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;  [C 


0  THE 

IIECHANIOAL  ENGINEER'S 
POCKET-BOOK 


A  REFBRENCE-BOOK  OF  RULES,   TABLES,  DATA, 

AKD  FORMULA,  FOR  THE  USE  OF 

ENGINEERS,  MECHANICS, 

AND  STUDENTS. 


BY 

WILLIAM  KENT,  A.M.,  M.E., 

CoMvUing  Engineer, 
Member  Amer,  Soc*y  Mechl.  Sngrt.  and  Amer,  Inst.  Mining  Slngra. 


J^IFTH  EDITION,  REVISED  AND  ENLARGED. 
EIGHTH    THOUSAN^D. 


NEW  YORK: 

JOHN   WILEY  &   SONS. 

Lokdon:   CJIAPMAN  &  HALL,  Limited. 

1901. 


HARVARD  COLLEGE  LIBRARY 
Pr?--   7:--  LSSRARY  OF 

FRA\..       PEAB03Y  MAGOUN 

IHt  GIFT  OF  HIS  SON 

MAY  8,  1929 


CopTniGHT,  isoe^ 

BY 

WILLIAM  KENT. 


Braunworth,  Munn  6f  Barbe       ,       ^\ 
Printers  and  Binders  .  ^ 

Brooklyn,  N.  Y.  -^     /^ 


PREPACK 


MoKA  than  twenty  years  ago  the  author  began  to  follow 
the  advice  given  by  Nystrom :  '*  Every  engineeer  should 
make  his  own  pocket-book,  as  be  proceeds  in  study  and 
practice,  to  suit  his  particular  business."  The  manuscript 
pocket-book  thus  begun,  however,  soon  gave  place  to  more 
modern  means  for  disposing  of  the  accumulation  of  engi- 
neering facts  and  figures,  viz.,  the  index  rerum,  the  scrap- 
book,  the  collection  of  indexed  envelopes,  portfolios  and 
boxes,  the  card  catalogue,  etc.  Four  years  ago,  at  the  re- 
quest of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to 
niecbanical  engineering,  and  of  condensing,  digesting,  and 
arranging  it  in  form  for  publication.  In  addition  to  this,  a 
careful  examination  was  made  of  the  transactions  of  engi- 
neering societies,  and  of  the  most  important  recent  works 
on  mechanical  engineering,  in  order  to  fill  gaps  that  might 
be  left  in  the  original  collection,  and  insure  that  no  impor- 
tant facts  had  been  overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  prepara- 
tion of  the  Pocket-book  that  will,  it  is  believed,  cause  it  to 
differ  from  other  works  of  its  class.  In  the  first  place  it 
was  considered  that  the  field  of  mechanical  engineering  was 
so  great,  and  the  literature  of  the  subject  so  vast,  that  as 
little  space  as  possible  should  be  given  to  subjects  which 
especially  belong  to  civil  engineering.  While  the  mechan- 
'Cal  engineer  must  continually  deal  with  problems  which 
'>elong  properly  to  civil  engineering,  this  latter  branch  is 
so  well  covered  by  Trautwine*s  **  Civil  Engineer's  Pocket- 
book"  that  any  attempt  to  treat  it  exhaustively  would  not 
only  fill  no  **  long-felt  want,"  but  would  occupy  space 
which  should  be  given  to  mechanical  engineering. 

Another  idea  prominently  kept  in  view  by  the  author  has 
been  that  he  would  not  assume  the  position  of  an  **  au- 
:bontj"  in  giving  rules  and  formuls  for  designing,  but 
only  that  of  compiler,  giving  not  only  the  name  of  the 
originator  of  the  rule,  where  it  was  known,  but  also  the 
rolame  and    page    from    which    it   was    taken,  so    that    its 

m 


*^  PREFACE. 

derivation  may  be  traced  when  desired.  When  different 
formulae  for  the  same  problem  have  been  found  they  have 
been  given  in  contrast,  and  in  many  cases  examples  have 
been  calculated  by  each  to  show  the  difference  between 
them.  In  some  cases  these  differences  are  <|utte  remark- 
able,  as  will  be  seen  under  Safety-valves  ^nd  Crank- pins. 
Occasionally  the  study  of  these  differences  has  led  to  the 
author's  devising  a  new  formula,  in  which  case  the  deriva* 
tion  of  the  formula  is  given. 

Much  attention  has  been  paid  to  the  abstracting  of  data 
of  experiments  from  recent  periodical  literature,  and  numer* 
ous  references  to  other  data  are  given.  In  this  respect 
the  present  work  will  be  found  to  differ  from  other  Pocket* 
books. 

The  author  desires  to  express  his  obligation  to  the  many 
persons  who  have  assisted  him  in  the  preparation  of  the 
work,  to  manufacturers  who  have  furnished  their  cata« 
logues  and  given  permission  for  the  use  of  their  tables, 
and  to  many  engineers  who  have  contributed  original  data 
and  tables.  The  names  of  these  persons  are  mentioned  in 
their  proper  places  in  the  text,  and  in  all  cases  it  has  been 
endeavored  to  give  credit  to  whom  credit  is  due.  The 
thanks  of  the  author  are  also  due  to  the  following  gentle- 
men who  have  given  assistance  in  revising  manuscript  or 
proofs  of  the  sections  named :  Prof.  De  Volson  Wood, 
mechanics  and  turbines;  Mr.  Frank  Richards,  compressed 
air ;  Mr.  Alfred  R.  Wolff,  windmills ;  Mr.  Alex.  C, 
Humphreys,  illuminating  gas ;  Mr.  Albert  E.  Mitchell, 
locomotives ;  Prof.  James  E.  Denton,  refrigerating-ina« 
chinery ;  Messrs.  Joseph  Wetzler  and  Thomas  W.  Varlcy, 
electrical  engineering  ;  and  Mr.  Walter  S.  Dix,  for  valuabU 
contributions  on  several  subjects,  and  suggestions  as  to  theii 
treatment.  William  Kent, 

Passaic,  N.  J.,  W>ri7, 1895. 

FIFTH    EDITION,  MARCH,  1900. 

Some  typographical  and  other  errors  discovered  in  the  fourt' 
edition  have  been  corrected.  New  tables  and  some  addition 
have  been  made  under  the  head  of  Compressed  Air.  The  nei 
(1899)  code  of  the  Boiler  Test  Committee  of  the  America 
Society  of  Mechanical  Engineers  has  been  substituted  for  tli 
old  (1885)  code.  W.  K,  I 


PREFACE  TO  FOURTH  EDITION. 

In  this  edition  many  extensive  alterations  have  been  made. 
Much  obsolete  matter  has  been  cut  out  and  fresh  matter  substi- 
tuted. In  the  first  170  pages  but  few  changes  have  been  found 
necessary,  but  a  few  typographical  and  other  minor  errors  have 
been  corrected.  The  tables  of  sizes,  weight,  and  strength  of 
materials  (pages  172  to  282)  have  been  thoroughly  revised,  many 
entirely  new  tables,  kindly  furnished  by  manufacturers,  having 
been  substituted.  Especial  attention  is  called  to  the  new  matter 
on  Cast-iron  Columns  (pages  250  to  253).  In  the  remainder  of 
the  book  changes  of  importance  have  been  made  in  more  than  100 
pagrs,  and  all  typographical  errors  reported  to  date  have  been 
corrected.  Manufacturers'  tables  have  been  revised  by  reference 
to  their  latest  catalogues  or  from  tables  furnished  by  the  manufac- 
turers especially  for  this  work.  Much  new  matter  is  inserted 
under  the  heads  of  Fans  and  Blowers,  Flow  of  Air  in  Pipes,  and 
Compressed  Air.  The  chapter  on  Wire-rope  Transmission  (pages 
917  to  922)  has  been  entirely  rewritten.  The  chapter  on  Electrical 
Engineering  has  been  improved  by  the  omission  of  some  matter 
that  has  become  out  of  date  and  the  insertion  of  some  new  matter. 

It  has  been  found  necessary  to  place  much  of  the  new  matter  of 
this  edition  in  an  Appendix,  as  space  could  not  conveniently  be 
made  for  it  in  the  body  of  the  book.  It  has  not  been  found  possi- 
ble to  make  in  the  body  of  the  book  many  of  the  cross-references 
which  should  be  made  to  the  items  in  the  Appendix.  Users  of  the 
book  may  find  it  advisable  to  write  in  the  margin  such  cross-refer- 
ences as  they  may  desire. 

The  Index  has  been  thoroughly  revised  and  greatly  enlarged. 

The  author  is  under  continued  obligation  to  many  manufacturers 
who  have  furnished  new  tables  and  data,  and  to  many  individual 
engineers  who  have  furnished  new  matter,  pointed  out  errors  in 
the  earlier  editions,  and  offered  helpful  suggestions.  He  will  be 
glad  to  receive  5imilar  aid,  which  will  assist  in  the  further 
Improvement  of  the  book  in  future  editions. 

William  Kent. 

PA5SA1C,  N.  J.,  Seftemher^  1898. 


CONTENTS. 


CFor  Alphabetical  Index  see  pace  1079.) 

MATHBMATIOS. 

Arithmetie. 

PAOB 

Arithmetical  and  Algebraical  Signti. 1 

Greatest  Common  iNTisor. 9 

Least  Common  Multiple ft 

FractloiM 2 

Decimals 8 

Table.    Decimal  Equiyalents  of  Fractions  of  One  Inch    8 

Table.    Products  of  Fractions  expressed  in  Dedmala 4 

Compound  or  Denominate  Numbers 6 

Reduction  Descending  and  Ascending 6 

BaCio  and  Proportion 5 

Involation,  or  Towers  of  Numbers 6 

Table.    First  Nine  Powers  of  the  First  Nine  Numbers 7 

Table.    First  Forty  Powers  of  8 7 

ETolution.     Square  Root •    7 

CubeBoot 8 

Alli«atlan 10 

Permutation 10 

Combination 10 

Arithmetical  Progression 11 

Geometrical  Progreesion 11 

Interest 18 

Disooont.. 18 

Compound  Interest 14 

Compound  Interest  Table,  8,  4,  fi,  and  6  per  cent 14 

Kqufttlon  of  Payments 14 

Partial  Pajmeuts 16 

Annuities 16 

TaUes  of  Amount,  Present  Values,  etc.,  of  Annuities 16 

Weights  and  Measures. 

Long  Measure 17 

OklLand  Measure 17 

Nautical  Measure  17 

Sqoare  Measure 18 

Sdid  or  Cubic  Measure 18 

Liqaid  Measure 18 

The  MiaersMnch 18 

Apothecaries*  Fluid  Measure 16 

Dry  Measure 18 

SfatpplQg  Measure 10 

AToirdnpois  Weight.  10 

Troy  W^bt. 10 

Apothecaries*  Weight 10 

ToWeigli  Correctly  on  an  Incorrect  Balance 10 

Circular  Measure 80 

Measure  of  time 80 

V 


E 


u 


-s   .^  'i 


I  0  I 


HARVARD  COLLEGE  LIBRARY 

fp::*:  t-:--  lscpary  of 

FRA-:..       FtAB02Y  MAGOUN 

IHL  GIFT  OF  HIS  SON 

MAY  8,  1929 


CopTniGHT,  isoe^ 

BY 

WILLIAM  KENT. 


Braunworth,  Munn  ^  Barbc       .  '^\ 

Printers  and  Binders  .      '    ^^ 

Brooklyn,  N.  y.  J        ^ 


PREPACE. 


More  than  twenty  years  ago  the  author  began  to  follow 
the  advice  given  by  Nystrom :  "  Every  engineeer  should 
make  his  own  pocket-book,  as  be  proceeds  in  study  and 
practice,  to  suit  his  particular  business.*'  The  manuscript 
pocket-book  thus  begun,  however,  soon  gave  place  to  more 
modern  means  for  disposing  of  the  accumulation  of  engi- 
neering facts  and  figures,  viz.,  the  index  rerum,  the  scrap- 
book,  the  collection  of  indexed  envelopes,  portfolios  and 
boxes,  the  card  catalogue,  etc.  Four  years  ago,  at  the  re- 
quest of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to 
mechanical  engineering,  and  of  condensing,  digesting,  and 
arranging  it  in  form  for  publication.  In  addition  to  this,  a 
careful  examination  was  made  of  the  transactions  of  engi- 
neering societies,  and  of  the  most  important  recent  works 
OQ  mechanical  engineering,  in  order  to  fill  gaps  that  might 
be  left  in  the  original  collection,  and  insure  that  no  impor- 
tant facts  had  been  overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  prepara- 
tion of  the  Pocket-book  that  will,  it  is  believed,  cause  it  to 
differ  from  other  works  of  its  class.  In  the  first  place  it 
was  considered  that  the  field  of  mechanical  engineering  was 
so  great,  and  the  literature  of  the  subject  so  vast,  that  as 
little  space  as  possible  should  be  given  to  subjects  which 
especially  belong  to  civil  engineering.  While  the  mechan- 
ical engineer  must  continually  deal  with  problems  which 
lelong  properly  to  civil  engineering,  this  latter  branch  is 
^o  well  covered  by  Trautwine*s  **  Civil  Engineer's  Pocket- 
Ixxtk"  that  any  attempt  to  treat  it  exhaustively  would  not 
onJy  fill  no  "long-felt  want,"  but  would  occupy  space 
vhich  should  be  given  to  mechanical  engineering. 

Another  idea  prominently  kept  in  view  by  the  author  has 
been  that  he  would  not  assume  the  position  of  an  '*  au- 
iboritj'*  in  giving  rules  and  formuls  for  designing,  but 
only  that  of  compiler,  giving  not  only  the  name  of  the 
originator  of  the  rule,  where  it  was  known,  but  also  the 
rolume  and   page    from  which    it  was    taken,  so    that    its 

iii 


t-  >•  1  ^^  '/  I  0  I 


HARVARD  COLLEGE  LIBRARY 
Pn:"   r;-  LIBPA'RY  OF 

FRAr.     .  FLAB03Y  MAGOUN 

Iht  GIFT  OF  HIS  SON 

MAY  8,  1929 


COPTHIOHT,  ISOB^ 
BY 

WILLIAM  KENT. 


Braunwoith,  Munn  &  Barbe  '^\ 

Printers  and  Binders  .  ^ 


Brooklyn,  N.  Y.  .^ 


•>) 


PREBACE. 


More  than  twenty  years  ago  the  author  began  to  follow 
the  advice  gWen  by  Nystrom :  "Every  engineeer  should 
make  his  own  pocket-book,  as  be  proceeds  in  study  and 
practice,  to  suit  his  particular  business."  The  manuscript 
pocket-book  thus  begun,  however,  soon  gave  place  to  more 
modern  means  for  disposing  of  the  accumulation  of  engi- 
neering facts  and  figures,  viz.,  the  index  rerum,  the  scrap- 
book,  the  collection  of  indexed  envelopes,  portfolios  and 
boxes,  the  card  catalogue,  etc.  Four  years  ago,  at  the  re- 
quest of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to 
mechanical  engineering,  and  of  condensing,  digesting,  and 
arranging  it  in  form  for  publication.  In  addition  to  this,  a 
careful  examination  was  made  of  the  transactions  of  engi- 
neering societies,  and  of  the  most  important  recent  works 
on  mechanical  engineering,  in  order  to  fill  gaps  that  might 
be  left  in  the  original  collection,  and  insure  that  no  impor- 
tant facts  had  been  overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  prepara- 
tion of  the  Pocket-book  that  will,  it  is  believed,  cause  it  to 
diScr  from  other  works  of  its  class.  In  the  first  place  it 
was  considered  that  the  field  of  mechanical  engineering  was 
so  great,  and  the  literature  of  the  subject  so  vast,  that  as 
little  space  as  possible  should  be  given  to  subjects  which 
especially  belong  to  civil  engineering.  While  the  mechan- 
xal  engineer  must  continually  deal  with  problems  which 
belong  properly  to  civil  engineering,  this  latter  branch  is 
s^o  well  covered  by  Trautwine*s  **  Civil  Engineer's  Pocket- 
book"  that  any  attempt  to  treat  it  exhaustively  would  not 
"nly  fill  no  "  long-felt  want,"  but  would  occupy  space 
vhich  should  be  given  to  mechanical  engineering. 

Another  idea  prominently  kept  in  view  by  the  author  has 
been  that  he  would  not  assume  the  position  of  an  "  au- 
thority" in  giving  rules  and  formuls  for  designing,  but 
only  that  of  compiler,  giving  not  only  the  name  of  the 
, originator  of  the  rule,  where  it  was  known,  but  also  the 
volume   and    page    from   which    it   was    taken,  so    that    its 

iii 


*^  PREFACE. 

derivation  may  be  traced  when  desired.  When  different 
formulae  for  the  same  problem  have  been  found  they  have 
been  given  in  contrast,  and  in  many  cases  examples  have 
been  calculated  by  each  to  show  the  difference  between 
them.  In  some  cases  these  differences  are  <|uite  remark- 
able, as  will  be  seen  under  Safety-valves  ^nd  Crank- pins. 
Occaaiooally  the  study  of  these  differences  has  led  to  the 
author's  devising  a  new  formula,  in  which  case  the  deriva- 
tion  of  the  formula  is  given. 

Much  attention  has  been  paid  to  the  abstracting  of  data 
of  experiments  from  recent  periodical  literature,  and  numer* 
ous  references  to  other  data  are  given.  In  this  respect 
the  present  work  will  be  found  to  differ  from  other  Pocket- 
books. 

The  author  desires  to  express  his  obligation  to  the  many 
persons  who  have  assisted  him  in  the  preparation  of  the 
work,  to  manufacturers  who  have  furnished  their  cata* 
logues  and  given  permission  for  the  use  of  their  tables, 
and  to  many  engineers  who  have  contributed  original  data 
and  tables.  The  names  of  these  persons  are  mentioned  io 
their  proper  places  in  the  text,  and  in  all  cases  it  has  been 
endeavored  to  give  credit  to  whom  credit  is  due.  The 
thanks  of  the  author  are  also  due  to  the  following  gentle- 
men who  have  given  assistance  in  revising  manuscript  ot 
proofs  of  the  sections  named :  Prof.  De  Volson  Wood, 
mechanics  and  turbines ;  Mr.  Frank  Richards,  compressed 
air;  Mr.  Alfred  R.  Wolff,  windmills;  Mr.  Alex.  C 
Humphreys,  illuminating  gas ;  Mr.  Albert  E.  Mitchell 
locomotives ;  Prof.  James  E.  Denton,  refrige rating-ma 
chinery;  Messrs.  Joseph  Wetzler  and  Thomas  W,  Varlcv 
electrical  engineering  ;  and  Mr.  Walter  S.  Dix,  for  valuabl 
contributions  on  several  subjects,  and  suggestions  as  to  tbei 
treatment.  WiLUAM  Kent. 

Passaic,  N,  J,,  Aprils  1895. 

FIFTH    EDITION,  MARCH,  1900. 

Some  typographical  and  other  errors  discovered  in  the  fourt 
edition  have  been  corrected.  New  tables  and  some  addition 
have  been  made  under  the  head  of  Compressed  Air.  The  nei 
(1899)  code  of  the  Boiler  Test  Committee  of  the  America 
Society  of  Mechanical  Engineers  has  been  substituted  for  th 
old  (1885)  code.  W.  K. 


PREFACE  TO  FOURTH  EDITION. 

In  this  edition  many  extensive  alterations  have  been  made. 
Much  obsolete  matter  has  been  cut  out  and  fresh  maiter  substi- 
tuted. In  the  first  170  pages  but  few  changes  have  been  found 
necessary,  but  a  few  typographical  and  other  minor  errors  have 
been  corrected.  The  tables  of  sizes,  weight,  and  strength  of 
materials  (pages  172  to  282)  have  been  thoroughly  revised,  many 
entirely  new  tables,  kindly  furnished  by  manufacturers,  having 
been  substituted.  Especial  attention  is  called  to  the  new  matter 
on  Cast-iron  Columns  (pages  250  to  253).  In  the  remainder  of 
the  book  changes  of  importance  have  been  made  in  more  than  100 
pagrs,  and  all  typographical  errors  reported  to  date  have  been 
corrected.  Manufacturers'  tables  have  been  revised  by  reference 
to  their  latest  catalogues  or  from  tables  furnished  by  the  manufac- 
turers especially  for  this  work.  Much  new  matter  is  inserted 
under  the  heads  of  Fans  and  Blowers,  Flow  of  Air  in  Pipes,  and 
Compressed  Air.  The  chapter  on  Wire-rope  Transmission  (pages 
917  to  922)  has  been  entirely  rewritten.  The  chapter  on  Electrical 
Engineering  has  been  improved  by  the  omission  of  some  maiter 
that  has  become  out  of  date  and  the  insertion  of  some  new  matter. 

It  has  been  found  necessary  to  place  much  of  the  new  matter  of 
this  edition  in  an  Appendix,  as  space  could  not  conveniently  be 
made  for  it  in  the  body  of  the  book.  It  has  not  been  found  possi- 
ble to  make  in  the  body  of  the  book  many  of  the  cross-references 
which  should  be  made  to  the  items  in  the  Appendix.  Users  of  the 
book  may  find  it  advisable  to  write  in  the  margin  such  cross-refer« 
ences  as  they  may  desire. 

The  Index  has  been  thoroughly  revised  and  greatly  enlarged. 

The  author  is  under  continued  obligation  to  many  manufacturers 
who  have  furnished  new  tables  and  data,  and  to  many  individual 
engineers  who  have  furnished  new  matter,  pointed  out  errors  in 
the  earlier  editions,  and  offered  helpful  suggestions.  He  will  be 
glad  to  receive  .similar  aid,  which  will  assist  in  the  further 
improvement  of  the  book  in  future  editions. 

Wjlliam  Kknt. 

Passaic,  S.  J.,  Se^tembtr^  1898. 


CONTENTS. 


(For  Alphabetical  Index  see  pace  1079.) 

MATHKMATIOS. 

Arltbmetlo. 

Arithmetical  and  Algebraical  Bigna. ~"l 

Greatest  Common  Diviflor. S 

Least  Oommon  Multiple. 8 

Fractions 8 

Decfmala 8 

Table.    Decimal  Equivalents  of  Fractions  of  One  Inch    8 

Table.    Products  of  Fractions  expressed  in  Decimals • 4 

Cbmpound  or  Denominate  Numbers 6 

BeductioD  Descending  and  Ascending 6 

Ratio  and  Proportion 6 

Involution,  or  rowers  of  Numbers 6 

Table.    First  Nine  Powers  of  the  First  Nine  Numbers 7 

Table.    First  Forty  Powers  of  8 7 

KvolutioD.     Square  Root 7 

CubeRoot 8 

AUigatloa 10 

Permutation 10 

Combination 10 

Arithmetical  Progression 11 

Geometrical  Progreasion • 11 

Interest 18 

DiKOOttnt. 18 

Compound  Interest 14 

Compound  Interest  Table,  8,  4,  8,  and  6  per  cent 14 

Equatkm  of  Payments 14 

Partial  Payments 15 

Annultlea 16 

Tables  of  Amount,  Preaent  Values,  etc.,  of  Annuities 10 

Weig^hta  and  Bleasures. 

LoagMeaaure 17 

Old  Land  Measure 17 

Nautical  Measure  17 

Souare  Measure 18 

Bokid  or  Cubic  Measure 18 

Liquid  Measure 18 

The  Miners*  Inch 18 

Apothecaries*  Fluid  Measure. 18 

Dry  Measure  18 

Shipping  Measure 10 

Avoirdupois  Weight  10 

Troy  Weigrht. 10 

Apotbec&Hes*  Weight 10 

To  Weigh  Correctly  on  an  Incorrect  Balance 10 

Circular  Measure SSO 

Measure  of  time 80 

V 


^^^  3n./iJ? 


HARVARD 
COLLEGE 
LIBRARY 


^n^  3^^,{)^ 


HARVARD 
COLLEGE 
LIBRARY 


0  THE 

MECHANICAL  ENGINEER'S 
POCKET-BOOK 


,    A  REFEBENCM-BOOK  OF  RULES,   TABLES,  DATA, 
AND  FORMULJB,  FOR  THE  USE  OF 
ENGINEERS,  MECHANICS, 
i  AND  STUDENTS. 


BY 

WILLIAM  KENT,  A.M.,  M.E., 

Confuting  Engineer, 
Member  Amer,  8oc*y  Mechl.  Engrs,  aiid  Amer,  Inst,  Mining  Engra. 


*      MFTH  EDITION,  REVISED  AND  ENLARGED. 
I  EIGHTH    THOUSAND. 


NEW   YORK: 

JOHN   WILEY  &   SONS. 

London:  CHAPMAN  &  HALL,  Limited. 

1901. 


t  >.-,  -5^/ 7,  c^/ 


u 


HARVARD  COLLEGE  LIBRARY 

pr-"   ,   ,-  L'BRARY  OF 

FRA-:..    .  I-EABODY  MAGOUN 

THE  GIFT  OF  HIS  SON 

MAY  8.  1929 


ConrmaiiT,  iflBB^ 

Br 

WILLIAM  KENT. 


Braunworth,  Munn  ^  Barbe 
Printers  and  Binders 
Brooklyn,  N.  Y.  \ 


.\^ 


'  PREEACE. 

More  than  twenty  years  ago  the  author  began  to  follow 
the  advice  given  by  Nystrom :  '*  Every  engineeer  should 
make  his  own  pocket-book,  as  be  proceeds  in  study  and 
practice,  to  suit  his  particular  business.'*  The  manuscript 
pocket-book  thus  begun,  however,  soon  gave  place  to  more 
modern  means  for  disposing  of  the  accumulation  of  engi- 
neering facts  and  figures,  viz.,  the  index  rerum,  the  scrap- 
book,  the  collection  of  indexed  envelopes,  portfolios  and 
boxes,  the  card  catalogue,  etc.  Four  years  ago,  at  the  re- 
quest of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to 
mechanical  engineering,  and  of  condensing,  digesting,  and 
arranging  it  in  form  for  publication.  In  addition  to  this,  a 
careful  examination  was  made  of  the  transactions  of  engi- 
neering societies,  and  of  the  most  important  recent  works 
on  mechanical  engineering,  in  order  to  fill  gaps  that  might 
be  left  in  the  original  collection,  and  insure  that  no  impor- 
tant facts  had  been  overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  prepara- 
tion of  the  Pocket-book  that  will,  it  is  believed,  cause  it  to 
differ  from  other  works  of  its  class.  In  the  first  place  it 
was  considered  that  the  field  of  mechanical  engineering  was 
so  great,  and  the  literature  of  the  subject  so  vast,  that  as 
little  space  as  possible  should  be  given  to  subjects  which 
especially  belong  to  civil  engineering.  While  the  mechan- 
<:al  engineer  must  continually  deal  with  problems  which 
belong  properly  to  civil  engineering,  this  latter  branch  is 
ro  well  covered  by  Trautwine*s  **  Civil  Engineer's  Pocket- 
>ook"  that  any  attempt  to  treat  it  exhaustively  would  not 
>n]y  fill  no  '*  long-felt  want,"  but  would  occupy  space 
rbich  should  be  given  to  mechanical  engineering. 

Another  idea  prominently  kept  in  view  by  the  author  has 
>^cn  that  he  would  not  assume  the  position  of  an  "  au- 
bority"  in  giving  rules  and  formuls  for  designing,  but 
r/slj  that  of  compiler,  giving  not  only  the  name  of  the 
ri^inator  of  the  rule,  where  it  was  known,  but  also  the 
olume  and    page    from   which    it  was    taken,  so    that    its 

ill 


*^  PREFACE. 

derivation  may  be  traced  when  desired.  When  different 
formuls  for  the  same  problem  have  been  found  they  have 
been  given  in  contrast,  and  in  many  cases  examples  have 
been  calculated  by  each  to  show  the  difference  between 
them.  In  some  cases  these  differences  are  quite  remark- 
able, as  will  be  seen  under  Safety-valves  ^nd  Crank* pins. 
Occasionally  the  study  of  these  differences  has  led  to  the 
Author's  devising  a  new  formula,  In  which  case  the  deriva* 
tion  of  the  formula  is  given. 

Much  attention  has  been  paid  to  the  abstracting  of  data 
of  experiments  from  recent  periodical  literature,  and  numer« 
ous  references  to  other  data  are  given.  In  this  respect 
the  present  work  will  be  found  to  differ  from  other  Pocket- 
books. 

The  author  desires  to  express  his  obligation  to  the  many 
persons  who  have  assisted  him  in  the  preparation  of  the 
work,  to  manufacturers  who  have  furnished  their  cata* 
logues  and  given  permission  for  the  use  of  their  tables, 
and  to  many  engineers  who  have  contributed  original  data 
and  tables.  The  names  of  these  persons  are  mentioned  in 
their  proper  places  in  the  text,  and  in  all  cases  it  has  been 
endeavored  to  give  credit  to  whom  credit  is  due.  The 
thanks  of  the  author  are  also  due  to  the  following  gentle- 
men who  have  given  assistance  in  revising  manuscript  or 
proofs  of  the  sections  named :  Prof.  De  Volson  Wood, 
mechanics  and  turbines ;  Mr.  Frank  Richards,  compressed 
air;  Mr.  Alfred  R.  Wolff,  windmills;  Mr.  Alex.  C. 
Humphreys,  illuminating  gas ;  Mr.  Albert  E.  Mitchell, 
locomotives ;  Prof.  James  E.  Denton,  refrigerating-ma. 
chinery  ;  Messrs.  Joseph  Wctzler  and  Thomas  W.  Varlcy, 
electrical  engineering  ;  and  Mr.  Walter  S.  Dix,  for  valuable 
contributions  on  several  subjects,  and  suggestions  as  to  thei] 
treatment.  William  Kent,  i 

Passaic,  N.  J,,  Aprils  1895. 

FIFTH    EDITION,  MARCH,  1900.  \ 

Some  typographical  and  other  errors  discovered  in  the  fourd 
edition  have  been  corrected.  New  tables  and  some  additioii 
have  been  made  under  the  head  of  Compressed  Air.  The  nei 
(1899)  code  of  the  Boiler  Test  Committee  of  the  America 
Society  of  Mechanical  Engineers  has  been  substituted  for  til 
old  (1885)  code.  W.  K 


PREFACE  TO  FOURTH  EDITION. 

In  ihis  edition   many  extensive   alterations   have   been  made. 
Much  obsolete  matter  has  been  cut  out  and  fresh  matter  substi- 
tuted.    In  the  first  170  pages  but  few  changes  have  been  found 
necessary,  but  a  few  typographical  and  other  minor  errors  have 
been  corrected.     The   tables   of  sizes,  weight,    and   strength   of 
materials  (pages  172  to  282)  have  been  thoroughly  revised,  many 
entirely  new  tables,  kindly  furnished   by  manufacturers,  having 
been  substituted.     Especial  attention  is  called  to  the  new  matter 
on  Cast-iron  Columns  (pages  250  to  253).     In  the  remainder  of 
ifae  book  changes  of  importance  have  been  made  in  more  than  100 
pagrs,  and  all  typographical  errors  reported   to  date   have  been 
corrected.     Manufacturers'  tables  have  been  revised  by  reference 
to  their  latest  catalogues  or  from  tables  furnished  by  the  manufac- 
turers  especially  for  this  work.     Much    new   matter   is   inserted 
under  the  heads  of  Fans  and  Blowers,  Flow  of  Air  in  Pipes,  and 
Compressed  Air.     The  chapter  on  Wire-rope  Transmission  (pages 
917  to  922)  has  been  entirely  rewritten.     The  chapter  on  Electrical 
Engineering  has  been  improved  by  the  omission  of  some  matter 
that  has  become  out  of  date  and  the  insertion  of  some  new  matter. 
It  has  been  found  necessary  to  place  much  of  the  new  matter  of 
this  edition  in  an  Appendix,  as  space  could  not  conveniently  be 
made  for  it  in  the  body  of  the  book.     It  has  not  been  found  possi- 
ble to  make  in  the  body  of  the  book  many  of  the  cross-references 
which  should  be  made  to  the  items  in  the  Appendix.     Users  of  the 
book  may  find  it  advisable  to  write  in  the  margin  such  cross-refer- 
ences as  they  may  desire. 
The  Index  has  been  thoroughly  revised  and  greatly  enlarged. 
The  author  is  under  continued  obligation  to  many  manufacturers 
who  have  furnished  new  tables  and  data,  and  to  many  individual 
engineers  who  have  furnished  new  matter,  pointed  out  errors  in 
the  earlier  editions,  and  offered  helpful  suggestions.     He  will  be 
glad    to    receive    similar    aid,  which  will    assist    in    the   further 
improvement  of  the  book  in  future  editions. 

William  Kknt. 

Passaxc,  N.  J.,  St^tembtr^  1898. 


0  THE 

MECHANICAL  ENGINEER'S 
POCKET-BOOK 


A  nEFERENCE-BOOK  OF  RULES,   TABLES,  DATA, 

AND  FORMULjE,  FOR  THE  USE  OF 

ENGINEERS,  MECHANICS, 

AND  STUDENTS. 


WILLIAM  KENT,  A.M.,  M.E., 

Conwiting  Engineer, 
Member  Amer.  Soc'y  Mechl,  Enffrs.  and  Amer,  Inti,  Mining  Engrs. 


MFTH  EDITION,  REVISED  AND  ENLARGED. 
EIGHTH    THOUSAND. 


NEW   YORK: 

JOHN   WILEY  &   SONS. 

I^ondon:  CJIAPMAN  &  HALL,  Limited. 

1901. 


0  THE 

MECHANICAL  ENGINEER'S 
POCKET-BOOK 


A  REFERENCE-BOOK  OF  RULES,    TABLES,  DATA, 

AND  FORMULA,   FOR  THE  USE  OF 

ENGINEERS,  MECHANICS, 

AND  STUDENTS, 


BT 


WILLIAM  KENT,  A.M.,  M.E., 

ConwiUing  Engineer^ 
Member  Amer,  8oc*y  Mechl,  Bngr9.  and  Amer.  Inst,  Mining  JSngrt. 


JflFTH  EDITION,  REVISED  AND  ENLARGED. 
EIGHTH    THOUSAND. 


NEW  YORK: 

JOHN   AVILEY  &   SONS. 

Ix)RDON:  CPAPMAN  &  HALL.  Limited. 

1901. 


£,.. 


'(  ■=>  -r  I  0 1 


u- 


HARVARD  COLLEGE  LIBRARY 
Fn?"'  7-.-  MBPARYOF 

FRA-:  rtABODY  MAGOUN 

^WL  GIFT  OF  HIS  SON 

MAY  8,  1929 


ConmiGHT,  isgo; 

BY 

WILLIAM  KENT. 


Braunworth,  Muon  ^  Bjrbc      .  ^  ^\ 

Printers  and  Binders  .  '  ^ 

Brooklyn,  N.  y.  /        "" 

'1  •>■ 


PREIACE. 


'  More  than  twenty  years  ago  the  author  began  to  follow 
the  advice  given  by  Nystrom :  '*  Every  engineeer  should 
make  his  own  pocket-book,  as  be  proceeds  in  study  and 
practice,  to  suit  his  particular  business."  The  manuscript 
pocket-book  thus  begun,  however,  soon  gave  place  to  more 
modern  means  for  disposing  of  the  accumulation  of  engi- 
neering facts  and  figures,  viz.,  the  index  rerum,  the  scrap- 
book,  the  collection  of  indexed  envelopes,  portfolios  and 
boxes,  the  card  catalogue,  etc.  Four  years  ago,  at  the  re- 
quest of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to 
mechanical  engineering,  and  of  condensing,  digesting,  and 
arranging  it  in  form  for  publication.  In  addition  to  this,  a 
careful  examination  was  made  of  the  transactions  of  engi* 
neering  societies,  and  of  the  most  important  recent  works 
on  mechanical  engineering,  in  order  to  fill  gaps  that  might 
be  left  in  the  original  collection,  and  insure  that  no  impor- 
tant facts  had  been  overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  prepara- 
tion of  the  Pocket-book  that  will,  it  is  believed,  cause  it  to 
differ  from  other  works  of  its  class.  In  the  first  place  it 
was  considered  that  the  field  of  mechanical  engineering  was 
so  great,  and  the  literature  of  the  subject  so  vast,  that  as 
little  space  as  possible  should  be  given  to  subjects  which 
especially  belong  to  civil  engineering.  While  the  mechan- 
ical engineer  must  continually  deal  with  problems  which 
belong  properly  to  civil  engineering,  this  latter  branch  is 
so  well  covered  by  Trautwine's  **  Civil  Engineer's  Pocket- 
book  "  that  any  attempt  to  treat  it  exhaustively  would  not 
only  fill  no  "long-felt  want,"  but  would  occupy  space 
irhich  should  be  given  to  mechanical  engineering. 

Another  idea  prominently  kept  in  view  by  the  author  has 
been  that  he  would  not  assume  the  position  of  an  **  au- 
thority'* in  giving  rules  and  formulae  for  designing,  but 
only  that  of  compiler,  giving  not  only  the  name  of  the 
originator  of  the  rule,  where  it  was  known,  but  also  the 
Volume  and    page    from   which    it  was    taken,  so    that   its 

iii 


**^  PREFACE. 

»• 

derivation  may  be  traced  when  desired.  When  different 
formula  for  the  same  problem  have  been  found  they  have 
been  given  in  contrast,  and  in  many  cases  examples  have 
been  calculated  by  each  to  show  the  difference  between 
them.  In  eome  cases  these  differences  are  quite  remark- 
able, as  will  be  seen  under  Safety-valves  ^nd  Crank* pins. 
Occasionally  the  study  of  these  differences  has  led  to  the 
author's  devising  a  new  formula,  in  which  case  the  deriva- 
tion of  the  formula  is  given. 

Much  attention  has  been  paid  to  the  abstracting  of  data 
of  experiments  from  recent  periodical  literature,  and  numer« 
ous  references  to  other  data  are  given.  In  this  respect 
the  present  work  will  be  found  to  differ  from  other  Pocket- 
books. 

The  author  desires  to  express  bis  obligation  to  the  many 
persons  who  have  assisted  him  in  the  preparation  of  the 
work,  to  manufacturers  who  have  furnished  their  cata* 
logues  and  given  permission  for  the  use  of  their  tables, 
and  to  many  engineers  who  have  contributed  original  data 
and  tables.  The  names  of  these  persons  are  mentioned  in 
their  proper  places  in  the  text,  and  in  all  cases  it  has  been 
endeavored  to  give  credit  to  whom  credit  is  due.  The 
thanks  of  the  author  are  also  due  to  the  following  gentle- 
men who  have  given  assistance  in  revising  manuscript  or 
proofs  of  the  sections  named :  Prof.  De  Volson  Wood, 
mechanics  and  turbines ;  Mr.  Frank  Richards,  compressed 
air;  Mr.  Alfred  R.  Wolff,  windmills;  Mr.  Alex.  C. 
Humphreys,  illuminating  gas ;  Mr.  Albert  E.  Mitchell, 
locomotives ;  Prof.  James  E.  Denton,  refrigerating-ma. 
chinery ;  Messrs.  Joseph  Wetzler  and  Thomas  W.  Varlcy, 
electrical  engineering  ;  and  Mr.  Walter  S.  Dix,  for  valuable 
contributions  on  several  subjects,  and  suggestions  as  to  tbeii 
treatment.  William  Kent. 

Passaic,  N.  J.,  Aprils  1895. 

FIFTH    EDITION,  MARCH,  1900. 

Some  typographical  and  other  errors  discovered  in  the  fourt] 
edition  have  been  corrected.  New  tables  and  some  additioni 
have  been  made  under  the  head  of  Compressed  Air.  The  ne« 
(1S99)  code  of  the  Boiler  Test  Committee  of  the  American 
Society  of  Mechanical  Engineers  has  been  substituted  for  tK 
old  (1885)  code.  W.  K. 


PREFACE  TO  FOURTH  EDITION. 

In  ihis  edilion  many  extensive  alterations  have  been  made. 
Much  obsolete  matter  has  been  cut  out  and  fresh  matter  substi- 
tuted. In  the  first  170  pages  but  few  changes  have  been  found 
necessary,  but  a  few  typographical  and  other  minor  errors  have 
been  corrected.  The  tables  of  sizes,  weight,  and  strength  of 
materials  (pages  172  to  282)  have  been  thoroughly  revised,  many 
entirely  new  tables,  kindly  furnished  by  manufacturers,  having 
been  substituted.  Especial  attention  is  called  to  the  new  matter 
on  Cast-iron  Columns  (pages  250  to  253).  In  the  remainder  of 
the  book  changes  of  importance  have  been  made  in  more  than  100 
pagrs,  and  all  typographical  errors  reported  to  date  have  been 
corrected.  Manufacturers*  tables  have  been  revised  by  reference 
to  their  latest  catalogues  or  from  tables  furnished  by  the  manufac- 
turers especially  for  this  work.  Much  new  matter  is  inserted 
under  the  heads  of  Fans  and  Blowers,  Flow  of  Air  in  Pipes,  and 
Compressed  Air.  The  chapter  on  Wire-rope  Transmission  (pages 
917  to  922)  has  been  entirely  rewritten.  The  chapter  on  Electrical 
Engineering  has  been  improved  by  the  omission  of  some  matter 
that  has  become  out  of  date  and  the  insertion  of  some  new  matter. 

It  has  been  found  necessary  to  place  much  of  the  new  matter  of 
this  edition  in  an  Appendix,  as  space  could  not  conveniently  be 
made  for  it  in  the  body  of  the  book.  It  has  not  been  found  possi- 
ble to  make  in  the  body  of  the  book  many  of  the  cross-references 
which  should  be  made  to  the  items  in  the  Appendix.  Users  of  the 
book  may  find  it  advisable  to  write  in  the  margin  such  cross-refer- 
ences as  they  may  desire. 

The  Index  has  been  thoroughly  revised  and  greatly  enlarged. 

The  author  is  under  continued  obligation  to  many  manufacturers 
who  have  furnished  new  tables  and  data,  and  to  many  individual 
engrineers  who  have  furnished  new  matter,  pointed  out  errors  in 
the  earlier  editions,  and  offered  helpful  suggestions.  He  will  be 
glad  to  receive  similar  aid,  which  will  assist  in  the  further 
improvement  of  the  book  in  future  editions. 

William  Kbnt. 

Passaic,  N.  J.,  Sepiembtr^  1898. 


CONTENTS. 


(For  Alphabetical  Index  lee  page  1079.) 

MATHBBIATIOS. 

Arithmetlo. 

PAGB 

Arithmetical  and  Algebraical  Blgna 1 

Greatest  Common  DiTiaor. 8 

Least  Common  Multiple 8 

FractioDS 3 

Decimate 8 

Table.    Decimal  Equivalents  of  Fractions  of  One  Inch    8 

Table.     Products  of  Fractions  expressed  In  Decimals 4 

Compound  or  Denominate  Numbers 5 

Reduction  Descending  and  Ascending 5 

Ratio  and  Proportion 5 

Involution,  or  Powers  of  Numbers 8 

Table.    First  Nine  Powers  of  the  First  Nine  Numbers 7 

Table.    FIrat  Forty  Powers  of  2 7 

Evohition.     Square  Booc 7 

CubeRoot 8 

Alligation 10 

Permutation 10 

Combination 10 

Arithmetical  Progression 11 

Geometrical  Progression 11 

Interest 18 

Discount 18 

Compound  Interest 14 

Compound  Interest  Table,  8,  4,  S,  and  6  per  cent 14 

Equation  of  Payments 14 

Partial  Payments 15 

Annuities 16 

TkUea  of  Amount,  Present  Values,  etc.,  of  Annuities 16 

Weig^hts  and  Bleasares. 

toag  Measure 17 

OldLand  Measure 17 

Ksutical  Meaaure  17 

Sqoare  Measure 18 

Solid  or  Cubic  Measure 18 

Liquid  Measure 18 

The  XineraMnch 18 

Apothecaries*  Fluid  Measure. 18 

DfT  Measure 18 

Supping  Measure 19 

Avoirdupois  Weight.  > 19 

Troy  Weight. 19 

Apothecaries*  Weij^t 19 

To  Weigh  Correctly  on  an  Incorrect  Balance 19 

Qrenlar  Measure SO 

Measure  of  time 80 

V 


E 


L^ 


3  -• 


I  0  / 


HARVARD  COLLEGE  LIBRARY 

Fr?"  7'.--  LICPA'RYOF 

FRAr  .        F-EAB03Y  MAGOUN 

IHt  GIFT  OF  HIS  SON 

MAY  8,  1929 

3         ; 

BY 

WILLIAM  KENT. 


Braunworth,  Munn  ^  Barbe       .        -  A 
Printers  and  Binders  •  "  ^ 

Brooklyn,  N.  y.  i        "^ 


PREIACE. 


More  than  twenty  years  ago  the  author  began  to  follow 
the  advice  given  by  Nystrom :  '*  Every  engineeer  should 
make  his  own  pocket-book,  as  be  proceeds  in  study  and 
practice,  to  suit  his  particular  business."  The  manuscript 
pocket-book  thus  begun,  however,  soon  gave  place  to  more 
modern  means  for  disposing  of  the  accumulation  of  engi- 
neering facts  and  figures,  viz.,  the  index  rerum,  the  scrap- 
book,  the  collection  of  indexed  envelopes,  portfolios  and 
boxes,  the  card  catalogue,  etc.  Four  years  ago,  at  the  re- 
quest of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to 
mechanical  engineering,  and  of  condensing,  digesting,  and 
arranging  it  in  form  for  publication.  In  addition  to  this,  a 
careful  examination  was  made  of  the  transactions  of  engi* 
neering  societies,  and  of  the  most  important  recent  works 
on  mechanical  engineering,  in  order  to  fill  gaps  that  might 
be  left  in  the  original  collection,  and  insure  that  no  impor- 
tant facts  had  been  overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  prepara- 
tion of  the  Pocket-book  that  will,  it  is  believed,  cause  it  to 
diflfer  from  other  works  of  its  class.  In  the  first  place  it 
was  considered  that  the  field  of  mechanical  engineering  was 
so  great,  and  the  literature  of  the  subject  so  vast,  that  as 
little  space  as  possible  should  be  given  to  subjects  which 
especially  belong  to  civil  engineering.  While  the  mechan- 
ical engineer  must  continually  deal  with  problems  which 
belong  properly  to  civil  engineering,  this  latter  branch  is 
so  well  covered  by  Trautwine's  **  Civil  Engineer's  Pocket- 
book"  that  any  attempt  to  treat  it  exhaustively  would  not 
only  fill  no  "long-felt  want,"  but  would  occupy  space 
which  should  be  given  to  mechanical  engineering. 

Another  idea  prominently  kept  in  view  by  the  author  has 
been  that  he  would  not  assume  the  position  of  an  **  au- 
thority "  in  giving  rules  and  formulae  for  designing,  but 
only  that  of  compiler,  giving  not  only  the  name  of  the 
originator  of  the  rule,  where  it  was  known,  but  also  the 
volume   and    page    from   which    it   was    taken,  so    that    its 

iii 


E 


I.  01 


HARVARD  COLLEGE  LIBRARY 
FR?"  v:-   L'BPARY  OF 

FRAP  ..    .  FtABODY  MAGOUN 

IHt  GIFT  OF  HIS  SON 

MAY  8,  1929 


CopTniGiiT,  isgo; 

Br 

WILLIAM  KENT. 


Braunworth,  Muon  &  Barbc      .       \  A 
Printers  and  Binders  ■     ^^ 

Brooklyn,  N.  y.  | 


PREIACE. 


[  More  than  twenty  years  ago  the  author  began  to  follow 
the  advice  given  by  Nystrom :  "  Every  engineeer  should 
make  his  own  pocket-book,  as  be  proceeds  in  study  and 
practice,  to  suit  his  particular  business."  The  manuscript 
pocket-book  thus  begun,  however,  soon  gave  place  to  more 
modern  means  for  disposing  of  the  accumulation  of  engi- 
neering facts  and  figures,  viz.,  the  index  rerum,  the  scrap- 
book,  the  collection  of  indexed  envelopes,  portfolios  and 
boxes,  the  card  catalogue,  etc.  Four  years  ago,  at  the  re- 
quest of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to 
mechanical  engineering,  and  of  condensing,  digesting,  and 
arranging  it  in  form  for  publication.  In  addition  to  this,  a 
careful  examination  was  made  of  the  transactions  of  engi- 
neering societies,  and  of  the  most  important  recent  works 
on  mechanical  engineering,  in  order  to  fill  gaps  that  might 
be  left  in  the  original  collection,  and  insure  that  no  impor- 
tant facts  had  been  overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  prepara- 
tion of  the  Pocket-book  that  will,  it  is  believed,  cause  it  to 
differ  from  other  works  of  its  class.  In  the  first  place  it 
was  considered  that  the  field  of  mechanical  engineering  was 
so  great,  and  the  literature  of  the  subject  so  vast,  that  as 
little  space  as  possible  should  be  given  to  subjects  which 
especially  belong  to  civil  engineering.  While  the  mechan- 
ical engineer  must  continually  deal  with  problems  which 
belong  properly  to  civil  engineering,  this  latter  branch  is 
so  well  covered  by  Trautwine*s  **  Civil  Engineer's  Pocket- 
book  "  that  any  attempt  to  treat  it  exhaustively  would  not 
>nly  fill  no  **  long-felt  want,"  but  would  occupy  space 
irhich  should  be  given  to  mechanical  engineering. 

Another  idea  prominently  kept  in  view  by  the  author  has 
been  that  he  would  not  assume  the  position  of  an  "  au- 
thority" in  giving  rules  and  formulae  for  designing,  but 
7nlj  that  of  compiler,  giving  not  only  the  name  of  the 
>ri£rinator  of  the  rule,  where  it  was  known,  but  also  the 
rolume   and    page    from   which    it   was    taken,  so    that    its 

m 


**^  PBEFACE. 

derivation  may  be  traced  when  desired.  When  different 
formula  for  the  same  problem  have  been  found  they  have 
been  given  in  contrast,  and  in  many  cases  examples  have 
been  calculated  by  each  to  show  the  difference  between 
them.  In  some  cases  these  differences  are  quite  remark- 
able, as  will  be  seen  under  Safety-valves  ^nd  Crank- pins. 
Occasionally  the  study  of  these  differences  has  led  to  the 
author's  devising  a  new  formula,  in  which  case  the  deriva- 
tion of  the  formula  is  given. 

Much  attention  has  been  paid  to  the  abstracting  of  data 
of  experiments  from  recent  periodical  literature,  and  numer« 
ous  references  to  other  data  are  given.  In  this  respect 
the  present  work  will  be  found  to  differ  from  other  Pocket- 
books. 

The  author  desires  to  express  his  obligation  to  the  many 
persons  who  have  assisted  him  in  the  preparation  of  the 
work,  to  manufacturers  who  have  furnished  their  cata* 
logues  and  given  permission  for  the  use  of  their  tables, 
and  to  many  engineers  who  have  contributed  original  data 
and  tables.  The  names  of  these  persons  are  mentioned  in 
their  proper  places  in  the  text,  and  in  all  cases  it  has  been 
endeavored  to  give  credit  to  whom  credit  is  due.  The 
thanks  of  the  author  are  also  due  to  the  following  gentle- 
men who  have  given  assistance  in  revising  manuscript  or 
proofs  of  the  sections  named :  Prof.  De  Volson  Wood, 
mechanics  and  turbines ;  Mr.  Frank  Richards,  compressed 
air ;  Mr.  Alfred  R.  Wolff,  windmills ;  Mr.  Alex.  C. 
Humphreys,  illuminating  gas ;  Mr.  Albert  E.  Mitchell, 
locomotives ;  Prof.  James  E.  Denton,  refrigerating-ma« 
chinery ;  Messrs.  Joseph  Wetzlcr  and  Thomas  W.  Varley, 
electrical  engineering  ;  and  Mr.  Walter  S.  Dix,  for  valuable 
contributions  on  several  subjects,  and  suggestions  as  to  their 
treatment.  William  Kent. 

Passaic,  N.  J.,  Apriit  1895. 

FIFTH    EDITION,  MARCH,  1900. 

Some  typographical  and  other  errors  discovered  In  the  fourth 
edition  have  been  corrected.  New  tables  and  some  additions 
have  been  made  under  the  head  of  Compressed  Air.  The  new 
(1S99)  code  of  the  Boiler  Test  Committee  of  the  American 
Society  of  Mechanical  Engineers  has  been  substituted  for  the 
old  (1885)  code.  W.  K. 


PREFACE  TO  FOURTH  EDITION. 

In  this  edition  many  extensive  alterations  have  been  made. 
Much  obsolete  matter  has  been  cut  out  and  fresh  matter  substi- 
tuted. In  the  first  170  pages  but  few  changes  have  been  found 
necessary,  but  a  few  typographical  and  other  minor  errors  have 
been  corrected.  The  tables  of  sizes,  weight,  and  strength  of 
materials  (pages  172  to  282)  have  been  thoroughly  revised,  many 
entirely  new  tables,  kindly  furnished  by  manufacturers,  having 
been  substituted.  Especial  attention  is  called  to  the  new  matter 
on  Cast-iron  Columns  (pages  250  to  253).  In  the  remainder  of 
the  book  changes  of  importance  have  been  made  in  more  than  100 
pagrs,  and  all  typographical  errors  reported  to  date  have  been 
corrected.  Manufacturers'  tables  have  been  revised  by  reference 
to  their  latest  catalogues  or  from  tables  furnished  by  the  manufac- 
turers especially  for  this  work.  Much  new  matter  is  inserted 
under  the  heads  of  Fans  and  Blowers,  Flow  of  Air  in  Pipes,  and 
Compressed  Air.  The  chapter  on  Wire-rope  Transmission  (pages 
917  to  922)  has  been  entirely  rewritten.  The  chapter  on  Electrical 
Engineering  has  been  improved  by  the  omission  of  some  matter 
that  has  become  out  of  date  and  the  insertion  of  some  new  matter. 

It  has  been  found  necessary  to  place  much  of  the  new  matter  of 
this  edition  in  an  Appendix,  as  space  could  not  conveniently  be 
made  for  it  in  the  body  of  the  book.  It  has  not  been  found  possi- 
ble to  make  in  the  body  of  the  book  many  of  the  cross-references 
which  should  be  made  to  the  items  in  the  Appendix.  Users  of  the 
book  may  find  it  advisable  to  write  in  the  margin  such  cross-refer* 
ences  as  they  may  desire. 

The  Index  has  been  thoroughly  revised  and  greatly  enlarged. 

The  author  is  under  continued  obligation  to  many  manufacturers 
who  have  furnished  new  tables  and  data,  and  to  many  individual 
engineers  who  have  furnished  new  matter,  pointed  out  errors  in 
the  earlier  editions,  and  offered  helpful  suggestions.  He  will  be 
glad  to  receive  5imilar  aid,  which  will  assist  in  the  further 
improvement  of  the  book  in  future  editions. 

William  Kknt. 

Passajc,  N.  J.,  September^  1898. 


CONTENTS. 

(For  Alphabetical  Index  lee  page  1079.) 

MATHBBIATICS. 

Arithmetlo. 

PAOB 

AritlimeticBl  and  Algebraical  Bigiw. 1 

Greatest  Common  DiTisor. 8 

Least  Conmion  Multiple. 8 

Fractions 8 

Decimals 8 

Table.    Decimal  Equivalents  of  Fractions  of  One  Inch    8 

Table.     Plroducts  of  Fractions  expressed  In  Decimals 4 

Oompouod  or  Denominate  Numbers 5 

Reduction  Descending  and  Ascending 5 

Batio  and  Proportion 6 

Invoiation,  or  Poirers  of  Nonbers 8 

Table.    First  Nine  Powers  of  the  First  Nine  Numbers 7 

Table.    First  Forty  Powers  of  2 7 

ETolntion.     Square  Boot 7 

CubeBoot... 8 

AlUgatioa 10 

Permutation 10 

Combination 10 

Arithmetical  Progression 11 

Geometrical  Progression 11 

Interest 18 

DisKonnt. 18 

Compound  Interest 14 

Compound  Interest  Table,  8,  4,  S,  and  0  per  cent 14 

Equation  of  Payments 14 

Partial  PaymeuU IS 

Annuities 16 

Tsbles  of  Amount,  Present  Values,  etc.,  of  Annuities 16 

Weights  and  Bfeasares. 

I^ng  Measure 17 

Old  Land  Measure 17 

Nautical  Measure  17 

Square  Measure 18 

Solid  or  Cubic  Measure 18 

Liquid  Measure 18 

The  Miners*  Inch 18 

Apothecaries*  Fluid  Measure. 16 

Dry  Measure 18 

Shipping  Measure 10 

Avoirdupois  Weight  10 

Troy  Weight. 10 

Apothecaries*  Weisrht 10 

To  Weigh  Correctly  on  an  Incorrect  Balance .••  10 

Circular  Measure SO 

Measure  of  time 80 

V 


E,: 


-\-'>'-ilol 


u 


HAf?VARD  COLLEGE  LIBRARY 
Fr?-'  T   ;•■  L'GPARY  OF 

FRA'...       PEABODY  MAGOUN 

lHi£  GIFT  OF  HIS  SON 

MAY  8,  1929 


COPTRIOBT,  1891^ 
BY 

WILLIAM  KENT, 


Braunworth,  Munn  fif  Barbc      .-  >    \ 
Printers  and  Binders  •;    '  ^ 

Brooklyn,  N.  y.  ^     ^^ 


PREiACE. 

More  than  twenty  years  ago  the  author  began  to  follow 
the  advice  given  by  Nystrom :  "  Every  engineeer  should 
make  bis  own  pocket-book,  as  be  proceeds  in  study  and 
practice,  to  suit  his  particular  business/'  The  manuscript 
pocket-book  thus  begun,  however,  soon  gave  place  to  more 
modern  means  for  disposing  of  the  accumulation  of  engi- 
neering facts  and  figures,  viz.,  the  index  rerum,  the  scrap- 
book,  the  collection  of  indexed  envelopes,  portfolios  and 
boxes,  the  card  catalogue,  etc.  Four  years  ago,  at  the  re- 
quest of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to 
mechanical  engineering,  and  of  condensing,  digesting,  and 
arranging  it  in  form  for  publication.  In  addition  to  this,  a 
careful  examination  was  made  of  the  transactions  of  engi- 
neering societies,  and  of  the  most  important  recent  works 
>n  mechanical  engineering,  in  order  to  fill  gaps  that  might 
>e  left  in  the  original  collection,  and  insure  that  no  impor- 
ant  facts  had  been  overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  prepara- 
ion  of  the  Pocket-book  that  will,  it  is  believed,  cause  it  to 
iffer  from  other  works  of  its  class.  In  the  first  place  it 
ras  considered  that  the  field  of  mechanical  engineering  was 
o  gTCAt,  and  the  literature  of  the  subject  so  vast,  that  as 
ttle  space  as  possible  should  be  given  to  subjects  which 
specially  belong  to  civil  engineering.  While  the  mechan- 
al  engineer  must  continually  deal  with  problems  which 
t\otig  properly  to  civil  engineering,  this  latter  branch  is 
>  well  covered  by  Trautwine's  *'  Civil  Engineer's  Pocket- 
>ok  "  that  any  attempt  to  treat  it  exhaustively  would  not 
ily  fill  no  "long-felt  want,"  but  would  occupy  space 
dich  should  be  given  to  mechanical  engineering. 
Another  idea  prominently  kept  in  view  by  the  author  has 
ten  that  he  would  not  assume  the  position  of  an  **  au- 
ority "  in  giving  rules  and  formule  for  designing,  but 
ily  that  of  compiler,  giving  not  only  the  name  of  the 
iginator  of  the  rule,  where  it  was  known,  but  also  the 
lume    and    page    from   which    it  was    taken,  so    that    its 

ill 


E ,, 


'(  -5  '-i  I  0 1 


L^ 


HAf?VARD  COLLEGE  LIBRARY 
FP?"  V--  IJBPARY  OF 

FRA".        PlABODY  MAGOUN 

THE  GIFT  OF  HIS  SON 

MAY  8.  1929 


coFTBioHT,  Ian; 

BY 

WILLIAM  KENT. 


Braunworth,  Munn  &  Barbc      .-  ^   A 
Printers  and  Bindca-s  .;   '     ^^ 

Brooklyn,  N.  V.  J       O" 


c 

''  PREPACK 

I 

Moke  than  twenty  years  ago  the  author  began  to  follow 
I  the   advice   given   by   Nystrom :    "  Every   engineeer  should 

make  his  own  pocket-book,  as  be  proceeds  in  study  and 
practice,  to  suit  his  particular  business."  The  manuscript 
pocket-book  thus  begun,  however,  soon  gave  place  to  more 
-modern  means  for  disposing  of  the  accumulation  of  engi- 
neering facts  and  figures,  viz.,  the  index  rerum,  the  scrap- 
'book,  the  collection  of  indexed  envelopes,  portfolios  and 
boxes,  the  card  catalogue,  etc.  Four  years  ago,  at  the  re- 
quest of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to 
mechanical  engineering,  and  of  condensing,  digesting,  and 
arranging  it  in  form  for  publication.  In  addition  to  this,  a 
careful  examination  was  made  of  the  transactions  of  engi- 
neering societies,  and  of  the  most  important  recent  works 
on  mechanical  engineering,  in  order  to  fill  gaps  that  might 
be  left  in  the  original  collection,  and  insure  that  no  impor* 
tant  facts  had  been  overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  prepara- 
tion of  the  Pocket-book  that  will,  it  is  believed,  cause  it  to 
lififer  from  other  works  of  its  class.  In  the  first  place  it 
ras  considered  that  the  field  of  mechanical  engineering  was 
)o  great,  and  the  literature  of  the  subject  so  vast,  that  as 
fttle  space  as  possible  should  be  given  to  subjects  which 
specially  belong  to  civil  engineering.  While  the  mechan- 
rai  engineer  must  continually  deal  with  problems  which 
elong  properly  to  civil  engineering,  this  latter  branch  is 
:>  well  covered  by  Trautwine's  **  Civil  Engineer's  Pocket- 
>oic  "  that  any  attempt  to  treat  it  exhaustively  would  not 
ily  fill  no  'Mong-felt  want,'*  but  would  occupy  space 
hicli  should  be  given  to  mechanical  engineering. 
Another  idea  prominently  kept  in  view  by  the  author  has 
ren  that  he  would  not  assume  the  position  of  an  **  au- 
ority"  in  giving  rules  and  formule  for  designing,  but 
fjy  that  of  compiler,  giving  not  only  the  name  of  the 
i^inator  of  the  rule,  where  it  was  known,  but  also  the 
lume   and    page    from   which    It  was    taken,  so    that    its 

ill 


*^  PREFACE. 

t. 

derivation  may  be  traced  when  desired.  When  different 
formula  for  the  same  problem  have  been  found  they  have 
been  given  in  contrast,  and  in  many  cases  examples  have 
been  calculated  by  each  to  show  the  difference  between 
them.  In  some  cases  these  differences  are  <iuite  remark- 
able,  as  will  be  seen  under  Safety-valves  ^nd  Crank* pins. 
Occasionally  the  study  of  these  differentes  has  led  to  the 
author's  devising  a  new  formula,  in  which  ease  the  deriva- 
tion  of  the  formula  is  given. 

Much  attention  has  been  paid  to  the  absiractlng  of  data 
of  experiments  from  recent  periodical  literature,  and  numer« 
ous  references  to  other  data  are  given.  In  this  respect 
the  present  work  will  be  found  to  differ  from  other  Pocket* 
books. 

The  author  desires  to  express  his  obligation  to  the  many 
persons  who  have  assisted  him  in  the  preparation  of  the 
work,  to  manufacturers  who  have  furnished  their  cata- 
logues and  given  permission  for  the  use  of  their  tables, 
and  to  many  engineers  who  have  contributed  original  data 
and  tables.  The  names  of  these  persons  are  mentioned  in 
their  proper  places  in  the  text,  and  in  all  cases  it  has  been 
endeavored  to  give  credit  to  whom  credit  is  due.  The 
thanks  of  the  author  are  also  due  to  the  following  gentle- 
men who  have  given  assistance  in  revising  manuscript  or 
proofs  of  the  sections  named :  Prof.  De  Volson  Wood, 
mechanics  and  turbines ;  Mr.  Frank  Richards,  compressed 
air;  Mr.  Alfred  R.  Wolff,  windmills;  Mr.  Alex.  C. 
Humphreys,  illuminating  gas ;  Mr.  Albert  E.  Mitchell, 
locomotives ;  Prof.  James  £.  Denton,  re  frige  rating-ma« 
chinery ;  Messrs.  Joseph  Wctzler  and  Thomas  W.  Varlcy, 
electrical  engineering  ;  and  Mr.  Walter  S.  Dix,  for  valuable 
contributions  on  several  subjects,  and  suggestions  as  to  their 
treatment.  WiLLlAM  Kent. 

Passaic,  N.  J.,  A^ri/^  1895. 

FIFTH    EDITION,  MARCH,  1900. 

Some  typographical  and  other  errors  discovered  in  the  fourtK 
edition  have  been  corrected.  New  tables  and  some  additions 
have  been  made  under  the  head  of  Compressed  Air.  The  new 
(1S99)  code  of  the  Boiler  Test  Committee  of  the  American 
Society  of  Mechanical  Engineers  has  been  substituted  for  the 
old  (1885)  code.  W.  K. 


PREFACE  TO  FOURTH  EDITION. 

In  this  edition  many  extensive  alterations  liave  been  made. 
Much  obsolete  matter  has  been  cut  out  and  fresh  matter  substi- 
tuted. In  the  first  170  pages  but  few  changes  have  been  found 
necessary,  but  a  few  typographical  and  other  minor  errors  have 
been  corrected.  The  tables  of  sizes,  weight,  and  strength  of 
materials  (pages  172  to  282)  have  been  thoroughly  revised,  many 
entirely  new  tables,  kindly  furnished  by  manufacturers,  having 
been  substituted.  Especial  attention  is  called  to  the  new  matter 
on  Cast-iron  Columns  (pages  250  to  253).  In  the  remainder  of 
the  book  changes  of  importance  have  been  made  in  more  than  100 
pagrs,  and  all  typographical  errors  reported  to  date  have  been 
corrected.  Manufacturers'  tables  have  been  revised  by  reference 
to  their  latest  catalogues  or  from  tables  furnished  by  the  manufac- 
turers especially  for  this  work.  Much  new  matter  is  inserted 
under  the  heads  of  Fans  and  Blowers,  Flow  of  Air  in  Pipes,  and 
Compressed  Air.  The  chapter  on  Wire-rope  Transmission  (pages 
917  to  922)  has  been  entirely  rewritten.  The  chapter  on  Electrical 
Engineering  has  been  improved  by  the  omission  of  some  matter 
that  has  become  out  of  date  and  the  insertion  of  some  new  matter. 

It  has  been  found  necessary  to  place  much  of  the  new  matter  of 
this  edition  in  an  Appendix,  as  space  could  not  conveniently  be 
made  for  it  in  the  body  of  the  book.  It  has  not  been  found  possi- 
ble to  make  in  the  body  of  the  book  many  of  the  cross-references 
which  should  be  made  to  the  items  in  the  Appendix.  Users  of  the 
book  may  find  it  advisable  to  write  in  the  margin  such  cross-refer- 
ences as  they  may  desire. 

The  Index  has  been  thoroughly  revised  and  greatly  enlarged. 

The  author  is  under  continued  obligation  to  many  manufacturers 
who  have  furnished  new  tables  and  data,  and  to  many  individual 
engineers  who  have  furnished  new  matter,  pointed  out  errors  in 
the  earlier  editions,  and  offered  helpful  suggestions.  He  will  be 
glad  to  receive  similar  aid,  which  will  assist  in  the  further 
improvement  of  the  book  in  future  editions. 

William  Kent. 

Passaic,  N.  J.,  September^  1898. 


CONTENTS. 


CFor  Alphabetical  Index  see  page  1070.) 

MATHEMATICS. 

Arlthmetle, 

PAOB 

Arithmetice]  and  Algebraical  Sigmi. 1 

Greatest  Common  InTiaor. 2 

Least  Common  Multiple 8 

Ftactions 8 

Dpcimala 8 

Table.    Decimal  Squlvalents  of  Fractions  of  One  Inch    8 

Table.     Producta  of  Fractions  ezpremed  In  Decimals 4 

Compound  or  Denominate  Numbers 6 

Reduction  Descending  and  Ascending 5 

Ratio  and  Proportion 6 

Invohitkm,  or  rowers  of  Numbers 6 

Table.    First  Nine  Powers  of  the  First  Nine  Numbers 7 

Tkble.    First  Forty  Powers  of  2 7 

Evolution.     Square  Boot 7 

CabeBoot 8 

Alligation 10 

Permutatloo 10 

Combination 10 

Arithmetical  Progression U 

Geometrical  Progression 11 

Interest 18 

Discount 18 

Compound  Interest 14 

Compound  Interest  Table,  8,  4, 6,  and  6  per  cent 14 

Equation  of  Payments 14 

Partial  Payments 15 

Annuities 16 

Tkblea  of  Amount,  Present  Valuea,  etc.,  of  Annuities 16 

Weights  and  Measures. 

Long  Measure 17 

Old  Land  Measure 17 

Nautical  Measure  17 

Square  Measure 18 

Boiid  or  Cubic  Measure 18 

Liquid  Measure 18 

The  Miners*  Inch 18 

Apothecaries*  Fluid  Measure. 18 

Dry  Measure. 18 

Shipping  Measure 19 

Aroirdupois  Weight.  10 

Troy  Weight. 10 

Apothecaries*  Weight 19 

To  Weigh  Correctly  on  an  Incorrect  Balance 19 

Circular  Measure SO 

Measure  of  time 20 

V 


0  THE 

lECHAKICAL  ENGINEER'S 
POCKET-BOOK 


A  REFERENCE-BOOK  OF  RULES,   TABLES,  DATA, 

AND  FORMULAE,  FOR  THE  USE  OF 

ENGINEERS,  MECHANICS, 

AND  STUDENTS. 


BT 

WILLIAM  KENT,  A.M.,  M.E., 

ConnUting  Engineer, 
Member  Amer,  8oc*y  MechL  Engrt.  and  Amer.  Inst.  Mining  JBngrs. 


MFTH  EDITION,   REVISED  AND  ENLARGED. 
EIGHTH    THOUSAND. 


NEW   YORK: 

JOHN   WILEY  &   SONS. 

Lokdon:  chapman  &  HALL,  Limited. 

1901. 


0  THE 

lECHANICAL  ENGINEER'S 
POCKET-BOOK 


1 

J 


A  REFERENCE-BOOK  OF  RULES,   TABLES,  DATA, 

AND  FORMULJE,  FOR  THE  USE  OF 

ENGINEERS,  MECHANICS, 

AND  STUDENTS, 


BT 

WILLIAM  KENT,  A.M.,  M.E., 

Conntlting  EngiJieer^ 
Member  Amer.  Soc*y  MeckL  JBngra,  and  Amer,  Inti,  Mining  Bngrs. 


MFTH  EDITION,  REVISED  AND  ENLARGED. 
EIGHTH    THOUSAND. 


NEW  YORK; 

JOHN    WILEY  &   SONS. 

Ia)Ndon:  chapman  &  HALL.  Limited. 

1901. 


t-  >•  I  ^-'lol 


HARVARD  COLLEGE  LIBRARY 

pr-"  T  .'  LIBRARY  OF 

FRa:  F£AE03Y  MAGOUN 

IHt  GIFT  OF  HIS  SON 

MAY  8,  1929 


COPTRIOHT,  IflQB^ 
BY 

WILLIAM  KENT. 


Braunworth,  Munn  &  Barbe 
Printers  and  Binders 
Brooklyn,  N.  Y.  ' 


.■'C\ 


PREIACE. 

MoRB  than  twenty  years  ago  the  author  began  to  follow 
the  advice  given  by  Nystrom :  "  Every  engineeer  should 
make  his  own  pocket-book ,  as  be  proceeds  in  study  and 
practice,  to  suit  his  particular  business."  The  manuscript 
pocket-book  thus  begun,  however,  soon  gave  place  to  more 
modern  means  for  disposing  of  the  accumulation  of  engi- 
neering facts  and  figures,  viz.,  the  index  rerum,  the  scrap- 
book,  the  collection  of  indexed  envelopes,  portfolios  and 
boxes,  the  card  catalogue,  etc.  Four  years  ago,  at  the  re- 
quest of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to 
mechanical  engineering,  and  of  condensing,  digesting,  and 
'  arranging  it  in  form  for  publication.  In  addition  to  this,  a 
I  careful  examination  was  made  of  the  transactions  of  engi* 
neering  societies,  and  of  the  most  important  recent  works 
on  mechanical  engineering,  in  order  to  fill  gaps  that  might 
be  left  in  the  original  collection,  and  insure  that  no  impor- 
tant facts  had  been  overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  prepara- 
tion of  the  Pocket-book  that  will,  it  Is  believed,  cause  it  to 
differ  from  other  works  of  its  class.  In  the  first  place  it 
was  considered  that  the  field  of  mechanical  engineering  was 
so  great,  and  the  literature  of  the  subject  so  vast,  that  as 
little  space  as  possible  should  be  given  to  subjects  which 
especially  belong  to  civil  engineering.  While  the  mechan- 
ical engineer  must  continually  deal  with  problems  which 
belong  properly  to  civil  engineering,  this  latter  branch  is 
so  well  covered  by  Trautwine*s  "  Civil  Engineer's  Pocket- 
book  "  that  any  attempt  to  treat  it  exhaustively  would  not 
only  fill  no  **  long-felt  want,"  but  would  occupy  space 
which  should  be  given  to  mechanical  engineering. 

Another  idea  prominently  kept  in  view  by  the  author  has 
been  that  he  would  not  assume  the  position  of  an  "  au- 
thority" in  giving  rules  and  formule  for  designing,  but 
only  that  of  compiler,  giving  not  only  the  name  of  the 
originator  of  the  rule,  where  it  was  known,  but  also  the 
rolume   and    page    from   which    it   was    taken,  so    that    its 

lii 


*^  PREFACE. 

derivation  may  be  traced  when  desired.  When  different 
formula  for  the  same  problem  have  been  found  they  have 
been  given  in  contrast,  and  in  many  cases  examples  have  < 
been  calculated  by  each  to  show  the  difference  between 
them.  In  some  cases  these  differences  are  <iutte  remark- 
able,  as  will  be  seen  under  Safety-valves  ^nd  Crank-pins, 
Occasionally  the  study  of  these  differences  has  led  to  the 
author's  devising  a  new  formula,  in  which  ease  the  deriva« 
tioa  of  the  formula  is  given. 

Much  attention  has  been  paid  to  the  abstracting  of  data 
of  experiments  from  recent  periodical  literature,  and  numer* 
ous  references  to  other  data  are  given.  In  this  respect 
the  present  work  will  be  found  to  differ  from  other  Pocket* 
books. 

The  author  desires  to  express  his  obligation  to  the  many 
persons  who  have  assisted  him  in  the  preparation  of  the 
work,  to  manufacturers  who  have  furnished  their  cata« 
logues  and  given  permission  for  the  use  of  their  tables, 
and  to  many  engineers  who  have  contributed  original  data 
and  tables.  The  names  of  these  persons  are  mentioned  in 
their  proper  places  in  the  text,  and  in  all  cases  it  has  been 
endeavored  to  give  credit  to  whom  credit  is  due.  The 
thanks  of  the  author  are  also  due  to  the  following  gentle- 
men who  have  given  assistance  in  revising  manuscript  or 
proofs  of  the  sections  named :  Prof.  De  Volson  Wood, 
mechanics  and  turbines ;  Mr.  Frank  Richards,  compressed 
air;  Mr.  Alfred  R.  Wolff,  windmills;  Mr.  Alex.  C. 
Humphreys,  illuminating  gas ;  Mr.  Albert  E.  Mitchell, 
locomotives ;  Prof.  James  E.  Denton,  refrigerating-ma« 
ciiinery  ;  Messrs.  Joseph  Wetzler  and  Thomas  W.  Varlcy, 
electrical  engineering  ;  and  Mr.  Walter  S.  Dix,  for  valuable 
contributions  on  several  subjects,  and  suggestions  as  to  their 
treatment.  WiLUAM  Kent. 

Passaic,  N.  J,,  Aprils  1895. 

FIFTH    EDITION,  MARCH,  1900. 

Some  typographical  and  other  errors  discovered  in  the  fourth 
edition  have  been  corrected.  New  tables  and  some  additions 
have  been  made  under  the  head  of  Compressed  Air.  The  nevr 
(1S99)  code  of  the  Boiler  Test  Committee  of  the  American 
Society  of  Mechanical  Engineers  has  been  substituted  for  tho 
old  (1885)  code.  W.  K. 


PREFACE  TO  FOURTH  EDITION. 

In  this  edition  many  extensive  alterations  have  been  made. 
Much  obsolete  matter  has  been  cut  out  and  fresh  matter  substi- 
tuted. In  the  first  170  pages  but  few  changes  have  been  found 
necessary,  but  a  few  typographical  and  other  minor  errors  have 
been  corrected.  The  tables  of  sizes,  weight,  and  strength  of 
materials  (pages  172  to  282)  have  been  thoroughly  revised,  many 
entirely  new  tables,  kindly  furnished  by  manufacturers,  having 
been  substituted.  Especial  attention  is  called  to  the  new  matter 
on  Cast-iron  Columns  (pages  250  to  253).  In  the  remainder  of 
the  book  changes  of  importance  have  been  made  in  more  than  100 
pagrs,  and  all  typographical  errors  reported  to  date  have  been 
corrected.  Manufacturers'  tables  have  been  revised  by  reference 
to  their  latest  catalogues  or  from  tables  furnished  by  the  manufac- 
turers especially  for  this  work.  Much  new  matter  is  inserted 
under  the  heads  of  Fans  and  Blowers,  Flow  of  Air  in  Pipes,  and 
Compressed  Air.  The  chapter  on  Wire-rope  Transmission  (pages 
917  to  922)  has  been  entirely  rewritten.  The  chapter  on  Electrical 
Engineering  has  been  improved  by  the  omission  of  some  matter 
that  has  become  out  of  date  and  the  insertion  of  some  new  matter. 

It  has  been  found  necessary  to  place  much  of  the  new  matter  of 
this  edition  in  an  Appendix,  as  space  could  not  conveniently  be 
made  for  it  in  the  body  of  the  book.  It  has  not  been  found  possi- 
ble to  make  in  the  body  of  the  book  many  of  the  cross-references 
which  should  be  made  to  the  items  in  the  Appendix.  Users  of  the 
book  may  find  it  advisable  to  write  in  the  margin  such  cross-refer- 
ences as  they  may  desire. 

The  Index  has  been  thoroughly  revised  and  greatly  enlarged. 

The  author  is  under  continued  obligation  to  many  manufacturers 
who  have  furnished  new  tables  and  data,  and  to  many  individual 
engineers  who  have  furnished  new  matter,  pointed  out  errors  in 
the  earlier  editions,  and  offered  helpful  suggestions.  He  will  be 
glad  to  receive  similar  aid,  which  will  assist  in  the  further 
improvement  of  the  book  in  future  editions. 

William  Kent. 

Passaic.  N.  J.,  Stpttmber^  1898. 


CONTENTS. 


(For  Alphabetical  Index  see  page  1079.) 

MATHEMATICS. 

Arithmetle. 

PAOB 

ArithmetiealandAlKebralcalSigiiB. 1 

Gnsalest  Common  DiTiaor. 9 

Least  Oommon  Multiple 8 

Fracrions 2 

D(«tmala 8 

Table.    Dedmal  Equivalents  of  Fractions  of  One  Inch    S 

Table.     Products  of  Fractions  expressed  In  Decimals 4 

Oomponnd  or  Denominate  Numbers 6 

Reduction  Descending  and  Ascending ft 

Ratk>  and  Proportion 6 

Involution,  or  Powers  of  Nmnbers 0 

Tftble.    First  Nine  Powers  of  the  First  Nine  Numbers 7 

Table.    First  Forty  Powers  of  2 7 

Evolution.     Square  Root 7 

CubeBoot 8 

Alligation 10 

Permutation 10 

Combination 10 

Arithmetical  Progression 11 

Geometrical  Progression 11 

Interest 18 

Discount. 18 

Compound  Interest 14 

Compound  Interest  Table,  8,  4, 6,  and  6  per  cent 14 

Equation  of  Payments 14 

Partial  Paymento 15 

Annuitiea 16 

Tables  of  Amount,  Present  Values,  etc.,  of  Annuities 16 

Weights  and  HeasuTes. 

Long  Measure 17 

OldLand  Measure 17 

Nautical  Measure  17 

Square  Measure 18 

Solid  or  Cubic  Measure 18 

Uqnid  Measure 18 

Tbe  Miners*  Inch 18 

Apothecaries*  Fluid  Measure. 18 

Dry  MesMire  18 

Shipping  Measure 19 

AvoirdupoU  Weight.  19 

Troy  Weight, 19 

Apothecariea' Weight 19 

To  Weigh  Correctly  on  an  Incorrect  Balance 19 

CIrcniar  Measure 80 

Measure  of  time 20 

V 


VI  ...  CONTENTS. 

Board  and  Timber  Measure iC 

Table.    ConteDU  in  BVet  of  Joists,  Scantlings,  and  Timber. 2( 

French  or  Metric  Mensures 21 

British  and  French  Equivalents. 2] 

Metric  Conversion  Tables , 2£ 

Compound  Units. 

of  Pressure  and  Weight 2^ 

of  Water,  Weight,  and  Bulk 21 

of  Work,  Power,  and  Duty Zi 

of  Velocity 21 

of  Pressure  per  unit  area 21 

Wire  and  Sheet  Metal  Gaums 26 

Twist-drill  and  Steel-wire  Gauges 2fi 

Music-wire  Gauge 2S 

Circular-mil  Wire  Gauge 8G 

NewU.S.  Standard  Wire  and  Sheet  Gauge,  1808 ..  80 

Decimal  Gauge 88 

Alfl^ebra. 

Addition,  Multiplication,  etc 89 

Powers  of  Numbers 89 

Parentheses,  Division 84 

Simple  Equations  and  Problems 84 

Equations  containing  two  or  more  Unknown  Quantities 8.1 

Elimination .  ..  8S 

Quadratic  Equations 85 

heory  of  Exponents 36 

Binomial  Theorem 80 

Geometrical  Problems  of  Construction 87 

of  Straight  Lines...-. 87 

of  Angles 88 

ofOircles 89 

ofTrlangles 41 

of  Squares  and  Polygons 42 

oftheElllpee 46 

of  the  Parabola 48 

of  the  Hyperbola 49 

oftbeOycloid 49 

of  the  Tractriz  or  Schiele  Anti-friction  Curve SO 

oftheSpiral 00 

of  the  Catenary 51 

of  the  Involute. 52 

Geometrical  Propositions 58 

Mensuration,  Plane  SurCaces* 

Quadrilateral,  Parallelogram,  eto 54 

Trapezium  and  Trapezoid. ,  54 

Triangles 64 

Polygons.    Table  of  Polygons 55 

Irregular  Figures ....  SB 

Properties  of  the  Circle. S7 

Values  of  ir  and  its  Multiples,  etc 57 

B«latlons  of  arc,  chord,  etc fl8 

Belations  of  circle  to  inscribed  square,  etc 59 

Sectors  and  Segments. 50 

Circular  Bing 50 

The  Ellipse 59 

TheHeliz. 60 

The  Spiral 00 

Mens  oration ,  Solid  Bodies. 

Prism...... 60 

Pyramid 80 

wedge 61 

The  Prismoidal  Formula 6i 

Rectangular  Prlsmoid 61 

Cylinder 61 

Cone 61 


PIGS 

Sphere 61 

Spherical  Triangle 61 

Spherical  PoiygOD ...••..  61 

^herical  Zone  68 

Spherical  Segment 69 

Spheroid  or  Ellipsoid 68 

Polyedron 62 

Cytindrical  Bins 62 

Solkla  of  BevoluUoD 68 

SiriJidJea 63 

Frusutun  of  a  Spheroid. 6S 

Parabolic  Goooid 64 

Tolume  of  a  Cask 64 

Irrefnilar  Solids 64 

Plane  Trigonometry. 

Solution  of  Plane  Trlangtee 66 

Sine,  TftsseDt,  Secant,  etc 65 

SilpM  of  the  Trtffononvttric  Functions 66 

TVigonometricalFormaln 66 

SohiHon  of  Plane  Right-angled  Triangles 66 

Solution  of  Oblique-angled  Trianglee 66 

Analytieal   Geometry. 

Ordlnates  and  Ahsctssaa 68 

EquatSona  of  a  Straight  Line,  Intersections,  etc 69 

Equations  of  the  Circle 70 

Equations  of  the  Ellipse TO 

Equations  of  the  Parabola : 70 

Equationa  of  the  Hyperbola. 70 

Logaritlunic  Curves. 71 

DIlTerentlal  Caleulns. 

Definttiona 7« 

I>Uferential8  of  Algebraic  Fonctlons ....  78 

Fonnulse  for  Differentiating 78 

Partial  Differentials 78 

Integrals 78 

Formulsfor  Integration 74 

Integration  between  Limits 74 

Quadrature  of  a  Plane  Surf  ace. 74 

Ouadratore  of  Surfaces  of  Revolution 75 

Cubature  of  Volumes  of  Revolution 76 

Second,  Third,  etc..  Differentials 75 

ltaclanriB*s  and  Taylor's  Theorems 76 

lf^Wi«^  aim!  Minima 76 

Differential  of  an  EziMnentlal  Function 77 

Ixsgarlthms 77 

Differential  Forms  which  have  Known  Integrals 78 

Exponential  Functions 78 

Circular  Functions. 78 

TbeQyelold 79 

Inteipml  Calculus 79 

Uaihen&atleal   Tables. 

BecipfYKsals  of  If  umbers  1  to  8000 80 

Squares,  Cubes,  Square  Roots,  and  Cube  Roohi  from  0.1  to  1600 86 

Squares  and  Cnbes  of  Decimals 101 

Fifth  Rooto  and  Fifth  Powers 102 

Circnmferenoes  and  Areas  of  Circles,  Diameters  1  to  1000.... 103 

Ctrcnmferenoea  and  Areas  of  Circles,  Advancing  by  Eighths  from  A  to 

100 108 

Deefmala  of  a  Foot  Equivalent  to  Inches  and  Fractions  of  an  Inch 118 

Ctrcnmferences  of  Circles  in  Feet  and  Inches,  from  1  loch  to  88  feet  11 

iocbee  la  diameter. 118 

Lengths  of  Circular  Arcs,  Degrees  Given 114 

Lengths  of  Circular  Arcs.  Height  of  Arc  Given  115 

Areas  of  the  Segments  of  a  Circle. lio 


Viii  OONTENTa 

PAOK 

Spheres 116 

Oontents  of  Pipes  and  Cylinders,  Cubic  Feet  and  Gallons i:ao 

Cylindrical  Vessels,  Tanks,  Cisterns,  etc 181 

Oallons  in  a  Number  of  Cubic  Feet 1«3 

Cubic  Feet  in  a  Number  of  Gallons 123 

Square  Feet  iit  Plates-S  to  88  feet  long  and  1  inch  wide 128 

Capacities  of  Rectangular  Tanks  in  Gallons 125 

Numberof  Barrels  in  CyUndrical  Cisterns  and  Tanks 126 

Lof(arithms 1«7 

Table  of  LoRarltbms 129 

Hyperbolic  J^iOgaritfams 156 

Natural  Trigonometrical  Functions 158 

Logarithmic  Trigonometrical  Functions ^ 168 

MATBKIAU. 

Chemical  Elements 16& 

Specific  Gravity  and  Weight  of  Materials 168 

Metals,  ProperUes  of 164 

The  Hydrometer 165 

Aluminum 166 

Antimony 166 

Bismuth 166 

Cadmium 167 

Copper 167 

Gold 167 

Iridium 167 

Iron 167 

Lead 167 

Magnesium 168 

Manganese 168 

Mercury 168 

Nickel 168 

Platinum 168 

Silver 168 

Tin 168 

Zinc 168 

BUsoellaneoas  Materials. 

Order  of  Malleabllitj,  etc.,  of  Metals 169 

FormulQ  and  Table  for  Calculating  Weight  of  Bods,  Plates,  etc 169 

Measures  and  Weighu  of  Various  Materials 169 

Commercial  Sixes  of  Iron  Bars 170 

Weights  of  Iron  Bars. 171 

of  Flat  Rolled  Iron ITS 

of  Iron  and  Steel  Sheets. 174 

of  Plate  Iron 175 

of  Steel  Blooms 17B 

of  Structural  Shapes 177 

Sizes  and  Weights  of  Carnegie  Deck  Beams 177 

^  '*       Steel  Channels 178 

"  "       ZBars 178 

"  **  Penooyd  Steel  Angles 179 

u  u  u       Tees lao 

**  **  **       Channels 1«^ 

•♦  ••  Roofing  Materials 181 

"  "  Terra-cotta. 181 

"  ••  Tiles 181 

••  "  Tin  Plates 18i 

"  ••  Slates 18S 

**  **  PineSblngles 189 

••  *'  Skv.light  Glass 184 

Weights  of  Various  Rooi-coverlngs 1 8i 

**  Cast-iron  Pipes  or  Columns IKS 

l«ft.  lengths 188 

-fltUngs. iset 

er  and  Gas-pipe 188 

"    and  thickness  of  Cast-iron  Pipes ]8i 

Safe  Pressures  on  Cast  Iron  Pipe 180 


*•     PIpe-l 
'*     Watei 


COKTElTTfl.  IX 

PAGK 

Sbeetriron  Hydraulic  Pipe 101 

SUuidard  Pipe  Flanges 192 

Pipe  Flanges  and  Cast-iron  Pipe 198 

Standard  Sises  of  Wrought-iron  Pipe IM 

Wrottght-iron  Welded  Tubes 196 

RiTeted  Iron  Pipes 197 

Weight  of  Iron  for  Riveted  Pipe 197 

Spiral  BtTeted  Pipe 198 

Seamless  Brass  Tubing 198,  199 

Coiled  Pipes 199 

Braas^  Copper,  and  Zinc  Tubing 200 

Lead  and  Tin-lined  Lead  Pipe SOI 

Weisrht  <tf  Copper  and  Brass  Wire  and  Plates SOS 

^      Round  Bolt  Copper 208 

"      Sheet  and  Bar  Brass 208 

Composition  of  Rolled  Brass 903 

Sizesof  Shot 204 

Screw-thread,  U.  B.  Standard 904 

Umit-gauges  for  Screw-threads 206 

Siaeoflron  for  Standard  Bolts 206 

Sixes  of  Screw-threads  for  Bolts  and  Taps 207 

Set  Screws  and  Tap  Screws 208 

Standard  Machine  Screws 209 

Siaea  and  Weights  of  Nuts 209 

Weight  of  Bolts  with  Heads 210 

TnuSc  Bolts 810 

W^eigfata  of  Nuts  and  Bolt-heads ^  211 

Rivets 211 

Shoes  of  Tnmbuckles 211 

Washers 212 

Track  Spikes 212 

RaawaySpikes 212 

BoatSplkes 212 

Wrought  Spikes 213 

Wire  Spikes 218 

CntNalfito 213 

Wire  Nails ,. 214,  216 

Iroo  Wire,  Size,  Strength,  etc 216 

Galvanized  Iron  Telegraph  Wire 217 

Tests  of  Telegraph  Wire 217 

Copper  Wire  Table,  B .  W.  Gauge 218 

^'^     '•         "     Edison  or  Circular  Mil  Gauge... 219 

••  "         *•     B.&S.Gauge 230 

losolated  Wire 221 

Copper  Telegraph  Wire 221 

EJectricCables 221,222 

Galvanised  Steel-wire  Strand 223 

Steel-wire  Cables  for  Vessels 223 

BpeeUcacions  for  Galvanized  Iron  Wire 224 

Strength  of  Piano  Wire 884 

Ploiqcfa-steel  Wire  224 

Wires  of  differen  t  metals 225 

Spedflcations  for  Copper  Wire 226 

Cable-traction  Ropes 226 

Wire  Ropes 226,  227 

Floagrbsteel  Ropes 227,  228 

Galvanized  Iron  Wire  Rope 228 

Steel  Hawsers 223,229 

Flat  Wire  Ropes 2-4;9 

Galvanized  Steel  Cables 230 

Streng^th  of  Chains  and  Ropes .. . 230 

Notes  OB  use  of  Wire  Rope 281 

Locked  Wire  Rope 231 

Crane  Chains 232 

Weights  of  Logs,  Lumber,  etc 232 

Siaea  of  Fh«  Brick 288 

Fire Claj, Analysia ■ ...  284 

k  Bricks 285 

286 


3t  C0KTRKT8. 

Strength  of  Material!. 

^  PAOK 

Htreiid  and  Strain » ».  ,.,., ^m 

EImUc  Ltiiiit »,,., ,. j96 

Yield  Point , »....  «? 

Modulus  of  Elasticity ,887 

Reiiillence ...*... »..»..  888 

Elastic  Limit  and  Ultimate  Stress ».», S38 

Repeated  Stresses , ,».  $18 

Hft«peat4*d  Sli<K!ks  ».  240 

Stresses  due  to  Sudden  Shocks , 841 

IncreasIuK  Tensile  Strength  of  Bars  by  Twisting » iM  t 

Tensile  Strength .» ,.»» »....»  d44 

Measurement  of  Elongation » »  S4^ 

Shapes  of  Test  Specimens »...» w....k...»  843 

Ck>inpres8ive  Strength ,» »,» , »  844 

Columns,  Pillars,  or  Struts 816 

Hodgkinson^s  formula , , 846 

Gordon's  Formula »,.,» »*.•.....,» 947 

Moment  of  Inertia i.»..i...» »..».»».....  847 

JUdl us  of  Gyration »  ♦ , ,....  847 

Elements  of  Usual  Sections , ».,..  848 

Strength  of  Cast-iron  Columns 860 
ransverse  Strength  of  Cast  Iron  Water-pipe Sal 

Safe  Load  on  Cast-iron  Columns        i 8&8 

fiirengthof  Brackets  on  Cast-iron  Columns 858 

£cceiitric  IxMidint;  of  Columns v.tt *... SM 

Wrought-iron  Columns SJ55 

Built  Columns 896 

Pbceniz  Columns  867 

Working  Form ulffi  for  Struts »...  Aw 

Merriman's  Formula  for  Columns > SAO 

Working  Strains  in  Bridge  Members %..  ^i 

Working  Stresses  for  Steel ^ 166 

Resistance  of  Hollow  Ci'linders  io  Collapse 864 

OoUapsine  Pressure  of  Tubes  or  Flues $6& 

Formula  for  Corrugated  Furnaces 866 

Transverse  Strength t 866 

Formulae  for  Flexure  of  Beams ...i........  96? 

Safe  Loads  on  Steel  Beams ».....»..  ...  6B0 

Elastic  Resilience  •..*».....►» 8^0 

Beams  of  Uniform  Strength » » •• ^St  1 

Properties  of  Rolled  Structural  Shapes. v % 878 

*'  "  Steel  1  BeaniH •  ..  .  876 

Spacing^of  Steel  I  Beams «.  .. ATI 

Properties  of  St H(^l  Channels »,  iit 

••  "TSliapes %  TTS 

"  *'  Angles S^78<k 

"  **  Z  bars 860 

Bise of  Beams  for  Floors » »..» 886 

Flooring  Material.. 661 

TieRod.sfor  Brick  Arches ».. 66t 

Torsional  Strength » *%,.»..  9Sk 

Elastic  Resistance  to  Torsion 881 

Combined  Stresses 6tt 

Stress  due  to  Temperature ..*•.,.  »..  9i6 

Strength  of  Flat  Plates 886 

Strength  of  Unstayed  Flat  Surfaces »..  8R4 

Unbraced  Heads  of  Boilers  «......«..  266 

Thickness  of  Flat  Cast-iron  Plates *.,. 866 

Strength  (if  Stayed  Surfaces    36i 

Spherical  Shells  and  Domed  Heads » 866 

Stresses  Ih  Steel  Plating  under  Water  Pressure »....%......  86^ 

Thick  Hollow  Cylinders  under  Tension 86( 

Thin  Cylinders  under  Tension 866 

Hollow  Copier  Balls  968 

Holding  Power  of  Nails,  Spikes,  Bolts,  and  Scree's 969 

Cut  verwM  Wire  Nails  9B6 

Strength  of  Wrought-iron  Bolts 996 


OOKTBITTS.  xi 

PAGE 

IniHal  Strain  on  BolU S9S 

SUnd  Pipes  and  their  Deflign 998 

Ittveced£eel  Water-pipes 8» 

If ^ yi»y^^f\M T» m%  Xubes •..••••••■•■•t* •«••••■«• •>.•••••••••■••  8M 

DrkaidT's  Tests  oCMAterisls SM 

Castlroa S9G 

IronCastings •  297 

Iron  Bars,  Porsings,  etc S97 

Steel  Balis  JUuTTires 806 

Steel  Axles,  Shafts,  Sprinc  Steel 899 

Riveted  Jointe 999 

Welds ^....  aOO 

Copper,  Brass,  Brooxe,  etc 900 

Wire,  Wira-rope •• 801 

Ropes,  Hemp,  sad  Cotton 901 

Betting,  GanTas 908 

Stones,  Briclc,  Cement 908 

Tensile  Strength  of  Wire 908 

Watertown  listing-machine  Tests 909 

Rireted  Joints 90S 

Wroocht'lron  Bsrs,  CompresBion  Tests .•.......,* 904 

Steell^e-bsn T. 90i 

Wroofffat-iron  Colomns • •••..• ...  905 

Cold  Drawn  Steel 908 

Amerioan  Wood» 909 

Sbeartns  Strength  of  Iron  and  Steel 908 

Holding  Power  of  Boilei^tubes 807 

Chains,  Weight,  Proof  Ttot,  etc 807 

Wrought-iron  Chain  Cables. 806 

8lz«i«thofGHnB.... 906 

Copper  at  HtRfa  Temperatnres 908 

Screngtb  of  limber 909 

Expansion  of  Timber • , 811 

Sbeartns  Strength  of  Woods 818 

StreagtB  <tf  Bnck,  Stone, etc .....••.••..«...  918 

^^      -    Flsgging 819 

«        **    Ume  and  Cement  Mortsr 818 

XodQH  of  Etasticity  of  Ysrious  Materials 814 

FSctoiB  of  asfetf 814 

Prvpertlcs of  Cork 818 

Vukanixed  India-rubber • 816 

Xf  lolith  orWoodstone 816 

AlomlaaaEi,  Properties  and  Uses .•* • 917 

AUoTs. 

AHofv  of  Copper  and  Tin,  Bronae 918 

Copper  and  Zinc,  Brass , 881 

Variation  in  Stnngth  of  Broaae 921 

Copper*Un-sinc Alloys... .».....• ...888 

Uqnatlon  or  Separation  of  Metals 8x8 

AflfoyaaoedinBrsasFoondries  .... 986 

Copper-tttokel  AiJora 886 

Copper-«ino4ron AJioyB • 8UI 

TbblaBronae aW 

FboqiAior  Bronae.. 


Akimiaam  Brass • 929 

CsuOoa  as  to  Strength  of  Alloys 989 

AJumiaiim hardened 8S0 

ABoys  of  Aluminum.  Silicon,  and  Iron • 380 

Tttncsten-alumiaum  Allogfs. 881 

Alumlaum-tin Alloys., 881 

Mangaoeae  Alloys 981 

Msuiisnenn  Bronae. • 981 

German  SilTer ,888 

ABoysof  Bismnth ,  889 

rmoble  Alloys 888 

~      -    rHetalAllc^ys. 818 


Ill  GOKTEKTS. 

PAOfl 

Alloys  contatniDg  Antlmonj 890 

White-metal  AIlojs , 884 

Type-metal Uj 

Babbitt  metals. 881 

Solders SS 

Ropes  and  Chains. 

Strength  of  Hemp,  Iron,  and  Steel  Ropes 33fi 

FlatBopes * , 83( 

WorkioK  Load  of  Ropes  and  Chains 8:)fi 

Strength  of  Ropes  and  Chain  Cables 34C 

Rope  xor  Hoisting  or  Transmission 3K 

Cordage,  Technical  terms  of 84] 

Splicing  of  Ropes »4] 

Coal  iioisting 84;! 

HanllaCordage.  Weight,  etc.. 844 

Knots,  how  to  make 844 

Splicing  Wh«  Ropes 341 

Springs. 

Laminated  Steel  Springs 84'a 

Helical  Steel  Springs 34^ 

Carrying  Capacity  of  Springs 84S 

Elliptical  Springs  852 

Fhosphor-bronse  Springs « 86:^ 

Springs  to  Resist  Torsional  Force 85^ 

Helical  Springs  for  Cars,  etc 859 

Riveted  Joints. 

Fairbalm*s  Experiments 854 

Loss  of  Strength  by  Punching    854 

Strength  of  Perforated  Plates .....854 

Hand  vs.  Hydraulic  Riveting 85S 

FormulsB  for  Pitch  of  Rivets 35*3 

Proportions  of  Joints 35C 

Efficiencies  of  Join  ts 85fl 

Diameter  of  Rivetfl 860 

Strength  of  Riveted  Joints •. 361 

Riveting  Pressures 869 

Shearing  Resistance  of  Rivet  Iron 863 

Iron  and  Steel. 

Classification  of  Iron  and  Steel 884 

Grading  of  Pig  Iron 365 

Influence  of  Silicon  Sulphur,  Phos.  and  Mn  on  Cast  Iron 86fi 

Tests  of  Cast  Iron 809 

Chemistiy  of  Foundiy  Iron 870 

Analyses  of  Castings 87^3 

Strength  of  Cast  Iron 874 

Speclflcations  for  Cast  Iron 874 

Mixture  of  Cast  Iron  with  Steel 87n 

Bessemerised  Cast  Iron 873 

Bad  Cast  Iron 875 

Malleable  Cast  Iron STB 

Wrought  Iron      877 

CSieinistryof  Wrought  Iron 877 

Influence  of  Rolling  on  Wrought  Iron 877 

Specifications  for  wrought  Iron 87^ 

Stay-bolt  Iron 879 

FormulsB  for  Unit  Strains  In  Structures 379 

Permissible  Stresses  in  Structures 881 

Proportioning  Materials  in  Memphis  Bridge 88:1 

Tenacity  of  Iron  at  High  Temperatures SSI 

BJfect  of  Cold  on  Strength  of  Iron S8t 

Expansion  of  Iron  by  Heat 885 

Durability  of  Cast  Iron 885 

Corrosion  of  Iron  and  Steel 886 

_  Preservative  Coailugs;  Paints,  etc 887 


coNTBKra  xiii 

PAOS 

Pou-oxidizinK  Prooen  of  Annealing: 887 

Ibuigaiieae  FlaUng  of  Iron 889 

8to«I. 

BBlatton  between  Chem.  and  Phys.  PropertiM • -  889 

Variation  In  Strength 891 

Open-hearth 809 


Banleninff  Soft  Steel 808 

Effect  of  Cold  BoUing 888 

Oomparlaott  of  FnlMaed  and  8m«n  Pleoea 8B8 

Treataoent  of  Structural  Steel 8M 

Inflnenoe  of  Annealing  upon  Magnetic  Oapadtj 8B8 

BpecUleatlona  for  Steel 807 

Boiler.  Ship  and  Tank  Flatea 800 

Steel  for  Springa,  Azlea.  etc 400 

XajOartwn  be  Burned  out  of  Sterir 408 

Becaleaceficcof  Steel '. 408 

Effectof  NIckingaBar 408 

Bleetite  ConductiTlt/ 408 

Spedfio  QruriXj 408 


408 

Begregation  In  ] 

Earliest  Usee  for^tructuroa 406 

Steel  CaatingB 406 

ManganeaeSted 407 

Hk:kel  Steel  407 

Aluminnm  Steel 400 

Chrome  Steel 409 

Tnngaten  Steel 400 

OompreaBed  Steel 410 

CrudUe  Steel 410 

Effect  of  Heat  on  Grain 41S 

»     ••  Hammering,  eto 412 

Heating  and  Forging 419 

Ttanpering  Steel 4ia 

MXOHANICS. 

Force,  Unit  of  Foroe 411^ 

Inertia 415 

Mewton^aLawBof  Motion 416 

Beaofaitlon  of  Forcea 415 

Parallelogram  of  Forces 410 

Moment  of  a  Force. 410 

Statical  Moment,  StabiUty 417 

StabOItT  of  a  Dam 417 

PandlelForcee 417 

Oooples 418 

EqniHhrlmnof  Forces 418 

Oentre  of  OravitT 418 

rinerOa., 


fc  of  Inertia 419 

Oentre  of  Oyiution • 490 

Badlna  of  Gyration 490 

Centre  of  OacOlation 491 

Centre  of  Percuaalon 499 

The  Pendulum 498 

Cboieal  Pendulum 498 

Centrifugal  Force 498 

Aooelmlion.; 498 

FaUlngBodiea 494 

Value  of  p. 494 

Angular  veloci^ • 496 

Height  doe  to  Velodiy 496 

Paraflelogram  of  Velocitiea 498 

MaflB 497 

Force  of  Acceleration 497 

Motion  on  InclhiedPliinea. 498 


:X1V  CONTEKT& 

VteVIva 498 

Work,  Foot-pound 4S8 

Power,  Horse-power 429 

Energy 429 

Work  of  Acceleration 430 

Force  of  a  Blow , 480 

Impact  of  Bodies 481 

Bnengy  of  Becoil  of  Guns 4S1 

Oonsenratlon  of  Energy 488 

Perpetual  Motion  4^18 

Sfllciencyof  aMachlne 488 

Aslmal-power,  Man-power 488 

WorkofaHorse 484 

Man-wheel 484 

Horse-sin 484 

Bastotance  of  Vehldee 485 

Elements  of  Maohlnes. 

The  Lever 486 

The  Bent  Lerer 486 

The  Moving  Strut 486 

The  Toffgle-joiot 488 

The  Inclinea  Plane 487 

The  Wedge 487 

TheScrew 437 

The  Cam 488 

ThePulley 488 

Differontial  PuUej iSS> 

DUTerential  WlndJasB 489 

DifferenUal  Screw 48C' 

WheelandAxle 489 

Toothed-wheel  Gearing 489 

IMlesB  Screw 4M 

Stresses  In  Fran&ed  Struotures. 

Cranes  and  Derricks 440 

Shear  Poles  and  Guys 448 

King  Post  Truss  or  Bridge. 448 

Queen  Post  Truss 448 

Burr  Truss 44S 

Pratt  or  Whipple  Truss 44S 

HoweTmss 445 

Warren  Girder 445 

Roof  Truss ; 4^ 

HBAT. 

Thermometeiv  and  Pyrometers 448 

Centigrade  and  Fahrenheit  degrees  compared 449 

Copper-ball  Pyrometer 461 

Thermo*eleotnc  FVrometer 451 

Tdniperatures  in  Furnaces 451 

Wlborgh  Air  pyrometer 458 

Seegers  Fire-Clay  Pyrometer 458 

Mesur6and  Nouel's  Pyrometer 468 

Uehling  and  BteinbarCs  Pyrometer 468 

Air-thermometer , 454 

High  Temperatures  Judged  by  Color 454 

BotliDg-polnts  of  Substances 465 

Melting-points 456 

0nftof  Heat 465 

Mechanical  Equivalent  of  Heat 486 

Heat  of  Combustion 466 

Specific  Heat 457 

Latent  Heat  of  Fusion 459»461 

Expansion  by  Heat 468 

Absolute  Temperature 461 

Absolute  Zero 461 


OOSTTEiriBi  XV 

PAGS 

Latent  HeAt 461 

Latent  Heat  of  Evaporation 4«d 

Total  Heat  of  Evaporation 408 

Evaporation  and  Drying.. 408 

Evaporation  from  Beaervoirs 408 

Evaporation  by  the  Kultlple  System 468 

BeElstance  to  B<riling 468 

Manuf actui«  of  Salt 404 

Solubility  of  Salt  and  Sulphate  of  lime 404 

Salt  CootenU  of  Brines 404 

Ooncentratlon  of  Sugar  Solutions 465 

Evaporating  by  Kxhaiist  Steam 466 

Drying  in  vacuum 466 

Radiation  of  Heat ; 467 

Conduction  and  Convection  of  Heat ..468 

Rate  of  Eztamal  Oondnotion 460 

Steam-pipe  Coverings 470 

Transmission  through  Plates 471 

**  in  Condenser  Tubes 478 

"  "       Cast-iron  Plates.  474 

"  from  Air  or  Gases  to  Water 4T4 

••  from  Steam  or  Hot  Water  to  Air 47B 

**  through  Walls  of  Buildings 478 

Thennodynamics 478 

PHTSICAI*  PBOFERTI£S  OF  OASES. 

Ezpaaalon  of  Oases 4T9 

Boyle  and  ICarriotte's  Law 479 

Law  of  Charles,  Avogadro*s  Law 479 

Saturation  Point  of  vapors 480 

Law  of  Gaseous  Pressure    480 

Flow  of  Gaaes 480 

Absorption  byLtqDidB 480 

AIB. 

Properties  of  Air 481 

Air-manometer 481 

Pressure  at  Different  Altitudes 481 

Barometric  Pressures. 488 

Levelling  br  the  Barometer  and  by  Boiling  Water 482 

To  find  Difference  in  Altitude 488 

Moisture  in  Atmosphere 488 

Weight  of  Air  and  Mixtures  of  Air  and  Vapor 484 

Specific  Heat  of  Ahr 484 

Flow  of  Air, 

Flow  of  Air  through  Orifloes 484 

Flow  of  Air  in  Pipes 486 

Effect  of  Bends  in  Pipe 488 

Flow  of  Compressed  Air 488 

Tables  of  Flow  of  Air 489 

Anemometer  Measurements 491 

Equalization  of  Pipes 491 

Loss  of  Fraasure  in  Pipes 498 

Wind. 

Force  of  the  Wfaid 498 

Wind  Pressure  hi  Storms 496 

Windmills 495 

Capacity  of  Wtodmills 497 

Economy  of  Windmills 498 

ElectricFOwer  from  Windmills 499 

Compressed  Air. 

499 

499 

600 


Heating  of  Air  hw  Compression 

Loss  of  Energy  m  Compressed  Air. 
Volomea  aparresBures » 


X?i  CONTElirTS, 

PiOl 

Lofls  due  to  Ezoess  of  Pressure 601 

Horse^wer  Required  for  Corapressloo 501 

Table  for  Adiabaiic  Compression ^ fiOsS 

Mean  Effective  Pressures  • ...608 

Mean  and  Terminal  Pressures 608 

Air-compressors 608 

Practical  Results 606 

Efficiency  of  Oompressed-air  Engines 606 

Requirements  of  Rock-drills 1 606 

Popp  Oompressed-air  System 607 

Small  Compressed-air  Motors 607 

Efficiency  of  Air-heatioK  Stoves 607 

Efficiency  of  Compressed-air  Transmission 60^ 

Shops  Operated  by  Compressed  Air 609 

Pneumatic  Postal  Transmission 609 

Mekarski  Compressed-air  Tramways 610 

Compressed  Air  Working  Pumps  in  Mines 611 

Fans  and  Blowers. 

Centrifugal  ^ans Sll 

Best  Proportions  of  Fans 513 

Pressure  due  to  Velocity 618 

Experiments  with  Blowers 614 

Quantity  of  Air  Delivered 514 

Kfflciency  of  Fans  and  Positive  Blowers 516 

Capacity  of  Fans  and  Blowers 517 

Table  of  Centrifugal  Fans 518 

Engines,  Fans,  and  Steam-coils  for  the  Blower  System  of  Heating. 519 

Sturtevant  Steel  Pressure-blower 519 

Diameter  of  Blast-pipes •••,. 519 

Efficiency  of  Fans •....•.•••••.•• ••  6S0 

Centrifugal  Ventilators  for  Mines S3I 

Experiments  on  Mine  Ventilators 6S8 

DiskFans , 694 

Air  Removed  by  Exhaust  Wheel 625 

Efficiency  of  Disk  Fans 585 

Positive  Rotary  Blowers 520 

Blowing  Engines 528 

Steam-let  Blowers 607 

Steam-Jet  for  Ventilation 627 

BEATING  AND  VENTILATION. 

Ventilation BBS 

Quantity  of  Air  Discharged  through  a  Ventilating  Duct. 590 

Artificial  Cooling  of  Air 581 

Mine-ventilation  681 

Friction  of  Air  in  Underground  Passages 581 

Equivalent  Orifices 588 

Relative  Efficiency  of  Fans  and  Heated  Chimneys 683 

Heating  and  Ventilating  of  Large  Buildings 684 

Rules  for  Computing  Radiating  Surfaces 688 

Overhead  Steam-pipes 687 

Indirect  Heating-surface 587 

Boiler  Heating-surface  Required 588 

Proportion  of  Grate-surface  to  Radiator-surface 538 

Steam-consumption  in  Car-heating 588 

Diameters  of  Steam  Supply  Mains 588 

Registers  and  Cold-air  Ducts 530 

Physical  Properties  of  Steam  and  Condensed  Water 540 

Size  of  Steam-pipes  for  Heating 510 

Heating  a  Greenhouse  by  Steam 541 

Heating  a  Greenhouse  by  Hot  Water 543 

Hot-water  Heating  642 

Law  of  Velocltv  of  Flow 54« 

Proportions  of  Radiating  Surfaces  to  Cubic  Capacities 543 

Diameter  of  Main  and  Branch  Pipes 543 

Rules  for  Hot-water  Heating 544 

Arrangements  of  Mains 544 


OOHTBNTa  Xvii 

FAOK 

fitowerSystetn  of  Hefttlng  and  Ventilating... <...*... 645 

KzperimenU  with  Aadiatore • 645 

Heating  a  Building  to  70»  P 645 

Beating  by  Electricity 646 

WATBR. 

Expansion  of  Water 647 

Wdglitof  Water  at  different  temperatures 547 

Preesure  of  Water  due  to  its  Weignt 640 

Head  (X^rresponding  to  Pressures 640 

BoiiWpotot*;./.;iy.!i!iiii'.!!;i;!;ii!!i;;;".!;!'/;^!;;;'.!!;/r.*'.!!!'/.;!"  eeo 

Freabtg-point 550 

Sea-water 640,560 

loe  and  Snow 590 

Specific  Heat  of  Water 550 

Compressibility  of  Water 651 

Impurities  of  water........ 551 

Causes  of  Incmstation ^ 661 

Means  for  FreTeoting  Incrustation ,, GS2 

Analyses  of  Boiler-scato 563 

Hardoess  of  Water 658 

Purifying  Feed-water 554 

Softening  Hard  Water 665 

Hydraulics.    Flow  of  Water. 

Fomuks  for  Discharge  through  Orifices 655 

Flow  of  Water  from  Orifloes 656 

Flow  in  Open  and  Closed  Channels 657 

General  Forroulae  for  Flow 557 

Table  Fall  of  Feet  per  mile,  etc ..  668 

Valnesof  Vr  for  Circular  Pipes 560 

Xntter*s  Formula 650 

Motosworth^s  Formula 56S 

Basin  *8  Formula 668 

IV  Arpy*s  Formula 568 

Older  FormuliB 664 

Velocity  of  Water  in  Open  Channels 664 

Mean,  Surface  and  Bottom  Velocities 664 

Safe  Bottom  and  Mean  Velocities 665 

Reristance  of  Soil  to  Erosion 665 

Abrading  and  Transporting  Power  of  Water 566 

Grade  of  Sewers 666 

BelatiQus  of  Diameter  of  Pipe  to  Quantity  discharged 660 

Flow  of  Water  in  a90-iochPipe 566 

Velocitlesin  Smooth  Cast-iron  Water-pipes 567 

Table  of  Flow  of  Water  in  Circular  Pipes 668-578 

Loasof  Head 573 

Flow  of  Water  in  Riveted  Pipes 574 

Frictioiial  Heads  at  given  rates  of  discharge 677 

Effect  of  Bend  andC^irves 578 

HydraoUc  Orade-Une 678 

Flow  of  Water  in  House-service  Pipes 678 

Air-bound  Pipes 570 

VerticaJJeta 570 

Water  Delivered  through  Meters 670 

Fire  Streams 570 

Friction  lioeses  in  Hose  580 

Head  and  Pressure  Losses  by  Friction 580 

Loss  of  Pressure  in  smooth  i^inch  Hose 580 

Bated  capacity  of  Steam  Fire-engines 680 

Pressures  required  to  throw  water  through  Nozzles 681 

The  Siphon 681 

Measurement  of  Flowing  ISsiCer 682 

Pfesometer 682 

PItot  Tnbe  Gauge       588 

TbeVentori  Meter 688 

Measurement  of  Discharge  by  means  of  Nozzles 684 


XVlll  COKTBHIS. 

flow  through  Bedaiigular  Oriflo«i 864 

MeuureoMiit  of  AQ  Open  Stream 064 

Minora*  Inch  Measuromente • 06B 

Flow  of  Water  over  Wein 086 

Francises  Fonnula  for  Weirs 586 

Weir  Table 687 

Baain^sExperimenta............. ..• 667 

Water»powefw 

^werofalUlorWater 586 

Horse-power  of  a  Running  Stream >■ K8B 

Currant  Motors 660 

Horse-power  or  Water  Flowing  in  a  Tube 560 

Maximum  BfflclencT  of  a  Long  Conduit 668 

Mlllpower f. 580 

Value  of  Wato^power 580 

The  Power  of  Ooean  Wavee 590 

UUliatlon  of  Tidal  Power 600 

•  Turbine  Wheels. 

Pmportlonsof  Turbines • 601 

Teste  of  Turbines 600 

Dimensions  of  Turbines 607 

The  Felton  Watei^wheel.. -••»•..  507 

Pumps. 

Theoretieal  eapadty  of  a  pump 601 

Depth  of  Suction 604 

▲mount  01  Water  raised  by  a  Single-acting  Lift-pump. 606 

Proportioning  the  Steam-cylinder  of  a  Direct^ictlng  Pump 600 

Speedof  Water  through  Pipes  and  Pump -passages 600 

Sues  of  Direct-acting  rumps 608 

TheDeanePump  606 

RAoienoy  of  Small  Pumps • •».•  606 

The  Worfchington  Duplex  Pump 604 

Speed  of  Piston .......% 665 

Speed  of  Water  through  ValTes- • 605 

Boiler-feed  Pumps... ».•....  • 605 

Pump  Valves 666 

Centrifugal  Pamps 606 

Lawreooe  Centrirugai  Pumps 607 

Bflloienoy  of  Centrifugal  and  Reciprocating  Pumps 605 

Vanes  of  Centrifugal  Pumps 605 

The  Centrifugal  Pump  used  as  a  Suction  Dredge 600 

Duty  Trials  of  Pumping  Sngines 600 

Leakage  Tests  of  Pumps ..•••« 611 

Vaouum  Pnmps • 616 

ThePulfloraeter... 61i 

TheJetPump ...614 

TlHsInlcwtor.... •• 614 

Airlift  Pump 6l4 

The  Hydrauiie  Ram 614 

Quantity  of  Water  Delivered  by  the  Hydraulic  Ram 515 

Hydraulio  Pressure  Transmission. 

Energy  of  Water  under  Pressure •.. 615 

Efllcienoy  of  Apparatus 615 

Hydraulic  Presses 617 

tdrauHc  Power  in  London 617 
drauUc  Riveting  Machines *  618 
draulio  Forging 618 
»  Aiken  IntensHler 610 

HydrauHo  Bagiae tV% 


ruBi*. 


liwory  of  Combustion 

Total  Heat  of  Combustion.. 


COKTENTS.  XIX 

• 

TAQM 

AttUyMBofGwMorOoailRistlOB «•• • «» 

TempenLCore of  the  Fire • *•»•••• •.•»  ttO 

Classiiication  of  Solid  Fuel 633 

Classification  of  Goals..... 634 

Analyses  of  Coals 6M 

^'««teni  Lifnites 6S1 

Analyses  oi  Foreign  Coals 6Si 

Nixon^s  Navigation  Coal 688 

SampIinfijDoal  for  Analyses ,...»•...• 632 

Itektive  Value  of  Fine  Sixes t»t 

Fmsed  Fuel 683 

BelaUve  Value  of  Steam  Coals 688 

Approximate  Heating  Value  of  Coals ».» • 684 

iCiod  of  Furnace  Adapted  for  Different  Coals 885 

Downward-draught  Fiimaces.. **..•.. 635 

CAiorimetric  Tests  of  American  Coals 636 

EvapoFatlTe  Power  of  Bituminous  Coals. 686 

Weathering  of  Coal ,....» 637 

Coke  687 

Szperlmentsin  Coking »..•, «•..»..  687 

Coal  Wasblns'. TT. : 688 

RecoTery  of  By-products  In  Coke  manufacture 688 

Making  Hard  Coke 638 

Cieoeration  of  Steam  from  the  Waste  Heat  and  Gases  from  Coke-ovens.  638 

Products  of  the  DistiUatfon  of  Coal • 689 

Wood  as  Fuel .  680 

Heating  Value  of  Wood 689 

Compoiitioii  of  Wood 640 

CbarT!Tial * 640 

Yield  of  CfaKTCoal  (krom  a  Cord  of  Wood 641 

Cbosmnptfon  of  Charcoal  In  Blast  Furnaces. 641 

Abaorpnon  of  Water  and  of  Oases  by  Charcoal 641 

Cmnposftion  of  Charcoals 64« 

Misceilajieous  Solid  Fuels 642 

Dost-f  uel— Dust  EzpIosiottS 643 

Peat  or  Turf 648 

Sawdust  as  Fuel *.%... 648 

Horse-manure  as  Fnd , » 618 

Wet  Tan-bark  as  Fuel 648 

Straw  as  Fuel • ....w... 648 

Bsgawwe  aa  Fuel  In  Sugar  Manufacture 648 

Petroleum* 

PHMlueUof  DistillaUon 646 

Lima  Petrotoora «....  046 

Value  of  Fetroteum  as  Fuel.. ,«..« 645 

Ofl«;.OoalasFtael 046 

Fuel  Gas* 

C^rtxmOaa 646 

Anthracite  Gas 6«7 

BttumfDons  Gas • ..  647 

Water  Oas 648 

Pitidaoer-gas  from  One  Ton  of  Coal 6¥9 

5atural  Oas  in  Ohio  and  Indiana 649 

0*mbustion  of  Producer-gas 660 

Use  of  aceam  in  Producers 680 

Gas  Fuel  for  Small  Furnaces.... 651 

lUaminatlng^  Gas* 

Coal-cas 661 

Water-gas 694 

Analywes  of  Wster-pn  and  Coal  ^as 668 

(^loriflc  ESquirafents  of  Constituents 654 

Efficiency  of  a  Water-gas  Plant 654 

<^)ace  Required  fbr  a  Water-cas  Plant 656 

fee^^atoe  of  Mtimiwitlne-gas 666 


211  OONTEKTS. 

PlOB 

Alloys  contalDiDg  Antimony ....^ 880 

White-metal  Alloys 886 


KtEbii 


bitt  metals. 886 

Solders 888 

Ropes  and  Chains. 

Strength  of  Hemp,  Iron,  and  Steel  Ropes «...  338 

FlatRopes , 889 

WorkiDff  Load  of  Ropes  and  CSialns 839 

Strength  of  Ropes  and  Chain  Gables 340 

Rope  lor  Hoisting  or  Transmission 840 

Cordage,  TechnloU  terms  of 341 

Splicing  of  Ropes 341 

Coal  Hoistlog 843 

ManllaCordage,  Weight,  etc 344 

Knots,  how  to  make 844 

Splicing  Wire  Ropes 846 

Springs. 

Laminated  Steel  Springs 847 

Helical  Steel  Springs 847 

Carrying  Capacity  of  Springs 849 

EUipUcai  Springs 858 

Phosphor-bronze  Springs « 9B2 

Springs  to  Resist  Torsional  Force 888 

Helical  Springs  for  Cars,  etc 858 

Riveted  Joints. 

Falrbalm*s  Experiments 854 

Loss  of  Strength  by  Punching 854 

Strength  of  Perforated  Plates 854 

Hand  TS.  Hydraulic  Riveting 855 

FormulsB  for  Pitch  of  Rivets 857 

Proportions  of  Joints 858 

Efficiencies  of  Joints 859 

Diameter  of  RIvetH  . .  380 

Strength  of  Riveted  Joints •. 861 

Riveting  Pressures 362 

Shearing  Resistance  of  Rivet  Iron 868 

Iron  and  Steel. 

Classification  of  Iron  and  Steel 864 

Grading  of  Pig  Iron 865 

Influence  of  Silicon  Sulphur,  Pbos.  and  Mn  on  Cast  Iron 865 

Tests  of  Cast  Iron 860 

Chemistry  of  Foundry  Iron 870 

Analyses  of  Castings 87S 

Strength  of  Cast  Iron 874 

Specltlcations  for  Cast  Iron 874 

Mixture  of  Cast  Iron  with  Steel 875 

Bessemerixed  Cast  Iron 875 

Bad  Cast  Iron 875 

Malleable  Cast  Iron 875 

Wrought  Iron      877 

Chemistry  of  Wrought  Iron 877 

Influenceof  Rolling  on  Wrought  Iron   877 

Specifications  for  Wrought  Iron 878 

Stay-bolt  Iron 879 

FormuliB  for  Unit  Strains  In  Structures 879 

Permissible  Stresses  In  Structures 881 

Proportioning  Materials  in  Memphis  Bridge 888 

Tenacity  of  Iron  at  High  Temperatures 881 

Effect  of  Cold  on  Strength  of  Iron 881 

Expansion  of  Iron  by  Heat 885 

Durability  of  Cast  Iron 885 

Corrosion  of  Iron  and  Steel 886 

,  Preservative  Coatings;  Paints,  etc 887 


COKTENTa  Xlll 

PAOB 

Kou-ozidizinff  Prooeas  of  AnDealiner 887 

SUngaoeae  Putting  of  Iron 889 

Steel. 

fielAlion  between  CShem.  and  Phyi.  FroportiM •.  889 

Variation  in  Strength 891 

Opeo*beart]i • 809 

** WT......  *'*^ 

ingSofI 

Effect  of  Cold  RoUIni 


HaideDing  Soft  Steel 888 

Effect  of  Cold  RoUIng 898 

Compartaon  of  FuU-elaed  and  Small  Pfeoea  , 


nent  of  Structural  Steel 804 

Influence  of  Annealing  upon  Magnetks  Capacity 808 

SpecifleayonsforStefa 807 

Boiler,  Ship  and  Tank  Plates 880 

Steel  for  Springs,  Axles,  etc 400 

May  Carbon  be  Burned  out  of  Stesl7 40S 

Becaleeoenceof  Steel '. 408 

Bffectof  Nlddngafiar 408 

Electric  ConductiTity 408 

Specific  QzaFitr 408 

Occaalonal  Failures 408 

Segregation  in  In«>ts 404 

Earliest  Uses  forStmctures ..  406 

Steel  Castings 406 

Manganese  Steel 407 

Kickel  Steel 407 

AlumiBum  Steel 400 

Chrome  Steel 400 

Tungsten  Steel 400 

Compressed  Steel 410 

Cmdble  Steel 410 

Effect  of  Heat  on  Grain 418 

'"     '*  Hammering,eto 412 

Heating  and  Forging 418 

Tempering  Steel 418 

MXGHANICS. 

Force.  Unit  of  Foroe 411^ 

Inertia 415 

Newt<m*s  Laws  of  Motion 416 

Besolutlon  of  Forces 415 

Parallelogram  of  Forces 418 

Moment  of  a  Force 418 

Statical  Moment,  StabOity 417 

Stability  of  a  Dam 417 

ParaUelForoes 417 

Couples 418 

Equilibrium  of  Forces 418 

Centre  of  OraTity 418 

Moment  of  Inerda 410 

Centre  of  Qyration 420 

Badlos  of  Oyratfon 480 

Centre  of  escalation 481 

Centre  of  Percussion.. 4S8 

The  Pendulum 488 

Conical  Pendulum 488 

Centrifugal  Foroe 488 

Acoeleratlon.'. 488 

Falling  Bodies 484 

Value  ofo. 484 

Angular  Velodty 485 

Height  due  to  Velocity 485 

Parallelogram  of  Velocities 486 

Mass 487 

Foroe  of  Acceleration 427 

Motion  on  Inclined  Planes. 488 

Momeotmu , 488 


211  CONTEKTS. 

PlOB 

Alloys  containing  Antimony , 880 

White-metal  Alloyi 886 

TJrpe-metal 888 

Babbitt  metals. 888 

Solders 888 

Bopes  and  Chains. 

Strength  of  Hemp,  Iron,  and  Steel  Ropes 838 

FlatRopes • , 880 

WorkiDff  Load  of  Ropes  and  Chains 8:)9 

Strength  of  Ropes  and  Chain  Gables 340 

Rope  lor  Hoisting  or  Transmission 340 

Cordage,  Technical  terms  of 841 

Splicing  of  Ropes 341 

Coal  Hoisting 843 

Manila  Cordage.  Weight,  etc....... 344 

Knots,  bow  to  make 814 

Splicing  Wire  Ropes 346 

Springs. 

Laminated  Steel  Springs 847 

Helical  Steel  Springs 847 

Carrying  Capacity  of  Springs 849 

Elliptical  Springs  ..    8a8 

Phosphor-bronze  Springs « 853 

Springs  to  Resist  lx>rsiona1  Force SSS 

Helical  Springs  for  Cars,  etc 858 

Riveted  Joints. 

Falrbalm*s  Experiments 854 

Loss  of  Strength  by  Punching 854 

Strength  of  Perforated  Plates 854 

Hand  vs.  Hydraulic  Riveting 855 

FormulsB  for  Pitch  of  Rivets 857 

Proportions  of  Joints 358 

Efficiencies  of  Joints 850 

Diameterof  Rivets 360 

Strength  of  Riveted  Joints •. 361 

Riveting  Pressures 868 

Shearing  Resistance  of  Rivet  Iron 868 

Iron  and  Steel. 

Classlflcation  of  Iron  and  Steel 864 

Grading  of  Pig  Iron 865 

Influence  of  Silicon  Sulphur,  Phos.  and  Hn  on  Cast  Iron 865 

Tests  of  Cast  Iron 869 

Chemistry  of  Foundiy  Iron 870 

Analyses  of  Castings 87S 

Strength  of  Cast  Iron 874 

Bpeclflcations  for  Cast  Iron 874 

Mixture  of  Cast  Iron  with  Steel 87S 

Bessemerixed  Cast  Iron 875 

Bad  Cast  Iron 875 

Malleable  Cast  Iron 878 

Wrought  Iron      877 

Chemistry  of  Wrought  Iron 877 

Influenceof  Rolling  on  Wrought  Iron   877 

Speciflcat  ions  for  Wrought  Iron 878 

Stay-bolt  Iron 879 

FormuUe  for  Unit  Strains  in  Structures STB 

Permissible  Stresses  in  Structures 881 

Proportioning  Materials  in  Memphis  Bridge 888 

Tenacity  of  Iron  at  High  Temperatures 89 

Effect  of  Cold  on  Strength  of  Iron 888 

Expansion  of  Iron  by  Heat 885 

Burabillty  of  Cast  Iron 885 

Corrosion  of  Iron  and  Steel 386 

,  Preservative  Coatings;  Paints,  etc 887 


COHMKTa  Xlii 

PAOB 

ITou-oxidisiiiff  Prooeas  of  ADneallnc 867 

Kanganeae  Pliating  of  Iron 889 

Steel. 

BbIaUou  between  CShem.  and  PhyB.  FropertiM -  889 

Variation  in  Strength 891 

Open-bearth 8» 

ingSoH 
rOoldl 


Hardening  Soft  Steel 888 

ESectdfOoldBoUing 808 

Comparison  of  FuU^ued  and  Small  Pieoea  . 


Treatment  of  Stmctural  Steel 804 

Inflnenoe  of  Annealing  upon  Magnetic  Oapadtj 886 

Specifksatfons  f or  StefQ 807 

Boiler.  Ship  and  Tank  Plates 899 

Steel  for  torings.  Axles,  etc 400 

May  Oartwn  be  Burned  out  of  Stesir 408 

Recalflsoenceof  Steel '. 408 

Bffectof  Nlckingafiar 408 

Electrio  ConducdTity 408 

SpecsUlo  OzafitT 408 

Oocasioiial  FalTures 408 

Segregation  in  Ingots 404 

Barliest  Uses  forStructures 406 

Steel  Castings 406 

Manganese  Steel 407 

Nickel  Steel 407 

Aluminum  Steel 409 

Chrome  Steel 409 

Tungsten  Steel 409 

Compressed  Steel 410 

Crucible  Steel 410 

Effect  of  Heat  OD  Grain 418 

**      **  Hammering,  etc 418 

Heating  and  Fbrging 418 

Tempering  Steel 418 

MBCHANICS. 

Force.  Unit  of  Foroe 4tS 

Inertia 415 

Mewt<m*s  Laws  of  Motion 415 

Resolution  of  Forces 415 

Parallelogram  of  Forces 416 

Moment  of  a  Force 416 

Statical  Moment,  StablUty 417 

StabUity  of  a  Dam 417 

PanillelForoes 417 

Couples 418 

Equilibrium  of  Forces 418 

Centre  of  Gravity 418 

Moment  of  InerUa 419 

Centre  of  Gyration 420 

Badios  of  Gyration 490 

Centreof  escalation 481 

Centre  of  Percussion... 4S8 

The  Pendulum 488 

Conical  Pendulum 488 

Centrifugal  Foroe 488 

AooelerMion.*. 488 

Falling  Bodies 484 

Value  ofo , 494 

Angular  Velocity 485 

Height  due  to  Velocity 485 

Paral]ek>gram  of  Velocities 486 

Mass 487 

Force  of  Acceleration 487 

Motion  on  Inclined  Planes. 488 

Momwitnm , 488 


."XIY  COKTEKTS. 

Vie  Viva 4S 

Work,  Foot-pound 49B 

Power,  Horse-power 499 

Energy 429 

Work  of  Acceleration 480 

Force  of  a  Blow 4ao 

Impact  of  Bodies 4S1 

Energy  of  Recoil  of  Guns 431 

Oonsenratlon  of  Energy 498 

Perpetual  Motion  4»i 

SIBclencyof  a  Machine  48S 

Animal-power,  Man-power 4Si 

Workof  aHorse 484 

Man-wheel 484 

Horse-gin 484 

Resistance  of  Vehicles 48S 

Elements  of  Machines. 

The  Lever 485 

The  Bent  Lever 436 

The  Moving  Strut 486 

The  Toarie-Jolnt 486 

The  Inclinea  Plane 487 

The  Wedge 487 

TheScrew 487 

The  Cam 488 

ThePulley 488 

Differential  PuUey 481) 

Differential  Windlass 489 

Differential  Screw 48(' 

WheelandAxle 489 

Toothed-wheel  Gearing 489 

ftidless  Screw 440 

Stresses  In  Framed  Struotures. 

Cranes  and  Derricks 440 

Shear  Poles  and  Guys 449 

King  Post  Truss  or  Bridge 449 

Queen  Post  Truss  449 

Surr  Truss 448 

Pratt  or  Whipple  Truss 448 

HoweTruss 446 

Warren  Girder 445 

Roof  Truss ; 446 

HEAT. 

Thermometers  and  Pyrometers  448 

Centigrade  and  Fahrenheit  degrees  compared 449 

Copper-ball  Pyrometer 461 

Thermo-eleotno  Pvrometer 451 

Temperatures  in  Furnaces 461 

Wlborgh  Air  Pvrometer 458 

Beegers  Fire-clay  Pyrometer 468 

Mesur^and  Nouel's  Pvrometer 468 

Uebling  and  Steinbart^s  Pyrometer 458 

Air-thermometer 454 

High  Temperatures  judged  by  Color 464 

BolllDg-points  of  Substances 456 

MeUing-points 4U 

TTnitofHeat 406 

Mechanical  Equivalent  of  Heat 496 

Heat  of  Combustion 466 

Speclflc  Heat 497 

Latent  Heat  of  Fusion 499,461 

Expansion  by  Heat 460 

Abnolute  Temperature 461 

Absolute  Zero 461 


OOKTEinSi  XY 

PAOB 

Latent  Heat 461 

Latent  Heat  of  Evaporation 40^ 

Total  Heat  of  Evanoration 4d8 

Evaporation  and  Drying: 4M 

Evaporation  from  Reservoirs 468 

Evaporation  by  the  Multiple  System 468 

Besistanoe  to  Boiling 468 

Manufacture  of  Salt 464 

SolubUity  of  Salt  and  Sulphate  of  lime 464 

Salt  Contents  of  Brines 464 

Conoentratlon  of  Sugar  Solutions 466 

Evaporating  by  Exhaust  Steam 466 

Drying  in  vacuum 466 

Radiation  of  Heat .' 467 

Ck>nduction  and  Convection  of  Heat 468 

Rate  of  External  ConduoUon 46Q 

Steam-pipe  Coverings 4T0 

Transmission  through  Plates 471 

**  in  Condenser  Tubes 478 

•*  **       Cast-Iron  Plates 474 

"  from  Air  or  Qaaes  to  Water 4T4 

•*  from  Steam  or  Hot  Water  to  Air 476 

"  through  Walls  of  Buildings 478 

niermodynamics 478 

PHTSICAI^  PBOPERTIES  OF  OASES. 

Expansion  of  Gases 479 

Boyle  and  Marriotte's  Lavr 479 

Law  of  Charles,  Avogadro's  Law 479 

Saturation  Point  of  vapors 480 

Law  of  Osseous  Pressure    480 

Flow  of  Oases 480 

Absorption  byLiqalds 480 

AIB. 

Properties  of  Air 481 

Air-manometer 481 

Pressure  at  Different  Altitudes 481 

Barometric  Pressures 482 

Levelling  by  the  Barometer  and  by  Boiling  Water 482 

To  find  Difierenoe  In  A I  tltude 483 

Moisture  In  Atmosphere 488 

Weight  of  Air  and  Mixtures  of  Air  and  Vapor 484 

Specillc  Heat  of  Air 484 

Flow  of  Air* 

Flow  of  Air  through  Orifices 484 

Flow  of  Air  in  Pipes 485 

Effect  of  Bends  in  Pipe 488 

Flow  of  Compressed  Air 488 

Tables  of  Flow  of  Air 489 

Anemometer  Measurements 491 

Equalization  of  Pipes 491 

Loss  of  Pressure  in  Pipes 498 

Wind. 

Force  of  the  Wind 498 

Wind  Pressure  in  Storms 495 

Windmills 495 

Capacity  of  Wind  mills 497 

Economy  of  Windmills 496 

ElectrlcPower  from  Windmills 499 

Compressed  Air. 

Heating  of  Air  bj  Compression 499 

Loss  of  Energy  m  Compressed  Air 499 

Volumes  and  rressures , , 609 


lioos  due  to  11x0688  of  Pressure ooi 

HorseHpower  Required  for  Compression 601 

Table  for  Adiabatic  CompressiOD i 5M 

Mean  EffectWe  Pressures 601 

Mean  and  Terminal  Pressures 608 

Alr-oompressors 608 

Practical  Results 6QS 

Efficiency  of  Compressed-air  Engines 606 

Requirements  of  Rock-drills .,.', 606 

Popp  Compressed-air  System 607 

Small  Compressed-air  Motors 607 

Efficiency  of  Air-heating  Stoves 607 

Efficiency  of  Compreesed-air  Transmission 60f< 

Shops  Operated  by  Compressed  Air 600 

Pneumatic  Postal  Transmission 609 

Mekarski  Compressed-air  Tramways 610 

Compressed  Air  Working  Pumps  in  Mines 611 

Fans  and  Blowers. 

Oentrifugal  ffans 611 

Best  Proportions  of  Fans 619 

Pressure  due  to  Velocity &1S 

Experiments  with  Blowers 614 

Quantity  of  Air  Delivered 614 

£fflciency  of  Fans  and  Positive  Blowers 516 

Capacity  of  Fans  and  Blowers 517 

Table  of  Centrifugal  Fans 618 

Engines,  Fans,  and  Steam-coils  for  the  Blower  System  of  Heating. 610 

Sturtevant  Steel  Pressure-blower 610 

Diameter  of  Blast-pipes 619 

Efficiency  of  Fans 690 

Centrifugal  Ventilators  for  Mines 621 

Experiments  on  Mine  Ventilators S8i 

DiskFans B«4 

Air  BemoTed  by  Exhaust  Wheel 686 

Efficiency  of  Disk  Fans 685 

Positive  Rotary  Blowers 886 

Blowing  Engines 686 

Steam-jet  Blowers 687 

Steam-Jet  for  Ventilation 687 

BKATING  AND  TJ&NTIUiTION. 

Ventilation 888 

Quantity  of  Air  Discharged  through  a  Ventilating  Duct. 580 

Artificial  Cooling  of  Air 681 

Mine-ventilation 681 

Friction  of  Air  in  Underground  Passages 6S1 

Equivalent  Orifices 688 

Relative  Efficiency  of  Fans  and  Heated  Chimneys 688 

Heating  and  Ventilating  of  Large  Buildings 584 

Rules  for  Computing  Radiating  Surfaces 686 

Overhead  Steam-pipes 687 

Indirect  Heating-surface 5S7 

Boiler  Heating-surface  Required 688 

Proportion  of  Grate-surface  to  Radiator-surface 588 

Steam-consumption  in  Car-heating 688 

Diameters  of  Steam  Supply  Mains 589 

Registers  and  Cold-air  Ducts 639 

Physical  Prop«>rties  of  Steam  and  Condensed  Water 540 

Size  of  Steam-pipes  for  Heating 540 

Heating  a  Greenhouse  by  Steam  541 

Heating  a  Greenhouse  by  Hot  Water  54S 

Hot-water  Heating  548 

Law  of  Velocitv  of  Flow 648 

Proportions  of  Radiating  Surfaces  to  Cubic  Capacities 548 

Diameter  of  Mai n  and  Branch  Pipes 548 

Rules  for  Hot-water  Heating 544 

Arrangements  of  Mains 644 


OONTEKTa  Xvii 

Blower  System  of  Reattng and  VeDtilatlng.. M5 

Ezperimentfl  with  Radiators « 545 

Heating  a  Buildinfr  to  TO*  F 545 

HeaUng  by  Electricity 540 

WATKR. 

Expansion  of  Water 647 

Weight  of  Water  at  different  temperatures 547 

Pressure  of  Water  due  to  its  Weight 549 

Head  Corresponding  to  Pressures 549 

Buoyancy 550 

Boiling-point , 560 

Freeauig-point 650 

Sea^water 549,560 

loe  and  Snow 650 

Specille  Heat  of  Water 550 

OompressibUity  of  Water 551 

Impurities  of  Water... 551 

Causes  of  Incrustation ^ 551 

Means  for  PreveDting  Incrustation 7, 5Kt 

Analyses  of  Boiler-seale 559 

Hardnees  of  Water 558 

Purifying  Feed-water 554 

Softening  Hard  Water 655 

Hydraulics.    Flow  of  Water. 

Fomuto  for  Discharge  through  Orifioes ...  555 

Flow  of  Water  from  Orifices 555 

Flow  In  Open  and  Closed  Channels 657 

G«ieral  Fx>rmuln  for  Flow 557 

Table  Fall  of  Feet  per  mile,  etc 558 

Vahiesof  Vr for  Circular  Pipes 659 

Kutter's  FormuU 569 

Molesworth's  Formula 663 

Bazin^s  Formula  ..  563 

D*Arcy*s  Formula 568 

Older  FormulflD 561 

Velodty  of  Water  in  Open  Channels 564 

Mean,  Surface  and  Bottom  Velocities 664 

Safe  Bottom  and  Mean  Velocities 665 

Resistance  of  Soil  to  Erosion 565 

Abrading  and  Transporting  Power  of  Water 665 

Grade  of  Sewers 660 

Relations  of  Diameter  of  Pipe  to  QuanUty  discharged 660 

Flow  of  Water  in  aSO-inchPipe 666 

Velocities  in  Smooth  Cast-iron  Water-pipes 567 

Table  of  Flow  of  Water  in  Circular  Pipes 66&-678 

Lossof  Head 578 

Flow  of  Water  in  Riveted  Pipes 574 

Frictional  Heads  at  given  rates  of  discharge 577 

Effect  of  Bend  andCurres •.  678 

Hydraulic  Orade-line 678 

Flow  of  Water  in  House-service  Pipes 678 

Air-bound  Pipes 679 

VerticalJets 679 

Water  Delivered  through  Meters 679 

FireStreams 679 

Friction  Losses  In  Hose  680 

Head  and  Pressure  Losses  by  Friction 580 

Loss  of  Pressure  in  smooth  3^-inch  Hose 580 

Rated  capacity  of  Steam  Fire-engines 580 

Pressures  required  to  throw  water  through  Nozzles 68t 

The  Siphon  581 

Measurement  of  Flowing 'VaCiBr 682 

Piezometer .T 582 

Pitot  Tnbe  Gauge        588 

The  Venturi  Meter 688 

Measurement  of  Dischaige  by  means  of  Nozzles 684 


PAOC 

flow  through  Reotangular  Oriflo«i » • »••»».• MM 

Meaauromeat  of  AQ  Open  Stream •..• 664 

Minora*  Inch  MeAsuremeats..... • fi6S 

Flow  of  Water  oTor  Wein •...•• 08S 

Francises  Formula  for  Weirs 686 

Weir  Table 687 

Baain^s Experimenta •%••....»...  6iSf 

Watei>powefw 

Power  of  a  VMl  of  Water 586 

fiorae-power  of  a  Runnlog  Stream ., 58B 

Current  Motors 680 

HorsO'powerof  Water  Flowing  in  a  Tube...  . 68D 

Maximum  Efficiency  of  a  Long  Conduit 660 

MIH.power :. 680 

Value  of  Water-power 800 

The  Power  of  Ocean  Waves 690 

UUliatlon  of  Tidal  Power 000 

•  Turbine  Wheela, 

Proportions  of  Turbines • 601 

Tests  of  Turbines « 600 

Dimensions  of  Turbines » * •.  607 

Tlie  Pelton  Water-wheel - 607 

PnmpB. 

Theoretical  capacity  of  a  pump •  •....«..••••.• 601 

Depth  of  Suction 604 

▲mount  01  Water  raised  by  a  Single-acring  Lift-pump. .  OQS 

Proportioning  the  Steam  cylinder  of  a  Direct-acting  Pump 600 

Speedof  Water  through  Pipes  and  Pump -passages 608 

Sues  of  Direct-acting  rumps 603 

TheDeanePump 000 

ftAoienoy  of  Small  Pumps O06 

The  Wonhington  Duplex  Pump 004 

Speed  of  Pisoon .. 006 

Speedof  Water  through  ValTes....  • 005 

Boiler-feed  Pumps....  ..*•.  • • 006 

Pnmp  Valves 006 

Centrifugal  Pumps 006 

lAwreooe  Centrifugal  Pumps 007 

Effioleaoy  of  Centrif^al  and  Reciprocating  Pumps 606 

Vanes  of  Centrifugal  Pumps 600 

The  Centrifugal  Pump  used  as  a  Suction  Dredge 600 

Duty  Trials  of  Pumping  Engines 600 

Leakage  Tests  of  Pumps ,... Oil 

Vaouum  Pnmps....  • 613 

ThePulsometer.... 610 

IlieJetPump • ••.....  614 

Thelnieotor ..»• 614 

AfrllftPump 614 

The  Hydraulic  Ram 614 

Quantity  of  Water  Delivered  by  the  Hydraulic  Ram Wi 

Hydraulic  Pressure  Transmission* 

Bn^rgy  of  Water  under  Pressure ......  616 

EAcieDcy  of  Apparatus 616 

Hydraulic  Presses 617 

Hydraulic  Power  in  London • 617 

Hjrdraulic  Riyeting  Machines • •  616 

mrdraulic  Forging 616 

1%e  Aiken  IntensHier 619 

Hydraulic  Engine 610 


FUBIto 


Theory  of  Combustion 

Total  Heat  of  Combustion.. 


COKTEKTfl.  XIX 

• 

9AQM 

AmaysBBof  GwMofOooibasllOB •« ••.*• «M 

Temperatun  of  the  Fire »• »»»•••» •»  ttO 

Classiflcation  of  Solid  Fuel 6S3 

Classification  of  Goals 634 

Analjs^ee  of  Coals ^ 

Wostern  Lfenites 681 

Analyses  of  Foreign  Coals 6S1 

Kixon^s  Navigation  Coal 632 

SampUneCoal  for  Analyses •.•»••• ..» ^ 

B«kti¥e  value  of  Fine  Sixes 6Stt 

Pressed  Fuel 682 

Belative  Value  of  Steam  Coals *. 663 

Approximate  Heating  Value  of  Coals •... » 634 

£ind  of  Furnace  Adapted  for  Different  Coals 6S& 

DowDward-draugbtFurnaces«„ »..«.. 635 

Caiorimetric  Tests  of  American  Coals 636 

Evaporative  Power  of  Bituminous  Coals.  • • 636 

Weathering  of  Coal • 697 

Coke 637 

£xperimenta  In  Coking «...*..  637 

Coil  WashinK 7. 1 m 

Recovery  of  By-products  in  Coke  manufacture 638 

Making  Hard  Cok:e » 638 

Generation  of  Steam  from  the  Waste  Heat  and  Gases  from  Coke-ovens.  638 

Products  of  the  Distmatfon  of  Goal 689 

Woodasf\iel .  630 

Heating  Value  of  Wood 6S9 

CompDBftion  of  Wood 640 

Charcoal 6« 

Yield  of  Ch&rooal  fiDm  a  Cord  of  Wood 641 

Consmnption  of  Charcoal  fn  Blast  Furnaces. • 641 

Absorption  of  Water  and  of  Oases  bj  Charcoal 641 

Composition  of  Charcoals 64)1 

Miftcellaneous  Solid  Fuels 642 

Dust-fuel— Dust  Ezplosiom 642 

Py»torTurf • 64« 

Sawdust  as  Fuel ...». .*  648 

Hone-manure  as  Fuel 648 

Wet  Tan-bark  as  Fuel 648 

Straw  as  Fuel 648 

Bsffasse  as  Fuel  in  JSugar  Manufacture 648 

Petroleum* 

Pn»duct80f  DiGUllatloQ 645 

Uma  Petroleum... •. «...»» .•«••....••..»...  640 

Value  of  Petroleum  as  Fad ••••••%..«« »..  64& 

Oatv^OoalAsFnel » 646 

Fuel  Gas. 

OnrtKmOaB 646 

Anthracite  Gas 617 

Bituminons  Gas 647 

Water  Gas 648 

Produeer^gas  from  One  Ton  of  Coal 049 

Natural  Gas  in  Ohio  and  Indiana 649 

Combustion  of  Producer^as..... 680 

Use  of  Steam  In  Producers » 6S0 

Gas  Fuel  for  Small  Furnaces 661 

lUuminatiag  Gas» 

Ooal'gas • 661 

Water-gas 668 

Analyses  of  Water-gas  and  Coal  f^ns 668 

Oaioriflc  Equivalents  of  Constituents 664 

KflftcleDcy  of  a  Water-gas  Plant 664 

^pace  Required  for  a  Water-gas  Plant 666 

fbel-^ahieot  Uhiminiiring'gas 666 


211  OONTEKTS. 

PAOB 

Alloys  contatniog  Antimony ,., 386 

White-metal  Alloyi SM 

Type-metAl 886 

Babbitt  metahk 886 

Solders 888 

Bopes  and  Chains. 

Strensthof  Hemp,  Iron,  and  Steel  Ropes 338 

FlatRopes , 839 

Workine  Load  of  Ropes  and  Chains S39 

Streneth  of  Ropes  and  Chain  Cables 840 

Rope  for  Hoisting  or  Transmission SiO 

Cordage,  Technical  terms  of 841 

Spliclnff  of  Ropes 341 

Coal  Hoisting      848 

Manila  Cordage.  Weight,  etc.. S44 

Knots,  bow  to  make 814 

Splicing  Wire  Ropes 346 

Springs. 

Laminated  Steel  Springs 847 

Helical  Steel  Springs 847 

Carrying  Capacity  of  Springs 849 

Elliptical  Springs  .,    852 

Phoepbor>bronze  Springs « 853 

Springs  to  Resist  Torsional  Force S5S 

Helical  Springs  for  Cars,  etc 858 

Riveted  Joints. 

Falrbalm*s  Experiments 854 

Loss  of  Strength  by  Punching       854 

Strength  of  Perforated  Plates 8M 

Hand  vs.  Hydraulic  Riveting 8S6 

Formuln  for  Pitch  of  Rivets 867 

Proportions  of  Joints 358 

Efficiencies  of  Joints  858 

Diameter  of  RivetR .360 

Strength  of  Riveted  Joints *. 861 

Rlvetuig  Pressures 862 

Shearing  Resistance  of  Rivet  Iron 863 

Iron  and  Steel. 

Classlfleation  of  Iron  and  Steel 884 

Grading  of  Pig  Iron 865 

Influence  of  Silicon  Sulphur,  Phos.  and  Mn  on  Cast  Iron 865 

Tests  of  Cast  Iron 869 

Chemistry  of  Foundiy  Iron  870 

Analyses  of  Castings 873 

Strength  of  Cast  Iron 874 

Specifications  for  Cast  Iron 874 

Mixture  of  Cast  Iron  with  Steel 875 

Bessemerized  Cast  Iron 875 

Bad  Cast  Iron 875 

Malleable  Cast  Iron 875 

Wrought  Iron      877 

Chemistry  of  Wrought  Iron 877 

Influenceof  Rolling  on  Wrought  Iron   877 

Speciflcations  for  wrought  Iron 878 

Stoy-boltlron 879 

Formulas  for  Unit  Strains  in  Structures 879 

Permissible  Stresses  in  Structures « 8Bi 

Proportioning  Materials  in  Memphis  Bridge 8B3 

Tenacity  of  Iron  at  High  Temperatures 888 

Effect  of  Cold  on  Strength  of  Iron 888 

Expansion  of  Iron  by  Heat 885 

Durability  of  Cast  Iron 885 

Corrosion  of  Iron  and  Steel S86 

,  Preservative  Coatings;  Paints,  etc 887 


CONTBKTa  Xiii 

5ou-ozidisiiiK  Process  of  Annealing 887 

Kaoganeae  Plating  of  Iron 889 

Steel. 

Belatlon  between  C9iem.  and  Phys.  Fropertiei -  889 

Variation  In  Strength 891 

OpeiFliearth 809 


Hardening  Soft  Steel 888 

Effect  of  Gold  Boiling 888 

Compariaon  of  FuUrtiaed  aiid  Small  Pieces 898 

Treatment  of  Structural  Steel 894 


Influence  of  Anuealiog  upon  Magnetic  OaBadty . , 

SpecUloatlona  for  Steel 897 

BoOer.  Ship  and  Tank  Plates 889 

Steel  for  Springs,  Aztes.  etc 400 

Kay  GariKm  be  Burned  out  of  Stesir 408 

Recaloecence  of  Steel '. 409 

Effeetof  Niddngafiar 408 

Eleetrle  Conductirity 408 

Bpedfie  GzaTitr 408 

Oocaaioiial  Failures 408 

Segregation  in  InwMs 404 

EsriicBtUses  forStnictuies 406 

Steel  Castings 406 

Manganese  Sted 407 

Nickel  Steel  407 

Alnralnnm  Sted 409 

Chnnne  Steel 409 

Toncrten  Steel ......••.••••..•.. • 409 

Oompressed  Steei'.'/.r.IlII.lIII..'.!...I..l..I.I...l  ....!...!.!'.*.'..!!*.!!!!  410 

Onidbie  Steel 410 

Bffect  of  Heat  on  Qraln 41S 

**     '*  Hammering,  etc 412 

Heating  and  Forging 418 

Tteipering  Steel 41» 

MXGHANICS. 

Foroe,Unitof  Foroe 41l( 

Inertia ...„ 415 

Newton's  Laws  of  Motion 415 

Resolution  of  Forces 415 

ParsIldogFam  of  Forces 418 

Moment  of  a  Force. 418 

Statical  Moment,  StabiUty 417 

StabiiilTroC  aDam 417 

PsraUd  Forces 417 

Ooupi« 418 

Bquilibriam  of  Forces 418 

Centre  of  Orarity 418 

TInerUa.. 


b  of  Inertia 419 

Centre  of  Gyration • 480 

BadinsofCgrration 490 

Oentreof  Oscillation 481 

Centre  of  Percussion... 488 

Tbe  Bendolnm 428 

Conical  Pendulum 488 

Centrifugal  Foroe 488 

Acceleration.-. 488 

FaUing  Bodies 494 

Value  of  o. 494 

Angular  Velocity 485 

Height  due  to  Velocity 485 

Parallelogram  of  Velocities 486 

MsmTTT 487 

Force  of  Acceleration. 487 

I  on  Inclined  PlMies. 488 


J 


Ill  OOKTEKTS. 


Alloys  containing  Antimony. , 

White-metal  Alloys 

Type-metal 

Babbitt  metals. 

Solders 


Ropes  and  Chains. 

Strength  of  Hemp,  Iron,  and  Steel  Ropes , 

FlatRopes * ., 

Working  Load  of  Ropes  and  Chains 

Strength  of  Ropes  and  Chain  Cables 

Rope  for  Hoisung  or  Transmission 

Cordage,  Technical  terms  of 

Splicing  of  Ropes 

Coal  Hoisting     

Manila Cordi^.  Weight,  etc.. 

Knots,  bow  to  make 

Splicing  Wire  Ropes 


Springs. 

Laminated  Steel  Springs 

Helical  Steel  Springs 


Carrying  Capacity  of  Springs. 
ElUptlcai  r  ^^ 


EUiptlcfU  Springs 

Phosphor-bronze  Springs 

Springs  to  Resist  lx>r8ional  Force. 
Helical  Springs  for  Cars,  etc 


Riveted  Joints. 

Falrbalm*s  Experiments 

Loss  of  Strength  by  Punching       

Strength  of  Perforated  Plates 

Hand  ts.  Hydraulic  Riveting 

FormulsB  for  Pitch  of  Rivets 

Proportions  of  Joints 

Efficiencies  of  Joints 

Diameter  of  Rivets  . .  

Strength  of  Riveted  Joints *. 

RlTetuig  Pressures 

Shearing  Resistance  of  Rivet  Iron 


Iron  and  Steel. 


Classiflca tion  of  Iron  and  Steel 

Grading  of  Pig  Iron 

Influence  of  Silicon  Sulphur,  Phos.  and  Mn  on  Cast  Iron. . 

Tests  of  Cast  Iron 

Chemistry  of  Foundiy  Iron 

Analyses  of  Castings 

Strength  of  Cast  Iron 

Specifications  for  Cast  Iron 

Mixture  of  Cast  Iron  with  Steel 

Bessemerized  Cast  Iron 

Bad  Cast  Iron 

Malleable  Cast  Iron 

WrotKht  Iron      

Chemistry  of  Wrought  Iron 

Influence  of  Rolling  on  Wroughtlron   

Speciflcations  for  wrought  Iron 

Stay-bolt  Iron 

FormulsB  for  Unit  Strains  in  Structures 

Permissible  Stresses  in  Structures 

Proportioning  Materials  in  Memphis  Bridge 

Tenacity  of  Iron  at  High  Temperatures 

Effect  of  Cold  on  Strength  of  Iron 

Expansion  of  Iron  by  Heat 

Durability  of  Cast  Iron 

Corrosion  of  Iron  and  Steel 

,  Preservative  Coatings;  Paiots«  etc 


COKTBKTa  Xiii 

FAOB 

5ou-ozidiminf  Process  of  Annealing 887 

Kaaganeee  Plating  of  Iron 880 

Steel. 

BeUtion  between  Oiem.  and  Pbys.  Fropeitiei ••  8811 

Variation  in  Strength 891 

Open-hearth 809 

BaseeniBr ••••••.•• ••••••••••>•••••••••••  ••• 809 

Hardening  Soft  Steel 888 

UtetoCOoldRoUIng 808 

OompariBon  of  FuU-ebed  and  Smatt  Fleoea 888 

Treatnunt  of  Structural  Steel 804 

Infloenoe  of  Annealing  upon  Magnetlo  Ctopadtj. , 


iforSteel 807 

Boiler,  Ship  and  Tank  Plates 800 

ated  for  Springs,  Axlea.  etc 4M 

XajOartionbeBuniedoutofStesir 408 

Recalesoenceof  Steel *. 408 

Effectof  NickingaBar 408 

Eleetrie  Conductivltj 408 

Specillc  QraritT 408 

Occasional  Fkdmres 408 

Segregation  in  Ingpca 404 

~~    "     > Usee  f orStructurM ...406 


Steel  Caatings 406 

KaaeaeSteel. 


407 

Nickel  Steel 407 

Atuminum  Steel 400 

Chrome  Steel 400 

Tnngrten  Steel 400 

OompreaBed  Steel 410 

CmcSle  Steel 410 

Effect  of  Heat  on  Grain 418 

**      '•  Hammering,  etc 412 

Beating  and  Forgtatg 418 

Tempering  Steel 4ia 

KBCHANIC8. 

roree,Unitof  Faroe 41» 

Inertia 415 

Newton's  Laws  of  Motion 416 

Beaolntion  of  Forces • 415 

Parallelogram  of  Forces 410 

Komentof  aForoe. 410 

Statical  Moment,  Stability 417 

Stability oC  aDam 417 

ParallelForcea 417 

Ooaples 418 

Eqoilibriimi  of  Forces 418 

Omtre  of  OraTity 418 

Moment  of  Inertia 419 

Gbntre  of  Oyratton • 480 

Badios  of  Gyration 480 

CentreoT  OscOlation 481 

Oentre  of  Percussion 483 

The  Fendolom 488 

Conical  Pendulom 428 

Oentrifugnl  Force 488 

Acceleration.-. 488 

FUOing  Bodies 484 

Value  of  o. 494 

Angular  Velocity 485 

Height  doe  to  Velocity 485 

Parallelogram  of  Vek)citiea 480 

Mass 487 

Force  of  Acceleration 487 

Motion  on  Inclined  Planes. 488 


J 


:X1Y  C01<rTEKI& 

Vis  Viva 4i8 

Work,  Foot-pound 4S8 

Power,  Horse-power 4S9 

Energy 4» 

Work  of  Acceleration 480 

Force  of  a  Blow 490 

Impact  of  Bodies 491 

Energy  of  Beooil  of  Quns 4S1 

Ctonaerration  of  Eneiigy 4SS 

Perpetual  If otion 4% 

BAelencyof  a  Machine  4Si 

▲nlmal-power,  Man-power 43S 

Workof  aHorse 434 

Man-wheel 484 

Horse-gin 484 

Resistance  of  Vehicles 435 

Slements  of  Machines. 

The  Lever 485 

TheBentLever 436 

The  Moving  Strut 436 

The  Toffgle-joiat 436 

The  Inclinea  Plane 487 

The  Wedge 487 

TheScrew 487 

The  Cam 488 

ThePulley 488 

DUrerentlal  PuUey 431^ 

Differential  Windlass 489 

Differential  Screw 48(^ 

WheelandAxle 48» 

Toothed-wheel  Gearing 488 

Endless  Screw 440 

SftrMses  In  Framed  Stmotures. 

Cranes  and  Derricks 440 

Shear  Poles  and  Ouys 442 

Xing  Post  Truss  or  Bridge 44S 

Queen  Post  Truss 449 

Burr  Truss 443 

Pratt  or  Whipple  Truss 448 

HoweTruss 44S 

Warren  Qlrder 445 

Boof  Truss : 440 

HKAT. 

Thermometers  and  Pyrometers  448 

Centigrade  and  Fahrenheit  degrees  compared 449 

Copper^Hill  Pvrometer 461 

Thermo-eleotno  fvrometer 451 

Temperatures  in  Furnaces 461 

Wiboivh  Air  Pvrometer 458 

Beegers  Fire-clay  Pyrometer 45S 

Mesurd  and  NouePs  Pvrometer 458 

Uehlfng  and  SteinbarOs  Pyrometer 493 

Air-thermometer , 454 

High  Temperatures  judged  by  Color 454 

Boil ing-polnts  of  Substances 455 

Melting-points 4S5 

Unltof  Heat 485 

Mechanical  Equivalent  of  Heat 466 

Heat  of  Combustion 456 

Specific  Heat 457 

Latent  Heat  of  Fusion 450,461 

Expansion  by  Heat 460 

Absolute  Temperature 461 

Absolute  Zero •• 461 


00HTE2n&  XV 

_  PAQB 

Latent  Beat 461 

Latent  Heat  of  Eraporatloii Mi 

Total  Heat  of  ETaporation 468 

Zvaporation  and  Drying 468 

XTaporation  from  Reservoirs 468 

Evaporation  by  the  Multiple  System 468 

BesistAooe  to  Boiling 468 

Manufacture  of  Salt 464 

Solubility  of  Salt  and  Sulphate  of  lime .'.  464 

Salt  Contenta  of  Brines 464 

Oonoentration  of  Sugar  Solutions 466 

Evaoorating  by  Exhaust  Steam 466 

Drying  in  vacuum 466 

SadlatioD  of  Heat .' 467 

Oondoctkm  and  Convection  of  Heat 468 

Rate  of  External  Oonduotion 460 

Steam-pipe  Coverings 470 

Transmission  through  Plates 471 

••  in  Condenser  Tubes 478 

•*  •*       Cast-iron  Plates.  474 

"  from  Air  or  Gases  to  Water 474 

•*  from  Steam  or  Hot  Water  to  Air 476 

••  through  Walls  of  Buildings 478 

niermodjnamics 478 

PHT8ICAI«  PKOPERTI£S  OF  GASBS. 

Expaufon  of  Oases 479 

Boyle  and  Maniotte^s  Law 470 

Law  of  Charies,  Avogadro's  Law 479 

Saturation  Point  of  vapors 460 

Law  of  Gaseous  Pressure    480 

Flow  of  Gases 480 

Absoiptloii  by  Liquids 480 

AIR. 

Properties  of  Air 481 

Air-manometer 481 

Pressure  at  Different  Altitudes 481 

Barometric  Pressures 488 

Levelling  by  the  Barometer  and  by  Boiling  Water 482 

To  find  Imferenoe  in  Altitude 488 

Moisture  in  Atmosphere 488 

Weight  of  Air  and  Mixtures  of  Air  and  Vapor 484 

^>ecillc  Heat  of  AJr 484 

Flow  of  Alr» 

Flow  of  Air  through  Orifices 464 

Flow  of  Air  in  Pipes 485 

Effect  of  Bends  in  Pipe 488 

Flow  of  Compressed  Air 488 

Tables  of  Flow  of  Air 489 

Anemometer  Measurements 491 

EquaJizatioo  of  Pipes 49I 

Loss  of  Pressure  in  Pipes 498 

Wind. 

Foroe  of  the  Wfaid 498 

Wind  Pressure  in  Storms 496 

WindmOOtf 405 

Capacity  of  WlndmOIs 497 

Economy  of  Windmills 496 

Electric  rower  from  Windmills 499 

Compressed  Air. 

Heating  of  Air  b^  Compression 409 

Loss  of  Energy  in  Compressed  Air 499 

ToiuiQM and  Pressures » .j «... 600 


xvi  coiirrBNTs. 

PAOl 

L0B8  due  to  Ezoen  of  Pressure 60 

Horae^wer  Required  for  Compression 50 

Table  for  Adiabatic  Oompression » 50 

Mean  Eftective  Pressures  60 

Mean  and  Terminal  Pressures 5(X 

Air-compressors 60i 

Practical  Results 50: 

Efficiency  of  Compressed-air  Engines. • 60< 

Requirements  of  Rock-drills 1 50< 

Popp  Compressed-air  System 60! 

Small  Compressed-air  Motors 50^ 

Efficiency  of  AiivheatinK  Stoves 50^ 

Efficiency  of  Compressed-air  Transmission 60^ 

Shops  Operated  by  Compressed  Air 601 

Pneumatic  Postal  Transmission 60i 

Mekarski  Compressed-air  Tramways 6U 

Compressed  Air  Working  Pumps  in  Mines 611 

Fans  and  Blowers. 

Centrifugall^ans 611 

Best  Proportions  of  Fans 61S 

Pressure  due  to  Velocity 51S 

Experiments  with  Blowers 6H 

Quantity  of  Air  Delivered bU 

Efficiency  of  Fans  and  Positive  Blowers 516 

Cap^icy  of  Fans  and  Blowers 617 

Table  01  Centrifugal  Fans 618 

Engines,  Fans,  and  Steam-coils  for  the  Blower  System  of  Heating. 519 

Sturtevant  Steel  Pressure-blower 510 

Diameter  of  Blastrpipes 51S 

Efficiency  of  Fans SiX 

Centrifugal  Ventilators  for  Mines 6S1 

Experiments  on  Mine  Ventilators 622 

DiskFans 684 

Air  Removed  by  Exhaust  Wheel 685 

Efficiency  of  Disk  Fans 529 

Positive  Rotary  Blowers 5M 

Blowing  Engines 680 

Steamjet  Blowers 523 

Steam-jet  for  Ventilation 6S? 

BEATING  AND  TEMTII«ATION. 

Ventilation 688 

Quantity  of  Air  Discharged  through  a  Ventilating  Duct 580 

Artificial  Cooling  of  Air 58t 

Mine-ventilation 681 

Friction  of  Air  in  Underground  Passages 68 

Equivalent  Orifices 58 

Relative  Efficiency  of  Fans  and  Heated  Chimneys 68 

Heating  and  Ventilating  of  Large  Buildings 6» 

Rules  for  Computing  Radiating  Surfaces.... St 

Overhead  Steam-pipes 51 

Indirect  Heating-surface  51 

Boiler  Heating-surface  Required 61 

Proportion  of  Grate-surface  to  Radiator-surface 51 

Steam-consumption  in  Car-hsaiing 5( 

Diameters  of  Steam  Supply  Mains 51 

Registers  and  Cold-air  Ducts 51 

Physical  Properties  of  Steam  and  Condensed  Water    64 

Size  of  Steam-pipes  for  Heating 61 

Heati ng  a  Greenhouse  by  Steam  54 

Heating  a  Greenhouse  by  Hot  Water 51 

Hot-water  Heating  54 

Law  of  Velocitv  of  Flow H 

Proportions  of  Radiating  Surfaces  to  Cubic  Capacities 51 

Diameter  of  Main  and  Branch  Pipes 51 

Rules  for  Hot-water  Heating 54 

Arrangements  of  Mains • 54< 


00KTSNT8.  XVll 

^  PAOK 

BIcnrer  System  of  Heating  ana  Ventilating « M5 

^qMriments  with  Iftadiators * 545 

HeatiDgaBuildinirto70*F 645 

Beating  by  ElectHci^ 640 

WATER. 

ExpansfoD  of  Water 547 

Weight  of  Water  at  different  temperatureB 547 

PresBore  of  Water  due  to  its  Weight 549 

Head  Oorresponding  to  Preasares 549 

Buojancy 590 

Bofmig-potet 660 

Freenbg-potnt 550 

Sea-water 540,560 

IceandSnow 550 

Specific  Heat  of  Water 550 

CoRipreesIbilitT  of  Water 651 

Imparities  of  Water 551 

Causes  of  Incrustation. ^ 561 

Means  for  PreTenting  Incrustation  7, 558 


AnalTses  of  Boiler-scale . . 
Hardness  c 


lof  Water 553 

Purifying  Feed-water 554 

Bofteolng  Hard  Water 665 

Hydraulics.    Flow  of  Water. 

FomubB  for  Discharge  through  Orifices 565 

Flow  of  Water  from  Orifices 555 

Flow  in  Open  and  Closed  Channels 557 

General  FbrmulsB  for  Flow 557 

Tsble  Fall  of  Feet  per  mile,  etc ..  568 

Taluesof  Vr for Qrcular Pipes 550 

Kntter*s  Formula 560 

Xolesworth's  Formula 562 

Bszin*s  Formula  ..  568 

D'Ansy's  Formula 668 

Older  Formulas 564 

Velocity  of  Water  in  Open  Channels 664 

Hean.  Surface  and  Bottom  Velocities 664 

Safe  BoUom  and  Mean  Velocities 665 

Resistance  of  Boil  to  Erosion 565 

AbradinfT  and  Transporting  Power  of  Water 566 

Orsde  orSewers 666 

Relati4?ns  of  Diameter  of  Pipe  to  Quantity  discharged 566 

Flow  of  Water  in  a  SO-inch  i>ipe 666 

VelocitSes  in  Smooth  Caat-iron  Water-pipes 567 

Table  of  Flow  of  Water  in  Circular  Pipes 666-578 

Lossof  Head ,  578 

Flow  of  Water  in  Riveted  Pipes 574 

Frictiooal  Heads  at  Kiven  rates  of  discharge 577 

Effect  of  Bend  and  Curres 678 

Hydraulic  Grade-line 578 

Flow  of  Water  in  House-serrioe  Pipes 578 

Air-bound  Pipes 579 

VerticalJeta 570 

Water  DellTered  through  Meters 679 

FlreStreama 579 

Friction  Losses  in  Hose  580 

Head  and  Pressure  Losses  by  Friction 580 

Loss  of  Pressure  in  smooth  ^inch  Hose 580 

Rated  capacity  of  Steam  Fire-engines 580 

Pressures  required  to  throw  water  through  Nozzles 581 

TbeSlpbon  581 

Measurement  of  Flowfaig  HMSer 58S 

Piezometer .T 582 

PItot  Tube  Gauge       5M 

TheVentttri  Meter 6W 

Measorement  of  Discharge  by  means  of  Nozzles • 686 


'J 


XVlU  C0KTBK18. 

PAQB 

flow  through  BeotangttlarOiifloei.... •..•.•••> 684 

Moasuremont  of  AD  Open  Btream fiBi 

Mlnera*  iDoh  MeMuremeots •.. 065 

Flow  of  Water  OTor  W«lra 085 

FrandB'B  Fonnula  for  Wein 586 

WelrTkble 687 

Barings  Experiments 5d7 

Water-powefv 

FowerofaFaUof  Watdr 588 

Horse-power  of  a  BunnlDg  Btroam K8B 

Currsnt  Motors 68B 

Horge-power  of  Wator  Flowing  In  a  Tube 688 

Maximum  Efficiency  of  a  Long  Conduit 580 

Mill-power S89 

Value  of  Wate^power 590 

Ttie  Power  of  Ocean  Waves •.... 599 

UUltntlon  of  Tidal  Power OOO 

•  Turbltte  Wheels, 

Proportions  of  Turbines » •«..  601 

Tests  of  Turbines 606 

Dlaiensions  of  Turbines • %••«••• 607 

The  Pelton  Water-wheel - 607 

Pumps. 

Theoretical  capacity  of  a  pump • • • 601 

Depth  of  Suction 602 

Amount  01  Water  raised  by  a  Slngleaciing  Lift-pump. 60el 

Proportioning  the  8teamcylinder  of  a  Direct-acting  Pump 6(tt 

Bpeedof  Water  through  Pipes  and  Pump -passages 603 

Sues  of  Direct-acting  rumps 603 

The  Deane  Pump 603 

Bttoienoy  of  Small  Pumps 60S 

The  Worfchington  Duplex  Pump 604 

Speed ofPisMm 606 

Speed  of  Water  through  ValTes 606 

Bollerfeed  Pumps » 605 

Pump  Valves 608 

Centrifugal  PHmpB 606 

Lawrence  Centrifugal  Pumps 607 

Bflddenor  of  Centrifugal  and  Reciprocating  Pumps 608 

Vanes  of  Centrifugal  Pumps 600 

The  Centrifugal  Pump  used  as  a  Suction  Dredge 609 

Duty  Trials  of  Pumping  Engines 60fl 

Leakage  Tests  of  Pumps ,*•. 611 

Vacuum  Pnmpe....  614 

ThePulsometer..*. 6U 

TlieJetPump »•...».  6U 

Tht)  Injector »*•••• 6U 

Air-lift  Pump 6i4 

The  Hydraulic  Ram • 614 

Quantity  of  Water  DeUvered  by  the  Hydraulic  Ram...., 014 

Hydraulic  Pressure  Transmiission, 

Energy  of  Water  under  Pressure • 61< 

Efficiency  of  Apparatus ....» 6ll 

Hydraulic  Presses 61' 

Hydraulic  Power  in  London • 6V 

Hydraulic  Riveting  Machines *  Cli 

I^drauiic  Forslnff 4S1 

The  Aiken  Intensiner «1 

hydraulic  Engine • 61 

FUSIi. 

tlieoryof  Combustion • •! 

Total  Heat  of  OombusUon • »«•..••••«•»  .  «l 


C0KTEKT8.  XIX 

PAOI 

AmljwmclQBamfiiCoiBaibaMcm i tttt 

Tempermciire  of  the  Fire • •...  m 

(lasilication  of  Solid  Fuel 038 

CtasificatioQ  of  Goals 634 

▲Mly:MS  of  Ck>al8 6ii4 

Western  Lifrnites 681 

ABAljaesof  Foreign  Coate 6S1 

NixiMi^fl  Navigation  Coal • 682 

SamplineCoal  for  Analyses »..••• ».» 6S3 

Aektive  value  of  line  Siies 688 

Praased  Fuel 692 

BalaUve  Value  of  Steam  Coals 688 

A|»proxiinate  Heating  Value  of  Coals ».., •  ..• 6S4 

Kindof  Furnace  Adapted  for  DifFereotCoaJs. 685 

Down  want-draught  Furnaces »«..•.. 635 

C^lorimetric  Tests  of  American  Coals 636 

EvapormtJ^e  Power  of  Bituminous  Coals.  • »....  686 

Weatberine  of  Goal , 637 

Ooke  68? 

fizperlmentfi In  OoUng • ••.•,•..••...».... • 687 

GoiiWashliiff. rr. ; 688 

Recovery  of  Br-products  In  Coke  manufacture • 688 

Making  Hard  Coke 638 

G«oeFation  of  Steam  from  the  Wasie  Heat  and  Gases  from  Coke-ovens.  638 

Prodocfs  of  the  Distillation  of  Coal 68i 

WoodasFdel 68D 

Hmting  Yaine  of  Wood 689 

CompoeiUoB  of  Wood « 640 

Charc«nl 640 

Yield  of  dmrooftl  flrrni  a  Oofd  of  Wood 641 

Ooosumntion  of  Charcoal  In  Blast  Fumacea 641 

Absorption  of  Water  and  of  Oases  by  Charcoal 641 

CnmpaaltioD  of  Charcoals 64l( 

MiAceJlaneous  Solid  Fuels 642 

Dust-foel— Dust  ExplosiODS 642 

PfeatorTorf 648 

Sawdust  as  Fuel »....• • 648 

HorBe-manare  as  Foel 643 

WetTto-barkasFuel....  648 

Straw  as  Fuel  .......  ....  • 648 

Bi«aase  as  PuM  In  Sugar  Hanufacture 648 

Petroleum* 

ProdocUof  DleUnatloa 646 

Lima  Petroieora «»...* ..• 646 

Value  of  Petroleum  as  Fwl « 646 

0ilc!s.O0ttlttsFttel 646 

Fuel  Gas. 

OrbooOas 646 

Anthracite  Oas 647 

Bttumioons  Gas • 647 

WsterCkuB 648 

PtTKiuoer-gas  from  One  Ton  of  Coal 649 

5&tunU  Oas  In  Ohio  and  Indiana 649 

Otmibuscion  of  Producer-gas 6M 

Ui«  of  Steam  hi  Producers 690 

(>as  Fuel  for  Small  Furnaces 661 

niuminatioir  Gas« 

Qial.|:aai 681 

Wacer-««B 6B8 

Analri"BR  of  Water-gas  and  Coal  gas 663 

r^iorifle  Equivalents  of  Constituents 664 

enctency  of  A  Water-gas  Plant 654 

•^lace  Bequf  red  for  a  Water-gas  Plant 666 

^Ml-imlnBOtllittmiBattliSVu 666 


;X1Y  COKTEKTS. 

Vis  Viva 498 

Work,  Foot-pound 49B 

Power,  Horse-power 499 

Energy 4S9 

Work  of  Acceleration 4ao 

Force  of  a  Blow 4ao 

Impact  of  Bodies 481 

Energy  of  Beooil  of  Guns 441 

Ck>n8ervation  of  Energy 498 

Perpetual  If  otion  4.« 

BAeiencyof  aMacbine  488 

▲nlmal-powerf  Man-power 438 

WorkofaHorse 484 

Man-wheel 484 

Horse-gin 434 

Resistance  of  Vehicles 485 

Slements  of  Maohlnes. 

The  Lever 485 

The  Bent  Lever 486 

The  Moving  Strut 486 

The  Toe»le-toInt 486 

The  Incunea  Plane 487 

The  Wedge 487 

TheScrew 487 

The  Cam 488 

ThePuUey 488 

Differantlal  PuUev 480 

Differential  Windlass 48» 

Differential  Screw 48S* 

Wheel  and  Axle  489 

Toothed-wheel  Gearing 488 

BndkMS  Screw 44<1 

Stresses  in  Framed  Straotures. 

Cranes  and  Derricks 440 

Shear  Poles  and  GHiys 442 

King  Post  Truss  or  Bridge 448 

Queen  Post  Truss 448 

Burr  Truss 443 

Pratt  or  Whipple  Truss 443 

HoweTross 446 

Warren  Girder 445 

Boof  Truss ; 446 

HKAT. 

Thermometers  and  Pyrometers  448 

Centigrade  and  Fahrenheit  degrees  compared 449 

Coppeivball  Pyrometer 451 

Thermo-eleotno  Pvrometer 451 

Temperatures  in  Fumaoes 461 

Wiborgh  Air  Pvrometer 458 

Seegers  Fire-clay  Pyrometer 458 

Me8ur6  and  KouePs  Pvrometer  458 

UehliDg  and  Steinbarrs  Pyrometer 45S 

Air-thermometer , 454 

High  Temperatures  judged  by  Color 454 

Boiling-points  of  Subetances 455 

MelUDg-points 455 

UnitofHeat 456 

Mechanical  Equivalent  of  Heat...  456 

Heat  of  Combustion 456 

Speclflc  Heat 457 

Latent  Heat  of  Fusion 459,461 

Expansion  by  Heat 460 

Absolute  Temperature 461 

Absolute  Zero 461 


G0NTE2n&  XT 

PAGK 

Latent  Heat 481 

Latent  Heat  of  Evaporation M^ 

Total  Heat  of  ETaporation «» 

ETaporation  and  Drying 448 

ByaporatioD  from  Resenroirs 468 

ETaporation  by  the  Multiple  System 468 

Reetstanoe  to  Boiling 468 

Manufacture  of  Salt 464 

SolubUity  of  Salt  and  Sulphate  of  lime 464 

Salt  Contents  of  Brines 464 

Concentration  of  Sugar  Solutions.... 466 

Eraporating  by  Exhaust  Steam 466 

Drying  in  vacuum 466 

Radiation  of  Heat 467 

Conduction  and  Convection  of  Heat 468 

Rate  of  External  Condootion..  460 

Steam-pipe  Coverings  470 

Transmission  through  Plates 471 

*'  in  Condenser  Tubes 478 

•*  *'       Cast-iron  Plates.  474 

**  from  Air  or  Qasies  to  Water 474 

••  from  Steam  or  Hot  Water  to  Air 476 

^  through  Walls  of  Buildings 478 

Thermodynamics 478 

PHTSIGAI*  PKOPERTIKS  OF  GASES. 

Expansion  of  Oases 479 

Boyle  and  Ifarriotte's  Law 470 

Law  of  Charles,  Avogadro*s  Law 470 

Saturation  Point  of  vapors 460 

Law  of  Gaseous  Pressure    480 

Flow  of  Gases 480 

Absorpticni  I7  Liquids 480 

AIR. 

Propertiee  of  Air 481 

Air-manometer 481 

Pressure  at  Different  Altitudes 481 

Barometric  Pressures 488 

Levelling  bv  the  Barometer  and  by  Boiling  Water 488 

To  find  Plfference  in  Altitude 488 

Moisture  in  Atmosphere 488 

Weight  of  Air  and  Mixtures  of  Air  and  Vapor 484 

Specific  Heat  of  Air 484 

Flow  of  Alr» 

Flow  of  Air  through  Orifices 484 

Flow  of  Air  In  Pipes 486 

Effect  of  Bends  in  Pipe 488 

Flow  of  Compressed  Air 488 

Tkbles  of  Flow  of  Air 489 

Anemometer  Measurements 491 

Equalization  of  Pipes 491 

Loss  of  Pressure  in  Pipes 498 

Wind. 

Force  of  the  Wind 498 

Wind  Pressure  in  Storms 495 

Windmills 406 

Capacity  of  Windmills 407 

Economy  of  Windmills 408 

ElectrlcPower  from  Windmills 409 

Compressed  Air. 

Heating  of  Air  bv  Compression 400 

Loss  of  Energy  m  Compressed  Air 400 

TohuoM  and  rassores , ^. 600 


Xvi  CONTBNTa 

PIO] 

L0B8  due  to  Ezcem  of  Pressure 501 

Horse-power  Required  for  Compression 601 

Table  for  Ad  iabatio  Cioinpression i 60:1 

Mean  Effective  Pressures 608 

Mean  and  Terminal  Pressures 503 

Air-compressors 508 

Practical  Results 508 

Efficiency  of  Oompressed-air  Engines !..  506 

Requii'emente  of  Rock-drills 1 506 

Popp  CJompressed-air  System 50^ 

Small  Oompressed-air  Motors 50! 

Efficiency  of  Air-heatinK  Stoves 601 

Efficiency  of  Compressed-air  Transmission 50^^ 

Shops  Operated  by  Compressed  Air 501] 

Pneumatic  Postal  Transmission 60fl 

Mekarski  Compressed-air  Tramways 51C 

Compressed  Air  Working  Pumps  in  Mines 51] 

Fans  and  Blowers. 

Oentrifugall^ans 511 

Best  Proportions  of  Fans 619 

Pi-essure  due  to  Velocity 618 

Experiments  with  Blowers 51 4 

Quantity  of  Air  Delivered 614 

Efficiency  of  Fans  and  Positive  Blowers 616 

Capacity  of  Fans  and  Blowers 617 

Table  of  Centrifugal  Fans  618 

Engines,  Fans,  and  Steam-coils  for  the  Blower  System  of  Heating. 51S 

Sturtevant  Steel  Pressure-blower 51fl 

Diameter  of  Blast-pipes • 619 

Efficiency  of  Fans 600 

Centrifugal  Ventilators  for  Mines 621 

Eaqperiments  on  Mine  Ventilators 629 

DiskFans 604 

Air  Removed  by  Exhaust  Wheel 68S 

Efficiency  of  Disk  Fans 68S 

Positive  Rotary  Blowers 626 

Blowing  Engines 626 

Steam-let  Blowers SS7 

Steam-Jet  for  Ventilation 627 

BEATING  AND  T£NTII^TION. 

Ventilation 528 

Quantity  of  Air  Discharged  through  a  Ventilating  Duct 590 

Artificial  Cooling  of  Air 531 

Mine-ventilation 631 

Friction  of  Air  in  Underground  Passages 631 

Equivalent  Orifices 633 

Relative  Efficiency  of  Fans  and  Heated  Chimneys 683 

Heating  and  Ventilating  of  Large  Buildings 684 

Rules  for  Computing  Radiating  Surfaces 586 

Overhead  Steam-pipes 687 

Indirect  Heating-surface 537 

Boiler  Heating-surface  Required 688 

Proportion  of  Grate-surface  to  Radiator-surface 588 

Steam-consumption  in  Car-heating 638 

Diameters  of  Steam  Supply  Mains 539 

Registers  and  Cold-air  Ducts 539 

Physical  Properties  of  Steam  and  Condensed  Water 540 

Size  of  Steam-pipes  for  Heating 510 

Heating  a  Greenhouse  by  Steam Ml 

Heating  a  Greenhouse  by  Hot  Water 542 

Hot- water  Heating 542 

Law  of  Velocity  of  Flow 642 

Proportions  of  Radiating  Surfaces  to  Cubic  Capacities 543 

Diameter  of  Main  and  Branch  Pipes 543 

Rules  for  Hot-water  Heating 544 

Arrangements  of  Mains 544 


00KTSKT8.  XVII 

PAOB 

filower  Systein  of  Heating  and  Ventilating * 545 

Experiments  with  lUdiators « 545 

Heating  a  BuildinR  to  70*  F 545 

Heating  by  Electricity 646 

WATER. 

Ezpanskm  of  Water 547 

Weight  of  Water  at  different  temperatures 547 

PresBore  of  Water  due  to  its  Wefgbt 540 

Head  Oorresponding  to  Pressures 549 

Buoyancy 550 

BoflW-point , 550 

Freediig-point 550 

Sea-water 549,550 

Ice  and  Snow 500 

foeciflc  Heat  of  Water 560 

CompresBlbility  of  Water 551 

Imparities  of  Water.... 551 

Causes  of  Incrustation ^ 551 

Means  for  FreTeotIng  Incrustation  T, SBH 

Analyses  of  Boiler-scale 563 

Hardness  of  Water 558 

Purifying  Feed-water 554 

Softening  Hard  Water 655 

Hydranlles.    Flow  of  Water. 

FomnlsB  for  Discharge  through  Orifices 555 

Flow  of  Water  from  Orifices 565 

Flow  in  ^len  and  Closed  Channels 557 

General  Formulae  for  Flow 557 

Tsble  Fsll  of  Feet  per  mile,  etc 668 

Valnesof  Vrforarcular Pipes 559 

Katter*s  Formula 650 

Xolesworth^s  Formula 503 

Bsxin^s  Formula  ..  668 

D*Arcy*s  Formula 568 

Older  Formule 564 

Velocity  of  Water  hi  Open  Channels 564 

Mean.  Surface  and  Bottom  Velocities 564 

Safe  Bottom  and  Mean  VeioclUes 665 

Resistance  of  Soil  to  Erosion 665 

Abrading  and  Transporting  Power  of  Water 666 

Grade  of  Sewers 566 

BehUiQns  of  Diameter  of  Pipe  to  Quantity  discharged 566 

Flow  of  Water  In  aSO-lnchripe 666 

Veioclclesin  Smooth  Csst-Iron  Water-pipes 667 

Table  of  Flow  of  Water  In  Circular  Pipes 668-673 

liossof  Head 678 

Flow  of  Water  in  Rireted  Pipes 574 

FricU<»al  Heads  at  given  rates  of  discharge 677 

Effect  of  Bend  and  Curres 578 

HydrmuUc  Grade-Une 678 

Flow  of  Water  in  House-senrloe  Pipes 678 

Air-bound  Pipes 670 

VertScalJets 670 

Water  Delivered  through  Meters 570 

FlreStreams 670 

Friction  Losses  In  Hose  680 

Head  and  Pressure  Losses  by  Friction 580 

Loss  of  Pressure  In  smooth  S^-inch  Hose 680 

Bated  capacity  of  Steam  Fire-engines 680 

Pressures  required  to  throw  water  through  Nozisles 681 

The  Siphon 681 

Measurement  of  Flowing  WaCer 563 

Piesometer : 582 

PItot  Tube  Gauge        588 

TbeVenturi  Meter 688 

Messufement  oC  Dischaige  by  means  of  Nozzles 684 


XVIH  C0KTEK18. 

PAGB 

flow  through  Beofeangular  Oiifloei 084 

MMMuremont  of  AD  Open  Stream 664 

Hlneni*  iBoh  Measurements flSB 

Flow  of  Water  oTer  Weirs » «...  685 

Francises  Foimula  for  Weirs 686 

Weir  Table 687 

Basin's  Experiments • 6d7 

Watei>-powofv 

PowerofaFanofWatef 888 

HoFse-power  of  a  Bunnlog  stream ■> S80 

Current  Motors 680 

Horse-power  of  Water  Flowing  in  a  Tube... 680 

Maximum  Efflcienoy  of  a  Long  Conduit 889 

Miil.power 680 

Value  of  Wat«^pow0r *.••  •• 680 

The  Power  of  Oceui  Waves • 690 

UUltntionofTi(Ua  Power OOO 

•  Turbltte  WhaeUk 

Proportions  of  Turbines • ••.•••..  60t 

1>Mt8  of  Turbines • *..••..»  648 

Dtmensions  of  Turbines •••••*....  607 

The  Felton  Water-wheel %••••.»,.••••••,..  647 

Pnmps. 

Theoretical  capadty  of  a  pump • 601 

Depth  of  Suction • 00^ 

Amount  ol  Water  raised  by  a  Sltigle-actl ng  Lift-pump. 604 

Proportioning  the  Steam  cylinder  of  a  Direct-acting  Tump 004 

Speed  of  Water  through  Pipes  and  Pump -passages 604 

Suees  of  Direct-acting  rumps OOS 

The  Deane  Pump 604 

Rttcienoy  of  Small  Pumps » * ».. 408 

The  Worfchington  Duplex  Pump 404 

Speed  of  Piston ..»«»«» 406 

Speed  of  Water  through  Valves  ..• 406 

Boiler-feed  Pumps.. k .»»»    • • 006 

Pvimp  Valves 406 

Centrifugal  Pumps 404 

Lawrence  Centrifugal  Pumps 407 

Bflddenoy  of  Centrifugal  and  Reciprocating  Pumps 406 

Vanes  of  Centrifugal  Pumps 404 

The  Centrifugal  Pump  used  as  a  Suction  Dredge 409 

Duty  Trials  of  Pumping  Engines 400 

Leakage  Tests  of  Pumps 411 

Vacuum  Pnmps 414 

ThePulsoraeter... 614 

nie  Jet  Pump «.  614 

The  Injector ..»••..» 614 

AtrllftPump 414 

The  Hydraulic  Ram •»..•.••  414 

Quantity  of  Water  Delivered  by  the  Hydraulic  Ram 614 

Hydranlio  Pressure  Transmission. 

Energy  of  Water  under  Pressure » .».  614 

fiAciency  of  Apparatus ...*» 414 

Hydraulic  Presses «....  617 

HydrauHc  Power  in  London • , 417 

Hydraulic  Riveting  Machines »  418 

wdraulio  Forslng 618 

The  Aiken  Intensiner « 419 

QydrauUc  Engine ....» 614 


FVSIi. 


Theory  of  Combustion 

Total  Heat  of  Combustion*, 


C0?TTEKT8.  XIX 

• 

PAOS 

AMlyaeB  of  Gases ^OombufltiaB ••••••«• »».»• t^ 

Temperature  of  tbe  Fire * • • .%  m 

ClassificaUoDofSoUdFuel 628 

ClassUlcation  of  Ooala 634 

Analyses  of  Coals » 9114 

Wf«teni  Llenites 681 

Analyses  of  Foreign  Coals.... , ,•.•.....••.....  6S] 

KixuQ^s  Navigation  Coal « • 682 

SampUnirCoal  for  Analyses •••.«»•.••• ».* 683 

fiektiTe  value  of  Fine  Sizes * 688 

Pressed  Fuel , 68'3 

ReJatiTe  Value  of  Steam  Coals 688 

Approximate  Heating  Value  of  Coals ....«» 684 

Kind  of  Furnace  Adapted  for  Different  Coals 685 

Downwani-draugbtFumacestk »..».. 635 

Calorimetric  Tests  of  American  Coals • 636 

EraporatiTe  Power  of  Bituminous  Coals • 636 

Weathering  of  Coal .,.•• »..•..  637 

Coke  687 

Experiments  In  Coking ,..•.•...•...« •••.•..  687 

Coal  WashlnK. 1 688 

Recoveryof  By-products  In  Coke  manufacture 688 

Making  Hard  Ooke 688 

Generation  of  Steam  from  the  Waste  Heat  and  Gases  from  Coke-ovens.  638 

Phxluetsof  tbeDistfUationofCoal 68i 

Wood  as  Fuel , .  680 

Heating  Value  of  Wood , 689 

Oompinftion  of  Wood * 640 

Charvoal ,... ...».  640 

Yield  of  Charcoal  from  a  Cord  of  Wood 641 

Coosmnption  of  Charcoal  In  Blast  Furnaces. 641 

Ataaorption  of  Water  and  of  Oases  by  Charcoal 641 

Ct>mpoBitlon  of  Charcoals Mt 

MisceilaDeousSolid  Fuels 642 

Dusc-f  oel— Dust  ExplosiOBS 642 

PmtorTurf 648 

Sawdust  as  Fuel » , 648 

Borae-raanure  as  Fttel 618 

WetlHan-barkasFuel....  w.  648 

StmwasFuel • • 648 

Bsgaase  as  Fuel  In  Sugar  Manufacture •••  648 

Petrolennu 

ProducUof  Distillaaoo 646 

lima  Petroleiini » •••...«•.•.•..«•.•....»..,»...  646 

Value  of  Petroleum  as  Fwl 646 

Oil  M.  Goal  as  Fuel 646 

Fael  Gas. 

QirttooQas 646 

AnthraciteOas 617 

Bitumioons  Gas 647 

WaterOas 648 

Prodaoer'^as  from  One  Ton  of  Goal 049 

Xatural  Oaa  in  Ohio  and  Indiana 649 

Cvmbtutioo  of  Producer^gas 650 

Use  of  Steam  in  Producers « 690 

Gas  Fuel  for  Small  Furnaces 661 

lUaminatinir  Oas« 

Onal-gas .«.••.• 661 

Vtier-fSaM 652 

Analywes  of  Water-gas  and  Coal  gas 668 

Otloriflc  Equivalents  of  Constituents 664 

Efficient  of  a  Water-gas  Plant 654 

(teace  Bequf red  fOr  a  Water-ipas  Plant. 656 

AetralDBOtlllUttiiflMi&K^^ 606 


.IIV  COUfTEKTS. 

Vis  Viva 49S 

Work,  Foot-pound 438 

Power,  Horse-power 429 

Energy 439 

Work  of  Acceleration 480 

Force  of  a  Blow 430 

Impact  of  Bodies 4«1 

Energy  of  BeooU  of  Quns 441 

Oonserration  of  Energy 4SS 

Perpetual  If  otion  43S 

BAeiencyof  aMachlne  439 

Antmal-poweTf  Man-power «» 

WorieofaHone 434 

Ifan-wheel 484 

Horse-gin 484 

Resistance  of  Vehicles 485 

Slements  of  Maohtnes. 

TheLeTor 485 

TheBent  Lever 436 

The  MoTlng  Strut 486 

The  Tofl»le-JoInt 486 

The  Inclinea  Plane 487 

The  Wedge 487 

TheSorew 487 

The  Cam 488 

ThePuUey 488 

Differential  PuUey 481* 

Differential  Windlass 489 

Differential  Screw 4» 

Wheel  and  Axle 489 

Toothed-wheel  Gearing 489 

Endless  Screw 440 

Strssses  in  Framed  Stmctiires, 

Cranes  and  Derricks 440 

Shear  Poles  and  Ouys 44S 

King  Post  Truss  or  Bridge 44S 

Queen  Post  Truss 44S 

Burr  Truss 443 

Pratt  or  Whipple  Truss 445 

HoweTruss 44: 

Warren  Qtrder 44! 

Roof  Truss ; 44< 

HEAT. 

Thermometen  and  Pyrometers  44( 

Centigrade  and  Fahrenheit  degrees  compared 441 

Copper-ball  Pyrometer 45: 

Thermo-etoctno  Pvrometer 45 

Temperatures  in  Furnaoes 45 

Wlbofgh  Air  Pvrometer 4h 

Seegers  Fire-clay  Pyrometer 45 

lfeBur6and  KouePs  Pvrometer  45 

Uehling  and  Steiabart^s  Pyrometer 45 

Air-thermometer , 45 

High  Temperatures  Judged  by  Color 45 

BoIling-pomtB  of  Substances 45 

Mel  ting-points 4*) 

UnitofHeat 45 

Mechanical  Equivalent <tf  Heat...  45 

Heat  of  Combustion 45 

Speolflo  Heat 45 

Latent  Heat  of  Fusion 459,  46 

B  xpaneion  by  Heat 46 

Absolute  Temperature 46 

Absolute  Zero • 46 


GOSTTSETEB.  XY 

PAGK 

Latent  Heat 461 

Latent  Heat  of  Braporatlon 4^ 

Total  Heat  of  Eraporation 408 

Evaporation  and  Drying 468 

Braporation  from  Reservoirs 468 

Eraporation  by  the  Multiple  System 468 

BesMtanoe  to  BfldliDg 468 

Manuf actuie  of  Salt 464 

Solubility  of  Salt  and  Sulphate  of  lime 464 

Salt  Ck>ntent8  of  Brines 464 

ConoKitration  of  Sugar  Solutions 466 

Evaporatlns  by  Exhaust  Steam 466 

Diyuig  in  vacuum 466 

Radiation  of  Heat 467 

GonducUon  and  Convection  of  Heat ..  468 

Rate  of  External  Conduction 460 

Steam-pipe  Coverings  470 

Transmission  through  Plates 471 

••  in  Condenser  Tubes 478 

"  "       Cast-iron  Plates 474 

••  from  Air  or  Gases  to  Water iU 

"  from  Steam  or  Hot  Water  to  Air 476 

••  through  Walls  of  Buildings 478 

Thermodynamics 478 

PHTSICAI*  PKOPERTIKS  OF  GASES. 

Expansion  of  Oases 479 

Boyle  and  ]farrlotte*8  Law 479 

Law  of  Charles,  Avogadro's  Law 479 

Saturation  Point  of  vapors 480 

Law  of  Gaaeotis  Pressnre 480 

Flow  of  Gases 480 

Absorption  hyIAqn\6s 480 

AIR. 

Properties  of  Air 481 

Air-manometer , 481 

Preesure  at  Different  Altitudes 481 

Barometric  Pressures 488 

Levelling  br  the  Barometer  and  by  Boiling  Water 482 

To  find  iniference  In  Altitude 483 

Hofstnre  In  Atmosphere 488 

Weight  of  Air  and  Mixtures  of  Air  aod  Vapor 484 

SpeSlle  Heat  of  Air 484 

Flow  of  Alr» 

Flow  of  Air  through  Orifices 484 

Flow  of  Afr  in  Pipes 485 

Effect  of  Bends  in  Pipe 488 

Flow  of  Compressed  Air 488 

Tables  of  Flow  of  Air 489 

Anemometer  Measurements 491 

Equalization  of  Pipes 491 

Loss  of  Pressure  in  Pipes 493 

Wind. 

Force  of  the  Whid 498 

Wind  Pressare  in  Storms 495 

Windmflls 496 

Capacity  of  Windmills 497 

Economy  of  Windmifls 496 

Electric  rower  from  Windmills 499 

Compressed  Air. 

Heating  of  Air  b7  Compression 499 

Loss  of  Energy  hi  Compressed  Air , 499 

Volwoef aoaProBsures i ,  609 


Xvi  CONTENTS. 

PIOI 

Loss  due  to  Excess  of  Pressure 60! 

Horse-power  Required  for  Compression 501 

Table  for  Ad  iabatic  Compression i fios 

Mean  Effective  Pressures fiOS 

Mean  and  Terminal  Pressures MK 

Air-compressors fiOf 

Practical  Results 6W 

Efficiency  of  Compressed-air  Engines AM 

Requirements  of  Boclc-driUs ...1 60( 

Popp  Compressed-air  System  6a; 

Small  Compressed-air  Motors 60; 

Efficiency  of  Air-heatinK  Stoves 60: 

Efficiency  of  Compressed-air  Transmission 60^ 

Shops  Operated  by  Compressed  Air 50S 

Pneumatic  Postal  Transmission 60h 

Mekarski  Compressed-air  Tramways 61( 

Compressed  Air  Working  Pumps  in  Mines 611 

Fans  and  Blowers. 

Centrifugal  Fftns 611 

Best  Proportions  of  Fans 61S 

Pi-essure  due  to  Velocity 619 

Experiments  with  Blowers 614 

Quantity  of  Air  Delivered tu 

Efficiency  of  Fans  and  Positive  Blowers 516 

Capacity  of  Fans  and  Blowers 617 

Table  of  Centrifugal  Fans 518 

Engines,  Fans,  and  Steam-colls  for  the  Blower  System  of  Heating. 519 

Sturtevant  Steel  Pressure-blower 6lfl 

Diameter  of  Blast^pipes 61fl 

Efficiency  of  Fans 62C 

Centrifugal  Ventilators  for  Mines 6S] 

Experiments  on  Mine  Ventilators 62S 

DiskFans , 824 

Air  Removed  by  Exhaust  Wheel 52£ 

Efficiency  of  Disk  Fans 62S 

Positive  Rotary  Blowers 6SC 

Blowing  Engines 52C 

Steam-jet  Blowers 527 

Steam-Jet  for  Ventilation 6Zi 

HEATING  AND  VENTII.ATION. 

Ventilation 628 

Quantity  of  Air  Discharged  through  a  Ventilating  Duct. 58G 

Artificial  Cooling  of  Air 581 

Mine-ventilation 581 

Friction  of  Air  in  Undeiiground  Passages 58] 

Equivalent  Orifices 589 

Relative  Efficiency  of  Fans  and  Heated  Chimneys 58fl 

Heating  and  Ventilating  of  Large  Buildings 534 

Rules  for  Computing  Radiating  Surfaces SK 

Overhead  Steam-pipes 68? 

Indirect  Heating-surface 53? 

Boiler  Heating-surface  Required 636 

Proportion  of  Grate-surface  to  Radiator-surface 538 

Steam-consumption  In  Car-heating NS8 

Diameters  of  Steam  Supply  Mains 53S 

Registers  and  Cold-air  Ducts 53S 

Physical  Properties  of  Steam  and  Condensed  Water  54G 

Size  of  Steam-pipes  for  Heating 6IC 

Heating  a  Greennouse  by  Steam 541 

Heating  a  Greenhouse  by  Hot  Water 549 

Hot- water  Heating  648 

Law  of  Velocity  of  Flow 548 

Proportions  of  Radiating  Surfaces  to  Cubic  Capacities 548 

Diameter  of  Main  and  Branch  Pipes 548 

Rules  for  Hot-water  Heating 644 

Arrangements  of  Mains 644 


CONTENTS  XVil 

PAOB 

Slower  System  of  Heating  and  Ventilating •. 545 

Expeiimente  with  Radiators ••... 545 

Heating  a  Buildinir  to  TO"  F 545 

Heating  by  Electiricity 54« 

WATER. 

Expaaiioa  of  Water 547 

Weight  of  Water  at  different  temperatures 547 

Preeaare  of  Water  due  to  its  Weight 549 

Head  OorreepoDdtng  to  PresBures 549 

Buoyancy 550 

Bollbg-point 650 

Freezfiig-point 550 

Bea^water 549,550 

loe  and  Snow 550 

Bpedflc  Heat  of  Water 550 

CompreesibilitT  of  Water 551 

Impurities  of  Water 551 

Causes  of  Incrustation ^ 561 

Means  for  Preventing  Incrustation 7. SSH 

Analyies  of  Boiler-scale 56S 

Hardness  of  Water 553 

Porifying  Feed-water 554 

Softening  Hard  Water 655 

Hydraulics.    Flow  of  Water. 

Fomnte  for  Discharge  through  Orifices ...  665 

Flow  of  Water  from  Orifices 556 

Flow  in  Open  and  Closed  Channels 557 

General  F^mulflB  for  Flow 557 

Tsble  Fall  of_Feet  per  mile,  etc 558 

Taluesof  Vr for Qrcular Pipes 569 

Kntter*s  Formula 669 

Molesworth's  Formula 6es 

Basin's  Formula 568 

D'Arcy*s  Formula 568 

Older  Formuls 564 

Velocity  of  Water  in  Open  Channels 664 

Mean  Surface  and  Bottom  Velocities 664 

Safe  Bottom  and  Mean  Velocities 565 

Besistance  of  Sou  to  Erosion 665 

Abradiog  and  Transporting  Power  of  Water 565 

Grade  of  Sewers 666 

BelatlQns  of  Diameter  of  Pipe  to  Quantity  discharged 566 

Flow  of  Water  in  a  80-inch  Pipe 566 

Veioeiilesin  Smooth  Castriron  Water-pipes 567 

Table  of  Flow  of  Water  in  arcular  Pipes 668-578 

LoesofHead 578 

Flow  of  Water  in  Riveted  Pipes 574 

FricUonal  Heads  at  given  rates  of  discharge 577 

Effect  of  Bend  and  Curves 578 

Hydraulic  Grade-line 578 

Flow  of  Water  in  House-service  Pipes 578 

Air-bound  Pipes 579 

VerticalJeU 579 

Water  Delivered  through  Meters 579 

Fire  Streams 579 

Friction  Losses  in  Hose 580 

Head  and  Pressure  Losses  bj  Friction 580 

Loss  of  Pressure  in  smooth  2^-ineh  Hose 580 

Bated  capacity  of  Steam  Fire-engines 580 

Pressures  required  to  throw  water  through  KosBles 581 

The  Siphon  581 

Measurement  of  Flowfaig  Wafer 582 

Piesometer T 582 

Pttot  Tnbe  Gauge       588 

The  Venturi  Meter 688 

Measurement  of  Discharge  by  means  of  Nozzles 684 


XVlll  C0KTBK18. 

_  PlOE 

flow  through  ReoftangularOrlfloet.. ••.»».• OM 

Hea«arem«Bt  of  aa  Open  Stream 664 

MfneraUnoh  Measuremeats •.. OSS 

now  of  Water  oTer  Wein 1160 

FrandB^s  Formula  for  Weirs fi86 

WeirTkble 687 

Baiiii'8  Experiments » fid7 

Waf;ei>powerw 

^werofsFUlofWater 568 

Horfle-power  of  a  Runnloi;  Stream ., G8B 

Current  Motors » 689 

Horae-powerof  Water  Flowing  in  a  Tube... • 66B 

Uaxlmum  Effieiency  of  a  Long  Conduit 680 

MUlpower 68B 

Value  of  Watca^power •....  600 

The  Power  of  Ooean  Waves » 690 

UtUfation  of  Tidal  Fower OOO 

•  Ttirbltte  Wheels. 

Proportions  of  Turbines »•...•..  601 

Tests  of  Turbines ••% 606 

Dimensions  of  Turbines ••»• 607 

llie  Pelton  Water-wheel - 607 

Pumps. 

Theoretical  capadty  of  a  pump • 601 

Depth  of  Suction 604 

JUnount  oi  Water  raised  by  a  Single-acting  Lift-pump 60a 

Proportioning  the  Steam  cylinder  of  a  Direct-acting  Pump OOt) 

Speed  of  Water  through  Pipes  and  Pump -passsges 603 

Sues  of  Dlrect>acting  Pumps 603 

Tlie  Deane  Pump •....• • OOS 

Kflloienoy  of  Small  Pumps * •  ...  ••*..  606 

The  Worfchlngton  Duplex  Pump • 604 

Speed  of  Piston ..>...» • 605 

Speed  of  Water  through  ValTes... » 605 

Boilerfeed  Pumps • 605 

PnmpValvee « 606 

Centrifugal  Pumps 606 

Lawrenoe  Centrifugal  Pumps 607 

EMoienqy  of  Centrifugal  and  Reciprocating  Pumps 606 

Vanes  of  Centrifugal  Pumps 600 

Tlie  Centrifugal  Pump  used  as  a  Suction  Dredge 60D 

Duty  Trials  or  Pumping  Engines 600 

Leakage  TesU  of  Pumps , 611 

Vacuum  Pnmps....  • 616 

ThePul8ometer..» k...  61i 

IlieJetPump •  •  »»..»».  514 

The  Injector •••••..•»..•». 614 

Air-lift  Pump 514 

The  Hydraulie  Ram »> •  514 

Quantity  of  Water  Delivered  by  the  Hydraulic  Ram..... 515 

Hydraulic  Pressure  Tranamission. 

Energy  of  Water  under  Pressure • 515 

fifliciency  of  Apparatus • 515 

ttydraulfc Presses 617 

Hydraulic  Power  in  London 617 

Hydraulic  Riveting  Machines 518 

Hydraulic  Forging 515 

1%e  Aiken  Intensmer 510 

Hydraulic  Bngitte 515 


FUBIto 


Theory  of  Combustion 

Total  Heat  of  Combustion., 


C0KTENT8.  XIX 

PAOI 

AMlrnBorGMesofOombostta «» 

T»inper«ture  of  the  Fire ••  AH 

Clasftiflcatioo  of  Solid  Fuel 628 

ClassiflcaUon  of  Coals 634 

Anelj-sas  of  Coals 624 

Western  Lignites 631 

ADslysesof  Foreign  Coals >...  68) 

NixoQ^s  Navigation  Coal 6S2 

SsmpIinKCoal  for  Analyses » 683 

ftftkUve  value  of  Fine  Sixes 68li 

Pressed  Fuel 68a 

Belatiye  Value  of  Steam  Coals 688 

A|»prox1mate  Heating  Value  of  Coals » 684 

Kind  of  Furnace  Adapted  for  Different  Coals 685 

DowDwafd-draugbt  Furnaces.  > ..».»..•.. 635 

Ghlorimetric  Tesis  of  American  Coals » 636 

£rsporative  Power  of  Bituminous  Coals. • • «..  686 

Weathering  of  Coal...  ,....« %...  697 

Coke  687 

Kzperiments in Oolcins • •.  ,•..„ ..• .^•..•..  687 

Coal  Washing 77. ; m 

B<ecc»Tei7  of  By-products  In  Coke  manufacture 688 

Making  Hard  Coke 638 

(jtfoeraiion  of  Steam  from  the  Waste  Heat  and  Gases  from  Coke-ovens.  638 

Products  of  the  DistlUatiOD  of  Coal 68» 

Wood  as  Fuel .  680 

HoatiDK  Value  of  Wood 680 

Compoiltlon  of  Wood » 640 

ChaiTosl 640 

Yield  of  Charcoal  ftom  E  Cord  of  Wood 641 

Consumption  of  Charcoal  In  BlaKt  Furnaces. 641 

Absorption  of  Water  and  of  Oases  by  Charcoal 641 

Oompositfon  of  Charcoals 64)1 

Mjaceilaneous  Solid  Fuels 643 

Dustrfuel— Dust  Ezploslom 643 

Beat  or  Turf • 648 

Sawdust  as  Fuel ..*..»• 648 

Hone-raanure as Ftid .......•» 643 

Wee  Tan-bark  as  Fuel 648 

Straw  as  Fuel 648 

Bagasse  as  Fuel  la  Sugar  ICanufacture 648 

Petroleam* 

P^isduetaof  DlsUIlation 646 

Lima  Petroleum. ••• • • »..,%...  646 

Valueof  FetroleumasFMl «.••*—* 646 

Oaea  Gold  as  Fuel 646 

Fael  Gas. 

O&rtxmGas • 646 

AnthrveiteGas 617 

Bttumiooas  Gas 647 

WaterOas 648 

Pit>daoerogss  from  One  Ton  of  Coal 649 

Natural  Gas  in  Ohio  and  Indiana 640 

Oimbttstion  of  Prodnoer^gas 6!i0 

Use  of  Steam  fan  Producers 6S0 

Gas  Fuel  for  Small  Furnaces 651 

lUamlnatlng  €kM» 

Ooal-gas , 661 

Water-ffas 660 

Analjwes  of  Water-gas  and  Coal  gas 6S3 

Oaloriftc  Equiralents  of  Constituents , 6M 

KSciency  of  a  Water-gas  Plant 664 

Hpace  Required  for  a  Water-^as  Plant 656 

iSiel'^aliifl  ol  iBinwIniUllig-gas OM 


XIV  GOKTEKT& 

VtoVlva 49S 

Work,  Foot-pound 4M 

Power,  Horse-power 499 

Energy 4» 

Work  of  Acceleration 480 

Force  of  a  Blow 490 

Impact  of  Bodies 431 

Enency  of  BecoU  of  Guns 481 

OonseryatioD  of  Enency 49B 

Perpetual  Motion  4» 

SIBciencyof  aHacbine 489 

Animal-power,  ]IIan>power 438 

WorkofaHorse 4S4 

Man-wheel 404 

Horse^n 484 

Besistanoe  of  Vehicles 485 

Blements  of  Machines. 

The  Lever 485 

TheBentLsTer 438 

The  Moving  Strut 486 

The  Toggle-Joint ■ 486 

The  Incunea  Plane 487 

The  Wedge 487 

TheScrew 437 

The  Cam 438 

ThePulloy 438 

DUTerantial  Pulley 4SD 

Differential  Windlass 489 

DUTerentJAl  Screw 481' 

WheelandAxle 48» 

Toothed-wheel  Gearing 488 

KwUesi  Screw 4«0 

Stresses  in  Framed  Struotnres. 

Cranes  and  Derricks 440 

Shear  Poles  and  Guys US 

King  Poet  Truss  or  Bridge. 4lt 

Queen  Post  Truss 449 

Burr  Truss 448 

Pratt  or  Whipple  Truss 44S 

HoweTmss 445  I 

Warren  Girder 44S 

Boof  Truss ¥i 

HEAT. 

Thermometere  end  Pyrometers 44 

Centigrade  and  Fahrenheit  degrees  compared 44t 

Copper-hall  Pvrometer 40 

Thermo-eleotno  Pvrometer fil 

Temperatures  in  Fumaoes 4SI 

Wlborgh  Air  promoter 4S 

Seegers  Fire-clay  Pyrometer 4SS 

Mesur^and  Kouel's  Pyrometer 40 

Uehling  and  Stelnbart^s  Pyrometer 49 

Air-thermometer , 4M 

High  Temperatures  judged  by  Color 4M 

Boiling-points  of  Subetaoces 4S 

Melting-points tf 

Unit  of  Heat ..  «l 

Mechanical  Equivalent  of  Heat fli 

Heat  of  Combustion el 

Specific  Heat tSf 

Latent  Heat  of  Fusion 4S>,«1 

Expansion  by  Heat # 

Abiiolute  Temperature IB 

Absolute  Zero « 


OONTESn&  XV 

PAQK 

Latent  Heat 461 

lAtent  Heat  of  Eyaporation 46^ 

Total  Heat  of  Evaporation 408 

ETaporatlon  and  Drying ..• 4(12 

Evaporation  from  Beeervoirs 468 

KTaporation  by  the  Multiple  System 468 

Reaisuuice  to  Boiling 468 

Manufacture  of  Salt 464 

SolubOity  of  Salt  and  Sulphate  of  Xime 464 

Salt  Contents  of  Brineg 464 

Conoentration  of  Sugar  Solutions....  465 

ETaporatins  by  Exhaust  Steam 466 

Vrymg  in  vacuum 466 

Radiation  of  Heat 467 

Oondoction and  ConyecUon  of  Heat ...468 

Rate  of  External  Conduction 460 

Steam-pipe  Coverings  470 

Transmission  through  Plates 471 

'*  in  Condenser  Tubes 478 

*•  **       Cast-iron  Plates 474 

**  from  Air  or  Oases  to  Water 474 

••  from  Steam  or  Hot  Water  to  Air 476 

*«  through  Walls  of  Buildings 478 

Thennodjnamics 478 

PHTSICAL  PROPERTIES  OF  GASES. 

Expansion  of  Gases 470 

Bojleand  Marriotte^s  Lav 470 

Law  of  Charles,  Avogadro*s  Law 470 

Batnration  Point  of  vapors 480 

Ijaw  of  Gaseous  Pressure 480 

Flow  of  Gases 480 

Absorptfon  by  Liquids 480 

AIR. 

Properties  of  Air 461 

Air-manometer 481 

Pressure  at  Different  Altitudes 481 

Barometric  Pressures 489 

Levelling  by  the  Barometer  and  by  Boiling  Water 482 

To  find  Imferenoe  in  Altitude 483 

Moisture  in  Atmosphere 488 

Weight  of  Air  and  Mixtures  of  Air  and  Vapor 484 

Specific  Heat  of  Air 484 

Flow  of  Air* 

Flow  of  Air  through  Orifices 484 

Flow  of  Air  in  Pipes 485 

Effect  of  Bends  in  Pipe 488 

Flow  of  Compressed  Air 468 

Tables  of  Flow  of  Air 480 

Anemometer  Measurements 401 

Eqrualization  of  Pipes 401 

liOflS  of  Pressure  in  Pipes 408 

Wind. 

Force  of  the  Wind 408 

Wind  Pressure  In  Storms 406 

Windmills 405 

Capacity  of  Windmills 407 

Economy  of  Windmills 408 

KlectricPower  from  Windmills 400 

Compressed  Air. 

Beatincr  of  Air  bj  Compression 400 

IxMB  of  Energy  bi  Compressed  Air 400 

Volumes  anaPreBBures * • .^ 600 


Xvi  CONTENTS. 

PlOl 

Loss  due  to  Excess  of  Presgure fiO] 

Horae-power  Required  for  Compression 601 

Table  for  Ad  labatic  Compression i BOi 

Mean  Effective  Pressures 6Q9 

Mean  and  Terminal  Pressures 603 

Air-compressors COS 

Practical  Results SOS 

Efficiency  of  Compressed-air  Engines 50e 

Requirements  of  Rock-drills 1 606 

Popp  Compressed-air  System 607 

Smflkil  Compressed-air  motors 607 

Efficiency  of  Air-heatinK  Stoves 607 

Efficiency  of  Compressed-air  Transmission 60^ 

Shops  Operated  by  Compressed  Air 60fl 

Pneumatic  Postal  Transmission 60d 

Mekarski  Compressed-air  Tramways 61C 

Compressed  Air  Working  Pumps  in  Mines 61] 

Fans  and  Blowers. 

Centrifugal  Fans 611 

Best  Proportions  of  Fans 619 

Pressure  due  to  Velocity 618 

Experiments  with  Blowers 614 

Quantity  of  Air  Delivered 61<l 

Efficiency  of  Fans  and  Positive  Blowers 516 

Capacity  of  Fans  and  Blowers 617 

Table  of  Centrifugal  Fans 618 

Engines,  Fans,  and  Steam-coils  for  the  Blower  System  of  Heating. 619 

Sturtevant  Steel  Pressure-blower 51fl 

Diameter  of  Blastrpipes 619 

Efficiency  of  Fans 82G 

Centrifugal  Ventilators  for  Mines 621 

Experiments  on  Mine  Ventilators 62S 

DlskFans 624 

Air  Removed  bv  Exhaust  Wheel 6S8 

Efficiency  of  Disk  Fans 63S 

Positive  Rotary  Blowers &M 

Blowing  Engines ftSC 

Steam-jet  Blowers 6*7 

Steam-Jet  for  Ventilation 627 

HEATING  AND  VENTII.ATION. 

Ventilation 828 

Quantity  of  Air  Discharged  through  a  Ventilating  Duct. 530 

Artlfldal  Cooling  of  Air 681 

Mine-ventilation  681 

Friction  of  Air  in  Underground  Passages 531 

Equivalent  Orifices 688 

Relative  Efficiency  of  Fans  and  Heated  Chimneys 688 

Heating  and  Ventilating  of  Large  Buildings 534 

Rules  for  Computing  Radiating  Surfaces 580 

Overhead  Steam-pipes 637 

Indirect  Heating-surface  687 

Boiler  Heating-surface  Required 588 

Proportion  of  Grate-surface  to  Radiator-surface 688 

Steam-consumption  In  Car-heating 638 

Diameters  of  Steam  Supply  Mains 539 

Registers  and  Cold-air  Ducts 539 

Physical  Properties  of  Steam  and  Condensed  Water 540 

Size  of  Steam-pipes  for  Heating 610 

Heating  a  Qreenhouse  by  Steam 041 

Heating  a  Greenhouse  by  Hot  Water 548 

Hot-water  Heating  548 

Law  of  Velocitv  of  Flow 548 

Proportions  of  Radiating  Surfaces  to  Cubic  Capacities 543 

Diameter  of  Mai n  and  Branch  Pipes 543 

Rules  for  Hot-water  Heating 544 

Arrangements  of  Mains • 544 


CONTENTS  Xvii 

-*  PAOB 

Bbwer  System  of  Heating  and  Ventilating 645 

Experiments  with  Radiators « 645 

Heating  a  Buildine  to  70*  F 645 

Heating  by  Electricity 646 

WATER. 

Expansion  of  Water 647 

W^ght  of  Water  at  different  temperatures 547 

Preasare  of  Water  due  to  Its  Weigbt 649 

Head  Oorrasponding  to  Pressures 649 

BoiSig-point*.!./.!l!l!I!I!iili!!lii!".r.y.;!;i!!!*!*^ '.;!!*.!;! ■".!**.;'.!*.!;.'*!  66o 

Freesmg-point 650 

Sea-water 649.560 

Ice  and  Snow 550 

Specific  Heat  of  Water 650 

Compressibility  of  Water 651 

Impurities  of  water........ 651 

Causes  of  Incrustation ^ 661 

Means  for  Preventing  Incrustation 7, 65'j 


Analyses  of  Boiler-scale., 
Hardness  < 


lof  Water 653 

Purifying  Feed-water 654 

Softening  Hard  Water 665 

Hydranllcs.    Flow  of  Water. 

Fomuls  for  Discharge  through  Orifices 665 

Flow  of  Water  from  Orifices 655 

Flow  In  Open  and  Closed  Channels 557 

General  Formuln  for  Flow 557 

Table  Fall  of_Feet  per  mile,  etc 668 

Valuesof  fr  for  Circular  Pipes 559 

Kntter*8  Formula 659 

Molesworth's  Formula 663 

Basin's  Formula 568 

IV  Arctr's  Formula 668 

Older  Formule 664 

Velocity  of  Water  in  Open  Channels 664 

Mean,  Surface  and  Bottom  Velocities 664 

Safe  Bottom  and  Mean  Velocities 665 

Resistance  of  Soil  to  Erosion 665 

Abrading  and  Transporting  Power  of  Water 665 

Grade  of  Sewers 666 

Belati^ns  of  Diameter  of  Pipe  to  Quantity  discharged 666 

Flow  of  Water  in  a  SO-inch  Fipe 666 

Veioclclesin  Smooth  Cast-Iron  Water-pipes 567 

Table  of  Flow  of  Water  in  Circular  Pipes 668-678 

Lossof  Head •578 

Flow  of  Water  in  Riveted  Pipes 574 

Frictional  Heads  at  given  rates  of  discharge 577 

Effect  of  Bend  and  Curves * 678 

Hydraulic  Grade-line 678 

Flow  of  Water  in  House-service  Pipes 678 

Air-bound  Pipes 679 

VertfcalJets 679 

Water  Delivered  through  Meters 679 

FIreBtreams 679 

Friction  Losses  in  Hose 580 

Head  and  Pressure  Losses  bv  Friction 580 

Loss  of  Pressure  in  smooth  2^-inch  Hose 580 

Rated  capacity  of  Steam  Fire-engines 680 

Pressures  required  to  throw  water  through  Kozssles 681 

The  Siphon 681 

Measurement  of  Flowhig  W«eier 688 

Piezometer 682 

Pilot  Tube  Gauge       683 

The  Ventttri  Meter 688 

Measurement  of  Dischai^  by  means  of  Nozzles 684 


XVIU  COKTEKT& 

PAQB 

flow  through  Beot&ngular  Orifloet 684 

HeasurenMBt  of  aa  Open  Stream 064 

Mlnera*  iBoh  Measurements •• 06B 

Plow  of  Water  oTor  Weirs •*., 088 

Francis's  Fonnula  for  Welfi 686 

WeirTkble 587 

Basin's  Experiments 6d7 

Wafeer^powerw 

^werofaFhUof  Water » Bd8 

Horfle-power  of  a  Running  8tt>Bam  M 

Current  Motors 68B 

Hors6>power  of  Water  Flowing  in  a  Tube 680 

Maximum  Efficiency  of  a  Long  Conduit 889 

Mill-power 689 

Value  of  Water-power • S90 

The  Power  of  Ooean  Waves 698 

UUliation  of  Tidal  Fower 000 

•  Ttirblne  Wheels. 

Proportions  of  Turbines ••» •••  001 

Tests  of  Turbines 600 

Dimensions  of  Turbines » 697 

llie  Pelton  Water-wheel • -• 807 

Pumps. 

Theoretical  capacity  of  a  pump • • 601 

0cpth  of  Suction 00< 

JUnoant  01  Water  raised  by  a  Single-acting  Lift-pump ••..  .  60a 

Proportioning  the  Steam  cylinder  of  a  Direct-acting  Pump 600 

Speed  of  Water  through  Pipes  and  Pump-passages • 009 

STses  of  Direct-acting  Pumps OOS 

The  Deane  Pump 000 

Rffioienoyof  Small  Pumps. *........>.  ••• 000 

The  Worthington  Duplex  Pump » 004 

Speed  of  Piston »»..> 006 

Speed  of  Water  through  ValTes ••• 005 

Bollerfeed Pumps ...».»•••. • 006 

Pump  Valves 006 

Centrifugal  Pumps 000 

Lawreooe  Centrifugal  Pumps 007 

Bfficienqy  of  CentrifUral  and  Reciprocating  Pumps 606 

Vanes  of^Centrlfugal  nimps 600 

The  Centrifugal  Pump  used  as  a  Suction  Dredge 000 

Duty  Trials  of  Pumping  Engines «..  000 

Leakage  Tests  of  Pumps ,.. Oil 

Vacuum  Pnmps 010 

ThePul8ometer..» 010 

The  Jet  Pump »..«..  614 

Thelo^tor 014 

Air-lift  Pump 014 

The  Hydraulic  Ram , 014 

Quantity  of  Water  Delivered  by  the  Hydraulic  Ram eW 

Hydraulic  Pressure  Transmission. 

Energy  of  Water  under  Pressure ....•• 010 

fiflicieiiey  of  Apparatus 010 

Hydraulfo  Presses .. .  017 

Hydraulic  Power  in  London • 617 

HydrauHc  Riveting  Machines *  018 

Hydraulic  Forging 018 

1%e  Aiken  Intensmer ^10 

HydrauHc  Engine 610 


FUKIf 


Theory  of  Combustion 

Total  Heat  of  Oombustioo.. 


CONTENTS.  XIX 

• 

PAOI 

AnaljiMorGaanofOoiiibastta » «tt 

Temperature  of  the  Fire »•••» ••»•  tttt 

CUssificatioD  of  SoUd  Fuel 628 

Ciasfitilcation  of  Coals 634 

Analys^ee  of  Coals 624 

Western  Llraitee 681 

Aaaljses  of  Foreig:n  Coals «. »...  681 

NixoD^s  NavifraUon  Coal 683 

SampIfDfrCoai  for  Analyses ,..•» ....,.» ».  682 

Hektive  value  of  Fine  Sizes 68ii 

Pressed  Fuel 6$^ 

Belative  Value  of  Steam  Coals 683 

Approximate  Heating  Value  of  Coals • 684 

Kind  of  Furnace  Adapted  for  Different  Coals 686 

Downward-draufl:htFurnaceB«> .»»..%.. 635 

Cslorimetric  Tests  of  American  Coals 636 

£TBporatlve  Power  of  Bituminous  Coals ••..• ••....  686 

Weathering  of  Coal... , 687 

Coke  637 

Experiments  in  Ookins »•....  ,..•. 687 

Coal  WasWnar !?. ; 688 

Recovenr  of  By-products  In  Coke  manufacture 688 

Making  Hard  Coke 688 

Generation  of  Steam  from  the  Waste  Heat  and  Gases  from  Coke-ovens.  638 

Products  of  the  DisUUaiion  of  Coal 680 

WoodasFiiel 680 

Hoating  Value  of  Wood 689 

CompOBitSon  of  Wood 640 

Charcoal ,... 640 

Yield  of  Cfaarcoftl  ftom  B  Cord  of  Wood 641 

ConKumndon  of  Clmrcoai  in  Blast  Furnaces. 641 

Absorption  of  Water  and  of  Oases  by  Charcoal.... , 641 

Com  positton  of  Charcoals 64« 

Miscellaneous  Solid  Fuels 642 

Dust-fuel— Dust  BxplosioDS 642 

PteatorTurf 648 

Sswdust  as  Fuel • » ....» 648 

Borse-manure  as  Fuel 648 

Wet  Tan-bark  as  Fuel....  648 

StmwasFuel • 648 

Bsgasse  as  Fuel  in  Sugar  lumufacture. 648 

Petrolenm* 

Praductoof  DtotiUatloa 646 

UmaPtotroleam • 646 

Vsiue  of  Petroleum  aaFMl 646 

OBet.  Goal  as  Fuel 646 

Fael  Gas. 

OifbonGas 646 

AnthnBiteOas 647 

Bttuminoas  Gas 647 

Water Oas 648 

Producer-gas  from  One  Ton  of  Coal 649 

Katnral  Oas  in  Ohio  and  Indiana 649 

Combustion  of  Producer-gas 6M 

Use  of  Sieam  In  Producers 6S0 

Gas  Fuel  for  Small  Furnaces 661 

XUnminatlng  Gas. 

Ooal-Kas , 661 

Water-gas 66t 

Analynes  of  Water-gas  and  Coal  km 868 

Oiloriflc  Equtralents  of  Constituents 654 

Efficiency  of  a  Water-ffas  Plant 664 

Space  Required  for  a  Water-yas  Plant 656 

rasl-Talna  of  IBimiinitting-gas OM 


•XIV  COKTEKT& 

VteVlTa 498 

Work,  Foot-pound 4S8 

Power,  Horse-power 4S9 

Energy 4» 

Work  of  Acceleration 480 

Force  of  a  Blow 430 

Impact  of  Bodies 481 

Energy  of  Recoil  of  Quns 481 

Oonservatton  of  EnenKj 488 

Perpetual  Motion  488 

SIBciencyof  aMachlne  488 

Antmal-power,  Man-power 488 

Workof  aHorae 484 

Man-wheel 484 

Horge-gin 484 

RaelBtanoe  of  Vehicles 485 

Blements  of  Maehlnes. 

The  Lever 485 

The  Bent  Lerer 436 

The  Moving  Strut 486 

The  Toggle-joint 486 

The  Inclined  Plane 487 

The  Wedge 487 

TheScrew 487 

The  Cam 488 

ThePulley 488 

IMfferential  Pulie/ 4m 

Differential  Windlass 480 

Differential  Screw 48S< 

Wheel  and  Axle 489 

1Vx>thed-wheel  Gearing 480 

IkidleH  Screw 44fl 

Stresses  in  Framed  Struotnres. 

Cranes  and  Derricks 440 

Shear  Poles  and  Guys 443 

King  Post  Truss  or  Bridge. 448 

Queen  Poet  Truss 44t 

Burr  Truss 443 

Pratt  or  Whipple  Truss 443 

HoweTruss 445 

Warren  Girder 445 

Roof  Truss : 4^ 

HEAT. 

ThermometeiB  and  Pyrometers 448 

Centigrade  and  Fahrenheit  degrees  compared 440 

Copper-ball  Pvrometer 451 

Thermo-eleotno  PVrometer 451 

Temperatures  in  Furnaces 451 

Wiborgh  Air  PVrometer 458 

Seegers  Fire-clay  Pyrometer 458 

Mesur^and  Kouel's  Pyrometer 458 

Uehling  and  Steinbart^s  Pyrometer 458 

Air-thermometer , 454 

High  Temperatures  judged  by  Color 454 

Boiling-points  of  Substances 455 

MelUng-points 455 

Unitof  Heat 465 

Mechanical  Equivalent  of  Heat 466 

Heat  of  Combustion 456 

Specific  Heat 457 

Latent  Heat  of  Fusion 450,461 

Expansion  by  Heat 460 

Absolute  Temperature 46t 

Absolute  Zero 461 


C0NTEKT8.  XV 

PAGK 

Latent  Heat 461 

Latent  Heat  of  Evaporation 46S 

Total  Heat  of  Evaporation 469 

Evaporation  and  Drying 468 

Evaporation  from  Reservoirs 468 

Evaporation  by  the  Multiple  System 468 

Resistance  to  fioiling 468 

Manufacture  of  Salt 464 

Solubility  of  Salt  and  Sulphate  of  lime 464 

Salt  Contents  of  Brines 464 

Concentration  of  Sugar  Solutions 466 

Evanoratins  by  Exhaust  Steam 466 

Drymg  In  vacuum 466 

Radiation  of  Heat 467 

Conduction  and  Convection  of  Heat ..468 

Rate  of  External  Conduction 460 

Steam-pipe  Coverings 470 

Transniiasion  through  Plates 471 

**  in  Condenser  Tubes 478 

"  **       Cast-iron  Plates 474 

••  from  Air  or  Gases  to  Water iU 

••  from  Steam  or  Hot  Water  to  Air 476 

••  through  Walls  of  Buildings 478 

Thermodynamics 478 

PHTSICAIi  PROPERTIES  OF  GASES. 

Expansion  of  Gases 470 

Boyle  and  Marriotte's  Lav 470 

liaw  of  Charles,  Avogadro's  Law 470 

Saturation  Point  of  vapors 480 

Law  of  Gaseous  Pressure    480 

Flow  of  Oases 480 

Absorption  by  Liquids 480 

AIR. 

Properties  of  Air 481 

Air-manometer 481 

Pressure  at  DiflTerent  Altitudes 481 

Barometric  Pressures 489 

Levelling  by  the  Barometer  and  by  Boiling  Water 482 

To  find  Differ  enoe  in  A I  ti  tude 483 

Moisture  in  Atmosphere 488 

Weight  of  Air  and  Mixtures  of  Air  and  Vapor 484 

Specillc  Heat  of  Air 484 

Flow  of  Air* 

Flow  of  Air  through  Orlfloes 484 

Flow  of  Air  in  Pipes 485 

Effect  of  Bends  In  Pipe 488 

Flow  of  Compressed  Air 488 

Tables  of  Flow  of  Air 480 

Anemometer  Measurements 401 

Equalisation  of  Pipes 401 

Loss  of  Pressure  in  Pipes 408 

Wind. 

Force  of  the  Whid 408 

Wind  Pressure  in  Storms 406 

Windmills 406 

Capacity  of  Windmills 407 

Economy  of  Windmills 408 

ElectricPower  from  Windmills 400 

Compressed  Air. 

Heatlngof  Air  by  Compression 400 

Loss  of  Energy  in  Compressed  Air 400 

Volumes  and  Pressures , , 600 


XVi  CONTENTS. 

PIGS 

Loss  due  to  Excess  of  Pressure 60i 

Horse-power  Required  for  Compression.... 60] 

Table  for  Adiabatic  Compression i 602 

Mean  Effective  Pressures 60i 

Mean  and  Terminal  Pressures 608 

Air-compressors • 608 

Practical  Results 606 

Eflflciency  of  Compressed-air  Engines. 606 

Requirements  of  Rock-driUs ..1 806 

Popp  Compressed-air  System 607 

Small  Compressed-air  Motors 607 

Efllciency  of  Air-heatinK  Stoves 607 

Efficiency  of  Compressed-air  Transmission 60R 

Shops  Operated  by  Compressed  Air 609 

Pneumatic  Postal  Transmission 609 

Mekarski  Compressed-air  Tramways 610 

Compressed  Air  Working  Pumps  in  Mines • 611 

Fans  and  Blowers. 

Centrifugal  fians 611 

Best  Proportions  of  Fans 619 

Pressure  due  to  Velocity 618 

Experiments  with  Blowers 614 

Quantity  of  Air  Delivered 614 

Efficiency  of  Fans  and  Positive  Blowers 516 

Capacity  of  Fans  and  Blowers 617 

Taole  of  Centrifugal  Fans 618 

Engines,  Fans,  and  Steam-coils  for  the  Blower  System  of  Heating. 619 

Sturtevant  Steel  Pressure-blower 519 

Diameter  of  Blast-pipes • 619 

Efficiency  of  Fans 620 

Centrifugal  Ventilators  for  Mines 6SI 

Experiments  on  Mine  Ventilators 688 

DiskFans 6»4 

Air  Removed  by  Exhaust  Wheel 685 

Efficiency  of  Disk  Fans 685 

Positive  Rotary  Blowers 686 

Blowing  Engines 686 

Steam-jet  Blowers 687 

Steam-jet  for  Ventilation 687 

HEATING  AND  VENTII^TION. 

Ventilation 688 

Quantity  of  Air  Discharged  through  a  Ventilating  Duct 680 

Artificial  Cooling  of  Air 581 

Mine-ventilation 581 

Friction  of  Air  In  Underground  Passages 581 

Equivalent  Orifices 588 

Relative  Efficiency  of  Fans  and  Heated  Chimneys 688 

Heating  and  Ventilating  of  Large  Buildings 684 

Rules  for  Computing  Radiating  Surfaces 686 

Overhead  Steam-pipes 687 

Indirect  Heating-surface 687 

Boiler  Heating-surface  Required 688 

Proportion  of  Grate-surface  to  Radiator-surface 588 

Steam-consumption  in  Car-hsatiiig 6S8 

Diameters  of  Steam  Supply  Mains 589 

Registers  and  Cold-air  Ducts 539 

Physical  Properties  of  Steam  and  Condensed  Water  540 

Size  of  Steam-pipes  for  Heating 640 

Heating  a  Oreennouse  by  Steam 541 

Heating  a  Greenhouse  by  Hot  Water 549 

Hot-water  Heating  548 

Law  of  Velocitv  of  Flow 548 

Proportions  of  Radiating  Surfaces  to  Cubic  Capacities 543 

Diameter  of  Mai n  and  Branch  Pipes 543 

Rules  for  Hot-water  Heating 544 

Arrangements  of  Mains 544 


/ 


OOJSTTENTS*  •    Xvii 

^  PAOK 

Blower  System  of  Heating  and  VentQatlng........ 645 

Sxperiments  with  Hadiatora • « 645 

Heating  a  Buildinir  to  70*  F c 545 

Heating  by  Electricity 546 

WATER. 

Exnansioii  of  Water 847 

W^ht  of  Water  at  different  temperatures 547 

Pressure  of  Water  due  to  ito  Weignt 549 

Head  Oorreepottdlng  to  Pressures 540 

Boiinig-potot*.!./.!IV.!!!l!li'.!!!Ii!'.".!*//.!!!l!!!*!!"/.!!l!!!r'.i!'. '/.!*//.];;  550 

Freeslng-point 550 

Sea-water 540,550 

Ice  and  Snow 650 

Specific  Heat  of  Water 550 

Compresslbiltty  of  Water 651 

Impurities  of  water.... 551 

Oauaes  of  Incrustation ^ 561 

Means  for  Preventing  Incrustation 65'^ 

Analyses  of  Boiler-scale 553 

HardnesB  of  Water 553 

Purifying  Feed-water 654 

Softening  Hard  Water 655 

Hydranlies.    Flow  of  Water. 

Fomnto  for  Discharge  through  Orifices 55S 

Flow  of  Water  from  Orifices 556 

Flow  in  Open  and  Closed  Channels 657 

General  Fx>rmul8B  for  Flow 657 

Table  Fsli  of_Feet  per  mile,  etc 668 

Valuesof  Vr for arcular Pipes 660 

Kutter*s  Formula 660 

Molesworth's  Formula 562 

Bazin 'a  Formula 568 

IVArcy's  Formula 668 

Older  Formule 664 

Velocity  of  Water  in  Open  Channels 664 

Mean.  Surface  and  Bottom  Teloclties 664 

Safe  Bottom  and  Mean  Velocities 665 

Resistance  of  SoU  to  Eroeion 666 

Abrading  and  Transporting  Power  of  Water 665 

Grade  ofSewers 666 

BelatiQns  of  Diameter  of  Pipe  to  Quantity  discharged 666 

Flow  of  Water  in  a  80-inch  Pipe 566 

Velocidesin  Smooth  Cast-iron  Water-pipes 567 

Table  of  Flow  of  Water  in  Circular  Pipes 668-678 

Loeeof  Head 578 

Flow  of  Water  in  Riveted  Pipes 574 

Frictional  Heads  at  given  rates  of  discharge 577 

Effect  of  Bend  and  Curves 678 

Hydraulic  Grade-line 578 

Flow  of  Water  in  House-service  Pipes 678 

Air-bound  Pipes 579 

VertlcalJeta 670 

Water  Delivered  through  Meters 670 

Fire  Streams 670 

Friction  Losses  in  Hose  660 

Head  and  Pressure  Losses  by  Friction 580 

Loss  of  Pressure  in  smooth  2^inch  Hose  . 580 

Rated  capacity  of  Steam  Fire-engines 580 

Pressures  required  to  throw  water  through  Nozzles 581 

The  Siphon 581 

Measurement  of  Flowfaig  Wafer 582 

Piesometer : 582 

Pilot  Tube  Gauge       688 

The  Venturt  Meter 688 

Measurement  of  Discharge  by  means  of  Nozzles 684 


XVIU  C0KTEK18. 

PAOB 

flow  through  BeoftangularOrifloet...*. 664 

Hea8urem«Bt  of  aa  Open  Stream 064 

Mfnem' iBoh  Measurements • 065 

Plow  of  Water  orer  Weirs 068 

Francis's  Formula  for  Weirs 686 

WeirTbble 687 

Basin's  Experiments 6d7 

Wafeer^powerw 

^werofsFhUofWater M 

Horse-power  of  a  Running  Stream 6w 

Current  Motors 680 

Horse-power  of  Water  Flowing  in  a  Tube 68D 

Maximum  Efllclency  of  a  Long  Conduit 880 

MUlpower :. 680 

Value  of  Water-power ,  500 

The  Power  of  Ocean  Waves • 690 

UUlbcation  of  Tidal  Power OOO 

•  Ttirblne  Whaeli. 

Proportions  of  Turbines » 601 

Tests  of  Turbines 606 

Dimensions  of  Turbines ••••»•• 607 

The  Pelton  Water-wheel •••-• 607 

Pumps. 

Theoretical  capaolty  of  a  pump , • 601 

Depth  of  Suction 6<M 

JUnoant  01  Water  raised  by  a  Single-acting  Lift-pump. 60(1 

Proportioning  the  Steamcy  Under  of  a  Direct-acting  pump 6w 

Speedof  Water  through  Pipes  and  Pump -passages 80) 

SuBes  of  Direct-acting  Pumps 60S 

The  Deane  Pump 006 

EAoiency  of  Small  Pumps.  *......*»»•  .» »  ...  ••*... 606 

The  Wonhington  Duplex  Pump 604 

Speed  of  Piston »> 605 

Speedof  Water  through  Valres-... 605 

BoUer-feed Pumps ...*»..*••.  006 

Pump  Valves « 000 

Oentrlfueal  Pumps 606 

Lawrenoe  Centrifugal  Pumps 007 

BMciency  of  CeotrifUgal  and  Reciprocating  Pumps >  606 

Vanes  ofCentrifugal  Pumps 600 

Tlie  Gentrifugal  Pump  used  as  a  Suction  Dredge 600 

Duty  Trials  of  Pumping  Engines 600 

Leakage  Tests  of  Pumps 611 

Vacuum  Pnmps 616 

ThePulsometer..* •»..  610 

TheJetPump ..,..614 

The  loieofior. ....••..».. 614 

Air-lift  Pump 614 

The  Hydraulic  Ram 614 

Quantity  of  Water  Delivered  by  the  Hydraulic  Ram 615 

Hydraulic  Pressure  Transmission. 

Energy  of  Water  under  Pressure 616 

Emciency  of  Apparatus » .*...  616 

Hydraulfo  Presses .. . 617 

Hydraulic  Power  in  London • • 617 

Hydraulic  Riveting  Machines 616 

Hydraulic  Forging 616 

The  Aiken  IntensKler... 610 

Hydraulic  Engine 610 


FUKIi. 


tlieory  of  Combustion 

Total  Heat  of  Gombustloo. 


CONTENTS.  XIX 

PAGB 

AottlyBeBofGaflMofOombiMtlOB • • •• •••».%» W« 

Tempentture  of  the  fire »••••.»•»••.•»  ttS 

Classification  of  Solid  Fuel 623 

ClaffiificatioQ  of  Ooala 634 

Analyses  of  Coals eoi 

Western  XJsnites 681 

Analyses  of  Foreign  Coals.... «.» «...  681 

Nizon^s  Kavigatlon  Coal 682 

SampUnirCoal  for  Analyses »••••• %.* ».  68S 

ftdctive  value  of  Fine  Slses *  CSS 

Prassed  Fuel 68^ 

Htlative  Value  of  Steam  Coals •• 688 

Approximate  Heating  Value  of  Coals », •  ..» 634 

Kind  of  Furnace  Adapted  for  Dilferent  Coals. 685 

Downward-draught  Furnaces. »..».. 635 

Oalorimetric Tests  of  American  Coals 636 

BTaporatiye  Power  of  Bltumi  nous  Coals •• • »....  686 

Weathering  of  Coal... ,...,.»..• 687 

Coke  687 

Experiments  in  Coking •»••.•.  ,•••.... »....» •• 687 

Coal  Washing. TT. 688 

Hecovenr  of  By-products  in  Coke  manufacture 688 

Making  Hard  Coke 688 

(veneration  of  Steam  from  the  Wadte  Heat  and  Gases  from  Coke-oyens.  638 

Products  of  the  DistiUaiion  of  Coal » 680 

Wood  as  Fuel 680 

Heating  Value  of  Wood 689 

Composition  of  Wood 640 

Charcoal ..640 

Yield  of  Chsrooal  fkt>m  a  Cord  of  Wood 641 

Ooosumptiott  of  Clmreoai  In  BlaKt  Furnaces. 641 

Absorption  of  Water  and  of  Oases  by  Charcoal 641 

Cr)mposltion  of  Charcoals 64)1 

Miscellaneous  Solid  Fuels 642 

Dust-fuel^Dust  Exploeioitt 642 

Peat  or  Turf • 64« 

Sawdust  as  Fuel ,..« »..«  618 

Horse-manure  as  Fuel •• » 648 

Wet  Tan-bark  as  Fuel , 648 

Straw  as  Fuel * 648 

Bsgaase  as  Fuel  In  Sugar  Hanufacture • 648 

Petroleum* 

Producteof  DistlUatloo , 646 

UmaPtetroleora..*. • ••»..• •• •*.•»...  646 

Value  <^Petx«leum  as  Fuel 646 

Oil  M.  Goal  as  Fuel , ...646 

Fuel  Gas. 

Oirtxmaas 646 

Anthracite  Gas 617 

BttuminoosGas 647 

WaterOaa 648 

Produeer^gas  from  One  Ton  of  Coal 649 

NatunU  Gas  in  Ohio  and  Indiana 649 

Combustion  of  Produoer^gas • 650 

?8e  of  Steam  in  Producers 690 

Gas  Fuel  for  Small  Furnaces 661 

Uluminatiog  Gas» 

Ooal-gss ^ 661 

Water-gas 659 

Analyses  of  Water-gas  and  Coal  gas 658 

C^lnriflc  Equiralents  of  Constituents 654 

CAciettey  of  a  Water-gas  Plant 654 

Space  Required  for  a  Water-gas  Plant 656 

ml-Tahieotldttminattiag-gas 0B6 


XX  CONTENTS. 

PACIS 

Flow  of  Gas  In  Piped •«, .•••». • «••••...    697 

Senrice  for  Lamps ». .« «.  :  • 6S8 

Tenoperatare  and  Pressure ..*...•.* 6W 

rrotal  Heat 669 

Latent  Heat  of  Steam 650 

Latent  Heat  of  Volume 660 

Specific  Heat  of  Saturated  Steam 660 

Density  andVolume 660 

Superheated  Steam 661 

RegnaulVs  Experiments 661 

Table  of  the  Properties  of  Steam 663 

Flow  of  Steam. 

Napler*s  Approximate  Rule 669 

Flow  of  Steam  in  Pipes ,..  669 

Loss  of  Pressure  Due  to  Radiation 6ri 

Resistance  to  Flow  by  Bends 673 

Siaes  of  Steam-pipes  for  Stationary  EoRlnes 673 

Sixes  of  Steam-pipes  for  Marine  Engines 674 

Stean&  Pipes. 

BurstlnflT-teets  of  Copper  Steam-pipes ••••• 674 

Thickness  of  Copper  Steam-pipes... 075 

Reinforcing  Steam-pipes 676 

Wire-wound  Steam-pipes 675 

BiTcted  Steel  Steam-pipes 676 

Valves  in  Steam-pipeA 675 

Failure  of  a  Copper  Steam-pipe 676 

The  Steam  Loop 67V 

Loss  from  an  Uncovered  Steam-plpe cn 

THIS  STEAM  BOILBB. 

The  Hon»*power  of  a  Steam-boiler. 077 

Measures  for  Comparing  the  Duty  of  Boilers 078 

Steam-boiler  Proportions 078 

Heating-surface    678 

Horse-power,  Builders*  Rating 679 

Grate-surface •., 680 

Areasof  Flues 680 

Air.passages  Throusrh  Grate-bars 6R1 

Performance  of  Boilers 681 

Conditions  which  Secure  Economy 68*^ 

Efficiency  of  a  Boiler 688 

Tests  of  Steam-boilers 685 

Boilers  at  the  Centennial  Exhibllion 685 

Tests  of  Tubulous  Boilers 686 

High  Rates  of  Evaporation 687 

Economy  Effected  by  Heating  the  Atr , 687 

Results  of  Tests  with  Different  Coals 688 

Maximum  Boiler  Efficiency  with  Cumberland  Coal 689 

Boilers  Using  Waste  Gases 689 

Boilers  for  Blast  Furnaces  68S 

Rules  for  Conducting  Boiler  Tests 696 

Table  of  Factors  of  Evaporaiiou 695 

Streuipth  of  Steam-boilers. 

Rules  for  Construction 700 

Shell-plate  Form  uln 701 

Rules  for  Flat  Plates 7D] 

Furnace  FormuliB 704 

Material  for  Stays 709 

Loads  allowed  on  Stays 70S 

Girders 703 

Rules  for  Constructir^n  of  Boilere  in  Merchant  Vessels  in  U.  8 706 


CONTENTS.  j  xxi 

PA« 

U.S.  Rule  for  AIIowabtoPreMares 706 

Safe- working  Pressures  707 

Rules  GoTemiof?  Inspection  of  Boilers  In  Philadelphia 708 

Fhies  and  Tubes  for  Steam  Boilers 709 

Flat-stayed  Surf  aoes 709 

Diameter  of  Staj-bolts 710 

Strengtli  of  Stays 710 

Stay-bolts  In  Curved  Surfaces 710 

Boiler  Attachments,  Famaces^  eto. 

Fusible  Plugs 710 

Steam  Domes 711 

Height  of  Furnace 711 

MeSianicat  Stokers 711 

The  Hawlev  Down  draught  Furnace 719 

Under-feed  Stokers 719 

Smoke  Prevention 719 

Oas-flred  Steam-boilerB 714 

Forced  Combustion 714 

Fuel  Economizers 715 

Incrustation  and  Scale 718 

Boiler-scale  Compounds. 717 

BemoTalof  Hard  Scale 718 

Corrosion  in  Marine  Boilers 719 

UseofZIno 790 

Effect  of  Deposit  on  Flues 790 

Dangerous  Boilers • 790 

Safety  Valves. 

Bnles  for  Area  of  Safety-valves 791 

Spring-loaded  Safety-valves 794 

The  Ii^ector* 

Equation  of  the  Inieetor 795 

Performanoe  of  Injectors 796 

BoOsr-feeding  Pumps 796 

Feed-water  Heaters* 

StrafauiOMised  by  Cold  Feed-water 787 

Steam  Separators* 

Eflldeiioy  of  Steam  Separators 798 

Determination  of  Moisture  In  Steam. 

Oolt  Oslorimeter 799 

Throttling  Calorimeters 799 

SeparaUng  Calorimeters 780 

Identification  of  Drv  Steam 780 

Usual  Amount  of  Moisture  in  Steam  781 

Chlmnejrs. 

Chimney  Draught  Theory 781 

Force  or  Intensitv  of  Draught 789 

Bate  of  Combustion  Due  to  Height  of  Chimney 783 

High  Chimneys  not  Necessary 784 

Heights  of  Chimneys  Required  for  Different  Fuels ..734 

Table  of  Sise  of  Chimneys 784 

Protection  of  Chimney  from  Lightning 786 

Some  Tall  Brick  Chimneys 787 

Stability  of  Chimneys 788 

Weak  Chimneys 789 

Steel  Chimneys 740 

Sheet-iron  Chfanneys 741 

THIS  STEAM  ENGINE. 

Expansion  of  Steam 749 

Mean  and  Terminal  Absolute  Pressures 748 


J 


XXll  CONTENTS. 

PAOK 

Oalcnlatfon  Of  Mean  Effective  Pressure....* • • 744 

Work  of  Steam  in  a  Single  Cylinder 746 

Measures  for  Comparing  the  Duty  of  Engines , ••.,  748 

Efficiency,  Thermal  Uulis  per  Minute 749 

Beal  Ratio  of  Expansion , 760 

Effect  of  Compression 751 

Clearance  in  Low  and  High  Speed  Engines 751 

Cylinder- condensation 752 

water-consumption  of  Automatic  Cut-off  Engines 753 

Experiments  on  Cylinder-condensation 753 

Indicator  Diagrams 754 

Indicated  Horse-power 755 

Rules  for  Estimating  Horse'power 756 

Horse-power  Constant 756 

Errors  of  Indicators 756 

Table  of  Engine  Constants 756 

To  Draw  Clearanoeon  Indicator-diagram 759 

To  Draw  Hyperbolic  Curve  on  Indicator-diagram 759 

Theoretical  Water  Consumption  ..  760 

Leakage  of  Steam 701 

Compound  Engines. 

AdTantoges  of  Compounding ,« ,.  709 

Woolf  and  Receiyer  Types  of  Engines 702 

Combined  Diagrams •..,  764 

Proportions  of  Cylinders  InCompound  Engines 706 

Beceiyer  Space 706 

Formula  for  Calculating  Work  of  Steam.... 767 

Calculation  of  Diameters  of  Cylinders 768 

Triple-expansion  Engines 709 

Proportions  of  Cylinders 709 

Annular  Ring  Method 709 

Rule  for  Proportioning  Cylinders 771 

Types  of  Three-stage  Expansion  Engines 771 

Sequence  of  Cranks 772 

Velocity  of  Steam  Through  Passages 772 

8 uadruple  Expansion  Engines 772 
iameters  of  Cylinders  of  Marine  Engines 773 

Pi-ogress  in  Steam-engines 7/3 

A  Double-tandem  Triple-expansion  Engine 773 

Principal  Engines,  World's  Columbian  Exhibition,  1898 774 

Steam  Eng^lne  Economy. 

Economic  Performance  of  Steam  Engines 775 

Feed-water  Consumption  of  Differ**nt  Types 775 

Sisesand  Calculated  Performances  of  \ertical  High-speed  Engines 777 

Most  Economical  Point  of  Cut-off  777 

Type  of  Engine  Used  when  Exhaust-steam  is  used  for  Heating 780 

Comparison  of  Compound  and  Single-cylinder  Engines .....  780 

Two-cylinder  and  Three-cy  Under  Engines 781 

Effect  of  Water  in  Steam  on  Efficiency 781 

Relative   Commercial  Economy  of  Compound  and  Triple-expansion 

Engines  781 

Triple-expansion  Pumplng-eogines 782 

Test  of  aTripIe-expansion  Engine  with  and  without  Jackets 783 

Relative  Economy  of  Engines  under  Variable  Loads 783 

Efficiency  of  Non-condenaing  Compound  Engines 784 

Economy  of  Engines  under  Varying  Loads 784 

Steam  Consumption  of  Various  Sizes 785 

Steam  Consumption  in  Small  Engines 780 

Steam  Consuniption  at  Various  Speeds 780 

Limitation  of  Engine  Speed 787 

Influence  of  the  Steam  Jacket 767 

Counterbalancing  Engines 788 

Preventing  Vibrations  of  Engines...  789 

Foundations  Embedded  in  Air 789 

Cost  of  Coal  for  Steam-power 7B9 


0#NTENT8.  XXlll 

PAOB 

Storinr  Steam  Heat •••«. 789 

Coet  of  Steam-power • 790 

Botary  8team««ii|;lnea» 

Steam  Turbines •••• 991 

The  Tower  Spherfoal  Eogine •• Ttti 

Dimensions  of  Parts  of  Bngines. 

^liDder 798 

Clearance  of  Piston 798 

ThlckDees  of  Cylinder 798 

Cjlinder  Heads 794 

CyUnder-head  Bolts 795 

Tbe  Piston 795 

Piston  Packiog-rings 796 

fit  of  Piston-rod 796 

Diameter  of  Piston-rods 797 

Piston-rod  Guides 798 

The  Connectiog-rod 799 

Connecting-rod  Bnds 800 

Tapered  &>nnecting-rod8 801 

TheOrank-pin ail 

Crosshead-pin  or  Wrist-ptai 804 

The  Crank-arm  809 

The  Shaft,  Twistins  Resistance .  806 

Besistance  to  Bendmg 808 

EquiTalent  Twisting  Moment 808 

Fly.wheel  Shafts 809 

Length  of  Shaft-bearings 810 

Crank<«hafts  with  Centre-crank  and  Double-crank  Arms 818 

Crank-shaft  with  two  Cranks  Coupled  at  90* 814 

ValTe-fltem  or  VolTe-rod 815 

Size  of  Slot-link 815 

The  Eccentric 816 

Tbe  Eooentric-rod ....•• 816 

Rerersing-gear 816 

Engine-frames  or  Bed-plates 817 

Flywheels* 

Weight  of  Flv-wheels 817 

Oentrifugal  Force  in  Fly-wheels 680 

Anns  of  Fly-wheels  and  Pulleys 880 

Diameters  for  Various  Speeds • •• • 881 

Strains  in  the  Rims 888 

Thickness  of  Kims 888 

A  Wooden  Rim  Flywheel 884 

Wire-wound  Fly-wheels • 694 

The  SUde-TalTe. 

Definitions.  Lap,  Lead,  eta 884 

Sweet's  ValTe^iagram • 8S6 

The  2Seuner  Valve-diagnun 887 

Port  Opening.. 898 

Lead 829 

Inside  Lead 8:29 

Ratio  of  Lap  and  of  Fort-openlDg  to  Valve-travel 849 

Crank  Angles  for  Connecting-rods  of  Different  Lengths • 880 

Relative  Motions  of  Crosshead  and  Crank 831 

Periods  of  Admission  or  Cut-off  for  Various  Laps  and  Travels. 881 

Diagram  for  Port-opening,  CutK>ff,  and  Lap 888 

Piston-valves 834 

Setting  the  Valves  of  an  Engine 884 

To  put  an  Engine  on  ite  Centre • 884 

Link-motion • 834 

Goremors. 

Fendnlam  or  Fly-baU  Gtovemors 886 

To  Change  the  Speed  of  an  Engine 887 


XXIT  CONTENTS. 

PAO« 

Fly-wheel  or  Shaft-go^ernon • «..  888 

Calculation  of  Springs  for  Shaft-governors 888 

Condensersy  Air-pumps,  Clronlating-pumps,  etc. 

Tlie  Jet  Condenser 889 

Ejector  Condensers 840 

The  Surface  Condenser.... 840 

Condenser  Tubes • 840 

Tube-plates 841 

Spacing  of  Tubes 841 

Quantity  of  Cooling  Water 841 

Air-pump 841 

Area  through  Valve-seats 84S 

drculating-pump 843 

Feed-pumps  for  Marlne-engioes 848 

An  EvaporatlTe  Surface  Condenser. 844 

Continuous  Use  of  Condensing  Water 844 

Increase  of  Power  by  Condensers 846 

Evaporators  and  Distillers 847 

GAS,  PBTBOI«BUM,  AND  HOT-AIB  ENGINES. 

Gas-engines 847 

Efllciency  of  the  Gas-engine 848 

Tests  of  the  Simplex  Gas  Engine 848 

A  8S0-H.P.  Gas-engine. 848 

Test  of  an  Otto  Gas-engine 849 

Temperatures  and  Pressures  Developed 840 

Test  of  the  Clerk  Gas-engine 849 

Combustion  of  the  Gas  in  the  Otto  Engine 849 

Use  of  Carburetted  Air  in  Gas-enghies 849 

The  Otto  Gasoline-engine 850 

The  Priestman  Petroleum-engine 8G0 

Test  of  a  5-H.P.  Priestman  Petroleumrengine 850 

Naptharengines 851 

Hot-air  or  Caloric-eiigine& 851 

Test  of  a  Hot^Ur  Engine 861 

I«OCOMOTlVES. 

Efftciency  of  Locomotives  and  Resistance  of  Trains 861 

Inertia  and  Resistance  at  Increasing  Speeds 868 

Efficiency  of  the  Mechanism  of  a  Locomotive  •,.  864 

Slse  of  Locomotive  Cylinders 854 

Size  of  Locomotive  Boilers 855 

Qualities  Essential  for  a  Free-steaming  Locomotive 866 

Wootten^s  Locomotive    865 

Grate-surface,  Smoke-stacks,  and  E^haust-noszles  for  Locomotives. .  ..  865 

Exhaust  Nozsles ..  856 

Fire-brick  Arches. 860 

Size,  Weight,  Tractive  Power,  eta  860 

Leading  American  Types 868 

Steam  Distribution  for  High  Speed • 868 

Speed  of  Railway  Trains. 880 

Dimensions  of  Some  American  Looomotives. 869-868 

Indicated  Water  Consumption 86S 

Locomotive  Testing  Apparatus ..  868 

Waste  of  Fuel  in  Locomotives 868 

Advantages  of  Compounding. ..  868 

Counterbalancing  Locomotives • 864 

Maximum  Safe  Load  on  Steel  Rails 685 

Narrow-guage  Railways. e.  865 

Petroleum* burning  Locomotives. 866 

Fireless  Locomotives.... 860 

SHAFTING, 

Diameters  to  Resist  Torsional  Strain 867 

Deflection  of  Shafting....   868 

Horse-power  Transmitted  by  Shafting: .  863 

Tftble  for  Laying  Out  Shafung. 871 


CONTENTS.  ^XXY 

puixsni 

PAOB 

Proportions  of  Pbllayt ••••^. ••••••• • 878 

Convexitr  of  Pulleys. •• .,« 874 

Cooo  or  B^p  Pulloys. ,« • 874 

Theonr  of  Belts  and  Banda 870 

CentrfftiSBl  Tension. • •.••••• 870 

Belting  rrsctioe,FormuliB  for  Belting...... 877 

Hone-power  of  A  Belt  one  inch  wide 878 

A.F.  Ka£le*8  Formula 878 

'Width  or  Belt  for  OiTen  Hone-power. 879 

Taylor's  Rules  for  Belting 880 

Koteson  Belting... 888 

Lacing  of  Belts. 888 

Setting  a  Belt  on  Quarter-twist 883 

To  Find  the  Lengtn  of  Belt. 884 

To  Find  the  Ani^e  of  the  Arc  of  Contact. 884 

To  Find  the  Length  of  Belt  when  Closely  Boiled 684 

To  Flzid  the  Approximate  Weleht  of  Belts .884 

Relations  of  the  Size  and  Speeds  of  Driving  and  Driven  Pulleys 884 

EtIIs  of  Tight  Belts. 880 

Sag  of  Belts 885 

Arrangements  of  Belts  and  Pttll^s 885 

Careof  Belts 880 

Strength  of  Belting. 880 

Adhesion,  Independent  of  Diameter. 886 

EndiessBelts. 880 

Belt  Data. 886 

Belt  Dressing. 887 

Oemeot  for  Cioth  or  Leather 887 

Rubber  Belting. 887 

GEARING. 

Pitch,  Pfteh-efrde,  eto 887 

Diametral  and  Circular  Pitch 888 

ChordalFitch R89 

Diameter  of  Pitch-line  of  Wheels  from  10  to  100  Teeth. 889 

Proportions  of  Teeth. 889 

Proportion  of  Qear-wheels 801 

Width  of  Teeth 891 

Bales  for  Oaleulating  the  Speed  of  Gears  and  Pulleys 891 

HiUing  ChittecB  for  Interchangeable  Geare 892 

Forms  of  the  Teeth. 

The  Cjrcioldsl  Tooth 893 

The  Involute  Tooth 894 

Approzimrtlon  by  Circular  Arcs 896 

Stepped  Gears 89? 

TwtSed  Teeth 897 

Spiral  Gears 897 

worm  Gearing • 897 

Teeth  of  Bevel-wheels ...  898 

Annular  and  Differential  Gearing 898 

Effldeopy  of  Gearing 899 

Strength  of  Gear  Teeth* 

Varloas  F6nnul»  for  Strength 900 

ComparisoDotFormulo..    008 

Maximum  Speed  of  Gearing ...••• 906 

A  Heavy  ICachine-cut  Spur-gear 906 

Frictlonal  Gearing 905 

FrietloQal  Grooved  Gearing 906 

HOISTING. 

Weight  and  Strength  of  Cordage 906 

Wofting  Strength  of  Blocks 906 


XXTi  CONTENTS. 

PAOB 

Sflloleiicy  of  Cfhain-blocks 907 

ProporUona  of  Hooks ..•« .• • OOT 

power  of  HoUtiii«  Euglnes ,.,, , OOS 

Effect  of  Slack  Rope  on  Strain  in  Hoisting • 908 

Limit  of  Depth  for  Hoisting , 908 

Large  Hoisti  n g  Reco rd s 906 

Pneumatic  Hoisting « 909 

Counterbalancing  of  Winding-engines 909 

Belt  Conveyors , , «#.•••  t 91t 

Bands  for  Canning  Grain , ,....,,.,,,.,.,,  9U 

Cranes. 

Classification  of  Cranes ' ».,...,•• 911 

Position  of  the  Inclined  Brace  In  a  Jib  Crane , , 919 

ALarge  TravelUng-crane ,,., 919 

A  150-ton  Pillar  Crane , ,.,.•.  ••.,...,  919 

Compressed-air  Travelling  Cranes ..••,..,..  919 

Wtre-rope  Hanlagv, 

Self-acting  Inclined  Plane ,..., «,,••. .,.,....,..  918 

Simple  Engine  Plane ,,.• ,.„, 918 

Tail-rope  System ., 918 

Endless  Rope  System , 914 

Wire-rope  Tramways ««t.*.«**f.t«.«.  ••.«••» 914 

Suspension  Cableways  and  Cable  Hoists ,  915 

Stress  in  Hoisting-ropes  on  Inclined  Planes 915 

Tension  Required  to  rreyene  Wire  Slipping  on  Drunif. .  • 910 

Taper  Ropes  of  Uniform  Tensile  Strength ,  ,.«•,...  910 

Effect  of  Various  Sized  Drums  on  the  Life  of  Wire  Ropes • 917 

WIRB-ROPE  TRANSMISSION. 

Elastic  Limit  of  Wire  Ropes  917 

Bending  Stresses  of  Wire  Ropes 918 

Horse-power  Transmitted 919 

Diameters  of  Minimum  Sheayes...  ■ '. 919 

Deflections  of  the  Rope WO 

Long-diatanoe  Transmission 9Gi  1 

ROPE  DRIVING. 

FormulsB  for  Rope  Driving 999 

Horse-power  of  Transmission  at  Various  Speeds , . , 9d4 

Sag  of  the  Rope  Between  Pulleys , , , .  • 925 

Tension  on  the  Slack  Part  of  the  Rope 029 

Miscellaneous  Notes  on  Rope»drlving 990 

FRICTION  AND  I«UBRICATION. 

Coefficient  of  Friction 998 

Rolling  Friction 998 

Friction  of  Solids 9>« 

Friction  of  Rest 92S 

Laws  of  Un  lubricated  Friotlon 098 

Friction  of  Slidlug  Steel  Tires 928 

Coefficient  of  Rolling  Friction , 0^9 

Laws  of  Fluid  Friction  989 

Angles  of  Repose , 9-^ 

Friction  of  Motion 9*^ 

Coefficient  of  Friotlon  of  Journal 980 

Experiments  on  Friction  of  a  Journal 081 

Coefficients  of  Friction  of  Journal  with  Oil  Bath 039 

Coefficients  of  Frioiion  of  Motion  and  of  Rest 089 

Value  of  Anti-friction  Metals ,  089 

Castrlron  for  Bearings 988 

Friction  of  Metal  Under  Steam-pressure OSU 

Morin*8  Laws  of  Friction ••*..• •  ....  083 


CONTENTS.  XXTXl 

PAOB 

Laws  of  Friction  of  welMubrlcated  Journals 964 

Allowable  PrsMuree  on  Bearing^Buif  ace. MS 

Oil-prefl8ure  in  a  Bearing 987 

Friction  of  Car-Journal  firaaiies Wf 

Experinoents  on  Overheatingr  of  Bearings 088 

Moment  of  FrioUon  and  Work  of  Friction 088 

FlTot  Bearings 089 

The  Schiele  Cunre 088 

Friction  of  A  Flat  FlTOt-bearing. 080 

XercuiyOMth  Pivot MO 

Ball  Bearings. 940 

FricUon  Boners. 940 

Bearings  for  Vei7  High  BotatlVe  Speed  041 

Friction  of  Steam-engines , 941 

Distributioo  of  the  Friction  of  Engines. 941 

IfUbricatloii. 

Durability  of  Lubricants 942 

Qualiiloations  of  Lubricants 948 

Amount  of  Oil  to  run  an  Engine 948 

Examination  of  Oils. 944 

F«ina.  R.  R.  Specifloations 944 

Solid  Lubricants 945 

Graphite,  Soapstone,  Fibre^rapbite,  MetaUue • 045 

THE  rOUMDBY. 

Cupola  Practice..  M6 

Charging  a  Cupola 948 

enlarges  in  StOTC  Foundries 949 

Resalts  of  Increased  Driving. , 949 

Pressure  Blowers 960 

IxMSoflroninMalUng 960 

Une  of  Softeners • 950 

Shrinkage  of  Castings. 961 

Weight  of  CasUngs  from  Weight  of  Pattem 958 

MouUOngSand 9Gii 

Foundiy  Ladles 988 

THE  MACHINE  SHOP. 

Speed  of  Cutthig  Tools 968 

*riible  of  Cutting  Speeds. 954 

Speed  of  Turret  Lathes ......  954 

r^rms  of  Cutting  Tools 955 

Rule  for  Gearing  Lathes 955 

Change-gears  for  Lathes 056 

Ketrle Screw-threads.. 056 

Setthag  the  Taper  in  a  Lathe. 056 

Speed  of  Drilling  Holes , 066 

Speed  of  Twis^driUs. 057 

lOlling  Cutters 057 

Speed  of  Cutters 968 

Brsolts  with  Milling-machines 959 

Killing  with  or  Aff&lnst  Feed 900 

Milling-machine  v«.  Planer 060 

Power  Required  for  Machine  Tods. 060 

Heavy  Work  on  a  Planer 960 

Honei>ower  to  mn  Lathes 061 

Power  used  by  Machine  Tools. 968 

Power  Required  to  Drive  Mschinery 964 

Powernsed  tai  Machlne^hops. 966 

Abrasive  Prooeases. 

The  Cold  Saw 006 

Beeae'sFttshig^lsk 960 

Cutting  Stone  with  Wire .  966 

The  Sand-blast ...  966 

Emery-wheels • 067-969 

Orindstonea 068-970 


XXVIU  CONTENTS, 

Tarlons  Took  and  Trooesseo, 

Taps  for  Machine-Borews. , • ~.~m 

TapDriUa..  , 9n 

Taper  Bolts,  Pins,  Reamers,  eta.. <,»> 978 

Punches,  Dies,  Presses 078 

Clearance  Between  Punch  and  Die.... 078 

Size  of  Blanks  for  Drawing^press 078 

Pressure  of  Drop-press.. -, 073 

Flow  of  Metals .r. 973 

Forcing  and  Shrinking  Fits 079 

Efficiency  of  Screws «< 074 

Poweirs  Screw-thread 978 

Proportioning  Parts  of  Machine. • 075 

Keys  for  Qearing,  etc • 075 

Holding-power  of  Set-screwB • .- 077 

Holding-power  of  Keys 078 

DTNAMOMETEICS, 

Traction  Dynamometers 078 

The  Prony  Brake 078 

The  Alden  Dynamometer 070 

Capacity  of  Friction-brakes 060 

Transmission  Dynamometers 980 

ICB  MAKIlfO  OB  BEFBIGEBATIlfO  MACHINES. 

Operations  of  a  Refrigerator-machine 061 

Pressures,  etc..  of  Available  Liquids 069 

Ice-melting  EflTect 08S 

Echer-machines 06S 

Air-machines 068 

Ammonia  Compression-machineB 068 

Ammonia  Absorption-machines. 0B4 

SulphttiMliozide  Machines.  066 

Performance  of  Ammonia  Compression-machines. 066 

Economy  of  Ammonia  Compression-machine 067 

Machines  UsingVapor  of  Water 068 

Efficiency  of  aitefrigerating-machine 088 

Test  Trials  of  Refrifcerating-machines 008 

Temperature  Range 901 

Metering  the  Ammonia 002 

Properties  of  Sulphur  Dioxide  and  Ammonia  Qas    008 

Properties  of  Brine  used  to  absorb  Ref  ligeratlng  EflTect. 094 

Chloride-of-calcium  Solution 004 

Actual  Performances  of  BefirlgerattDg  Machines. 

Performance  of  a  75-ton  Ref rigerating-machine 004, 006 

Cylinderheating 007 

Tests  of  Ammonia  Absorption-machine i 907 

Ammonia  Compression-machine,  Results  of  Tests •... 000 

Means  for  Applying  the  Cold 000 

Artlfloial  Io« -manufacture. 

Test  of  the  New  York  Hygeia  loe-making  Plant. 1000 

MABINE  ENGINBEBINO. 

Rules  for  Measuring  Dimensions  and  Obtaining  Tonnage  of  Vessels. . ..  1001 

The  Displacement  of  a  Vessel 1001 

Coefficient  of  Fineness lOfti 

Coefficient  of  Water-lines 1008 

Resistance  of  Ships. 1008 

Coefficient  of  Performance  of  Vessels. 1008 

Defects  of  the  Common  Formula  for  Resistance 1008 

Rankine^s  Formula. • lOOS 

Dr.  Kirk's  Method 1004 

To  And  the  I. H. P.  from  the  Wetted  Surface 1006 

E.  R.  Mumford^a  Method 1O08 

Belative  Horse-power  required  for  'litferent  Speeds  of  Vessels 1000 


COiJTENTS.  IXIX 

PAOB 

BnifltiMioojMr  Hono*powor  for  dlffsrent  Spoods..  ••••••.••••••••  •••••••  1000 

Results  of  Trials  of  Steam-Tesaels  of  Yarious  Sixes 1007 

Speed  on  Ckuials, 1008 

Results  of  ProgresslTe  Speed-trials  Id  laical  Vessels. 1006 

Zsttmatod  Displaoement,  Horse-power,  ete.,  of  Steam-Tessels  of  Tarious 


Tlie  Sorow-propollMw 

8Iie  of  Sereir. • 1010 

Propeller  Ooefflctents 1011 

£fflcieoc7  of  the  Propeller 1013 

Pitch-ratio  and  Slip  for  Screws  of  Standard  Fonii..., 1018 

Results  of  Recent  Researches. 1018 

The  Paddle-wheel* 

Fsddle-wheel  with  Radial  Floats. 1018 

Feathering  Paddle-wheels • 1018 

EffldemgrofFaddle-wheels 1014 

Jet-propvlsioii. 

BesctioaoCaJet 1016 

Beeent  PnMstlee  In  Harlne  Bni^lnea. 

Forced  Draught 1015 

Boilers.. 1015 

Piston-Talvea. 1016 

Steam-pipes 1016 

AuxiliaiT  Supply  of  Fresh-water  Eraporators. 1016 

Weir*s  Feed-water  Heater. 1016 

Passenger  Steamers  fitted  with  Twin-screws. 1017 

OomparatlTte  Results  of  Working  of  Marine-engine,  187S,  1881,  and  1801..  1017 

WeJid^tof  Three*etageEzpaDfdonenglne8 • 1017 

Partlonlars  of  Three-stage  EzpansioD^Dgines.  1018 

OONSTBUCTION  OF  BUIU>ING8. 

Walls  of  Warehouses,  Stores,  Factories,  and  Stables 1010 

Strength  of  Floors,  Roofs,  and  Supports. 1019 

Columns  and  Poets....  1010, 10s» 

Fireproof  Buildings 10*20 

Iron  and  Steel  Columns 1020 

lintels.  Bearings,  and  Supports. 1020 

Strains  on  Oirders  and  RfTcts. 1030 

Maxlmnm  l4>ad  on  Floors 1031 

Strenctli  of  Floors 1031 

Safe  Mtribated  Loads  on  Southern-pine  Beams ..  1038 

BLBCTRICAI.  ENOIMEBBING. 
Standards  of  M easarement* 

CL  0. 8.  t^ystem  of  Physical  Measurement 1034 

Practical  units  used  in  Electrical  Calculations 1034 

Relations  of  Various  Units 1085 

EqniTalent  Electrical  and  Mechanical  Units 1036 

Analogies  between  Flow  of  Water  and  Electricity 10S7 

Analogy  between  the  Ampere  and  Miner's  Inch 1087 

Blectri«ttl  Beslstanee* 

Laws  of  Sleotrleal  Resistance 1088 

Equivalent  Conductors 1088 

BectricalConductfri^  of  Different  Metals  and  Alloys    1088 

BelatiTeConductlrity  of  Different  Metals lOSO 

Conductors  and  Insulators ...••• 1080 

Resistance  Varies  with  Temperature , 1080 

Annealing 1080 

Standard  of  ResfstSDoe  of  Copper  Wire 1000 

Eleoirio  Oorrents. 

Ohm^Law 1000 

DIfldsdCbentti lOU 


XXX  COKTKKTS. 

9Aam 

Conductors  In  Series • • • • 1061 

Internal  Resistance • 1081 

Joint  Resistance  of  TwoBraii6be8 ..••• 1088 

KlrchholTs  Laws 108S 

Power  of  the  Circuit •••. 1088 

Heat  Generated  by  a  Current • 1088 

Heating  of  Conductors 1033 

HeaUng  of  Wires  of  Cablet 1063 

Oopper-wire  Table 1084»  1085 

HeaUngof  Colls 1086 

Fusion  of  Wires • 1087 

BI«etrf«  Trftiismlssloiu 

Section  of  Wire  required  for  a  Given  Current 1038 

Constant  Pressure 1038 

Short-circuiting 1039 

Economy  of  Electric  Transmission 1039 

Table  of  Electrical  Horse-powers 1041 

Wiring  FormulflB  for  Incandencent  Lighting ]04*J 

Wire  Table  for  100  and  600  Volt  Circwts 1043 

Cost  of  Copper  for  Long-distance  Transmission 1044 

Weifcht  of  Copper  for  Long-distance  Transmission 1044 

Efficiency  of  Long-distance  Ti-ansmission : 1045 

Systems  of  Electrical  Distribution 1046 

Ismclency  of  a  Combined  Engine  and  Dynamo 1047 

Electrical  Efficiency  of  a  Generator  and  Motor —  1047 

Efficiency  of  an  Electrical  Pumping  Plant 1048 

£leotrlc  Hallways. 

Test  of  a  Street-railway  Plant 1046 

Bleetrle  Lighting. 

Life  of  Incandescent  Lamps 1040 

Life  and  Efficiency  Tests  of  Lamps 1049 

Street  Lighting  1049 

Lighting-power  of  Arc-lamps 1060 

Candle-power  of  the  Arc-light 1050 

Blectric  Welding ' 1051 

JBlectrlo  Heaters 1058 

Electric  Aooumulators  or  Storage-batteries. 

Sixes  and  Weights  of  Storage-batteries .' 1064 

Use  of  Storage-batteries  in  Power  and  Light  Stations 1055 

Working  Current  of  a  Storage-cell 1055 

Slectro-chemloal  Bqulvalents 10.VO 

Kleotrolysls  1056 

Bleotro-m  agnets. 

Units  of  Electro-magnetic  Measurement 1067 

Lines  of  Loops  of  Force. 1068 

Strength  of  an  Electro^magnet 1058 

Force  in  the  Gap  between  Two  Poles  of  a  Magnet )0'>9 

The  Magnetic  Circuit..  1009 

Determining  the  Polarity  of  Electro-magnets 1050 

I>yiiaiiio*Electrlc  Machines. 

Kinds  of  Dynamo-electric  Machines  as  regards  Manner  of  Winding 1060 

Current  Generated  by  a  Dynamo-electric  Machine 1060 

Torque  of  an  Armature 1061 

Electro-motive  Force  of  the  Armature  Circuit 1061 

Strength  of  the  Magnetic  Field 1062 

Application  to  Designing  of  Dynamos 1068 

Permeability 1064 

Permissible  Amperage  for  Magnets  with  Cotton-covered  Wire . .  ,  1065 

Form ulflB  uf  Efficiency  of  Dynamos IOCS 

The  Electric  Motor 1066 

Table  of  Standard  Belted  Motors  and  Generators 1067 


CONTENTS.  ■     XXXI 

API'KNDIX. 

Str«iig^1i   of  Timber. 

PAOK 

Safe  Load  on  Wbite-oak  Beams lUGi: 

Mathematics. 

Formula  for  Interpolation 1070 

Maxima  and  Minima  without  the  Calculus lOTO 

Riveted  JoiiitH. 

Pressure  Required  to  Drive  Hot  Rivets 1070 

Heating  and  Ventilation. 

(Capacities  for  Hot-biast  or  Plenum  Heating  witU  Fans  and  Blowers.  ..  1071 

Water-wheels. 

Wat«T-powpr  Plants  OperatiitR  under  High  Pressure ......  1071 

FormulsB  for  Power  of  Jet  Water-wheels 1079 

Gaa  Fuel. 

Composition,  Energy,  etc.,  of  Various  Oases 10?2 

Steann-bollers. 

Rules  for  Steam-boiler  Construction lOTS 

The  Steam-engine. 

Current  Practice  in  Engine  Proportions 1074 

Work  of  Steam-turbines 1075 

BelativeCostof  Different  Sizes  of  Engines 1075 

I^iocomo  lives. 

Resistance  of  Trains 1075 

Performance  of  a  High-speed  Locomotive 107ft 

Ijocomotive  Link  Motion 1077 

Gearing. 

ElBcieDcy  of  Worm  Gearing 10?fi 


NAMES  AND  ABBREVIATIONS  OF  PERIODICALS 
AND  TEXT  B00K8  FJiEQUENTLY  REFERRED  TO 
IN  THIS  WORK. 


Am.  Mach.    American  Machinist. 

App.  Cyl.  Mech.    Appleton's  Cyclopiedia  of  Mecbanlcii,  Vols.  I  and  IL 

Bull.  I.  &  8.  A.  Bulletin  of  the  American  Iron  and  Steel  Association 
(Philadelphia). 

Burr'A  Elasticity  and  Resistance  of  Materials. 

Clarlc,  K  T.  D.  1>.  K.  Clark's  Rules,  Tables,  and  Data  for  Mechanical  En- 
jrineers. 

Clarlc,  S.  E.    D.  K.  Clark's  Treatise  on  the  Steam-engine. 

Engg.    Engineering  (London). 

Bng.  News.    EnKineeiing  News. 

Engr.    The  Engineer  (London). 

Fairbaim's  Useful  Informaiion  for  Engineers. 

Flynn's  Irrigaiion  Canals  and  Flow  of  water. 

Jour.  A.  C.  L  W.    Journal  of  American  Charcoal  Iron  Workera'  Association. 

Jour.  F.  I.    Journal  of  the  Franklin  Institute. 

Kapp's  Electric  Transmission  of  Energy. 

Lanza's  Applied  Mechanics. 

Merriman^s  Strength  of  Materials. 

Modern  Mechanism.  Supplementary  Tolume  of  Appleton*s  CyclopSBdia  of 
Mechanics. 

Proc.  Inst.  C.  E.    Proceedings  Institution  of  CItII  Engineers  (London). 

Proc.  Inst.  M.  E.  Proceedings  Institution  of  Mechanical  Engineers  (Lon- 
don). 

Peabody*s  Thermodynamics. 

Proceedings  Engineers*  Club  of  Philadelphia. 

Rankine.  S.  E.    Rankine's  The  Steam  Engine  and  other  Prime  Movers. 

Rankitie*s  Machinery  and  Mill  work. 

Rankine,  R.  T.  D.    Rankine's  Rules,  Tables,  and  Data. 

Reports  of  U.  S.  Test  Board. 

Reports  of  U.  S.  Testing  Machine  at  Watertown,  Massachusetts. 

Rontgen's  Thermodynamics. 

Seatoii's  Manual  of  Marine  Engineering. 

Hamilton  Smith,  Jr.*8  Hydraulics. 

The  Stevens  Indicator. 

Thompson's  Dynamo-electric  Machln*»ry. 

Thurston's  Manual  of  the  Steam  Engine. 

Thurston's  Materials  or  Engineering. 

Trans.  A.  I.  E  E.    Transactltins  American  Institute  of  Electrical  Engineers. 

Trans.  A.  I.  M.  K.    TrnnsactionH  American  Institute  of  Mining  Engineers. 

Trans.  A.  S.  O.  E.    Transactions  American  Society  of  Civil  Engineers. 

Trans.  A.  S.  M.  E.    Transactions  American  Soc'ty  of  Mechanical  ElnglneerB 

Trautwlne's  Civil  Engineer's  Pocket  ik>ok. 

The  Locomotive  (Hartford,  Connecticut). 

Unwinds  Elements  of  Machine  Design. 

Weishach's  Mechanics  of  EngineerU)^ 

Wood's  Resistance  or  Materiaia 

Wood's  Tbermodjuamios. 

zxxli 


MATHEMATICS. 


Arttbmettcal  and  Alfl^brmical  Slirns  and  AbbreTlatlons« 


^  plus  (addition). 
-r  positive. 

-  miDus  (subtraction). 

-  negative. 

±  plus  or  minus. 
T  minus  or  plus. 
=  equals. 
X  multiplied  by. 
ah  or  a.b  =  a  x  b. 
't-  divided  by. 
/    divided  by. 


—  =  a/b  =  a-t-b. 


,M.=  L». 


^  =:: 


.002  = 


_8_ 
10'  •"***  •"  1000* 

V  square  root. 

V  cube  root. 

V  4th  root. 

:   is  to,  s  so  !s. :  to  (proportion). 

2;  4s8:6,as2isto4aoi88to6. 

:  ratio;  divided  by. 

2  :  4.  ratio  of  2  to  4  =s  2/4. 
.*.  therefore. 
>  greater  than. 
<  le£«  than. 
□  square. 
O  round. 

»  degrees,  arc  or  thermometer. 

'  minutes  or  feet. 

''  seconds  or  inches. 
"""  accents  to  distinguish  letters,  as 

a',  a",  a'". 
oi,  09'  Os*  Ok«  Atf-  i'«*d  a  mib  1,  a  sub  b. 

PtC. 

()  [  1   }  }  vincula,    denoting 

that  (he  numbers  enclosed  are 
to  be  taken  together ;  as, 

(a  +  5)c  =  4  +  8x5  =  85. 
a*,  a*,  a  squared,  a  cubed. 
u^  a  raised  to  thejtth  power. 

a-i  =  !,«-.  =  1. 
a  a* 

10»  =  10  to  the  0th  power  =  1,000,000,- 

Rin.  a  rr  the  sine  of  a. 

ijn.-i  a  s  the  arc  whose  sine  is  a. 

sin.  a-»  =  -j-i— 

sin.  a. 

log.  =  logarithm. 

*°^e ^«:  Vp.  log.  =  hyperboUc loga- 
rithm. 


Z  angle. 

L  right  angle. 

±  perpeudkular  to. 

sin.,  sine. 

COS.,  cosine. 

tang.,  or  tan.,  tangent. 

sec.,  secant. 

▼ersin.,  versed  sine. 

cot.,  cotangent. 

cosec,  cosecant. 

covers.,  co- versed  sine. 

In  Algebra,  the  first  letters  of  the 
alphabet,  a,  2>,  c,  d,  etc.,  are  gener- 
ally used  to  denote  known  quantities, 
and  the  last  letters,  w^  or,  y^  2,  etc., 
tmknown  quantities. 

AbbreviatiwiB  and  Symbols  com- 

monly  used, 
d,  differential  (in  calculus). 
y,  integral  (in  calculus). 

y  *,  integral  between  limits  a  and  5. 

d,  delta,  difference. 

2.  Sigma,  sign  of  summation. 

*,  pi,  ratio  of  circumference  of  circle 

to  diameter  =  S.  14159. 
y,  a<;celeration  due  to  gravity  =  82.16 

ft.  per  sec. 

Abbreviations  frequently  used    t» 

this  Book. 
L.,  1.,  length  in  feet  and  inchee. 
B.,  b.,  breadth  in  feet  and  inches. 
D.,  d.,  depth  or  diameter. 
H.,  h.,  height,  feet  and  inches. 
T.,  t.,  thickness  or  temperatura 
v.,  v.,  velocity. 
F.,  force,  or  factor  of  safety. 
f.,  coefficient  of  friction. 
E.,  coefficient  of  elasticity. 
R.,  r.,  radius. 
W.,w.,  weight 
P.,j>.,  pressure  or  load. 
H.P.,  horse-power. 
I.H.P.,  indicated  horse-power. 
B.H.P.,  brake  horse-power, 
h.  p.,  high  pressure, 
i.  p.,  intermediate  pressure. 
1.  p.,  low  pressure. 

A.  W.  Q.,  American  Wire  Qauge 
(Brown  &  Sharpe). 

B.  W.G.,  Birmingham  Wire  Gauge, 
r.  p.  m.,  or  revs,  permln.,  revolutions 

per  minute. 


KATHEHATIC& 


ABITHMETia 

The  user  of  this  book  is  supposed  to  have  had  a  training  in  arithmetic  as 
well  as  in  elementaiy  algebra.  Only  those  rules  are  given  here  which  are 
apt  to  be  easily  forgotten. 

ORBATRST  CORiniON  IHBASVRE,  OR  GRBATE8T 
GOniJIEON  DIVISOR  OF  TWO  NUMBBR8. 

Rule*-  Divide  the  greater  Dumber  by  the  less ;  then  divide  the  divinor 
by  tile  leniainder,  and  so  on,  dividing  always  the  last  divisor  by  the  last 
remainder,  until  there  is  no  remainder,  and  the  last  divisor  is  the  greatest 
common  measure  required. 

I<BA8T   COMMON   M17I<TIPI<B   OF   TWO  OR   MORB 
N17MBBR8. 

Rule.— Divide  the  given  numbers  by  any  number  that  will  divide  the 
greaiettt  number  of  them  without  a  remainder,  and  set  the  quotients  wiih 
the  undivided  numbers  in  a  line  beneath. 

Divide  the  second  line  as  before,  and  so  on,  until  there  are  no  two  numbers 
that  can  be  divided  ;  then  the  continued  product  of  the  divisors  and  last 
quotients  will  give  the  multiple  required. 

FRACTIONS. 

To  reduce  a  eominon  fyactlon  to  Its  longest  terms.— Divide 
botii  Ufrma  by  tlielr  greiiiest  common  divisor:  if  =  f 
To  cltaii|i:e  an  Improper  fraction  to  a  mixed  numlMr.  — 

Divide  the  numerator  by  the  denominator;  the  quotient  is  the  whole  number, 
and  the  remainder  place<l  over  the  denominator  is  the  fraction:  V  =  ^V 
To  change  a  mixed  number  to  an  Improper  fWtetlon.— 

'   '"ply  the  whole  number  by  the  denominator  of  the  fraction;  to  the  prod- 


uct add  the  numerator*  place  the  sum  over  the  denominator:  1{  =  V. 

To  express  a  irnole  number  In  the  form  of  a  fraction 
ivltli  a  fflTcn  denominator.  ~Mu I ti ply  the  whole  number  by  ilie 
given  df  noininaior,  and  place  the  product  over  that  denominator:  18  =  V- 

To  reduce  a  compound  to  a  simple  fWictlon»  also  to 
multiply  fractions.— Multiply  Uie  numerators  together  for  a  new 
numerator  and  the  denominators  together  for  a  new  denominator: 

8-4      8    ..        2^4      8 
-of-  =  -,  also    -Xj-j,. 

To  reduce  a  complex  to  a  simple  Aractlon.— The  numerator 
and  denominator  must  each  flrnt  be  given  the  form  of  a  simple  fraction; 
then  multiply  the  numerator  of  the  upper  fraction  by  the  denominator  of 
the  lower  for  the  new  numerator,  and  the  denominator  of  the  upper  by  the 
numerator  of  the  lower  for  the  new  denominator: 

To  dlTlde  ftmctlons.—Reduoe  both  to  the  form  of  simple  fraotiong, 
invert  the  divisor,  and  proceed  as  in  multiplication: 

8-^^*  =  8-^8-  =  8^4==12- 

Cancellation  of  Aractlons.— In  compound  or  multiplied  fractions, 
divide  any  numerator  and  any  denominator  by  any  number  which  will 
divide  them  i)olh  without  remainder,  Htrikine;  out  the  nunibei'S  thus  divided 
and  setting  down  the  quotients  in  tlieir  stead. 

To  reduce  ft*actlons  to  a  common  denominator. ^-Reduce 
each  fraction  to  tlie  form  of  a  simple  fraction;  then  multiply  each  numera- 


DECIMALS.  3 

tor  by  all  the  denominators  except  Ite  own  for  the  new  numerators,  and  all 
the  denominators  together  for  the  common  denominator: 

1     1     8^21     14     18 
2'    8'    7      42'    42*    42' 

To  mdd  fyaetloDS.— Reduce  them  to  a  common  deooroinator.  then 
add  Uie  iiuiiieraiors  and  place  their  sum  over  the  common  denominator: 

118^  21-1-14-1-18  ^68^ 
2^8      7  42  42       "' 

To  ■vbtimct  fkmcUoiis«~Reduce  them  to  a  common  denominator, 
piibtriict  the  uumeratoni  and  place  the  difference  over  the  common  denomi- 
nator: , 

1  _ 8  _ 7-6 _ 2. 

2  7        14    "14* 


DECIlHAIiS. 

To  add  decimals.— Set  down  the  flgures  so  that  the  decimal  points 
are  one  akK>ve  tiie  other,  then  proceed  as  in  simple  addition:  18.764-  .012  = 

To  unMraet  deelmals.— Set  down  the  fl^riires  so  that  the  decimal 
poinrH  art-  nnt*  utMve  the  other,  then  proceed  as  in  simple  subtraction:  18.75 
-  .012  =  18  7**, 

To  maltlply  decimals.— Multiply  as  in  multiplication  of  whole 
numbers,  iben  point  off  as  many  decimal  places  as  there  are  in  multiplier 
and  muliiplicAnd  taken  tosretlier:  1.5  X  .02  =  .060  =  .08. 

To  dlTlde  deelmals.— Divide  as  in  whole  numbem,  and  point  off  in 
the  quotient  as  many  decimal  places  as  those  in  the  dividend  exceed  those 
in  Llie  divisor.  Ciphers  mnst  be  added  to  the  dividend  to  make  its  decimal 
places  at  least  equal  those  in  the  divisor,  and  as  many  more  as  it  is  desired 
to  have  in  the  quotient:  1.5  -«-  .25  =  6.    0.1  ■+■  0.3  =  0.10000  -t-  0.3  =  0.8833  -h 

Decimal  EqnlTalents  of  Fractions  of  One  Inch. 


1-64 
1-8-.' 
8-64 
1-16 

.015625  ! 
.0:J125 
.046875 
.0625 

17-64 
9-32 
19-64 
6-16 

.265625 
.28125 
.296875 
.8125 

38-64 
17-82 
85-64 
0-16 

.515625 
.58125 
.546875 
.5625 

'jn-64 
25-82 
51-64 
18-16 

.765625 
.78125 
.796875 
.8125 

5-64 
:j-82 
7-*# 

1-8 

.078196 
.00875 
.109875 
.125 

21. 64 

11-82 

28-64 

S-8 

.828125 
.84875 
.850875 
.87? 

37-64 

19-82 

8»-64 

6-8 

.578126 
.59875 
.609375 
.685 

58-64 
27-^ 
56-64 

7-8 

.828125 
.84375 
.«S9875 
.875 

9-64 
5~:« 
11-61 
S-i6 

.140625 
.15685 
.171875 
.187ir 

25-64 
18-82 
27-64 
7-16 

.800625 
.40625 
.421875 
.4875 

4!-64 
ai-32 
48-64 
11-16 

.640625 
.65625 
.671875 
.6875 

57-64 
2d-32 
59-64 
16-16 

.890625 
.90625 
.921875 
.9375 

18-61 
7-8^ 

1.V64 
1-4 

.208125 
.21875 
.284875 
.25 

29-64 

15-82 

81-64 

l-« 

.453125 
.46875 
.484875 
.80 

45-04 

28-82 

47-64 

8-4 

.706125 
.71875 
.734375 
.75 

61-64 
31-82 
68-64 

1 

.953125 
.96875 
.984375 
1. 

To  conwert  a  common  fVmetlon  Into  a  decimal.— Divide  the 
nuiiifrator  by  the  denominAbor,  adding  to  che  niimfraior  as  mnnv  ciphers 
prpflxed  by  a  decimal  point  as  are  n^cHssary  to  give  the  number  of  decimal 
places  desired  in  the  result:  U  =  1  <l0u0-i-8  =  0.8333  -f. 

To  eoBwert  a  decimal  Into  a  common  fkmetlon.— Set  down 
the  decimal  as  a  numerator,  and  place  as  the  denominator  1  with  as  many 
cioberv  annexed  as  there  are  decimal  places  in  the  numerator;  eras^U^e 


ABITHMETIO. 


ooh" 


ill  i 


•^o. 


g    S 


2    § 
8    S 


§ 


< 


S    s 
S    fi 


o     o 


iiiilil 


S    51 


HiSiiii 


iliiiiiggii 


m^iiiiiii 


H: 


i  i 1 1  iT 


ill 

3  8  & 


S  S  S  S  S  £: 

I  i  §  §  I  i 


I  i 


=  s  § 

o  o  o 


5  S 


ii 


'H-'^nSr-. 


COMPOUND  KUMBEBS.  5 

d(H.-iuial  point  in  the  numerator,  and  raduoe  the  fraction  tbua  fonned  to  lia 
lowest  temM: 

•*  =  io6'i'  -^^  =  10000 '8' "~^- 

To  redvee  a  reennrlnc  decfmal  to  a  coBmiOM  flraetloii.— 

Subtract  Ujo  decimal  Hffurea  tliat  do  not  recur  from  the  whole  decimal  in- 
cluding one  set  of  recurrinic  flfcures;  set  down  the  remainder  as  the  numer- 
ator or  the  fraction,  and  as  many  nines  as  there  are  reeurrinc  figures,  fol- 
lowed by  as  many  ciphers  as  there  are  non-recurring  figures,  m  toe  denom- 
inator.   Thus: 

.79064054,  the  recurring  figures  being  054. 
Subtract  79 

^^  =z  (reduced  to  ito  lowest  terms)  |>g. 

conpoinvD  on  denooeinatv  nuhbess. 

Redaction  desc^ndlnff .--To  reduce  a  compound  num  ber  to  a  low«*r 
denoro inailon.  M uUiply  the  n umber  by  as  many  units  of  the  lower  denoml- 
nation  as  makes  one  of  the  higher. 

8  yards  to  inches:    8  X  86  =  108  Inches. 

.01  square  feet  to  square  inches:    .04  X  144  s  6.70  sq.  in. 

If  tho  given  number  Is  in  more  than  one  denomination  proceed  in  steps 
from  the  highest  denomination  to  the  next  lower,  and  so  on  to  the  lowest, 
adding  In  the  units  of  each  denomination  as  the  oper.itloii  proceeds. 

8  yds.  1ft.  7  in.  to  inches:  8x  3  =  9,  +  1  s  10,  ]0xl8=>  190,  +  7  s  1:27  in. 

llodaetloii  ascendlns*— To  express  a  number  of  a  lower  denomi- 
nation in  terms  of  a  higher,  divide  the  number  by  the  numb'  r  of  units  of 
the  lower  denomination  contained  In  one  of  the  next  higher;  the  quotient  is 
in  the  higher  denomination,  and  the  remainder,  if  any.ln  the  lower. 

1-/7  inches  to  higher  denomination. 

is;-*- 12  =  10  feet  +  7  inches;    10  feet  i-  8  =  8  yardn  + 1  foot. 

Ans.  8  yds.  1  ft.  7  in. 

To  express  the  result  in  decimals  of  the  higher  denomination,  divide  the 
riven  number  by  tbe  number  of  units  of  the  given  denomination  contained 
in  one  of  the  required  denomination,  carrying  the  result  to  as  many  places 
of  dednutls  as  may  be  desired. 

197  loches  to  yards:    197  -i-  86  =  8|t  =  8.5877  +  yards. 
RATIO  AND  PROPORTION. 

Ratio  is  the  relatiou  of  one  number  to  another,  as  obtained  by  dividing 
one  by  the  other. 

BAtioof9to4,or9  :  4a9/4=s1/8. 
Ratio  of  4  to  S,  or  4  :  2  =  3. 

Proportion  is  the  equality  of  two  ratios.  Ratio  of  2  to  4  equals  ratio 
of  .1  CO  0,  2/4  =  8/6:  expressed  thus,  9  :  4  :  :  8  :  0;  read,  2  is  to  4  as  3  is  to  6. 

Tbe  first  and  fourth  terms  are  called  the  extremes  or  outer  terms,  the 
Moond  and  third  the  meftns  or  inner  terms. 

The  product  of  the  means  equals  the  product  of  the  extremes: 

9  :  4  : :  8  :  6;    2  x  6  =  12;   8  X  4  =  19. 

Hence,  given  the  first  three  terms  to  find  the  fourth,  multiply  the  second 
and  third  terms  together  and  divide  by  the  first. 

2 :  4  :  :  8 :  what  number?    Ans.    ^  ^  -  =  6. 


6  ABITHHETIC. 

Alff«bralc  expreMlon  of  proportion.— a  :  b  :  :  e  :  d;  ^  s  -i;a(l 

.-  ...  be     ,     be    ,       ad  ad 

=  be;  from  which  a=^;d=— ;o  =  — -;  c  =  -r-. 

]VIeaift  proportional  between  two  given  numbera,  Ist  and  2d.  Is  Ruch 
a  number  chat  the  ratio  which  the  first  bears  to  it  equals  the  ratio  which  it 
bears  to  the  second.  Thus,  2  :  4  : :  4  :  8;  4  is  a  mean  proportional  between 
fi  and  8.  To  find  the  mean  proportional  between  two  numbers,  extract  the 
square  root  of  their  product. 

Mean  proportional  of  2  and  8  =  1^2  X  8  =  4. 

fllnffle  Rule  of  Tlireo  ;  or,  finding  the  fourth  term  of  a  proportion 
when  three  terms  are  given.— Rule,  as  above,  when  the  terms  are  stated  in 
their  proper  order,  multiply  the  second  by  the  third  and  divide  by  the  first. 
The  difficulty  is  to  state  the  terms  in  their  proper  order.  The  term  which  is 
of  the  same  kind  as  the  required  or  fourth  term  is  made  the  third;  the  first 
and  second  must  be  lilce  each  other  in  kind  and  denomination.  To  deter- 
mine which  is  to  be  made  second  and  which  first  requires  a  little  reasoning. 
If  an  inspection  of  the  problem  shows  that  the  answer  should  be  greater 
than  the  third  term,  then  the  greater  of  the  other  two  given  terms  should 
be  made  the  second  term— otherwise  the  first.  Thus,  8  men  remove  54  cubic 
feet  of  rock  in  a  day;  how  many  men  will  remove  in  the  same  time  10  cubic 
▼ards  ?  The  answer  is  to  be  men— make  men  third  term;  the  answer  is  to 
be  more  than  three  men.  therefore  make  the  greater  quantity.  10  cubic 
yards,  the  second  term ;  but  as  it  is  not  the  same  denomination  as  the  other 
term  it  must  be  reduced,  =  270  cubic  feet.    The  proportion  is  then  stated: 

8  X  STO 
64  :  270  :  :  8  :  X  (the  required  number) ;    x  =  — r-r—  =  15  men. 

The  problem  is  more  complicated  if  we  increase  the  number  of  given 
terms.  Thus,  in  the  above  question,  substitute  for  the  words  ''  in  the  same 
time  "  the  words  "  in  8  days."  First  solve  it  as  above,  as  if  the  work  were 
to  be  done  in  the  same  time;  then  make  another  proportion,  stating  it  thu^: 
If  15  men  do  it  in  the  same  time,  it  will  take  fewer  men  to  do  it  in  8  days; 
make  1  day  the  2d  term  and  8  days  tlie  first,  tenn.    S  :  1  :  :  15  men  :  6  men. 

Compound  Proportion^  or  Double  Rule  of  Tliree*— By  this 
rule  are  nolved  questions  like  the  one  just  given,  in  which  two  or  more  stac- 
ingsare  requinxi  by  the  single  rule  of  three.  In  it  as  in  the  single  rule, 
there  is  one  third  term,  which  is  of  the  same  kind  and  dt  nomination  as  ihe 
fourth  or  required  term,  but  there  may  be  two  or  more  first  and  second 
terms.  Bet  down  the  third  term,  take  each  pair  of  terms  of  the  same  kind 
separately,  and  arrange  them  as  first  and  second  by  the  same  reasoning  as 
is  adopted  in  the  single  rule  of  three,  making  the  greater  of  ihe  pair  the 
second  if  this  pair  considered  alone  should  require  the  answer  to  be 
greater. 

Set  down  all  the  first  terms  one  under  the  other,  and  likewise  all  the 
second  terms.  Multiply  all  the  first  terms  together  and  all  the  second  terms 
together.  Multiply  the  product  of  all  the  second  terms  by  the  third  term,  and 
divide  this  product  by  the  product  of  all  the  first  terms.  Example:  If  8  men 
remove  4  cubic  yards  in  one  day,  working  12  hours  a  day,  how  many  men 
working  10  hours  a  day  will  remove  20  cubic  yards  in  8  days  Y 

Yards  4:    201 

Days  8  :      1  :  :  8  men. 

Hours        10  ;    12| 

Products  120  :  240  :  :  8  :  0  men.  Ans. 

To  abbreviate  by  cancellation,  any  one  of  the  first  terms  may  cancel 
either  the  third  or  anv  of  the  second  terms;  thus.  8  in  first  cancels  8  in  third, 
making  it  1,  10  cancels  into  20  making  the  latter  2,  which  into  4  makes  it  2, 
which  into  12  makes  it  0,  and  the  figures  remaining  are  only  1  :  6  :  :  1  :  6. 

IIVVOIilTTION,  OR  POWBRS  OF  NITnBKBS. 

InTolntlon  is  the  continued  multiplication  of  a  number  by  itself  a 
given  numl)er  of  times.  Tiie  nunil>er  is  called  the  root,  or  first  power,  and 
the  products  are  called  powers.    Ttie  second  power  is  ci^Ued  the  square  and 


POWERS  OP  NUMBERS. 


the  third  power  the  cube.  The  operation  mav  be  indicated  without  being 
perf ormea  by  writincr  a  small  figure  called  tne  index  or  exponent  to  the 
ri^ht  of  and  a  little  above  the  root;  thus,  8*  =:  cube  of  8,  =  27. 

To  multiply  two  or  more  powers  of  the  same  number,  add  their  exponents; 
thiis,  ««  X  2*  =  a».  or  4  X  8  =  88  =  2». 

To  divide  two  powers  of  the  same  number,  subtract  their  exponents;  thus, 

a»  -I-  2«  =  2>  =  S;  2*  -•-  2*  =  2"~*  =  —  =  -.  The  exponent  may  thus  be  nega- 
tive. 2*  ■•>  2>  =  2*  =  1,  whence  the  asero  power  of  any  number  =  1.  The 
first  power  of  a  number  is  the  number  itself.  The  exponent  may  be  frac- 
tional, as  2^,  2i,  which  means  that  the  root  is  to  be  raised  to  a  power  whose 
exponent  is  the  numerator  of  the  fraction,  and  the  root  whose  sign  in  the 
denominator  is  to  be  extracted  (see  Evolution).  The  exponent  may  be  a 
decimal,  as  2***,  2^**;  read,  two  to  the  five-tenths  power,  two  to  the  one  and 
five-tenths  power.  These  powers  are  solved  by  means  of  Logarithms  (which 
see;. 

Flrat  Nine  Ponrers  of  tUe  First  Nine  Numbers. 


Ist 

•2d 

8d 

4th 

5th 

6th 

7th 

8th 

9th 

Pow'r 

Pow'r 

Power. 

Power. 

Power. 

Power. 

Power. 

Power. 

Power. 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

4 

8 

16 

82 

64 

128 

256 

512 

8 

9 

27 

81 

248 

729 

2187 

6561 

19688 

4 

16 

64 

256 

1024 

4096 

16884 

65586 

262144 

5 

25 

125 

6;» 

8125 

15625 

78125 

890625 

1958125 

6 

86 

216 

1296 

7776 

46656 

279986 

1679616 

10077696 

7 

49 

848 

2401 

16807 

117649 

828548 

5764801 

40858607 

8 

64 

512 

4096 

8er68 

20SS144 

2097152 

16777216 

134217728 

9 

81 

729 

6681 

69049 

581441 

4782969 

48046721 

887420489 

The 

First  Forty  Ponrers  of  3. 

i 

i 

> 

1 

> 

i 

1 

> 

1 

> 

1 

0 

1 

9 

512 

18 

262144 

27 

184217728 

86 

68719476736 

1 

2 

10 

1024 

19 

624288 

28 

268435466 

37 

137438968472 

2 

4 

11 

2048 

20 

1048576 

20 

636870912 

88 

274877906944 

S 

8 

12 

4096 

21 

2007152 

:» 

1073741824 

89 

54971»813888 

4 

16 

18 

8192 

22 

4194804 

81 

2147483048 

40 

1099511627776 

5 

82 

14 

16884 

23 

8888606 

32 

4294967296 

6 

64 

15 

32768 

24 

16777216 

83 

8589984592 

7 

128 

16 

655.36 

25 

38554482 

84 

171T»«9184 

8 

256 

17 

181072 

26 

67108864 

36 

84350788868 

BFOIiVTION. 

Birolntlon  is  the  finding  of  the  root  (or  extracting  the  root)  of  any 
number  the  power  of  which  is  given. 

The  sign  y  indicates  that  the  square  root  is  to  be  extracted :  V  V  V'*  (tie 
cube  root,  4th  root,  nth  root. 

A  fractional  exponent  with  1  for  the  numerator  of  the  fraction  is  also 
used  to  indicate  that  the  operation  of  extracting  the  root  is  to  be  performed; 

thus,  2*,  2*=  V2,\% 

When  the  power  of  a  number  i«  indicated,  the  fnvohiMon  not  heiii);  p4*r- 
furmcd,  the  extraction  of  any  root  of  that  power  may  also  be  indicated  by 


8  AKITHMETIO.    * 

dividing  the  Index  of  the  poorer  by  the  index  of  the  root,  Indicating:  the 
division  bj  a  fraction.    Tims,  extract  the  square  root  of  the  6th  power  of  2: 

|/i^=:2'  =  2^  =  8*  =  8. 

The  6th  power  of  9»  aa  hi  the  table  above,  is  64  ;  4/64  m  a 

Difficult  problems  in  evolution  are  performed  by  logarithms,  but  the 
square  root  and  the  cube  root  may  be  extracted  directly  according  to  the 
rules  given  below.  Tlie  4th  root  is  the  square  root  of  the  square  root.  The 
6th  root  is  the  cube  root  of  the  square  root,  or  the  square  root  of  the  cube 
root ;  the  8th  root  is  the  cube  root  of  Ute  cube  root  •  etc. 

To  Kxtraet  tbo  Sqnare  Root.— Point  off  the  given  number  into 
periods  of  two  places  each,  beghming  with  units.  If  there  are  decimals, 
point  these  off  likewise,  bejginning  m  the  decimal  point,  and  supplying 
as  many  ciphers  as  may  be  needed.  Find  the  greatest  number  whoee 
square  is  less  than  the  first  left-hand  period,  and  place  it  as  the  first 
figure  in  the  quotient.  Subtract  its  square  from  the  left-hand  neriod. 
and  to  the  remainder  annex  the  two  figures  of  the  second  period  for 
a  dividend.  Double  the  first  figure  of  the  quotient  for  a  partial  divisor ; 
find  how  many  times  the  latter  is  contained  in  the  dividend  exclusive 
of  the  right-hand  figure,  and  set  the  figure  representing  that  number  of 
times  as  the  second  figure  in  the  quotient,  and  annex  It  to  the  right  of 
the  partial  divisor,  forming  the  complete  divisor.  Multiply  this  divisor  bv 
the  second  figure  In  the  quotient  and  subtract  the  product  from  the  divi- 
dend. To  the  remainder  bring  down  the  next  period  and  proceed  as  before. 
In  each  case  doubling  the  figures  in  the  root  already  found  to  obtain  ihe 
trial  divisor.  Should  the  product  of  the  second  figure  in  the  root  by  the 
completed  divisor  be  greater  than  the  dividend,  erase  rhe  second  filfrore  both 
from  the  quotient  and  from  the  divisor,  and  substitute  the  next  smaller 

Sture,  or  one  small  enough  to  make  the  product  of  the  second  figure  by  the 
visor  less  than  or  equal  to  the  dividend. 

8.14168866S6I1.77846  + 

87W4 
1189 
84712515 
12429 
864218692 
71064 


85444'160866 
J141776 


85448511908936 
11772425 

To  extract  ths  square  root  of  a  fraction,  extract  the  root  of  numeratob 
and  denominator  separately.    a/-t  ^  j^  or  first  convert  the  fraction  into  a 

decimal,i/^=:  /iSTf  =  .6666 -f . 

To  Rztraet  tbe  Cube  ]Koot«~Foint  off  the  number  Into  periods  of 
8  figures  each,  beginning  at  the  right  hand,  or  unites  jpUce.  Point  off  deci- 
mals In  periods  of  3  figures  from  the  decimal  point.  Find  the  greatest  cube 
that  does  not  exceed  tne  left-band  period ;  write  its  root  as  the  first  figure 
In  the  required  root.  Subtract  the  cube  from  the  left-hand  period,  and  to 
the  remainder  bring  down  the  next  period  for  a  dividend. 

Sqaare  the  first  figure  of  the  root;  multiply  by  300,  and  divide  the  product 
Into  the  dividend  for  a  trial  divisor ;  write  the  quotient  after  the  first  figure 
of  the  root  as  a  trial  second  figure. 

Complete  the  divisor  by  adding  to  SCO  times  the  square  of  the  first  figure, 
80  times  the  product  of  the  first  by  the  second  ftgur&  and  the  square  of  the 
second  figure.  Multiply  this  divisor  by  the  second  figure;  subtract  the 
product  from  the  remainder.  (Should  the  product  be  greater  than  the 
remainder,  the  last  figure  of  the  root  and  the  complete  divisor  are  too  lar^e ; 


CUBE  BOOT.  9 

snbfltttote  for  Uie  last  figure  the  next  anoaller  number,  aad  ootreet  tbe  trial 
divhK>r  aocordiDfrly.) 

To  the  remainder  bring  down  the  next  period,  and  proceed  as  before  to 
find  the  third  figure  of  the  root — that  Is,  square  the  two  figures  of  the  root 
already  found;  multiply  bv  800  for  a  trial  divisor,  etc. 

If  at  any  time  the  trial  dmsor  is  greater  than  the  diyldend,  bringdown  an- 
other period  of  3  figures,  and  place  0  in  the  root  and  proceed. 

The  cube  root  of  a  number  wlU  contain  as  many  figures  as  there  are 
periods  of  S  in  the  number. 

Siiorter  Hetbods  of  BxtracUng:  the  €nbe  Boot*— 1.  From 
Wentworth^s  Algebra: 


800  X  1«        =       800 
80x1x8=        80 


«•  = 


1,881,885,068,826118845 
798 


_64_  I   168885 
800x19*        s:   ^4Srno\ 
80  X  IS  X  8   =       lOdOl 
8*=:     9 

44989 
1060 


182887 


800  X  ]88«        =   45387tX) 
80  X  19S  X  4  =       14760l 


90406988 


78M 


4568478  M8218904 
HTTOJ    2S2800B0885 
80O  X  1284> 
80  X  1984  X  5  « 
5«=: 


457011995 


After  the  first  two  figures  of  the  root  are  found  the  next  trial  divisor  is 
f^jnd  by  bringing  down  the  sum  of  the  80  and  4  obtained  in  completing  the 
preceding  diTisor ,  then  adding  the  three  lines  connected  by  the  brace,  and 
annexing  two  ciphers.  This  method  shortens  the  work  in  long  ezamplet),  as 
is  seen  in  the  case  of  the  last  two  trial  divisors,  saving  the  labor  of  squaring 
193  and  1984.  A  further  shortening  of  the  work  is  made  by  obtaining  the 
last  two  figures  of  the  root  by  division,  the  divisor  employed  being  three 
times  the  square  of  the  part  of  the  root  already  found;  thus,  after  finding 
the  first  three  figures: 

8  X  198<  s  46387190496063145. 1  + 
—181548  ' 

984416 


74813 


The  error  due  to  tlie  remainder  if  not  sufficient  to  change  the  fifth  figure  of 
the  root. 
2,  Br  Prof.  H.  A.  Wood  (atewfU  Indicator,  Julv,  1890): 

I.  ^Ting  sraarated  the  number  into  periods  of  three  figures  each,  count- 
ing from  toe  right,  divide  by  the  square  of  the  nearett  root  of  the  first 
period,  or  first  two  periods ;  the  nearett  root  is  the  trial  root. 

II.  To  the  quotient  obtained  add  twice  the  trial  root,  and  divide  by  8. 
This  gives  the  root,  or  first  approximation. 

m.  By  using  the  first  approximate  root  as  a  new  trial  root,  and  proceed- 
ing as  before,  a  nearer  approximation  is  obtained,  which  process  may  be 
repeated  until  the  root  has  oeen  extracted,  or  the  approximation  carried  at 
far  as  desired. 


10  AKITHMETIO. 

ExAHPLB.-— Required  the  cube  root  of  80.    The  nearett  ciibe  to  20  is  S*. 
8<  =  9)20.0 
2.2 
«_ 
8)8^ 
2.7  IstT.  B. 
».7«=:  7.29)20.000 
2.748 
5.4 

8)8.148 
2.714,  let  ap.  cube  root 
«.714«  a  7.865796)80.0000000 
2.7I62S84 
6.4g8 
8)6.1482584 
2.7144178  2d  ap.  cube  root 

Rbhark.— In  the  example  it  will  be  obeerved  that  the  second  term,  or 
flr«t  two  figures  of  the  root,  were  obtained  by  uslngr  for  trial  root  the  root  of 
the  first  period.  Using:,  in  like  manner,  these  two  terms  for  trial  roor«  we 
obtained  four  terms  of  the  root ;  and  these  four  terms  for  trial  root  save 
seven  flgrures  of  the  root  correct.  In  that  example  the  last  figure  efhould  be 
7.  Should  we  take  these  eight  figures  for  trial  root  we  should  obtain  at  least 
fifteen  figures  of  the  root  correct. 

To  Extract  a  mffber  Root  tban  tUe  Cnbe*— The  fourth  root  is 
the  square  root  of  the  square  root ;  the  sixth  root  Is  the  cube  root  of  the 
square  root  or  the  square  root  of  the  cube  root.  Other  roots  are  most  con- 
Teniently  found  by  the  use  of  logarithms. 

ALLIGATION 

shows  the  value  of  a  mixture  of  different  ingredients  when  the  quantity 
and  value  of  each  Is  known. 

Let  the  ingredients  be  a,  &,  c,  d,  eta,  and  their  respective  values  per  unit 
v't  ^«  V$  «t  etc. 

X  =  the  sum  of  the  quantities  =  a  +  b-{-e-{-dt  etc. 

P  ss  mean  value  or  price  per  unit  of  A. 

AP  =  ato -{■  bx  +  cy -{■  dz^  etc. 

^aw-^-bx  +  cy  +  dz 

A 

PERIHUTATION 

shows  in  how  many  positions  anv  number  of  things  may  be  arranged  In  a 
row;  thus,  the  letters  a,  &,  c  may  be  arranged  Id  six  positions,  viz.  ahc,  acb, 
cctb,  c6a,  hoc,  bca. 

Rule.— Multiply  together  all  the  numbers  used  in  counting  the  things;  thus, 
permutations  of  1,  a,  and  8  =  1x2x8  =  6.  In  how  many  positions  can  9 
things  in  a  row  be  placed  ? 

1X2X8X4X6X6X7X8X9  =  862880. 

COMBINATION 

shows  how  many  arrangements  of  a  few  things  may  be  made  out  of  a 
greater  number.  Rule :  Set  down  that  figure  which  indicates  the  greater 
number,  and  after  it  a  series  of  flgui*e8  diminishing  by  1,  until  as  many  are 
set  down  as  the  number  of  the  few  things  to  be  taken  in  each  combination. 
Then  beginning  under  the  last  one  set  down  said  number  of  few  things  ; 
then  going  backward  set  down  a  serien  diminishing  by  1  until  arriving  under 
the  first  of  the  upper  numbers.  Multiply  together  all  the  upper  numbers  to 
form  one  product,  and  all  the  lower  numbers  to  form  another;  divide  the 
upper  product  by  the  lower  cno. 


GEOMETRICAL   PROGRESSIOK.  11 

Row  many  combinations  of  9  things  can  be  made,  taking  8  in  each  com- 
btuationr 

9X8X7  ^  ??1 «  84 
1X2X8        6 

ARrraniETICAIi  PBOGRBSSIONy 

in  a  series  of  numbers,  is  a  progressive  increase  or  decrease  io  each  succes- 
sive number  by  the  addition  or  subtraction  of  the  same  amount  at  each  step, 
as  1.  2,  3,  4,  5,  etc.,  or  16,  12, 9, 6,  etc.  The  numbers  are  called  terms,  and  the 
equal  increase  or  decrease  the  difference.  Examples  in  arithmetical  pro> 
gression  may  be  solved  by  the  foUowiog  formulie : 

I-et  a  =  first  term,  I  =  last  term,  d  s  common  difference,  n  =  number  Of 
Urms,  M  =K  sum  of  the  terms: 

I  =  a  +  (n-l>l,  --id±|/2d.  +  (a-|d),* 

2a                                                    8   .  jn^Dd 
«--«,  *»+— 2 

.  =  ^»[3a  +  (n-l>cfl,  =     S    +-8d"' 

=  «  +  a)^,  =^n[2i~(n-l)cl]. 


:I-(»-l)d, 


=  |.V('  +  i'')'-««^ 


2f 


I  — a  __  g^g  -  cm) 

^  =  ^TH'  •*  n{n  -  1)' 
It  ^a*  2(nf  ~  8) 

=  2«  -  «  -  a'  ""  n(H  -  1)' 


l-a 


d-2a±|/(2a-d)«  +  8d* 


+  1.  = ad" 


2« 


2Z  +  </  ±|/(2l  +  d)«  -  8ds 


=  Z+a  ""  2d 

4SiB01!IlBTAICAli  PROGRB8SION, 

in  a  series  of  numbere,  is  a  propressive  increase  or  decrease  in  each  sue* 
ceiwive  number  by  the  same  multiplier  or  divl8or  at  each  step,  as  1,  2,  4,  8, 
16.  etc.,  or  :M3,  81,  27,  9.  etc.    The  common  multiplier  is  called  the  ratio. 

Lpt  a  =s  first  term,  I  =  last  term,  r  =  ratio  or  constant  multiplier,  n  » 
number  of  terms,  m  =  any  term,  as  1st,  2d,  etc.,  a  =  sum  of  the  terms: 

i-ar^     ^  r  r*  - 1 

log  I  =  log  a  +  (tt  -  1)  log  r,  |(£  -  I)*  -  *  -  a(«  -  o)«  -  1  =  a 

m  =  a»** ""  ^  log  m  =  log  a  +  (m  -  1)  log  r. 

r-1    •  r-r  -    n-i-       n-l.- 

y/  -       Va 


r*-.r«-l 


12 


Aun    iGTia 


o« 

1 

ys 

•VJ 

r* 

a           a 

=  0. 

logl-lopfl 

+  1. 

logr 

loga  =  log  I  ^  (n  -  1)  log  r. 


=:  *  -**.  log r  =  ?2«.izJ2»?. 


n-1 


log  ?  -  log  o 


'  log  (»  -  o)  -  log  (8-1) 


+  1. 


_  log  [g  +  (r  -  l)g]  -  log  g 
"  log  r 

^  log  t  -  log  [tr  -  (r  - 1)«) 
log  r 


+  1. 


Population  of  tlie  ITnlted  Statos* 

(A  problem  id  geometrical  progression.^ 


Tear. 
1860 
1870 
1880 
1890 
1900 
1906 
1910 


Population. 
81,448,821 

89.818,449^ 
50,156.788 

«»,e9s;B0 

76,*496,»» 

Est.  83,577,000 

**    91,554,000 


Increase  In  10    Annual  Increase. 
Years,  per  cent.        per  cent. 


S6.68 

8.89 

25.96 

8.88 

84.86 

8.86 

81.884 

1.994 

Est  1.840 

20.0 

•*    1.840 

Estimated  Population  in  Each  Yearfrovi  1870  to  1909. 
(Based  on  the  above  rates  of  increase,  in  even  thousands.) 


1870.... 

89,818 

1880.... 

60,166 

1890.... 

62.622 

1900.... 

78,29.5 

1871  .. 

40.748 

1881... 

61,281 

1891.  . 

68,871 

1901.... 

77,609 

1872.     . 

41,699 

1888  ... 

52.433 

1802.... 

65,145 

1902  .. 

79,1-.»U 

1878.... 

4i,673 

1883.... 

58,010 

1893  ... 

66,444 

1909.... 

80,5K5 

18T4... 

48,070 

1884.... 

54,813 

1894... 

67,770 

1904.... 

82,007 

1875.... 

44.G90 

1886.... 

56,048 

1895  ... 

69,122 

19C5.... 

88,677 

1876.... 

45,878 

1886.... 

57,301 

1896.... 

70,500 

1906.... 

86,115 

1877.... 

4(J,H00 

1887.... 

58,588 

1897. . . . 

71,906 

1007.... 

86,6Kl 

1878  .. 

47,888 

1883... 

59.903 

1898.... 

78,841 

1908.... 

88.276 

1879.... 

49,011 

1889.... 

61,247 

1899.... 

74,803 

1909.... 

80,900 

The  above  table  has  been  calculated  by  logarithms  as  follows  : 
log  J-  =  log  I  —  log  a  -•-  (II  -  1),  log  m  =  log  a  +  (mi  —  1)  log  r 

Pop.  1900. . . .  76,296,220  log  =  7.88SM988  =  log  I 

**      1890  . .  62,682,260  log  =  7.7907285  =  log  a 


n&=  ll,n 


difl.  = 
1  =  10;  diff.  +  10  = 
add  log  for  1890 

log  for  1891  : 
add  again 


.0857708 
.00867708 
7.7967286 


=  log  r, 
=  log  a 


7.80530568  No.  =  68.871 
.00857708 


log  for  1898      7.81888256  No.  =  65,145  . 

Compouiui  Interest  is  a  form  of  geometrical  progression  ; 
ing  1  plus  the  percentage. 


the  ratio  be- 


*  Corrected  by  addition  of  1 ,260.078,  estimated  error  of  the  census  of  1870, 
Census  Bulletin  No.  16.  Dec.  12, 1890. 


DISCOUNT.  LO 

INTBBB8T  AND  BISCOtJNT. 

Interest  biiDone J  paid  for  the  ase  of  money  for  a  given  time;  the  fac 
tors  are : 

p.  the  Ruu)  loaned,  or  the  principal: 
f,  the  time  in  years; 
r,  the  rate  of  fntereflt; 

t,  the  amount  of  interest  for  the  ^ven  rate  and  time; 
a  =  p  + 1  =  the  amount  of  the  principal  with  interest 
at  the  end  of  the  time. 
Formulee : 

i  =  mterest  =  principal  X  time  X  rate  per  cent  =  t  =  j^; 

a  =  amount  =  principal  +  interest  =  p-r  ^; 

lOOt 
r=rate  =  — ; 


p  =  principal  =  ?^=a.^^; 


*  =  time  = . 

pr 

If  the  rate  is  expressed  decimally  as  a  per  cent,— thus,  6  per  cent  =  .06,— 
thb  formulae  become 

/  =  p,-f,„  =  p(l+rO;     r  =  ±;      *  =  ^;     P  =  s  =  ,-frt- 

Roles  for  flndlnjir  Interest*— Multiply  the  piincipal  by  the  rate 
per  annum  divided  by  100,  aud  by  the  time  in  years  and  fractions  of  a  year. 
U  the  tln»  te  Kiven  in  day.  intereet  =  pri5?'g^>|g|X»o.  of  dvt_ 

In  banks  interest  is  sometimes  calculated  on  the  basis  of  800  days  to  a 
year,  or  12  montlis  of  80  days  each. 
Short  rules  for  interest  at  6  per  cent,  when  360  davs  are  taken  as  1  year: 
Multiply  the  principal  by  number  of  days  and  divide  by  0000. 
Multiply  the  pnnci[>al  bV  number  of  months  and  divide  by  200. 
Tlie  interest  of  1  dollar  for  one  month  is  ^  cent. 

Intere»t  of  lOO  Dollars  for  DlflTerent  Ttmes  and  Rates, 

Time,           t%          %%  A%  h%           ^%  S%  lOi 

lyear                      $2.00  $3.00  $4.00  $5.00  $6.00  $8.00  $10  00 

1  month                       .16}         .25  .83}  .4]|         .50  .603  Ml 

1  day  =  ,iv  year  .00551  .0063}  .01  lU  -OlSSf  .0166|  .0222}  .0277} 

1  day  =  ^  year  .005479  .008219  .010959  .018699  .016438  .08191^$  .0273973 

DIseonnt  if>  interest  deducted  for  payment  of  money  before  it  is  due. 

True  discount  is  the  difference  between  the  amount  of  a  debt  pay- 
able at  a  future  date  w^ithout  interest  and  its  present  worth.  The  present 
worth  is  that  sum  which  put  at  interest  at  the  legal  rate  will  amount  to  the 
debt  when  it  is  due. 

To  And  the  present  worth  of  an  amount  due  st  future  date,  divide  the 
amount  by  the  amount  of  $1  placed  at  interest  for  the  given  time.  Thtt  dis- 
count equals  the  amount  minus  the  present  worth. 

What  discount  ^ould  be  allowed  on  $106  paid  six  months  before  it  is  due, 
interest  being  0  per  cent  per  annum  ? 

=  $100  present  worth,  discount  =  3.00. 

1  +  1  X  .06  X  5 
2 

Bank  discount  is  the  amount  deducted  by  a  bank  as  interest  on 
money  loaned  uu  promissory  notes.  It  is  interest  calculated  not  on  tlie  act- 
ual sum  loaned,  nut  on  the  gross  amount  of  the  note,  from  wliich  tlie  dis- 
Cfiunt  IS  deducted  in  advance.  It  is  also  calculated  on  the  basis  of  30()  da.^  s 
in  the  year,  and  for  8  (In  some  banks  4)  days  more  than  the  time  specified  in 
the  note.  These  are  called  days  of  grace,  and  the  note  is  not  payable  ull 
the  last  of  these  days.    In  some  States  days  of  grace  have  been  abolished. 


14 


AKITHMBTIC. 


What  discount  will  be  deducted  by  a  bank  fn  discounting  a  note  for  $103 
tmyable  6  months  hence  ?  Six  months  =  182  days,  add  3  days  grace  =  135 
-       ,  108  X  186      „  ,„ 

Compound  Interest*— In  compound  interest  the  interest  Is  added  to 
the  principal  at  the  end  of  each  year,  (or  shorter  period  if  agreed  upon). 

Letp  =  the  principal,  r  =  the  rate  expressed  decimally,  n  =  no  of  years, 
ftud  a  the  amount : 


a  =  amount  =  p  <1  +  »")»;  r  =  rate 


■VI 


1, 


log  g  -  log  p 


p  =  principal  =  ^^-^^ ;  «o.  of  years  =  n  =  '^^^  ^^  ^  ^^ 


Compound  Interest  Table. 

(Value  of  one  dollar  at  compound  interest,  compounded  yearly,  at 
8,  4,  5,  and  6  per  cent,  from  1  to  fiO  years.) 


i 

t% 

i% 

^% 

W 

i 

t% 

4^ 

^ 

9% 

►* 

>* 

1 

1.08 

1.04 

1.06 

1.06 

16 

1.6047 

18780 

2.1829 

2.5408 

3 

1.0609 

1.0816 

1.1025 

1.1286 

17 

1.6528 

1.9479 

2.2920 

2.6928 

8 

1.095»7 

1.1249 

1.1576 

1.1910 

18 

1.7084 

2.0258 

2.4066 

2.8543 

4 

1.1255 

1.1609 

1.2155 

1.2626 

19 

1.7585 

2.1068 

2  5269 

8.02.'i6 

6 

1.1598 

1.2166 

1.2768 

1.8882 

20 

1.8061 

2.1911 

2.6588 

8.2071 

6 

1.1941 

1.2663 

1.3401 

1.4186 

21 

1.8008 

2.2787 

2.7869 

8.3995 

7 

1.S299 

1.81.50 

1.4071 

1.5036 

22 

1.9161 

2.8890 

2.9252 

8.60:36 

8 

1.2688 

1.8686 

1.4774 

l..Mn8 

88 

1.9786 

2  4647 

8.0715 

8.8197 

0 

1.8048 

1.42^» 

1.5618 

1.6895 

24 

2.0828 

2.5638 

812251 

40487 

10 

1.8439 

1.4802 

1.6280 

1.7908 

25 

2.0937 

2.6658 

8.3864 

4.2919 

11 

1..3842 

1.5394 

1.7108 

1.8083 

30 

2.4272 

3.2484 

4.3219 

5  7435 

12 

1.4268 

1.6010 

1.79.58 

2.0122 

86 

2.8188 

8.9460 

5.5166 

7.6«R1 

13 

1.4685 

1.6651 

18856 

2  1329 

40 

8.2620 

4.8009 

7  0100 

10.-J858 

14 

1.5126 

1.7817 

1.9799 

2.2609 

45 

8.7815 

5.8410 

8.9860 

13.7646 

15 

1.5580 

1.8009 

2.0789 

2.3965 

CO 

4.3838 

7.1064 

11.6792 

18.4190 

At  compound  interest  at  8  per  cent  money  will  double  itself  in  23^  year!^ 
at  4  per  cent  In  17^^  years,  at  5  per  cent  in  14.2  years,  and  at  6  per  cent  in 
11.9  years. 

E41I7ATION  OF    PAYHIEFITS. 

By  equation  of  payments  we  find  the  equivalent  or  average  time  In  which 
one  payment  should  be  made  to  cancel  a  number  of  obligations  due  at  dif- 
ferent dates ;  also  the  number  of  days  upon  which  to  calculnte  interest  or 
discount  upon  a  gross  sum  which  is  composed  of  several  smaller  sums  pay- 
ab1f>  nt  different  dates. 

Rnle.— Multiply  each  Item  by  the  time  of  its  maturity  in  days  from  a 
fixed  date,  taken  as  a  standard,  and  divide  the  sum  of  the  products  by  the 
sum  of  the  items:  the  result  is  the  average  time  in  days  from  the  standard 
date. 

A  owes  B  $100  due  in  80  days,  $-300  due  in  60  days,  and  $300  due  in  90  days. 
In  how  many  days  may  the  whole  be  paid  In  one  sum  of  $600  ? 

100  X  30  +  200  K  60  +  800  X  90  =  42,000;    42,000 h- 600  =  70  days,  an$. 

A  owes  B  $100,  $200,  an<l  $300,  which  amounts  are  overdue  respectively  80. 
60,  and  90  days.  If  he  now  pays  the  whole  amount,  $600,  how  many  days* 
interest  should  he  pay  ou  limi  snm  y    Au»,  70 days. 


ANNUITIES. 


15 


PARTI  All    PAY1HBNT8. 

To  compute  interest  on  notes  and  bonds  when  partial  payments  haTe  been 

Unlteil  Stmt«s  Role.— Find  the  amount  of  the  principal  to  the  time 
of  I  be  flrat  payment,  and,  subtracting  the  payment  from  it.  And  the  amount 
of  the  reraamder  as  a  new  principal  to  the  time  of  the  next  payment. 

If  the  payment  is  less  than  the  interest,  And  the  amount  of  the  principal 
to  the  time  when  the  sum  of  the  imyments  equals  or  exceeds  the  interest 
due,  and  subtract  the  sum  of  the  payments  from  this  amount. 

Proceed  in  this  manner  till  the  time  of  settlement. 

Note*— The  principles  upon  which  the  precediuf;  rule  is  founded  are: 

1st.  That  payments  must  be  applied  first  to  discban^  accrued  interest, 
and  then  the  remainder.  If  any,  toward  the  discharge  of  the  principal. 

2d    That  only  unpaid  principal  can  draw  interest. 

Mercantile  niettaod.— When  partial  payments  are  made  on  short 
notes  or  interest  accounts,  business  men  commonly  employ  the  following 
method : 

Find  the  amount  of  the  whole  debt  to  the  time  of  settlement ;  also  find 
the  amount  of  each  payment  from  the  time  it  was  made  to  the  time  of  set- 
tlement. Subtract  the  amount  of  payments  from  the  amount  of  the  debt; 
the  remainder  will  be  the  balance  due. 

ANNVITIES. 

An  Annultir  Is  a  fixed  sum  of  money  paid  yearly,  or  at  other  equal  times 
agrved  upon.  The  values  of  annuities  are  calculated  by  the  principles  of 
compound  interest. 

1.  Let  t  denote  interest  on  $1  for  a  year,  then  at  the  end  of  a  year  the 
amount  will  be  1  +  i.    At  the  end  of  n  years  it  will  be  (1  +  ^>*^. 

2.  The  sum  which  hi  n  years  will  amount  to  1  is  or  (1+0"  *  or  the 
present  value  of  1  due  In  n  years. 

8.  The  amount  of  an  annuity  of  1  in  any  number  of  years  n  is 

4.  The  present  value  of  an  annuity  of  1  for  any  number  of  years  n  is 
1  J(14-t)-n 

5  ITie  annuity  which  1  will  purchase  for  any  number  of  years  n  is 
i 


(1+0* 


i-(l-|-t)-»' 
6.  The  annuity  which  would  amount  to  1  in  n  years  is 


(1+i)»-l 


Amounts,  Present    Talnes,  etc.,  at  &%  Interest. 


Years 

(l+i)" 

(2) 

(1  +  /)-»• 

(«) 

(1  4.  i)n  ^  1 

(4) 

i-ci+o-* 

(6) 
t 

(6) 

t 

i 

i 

i-a+o-" 

a+t)*»-i 

1 

2  .... 

8 

4 

5 

6 

7 

8 

9 

10 

1.05 

l.lOiSS 

1.15:625 

1.215606 

1.276182 

1.840096 
1.407100 
1.477456 
l.S5l8i8 
1.688896 

.952%] 
.907029 
.669888 
.8*^702 
.'re3636 

.746815 
.710681 
.678889 
.644609 
.618913 

1. 

2.05 

8.1525 

4.3I0I25 

5.525631 

6.801918 
6.142006 
9.549109 
11.026564 
12.677898 

.962881 
1.859410 

3.645951 
4.329477 

5.075692 
5.786373 
6.4fi:«i3 
7.107822 
7.721735 

1.05 
.587805 
.867209 
.282012 
.230975 

.197017 
.i;'2820 
.154722 
.140690 
.129505 

1. 

.487806 
.317209 
.282012 
.180975 

.147018 
.122820 
.104782 
.090690 
.079506 

ABITHMETIC. 


,■« 

119.18 
101.08 
87.02 
75.87 
66.79 

to 

S?!SS8 

SisS98 

JO  — Q0»^ 

am 

«0«J0»t-i0 

^ 

8SSSS 

c;^eodadtD 

^ 

sosgse 

gS?^2S 

S28S? 

2«S^S 

SSt:£S 

?ggs§ 

^SSSS 

^5£S$ 

9StiSS 

ss;;«" 

3! 

00 

^a5S$5 

^^Z^B 

$S'^SS 

SSSS9& 

&8S$S 

§gi?s 

ssssgs 

ssss<^ 

9$So£2S 

OIO*^0»I> 

5 

00 

01 
01 

essss 

5^^5«;: 

5SSf:S 

8fes:!:sj 

e8j&9 

l§ISS 

grggs 

^ssss 

i;9;;ssi 

gjQOjrOJO 

S55S;s:5 

S2J8SS 

£8Sc:3S 

e*eo"*ioo 

l>  QO  0>  ©  ^ 

9*  CO  "^  o  «d 

t?22^«5 

S5?$«S 

WEIGHTS  AND   MBASURES. 


17 


TABLES   FOR    CAI^CULATING    SINKING-FIJNIIS   AND 
PBBSBNT   TAI^ITES. 

Engineers  aad  others  connected  with  municipal  work  and  industrial  enter* 
priiies  often  find  it  necessary  to  calculate  payments  to  sinking-funds  which 
vill  provMe  a  sum  of  money  sufficient  to  pay  off  a  bond  issue  or  other  debt 
at  the  end  of  a  giren  period,  or  to  determine  the  present  value  of  certain 
annual  charges.  The  accompanying  tables  were  computed  by  Mr.  John  W. 
Hill,  of  Cincinnati,  Eng^g  News,  Jan.  85,  1894. 

Table  I  (opposite  page)  shows  the  annual  sum  at  rarious  rates  of  interest 
required  to  net  $1000  in  from  2  to  50  years,  and  Table  n  shows  the  present 
value  at  various  rates  of  interest  of  an  annual  charge  of  $1000  for  from  5  to 
60  years,  at  five-year  intervals  and  for  lOO  years. 

Tmhle  II«— CapttaltaEatlon  of  Annuity  of  81000  for 
flrom  5  to  100  Years* 


Rate  of  Interest,  per  cent. 


2» 


5  4,645 
10  8.758. 
1512,881. 
so!  15.589. 
25  18,4-^. 
I 


f.59 

1.58 

.15 

L48 

10038,614.81 


80  ;»,980.i 

85;sH,145.J 

40*^5.103.1 

45S 

60  28,989.^ 


4,679.60 
8,580.18 
11,937.80 
14,877.27 
17,418.01 

19.600.21 
21,487.04 
88,114.86 
84,518.49 
85,789.58 
81,598.81 


SH 


4.514.98  4,451.68 
6,816.45  8,110.74 
11,517.83,11,118.06 
14,212.181 18,590.81 
16,481.88,15,621.98 

18,891.86  17,891.86 
80,000.48  18,664.87 
8!  ,354.83' 19,792.65 
82,495.83  80,719.89 
23,456.21 121,482. 06 
27,655.86  24,504.96 


4« 


4,889.91 
7.912.67 
10,789.48 
13,007.88 
14,828.12 

16,888.77 
17,460.89 
18,401.49 
19,156.84 
19,761  98 
21,949.21 


4,889.45 
7,721.78 
10,879.53 
12,468.13 
14,093.86 

15,878.36 
16,374.36 
17,159.01 
17,778.99 
18,855.86 
19,847.90 


6» 


4,268.09 
7,587.64 
10,087.48 
11,950.86 
18,413.88 

14,533.63 
15,890.48 
16.044.98 
16,547.65 
16,931.97 
18,095.68 


4,818.40 
7,860.19 
9,718.80 
11,469.96 
18,788.88 

13,764.85 
14,486.66 
15,046.81 
15,466.85 
15,761.87 
16^618.64 


WEIGHTS  AND  IfEASXJBES. 
Iions  Measure.— Measures  of  Ijengtli* 

12  inches  =  1  foot. 

8  feet  =  1  yard. 

6^  yards,  or  16^  feet  =  1  rod,  pole,  or  perch. 

40  poles,  or  280  yardfl  =  1  furlong. 

8  furlongs,  or  1760  yards,  or  5880  feet  =  1  mile. 
8  miles  =  league. 

Additional  measures  of  length  in  occasional  use :  1000  mils  =  1  inch; 
4  inches  =  1  hand  ;  9  inches  =  Ispan  ;  8^  feet  =  1  military  pace  ;  2  yards  = 
1  fathom. 

Old  I«and  Measnre.— 7.98  inches  =  1  link;  100  links,  or  66  feet,  or  4 
poles  =  1  chain;  lO  chains  =  1  furlong;  8  furlongs  =  1  mile;  10  square  ciiains 
=  1  acre. 

Nautical  Measure. 

^te'milM^  ^^**^  ^^''  \  =  *  °*""^*'  °^*^**'  ^^  ^°°'-* 
3  nautical  miles  =  1  league . 

^  "Sltmi  SilS'  ^^  ^^'^^  \  =  ^  ^^^  ^'^  ^*  equator). 
860  degrees  =  circumference  of  the  earth  at  the  equator. 

♦The  British  Admiralty  takes  the  round  figure  of  6080  ft.  which  is  the 
lensth  of  the  '*  measured  mile''  used  in  trials  of  vessels.  The  value  varies 
from  6080.26  to  6088.44  ft.  according  to  different  measures  of  the  earth's  di- 
ameter. There  to  a  difference  of  opinion  among  writers  as  to  the  use  of  the 
word  **  knot  ^*  to  meao  length  or  a  distance-Hsome  holding  that  It  should  be 


18  ARITHMETIC. 

Square  Memaure,-  me^mnrem  ofSnrfece. 

m  sauare  inches,  or  1H3.35  circular  I      .  .     . 

Inches  f  =  ^  square  foot. 
9  square  feet  =  1  square  yard . 

80i  square  yaixls,  or  272J  square  feet         =  1  square  rod,  pol<»,  or  perclu 
4U  square  poles  =  i  rood. 

4  roods,  or  10  sq.  chains,  or  160  sq.  ) 

poles,  or  484U  sq.  yards,  or  48M0  V  =  1  acre, 

sq.  feet,  ) 

«0  acres  =  i  square  mile. 

An  acre  equals  a  square  whose  side  is  208.71  feet. 

Circular  Incli;  Circular  Jllll.-A  circular  inch  is  the  area  of  a 

circle  1  inch  in  diameter  =  0.7854  square  inch. 

1  square  inch  =  1.2782  circular  inches. 

A  circular  mil  is  the  area  of  a  circle  1  mil,  or  .001  inch  in  diamet«r- 
1000*  or  1.000,000  circular  mils  =  1  circular  inch. 

1  square  inch  =  1,278,288  circular  mils. 

The  mil,  and  circular  mil  are  used  in  electrical  calculations  involving 
the  diameter  and  area  of  wires. 

Solid  or  Cubic  Rleaau re.— measures  of  VoIudbc. 

1728  cubic  inches  =  1  cubic  foot. 
27  cubic  feet     =  1  cubic  yard. 
1  cord  of  wood  =  a  pile,  4x4x8  feet  -  128  cubic  feet 
1  perch  of  masonry  =  16f  X  H  X  1  foot  =  24{  cubic  feet 

Ijtquid  measure. 

4  grills  =  1  pint 

2  pints  =  1  quart. 

A  #itiai>ta  —  \  <r.ii/^ti  i  U.  8.  231  cubic  inches. 

^  ^^^^  =  ^  ^^^^  1  Eng.  277.274  cubic  inches. 

8U  frallons  =  1  barrel. 

43  fcaU'^ns  =  1  tierce. 

2  barreifi,  or  68  eallous        =  1  hogshead. 
84  fifallons,  or  2  tierces  =  1  puncheon. 

2  hogsheads,  or  126  gallons  =  1  pipe  or  butt 
2  pipes,  or  8  puncheons       =  1  tun. 
The  U.  8.  gallon  contains  281  cubic  inches;  7.4805  gallons  =  1  cubic  foor. 
A  cylinder  7  In.  diam.  and  6  in.  high  contains  1  gallon,  very  nearlv.  or  230.9 
cubic  inches.     The  British  Impeiial  gallon  contains  277.S74  cubic  Inches 
£=  1.20082  U.  8.  fsrallnn. 

Tbe  miner^s  I ncli.— (Western  U.  8.  for  measuring  flow  of  a  stream 
of  water). 

The  term  Miner's  Inch  is  more  or  less  indefinite,  for  the  reason  that  Call- 
fornfa  water  companies  do  not  all  use  the  same  head  above  the  centre  of 
the  aperture,  and  the  inch  varies  from  1.86  to  1.78  cubic  feet  per  minute 
each;  but  the  most  common  measurement  is  through  an  apeilure  2  inches 
high  and  whatever  length  is  required,  and  through  a  plank  U  inches  thick. 
The  lower  edge  of  the  aperture  should  be  2  inches  above  the  bottom  of  the 
measuriug-box,  and  the  plank  5  inches  high  above  the  aperture,  thus  mak- 
ing a  6-inch  head  above  tue  centre  of  the  stream.  Each  square  inch  of  ihis 
opening  represents  a  miner's  inch,  which  is  equal  to  a  flow  of  H  cubic  fee'; 
per  minute. 

Apotbecartes'  Fluid  measure. 
60  minims  =  1  fluid  drachm. 

8  drachms,  or437i  grains,  or  1.732  cubic  inches  =  1  fluid  ounce. 

Dry  measure^  IT.  S, 

2  pints  =:  1  quart. 
8  quarts  =  1  peck. 
4  pecks  =  1  bushel. 

used  soJy  to  denoie  a  rate  of  speed.  The  length  between  knots  on  tlie  log 
line  is  tIv  ^f  A  nautical  mile  or  50.7  ft.  when  a  half-minute  glass  is  used;  so 
that  a  speed  of  10  knots  is  equal  to  10  nautical  miles  per  hour. 


WBIGHtS  AKD  ll£ASU&£d.  19 

Hie  standard  U.  8.  bushel  is  the  WiDchester  bushel,  which  Is  in  cylinder 
form,  18i  inches  diameter  and  8  Inches  deep,  and  contains  2150.4^  cubic 
inches. 

A  struck  bushel  contains 2150.4*2  cubic  inches  =  1.S445  cu.  ft.:  1  cubic  foot 
=  0.803!yS  struck  bushel.  A  heaped  bushel  is  a  cylinder  18^  inches  diam- 
eter and  8  inches  deep,  with  a  heaped  cone  not  less  than  6  inches  high. 
It  is  eqtial  to  Ij  struck  bushels. 

The  British  Imperial  bushel  is  based  on  the  Imperial  gallon,  and  contains 
8  such  gallons,  or  2318.  I9<  cubic  inches  =  1.2887  cubic  feet.  The  English 
quarter  =  8  Imperial  bushels. 

Capacity  of  a  cylinder  in  U.  8.  gallons  =  square  of  diameter,  in  inches  X 
height  in  inches  X  .0084.    (Accurate  wlthhi  1  part  in  100,000.) 

Capacity  of  a  cylinder  in  U.  8.  bushels  =  square  of  diameter  in  inches  X 
height  in  inches  X  .0008662. 

SUpplng  JHeasure. 

BegiMter  Ton.— For  register  tonnage  or  for  measurement  of  the  entir*) 
internal  capacity  of  a  yessel : 

100  cubic  feet  =  1  register  ton. 

This  mimber  is  arbitrarily  assumed  to  facilitate  computation. 
Shipping  Ton,— For  the  measurement  of  cargo : 

(1  U.  S.  shipping  ton. 
40  cubic  feet  =  •<  81.16  Imp.  nushels. 
( 82.148  U.  8.      '* 
( 1  British  Rhipping  ton. 
42  cubic  feet  =  •<  82.719  Imp.  bushels. 
1 88.75  U.  8. 
Carpenier^s  £tt2e.— Weight  a  yessel  will  carry  =  length  of  keel  X  breadth 
at  main  beam  X  depth  of  hold  in  feet  -i-96  (the  cubic  feet  allowed  for  a  ton). 
The  result  will  be  the  tonnage.    For  a  double-decker  instead  of  the  depth 
of  the  hold  take  half  the  breadth  of  the  beam. 

WLemmnrem  of  Wetflit.'-ATolrdiipolM.  or  Commercial 
Welffht. 

16  drachms,  or  487.5  grains  =  1  ounce,  oz. 
16  ounces,  or  7000  grains  =  1  pound,  lb. 
28  pounds  =  1  quarter,  qr. 

4  quarters  =  1  hundredweight,  cwt.  =  112  lbs. 

20  hundred  weight  =  1  ton  of  2240  pounds,  or  long  ton. 

3000  pounds  =  1  net,  or  short  ton. 

2801.6  pounds  =  1  metric  ton. 

1  stone  =  14  pounds  ;  1  quintal  =  100  pounds. 

Troy  mrelffbt. 

34  grains  =  1  pennyweight,  dwt. 

20  pennyweights  =  1  ounce,  07..  =  480  grains. 

12  ounces  =  1  pound,  lb.  =  5700  grains. 

Tray  weight  is  used  for  weighing  gold  and  silver.  The  grain  Is  'he  same 
in  Avoirdupois,  Troy,  and  Apothecaries^  weights.  A  carat,  used  in  weighing 
««^pyMMifl  -s  8.168  grains  =  .205  gramme. 

Apotbecarlea'  ITelebt. 

20  grains     =  1  .scruple,  3 
8  scruples  =  1  drachm.  3    =     60  grains. 
8  drachms  =  1  ounce,  1       =    480  grains. 

12  ounces    =  1  pound,  lb.     =  5760  grains. 

To  detcnnliie  urbetber  a  lialance  lias  unequal  arms.— 

Affer  weighing  an  article  and  obtaining  equilibrium.  trauHpose  the  article 
anfl  the  freights.  If  the  l>a1ance  is  true,  it  will  remain  in  equilibrium  ;  if 
untrue,  the  nan  suspended  from  the  longer  arm  will  descend. 

To  ireligk  eonreetlT  om  an  Incorrect  balance.— First,  by 
sabstituUun.    Put  the  article  to  be  weighed  in  one  pan  of  the  balance  and 


20  ARITHMETIC. 

couQlerpoiae  it  bv  any  convenient  heavy  articles  placed  on  the  other  pan. 
Remove  the  article  to  be  welched  and  subBUtute  for  it  standard  weif^rhta 
until  equipoise  is  a^ain  established.  The  amount  of  these  weights  is  the 
weight  of  the  article. 

Second,  by  transposition.  Determine  the  apparent  weight  of  the  article 
as  usual,  then  its  apparent  weight  after  transposing  the  article  and  the 
weights.  If  the  diffei-ence  is  small,  add  half  the  difference  to  the  smaller 
of  the  apparent  weights  to  obtain  the  true  weight.  If  Uie  difference  is  2 
per  cent  the  error  of  this  method  Is  1  iiart  in  10.000.  For  larger  differences, 
or  to  obtain  a  perfectly  accurate  result,  multiply  the  two  apparent  weights 
together  and  extract  the  square  root  of  tlie  product. 

Olrciilar  IHemsiire* 

60  seconds,  "  =  1  minute, '. 
60  minutes, '  =  1  degree,  ". 
00  degrees      =  1  quadrant. 
860      ''  =  circumference. 

Time, 

60  seconds  =  1  minute. 
60  minutes  =  1  hour. 
S4  hours     =  1  day. 
7  da3rs       =  1  week. 
885  daySf  5  hours,  48  minutes,  48  seconds  =  1  year. 

By  the  Qregorian  Calendar  every  year  whose  number  is  divisible  by  4  Is  a 
leap  year,  and  contains  866  days,  the  other  years  containing  865  days,  ex- 
cept that  the  centesimal  years  are  leap  years  only  when  the  number  of  the 
year  is  divisible  by  400. 

The  comparative  values  of  mean  solar  and  sidereal  time  are  shown  by  the 
following  relations  according  to  Bessel : 

866.84223  mean  solar  days  =  866.21282  sidereal  days,  whence 
1  mean  solar  day  =  1.00273T91  sidereal  days; 
1  sidereal  day  =  0  00726957  mean  solar  day; 
24  hours  mean  solar  time  =  24*  8f  56•..^^5  sidereal  time; 
24  hours  sidereal  time  =  2S>'  56n  4«.091  mean  solar  time, 

whence  1  mean  solar  day  is  S»  56^.01  longer  than  a  sidereal  day,  reckoned  in 
mean  solar  time. 

BOARD    AND   TIMBER   REBASirBfi. 

Board  measure. 

In  board  measure  boards  are  assumed  to  be  one  inch  in  thickness.  To 
obuiii  the  number  of  feet  board  measure  (B.  M.)  of  a  board  or  stick  of 
square  timber,  multiply  together  the  length.in  feet,  the  breadth  in  feet,  and 
tb**  thickness  in  inches. 

To  compute  tbe  measure  or  surface  in  square  feet.—When 
r11  diiiiensiuus  are  in  feet,  nmltiplv  the  length  by  the  breadth,  and  the  pro- 
duct will  give  the  surface  lequired. 

When  either  of  the  dimensions  are  in  inches,  multiply  as  above  and  divide 
the  product  by  12. 

When  all  dimensions  are  in  inches,  multiply  as  before  and  divide  prodoci 
by  144. 

Timber  Measure. 

To  compute  tbe  volume  of  round  timber.— When  all  dimen- 
sions ai-e  in  feet,  multiply  the  length  by  one  quarter  of  the  product  of  the 
mean  girth  and  diameter,  and  the  product  will  Ktve  the  measurement  in 
cubic  feet.  Wlien  length  is  given  in  feet  and  girth  and  diameter  in  Indies, 
divide  the  product  by  144  ;  when  all  the  dimensions  are  in  inches,  divide  bv 
172R. 

To  compute  tbe  volume  of  square  timber.— When  all  dimen- 
sions ara  in  feet,  multiply  together  the  length,  breadth,  and  depth;  the 
£roduct  will  t>e  tbe  volume  in  cubic  feet.  When  one  dimension  ia  given  in 
lehee,  divide  by  12;  when  two  dimensions  ai«  in  Inches,  divide  by  144;  when 
all  tJiree  dimensioDS  are  in  iuchea,  divide  by  1728. 


WEIGHTS  AND  MlsiASCRES. 


21 


€ont«nto  In  Feet  of  Jotirta,  BeaMillng,  and  Timber. 

Length  in  Feet. 


12        14        16        18 


32        84 


Feet 

Board  Measure. 

«X  4 

8 

9 

11 

18 

18 

15 

16 

17 

19 

90 

8X  6 

12 

14 

16 

18 

20 

22 

91 

86 

28 

80 

2X  8 

16 

19 

21 

24 

27 

29 

82 

85 

87 

40 

8X  10 

90 

28 

27 

80 

88 

87 

40 

48 

47 

50 

2X  IS 

24 

28 

S2 

36 

40 

44 

48 

52 

ts 

60 

2X  14 

28 

88 

87 

42 

47 

51 

56 

61 

65 

70 

8x  8 

24 

88 

82 

86 

40 

44 

48 

52 

56 

60 

8X  10 

ao 

85 

40 

46 

60 

65 

80 

65 

70 

75 

3X  1« 

88 

42 

48 

54 

60 

66 

72 

78 

84 

90 

SX14 

42 

49 

66 

68 

70 

77 

84 

91 

96 

105 

4X  4 

16 

10 

21 

24 

97 

99 

8-i 

85 

87 

40 

4X  6 

24 

28 

82 

86 

40 

44 

48 

52 

56 

60 

4X  8 

82 

87 

48 

48 

58 

50 

64 

69 

75 

80 

4X10 

40 

47 

58 

60 

67 

78 

80 

87 

93 

100 

4X  W 

48 

66 

64 

72 

80 

88 

96 

104 

112 

120 

4X14 

56 

65 

75 

84 

93 

108 

112 

121 

181 

140 

«X  6 

86 

42 

48 

64 

60 

66 

72 

78 

84 

90 

«X  8 

48 

66 

64 

7S 

80 

88 

96 

104 

118 

120 

cxio 

60 

70 

80 

90 

100 

110 

190 

180 

140 

150 

6X12 

72 

81 

96 

108 

120 

182 

144 

166 

168 

180 

6X14 

84 

96 

112 

126 

140 

164 

188 

182 

196 

210 

8X  8 

64 

75 

86 

06 

107 

117 

128 

139 

149 

160 

8x  10 

80 

98 

107 

120 

188 

147 

160 

178 

187 

200 

8X12 

96 

lis 

128 

144 

160 

176 

192 

208 

224 

240 

8X14 

112 

181 

149 

168 

187 

205 

224 

248 

261 

280 

roxio 

100 

117 

188 

160 

167 

ISS 

200 

917 

988 

250 

10  X  12 

120 

140 

160 

180 

200 

2-iO 

240 

960 

980 

300 

10  X  14 

140 

J68 

187 

210 

288 

257 

280 

803 

827 

850 

U  X  12 

144 

168 

192 

216 

240 

264 

288 

312 

886 

360 

12  X  14 

168 

188 

sm 

252 

280 

806 

886 

864 

892 

420 

14  X  14 

196 

229 

261 

'  294 

827 

859 

802 

425 

457 

490 

FRBNCn  OB  nSTBIO  aiBASCTRSS. 

Tbe  metric  unit  of  lenfrth  is  the  metre  s  39.87  inches. 
The  metric  unit  of  weight  is  the  gram  =  15.482  grains. 
The  following  prefixes  are  used  for  subdivisions  and  multiples ;  Millf  =  x^n, 
Centi  =  1^9.  Dec)  =  ^,  Deca  =  10,  Hecto  =  100,  Kilo  =  1000,  Myria  =  10,000. 

VBEHCM  AND  BBITI8H  (AND  AIHBRICAlf) 
BQ1JITAI.BNT  MBASVBSflU 

Keaenres  of  lienstb. 

FBiorcH.  British  and  U.  S. 

1  metre  =  89.87  inches,  or  8.28068  feet,  or  1.09861  yards. 

.8048  metre  ts  i  foot. 

1  centimetre  s  .8887  inch. 
2154  centimetres  s  l  inch. 

1  millmetre    =  .08037  inch,  or  1/25  inch,  nearly. 
86. 4  millimetres  s  l  inch. 

1  kilometre    s  1008.61  yards,  or  0.62197  mlla 


22  ARITHMETIC. 

Measnres  of  SarOtcA. 

Frknch.  Britisb  and  U.  8. 

1  <x«..a.^  ...<>»»>  i  10.761  square  feet, 

1  square  metre  =  -^    ,.196  square  yartlB. 

.886  square  metre  =  1  square  yard. 

.09si9  square  metre  =  1  square  foot. 

1  square  centimetre  =  Abb  square  inch. 
6.452  square  centimetres  =  I  square  incb. 

1  square  millimetre    =  .00155  square  inch. 
646.^  square  millimetres  =  1  square  inch. 
1  centiare  =  1  sq.  metre  =  10  764  square  feet. 

1  are  =  1  Hq.  decametre  =  1076.41     *' 

1  hectare  =  100  ares  =  107641      "         '*  =  9.4711  acres. 

1  sq.  kilometre  =  .886109  sq.  miles   s  247.U     *' 

1  sq.  myriametre  =  88.6109  "       '< 

or  Volume, 

Frbnob.  British  and  U.  S. 

.7645  cubic  metre  =  1  cubic  yard. 

.02832  cubic  metre  =  1  cubic  foot. 

.cubic  decimetre    =  ^'iSSaSSaSi^S."- 

28.83  cubic  decimetres  =  1  cubic  foot. 
1  cubic  centimetre  =  .061  cubic  inch. 

16.387  cubic  centimetres  =  1  cubic  inch. 
1  cubic  centimetre  =  1  miUilitre  =  .061  cubic  inch. 
1  centilitre  =  =      .610     " 

1  decilitre  =  =    6.108     "       " 

1  litre  =  1  cubic  decimetre  =  61.033      "       "      =  1.05671  quarts,  U.  a 

1  hectolitre  or  decisiere  =    8.6814  cubic  feet  =   2.8875  burtiels,  " 

1  stere,  kiloUtre,  or  cubic  metre  —    1.806  cubic  yards  =     28.37  bushels,  " 

or  Capacity, 

Frbvoh.  British  and  U.  S. 

{61.023  cubic  inches, 
i^'g^lonfrm-ericiu.). 
2.202  pounds  of  water  at  62^  F. 
88.317  litres  =  1  cubic  foot. 

4.543  litres  =  1  gallon  (British). 

8.785  litres  =  1  gallon  (American). 

or  l¥elsht. 

French.  British  and  U.  8. 

1  gramme  =  15.482  grains. 

.0648  gramme  =  1  grain. 

28.35  gramme  =  1  ounce  avoirdupois. 

1  kilogramme  =  2.2046  pounds. 

.4536  kilogramme  =  1  pound. 

1  tonne  or  metric  ton  =  ( '^^  J.^°  ^'  «^  ^^^^ 
1000  kilogrammes  =  ]  2^6  ^?inds. 

1.0 1 «  metric  tons  =  i  1  ton  of  SSUn  tv^nnHa 

1016  kilogrammes  ^  ^  1  ton  or  -»40  pounds. 

Mr.  O.  H.  Titmann,  in  Bulletin  No.  9  of  the  U.  8.  Coast  end  Geodetic  Sur- 
vey, discusses  the  work  of  various  authorities  who  have  compared  the  yard 
and  the  metre,  and  by  referring  all  tJie  observations  to  a  common  standard 
has  Hucceeded  in  reconciling  the  discrepancies  within  very  narrow  limits. 
The  following  are  his  results  for  the  number  of  inches  in  a  metre  according 
to  the  comparisons  of  the  authorities  named: 

1817.  Hassler 89.86991  inches. 

1818.  Kater 39.86990      " 

1835.     Bailv 39.86978      " 

1866.    Clarke 39.86JW0      " 

1885.    Conistock 39.86984      " 

The  mean  of  these  is 80.86988      ** 


METEIC   WEIGHTS  AND  MEASURES.  23 

ntSTBIO  CONVBR8ION  TABLES. 

The  followfne  tables,  with  the  subjoined  memoranda,  were  published  in 
1890  by  the  United  States  Coast  ana  Qeodetic  Survey,  office  of  standard 
weights  and  measures,  T.  C.  Hendenhall,  Superintendent. 

Tables  for  CoBvertlns  IT.  8.  mrelffbtai  and  IIEeaaiire»-i 
Customary  to  netrle. 

LINEAR. 


Inches  to  Hllli- 
metres. 

Feet  to  Mecree. 

Tarda  to  Metres. 

Miles  to  Kilo- 
metres. 

i  = 

2  = 

3  = 

4  = 

5  = 

6  = 

7  = 

8  = 

9  = 

86.4001 
60.8001 
76.8002 
101.6008 
127.0008 

168.4008 
177.8004 
803.2004 
288.6006 

0.804801 
0.609601 
0.914402 
1.219202 
1.524006 

1.828801 
8.188604 
8.488406 
8.743206 

0.914402 
1.828804 
2.748206 
8.657607 
4.672009 

5.486411 
6.400813 
7.815215 
8.829616 

1.60935 
821860 
4.82804 
6.43789 
8.04674 

9.65606 
11.86548 
12.87478 
14.48412 

SQUARE. 


Square  Inches  to 
Square  Centi- 
metres. 

Square  Feet  to 
Square  Deci- 
metres. 

Square  Yards  to 
Square  Metres. 

Acres  to 
Hectares. 

1  = 

2  = 
8  = 

4  = 

5  = 

6  = 

8  = 

9  = 

6.453 
12.906 
19.850 
25.807 
82.268 

88.710 
45.161 
51.618 
68.066 

9.290 
18.581 
27.871 
37.161 
46.458 

56.748 
65.032 
74.823 
83.618 

0.836 
1.672 
2.608 
8.844 
4.181 

6.017 
6.858 
6.680 
7.626 

0.4047 
0.8094 
1.2141 
1.6187 
2.Q23I 

8.4881 
2.8328 
3  2375 
8.6422 

CfUBIO. 


Cubic  Inches  to 
Cubic  Centi- 
metres. 

Cubic  Feet  to 
Cubic  Metres. 

Cubic  Yards  to 
Cubic  Metres. 

Bushels  to 
Hectolitres. 

1  = 

2  = 

3  = 

4  = 

5  = 

6  = 

8^ 
9  = 

16.387 
88.774 
48.161 
65.549 
81.996     - 

98.383 
114.710 
181.097 
147.484 

0.02832 
0.a'V668 
0.08405 
0.1 1327 
0.14158 

0.16990 
0.198i» 
0.226M 
0.85486 

0.765 
1.529 
2.294 
3.058 
S.tfiS 

4.587 
5.3.'S2 
6.116 
6.881 

0.35212 
0.70485 
1.06727 
1.40969 
1.76211 

2.11454 
2.46696 
2.81938 
8.17181 

24 


ARITHMETIC. 
CAPACITY. 


Fluid  Dracbms 

to  Millilitres  or 

Fluid  Ounces  to 

Quarts  to  Litres. 

QalloDs  to  Litres. 

Cubic  Centi- 

Millilitres. 

metres. 

1  = 

3.70 

29.57 

0  946.36 

8.78544 

2  = 

7.39 

59.15 

1.89272 

7  57088 

8  = 

11.09 

88.72 

2.83908 

11.86682 

4  = 

14.79 

11880 

8.78544 

15.14176 

6  = 

18.48 

147.87 

4.78180 

18.927a) 

6  = 

22.18 

177.44 

5.67816 

82.71264 

7  = 

25.88 

207.02 

6.62462 

26.49808 

8  = 

29.07 

286.59 

7.57088 

80.28352 

9  = 

88.28 

266.16 

8.61724 

84.06896 

WEIGHT. 


Grains  to  MUli- 
gramroes. 

ATolrdupois 
Ounces  to 
Gfluiiniee. 

AToirdupois 

Pounds  to  Kilo- 

gramtues. 

Troy  Ounces  to 
Grainmes. 

1  = 

2  = 
8  = 

4  = 

5  = 

6  = 

7  = 

8  = 

9  = 

64.7989 
129.5978 
194.8968 
259.1957 
828.9946 

888.7986 
453.5924 
518.3914 
683.1903 

28.8495 
66.6991 
85.0486 
118.8981 
141.7476 

170.0972 
198.4467 
226.7962 
255.1457 

0.45859 
0.90719 
1.86078 
1.8HS7 
8.80796 

S.72156 
8.17516 
3.62874 
4.08288 

81.10348 
62.20696 
98.81044 
121.41892 
166.51740 

186.62089 
217.72487 
248.82785 
279.98188 

1  chain  zz      20.1169  metres. 

1  square  mile    =  259  hectares. 
1  fathom           =        1.829  metres^ 

1  nautical  mile  =  1853J27  metres. 
1  foot                 =        0.804801  metre. 

1  avoir,  pound  r=  458.6924277  gram. 
16432.35689  grains    =        1  kilogramme. 


Tableii  for  Convertlns  IT,  fl.  Welerhta  and  jlleasares 
metric  to  Onstoinary. 


LINEAR, 


Metres  to 
Inches. 

Metres  to 
Feet. 

Metres  to 
Yards. 

Kilometres  to 
Miles. 

1  = 
8  = 
6  = 
6  = 

8  = 

9  = 

89.8700 
78.7400 
118.1100 
157.4800 
196.8500 

286.2200 
275.5900 
314.9000 
854..3300 

3.28088 
6.56167 
9.84250 
13.12333 
16.40417 

19.68500 
82.96.^83 
26.24667 
89.62750 

1.093611 
2.187222 
3.-.>80833 
4.374444 
5.468a56 

6.561667 
7.655278 
8.748889 
9.842500 

0.62187 
1 .24274 
1  86411 
2.48548 
8.10685 

8.72822 
4.34959 
4.97096 
6.69283 

METRIC  COKrEBSlON  TABLES. 
SQUARE. 


25 


Square  Oenti- 

metresto 
Sqiuire  Inches. 


Square  Metres 
to  square  Feet 


Square  Metres 
to  Square  Tarda. 


Hectares  to 
Acres. 


0.1550 
0.8100 
0.4650 
0.6200 
0.7750 

0.9800 
1.0680 
1.2400 
1.8860 


10.764 
21.688 
82.292 
48.065 
63.819 

64.688 
75.847 
86.111 
06.874 


1.196 
2.892 
8.588 
4.784 
6.960 

7.176 
8.873 
9.668 
10.764 


2.471 
4.942 
7.418 
9.884 
12.855 

14.826 
17.297 
19.768 
28.880 


CUBIC. 


Cubic  Oeiitl- 

metres  to  Cubic 

Inches. 

Cubic  Deci- 

metres  to  Cubic 

Inches. 

Cubic  Metres  to 
Cubic  Feet. 

Cubic  Metres  to 
Cubic  Yards. 

1  = 

0.0610 

61.028 

86.814 

1.808 

2  = 

0.12% 

122.047 

70.629 

2.616 

8  = 

0.1881 

188.070 

106.948 

8.924 

4  = 

0.M41 

244.098 

141.256 

6.282 

5  = 

0.8061 

806.117 

176.572 

6.540 

6  = 

0.8661 

866.140 

211.887 

7.848 

7  = 

0.4m 

427.168 

»I7.801 

9.156 

8  = 

0.4888 

488.187 

282.616 

10.464 

9  = 

0.6488 

649.810 

817.880 

11.771 

CAPACITY. 


MtlUlitres  or 
Cubic  Oenti 
litres  to  Fluid 
1    Drachms. 

Oentilitrw 
to  Fluid 
Ounces. 

Litres  to 
Quarts. 

Dekalitres 

to 

QalloDB. 

Hektolitres 

to 

Bushels. 

1  =             0.87 
2=            0.54 
3  =             0.81 
4=             1.08 
5=             1.85 

6=r               1.02 
7=    ,          1.89 
H=            2.16 
9=             8.4S 

0.888 
0.676 
1.014 
1.852 
1.691 

2.020 
2.868 
8.706 
8.048 

1.0667 
2.2181 
8.I70O 
4.2207 
5.2834 

6.3401 
7.3968 
8.4534 
9.5101 

2.6417 
5.2834 
7.9261 
10.6668 
18.2086 

15.8602 
18.4919 
21.1886 
23.7758 

2.8875 
5.6760 
8.6125 
11.3500 
14.1875 

17.0250 
19.8625 
22.7000 
25.5376 

36 


ARITHMETIC. 
WEIGHT. 


MillifframmeB 
to  Grains. 

Kilogrammes 
to  Grains. 

HectoRrrammes 
(100  grammes) 
to  Ounces  Av. 

Ktlograrnmes 

to  Pounds 

Avoirdupois. 

1  = 

8  = 
8  = 

4  = 
6  = 

6  = 

8  = 

9  = 

0.01648 
0.08086 
0.046.« 
0.06178 
0.07716 

0.09850 
0.10808 
0.18846 
0.18880 

15488.86 
80864.71 
46897.07 
61789.48 
77161.78 

92594.14 
108086.49 
188458.86 
188891.81 

8.6274 
7.0648 
10.6888 
14.1006 
17.6870 

21.1644 
24.6918 
28.2192 
81.7466 

2.20462 
4.40984 
6.61886 
8.81849 
11.08811 

18.28778 
15.48885 
17.68607 
10.84150 

WEIGHT— (Continued). 


1  = 

2  = 
8  = 

4  = 

5  = 

6  = 

7  = 

8  = 
0  = 


Quintals  to 
Pounds  Ay. 


280.46 
440.98 
661.88 
881.84 
1108.80 

1828.76 
1548.88 
1768.68 
1984.14 


Milliers  or  Tonnes  to 
Pounds  Av. 


22046 
4400.2 
6613  8 
8818.4 
11083.0 

18287.6 
15482.2 
17686.8 
19641.4 


Grammes  to  Ounces, 
Troy. 


0.08215 
0.06480 
0.09645 
0.18860 
0.16075 

0.19890 
0.8S506 
0.25781 
0.8 


The  only  authorized  material  statidard  of  customary  length  is  the 
Troughton  scale  belonging  to  this  office,  whose  length  at  59*.62  Fahr.  con- 
forms to  the  British  standard.  The  yard  in  use  in  the  United  States  is  there- 
fore equal  to  the  British  yard. 

The  only  authorized  material  standard  of  customaiy  weight  is  the  Troy 
pound  of  the  mint.  It  is  of  brass  of  unknown  density,  and  therefore  not 
suitable  for  a  standard  of  mass.  It  was  derived  from  the  British  standard 
Troy  pound  of  1758  by  direct  comparison.  Tlie  British  Avoirdupois  pound 
was  aiHO  derived  from  the  latter,  and  contains  7000  grains  Troy. 

The  grain  Troy  is  therefore  the  same  as  the  grain  Avoirdupois,  and  tiie 
pound  Avoirdupois  in  use  in  the  Uuited  States  is  equal  to  the  British  pound 
Avoirdupois. 

The  metric  system  was  legalized  in  the  United  States  in  1866. 

By  the  concurrent  action  of  the  principal  governments  of  the  world  an 
International  Bureau  of  Weights  and  Measures  has  been  established  near 
Paris. 

The  International  Standard  Metre  is  derived  from  the  Mdtre  des  Archives, 
and  its  length  is  defined  by  the  distance  between  two  lines  at  0**  OenClgrade, 
on  a  platinum-iridium  bar  deposited  at  the  lotematlonal  Bureau. 

The  International  Standard  Kilogramme  is  a  mass  of  platinum-lrtdlum 
deposited  at  the  same  place,  and  its  weight  in  vacuo  is  the  same  as  that  of 
tlie  Kilogramme  des  Archives. 

Copies  of  these  international  standards  are  deposited  in  the  office  of 
Btauaard  weights  and  meaHures  of  the  U.  S.  Coast  and  Geodetic  Survey. 

The  litre  is  equal  to  a  cubic  decimetre  of  water,  and  it  is  measured  by  the 

auantity  of  distlUed  water  which,  at  its  maximum  density,  will  counterpoise 
iie  standard  kilogramme  in  a  vacuum;  the  volume  of  such  a  quantity  of 
water  being,  as  nearly  as  has  been  ascertained,  equal  to  a  cubic  decimetre. 


WEIGHTS  AND  MBA8UBES — COMPOUND  UNITS.      37 


COMPOUND   UNITS. 

leasures  of  Pressure  and  IVeli^lit. 


1  lb.  per  square  inch. 


1  atmosphere  (14.7  lbs.  per  sq.  Id.).  = 


I  inch  of  water  at  es?  F. 


1  inch  of  water  at  88*  F. 


1  foot  of  water  at  O^^"  F. 


1  inch  of  mercury  at  eaf  F. 


144  lbs.  per  square  foot. 

sj.0856 108.  of  mercury  at  82*  F. 

2.0416 («•  F. 

2.809  ft.  of  water  at  6*j*  F. 
27.71  ins.  *♦      "     '»  6-2*  F. 
2116.3  lbs.  per  square  foot. 

83.947  ft.  of  water  at  6-2*  F. 
80  ins.  of  mercury  at  62*  F. 

29.922  Ins.  of  mercury  at  8-2«  F. 
.760  millimetres  of  mercury  at  3;!*  F. 
.0861  lb.  per  square  inch. 
6.196  lbs.   "       "       foot. 
.0786  in.  of  mercury  at  62*  F. 
.  .  5.2021  lbs.  per  square  foot. 
-}     .086126  lbs.  per  *'      inch. 
.488  lb.  per  square  inch. 
62.356  lbs.  "         '»      foot. 
.88:i  in.  of  mercury  at  02*  F. 
.49  lb.  per  square  inch. 
msOlbs.  "        '•      foot. 
1.132  ft.  of  water  at  62*  F. 
18.58  ina 62*  F. 


HFeUrlit  of  One  Cubic  Foot  of  Pure  Water. 

At  82*  F.  (frwalnff-pofnt) 02.418  lbs. 

''   89.1*  F.  (maximum  deusity) 6*2.425  " 

-  62*  F.  (Standard  temperature) 62.8.^5  " 

"  21  <•  F.  (boiling-point,  under  1  atmosphere) 69.76     " 

American  gallon  =  281     cubic  Ins.  of  water  at  62*  F.  =  8.3856  lbs. 

British  "       =  277.274  "       "     '^       =  10  lbs. 

measures  of  Work,  Poirer,  and  Duty. 

Work.— The  sustained  exertion  of  pressure  through  space. 

Unit  of  irork.— One  foot-pound,  i.e.,  a  pressure  of  one  pound  exerted 
through  a  space  of  one  fopt. 

Horse-poirer.— The  rate  of  work.  Unit  of  horse-power  =  83,000  ft.  - 
lbs.  per  minute,  or  550  ft.-lbe.  per  second  ==  1,960,000  ft. -lbs.  per  hour. 

Heat  imlt  =  heat  required  to  raise  1  lb.  of  water  1*  F.  (from  89*  to  40*). 

88000 

Hone-power  expressed  in  heat  units  =  -==^-  =  42.416  heat  units  per  min- 
ute =  .707  heat  unit  per  second  =  2545  heat  units  per  hour. 

1  Ih  of  tnt^  Mr  H  l»  mr  honi—  i  ^WO.OOO  ft.-lb8.  per  lb.  of  fuel. 
I  ID.  or  ruei  per  u.  i .  per  nour=  ^  g^g^  j^^^^^  ^^^^       „ 

1.000,000  ft.-lbs.  per  lb.  of  fuel  s  1.98  lbs.  of  fuel  per  H.  P.  per  hour. 
5280      22 
Yeloelty.— Feet  per  second  =  ^^^  ~  15  **  ni>>««  per  hour. 

Gross  tons    per 


lUe  =  ^3^  =  ~  lbs.  per  yard  (single  rail.) 


Vrenek  and  Brtttsk  Bqnlvalents  of  UTel^kt  and  Press- 
ure per  Unit  of  Area. 

FanrcH.  British. 

1  gramme  per  square  millimetre  -       1.422  lbs.  per  square  inch. 

1  kUoirramme  per  square  **  =1422.82     "      " 

1  '*  **         »•      centimetre  =     14.228   *»      "       •*         " 

1.0835  kilogrammes  per  square  centimetre  (.-.it'-      •<     .«       >.         >« 

(1  atmosphere)  \  ' 

0.070908  kilogramme  per  square  centimetre  =  I  lb.  per  square  inch- 


98 


ABITUJIBTIC. 


WIBB   AND  SHBBT-lVBTAEi 

CtAVGBS  GOMPARBD. 

Number  of 
Gauge. 

III 

III 

^      CO 

hi 

"  1 

Erillsh  Imperial 

Standard 

Wire  Gauge. 

(Legid  Standard 

in  Great  Britain 

since 

Marvh  1, 18Si.) 

Iflilt 

II 

incb. 

Inch. 

inch. 

iDCU. 

inch. 

milUm. 

inch. 

0000000 

.49 

.500 

12.7 

.5 

7/0 

000000 

.46 

.464 

11.78 

.409 

6,^0 

00000 

.43 

.432 

10.97 

.488 

5/'0 

0000 

.454 

.46 

.898 

.4 

10.16 

.406 

4/0 

000 

.425 

.40964 

.862 

.878 

9.46 

.875 

8/0 

00 

.88 

8648 

.881 

.848 

8.84 

.844 

2/0 

0 

.84 

.82480 

.807 

.824 

6.38 

.818 

0 

1 

.8 

.2898 

.288 

.227 

.8 

7.88 

.261 

1 

2 

.284 

.26768 

.268 

.219 

.276 

7.01 

.266 

8 

8 

.259 

.22942 

.244 

.812 

.252 

6.4 

.85 

8 

4 

.288 

.20181 

.236 

.207 

.283 

6.89 

.284 

4 

5 

.22 

.18194 

.207 

.204 

.212 

6.88 

.219 

6 

6 

.208 

.16202 

.192 

.201 

.192 

4.88 

.203 

6 

7 

.18 

.144-28 

.177 

.199 

.176 

4.47 

.188 

7 

8 

.165 

.12849 

.162 

.197 

.16 

4.06 

.172 

8 

0 

.148 

.11443 

.148 

.194 

.144 

8.66 

.156 

9 

10 

.184 

.10189 

.136 

.191 

.128 

8.26 

.141 

10 

11 

.18 

.09074 

.12 

.188 

.116 

2.96 

.125 

11 

18 

.109 

.08081 

.106 

.185 

.104 

9.64 

.109 

12 

18 

.095 

.07196 

.092 

.1S8 

.092 

9.84 

.094 

18 

14 

.068 

.06408 

.08 

.180 

.06 

2.08 

.078 

11 

15 

.078 

.05707 

.072 

.178 

.072 

1,88 

.07 

15 

16 

.065 

.06068 

.063 

.175 

.064 

1.68 

.0625 

16 

17 

.058 

.(M526 

.054 

.172 

.056 

1.48 

.0568 

17 

18 

.049 

.0408 

.047 

.168 

.048 

1.22 

.06 

18 

10 

.042 

.08569 

.041 

.164 

.04 

1.01 

.0488 

19 

20 

.085 

.03196 

.085 

.161 

.086 

.91 

.0875 

20 

21 

.033 

.02846 

.082 

.157 

.082 

.81 

.0844 

81 

22 

.028 

.02535 

.028 

.156 

.028 

.71 

.0318 

88 

83 

.085 

.02257 

.025 

.158 

.034 

.61 

.J0981 

88 

24 

.022 

.OiiOl 

.0)28 

•^51 

.022 

.66 

.086 

91 

25 

.02 

.0179 

.03 

.148 

.02 

.61 

.0919 

85 

26 

.018 

.01594 

.018 

.146 

.018 

.46 

.0188 

86 

27 

.016 

.01419 

.017 

.143 

.0164 

.42 

.0178 

87 

98 

.014 

.01864 

.016 

.139 

.0148 

.88 

.0156 

88 

29 

.018 

.01126 

.015 

.184 

.0186 

.85 

.0141 

29 

80 

.012 

.01009 

.014 

.187 

.0124 

.81 

.0125 

80 

81 

.01 

.00698 

.0185 

.120 

.0116 

.29 

.0109 

81 

82 

.009 

.00795 

.018 

.115 

.0108 

.27 

.0101 

32 

88 

.008 

.00708 

.011 

.112 

.01 

.85 

.0094 

83 

84 

.oor 

.0068 

.01 

.110 

.0092 

.28 

.0086 

84 

85 

.005 

.00561 

.0095 

.106 

.0084 

.21 

.0078 

35 

86 

004 

.006 

.009 

.106 

.0078 

.19 

.007 

86 

87 

.00445 

.0085 

.108 

.0068 

.17 

.0066 

87 

88 

.00896 

.00*< 

.101 

.006 

.15 

.0068 

36 

89 

.00853 

.0075 

.099 

.0052 

.18 

89 

40 

.00814 

.007 

.097 

.0048 

.12 

40 

41 

.006 

.0044 

.11 

41 

42 

.092 

.004 

.10 

48 

43 

.088 

.0038 

.09 

48 

44 

.065 

.0032 

.06 

44 

46 

.081 

.0098 

.07 

45 

46 

.079 

.0034 

.08 

46 

47 

.077 

.008 

.05 

47 

48 

.076 

.0016 

.04 

48 

40 

.072 

.0012 

.08 

40 

50 

.069 

.001 

.086 

60 

WIRE  QAUa£  TABLES. 


29 


BBISOlf ,  OI 


OmCIJIiAR  Mill  OAUOK,   FOB  EIiBC* 
TBIOAIi  uriRBS. 


(Huge 
Num- 

Circular 
Mils. 

Diam- 
eter 

Gauge 
Num- 

Circular 
Mils. 

Diam- 
eter 

Gauge 
Num- 

Circular 
Mils. 

Diam- 
eter 

ber. 

Id  Mils. 

oor. 

in  Mils. 

ber. 

in  Mils. 

3 

8,000 

54.78 

TO 

70,000 

264.58 

190 

190,000 

485.89 

5 

6,000 

70.72 

75 

75,000 

273.87 

300 

200,000 

447.32 

8 

8,000 

80.45 

80 

80,000 

28*^.85 

220 

220.000 

469.06 

12 

l-.»,000 

109. .% 

86 

85,000 

291.55 

240 

240,000 

489.90 

IS 

15,000 

ldsi.48 

90 

90.000 

300.00 

260 

2Q0.000 

509.91 

80 

ao,ooo 

141.48 

95 

95,000 

308.23 

280 

280,000 

589.16 

» 

25.000 

168.1? 

100 

100,000 

816.23 

800 

800,000 

547.73 

80 

90,000 

17S.81 

no 

110,000 

331.67 

8:20 

320.000 

665.69 

35 

35,000 

187.00 

120 

120,000 

U6.42 

840 

840,000 

588.10 

40 

40,000 

800.00 

180 

180,000 

300.56 

860 

860.000 

600.00 

45 

45,000 

212.14 

140 

140,000 

874.17 

BO 

60,000 

a!8.61 

150 

160,000 

887.30 

65 

65,000 

234.58 

160 

160,000 

400.00 

60 

60.000 

244.96 

170 

170,000 

412.32 

65 

66,000 

254.96 

180 

180,000 

4-44.27 

TDTIST  DRII^Ii  AND  8TSBI«   WIRE  GAVGR. 

(Morse  Twist  Drill  and  Machine  Co.) 


Xo. 

«».l 

No. 

8ise. 

No. 

Sise. 

No. 

Sise. 

jNo. 

Size. 

No. 

Size. 

ipcb.  1 

inch 

inch. 

locb. 

incli. 

Inch. 

.2«0  ' 

11 

.1910 

21 

.1590 

31 

.1200 

41 

.0960 

61 

.0670 

.2<10  < 

12 

.1890 

22 

.1670 

88 

.1160 

42 

.0985 

52 

.0635 

.2130  , 

18 

.1860 

23 

.1540 

38 

.1180 

43 

.0890 

53 

.0595 

.2000 

14 

.1820 

24 

.1580 

Zi 

.1110 

44 

.0860,1  54 

.0550 

.8055  1 

15 

.1800  1 

25 

.1495 

35 

.1100 

45 

.08301    55 

.0620 

.2010       16 

.1770  1 

26 

.1470 

86 

.1065 

40 

.0810  I  56 

.0465 

.2010    1  17 
.190J   I  18 

.1730 

27 

.1440 

37 

.1040 

47 

.0786     57 

.0430 

.1605  1 

^8 

.1405 

38 

.1015 

48 

.0700     58 

.0420 

.1900      19 

.1660 

29 

.1860 

89 

.0995 

49 

.0780     59 

.0410 

10 

■'•"II* 

.1610  j 

80 

.1285 

40 

.0U80 

50 

.OruOi    00 

.0400 

ST1JR89  8TEBI«  UTIRK  GAUGE. 

(F*or  Nos.  1  to  50  see  table  on  page  28.) 


Ko. 

Size. 

No. 

Sise.    ! 

No. 

Size. 

"No.I 

Size. 

'No.|  Size.';  No.' Size. 

inch. 

inch.    ' 

inch. 

,1 

inch. 

,  inch  ,        i  inch. 

Z 

.413 

P 

.888    . 

F 

.257 

'■  51 

.066 

,  61  1    038   1  71      .086 

\ 

.401 

O 

.816    1 

.802    1 

E 

.280 

t  62 

.068 

1  62  1   .037  li  72      .024 

X 

.897 

N 

D 

.846 

|l  63 

.058 

63  I   .086  i|  73  ;   .0« 

w 

.386 

M 

.895 

C 

.248 

|i  54 

.065 

64  I   .035  \-  74 

.082 

V 

.877 

I> 

.290    1 

B 

.288 

1  ^ 

.060 

65  ;  .088  li  75 

.020 

u 

.868 

K 

.881     1 

A 

.284 

.1  66  1 

.045 

,  66  1  .062    1  76 

.018 

T 

.358 

J 

.277    1 

1 

See 

i    57 

.042 

67  '  .081       77 

.016 

8 

.848 

1 

.872    1 

to 

-{page 

1  56  1 

.041 

1  68  1  .030      78 

.015 

K 

.888 

H 

.866 

SO 

a 

11  59  1 

.040 

69  1  .089  11  79 

.014 

<^ 

.382 

G 

.261    1 

II  001 

.089 

1  70  :  .027  1'  80 
t        1            it 

.018 

The  Stubs'  Steel  Wire  Gauge  is  used  in  measuring  drawn  steel  wire  or 
drill  rods  of  Stubs'  make,  and  Is  also  used  by  many  makers  of  American 
drill  rods. 


30  ARITHMETIC. 

THB  BDI80N  •»  €IBCVI«AR  Bill.  HimB  GA1JGB. 

(For  table  of  copper  wires  by  thi8*Kttuge«  Klviiif?  weights,  electrical  resist- 
aoces,  etc..  fwe  Copper  Wire.) 

Mr.  O.  J.  Field  {Stevens  Iivdicator^  July,  1887)  thus  describes  the  origin  of 
the  Edison  gauge: 

The  Edison  company  experienced  inconvenience  and  loss  by  not  having  a 
wide  enough  range  nor  suffleienr.  number  of  sizes  in  the  existing  gauges. 
This  was  felt  more  particularly  in  the  central-station  woik  in  making: 
electrical  determinations  for  the  street  system.  Tliey  were  compelled  to 
make  use  of  two  of  the  existing  gauges  at  least,  thereby  introducing  a 
complication  that  was  liable  to  lead  to  mistakes  by  the  contractors  and 
linemen. 

In  the  incandescent  system  an  even  distribution  throughout  the  entire 
system  and  a  uniform  pressure  at  the  point  of  delivery  are  obtained  by  cal- 
culating for  a  given  maximum  percentage  of  loss  from  the  potential  ss 
delivered  from  the  dynamo.  In  carrying  this  out,  on  account  of  lack  of 
.  regular  sizes,  it  was  often  necessary  to  use  larger  sizes  than  the  occnslon 
demanded,  and  even  to  assume  new  sizes  for  large  underground  conductors. 
It  was  also  found  that  nearly  all  manufacturers  cased  their  calculation  for 
the  conductivity  of  their  wire  on  a  varic^ty  of  units,  and  that  not  one  used 
the  latest  unit  as  adopted  by  the  BiitiKh  Association  and  determined  from 
Dr.  Matthiessen's  experiments  ;  and  as  this  was  the  unit  employed  in  the 
manufacture  of  the  Edison  lamps,  there  was  a  further  reason  for  construct- 
ing a  new  gauge.  The  engineering  department  of  the  Edison  company, 
knowing  tlie  requirements,  have  designed  a  gnuge  that  has  the  widest 
range  obtainable  and  a  large  numbei*  of  sizes  which  increase  in  a  regular 
and  uniform  manner.  Tlie  baMiti  of  the  graduation  is  the  sectional  area,  and 
the  number  of  the  wire  corresponds.  A  wire  of  100,000  circular  mils  area  is 
No.  100 ;  a  wire  of  one  half  the  size  will  be  No.  60  ;  twice  the  size  No.  300. 

In  the  older  gauges,  an  the  number  increased  the  size  decrcai-^i.  With 
this  gauge,  however,  the  number  increases  with  the  wire,  and  the  number 
multiplied  by  10U0  will  K'ive  the  circular  mils. 

Tlie  weight  per  mil-foot,  0.0000030*2705  pounds,  agrees  with  a  specific 
gravity  of  8.889,  which  is  the  latest  figure  given  for  copper.  The  ampere 
capacity  which  is  given  was  deduced  from  experiments  made  in  the  com- 
pany's laboratory',  and  is  based  on  a  rise  of  temperature  of  60®  F.  in  the  wire. 

In  1898  Mr.  Field  writes,  concerning  gauges  In  use  bj'  electricnl  engineers: 

The  B.  and  8.  gauge  seems  to  be  in  general  use  for  the  smaller  sizes,  up 
to  100,000  c.  m..  and  in  some  cases  a  little  larger.  From  between  one  and 
two  hundred  thousand  circular  mils  upwards,  the  Edison  gauge  or  ita 
equivalent  is  practically  in  use,  and  there  is  a  general  tendency  to  designate 
all  sizes  above  this  In  circular  mils,  specifying  a  wire  as  200,000,  400,000,  500,- 
000,  or  1.000.000  c.  m. 

In  the  electrical  business  there  Is  a  large  use  of  copper  wire  and  rod  and 
other  materials  of  these  large  sizes,  and  in  ordering  them,  speaking  of  them, 
specifying,  and  in  every  other  use,  the  general  method  is  to  stniplj'  Hpecify 
the  cii^ular  milage.  I  think  it  is  going  to  be  the  only  system  in  the  ruture 
for  the  designation  of  wires,  and  the  attaining  of  it  means  practically  the 
adoption  of  the  Rdison  gauge  or  the  method  and  basis  of  this  gauge  as  the 
correct  one  for  wire  sizes. 

THB   V.  S.  STANDARD  GAITGE  FOR  SHKBT  AND 
PLATK  IRON  AND  STEKL,  1893. 

Th^'re  Is  in  this  country  no  uniform  or  standard  gauge,  and  the  same 
numbers  in  different  gauges  represent  different  thicknesses  of  sheets  or 
plates.  This  has  given  rise  to  much  misunderstanding  and  friction  between 
employers  and  workmen  and  mistakes  and  fraud  l>etween  dealers  and  con- 
sumers. 

An  Act  of  Congress  in  1893  established  the  Standard  Gauge  for  sheet  iron 
and  steel  which  is  given  on  the  next  page.  It  is  based  on  the  fact  that  a 
cubic  foot  of  iron  weighs  480  pounds. 

A  sheet  of  iron  1  foot  square  and  1  inch  thick  weighs  40  pounds,  or  640 
ounces,  and  1  ounce  in  weight  should  be  1/640  inch  tliick.  The  scale  has 
been  arranged  so  that  each  descriptive  number  represents  a  certain  number 
of  ounces  in  weight  and  an  equal  nunibtfr  of  640ths  of  an  inch  in  thickness. 

The  law  enacts  that  on  and  after  July  1, 1H98,  the  new  gauge  shall  be  used 
in  det«miiniug  duties  and  taxes  levied  on  sheet  and  plate  iron  and  steel;  and 
tlu^t  in  its  applicatiou  a  variation  of  "iy^  |)er  cent  either  way  may  be  allowed. 


GAUGlS   FOK  SHEET  AND   PLATK  IRON  AND  STEEL.   31 


S.  STANDARD  GA176B  FOR  8HBKT  AND  PI«ATB 
IRON  AND  STBKI.,   1893. 


II 

Aiiproxiniate 

Thick  neti-s  in 

Fractions  of 

an  Inch. 

Approximate 
Thickness  in 

Decimal 

ParU  of  an 

Inch. 

Approximate 
Thickness 

in 
Millimeters. 

Weight  per     1 
Square  Foot 

in  Ounces 
Avoirdupois. 

Weightper 

Square  Foot 

in  Pounds 

Avoirdupois. 

^1 

III 

Weigiitper 
Square  Meter 

m  Pounds 
Avoirdupois. 

>3iJO0O0 

1-a 

0.5 

12  7 

820 

20. 

9.072 

97.65 

216.28 

ooixiao 

15-82 

0.46875 

11.00626 

800 

18.75 

S.505 

91.55 

201.92 

(W)00 

7-16 

0.4375 

11.1126 

280 

17.60 

7.938 

86  44 

188.37 

oooo 

18-32 

0.40625 

10.81875 

260 

16.25 

7.871 

79.38 

174.91 

000 

8-8 

0.875 

0.525 

240 

15. 

6.804 

73.24 

161.46 

OQ 

11-82 

0.84875 

8.78125 

220 

18.76 

6  287 

67.13 

148  00 

o" 

6-16 

0.8125 

7.9875 

200 

12.60 

5.67 

01.08 

184.55 

1 

9-82 

0.28125 

7.14875 

180 

11.25 

5.108 

54.9.S 

121.09 

1 

17-64 

0.266G25 

6.746875 

170 

10.625 

4.819 

51.88 

114.87 

8 

1-4 

0.25 

6.36 

160 

10. 

4.536 

48.82 

107.64 

4 

15-64 

0.234375 

5.953125 

150 

9.375 

4.252 

46.77 

100.91 

6 

7-82 

0.21875 

5.65625 

140 

8.75 

3.960 

42.72 

94.18 

6 

I!{-«4 

0.20»125 

5  159376 

180 

8.125 

3.6»> 

39.67 

87.45 

8-16 

0.1875 

4.7625 

120 

7.5 

3.402 

36.62 

80.72 

8 

11-64 

0.171875 

4.865025 

110 

6.875 

3.118 

38.57 

74.00 

9 

5-32 

0.156-^5 

8.95875 

100 

6.25 

2.835 

30.52 

67.27 

10 

9-64 

0.140626 

3.571875 

90 

5.625 

2  552 

27.46 

60.55 

11 

1-8 

0.125 

8.175 

80 

5. 

2.268 

24.41 

58.82 

\l 

7-64 

0.108875 

2.778125 

70 

4.375 

1.984 

21.86 

47.09 

IS 

8-32 

0.09875 

2.38125 

60 

8.75 

1.701 

18.81 

40.86 

14 

5-64 

0.07B12S 

1.084375 

50 

3.125 

1.417 

15.26 

38.64 

15 

9-128 

0.0708125 

1.7869375 

45 

2.8125 

1.276 

13.73 

80.27 

16 

1-16 

0.0625 

1.5875 

40 

2.5 

1.134 

12.21 

26.91 

17 

9-160 

0.06625 

1.42875 

86 

2.25 

1.021 

10.09 

24.22 

-   18 

1-20 

0.06   - 

1.27  - 

32 

2. 

0.9072 

9.765 

21.58 

19 

7-160 

0.04877S 

1.11125 

28 

1.75 

0.7988    8.544 

18.84 

90 

8-8U 

0.0375 

0.9525 

24 

1.50 

0.6804    7.324 

16.15 

%\ 

n-8i0 

0.084375 

0.878125 

22 

1  875 

0.6287 

6.713 

14.80 

« 

1-82 

0.08125 

0.793750 

20 

1.25 

0.567 

6.ia3 

13  46 

23 

8-^20 

0.028125 

0.714375 

18 

1.125 

0.5103 

5.493 

12.11 

t4 

1-^ 

O.0S5 

0  685 

16 

1. 

0  4536 

4.882 

10.76 

25 

7-320 

0.0-il875 

0.555625 

14 

0.875 

0.8960 

4.272 

9.42 

S6 

8-lGO 

0.01876 

0.47025 

12 

0.75 

0.3^02 

3.662 

8.07 

27 

11-M) 

0.0171875 

0.4865625 

11 

0.6875 

0.8119 

3.857 

7.40 

» 

1-64 

0.015625 

0.896875 

10 

0.625 

0.2835 

8.052 

6.73 

29 

9-640 

0.0140825 

0.8571875 

9 

0.5625 

0.2551 

2.746 

6.05 

30 

1«) 

0.0:25 

0.8175 

8 

0.5 

0.22G8 

2441 

5  as 

81 

7-6lrt 

0.0109375 

0.2778126 

7 

0  4375 

0.19H4 

2.l:i6 

4.71 

%Z 

IS~1-J80 

O.OIOI.VWS 

0.25796875 

6^ 

0. 40625 

0.1848 

l.fl«3 

4.37 

83 

8-820 

0.009875 

0.288125 

6 

0.375 

0.1701 

1.831 

4.04 

84 

11-1280 

0  00650875 

0.218S8125 

5^ 

0..S4875 

0  1559    1.6:8 

8  70 

^ 

5-640 

0.0078125 

0.1984375 

5 

0.3125 

0.1417    1.526 

3  86 

86 

»-13H0 

0  00708125 

0  17850375 

J^ 

o-esi-i.'. 

0.1276    1.373 

8.03 

87 

17-2BO0 

0.006640625 

0.168671875 

o.2t'>r,e25 

0.1205    1  2«7 

2.87 

« 

1-160 

0.00625 

0.15876 

4 

0.25 

0.1  1:M    1  221 

1 

2.69 

32 


MATHEMATICS. 


The  Decimal  Gauffe*— The  legalization  of  the  standard  sheet-metal 
gaufce  of  189S  and  its  adoption  by  some  manufacturers  of  sheet  iron  have 
only  added  to  the  existing  confusion  of  grauges-  A  ioint  committee  of  the 
American  Society  of  Mechanical  Enjdneers  and  the  American  Railway 
Master  Mechanics'  Association  in  18!)5ajrreed  to  recommend  the  use  of  the 
decimal  gauge,  that  is,  a  gauge  whose  number  for  each  thickness  Is  the 
number  of  thousandths  of  bn  inch  In  that  thickness,  and  also  to  recommend 
**  llie  abandonment  and  disuse  of  the  various  other  gauges  now  in  use,  as 
tending  to  confusion  and  error/*  A  notched  gauge  of  oval  form,  as  shown 
in  the  cut  below,  has  come  into  general  use  as  a  standard  form  of  the  dec- 
imal gauge,  but  for  accurate  measurement  Ites  indications  should  be  checked 
by  the  use  of  a  micrometer  gauge  reading  to  thousandths  of  an  inch. 
UTelffbt  of  Sheet  Iron  and  SteeK  Thlckne»»  bj  Decimal 
Gauge* 


09 

B 

1 

Weightper 
Square  Foot 

OB 

c 

1 

Weik!ht_per 
Square  Foot 

, 

£ 

? 

in  Pounds. 

. 

o 

o 

in  Pounds. 

1 

it 

B 

i 

1 

08 
O 

1 

a-: 

1? 

ty 

a«-i 

CO 

a 

g& 

|35 

"§ 

g^ 

g 

P 

"^^5 

ft 

-< 

< 

►"• 

CC 

ft 

< 

< 

GO 

0.002 

1/500 

0.05 

0.08 

0.082 

o.oocT 

1/16  - 

1.82 

8.40 

8.448 

0.00* 

1/250 

0.10 

0.16 

0.1G3 

0.065 

18/200 

1.65 

8.60 

2  6.52 

0.006 

3/r,oo 

0.15 

0.24 

0.245 

0.070 

7/100 

1.78 

8.80 

2.H56 

0.008 

1/125 

0.20 

0.82 

0.326 

0.075 

3/40 

1.90 

8.00 

3.060 

0.010 

1/100 

0.25 

0.40 

0.408 

0.080 

2/:i5 

8.08 

8.80 

8.261 

0.012 

3/250 

0.30 

0.48 

0.490 

0.085 

17/200 

2.16 

8.40 

3.4(W 

O.OU 

7/500 

0.86 

0.66 

0.571 

0.090 

9/100 

8.28 

8.60 

3.672 

0.016 

1/64  4- 

0  41 

0.64 

0G53 

0.095 

19/200 

8  41 

8.80 

3.876 

0.018 

9/500 

0.46 

0.78 

0.784 

0.100 

1/10 

2.64 

4.00 

4.080 

0.020 

1/50 

0  61 

0.80 

0.816 

0.110 

11/100 

8.79 

4.40 

4.488 

0  022 

11/500 

0.56 

0.88 

0  898 

0.125 

1/8 

8.18 

6.00 

6  100 

0.025 

1/40 

0.64 

1.00 

1.020 

0.135 

27/200 

3.48 

6.40 

5.508 

0.028 

7/2fS0 

0.71 

1.12 

1.142 

0.1.50 

8/20 

8.81 

6.00 

6.120 

0.0:12 

1/82  -h 

0.81 

1.28 

1.306 

0.165 

3:^/200 

4.19 

6.60 

6  73i 

0.036 

9/250 

0.91 

1.44 

1.469 

0.180 

9/.0O 

4.67 

7.20 

7.344 

0.040 

1/26 

1.02 

1.60 

1.632 

0.200 

l/.'S 

6.08 

8.00 

8.  ICO 

0.045 

9,-200 

1.14 

1.80 

1.836 

0  220 

11.  ro 

5.59 

8.80 

8.970 

oav) 

1/20 

1.27 

200 

2.040 

0.240 

6/-,'5 

6.10 

9  60 

9.79i 

O.OM 

11/200 

1.40 

2.20 

2.244 

0.250 

1/4 

0.86 

10.00 

10.200 

ALGEBRA.  88 


ALGEBBA. 

Addition.— Add  a  and  b.   Ans.  a-f  &•   Adda»6,and~e.  An8.a4-b-e. 

Adii  iu  and  —  8a.    Ans.  —  a.    Add  Sob,  —  8a6,  —  o,  —  8c.    Ads.  ^ab^4e, 

Bubirmetlon.— Subtract  a  from  b.  Ana.  b  -  a.  Subtract  —  a  from  —  6. 
Ap#.  —  ^  4-  a. 

Subtract  6  +  c  from  a.  An8.a  — b-o.  Subtract  8a*6— 9o  from  4a*6  +  c. 
Ana.  a*&  +  lOe.  Bhlk:  Caiauge  the  signs  of  the  subtrahend  and  proceed  as 
in  additioD. 

lIaltlPlleaUoii.-Multipl7  a  by  6.  Ana.  ab.  HulUpIy  ob  bya  +  b. 
Ana.  a*b  4-  ab^, 

MulUply  o  -h  6  by  a  +  b.    Ans.  (a  +  b)(a  +  b)  =  o«  +  Sob  +  &*. 

Muldply  —  a  by  ~  b.  Ans.  ab.  MulUply  -  a  by  b.  Ans.  -  ab.  Like 
signs  jjpve  plus,  unlike  siffiis  minus. 

rowers  of  iiniiibers.— The  product  of  two  or  more  powers  of  any 
number  is  the  number  with  an  exponent  equal  to  the  sum  of  the  powers: 
a*  X  a*  B  a*;  a*b*  xab  =  o«b»;  -  7ab  x  2ac  =  —  14  o'bc 

To  multiply  a  polynomial  by  a  monomial,  multiply  each  term  of  the  poly- 
nomial by  the  monomial  and  add  the  partial  products:  (Oa  —  8b)  x  8o  c=  ISiic 

—  9bc. 

To  multiply  two  polynomials,  multiply  each  term  of  one  factor  by  each 
term  of  tlie  other  and  add  the  partial  products:  (5a  -  6b)  x  (8a  -  4b)  = 
15a*-88ab  +  a4b«. 

The  square  of  the  sum  of  two  numbers  =  sum  of  their  squares  +  twice 
their  product. 

The  square  of  the  diiference  of  two  numbers  =  the  sum  of  their  squares 

-  twice  their  product. 

The  product  of  the  sum  and  difference  of  two  numbera  s  the  difference 
of  their  squares: 

(a  +  b)«  =^a'»  +  idb  +  b*;    (a  -  b)«  =a«  -  2ab  +  b«; 
(a+b)  x{a--b)  =  a*'-bK 

The  square  of  half  the  sums  of  two  quantities  is  equal  to  their  product  plus 
the  sqoara  of  half  their  difference:  (^^)'  =  ob  +  (^-^)'' 


The  square  of  the  sum  of  two  quantities  is  equal  to  four  times  their  prod- 
octii,  plus  the  square  of  their  difference:  (a  -\-  b)*  =  4ab  +  (a  -  b)* 

The  sum  of  the  squares  of  two  quantities  equals  twice  their  product,  plus 
the  square  of  their  difference:  a*  -V  b*  =  2ab  +  (a  —  b)*. 

The  square  of  a  trinomial  =  the  square  of  each  term  4-  twice  the  product 
of  each  term  by  each  of  the  terms  that  follow  it:  (a  +  b  +  c)*  =  a*  +  b*  -h 
e*4-2ab-{-2ae+9bc;  (a  -  b -c)«  =  o«-f  b«H-c« -8ab -8ac+«bc. 

The  square  of  (any  number  -^H)  »  square  of  the  number -f  the  number 
-r-  li;  =  the  number  x  (the  number  4*  1)  +  M'y 

The  product  of  any  number  +  H  hy  any  other  number  4-  ^  =  product  of 
th«  numbers  4-  half  their  sum  +  3|.  (a  +  H)  X  b 4-  V^)  =s  ab  4-  ^(a + b)+  ^. 
4Hx(H<=4X64-«(4+6)  +  ^-M4-r+M=3M.     .,       ,^ 

S^iuuro,  enbe,  4th  poiwer^  ete.^  of  a  binomial  a  +  b. 

(o  +  b)«  =  a«  +8ab  +b";   (a-^b)*  =  a» -f 8o«b 4 8ab« 4-b«; 
(a4-b)«  sza*  4-4aSb  +  6a*b<  +4ab*  4-b«. 

In  each  case  the  number  of  terms  is  one  greater  than  the  exponent  or 
the  power  to  which  the  binomial  is  raised. 

i.  In  the  first  term  the  exponent  of  a  is  the  same  aa  the  exponent  of  the 
power  CO  which  the  binomial  is  raised,  and  it  decreases  by  1  in  each  succeed- 
mfcterm. 

1.  b  appears  in  the  second  term  with  the  exponent  1,  and  its  exponent 
increases  by  1  in  each  succeeding  term. 

4.  The  coefficient  of  the  first  term  is  1. 

5.  The  coefficient  of  the  second  term  is  the  exponent  of  the  power  to 
which  the  binomial  is  raised. 

6.  The  coefficient  of  each  succeeding  term  is  found  from  the  next  pre- 
eedlog  term  by  multtplying  its  coefficient  by  the  exponent  of  a,  and  divid- 
|ax  the  product  by  a  number  greater  by  1  than  the  exponent  of  b.  (See 
Binomial  Theorem,  below.) 


84  iXGEBai. 

PArentliesMi*— When  a  narenthesis  is  preceded  by  a  plus  sign  It  may  be 
remoTed  without  cbaniriDer  the  value  of  the  expression:  a  +  6  +  (u  +  o)  = 
Sa  +  ^-  When  a  parentaeeiB  i8  preceded  by  a  minus  siffn  it  may  be  removed 
If  we  change  the  signs  of  all  the  terms  within  the  parenthesis:  1  —  (a  —  6 
.—  e)  =  1— a  +  6  +  c.    When  a  parenthesis  is  within  a  parenthesis  remove 

the  imer  one  first:  o-r6-]o-(d-e)[l  =a-  r6-|c-d  +  c[] 

A  multiplioation  sign,  X,  has  the  effect  of  a  parenthesis.  In  that  the  oper- 
ation indicated  by  it  must  be  performed  before  the  operations  of  addition 
or  subtraction.  o  +  6xa-f6  =  a+a!)  +  6;  while  (a  -f  6)  x  (a  -f  6)  = 
a«  -f  2a6  4-  ft",  and  (a  -f  6)  X  o  +  6  =  a«  -f  a6  -f  5. 

IHtIbIoii.— The  quotient  is  positive  when  the  dividend  and  divisor 
have  Ulce  signs,  and  negative  when  they  have  unlike  signs:  abc  -t-b  —  ae; 
abe  H —  b=  —ae. 

To  divide  a  monomial  by  a  monomial,  write  the  dividend  over  the  divisor 
with  a  line  between  them.  If  the  expressions  have  common  factors,  remove 
the  common  factors: 

,.  .         a*bx       ax ,      a*  a*        1  _t 

a«te  +  a*y=-^^5j^  =y;     -,=a;        -  =  _=«- 

To  divide  a  polynomial  by  a  monomial,  divide  each  term  of  the  polynomial 
by  the  monomial:  (8a6  -  18ac)  -♦-  4a  =  86  —  3c. 

To  divide  a  polynomial  by  a  polynomial,  arrange  both  dividend  and  divi- 
sor in  the  order  of  the  ascending  or  descending  powers  of  some  common 
letter,  and  keep  this  arranirement  throughout  the  operation. 

Divide  the  first  term  of  the  dividend  by  the  flrst  term  of  the  divisor,  and 
write  the  result  as  the  first  term  of  the  quotient. 

Multiply  all  the  terms  of  the  divisor  by  the  flrst  term  of  the  quotient  and 
subtract  the  product  from  <;he  dividend.    If  there  be  a  remainder,  consider 
It  as  a  new  dividend  and  proceed  as  before:   (a*  —  6*)  -•-  (a  +  6). 
a»-6«|a-|-6. 
o*  -f  gfc  I  g  -  6. 

-  o6  -  fe«. 
-ab-  fe«. 

The  difference  of  two  equal  odd  powers  of  any  two  numbers  Is  divisible 
by  their  difference  and  also  by  their  sum: 

(a«  -  6«/  -H  (a  -  6>  =  a«  +  oft  4-  6*  ;  (a*  -  b«)  ■«-  (o  +  6)  =  o«  -  a5  -f  6«. 

The  diffAenoe  of  two  equal  even  powers  of  two  numbers  Is  divisible  by 
their  difference  and  also  by  their  sum:  (a*  —  &*)-•-  (a  —  6)  =  a  -f  b. 

The  sum  of  two  equal  even  powers  of  two  numben*  is  not  divisible  by 
either  the  difference  or  the  stun  of  the  numbers;  but  when  the  exponent 
of  each  of  the  two  equal  powers  is  composed  of  an  odd  and  an  even  factor, 
the  sum  of  the  givenpower  is  divisible  by  the  sum  of  the  powers  expressed 
by  the  even  factor.  Thus  a?*  -4-  ^  is  not  divisible  by  a;  -f  tf  or  by  a;  —  y,  but  is  i 
Hvislbie  by  a?» -f- !(•.  j     -r  m        j         m^ 

Simple  eqaaUoiis*— An  equation  is  a  statement  of  equality  between  i 
twoexpressions;a8,a4-6=  c-f  d.  I 

A  simple  equation,  or  equation  of  the  flrst  degi-ee.  Is  one  which  contains 
only  the  flrst  power  of  the  unknown  quantity.  If  equal  cltanges  be  iiiailel 
(by  addition,  subtraction,  multiplication,  or  division;  in  both  hides  of  aa| 
equation,  the  results  will  be  equal. 

Anv  term  may  be  changed  from  one  side  of  an  equation  to  another,  pro>{ 
Tided  its  sign  be  changed:  o  -f  6  =  c  4-  d;  a  =  c  4-  d  -  6.  To  solve  a 
equation  having  one  unknown  quAntitv,  trannpose  all  the  terms  involvin 
the  unknown  quantity  to  one  side  of  the  equation,  and  all  the  other  term 
to  the  other  side;  combine  like  terms,  and  divide  both  sides  by  the  ooefflcien 
of  the  unknown  quantity. 

Solve  &p  -  29  =  86  -  &r.    &t  4-  «*  =  »  4-  ^:  11«  =  56; «  =  5,  ans. 

Simple  algebraic  problems  containing  one  nnlcnoxAn  quantity  are  solve 
by  making  x  =  the  unknown  qiianllry,  and   Kiating  the  conditions  of  ^^ 

Sroblem  in  the  form  of  an  algebraic  **quation,  and  then  solving  the  er 
on.    What  two  numbers  are  those  whose  sum  is  48  and  difference  14  7 
X  =  the  smaller  number,  a;  4- 14  the  greater,    x -\- x -\- \A  =  4&.    8fl?=:84,  i 
=  17;  *  + 14  =  81,  ans. 

Find  a  number  whose  treble  exceeds  50  as  much  as  Its  double  falls  shoi| 
of  40.    Let  X  =  the  number.    &c  -  50  =  40  -  2ar;  5a;  =  M):  a;  =  18,  ans.    Pr 
iag,  64-60  =  40-80. 


ALGEBRAr  35 

LvmtlaBs  coiitetiiliiir  tiwo  nBknoira  qaaiitlll«i*~If  one 

. , Jon  contains  two  unknown  quantities,  x  and  y,  an  indefinite  number  of 

pairs  of  values  of  x  and  y  maj  be  found  tliat  will  aatiafy  the  equation,  but  if 
a  second  equation  be  gireu  only  one  ]Miir  of  values  can  be  found  that  will 
satisf  J  both  equations.  Simultaneous  equations,  or  those  that  may  be  satis- 
fied by  the  same  values  of  the  unknown  quantities,  are  solved  by  combining 
the  equations  so  as  to  obtain  a  single  equation  containing  only  one  unknown 
quantit  V.    This  prooess  is  called  eilralnation. 

JSUmtnation  by  addition  or  «u6/}-act<on. —Multiplv  the  equation  by 
puch  numbers  ss  will  make  the  coeiBcients  of  one  of  the  unknown  quanti« 
ties  equal  in  the  resulting  equation.  Add  or  subtract  the  resulting  equar 
Uona  according  as  they  have  unlike  or  like  signs. 

c^i—  j  ar  +  «y  =  7.   Multiply  by  2:   4*  +  6y  =  14 

*^*^*  1  4«  -  5y  =  8.   Subtract:  4ac  -  5y  =   8        lly  :=  11;  y  s  1. 

Substituting  value  of  v  in  first  equation,  ftv  +  8  »  7;  »  =  9. 

ElimincUion  6y  9uMitutiati,^From  one  of  the  equations  obtain  the 
value  of  one  of  the  unknown  quantities  in  terms  of  the  other.  Substltu- 
tnte  for  this  unknown  quantity  Its  value  In  the  other  equation  and  reduce 
the  resulting  equations. 

J.  .      iar  +  8y=r8.    a).    From  (1)  we  find  a?  = -i^ . 

Sobstitute  this  value  hi  (8):  8(^^^)  +  7y  =  7;   =»  94  -  «y  +  14y  =  1< 

whence  y  =  ~  9.    Substitute  this  value  in  (1):  e»  —  8  =  8;  x  =  7. 

Elimination  by  oomparison.'—Vrom  each  equation  obtain  the  value  of 
one  of  the  unknown  quantities  in  terms  of  the  other.  Form  an  equatioo 
(rum  these  equal  values,  and  reduce  this  equation. 


Solve 


2x-'9y=U,   (1).    From  (1)  we  find  xs^^-^t^. 
dx-4y  =  7.   (2).    From(«)weflndaj  =  ^i^. 


EquaUng  these  values  of  a;,  ^^  "^  ^'^  =   '^\*^  ;  l«y=  -  1»;  y=:-l. 

Substitute  this  value  of  y  in  (1):  2x  +  9  =  n;z  =  l. 

If  three  simultaneous  equations  are  given  containing  three  unknown 
quantities,  one  of  the  unknown  quantities  must  be  eliminated  between  two 
pairs  of  the  equations;  then  a  second  between  the  two  resulting  equations. 

4|«m4nttle  eqitatloiis*— A  quadratic  equation  contains  the  square 
of  ihe  unknown  quantity,  but  no  higher  power.  A  pure  quadraiw  contains 
the  square  only;  an  affected  quadratic  both  the  square  and  the  first  power. 

To  joJve  a  pure  quadratic^  collect  the  unknown  quantities  on  one  side, 
and  the  known  quantities  on  the  other;  divide  by  the  coefficient  Of  the  un- 
known quantity  and  extract  the  square  root  of  each  side  of  the  resulting 
eqastion. 

Solve  &r< -15_=0.    Sx*  =  15;  a;>  =  6;  a;  =  ^5 

A  root  like  ^57  which  is  indfcated,  but  which  can  be  found  only  approzi- 
Bately,  Is  called  a  turd. 

Solve  8x*  + 18  =  0.    8aji  =  -  16;  ar«  =s  -  6;  a:  =  4^^. 

The  square  root  of  —  6  cannot  be  found  even  approximately,  for  the  square 
«f  any  number  positive  or  negative  is  positive;  therefore  a  root  which  is  in- 
dicated, but  cannot  be  found  even  approximately,  is  called  imaginary. 

To  tolve  an  </ffected  mutdratie.^\.  Convert  the  equation  into  the  form 
S'Z*  ±  iabx  =  c,  multipnring  or  dividing  the  equation  if  necessary,  so  as 
Id  make  the  coefficient  of  x*  a  square  number. 

S.  Complete  the  square  of  the  first  member  of  the  equation,  so  as  to  con- 
fm  it  to  the  form  of  a*dB*  ±  2abx  -f  b*,  which  is  the  square  of  the  binomial 
tJc  ±  b,  as  follows:  add  to  each  side  of  the  equation  the  square  of  the  quo- 
tient obtained  by  dividing  the  second  terra  by  twice  the  square  root  of  the 
8m  term. 

1  Extract  the  square  root  of  each  side  of  the  resulting  equation. 

Solve  Sas*  —  42  =  89.  To  make  the  coefficient  of  x*  a  square  number, 
femUiply  by  8:  ftr«  -  12r  =  96;  ISiT  -1-  (2  X  ar)  =  :i;  2«  =  4. 

Complete  the  square:  ite*  -  12sb  +  4  =  100.    Extract  the  root:  8a;  -  2  =  ± 


I 


86  ALQBBft^ 

10,  whenoe  «  n  4  or -•  9  v.  The  niiare  rod  of  160  It  eMber  4<  10  or  *  10, 
stnoe  the  square  of  >-  10  aa  well  aa  +  10*  s  lOO. 

Problema  involving  quadratic  equations  bave  apparently  two  aolutiOBS,  ai 
a  quadratic  bas  two  roots.  Bometlmes  both  will  be  true  solutlont,  but  Reu- 
erally  one  oolv  wiU  be  a  solution  and  the  other  be  inooualatent  with  ihe 
conditions  of  the  problem. 

The  sum  of  the  squares  of  two  consecutive  positive  numbers  is  481.  Find 
the  numbers. 

I«tap  =  oneiiumber.«  +  l  the  other.  a;«4- (x  +  1)*  =  481.  9tv*  +  ftr  +  l 
«481. 

«•  +  X  3  S40.  Oompletinic  the  square,  «•  +  9  +  0.iK  m  M0.S5.  EztractinK 
the  root  we  obtain  x  4-  0.5  s  ±  16.5;  «  ss  15  or  —  10. 

The  positive  root  gpives  for  the  numbers  15  and  16.  The  Begative  root  - 
16  is  inconsistent  with  the  conditions  of  the  problem. 

Quadratic  equations  containinir  two  unknown  quantities  require  different 
methods  for  their  solution,  according  to  the  form  of  the  equations.  For 
these  methods  reference  must  be  mside  to  works  on  algebra. 

Theory  of  exponeiit0.>-r  o  when  n  is  «  positive  intecer  is  one  of  m 

equal  factors  of  a.  y  a^  means  a  is  to  be  raised  to  the  mth  power  and  the 
itih  root  extracted. 

(r  "a)""  means  that  the  nth  root  of  a  is  to  be  taken  and  the  result 
raised  to  the  mth  power. 

Va^  :=  Kya)     s  a  «.    When  the  exponent  tea  fraction^e  numera- 
tor indicates  a  power,  and  the  denominator  a  root    a^  =  r  <**  =  a«;  al  = 

To  extract  the  root  of  a  quantity-  raised  to  an  indicated  power,  divide 
the  exponent  by  the  index  of  the  required  root;  as, 

Vo^  =  a'i'*  Va«  =  o*  =  a*. 

Subtracting  1  from  the  exponent  of  a  is  equivalent  to  dividing  by  a  : 

,o«-»  =a>  =  a:    a» -»  =  a«  =  -  =  1;  a«->  =  a  -»  = -;  o  -»  -«  =  a-«=-i 

A  number  with  a  negative  exponent  denotes  the  reciprocal  of  the  number 
with  the  corresponding  po:titive  exponent. 

A  factor  under  the  radical  sign  whofle  root  can  be  taken  may.  by  having 
the  root  taken,  be  removed  from  under  the  radical  sign: 

^cflh   B  |/a*  )(  |/b  »  a  4/6? 

A  factor  outside  the  radical  sign  may  be  raised  to  the  corresponding 
power  and  placed  under  it: 

Binomial  Theorem.— To  obtain  any  power,  as  the  nth,  of  an  ex« 

I  esMon  of  the  form  x-^-a 

etc. 
The  following  laws  hold  for  any  term  In  the  expansion  of  (a  •{•  ar)". 
The  exponent  of  x  is  less  by  one  than  the  number  of  terms. 
The  exponent  of  a  is  n  minus  the  exponent  of  x. 

The  lost  factor  of  the  numerator  is  greater  by  one  than  the  exponent  of  a. 
The  laMi  factor  of  the  denominator  is  the  same  as  the  exponent  of  x. 
In  the  rth  term  the  exponent  of  a;  will  be  r  -  1. 
The  exponent  of  n  will  be  n  —  (r  —  1).  or  n  -  »'  +  1. 
The  last  factor  of  the  numerator  will  be  n  -  »H-  2. 
The  last  factor  of  the  denominator  will  be  =s  r  —  1. 

Hence  the  rth  term  =-^ -—x  ——■ ---— —  o«  "  »^  +  1  «^-» 

1  .  s  t  a  .  .  .  .  ^i    —  1) 


OaOVKTBlCAl.  PROBIiBXa, 


87 


OSOXBTBXOAXi  FBOBLEMS. 


f 

^ 

ft 

} 

■■; 

■•) 

"iC 

" 

>t 

Fia. 

5. 

c 

O 

1 
1 

1 

* 

1 

..  ..|. 

n« 

^ 

B 

1«  To  bl»«ct  •  strAlslit  line, 
or  an  aro  of  a  circle  (Fig.  i).— 
From  the  ends  A-,  B^  an  centres,  de- 
pcribe  arci  interaectinK  at  C  and  A 
and  draw  a  line  through  C  and  D 
which  will  bisect  the  line  at  i?  or  the 
ftfcat^. 

S*  To  dntiv  a  perpendicular 
to  a  ctraUdlt  Une,  or  a  radial 
line  to  a  arcnlar  arc*— Same  as 
in  Problem  1.  CZ>  is  perpendicular  to 
the  line  A  B^  and  also  radial  to  the  arc. 

8.  To  draiw  a  perpendicular 
to  a  straight  line  front  a  slT«n 
point  Intliat  line  (Fig.  2).-With 
any  radius,  from  the  given  point  A  in 
the  line  B  C,  cut  the  line  at  B  and  C. 
With  a  longer  radius  describe  arcs 
from  B  and  C,  cutting  each  <^her  at 
i>,  and  draw  the  perpendicular  D  A. 

Am  From  the  end  ^ofatflTen 
line  ^  l>  to  erect  a  perpendlc" 
nlar  A  M  (Fig.  8).-^Prom  any  centre 
>',  above  A  2>,  describe  a  circle  patising 
through  the  given  point  JL  and  cut- 
ting the  given  line  at  D.  Draw  D  F 
and  produce  it  to  cut  the  circle  at  E^ 
and  draw  the  perpendicular  A  E. 

Second  Method  (Fig.  4).— From  the 
given  point  A  set  off  a  distance  A  E 
equal  to  three  parts,  bv  any  scale : 
and  oil  the  centres  A  and  E^  M'lth  radii 
of  four  and  Ave  parts  respectlvfly, 
describe  arcs  intersecting  at  C  Draw 
the  perpendicular  4  C, 

NoTB.— This  method  Is  most  useful 
on  very  large  scales,  where  straight 
edges  are  inapplicable.  Any  multiples 
of  the  numb«*rs  9.  4,  5  may  be  taxen 
with  the  same  effect  as  6,  8, 10,  or  9, 
12, 15. 


6«  Todra^ra 
to  a 


To  dra^r  a  perpendlcnli 

•tralfflit  fine  Arom  ai 

It  Wltfiont  It  (Fig.  5.)-Fn 


lar 


Solnt  wltnont  It  (Fig.  5.)- From 
le  point  4,  with  a  sufficient  radius 
cut  the  given  line  at  F  and  (?,  and 
from  these  points  describe  arcs  cut- 
ting at  E,    Draw  the  perpendicular 

6.  To  dra^r  a  etralsbt  line 
parallel  to  a  slTcn  line,  at  a 
fflTcn  dUtance  apart  (Fig.  O).— 
From  the  centres  A^  /«,  in  the  given 
line,  with  the  given  distance  as  radius, 
describe  arcs  C.  D,  and  draw  the  par- 
allel lines  C  J>  touching  the  arc9. 


GEOMBTRIOAL  PROBLBUS. 


Fio.  8. 


To  dlTlde  a  stnlcht  Una 
»  a  namber  of  equal  narto 

.  7).-To  divide  the  line  A  B  into, 


Into  I 

say,  Ave  parte,  draw  the  line  ^  C  at 
an  angle  from  A;  set  off  live  equal 
parts:  draw  B  6  and  draw  parallels  to 
it  from  the  other  points  of  division  in 
A  C.  These  parallels  divide  A  B  aa 
required. 

KoTB.— Bya  similar  process  a  line 
may  be  divided  into  a  number  of  un- 
equal parts;  setting  off  divisions  os 
A  C,  proportional  by  a  scale  to  the  re- 
quired divisions,  and  drawing  parallrl 
cutting  A  B,  Tlie  triangles  All^  A^ 
^88,  etc.,  are  similar  Manglea, 


•tralslit  line  to 
Kle   eqnal  to 


8*  Upon 
draw  an  anjrle  eqnal  to  a 
tfiwen  anffle  (Fig.  6).— Let  A  be  the 
given  angle  and  F  G  the  line.  From 
the  point  A  with  any  radius  describe 
the  arc  D  E.  From  F  witli  the  same 
radius  describe  J  H.  Set  off  the  arc 
/tfequaltoDf.anddrawir'JEr.  The 
angle  F  Is  equal  to  ^,  as  required. 


9«  To  dra^r  anarl^*  of  60* 
and  80<*  (Fig.  »).— T'rom  F,  %vith 
any  radius  F  /,  describe  an  arq^  J  H  ; 
and  fruiii  7,  with  the  same  radiAs,  cut 
the  arc  ax  H  and  draw  FH  to  form 
the  required  angle  7 F  JET.  Draw  the 
perpendicular  HK  to  the  base  line  to 
form  the  angle  ot  20*FHK, 


10*  To  dra^r  an  angle  or45« 

(Fig.  10).— Set  off  the  distance  FJi 
draw  the  perpendicular  1 H  equal  to 
I  Ft  and  join  HF  to  form  the  angle  at 
F.    The  angle  at  His  also  45«. 


11.  To  bleeet  an  angle  (Fig. 
11).— Let  AC  Bhe  the  angle;  with  O 
as  a  centre  draw  an  arc  cutting  the 
sides  at  A^  B.  From  A  and  B  as 
centres,  describe  arcs  cutting  each 
other  at  D.  Draw  C  D,  dividing  the 
angle  Into  two  equal  parts. 


Fio.  12. 


19*  Tliroagli  t^ro  glwen 
points  to  deacrlbe  an  are  or 
a  circle  wltli  a  glTen  radlna 

(Fig.  12).— From  the  points  A  and  B 
an  centres,  with  the  given  radius,  de- 
Bcri))e  arcs  cutting  at  C  \  and  from 
Cwith  the  same  radius  desoribe  an 
arc  A  B. 


OBOMBTfilCAL  PB0BLEH6. 


39 


Fio.  18, 


Fig.  14. 


Fio.  15. 


18.  To  flnil  the  eeiitre  of  a 
eirele  or  of  an  are  of  a  circle 

(Fiff.  laX'-Select  three  points,  A^  B, 
C%  In  tbe  oiteumferenoe,  well  apart; 
with  the  same  radius  describe  arcs 
from  these  three  points,  cutting  each 
other,  and  draw  the  two  lines,  D  E^ 
F-&^  through  their  intersections.  The 
point  O,  where  they  cut,  is  the  centre 
of  the  circle  or  arc. 

To  describe  a  circle  paesliiir 
Uuronslft  three  kItch  points* 
~Ijet  A^  B,CY>e  the  given  points,  and 
proceed  asin  last  problem  to  find  the 
centre  O,  from  which  the  circle  may 
be  described. 

14.  To  describe  an  arc  of 
a  circle  passing  thronsb 
three  slTcn  points  ivhen 
the  centre  Is  not  aTallable 
(Fig.14)  — From  the  extreme  points 
A,  B,  as  centres,  describe  arcs  A  H, 
B  O.  Through  the  third  point  O 
draw  AE,  B  F,  cutting  the  arcs. 
DlTide  A  F  and  B  E  into  any  num- 
ber of  equal  parts,  and  set  off  a 
series  of  equal  i>arts  of  the  same 
length  on  the  upper  portions  of  the 
arcs  beyond  the  points  E  F.  Draw 
straight  lines,  B  L,  B  M,  etc.,  to 
the  divisions  in  A  F,  and  AI,AK, 
etc.,  to  the  divisions  in  E  Q.  The 
succeissive  intersections  N^  O,  etc., 
of  these  li  es  are  points  in  the 
circle  required  between  the  given 

Soints  A  and  C.  which  mav  be 
rawn  in  ;  similarly  tbe  reraunlng 
Sart  of  tbe  curve  B  C  may  be 
escribed.    (See  also  Problem  64.) 

15*  To  dra^r  a  tangent  to 
a  circle  Aroni  a  slTcn  point 
In  the  elrcomference  (Fig.  15). 
—Through  the  fdven  point  A^  draw  the 
radial  line  A  C,  and  a  perpendicular 
to  it,  F  &,  which  is  the  tangent  re- 
quired. 


16*  To  dra^r  tansrents  to  a 
circle  ttont  a  point  without 

It  (ITig.  16).— From  A,  with  tht*  radius 
A  C,  desci-ibe  an  arc  B  C  D^  and  from 
C,  with  a  radius  eaual  to  the  diameter 
of  the  circle,  cut  the  arc  at  B  D,  Join 
BC,  CD,  cutting  the  circle  at  EFy 
and  draw  A  E^  A  F,  the  tangents. 

Note.- When  a  tangent  Is  already 
drawn:  the  exact  point  of  contact  may 
be  found  by  drawing  a  perpendicular 
to  it  from  the  centre. 


17.  Betireen  tw^o  Inclined  lines  to  draur  a  series  ofelT^ 
eles  tonchlnc  these  lines  and  tonchlns  each  other  (Fig.  IT). 
-Bbtect  the  iiicUnation  of  the  given  lines  A  /?,  CD,  by  the  line  N  O.  From 
a  point  F  In  this  line  draw  the  perpendicular  P  ^  to  tbe  line  A  B^  and 


GEOMETRICAL  PBOBLEMS. 


on  P  describe  the  circle  B  P,  touching 
the  lines  and  cutting  the  centre  line 
&t  E.  From  JSdraw  JCFperpendicular 
to  the  centre  line,  cutting  ^  i^  at  ^, 
and  from  ir*  describe  an  arc  £  6.  cut- 
ting ABaXG.  Draw  O  H  parallel  to 
B  P„  giving  J7,  the  centre  of  the  next 
circle,  to  be  described  with  the  radius 
H  E,  and  so  on  for  the  next  circle  IN. 
Inversely,  the  largest  circle  may  be 
described  nrst,  and  the  smaller  ones 
in  succession.  This  problem  is  of  fre- 
quent use  in  scroll-work. 

18*  Bet'lveen  two  Inclined 
llnea  to  drm^r  a  drenlar  •««*- 
ment  tansent  to  the  lines  and 
paaalnfT  throoffli  a  point  F 
on  the  line  F  C  whleh  bisects 
the  ancle  of  the  lines  (Fig.  18). 
—Through  jPdraw  D  ^  at  right  angles 
to  FC;  bisect  the  angles  A  and  A  as 
in  Problem  11,  by  lines  cutting  at  C, 
and  from  C  with  radius  CFdraw  the 
arcHFO  required. 

19.  To  dra^r  a  clircniar  are 
that  will  be  tangent  to  t^ro 
flTlven  lines  ^  Ji  and  V  J>  In- 
clined to  one  another,  one 
tangential  point  M  helnc 
alTcn  (Fig.  19).>-Draw  the  centre 
hne  O  F.  From  Ednvr  EFat  right 
to  angles  A  B ;  then  F  is  the  centre 
of  the  circle  required. 

20*  To  describe  a  circular 
arc  Joining  tw^o  circles,  and 
tonchlns  one  of  them'  at  a 
SlTcn  point  (Fig.  90).— To  johi  the 
circles  AB^FQ.hy 9Ji  arc  touching 
one  of  them  at  F,  draw  the  radius  B  F, 
and  prodiiceit  both  ways.  Setoff  jPfi 
equal  to  the  radius  A  C  ot  the  oUier 
circle;  join  CH  and  bisect  it  with  the 
perpendicular  LI,  cutting  EF  At  I. 
On  the  centre  I,  with  radius  IF,  de- 
scribe the  arc  F  il  as  required. 

21  •  To  draw  a  circle  wrfth  a 

STcn  radios  M  that  will  be 
nsent  to  two  fclwen  dreles 

A  and  B  (Fig.  21).— From  centre 
of  circle  A  with  radius  equal  R  plus 
radius  of  ^,  and  from  centre  of  B  with 
radius  equal  to  /Z  +  radius  of  B,  draw 
two  arcs  cutting  each  other  in  C,  which 
will  be  the  centre  of  the  circle  re- 
quired. 

ft2.  To  construct  an  eanl- 
lateral  trlanale«  the  sides 
belns  tflTcn  (Fig.  «<).— On  the  ends 
of  one  side,  A^  B,  witli  ABas  radius, 
describe  arcs  cutting  at  O,  and  draw 
A  O,  CB. 


OBOXBIBIOAL  FB0BLBM8. 


41 


28.  To  convCntet  m,  trlansle 
of  nneaiua  atde*  (Fl«r.  88).~Oa 
either  end  of  the  hase  A  D,  with  the 
Bide  B  ag  radius,  describe  an  arc; 
and  with  the  side  C  as  radius,  on  the 
other  end  of  the  base  as  a  centre,  cut 
the  arc  at  E,    Join  AE,DE, 


Fio.  23. 


"  ';< 


Hi fi 


S4«  To  iKoiistniet  H  aqnare 
on  a  ^Ten  atmifflit  line  A  B 

(FIs:.  84).— With  AB  B»  radius  and  A 
and  B  as  centres,  draw  arcs  i4  Dand  B 
C,  intersection;  at  E.  Bisect  EBAiF. 
'With  fas  centre  and  RFbm  radius, 
cut  the>arc8  A  D  and  B  C  In  D  and  C. 
Join  A  C\  C  i>,  and  i>^  to  form  the 
square. 


%S»  Vo    eonstraet    a  reet- 
ancle  witlijrtTen  Imum  J7  :p 

maA  beiclftt  jTlf  (Fig.  85).— On  the 
base  E  Fartkw  the  perpendiculars  EH, 
F  0  equal  to  the  height,  and  Join  O  H. 


aboi 


6.  Vo    describe    a    elrele 


_  Dai  a  triankle  (Fifr.  86).- 
Bisect  two  sides  AB,  A  C  of  the  tri- 
angle at  E  Jr\  and  from  these  points 
d  raw  perpendiculars  cutting  at  k.  On 
the  centre  K^  with  the  radius  KA, 
draw  the  circle  ABC, 


97.  To  tneeribe  a  elrele  In 
a  triangle  (Fig.  87).~Bi8ect  two  of 
the  angles  A^  C,  of  the  triangle  by  lines 
cutting  At  JD ;  from  D  draw  a  per- 
pendicular De!  to  any  side,  and  with 
D  Eas  radius  describe  a  circle. 

When  the  triangle  is  equilateral, 
draw  a  perpendicular  from  one  of  the 
angles  to  the  opposite  side,  and  from 
the  side  set  off  one  third  of  the  per> 
pendicular. 

S8.  To  desert  be  a  clrele 
about  a  aiinare.  and  to  In- 
■crtbe  a  square  In  a  elrele  (Fig. 
£8).— To  describe  the  circle,  draw  the 
diagonals  ^  B,  C  D  of  the  square,  cut- 
tine  at  E.  On  the  centre  E,  with  the 
radius  A  JST,  describe  the  circle. 


FlO.88. 


To   Inseribe   tMte   sqni 

Draw  the  two  diameters,  AB,  OD,  at 
right  angles,  and  join  tlie  points  A,  B, 
C  D,Xo  form  the  square. 

Note.— In  the  same  way  a  circle  may 
be  described  abvut  A  rectangle.   • 


42 


GEOMETRICAL  PROBLEMS. 


A  Q  C 


At 


29.  To  Inseiibe  a  drde  tn  • 
tqnare  (Fi^.  29).— To   inscribe  the 

slrcle,  draw  the  diagonals  A  B^  C  D 
jf  the  square,  cutting  at  E;  draw  the 
perpendicular  E  F  to  one  side,  and 
with  the  radius  B  F  describe  the 
circle. 


30*  To  dosoHbe  a  B^iiare 
aboot  a  cirelo  (Fig.  80).— Draw  two 
diameters  A  B,  CD  at  right  angles. 
ViXth  the  radius  of  the  circle  and  J,  B^ 
C  and  D  as  centres,  draw  the  four 
half  circles  which  cross  one  anotfaar 
in  the  comers  of  the  square. 


81.  To  Inscribe  apontacon 
tn  a  drele  (Fig.  81).— Draw  cflam- 
eters  AC^B  DtX  right  angles,  cutting 
at  o.  Bisect  Ao  tX  E,  and  from  £, 
with  radius  £  ^,  out  ^  C  at  ^ ;  from 
B,  with  radius  B  F,  cut  the  circumfer- 
ence at  Oy  H,  and  with  the  same  radius 
step  round  the  circle  to  /and  K ;  join 
the  points  so  found  to  fonn  Uie  penta- 
gon. 


Fio.84. 


Bflm  To  constraet  a  penta^ 
iron  on  a  jglwen  line  A  B  (Fig. 
JW).— From  ^  erect  a  perpendicular 
B  G  half  the  length  of  A  B;  join  A  C 
and  prolong  it  to  />,  maicing  C  2>  =  BC. 
Then  B  D  in  the  radius  of  the  circle 
circumscribing  the  pentagon.  From 
A  and  ^as  centres,  with  BDbb  radius, 
draw  arcs  cutting  each  other  lu  O, 
which  is  the  centre  of  the  circle. 

88.  To  ronatmet  a  bozairon 
upon  a  slwen  atralsbt  nno 

(Fig.  S8).~From  A  and  BTthe  ends  of 
the  given  line,  with  radius  A  B,  de- 
scribe arcs  cutting  at  g ;  from  g,  with 
the  radius  g  A^  describe  a  circle;  with 
the  same  radius  set  off  the  arcs  A  O, 
O  F,  and  BD.DE,  Join  the  points  so 
found  to  form  the  hexagon.  The  aide 
of  a  hexagon  =  radius  of  its  circum- 
scribed circle. 

34»  To  Inscribe  a  bexag^on 
In  a  circle  (Ffg.  84).— Draw  a  diam- 
eter A  CB.  From  A  and  B  as  centres, 
with  the  radius  of  the  circle  A  C,  cut 
the  circumference  at  D,  E^  F^  O,  and 
draw  A  D,DE,  etc.,  to  form  the  hexa- 
gon. The  radius  of  the  circle  is  equal 
to  the  Ride  of  the  hexagon;  therefore 
the  points  D,  Ej  etc..  may  also  be 
found  by  stepping  the  radius  six 
times  round  the  circle.  The  angle 
between  the  diameter  and  the  sidea  of 
a  hexagon  and  also  the  exterior  angfle 
between  a  side  and  an  adjacent  side 
prolonged  Is  60  degrees;  therefore  a 
hexagon  may  conveniently  be  drawn 
by  the  use  of  a  60-degree  triangle. 


GEOMETRIGAL  FBOBLEMS. 


43 


F10.8& 


85.  To  describe  a  hexagon 
aboot  a  elrele  (FIr.  85).— Draw  a 
diameter  A  D  B,  and  with  the  radius 
A  A  on  the  centre  A^  cut  the  circum- 
ference at  C ;  join  A  0,  and  bisect  it 
with  the  radius  D  E ;  through  E  draw 
FQ^  parallel  to  ^  C,  cutting  the  diam* 
eter  at  F,  and  with  the  radius  D  F  de- 
scribe the  circumscribing  circle  ^J7. 
Within  this  circle  describe  a  hexagon 
by  the  preceding  problem.  A  more 
convenient  method  is  by  use  of  a  00- 
degree  triangle.  Four  of  the  sides 
make  angles  of  60  degrees  with  the 
diameter,  and  the  other  two  are  par- 
allel to  the  diameter. 

86*  To  deaerlbe  an  oeCasoB 
on  a  KlT«n  atralfflit  line  (l«lg. 
86).— Produce  the  given  line  A  B  botl 

V} 

BV, 

equal  to^B.  Draw  C X> and  H O par- 
aflel  toAE,  and  equal  UiAB\  from 
the  centres  O^  A  with  the  radius  A  B, 
cut  the  perpendiculars  at  ff,  F,  and 
draw  EFto  complete  the  ocUgon. 

87.  To  convert  a  Minare 
Into  an  octagon  (Fig.  87).— Draw 
the  diagonals  of  the  square  cutting  at 
e ;  from  the  corners  A^  B,  C7,  D,  with 
^  «  as  radius,  describe  arcs  cuttlne 
the  sides  at  gn,  fk,  Am,  and  ol,  and 
join  the  points  so  found  to  form  the 
octagon.  Adjacent  sides  of  an  octa- 
gon make  an  angle  of  186  degrees. 


88.  To  Inscribe  an  octagon 
In  a  circle  (Fig.  88).— Draw  two 
diameter8»  A  C,  B  D  at  right  angles; 
bisect  the  arcs  A  B^  B  C,  etc.,  at  e/, 
etc.,  and  join  Ae^eB,  etc.,  to  form 
the  octagon. 


89*  To  describe  an  octagon 
about  a  circle  (Fig.  99).— Describe 
a  square  about  the  given  circle  A  B ; 
draw  perpendiculars  h  k,  etc.,  to  the 
diagonals,  touching  the  circle  to  form 
the  octagon. 


40.  To  describe  a  polygon  of  any  number  of  sides  upon 
ft  Klwen  strali^t  line  (Fig.  40).— Produce  the  given  line  A  B,  and  on  A, 


44 


OBOHKtRtOAL  t>fiOBLfiKS. 


with  the  radius  A  S^  di»ffcribe  a  semi- 
circle; divide  the  seml-oircumference 
into  as  roftAy  equal  parts  as  therts  are 
to  be  sides  in  the  polj-gon^say,  in  this 
example,  Ave  Sides.  Draw  lineH  from 
A  through  the  divisional  points  D,  b. 
and  c,  omitting  one  point  a  ;  and  on 
the  centres  B,  Z>,  u  ith  tlie  radius  A  B, 
cut  ^5  at  J?  and  ^  cat  ii^.  DrawDf, 
^  ^,  ^B  to  complete  the  polygon. 
41,.    Vo    ln(i«rtbe    a   eirele 


HVlUlln  a  poljrg^oil  (Figs.  41, 45!).— 
When  thepoTygon  hai«  an  even  number 
of  sides  (Fig.  41),  bisect  two  opposite 


sides  at  ^  and  ^;  draw  ^  B.  and  bisect 
it  at  C  by  a  diagonal  D  E,  and  with 
the  radius  C^  describe  the  circle. 

When  the  number  Of  sides  is  odd 
(Fig.  43),  bisedt  two  of  the  sides  at  A 
and  B.  and  dr4w  lines  A  E,BD  to  the 
opposite  Angles,  intersecting  at  C; 
from  a  with  the  radius  C  A,  describe 
the  circle. 


42.    IPo    deseiilM   m    drele 

'Wlthoot  a  polyKton  (Figs.  41,  4*.'). 
—Find  tiie  Centre  (J  as  before,  and  with 
the  radius  C  Z>  describe  the  circle. 


48.  To  inijerlbe  a  polygon 
of  anj  nomber  of  ftlde*  iv^lUf 
In  a  circle  (Fig.  48).— Draw  the 
diameter  A  B  and  through  the  centre 
^draw  the  perpendicular  EC^  cutting 
the  circle  at  S*.  Divide  E  F  into  four 
equal  parts,  shd  set  off  three  parts 
equal  to  those  from  F  to  C.  Divide 
the  diameter  A  B  into  as  many  equal 
parts  as  the  polygon  is  to  have  siden  ; 
and  from  C  draw  CA  through  the 
second  point  of  division,  Cutting  the 
circle  at  D.  Then  ^  Z>  is  equal  to  one 
side  of  the  polygon,  and  by  stepping 
round  the  dircumfet'ence  wiih  the 
length  A  D  the  polygon  may  be  com' 
pleted. 


TABLE  OF  POLYGONAL  ANGLES. 


Number 

Angle 

Nttmbel» 

AnRle 

Number 

Angle 

of  Bides. 

at  Centtv. 

,   Of  Sides. 

at  Centre. 

of  Sides. 

at  Centre. 

No. 

Degrees. 

No. 

Degrees. 

No. 

Degrees. 

lao 

9 

40 

16 

94 

90 

10 

86 

16 

^ 

72 

11 

88A 

17 

60 

18 

80 

18 

80 

S» 

13 
14 

^ 

IS 

10 
18 

OlSOMBtRlCAL  PROBLEMS. 


45 


In  this  table  the  Mgle  at  th«  centre  is  round  hf  dividing  860  deRroes,  the 
number  oC  deKreee  in  a  cfreir,  by  the  number  of  sides  fn  Uie  polytcon;  and 
by  seititir  off  roand  the  centre  or  the  circle  a  succession  of  angles  by  means 
o(  the  protractor*  equal  to  Vbin  aiu^e  in  the  table  due  to  a  fflven  number  of 
sHtee,  the  radii  so  drawn  will  divide  the  circumference  into  Uie  sanae  number 


of  parts. 


Fio.  45. 


44.  To  deaerlbe  mn  «lllMe 
^rlieii  tbe  lenstli  antt  breadtli 
are  clvett  (Pig.  44). —^  B,  transverse 
axis;  C />,  conjugate  axis;  F0t  foci. 
The  sum  of  the  disianoes  from  C  to 
F  and  Ot  also  the  sum  of  ihe  distances 
from  F  and  O  to  any  other  poiut  in 
the  curve*  is  equal  to  the  transverse 
axis.  From  the  centre  C,  with  A  Em 
radius*  cut  the  axis  .^  If  at  Fand  G, 
the  foci;  fix  a  couple  of  pins  into  the 
axis  at  F  and  O,  and  loop  on  a  thread 
or  cord  upon  them  equail  In  length  to 
the  axis  ^  £,  so  as  when  stretched  to 
reach  to  the  extremity  C  of  the  cou- 
jugate  axis,  as  shown  in  dot-lining. 
Place  a  pencil  inside  ibe  cord  as  at  /f  , 
and  guiding  the  pencil  in  this  way, 
keeping  the  Oord  equally  In  tenBion* 
carry  the  pencil  found  the  pins  F^  <?, 
and  so  describe  the  ellipse. 

NoTS.— This  method  is  employed  in 
setting  oif  elliptical  garden-plots, 
walks,  etc. 

2d  Method  (Fig.  46). —Along  the 
straight  edge  of  a  slip  of  stiff  paper 
mark  off  a  distance  a  c  equal  to  A  C, 
half  the  transverse  axis;  and  from  the 
same  point  a  distance  ab  equal  to 
C  A  half  the  conjugate  axis.  Place 
the  slip  so  as  to  bring  the  point  b  on 
the  line  A  B  ot  the  transverse  axis, 
and  the  point  c  on  the  line  D  E ;  and 
set  off  on  the  drawing  the  position  of 
the  point  a.  Shifting  the  slip  so  that 
the  point  b  travels  on  the  transverse 
axis,  and  the  point  c  on  the  conjugate 
axis,  any  number  of  points  in  the 
curve  may  be  found,  through  which 
the  curve  may  be  traced. 

8d  Mtthnd  (Fig.  40).— The  action  of 
the  preceding  method  may  be  em- 
bodied so  as  to  afford  the  means  of 
describing  a  large  curve  continuously 
by  means  of  a  bar  m  le,  with  steel 
points  m,  I,  Jb,  riveted  into  brass  slides 
adjusted  to  the  length  of  the  semi- 
axis  and  fixed  with  set-screws.  A 
rectangular  cross  E  O,  with  guiding- 
slots  is  placed,  coinciding  with  the 
two  axes  of  the  ellipse  A  C  and  B  H. 
By  sliding  the  points  k^  I  in  the  slots, 
and  carrying  round  the  point  m.  the 
curve  may  be  continuously  described. 
A  pen  or  pencil  may  be  fixed  at  m. 

Ath  Method  (Fig.  47).-BiseOt  the 
transverse  axis  at  C.and  through  0 
draw  the  perpendicular  D  E,  making 
O  D  and  0  £  each  equal  to  half  the 
conjugate  axis*  From  i>  or  E,  with 
the  radius  A  C,  cut  the  transverse 
axis  at  F^  F\  for  the  foci.  Divide 
A  C  into  a  number  Of  parts  at  the 


46 


GEOMETRICAL  PROBLEMS. 


points  1,  2.  8,  etc.  With  the  radius  A  I  on  F  and  F'  as  oentres,  describe 
Arcs,  ana  with  the  radius  B  /  on  the  same  centres  cut  these  arcs  as  shown. 

Repeat  the  operation  for  the  other 
diTisions  of  the  transverse  axis.  The 
series  of  intersections  thus  made  are 
points  in  the  curve,  through  which  the 
curve  may  be  traced. 

6tk  Method  (FiR.  48).— On  the  two 
axes  A  B^  D  Eaa  diameters,  on  centre 
C,  describe  circles;  from  a  number  of 
points  a,  5,  etc.,  in  the  circumference 
AFB,  draw  radii  cuttinf?  the  inner 
circle  at  a%  b\  etc.  From  a,  6,  etc., 
draw  perpendiculars  to  AB;  and  from 
a\  b\  etc.,  draw  parallels  to  ^  B,  cut- 
ting the  respective  perpendiculars  at 
n,  o.  etc.  The  Intersections  are  points 
in  the  curve,  through  which  the  curve 
may  be  traced. 

6th  Method  (Fig.  49).  — When  the 
transverse  and  conjugate  diameters 
are  given,  A  B,  C  2>,  draw  the  tansrent 
fJi^^ parallel  to  A  B.  Produce  CD, 
and  on  the  centre  O  with  the  radius 
of  half  A  B,  describe  a  semicircle 
H DK;  from  the  centre  O  4raw  any 
number  of  straight  lines  to  Uie  points 
E,  r,  etc.,  in  the  line  BF^  cutting  the 
circumference  at  Z,  m,  n,  etc.;  from 
the  centre  O  of  the  ellipse  draw 
siraiKht  lines  to  the  points  17,  r,  etc.; 
and  f iom  the  points  I,  m,  1^  etc.,  draw 
parallels  to  (?  C,  cutting  ihe  lines  O  J?, 
O  r,  etc.,  at  L,  Af,  JV,  etc.  These  are 
points  in  the  circumference  of  the 
elllpKe,  and  the  curve  may  be  traced 
through  them.  Points  in  the  other 
half  of  the  ellipse  are  formed  by  ex- 
tending the  intersecting  lines  as  indi- 
cated in  the  figure. 

45,  To  deacribe  an  ellipse 
approxliiiatel]r  by  meaD*  of 
clrcDlar  area,— ^'»«^— With  arcs 
of  tuu  radii  (Kig.  50).— Find  the  dUTer- 
euce  of  the  semi-axes,  and  set  it  oif 
from  the  centre  O  to  a  and  c  on  O  ii 
and  O  C ;  draw  a  c.  and  set  off  half 
a  c  to  d  ;  draw  d  i  parallel  to  a  c:  set 
off  O  ^  equal  to  O  a\  join  e  t,  and  draw 
tlie  parallels  em,  dm.  From  m,  with 
radius  in  C,  describe  an  arc  through 
C ;  and  from  t  describe  an  arc  through 
B;  from  d  and  <^  describe  arcs  through 
A  and  B.  The  four  arcs  form  the 
ellipse  approximately. 

Nora.— rhis  method  does  not  applv 
satisfactorily  when  the  conjugate  axis 
is  less  than  two  thirds  of  the  trans- 
verse axis. 

2d  Method  (by  Carl  G.  Earth, 
Fig.  51).-  In  Fig.  51  a  b  is  the  major 
and  c  a  the  minor  axis  of  the  ^lipee 
to  be  approximated.  Lay  off  6  e  equal 
to  the  semi-minor  axis  c  O,  and  use  a  e 
as  radius  for  the  arc  at  each  extremity 
of  the  minor  axis.  Bisect  e  o  at  /  and 
lay  off  6  (7  equal  to  e/,  and  use  gbaa 
radius  for  the  arc  at  each  extremity 
Fio.  61.  of  the  major  axis. 


Pro  49. 


OBOHETBICAL  FBOBLEHS. 


« 


Ths  mettiod  Ib  not  oonsldered  sppUcable  for  cases  in  which  the  minor 
ujs  is  lees  than  two  thirds  of  the  major.  .  , 

Zd  Method :  With  arcs  of  three  radii 
(Fife.  5i0.— On  the  transverse  axis  A  B 
draw  the  rectangle  BGon  the.beifrht 
OC;  to  the  diagonal  A C  draw  the 
perpendicular  G  H  Di  set  off  O  Jt 
equal  to  O  C,  and  deecribe  a  semi- 
circle on  A  K,  and  produce  O  C  to  L; 
set  off  O  Jf  equal  to  C  L,  and  from  X> 
describe  an  arc  with  radius  D  M ;  from 
Aj  with  radius  O  L,  cut  ^  B  at  Ni  from 
H,  with  radius  HN,  cut  arc  ad  at  a. 
Thus  the  five  centres  2>.  a»  6,  H,  H' 
are  found,  from  which  the  arcs  are 
described  to  form  the  ellipse. 

This  process  works  well  for  nearly 
all  proportions  of  ellipses.  It  is  used 
in  striking  out  vaults  and  stone  bridges. 
Uh  Method  (by  F.  R.  Honey,  Figs.  58  and  54).— Three  radii  are  emoloyed. 
With  the  shortest  radius  describe  the  two  arcs  which  pass  through  the  ver- 
tices of  the  major  axis,  with  the  longest  the  two  arcs  which  pass  through 
the  vertices  of  the  minor  axis,  and  with  the  third  radius  the  four  arcs  which 
counect  the  former.  ^  . 

A.  simple  method  of  determinhig  the  radii  of  curvature  is  illustrated  in 

Fig.  68.  Draw  the  straight 
lines  a/  and  a  c»  forming  any 
angle  at  a.  With  a  as  a  centre, 
and  with  radii  a  b  and  a  e,  re- 
spectively, equal  to  the  semi- 
minor  and  semi-major  axes, 
draw  the  arcs  6  e  and  ed.  Join 
ed,  and  through  6  and  c  re- 
spectively draw  6  g  and  e  f 
parallel  to  e  d,  interseoting  a  e 
at  a,  and  af  at/;  a/  is  the 
radius  of  curvature  at  the  ver- 
tex of  the  minor  axis;  and  a  g 
the  radius  of  curvature  at  the 
vertex  of  the  major  axis. 
'        -  -- '—     —  ighthofftd.    Join  c^  and  draw  efe and 

longest  radius  {^R\al  for  the  shortest 

„  -    ean,  or  one  half  the  sum  of  the  semi-axes, 

for  the  third  radius  (=!>>,  aud  employ  these  radii  for  the  eight-centred  oval 
as  follows: 

Let  a  b  and  c  d  (Fig.  54) 
be  the  major  and  minor 
axes.  Lay  off  as  equal 
to  r,  and  a/  equal  to  p; 
also  lay  off  cy  equal  to  S, 
and  c  h  equal  to  p.  With 
9  as  a  centre  and  y  A  as  a 
radius,  draw  the  arc  h  k\ 
with  the  centre  e  and 
radius  0  /  draw  the  are  /  Jb, 
J.  intersectingAib  at  le.  Draw 
1^  the  line  gfc  and  produce  it, 
makine  g  I  equal  to  R, 
Draw  k  e  and  produce  it, 
making  h  m  equal  to  p. 
With  the  centre  g  and 
radius  ge{=B)  draw  the 
arc  c  I :  with  the  centre  k 
and  radius  kl  (=p)  draw 
the  arc  { m,  and  with  the 
centre  e  and  radius  em 
<=  r)  draw  the  arc  m  a. 
Fio.  54.  The  remainder   of    the 

work  is  symmetrical  with 
respect  to  the  axes. 


Tenex  oi  uie  major  axis. 

lAy  oBdh  (Fig.  58)  equal  to  one  eighth 
b  Iparallel  to  e  h.  Take  a  k  for  the  long< 
radius  (=  r).  and  the  arithmetical  mean,  c 


48 


GEOMSTBICAL  PBOBLEHS. 


Fig.  65. 


r  46.  Tlfte  Parabola*— A  parabola 

(Z>  ^  C,  Fi«.  65}  Is  a  curve  nich  that 
every  point  In  the  curve  is  equollj 
distant  from  the  directrix  KL  axid  the 
focus  F.  The  focus  lies  in  the  axis 
A  B  drawn  from  the  vertex  or  head  of 
the  curve  ^4,  so  as  to  divide  the  figure 
into  two  equal  i>arts.  The  vertex  A 
is  equidistant  from  the  directrix  and 
the  focus,  or  A  e^AF.  Any  line 
parallel  to  the  axis  is  a  diameter.  A 
straight  line,  na  EO  or  DC,  dra^in 
across  the  figure  at  right  angles  to  the 
axis  is  a  double  ordinate,  and  either 
half  of  it  is  an  ordinate.  The  ordinate 
to  the  axis  EFO,  drawn  through  the 
focus,  is  called  the  parameter  of  the 
axia  A  segment  of  the  axis,  reckoned 
from  the  vertex,  is  an  abscissa  of  the 
axis,  and  it  is  an  abscissa  of  the  ordi- 
nate drawn  from  the  base  of  the  ab- 
scissa. Thus,  ^  B  is  an  abscissa  of 
...  -  ^  ,  .        the  ordinate  B  a 

AbscissflB  of  a  parabola  are  as  the  squares  of  their  ordinatea. 
To  doaertbe  a  parabola  wben  an  abrolsM  and  Ita  or^- 
nate  are  fftven  (Pig.  56).-Bi8ect  the  given  ordinate  B  Cat  a,  draw  A  a, 
and  then  o  6  perpendicular  to  it,  meeting  the  axis  at  b.  Bet  oil  A  e^  A  F, 
each  equal  to  B  6;  and  draw  Ke  L  perpendicular  to  the  axis.  Then  K  L  is 
the  directrix  and  F  is  the  focus.  Through  F  and  any  number  of  points,  o,  o. 
etc.,  in  the  axis,  draw  double  ordinates,  non,  etc.,  and  from  the  centre  F, 
with  the  radii  Fe,o  e,  etc.,  out  the  respective  ordinates  at  £L  <?,  n,  t^  etc. 
The  curve  may  be  traced  through  these  points  as  shown.       --»    »  t  •»    "^ 


2d  Method :  By  means  of  a  square 
and  a  cord  (Fig.  56).— Place  a  straight- 
edge to  the  directrix  E  N,  and  apply 
to  it  a  square  LEO.  Fasten  to  the 
end  O  one  end  of  a  thread  or  cord 
equal  in  length  to  the  edge  E  O,  and 
attach  the  other  end  to  the  focus  F ; 
slide  the  square  along  the  straight- 
edge, holding  the  cord  taut  against  the 
edge  of  the  square  by  a  pencil  D^  by 
which  the  curve  is  described. 


Fia.  56. 


If  a  B  a  if  cii 
Fia.  67. 


3d  Method :  When  the  height  and 
the  base  are  given  (Fig.  67).— Let  A  B 
be  the  given  axis,  and  C  D  &.  double 
ordinate  or  base:  to  desciibe  a  para- 
bola of  which  the  vertex  is  at  A. 
Through  A  draw  J^F  parallel  to  CI>, 
and  through  C  and  D  draw  C  E  and 
Di^  parallel  to  the  axis.  Divide  B  O 
and  BD  into  any  number  of  equal 
parts,  say  five,  at  a,  5,  etc.,  and  divide 
C  E  and  D  F  into  the  same  number  of 
parts.  Through  the  points  a,  6.  c,  d  in 
the  base  CD  on  each  side  of  the  axis 
draw  perpendiculars,  and  through 
a.&,c,  din  CE&nd  D.F draw  lines  to 
the  vertex  A,  cutting  the  perpendicu- 
lars at  c.  /,  g,  h.  These  are  points  in 
the  parabola,  and  the  curve  CAD  may 
be  traced  as  shown,  pasving  throqgh 
then;. 


GEOHETRIGAL  PROBLEMS. 


49 


Flo.  68. 


47*  The  07perlN»la  (Fi^.  58)  .—A  hyperbola  Is  a  plane  curve,  such 
that  the  differentM  of  the  distances  from  anv  point  of  It  to  two  fixed  points 

is  equal  to  a  spi  ven  distance.    The  fixed 
points  are  called  the  foci. 

To  conatmot  a  li]rperlN»la* 
—Let  W  and  Jf"  be  the  foci,  and  F'  F 
the  distance  between  them.  Take  a 
ruler  longer  than  the  distance  J^'  F, 
and  fasten  one  of  its  extremities  at  the 
focus  F'.  At  the  other  extremity,  ff, 
attach  a  thread  of  such  a  length  that 
the  length  of  the  ruler  shall  exceed 
the  length  of  the  thread  by  a  given 
distance  A  B.  Attach  the  other  ex- 
tremity of  the  thread  at  the  focus  F. 

Press  a  pencil,  P,  against  the  ruler, 
and  keep  the  thread  constantly  tense, 
while  the  ruler  is  turned  around  F'  as 
a  centre.  The  point  of  the  pencil  will 
describe  one  branch  of  the  curve, 

2(i  MeViod:  By  points  (Fig.  aO).— 
From  the  focus  S"  lay  off  a  distance 
F'  J^  equal  to  the  transverse  axis,  or 
distance  between  the  two  branches  of 
the  curve,  and  take  any  other  distance, 
as  F'Hy  greater  than  F'N. 

With  J^'  as  a  centre  and  F'H  as  a 
radius  describe  the  arc  of  a  circle. 
Then  with  Jr*  as  a  centre  and  NU  •»& 
radius  describe  an  arc  intersecting 
the  arc  before  described  at  p  and  q. 
These  will  be  jpohits  of  the  hyperbola,  torF^q-Fq  is  equal  to  the  trans- 
verse axis  AB, 

If,  with  F  as  a  centre  and  F'  H^  as  a  radius,  an  arc  be  described,  and  a 
second  arc  be  described  with  i«^'  as  a  centre  and  NHasA  radius,  two  points 
in  the  other  branch  of  the  curve  will  be  determined.  Hence,  by  changing 
the  oentma,  each  pair  of  radii  will  determine  two  points  in  each  branch. 

Xlie  BqntlAieiml  Hyperbola.— The  transverse  axis  of  a  hyperbola 
is  the  distance,  on  a  line  joining  the  foci,  between  the  two  branches  of  the 
curve.  The  conjugate  axis  is  a  line  perpendicular  to  the  transverse  axis, 
drawn  from  its  centre,  and  of  such  a  length  that  the  diagonal  of  the  rect- 
angle of  Uie  transverse  and  conjugate  axes  is  equal  to  the  distance  between 
the  fod.  The  diagonals  of  this  rectangle,  indefinitely  prolonged,  are  the 
cuympfoles  of  the  hyperbola,  lines  which  the  curve  continually  approaches, 
but  touches  only  at  an  infinite  distance.  If  these  asymptotes  are  perpen- 
dicular to  each  other,  the  hyperbola  is  called  a  rectanffular  or  equilateral 
hpperboia.  It  is  a  property  of  this  hyperbola  that  if  the  asymptotes  are 
taken  as  axes  of  a  rectangular  system  of  coordinates  (see  Analytical  Geom- 
etry), the  product  of  the  abscissa  and  ordinate  of  any  point  in  the  curve  is 
equal  to  the  product  of  the  abscissa  and  ordinate  of  any  other  point ;  or,  if 
p  is  the  ordinate  of  any  point  and  v  its  abscissa,  and  Pi  and  v,  are  the  ordi- 
nate and  abscissa  of  any  other  point,  pv=pi  v, ;  or  pv  =  a  constant. 

48.  The  Cyelold 
(Fig.  (iO).-lf  a  circle  A  d 
be  roiled  along  a  strarght 
line  ^6,  any  point  of  the 
circumference  as  A  will 
describe  a  curve,  which  Is 
called  a  cycloid.  The  circle 
is  called  the  generating 
circle,  and  A  the  generat- 
ing point. 

To  dranv  a  eyelold. 
— Divide  the  circumference 
of  fbe  generating  circle  Into  an  even  number  of  equal  parts,  as  A  1, 12,  etc., 
and  set  off  these  distances  on  the  base.  Through  the  points  1,  8,  8,  etc.,  on 
tbe  circle  draw  horizontal  lines,  and  on  them  set  off  distances  la  =  Al, 
ibszA^^  =  A^  etc.  The  points  A^  a,  6,  c,  etc.,  wiU  be  points  in  the  cycloid, 
throog^  which  draw  the  curve. 


50 


GSOMETRICAL  PROBLEMS. 


49.  The  Bpleyelold  (Fig.  61)  is 
irenerated  by  a  point  D  in  one  circle 
D  C  roliinff  upon  the  circumference  of 
anotlier  circle  A  C  B,  instead  of  on  a 
flat  surface  or  line;  the  former  beini; 
tiie  generatinK  circle,  and  the  latter 
the  fundamental  circle.  The  generat- 
ing circle  is  shown  in  four  positions,  in 
which  the  generating  point  Is  succes- 
sively marked  A  ly,  iy\  D"'.  A  W  B 
is  the  epipydotd. 


50.  The  0ypoeyelold(Fig.  02) 

Is  generated  bv  a  point  in  the  gener- 
ating circle  rolling  on  the  inside  of  the 
fundamental  circle. 

When  the  generatinflp  circle  =  radius 
of  the  other  circle,  uie  hypocydoid 
becomes  a  straight  line. 


51*  The  Trmetrtx  or 
Sehlele's  mntl-fMetlon  enrre 

(Fig.  08).^/;  is  the  radius  of  the  shaft, 

C,  1,  2,  etc.,  the  axis.    From  O  set  off 

on  17  a  small  distance,  oa\  with  radius 

B  and  centre  a  cut  the  axis  at  1,  join 

a  1,  and  set  off  a  like  small  distance 

a  h\  from  h  with  radius  B  cut  axis  at 

S,  Join  6  S,  and  so  on,  thus  findinsr 

points  o,  a,  &,  c,  d,  etc.,  through  which 

.^     ^  the  curve  is  to  be  drawn. 

Fio.  68. 

62*  The  8plral.-*The  spiral  is  a  curve  described  by  a  point  which 

moves  along  a  straight  line  accortltng  to  any  given  law,  the  line  at  the  same 

time  having  a  uniform  angular  motion.    Tlie  line  is  called  the  radius  vector. 

If  the  radius  vector  increases  directly 
as  the  ineasuring  angle,  the  spires, 
or  parts  described  in  each  revolution, 
thus  gradually  increasing  their  dis- 
tance from  each  other,  the  curve  is 
known  as  the  spiral  of  Archimedes 
(Fig.  64). 

This  curve  is  commonly  used  for 
cams.  To  describe  It  draw  the  radius 
vector  in  several  different  directions 
around  the  centre,  with  equal  angles 
between  them;  set  off  the  distances  1,  2, 3,  4,  etc.,  corresponding  to  the  scale 
upon  which  the  curve  is  drawn,  as  shown  in  Fig.  04. 

In  the  common  spiral  (Fig.  61)  the  pitch  is  uniform;  that  is.  the  spires  are 
equidistant.    Such  a  spiral  is  made  by  rolling  up  a  belt  of  uniform  thickness. 
/ 

To  eonstrnct  a  spiral  ^rltlt 
four  centres  (Fig.  66).— Qiven  the 
pitch  of  the  spiral,  construct  a  square 
about  the  centre,  with  the  sum  of  the 
four  sides  equal  to  the  pitch.  Prolong 
the  sides  in  on^  direction  as  shown; 
the  comers  are  the  centres  for  each 
arc  of  the  external  angles,  formlD£f  a 
quadrant  of  a  spire. 

Fig.  66. 


37     12  8   4    56 
s,^4 .«» -^ 


Fio.  64. 


GEOVETBIGAL  PBOBLEKS. 


51 


53.  To  find  tike  dfmineter  of  a  etrele  Into  urbleb  a  eertaln 
aamlMr  of  lines  will  fit  on  Its  Inside  iPig.  66).— For  instanoe, 
what  is  ihe  diameter  of  a  circle  Isto  which  twelve  ^-inch  rlnss  will  fit,  as 
per  aketch  f    AMume  that  we  have  found  the  diameter  of  the  required 

ci rcle,  and  have  drawn  the  riuss  Ineride 
of  It.  Join  the  centres  of  the  rinjirg 
bv  straight  lines,  as  shown  :  we  then 
obtain  a  regular  polygon  with  18 
sides,  each  side  being  equal  to  the  di- 
ameter of  a  Riven  ring,  we  have  now 
to  And  the  diameter  of  a  circle  cir- 
cumscribed about  this  polygon,  and 
add  the  diameter  of  one  ring  to  it;  the 
sum  will  be  the  diameter  of  the  drole 
into  whicli  tlie  rings  will  fit.  Through 
the  centres  A  andZ)  of  two  adjacent 
rings  draw  the  radii  CA  and  CD; 
since  the  polygon  has  twelve  sides  the 
angle  ACD  =  W>  and  ACB=l6\ 
One  half  of  the  side  ^  D  is  equal  to 
A  B.  We  now  give  the  following  f^ro- 
portlon :  The  sme of  the  angle  ACB 
isto^Baslisto  the  required  ra- 
dius. From  this  we  get  the  following 
Hjjd :  IXIvide  A  B  by  the  sine  of  the  angle  ACB  ;  the  quotient  will  be  the 
radius  of  the  circumscribed  circle  :  add  to  the  corresponding  diameter  the 
diameter  of  one  ring  :  the  sum  will  be  the  required  diameter  FG. 

64.  To  describe  an  are  of  a  elrcle  nrlileli  Is  too  lar^e  to 
be  drasm  by  a  beam  compass,  by  means  of  points  In  tbe 
are,  radlns  belns  slTen.— Suppose  the  radius  is  )M)  feet  and  it  is 
desired  to  obtain  five  points  in  an  arc  whose  half  chord  is  4  feet.  Draw  a 
line  equal  to  the  half  chord,  full  size,  or  on  a  smaller  scale  if  more  con- 
venient, and  erect  a  perpendicular  at  one  end,  thus  making  rectangular 
axes  of  coordinates.  Erect  perpendiculars  at  points  1,  8,  8,  and  4  feet  from 
tlM  first  perpendicular.  Find  values  of  y  in  the  formula  of  the  circle. 
j«  +  ^  =  IP  by  substituting  for  x  the  values  0, 1,  8,  8,  and  4,  etc..  and  forJB* 
the^uare  of  ^e  radius,  or  400.  The  values  will  be  y  =  ^K»  -x*=  «'400, 
<^a99,  t".^,  «'89].  4^884;  =  80,  19.975,  19.90,  19.774,  19.596. 
Subtract  the  smallest, 

or  19.S06,  leaving  0.404,     0.879,     0.804.    0.178,     0        feet, 

liiy  off  these  distances  on  the  Ave  perpendiculars,  as  ordlnates  from  the 
hjjf  chord,  and  the  positions  of  five  points  on  the  arc  will  be  found. 

Through  these   the  curve  may  be 
drawn.    fSee  also  Problem  14.) 

55*  Tbe  Catenary  Is  the  curve 
assumed  by  a  perfectly  flexible  cord 
when  its  ends  are  fastened  at  two 
points,  the  weight  of  a  unit  length 
being  constant. 
The  equation  of  the  catenary  Is 


e  Is  the 


y=  ?(«*'  +  «    "It  *n  which 

base  of  the  Naperlan  system  of  log- 
arithms. 
To  plot  the  catenary,— Let  o 

(Fig.  67)  be  the  origin  of  coordinates. 
Assigning  to  a  any  value  as  8,  the 
equation  becomes 


t  =  l(^  +  e~^y 


M" 


Vl)  =  8. 


52 


OBOHSTBIGAL  PROBLEMS. 


Then  put  a;  =  1;  .*.  y 


Put  a;  =  2; 


:|(i.896  +  o.rir)a 


«.17. 


(1.948  4- 0.618)  =  3.69. 


Put  a;  ^  8,  4,  ft,  <itc.,  etc.,  aud  And  the  correspondinft  Taluee  Ot  y.    For 
each  value  Of  y  we  obtain  two  syiumetrical  points,  as  for  example  p  and  p^ 
In  this  way,  by  making  a  successiyely  equal  to  2,  3,  4,  5,  6^  7,  and  8,  the 
curves  of  Fig.  87  were  plotted. 

In  each  case  the  distance  from  the  origin  to  the  lowest  point  of  the  curve 
is  equal  to  a  ;  for  ptittlng  x=o,  tlie  general  equation  reduces  to  y  =  a. 

For  values  of  a  =  6, 7,  and  8  the  catenary  closely  approaches  the  parabola. 

For  derivation  of  the  equation  of  the  catenary  see  Bowser^s  Analytic 

Mechanics.    For  com po risen  of  the  catenary  with  the  parabola,  see  article 

by  F.  a.  Hohev.  Amer.  Machinist,  Feb.  1, 1W4. 

56*  T]i«  InTOlnte  is  a  name  given  to  the  curve  which  is  formed  by 

the  end  of  a  string  which  is  unwound 
from  a  cylinder  and  kept  taut ;  con- 
sequently the  string  as  it  is  unwound 
will  always  lie  in  Ihe  direction  of  a 
tangent  to  the  cylinder.  To  describe 
the  involute  olf  any  given  circle.  Fig. 
68,  take  any  point  A  on  Its  circum- 
ference,  draw  a  diameter  AB^  and 
from  B  draw  B  b  perpendicular  to  AB. 
Make  Bb  equal  in  length  to  half  the 
circumference  of  the  circle.  Divide 
Bb  and  the  semi-circumference  intt) 
the  same  number  of  equal  part^ 
say  six.  Fi-om  each  point  of  division 
1, 2, 3,  etc.,  on  the  circumference  draw 
lines  to  the  centre  C  of  the  circle. 
Then  draw  1  a  perpendicular  to  C 1 ; 
2  ns  perpendicular  to  02;  and  00  on. 


Fta.  68. 


Make  1  a  equal  to  b  b,  ;  2«r*  equal 
to  &  6)  ;  8  as  equal  to  6  6| ;  ana  so  on. 


Join  the^polnts^,  ai\  a^,  a^,  etc.,  by  a  curve;   this  curve  will  be  the 
required  involute. 
67«  netliod  of  plotting  angles  ^irliliont  nslnga  prAtrae* 

tof.— The  radius  of  a  circle  whose  circumrerence  is  360  is  57. S^ (more  ac- 
curately 57.296).  Striking  a  semicircle  with  a  radius  57.3  by  any  scale, 
spacers  set  to  10  by  the  same  scale  will  divide  the  arc  into  18  spaces  of  10^ 
each,  and  intermediates  can  be  measured  Indirectly  at  the  rate  of  1  by  ecale 
for  each  iVor  interpolated  by  eye  according  to  the  degree  of  accurtury 
required.  The  following  table  shows  the  chords  to  the  above-mentioned 
radius,  for  every  10  degrees  from  0^  up  to  110"*.    By  means  of  one  of  these. 


Ani 


igle.  Chord. 

!• 0.999 

lO* 9.988 

2(r» 19.899 

30«> 29.658 

40» 89.192 

60» 48.429 


Angle.  Chord. 

60» 67.296 

70» 66.73? 

80" 78.668 

90** 81.029 

lWy> 87.782 

110» 93.809 


a  10°  point  is  Oxed  upon  the  paper  next  less  than  the  required  angle,  azid 
the  remainder  is  laid  off  at  the  rate  of  1  by  scale  for  each  degree. 


GEOMETBICAL    FBOt»0SITIONS.  5B 


QEOMETBICAL  PROPOSITIONS. 

la  a  rightanKled  trlaagl«  the  square  on  the  hjpothcnuse  is  equal  to  the 
■uiD  of  the  squares  on  tm  Other  two  sidett. 

Ir  a  trianifle  is  equilateral,  it  is  equiang^ular,  and  vice  ver$a. 

If  a  straight  line  from  the  vertex  of  an  isoMCeles  trlauitle  bisecti  th«  iMse, 
ft  biveotA  me  verifeal  angle  and  is  perpendicular  to  the  base. 

If  one  side  of  a  triangle  Ia  produced,  the  exterior  angle  is  equal  to  the  earn 
of  the  two  interior  ahaopposlte  angles. 

If  two  ti-laiigles  are  mutually  equiangular,  they  are  similar  and  theft* 
corresponding  sides  are  proportional. 

If  the  sides  of  a  polygon  are  produced  la  the  same  order,  the  ftum  of  the 
exterioir  angles  equals  four  rignt  angles. 

In  a  quadrilateral,  tbe  sum  of  the  Interior  angles  equals  four  right  angles. 

In  a  parallelogram,  th*  opposite  sides  are  equal  t  the  oppoilte  augles 
are  equal;  it  Is  oisected  by  Its  diagonal;  and  its  diagonals  bisect  e».ch 
other. 

If  three  points  are  not  in  the  same  straight  line,  a  drole  may  ba  paired 
throuith  tbetn* 

If  two  arcs  are  intercepted  on  the  same  circle,  they  are  proportional  to 
the  corresponding  angles  at  the  centre. 

If  two  arcs  are  simtuur,  they  are  proportional  to  their  radii. 

The  areas  of  two  oirdes  are  proportional  to  the  square*  of  their  radii. 

If  a  radius  is  perpendioular  to  a  chord,  it  bisects  the  chord  and  It  biseoti 
the  are  subtended  by  the  chord. 

A  straight  line  tangent  to  a  circle  meets  it  in  only  one  point,  and  It  It 
perpendicular  to  the  radius  drawn  to  that  point. 

If  frotn  a  point  without  a  ch«le  tangents  are  drawn  to  touch  the  circle, 
there  are  but  two;  they  are  equal,  and  they  make  equal  angles  wilh  th« 
chord  Joining  the  tangent  points* 

ir  two  lines  are  parallel  chords  or  *  tangent  and  parallel  chord,  they 
intercept  equal  arcs  of  a  circle. 

If  an  angle  at  the  circumference  of  a  circle,  between  two  chords,  H  sub- 
tended 1^  the  same  arc  as  an  angle  at  the  centre,  between  two  radii,  the 
sfigla  at  tbe  oinmmference  is  equal  to  half  the  angle  at  the  centra^ 

Ir  a  triangle  is  inscribed  in  a  semiolrcli*,  it  is  rignt-anglrd. 

If  an  angle  is  formed  by  a  tangent  and  chord,  it  is  measured  by  obe  half 
ef  the  aro  intercepted  by  the  chord;  that  is,  it  is  equal  to  hair  the  angle  at 
Ihe  centre  subtended  by  the  chord. 

If  two  abords  intersect  each  other  in  a  drole,  the  rectangle  of  the  seg- 
ments of  the  one  equals  the  rectangle  of  the  segments  of  the  other. 

And  if  one  chord  is  a  diameter  and  the  other  perpendicular  to  ft-,  the 
rectangle  of  the  segments  of  the  diameter  Is  equal  to  the  square  on  half  the 
other  chord,  and  the  half  chord  is  a  mean  proportiotial  betweeu  the  ^g- 
menta  of  the  diameter. 


M  XBKBUBATIOV. 

MENSUBATION. 

PI«ANE  S17RFACE8, 

anadrllateral.— A  four-sided  figure. 

Paralleloffram.— A  quadrllatemi  with  opposite  sides  parallel. 

Fanetiei.— Square :  four  sides  e<iual,  all  angles  right  angles.  Bectangle: 
opposite  .sides  equal,  ali  augles  right  angles.  Rhouibus:  four  sides  equal, 
opposite  angles  equal,  angles  not  right  angles.  Rhomboid:  opposite  sides 
equai,  opposite  angles  equal,  augles  not  right  angles. 

Trapeslom.— A  quadrilateral  with  unequal  sides. 

Trapexold.-A  quadrilateral  with  only  one  pair  of  opposite  sidea 
parallel.  

IMaffonal  of  a  sqaare  =  4/8  x  i*ide«  =  1.4148  x  side. 


IHair,  of  a  rectangle  =  4/sum  of  squares  of  two  adjacent  sides. 

Area  of  any  parallelogram  =  base  x  altitude. 

Area  of  rliombas  or  rEombold  =  product  of  two  adjacent  sides 
X  sine  of  angle  included  between  Lhem. 

Area  of  a  trapezium  =  half  the  product  of  the  diagonal  by  the  sum 
of  the  perpendieulars  let  fall  on  it  from  opposite  angles. 

Area  of  a  trapezoid  =  product  of  naif  the  sum  of  the  two  parallel 
sides  by  the  |>erpendicuiar  distance  between  thefn. 

To  find  tlie  area  of  any  quadrilateral  flcrure.— Divide  the 
quadrilateral  into  two  triangles;  the  sum  of  the  areas  of  ih«  triangles  is  the 


Or,  multiply  half  the  product  of  the  two  diagonals  by  the  sine  of  the  angle 
at  their  intersection. 
To  find  tlie  area  of  a  quadrilateral  Inscribed  In  a  circle* 

^From  half  the  sum  of  the  four  sides  subtract  each  side  severally;  multi- 
plythe  four  remainders  together;  the  square  root  of  the  product  is  the  area. 

Trlanfrle.— A  three-sided  plane  figure. 

Fiat-ietiM.— Right-angled,  having  one  right  angle;  obtuse-angled,  having 
one  obtuse  anf^e ;  isoweles,  having  two  equal  angles  and  two  equal  sides; 
equilateral,  having  three  equal  sides  and  equal  angles. 

The  sum  of  the  three  angles  of  every  triangle  =  180**. 

The  two  acute  angles  of  a  right-angled  triangle  are  complements  of  each 
other. 

Hypothenuse  of  a  right-angled  triangle,  the  side  opposite  the  right  angla 

=  |/sum  of  the  squares  of  the  other  two  sides. 
To  find  tbe  area  of  a  triangle  s 

RuLK  1.  Multiply  the  base  by  half  the  altitude. 

RuLB  8.  Multiply  half  the  product  of  two  sides  by  the  sine  of  the  Included 
angle. 

RiTLK  8.  From  half  the  sum  of  the  three  sides  subtract  each  side  severally; 
multiply  together  the  half  sum  and  the  three  remainders,  and  extract  the 
square  root  of  the  product. 

The  area  of  an  equilateral  triangle  is  equal  to  one  fourth  the  square  of  one 

of  Its  sides  multiplied  by  the  square  root  of  8,  =  - — ^  a  being  the  side;  or 

a«  X  .438018. 

Hypothenuse  and  one  side  of  right-angled  triangle  given,  to  find  other  side, 
Requii'ed  side  =  Vhyp«  —  given  8ide«. 

If  the  two  sides  are  equal,  side  =  hyp  -•- 1.4148;  or  hyp  X  .7071. 

Area  of  a  triangle  given,  to  find  base:  Base  =  twice  area  -1-  perpendicular 
height 

Area  of  a  triangle  given,  to  find  height:  Height  =  twice  area  •*-  base. 

Two  sides  and  base  given,  to  fin^  perpendicular  height  (in  a  triangle  in 
which  both  of  the  angles  at  the  base  are  acute). 

RuLB.— As  the  base  Is  to  the  sum  of  the  sides,  so  Is  the  difference  of  the 
sides  to  the  diflTerence  of  the  divisions  of  the  base  made  by  drawing  the  per- 
pendicular. Half  this  difference  being  added  to  or  subtracted  from  naif 
the  base  will  give  the  two  divisions  thereof.    As  each  side  and  its  opposite 


PLANE  SUBFAGES. 


55 


dirisfoB  of  (he  base  constitutes  a  right-angled  triangle,  the  perpendicular  Is 
aso»lalned  by  the  rule  perpendicular  =  Vhyp*  —  base*. 

Polygon.  —  A  plane  figure  haying  three  or  more  sides.  Regular  or 
irregular,  according  as  the  sides  or  angles  are  equal  or  unequal.  Polj'gons 
are  named  from  the  number  of  their  sides  and  angles. 

To  find  the  area  of  an  Irresnlar  polyson.— Draw  diagonals 
dlTiding  the  polygon  into  triangles,  and  find  the  suiu  of  the  areas  of  these 
triangles. 

To  find  the  area  of  a  regular  polygon  s 

RuLX.— Multiply  the  length  of  a  side  by  the  perpendicular  distance  to  the 
centre;  multiply  the  product  bv  the  number  of  sides,  and  divide  it  by  2. 
Or,  multiple  hau  the  perimeter  by  the  perpendicular  let  fall  from  the  centre 
on  one  of  the  sidea 

The  perpendicular  from  the  centre  Is  equal  to  half  of  one  of  the  sides  of 
the  polygon  multiplied  by  the  cotangent  of  the  angle  subtended  by  the  half 
side. 

The  angle  at  the  centre  =  SOO"  divided  by  the  number  of  sides. 


TABLE  OF  REGULAR  POLYGONS. 

Radius  of  Cir- 

cumscribed 

If 

4i 

1 

II 

Circle. 

^ 

% 

1 

6 

H 

< 

Triangle 

.4380127 

2. 

.6778 

.2887 

1.788 

120» 

60» 

Square 

1. 

1.414 

.7071 

.5 

1.4142 

90 

90 

Pentagon 

1.7204774 

1.288 

.8506 

.6888 

1.1756 

72 

106 

Hexagon 

8  5SM0782 

1.156 

1. 

.866 

1. 

60 

120 

Heptagon 

8.0389124 

l.U 

1.1524 

1.0388 

.8677 

51  2G' 

128  4-7 

Octagon 

4.8284271 

1.068 

1.3066 

1.2071 

.7658 

45 

185 

Nonagon 

6.1818212 

1.004 

1.4619 

1.8787 

.684 

40 

140 

10 

Decagon 

7.0942068 

1.061 

1.618 

1.5.^88 

.618 

36 

144 

11 

Undecagon 

9.3066890 

1.042 

1.7747 

1.70« 

.5634 

82  43' 

147  3-11 

» 

Dodecagon 

11.1961524 

1.087 

1.9319 

1.866 

.5176 

80 

150 

To  And  the  area  of  a  resnlar  polygon,  nrlieii  the  length 
of  a  side  only  to  ciTen  s 

KnjB. — Multiply  the  uquare  of  the  side  by  the  multiplier  opposite  to  the 
Djinie  of  the  polygon  in  the  table. 

To  And  the  area  of  an  Ir- 
regular Acnre  (Fig.  69).— Draw  or- 
diiiates  across  its  breadth  at  equal 
distances  apart,  the  first  and  the  last 
onlinate  each  being  one  half  space 
from  the  endt  of  the  figure.  Find  the 
average  breadth  by  adding  together 
the  lengths  of  these  lines  included  be- 
tw<*en  the  boundaries  of  the  figure, 
and  divide  by  the  number  of  the  lines 
added;  multiply  this  mean  breadth  by 
tbti  length.  The  greater  the  number 
of  lilies  the  nearer  the  approximation. 

In  a  figure  of  very  irregular  outline,  as  an  Indif^itor-diagram  from  a  high- 
speed steam-engine,  mean  lines  may  be  substituted  for  the  actual  lines  of  the 
figure,  being  so  traced  as  to  intersect  the  undulations,  so  that  the  total  area 
of  the  spaces  cut  off  may  be  compensated  by  that  of  the  extra  spaces  in- 
closed. 


86  HE2)8URATIOK. 

fbd  Method :  Tm  Trapbsoidal  Rulb.  —  Divide  the  figure  Into  any  euffl. 
dent  nunibtr  of  equal  parte:  add  half  the  gum  of  the  two  end  ordinaten  to 
the  sum  of  all  the  other  ordinates:  divide  by  ihe  number  of  spaoen  ((hat  is. 
one  less  than  the  number  of  ordinates)  to  obtain  the  mean  ordinate,  and 
multiply  this  by  the  length  to  obtain  the  area. 

8d  Method :  Simpsom^b  Rulb.— Divide  the  length  of  the  figure  into  any 
even  number  of  equal  parts,  at  the  common  distance  D  apart,  and  draw  or. 
dinates  through  uie  points  of  division  to  touch  the  boundary  lines.  Add 
together  the  first  and  last  ordinates  and  call  the  sum^;  add  together  the 
eveu  ordinates  and  call  the  sum  i';  add  together  the  odd  ordinates,  except 
the  first  and  last,  and  call  the  sum  0.   Then, 

area  of  the  figure  =  ^-^^^  +  ^<^  x  D. 

4th  Method :  Durand^s  Rulb.— Add  together  4/10  the  sum  of  the  first  and 
last  ordinates,  1 1/10  the  sum  of  the  second  and  the  next  to  the  last  (or  the 
penultimates),  and  the  sum  of  all  the  intermediate  ordinates.  Multlplv  the 
wum  thus  gained  by  the  common  distance  between  the  ordinates  to  obtain 
the  area,  or  divide  this  sum  by  the  nmnber  of  spaces  to  obtain  the  mean  or- 
dinate. 

Prof.  Durand  describes  the  method  of  obtaining  his  rule  in  Engineering 
Newt,  Jan.  18. 1804.  He  (dalms  that  it  is  more  accurate  than  Simpson's  rule, 
and  practically  as  simple  as  the  trapezoidal  rule.  He  thus  describes  Its  ap- 
plication for  approximate  integration  of  diffenential  equations.  Any  defi- 
nite integral  may  be  represented  graphically  by  an  area.    Thus,  let 


Qz=yudx 


be  an  integral  In  which  u  Is  some  function  of  x,  either  known  or  admitting  of 
computation  or  measurement.  Any  curve  plotted  with  z  as  abscissa  and  u 
as  ordinate  will  then  represent  the  variation  of  u  with  x,  and  the  area  o«- 
tween  such  curve  and  the  axis  X  will  represent  the  integral  in  question,  no 
matter  how  simple  or  complex  may  be  the  real  nature  of  ibe  function  «. 

Substituting  in  the  rule  as  above  given  the  word  ''volume"  for  "area  ' 
and  the  word  **  section  **  for  **  ordinate,"  it  becomes  applicable  to  the  deter- 
mination of  volumes  from  eqnidbtant  sections  as  well  as  of  areas  from 
equidistant  ordinates. 


nates  +  sum  of  the  other  ordinates)  1/10  of  (sum  of  penultimates— sum  of 
first  and  last)  and  multiplying  by  the  common  distance  between  the  ordl- 

^th  Method  —Draw  the  figure  on  croes-sccilon  poper.  Count  tlie  number 
of  squares  that  are  entirely  Included  within  the  boundary;  then  esUmate 
the  fractional  parts  of  squares  that  are  cut  by  the  boundary,  add  together 
these  fractions,  and  add  the  sum  to  the  number  of  whole  squares.  The 
result  is  the  area  in  units  of  the  dimensions  of  the  squares.  The  finer  the 
ruling  oi'  tlie  cross-section  paper  the  more  accurate  the  result. 

Mh  Method.-Vrui  a  planimeter.  

7th  Mt:thf)d.—'Witli  a  chemical  balance,  Rensitive  to  one  milligram,  draw 
thf  flKure  on  paper  of  uniform  thickness  and  cut  It  out  carefully;  weigh  the 
piece  cut  out,  and  compare  its  weight  with  the  weight  per  square  Inch  of  the 
oaper  as  tested  by  weighing  a  piece  of  rectangular  shape. 


THB  CIBCLB. 


67 


THJB   €Ilft€I<S* 

Circiiinferenoe  s  diameter  x  8.1418,  nearly;  more  McuraMy,  8.141RM66S50. 
Approximations,  j  =  8.148;  ^  =  8.1415089. 
The  ratio  of  circum.  to  diam.  is  represented  by  the  symbol «-  (called  Pi), 


Multiples  of  V. 
lv=  8.14150965850 


«rs  6.88818580718 
a«-=  0.48477796077 
4«  =  18.66687061486 
&r  =  15.70706886:96 
6«  =  18  84056598154 
7«  =  21.00114857518 
8r  =  25.18874128878 


'  )c3  =  l. 5707908 
'  X  3  =  2.8561045 
X  4  =  8.1415027 
X  5  =  8.0800006 
X  6  =  4.7123890 
X  7  =  5.4077871 
X  8  =  6.8881858 
X  0  =  7.068je85 
Batio  of  diam.  to  circumference  =  reciprocal  of  r  =  0.8183009. 


Multiples  of  <. 
[*        =    .7853062 


Btfciprocal  of  |v  =  1 .27824. 
Multiples  of  -. 


1 


.81881 

r 

=   .68668 

=  .05108 
=  1.27884 
=  1.50156 


•=1. 


-  =  2.28817 

V 

5.  =  2.54618 
ir 

-  =  2.86470 

w 

-=8.18810 

n 

-  =  8.81072 


^»  =  1.5'n)796 
■ir=  1.647197 
>  =  0.523600 


M=     0.261700 


^=z     0.0G87866 
—  =  114.6015 


««=     0.86060 


-=-  =  0.101321 


1  772458 
0.564180 


Logirs    0.49714067 
Lofi;  ^»  =  T.895090 


^  =  area. 


Diam.  in  Ins.  =  18.5105  4^area  in  sq.  ft. 

Area  in  sq.  ft.  =  (.llam.  In  inches)^  x  .0)54542. 

D  =  diameter,     B  =  radius,      G  =  circumference, 

O  =  irD;  =  2irB;  =  1^;  =  2  V'l^^;  =  8.545  VJ  ; 
il=i>>x  .7854;  =^;  =4i2«  x  .7854;  =»/?•;  =J«i>«;  =  ^;  =.07058C»;  =  ^- 


1)  =  ^ 


=  0.81881  C;    :=2V^;    =  1.18888 V?; 
=  0.160156C;  =  V  |-;    =  0.564180  VI. 


Areas  of  drelss  are  to  each  other  as  the  squares  of  their  diameters. 
To  And  tlie  len^^  of  an  are  of  a  circle  t 

anus  1.  As  860  is  to  the  number  of  degrees  in  ihe  arc,  so  is  the  circum- 
ference of  the  circle  to  the  length  of  the  arc. 

BiTLa  2.  Multiply  the  diameter  of  the  circle  by  the  number  of  degrees  in 
the  aic,  and  this  product  by  0.0067866. 


58  [mbnsubatiok. 

Relation*  of  Are,  Cliord,  CltoWl  of  Half  the  Are^ 
ITereed  Sine,  ete« 

Let  B  =  radius,      D  =  diameter,       Ai-c  =  length  of  arc, 

Cd  =  chord  of  the  arc,       ch  =  chord  of  half  the  arc, 

F=  versed  sine,       D—V  =  diam.  minus  ver.  sin., 

Mi-cd,             ,,        v^aTTF*  X  ior«  ,  „  , 
Arc  = — (very  nearly).    =  — i5c;a»  +  8Sr« ^  ^'*'  nearly. 


Chord  of  the  arc  =  2  Vcfc«-r«;  =  VDa-(2)-ar)«;  =8cA-8^rc 

=  8ViJ»-(«-F)«;  =2V(D-.r)x  F. 
Chord  of  half  the  arc.  cfc=:5^Ca»  +  4K«;  =«^^TF;  ^^^^  +  0^, 


Diameter 


cfc« 


(^ca)«+r» 


Versed  sine  =  ~ ;  =  g(0  "  ♦'^-  C«*; 


(or   i(i)  +  Vz)a-Cd«),    if  F  Is  greater  than  radius. 


=  / 


4  . 


Half  the  chord  of  the  arc  is  a  mean  proportional  between  the  versed  sine 
and  diameter  minus  versed  sine: 


\cd  =  VK  X  (Z)-  F). 


Ijenctli  of  a  Circular  Arc*— Hnjrjglieiis'e  Approximation. 

Let  C  represent  the  length  of  the  choid  octhe  arc  ana  c  the  length  of  the 
chord  of  half  the  arc;  the  length  of  the  arc 

^  =  ""8"- 
Professor  Williamson  shows  that  when  the  arc  subtend  9  an  angle  of  80«,  the 
radius  being  100.000  feet  (nearly  19  miles),  the  error  by  this  formula  is  about 
two  inches,  or  1/600000  part  or  the  radius.  When  the  length  of  the  arc  la 
equal  to  the  radius,  i.e.,  when  it  subtends  an  angle  of  ST".:!,  the  error  is  Iei« 
than  1/7080  part  of  the  radius.    Therefore,  if  the  radius  Is  100,000  feet,  the 

100000 
error  is  less  than    ^^  =  18  feet.    The  error  increases  rapidly  with  the 

increase  of  the  angle  subtended. 

In  the  measurement  of  an  arc  M'hich  Is  described  with  a  short  radius  the 
eiTor  is  so  small  tl^at  it  may  be  neglected.  Describing  an  arc  with  a  radius 
of  12  inches  subtending  an  angle  of  80°,  the  error  is  1/50000  of  an  Inch.  For 
570.8  the  error  is  less  than  0''.U015. 

In  order  to  measure  an  arc  when  It  subtends  a  large  angle,  bisect  it  and 
measure  each  half  as  before— in  this  case  making  B  =  length  of  the  chord  of 
half  the  arc,  and  b  =  length  of  the  chord  of  one  fourth  the  arc ;  then 
_      166-25 

■^= — r~- 

Relation  ot  tlie  Circle  to  Its  Bqnai,  Inscribed^  and  €tr* 
enmscrlbed  Squares* 

Diameter  of  circle  x  .88623 »  _    , .     -         ,  ^..^^ 

.      arcumference  of  circle  x  .28300  f  -  8»"e  of  equal  square. 
Circumference  of  circle  x   l.l28i    =  perimeter  of  equal  square. 


THE  ELLIPSfl.  59 

Diameter     of     circle  x    .70711 

Clrcumfereuoe  of  circle  x  .22508  >  s  side  of  inscribed  square. 

Area  of  circle  k  .90061  •«-  diameter ) 

Area  of  circle  x  1.S78-2  =  area  of  circumscribed  square. 

Area  of  circle  x  .68663  =  area  of  ioscrlbed  square. 

Side  of  square  x  1.414S  =  diam.  of  cii*cumscrA)ed  circle. 

'*     X  4.4428  =circum. * 

"          ••     X  1.1284  =  diam.  of  equal  circle. 

"  8.6*49  =circum. 


Perimeter  of  square  x         0.8 

Square  liiebes  x  LiiTS^     s  circular  inches. 

Sectors  and  Smgnkentm^—To  find  the  ca-ea  of  a  sector  of  a  eirOe, 

RuLB  1.  KultiplT  the  arc  of  the  sector  by  half  its  radius. 

RuLK  8.  As  860  18  to  the  number  of  degrees  in  the  arc,  so  is  the  area  of 
the  circle  to  the  area  of  the  sector. 

RuLB  8.  Multiply  the  number  of  degrees  in  the  arc  by  the  square  of  the 
radius  and  by  .000787. 

To  find  the  area  of  a  segment  of  a  eirde:  Find  the  area  of  the  sector 
which  has  the  same  arc,  and  also  the  area  of  the  triangle  formed  by  the 
diord  of  the  segment  and  the  radii  of  the  sector. 

Then  take  the  sum  of  these  areas,  if  the  segment  is  greater  than  a  semi- 
circle,  but  take  their  difference  if  it  is  less. 

Another  Method:  Area  of  segment  = -^  (<^*^  "  ^^  ^)  '^  which  A  Is  the 

central  angle,  R  the  radius,  and  arc  tlie  length  of  arc  to  radius  1. 

To  find  the  area  of  a  segment  of  a  circle  when  Its  chord  and  height  or 
rersed  sine  only  are  given.    First  find  radius,  as  follows : 

.,  1  fsquare  of  half  the  chord  ,  ,    ,  .  ."I 

8.  Find  the  angle  subtended  by  the  arc,  as  follows:  — ^.         =  sine 

of  half  the  angle.    Take  the  corresponding  angle  from  a  table  of  sines,  and 
double  it  to  get  the  angle  of  the  arc. 
8.  Find  area  of  the  sector  of  which  the  segment  is  a  part ; 

M    1    ,       degrees  of  arc 
area  of  sector  =  area  of  circle  x  — = — 5^- . 

C  Subtract  area  of  triangle  under  the  segment: 

Area  of  triangle  =  ^^^  x  (radius  -  height  of  segment). 

Tlie  remainder  is  the  area  of  the  segment. 

When  the  chord,  arc,  and  diameter  are  given,  to  find  the  area.  From  the 
length  of  the  arc  subtract  the  length  of  the  chord.  Multiply  the  remainder 
by  the  radhis  or  one-half  diameter;  to  the  product  add  the  chord  multiplied 
by  the  height,  and  divide  the  sum  by  2. 

Atiother  rule:  Multiply  tlie  chord  oy  the  height  and  this  product  by  .6884 
plus  one  tefith  of  the  square  of  the  height  divided  bv  the  radius. 

To  find  the  chord:  From  the  diameter  subtract  the  height;  multiply  the 
remainder  by  four  times  the  height  and  extract  the  square  root. 

When  the  chords  of  the  arc  and  of  half  the  arc  and  the  versed  sine  are 
given:  To  the  chord  of  the  arc  add  four  thirds  of  the  chord  of  half  the  arc; 
multiply  the  sum  by  the  versed  sine  and  the  product  bv  .40426  (approximate). 

ClrcnlAr  Wttn§[.—To  find  the  area  of  a  ring  included  betioeen  the  cir- 
cumferencea  of  two  concentric  circles:  Take  the  difference  between  the  areas 
of  the  two  circles;  or,  subtract  the  sqnare  of  the  less  radius  from  the  square 
of  the  greater,  and  multiply  their  difference  by  8.14150. 

The  area  of  the  greater  circle  is  equal  to  wR*; 
and  the  area  of  the  smaller,  •  irr*. 

Their  difference,  or  the  area  of  the  ring.  Is  tr(R*  -  r»). 

Tl^e  BIltf«««— Area  of  an  ellipse  =  product  of  Its  semi-axes  x  8.141S9 

¥=  product  of  its  axes  x  .785898. 

TheEIUpae.'-CiTcamterence  (approximate)  =  8,1416  V^-^J — ,  D  and  d 

being  the  two  axes. 

Trmutwine  gives  the  following  as  more  accurate:  When  the  longer  axis  J) 
i<  not  more  than  five  times  the  length  of  the  shorter  axis,  d, 


60  HJBirSU&AnON, 

aroumferenoe  =5  8.1416  Y  — ^^ ti.H    ' 

When  P  is  mow  tliim  Sd,  th^  divisor  8.8  ia  to  be  replaced  by  the  following : 
For5/d  =  8     7       8        9       10       12      U        16       IS       80       80       40       60 
Divliior    -  9  ».«    »  3    9,35  9.4     9.5     9.6    9.C8    0.T5    9  8    0.93    9,98     10 

An  accurate  formula  is  Cm  w(a  +  b){l  +  Y  "^  76  "^ 250  "^  16384"^  . . .),  in 
which  A  =  ^-^.— /w«ni*ei*r»  Taichenbuch,  1896. 

Carl  G.  Barth  {Mo/ehiMry,  Sept.,  1900)  give*  as  a  very  cIom  approzliqation 
to  thl»  (grmula 

<?^^<<*  +  <>)e4^io^r 

^rea  of  a  aegttkent  of  an  eUip§e  the  baae  of  which  ia  parcel  to  em  of 
the  loea  of  the  ellipia.  Divide  the  height  of  th«  Begment  by  the  ox te  nt 
whjch  it  19  part,  and  And  the  area  of  a  circular  segment.  In  a  table  of  circa- 
Ur  HegmenU,  of  which  the  height  is  equal  to  the  quotient;  multiply  the  area 
thuH  found  by  the  product  of  the  two  axes  of  the  ellipee. 

Cydoldf— A  curve  generated  by  the  rolling  of  a  circle  on  a  plane. 
Length.of  a  cycloldal  curve  =  4  X  diameter  of  the  generating  Qlrcle. 
Length  of  the  base  =  circumference  of  the  generating  clrele. 
Ar^ft  of  a  pycloid  3=  S  x  area  of  generating  circle. 

Helix  (9er«W).-A  Up©  generated  by  the  progressive  rotation  of  a 
poiut  around  an  axis  and  equidistant  from  its  centre,  ^,   ^  ,.   *». 

Length  of  a.  helix.— To  the  gquare  of  the  circumference  described  by  the 
seneratUig-poInt  add  the  square  of  the  distance  advanced  in  one  re^rolutlon, 
and  take  the  square  root  of  their  sum  multiplied  by  the  number  of  revobi- 
tlous  of  the  generating  point.    Or, 

y(c«  +  h*)n  =  length,  n  being  number  of  revolutions, 

Splrml««— Unes  generated  by  the  progressive  rotation  of  a  point  around 
a  fixed  axis,  with  a  constantly  increasing  distance  from  the  axia. 

A  vlane  spiral  Is  when  the  point  rotates  in  one  plane. 

A  conical  spiral  is  when  the  point  rotates  around  an  axis  at  a  progressing 
distance  from  ita  centre,  and  advancing  in  the  direction  of  the  axis,  as  around 

*  l^mgth  of  a  plane  spiral  J»nP,— When  the  distance  between  the  polls  is 

RuLB.— Add  together  the  greater  and  less  diameters;  divide  their  sum  by 
2-  multiply  the  quotient  by  8.1416,  and  again  by  the  number  of  revolutions. 
Or  take  the  mean  of  the  length  of  the  greater  and  less  circumferences  and 
multiply  ft  by  the  number  pf  revolutions.    Or, 

length  ^  vn  ^\^\  d  and  d'  being  the  Inner  and  outer  dlameteiv. 

Length  of  a  conical  spiral  Wn«.-Add  together  the  greater  wd  less  diam- 
eters; divide  their  sum  by  8  and  multiply  the  quotient  by  8.14J6,  To  the 
souare  of  the  product  of  this  circumference  and  the  number  of  revolutions 
of  the  spiral  add  the  square  of  t4ie  height  of  ite  axis  and  take  the  square 
root  of  Uie  sum. 

Or,  lengtli  1 


80LI9  BOPTBti, 

Xbe  Priam,— TV)  iind  the  surface  of  aright  pri9m :  Multiply  the  perim- 
eter of  the  base  by  the  altitude  for  the  convex  surface.  To  thi«  add  the 
4feas  of  the  two  ends  when  the  entire  surface  is  required. 

Volume  of  a  prism  «  area  of  ita  base  x  ita  altitude. 

The  pywimld.-Convex  surface  of  a  regular  pyramid  =  Pfrtmeter  of 
its  base  X  half  the  slant  height.  To  tliis  add  area  of  the  base  if  the  whole 
surface  is  required. 

Volume  of  a  pyramid  =  area  of  base  X  one  third  of  the  altitude. 


SOLID  BODIES.  61 

To  find  the  aurface  vf  afnutuni  of  a  regular  pyramid :  Multiply  half  the 
slant  height  by  the  sum  of  the  perimeters  of  the  two  bases  for  the  couvez 
surface.  To  this  add  the  areas  of  the  two  bases  when  the  entire  surface  is 
reqalnHL 

To  find  the  volume  of  a  frustum  of  a  pyramid :  Add  together  the  areas  of 
tlie  two  bases  and  a  mean  proportional  between  them,  and  multiply  the 
sum  by  one  third  of  the  altitude.  (Mean  proportional  between  two  numbers 
=  square  root  of  their  product.) 

wedipe*— A  wedge  is  a  solid  bounded  by  Ave  planes,  yIz,:  a  rectangular 
base,  two  trapezoids,  or  two  rectangles,  meeting  in  an  edge,  and  two  tri> 
angular  ends.  The  altitude  is  the  perpendicular  drawn  from  any  point  in 
the  edge  to  the  plane  of  the  base. 

Tomtd  the  volume  of  a  wedge :  Add  the  length  of  the  edge  to  twice  the 
leogtli  of  the  beae,  and  multiply  the  sum  by  one  sixth  of  the  product  of  the 
height  of  the  wedge  and  Uie  breadth  of  the  base. 

Wt^eetmngutmr  prlsmold*— A  rectangular  prismoid  is  a  solid  bounded 
by  six  plaues,  of  which  the  two  bases  are  rectangles,  baying  their  corre« 
sponding  sides  parallel,  and  the  fotu*  upright  sides  of  the  solidii  are  trape- 
zoids. 

To  find  the  volume  of  a  rectangular  prigmoid:  Add  together  the  aresa  of 
the  two  bases  and  four  times  the  area  of  a  pamllel  section  equally  dlstaut 
from  the  bases,  and  multiply  the  sum  by  one  sixth  of  the  altitude. 

Cylinder*— Ck>n  vex  surface  of  a  cylinder  =  perimeter  of  bane  x  altitude. 
To  this  add  the  areas  of  the  two  ends  when  the  entire  surface  is  required. 
Volume  of  a  cylinder  =  area  of  base  X  altitude. 

CToae.— Convex  surface  of  a  oone  =?  oircumf erenoe  of  base  x  half  the  slant 
aide.    To  this  add  the  area  of  the  base  when  the  entire  surface  is  required. 

Volume  of  a  oone  s  area  of  base  x  g  altitude. 

3b  find  the  aurfaoe  of  a  frustum  of  a  cone :  Multiply  half  the  side  by  the 
snm  of  the  circumferences  of  the  two  bases  for  the  convex  surface;  to  this 
add  the  areas  of  the  two  bases  when  the  entire  surface  is  requirsd. 

To  find  the  volume  ofafnutum  of  a  cone :  Add  together  the  areas  of  the 
tiro  bases  and  a  mean  proportional  between  them,  and  multiply  the  sum 
by  one  third  of  the  altitude. 

Spli«re.—7\>  And  the  turf  ace  of  a  sphere :  Multiply  the  diameter  by  the 
circumference  of  a  great  circle;  or,  multiply  the  square  of  the  diameter  by 
8.141seL 

Surface  of  sphere  =  4  x  area  of  its  great  circle. 

**        ••      *'      =s  convex  surface  of  its  circumscribing  cylinder. 

Surfaces  of  spheres  are  to  each  other  as  the  squares  of  their  diameters. 

To  find  thm  volume  of  a  apJiere :  Multiply  the  surface  by  one  third  of  tbs 
radius;  or,  multiply  the  cube  of  the  diameter  by  l/Ov;  that  is,  by  O.fi^. 

Value  of  |ir  to  10  decimal  places  =  .588^087766. 

The  Tolume  of  a  sphere  =  S/8  the  volume  of  its  dronmscribing  cylinder. 

Volumes  of  spheres  are  to  each  other  as  the  cubes  of  their  diameters. 

8pherlesU  tritLnjgle.^To  find  the  areaqfa  splieiioal  triangle :  Com- 
pute the  surface  of  the  quadrantal  triangle,  or  one  eighth  of  the  surface  of 
the  sphere.  From  the  sum  of  the  three  angles  subtract  two  right  angles; 
divide  the  remainder  by  SX),  and  multiply  the  quotient  by  the  area  of  the 
quadrantal  triangle. 

Spherleal  poljgonm— To  find  the  area  of  a  spherical  polygon:  Com- 
pQie  the  snrface  of  the  quadrantal  tiiangle.  From  the  sum  of  all  the  angles 
subtract  the  product  of  two  right  angles  by  the  number  of  sides  less  two; 
divide  the  remainder  by  90  and  multiply  the  quotient  by  the  area  of  the 
quadrantal  triangle. 

The  prlmnold.— The  prismoid  is  a  solid  having  parallel  end  areas,  and 
mav  be  composed  of  any  combination  of  prisms,  cylinders,  wedges,  pyra- 
mids, or  cones  or  frustums  of  the  same,  whose  bases  and  apices  lie  in  the 
end  areas. 

Inasmuch  as  cylinders  and  cones  are  but  special  forms  of  prisms  and 
pyramid^  and  warped  surface  solids  mav  be  divided  into  elementary  forms 
of  them,  and  since  frustums  may  also  be  subdivided  into  the  elementary 
forms,  it  Is  sufflcient  to  sav  that  all  prismoid s  may  be  decomposed  into 
prisms,  wedges,  and  pyramids.  If  a  formula  can  be  found  which  is  equally 
applicable  to  all  of  these  forms,  then  it  will  apply  to  any  combination  of 
them.    Such  a  formula  is  called 


62  MENSURATION. 

The  Prlsmoldml  Foratnta. 

Let  A  =  area  of  the  base  of  a  prism,  wedge,  or  pjramld; 
^j,  ^t,  Am  =  the  two  end  and  the  middle  areas  of  a  pruunoid,  or  of  any  of 
its  elementary  solids; 
h  =  altitude  of  the  prismoid  or  elementary  solid; 
V=  its  volume; 

For  a  prism  A^  Am  and  A^  are  equal,  =A\  V=-^x^A^  hA. 

For  a  wedge  with  paraUel  ends,  A^  =  0.  ^m  =  |ii, ;  r=  |u,  +  2Ao  =  —- 

For  a  cone  or  pyramid,  At  =  0,  Am  =  7^1 ;  V  s=  ^(4,  +  Ai)  =  -^. 

The  prismoldal  formula  is  a  rigid  formula  for  all  prismoids.  The  only 
approximation  involved  in  its  use  is  in  the  assumption  that  the  given  solid 
may  be  generated  by  a  right  line  moving  over  tne  boundaries  of  the  end 


The  area  of  the  middle  section  Is  never  the  mean  of  the  two  end  areas  if 
the  prismoid  contains  any  pyramids  or  coues  among  Its  elementary  forma 
When  the  three  sections  are  similar  in  form  the  dimeiinoru  of  the  middle 
area  are  always  the  means  of  the  corresponding  end  dimensions.  This  fact 
often  enables  the  dimensions,  and  hence  the  area  of  the  middle  section,  to 
be  computed  from  the  end  areas. 

Polyedronsa—A  polyedron  is  a  solid  bounded  by  plane  polygons.  A 
regular  polyedron  Is  one  whose  sides  are  all  equal  regular  polygons. 

To  find  the  aurface  of  a  regular  po/^edrou.— Multiply  the  area  of  one  of 
the  faces  by  the  number  of  faces  ;  or,  multiply  the  square  of  one  of  the 
edges  by  the  surface  of  a  similar  solid  whose  edge  is  unity. 

A  Tabub  of  the  Rboular  Poltbdbons  whoss  Edoks  ark  Unity. 

Names.                                      No.  of  Faces.  Surface.  Volume. 

Tetraedron 4  1.7330608  0.1178513 

Hexaedron 6  6.O00O00O  1.0000000 

Octaedron  8  8.4041016  0.4714045 

Dodecaedron 18  I«).6I57288  7.6681189 

Icosaedron 90  8.060^540  2.1816950 

To  flnd  tb«  Tola  me  of  a  reralar  polyedron.— Multiply  the 

surface  by  one  third  of  the  perpendicular  let  fall  f  1  oin  tliM  centre  on  one  of 
the  faces ;  or,  multiply  the  cube  of  one  of  the  edges  by  the  solidity  of  a 
similar  polyedron  whose  edge  is  unity. 

Solid  of  reTolatlon.— The  volume  of  any  solid  of  revolution  Is 
equal  to  the  product  of  the  area  of  its  generating  surface  by  the  length  of 
the  path  of  the  centre  of  gravity  of  that  surface. 

The  convex  surface  of  any  soUd  of  revolution  is  equal  to  the  product  of 
the  perimeter  of  Its  generating  surface  by  the  length  of  path  of  its  centre 
of  gravity. 

Cylindrical  rlnff.— Let  d  =  outer  diameter ;  d'  =  inner  diameter ; 

s  (ri  -  d')  =  thickness  =  t ;  7  » f*  =  sectional  area  ;  -Ad-^-d')  =  mean  diam> 

s  4  « 

eter  =  3f ;  wt  =  circumference  of  section  \  vM=^  mean  circumference  of 
ring;  surface  =  irt  x  nM\  =  iw«(d*  -  (!'«);=  9.86965 < If;  =  8.46741  (cl»  -d'«); 

volume  =  i  »  «« If  it;  =  8.4674U«  M. 

4 

Splierleal  momt*— Surface  of  a  aphericaf  gone  or  segment  of  a  sphere 
=  its  altitude  x  the  circumference  of  a  great  circle  of  the  sphere.  A  great 
circle  Is  one  whose  plane  passes  through  the  centre  of  the  sphere. 

Volume  of  a  tone  of  a  sphere.^To  the  sum  of  the  squares  of  the  radii 
of  the  ends  add  one  third  of  the  square  of  the  height ;  multiply  the  sum 
by  the  helirht  and  by  1.5706. 

Spherical  •enrment.— Volume  of  a  tpherical  segment  tcith  one  6ase.~ 


SOLID  BODIES.  63 

MaltlpW  half  the  helRht  ot  the  segment  by  the  area  of  the  base,  and  the 
cube  or  the  heleht  by  .62S6  and  add  the  two  products.  Or,  from  three  times 
the  diameter  of  the  sphere  subtracl  twice  the  height  of  the  segment;  multi- 
ply the  difference  br  the  square  of  the  height  and  by  .5286.  Or,  to  three 
times  the  square  of  the  radius  of  the  base  of  tne  segment  add  the  square  of 
its  height,  and  multiply  the  sum  by  the  height  and  oy  .5286. 

^berold  or  •lUpsold.— When  the  revolution  of  the  spheroid  Is  about 
the  trausverse  diameter  it  is  prolate^  and  when  about  the  conjugate  it  is 
oblate. 

Convex  swf/aee  of  a  §effment  of  a  mAero^ —Square  the  diameters  of  the 
spheroid,  and  take  the  square  root  of  half  their  sum  ;  then,  as  the  diameter 
from  which  the  segment  is  cut  is  to  this  root  so  is  the  height  of  the 
segment  to  the  proportionate  height  of  the  segment  to  the  mean  diameter. 
Multiply  the  product  of  the  other  diameter  and  8.1410  by  the  proportionate 
height. 

Convex  mirfaee  of  a  fnutwn  or  zone  of  a  tpheroid.— Proceed  as  by 
prevloDS  rule  for  the  surface  of  a  segment,  and  obtain  the  proportionate 
height  of  the  frustum.  Multiply  the  product  of  the  diameter  parallel  to  the 
base  of  the  frustum  and  8.1416  by  the  proportionate  height  of  the  frustum. 

Folttme of  a  mheroid is  equal  to  theproduct  of  the  square  of  the  revolving 
axis  by  the  fixed  axis  and  by  .6886.  The  volume  of  a  spheroid  is  two  thirds 
of  that  of  the  circumscribing  cylinder. 

Volume  of  a  tegment  of  a  mkeroid.'-l.  When  the  base  is  parallel  to  the 
revolviog  axis,  multipW  the  difference  between  three  times  the  fixed  axis 
and  twice  the  height  of  the  segment,  by  the  square  of  the  height  and  by 
jex.  Multiply  the  product  by  the  square  of  the  revolving  axis,  and  divide 
by  the  square  of  the  fixed  axis. 

t.  When  the  base  is  perpendicular  to  the  revolving  axis,  multiply  the 
difference  between  three  times  the  revolving  axis  and  twice  the  height  of 
the  segment  by  the  square  of  the  height  and  by  .6286.  Multiply  tlie 
product  by  the  length  of  the  fixed  axis,  and  divide  by  the  length  of  the 
revolving  axis. 

Volume  of  ike  middle  fniBtum  of  a  spheroid.—l.  When  the  ends  Are 
circular,  or  parallel  to  the  revolving  axis :  To  twice  tlie  square  of  the 
middle  diameter  add  the  square  of  the  diameter  of  one  end  ;  multiply  the 
sum  by  the  length  of  the  frustum  and  by  .2618. 

SL  when  the  ends  are  elliptical,  or  perpendicular  to  the  revolving  axis : 
To  twice  the  product  of  the  transverse  and  conjugate  diameters  of  the 
middle  section  add  the  product  of  the  transverse  and  conjugate  diameters 
of  one  end  ;  multiply  the  sum  by  the  length  of  the  frustum  and  by  .2618. 

SpiDdles*— Figures  generated  bv  the  revolution  of  a  plane  area,  when 
the  curve  is  revolved  about  a  chord  perpendicular  to  its  axis,  or  about  its 
double  ordinate.  They  are  designated  by  the  name  of  the  arc  or  curve 
from  which  they  are  generated,  as  Circular,  Elliptic,  Paiabolic,  etc.,  etc. 

Convex  aurface  of  a  circular  apindle^  zone^  or  tegmeiit  of  it  —Rule:  Mul- 
tiply the  length  by  the  radius  of  the  revolving  arc;  multiply  this  arc  by  the 
central  distance,  or  distance  between  the  centre  of  the  spindle  and  centre 
of  the  revolving  arc  ;  subtract  this  product  from  the  former,  double  the 
remainder,  and  multiply  it  bv  8.1416. 

Foliime  o/ a  c/nnttor  «ptndle.— Multiply  the  central  distance  by  half  the 
area  of  the  revolving  segment;  subtract  the  product  from  one  third  of  the 
cube  of  half  the  length,  and  multiply  the  remainder  by  12.5664. 

Viflume  offi^utum  or  tone  or  a  circular  spindle.— From  the  square  of 
half  the  length  of  the  whole  spindle  take  one  third  of  the  square  of  Irnlf  the 
length  of,  the  frustum,  and  multiply  the  remainder  by  the  said  half  length 
of  the  frustnm  ;  multiply  the  central  distance  by  the  revolving  area  which 
f^enerates  the  frustum  ;  subtract  this  product  from  the  former,  and  multi- 
ply the  remainder  by  6.888S. 

Volume  of  a  aegment  of  a  ciixular  aptndle.— Subtract  the  length  of  the 
segment  from  the  half  length  of  the  spindle  :  double  the  remainder  and 
ascertain  the  volume  of  a  middle  frustum  of  this  length  ;  subtract  the 
result  from  the  volume  of  the  whole  spindle  and  halve  the  remainder. 

Volume  of  a  eydoidal  mindle  =  five  eighths  of  the  volume  of  the  circum- 
scribing cylinder.— Multiply  theproduct  of  the  square  of  twice  the  diameter 
of  the  generating  circle  and  8.927  by  its  circumference,  and  divide  this  pro- 
duct by  & 

Parabolic  conoid.— Fbliime  of  a  parabolic  conoid  (generated  by  the 
revolution  of  a  parabola  on  its  axis).- Multiply  the  area  of  the  base  by  half 
the  height. 


64  MENSURATION. 

Or  multiplxthe  square  of  the  diameter  of  the  base  by  the  height  and  bj 
•8827. 

Volume  of  a  frustum  of  a  parabolic  eonotd.—Multipbr  half  the  sum  of 
the  areas  of  the  two  ends  by  the  heig^ht. 

Volume  of  a  parabolic  spindle  (generated  bv  the  reToluUon  of  a  parabola 
on  Its  base).— Multiply  the  square  of  the  middle  diameter  by  the  lengrth 
and  by  .4188. 

The  volume  of  a  parabolic  spindle  is  to  that  of  a  cylinder  of  the  same 
heif  ht  and  diameter  as  8  to  15. 

volume  of  the  middle  frustum  of  a  parabolic  spindle.— Add  together 
8  times  the  square  of  the  maximum  diameter,  8  times  the  square  of  the  end 
diameter,  and  4  times  the  product  of  the  diameters.  Multiply  the  sum  by 
the  leoRth  of  the  frustum  and  by  .05286. 

This  rule  is  applicable  for  calculating  the  content  of  casks  of  parabolic 
form. 

Caaks.— To  find  the  volume  of  a  cask  of  any  /oitn.— Add  together  88 
times  the  square  of  the  bung  diameter,  25  times  the  square  of  the  head 
diameter,  and  26  times  the  product  of  the  diameters.  Multiply  the  sum  by 
tlie  length,  and  divide  by  81,778  for  the  content  in  Imperial  gallons,  or  by 
«6j470  for  U.S.  gallons. 

This  rule  was  framed  by  Dr.  Hutton,  on  the  supposition  that  the  middle 
third  of  the  length  of  the  casir  was  a  frustum  or  a  parabolic  spindle,  and 
each  outer  third  was  a  frustum  of  a  cone. 

To  find  the  ullage  of  a  cask,  the  quantity  of  liquor  in  it  when  it  is  not  full. 
1.  For  8k  lying  cask :  Divide  the  number  of  wet  or  dry  inches  by  the  bung 
diameter  in  Inches.  If  the  Quotient  is  less  than  .5,  deduct  from  it  one 
fourth  part  of  what  it  wants  of  .5.  If  it  exceeds  .5,  add  to  it  one  fourth  part 
of  the  excess  above  .5.  Multiply  the  remainder  or  the  sum  by  the  whole 
content  of  the  caslr.  The  product  is  the  quantity  of  liquor  in  the  cask,  in 
gallons,  when  the  dividend  is  wet  Inches;  or  the  empty  space,  if  dry  inches. 

2.  For  a  standing  cask :  Divide  the  number  of  wet  or  dry  inches  by  the 
length  of  the  cask.  If  the  quotient  exceeds  .6,  add  to  it  one  tenth  of  its 
excess  above  .5;  if  less  than  .5,  subtract  from  it  one  tenth  of  what  it  wants 
of  .5.  Multiply  the  sum  or  the  remainder  by  the  whole  content  of  the  cask. 
The  product  is  the  quantity  of  liquor  in  the  cask,  when  the  dividend  is  wet 
inches;  or  the  empty  space,  if  dry  inches. 

Volume  of  cask  (approximnte)  U.  8.  gallons  =  square  of  mean  dlam. 
X  lengtli  in  inches  X  .0084.  Mean  dlam.  =  half  tlie  sum  of  the  bung  and 
head  dlams. 

Tolmne  of  mn  Irre/gnlar  solid.— Suppose  it  divided  into  parts, 
resembling  prisms  or  other  bodies  measurable  by  preceding  roles.  Find 
the  content  of  each  part;  the  sum  of  the  contents  is  the  cubic  contents  of 
the  solid. 

The  content  of  a  small  part  is  found  nearly  by  multiplying  half  the  sum 
of  the  areas  of  each  end  by  the  perpendicular  distance  between  them. 

The  contents  of  small  frr^ular  solids  mny  sometimes  be  foimd  by  im- 
mersing them  under  water  in  a  prismatic  or  cylindrical  vessel,  and  observ* 
ing  the  amount  by  which  the  level  of  the  water  descends  when  the  solid  is 
w  ithdrawn.  The  sectional  area  of  the  vessel  being  multiplied  by  the  descent 
of  the  level  gives  the  cubic  contents. 

Or,  weigh  the  solid  in  air  and  in  water;  the  difference  Is  (he  weight  of 
water  it  displaces.  Divide  the  weight  In  pounds  by  62.4  to  obtain  volume  in 
ciil>ic  feet,  or  multiply  it  by  27.7  to  obtain  the  volume  In  cubic  inches. 

When  the  solid  is  very  large  and  a  great  degree  of  accuracy  is  not 
requisite,  measure  its  length,  breadth,  and  depth  in  several  oifferent 
places,  and  take  the  mean  of  the  measui«ment  for  each  dimension,  and 
multiply  the  three  means  together. 

When  the  surface  of  (he  solid  is  very  extensive  it  Is  better  to  divide  it 
into  triangles,  to  And  the  at-ea  of  each  triangle,  and  to  multiply  it  by  the 
mean  depth  of  the  triangle  for  the  contents  of  each  triangular  portion;  ihs 
contents  of  the  triangular  sections  are  to  be  added  together. 

The  mean  depth  of  a  triangular  section  is  obtained  by  measuring  Uie 
depth  at  each  angle,  adding  together  the. three  measurements,  and  taking 
one  third  of  the  sum. 


PLA.NB  TBtaOlsrolCBTBT*  6S 


VLAITE  TBIGK>HOMET&Y« 


Trtconom«trlcal  FuneUons. 

Erery  tiiAngto  has  six  parts— three  angles  and  thrM  sides.  When  any 
hn-e  of  these  parts  are  given,  provided  one  of  them  is  a  side,  the  other 
>-irts  may  be  determined,  uy  the  solution  of  a  triangle  is  meant  the  detet^> 
iiinaiion  of  the  unknown  parts  of  a  triangle  when  certain  parts  are  given. 

The  complement  of  an  angle  or  arc  is  what  remains  after  subtracting  the 
in^le  or  arc  from  Wf*., 

In  general,  if  we  represent  any  arc  by  A,  its  complement  is  90^  —  ^. 
Hf  Dce  the  complement  of  an  arc  that  exceeds  90**  is  negative. 

Since  the  two  acute  angles  of  a  right-angled  triangle  are  together  equal  to 
I  right  angle,  each  of  them  Is  the  complement  of  the  other. 

The  supplement  of  an  angle  or  arc  is  what  remains  after  subtracting  the 
ingle  or  arc  from  I9ff*.  If  ^  is  an  arc  its  supplement  Is  ISO**  —  A,  The  sup- 
^rnent  of  an  arc  that  exceeds  180°  is  negative. 

Tke  Bum  of  the  three  angle$  of  a  triangle  u  eguaZ  to  180».  Either  angle  is 
\be  supplement  of  the  other  two.  In  a  nght-angled  triangle,  the  right  angle 
being  equal  to  90*,  each  of  the  acute  angles  is  the  complement  of  the  other. 

In  ail  right-angled  triangles  having  the  same  acute  angle,  the  sides  have 
lo  each  other  the  same  ratio.  These  ratios  have  received  special  names,  as 
billows: 

If  ^  is  one  of  the  acute  angles,  a  the  opposite  side,  b  the  adjacent  side, 
md  c  the  hypothenuse. 

The  sliie  of  the  angle  A  is  the  quotient  of  the  apposite  tide  divided  by  the 
a 
kfpothenum.     Sin.  A^ -^ 

Tlie  ta.Bsemt  of  the  angle  A  is  the  quotient  of  the  opposite  side  divided  by 
a 
tke  adjacent  tide.   Tang.  A  =  ^ 

The  — eant  of  the  angle  A  is  the  quotient  of  the  hypothenuse  difftded  by 
o 
Ike  adj€teeni  side.    Sec.  A  =  -y 

The  eoslBe^  cotmnipeiit,  and  eoseeant  of  an  angle  are  respeo- 
tirely  the  sine,  tangent,  and  secant  of  the  complement  of  that  angle.  The 
terms  sine,  cosine,  etc.,  are  called  trigonometrical  functions. 

In  adrcle  whose  radius  is  unity,  tbe  sine  of  an  arc^  or  of  the  angle  at  tfie 
centre  metuured  by  that  are^  is  the  perpendicular  let  fall  from  one  extreme 
ii\*}f  the  arc  upon  the  diameter  passing  through  the  other  extremity. 

The  tfluscent  of  an  arc  is  ths  line  lokieh  touches  the  circle  at  one  extreme 
i(y  o/  the  arc.  and  is  limited  by  the  diameter  {produced)  passing  through 
&>  other  extremity. 

The  eeesiht  o/  an  arc  is  that  pari  of  the  produced  diameter  which  is 
intfrcepted  bet'reen  the  centre  and  the  tangent. 

The  wemed  sine  of  an  arc  is  that  part  of  the  diameter  intercepted 
btttceen  the  extremity  of  the  arc  and  the  foot  of  the  sine. 

Tn  A  circle  whoee  radius  is  not  unitv,  the  trigonometric  functions  of  an  arc 
viil  be  equal  to  the  lines  here  defined,  divided  by  the  radius  of  ihe  circle. 

If  /  C  ^  (Fig.  70)  Is  an  angle  in  the  first  quadrant,  and  0  Fsa.  radius, 

Tbescoeof  th.««le=^.  00.  =  ^  =  ^^ 

T««.  =  iSd.-  Secant  =  ^^.  Cot.  =  ^ ; 
CL    „     ,         CfA 
^^**^^'  =  Bad.*  VerslD.  =  g^.  B 

If  radius  Is  1,  then  Rad.  In  the  denominator  is 
C'lnitLed,  and  sine  as  FQ^  ete. 

The  erne  of  an  arc  a  half  the  chord  of  tioiee  ihe 
srv. 

Tbe  sine  of  the  supplement  of  the  arc  is  the  same  fj/ 
SR  that  of  the  arc  itself  .    Bine  of  arc  B  i^  i^' =  J^  (?  = 
riaare^*^  Fio.  70. 


68 


PLAKB  TBIGOKOHETBY. 


The  tangent  of  the  supplement  is  equal  to  the  tangent  of  the  arc,  but 
a  contrary  sign.   IVing.  BDF=  B  M. 

The  secant  of  th6  supplement  is  equal  to  the  secant  of  the  arc,  but  with 
contrary  sign.    Sec.  BDF=  CM. 

Mens  of  the  nmetloniB  in  tbe  four   qamdrante,— If 
dWide  a  circle  into  four  quadrants  by  a  vertical  and  a  hurisontal  dif- 
fer, the  upper  right-hand  quadrant  is  called  the  first,  the  upper  left  the  f 
ond,  the  lower  left  the  thira,  and  the  lower  right  the  fourth.    The  signs  ( 
the  functions  in  the  four  quadrants  are  as  follows:  j 

F«r«fquadL  5eoo»dquad.  STb^rdquad.  Jrburf ft  qusd 
Sine  and  cosecant,   -       +                    +                   —  —       i 

Cosine  and  secant,  4-  —  —  4-      ! 

Tangent  and  cotangent,  +  -*  +  — 

The  values  of  the  functions  are  as  follows  for  the  angles  specified: 


Angle 

Sine 

Ckwine 

Tangent 

Cotangent.. 

Secant  

Cosecant... 

Versed  sine 


80 
j_ 

2 
2 


45 

_L 

1 
1 

V2 

V5-1 


^2 


90     180 

8 

_  1 
8 

-8 
8 

8 


185 
_1_ 

1_ 

^2 
-1 
-1 

V2 

£?+-' 

V8 


150 

1 

.  8 

8 

J_ 
V8 

•  V8 

8 

8 


1801870 
0     -1 

-1 
0 


e..    J 


TRIGONOlOLBTIUCAIi  FORJIiUIi.SU 

The  following  relations  are  deduced  from  the  properties  of  similar  U 
angles  (Kaditis  =  1): 

sin  A 

cos  .^ :  sin  ul  n  1 1  tan  ji,  whence  tan  A  = r : 

cos  .<1* 


sin  A  t  cos  ^  a  1 1  cot  A,      **  cotan  A  = 

cos  ul :  1         a  1 :  sec  .<1,      "  sec  ^  = 

sin  ^  1 1         a  1 :  cosec  A,  "  oosec  A  = 

tanul:!         alxcot^       "  tan^  = 


cos.<i 

8ln  A 

_J 

cos  A 

J[ . 

sin  A' 

_1 

cot.<l' 


The  sum  of  the  square  of  the  sine  of  an  arc  and  the  square  of  its  cosi^ 
equals  unity.    Sln«  A  4-  cos*  A  =  1. 
AlBo,  1  4-  tan«  A  =  sec*  A:       1  +  cot«  A  =  cosec*  A, 

Fimctlons  of  tlte  anna  and  dllTerenee  of  tivo  nnsloa  i 

•    Let  the  two  angles  be  denoted  by  A  and  i?,  their  sum  A-i-  B  =  C,  a^ 
their  difference  A  -  P  hj  D, 

sin  (^  4- 1;)  =  sin  ^  cos  £  +  cos  ^  sin  2^; 


TBIGOKOMBTBICAL  FOBMULiB. 


o(M  (A -{- S)  =  CM  A  cot  B  -  Bin  A  tkn  B;  .  .  • 

9ln  {A  ^  B)  =  iAn  A  oob  B  —  ooa  ^  sin  B;   .  .  • 

COS  {A  —  B)  =  cos  A  cw  B  i- sin  A  aia  B.   .  .  . 
From  tbflte  four  formiilaB  by  addition  and  subtraction  we  obtain 

Bin  U  +  ^)  +  sin  U  -  B)  =  2  sin  ^  cos  B;  .  .  . 

BinU  +  iO-8in  U~B)  =  8co8^8la  B;  .  .  . 

O08  M  +  B)  +  000  (il  -  B)  =  2  ooe  >.  cofl  J^;  .  .  . 

coBU-Bj^CM(A  +  B)  =  9tinAaiBB..  .  . 


(«) 
(8) 

(4) 

(5) 
(«) 
(7) 
(8) 

If  we  put  wl  +  B  =  C.  and  ^  -  B  =  B,  then  A  s  mc  +  D)  and  B  »  ^C  - 
B),  and  we  hare 

sinC+BinBsS8inH<^+B)co«Vi(0- B);  .  ...  (9) 
rinC-ilnB=:2coeH<C+I>)8lnH(C- B):  .  .  .  .  (10) 
co8C4-cosB=r2co8H(C+B)co8H(C-B);  .  .  .  .  (11) 
oosB-oos(7=28in  H(C+B)BinH(C- B) (12) 

Equation  (9)  may  be  enunciated  thus:  The  sum  of  the  sines  of  any  two 
amrles  ifl  equal  to.  twice  the  sine  of  half  the  sum  of  the  ang^les  multiplied  by 
the  cosine  of  lialf  th«>ir  difference.  These  f ormulss  enable  us  to  transform 
a  imm  or  difference  into  a  product.  .    . 

Th«*  sum  of  the  sines  of  two  angrles  is  to  their  difference  as  the  tangent  of 
Lalf  the  sum  of  yifise  angles  is  to  the  tangent  of  half  their  differenoe. 

sin  ^  -I-  sin  B      2  sin  H(^  +  B)  cos  H(wi  -  B)  _  tnn  H(^  4-B)       ^ 
Bin  ^  -  sin  B  "^  2  cos  y^A  +  B)  sin  H(4  -  B)  ~  lati  ^A  -  BY     ^    ' 
The  sum  of  the  cosines  of  two  angles  is  to  their  differencaas  the  ootangenl 
of  half  the  sum  of  those  angles  Is  to  the  tangent  of  half  their  difference. 
CM^+oosB      2oosH<i4  +  B)cos^M-B)      cot  ^(^  +  B) 
ooeB-cOS-4  *  «8in  H(^  +  B)  sin  H(^  -  B)  "^  tan  M(^  -  B)'     ^    ' 
The  moe  of  the  sum  of  two  angles  is  to  the  sine  of  theirdifreneooe  as  the 
sum  of  the  tangents  of  those  angles  is  to  the  difference  of  the  tangents. 

sin  (^  +  B)  _  tan  ui  +  tan  B 


sin  (A  -  B) 

^iLl4Jl^=tanu4  +  tanB; 
oos^oosB  ^ 


■^^^j*--^  =  tan^-tanB; 
oos^cosB 

®?lil±:^  =  1  -  tan  ^  tan  B; 
cos^cosB 

???Ltd— -^  =  1  +  tan  4  tan  B; 
cos^oosB 

FaisetloBS  of  thrice  an  anffle  i 

«in2^  s  2  sin  ^  cos  ^; 

.^         2tan^ 
^«^  =  l^tan«a- 
Fanettons  of  Half  an  an^le  i 


tan  ^  >-  tan  B*  * 

tan  (^  +  B)  = 
tan  (^  -  B)  = 
cot  (^  +  B)  = 


(15) 


cot  (il  -  B)  = 


tan  ^  4-  tan  B  . 
1  ~  tan  ^  tan  B' 

tan  i4  -  tan  B  ^ 
1  +  tan  ii  tan  B* 
cot  >4  cot  B  -  1 . 

cot  B  4- cot  ^  * 
cot  ^  cot  f?  4- 1 

cot  B  —  cot  A  ' 


cos  ZA  =■  cos*  A  -  sin*  A\ 

*  «  .      «"t«  A  -  1 
cot  ZA  = 


2co(^ 


HA 


lux  HA 


—  cos^ 


cosH^ 


../^ 


4-  cos  A 


-  cos^. 
cos^* 


cot  Hi4  =  ±  , 


/I  -f  cow  A 
'  1  -  cos -4* 


68  PLAKB  TJUOOKOKET&Y. 

flolutlOB  oir  Plan*  Rlcl&t-«ii«l«d  TrUmcIes. 

liBt  A  and  S  be  the  two  acute  angles  and  C  tbe  rig^t  an«:le,  and  a,  6,  and 
c  the  sides  opposite  these  angles,  respectiFely,  then  we  have 

1.  sin  ^  =  oosB  «=  - ;     8.  tan^  =  cot B  =  ^; 

S.  COS  ^  =  sin  B  XI  -;      4.  cot ^  =  tan  B  =  -. 
c  a 

1.  In  any  plane  right-aogled  trlMiffle  the  sine  of  either  of  the  acute  angles 
is  equal  to  the  quotient  ofthe  opposite  leg  divided  by  the  hypothenuse. 

2.  Tlie  cosine  of  eiiher  of  the  acute  angles  is  equal  to  the  quotient  of  the 
adjacent  leg  divided  by  the  hypothenuse. 

3.  The  tangent  of  either  of  the  acute  angles  Is  equal  to  the  quotient  of  the 
opposite  leg  divided  by  the  adjacent  leg. 

4.  The  cotangent  or  either  of  the  acute  angles  is  eqnal  to  the  quotient  of 
the  adjacent  leg  divided  by  the  opposite  leff. 

5.  The  square  of  the  hypothenuse  equals  the  sum  of  the  squares  of  the 
other  two  sides. 

SolatlojOL  of  Obliqne-SLiiffled  Trlancles, 

The  following  propositions  are  proved  In  works  on  plane  trigonometry.  In 
any  plane  triangle— 

Theorem,  1.  The  sines  of  the  angles  are  proportional  to  the  opposite  aides. 

Tlworem  9.  The  sum  of  any  two  siden  is  to  their  difff  rence  as  tbe  tangent 
of  half  tbe  sum  of  the  opposite  angles  is  to  the  tangent  of  half  tbeir  differ- 


Theorem  3.  If  from  any  angle  of  a  triangle  a  perpendicular  be  drawn  to 
the  opposite  side  or  base,  the  whole  base  will  be  to  the  sum  of  the  oUier  two 
sides  as  the  difference  of  those  two  sides  is  to  the  difference  of  the  aegments 
of  the  base. 

Cask  I.  Given  two  angles  and  a  side,  to  And  the  third  angle  and  tbe  other 
two  sides.  1.  The  third  angle  =  1B0<>  —  sum  of  the  two  angles.  S.  The  sides 
may  be  fonnd  by  the  following  proportion  : 

The  sine  of  the  an^le  opposite  the  given  side  is  to  the  sine  of  the  angle  op- 
posite the  required  side  as  the  pri^en  s^de  is  to  the  required  side. 

Cabs  II.  Given  two  sides  and  an  angle  opposite  one  of  them,  to  find  the 
third  side  and  the  remaining  angles. 

The  side  opposite  the  given  angle  is  to  the  side  opposite  the  required  angle 
as  the  sine  of  the  given  angle  is  to  the  nine  of  the  required  angle. 

The  third  angle  is  found  by  subtracting  the  sum  of  the  other  two  from  180*, 
and  the  third  Ride  is  found  as  in  Case  I. 

Case  m.  Given  two  sides  and  the  included  angle,  to  And  the  third  aide  and 
the  remaining  angles. 

The  sum  of  the  required  angles  is  found  by  subtracting  the  given  angle  j 
from  180**.  The  difference  of  the  required  angle:*  is  then  found  by  Theorem 
II.  Half  the  difference  added  to  half  the  sum  gives  the  greater  angle,  audi 
lialf  ihe  difference  subtracted  from  half  the  sum  gives  the  less  angle.  The 
third  Bide  1»  then  found  by  Theorom  I. 

Another  method  : 

Given  the  sides  c,  6,  and  the  included  angle  A^  to  find  the  remaining  side  a 
and  the  remaining  angles  B  and  C. 

From  either  of  the  unknown  angles,  as  B,  draw  a  perpendlcuUr  ^  e  to  tht 
opposite  side. 

Then 

Ae  =  cQo»  A^    Be  =  c^XnA^    eC=h  -  Ae,    Be-*-eC=  tan  C. 

Or,  in  other  words,  solve  Be.Ae  and  B  e  CaA  right-angled  triangles. 
Ca8B  IV.  Given  the  three  sides,  to  And  the  angles. 


Let  fall  a  perpendicular  upon  the  longest  side  from  the  opposite  angk| 
lividiiig  the  given  triangle  into  two  right-angled  triangles.  The  two  sea 
meiits  of  the  base  may  be  fonnd  by  Theorem  III.    There  will  then  be  givef 


the  hypothenuse  and  one  side  of  a  right-angled  triangle  to  flud  the  angles. 
For  areas  of  triangles,  sec  Mensuration. 


A^^ltlQAJU  a5Q¥OTllT.  S9 


AlTALYTICAXi  (JBOMBTBY. 

Anmljrtleml  geometry  is  that  branch  of  Mathematics  which  hap  for 
its  ob^i  ih«  deiermioatiou  of  the  fonns  and  magultudea  of  geometrical 
masmi'iideA  by  means  of  analysis. 
OrdlDstes  and  abselMAS*— In  analytical  geometry  two  intersecting 
lilies  YY\  XX'  are  used  as  coordinate  axea, 
XX'  being  the  axis  of  abscissas  or  axis  of  X 
and  YY'  Uie  axis  of  ordlnatea  or  axia  of  Y. 
A.  the  intersection,  is  ealled  tba  origli\  of  oo* 
Qrdinates.  The  distance  of  any  point  P  from 
the  axis  of  Y  measured  parallel  to  the  axis  of 
X  is  called  the  abscissa  o(  the  point,  as  AD  or 
(7P,  Fig.  71.  Its  distance  from  the  axis  of  X. 
measured  parallel  to  the  axis  of  F,  is  called 
the  or  din  ate,  as  AC  or  PD.  The  abscissa  and 
ordinate  taken  together  are  called  the  coor- 
dinates of  the  point  P.  The  angle  of  intersec- 
tion is  usually  takeo  as  a  right  angle,  in  which 
case  ihe  axes  of  X and  Fare  called  rectangu- 
lar oooi'd/na^es. 

The  abscissa  of  a  point  is  designated  by  the  letter  x  and  the  ordinate  by  y. 

The  equations  of  a  point  are  the  equations  which  express  the  distances  of 

(he  point  from  the  axis.    Thun  a;  =  »,  9  =  6  ara  the  equations  of  the  point  P. 

Eqn«ttoii0  referred  to  rectADKnlar  cotfrdtnates.— The  equa- 

UoQ  of  a  lint)  expresiMM  the  rehition  which  exists  between  the  qoOpdinatea  of 

every  poini  of  ine  line. 

Equation  of  a  straight  line,  y  =  ax±h^\n  which  a  is  the  tangent  of  the 
angle  the  line  makes  with  the  axis  of  X,  and  b  the  distance  above  A  in  which 
the  line  cuts  the  axis  of  F. 

Every  equalioii  of  the  flrat  degree  between  two  variables  is  the  equation  of 
»  straight  line,  as  ^y  +  Bx  -j-  C  =  0,  which  can  be  reduced  to  the  form  y  = 
ax  ±b. 
Equation  of  the  distance  between  two  points: 


coordinates  of  the  t^ 
;  through  a  given  poi 

j^  -  y'  =  a(a;  -  x'). 


In  which  x'y',  x"y"  are  the  coordinates  of  the  two  points- 
Equation  of  a  hne  passing  through  a  given  point : 


in  which  rr'w'  are  the  coordinates  of  the  given  point,  a,  the  tangent  of  the 
angle  the  line  makes  with  the  axis  of  x,  being  undetermined,  since  any  num- 
ber of  lines  may  be  drawn  through  a  given  point. 
Equation  of  a  line  passing  through  two  given  points : 

Equation  of  a  lUie  parallel  to  a  given  line  and  through  a  given  point; 

y  ^  y'  cz  aix  —  a?'). 
Equation  of  an  angle  K included  between  two  given  lines: 

'^  1  +  a'a 

in  which  a  and  a'  are  the  tangents  of  the  angles  the  lines  make  with  the 
axis  of  abscissas. 
H.  the  lines  are  at  right  angles  to  each  other  tang  T  =:  oo ,  and 

1  4-  ^'o>  =  0,  r 
Equation  of  an  intersection  of  two  lines,  whose  equations  are 
y  =  ax  -\-  by      and    y  =  a'x  +  fc', 

b-  h'         ^  ah'  -  a'b 

a;  = ;,   and    y  = -. 

a-^  a'  a  -  a' 


70  AKALTTIOAL  GEOMETBT. 

EquAtion  of  a  perpendicular  from  a  given  point  to  a  given  line: 

Equation  oC  the  length  of  the  perpendicular  F: 

The  elrele.— BquaUon  of  a  drole,  the  origin  of  ooOrdlnatee  being  at  the 
centre,  and  radius  s  B : 

If  the  origin  is  at  the  left  extremity  of  the  diameter,  on  the  axis  of  X :     . 

If  the  origin  is  at  any  point,  and  the  coOrdlDates  of  the  centre  are  x'y^ : 

(X  -  ar')*  +  (y  -  y')*  =  i2». 

Equation  of  a  tangent  to  a  circle,  the  coordinates  of  the  point  of  tangency 
being  x' V'  and  the  origin  at  the  oentre, 

The  ellipse,— Equation  of  an  ellipse,  referred  to  rectangular  coOrdi' 
•nates  with  axis  at  the  centre: 

^  V  +  B^x^  =  A^B*, 

in  which  A  is  half  the  transverse  axis  and  B  half  the  conjugate  axis. 

Equation  of  the  ellipse  when  the  origin  is  at  the  vertex  or  the  transverse 
axis: 

The  eccentricity  of  an  ellipse  is  the  distance  from  the  centre  to  either 
focus,  divided  by  the  semi-transverse  axis,  or 

_  VA*^B* 
'-        A       • 

The  parameter  of  an  ellipse  is  the  double  ordinate  passing  through  the 
focus.    It  is  a  third  proportional  to  the  transverse  axis  and  its  conjugate,  or 

SB* 
iiA:2B  ::2B  :  parameter;  or  parameter  =  -j-. 

Any  ordinate  of  a  circle  circumscribing  an  ellipse  is  to  the  corresponding 
ordinate  of  the  eiiipse  as  the  semi-transverse  axis  to  the  aemi-conjugate. 
Any  ordinate  nf  a  circle  inscribed  in  an  ellipse  is  to  the  corregponding  ordi- 
nate of  the  ellipse  as  the  semi-conjugate  axlH  to  the  seuii-transversa 

Equation  of  the  tangent  to  an  ellipse,  origin  of  axes  at  the  centre : 

A*w"  -f  B^xx"  =  A^B*, 

yf'xf'  being  the  coordinates  of  the  point  of  tangencv. 

Equation  of  the  normal,  passing  through  the  point  of  tangency,  and  per- 
pendicular to  the  tangent: 

The  normal  bisects  the  angle  of  the  two  lines  drawn  fron}  the  point  of 
tangency  to  the  foci. 

The  lines  drawn  from  the  foci  make  equal  angles  with  the  tangent. 

Tlie  parabola.  -Equation  of  the  parabola  referred  to.  rectangular 
coordinates,  the  origin  being  at  the  vertex  of  its  axis,  y*  =  Sfpa;,  in  which  2p 
is  the  parameter  or  double  ordinate  through  the  focus. 


ANALYTICAL  OEOMETBY.  71 

The  parameter  is  a  thfrd  proportional  to  any  abeciflsaand  lUoorrespoiidiiig 
ordinate,  or 

Equation  of  the  tangent: 

tr''x"  beinff  coordinates  of  the  point  of  tangenoy. 
Equation  of  the  normal: 

The  sub  normal,  or  projection  of  the  normal  on  the  axis,  Is  constant,  and 
equal  to  half  the  parameter. 

The  tangent  at  any  point  makes  equal  angles  with  the  axis  and  with  the 
]in«*  drawn  from  the  point  of  tangenoy  to  the  focus. 

Tlie  liyperbola.— Equation  of  the  hyperbola  referred  to  rectangular 
coOrdioates,  origin  at  the  centre: 

in  which  A  is  the  fleml-transverse  axis  and  B  the  semi-conjugate  axis. 
Equation  when  the  origin  is  at  the  right  Tert«sx  of  the  transverse  axis: 

1/*^^^{2Ax  +  X*). 

ConJncACe  and  eqallateral  ltyperbola».— If  on  the  conjugate 
axis,  as  a  transverse,  and  a  focal  distance  equal  to  VA*  +  B*,  we  construct 
the  two  branches  of  a  hyperbola,  the  two  hyperbolas  thus  constructed  are 
called  coidugate  hyperbolas.    If  the  transverse  and  conjugate  axes  are 

' ,  the  iiyperboiaiB are  called  equilateral,  in  which  case  ifi—afl=  —  A* 

^  is  the  transverae  axis,  and  jt*  -  y*  =  -  i?*  when  B  is  the  trans- 


equal, 
when 


The  parameter  of  the  transverse  axis  is  a  third  proportional  to  the  trans- 
verse axis  and  its  conjugate. 

iA:ZB::fiB :  parameter. 

The  tangent  to  a  hyperbola  bisects  the  angle  of  the  two  lines  drawn  from 
the  point  of  tangenoy  to  the  foci. 

Tne  msymptotes  of  a  byperbola  are  the  diagonals  of  the  rectangle 
described  on  the  axes.  Indefinitely  produced  in  both  directions. 

In  an  equilateral  hyperbola  the  asvmptotes  make  equal  angles  with  the 
transveme  axis,  and  are  at  right  angles  to  each  other. 

The  asymptotes  continually  approach  the  hyperbola,  and  become  tangent 
to  it  at  an  infinite  rtlstanoe  from  the  centre. 

Conle  seetlon8.>-Every  equation  of  the  second  degree  between  two 
vsriables  will  represent  either  a  circle,  an  ellipse,  a  parabola  or  a  hyperbola. 
These  curves  are  those  which  are  obtained  by  intersecting  the  surface  of  a 
cone  by  planes,  and  for  this  reason  they  are  called  conic  sections. 

liC^Cwrftltiiile  curve.— A  logMrithmic  curve  is  one  in  which  one  of  the 
coftrdiiiates  of  any  point  is  the  logarithm  of  the  other. 

The  coordinate  axis  to  «  hich  the  lines  denoting  the  logarithms  are  parallel 
is  called  the  axU  of  logarithmt,  and  the  other  the  axis  of  numberg.  If  y  is 
the  axis  of  logarithms  and  x  the  axis  of  numbers,  the  equation  of  the  curve 
isv  =  \ogx. 

If  the  base  of  a  system  of  .logarithms  is  a,  we  have  aV  =  x,  in  which  y  Is  the 
knrarithm  of  x. 

Each  system  of  logarithms  will  give  a  different  logarithmic  curve.  If  y  = 
0.  X  =  1.  Hence  every  lomrithmic  curve  will  intersect  the  axis  of  numbers 
St  a  distance  from  the  origin  equal  to  1. 


72  DIFFERENTIAL  CALCULUS. 


DIFFEBENTIAL  CALCULUS. 

The  differential  of  a  variable  quantity  is  the  difference  between  any  two 
of  its  consecutive  values;  hence  it  is  indefinitely  small.  It  is  expressed  bjr 
writing  d  before  the  quantity,  as  dx,  which  is  read  differential  of  x. 

The  term  ^  is  called  the  differential  coefficient  of  y  regarded  as  a  f uno- 

tion  of  X. 
The  differential  of  a  function  is  equal  to  its  differential  coefficient  inul< 

tiplied  by  the  differential  of  the  independent  variable;  thus,  -^dx  =  dy. 

The  limit  of  a  variable  quantity  Is  that  value  to  which  it  contiiinallj 
approaches,  so  as  at  last  to  differ  from  it  by  less  than  any  assignable  quan- 
tity. 

The  differential  coefficient  is  the  limit  of  the  ratio  of  the  increment  of  the 
independent  variable  to  the  increment  of  the  function. 

The  differential  of  a  constant  quantity  is  equal  to  0. 

The  differential  of  a  product  of  a  constant  by  a  variable  Is  equal  to  the 
constant  multiplied  by  the  differential  of  the  variable. 

If   u  =:  AVf    du  =  Adv. 

In  any  curve  whose  equation  is  y—f{x\  the  differential  coefficient 

:r  =  tfl^n  <z;  hence,  the  rate  of  increase  of  the  function,  or  the  ascension  of 

cut 

ihe  curve  at  any  point,  Is  equal  to  the  tangent  of  the  angle  which  the  tAOgent 

line  makes  witn  the  axis  of  abscissas. 

All  the  operations  of  the  Differential  Calculus  comprise  but  two  objects: 

1.  To  find  the  rate  of  change  In  a  function  when  it  passes  from  one  8tat« 
of  value  to  another,  consecutive  with  It. 

S.  To  find  the  actual  change  in  the  function :  The  rate  of  change  te  the 
differential  coefficient,  and  the  actual  chaufre  the  differential. 

Dlfferenttals  of  algebraic  fnnctlons,— The  differential  of  the 
sum  or  difference  of  any  number  of  functions,  dependent  on  the  same 
variable,  is  equal  to  the  sum  or  difference  of  their  differentials  taken  sepa- 
rately: 

If    u  —  y-\-z  —  v}^    du  —  dy-\-dz—  dw. 

The  differential  of  a  product  of  two  functions  dependent  on  the  same 
variable  is  equal  to  the  sum  of  the  products  of  each  by  the  differential  of 
the  other : 

,.    .         ,     ,      ,        diuv)     dn  ,  dv 
dCuv)  =  vdu  +  udv.      — -  ==ii^  +  —' 

The  differential  of  the  product  of  any  number  of  functions  Is  equal  to  the 
sum  of  the  products  which  arise  bv  multiplying  the  differential  of  each 
function  by  the  product  of  all  the  others: 

d{ut*)  3  tedu  +  nsdt  -4-  utd$. 
The  differential  of  a  fraction  equals  the  denominator  Into  the  differential 
of  the  numerator  minus  the  numerator  into  the  differential  of  the  denom- 
inator, divided  by  the  square  of  the  denominator  :  , 


dt 


„/u\     vdu —  udv 


If  the  denominator  Is  constant,  dv  =  0,  and  dt  =  —^  =  ~<. 

udv 
If  the  numerator  is  constant,  du  =  0,  and  dt  = r- 

The  differential  of  the  square  root  of  a  quantity  is  equal  to  the  differen* 
tial  of  the  quantity  divided  by  twice  the  square  root  of  the  quantity: 

If    V  =  it^,    or   v=i'u,   dv  =  — -;  =  -u^^du* 
8  i^u        8 


DIFFERENTIAL  CALCULUS.  73 

The  differential  of  any  power  of  a  f  onotion  is  equal  to  the  exponent  multi- 
plied by  the  function  raixed  to  a  power  less  one,  multiplied  by  the  differoR- 
lial  of  the  function,  d(M")  =  nt**  -  irfu. 

Ponnnlaa  for  OUTerenttrnttiig  nlKebrale  Aincttoiui, 

1.  d  (o)  =  0. 


2.  d  (ax)  =3  adx, 

4.  d  (x  —  y)  =  dx  —  dy, 

5.  d  (jcy)  =  xdy  +  ycte» 


e  jj  /?\  _  ytto-ardy 


\vf  y* 

7.  d  («"•)=  m*"*- 'da?. 
dx 


9.  d 


2  Va: 
t"*)r=-ra?''*"W 


To  find  the  differential  of  the  form  «  =  (a+  to")*": 

Multiply  the  exponent  of  the  pareuthesis  into  tlie  exponent  of  the  varia- 
ble within  the  parenthesis,  into  the  coefficient  of  the  variable,  into  the  bi- 
nomial raised  to  a  power  leas  1,  into  the  variable  witbin  the  pareuthesis 
raised  to  a  power  less  I,  into  the  differential  of  the  variable. 

dw  =  d{a  +  te*)**  =  mnb{a  +  6x*)*  "  *  ar »  "  *da?. 

To  find  the  rate  of  change  for  a  given  valtie  of  the  variable : 
Find  the  differential  coefficient,  and  substitute  the  value  of  the  variable  in 
the  second  member  of  the  equation. 

ExAifPT^.— If  X  fs  the  side  of  a  cube  and  u  its  volume,  tt  =  «»,  ~  =  8a:*. 

ax 
Henoe  the  rate  of  change  in  the  volume  is  three  times  the  square  of  the. 
edge.    If  the  edge  la  denoted  by  1,  the  rate  of  change  is  3. 

Application.  The  ooeffloient  of  expansion  by  heat  of  the  volume  of  a  body 
is  three  times  the  linear  coefficient  of  expansion.  Thus  if  the  side  of  a  cube 
exnands  .001  inch,  its  volume  expands  .008  cubic  inch.    1.001*  =  1.003003001. 

A  pajrttal  diflRDFentlal  eoeflletent  is  the  differential  coefficient  of 
a  function  of  two  or  more  variables  under  the  supposition  that  only  one  of 
them  has  changed  its  value. 

A  partial  differential  is  the  differential  of  a  function  of  two  or  more  vari- 
ables under  the  supposition  that  only  one  of  them  has  changed  its  value. 

The  total  differential  of  a  function  of  any  number  of  variables  is  eqiuil  to 
the  sum  of  the  partial  differentials. 

If  tt  =/(ary),  the  partial  differentials  are  7-dar,  -fdy. 

Ifu  =  a:«  +  y*-»,dttr=^*daj  +  ^dy  +  ?^;  =8a;dar4-3i/«dy-d«. 
ax  ay  dz 

Intesralfl.— An  Integral  is  a  functional  expression  derived  flrom  a 
differential.  Integration  Is  the  operation  of  finding  the  primitive  function 
from  the  differential  function.  It  is  Indicated  by  the  sign  /,  which  is  read 
'*the  integral  of."    Thus/SLrdx  =  x*  ;  read,  the  integral  of  2xdx  equals  x*. 

To  inteirrate  an  expression  of  the  form  nu^  ~  ^d»  or  x^dx.  add  1  to  the 
exponent  of  the  variable,  and  divide  by  the  new  exponent  and  by  the  differ- 
ential of  the  variable:  fSx^dx  =  x*,    (Applicable  in  all  cases  except  when 


For /x       dx  see  formula  2  page  78.) 


The  integral  of  the  product  of  a  constant  by  the  differential  of  a  vari- 
able is  equal  to  the  constant  multiplied  by  the  integral  of  the  differential; 


fas^dx  =  a/l^dx  =  a~-r-  a-m  + » 


The  integral  of  the  algebraic  sum  of  any  number  of  cdfferentials  is  equal  to 
the  algebraic  sum  of  their  integrals: 

du  =  ikuMx  -  bydy  -  z^dz;   fdu  =  ^ax*  -  sJ'*  -  ^• 

fince  the  differential  of  a  constant  is  0,  a  constant  connected  with  a  vari- 
able by  the  sign  -for  -  disappears  in  the  differentiation;  thus  dia  +  a?*)  = 
ds^  ss  ms^  '  'd«.    Hence  in  integrating  a  differential  expression  we  must 


74  DIFFEBENTIAL  CALCULUS. 

annex  to  the  intofcnd  obtained  a  oonstant  represented  by  O  to  compensate 
for  tbe  term  whion  may  have  been  lost  in  differentiation.  Thus  if  we  hare 
dt  s  adx'y  Jdy  =  afdx.    Integrating, 

y  =  ax±C. 

The  oonstant  C,  which  is  added  to  the  first  intefrral,  must  have  such  a 
YiUue  as  to  render  thefunctiooal  equation  true  for  every  possible  value  that 
may  be  attributed  to  the  variable.  Hence,  after  having  found  the  flrst 
integral  equation  and  added  the  constant  C,  if  we  then  make  the  variable 
equal  to  zero,  the  value  which  the  function  assumes  will  be  the  true  value 
of  a 

An  indefinite  Integral  is  the  first  integral  obtained  before  the  value  of  the 
constant  Cis  determined. 

A  particular  Integral  is  the  integral  after  the  value  of  C  has  been  found. 

A  definite  integral  is  the  integral  corresponding  to  a  given  value  of  the 
variable. 

Intecimtton  iMtween  limtta.— Having  found  the  indefinite  Inte- 
gral and  the  particular  integral,  the  next  step  Is  to  find  the  definite  integral, 
and  then  the  definite  integral  between  given  limite  of  the  variable. 

The  integral  of  a  function,  taken  between  two  limits,  indicated  by  given 
values  of  X,  is  equal  to  the  difference  of  the  definite  integrals  oorreepond- 
ing  to  those  limits.    The  expression 


i  dy  =  a  j  dx 


Is  read:  Integral  of  the  differential  of  y,  taken  between  the  limits  x^  and  tee- 
the least  limit,  or  the  limit  corresponding  to  the  subtractlve  integral,  being 
placed  below. 

Integrate  du  =  fisesda;  between  the  limits  x  =  1  and  a;  =  8,  u  being  equal  to 
81  when  x  s 0.   /du  s/to'dx  s  &r*  +  C;  C=  81  when  x  =  0,  then 


I 


»X-8 

du  =  8(8)>  +  81,  ndnus  8(1>*  +  SI  s  7& 
x»l 


Int^gmtlon  of  partlenlar  forms. 

To  integrate  a  differential  of  thefoi-m  du  =  {a-\-  bx^y^x*  '  'dx. 

1.  If  there  is  a  constant  factor,  place  it  without  the  sign  of  the  Integral, 
and  omit  the  power  of  the  variable  without  the  parenthesis  and  the  differ, 
ential; 

2.  Augment  the  exponent  of  the  parentheslsi  by  1,  and  then  divide  this 
quantity,  with  the  exponent  so  increased,  bv  tlie  exponent  of  the  paren< 

Into  the  exponent  of  the  variable  within  the  parenthesis,  into  the  co> 
'"     variabi       '"" 


quantity, 
thesis,  in 


efficient  of  the  variable.    Whence 


> 


{m  +  l)nb 


The  differential  of  an  arc  Is  the  hypothenuse  of  a  right-angle  triangle  of 
which  the  base  Is  dx  and  the  perpendicular  dy. 

Ifsisanarc,  d£=  VcU*  +  dy^     z=fVdx*  +  dy*\ 

anadrature  of  a  plane  flu^nre. 

The  differential  of  the  area  of  a  plane  surface  is  equal  to  the  ordinate  into 
the  differential  of  the  abscissa. 

dt  =  ydx. 

To  apply  the  principle  enunciated  in  the  last  equation,  In  finding  the  area 
of  any  particular  plane  surface : 

Find  the  value  of  y  in  terms  of  x,  from  the  equation  of  the  bounding  line; 
substitute  this  value  In  the  differential  equation,  and  then  integrate  between 
the  required  limits  of  x. 

Area  oftlte  parabola  ^^Fiud  the  area  of  any  portion  of  the  com- 
mon parabola  whose  equation  Is 

y*  =  ftpx;      whence   y  =  j^2px. 


DIFFERENTIAL  CALCULITS.  75 

SubsUtuUiiK  this  value  of  y  in  the  differential  equation  d$  =  ydx  gives 
/  <^=  /  f^«ete=  i/^J  x^dx=  — ^— al  +  C; 

or.       •=-^       =3*F+C. 

If  we  eetimate  the  area  from  the  principal  vertex,  x  :=:  0.  y  =  0,  and  (7=0; 

2 
and  denoting  the  particular  Integral  by  y,  «'  =»  £  'V* 

Thai  is,  the  area  of  any  portion  of  the  parabola,  estimated  from  the  ver- 
tex, is  eanal  to  %  of  the  rectangle  of  the  abscissa  and  ordinate  of  the  extreme 
point.    'The  curve  is  therefore  quadrable. 

Aaadrmtnre  of  ■nrteeMi  of  reTolatlon.— The  differential  of  a 
surface  of  revolution  is  equal  to  tlie  circumference  of  a  circle  perpendicular 
to  the  axis  into  the  differential  of  the  arc  of  the  meridian  curve. 


d$  =  ftwy^dx*  •{- dy*; 

in  wliicli  y  is  the  radius  of  a  circle  of  the  boundfaig  surface  in  a  plane  oer- 
pendlcular  to  the  axis  of  revolution,  and  x  is  the  abscissa,  or  distance  of  the 
plane  from  the  orif  in  of  coordinate  axes. 

Therefore,  to  fina  the  volume  of  anv  surface  of  revolution: 

Find  the  value  of  y  and  dy  from  the  equation  of  the  meridlao  curve  in 
terms  of  x  and  dx,  then  substitute  these  values  in  the  differential  equattoui 
and  integrate  between  the  proper  limits  of  x. 

Bv  application  of  this  rule  we  may  And: 

The  curved  surface  of  a  cylinder  equals  the  product  of  the  circumference 
of  the  base  Into  the  altitude. 

The  convex  surface  of  a  cone  equals  the  product  of  the  circumference  of 
the  base  Into  half  the  slant  height. 

The  surface  of  a  sphere  is  equal  to  the  area  of  four  great  dreles,  or  equal 
tn  the  curved  surface  of  the  circumscrlbinjc  cylinder. 

Cakttf «re  of  Tolvns^s  of  reTolatlon.— A  volume  of  revolution 
ii  a  volume  fceneraied  by  the  revolution  of  a  plane  figure  about  a  fixed  line 
called  the  axis. 

If  we  denote  the  volume  by  F,  dV  =  «y"  dx. 

The  area  of  a  circle  deecrlbed  by  any  ordinate  y  is  «y*;  hence  the  differ* 
ential  of  a  volume  of  rovolution  Is  equal  to  the  area  of  a  ciixsle  perpendicular 
to  the  axis  into  the  differential  of  the  axis. 

The  differential  of  a  volume  generated  by  the  revolution  of  a  plane  figure 
about  the  axis  of  Y  Is  9X*dy. 

Tn  find  the  value  of  Ffor  any  fj^ven  volume  of  revolution : 

Find  thfl  value  of  y*  In  terms  of  x  from  the  equation  of  the  meridian 
curve,  substitute  this  value  In  the  differential  equation,  and  then  integrate 


between  the  required  limits  of  x. 
By  application  of  this  rule  we  may  find : 
The  volume  of  a  cylinder  Is  equal  to  the  1 


i  cylinder  Is  equal  to  the  area  of  the  base  multiplied  by  the 
sltitnde.  *  -• 

The  volume  of  a  cone  is  equal  to  the  area  of  the  base  into  one  third  the 
siatiide. 

The  volume  of  a  prolate  spheroid  and  of  an  oblate  spheroid  (formed  by 
the  revolution  of  an  ellipse  around  its  transverse  and  Its  conjugate  axis  re- 
spectively) are  each  equal  to  two  thirds  of  the  clreumscriblng  cylinder. 

If  the  axes  are  equal,  the  spheroid  becomes  a  sphere  and  its  volume  => 

^IP  sc  i>  =  2  *^«  ^  being  radius  and  D  diameter. 
9  o 

The  volume  of  a  paraboloid  is  equal  to  half  the  cylinder  having  the  same 
hsse  and  altitude. 

The  volume  of  a  pyramid  equals  the  area  of  the  base  multiplied  by  one 
third  the  alUtnda 

floeonid^  tliirdf  ete*^  dlil^reiitlals.— The  differential  coefficient 
bdnir  a  function  of  tne  independent  variable,  it  may  be  differentiated,  and 
«e  thus  obtain  the  second  dCfferantial  coefficient: 

d(^)  s  ^.    Dividtaig  by  dx,  we  have  for  the  second  differential  ooefll- 
\fgx-^      ax 


76  DlFFBRfiKTlAL  CALCULUS. 

dent  -z-^,  which  is  read:  second  differential  of  u  divided  by  the  square  oi 

the  differential  of  t  (or  dx  squared). 

The  third  differentiHi  coefficient  ^  is  read:  third  differential  of  %i  divided 

by  dx  cubed. 
The  differentials  of  the  different  orders  are  obtedned  by  multiplyio^  the 

differential  coeffloients  by  the  corresponding  powers  of  rte;  thus^-g  <to*= 

third  differential  of  u. 

St^rn  of  tlte  first  diiTereiltliil  coettelent.— If  we  hate  a  curre 
wboHe  equation  is  ^  =  /s,  referred  to  rectangular  coordinates^  the  curve 

will  recede  from  the  &xis  of  X  when  ^  is  positive,  and  approach  Uie 

axis  when  it  Is  negatiTe^  when  the  curve  lies  within  the  first  ant^le  of  the 
'eo<(rdinate  aares.  For  all  angles  and  every  relation  of  v  and  x  the  cur%*e 
will  recede  from  the  axis  of  X  when  the  ordinate  and  fli*8t  differential  co- 
efflcient  have  the  some  sign,  and  approach  it  when  they  have  different 
signs.    If  the  tangent  of  the  curve  becomes  parallel  to  the  axis  of  X  at  any 

p6ilit  x^  —  0.    If  the  tangent  becomes  perpendicular  to  the  astis  of  X  nt  any 

point  ^  =  00. 

Slj^  ortlk«  second  dlflnsreAtlal  coellleleiit.— tte  second  dif- 
fsrenual  coefficient  has  the  same  sign  as  the  ordinate  when  the  curve  Is 
convex  toward  the  axis  of  abscissa  and  a  contrary  sign  when  it  is  concave. 

MaclauHn's  Theorem.— For  developing  into  a  series  any  function 
M  a  single  variable  &a  n-A^Bx  +  <}afl-\-  Dx^  +  Ex*^  etc..  In  which  A,  £, 
C,  etc.,  are  independent  of  v: 

In  applying  the  formnia,  omit  the  expressioBs  «  s  0^  althougli  tfa*  ooeffi- 
oiente  are  always  found  under  tiiis  hypothesis. 
^Examples  : 

+   -(j!!^<J!ir«)«--»^.  +  etc. 


« -f «       a      o«    '  «»      a*  ^   '  *  '  <ju  + 1 ' 

Taylor's  Theorem.— For  develop! ng'into  a  series  any  function  of  the 

sum  or  difference  of  two  independent  variables,  as  a'  te  /(<r  ±  y): 

in  which  u  is  what  u'  becomes  when  y  "=  0»  x.  ^  what  -.-   beoomes  when 

y  ts  0.  etc. 

niaixima  and  mintmn.— To  find  the  maximum  or  minimum  value 
of  a  function  of  a  single  variable: 

1.  Find  the  first  differential  coeffiolent  of  the  f  unctloa,  place  it  equal  to  0, 
and  determine  the  roots  of  the  equation. 

8.  Find  the  second  differential  coefficient,  and  substitute  each  real  root, 


In  succession,  for  the  variable  m  the  second  member  of  tlie  equation.  £acb 
root  which  gives  a  negative  result  will  correspond  to  a  maximum  value  of 
the  function,  and  eaon  which  gives  a  positive  result  will  correspond  to  a 
minimum  value. 

JSXAIIPI.B.— To  find  the  value  of  x  which  will  render  the  ftttntlon  y  s 
maximum  or  minimum  in  the  equation  of  the  circle,  y*  4-  «•  sx  J2«; 

^=  -  *    making  -  -  =  Ogives  a?  =  0. 


DIFITEBBKTIAL  CALCULUS.  7T 

The  second  differential  coefficient  is:  ^  =  -  ^'"t*^. 

jf-.  « 

When  X  =  0,  y  =  R;  hence  ~  ~  "B*  ^^^h  being  negatlTO,  y  is  a  maxi- 
mum for  B  poeitiva 

In  applying  the  rule  to  practical  examples  we  first  find  an  expression  for 
(he  function  which  Is  to  be  made  a  maximum  or  minimum. 

S.  If  in  such  expressloD  a  constant  quantity  is  found  as  a  faotor,  it  mav 
be  omiOed  in  the  operation;  for  the  praduct  will  be  a  maximum  or  a  mini- 
mum when  the  variable  factor  is  a  maximum  or  a  minimum. 

S.  An  J  Talue  of  Uie  independent  variable  which  rendera  a  function  a  maz- 
imura  or  a  minimum  will  render  any  power  or  root  of  that  function  a 
maximum  or  minimum;  hence  we  may  square  both  members  of  an  equa- 
tion to  free  it  of  radicals  before  differentiaung. 


Bf  thane  ruk*  we  may  find: 
Tliei 


)  maximum  rectangle  which  can  be  inscribed  in  a  triangle  Is  one  whose 
altitude  is  luilf  the  altitude  of  the  triangle. 

The  altitude  of  the  maximum  cylinder  which  can  be  inscribed  in  a  cone  is 
one  third  the  altitude  of  the  cone. 

The  surface  of  a  cylindrical  vessel  of  a  given  volume,  open  at  the  top,  is  a 
minimum  when  the  altitude  equals  half  the  diameter. 

Tlie  altitude  of  a  cylinder  inscribed  in  a  sphere  when  its  convex  surface  is 
a  maximum  is  r  ^2.    r  =  radios. 

The  altitude  of  ajcyllnder  inscribed  in  a  sphere  when  the  volume  is  a 
maximum  is  2r  -«-  VS. 

(For  nuucima  and  minima  without  the  calculus  see  Appendix,  p.  1070.) 

JMfl'erentlal  of  an  exi^onentlal  Ametlon. 

If    «  =  o* 0) 

thendttcd^^  =a^fcda;, (9> 

hi  which  Jb  is  a  constant  dependent  on  a. 

The  relation  between  a  and  I;  is  a^  =  e;  whence  a  s  e*,     .....    <8) 

in  which  e  =  2.718S818  .  .  .  the  base  of  the  Naperian  system  of  logarithms. 
Iiosmritliiiis.— The  logarithms  in  the  Naperian  system  are  denoted  by 
2,  Nap.  log  or  hyperbolic  log,  byp.  log,  or  log^;  and  in  the  common  system 
always  by  log. 

k  =3  Nap.  log  a,    log  a  =  I;  log  e (4) 

The  common  logarithm  of  e,  =r  k)g  2.718S8I8  .  .  .  =  .4842M5  ....  is  called 
the  modulus  of  the  common  system,  and  is  denoted  by  M.  Hence,  if  we  have 
the  Naperian  logarithm  of  a  number  we  can  And  the  common  logarithm  of 
tlie  same  numwr  by  multiplying  by  the  modulus.  Beciprocally,  Nap. 
ioK  ^  com.  log  X  2.S0858S1. 

U  in  equation  (4)  we  make  a  =  10,  we  have 

1  8  fc  log  e,   or  -  s  log  e  =  If. 

That  Is,  the  modulns  of  the  common  system  is  equal  to  1,  divided  by  the 
Naperian  logarithm  of  the  common  base. 
From  equation  (IQ  we  have 

«       a* 
If  we  make  a  s  10;  the  base  of  the  common  system, «  s  log  ti,  and 
jy.         *       J         di*       1       dw       _. 

d(IOg  tt)ad«S    Kr-CB  —    xjtf. 

That  is,  the  differential  of  a  common  logarithm  of  a  quantity  is  equal  to  the 
differential  of  the  quantity  divided  by  the  quantity,  into  the  modulus. 
If  we  make  a  =s  e,  the  base  of  the  Naperian  system,  x  becomes  the  Nape* 


78  DIFFERENTIAL  CALCULUS. 

rlan  logarltnm  of  u,  and  k  becomeB  1  (see  equation  (8));  bonce  If  »  1,  and 

iKNap.lo«t*)r=ifx=^;  =  ^. 
a*  u 

That  is,  the  differential  of  a  Naperlan  logarithm  of  a  quantity  is  equal  to  the 
differential  of  the  quantity  divided  by  the  quantity;  and  In  the  Naperlan 
system  tlie  modulus  is  1. 

Since  fc  is  the  Naperlan  logarithm  of  a,  du  s  a^  I  a  cte.  That  Is,  the 
differential  of  a  fuuctlon  of  the  form  a^  is  equal  to  th«  fuoction,  into  the 
Naperlan  logarithm  of  the  base  a,  into  the  differential  of  the  exponent. 

If  we  have  a  .differential  in  a  f  raetioual  form.  In  which  the  numerator  is 
the  differential  of  the  denominator,  the  integral  is  the  Naperlan  logarithm 
of  the  denominator.  Integrals  of  fractional  differentials  of  other  forms  are 
given  lielow: 

IMllbreiitla]  forma  iv^bleli  Itave  knoiv^n  InteKral*}  esc- 
ponenUal  ftanettoiui*   d  =  Nap.  log.) 

1.  I  aP^ladx  =  ar^-\-C; 

dxx~  *  =  lx-\-0\ 


dx 

dx 


=  Kx  +  j^x*±a*)  +  C; 


^x*  ±  lUix 

Clrenlar  Ainetloiia.-Let  z  denote  an  arc  in  the  first  quadrant,  y  fts 
Bine,  X  its  cosioe,  v  its  versed  sine,  and  i  Its  tangent;  and  the  following  nota- 
tion be  employed  to  designate  an  arc  by  any  one  of  its  functions,  vis., 

sin  "^  If  denotes  an  arc  of  which  y  is  the  sine 

^jQg-ljp     M         «    «    u       «.     a;  is  the  cosine, 

tan-*«     "         ••    "    **       "     Ms  the  tangent 


OIFFEBENTIAL  CALCULUK 


79 


*md  "arc  whom  sine  is  y,**  etc.).— we  hare  the  foUowing  differential  fonns 
vhidi  hare  known  integrals  (r  =  radius): 


/  cos  sdx     =  sin  c  -f  C^f 
/  -  sin  s  dx  =  cos  m+C; 


r^i 


dx 


=  coe-*af  C; 


=  yer-sin  -*«  +  (?; 


—==z  =co»    • 


«+C; 


Kdz  =  yer-sin  Z'{-C\ 


dz 

C06*S 

rd  t> 


=  tan  c  +  C; 


4/*;;;+^ = ^«''-"*»  "*»+<?; 


/: 

—: rr:^.  =  COS      * 


■»^  +  C; 


l/'^tai*  -  u* 


u.       =*--*i  +  <^. 


The  eyelold*— If  a  circle  be  ro11<*<1  along  a  straight  line,  any  point  of 
the  circumference,  as  P,  will  dt^sciibe  a  curve  which  \»  called  a  cycloid.  The 
circle  is  called  the  generating  circle.  ao<l  Pthe  geuerating  point. 

The  transcendental  equation  of  the  cycloid  i« 


X  =  ver-sln-  >  y  —  J^try  -  p\ 


tad  the  differential  equation  is  dx  - 


^^-y  -  y*. 


The  area  of  the  cycloid  is  equal  to  three  times  the  area  of  the  generating 
tircle. 

The  Mjrfaee  descrllMrd  by  the  arc  of  n  cycloid  when  revolved  about  its  base 
fe  eqtial  to  04  thii'dM  of  the  enierHtiii?  circle 

The  volume  of  the  M'>lid  K^^nnrnted  hv  revolving  a  cycloid  about  its  base  is 
Moal  to  fli-e  eiphUifi  of  fh-  ciri-iiniscribinir  cylinder. 

InCearrsil  eftlcolna«~In  the  integral  calculus  we  have  to  return  from 
tiie  differencial  ii>  the  fiiiH-tlon  from  which  it  waM  derived  A  number  of 
liffervntial  «>xpressions  are  triven  abovf».  «>aoh  of  which  has  a  known  in- 
vgral  corresponding  10  it,  and  which  being  different.ated,  will  produce  the 
iziveii  differential 

In  all  cUumes  of  functions  any  differential  expression  may  be  integrated 
when  it  ia  retiuceil  to  one  of  ilin  known  forms;  and  the  operations  of  the 
loreirral  calculiiH  cotisisr  nminlv  In  making  such  irai informations  of  given 
(iifferentiaJ  expressions  as  Mhalf  nxlnce  them  to  equivalent  ones  whose  in- 
ieirra>ls  are  known. 

For  inctliods  of  making  these  transformations  reference  must  be  made  to 
tie  text^booka  on  differential  and  Iniegral  calculus. 


80 


HATHEMATICAL  TABLES. 
BBCIPBO€AI<9  OF  NUMBERS. 


No. 

Recipro- 
cal. 

No. 

Reclpro- 

No. 
127 

Reclpro- 

No. 

Recipro-  ' 

No. 

253 

Recipro- 
cal. 

1.00000000 

64 

.01662500 

.00787402 

190 

.00626816 

.oaj&5e5: 

.60000000 

6 

.0158^61 

$ 

.00781280 

1 

.00628560 

4 

.OOSSMTin 

.3S8833W 

0 

.01516161 

9 

.00^75194 

2 

.00620888 

6 

.008021.51 

,26000000 

7 

.01492687 

180 

.0076928: 

3 

.00.-,l8l85 

6 

.00»Wfi2S 

.90000000 

8 

.01470588 

1 

.00768:i')9 

4 

.00515404 

7 

.008«yi(R 

.16666«ST 

9 

.01449275 

8 

.(10757576 

5 

.00512820 

8 

.00:^875'/' 

.14«85rN 

70 

.01428571 

8 

.aJ751880 

6 

.00510204 

0 

.0l»»6liij 

.i->6no<KKi 

7 

.014064:.! 

4 

.00r40-,'(i9 

7 

.oftiorou 

260 

. 00:^401' 

.11111111 

2 

.01:^88880 

6 

.00740741 

8 

.0O5O5(j51 

1 

.00^^141 

.lUOOOOOO 

8 

.0l86n868 

e 

.00735294 

9 

.00502518 

2 

.OOfJHir,';! 

.0009U909 

4 

.01851 «5| 

7 

.00729927 

200 

.00500000 

8 

.0(8SOe2l 

.08*J133:i 

5 

.01838  533 

8 

.007240:^8 

1 

.(X)497512 

4 

.00:i7K8J 

.0T69J80H 

6 

.018157M9 

9 

.00719424 

2 

.00495049 

6 

.008778:»i 

.07141X67 

7 

.012»»870: 

140 

.0<  ►714280 

8 

.0< '492011 

6 

.003759* 

.066r.6lHJ7 

8 

.01282051 

1 

.00709220 

4 

.00490196 

7 

.00:17458! 

.06i50000 

9 

.01J65823 

2 

0«>704225 

6 

.0W87805 

8 

.003781* 

.05'58.'.V.8 

80 

.012,VXXH) 

8 

.0G699801 

6 

.00485487 

9 

.00:17174 

.0555.\556 

1 

.01284568 

4 

.00694444 

7 

.00488092 

270 

.0087(371 

.O.V^1i:8 

2 

.01219512 

6 

00689655 

8 

.00480769 

1 

.0086000 

.OiOOOOOO 

8 

.01204819 

0 

.00084981 

9 

.00478469 

2 

.0036764 

.047610)6 

4 

.01190476 

.00680272 

210 

.00476190 

8 

.00:MiG:m 

.04M64:>5 

5 

.01176471 

8 

.0(»675676 

11 

.00473984 

4 

.0086496 

.048I76M 

6 

.01162791 

9 

.00671141 

12 

.00471698 

6 

.0a3686» 

.0416CCC7 

7 

.01149425 

150 

.00666667 

13 

.00469484 

6 

.0080-231! 

.04000000 

8 

.01136864 

1 

.006622.52 

14 

.00467290 

7 

.00:56101 

.08846154 

9 

.01123595 

2 

.00667895 

15 

.00466116 

8 

.003.-.&7I 

.08703704 

00 

.01111111 

« 

.00658595 

16 

.00462968 

9 

.00:^5842; 

.085714J9 

1 

.01008901 

4 

.00649351 

17 

.00460829 

280 

.003.571 41 

.08448276 

2 

.01086956 

6 

.00645161 

18 

.004.58716 

1 

.0a'J.55.s7 

.o^aasasij 

8 

.01076269 

6 

.00041026 

19 

.00456621 

3 

.0(Vi.546!< 

.09«?S8i)6 

4 

01(108830 

7 

.00086943 

220 

.00454545 

8 

.003588-. 

.081.25000 

5 

010oJti32 

8 

.0068291 1 

1 

.00452489 

4 

.0O5j.->2n; 

.aH0.W303 

G 

.01041607 

9 

.00628931 

2 

.00450450 

6 

.0(»:i.-»0N7 

.0^41176 

7 

.01080928 

160 

.00625000 

8 

.00448480 

6 

.00:^4  9:  .Til 

.Oi«37l4:J 

8 

.01020408 

1 

.00621118 

4 

.00446429 

7 

.0O84S18 

.02777778 

9 

.01010101 

2 

.00617284 

5 

.00444444 

8 

.00517221 

.02702708 

100 

.01000000 

8 

.00018497 

6 

.00442478 

9 

.00^4002 

.02631579 

1 

.00990090 

4 

.00609766 

7 

.00440629 

290 

.0034  48-J 

.02564103 

2 

.00980892 

6 

00606061 

8 

.00488596 

1 

.0(W430li 

.02500000 

8 

.00970874 

6 

.00602410 

9 

.00486681 

2 

.00M24& 

.0^:«02< 

4 

.00961538 

7 

.00598802 

980 

.00481788 

8 

.0034129 

.0;.'380052 

6 

.00952881 

8 

.00595238 

1 

.00432900 

4 

.00*40131 

.02325681 

6 

.00948896 

9 

.00591716 

2 

.00431034 

6 

.003.H8aH; 

.023?^727 

7 

.00934579 

170 

.00588235 

3 

.00429184 

6 

.oo3rr.<a 

.0»2222-.»2 

8 

.00926926 

1 

.0a584795 

4 

.0a427:i50 

7 

.00:i3«7(»< 

.02178913 

9 

.00917481 

2 

.Oa581395 

6 

.0042.55.8'> 

8 

.0(Ki:l.V)7l 

.02127660 

no 

.00909091 

8 

.00.578085 

6 

.00423729 

9 

.0a88144l 

.02083;Wi 

11 

.00900901 

4 

.00674713 

7 

.00421941 

300 

.O0:j:»j:t 

.02040816 

12 

.00892g57 

6 

.0057 J 429 

8 

.00420168 

1 

.008:«22t 

.02000000 

18 

.0088495U 

0 

.00.568182 

9 

.00418450 

a 

.003>in2l 

.01900784 

14 

.00877193 

7 

.00564972 

340 

.(X)Vi(m7 

3 

.003:1003! 

.01»2:i077 

16 

.OftWOMJS 

6 

.0a56l798 

1 

.0041 49:« 

4 

.0082894: 

.01886792 

16 

.00862009 

9 

.00558059 

2 

.004l:«»8 

5 

.OOS-T^li! 

.01851852 

17 

.00854701 

180 

.00.V>.55.-HJ 

8 

.00411.523 

6 

.00^2679: 

.0181818-' 

18 

.008174.5-* 

1 

.005524Hft 

4 

.00409S80 

7 

.0031-::^^ 

.01786714 

19 

.0«;840:J3G 

2 

.0l):>494f)l 

5 

.0040M6:i 

8 

iit«:.Ni;7^ 

.01784886 

120 

.00S838.38 

8 

.0O.-)4644H 

6 

.00106504 

9 

.0(«2.^»W 

.01724188 

1 

.008.'64I6 

4 

.00548478 

7 

.004018.*<8 

810 

.0a8*2,V< 

.01094915 

2 

00819672 

5 

.0O.->4O5in 

8 

.0040:1220 

11 

.00*21.^13 

.01686607 

8 

.00.Si:W(W 

0 

.0053ro:i4 

9 

.00401000 

12 

00.120.-,  1; 

.01689844 

4 

.0080I545J 

•J 

.00581759 

250 

.00400000 

18 

. 0031 94 W 

.01012903 

5;  .oasooooo 

01  .00793651 

8 

.0«).581914 

1 

.00398406 

14|  .0a81Kl7I 

.01587802 

1   9 

.00529100 

21  .00.J96S25 

l&l  .0081740< 

BECIPBOOAIA  07  KUMBXBS. 


81 


No 

Rc«ipro* 

No. 

Raclpro- 

No. 
446 

Reclpro- 

No. 

Redpro- 

No. 

R^r<. 

816 

.00316456 

381 

.00862467 

.00224215 

611 

.00195695 

576 

.00173611 

17 

.0031M67 

2 

.00281780 

7 

.00223714 

12 

.00195812 

7 

.00i;8810 

18 

.00314465 

3 

.00;»1097 

6 

.00223214 

18 

.00104932 

8 

.00178010 

1» 

.00818480 

4 

.00860417 

9 

.00222717 

14 

.00194552 

9 

.00172712 

3390 

OOSl^iQOO 

6 

.00259740 

460 

.00228222 

15 

.00194175 

580 

.00172414 

1 

.00311S86 

6 

.002«K)fi7 

1 

.00221729 

16 

.00193798 

1 

.00172117 

a 

.0O3tO55O 

7 

.0025K898 

2 

.00221289 

17 

.00193424 

2 

.00171821 

8 

.0090958: 

8 

.002577821 

8 

.00220751 

18 

.00193060 

8 

.00171527 

4 

.00908642 

9 

.00257009! 

4 

.00220264 

19 

.00192678 

4 

.0017123:) 

6 

.00807692 

890 

.00256410 

6 

.00219780 

KO 

.00192808 

5 

.00170940 

e 

.00906748 

1 

.00255754 

6 

.00219298 

1 

.00191939 

6 

.00170648 

7 

.00805810 

9 

.00255102 

7 

.00218818 

2 

.00191571 

7 

.00170358 

8 

.00804878 

8 

.00354453 

8 

.00218341 

8 

.00191905 

8 

.OO170OG8 

9 

.00808951 

4 

.00253807 

9 

.00217865 

4 

.00190840 

9 

.00169779 

sao 

.00303030 

6 

.00253ia5 

460 

.00217,391 

6 

.00190476 

590 

.00169491 

1 

.0090-2115 

6 

.0O,>52525 

1 

.00216920 

6 

.00190114 

1 

.00169-205 

8 

.00301306 

7 

.00251889 

2 

.00216450 

7 

.00189753 

2 

.00168019 

8 

.00800300 

8 

.00251250 

8 

.00215983 

8 

.00189394 

3 

.00168634 

4 

.00299101 

9 

.00250627 

4 

.00216617 

9 

.00189036 

4 

.001083.50 

6 

.oojfl8:.o: 

400 

.0025000n 

6 

.00215054 

580 

.00188679 

5 

.001680«i7 

6 

.00297619 

1 

.00249377 

6 

.00214592 

1 

.00188324 

6 

.00167785 

7 

.00296736 

2 

.0024S75C 

7 

.0O21413;J 

2 

.00187970 

7 

.00167504 

8 

.00295858 

3 

.00248139 

8 

.00218675 

8 

.00187617 

8 

.00107-224 

9 

.0029408.-, 

4 

.00247525 

0 

.00213220 

4 

.00187266 

0 

.00166945 

SIO 

.00294118 

» 

.00246914 

470 

.00212766 

5 

.00186916 

600 

.00166667 

1 

.ooaBefts 

6 

.00246305 

1 

.00212:^14 

6 

.00186567 

1 

.00166389 

9 

.OO-.-OiSOP 

7 

.00245700 

2 

.00211864 

7 

.00186220 

2 

.00166118 

8 

.00291 M5 

8 

.00245098 

8 

.00211416 

8 

.00185874 

8 

.00165837 

4 

.0029060* 

9 

.002444911 

4 

.00210970 

9 

.00186528 

4 

.00165563 

5 

.00SiS98&5 

410 

.00248902 

5 

.00210526 

640 

.00185185 

5 

.00165280 

6 

.00289017 

11 

.00243309 

6 

.00210064 

1 

.C0181<43 

6 

.00165016 

7 

.(0288184 

12 

.00242718 

7 

.00209644 

2 

.00184502 

7 

.00164746 

A 

.00287!»6 

13 

.00242131 

8 

.00209205 

8 

.00184162 

8 

.00164474 

9 

.00286.V» 

14 

.00241546 

0 

.00208768 

4 

.00183823 

9 

.00164204 

850 

.00285714 

15 

.00210961 

480 

.00208:^ 

5 

.00183486 

610 

.00163934 

1 

.00284000 

16 

.00240:«5 

1 

.002a790(' 

6 

.00188150 

11 

.00168666 

9 

.00*284091 

17 

.00239808 

2 

.00207469 

7 

.0018-2815 

12 

.00163399 

8 

.0ftA)8288 

18 

.00J89284 

8 

.002070:11) 

8 

.00182482 

13 

.00163132 

4 

.0O-.'8248C 

10 

.00238603 

4 

.00206612 

9 

.00182149 

14 

.00162866 

b 

.00281680 

420 

.0028809*) 

5 

.00-206180 

C50 

.00181818 

15 

.00162602 

6 

.Qoamm 

1 

.00237530 

6 

.00205761 

1 

.00181488 

16 

.001623.38 

7 

.002801 U 

2 

.00286967 

7 

.002058.^9 

2 

.00181159 

17 

.00162075 

8 

.00279:530 

3 

.002.16407 

8 

.00204918 

8 

.00180832 

18 

.00161812 

9 

.002785.M 

4 

.0023.5849 

0 

.00-2(M4D9 

4 

.00180505 

19 

.00161551 

860 

.00277778 

6 

.0023.5294 

490 

.0020408-2 

5 

.00180180 

6-20 

.00161-290 

I 

.0027700F 

6 

.00*^742 

1 

.ooeo36r.G 

6 

.00179856 

1 

.ooioiasi 

2 

.00276243 

7 

.0023419? 

2 

.002032.52 

7 

.00179533 

2 

.00160772 

8 

.00276482 

8 

.0O2:i'J64r) 

8 

.00202840 

8 

.00170211 

3 

.00160514 

4 

.0027472.T 

9 

.0023dl0i) 

4 

.00202429 

0 

.00178891 

8 

.00160256 

5 

.002789r3 

430 

.00232^^8 

6 

.00202020 

560 

.00178571 

5 

.00160000 

6 

.00/78224 

1 

.00282019 

6 

.00201613 

»1 

.00178253 

6 

.001.59744 

7 

.002W480 

9 

.00231481 

7 

.00-20120'; 

2 

.00177936 

.00159490 

8 

.00271:39 

8 

,00230947 

8 

.00200803 

8 

.00177620 

8 

.001 59. '36 

9 

.owioiw 

4 

.002:^0115 

9 

.00200401 

4 

.00177305 

9 

.00158982 

870 

.00270270 

6 

.00229885 

600 

.00200000 

6 

.00176091 

630 

.001.58730 

3 

.00961L542 

6 

.00-.'2»3.-8 

1 

.001996(^1 

6 

.00170678 

1 

.00158479 

9 

.0U2et«l7 

7 

.C0228a3:5 

2 

.00199-203 

.0017C367 

2 

.001.58-228 

8 

.00268096 

8 

.002CH.S10 

3 

.0(M  98807 

8 

.00176056 

8 

.00157978 

4 

.0Oi6788() 

9 

.00227790 

4 

.00198413 

9 
570 

.0017.5747 

4 

.001577-29 

5 

.00260607 

440 

.00227273 

5 

.00198020 

.00175439 

5 

.00157480 

6 

.00265957 

1 

.00226757 

6 

.001976-28 

1 

.0017.5131 

6 

.00157233 

7 

00265652 

a 

.00228244 

7 

.0019?239' 

2 

.001748-25 

r- 

.00156986 

8 

.(xmaao 

3 

.00225784 

8 

.001968oO; 

3 

.00174520 

8 

.00156740 

0 

.00260852 

4 

.0022.'i225 

9 

.01U1J6464 

4 

.00174216 

9 

.00156491 

880 

.00288158 

s 

.00294719 

510 

.001960781 

6 

.00173913 

640 

.00166250 

82 


MATHEMATICAL  TABLES. 


No. 

Htjtfpro- 
cal. 

No. 

Reclpro 
cul. 

No 

l_ 

771 

Recipro- 

No. 

Recl->rD' 
eal. 

No. 
901 

Redpro- 

on 

.00156006 

T06 

00141643 

.00129702 

886 

.00119617 

.00110968 

2 

.00l5r,T6:j 

7 

.00141443 

S 

.001296*1 

7 

.00119474 

2 

.00110865 

8 

.00  .'VVS-.M 

8 

.00141243 

8 

.00129366 

8 

.00119&32 

3 

.001 10742 

4 

.00j55;?r9 

9 

.00141044 

1   4 

.00129199 

9 

.00119189 

4 

.00110619 

5 

.00:. 55089 

710 

.00140815 

6 

.00129082 

840 

.00119048 

6 

.001 10497 

6 

.001.54799 

11 

.00140647 

6 

.0012aS66 

1 

.00118006 

6 

.00110375 

7 

.00I.',45.'»9 

12 

.00110149 

7 

.00128700 

2 

.00118765 

7 

.00110254 

8 

.00r»432I 

13 

.00140252 

8 

.00128535 

8 

.00118024 

8 

.00110192 

9 

.0«)l540b3 

14 

.00140056 

9 

.00128370 

4 

.0011»188 

9 

.00110011 

6.V) 

.00ir)88lii 

15 

.00189880 

780 

.O0128'a05; 

5 

.00118843 

910 

.00109890 

1 

.00I.586I0 

16 

.00139665 

1 

.00128041 

6 

.00118203 

]l 

.00109760 

2 

.001.1*^74 

17 

.00189170 

8 

.00127877, 

7 

.00118064 

12 

.00109649 

8 

.00  53140 

IH 

.00139276 

3 

.00127714 

8 

.00117924 

13 

.00109539 

4 

.00I.53905 

19 

.00139082 

4 

.00127551' 

9 

.00117786 

14 

.00109409 

5 

.00I5«7,J 

720 

.00138889 

6 

.00127888: 

850 

.00117647 

15 

.00109890 

6 

.00152489 

1 

.00i:i8696 

6 

.00127226 

1 

.00117509 

16 

.00109170 

7 

.oovrijn: 

2 

.00138501 

7 

.00127065, 

2 

.00117871 

17 

.00109051 

8 

.00151975 

3 

.00138313 

8 

.00126904 

8 

0011?283 

18 

.00108982 

9 

.00151745 

4 

.00138121 

9 

.00126743 

4 

.00117096 

19 

.00108814 

6G0 

.00151515 

5 

.00187981 

790 

.00121/582, 

ft 

.OOI169ft9 

920 

.00108696 

1 

.00151*6 

6 

.00137741 

1 

.00126422 

6 

.00116822 

1 

.00106578 

2 

.00151057 

7 

.00187552 

2 

.001»263l 

7 

.00116686 

8 

.00108460 

3 

.00150830 

8 

.0013736:^ 

3 

.00126108 

8 

.00116650 

8 

.0010834^ 

4 

.0015060^ 

9 

.00187174 

4 

.00125945! 

9 

.00116414 

4 

.001082S5 

5 

.OOloOSItt 

730 

.00180986 

6 

.001257861 

860 

.001^279 

fi 

.00108106 

6 

.00130150 

1 

.00136799 

6 

.00125628, 

1 

.00116144 

6 

.00107991 

7 

.001499-25 

2 

.00i:J6612 

1   ' 

.00125170 

2 

.00116009 

7 

.00107875 

8 

.00149701 

3 

.00130426 

8 

.00125313 

8 

.00115875 

8 

.00107759 

9 

.00119177 

4 

.00136240 

1   0 

.00125156 

4 

.00116741 

9 

.0010764.H 

670 

.00149;.'54 

5 

.00136054 

•  800 

.00125000 

6 

.00115607 

090 

.00107527 

1 

.OOHOaSl 

6 

.00135870 

:  1 

.00124844' 

6 

.00115473 

1 

.0010741 t 

2 

.00148809 

^ 

.00135685 

!  2 

.001246881 

7 

.00115840 

2 

.00107296 

8 

.00148588 

8 

.00135501 

'  a 

.0012458:1, 

8 

.00116207 

a 

.00107181 

4 

.00148368 

9 

.00185;J18 

4 

.00124878 

9 

.00115075 

4 

.00107066 

5 

.00148148 

740 

.00185135 

B 

.00124224 

870 

.00114942 

5 

.00100962 

e 

.001  79',»9 

1 

.00184953 

1   ^ 

.00124009 

1 

.00114811 

6 

.00106888 

7 

.00147710 

2 

.00134771 

7 

.00123916 

2 

.00114679 

7 

.00106724 

8 

.00147498 

3 

.00134589 

8 

.00123762 

8 

.00114547 

8 

00I0601O 

g 

.CO 14727 5 

4 

.001341(»9 
.00134228 

1   8 

.00128609 

4 

.00114416 

9 

.00106496 

68U 

.00147059 

6 

1  810 

.001284571 

5 

.00114286 

940 

.00106888 

1 

.0014r>813 

6 

.00134018 

11 

.00123305' 

6 

.00114155 

1 

.00106270 

2 

.001406 JH 

ly 

.00l33v%9 

1  ^'-^ 

.00123153, 

7 

.00114025 

8 

.00106157 

8 

.00I4G413 

8 

.0013:1690 

'  13 

.00128001! 

8 

.0011.3^95 

8 

.00106044 

4 

.0<M  46199 

9 

.00138511 

1  54 

.00128850 

9 

.00118766 

4 

.oaio.5a32 

5 

.00145985 

750 

.0013*138 

1  15 

.00122699 

880 

.00113636 

ft 

.00105880 

G 

.00 1 4:.:  78 

1 

.00133156 

;  16 

.00122549 

1 

00118507 

e 

.00105708 

7 

OOH-Vj^JO 

2 

.00132979 

1  17 

.001223901 

2 

.00113879 

7 

.0niaVM»7 

8 

.OU145J4U 

3 

.0013J802 

(  '« 

.00122249 
.00122100 

3 

.00113250 

8 

.00105485 

9 

.00145137 

4 

.00182026 

!  19 

4 

.00118122 

9 

.00105874 

690 

.0OI419-,>7, 

5 

.00:32450 

,  820 

.00121951 

ft 

.00112994 

950 

.00106268 

1 

001 1471 S 

6 

.00132275 

1 

.00121808 

6 

.00112867 

1 

.00105153 

j» 

.00144501), 

7 

.00182100 

1   2 

.(X)121654| 

r- 

.00112740 

8 

.00106048 

S 

.00144:101)1 

8 

00I3I926 

« 

.00121507 

8 

.00112613 

8 

.00104982 

4 

.00I4401« 

9 

.001317.52 

1   4 

.00121:159' 

9 

.00112486 

4 

.00104822 

5 

,0014888.-. 

700 

.00181579 

1   6 

.001212l:» 

890 

.00112360 

ft 

.00104712 

6 

.OOII36<S' 

J 

00181106 

6 

.00121065 

1 

.0011228:1 

6 

60104602 

7 

.00M817-.'| 

2 

.00 1 81  •.'84 

7 

.  00 1  ,'0919 

2 

.00118108 

7 

.00104493 

8 

OONJ:^;^ 

3 

.OOI8:0<>2 
.001. 10890 ' 

8 

.0012077.81 

8 

.00111982 

8 

.00104884 

» 

OOI4*)6l 

4 

9 

.0012U627I 

4 

.00111867 

9 

.00104275 

700 

.00 14. '.157! 

5 

.0011071  HI 

830 

.001-J04K2. 

ft 

.00111782 

960 

.00104167 

1  (nii  r-.'Gr,?i 

6 

.00  .805181 

1 

.001203371 

6 

.00111607 

1 

.00104058 

2   (K)l  l-.U.'iit' 

7  .00j:w:i78: 

2 

. 0012019.'! 

7 

.001114&8 

2 

.00106960 

s  .o^mtu:' 

8  .0();i0w'08| 

8 

.001200481 

8 

.00111859 

8 

.00108842 

4      00  H'^ir.l 

9  .00i:^008«M 

4 

.00119904 

9 

.00111235 

4 

.00108764 

•M  iw..ii>lii 

::o  .001'J9F70,' 

ft  .001197601' 

900 

.00111111 

6 

.00108087 

BECIPBOCALS  OF  ITUHBEBS. 


83 


Ho. 

Recipro- 

No. 

Recipro- 

No. 

BecfDro- 

No. 

Eecjyro- 

No. 

Recipro- 

986 

.0O1035» 

1061 

.00096993-2 

1096 

.000918409 

1161 

.000861826 

1826 

.000616661 

r- 

.00108413 

2 

.000968992 

7 

.000911577 

8 

.000860585 

7 

.009614996 

8 

.00103906 

.000088054 

8 

.000910747 

8 

.000859845 

8 

.000614388 

0 

.00108199 

.000967118 

9 

.000909918 

4 

.000859106 

9 

.000618670 

970 

.00103093 

.000966184 

1100 

.000909091 

6 

.000868869 

1880 

.000818006 

1 

.0O10S987 

.000965251 

1 

.000908265, 

6 

.000857688 

1 

.000812846 

S 

.00l0e2881 

.000964320 

8 

.000907441 

7 

.000856898 

8 

.000811686 

s 

.00102775 

.000968391 

8 

.000906618 

6 

.000856164 

8 

.000611080 

4 

.00109069 

.000962464 

4 

.000905797 

0 

.000855432 

4 

.000610878 

5 

.00102564 

1040  .0009615881 

5 

.000904977 

1170 

.000854701 

5 

.000809717 

6 

.00108459 

.000960615 

6 

.000904159, 

1 

.000858971 

6 

.000809061 

7 

.0010SS54 

.000959693 

7 

.000903342 

2 

.00085&!42 

7 

.000806407 

8 

00102860 

.000956774 

8 

.0009025-,'7 

8 

.000852515 

6 

.000807754 

9 

.00109145 

.000957854 

9 

.000901713 

4 

.000851789 

9 

.000807102 

960 

.00109041 

.000956988 

1110 

.000900901 

5 

.000851064 

1840 

.000806452 

J 

.00101987 

.000956028 

11 

000900090 

6 

.000850840 

1 

.000805802 

2 

.00101833 

.000956110 

12 

.000899281 

7 

.000849618 

8 

.000806153 

S 

.00I01?29 

.000954198 

13 

.000898473 

8 

.000848896 

8 

.000604506 

4 

.00101696 

.000958289 

14 

.0008976C6 

9 

.000848176 

4 

.000808856 

5 

.00101583 

1060 

.000952381 

15 

.0008968611 

1180 

.000847457 

6 

.000803218 

6 

.00101420 

.000951475 

16 

.000896057 

1 

.000816740 

6 

.000802568 

7 

.00101817 

.000950570 

17 

.000805255 

8 

.000846024 

7 

.000801925 

e 

.00101215 

.000949668 

18 

.000894454 

8 

.000845308 

8 

.000801288 

.00101112 

.00094871^7 

19 

.000893655 

4 

.000844595 

9 

.000800640 

99i] 

.00101010 

.000947867 

1120 

.000892867 

6 

.000843882 

1260 

.000800000 

.00100906 

.000046070 

1 

.000892061 

6 

.000843170 

1 

.000799860 

00100606 

.000946074 

2 

.000801266 

7 

.000842400 

8 

.000798;'28 

.00100706 

.000945180 

8 

.000890472 

8 

.000841751 

8 

.000798085 

.00100601 

.000944287 

4 

.000889680 

9 

.000841043 

4 

.000797446 

.00100602 

1()6C 

.000948396 

6 

.000888889 

1190 

.00084033€ 

5 

00071*6818 

.00100102 

.000942507 

6 

.000888099 

1 

.000889631 

6 

.000796178 

.00100801 

.000941.620 

7 

.000687311 

8 

.OOOi'38926 

7 

.000795645 

.00100200 

.000940734 

8 

.000886525 

8 

.000838222 

8 

.000794913 

00100100 

.000939650 

9 

.000885740 

4 

.000837521 

9 

.OOO".  94281 

lOOC 

.00100000 

.000938967 

1180 

.000884956 

5 

.000836820 

1260 

.000793051 

.000990001 

000938086 

1 

.00C8&I173 

6 

.000836120 

1 

.000798021 

.000988001 

.000937207 

2 

.000683892 

7 

.00083:>422 

2 

.000792893 

.000997009 

.0009^6330 

8 

.000882612 

8 

.O0OSM724 

8 

.000791766 

.000935454 
.000934579 

4 

.000881834 

9 

.000884028 

4 

.000791139 

000095025 

107( 

6 

.000881067 

1200 

000838833 

6 

.000790514 

!000094O86 

.000938707 

e 

0008Maj82 

1 

.00U832689 

6 

.000780889 

.000993049 

.000932836 

7 

.000879508 

2 

.000881947 

7 

.000789266 

.0009fti063 

.000931966 

8 

.000878735 

8 

.000831255 

8 

.00078H643 

.000991060 

.000931099 

9 

.0006779e8 

4 

.00088a>65 

9 

.000788022 

1011 

.000990090 

.000980233 

1140 

.000877193 

5 

.000829875 

1270 

.000787402 

.000969120 

.000929868 

1 

.000876424 

6 

.0008V9187 

1 

.000786782 

.000968142 

.000988605 

a 

.000875057 

7 

.00082K500 

8 

.000786163 

.000087167 

.000927644 

s 

.000874891 

8 

.000827815 

8 

.OOir,  85546 

000966199 

.000926784 

4 

.000874126 

9 

.000827180 

4 

.000784929 

.000985822 

loec 

.000925926 

6 

.000873362 

1210 

.000826446 

5 

.000784314 

.0cn0S4262 

.000925069 

6 

.000872600 

11 

.000825764 

6 

.000783699 

.000083-^84 

.000984..M4 

7 

.000871840 

12 

.000825082 

7 

.000783085 

.000962318 

.000923361 

8 

.000871080 

18 

.000824402 

8 

.000782473 

.000961351 

.000922509 

9 

.000870322 

14 

.00a^«8728 

9 

.000781861 

ICtiO 

.000980892 

.000921659 

1150 

.000869565 

15 

.000823045 

1280 

.000781250 

.000970488 

.000920610 

1 

.000868810 

16 

.000822;HC8 

1 

.0007J-43640 

0000:6474 

.000919963 

2 

.000868056 

17 

.00082169.M 

2 

.000780031 

.000977517 

.000919118 

8 

.000867303 

18 

.000821018 

8 

.000779423 

.000076562 

000918274 

4 

.000866551 

19 

.000820344 

4 

.000778816 

.000975610 

1000  .000017431 

5 

.00086r.801 

1280 

.000819672 

5 

.000778210 

.000974659 

1  .0U0916590 

6 

.00l)«6r»0.V2 

1 

.000819001 

6 

.000777-605 

.000078710 

2  .000915761 

7 

.000861304 

2 

.000818381 

7 

.000777001 

s 

.000978783 

8  .000914913 

8 

.001J86a'i.'>8 

3 

.000817661 

8 

001)770397 

9 

.000071817 

4I.0U09HO77 

9 

.oc-osoaais 

4 

.000816993 

9 

.0m)77.^795 

KM 

.O00OSW74 

5 

.000913242 

1160 

.OOOHOOOTO 

5 

.000816326 

1290 

.000775194 

84 


MATHEMATICAL  TABLES. 


No. 

ReciDro- 

No. 

Recinro- 

No. 

Recipro- 

'no. 

Recioro- 

No. 

Recioro- 

1801 

.000774503 

1856 

.000737468 

1421  .000708780 

1486 

.000672048 

1651 

.0006447* 

S 

.000778994 

7 

000736920, 

2.000708235 

7 

.000678405 

8 

.000644a3< 

8 

.000778395 

8 

.000786:177 

8   000702741 

8 

.000679048 

8 

.00064891,' 

4 

.000772797 

9 

.0U07358:i5 

4  .000702247 

01.000671502 

4 

.000&485O 

K 

.0007WJ01 

1880 

.00a7S5'294i 

6  .OU0701754 

14901.000671141 

5 

.000643081 

6 

.000771605 

1 

.0007^4754 

6  .000701262 

1 1.000670601 

6 

.000645KJ7; 

7 

.OOOTHOIO 

2 

.000794214, 

7  .000700771 

2;.  000670241 

7 

.00064226J 

8 

.000770416 

8 

.0007380761 

8  .010700280 

81.000660702 

8 

.00061  IS  It 

9 

.000760&J3 

4 

.0007^138 

9  .000090790 

4  .000660344 

0 

.00064143' 

1800 

.000:69-^1 

5 

. 00073  aoit 

1430  .000690;j01 

51.000668806 

1500 

.00064 10:>( 

1 

.00076t(639 

6 

.0007^«064 

1  .000698812 

6'.  000668440 

1 

.00064061,'! 

2.000768W9 

7 

.000781529 

2  .000008324 

7.000668008 

S 

.0006402QE 

8  .0007tf7459 

8 

.000730094 

8  .000697837 

8  .000667557 

8 

.000630793 

4  .0007C6871 

9 

.000730480 

4  .000U97.i60 

1      9.000667111 

4 

.OOOOSKISO 

6  .00076C883, 

1870 

.0007<0927 

6.000606664! 

1500.000666667 

5 

.000638978 

6;. 000755697 

1 

.0007203951 

6  .0006JW379| 

1      11.000666228 

« 

.000638570 

7..  0007651  111 

2 

.000728863 

7  .000695894' 

2'.  000665779 

7 

.000688162 

8 

.000761526 

8 

.0007^»2l 

8.000605410; 

8  .000665836 

8 

.000687755 

0 

.000768942 

4 

.000727802 

0  .000604027, 

4  .0006648041 

9.000637819 

1810 

.00076S:«9 

5 

.0007Vr278 

1440  .000604444' 

5  .000664452 

I570;.00063C943 

11 

.000762776 

6 

.000726744 

11.000693062; 

6.000664011 

1  .0000866:^7 

18 

.000762195 

7 

.000726216 

2.000693481' 

7  .000668570 

2' .0006381  .%> 

18 

.000761616 

8 

.000726689 

8  .0006980011 

8  .000668130 

8.0006857-2S 

14 

.000761035 

9 

.00072516-^ 

4  .00060-25211 

0<. 000602891 

4  .000685324 

15 

.000760466 

1890 

.000724638 

6  .000602041 

15101.000662252 

5  .000634021 

16 

.000750878 

1 

.000724113 

61.0006015631 

111.000661813 

6  .000684518 

17 

.000750301 

2 

.000723589 

7  .0006010851 

I2I  .000661876 

71.000634115 

18 

.000768725 

3 

.00072:»06 

8<. 000600608 

18.000660930 

8  .000633714 

10 

.000758150 

4 

.000722543 

0  .000600131 

14  .000660502 

0  .  000688:112 

1820 

.000757576 

6 

.000722022 

1450;.00068D655 

15.000600066 

1580  .000682911 

1 

000767002 

6 

.000721501 

1  .000680180 

16;.OH0660631 

11.000682511 

2 

.000766430 

7 

.  0007520980 

2'. 000688705! 

17i.000(i50lP6 

«!. 000632111 

8 

.000755858 

8 

.000720401 

8.000688231 

18!. 000658761 

8!. 000631712 

4 

.000765-J87 

9 

.000719912 

41.000687758 

191.000658328 

4'. 000631318 

5 

.000754717 

1300 

.000719424 

6'.  000687285 

1520  .0006578951 

5. 000030915 

6 

.000754148 

1 

.000718907 

6.000686813 

1 

.000657462 

6.000630517 

7 

.000753679 

2 

000718391 

7  .000086341 

2 

.0006.57030 

7  .000680I'20 

8 

.0007^8013 

8 

.000717875 

8  .000685871 

8 

.000656598 

8.000629723 

»!. 000752445 

4 

.000717300 

0  .000685401 

4 

.000656168, 

0  .0006203-27 

isao 

.000751880 

6 

.000716846 

1460  .0006849321 

5;. 000665738 

1600  .0006289.^1 

1 

.000751315 

0 

. 00071 63:« 

1  .000684463, 

6.000655308 

1  .000628.>36 

2 

.000r507.')0 

7 

.000715820 

2  .00008:1994! 

2  .00062X141 

8 

.000750187 

8 

.0007153081 

8  .0006885271 

81.000654450; 

8  .000627746 

4 

.0007496.25 

9 

.000714790i 

4  .0006830001 

0|.  000654022' 

4 

.000627353 

5 

.000749064 

1400 

.000714286 

5. 00068-2594' 

1580'.  000653595 

6 

.000626958 

6 

.000748503 

1 

.0007187761 

6' .000682128 

It. 000658168 

6 

.000626566 

.000747943 

2 

.0007132671 

7. 000681 663 

2.000652742 

7 

.000626174 

8 

.000747384 

8 

.000712758 

8  .000681199 

8;.0006523I6 

8 

.000625788 

9 

.000746826 

4 

.0007122511 

0'.000(«0735 

4l.CH)0651890 

0 

.000625391 

1340 

.OOOJ  46269 

6 

.000711741' 

1470  .000680272 

JSI.00065146C 

1600 

.000625000 

1 

.000746712 

6 

.000711238 

1  .000079810 

61.0006.51042 

2 

.0006-24219 

2 

.000745156 

7 

.000710732 

2  .000079318 

71.000650618 

4 

.000623441 

8 

.00074400.; 

8 

.0007102271 

8  .000678S87 

8  .000650195 

6 

.00062J665 

4 

.000744018 

9 

.0007097-28] 

4  .000678426 

91.000649778 

8 

.000621H90 

5 

.000743494 

1410 

.000709220 

5  .000077966 

15401.000649351 

1610 

.000621118 

6 

00074294-2 

11 

.000708717' 

6  .00O(r775O7 

1:.  000648929 

8 

.000620847 

7 

.000742390 

12 

.0007082151 

71. 000677048 

2 

.000648508 

4 

.000619578 

8 

.000741840 

13 

.000707714' 

8  .000676590 

3 

.000(*^OH8 

6 

.0006ISS1S 

0 

.000741290 

14 

000707214, 

9  .000076182 

4 

.000047608 

8 

.00061804/ 

1850 

.000740741 

16 

.000706714 

1480    000675676 

5 

.000647249 

1620 

,00061728* 

1 

.000740192 

16 

.000700215 

1  .00^575219 

6 

.000646a30 

2 

.0006165^ 
.0006157^ 

2 

000739645 

17 

.000705716 

2  .000«r4-64 

7'.  0006464 12 

4 

3 

.000789098 

18 

.0(»705219 

8  .000674309 

8. 000045995 

6 

.000615006 

4 

.000788552 

19 

.000704722 

4  .0no«}7TJ8.M 

1       9|  .000645.578 

8 

.0006142M 
.000618407 

6 

.000788007. 

1420 

.000704225 

5'.0006'^3»01 

15501.000645161 

1680 

BBGIPROCALS  OF  NUMBERS. 


86 


No. 


Redpro- 
coil. 


ISttJ  .•00612745 
4' .000611996 
6'  0006ll«47 
R   000610300 

16i0{  .000609:96 
S. 000600018 
.000608272 


8 
16S0 


i|.oooeon»3 

.000606796 
^  .000606061 
ti. 0006058-27 
4i.0006015l» 
V .000609865 
8;  .000808186 

16601.000602410 
2i.  000601685 
4.00n600W9 
6.000600MO 
8.0006995SO 

26^)1  .OOQSflWOf 
». 000698066 
4  .000697371 
e:  .000596658 
8.00059504T 

16<»  .000595i38 
ft. 000594530 
4).000988«M 
6i.O0OGO31id0 
8  .00(fi9d417| 

1680  .000601716 
8  .000601017; 
4.000680819 
6.0005806'S 
8.000688928 

1700.000688386 
8.00058iS44 
4.00(680854 


No. 


1706 
8 

1710 
12 
14 
18 
18 

IT* 
2 
4 
6 
8 

1780 
9 
4 
6 
8 

1740 
2 
4 
6 
8 

1790 
8 
4 
6 
8 

1760 
8 
4 
6 
8 

1770 
2 
4 
6 
8 


Recipro- 
cal. 


.000686166 
.0005854801 
.000584795 
.000584112 
.0005834801 
.000582750 
.0005820721 
.000581395 
.000580720 
.00(»80046 
.000579374 
.0005787t)4 
.0005780:^5 
.000577367, 
.000676701 
.0005760^7 
.0005759r4 
.000574713 
.000574avJ 
.000573394, 
.00ai727a7 

0005720Hi 
.000571429 
.000570776! 
.0005701»5 
.000569476 
.000568828 
.000568182 
.000667587 

000566898 
.000566251 

000565611 

000564334; 
,000563698 
.00056806;i 
.0005624301 


No. 


Reclpro- 


tecipi 


4' 
6 

8| 
1700 

4 
6 
8 
1800. 

2; 

4. 

6 

8 

1810 
12i 
14 
161 
18) 
1820 

2 

^! 
«; 

8l 
1830 
2 
4 
6 
8 

1840. 
2 
4 

1850| 
2 


No. 


000561798  1854 
000561167  I   6 

.0005605381   8 

.000659910.  I860 

.000550284 

.000558659; 

.000558aS5 

.000557413 

.000556798 

.000556174 

.000555556 

.000554989 

.0005543:24; 

.OOa'^710  11880 

.000563097 

.000552486 

.000551876 

.000651268 

.00a'j50661 

.000550055: 

.000549451 

.000548848 

.000548240 

.000547645 
000547040! 

. 0005464 ]8| 

.000545851 

.000545259 

.000544002 

.000544069, 

.000543478] 

.00054-JH88I 

.000542299,   _ 

.000541711!  1920 

.000541125  1   a 

.000540540    4 

.00058095711   6 


1870 
2 

4 
6 
8 


2 

4 

6 

8 

1890 

2 

4 

6 

8 

1900 

2 

4 

6 

8 

1910 

12 

14 

16 

18 


Recfpro- 


'^: 


No. 


.000539874  1928 

.000538793  1980 

.000588213!!   2 

.0005876841 

.000587057, 

.000586480; 

.000535905; 

.000535332 

.0006847591 

.000534188 

.000538618 

0005S8049 
.000582481) 
.000531915 
.000581350 

aKl530785' 
.000530222 
.000529661 
.000520100 
.0005:28541 
.000527983 
.000527426 
.000526870, 
.000526816 
.000525762 
.000525210 
.000624050, 
.000524109 
.000528560 
.000523012 
.000622466 
.000521990; 
.000521376 
.000520833, 

.ooa')202gi 

000519750, 


4 
6 
8 

1940 
9 
4 
6 
8 

1950 
2 
4 
6 
8 

1660 
2 
4 
6 
8 

1970 

4 

8 

8 
1980 
2 
4 
6 


1990 
2 
4 
6 

8 


000519211 1  2000 


Reel 


ar 


,000518678 
000518188 
,000517599 
.000517003 
.000516528 
.000515990 
.000515464 
.000514988 
.000514408 
.000513974 
.000513847 
.000512880 
.000512295 
.000511770 
.00tt51l247 
000510785 
.00U5102(»4 
.00U5O9684 
.000509166 
.000508647 
.000508180 
.0005071)14 
.000507099 
.000506585 
.000506078 
.000506661 
.000605051 
.000604541 
.000504082 


.000503018 
.000502^18 
.000502006 
.000501504 
.000501009 
.000500601 
000500000 


Use  of  reciprocals.— Reciprocals  niay  be  conveniently  used  to  facili- 
tate computations  in  longr  division.  Instead  of  dividing  as  usual,  multiply 
ihe  divideud  by  the  reciprocal  of  the  divisor.  The  method  is  especially 
useful  whcMi  many  different  dividends  are  required  to  be  divided  by  the 
same  divisor.  In  this  caso  find  the  reciprocal  of  the  divisor,  and  make  a 
small  fable  of  iis  multiples  up  to  9  times,  and  use  tliis  as  a  multiplication- 
table  instead  of  actually  performing  the  multiplication  in  each  case. 

Example. —9671  and  several  other  numbers  are  to  be  divided  by  1688.    The 
reciprocal  of  1688  is  .000610600. 
XolUp 


lolUtiles  of  the 
redprocAl: 
I.  .0006106 
SL  .0019910 
8.    .0018816 

4.  .O0S4420 

5.  .0080525 

6.  .0096680 

7.  .0042786 

8.  .0046640 

9.  .0064045 
10.  .0061060 


The  table  of  multiples  Is  made  by  continuous  addition 
of  6105.    The  tenth  Ime  Is  written  to  check  the  accuracy 
of  the  addition,  but  it  is  not  afterwards  used. 
Operation: 

Dividend         9871 

Take  from  table  1 0006105 

7 0.0427:« 

8 00.48S40 

9 005.4945 


Quotient 6.02G9455 

Oorteet  quotient  by  direct  diviKion 6 .026251 5 

Tbe  result  will  generally  be  correct  to  as  many  figures  as  tliere  are  signifi- 
cant figures  in  the  reciprocal,  less  one,  and  the  error  of  the  next  figure  will  In 
general  not  exceed  one.  In  the  above  example  the  reciprocal  has  six  aig^* 
niflcaat  figures,  610600,  and  the  result  is  correct  to  five  places  of  figures. 


86 


HATHEHATICAL  TABLES. 


MII7ARE8,   CUBBS,   S<|UARE  ROOTS   AflD  CtJBB 
ROOTS  OF  MUniBKRS  FROM  .1   TO  1600. 


No. 

Square. 

Cube. 

8q. 
Boot 

Cube 
Root. 

No. 
8.1 

Square. 

Cube. 

• 

8q. 
Boot. 

Cube 
Boot. 

.1 

.01 

.001 

.8162 

.4642 

0.61 

29.791 

1.761 

1.4.58 

.15 

0225 

.0084 

.3878 

.5313 

.2 

10.24 

32.768 

1.789 

1.474 

.2 

.04 

.006 

.4472 

.5848 

.8 

10.89 

85.987 

1.817 

1.489 

.26 

.0625 

.0156 

.500 

.6300 

.4 

11.56 

89.804 

1.844 

1.604 

.3 

.09 

027 

.6477 

.6694 

.5 

12.25 

42  875 

1.871 

1.518 

.85 

.1225 

.0429 

.5916 

.7047 

.6 

12.96 

46.666 

1.897 

1.5SS 

.4 

.16 

.064 

.6825 

.7868 

.7 

18.69 

60.663 

1.924 

1.547 

.45 

.2025 

.0911 

.6708 

.7668 

.8 

14.44 

64.878 

1.949 

1.500 

.5 

.25 

.125 

.7071 

.7987 

.9 

16.81 

59.819 

1.975 

1.674 

.55 

.3025 

.1664 

.7416 

.8193 

4. 

16. 

64. 

8. 

1.5874 

.6 

.86 

.216 

.7746 

.8434 

.1 

16.81 

68.921 

8  085 

1.601 

.66 

.4225 

.2746 

.8062 

.8662 

.2 

17.61 

74.088 

2.049 

1.618 

.< 

.49 

.843 

.a367 

.8879 

.8 

18.49 

79.607 

8.074 

1.G26 

.75 

.56% 

.4219 

.8660 

.9086 

.4 

19.36 

86.184 

8.096 

1.680 

.8 

.64 

.512 

.8944 

.9283 

.5 

20.25 

91.186 

8.181 

1.651 

.85 

.7225 

.6141 

.9219 

.9478 

.6 

21.16 

97.836 

8.145 

1.668 

.0 

.81 

.729 

.M«7 

.9655 

.7 

22.09 

108.828 

2.168 

1,675 

.96 

.9025 

.8574 

.9747 

.9830 

.8 

23.04 

110.602 

2.101 

1.687 

1. 

1. 

1. 

1. 

1. 

.9 

24.01 

117.649 

2.814 

1.006 

1.05 

1.1025 

1.158 

1.025 

1.016 

6. 

25. 

126. 

8.8861 

1.7100 

1.1 

1.21 

1.881 

1.049 

1.032 

.1 

26.01 

182.661 

8.868 

1.721. 

1.15 

1.8225 

1.521 

1.072 

1.0-18 

.2 

27.04 

140.606 

8.280 

1.788 

1.2 

1.44 

i.-na 

1.095 

1.063 

.8 

28.09 

148.877 

2.802 

1.744 

1.25 

1.56^5 

1.953 

1.118 

1.077 

.4 

29.16 

167.464 

8.884 

1.754 

1.8 

1.69 

2.197 

1.140 

1.091 

.5 

30.25 

166.875 

8.846 

1.765 

1.85 

1.8225 

2.460 

1,162 

1.105 

.6 

81.36 

175.616 

8.366 

1.776 

1.4 

1.96 

2.744 

1.183 

1.119 

.7 

82.49 

185.193 

8.387 

1.786 

1.45 

2.1025 

8.049 

1.204 

1.182 

.8 

83.64 

195.118 

2.406 

1.797 

1.5 

2.25 

8.375 

1.2247 

1.1447 

.9 

34.81 

205.379 

2.429 

1.807 

1.55 

2.4025 

8.721 

1.245 

1.157 

6. 

86. 

216. 

2.4495 

1.8171 

1.6 

2. .56 

4.096 

1.265 

1.170 

.1 

87.21 

226.981 

2.470 

1.827 

l.Oo 

2.7225 

4.492 

1.285 

1.182 

.2 

88.44 

2:i8.328 

2.490 

1.837 

l.T 

2.89 

4.918 

1.804 

1.193 

.8 

39.69 

250.047 

2.510 

1.847 

1.75 

3.0625 

5.359 

1.323 

1.205 

.4 

40.96 

268.144 

2.5.30 

1.867 

1.8 

8.24 

5.832 

1.842 

1.216 

.5 

42.25 

274.625 

2.660 

1.866 

1.85 

3.4225 

6.832 

1.360 

1.228 

.6 

48.56 

287.496 

2.569 

1.876 

1.9 

3.61 

6.&19 

1.878 

1.239 

y 

44.89 

800.763 

2.688 

1.885 

1.05 

8.8025 

7.415 

1.396 

1.249 

.'8 

46.24 

314  482 

2.608 

1.895 

S. 

4. 

8. 

1.4142 

1.2599 

.9 

47.61 

328.509 

2  627 

1.004 

.1 

4.41 

9.261 

t449 

1.281 

7. 

49. 

848. 

2.6458 

1.9129 

.2 

4.84 

10  648 

1.483 

1.801 

.1 

50.41 

857.911 

2.665 

1.928 

.8 

5.29 

12  167 

1.617 

1.3J0 

.2 

51.84 

378.248 

2.688 

1.981 

.4 

5.76 

18.8','4 

1.549 

1.839 

.3 

53.29 

389.017 

2.708 

1.940 

.5 

6.25 

15.625 

1.581 

1.357 

.4 

54.76 

405.224 

2.780 

1.949 

.0 

6.76 

17.576 

1.612 

1.375 

.5 

56.25 

421.876 

2.789 

1.967 

.7 

7.29 

19.083 

1.643 

1.392 

.6 

57.76 

438.976 

8.757 

1.966 

.8 

7.84 

21.952 

1.673 

1.400 

.7 

59.29 

456.533 

8.775 

1.975 

.9 

8.41 

24.889 

1.703 

1.426 

.8 

60.84 

474.652 

2.793 

1.983 

3. 

9. 

27. 

1.7321 

1.4422 

.9 

62.41 

498.080 

2  811 

1.998 

SQUABES,  CUBES,  SQUASB  AND  GCBE  BOOTS.        87 


No. 

Square. 

Cube. 

Sq. 

Cube 
Boot 

No. 

Square. 

Cube. 

Bq. 
Root. 

Cube 
Root. 

8. 

G4. 

618. 

2.8884 

8. 

45 

20SS 

91185 

6.7088 

8.5569 

.1 

65.81 

581.441 

8.846 

8  008 

46 

^ 

97886 

6.7883 

3.5830 

.« 

S:IS 

551.868 

8.864 

8.017 

47 

103888 

6.8557 

8.6068 

.8 

571.787 

8.881 

8  085 

48 

8804 

110598 

0.9888 

3.6348 

.4 

70.56 

6O0.7O4 

8.808 

8.038 

49 

8401 

117649 

7. 

8.6598 

.5 

72.85 

614.185 

8.015 

8.041 

50 

8500 

185000 

7.0711 

8.6840 

.6  '    73^ 

686.056 

8.938 

8.040 

51 

8601 

138651 

7.1414 

3.7084 

.7 

75.0d 

666.508 

8.950 

8.057 

58 

8704 

140606 

7  8111 

3.7885 

.8 

77.44 

681.478 

8.966 

8.065 

53 

2809 

148877 

7.2801 

3.7B63. 

.9 

7!9.«1 

701.969 

2.968 

8.078 

54 

8916 

167464 

7.3485 

3.7798 

t. 

81. 

780. 

8. 

8.0601 

55 

8085 

166875 

7.4168 

3.8030 

.1 

».81 

758.571 

8.017 

8.088 

56 

8186 

175616 

7.4883 

8.8859 

i 

81.64 

778.688 

8.088 

8.095 

57 

3849 

185193 

7.5498 

8.S485 

.8 

86.40 

804.857 

8.050 

8.108 

58 

8364 

ia51I8 

7.6158 

8.8700 

.4 

88.96 

880.564 

8.066 

8.110 

69 

3481 

905879 

7.6811 

8.8930 

.5 

S0.85 

857.875 

8.089 

8.118 

60 

3600 

816000 

7.7460 

3.9149 

.6 

flS.16 

881.786 

3.096 

8.126 

61 

8781 

286981 

7.8108 

8.9865 

.7 

M.Od 

918.678 

3.114 

8.188 

08 

8844 

288888 

7.8740 

8.9579 

.8 

96.M 

•41.108 

8.130 

8.140 

63 

8969 

260047 

7.9378 

3.9791 

.9 

98.01 

Sy70.890 

8.146 

8.147 

64 

4096 

868144 

8. 

4. 

10 

100 

1000 

3.1683 

8.1544 

66 

4885 

274685 

8.0623 

4.0307 

11 

121 

1381 

3.3166 

8.2240 

66 

4856 

287496 

8.1340 

4.0418 

w 

144 

1783 

3.4641 

8.2894 

67 

4489 

800768 

8.1854 

4.0615 

13 

160 

8197 

3.6056 

8.3513 

68 

4684 

814438 

8.2462 

4.0817 

14 

196 

8744 

3.7417 

8.4101 

69 

4761 

S-J8509 

8.3066 

4.1016 

15 

»5 

8875 

3.8780 

8.4668 

70 

4900 

348000 

8.8666 

4.1818 

16 

956 

4096 

4. 

8.5198 

71 

5041 

3.57911 

8.4861 

4.1408 

17 

889 

4918 

4.1831 

8.5713 

72 

5184 

373848 

8.4858 

4.1608 

18 

884 

5888 

4.3486 

8.6907 

73 

5389 

389017 

8.5440 

4.1798 

19 

861 

60B9 

4.3589 

8.6684 

74 

5476 

405284 

8.6083 

4.1983 

90 

400 

8000 

4.4731 

8.7144 

75 

5635 

481875 

8.6603 

4  2172 

21 

441 

0961 

4.5686 

8.7689 

76 

6776 

438976 

8  7178 

4.8358 

Si 

484 

10048 

4.6904 

8.8080 

77 

6039 

456533 

8.7760 

4.8543 

SS 

m 

18167 

4.7968 

8.8439 

78 

6064 

474558 

8.8318 

4.2787 

24 

576 

13894 

4.8990 

8.8845 

70 

6841 

498039 

8.8888 

4.8908 

O 

095 

15685 

5. 

8.9840 

80 

6400 

512000 

8.9443 

4.3089 

a 

676 

17576 

5.0990 

8.9685 

81 

6561 

531441 

9. 

4.3867 

97    7» 

19688 

5.1968 

3. 

88 

6724 

551368 

9  05.54 

4.3(45 

88    784 

8108S 

5.8915 

3  0866 

88 

0880 

571787 

9.1104 

4.3681 

29 

841 

94889 

5.3858 

3.0788 

84 

7056 

59-^704 

9.1658 

4.3795 

10 

900 

87000 

5.4778 

3.1072 

85 

7285 

614125 

0.8195 

4.3968 

81 

961 

89791 

5.5678 

3.1414 

86 

7896 

636056 

9.8736 

4.4140 

82 

1QS4 

88768 

5.6560 

3.1748 

87 

7.'>69 

65&'n8 

9  3-.T(5 

^.4^J10 

83 

1089 

38987 

5.7446 

3.8075 

88 

7744 

0^1478 

9.3H08 

4.4480 

SI 

1156 

89804 

5.8810 

8.8886 

80 

7981 

704969 

0.4M0 

4.4647 

& 

1285 

48875 

5.9161 

3.2711 

90 

8100 

739000 

9.4868 

4.4814 

88  1996 

46660 

6. 

8.8010 

91 

8881 

7Jmn 

9.5394 

4.4979 

37  1809 

50668 

6.0888 

3.8388 

98 

8464 

778688 

0  .5917 

4.5144 

88 

1444 

64879 

6.1644 

8.8690 

93 

8649 

804357 

9  6437 

4.5307 

39 

1581 

69319 

6.8450 

3.8918 

94 

8836 

830584 

9.6954 

4.5468 

40 

1600 

64000 

6.8848 

3.4900 

95 

9025 

9  7466 

4.5680 

41 

1081 

68»»1 

6.4081 

3.4488 

96 

9216 

884736 

9.7980 

4.5780 

48 

1764 

74088 

6.4807 

3.4700 

97 

9409 

918678 

9.84K0 

4.5947 

4S 

1840 

79607 

6.5574 

3.5034 

9H 

9604 

941198 

9.8995 

4.6104 

44 

1986 

851M 

6.6888 

3.5808 

99 

9801 

970899 

9.9499 

4.6861 

88 


HATHEUATIOAL  TABLES. 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

100 

10000 

1000000 

10. 

4.6416 

155 

24025 

8728875 

12.4499 

58717 

101 

ioa)i 

IU.30801 

10.0199 
10.0905 

4.6570 

156 

243:i6 

8796416 

12.4900 

5.3832 

10;! 

10404 

1061208 

4.6728 

157 

24649 

3869893 

12.5800 
12.660i 

5.3947 

108 

10609 

1092727 

10.1489 

4.6875 

158 

24964 

8944313 

6.4061 

104 

10816 

1124864 

10.1980 

4.7027 

159 

25281 

401967V 

12.6005 

6.4175 

106 

1102S 

1157626 

10.2470 

4.7177 

160 

25600 

4096000 

18.M91 

6.4288 

106 

112  6 

1191016 

10.2956 

4.7326 

161 

25921 

4178261 

12.6686 

6.4401 

107 

11449 

1225043 

10.3441 

4.7476 

162 

26244 

4251528 

12.7879 

5  4514 

108 

11664 

1259712 

10.3923 

4.7622 

163 

20569 

4380747 

12.7671 

5.4«26 

109 

11881 

1295029 

10.4403 

4.7769 

164 

26896 

4410044 

12.6062 

5.4737 

110 

12100 

1831000 

10.4881 

4.7914 

166 

27225 

4492185 

12.8452 

5.4848 

111 

ia8;Jl 

1367631 

10.6857 

4.8050 

166 

27556 

4574296 

12.8841 

6.4959 

112 

12514 

1404928 

10.5880 

4.8203 

167 

27889 

4657463 

12.9228 

5.5069 

118 

12709 

1442897 

10.6301 

4.8S46 

108 

28v»24 

4741682 

12.9615 

5.5178 

114 

12996 

1481544 

10.6771 

4.8488 

169 

28561 

4826800 

18.0000 

5.5288 

115 

132« 

1520676 

10.7288 

4.6629 

170 

28900 

4918000 

18.0884 

5.53fR' 

116 

13456 

1660896 

10.7708 

4.8770 

171 

29241 

6000211 

18.0767 

5.5505 

117 

18689 

1601613 

10.8167 

4.8910 

172 

29584 

6088448 

13.1149 

5.5613 

118 

18924 

1613032 

10.8628 

4.9049 

173 

29929 

5177717 

18.1529 

5.5721 

110 

14161 

1685159 

10.9087 

4.9187 

174 

80276 

5268024 

13.1909 

5.5886 

120 

14400 

1728000 

10.9545 

4.9324 

175 

80625 

5859375 

18.2288 

5.5934 

121 

14641 

1771561 

11.0000 

4.9461 

176 

80976 

6451778 

13.2665 

5.6041 

li^ 

14884 

1815848 

11.0454 

4.9597 

177 

31329 

5545238 

13.8041 

6.6147 

123 

15129 

1800867 

11.090) 

4.9732 

178 

31684 

66:«758 

18.8417 

6.6253 

m 

15876 

1906624 

11.1355 

4.9866 

179 

&2011 

5735889 

13.8791 

5.6357 

125 

15025 

1953125 

11.1808 

5.0000 

180 

32400 

6833000 

13.4164 

5.6468 

190 

15876 

2000876 

11.2250 

5.0138 

181 

32761 

5929741 

13.4.')36 

6.6567 

1« 

16129 

•.•018883 

11.2694 

5  0265 

182 

38124 

602^566 

13.4907 

66671 

128 

16884 

2097152 

11.8187 

5.0897 

183 

88489 

6128487 

13.5277 

6.6774 

120 

16641 

2146660 

11.3578 

5.0528 

184 

83856 

6229504 

13.5647 

6.6«77 

180 

16900 

2197000 

11.4018 

6.0658 

186 

342-25 

6831685 

13.6015 

6.6060 

ISI 

17161 

2248091 

11.4455 

5.0788 

186 

84596 

6434856 

13.&S82 

6.7088 

laz 

17424 

229'J968 

11.4891 

5.0916 

187 

34960 

6639208 

13.6748 

6.7165 

188 

17689 

2352637 

n.  5-^26 

*.1045 

188 

35344 

6644672 

18.7113 

5.r287 

184 

17956 

2406104 

11.5758 

5.1172 

189 

85?21 

6751269 

18.7477 

5.7388 

185 

18226 

2460375 

11.6190 

6.1299 

190 

86100 

6850000 

13.7840 

6.7469 

136 

18496 

2515456 

11.6619 

5.1486 

101 

86481 

6967871 

13.8203 

5.7590 

187 

18769 

2571353 

11.7047 

5.1551 

192 

36864 

7077888 

13.8564 

5.7690 

188 

190J4 

•J628072 

11.7473 

5.1676 

198 

37249 

7189a'57 

13.8924 

6  7790 

139 

19321 

'J68otil9 

11.7893 

5.1801 

194 

37636 

7301384 

13.9284 

5.7890 

140 

19600 

2744000 

11.a332 

5.1926 

195 

38025 

7414875 

18.9642 

6.7989 

141 

19881 

2803221 

11.8743 

5.2048 

196 

38116 

76295^16 

14.0000 

5.8068 

14*2 

20164 

2863288 

11.9164 

5.2171 

197 

JJ8809 

7615378 

14.0357 

5.8188 

143 

W449 

29i4207 

11.9583 

5.2293 

196 

39204 

7762392 

14.0712 

5.8286 

144     vH)r3U 

2985984 

12.0000 

5.2425 

199 

89601 

7880599 

14.1067 

5.8383 

145 

21085 

3048625 

12.0416 

5.2536 

200 

40000 

6000000 

14.1421 

B.84S0 

146 

21316 

8112136 

12.08.W 

5.2656 

201 

40401 

8120601 

14.1774 

5.8578 

147 

21609 

3170523 

12.1244 

5.2776 

202 

40804 

8242406 

14.2127 

6.867B 

148 

21M)4 

3241792 

12.16."« 

5.2896 

203 

41209 

ft365427 

14.2478 

5.8771 

149 

22201 

3307949 

12.2066 

5.8015 

204 

41016 

8489064 

14.2829 

6.8808 

ISO 

22500 

3375000 

12.2474 

5.8133 

205 

42025 

6615125 

14.3178 

6.6964 

151 

2-2801 

3442051 

12.2H82|  5.1251 

206 

42436 

6741816 

14.3527 

69069 

152 

23104 

3511808 

12.328.**,  5,8368 

2t>7 

42849 

8860743 

14.8875 

6.9166 

168 

23409 

3681577 

12.36'.<3i  5.3485 

208 

48264 

8998913 

14.4288 

6.98fiO 

154 

23716 

3652264 

12.40971  5.8601 

209 

48681 

9129339 

14.4566 

6.9846 

SQUARES,  CUBES,  SQUARE  AKD  CUBE   ROOTS.        89 


Ko. 

«10 

Square. 

Cube. 

&. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 

Cube 
Root. 

44100 

9961000 

14.4914 

5.9489 

865 

70886 

18609086 

16.8788 

64888 

SU  '  44»ei    i 

9893981 

14.6866 

5.9588 

866 

707A6 

18881096 

16.8095 

6.4818 

itt 

44014 

06S8138 

14.5608 

5.9687 

807 

71889 

19084168 

16.*401 

6.4398 

»a 

46809 

9668597 

14.5945 

5.9?81 

868 

71884 

19848838 

16.8707 

6.4478 

814 

45700 

9800844 

14.0887 

5.9814 

800 

?2861 

19466100 

16.4018 

6.4568 

SIS 

40989 

9988870 

14.6089 

59907 

«70 

78900 

10688000 

16  4817 

6.4688 

SIO     40666 

loonooo 

14.6960 

6.0000 

871 

73441 

100086U 

16.4681 

6.4718 

tn     470B0 

10«18818 

14.7809 

6  009-^ 

878 

73984 

80188648 

16.4984 

6.4798 

«1H 

47924 

1086098;] 

14.7648 

6.0185 

873 

74589 

20^6417 

16,5287 

6.4878 

S19 

47061 

10B00450 

14.7986 

6027T 

874 

76076 

80570834 

16.5589 

6.4961 

2» 

48400 

10648000 

14.8884 

6.0866 

875 

75685 

80706876 

16.6881 

6.6080 

sa 

48841 

10793801 

I4.866t 

6.0459 

876 

76176 

81084576 

16.6182 

6.5108 

ae '  4ne4 

10941048 

14.8997 

60560 

877 

70'i'89 

81858088 

16.6438 

6.5187 

ea 

497SI9 

11089567 

14.03:i8 

6.0641 

878 

77884 

21484052 

16.6733 

6.5866 

SM 

60176 

118891i4 

14.9666 

6.0788 

879 

77841 

81717680 

16.7088 

6.6348 

tta 

50085 

11890885 

15.0000 

6.0888 

880 

78400 

81068000 

16.7882 

6.5481 

Stf 

51076 

11548176 

15.0888 

6.0918 

881 

78961 

82188041 

16.7681 

6.r>499 

an 

515S9 

11697088 

15.0666 

6.100;> 

.J88 

79584 

224«5768 

16.7989 

6.5677 

«e 

51084 

11868868 

15.0997 

6.1091 

888 

80039 

28066187 

16.8886 

6.6664 

XO     SM41 

18008989 

15.1887 

6.1180 

884 

80666 

28006304 

16.8683 

6.5781 

tso 

SSOOO 

18167000 

15.1696 

6.186P 

886 

81886 

88140186 

16.8819 

6.6808 

»1 

53861 

I88»Sd91 

15.1987 

6.1856 

286 

81796 

8:^08656 

16.9115 

6.5886 

i8i 

53884 

19487168 

15.8815 

6.1446 

887 

S8869 

23680008 

16.9411 

6.5968 

8» 

51889 

18649887 

15.8648 

6.15^ 

888 

88944 

23887878 

16.9706 

6.60B9 

ai 

54796 

1«1^9904 

15.8971 

6Am 

880 

88581 

84137560 

17.0000 

6.6116 

S95 

56889 

18977875 

15.8897 

6.1710 

890 

84100 

84880000 

17.0894 

6.6191 

8» 

50606 

1S144866 

15.8688 

6.179? 

8tfl 

84681 

24642171 

17.0587 

6.6967 

»7 

56169 

18818058 

15  3948 

6.1885 

898 

85864 

24807088 

17.0880 

6.6848 

»8 

56644 

14461878 

15.4178 

6.197a 

808 

85849 

2516:3757 

17.1179 

6.6419 

SW 

571«1 

18651919 

15.4596 

6.8058 

894 

86436 

25418184 

17.1464 

6.6494 

MO 

67600 

18884000 

15.4919 

6.8145 

895 

87025 

2667^875 

17.1766 

6.6600 

«1 

56081 

18097681 

15.6848 

6.8831 

81i6 

87016 

25934336 

17.2047 

6.6644 

S41 

58564 

14178488 

15.6668 

6.8817 

897 

88209 

26198073 

17.8:337 

6.6710 

M3 

50040 

14848907 

15.5885 

6.»4OT 

298 

88804 

264G3592 

17.2687 

6.6794 

m 

58086 

14586784 

15.6803 

6.8488 

899 

89101 

26730899 

17.8916 

6.6869 

i» 

60085 

14706185 

15.6685 

6.8573 

800 

90000 

-27000000 

17.8806 

6.6948 

M 

00016 

14886086 

15.6814 

6.8658 

;301 

90601 

27270901 

17.3494 

6.7018 

247 

61009 

15009488 

15.7168 

6.8743 

;«B 

91804 

2764360S 

17.3781 

6.709B 

:;44 

C1604 

16858998 

15.7480 

6.8888 

:i03 

91800 

27818127 

17.4069 

6.7166 

»19 

eeooi 

15488M9 

15.7797 

6.8912 

304 

08416 

28094464 

17  4866 

6.7840 

SO 

02500 

15696000 

15.8114 

6.8996 

305 

98085 

28372685 

17.4648 

6.7318 

»1  :  64001 

15818«1 

16.8480 

6.8060 

306 

93636 

28658616 

17.4929 

6.7387 

« 

6S604 

16008008 

15.8745 

6  81(^4 

307 

04849 

28934443 

17.5214 

6.7460 

ss 

04009 

16194  <77 

16.9060 

6.a»47 

306 

94864 

29218112 

17.6499 

0.7538 

»i 

54516 

16887064 

15.9074 

6.8880 

309 

95481 

29503629 

17.5784 

6.7606 

» 

68005 

16681875 

15.9687 

6.8413 

310 

96100 

29791000 

17.6068 

6.7670 

a6 

66080 

16777816 

16.0000 

6.3496 

311 

96781 

800602:)1 

17.6:352 

6  7768 

»7 

66049 

16974508 

16.0812 

6.3579 

313 

97314 

30371328 

17.6635 

6.7884 

2» 

66664 

17178613 

16.06-24 

6.8661 

313 

97960 

30664^97 

17.6918 

6.7897 

2S0  1  67061 

17878979 

16.0985 

6.3743 

314 

98596 

30959144 

17.7800 

6.7969 

SGO 

67000 

17576000 

16.1845 

6  8385 

315 

99225 

81255875 

17.7482 

6.8041 

»1 

OKlil 

17779581 

16.1555 

6.3007 

316 

i«)S5C 

31554496 

17.7764 

6.8118 

»» 

68644 

17964788 

16.1864 

6.89«8 

■in    100489 

8185.5013 

17.8045 

6.8186 

»3 

eoi60 

18191447 

16.8178 

6.4070 

318  1101134 

32157432 

17.83-,»G 

6.8256 

asi 

60606 

18889744 

16.9461 

6.4151 

319  1101761 

32461759 

17.8606 

6.8:388 

90 


VATREUATICAL  TABLES. 


No. 

Square. 

Cube. 

8q. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Root. 

Cube 
Root. 

8?0 

102400 

82768000 

17.8886 

6.8800 

•375 

140625 

58784875 

19.8610 

7.2118 

321 

108041 

88076161 

17.9165 

6.8470 

876 

141376 

53167876 

19.8007 

7.2177 

92i 

103C84 

33386248 

17.9444 

6.8641 

877 

142129 

58582688 

19.4166 

7.2240 

S^ 

104329 

38696267 

17.9722 

6.8612 

378 

142884 

54010158 

19.4422 

7.2804 

8^ 

104976 

34012224 

18.0000 

6.8683 

879 

148641 

64489980 

19.4670 

7.2868 

8:25 

105625 

84888125 

18.0278 

6.8768 

880 

144400 

54872000 

10.4986 

7.8482 

8S6 

106276 

84645076 

18.0556 

6.8824 

381 

146161 

65806341 

10.5102 

7.2405 

937 

106929 

84965788 

18.0631 

6.8804 

882 

146924 

55748008 

10.5448 

7.2558 

328 

107584 

85287552 

18.1108 

6.8064 

888 

146680 

66181887 

10.5704 

7.2622 

829 

108241 

85611289 

18.1884 

6.0084 

384 

147456 

50683104 

10.5050 

7.8685 

830 

108900 

35987000 

18.1659 

6.0104 

886 

148225 

67066025 

10.6814 

7.2748 

881 

109561 

86264691 

18.1034 

6.0174 

886 

148006 

57512456 

10.6460 

7.2811 

832 

110224 

86594368 

18.2209 

6.0244 

387 

140760 

57060608 

10.6«8 

7.2874 

883 

110689 

80926087 

18.2488 

6.0318 

388 

160644 

68411078 

10.6977 

7.2936 

884 

111556 

37259:04 

18.2757 

6.0382 

889 

151821 

58868860 

19.7281 

7.2009 

885 

112225 

87595875 

18.3080 

6.0451 

890 

162100 

50810000 

19.7484 

7  8061 

830 

112806 

37983056 

18.3303 

6.9521 

891 

162881 

60776471 

10.7787 

7.8184 

887 

118569 
114214 

38272753 

18.8576 

6.9589 

892 

158604 

60836288 

10.7990 

7. .31 88 

888 

38614472 

18.8848 

6.9658 

898 

154440 

60608467 

19.8848 

7.8248 

880 

114921 

88958219 

18.4120 

6.97JJ7 

894 

155286 

61168064 

19.8404 

7.3310 

840 

115600 

89304000 

18.4891 

6.9795 

305 

156025 

61620875 

19.8746 

7.8872 

841 

116281 

89661821 

18.4602 

6.9864 

306 

156816 

68009136 

19.8907 

7.8434 

842 

116964 

40001688 

18.4932 

6  9982 

307 

1.57600 

62670778 

10.0240 

7..3496 

843 

117649 

40358607 

18.5203 

7.0000 

396 

158404 

68044792 

10.9400 

7.8568 

344 

118836 

40707684 

18.5472 

7.0068 

809 

150001 

68581100 

10.9760 

7.8619 

845 

11902S 

41063625 

18.5742 

7.0186 

400 

160000 

64000000 

20.0000 

7.8681 

846 

119716 

41421786 

18.6011 

7.0208 

401 

160801 

64481201 

20  02S(^ 

7.8742 

847 

120409 

41781923 

18.6279 

7.oen 

402 

161604 

64064806 

20.0499 

7. .3803 

848 

121104 

42144192 

18.6548 

7.0338 

408 

162400 

65450S27 

20  0749 

7.8864 

849 

121801 

42506549 

18.6815 

7.0406 

404 

168216 

65989264 

20.0908 

7.8925 

860 

122500 

42875000 

187083 

7.0478 

406 

164085 

66430125 

20.1846 

7.8086 

851 

123201 

43248561 

18.7850 

7.0540 

406 

164886 

6692.3416 

80.1404 

7.4047 

852 

123904 

43614208 

18.7617 

7.0607 

407 

166640 

67419148 

20.1748 

7.4108 

853 

124609 

43986977 

18.7883 

7.0674 

408 

166464 

67917812 

20.1990 

7.4169 

854 

125316 

44361864 

18.8149 

7.0740 

409 

167881 

68417929 

2Q.8287 

7.4229 

855 

126025 

44788876 

18.8414 

7.0607 

410 

108100 

66921000 

20.8486 

7.4290 

8-)6 

126786 

45118016 

18.8680 

7.0873 

411 

168021 

69426681 

80.8731 

7.4850 

857 

127449 

45499293 

18.8944 

7.0940 

412 

160744 

69934528 

80.2976 

7.4410 

858 

128164 

45H82712 

18  9209 

7.1006 

413 

170560 

70444997 

80.8284 

7.4470 

859 

128881 

46268279 

18.9473 

7.1072 

414 

171896 

70967944 

80.8470 

7.468t) 

360 

129600 

46666000 

18.9737 

7.11.38 

416 

172225 

80.8715 

7.4690 

861 

130321 

47045881 

19.0000 

7.1204 

416 

178056 

71991296 

20.8961 

7.4650 

362 

181044 

47437«28 

19.0263 

7.1269 

417 

173889 

72511713 

80.4206 

7.4710 

863 

131769 

47832147 

10.0626 

7.1385 

418 

17472* 

73084688 

80.4450 

7.4rro 

864 

13-^496 

48228544 

19.0788 

7.1400 

419 

175661 

78560059 

20.4605 

7.4829 

365 

183225 

48627125 

19.1060 

7.1460 

420 

176400 

74068000 

80.4080 

7.4889 

866 

133956 

49027896 

19.1311 

7.1,581 

421 

177241 

74618461 

20.6188 

7.4948 

867 

134689 

49430863 

19.1572 

7.1596 

422 

178084 

75151448 

80.5426 

7.5007 

868 

1354-.'4 

49836032 

19.1833 

7.1661 

423 

178929 

7.5686967 

20.6670 

7.5067 

869 

130161 

50243409 

19.2094 

7.1726 

424 

179776 

76225024 

80.6018 

7.5126 

870 

130900 

60658000 

19.2354 

7.1T91 

425 

180625 

7676.5625 

20.61.55 

7.5185 

871 

187041 

51064811 

19.2614 

7.  law 

426 

181476 

77308776 

20.6896 

7.5244 

872 

138384 

5I4r884sS 

19.2873 

7.1920 

427 

182329 

778,5448:1 

20.6640 

7.5302 

:-73 

189129 

51895117 

19.3132 

7.1984 

428 

188184 

78402752 

20  6888 

7.5.^1 

874 

139876 

62313624 

19.3391 

7.2018 

429 

184041 

78953589 

80.7188 

7.6420 

SQUASES,  0UBS8^  SQUABS  AJXD  CUBE  SOOTS.       91 


No. 


Square. 


18KV1 
180ftM 
187480 
188896 


«4 


441 
4«i 
4a 
441 

415 

446 
447 
448 


490 

4SI      aOMOl 

4M  !  804804 

493 

494     806110 


101844 
1W781 

196000 
194481 
190804 
196849 
197180 


198910 
199809 

ooonM 

801001 


430 
496 

497 

<99 


461 
403 


407 
408 


470 
471 
473 
478 
474 

475 
470 
477 
478 
479 


481 
482 


404 


807020 
807988 
806840 
8D0;04 

210061 

911000 
81481 
813444 

814860 
SlSfiVO 

810889 
817180 


219084 

819901 


821841 

2887B4 


tMOTO 


226976 


828484 
289441 


280400 
831861 


284896 


Cube. 


TKOrooo 

ooooeooi 

80021968 
81182787 
61746004 


6S40845S 

81087673 
84001510 

86184000 
85766181 


86988807 
87888881 

88181185 
S8716986 
89814688 
80015898 
90918U9 

91199000 

91788891 
9:2845108 
9-2998677 
88570064 

94196875 
94818B16 


06071918 
90709979 


onaoooo 

97938181 
98011128 


99887811 

100544ee5 
101194090 
101647068 
108508888 
108101709 

108898000 
104487111 
109154048 
109ae8817 
10049M24 

107171875 
107800170 
1065SM88 
109816808 
108908289 

110608000 
111984641 
111980108 


118879904 


Sq. 
Boot. 


90.7804 
20.7805 
:M.7840 
80.8087 
«).8887 

80.8007 
80.8806 
90.9015 
80.9tt4 
80.9088 

90.0768 
81.0000 
81.0888 
81.0476 
81.0718 

81.0960 
81.1187 
81.1484 
21.1660 
81.1696 

91 .8182 

81.8868 

81.8606 

81.81 

81.8073 

81.8807 
81.3948 
81.8776 
81. « 
81.4818 

31.4476 
81.4709 
81.4948 
81.5174 
81.5407 

81.5089 

81.9870 

81.6108 

81.6 

81.0604 

81.6795 
81.7025 
81.7856 
81.7486 
31.7715 

21.7945 
81.8174 
21.8406 
21.8688 
21.8661 

81.9080 
21.9617 
21.0645 
81.9778 
«2.0000 


Cube 
Boot. 


7.5478 
7.5587 
7.9595 
7.5664 
7.5718 

7.5770 
7.58S» 
7.9886 
7.5044 
7.0001 

7.6090 
7.6117 
7.6174 
7.6832 
7.0889 

7.6846 
7.6408 
7.6460 
7.6917 
7.6974 

7.0681 
7.0688 
7.6744 
7.0800 
7.0837 

7.6914 
7.0970 
7.7026 
7.7082 
7.7188 

7.7194 
7.7850 
7.7806 
7.7863 

7.7418 

7.7478 
7.7530 
7.7984 
7.7689 
7.7695 

7.7780 
7.7806 
8.7800 
7.7915 
7.7970 

7.8089 
7.8079 
7.8184 
7.8188 
7.8846 

7.8897 
7.8852 
7.8406 
7.8460 
7.8914 


No. 


485 
460 
487 
488 
480 

490 
491 
408 
498 
494 

499 
496 
497 
498 
499 

600 
901 
608 
508 
504 

905 
506 
507 
908 
509 

910 
911 
913 
518 
614 

915 

616 
517 
518 
519 

530 
681 
528 
988 
584 

596 
586 
587 
688 
939 

980 
981 
982 
988 
984 

986 
986 
587 
588 
589 


Square. 


886196 
337160 
838144 
889131 


Cube. 


114064139 
114791396 
119601308 
116214273 
116880160 


940100  117649000 
341081  118370771 
342064  '119009488 
843049  !n9628l67 
944066  180598784 


349005 
346016 
947000 


121287875 
132038936 
133708473 


M8004  :  123909993 
949001  134391499 


390000 

351001 
392004 
858009 


135000000 

139791901 
126506006 
187268527 


394016  138034064 


399085 
256086 
267040 

858064 

£>ya8i 

360100 
261131 
262144 
363169 
2(M196 


366896 
867289 
368324 
369361 

270400 
371441 
372484 
373939 
374976 

275685 
276676 
377739 
278784 
279841 

280900 
281961 


384069 
389196 


387396 


289444 
300521 


138787889 
129»43IC 
130823813 
131096512 
131»72:tt9 

133661000 
133432831 
184217728 
1:^5005697 
135796744 

!  186600875 
,187388096 
138188418 
1188991882 
I 189798859 

' 140608000 
141420761 
142286648 
143055667 
|1438778-,^ 

^44708138 
146531576 
146363183 
147197952 
148085868 

'148877000 
149731291 
150568768 
151419487 
152278304 


1153130875 
153990656 
154854153 
.155720873  28.1948 
'15C590619  .23.3164 


Sq. 
Root. 


22.0837 
32.0454 
22.0681 
32.0907 
22.1183 

33.1869 
22.1586 
22.1811 
83.3086 
32.3261 

33.3480 
22.2711 
22.2985 
22.3159 
22  8868 

33.8607 
32.1»30 
22.4054 
32.4277 
22.4499 

32.4732 
22.4944 
22.5167 
32.5889 
3-^.9610 

32.5832 
22.6053 
23.6274 
2  i.  6195 
32.6716 


32.7156 
2i.7876 
22.7590 
22.7816 

32  8035 
22.8254 

22.8473 
22.8692 
23.8910 

23.9129 
23  931' 
22.9665 
22.9783 
33.0000 

28.0317 
23.0434 
23.0651 
28.0868 
23.1064 


38.180 

28.1517 

23.1733 


Cube 
Root 


7.8568 
7.8683 
7.8676 
7  8780 
7.8re4 

7.8887 
7.8891 
7.6944 
7.8996 
7.9051 

7.9105 
7.9158 
7.9211 
7.9264 
7.9317 

7.9870 
7.9438 

7.9476 
7.9528 
7.9581 

7.9684 
7.9686 
7.9789 
7.9791 
7.9848 

7.9896 
7.9948 
8.0000 
8.0053 
8.0104 

8.0166 
8.0208 
8.0260 
8.0311 
8.U3G3 

8.0415 
8.0166 
8.0517 
8.0:>69 
8.0620 

8.0671 
8.0728 
H.0774 
8.0835 
8.0676 

8.0987 
8.0978 
8.1028 
8.1079 
8.1130 

8.1180 
8.1231 
8.1281 
8.1&32 
8.1382 


92 


MATHEMATICAL  TABLC8. 


Square. 


291600 


896764 
994849 
995986 

897025 
298116 


800804 
801401 

803500 
808601 
804704 
805809 
806916 

806085 
809186 
810249 
811864 
312481 

818600 
314721 
815844 
810909 
818096 

819225 
320856 
321489 


383761 

324900 
820041 
327184 
328329 
829476 


331776 
332929 
334084 
335241 

886400 
837561 
338724 


311056 

342225 
843396 
344569 
345744 
346921 

348100 
349281 
350464 
&51649 


Cube. 


157464000 
158840421 
159220088 
160103007 
160969184 

161878625 
162771886 
168667823 
1&;666592 
165469149 

166876000 
167284151 
168196606 
169112877 
170031464 

170958875 
171879616 
172806698 
173741112 
174676879 

175616000 
176558481 
177504328 
178453547 
179406144 

180862125 
181321496 
1S2284268 
183250432 
184220000 

185193000 
186169411 
187149248 
188182517 
189119224 

190109875 
191102976 
192100033 
193100552 
194104539 

195112000 
196122941 
197137368 
1981 55-^7 
199176704 


Sq. 
Boot. 


28.2879 
28.2594 
23.2809 
23.3024 
23.3238 

23.3452 
28.3666 
28.3880 
28.4094 
28.4307 

23.4521 
23.4734 
28.4947 
23.5160 
23.5372 

28.5584 
23.5797 
2:^.6008 
23.6220 
28.6432 

23.6648 
23.6854 
28.7066 
23.7276 
28.7487 

23.7697 
28.7908 
23.8118 
23.8328 
23.8537 

28.8747 
23.8956 
2:3.9165 
28.9374 
23.9583 

23.9792 
24.0000 
24.0208 
24.0416 
24.0(fiM 

24.0882 
24.1039 
24.1247 
24.1454 
24.1661 


Cube 
Boot. 


200201625  24.1868 

201280056  24.2074 

202262008  24.2281 

203297472  24.2487 

204386469  24.2693 


205379000 
206425071 

207474688 
208527«S7 
209.'>S4584 


24.2899 
24  3105 
24.3311 

24.3516 
24.3721 


8.1488 
8.1488 
8.1533 
8.1583 
8.1083 

8.1688 
8.1738 
8.1788 
8.1838 
8.1882 

8.1982 
8.1962 
8.2081 
8.2081 
8.2180 

8.2180 
8.2229 
8.2278 
8.2327 
8.2877 

8.2426 
8.2475 
8.2524 
8.2.'i73 
8.2621 

8.2670 
8.2719 
8.2768 
8.2816 
8.2865 

8.2918 
8.2962 
8.3010 
8.3059 
8.3107 

8.8155 
8.3203 
8.8251 
8.3300 
8.8348 

8.8396 
8.3443 
8.3491 
8.3539 
8.3587 

8.3634 
8.3682 
8.3730 
8.3777 
8.3825 

8.3872 
8.3919 
8.3<i67 
8.4014 
8.4061 


No. 


Square. 


680 


854085 
855816 
866409 
857604 


860000 
861801 
862404 


864816 

866025 
867286 
868449 
869664 
370881 

878100 
878881 
874544 
875769 
376996 


879456 


381924 
883161 


384400 
385641 


388129 


390625 
391876 
393129 
394384 
805641 


398161 


400689 
401956 


404496 
405769 
407044 
408821 

409600 
410881 
412164 
413449 
414736 

416025 
417816 
418609 
419904 
421201 


810644875 
211706786 
212776178 
818847192 
214981799 

816000000 
817081801 
818167808 
219856287 
880348864 

881445185 
228545016 
228648548 
284755718 
225866589 


228009181 
229220088 
280346397 
231475544 


238744896 
234885118 
286029088 
237176659 


Cube. 


239483061 
240641848 
241804867 
242970624 

244140685 
24.5314376 
246491883 
5M7678152 
248858189 

350047000 
251239591 
252435968 
253636137 
2&48401O4 

256047875 
257259456 

258474863 
25969407S 
260917119 

262144000 
263374721 
264609288 
265847707 
267069984 

268886185 
269586130 
270840028 
272097792 
27.^3.^449 


Boot. 


84.3886 
84.4181 
94.4886 
84.4540 
84.4745 

84.4949 
84.5158 
84.5857 
84.5861 
84.5764 

a4.6M7 
84.6171 
84.6874 
84.0677 
81.6779 

94  6888 
91.7184 
94.7866 
84,7688 
84.7790 

84.7908 

84.8198 
94.8895 
84.8596 
84.8797 

94.8096 
84.9199 
84.9899 
84.9600 
94.9800 

85.0000 
25.0200 
26.0400 
85.0599 
25.0799 

85.0998 
85.1197 
25.1896 
25.1605 
25.1794 

85.1999 
85.2190 
25.2889 
85.2587 
25.2784 

25.2969 
35.8160 
85.8877 
25.3674 
26.3772 

25.8969 
25.4165 
35.4868 
35.4568 
25.4755 


SQUARES,  CUBES,  SQUABB  AND  CUBE  BOOTS.         93 


No.  Sqnare. 


C50 


6U 

657 
6&S 
«5» 

660 
661 
662 
66S 
664 


667 

6e» 

609 

670 
671 
67^ 
674 
674 

675 
676 
677 
67d 
679 

680 
6S1 

eisi 

688 

6M 

6m 

6« 
6M7 
0« 


601 

oaee 


606 
697 
606 
690 

TOO 

^9i 
70S 
704 


4.3801 
425101 
4:96400 
4:^716 

4S9QaS 

4ao«» 

431649 
4.t:S64 
43*281 

48S600 

4.M0Oi 
436;B44 
480969 

440606 

44iSS6 
4469G6 

444809 
446i»4 
447561 

448000 

45QM1 
451564 


974699000 
275804451 
-.{77167808 
978445077 
3i797MU64 

981011875 
;t8a»(Nl6 


284890819 
986191179 

S87496000 
^i8880478l 
9901I7S98 
991484ai47 
9SEi754944 

994079686 
295408896 
996740968 
998077689 
299418809 


454276 

456076 
458890 


461011 

469400 
468761 
465194 
466489 

467866 


470396 
471969 

474791 

476100 
477481 
478864 
480949 
481636 


484416 
486809 


487204 

488601 


491401 
492801 
494909 


Cube. 


802111711 
806464448 
801821917 
806182094 

80n»l6876 
808915776 
810988783 
811665799 
418046889 

814488000 

816891941 
817914668 
818611987 
8J0018904 

831419195 


894949708 
8SS660879 
:«706976O 

388609000 

829989871 
881878888 
882812567 
884955884 

885708876 
887158586 
888608878 
840068899 
841689099 

848000000 

844479101 
845048408 
847498997 
848918064 


8q. 
Root. 


25.4961 
25.5147 
85.6848 
25.5580 
95.5784 

95.5980 
95.6125 
95.6820 
25.6615 
25.6710 

95.6905 
25.7099 
95TS94 
25.7488 
25.7689 

25.7876 
25.8070 
25.8968 
25.8467 
25.8650 

25.8844 
25.0087 
25.9980 
25.9492 
25.0615 

95.9808 
96.0000 
26.0192 
26.0884 
26.0576 

96.0768 
26.0060 
26.1151 
96.1848 
26.1584 

96.1795 
26.1916 
98.9107 
26.9986 
26.2488 

26.9679 
96.9860 
26.8060 
26.8249 
26.8489 

96.8089 
26.8816 
26.4006 
28.4197 
26.4886 

96.4576 
96.4764 
26.4968 
20.6141 
26.5880 


Cube 
Root. 


8.6694 
8.6666 
6.6713 
8.6757 
8.6801 

8.6645 
8.6890 
8.6084 
8.6978 
8.7022 

8.7060 
8.7110 
8.7154 
8.7198 
8.7941 

8.7985 
8.7829 
8.7873 
8.7416 
8.7460 

8.7608 
8.7547 
8.7590 
8.7681 
8.76; 

8.7721 
8.7764 
8.7807 
8.7850 
8.7898 

8.7987 
8.7980 
8.8023 
8.8066 
8.8109 

8.8152 
8.8194 

8.8287 
8.8280 
8.8823 

8.8! 

8.8408 

8.8451 

8.8493 

8.8586 

8.8678 
8.8021 
8.8663 
8.870C 
8.8748 

8.8790 
8.8883 
8.8875 
8.8917 
8.8959 


No. 


Square. 


Cube. 


497025  850402695 

498486  851895816 

499849  868808918 

501261  354894912 

502681  856100629 


604100 
505521 
506044 


509796 

511225 
512656 
514089 
515591 
516961 

518400 
519841 
521281 
522729 
524176 


527076 
62bo29 
529984 
531441 

589900 
5:34361 
5358-^ 

5:«'289 
538756 

510225 
541696 
.513169 
514611 
546121 

547600 

510801 

552049 
558536 


566095 
556516 
558009 
559501 
561001 


568500 
564001 
566504 
567009 
568516 


857911000 
359125(81 
860944128 
862467007 
868994344 

866686875 
867061696 
868601818 
870146288 
871694950 

878948000 
871805361 
876367048 
877983067 
879503424 

881078195 
882G57176 
38l240.')88 
3a')828359 
387120489 

889017000 
890617891 


89383S837 
395446901 


307065375 


40031.55.53 
401947272 
403568119 

405294000 
406869021 
408518488 
4101?2407 
411830784 


Sq. 
Root. 


26.6518 
26.5707 
26.5895 
26.6088 
26.6271 

26.6458 
26.6646 
26.6683 
26.7091 
26.7208 

96.7896 
26.7689 
26.7769 
26.7965 
26.8142 

26.8888 
26.8514 
26.8701 
28.8887 
26.9079 

26.9858 
26.9444 
26.9629 
26.9815 
27.0000 

27  0185 
27.0870 
27.0656 
27.0740 
27.0924 

27.1109 
27.1998 
27.1477 
27.1662 
27.1846 

97.2029 
27.2213 
27.289' 
27.2580 
27.2764 


Cube 
Root. 


418498625   27.2947  9.0654 

4I5I60936   27.3130  9.0694 

4IC832723  '£7.3313  9.0785 

418508992    e7.8496  9.0775 

420189749   27.8679  9.0816 


421875000 
42a')64751 
425259008 

426957777 
428661064 


570025  430366875 

571536  432081216 

573040  1433798093 

574.564  1435519512 

.576081  1417245479 


27.8861 
27  4044 
27.4226 
27.4408 
27.4591 

27.4778 
27.4955 
27.5136 
27.5318;  9.1178 
27.5500!  9.1218 


94 


UATHEHATIGAL  TABLES. 


No. 

Square. 

760 

577600 

781 

5791-il 

7te{ 

580644 

763 

582169 

764 

58d6»6 

766 

585325 

766 

580756 

767 

588289 

768 

5898..>4 

76U 

591361 

770 

592900 

771 

594141 

772 

595984 

773 

697539 

774 

599076 

775 

600625 

TTC 

602176 

777 

6a3r.J9 

778 

605:.'84 

779  600841 

780  008400 

781  609961 
61]5'J4 
613089 
614656 


783 

784 

786 
786 
78^ 
78S 
789 

790 
791 
792 
7l>8 


616225 
617796 


6J0944 
628521 

624100 
C25681 
G572C4 
G28M9 


794  680436 


795 
796 

797 
798 
799 

800 
801 
8U2 
803 
804 

806 
806 

807 
808 
800 

SIO 
811 
812 
818 
814 


682025 
633616 
635209 

036804 
638401 

610000 
641U01 
G43^>04 
G14N09 
646416 

648025 
649636 
651249 
652864 
654481 

656100 
657721 
659;jM 
660969 
6«.»596 


Cube 
Root. 


9.1258 
9.1298 
9.1888 
9.1378 
9.1418 

9.1458 
9.1498 
9.1587 
9.1677 
9.1617 

9.1657 
9.1696 
9.1786 
9.1775 
9.1815 


465484376  27.8388  9.1865 

4672885T6  27.8668  9.1894 

469097433  27.8747  9.1938 

470910952  27.89271  9.1973 

472729139:27.9106  9.2012 

474552000  27  9285'  9.2052 
47687954 1]27. 9464  V.2091 
47821 1 70H  27.9643  9.2180 
4800l8li8T;27.98-.'l,  9.2170 
48l89O3a4'28.UO00   9.2209 


27  7489 
27.7869 
27.7849 
27.8029 
27.8209 


4a3736625' 
4a'i58T()5« 
487444408: 
489303ST2 
491169009 

4980390001 
494918071 
49679:^088! 
498677257 
5005661841 


28.0179 
28.0357 
28.0583 
28.0713 
28.0891 

28.10C9 
28.1247, 
2<4.1425' 
28.16031 
28.1780; 


9.2248 
9.2287 
9  2326 
9.2365 
9.;M04 

9.2443 
9.2482 
9,2521 
9.2560 
9.2599 


502469875  28.1957!  9.2638 
504a5a336  28.21851  9.2677 
50C86l5r<j:28.2312  9.2716 
508169592  28.2489;  9.2754 
510082399|28.2666  9.2798 

51200000o'28.284S  9.2832 
618922401 128.8010'  9.2870 
615849608  28.81961  9.2909 
517781627128.3373,  9.2918 
5197l8464;28.3&49l  9.2986 


621660125  28 
523606616  28 
525557948  28 
627514112,28 
629475129  28 

531441000  28 
53341173128 
535887328  28. 
537867797  28 
5:)93.53144  ^ 


87251 
890l! 
4077 
4253 
4420 

4605 
,4781 
49.')6 
51*2 
5307 


9.3025 
9.3003 
9.3102 
9.3140 
9.8179 

9.8217 
9.8255 
9.3294 
9.3.S:i2 
{)  aS70 


No.  Square. 


815  664225 

816!  665856 

817'  667489 

8181  669184 

819|  670761 

8S0l  672400 

821 1  674041 

8221  675684 

828  677829 

824  678976 

680025 
826  682276 
827 


829 


831 


837 


685584 
687241 


690561 
692224 


695556 
697S25 


700569 
702244 
708921 

706600 
707281 
708964 
710649 


Cube. 


64184^376 
543388496 
&4688851S 
647843482 
649853S59 

551868000 
658387061 
656412246 
557441767 
559476S24 

661515626 
668659976 
665609283 
667663562 
66972S789 

671787000 
573866191 
575980368 
678009587 
68008S704 

582182875 
684277066 
586876253 
688480472 
590689719 

592704000 
694823321 
6969476S8 
599077107 


12336  601211684 


714025 
715716 
717409 
719104 
720801 

722500 
724201 
72.')904 
727009 
729316 

731025 
782736 
734449 
736164 
787881 

739600 
741321 
743044 
744769 
746496 

748285 
749956 
751689 
753424 
755161 


Sq. 
Boot. 


28.566: 
28.5882 
28.6007 
28.6182 

28.6856 
28.6531 
28.6705 
28.6880 
28.7064 

28.7288 
28.7402 
28.7576 
28.7750 
28.7984 

28.8097  9.8978 

28.8871  9.40l« 

28.8444  9  4058 

28.8617  9.4091 

28.8791  9.41S9 

88.8964 
28.9187 
28.9810 
28.9482 
28.9666 


29.0000 
29.0172 
29.0845 
29.0617 


89.0689 
29.0861 
29.1033 


608851125 
605495r86 
607645428 
609800192  29.1204 
611960049:29.1876 

614125000*89.1548 
616295051 189.1719 
618470208,29.1890 
620650477  29.2062 
628885864|29.228S 

625026375  29.8404 
6272-J20I6.29  2575 
629422:03  29.2746 
631628712  29.8916 
638889779  29.8067 

686056000  29.8858 
63827T881  ]29  8428 
640508928:29.  a598 
6427^5647129.8769 
644972544  89.8989 

647214685  29.4109 
649461896  29.4279 
651714863  89.4449 
653972a32|29.4618 
656234909129.4788 


SQUARES,  CUBES,  BQUAHE  AND  CUBE  ROOTS.        95 


No. 


Square. 


87D 

871 
B» 
873 
674 

875 
876 
877 
878 
St9 

880 
881 
882 
8tt 
864 


887 


97i6000 
758641 
760884 
76ei.» 
763876 

7666» 
767378 
7691M 
770884 
77:»4l 

774400 
776161 
TTTftW 


781456 

TR895 
n)4996 
796760 
788541 
i9a»l 


708100 
^83881 
80S;  795664 
88S.  797440 


800 
891 


801035 
806  802816 
807,  804600 
808'  806404 

806;»1 


900 

901 

mm 


903  815400 


904 

flOO 
90S 
907 
908 

900 

010 

oil 
ot« 

918 
014 

015 
916 
01 

919 

3» 

0:i 

m 

088 
084 


810000 
811801 
818004 


8IK16 

810K5 
820886 
8SW49 
824464 
&MH81 

828100 


831744 


835896 


837'2!» 
839066 


84i73i4 
844561 


Cabe. 


658B0000O 

660770811 
668064848 


667687684 

6600S1875 
67tfci8l876 
674SJM1S8 
67B8S6150 
679161489 


Sq. 
BooC. 


89.4968 
W.6127 
29.6;!96 
29.6466 
29.5685 

99.5804 
20  5978 
VO.6142 
29.6811 
29.6479 


681472000  29.6648 


688797841 


688465887 
690807104 

0961541S5 
605506456 
607864103 
7002SiO7^ 
702805800 


29.6816 
29.6085 
29.7158 
80.7821 

90.7489 

29, 

29.7825 

29.7998 

29.8161 


704969000  20.ai20 
7t)7347971 129.8496 
700732288  29.8664 
712WlQ67'.».R88t 
714510084  29.8098 


716017875 
710828186 
7'il734«73 
724160702 
79657«»0 


29.9166 
29.9338 
89.9500 
29.9606 
89.9888 


73900000080  0000 


781432701 
733870806 
786814827 
788703264 


80.0167 
8U.0388 
80.0600 
80.0066 


741817085  80.0882 
748677416  80.0906 
746148648  80.1164 
748618812  80.1880 
751080429  80.1496 


758571000 
756068031 


761048497 
768551944 

760060875 
768576896 
771096818 
773690882 
7761515S0 


846400  778688000 

848041  781829961 

860084  783777448 

851089  ,  786380167 

K8T7B  ' 


30.1062 
30.1888 
30.1998 
80.2159 
80.8324 

80.8400 
80.8655 
80.2820 
80.8886 
80.8150 

80.3315 
30.3480 
30.8645 
80.8809 
30.8974 


Cube 
Root. 


0.6464 
0.5601 
0.5537 
0.5574 
9.6610 

9.5647 
0.60&8 
9.5719 
9.6756 
9.5792 

0.5828 
9.5365 
9.5901 
0.5937 
0.5078 

0.6010 
9.6046 
9.6082 
9.6118 
0.6154 

9.6190 
9.6226 
9.6262 
9.6896 
9.6334 

9.6406 
9.6442 
9.6477 
9  6513 

9.6549 
9.0686 
9.6620 
9.6056 
9.6692 

0  6727 
9.6763 
9.6790 
9.6334 
9.6870 

9.6905 
9.6941 
9.6976 
9.7012 
9.7047 

9.7082 
9.7118 
9.7153 
9.7188 
9.7824 

9.7S6fl 
9.7294 
9.7329 
9.7864 
9.7400 


No. 


857476 
859329 
861184 
868041 


864000 
866761 


980 
981 
982 

933  870489 

934  8^2366 


0391 


874326 
876096 
877969 
870844 
881781 


040  883600 

041!  885481 

942  887854 

943  889249 

944  891186 

945'  893085 

946|  804916 

947  806809 

948  898704 

949  900001 

050  908500 

951  904401 

962  906804 

953  008209 

954  910116 

955  912025 

956  913986 
957;  915849 

958  917764 

959  919681 


960 
961 
962 
968 
964 

905 
966 
067 
9G8 
969 

970 
971 
972 
973 
974 

975 
976 
97' 
078 
979 


981600 


985444 
927860 


981885 
933156 
935089 
937024 
038961 

940900 
942841 
R44784 
946729 
948676 

950635 
952576 
954r)2H 
956484 
958441 


791463185  30.4138 
794022776:30.4302 
796597983  80.4467 
799178752'80.4631 
801766080:80.4795 

80485700o'80.4959 
806954491180.5123 
800657568  30.5287 
812166237130.5450 
814780504  80.6614 

817400875I30.5778 
8«)02S8S6<30.6941 
828666058'80.6105 
825293672|80.6268 
887906019  30.6431 

880584000I80  6504 
888287621  ;80.675^ 
835806888|30.6920 
888661807  80.7083 
841282884  80.7246 

843908625  30.7409 
84659a'>36  80.7571 
8492781^8  30.7734 
851971S92.30.7896 
854670849  30.8068 


857375000 
860085351 
862801406 
805528177 
868250604 


80.8281 
30.8388 
30.8545 
30.8707 
30.8869 


870988875  30.0031 
873728816  30:9192 
876467493  30.9354 
879217912  80.9516 
88197407%  30.9677 


S84736000 
887503681 
8902771-^8 
89805(3347 
885841344 

898682125 
901428696 
904281063 
907OT9V82 
909853209 

912673000 
915498611 
918880048 
921167317 
924010424 

926859375 
929714176 
932574aS8 
93.'V44ia52 

g3a3].'n'89 


80.9839 
31.0000 
31.0161 
31.0322 
31.0483 

31.0644 
31.0805 
31.0966 
31.1127 

31.1288 

31.1448 
81.1609 
81.1769 
31.1929 
:n.2090 

81.2250 
31 .2410 
31.2570 
31.2730 
31.2890 


96 


HAtHEMATIOAL  TABLES. 


Square. 


960400 
964801 
904894 
966889 


970S95 
9792196 
974169 
976144 
978181 

960100 
982061 
964064 
986049 
988086 

990085 
998016 
994009 
996004 
998001 

1000000 
100900] 
1004004 
1006009 
1006016 

1010085 
1018036 
1014040 
10HH)64 
1018081 

10-20100 
1088181 
1084144 
1086169 
1038196 

1090885 
1088856 
1034880 
10368:14 
1038861 

1040400 
1048441 
10444S4 
1046589 
1048576 

1050635 
105867C 
1054789 
1056784 
1058841 

1060900 
1068961 
1065084 
1067089 
10691 5C 


Cube. 


941198000 
944070141 
946966168 
94986S1U87 
958768904 

056671685 
958686856 
961504808 
964480878 
967861600 

970890000 
978S4*i871 
976191488 
979146657 
988107784 

966074875 
988047986 
991086078 
994011098 
99700S099 


1000000000 
1008006001 
1006018008 
1009087087  81.6708 
1018048064  81.6660 


8q. 
Root. 


81.8050 
81.8800 
81.8869 
81.8588 
81. 

81.8847 
81.4006 
81.4166 
81.4885 
81.4484 

81.4643 
81.4808 
81.4960 
81.5119 
81.5878 

81.5486 
81.6{»5 
31.5758 
81.5911 
81.6070 


Cube. 
Root. 


9.9880 
9.9868 
9.9896 
9.9480 
9.9464 

9.9497 
9.0681 
9.9565 
9.9596 
9.9688 

9.9666 
9.9699 
9.9788 
9.9766 
9.9600 

9.9888 
9.9866 
9.9900 
9  9988 
9.9967 


81.688610.0000 
81.6386  10.0088 


81.6544 


1016075125 
1018106816 
1081147848 
1084198518 
1087843789 


10.006: 
10.0100 
10.0188 


81.7017  10.0166 
81. '5175  10.0800 
81.7888110  0288 
81. 74901 10. 0866 
81.7648,10.0899 


1080801000  81.7605  10.0888 
10338643;^  31  7968  10.0865 
10S6433788I8I  .81 19, 10.0898 
1039509197  31 .88771 10.0481 
1048590744  81.8484  10.0465 


1046678375 
1048778096 
1051871918 
1054977888 
1058089859 

1061808000 
1064338801 
1067468648 
1070)9916: 
1078741884 

1076890685 
1080045570 
1083806688 
1086373952 
10e9647<J80 

1092787000 
1095918791 
1099104768 
1108:)08037 
1105507804 


81.8601 
81.8748 
81.8904 
81.9061 
81.9818 

81.9874 
81.9531 
31.9687 
31.9844 
38.0000 


10.0498 
10.0581 
10.0568 
10.0696 
10.0689 

10.0668 
10.0605 
10.0788 
10.0761 
10.0704 


32.0156  10.0626 
88.0318  10.0659 
82.0468  10.0898 
32.0684  10.0985 
88.078010.0957 

88.0986  10.0090 
.33.1098  10.1088 
32. 12481 10. 1055 
.32.1403  10.1088 
32.1559110. 1121 


No. 


Square. 


1065 
1080 
1087 
1088 
1039 

1040 
1041 
1048 
1043 
1044 

1045 
1040 
1047 
1048 
1049 

1050 
1051 
1058 
1053 
1054 

1065 
1050 
1067 
1058 
1059 

1060 
1061 
1068 
1063 
1064 

1065 
1066 
106: 
1068 
1060 

1070 
1071 
1078 
1078 
1074 

1075 
1076 
1077 
1078 
1079 

1060 
1081 
1068 
1083 
1084 

1065 
1066 
1087 
1088 
1089 


Cube. 


8q. 
Root. 


1071835  1106717876  82.1714 
1073896  1 11 1934656i82. 1870 
1075809  1115167653188.3085 
1077444i  11 18386878  88.8180 
1079081  U81688819  88.8885 

108160o'l  194804000  88.9400 
1088681 1 1186111981  88.8645 
1065764  1181866088  88.8800 


109784911134086507 
1080936  1187603184 


1098086 
1094116 
1096809 
1098804 
1100401 

1108600 
1104601 
1106704 
1108800 
1110916 

1118085 
1110186 
1117849 
1119364 
1181481 

1188000 
1185781 
1187644 
1189969 
1188096 


88.8955 
82.8110 


1141166125  82.8866 
1144445886  82.8419 
1147730888,88  8574 
11510885981.38.8788 
1154880649  88.8688 

1157689000  88.4037 
1160986651  88.4191 
1164858606.88.4845 
1167576877  82.4500 
1170905464  83.4654 


1174841875 
1177688616 
1180988198 
1184887118 
1187648879 


82.4606 
82.4968 
88.6116 
88.6860 
88.5488 


1191016000  82.8676 
119438998138.5780 
119777C388  33.5868 
1801157047  33.6066 
1804660144  88.6190 


1184885  1807940686 
1136356' 181 1855496 
118648911814767763 
1140684' 1818186438 
1148761  1881611509 

11449001 1325049000 
1147041;  1886480911 
1149184  1831985848 
11618891236876017 
1158476<1888883«I4 


88.6497 
88  6660 
88 
38 

82.n09 

as.'nwi 

38.7414 
83.7567 
38.7719 


1156685!l348896875  38.7878 
1157776  lS4,'i76697«  88.8084 
1150989  12498485.33  38.8177 
1168084  1858726658  88.8389 
1164841 1 !856816089  38.6481 


116640011859718000 
116866111268814441 
1170784' 1866728868 
1178889,1270888787 
1176056  1878760704 

1177885  1277S99195 
1179896  1280684056 
1181569  1884.365503 
11637441 J  88791 8478 
1185981,1891467960 


82.8684 
88.8766 
33.8986 
33.9090 
88.9848 

82.9898 
88.9545 
38.960; 
38.9848 
33.0000 


Cube 
Root. 


10.115& 
10.1186 
10.1818 
10.1851 
10.1868 

10.1816 
10.1848 
10.1881 
10.1418 
10.1446 

10.14TB 
10.1510 
10.1548 
10.1576 
10.1607 

10.1640 
1O.1078 
10.1704 
10.1786 
10.1760 

10.1801 
10.1688 
10.1865 
10.1897 
lO.lflECO 

10  1901 
10.1998 
10.8086 
10  8067 
10.8068 

10  8191 
10.8158 
10  8186 
10.8817 
10.«M9 

10.9881 
10.8813 
10.8845 
10.8876 
10.8406 

10.8440 
10.847^ 
10.8608 
10.8586 
10.8067 

10.8599 
10.8680 
10.8668 
10.8098 
10.8786 

10.9757 
10.9788 
10.8880 
10.9861 
10.9688 


SQUARES,  CUBES,  SQUARE  AKD  CUBE   ROOTS.        97 


No. 


Square. 


1090 
S091 
lOBJ 
109S 
10M 

10B6 
1096 
1097 
1096 
1009 

1100 
1 101 

1103 
1 104 

1105 
1106 
1107 
1108 
1109 

1110 

nil 

1112 
1113 
1114 

1115 
1110 
1117 
1118 
1119 

11» 

mi 
im 

1128 
ItM 

1125 

11« 
1127 
IIJB 
1120 

iiao 

II31 
1182 
11S8 
1184 

im 

1188 
1187 
1138 
1180 

1)40 
1141 
!I43 
1148 
1144 


1188100 
1190881 
119aM8l 
11M649 
11988M 

1199085 
1201216 
1208409 
1206004 
1207801 


1210000  188100000088 


1212901 
1214404 
1218009 
1218810 

12210S> 


1225449 

1227604 
l;89681 

1282100 
12S4821 
1288544 

1288709 
1240096 

1248225 
1245456 
1247089 
1249924 
12»161 


1267876 
1270129 
1272884 
1274641 

1270900 
U79161 
1281424 
1288689 
1285066 


1290496 
1292709 
I29S044 
1207821 

1209600 
1801881 
1804164 
1806449 

18087861 


Cube. 


1206029000 

1296606971 
1808170688 
l.^i06751857 
1809888664 

1812982875 
1816582786 
1820189678 
1828758198 
1827878899 


88.0151 
83.0803 
8S.0454 
83.0606 
0767 

88.0906 
88.1069 
83.1910 
83.1861 
88.1618 


18<f468880l 
1888278906 
1841919797 
1845572664 


1352899016 
185657'J048 
I86025m2 
1868088099 

1807681000 
1871880681 
1875086926 
1878749697 
1882409644 

188619687S 
1889928696 
1808668618 
1897415082 
I40I 166150 


1254400  1404988000 


1296641 

1286884 

1261189  i41flM7867 

1288876 


Sq. 

Root. 


1662 
88.1818 
88.1964 
88.2114 
88. 

88.9415 
88.2566 
88.8716 
83.2666 
88.8017 

83.8167 
83.8817 
83.8467 
88.8617 
88.8766 

88.8916 
88.4066 
83.4n5 
88.4865 
88.4515 


88.4664 

1408694561  88.4618 

1412407646  83.4968 

83.5119 

1420084624  38.5261 

1428826125  88.5410 
1427626876'33.6660 
1481485868  83.5706 
1485249159  83.5667 
1489009689^38.6006 

1442697000  88.0165 


1446781091 
1450571966 
1454419687 
1458274104 

1462185875 

146600846688 

I460W8858 

1478760072 

1477646619 


33.6803 
33.6452 
33.6601 
83.0749 

38.6686 
7046 
33.7174 
88.7342 
83.7491 


146154400088 


1485446^21 
1489355268 
1498271907 


149719098488 


7688 
83.7787 

7986 
83.8068 

8881 


Cube 
Root. 


10.9014 
10.2946 
10.2977 
10.8009 
10.8040 

10.8071 
10.8108 
10.8184 
10.8165 
10.8197 

10.88S8 
10.8269 
10.8290 
10.8822 
10.8853 

10.8864 
10.3415 
10.8447 
10.8478 
10.8509 

10.8540 
10.8571 
10.8602 
10.3688 
10.8664 

10  8606 
10.8726 
10.8767 
10.8788 
10.8619 

10.8660 
10.8681 
10.8912 
10.8948 
10.8978 

10.4004 
10.4086 
10.4066 
10.4007 
10.4127 

10.4158 
10.4189 
10.4219 
10.4260 
10.4261 

10.4811 
10.4842 
10.4378 
10.4404 
10.4434 

10.4464 
10.4405 
10.4525 
10.4656 
10.4566 


No. 


1146 
1146 
1147 
1148 
1149 

1150 
1151 
1152 
1158 
1154 

1166 
1166 
1157 
1158 
1159 

1160 
1161 
1162 
1168 
1164 

1165 
1166 
1167 
1168 
1160 

1170 
1171 
11T2 
1178 
1174 

1175 
1176 
1177 
1178 
1179 

1180 
1181 
1182 
1188 
1184 

1185 
1186 
1167 
1188 
llb9 

1190 
1191 
1192 
1193 
1194 

1195 
1196 
1197 
1198 
1199 


Square. 


1311085 
1818816 
1315009 
1317904 
1320901 

1829500 
1824801 
1327104 
1389409 
1881716 

1884025 
1386886 
1338649 
1840864 
1343281 

1345600 
1347921 
1350244 
1SS2069 
1854896 

1357285 
1859656 
1361889 
1364224 
1366561 

1366900 
1371^1 
1373564 
1375929 
1378276 

1360825 
1382976 
1385829 
1867684 
1890041 

1302400 
1394761 
1397124 
1399489 
1401656 

1404225 
1406586 
1406869 
1411344 
1413721 

1416100 
1418481 
1420664 
1423249 
1425636 


1430416 
1432809 
1435204 
1187601 


Cube. 


1501128825 
1505060136 
1509003523 
1512958708 
1516910949 


33.8878 


83.8674 
83.8821 


1520676000 
158484596133 


9116  10, 


1532606677 
1536800264 

1540796875 
1544804416 
1548816803 
1558836812 
1556862679 

1560696000 
1564936S81 
1568968528 
1578087747 
1577006044 

1681167125 


1689324463 
1593418632 
1597509600 

1601618000 
1605723211 
1609640448 
1618964717 
1618096024 

1622234875 
16S8379776 
168058-^233 
1684601762 


33. 

9264 
33.9411 
33.9559 
33.9706 

33.9W} 
34.0000 
34.0147 
34.0294 
31.0441 

34.0688 
34.0735 
34.0881 
34.1098 
84.1174 

34.1821 

84.1467 

34.1614 

34.1 

34.1906 


1648082000 
1647212741 
1051400566 
1655505487 
1659797504 


1664006625  34 


1672446203 
16766T6672 
1680914269 

1685159000 
1689410871 


1697986057 
1702209884 

170M89875 
1710777536 
1715072873 
1719874892 
1723683590 


Sq. 
Root. 


'60  10 


34.9053 
34.2109 
84.2345 
34.2491 
34.2837 

84.2788 
34.2029 
34.8074 
34.3220 
34.3866 

34.3511 
34.3657 
34.8804 
34.394S 
34.4098 


34.4384 
34.4529 
34.4674 
34.4819 

34.4964 
34.5109 
34.5254 
34.539S 
34.5543 

34.6688 
34.683:2 
34.6977 
34.6121 
34.6266 


Cube 
Root. 


10.4617 
10.4647 
10.4678 
10.4706 
10.4789 


.4769 

10.4799 
10.4880 
10.4860 
10.4890 

10.4921 
10.4961 
10.4961 
1U.501I 
10.504:2 

10.6072 
10.5102 
10.5182 
10.5162 
10.5198 

10.5228 
10.5258 
10.5288 
5818 
10.5848 


10.5878 
10.5408 
10.5438 
10.5468 
10.5498 

10.5528 
10.5558 
10.5688 
10.5618 
10.5642 

10.5678 
10.5708 
10.5782 
10  5768 
10.5791 

10.5821 
10.5651 
10.5681 
10.5010 
10.5910 

10.5970 
10.6000 
10.6(»9 
10.6050 
10.6068 

10.6118 
10.6148 
10  6177 
10.6207 
10.6236 


HATHBMAtlCAL  lAfl££8. 


Square. 


1900  1440000 

l:i01  144:M01 

3S0-J  1444804 

1908'  1447209 

1904  1449616 

1452035 
1454436 
1466849 
1469«64 
1461681 

1464100 
14665»!1 
1468944 
1471S69 
1478796 

1476885 
1478656 
1481089 
1488594 
1465961 

1488400 
1490641 
I498S84 
1495729 
1496176 

1500685 
1506076 
15055'J9 
1507964 
1510441 

151)f900 
1515861 
15178M 


1&22756 

II 

1597696 

153U169 

158^644 

1585191 

1587600 
1540061 
1549564 
1545049 
1547686 

1560095 
1552516 
1665009 

1557504 
1560001 

1569500 
1565001 
1567504 
1570009 
lOT'^lO 


Cube. 


Sq. 
Boot. 


1798000000  84.6410 
1789898601  34.6554 
1786654406  84.6699 
17409994<i7  84.6843 
1745387664  84.6967 

1749690195  34.7181 
1754049816,34.7975 
175641674384.7419 
176:nW9l2ld4.7563 
1767179389  34.7707 


1771561000 
1775056031 
1780860198 
1784770597 
1789188344 

1798618875 
1796045690 
1809485313 
1806982*^39 


84.7851 
31.7994 
34.8138 
34.8981 
34.8425 

34.8569 
34.8712 
34.8865 
34.80D9 


1811886459  34.914 


1815848000 
I8906l6b61 
18:M798048 
l829-.rt-6:H>7 
1H83767424 


1838'2fi5625  35.0000 


34.9285 
34.0428 
84.9571 
:W.J»7I4 
84.9857 


1842771176 
1847284083 
1851804352 
1850381069 

1860667000 
1865409391 
1869959168 
187451683; 
1879060904 

1888659875 


1892819053 
1897418272 
1909014919 

1906694000 

1911940521 
1015864488 
1920495907 
1925184764 

1999781125 
1984484986 
193809(»28 
1943764992 
1948441949 


:^.0148 
:i'j.0286 
35.0428 
35.0571 


Cube 
Root. 


10.6966 
10.6295 
10.6385 
10.6354 
10.6884 

10.6418 
10.6443 
10.6479 
10.6501 
10.6580 

10.6660 
10.6590 
10.6619 
10.6648 
10.6678 

10.6707 
10.6786 
10.6765 
10.0795 
10.6894 

10.68iS8 
10.6882 
10  6911 
10.6940 
10.6970 

10.61 

10.7028 

10.7057 

10.7086 

10.7115 


35.0714  10.7144 
35.0656  10.7173 
35.0909  10.7202 
35.1141  10.7281 
35.1963  10.7960 

85.149610.7980 
35.15681 10.7818 
85.1710  10.7347 
35.1852  10.7876 


85.1994 

85.9186 

35.2278 
35.9490 
35.9562 
35.2704 

85.9846 
35.2087 
35.3129 
35.3270 
36.8412 


10.7406 

10.7434 
10.7463 
10.7491 
10.7520 
10.7549 

10.7578 
10.7*507 
10.7635 
10.7664 
10  7693 


1958125000  35.8553  10.77^ 
1967816251  85.8695|10.r7.'j0 
1962515008i;«.3K36|  10.7779 
1967221277,:»  3077.10  7808 
1971935004!3.5  41imi0  7sa7 


No, 


1955 
1956 
1257 
1958 
1959 

1260 
1261 
1962 
1968 
1964 

1966 
1966 
1967 
1268 
1969 

1970 
1971 
1272 
1273 
1974 

1975 
1276 
1977 
1978 
1979 

1980 
1981 
1262 
1268 
1284 

1986 
1286 
1287 
1988 
1269 

1990 
1291 
1299 
1203 
1994 

1295 
1296 
1207 
lJi9H 
121^9 

1800 

1801 
1302 
1303 
1304 

1805 
i:)06 
1307 
1808 
1309 


Square. 


1575095 
1577586 
1580049 
15825M 
1565061 

1587000 
\1590121 
1592644 
1595169 
159769G 

1600995 
1602756 
1605269 
16078;M 
1610361 

1619900 
1615441 
1617964 
1690520 
1693076 

1695695 
162817C 
1630799 
1038284 
1635841 

1688400 
1640961 
1643524 
1646069 


1 
1976666375  85. 
1961885216  85. 
1966121593  36. 
1990865.519  85. 
1996616979  85. 

9000876030  86. 
9005142581  35. 
2009916798  35. 
2014698447  35. 
9019487744,85. 


9094964695  85.6668 
9099069096  86.5809 


1661925 
1653796 
1656369 
1658944 
1661521 

1664100 
1666681 
1669264 
1671849 
167418G 


Cube. 


Sq. 
Root. 


.4960 
.4401 
4549 
.4688 
4894 

4965 
6106 
6946 
5887 
5S96 


2088901163 
9036790839 
9043548109 

2048888000 

9058925511 
2056075648 
206293341 
9067706894 

2079671875 
2077652576 
2089440933 
2087886952 
2099940689 

9007159000 
9102071041 
2106997768 
2111982187 


1648656  9116874304 


9191894196 

9126781666 
2131746903 
2136719879 
2141700560 

2146689000 
2151685171 
2156689068 
2161700757 
216G?i0164 


167702.*)  91717473:5 

16796lC.,2l7678-.i836 
168;i209|  21  HI  820073 
1684804  218687.5502 
1667401  2191933890 


1690000  2197000000 
1692001  2202073901 
1695204  2207155608 
1697800 1 22 12945127 
1700416.2217342464 

170802512229447695 
1705636  9297660616 
1708249  22.32681443 
1710864  2287810112 
171348119242946629 


85.5049 
&5.6000 
36.6930 

35.6871 
85  6511 
35.6651 
35.6:91 
35.6081 

86.7071 
85.7911 
35,7351 
35.7491 
86.7631 

88.7771 
35.7911 
35.8050 
35.8190 
35.8899 

35.8460 
35.8606 
35.8748 
36.8887 
36.9096 

35 .0166 
35.9.^') 
35.9444 
35.9583 
35.9722 

35.9861 
36  0000 
36.0139 
36.0278 
36.0416 

86.0655 
36.0604 
36.0689 
36.0971 
36.1109 

36.1948 
36.1866 
36.1596 
36.1663 
36.1801 


Cube 
Root. 


10.7865 
10.7694 
lO.TOiS 
10.7951 
10.7880 

10.8006 
10.8087 
10.8065 
10.8094 
10.8129 

10.81.M 
10.8179 
10  K906 
10  8236 
10.8265 

10.8998 
]0.Ki92 
10.K»50 
10  8.^78 
10.6407 

10.8485 
10.6463 
10.6409 
10.8&40 
10.6548 

10.8577 
10.8806 
10.6688 
10.8661 
10.6690 

10.8718 
10.8746 
10.8774 
10.8809 
10.8631 

10.8859 
10.8887 
10.61115 
10.8043 
10.6971 

10.8990 
10.9097 
10.9065 
10.0083 
10.0111 

10.0189 
10.9167 
10.9195 
10.99S3 
10.9951 

10.9979 
10.9807 
10.988& 
10.986S 
10.9891 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS. 


No. 


1S10 
ISlI 
]3iS 
131$ 
1314 


SqiiAre. 


Cube. 


1716100  m»mof» 

171  tmi  StiSZTH'^l 
17il344  2458408388 
17S890O  2868371297 
17MBM£i8874ni4 


36.1939 
36.«r77 
3tf.£8l6 
36.3858 
36.8491 


1315  17^90385  28nn3067&  36.8689 

13161  17818S6  8879188496  86.2767 

1317  1734489  2»4.%88013  86.8905 

1318i  1787184  888998943836.3048 

1319,  1739761  2891744729  86  3180 

ISaol  1749400  22999660OO  36.8818 

1381  >  1745041  8806199161  86.3456 

1882,  1747684  8310438848  86.3698 

lS8di  1790389  8415666067  86.3^11 

IXUi  1733)9:6  8380940884  86.8888 


13S5   1733685 
1386;  1758876 

i3s; 

IttSl 

1389   1760841 


8831478976 
8336738783 
«)48089568 
8317334889 


1760M9  8336738783 
1768664  «)48089568 


Boot. 


86.4005 

86.4143 
86.4880 
86.4417 
36.4566 


1330i  17698008358637000  36.4698 
1331  mi561hi%7947691  36.4889 
191'  1774884  8368866868  36.4966 
1333  1776889  8868603067  36.5106 
13MJ  1779666  J873987704  86.5840 


:31S| 

1386; 
1337 
1318 
1339 


8379870673 
1784896  2884681056 


1787669 
179W44 
1798881 


2889979758 
3895346478 
8400»1219  86. 


1348 

1^ 
1344 


:M0610400036. 
1798881  2411494881 

8416898088  86 
2428300607 


1340   1796000 
ISII 

1800964 

1808649 


1806830  2427715664 


1345  1800085 

1346  1811716 
1347!  1814409 
1348!  1817104 
l»l»:  1810801 


ISO] 

mi 


1353 
I»4 


188B00 
18i5-J0] 


13S8  1S87904 


1880009 

1838816 


1355,  __ 

166  1838786 

last,     :     ~ 

13S6  1844164 

1S9  1846881  2609911879 


8615486000 
Ml   1862881  2681008881 


86.6377 
86.6513 
36.5650 
36.5787 


2433188085 
2488660786 
2444006028 
2449456198 
2454911549 

2460675000 
2465846561 
2471880806 
8476813077 
24fre809864 


2487813875  36 
2498886016  86 


1841449  9498846886 
2904874712 


1849600 

1862881 

1886044 
I  18B7760  9688189147 
I  1860496^87716544 


6060 
86.6197 

6888 
86.6460 
86.6606 

86.6748 
86.6879 
86.7015 
86.7151 
86.7887 


86.7560 


7881 
7967 


.810811 
11 
8875 
8611 
8646 


86.8788 
86.8917 
86.9053 
36.9188 
86.9884 


Cube 
Boot. 


10.9418 
10.9446 
10.9474 
10.9608 
10.9580 

10.0657 
10.9565 
10.9613 
10.9640 
10.9668 

10.9696 
10.9784 
10.9758 
10.9779 
10.9807 

10.9684 
10.9868 
10.9890 
10.9017 
10.9945 

10.9978 
11.0000 
11.0088 
11.0065 
11.0088 

11.0110 
11.0138 
11.0165 
11  0193 
ll.(»20 

11.0247 
11.0875 
11.0808 
11.0830 
11.0857 

11.0884 
11.0418 
11.0439 
11.0466 
11.0494 


86.748811.0681 
.0648 
.057^ 
.0603 
.0680 


.0657 
.0684 
.0712 
.0789 
0766 


11.0798 
11.0680 
11.0847 
11.0875 
11.0902 


No. 


1365 
1866 
1887 
1868 
1869 

1870 
1871 
1878 
1873 
1374 

1375 
1876 
1377 
1378 
1379 

1380 
1381 
1382 
1388 
1884 

1885 
1886 
1887 
1888 
1889 

1390 
1891 
1398 
1803 
1894 

1895 
i:i96 
1391 
1896 
1899 

1400 
1401 
1408 
1403 
1404 

1405 
1406 
1407 
1408 
1400 

1410 
1411 
1413 
1418 
1414 

1415 
1416 
1417 
1418 
1419 


Square. 


1868885 
1865056 
1868689 
1871484 
1874161 

1876000 
1879641 
1888384 
1885120 
1887876 


8543808125 
8548895896 
8554497868 
8560108088 
8565786409 

8671868000 
8576987811 
8588630848 
8688888117 
8593941684 


1890085  2699600875 


1698876 
1896180 
1896884 
1901641 

1904400 
1907161 
1909984 
191-2689 
1915456 

1918885 
1980996 
1988769 
1986544 
1989881 

1988100 
1984881 
1937664 
1940449 
1948836 

1946085 
1948816 
1951609 
1954404 
1960^1 

1960000 
196-2801 
1066604 
1968409 
1971816 

1974085 
1976886 
1979649 
1988464 
1985881 

1988100 
1900981 
1993744 
1996569 
1999896 

2008285 

20t)r889 
20107^4 
8013561 


8605885876 
8610969688 
8616668158 
8688868989 


2688079000 
8683780341 
8639514968 
8645848887 
8650991104  87 


865674168687 
8668500466 


Cube. 


86.9469 
86.9594 
86.9780 
86.9865 
37.0000 

87.0185 
37.0870 
87.0405 
87.0540 
87.0675 


87.081011.1199 
87  0945  11.1*226 


87.1080 
87.1814 
37.1849 


867404307:1 


2685619000 
8691419471 


2708045457 
8708870964 

8n4704876 
878054n86 
8786397773 
873-2266798 
8788184199 


8744000000 
■2749681801 
8755776808 
2761677827  87.4566 
8767587864  87.4700 


8q. 
Boot. 


Cube 
Boot 


11.0989 
11.0966 
11.0988 
11.1010 
11.1087 

11.1064 
11.1091 
11.1118 
11.1145 
11.1178 


87.1484 
37.1618 
87.1768 
87.1887 
8081 


.8166 
37.8290 
37.8424 
87.2559 
37.8090 


87.8827 
87.2961 
87.8095 
87.3889 
87.8863 

87.8497 

87.3681 
37.8765 
87.; 
37.4088 


87.4166 
87.4899 
87.44-18 


8773505185 
8779481416 
2785866143 
2791309318 
8797860989 

8808881000 
8H09189581 
2815166528 
2821151997 
■2887145944 


28891  .^9■296 
2845178713 
2851206632 
2857843059 


87.4838 
37.4967 
87.5100 
87.5238 
87.5866 


11.1858 
11.1880 
11.1307 

11.1834 

11.1861 
11.1387 
11.1414 
11.1441 

11.1468 
11.1495 
11.1528 
11.1548 
11.1575 

11.1608 
11.1689 
11.1665 
11.1688 
11.1709 

11.1736 
11.1768 
11.1789 
11.1816 
11.1842 

11.1809 
11.1896 
11.1928 
11.1949 
11.1975 

11.8008 
11.8088 
11.8055 
11.8088 
11.8106 


37.5500,11.2185 
37.563311.8161 


•S7.5766 
87.5899 
87.1 

87.6165 
87.6898 
87.6481 
87.6r>63 


11.2188 
11.8214 
11.8240 

11.2887 
11  2293 
11.2820 
11.2846 
11.2373 


100 


ITATHEMATICAL  TABLES, 


No. 


1490 
1491 
14^ 
148S 
1444 

1485 
14M 
1427 
1428 
1429 

14S0 
14.S1 
1482 
1433 
1484 

1485 
148(5 
1487 
1488 
1489 

1440 
1441 
1443 
1443 
1444 

1446 
1446 
J447 
1448 
1449 

14.% 
1451 
145^ 
1453 
1434 

1466 
1456 
145: 
Ur^H 
1459 

1460 
1461 
146-2 
1403 
1464 

1465 
]4«fl 
1467 
1408 
1469 

1470 
1471 
1472 
1473 
1474 


Square 


2016400 
2019-^41 
20-J2084 
9024929 
2087770 

9080025 
9088476 
90868S9 
9089184 
9042041 

9044900 
9047761 

9058480 
9066856 


9069096 
9U64969 
8067844 

9079000 
207W81 
S079W4 
9082240 
9085186 


2090916 
1^098809 
9096704 
9099601 

9102500 
9105401 
9108304 
2111209 
2114116 


Cube. 


8q. 
Boot. 


S9«Ib»8000'87.6899 
2869841461  37.6962 
2875408448  37.7094 
2881478967  87.7227 
2887558024|87.7859 

2808840635'87.7492 
28997867T6;87.7644 
2905841488  87.7767 
39119647B2I87.7889 
2918076689  87.8021 

2994207tX)0  87.8158 
298084509187.8986 
..>986493568  87.8418 
2042649787  87.8660 
2948814504187.8089 

2954987879  87.8814 
2961l6g656'87.8946 
2907860458,87.9078 
2978559672187.9210 
9979767519,87.9342 


Cube 
Root. 


11.9899 
11.9485 

11.2459 
11.9478 
11.9605 

11.8581 
11.8557 
11.9588 
11.9010 
11.2686 

11.9009 
11.9689 
11.9715 
11.9741 
11.9767 

11.9798 
11.2fi«) 
11.9846 
11.9879 
11.9896 


9986984000  87.9478  11 .9994 
2992209121  87.9006  11.9950 
299844J888  87.9787  11 .9977 
8004685307,87.9888  11.3008 
8010986884  88.0000,11.9099 

8017190196  88.018211.8066 
8O234045d6}88.O268  11 .8061 
8029741628  88.0895  11.8107 
80:)6027892  38.0626  11.8188 
8042821849  88.0057111.8159 


8048695000 
3a-}4g:)6851 
306] 257408 
8067686677 
8073924064 


2117086  8060271875 

21 I993G  3086626818 
2122849,3092990998 
212570l';?0ft9863912 
212808113105745579 


88.078911.8186 
88.0920  11.8211 
88.1051  11.8237 
:».  1182' 11. 8268 
88.1814|ll.Se89 

88.1445111. 8816 
88. 1576' 11. 8841 
38.1707111.8867 
38. 1888M  1.8898 
88. 1969111. 8419 


213100013119186000  88.9099  11.8446 
21315. M 13118535181  38.9880  11  8471 
2137444  3124948128  38.9361  11.8496 
2140;i09l8181.359847  88.2492  11  .a')28 
2143296  3187785344  88.2693  11.8548 


9146325 
2149156 
21.'i2089 
2155<)24 
2157961 

9160900 
9163841 
2106784 
2169729 
9172676 


8144219625  88.977>8 
815066:696  3S.2884 
31571H563'38.8014 
810357523813^.8145 
31700447T)9  38.8276 


8176628000 

318801011 
818{)500048 
8190010817 
8202.524124 


88.8400 
3S.8680 
88.3607 
38.3797 
38.3997 


11.&574 
11.3600 
11.8626 
11.8(»2 
11.8677 

11.8708 
11.8729 
11.8756 
11.8780 
11.8806 


No, 


Square. 


1476 
1476 
1477 
1478 
1479 

1480 
1481 
1489 
1488 
1484 

1486 
1480 
1487 
1488 
1489 

1490 
1491 
1499 
1498 
1494 

1496 
1496 
1497 
1498 
1499 

1600 
1601 
1502 
1503 
1604 


9175685 
9178676 
9181599 
9184484 
9187441 

9190400 
9108861 
9190891 
91099B9 


8909046876 
8916578170 
3822118888 
8228687868 


8841799000 
8948807041 
8254959108 
8961646687 
8908147904  88 


9906190 
8911109 
9214144 


8974760195 
8961S70968 


8994040972 


9317191  8801298109 


9890100 


9890004 
2930049 


9988010 
2941009 
9244004 
9947001 

9960000 
6968001 
9950004 
9859009 
9969016 


1607 
1508 
1509 


1510 
1511 
1512 
1513 
1514 

1515 
1510 
1517 
1518 
1619 

1690 
1591 
1522 
1598 
1524 

1595 
1526 
1527 
1528 
1529 


1505  9906025 

1606 

2271049 
2274004 
2277081 


Cube. 


86.4067 
88.4187 
88.4818 
88.4448 
88.4678 


88.4706 

88!4908 
88  5007 


8807940000 
8814018771 
8821987488 
8827970167 
8084001784  88, 


8841809876 
8818071980 
8864790478 
8861517992 
8868954499 

8875000000 
8881764601 
8888518006 
8895290627 
840-.K>79064 


Sq. 
Root. 


88.5857 
88.6467 
86.6010 
88.6740 
88.6870 


88.0006 
88.0185 
88.0904 
88.0804 


88.00ia 

88.0789 
88.0911 
88.7040 
88.7109 

88.7996 
88.7497 
88.7660 
88.7086 
88.7814 


8408808025  88.7948  11  4598 


Cube 


11.8882 
11.8868 
11.8888 
11.8909 
11.8985 

ll.MGO 
11.8966 
11.4012 
11.4087 
11.4063 

1.4089 
11.4114 
11.4140 

n.4i» 

11.4191 

11.4910 
11.4942 
11.4268 
11.4203 
11.4819 

11.4844 
11.4370 
11.4895 
11.4421 
11.4446 

11.447! 
11.4497 
n  .45<f2 
1I.4.'>4R 
11.4673 


3415602816 
8422470843 
3429288512 
3486116999 

8449951000 
8449795831 
3466649728 
3468512697 


9880100 
2288121 
2980144 
9289109 
9292196  8470884744 


8298950 
2301280 
8304324 
8807861 

8810400 
8818441 
2310484 
2819520 


3477206875  88.9980 
3484150096  88.9868 
8491055418  88.9487 
8497968882  88.9615 
3504881859  88.9744 


2«i1729 
2834784 
2887841 


88.8079,11.4624 
88.6901  11. 4n49 
38.83.W1 1.4615 
88.846811.4700 

88.8667  11.4725 
88  8716  1I.4T.M 
88  8844'll.4r70 
88.8973  11. 4Kn 
88.9102  11. 4tfi2a 


3611808000 
8618748701 
3525688048 
3582042667 
8589605824 

8540678196 
8553560670 
8560550188 
3667549969 
3574558869 


88.9678 
89.0000 
89.0198 
89.0260 
89.0884 

80.0618 
80.0040 
89.0768 
89.0600 
89.1094 


11.4a'(2 
11.4877 
11.4909 
11.4997 
11.4958 

11.4078 
11  6O08 
11.5028 
11  (X)54 
11.5079 

11.5101 
11.6129 
11.6154 
11.6179 
11.5W4 


SQUABBS,  CUBES,  SQUARE  AND  CUBE  BOOTS.      101 


Xo 


Square. 


1530 
15M 


2SIO0OO 

SM7(»4 
SKOOtO 


3581577000 
»a8604«)l 
85Q5(H07l{8, 

360S74130A 


1S«I  2tS62&5 

1536   2859296 

1587 

158s   238&U4 

lS39t  8868581 

IMO  8871600 

IMl  ^f7468l 

U42  S3T7761 

1518  3880849 
1544 


1346 

15t7 


$616S0S375  89.1791 
8688878656  88.1918 
8880961158  88.8046 
868^<06d8?e88.S178 
8645153819  88.8801 


869SQ64000  89. 
369088^)481 
8866512086  89 
3678660007 
8680797184 


8408500 
8405601 
8406704 

8411809 
8414916 

8418085 
8421188 
8484^19 
848r364 
8480481 

8483600 


3695119836 
37(l;>894888 
3709476698 
3716678148 

8?18875000 
8731087151 
87.18306606 
8745538877 
3758779464 


\^  888^)85  86^7968685 
"••    *«»I16**-"'**"-^ 

8803809 

8896301 
1549i  8880101 


1330 

1551. 

1553! 

ISolj 

1S55 
1556 
1357 
1558 
156S^{ 

!360l 
1561 
156sS 
15G3 
1564 


84861^1 


8448969 
8446006 


Cube. 


Bq. 
Boot. 


39.1158 
88.1880 
89.1408 
89.1635 
39.1663 


39.8556 


8810 
8938 

8065 
3198 
8319 
8446 
8578 


39.8700 
39.3837 
89.8834 
89.4081 
39.4806 


8760098875  39.4336 
8797887610:394468 
877455569830.4588 
3781833112I89.4715 
8789119879  89.4648 


8796416000 
3803781481 


8489844  3d  1 1086388 


381836054' 
8883604144 


Cube 
Root. 


11.5830 
11.6865 
11.6880 
11.5305 
11.5830 

11.5365 
11.5380 
11.5406 
11.5430 
11.6455 

11.5480 
11.5605 
11.5680 
11.5565 
11.5580 

11.5605 
11.5680 
11.9666 
11.5680 
11.5706 

11.5790 
11.5764 
11.5779 
11.5804 
11.5829 

11.6664 
ll.58t9 
11.5908 
11.5988 
11.5958 


80  496811.5978 
89  eoa-)  11.6003 
39.588111.6037 
89. 634d  11.6053 
89.5474  U. 6077 


No. 


1565 
1566 
1567 
1568 
1569 

1579 
1571 
157% 
1573 
1574 

1575 
1576 
1577 
1578 
1579 

1580 
1581 
1583 
1588 
1584 

1586 
1586 
1587 
1588 
1589 

1590 
1591 
1593 
1593 
1594 

1505 
1596 
1597 
1598 
1599 


Square. 


Cube. 


8449335  3833087135 
8453856;3840889496 
8455469!3847751363 
8468634  386513348*^ 
8461761  j386250«)09 

8464000  3890693000 
8468041387739-^411 
a4711B4,3()84701848 
8474339  3893119517 
8477476,38095478^ 

8480635  3906984875 
8483770  3914430076 
8466939,3981887038 
8490084, 4930a')355<J 
84933413936837539 

9406400  8044313000 
84095613651805941 
2603734  3969309668 
8605889  896683»S87 
8609066  3Or4344704 

051283513981876635 
85158963989418056 
8518569  3996069008 
3681744  4004539473 
3584931  4013099469 


8588100 
8581281 
3584464 
85B7649 


4019679000 
4037368071 
4034866688 
404347485; 


8540836  4050094684 


2544035 
3547316 
3560409 
3553604 


4057719875 
4065356736 
4073003173 
4060659193 


3556801,4088334790 


1600  3360000'4Q96000000  40.0000'll.6961 


Sq. 
Root. 


39.5601 
89.5737 
39.5854 
;i9.508O 
39.6106 

89.6383 
89.6358 
89.6485 
30.6611 
80.6737 

89.6868 
89.6980 
89.7115 
.H9.7340 
89.7366 

30.7403 
89.7618 
89.7744 
369 
89.7995 


89.8181  11.6604 
39.894611.6619 
30.887311.6648 
80.8407ill.8668 
30,863311.6693 

89.874811.6717 
89.8873  11.6741 
39.8999  11.6765 
89.9134  11.6790 
39.984911.6614 

89.9375'll.7839 
89.0900  11.6868 
9635|11.6668 
89.075011.6913 
89. 9875,11. 6936 


Sai^ABBS  ANB  CVBBS  OF  BBCIMAM. 

5Eo. 

Square. 

Cube. 

No. 

Square. 

Cube. 

No. 

Square. 

Cube. 

.1 

.01 

.001 

.01 

.0001 

.000  001 

.001 

.00  00  01 

.000  000  001 

.2 

.04 

.006 

.03 

.0004 

.000  008 

.008 

.00  00  04 

.ooaooo  003 

8 

.09 

.037 

.03 

.0009 

.000  037 

.003 

.00  00  09 

.000  000  037 

4 

.16 

.064 

.04 

.0016 

.000  064 

.004 

.00  00  16 

.000  000  064 

.5 

.25 

.135 

.05 

.0035 

.000  135 

.005 

•00  00  35 

.000  000  125 

.6 

.36 

.816 

.06 

.0036 

.000  216 

.006 

.00  00  36 

.000  000  316 

.7 

.49 

.843 

.07 

.0040 

.000  34:^ 

.007 

.00  00  49 

.000  000  843 

.« 

.64 

.618 

.08 

.0064 

.000  513 

.008 

.00  00  64 

.000  000  51 -i 

.0 

.81 

.730 

.00 

.0061 

.000  739 

.009 

.00  00  81 

.000  000  739 

1.C 

1.00 

1.000 

.10 

.0100 

.001  000 

.010 

.00  01  00 

.000  001  000 

It 

1.44 

1.788 

.13 

.0144 

.001  738 

.013 

.00  01  44 

.000  001  728 

Nolo  that  the  f^qiiare  has  twice  as  many  decimal  places,  and  the  cube  three 
times  as  many  decimal  places,  as  the  root. 


102 


MATHEMATICAL  TABLES. 


FIFTH  ROOTS  ANB  FIFTH  POWERS. 

(Abridged  from  Trautwinb.) 


g^ 

o  ^ 

^o 

o^' 

H 

ll 

Power. 

68 

Power. 

6  0 

Power. 

dS 

Power. 

c  0 

Power. 

»« 

5?« 

&» 

J5« 

.10 

.000010 

3.7 

098.440 

0.8 

90392 

21.8 

4083507 

40 

102400000 

.15 

.000076 

3.8 

792.852 

9.9 

05099 

22.0 

61&3632 

41 

11585«-?01 

.90 

.000820 

8.9 

002.242 

lO.U 

100000 

22.2;     6392188 

42 

130691-^32 

.85 

.000977 

4.0 

1024.00 

10.2 

110408 

22.4|    5639403 

48 

147006443 

.80 

.00;i430 

4.1 

1158.56 

10.4 

121665 

22.6,    6895793 

44 

164916224 

.86 

.005252 

4.2 

i;«6.9i 

10.6 

133828 
140933     ' 

22.8     6161827 

45 

184588125 

.40 

.010240 

4.3 

1470.08 

10.8 

23.  o;    6436343 

46 

805062976 

.45 

.018453 

4.4 

1649.16 

11. 0 

161051 

28.2,    6721093 

47 

289345007 

.CO 

.031250 

4  6 

1845.28 

11.2 

176284 

23.41     7015834 

48 

254803008 

.66 

.0508aJ 

4.6 

2050.63 

n.4 

192541 

28.6,    7820825 

40 

288475240 

.60 

.077760 

4.7 

2293.46 

11.6 

2101184 

23.8     7686832 

60 

318500000 

.06 

.116029 

4.8 

2548.04 

11.8 

228776 

24.0     706J624 

61 

345025851 

.70 

168070 

4.9 

2824.75 

12.0 

248832 

24.2     8299976 

58 

38020ltW3 

.75 

.2:J7805 

60 

8126.00 

12.2 

270271 

24.4     864^666 

53 

418105498 

.80 

.827680 

6.1 

8450.26 

12.4 

293163 

24.61     900H978 

64 

4501C5024 

.86 

.443705 

5.2 

8802  04 

12.6 

817580 

24.8,    9881200 

66 

503284375 

.90 

.600490 

6.3 

4181.95 

12.8 

843597 

85  0     9765626 

66 

550731776 

.06 

.778781 

6.4 

4591.65 

13.0 

871298 

25.2'  10162550 

67 

6016iKa'J7 

1.00 

1.00000 

6.6 

6032.84 

13.2 

400746 

25.4    10572278 

68 

666356708 

1.05 

1.27628 

6.6 

5.5<J7.32 

13.4 

482040 

25.6    10995118 

50 

714924899 

1.10 

1.61061 

5.7 

6016.92 

13  6 

465259 

85.8    11431377 

60 

777eCKW00 

1.16 

2.01135 

6.8 

«6«3.57 

13.8 

600490 

26.0    11881376 

61 

84459G301 

i.ao 

2.48832 

6.9 

7149.24 

14.0 

687824 

26.2    12345487 

62 

9161. '^»38 

1.S5 

3.05176 

6.0 

7776.00 

34.2 

677358 

26.4!  12828^86 

68 

992436543 

1.80 

8.71298 

6.1 

8445.96 

14.4 

619174 

26.6    133170f>5 

64 

1W3741824 

1.85 

4.46408 

6.2 

9161.33 

14  6 

663388 

26.8'  1882f)281 

65 

11602900V5 

1.40 

5.87824 

6.8 

9924.87 

14.8 

710082 

27.0,  14348907 

66 

1252882r76 

1.45 

6.40978 

64 

10737 

15.0 

759375 

27.2    14888280 

67 

1850185107 

l.SO 

7.59875 

6.5 

11603 

16  2 

811368 

27. 4 1  15413762 

68 

14589:«568 

1.56 

8.94661 

6.6 

125J8 

15.4 

866171 

27.6    16015681 

60 

1564U31349 

1.60 

10.4858 

6.7 

18501 

15.6 

923H96 

27.81  16604430 

70 

16W)7a)m>0 

1  66 

12.2898 

6.8 

14539 

15.8 

984658 

28.0    17210308 

71 

1804289351 

1  70 

14.1986 

6.9 

15C40 

16.0 

1048576 

28.2    17t'a3K0« 

72 

1934917032 

1.75 

16.4i:n 

7  0 

1C807 

16.2 

1115771 

28.41  1W;5309 

78 

2073071693 

1.80 

18.8957 

7.1 

18042 

16.4 

1186367 

28.6'  1«1850:6 

74 

22l90U6fr.'4 

1.85 

21.6?00 

7.2 

19849 

16.6 

1260408 

28.8    198I8&57 

75 

23':  8046875 

l.«0 

24.7610 

7.8 

20781 

16  8 

13:«'v>78 

29.0    20511149 

76 

95:^5516376 

1.95 

28.1951 

7.4 

22190 

17.0 

1419857 

29.8   212-J8253 

77 

2706784157 

:i.00 

32.WH)0 

7.5 

28780 

17.2 

1505386 

20. 4i  21965275 

78 

2887174368 

2.(H> 

36.2051 

7.6 

25356 

17.4 

15041)47 

a9.6,  2272x'628 

70 

3077066399 

2.10 

40  8410 

7.V 

27068 

17.6 

1688742 

29  8'  yS.^00728 

80 

3276800000 

2.15 

45.9101 

7.8 

28872 

17.8 

1786H90 

30.0;  24dO0(K)O 

81 

3486781401 

2  v'O 

61.5:^ 

7.9 

aorri 

18.0 

1880568 

30. 5I  20H93634 

82 

3707308482 

2.25 

67.6650 

8.0 

32768 

18.2 

1996908 

81.0,  28629151 

83 

3989040648 

2.30 

64.3634 

8.1 

84868 

18.4 

2109061 

31.61  81013642 

84 

41H21 19424 

2.. 35 

71.6708 

82 

37074 

18.6 

2226203 

32.0,  835M432 

86 

4437053125 

2.40 

79.6-J62 

8.8 

89390 

18.8 

2348498 

82. 5I  3625«()«2 

66 
1  87 

4704270176 

2.45 

88.2785 

8.4 

41821 

19.0 

2476099 

33. 0|  39185303 

4984209207 

2.50 

97.6562 

8.5 

44371 

19.2 

2609193 

33.5'  42191410 

88 

5277819168 

2.55 

107.820 

8.6 

47048 

19.4 

2747M9 

34  0,  45435424 

80 

6684060449 

2.60 

I  118.814 

8.7 

49842 

19.6 

2892547 

81.5    48875980 

00 

5904900000 

2.70 

143.489 

8.8 

527:8 

19.8 

3043168 

35.0   52:j21875 

01 

6840821451 

2.80 

172.104 

8.9 

65841 

20.0 

8200000 

35.5   66382167 

02 

6500616288 

8.(» 

'  206.111 

9.0 

61K)49 

20.2 

3863232 

86.0'  60466176 

08 

6966888603 

3.00 

243  000 

9.1 

62403 

20.4 

3533a59 

86  5;  W:a3487 

94 

73300)0824 

8.10 

286.292 

9.2 

65908 

20.6 

3709677 

37.0   60343957 

96 

TnJ7«00875 

8.20 

335.544 

9.3 

69569 

20.8 

8893289 

37.5,  74157716 

96 

8158786076 

3.80 

391.354 

9.4 

73390 

21.0 

4084101 

38. 0:  79235168 

97 

8587340257 

8.40 

454.854 

9.5 

7r378 

21.2 

4282822 

88.5,  84587005 
89.01  00224199 

98 

9030807068 

3.60 

625.219 

9.6 

81587 

21.4 

4488166 

99 

9509900400 

8.60 

604.662 

9.7 

85878 

21.6 

4701'^50 

39.5,  96158012 

OIBCUKFEBENCES  AND  ABEAS  OF  CIBOLES.       103 


OUr€tinFKKJfiM€l£ll  ANJil  AREAS  OF  CIBOIiBS. 

Ptom. 

ClrcQin. 

Area. 

Dlam. 

Circum. 

Area. 

Diaro. 

Circum. 

Area. 

1 

8.1416 

0.7854 

65 

204.20 

8818.31 

129 

406.87 

13069.61 

t 

e.ssae 

8.1416 

66 

207.84 

3421.19 

ISO 

406.41 

18278.83 

8 

0.4:M8 

7.0666 

67 

210.49 

8525.66 

131 

411.56 

18478.28 

4 

19.5664 

12.5664 

68 

218.68 

8631.68 

182 

414.69 

13684  78 

5 

15.7060 

19.635 

69 

216.77 

8739.28 

133 

417.88 

13802.91 

6 

18.850 

88  274 

70 

219.91 

8848.45 

134 

420.97 

14102.61 

7 

21.901 

88.486 

71 

223.00 

8859.19 

185 

424.12 

14318.88 

8 

«6.138 

60.266 

72 

226.19 

4071.50 

136 

427.26 

14526.72 

9 

88.274 

68.617 

78 

229.34 

4185.89 

187 

480.40 

14741.14 

10 

81.416 

78.510 

74 

232.48 

4300  84 

138 

433.54 

14957.18 

11 

84.556 

95.083 

75 

235.62 

4117.86 

139 

486.68 

15174.66 

S3 

87.699 

118.10 

76 

288.76 

4536.46 

140 

439.82 

15383.80 

28 

40.641 

132.73 

77 

811.90 

4656.68 

141 

442.96 

15614.50 

11 

48.962 

153.94 

78 

245.04 

4778.36 

142 

446.11 

15886.7? 

15 

47.  la* 

176.71 

79 

248.19 

4901.67 

143 

449.25 

16060.CI 

16 

50.265 

201.06 

80 

251.88 

6026.55 

144 

452.89 

16286.02 

17 

53.407 

8^.96 

81 

254.47 

5158.00 

115 

455.58 

16513.00 

18 

56.549 

854.47 

82 

257.61 

5281.02 

146 

458.67 

16741.55 

19 

50.080 

283.53 

88 

860.75 

5410.61 

147 

461.81 

16971.67 

SO 

03.8»S 

814.16 

84 

863.89 

5541.77 

148 

464.96 

17203.86 

21 

65.973 

816.36 

85 

267.04 

5674  50 

149 

468.10 

17486.W 

a 

60.115 

880.13 

86 

270  18 

6808.80 

loO 

471.84 

17671.46 

23 

T5f.857 

415.48 

87 

273.88 

5914.68 

151 

474.88 

17907  86 

24 

75.896 

452.39 

88 

276.46 

&0tSi.l2 

152 

477.62 

18145.84 

25 

78.540 

490.87 

89 

279.60 

6^1.14 

153 

480.66 

18885.89 

» 

81.661 

530.98 

00 

282.74 

6381.78 

154 

483.81 

18626.50 

27 

64.828 

572.56 

91 

285.86 

6.V)8.88 

155 

486.95 

18869.19 

28 

67.965 

615.75 

92 

289.03 

6647.61 

156 

490.09 

19113.45 

» 

01.106 

660.62 

98 

292.17 

6792.91 

157 

498.23 

19359.26 

SO 

04  816 

706.86 

94 

205.31 

6939.78 

158 

496.37 

19606.68 

81 

97.889 

754.77 

95 

296.46 

7088.22 

159 

499.51 

19856.65 

» 

100.58 

804.25 

96 

801.69 

7236.23 

100 

502.66 

20106.19 

S3 

103.67 

855.30 

97 

801.78 

7389.61 

161 

505.80 

20858.81 

81 

106.81 

907.92 

96 

807.88 

7542.96 

162 

608.94 

20611.99 

S 

109.96 

962.11 

99 

311.02 

7697.69 

168 

512.06 

80867.24 

86 

118.10 

1017.88 

100 

814.16 

7853.96 

164 

515.22 

21124.07 

87 

116.84 

1075.21 

101 

817.30 

8011.85 

165 

.M8.86 

21882.46 

as 

119.86 

1184.11 

102 

3^.44 

8171.28 

166 

521.60 

21642.48 

89 

128.58 

1191.59 

103 

323.58 

8382.29 

167 

524.65 

21908  97 

40 

125.60 

1256.64 

104 

326.73 

8494.87 

168 

527.79 

22167  06 

41 

128.81 

1320.25 

105 

829  87 

8659.01 

169 

580.98 

22481.76 

42 

131.95 

1885.44 

106 

333.01 

8824.78 

170 

534.07 

28606.01 

43 

135.00 

1452.20 

107 

336.15 

8992.0S 

171 

537.21 

22965.88 

44 

188.28 

1520.53 

106 

389.29 

9160.88 

172 

510.85 

2:«i85.22 

45 

141.87 

1590.43 

109 

342.48 

9831.32 

173 

543.50 

28506.18 

45 

14451 

1661.90 

110 

345.58 

9503.32 

174 

546.64 

28778.71 

47 

147.65 

1734.94 

111 

348.78 

9676.89 

175 

549  78 

24052.82 

48 

150.80 

1809.56 

112 

351.86 

9852.08 

176 

552.92 

24828.49 

49 

158  94 

1885.74 

118 

355.00 

10028.75 

177 

566.06 

24605.74 

(0 

157.08 

1968.50 

114 

858.14 

10207.08 

178 

559.20 

84884.56 

51 

160.23 

2012.82 

115 

861.28 

10886  89 

179 

562.85 

25164.94 

52 

168.86 

2128.72 

116 

864.42 

10568.32 

160 

665.49 

25446  90 

&3 

166.50 

2806.18 

117 

867.57 

10751.82 

181 

568.68 

25780.43 

54 

109.05 

2290.22 

118 

370.71 

10985.88 

182 

571.77 

26015.58 

96 

1W.79 

2875.88 

119 

873.85 

11122.02 

183 

574.91 

26302.20 

56 

175.93 

2463.01 

180 

876.99 

11809.78 

181 

578.05 

26.')90.44 

57 

179.07 

2551.76 

121 

380.18 

11409.01 

185 

581.19 

26880.85 

58 

182.21 

2612.06 

122 

383.27 

11689.87 

186 

584.34 

27171.63 

59 

185.35 

8788.97 

188 

886.42 

11882.29 

187 

587.48 

27464.50 

60 

188.60 

8827.48 

124 

389  56 

13078.28 

188 

590.62 

2n59.ll 

61 

191.64 

2932.47 

125 

392.70 

12-J71.85 

189 

593.76 

28055.81 

ti 

194.78 

8019.07 

126 

395.81 

12468.98 

100 

596.90 

28:«»2  87 

63 

107.18 

8117.25 

127 

896.96 

iaK57.69 

191 

GOO.Ol 

28652.11 

64 

HOI  .00 

8216.99 

128 

402.12 

12867.96 

192 

603.19 

28952.92 

104 


MATHBMATICAI.  TABLES. 


Clrcum. 

Area. 

Dlam.  Clrcum. 

Area. 

Diain.  Clrcum. 

1 

Area. 

103 

606.88 

89865.80 

860 

816.81 

53092.92 

827 

1027.30 

89981.84 

194 

600.47 

29559.25 

261 

819.96 

53502.11 

828 

1030.44 

&I496  28 

m 

612.61 

29864.77 

262 

823.10 

53912.87 

829 

1033.68 

85013.28 

196 

615.75 

80171.86 

268 

820.24 

54325.21 

880 

1036  78 

a'il)2d.86 

197 

618.89 

80480.62 

264 

829.83 

64739.11 

331 

1039.87 

86049.01 

196 

622  04 

80790.75 

265 

aS2.52 

65154.59 

832 

1043.01 

86609.73 

199 

625.18 

81102.65 

266 

8:«.66 

55571.63 

838 

1046.16 

871098.02 

soo 

628.32 

81415.93 
81730.87 

267 

838.81 

55990.26 

8»l 

1049.29 

87615.^ 

201 

681.46 

268 

841.95 

66410.44 

885 

1052.48 

88141.31 

90-i 

684.60 

82047.89 

269 

845.09 

66832.20 

886 

1055.58 

88668.81 

903 

687.74 

82365.47 

870 

848.88 

67255.5JJ 

837 

1058.72 

89106.88 

204 

640.88 

82685.18 

271 

851.37 

67680.48 

9SS 

1061  86 

89727.03 

205 

644.06 

88006.86 

272 

854.51 

68106.90 

889 

1065.00 

9025x«4.74 

200 

647.17 

88329.16 

273 

857.65 

58584.94 

840 

1068.14 

90rJl8  U3 

207 

650.31 

88663.53 

874 

660.80 

58964.56 

841 

1071.28 

91326.88 

206 

653.46 

88979.47 

276 

863.94 

60395.74 

842 

1074.42 

91863.81 

209 

656.59 

84306.96 

876 

867.08 

69^8.49 

843 

1077.57 

98401  81 

210 

659.78 

346:i6.06 

877 

870.22 

60262.82 

344 

1080.71 

92940.88 

811 

662.88 

84966.71 

878 

873.36 

60698.71 

845 

1063.86 

93482.02 

2ri 

666.08 

85298.94 

279 

876.50 

61186.18 

846 

1066.99 

94021.73 

SIS 

669.16 

86688.78 

880 

879.66 

61575.82 

847 

1090.18 

94669.01 

S14 

672.80 

85968.09 

281 

882.79 

62015.88 

848 

1093.87 

95114.86 

215 

675.44 

86805.08 

882 

885.93 

62458.00 

849 

1096.42 

95662.28 

916 

678.58 

36648.64 

888 

889.07 

62901.75 

860 

1099.56 

90811.88 

817 

681.78 

86983.61 

284 

892.21 

68347.07 

851 

1108.70 

96761.84 

8)8 

084.87 

37325.26 

286 

895.85 

68798.97 

868 

1106.84 

97B18.97 

819 

668.01 

87668.48 

286 

898.50 

64242.48 

868 

1106.98 

97B67.68 

880 

G91.15 

88013.87 

287 

901.64 

64692.46 

854 

1118.12 

98422.96 

221 

694.29 

88359.68 

888 

904.78 

65144.07 

355 

1115.27 

98079.80 

2i» 

697.48 

88707.66 

889 

907  92 

65597.81 

856 

1118.41 

99538.22 

»d 

700.58 

89067.07 

290 

911.06 

66051.99 

a^7 

1121.55 

100098.81 

8si4 

703.72 

89408.14 

291 

914.20 

66508.30 

858 

1124.69 

100659.77 

iB5 

706.86 

89760.78 

292 

917.35 

669e6.l9 

859 

1127.88 

10182:2.90 

226 

710.00 

40115.00 

293 

920.49 

67425.65 

800 

1130.97 

101787.60 

227 

718.14 

40470.78 

294 

923.68 

67886.68 

861 

1134.11 

108853.87 

828 

716.28 

40828.14 

895 

926.77 

68349.28 

362 

1187.26 

102921.72 

829 

719.42 

41187.07 

206 

929.91 

68813.45 

868 

1140.40 

108491.13 

2S0 

722.67 

41547.56 

297 

9.33.06 

69279.19 

364 

1148.54 

104062.12 

281 

725  71 

41909.68 

298 

936.19 

69746.50 

365 

1146.68 

104634.67 

fi»2 

7:28.85 

42278.27 

299 

939.34 

70215  88 

SC6 

1149.82 

105808.80 

233 

781.99 

42688.48 

800 

942.48 

70685.63 

867 

1158.96 

105784.49 

284 

735.18 

43005.26 

801 

945.62 

71157.86 

368 

1156.11 

106861  76 

835 

788.27 

48373.61 

802 

948.76 

71681.45 

369 

1159.25 

106940.60 

836 

741.42 

48743.54 

808 

951.90 

72106.62 

870 

1168.89 

107521.01 

887 

744.56 

44115.08 

804 

955.04 

72588.86 

371 

1105.58 

108102.99 

888 

747.70 

44488.09 

805 

958.19 

78061.66 

372 

1168.67 

108686.51 

239 

750.84 

44862.73 

806 

961.83 

78541.64 

87« 

1171.81 

109871.66 

240 

753  98 

452:)8.98 

807 

964.47 

74022.99 

874 

1174  98 

109858.35 

241 

757,12 

45616.71 

806 

967.61 

74506.01 

875 

1178.10 

110446. 68 

212 

760.27 

45996.06 

809 

9T0.75 

74990.60 

376 

1181.24 

111036.45 

243 

763.41 

46876.98 

810 

973.89 

75476.76 

877 

1184.88 

111627.86 

244 

766.55 

46759.47 

811 

977.04 

75964.60 

878 

1187.52 

118220.83 

215 

769.69 

47143.52 

812 

980.18 

76468.80 

879 

1190.66 

112815.88 

846 

772.88 

47529.16 

818 

963.32 

76944.67 

380 

1198.81 

118411.49 

247 

775.97 

47916.86 

814 

986.46 

77487.12 

381 

1196.95 

ll40m).18 

248 

779.11 

48305.18 

815 

989.60 

77981.13 

382 

1200.08 

114608.44 

249 

782.26 

48695.47 

816 

992.74 

784-26.?2 

888 

1208.28 

115909.87 

850 

785.40 

49087  89 

817 

995.88 

78923.88 

384 

1206.87 

115811.67 

251 

788.54 

494H0.87 

318 

999.03 

79422.60 

C% 

12C9.51 

116415.64 

2.M 

791.68 

49875.92 

819 

1002.17 

79922.90 

386 

1218.65 

117021.18 

253 

794.82 

50272.56 

880    1005.31 

80424.77 

387 

1815.80 

117628.80 

254 

;97.96 

50670.75 

821    1008.45 

60928.21 

888 

1218.94 

118886.98 

855 

801.11 

61070.52 

822   1011.59 

81483  22 

380 

1223.08 

118847.24 

856 

804.25 

51471.55 

823    1014  73 

81939.80 

800 

1226.82 

119159.0(> 

257 

807.89 

51874.76 

824 

1017.88 

82447.96 

391 

1228.36 

180078.46 

256 

810.58 

52279.21 

325 

1021.02 

82957.68 

392 

1281.80 

180687.4:tt 

259 

813.67 

52085.29 

326 

1024. IG 

83468.98 

898 

1234.65 

181808.96 

CIRCUHFERBNCES  AI^D  AREAS  OF  CIRCLES.       J  05 


Oum. 

Circum 

Area. 

Dlam. 

Clreum. 

Area. 

Dlam. 

Clrcam. 

Atml 

394 

1^87.79 

121922.07 

461 

1448.27 

166918.60 

628 

1668.76 

SI 8956.44 

3» 

1340.03 

122541.75 

462 

1451 .42 

167638.53 

529 

1661.90 

219786.61 

3« 

1-444.07 

123168.00 

468 

1454.56 

168366.02 

680 

1665.04 

220618.84 

•W 

1-^47.21 

123786  82 

464 

1457.70 

169098.08 

531 

1G68.19 

2214.51.65 

3* 

ri5U.35 

1-^4110.21 

465 

1460.84 

169822.72 

58-4 

1671.33 

a42286.68 

3)9 

1^^33  50 

125036  17 

466 

1463.98 

170553.9-4 

633 

1674.47 

228122.98 

«oa 

1456.64 

125663.71 

467 

1467.1« 

171286.70 

584 

1677.61 

228961.00 

101 

1239.7« 

128292.81 

408 

1470.27 

1720-41.05 

535 

1680.75 

224800.59 

•XH 

ISOi^i 

1:W623.48 

469 

1473.41 

172756.97 

636 

1683.89 

225641.75 

4^ 

1:366.06 

127S55.73 

470 

1476.65 

173494.45 

637 

1687.04 

226484.48 

^iM 

1269.20 

128189.55 

471 

1479.69 

174-438.61 

538 

1690.18 

227828.79 

K» 

l3S7i.85 

128884.93 

472 

1482.88 

174974.14 

539 

1C93.32 

228174.66 

*« 

1;!73.49 

129461.69 

473 

1485.97 

1757l«.ai 

640 

1696.46 

229022.10 

■lor 

I3r78.6» 

180100.42 

474 

1489.11 

176460  12 

Ml 

1699.60 

229871.12 

•lOS 

iai.77 

130740.52 

475 

1498.26 

177205.46 

542 

1702.74 

280721.71 

4'.i9 

1C&I.91 

181382.19 

476 

1496.40 

177952.37 

548 

17«»5.8b 

2815:8.66 

410 

i:08S.o& 

183»26.43 

477 

1498.54 

178r00.8ti 

544 

1709.08 

282427.59 

411 

1:291.19 

18i670.24 

478 

1501.68 

179450.01 

546 

1712.17 

2332;j2.89 

412 

1294.84 

133316.63 

479 

1504.8* 

180202.64 

646 

1715.81 

284139.76 

413 

1297. 4« 

133964.68 

480 

1607.96 

180955.74 

547 

1718.45 

284098.20 

4U 

\300.64 

181614.10 

481 

1511.11 

181710.60 

548 

1721.59 

285858.21 

415 

1303.76 

1855»6.20 

482 

1514.25 

]8:?466.84 

549 

17-44.73 

286719.79 

419 

1306.90 

185917.86 

483 

1617.89 

188-2d4.75 

650 

17-47.88 

287682.94 

417 

1310.04 

180672.10 

484 

155».53 

183984.23 

651 

1731.0-4 

288447.67 

4ie 

1313.10 

187227.91 

485 

1523.67 

184746.28 

652 

1734.16 

239818.9G 

419 

131633 

187885.29 

486 

1526.81 

185507.90 

553 

1737.80 

240181.88 

4iO 

1319.47 

188544.24 

487 

1529.96 

186278.10 

554 

1740.44 

241051.26 

Ul 

13;8.6i 

139»l.76 

488 

1633.10 

187087.86 

556 

1743.58 

241922.27 

4tS 

1135. 73 

139866.85 

480 

]5;j6.24 

187805.19 

656 

1746.73 

242794.85 

4S 

I3«.t« 

140530.51 

490 

1539.38 

183574.10 

557 

1749.87 

243668.09 

4:il 

133)2  04 

141195.74 

491 

1642.52 

189344.57 

556 

1758.01 

2445t4.n 

445 

1335.18 

141862  M 

492 

1645.66 

190116.62 

559 

1756.15 

245422  00 

4:90 

13«.8i 

142580.92 

498 

1548.81 

190890.24 

600 

1759.29 

246300.86 

ur 

1341.46 

143200  86 

491 

1651.05 

191666.48 

561 

1762.43 

247181.80 

4S 

1344  60 

143872.88 

495 

1555  09i  194442.181 

562 

1765.58 

248063.80 

4t» 

1347.74 

144545.40 

496 

1558.281  19:^420.51 1 

668 

17tfs.72 

248046.87 

IM 

1350.88 

145220.1-4 

497 

1661.37 

194000.41 

664 

1771.86 

240632.01 

431 

13:V4.03 

145896.35 

498 

1564.51 

194781.89 

566 

1775.00 

250718  73 

43« 

1837.  (7 

146574  15 

499 

1567.65 

195564.93 

666 

1778.14 

251607.01 

in 

1360.31 

147258.52 

600 

1570.80 

196849.54 

667 

1781.28 

862496.87 

431 

1363.40 

14798146 

601 

1578.94 

197185.72 

566 

1784.42 

253386.30 

4« 

1366.69 

14^16.97 

502 

1677.08 

197948.48 

669 

1787.57 

254281 .29 

4» 

1369.73 

149301.05 

508 

1580.22 

198712.80 

670 

1790.71 

255175.66 

437 

137«.88 

149986.70 

604 

1688.86 

199508.70 

671 

1793.85 

256072.00 

m 

1376.0:: 

150673.93 

605 

1586  50 

200296.17 

672 

1706.99 

250969.71 

4» 

1379.16 

151362.7^ 

506 

1680.65 

201090.20 

678 

1800.13 

267808.99 

4I# 

138^.30 

152053.08 

607 

1594.79 

201885.81 

674 

1803.27 

25H7t>9.85 

411 

1385.44 

l&-i743.U2 

608 

1595.93 

202682.99 

r75 

1806.42 

259672.27 

4«e 

1386.68 

163438  53 

600 

1599.07 

203481.74 

576 

1809.56 

360576.26 

4U 

1391.78 

]54l3i.60 

610 

1602.21 

204282.06 

577 

1812.70 

261481  83 

4i4 

1394.87 

154880.25 

511 

1G05  85   206083.95 

678 

1815  84 

«6238H.06 

443 

1398  01 

155548.47 

512 

1608.501  805887.42 

679 

1818.98 

268497.67 

444 

1401.15 

15e2«.26 

613 

1611.641  20G692.45 

680 

1842  12 

264207.9^ 

447 

1404.29 

160M9.62 

614 

1614.78   207499.05 

581 

1843.27 

265119.70 

444 

1407.43 

157632  55 

616 

1017.92   208307.23 

bSi 

1828.41 

266088.21 

449 

1410.68 

158337  06 

616 

1621.06   209116  97 

583 

1831.55 

266948.20 

4»9 

14I37< 

159043.13 

617 

16*44.20   2099:88.29 

584 

18:)4.69 

267864.76 

451 

1416  86 

160790.77 

618 

1627.84;  210741.18 

586 

1837.83 

268782.89 

45i 

t4:«>.00 

160489.90 

510 

16:».49i  211555  63 

586 

1840.07 

269702.69 

45S 

1423.14 

161170.77 

420 

1638.63   212J71.66 

6S7 

1844.11 

270628.66 

454 

14:36.28 

161883.13 

521 

1636.77:  213189.26 

588 

1847.26 

271546.70 

tfft 

1429  42 

16«97  06 

522 

1689.91    214008.43 

589 

18.50.40 

272471.12 

«9t 

1432.67 

168312.55 

628 

1643.05,  2148-49.17 

600 

1853.54 

273897.10 

457 

1435.71 

161029.02 

524 

1646.10    21 .7651.49 

591 

1856.68 

974:^24.66 

4SB 

1438.85 

16474S.26 

6« 

1619.84    216475.37 

5U2 

1859.82 

275258.78 

4J9 

1441.99 

16546S.47 

526 

1652.48,  217300.8:4 

693 

1862.96 

276184.48 

4W 

1445.18J 

106199.26 

697 

1656  621  218127.85 

594 

1866.11 

277116.75 

106 


MATHEMATICAL  TABLES. 


Biam. 

Clrcam. 

Area. 

Dlam- 

Clrcam. 

Area. 

Dlam*  Clrcum. 

Area. 

&»6 

1869.86 

878050.58 

663 

8088.88 

845836.69 

731   i  8896.60 

419686.15 

596 

18^^.89 

278985.99 

664 

9086.08 

846278.91 

788  1  2890.65 

480835.19 

597 

1875.53 

279988.97 

665 

2089.16 

347888.70 

733  1  2808.79 

421985.79 

5y8 

1878.67 

280861.58 

666 

2098.80 

348368.07 

781 

2305  93 

428187.97 

599 

1881.81 

881801  65 

667 

2095.44 

849415.00 

735 

2309.07 

424891 .78 

600 

1884.96 

283743.84 

668 

2098.58 

350463.51 

736 

2812.81 

425447.04 

001 

1888.10 

883686.60 

669 

8101.78 

851518.59 

737 

2315.85 

486003.94 

608 

1891.24 

884631.44 

670 

8104.87 

858565.24 

738 

23i8.50 

427768.40 

60S 

1894.38 

885577.84 

671 

2108.01 

853618.45 

739 

2881.64 

428982.43 

604 

1897.68 

286585.88 

678 

2111.15 

854673  24 

740 

2384.78 

480084.03 

605 

1900.66 

887475.36 

673 

2114.29 

355789.60 

741 

2827.98 

431247.81 

606 

1908.81 

888486.48 

674 

2117.43 

856787.54 

742 

8381.06 

432411.95 

607 

1906.96 

889879.17 

675 

2120.58 

857847.04 

748 

2834.80 

438578,87 

606 

1910.09 

290688.43 

676 

2123.72 

358908.11 

744 

2837.34 

484746.16 

600 

1918.23 

291.889.26 

677 

2186.86 

859970.75 

746 

2840.49 

435915.68 

«10 

1916.87 

898846.66 

678 

2130.00 

861034.97 

746 

2343.68 

487086.61 

611 

1919  51 

293205.63 

679 

2188.14 

362100.75 

747 

£846.77 

488259.84 

61SS 

1928.65 

294166.  r< 

680 

8186.28 

868168.11 

748 

2349.91 

439488.41 

618 

1985.80 

295188.88 

681 

2139.42 

864237.04 

749 

2353.05 

440009  16 

614 

1928.94 

296091.97 

688 

2142.57 

365807.54 

760 

2856.19 

441786.47 

615 

1988.08 

897057.82 

688 

2146.71 

886379.60 

751 

2859.34 

448965.35 

616 

1935.22 

298084.05 

684 

2148.85 

867458.84 

762 

2362.48 

444145. ») 

617 

1938.36 

898998.44 

685 

2151.99 

368528.45 

753 

2365.62 

445887.553 

618 

1941.50 

899968.41 

686 

2155.13 

869605.88 

754 

2868.76 

446511.48 

619 

1914.65 

300933.95 

687 

2158.27 

870683.59 

755 

2871.90 

447696.f.9 

680 

1947.^9 

301907.05 

688 

2161.42 

371768.51 

756 

8875.04 

448888.38 

63il 

1950.93 

808881.73 

689 

2164.56 

878845.00 

757 

2378.19 

450071 .63 

622 

1964.07 

803857.98 

690 

2167.70 

878988.07 

758 

2881.83 

451861.51 

688 

1957.21 

304885.80 

691 

2170.84 

875012.70 

759 

8384.47 

462452.96 

684 

1960.35 

805815.20 

692 

2173.98 

376098.91 

760 

8387.61 

458645  98 

685 

1963.60 

806796.16 

693 

2177.12 

877186.68 

761 

2390.75 

464840.57 

686 

1966.64 

3Ui7'i^.69 

694 

2180.87 

878876.08 

762 

2893.89 

456036.73 

627 

1969  78 

808768; 79 

695 

2188.41 

879366.95 

763 

S897.04 

457284.46 

688 

1972.98 

309748.47 

696 

2186.55 

380459.44 

764 

M400.18 

468483.77 

689 

1976.06 

810785  71 

697 

2189.69 

381558.50 

766 

2408.88 

469684  64 

680 

1979.80 

311784.53 

698 

2192.83 

888649.13 

766 

8406.46 

460837.08 

631 

1988.35 

818714.92 

699 

2195.97 

883746.88 

767 

2409.60 

468041.10 

638 

1985.49 

818706.88 

700 

2199.11 

384845.10 

768 

2412.74 

463846.69 

688 

1988.63 

314^00.40 

701 

2208.26 

885945.44 

769 

2416.88 

464458  84 

834 

1991.77 

815695.50 

702 

2805.40 

887047.36 

770 

2419.08 

46566B2.57 

635 

1994.91 

816692.17 

703 

2208.54 

388150.84 

771 

2422.17 

466872.87 

636 

1908.05 

817«90.48 

704 

2211.68 

889256.90 

778 

2485.81 

468084  74 

687 

2001.19 

818690.23 

705 

2814.82 

890368.52 

778 

2488.45 

469208.18 

638 

8004.34 

319691.61 

706 

2817.96 

891470.72 

774 

2431.59 

470518.19 

689 

2007.48 

380694.56 

707 

2281.11 

892580.49 

776 

2434.78 

471729.77 

640 

8010.68 

381690.09 

708 

2284.25 

893691 .82 

776 

2487.88 

47^2947.0^! 

641 

8018.76 

388705.18 

709 

2887.89 

894804.73 

777 

2441.02 

474167.05 

64:? 

8016.90 

383718.85 

710 

2830  53 

89r>919.81 

778 

2444. 1C 

475888.94 

643 

2080.04 

38478?2.09 

711 

2833.67 

397085.26 

779 

JW47.80 

476611.81 

644 

2083.19 

825788.89 

712 

2836.81 

398158.89 

780 

2450.44 

47T836.24 

645 

8086.33 

888745.87 

718 

2239.96 

899872.08 

7bl 

2458.58 

470U62.85 

646 

8089.47 

887759.88 

714 

2248.10 

400392.84 

782 

£466.73 

480280.83 

647 

208261 

888774.74 

715 

2246.24 

401515.18 

7«3 

2459.87 

481618.97 

648 

2035.75 

889791.83 

716 

2849.38 

408689.08 

784 

2463.01 

482749.69 

649 

8038.89 

3:30810.49 

717 

2858.58 

403764.50 

785 

2466.15 

488081.98 

660 

9012.04 

331830.78 

718 

2855.66 

4(M891.60 

786 

2469.29 

485815.84 

661 

2045.18 

338858.58 

719 

2858.81 

406080.82 

787 

2472.48 

486451.28 

668 

8048.88 

388875.90 

720 

8861  95 

407150.41 

788 

2475.58 

487688.88 

653 

2051.46 

8JH900.86 

721 

2865.00 

408282.17 

789 

8478.72 

488986.85 

654 

8054.60 

a3.5U87.36 

782 

2868.23 

409415.50 

700 

2481.86 

490166.99 

655 

2057.74 

336955.45 

783 

2871.87 

410550.40 

791 

2485.00 

491408.71 

656 

8060.88 

337985.10 

721 

2874.51 

411686.87 

792 

2488.14 

492651 .99 

657 

8064.03 

839016.33 

725 

2-.'77.65 

412824.91 

798 

2491.28 

403896.85 

658 

8067.17 

840049.13 

786 

2880.80 

418964.62 

794 

2494.42 

495148.28 

659 

8070.31 

341083.50 

787 

88f>5.94 

415105.71 

796 

2497.57 

496391.27 

660 

2073.45 

348119.44 

728 

2887.08 

416848.46 

796 

2500.71 

497640  84 

661 

8076.59 

3431.')6.93 

789 

8890.88 

417392.79 

797 

2508.85 

498891.98 

668 

8079.73 

344196.03 

780 

8898.36 

418538.68 

796 

2606.99 

600144.69 

CIECUMFEREKCES  ANt>  AREAS  OF  CIRCLES.       107 


DlanLJClrciun. 

Area. 

Diain.|Clrcum. 

Area. 

Dlnm. 

CIrcum. 

Area. 

799 

2510.  M 

50l89ri.97 

867 

2723.76 

590375.16 

936 

2987.89 

686614.71 

800 

2518.27 

502654.82 

868 

2?26.n0 

591787.8:3 

936 

2940.63 

688084.19 

801 

2516.42 

50:«I2.25 

869 

2730.04 

598102  06 

937 

2948.67 

689555.24 

8(tt 

2519.56 

505171.24 

870 

2783.19 

694167.87 

938 

2946  81 

691027. 86 

m 

252;!.  70 

506431.80 

871  ]  2736.83 

595835.25 

939 

2949.96 

692502.05 

8M 

•i5i5.84 

507693.94 

872  1  2739.47 

597204.20 

940 

2953.10 

693977.82 

805 

2528  98 

5U8057.61 

873     2742.61 

598574.72 

941 

2956.24 

695455.15 

9» 

2532.121  510222.92 

874     2745.75 

599946.81 

942 

2959.38 

696934.06 

W7 

2585.27 

511489.77 

875 

2748.89 

601320  47 

948 

2962.52 

698414.58 

«M 

:»38.41 

512758. 19 

876 

2752.04 

602695.70 

944 

2965.66 

699896.58 

H09  •  2311.55 

514028.18 

877 

2755.18 

604072.50 

945 

8968.81 

701380.19 

910 

2344.69 

515299.74 

878     2758.82 

(J05450.88 

946 

2971.95 

702865.88 

811 

2547.88 

51(3372.87 

879 

2761 .46 

606830.82 

947 

2975.09 

704352.14 

812 

2550.97 

517847.57 

TJ80 

2764.60 

606212.34 

948 

2978.28 

705840.47 

813 

2554.11 

51912^)  84 

881 

2767.74 

009595.42 

949 

2981.87 

707830.37 

814 

)»57.26 

520401.68 

882 

2770.88 

610960.08 

960 

2984.51 

706821.84 

813 

2.MS0.40 

521681.10 

883 

2774.03 

612366.31 

951 

2987.65 

710314.88 

81« 

2563.54 

522962  08 

884 

2777.17 

613754.11 

952 

2990.80 

711809.50 

817 

2566.68 

524244.68 

883 

2780.81 

615143.48 

958 

2990.94 

718305.66 

818 

2569.82 

525528.76 

886 

2783.45 

616534.42 

954 

2997.08 

714803.43 

819 

2572  S6 

526814  46 

887 

2786.59 

617926.93 

955 

3000.22 

716302.78 

htO 

2376.11 

528101.78 

888 

2789.78 

619321.01 

956 

3008.36 

717806.66 

tiil 

2579.25 

529390.56 

889 

2792.88 

620716  66 

957 

8006.50 

719306  12 

9U 

2582.39 

530680.97 

800 

2796.02 

622113.89 

968 

8009  65 

720610.16 

8i3 

^85.53 

531972.96 

891 

2799.16 

623512.68 

959 

3012.79 

722315.77 

im 

2588.67 

533266.50 

892 

28(12.30 

624913.04 

900 

8015  93 

728822.96 

8» 

2591.81 

534561.62 

893 

2805.44 

626314.98 

961 

3019.07 

725331.70 

8:96 

2594.96 

535858.32 

894 

2808.58 

027718  49 

962 

8022.21 

726842.02 

847 

2598.10 

537156.58 

896 

2811.78 

629123.56 

968 

3025.85 

728853.91 

838 

2601 .24 

53S456  41 

896 

2814.87 

630530.21 

964 

3028.50 

729867.37 

(fi» 

2604.38 

539757.82 

897 

2818.01 

6:31938.48 

965 

8031.64 

731882.40 

sso 

260r.52 

541060.79 

808 

2821.16 

63:3:348.22 

966 

8034.78 

782890.01 

Ml 

2610.66 

512365.34 

899 

2824.29 

634759. 5S 

967 

3037.92 

734417.18 

«3-* 

2613.81 

54SG71.46 

000 

2827.43 

636172.51 

968 

8041.06 

rd6936.93 

884 

2616.95 

544979.15 

901 

2«».58 

6:37587.01 

969 

3044.20 

737458.24 

834 

2620.09 

546288.40 

902 

2833.72 

639003.09 

970 

8047.34 

738981.13 

8» 

2623.23 

517599.23 

903 

2836.86 

640420.7:3 

971 

3050.49 

740505.59 

836 

2626.37 

518911.68 

904 

2840.00 

641839.93 

972 

3058.63 

742031.62 

837 

2629.51 

530225.61 

905 

2843. 14 

643260.78 

978 

8056.77 

743569.22 

8« 

2682.65 

551541.15 

906 

2846.28 

644683.09 

974 

8059.91 

745068.39 

K» 

2635.80 

552868.26 

907 

2849.42 

640107.01 

975 

3063  05 

746619.13 

840 

2688.94 

554176  94 

S08 

2852.57 

6473:32.51 

976 

3066.19 

748151.44 

841 

2642.08 

555497.20 

909 

2853.71 

648959.58 

m 

3069.84 

749685.82 

812 

2645.22 

656819.02 

910 

2858.85 

68a388.22 

978 

3072.46 

751220.78 

^) 

2648  36 

558142.42 

911 

2861.99 

651818.48 

979 

8075.62 

752757.80 

84t 

2651.50 

559467.39 

912 

2865.13 

653230.21 

980 

8078.76 

754296.40 

»15 

2654.65 

56U'/»8.92' 

913 

2868.27 

654683.56 

961 

3081  90 

755886.56 

816 

2857.79 

562122.08 

914     2871.42 

650118.48 

982 

8085.04 

757878.80 

847 

2660.94 

563451.71 

915  1  2874.56 

6.37554.98 

983 

3088.19 

758921.61 

818  ■  9664.07 

564782.96 

916  ,  2877.70 

658993.04 

984 

3091.33 

760466  48 

849     ^667. 21 

566115.78 

917  i  2880.81 

660432.68 

966 

3094.47 

762012.93 

8eO 

2670.35 

567450.17 

918     28K3.98 

661873.88 

986 

8097.61 

7t>35(;0.95 

851 

2678.50 

568786.14 

919     2887.12 

663316  66 

967 

3100.75 

765110  54 

ssa 

3676.64 

670128.67 

920  :  2890.27 

664761.01 

988 

3108.89 

766661.70 

858 

2679.78 

571462.77 

921  ;  2893.41 

666206.92 

9S9 

8107.04 

768214.44 

854 

2682  92 

572803.45 

922  .  2896.55 

667654.41 

990 

3110.18 

769768.74 

S5S 

2686.06 

574145.69 

923 

2899.69 

669103.47 

991 

3113.32 

771324.61 

856 

2689.20 

575480.61 

924 

:>90J.83 

670554.10 

992 

3116.46 

772882.06 

857 

2692.34 

576884.90 

926 

8905.97 

672006.30 

993 

811960 

774441,07 

858 

9696.49 

578181.85 

926 

2909.11 

6'i:3400.08 

994 

3122.74 

776001.66 

859 

2896.68 

579580.38 

927  1  2912. 2fi 

674915.42 

995 

3125.88 

777563.82 

800 

2701.77 

580880.48 

928     2915.40 

67(^72.33 

996 

3129.03 

779127.54 

861 

2704.91 

6822SS.15 

929  •  2918.54 

677h80.82 

997 

3132.17 

780(i92.84 

ett 

S708.06 

568585.89 

9S0  1  2921.68 

(579290.87 

998 

3135.81 

782259  71 

888 

9711.19 

684940.20 

931   1  2924.  K2 

680r.V2.50 

999 

3138.45 

783R28.1fi 

864 

2714  84 

588*96.69 

932     2927.% 

6^2215.69 

1000 

8141.59 

785398.16 

880 

8717.48 

68^54.54 

988     29:11.11 

68:3680.46 

886 

2390  6^ 

980014.07 

984     2934.25 

685146.80 

108 


MATHEMATICAL  TABLES. 


CIBCUMFERENCBS   AND   AHBAS  OF  CIACJLBS 

Advanolus  by  Elslitli*. 


Dlam. 

Ciroum. 

Area. 

Plain. 

Clrcum. 

Area. 

Dlam. 

Ciroum. 

Area. 

•1/M 

.04009 

.00019 

2   H 

7.4613 

4.4301 

0  H 

19.949 

99.465 

^m 

.00818 

.00077 

7/16 

7.6576 

4.6664 

H 

10.630 

80  680 

8/64 

.14796 

.00173 

H 

7.8540 

4.9067 

% 

90.098 

31.019 

1/10 

.19635 

.00807 

V 

8.0508 

5.1579 

V6 

90.490 

38.183 

.99459 

.00690 

8.9467 

5.4119 

^ 

90.613 

34.479 

^ 

.89270 

.01997 

11/16 

8.4480 

5.8797 

P 

91  900 

35.7«5 

b/oi 

.490B7 

.01017 

18/16 

8.6394 

5.9896 

% 

91.598 

87. 199 

8/10 

.58905 

.09761 

8.8357 

6.9196 

7. 

91.091 

88.485 

7/ai 

.68799 

.08758 

k 

9.0891 

6.4918 

99.884 

39.871 

15/16 

9.9984 

6.7771 

^ 

99.770 

41   982 

9%i 

.78540 

.04909 

3|l 

93.109 

49.718 

.88857 

.06;il3 

8. 

9.4948 

70680 

7* 

93.5«i 

44-179 

5/16 

.98175 

.07670 

1/16 

9.6911 

7.8069 

M 

98.956 

46  664 

lim 

1.0799 

.00981 

k 

9.8175 

7.6699 

% 

94.847 

47.173 

1.1781 

.11045 

8/16 

10.014 

7.9798 

yi  1 

94.740 

48.707 

izm 

1.9768 

.1900.J 

M 

10.910 

8.9968 

8. 

95.183 

50  96.-) 

7/16 

1.8744 

.160:33 

6/16 

10.407 

8.6179 

/i 

95.595 

61.849 

15/8;) 

1.47y6 

.17937 

H 

10.008 

8.9469 

M 

95.918 

58.456 

7/16 

10.7119 

9.9806 

96.3U 

50  088 

1754l 

1  5708 

.19635 

9% 

10.996 

9.6911 

1 1 

90.704 

56.745 

1.0000 

.99166 

11.199 

9.0678 

H  \ 

97.090 

58.426 

»/16 

1.7«71 

.94850 

H 

11.888 

10.881 

k 

97.480 

00.189 

19^3 

1.8668 

.97688 

4' 

11.585 

10.680 

H 

97.889 

01.869 

1.9G85 

.80080 

11.781 

11.045 

9. 

98.974 

08.617 

31^ 

a  061? 

.38894 

13/16 

ii.»rr 

11.416 

M 

98.667 

0.5  807 

11/10 

9.1598 

.87199 

155^6 

19.174 

11.793 

^ 

99.060 

67.901 

98/84 

2.9580 

.40674 

19.870 

19.177 

fl 

90.459 

69.0199 

4. 

19.566 

19.666 

L , 

90.845 

70.889 

95/1) 

9.8569 

.44179 

■a* 

19.768 

19.909 

yi 

30.988 

7«.Teo 

2.4544 

.47937 

19.059 

13.864 

^ 

30.681 

74.069 

13/10 

9.5.595 

.51849 

3/10 

13.156 

13.779 

tZ 

31.098 

76.689 

97/89 

9.6507 

.55914 

5/16 

13.358 

14.186 

10. 

31.416 

78  640 

k 

9.7489 

.60139 

13.548 

14.607 

H 

31.809 

80.616 

90/B-2 

9.8471 

.64504 

7/16 

13.744 

15.083 

H 

89.901 

89  516 

15/16 

9  9459 

.69099 

18.941 

15.466 

% 

89.594 

84.541 

81/39 

3.0484 

.78708 

i2 

14.187 

15.9(H 

K 

39.987 

86.590 

f 

14.834 

16.849 

K 

88.879 

86.664 

1. 

3.1416 

.7854 

14.530 

16.800 

» 

88.779 

90.7li3 

1/16 

3.8879 

.8866 

11/16 

14.796 

17.987 

U 

34.165 

d9.886 

H 

8.5848 

.9940 

N 

14  998 

17.781 

11. 

84.558 

96.083 

V 

3.7806 

1.1075 

X 

15.110 

18.190 

H 

34.050 

97.905 

8.9S70 

l.«79 

15.815 

18.665 

u 

85.348 

99.409 

5/16 

4.1988 

1.8580 

15/16 

15  519 

19.147 

?i 

85.780 

101.69 

9^ 

4.8197 

1.4849 

6. 

15.708 

19.685 

a 

86.198 

108.87 

7/T6 

4.5160 

1.6980 

1/16 

15.004 

90.199 

H 

86.591 

106.14 

k 

4.7194 

1.7671 

k 

16.101 

90.699 

S 

80.914 

108.43 

9/16 

4  0087 

1.9175 

3/16 

16.997 

91.185 

H 

87.800 

110.75 

5.1051 

9.0780 

5/l6 

16.499 

91.648 

12. 

87.090 

118.10 

11/16 

5.8014 

9.9365 

16.690 

99.166 

H 

88.099 

115.47 

6.49« 

9.4053 

% 

16.886 

99.691 

b 

88.485 

117.86 

la/te 

5.6941 

9.6909 

7/16 

17.088 

98.991 

n 

88.877 

190.98 

H 

58905 

9.7619 

H 

17.979 

93.758 

» 

80.970 

199.73 

13/J6 

6.0668 

9.9488 

''a' 

17.475 

94.801 

H 

89.068 

195.19 

17.671 

94.850 

H 

40.066 

197.68 

S. 

6.9889 

3.1416 

11/16 

17.868 

95.406 

H 

40.448 

1W.19 

'a" 

6.4795 

8  8410 

H 

18.064 

95.907 

18. 

40.841 

13Bi.73 

6.6759 

8  5466 

13-16 

18.961 

96.685 

H 

41.988 

185.80 

8^6 

6  8799 

8.7583 

15^6 

18.4.'i7 

97.109 

M 

41.690 

187.89 

H 

7.0086 

3.97G1 

IB. 653 

97.088 

% 

49.019 

140.50 

6/16 

7.9649 

4.9000 

«. 

Ift-R-Ml 

98.974 

« 

49.419 

148.14 

CIRCUMFERBNOES  AND   AREAS  OP  CIRCLES.        109 


Dtein 

L 

Cfrcttui. 

Area. 

13^ 

42.804 

145.80 

Sa 

«.!97 

148  49 

%  1 

48.»W 

151.90 

14. 

4B.mA 

153.94 

H 

44  JW6 

156.70 

4 

44.768 

159.48 

i 

45.160 

16:i.a0 

i 

45.583 

165.13 

^ 

45.846 

167.99 

% 

46.8a8 

170.87 

H 

46.731 

173.78 

15 

47.1J4 

176.71 

47.617 

179.67 

47.900 

182.65 

4S.30ii 

185.66 

48.605 

183.69 

'h 

49.087 

191.75 

!|| 

49.480 

194.88 

i2 

49.873 

197.03 

i« 

50.985 

201.06 

^ 

£0.668 

204.9-<i 

1 

51.051 

a07.89 

i 

51.414 

210.60 

4 

61.816 

213.82 

'« 

52.229 

217.08 

^ 

59.692 

220.35 

5i 

58.014 

238.ftS 

17 

58.407 

226.98 

H 

68.800 

280.33 

:    ; 

54.199 

233.71 

'^f 

54.585 

237.10 

*.l 

ti4.978 

240.63 

'^; 

56.371 

248.98 

■fc 

65.768 

247.45 

fi 

56.156 

250.95 

18 

56.549 

254.47 

u 

56.941 

258.02 

■i 

, 

57.:^ 

261.59 

■^ 

1 
( 

57.727 

265.18 

^ 

■ 

68.119 

268.80 

'^ 

66.518 

279.45 

14 

56.905 

276.19 

69.288 

279.81 

19 

69.600 

288.53 

^ 

60  063 

287.27 

•^ 

60.476 

291.04 

'^ 

1 

60.8W 

294.83 

■' 

1 

61.961 

208.65 

'1 

1 

61.654 

309.49 

«< 

62.046 

306.33 

Jl 

61.439 

310.24 

t% 

6S.889 

314.16 

h 

63.23!5 

318.10 

■i 

63.617 

329.06 

ji 

64.010 

328.05 

■  1 

6I.40S 

330.06 

ii 

6I.7B5 

3:i4.10 

ife 

65  188 

838.16 

'I 

66.S8t 

349.25 

« 

66.978 

346.36 

4 

66.886 

890.60 

t 

66.759 

354.66 

^\ 

67.158 

358.84 

1  ; 

67.544 

868.a5 

'^1 

67.987 

807.28 

k 

I 

68.8» 

S71.M 

Diam. 


89. 


28. 


24. 


26. 


26. 


27. 


28. 


29. 


90. 


CirouiB. 


68.729 
69.116 
69.508 
69.900 
70.296 
70.686 
7l.0i9 
n.471 
71.864 
72.257 
79.649 
78.049 
78.435 
78.827 
74.280 
74.613 
75.006 
75.898 
75.791 
76.184 
76.576 
76.969 
77.862 
77.754 
78.147 
78.540 
78.933 
79.825 
79.718 
80.111 
80.508 
80.886 
81.289 
81.681 
82.074 
82.467 
82  860 
83.252 
88.645 
»1.088 
84.480 
84.883 
85.216 
85.608 
86.001 
86.304 
86.786 
87.179 
87.679 
87.966 
88.357 
88.750 
89.143 
89.535 
89.988 
90.391 
90.713 
91.106 
91.499 
91.89B) 
92.284 
92. 6?? 
9.^.070 
93.462 
98.8.55 
94.»t8 


Area. 


375.88 
380.13 
884.46 


397.61 
402.04 
406.49 
410.97 
415.48 
420.00 
424.66 
429.13 
4^3.74 
438.86 
443.01 
447.69 
452.89 
457.11 
461.86 
466.64 
471.44 
476.26 
481.11 
485.96 
490.87 
495.79 
500.74 
506.71 
510.71 
515.72 
520.77 
525.84 
530.93 
536.05 
541.10 
546.35 
551.55 
556.76 
562.00 
567.27 
.079.56 
577.87 
583.91 
588.57 
593.96 
599.37. 
604.81 
610.27 
615.75 
621.26 
626.80 
632.36 
637.94 
643. .55 
649.18 
654.84 
600.52 
066.23 
671.96 
677.71 
1083.49 
689.30 
696.13 
700.98 
706  86 


Diam 


81. 


92. 


SS. 


94. 


86. 


87. 


88. 


Circum* 


91.640 
95.038 
96.426 
95.819 
96.211 
96.604 
96.997 
97.889 
97.789 
98.175 
98.667 
98.960 
99.358 
99.746 
00.138 
00.531 
00.924 
.316 
101.709 
102.109 
02.494 
102.887 
08.280 
103.678 
04.065 
104.458 
104.851 
105.243 
105.636 
106.029 
106.421 
106.814 
107.207 
07.600 
107.999 
106.385 
08.778 
09.170 
109.563 
09.966 
10.848 
10.741 
11.134 
11.527 
11.919 
12.312 
12.705 
13.097 
13.490 
13.883 
14.275 
14.G68 
16.061 
15.454 
15.846 
16.239 
16.6;i2 
17.024 
17.417 
17.810 
18.202 
18.596 
18.988 
19.381 
19.773 
20.166 


110 


ItATHEMATICAL  TABLES. 


Diam. 

Circum. 

Area. 

Diiuii. 

Circum. 

Area. 

DianL 

Circum. 

Area. 

ZSfi 

120.. '»9 

1156.6 

I<5?.^ 

146.477 

1707.4 

o4% 

172. 395 

2865. 0 

,i 

120.951 

1164.2 

■}4 

146.869 

1716.5 

55. 

172.788 

2875.8 

'1 

121.344 

1171.7 

147.262 

1725.7 

M 

178.180 

8886.6 

;l 

121.787 

1179.3 

47    "" 

147.655 

1734.9 

173.673 

2897.5 

% 

12:1.129 

1186.9 

l-H 

148.048 

1744.2 

9^ 

173.966 

8408.3 

Z9 

122.52-^ 

1194.6 

^l 

148  440 

1753.5 

l2 

174.358 

8410.:: 

1-42.915 

1202.3 

'?M 

148  883 

1762.7 

7B 

174.751 

2480.1 

]a 

m.308 

1210.0 

H 

149  226 

1772.1 

i/t 

175.144 

2441.1 

vk 

123.700 

1217.7 

149.618 

1781.4 

175.686 

2458. 0 

'ii 

1*44  093 

1225.4 

?1 

150.011 

1790.8 

56. 

175.929 

2463. 0 

1^ 

124.486 

12.33.2 

150.404 

1800.1 

1^ 

176.828 

2474.0 

ill 

1:^4. 87« 

1241.0 

i^'"^ 

150.796 

1809.6 

L 

178.715 

2485. 0 

''1 

125.271 

1248.8 

'-i 

151.189 

1819.0 

&  1 

177.107 

2196.1 

40. 

125. 004 

1256.6 

'  i 

151.582 

1828.5 

£2 

irr.500 

2507. « 

H 

128.056 

1264.5 

151.975 

1837.9 

7\  1 

177.893 

2518.3 

H 

126.419 

12^2.4 

!    . 

162.367 

1847.5 

7* 

178.285 

8520.4 

i| 

126.842 

1280.3 

152.760 

1857.0 

yk 

178.678 

8540.6 

1 

127.2.i5 

1288.2 

'  1 

158.153 

1866.5 

57. 

179.071 

2551.8 

S 

127.627 

1296.2 

153  545 

1876.1 

^ 

179.468 

2563.0 

^ 

128. 0*^ 

1304.2 

151 

158.988 

16*5.7 

^ 

179.858 

2574.2 

^ 

128.413 

1312.2 

'h 

154. 3;)! 

1895.4 

98 

180.249 

2585.4 

41 

1^.805 

1320.3 

'  i 

154.723 

1905.0 

Lc 

180.642 

2506.7 

H 

129.198 

1328.3 

155.116 

1914.7 

tN 

181.081 

2608.0 

^ 

129.591 

13:36  4 

Uj 

155.509 

1924.4 

s 

181.427 

2610.4 

^1 

129.983 

1344.5 

■'h 

1.^5.l>02 

1984  2 

181.820 

2630.7 

1 

180.370 

135;'.7 

'>.] 

1.'>(;.294 

1943.9 

58. 

182.212 

2042.1 

3 

130.769 

1360.8 

150  Gb7 

1958.7 

^ 

182.605 

2658.5 

^ 

131.161 

1309.0 

.'lO  ■■ 

157.080 

1968.5 

i3 

182.998 

2604.9 

^ 

181.554 

1377.2 

1  ^ 

157.472 

1978.3 

84 

183.390 

2676.4 

4a 

131  947 

1385  4 

'  ( 

157. MJ5 

1983.2 

79 

183.788 

2C87.8 

H 

182.. ^40 

1393.7 

158.256 

1993.1 

^ 

184.176 

2690.3 

1 

132.732 

HUJ.O 

1 ., 

168.650 

2003.0 

ft 

184.569 

2710.9 

% 

133. 12^ 

1410  3 

■•  ^ 

159.048 

2012.9 

184.961 

2722.4 

1 

13:^.518 

1418.6 

■'■J 

159.436 

2022.8 

59. 

185. a54 

27JM.O 

^ 

13i.9l0 

1427.0 

159.829 

2032.8 

H 

185.747 

2745.6 

^ 

134.303 

1435.4 

.M    ^ 

160  221 

2042.8 

186.189 

8757.2 

fl 

134.696 

1443  8 

1  -^ 

160.614 

2052  8 

a^ 

166.532 

2768.8 

4S 

m.oes 

1452.2 

1  , 

161.007 

2062.9 

zi 

186.925 

2:80.5 

135.481 

1460.7 

:-.^ 

161.399 

207:3.0 

z8 

187.317 

2792.2 

/4 

135.874 

1469.1 

1  .. 

161.792 

2083  1 

n 

187.710 

2H03.9 

b2 

136.267 

1477  6 

r.  ^ 

162.185 

2093  2 

188.108 

2815.7 

S 

136.659 

1486.2 

"  ] 

162  577 

2103  8 

60. 

188.496 

2827.4 

7ft 

187.052 

1494.7 

162.970 

2113.5 

i 

188.888 

2889  2 

^ 

137.445 

1503.3 

163.363 

2128.7 

189.281 

2851.0 

137.887 

1511.9 

163.756 

21:33.9 

189.674 

2862.0 

44. 

138.230 

1520  5 

■  J 

164.148 

2144.2 

h^ 

190.066 

2874  8 

138.023 

1529.2 

164.541 

2154.5 

78 

190.450 

2886.6 

L 

189.015 

1587.9 

164.934 

2164. H 

f4 

190.852 

2898.6 

9f  i 

139.408 

1546.6 

■''4 

165.326 

2175.1 

yk 

191.244 

2010.5 

12 

139.801 

1655.3 

■'  I 

165.719 

2185.4 

61. 

191  687 

2922.5 

ill 

140  194 

1664.0 

166.112 

2195.8 

^ 

192  030 

2934.5 

i 

140.586 

1572.8 

:»:t 

166.504 

2206.2 

192.42:1 

2946.5 

140.979 

1681.6 

) 

166.897 

2216.6 

&^ 

192.816 

2058.5 

46. 

141.372 

1690.4 

'  1 

167.290 

2227.0 

zi 

103.208 

2070.6 

^ 

141.764 

1699.8 

■'K 

167.8*3 

2237.5 

&g 

193.601 

2082.7 

'1 

142.157 

1608.2 

i^4 

168.076 

2248.0 

a 

193.998 

2004.8 

j| 

142.550 

1617.0 

4 

168.488 

2258.5 

104.386 

8006  9 

ll 

142.942 

16:i6.0 

^\ 

168.861 

2269.1 

68. 

194.770 

8010.1 

<l 

148.3:35 

1634.9 

"^-ri 

160.253 

2279.6 

^ 

195.171 

8U81.3 

2 

143.728 

1643.9 

r,i 

169.646 

2290.2 

M 

195.664 

8043.5 

% 

144.121 

1652.9 

1 . 

170.  a39 

2800.8 

s2 

195.957 

8055.7 

46. 

144.513 

1661.9 

^■1 

170,431 

2311.5 

1^ 

196  850 

3068.0 

li 

144.906 

1670.9 

'•^H 

170.824 

2322.1 

78 

196.742 

808»i..^ 

'  < , 

145.299 

1680.0 

'•i 

171.217 

2332.8 

81 

197.186 

8002  6 

' 

14.).  691 

1689.1 

iV  " 

171.609 

2343.5 

78 

197.528 

3104.9 

1 ' ' 
H 

146.064 

1698.2 

H 

172.002 

2354.3 

68. 

197.980 

8117.8 

CIBOUMFERENCES  AND   AREAS  OF   CIRCLES.        Ill 


Diam 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

M^ 

196.313 

81296 

71H 

224.281 

4001.1 

250.149 

4979.5 

^ 

1W.706 

8142.0 

H 

284.624 

4015.2 

» 

250  542 

4995.2 

199.096 

3154.5 

II 

225.017 

4029.2 

% 

2S0.935 

5010.0 

L^ 

199.491 

8166.9 

R 

225.409 

4043.3 

80. 

251.327 

5026.5 

71 1 

199.864 

3179.4 

% 

225.802 

4067.4 

251.720 

5042.3 

^ 

aoo.«77 

8191.9 

72. 

!d26.195 

4071.5 

7' 

252.118 

5058.0 

^  t 

U00.660 

3201.4 

'% 

228.687 

4085.7 

9t  1 

252.506 

5073.8 

C4. 

201  .(XU 

8217.0 

i 

886.980 

4099.8 

■ii 

252.898 

5069. G 

4 

8)1.455 

3229.6 

227.378 

4114.0 

25».201 

5106.4 

aOl.847 

8242.2 

227.786 

4128.2 

\\i 

258.684 

5121.8 

'  v 

202.240 

8254  8 

228.158 

4142.5 

M  I 

254.076 

5187.1 

^ 

202.688 

3267.5 

228.551 

4156.8 

81. 

254  469 

5153.0 

1 14 

208.026 

3280.1 

228.944 

4171.1 

M 

254.862 

5168.0 

'  ''^ 

208.418 

8298.8 

*% 

229.386 

4165.4 

255.254 

5184.9 

'  i 

208.811 

8305.6 

U 

229.7S9 

4199.7 

78 

255.647 

5200.8 

6S. 

204.204 

3318.8 

'•.t 

230.122 

4214.1 

I4 

256.040 

5216.8 

^ 

204.506 

8831.1 

% 

280.514 

4226.5         K 

256.433 

5282.8 

^ 

204.969 

8343.9 

i.i 

230.907 

4242.9 

» 

256.826 

5248.9 

9l  1 

205.882 

3856.7 

f^^ 

231.300 

4257.4 

H 

257.218 

5264.9 

u , 

206.774 

3369.G 

i^t 

231.692 

4271.8 

82. 

257.611 

5281.0 

78 

-•06  167 

8382.4 

""h 

232.065 

4286.3 

A 

258.008 

5297.1 

» 

2U6.5a0 

3395.3 

74 

282.478 

4300.8 

A 

258.396 

5313.8 

H 

206.952 

8406.2 

H 

282.871 

4315.4 

'1 

258.789 

5829.4 

M. 

207.345 

3421.2 

'4 

233.268 

4829.9 

I 

259.181 

5345.6 

^ 

207.736 

3434.2 

H 

233  656 

4344  5 

'1 

259.574 

5361.6 

H 

206.131 

8447.2 

U. 

234.049 

4359.2 

H 

259.967 

5378.1 

H 

208.52S 

3460.2 

^S 

234.441 

4373.8 

% 

260.359 

5394.8 

R 

206.916 

3473.2 

^ 

234. 8:M 

4388.5 

88. 

260.752 

5410  0 

^ 

209.309 

8486.3 

285.227 

4403.1 

H 

261.145 

5426.0 

H 

209.701 

3499.4 

To'"* 

235.619 

4417.9 

H 

261.538 

6443.8 

?2 

210.094 

8512.5 

'k 

286.012 

4432.6 

y 

261.930 

5459.6 

t7. 

210.487 

3525  7 

'1 

236.406 

4447.4 

4 

262.823 

5476.0 

-6 

'4 

210.879 

8538.8 

H 

236.796 

4462.2 

rk 

268.716 

5492.4 

211  272 

8552.0 

I,. 

237.190 

4477.0 

S 

263.106 

5608.6 

^ 

211.665 

S)65.2 

'*l 

237»583 

4491.8 

% 

283.501 

5625.8 

4 

212.058 

3578.6 

ly 

237.976 

4506.7 

84. 

268.804 

5541.8 

<s 

212.450 

3591.7 

-    ^ 

288.868 

4621.5 

H 

264.286 

6658.8 

'^ 

212.843 

8605.0 

70 

238.761 

4536.5 

» 

264. 6T9 

6574.8 

% 

213.236 

8618.8 

1  K 

239.154 

4551.4 

% 

265.072 

5591.4 

68 

218.628 

8631.7 

'l 

239.546 

4566.4 

% 

265.465 

5607.9 

4 

214.021 

8645.0 

''n 

239.989 

4581.3 

1 

266.857 

6624.6 

214.414 

8658.4 

'\,j. 

240.832 

4596.8 

R 

266.250 

5641.2 

i 

214.806 

3671.8 

'''h 

240.725 

4611.4 

H 

266.643 

5657.8 

i 

215.199 

8685.3 

'\ 

241.117 

4626.4 

80 

267.085 

5674.5 

i 

215.592 

3698.7 

241.510 

4641.6 

% 

267.428 

6U91.2 

^ 

215.961 

8712.2 

J« . 

241.903 

4656.6 

267.821 

5707.9 

^ 

216.377 

8725.7 

242.295 

4671.8 

'98 

268.213 

5724.7 

w 

216.770 

3789.8 

7* 

242.688 

4686.0 

2 

268.606 

5741.5 

^ 

217.163 

8752.8 

7I 1 

243.081 

4702.1 

9r 

2C8.9D9 

5758.8 

H 

217.555 

3766.4 

Z9 

243.478 

4717.3 

R 

269.392 

5775.1 

!^ 

217.948 

8780.0 

rk 

243.866 

4732.5 

% 

269.784 

5791.9 

1 

218.311 

3793.7 

» 

244.259 

4747.8 

86 

270.177 

5808.8 

'^ 

218.738 

3807.3 

^ 

244.652 

4763.1 

270.570 

5825.7 

;1 

219  126 

3821.0 

78. 

245. OU 

4778.4 

7^ 

270.962 

5842.6 

^ 

219.519 

8884.7 

H 

245  437 

4798.7 

9s 

271.355 

5859.6 

;o 

819.911 

3'<48.5 

h 

245.830 

4809.0 

79 

271.748 

6876.6 

4 

220.304 

8862.2 

H 

246.222 

4824.4 

78 

272.140 

5898.5 

4 

220.697 

3876.0 

» 

246.616 

4839  8 

8^ 

272.533 

5910.6 

i 

221.000 

8889.8 

n 

247.008 

4855.2 

tZ 

272.926 

5927.6 

i 

221.462 

3908.6 

s 

247.400 

4870.7 

87. 

273.319 

5944.7 

'3 

221.875 

3917.5 

% 

247.793 

4880. 2 

273.711 

6961.8 

3 

222.268 

8881.4 

79. 

248.186 

4901.7 

t2 

274.104 

5978.9 

« 

222.660 

8045.8 

H 

248.579 

4917.2 

9h 

274.497 

5996.0 

71. 

228.058 

8959.2 

^ 

248.971 

4932.7 

1^ 

274.889 

6018.2 

^ 

223.446 

8973.1 

K 

249  364 

4948.3 

tS 

275.282 

6030.4 

228.8I« 

8987.1 

« 

249.757 

4963.9 

94 

275.675 

6047.6 

112 


UATHBMAllCAL  TA13LE8. 


DIam. 

Cfrcum. 

Area. 

Diam. 

Cli*cuni. 

Area. 

Hmm. 

Circuin. 

Arecu 

87% 

2r:tjo«7 

6064  9 

03. 

2H9.027 

0647  € 

301  986 

7!Ki7  1 

88 

27«.4*iO 

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289.419 

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302  378 

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v& 

37».85:i 

6099.4 

C 

289.818 

6683.8 

''B 

;302.771 

7>!«4   9 

lA 

277^6 

6118.7 

ftj  1 

290.206 

6701.0 

l2 

.S03  llU 

7813. S 

'  'M 

877.  (W8 

6134.1 

L . 

290.597 

67-.'0.1 

h\ 

30:4.666 

7S«,'  8 

'  "i 

278  081 

6151.4 

7\\ 

290.990 

6;-88.32 

'i 

8(«  949 

7».M.rt 

1 2 

278. 45M 

6168.8 

Bj 

291.888 

6756.4 

304  .M42 

7«ro.s 

<  4 

'J78.S16 

6186.2 

y|  I 

291.775 

6774.7 

i'^4 

304  734 

73S$>  H 

''Z 

279  209 

6203.7 

98. 

298.168 

6792.8 

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806. 127 

74ll^*  M 

«». 

279. 602 

6221.1 

H 

292.561 

68tl.2 

:^05.520 

74^8  0 

^ 

279.994 

623K.0 

H 

292.954 

6889.5 

i.t| 

305.918 

7447    I 

^ 

280.387 

6350.1 

U 

298.816 

6847.8 

4 

306.805 

74«;ti  V 

a2 

280  780 

6273.7 

7% 

298.789 

6866.1 

''1 

.306.098 

74H.-i  :■% 

ZS 

281.178 

6291.2 

fl 

294.182 

6884.5 

807  091 

75iM   5 

^ 

ySl.wC". 

6  08.8 

n 

294.. •>24 

6902  9 

307.488 

7fi'».S   7 

•>4 

281.958 

6826.4 

H 

294  917 

6921.3 

IIS 

307.876 

754-^  O 

'/i. 

282.351 

6344. 1 

94. 

295  310 

69898 

'\ 

808  289 

7.''.<W   '2 

0 

2H2.748 

6361.7 

295.702 

6058.2 

308.661 

7581.5 

^ 

28:)  ]8tf 

63T9  4 

V 

296  095 

6976  7 

309  054 

76CIO.S 

288.529 

6397.1 

7\\ 

206.488 

6995.3 

.309.447 

765JO    1 

f^ 

28:1921 

6414.9 

12 

296.881 

7013  8 

309  840 

7WIW   5 

^ 

281.814 

6432.0 

Tt 

297.278 

7a3i.4 

.  ? 

310.232 

7tt.%8  9 

2^.707 
£«6J00 

6450.4 

A^ 

297.666 

7051.0 

810.625 

767K  3 

^ 

64682 

7\\ 

298  059 

7069.6 

li;i 

811.018 

7GI>7  7 

285.492 

6486  0 

9o. 

298.451 

7088. '2 

II 

311.410 

7717-1 

91. 

2a%.88B 

6503  9 

L^ 

298.844 

7106.9 

311.803 

TT^ttJ  t$ 

t^ 

286.278 

6521.8 

M 

299.237 

7125.6 

:412  198 

77R6    1 

C 

288.670 

6539.7 

s2 

299  629 

7144.8 

312.588 

7r7r,.6 

ii2 

287.063 

6557.6 

12 

300.022 

7io:).o 

812.981 

7r9r>  ;; 

2 

5-87.456 

6575.5 

zB 

300.415 

7181.8 

313  874 

7814  8 

'^ 

287.848 

6593.5 

a 

300.807 

7200.6 

813  767 

7834   4 

'1 

288.241 

6611.5 

301.200 

7219.4 

1  00 

814.159 

7864.0 

8 

288.634 

6629.6 

90. 

801.598 

7238.2 

BECimALS  OF  A  FOOT  EQUIVALCNT  TO  INCHKS 
AND  FRACTIONS  OF  AN   INCH. 


Inches. 

0 

% 

H 

% 

% 

% 

% 

H 

0 

0 

.01012 

.02083 

.03125 

.01166 

.06208 

.00250 

.mii»i 

1 

.0833 

.09;J7 

.1042 

.1146 

.1250 

.1.354 

.1459 

.15<i3 

2 

.1067 

.ITil 

.1875 

.1979 

.2063 

.2188 

.2292 

2896 

8 

.2500 

.2001 

.2708 

.2813 

.2917 

.3021 

.8125 

.8229 

4 

.83.^3 

.8137 

.3542 

..3646 

.:C50 

..-{854 

.3958 

.40(S8 

5 

.4167 

.4271 

.4:575 

.4479 

.4588 

.4688 

.4792 

.4896 

6 

.5000 

.5104 

.5208 

.5313 

.5417 

.5521 

.5025 

.57"^ 

7 

.5833 

.6937 

.6042 

.6146 

.62.V) 

.6a'>4 

.6159 

.6568 

8 

.6667 

.em 

.6875 

.6979 

.7083 

.7188 

.7292 

.7396 

9 

.7500 

.7604 

.7708 

.7818 

.7917 

.8021 

.8125 

.8.S9 

10 

.«m 

.84:^7 

.8512 

.8646 

.8750 

.88M 

.8958 

.9068 

11 

.9167 

.9271 

.9375 

.9479 

.9583 

.9688 

.9792 

.9696 

CIBCVJIFERBNCBS  OF  CIRCLES. 


113 


8   ! 


m 

V 


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114 


KATHEKATICAL  TABLES. 


liENOTHS  OF  CIBCUIiAB  ARCS. 
(Mk^tpreeu  betns  ffiveii*    Hmdtlis  ofCttrele  =  !•> 

Formula.— Length  of  arc  =        --      X  radius  X  number  of  def^rees. 

RuLB.— Multiply  the  factor  in  table  for  any  given  number  of  degi^tsa  by 
the  radius. 

ExAMPLB.— Given  a  curve  of  a  radius  of  6S  feet  and  an  angle  of  78<*  90'. 
What  is  the  length  of  same  in  feet  ? 

Factor  from  table  for  780 1.8618548 

Factor  from  table  for  aK .0058178 

Factor 1.3671746 

1.8671746X55  =  75.19  feet. 


I>effree8. 

'     Mlnntca. 

^0t71&33 

61 

)  n^^&ofl 

121 

2.11IM}^ 

1 

.M08M8 

68 

LOAiimL 

128 

8.1?^WS7 

% 

.0006818 

*fXMSSt9 

68 

i.vmi^H 

123 

tM^:i^*i 

8 

.0008787 

iMHI82i 

61 

MiTom; 

124 

8    1«*#L^ 

4 

.6011636 

.gmtm 

65 

I  1^4040 

128 

i.1HLe«l6 

6 

.0014M4 

.IHTlif^ 

66 

1  iM«i7:^ 

126 

a.iswiuv 

6 

.0017463 

.1111780 

67 

1   IftKtVOft 

127 

1  SIOMffi 

7 

.0080968 

.1198183 

68 

1    lS4^flE» 

128 

a  ijruosn 

8 

.0083871 

.lATmM 

69 

1.304Ejr« 

199 

^  se5H747 

• 

.ogoiao 

10 

J74tlS& 

70 

1.1217305 

130 

l.lie^^1^!llO 

10 

11 

.l9]fM3 

71 

i  'e?'jin;i,K 

131 

t  iMA.tML3 

U 

.0031808 

Ifl 

.10M»& 

78 

1      ■.   ■  ■  I 

138 

2.lci«c34a 

18 

.0084907 

IS 

78 

<    mt-wvwvm 

133 

;E,  321979 

18 

omrmj 

14 

'f 443441 

74 

1.2915438 

134 

a.M«71l? 

14 

OMu7t4 

lA 

.»1T»M 

76 

136 

2  3^1945 

U 

iMHSAn 

16 

.wnawj 

76 

l!326l&08 

138 

t  S73fl47Jt 

16 

,a(H£6ii 

17 

.IBSTWU 

n 

1.3439086 

137 

2  SUilOll 

17 

OOiMtl 

18 

.5141m:i 

78 

1.3618668 

138 

j!.1(W>£pH 

18 

jtoMsm 

19 

.TSTflt^fl 

79 

1.3788101 

139 

%  imMTi 

19 

OQfiCkMf 

» 

."1 1  \H  \t\  \'f 

80 

1.3868834 

140 

^  4434(110 

80 

JKHUTI 

21 

.KHi,.-,'.'il 

81 

1.4137167 

141 

^mum 

81 

Mnm 

tt 

:iA  ur^Ji 

88 

1.4311700 

148 

«  I7SM75 

88 

.oooaat 

» 

.*iiHi'N 

88 

1.1488833 

143 

t.i9M8(M 

23 

.OOOBfiil 

U 

.IIW7lhP 

84 

1.4660706 

144 

8.613*741 

84 

.OQWlt 

» 

86 

146 

8.65107874 

86 

-ttWllTPf 

S6 

A^lT^'*y 

86 

:  ..-...;__: 

146 

i.Mdiwg 

86 

mi^^\ 

S7 

+ ;  1  ;<.'it 

87 

i-M.S4!^ 

147 

B.flif'rfim-i 

87 

.SMt'imftti 

» 

l-A-Vi;. 

88 

1  J)3&llMr 

148 

2.^*;-!'^«t:! 

88 

.008144V 

S9 

'A^.-\  \\.. 

89 

1  &5XMi»l 

140 

89 

.0004364 

80 

'.■.■■L',.»M^v 

90 

1   SiTCI^WEI 

150 

8.6179990 

80 

.0007816 

31 

.■.JI-'.JL 

91 

l.Mt<249a 

161 

8.6354478 

81 

.0000175 

SS 

■,,,K-*1-,| 

98 

t  QOTNirai 

188 

8.66C9006 

as 

.0003084 

88 

". ;  'rv  .'^ ; 

93 

i.«ji3t.'Vfli 

153 

8.6708588 

88 

34 

I'l;  1 1 1'J 

94 

i^^voBfrn 

164 

2.6878070 

84 

.0098988 

85 

1.    rl-..      ' 

96 

1  65IMM8 

166 

2.7068608 

36 

.0101811 

88 

1 .  ;  h  '  1  . ', 

96 

i.nauii 

166 

m    >Ma».Aa 

86 

.0104780 

87 

u\  ..-.•'■^ 

97 

i.i6«m»4 

157 

S7 

.0107089 

38 

I"' "'.'.■ 

98 

I.JIMOT 

168 

^."ki'y^K 

88 

.0110638 

39 

l',f^|^*!.7^| 

99 

1  TSTS7»f) 

160 

a,776or3a 

80 

.0113446 

40 

\,-\*-\  .1- 

100 

1  utisim. 

160 

%7w^m. 

40 

.0116366 

41 

1      -  ^' 

101 

1  rnsjusw 

161 

twmmi 

41 

.0U99U 

48 

iwwvwow 

102 

1   7Wȣ>.'* 

168 

%^ir{iifA% 

48 

43 

!7501916 

103 

1   7970BSH 

163 

2  lt4iJ4?«7 

48 

.0185082 

44 

.7679449 

104 

}   HI5UT1 

164 

H.wyjioo 

44 

.0187991 

a 

.7853968 

106 

t  ^:>-I,-p*7 

166 

2.»TV793a 

46 

.0130900 

40 

.80)!»516 

106 

L  -..Vh.J>-' 

166 

s^-aiM 

46 

.0133809 

47 

oa/>oA4^ 

107 

k.tmiiiM-^ 

167 

1  SlMiKW 

47 

.0186717 

48 

106 

1.8^9566 

168 

2  KttlMI 

48 

.0139086 

49 

109 

1.9024069 

169 

12  MMOOi 

49 

.0148636 

fiO 

no 

1.9198622 

170 

z  wfhJir*: 

60 

.0146444 

51 

111 

1.9373165 

171 

1  mkfx\M 

61 

.014838& 

68 

112 

1.9647688 

178 

N  ip'LiMfi:! 

68 

.0161862 

63 

"f;.  '1  ■|."i 

113 

1.9782281 

173 

63 

.0164171 

64 

•>ivr  - 

114 

1.9896753 

174 

0     VUUDI*^ 

64 

.0167080 

66 

■y  »i.::i 

116 

8.0071286 

176 

3.0643868 

66 

.0160989 

58 

.yi::sJiHHi 

116 

2.0245819 

176 

8.0717796 

86 

.0188897 

87 

wijii;: 

117 

2  0420352 

177 

8.0892328 

67 

.0166806 

68 

1  MlS.lJ](i 

118 

2.0694886 

178 

8.1066861 

68 

.0168715 

69 

1    flPn-Ttrt 

119 

2.0769418 

179 

3.1241394 

69 

.0171684 

60 

1  i.lTi'A-i. 

120 

2.0943951 

180 

S.1416087 

iO 

.0174633 

LSKGTHS  OF  CIROULAB  AllCS. 


116 


ILKNGTHS  OP  €m€ri<A»  ARCH. 
CBlmmeter  =  1«     Given  tlte  Cbord  mud  Heicl^t  of  tlie  Arc.) 

Bulk  worn.  Uss  or  the  Tabxa.— Divide  the  height  by  the  chord.  Find  in  the 
eolnmn  of  beifrhtii  the  number  equal  to  this  quotient.  Take  out  the  corre- 
spODdtns  number  from  the  column  of  lengths.  Multiply  this  last  number 
by  the  length  of  the  given  chord ;  the  product  will  be  length  of  the  arc. 

1/  the  are  is  ffreaier  than  a  9emicircle,  flrst  And  the  diameter  from  the 
formiila,  Dijun.  =  (square  of  half  chord  -*-  rise)  +  rise;  the  formula  is  true 
whether  the  arc  exceeds  a  semicircle  or  not.  Then  And  the  circumference. 
FYom  the  diameter  subtract  the  given  height  of  arc,  the  remainder  will  be 
height  of  the  smaller  arc  of  the  circle;  find  its  length  according  to  the  rule, 
and  subtract  It  from  the  circumference. 


Hgts. 

Lffths. 

Hgts. 

Lgths. 

Hgts. 

Lgths. 

Hgts. 

Lgths. 

Hgts. 

Lgths. 

.001 

i.ooooe 

.15 

1.06806 

.288 

1.14480 

.386 

1.86288 

.414 

1.40788 

.005 

1.00007 

.168 

1.06061 

.24 

1.14714 

.328 

1.26588 

.416 

1.41145 

.01 

1.00027 

.154 

1.06200 

.842 

1.14951 

.38 

1.26892 

.418 

1.41608 

.015 

1.00061 

.156 

1.06368 

.844 

1.15189 

.832 

1.27196 

.42 

1.41861 

.02 

1.00107 

.158 

1.08580 

.846 

1.15428 

.384 

1.27502 

.422 

1.42221 

.OS 

1.001G7 

.16 

1.06608 

.248 

1.15670 

.386 

1.27810 

.424 

1.42583 

.01 

1.00040 

.162 

1.06858 

.25 

1.15912 

.838 

1.28118 

.426 

1.42945 

.036 

1.00327 

.164 

1.07025 

.252 

1.16166 

.84 

1.28428 

.428 

1.43300 

.01 

1.004S6 

.166 

1.07194 

.254 

1.16402 

.342 

1.28T39 

.43 

1.43678 

.045 

1.00689 

.168 

1.07365 

.256 

1.16660 

.344 

1.29059 

.432 

1.4^039 
1.44405 

.06 

1.00065 

.17 

1.07537 

.258 

1.16899 

.346 

1.80366 

.484 

.005 

1.O0606 

.178 

1.07711 

.86 

1.17150 

.848 

1.29681 

.436 

1.44778 

.06 

1.00057 

.174 

1.07988 

.262 

1.17408 

.85 

1.29907 

.488 

1.46142 

.065 

1.01128 

.176 

1.08066 

.864 

1.17657 

.352 

1.80315 

.44 

1.45613 

.07 

1.01802 

.178 

1.06246 

.266 

1.17912 

.354 

1.30634 

.448 

1.45883 

.0» 

1.01498 

.18 

1.06428 

.268 

1.18169 

.356 

1.80054 

.444 

1.46856 

.08 

1.01098 

.182 

1.08611 

.27 

1.18429 

.358 

1.81276 

.446 

1.46628 

.085 

1.01916 

.184 

1.08797 

.278 

1.18689 

.86 

1.81599 

.448 

1.47008 

.00 

1.02146 

.186 

1.08964 

.874 

1.18951 

.862 

1.81923 

.45 

1.47377 

.005 

1.02889 

.198 

1.O0174 

.876 

1.19214 

.364 

1.82849 

.458 

1.47753 

.10 

1.08646 

.19 

1.00365 

.278 

1.19479 

.366 

1.32677 

.454 

1.48131 

.102 

1.02752 

.192 

1.09557 

.88 

1.19746 

.368 

1.32905 

.466 

1.48609 

.101 

1.08860 

.194 

1.09752 

.282 

1.90014 

.37 

1.38234 

.458 

1.48689 

.106 

1.02970 

.196 

1.09949 

.284 

1.20284 

.378 

1.33564 

.46 

1.49269 

.108 

1.0:1062 

.198 

1.10147 

.286 

1.2a5.\5 

.374 

1.33896 

.462 

1.49651 

.11 

1.03196 

.20 

1.10847 

.288 

1.20827 

.376 

1.34229 

.464 

1.60088 

.m 

1.03312 

.202 

1.10548 

.29 

1.21102 

.378 

1.34568 

.466 

1.S0416 

.114 

1.03480 

.204 

1.10752 

.292 

1.21377 

.88 

1.34899 

.468 

1.60600 

.tio 

1.08561 

.206 

1.10968 

.294 

1.21664 

.382 

1.86237 

.47 

1.M185 

.118 

1.08672 

.208 

1.11165 

.296 

1.21938 

.384 

1.35575 

.478 

1.51571 

.18 

1.09797 

.21 

1.11374 

.298 

1.22213 

.386 

1.35914 

.474 

1.51958 

.128 

1.09928 

.212 

1.11584 

.30 

1.22495 

.388 

1.86254 

.476 

1.52346 

.194 

1.04061 

.214 

1.11796 

.802 

1.22778 

.89 

1.36596 

.478 

1.62736 

.126 

1.04181 

.216 

1.12011 

.804 

1.23068 

.392 

1.86939 

.48 

1.53126 

.128 

1  04818 

.218 

1.12226 

.806 

1.23849 

.394 

1.37288 

.488 

1.58518 

.13 

1.04447 

.22 

1.12444 

.308 

1.23686 

.896 

1.87628 

.484 

1.58910 

.IS 

1  04584 

.222 

1.12664 

.81 

1.28926 

.398 

1.37974 

.486 

1.54308 

.184 

1.04722 

.824 

1.12886 

.813 

1.24216 

.40 

1.38322 

.488 

1.54696 

.130 

1  04862 

.820 

1.18108 

.814 

1.24507 

.402 

1.88671 

.49 

1.55091 

.196 

1  06008 

.828 

1.13881 

.816 

1.24801 

.404 

1.39021 

.492 

1.55487 

.14 

1  05147 

.28 

1.18657 

.318 

1.25095 

.406 

1.39372 

.494 

1.65854 

.142 

1.'05298 

.2S8 

1.18786 

!   .88 

1.25391 

.408 

1.89784 

.496 

1.66282 

144 

1  06441 

.284 

1.14015 

.822 

1.25689 

.41 

1.40077 

.496 

1.66681 

.145 

1.06691 

.286 

1.14247 

.824 

1.85988 

.412 

1.40438 

.50 

1.57080 

.148 

1.06748 

1 

1               1 

116 


MATHEMATICAL  TABLB3. 


AREAS  OF  THB  8BOHBNT8  OF  A  €IB€I<S. 

(Illameter  =  1 :  Alse  or  Versed  Sine  In  parts  of  nimmeter 
fcelugr  Stveu.) 

RDI.K  SOR  UsB  or  tBB  TABi*B,~Dlvide  the  rise  or  height  of  the  segment  by 
the  diameter  to  obtain  the  Tersed  sine.  Multiply  the  area  ih  the  table  coi> 
responding  to  this  yeraed  sine  by  the  square  of  the  diameter. 

If  the  aegmtnt  escceedt  a  «emictrdc  its  area  is  aroa  of  oirole*area  of  seg- 
ment whose  rise  is  (diam.  of  circle— rise  of  giveo  segm^it). 

Given  chord  and  rifie,  to  And  diameter.  Diam.  s  (square  of  half  chord  •«- 
rise)  ■+  ri«e.  The  half  chord  in  a  mean  proportional  between  the  two  parts 
into  which  the  ohord  divides  the  diameter  which  is  perpendicular  to  f  u 


V«r»d 
Sine. 

Araiu 

VwMd 

Sine. 

Area. 

Vetwd 
Sine. 

Are.. 

Vened 

Sine. 

Ana. 

VmmiI 

Sine. 

An*. 

.001 

.00004 

.054 

.01646 

.107 

.04514 

.16 

.08111 

.218 

.ia2:i5 

.004 

.00018 

.056 

.01691 

.108 

.04576 

.161 

.08185 

.914 

.18817 

.Oft3 

.00038 

.056 

.01737 

.109 

.04638 

.168 

.08858 

.216 

.18399 

.004 

.00034 

.057 

.01783 

.11 

.01701 

.163 

.08338 

.216 

.18481 

.005 

.00047 

.058 

.01830 

.111 

.04763 

.164 

.08406 

.217 

.18S68 

.006 

.00068 

.069 

.01877 

.118 

.04836 

.165 

.08480 

.918 

.12646 

.007 

.00078 

.06 

.01934 

.113 

.04889 

.166 

.08654 

.919 

.187^ 

.008 

.00005 

.061 

.01973 

.114 

.04958 

.167 

.08689 

.89 

.19611 

.009 

.00118 

.068 

.08080 

.115 

.05016 

.168 

.08704 

.981 

.198»1 

.01 

.00183 

.068 

.08068 

.116 

.06080 

.169 

.08779 

.999 

.12977 

.011 

.00153 

.064 

.08117 

.117 

.05146 

.17 

.08854 

.993 

.18060 

.018 

.00175 

.066 

.08166 

.118 

.06800 

.171 

.08939 

.994 

.18144 

.018 

.00197 

.066 

.08815 

.119 

.05874 

.ITS 

.09004 

.986 

.18927 

.014 

.0088 

.067 

.08865 

.19 

.05838 

.178 

.09080 

.996 

.18811 

.015 

.00844 

.068 

.08315 

.131 

.05404 

.174 

.09155 

.997 

.18805 

.016 

.00868 

.069 

.08366 

.133 

.03469 

.175 

.09331 

.998 

.18478 

.017 

.00891 

.07 

.08417 

.183 

.05585 

.ITO 

.09307 

.999 

.135G8 

.018 

.00*8 

.071 

.0i468 

.134 

.05600 

.177 

.09:384 

.33 

.18646 

.019 

.00347 

078 

.08580 

.136 

.06666 

.m 

.09460 

.931 

.137^1 

.0» 

.00375 

.076 

.08571 

.136 

.05783 

.179 

.09587 

.289 

.18815 

.041 

.0040:3 

.074 

.08684 

.127 

.05799 

.18 

.09613 

.383 

.13900 

.Oti 

.00438 

.075 

.08676 

.138 

.05866 

.181 

.09690 

.384 

.18984 

.0^3 

.00468 

.076 

.03789 

.139 

.05938 

.188 

.09767 

.385 

.14069 

.094 

.00498 

.077 

.03788 

.18 

.06000 

.188 

.09^5 

.286 

.14154 

.005 

.00SS3 

.078 

.08886 

.181 

.06067 

.184 

.09938 

.987 

.14239 

.o-w 

.00655 

.079 

.03889 

.133 

.06186 

.186 

.10000 

.988 

.148,*4 

.087 

.00587 

.08 

.08943 

.188 

.06808 

.186 

.10077 

.989 

.14400 

.0« 

.00619 

.081 

.08998 

.184 

.06271 

.187 

.10155 

.94 

.144W 

.029 

.00658 

.088 

.08053 

.185 

.06339 

.188 

.10933 

.941 

.14580 

.06 

.00687 

.063 

.08108 

.186 

.06407 

.189 

.10313 

.949 

.14666 

.081 

.00781 

.084 

.08168 

.137 

.06476 

.19 

.10890 

.343 

.147^1 

Mi 

.00756 

.085 

.03819 

.138 

.06545 

.191 

.10469 

.944 

.14S17 

.OW 

.00791 

.086 

.03875 

.139 

.06614 

.193 

.10547 

.846 

.149M8 

.081 

.00887 

.087 

.08331 

.14 

.06683 

.103 

.10686 

.346 

.l.WOO 

.085 

.00864 

.088 

.08887 

.141 

.06758 

.m 

.10705 

.247 

.15095 

.096 

.00901 

.089 

.08444 

.143 

.06832 

.195 

.10784 

.248 

.15188 

.067 

.009:18 

.09 

.08.101 

.143 

.06892 

.196 

.10864 

.949 

.lo268 

.088 

.00976 

.091 

.a3559 

.144 

.06968 

.197 

.10948 

.95 

.16866 

.0?» 

.01015 

.098 

.08616 

.145 

.07083 

.198 

.11093 

.851 

.16441 

.04 

.01054 

.093 

.08674 

.146 

.07103 

.199 

.11108 

.969 

.15606 

.041 

.01098 

.094 

.08788 

.147 

.07174 

.9 

.11182 

.963 

.15615 

.048 

.01133 

.096 

.03791 

.148 

.07845 

.301 

.11362 

.964 

.1571)8 

.048 

.01173 

.096 

.03850 

.149 

.07316 

.308 

.11843 

.965 

.157W 

.044 

.01814 

.097 

.03909 

.15 

.07887 

.308 

.11493 

.956 

.15876 

.045 

.01355 

.096 

.08968 

.151 

.07469 

.9M 

.11504 

.857 

.15964 

.046 

.01897 

.099 

.04088 

.158 

.07531 

.305 

.11584 

.938 

.16051 

.047 

.01339 

.1 

.04087 

.158 

.0760} 

.906 

.11665 

.959 

.16189 

.048 

.01888 

.101 

.04148 

.164 

.07675 

.907 

.11746 

.96 

.lftM6 

.049 

.01435 

.108 

.04208 

.l.'iS 

.07747 

.808 

.11887 

.961 

.16314 

.06 

.01468 

A(Xi 

.04-JG9 

.156 

.07819 

.809 

.11908 

.263 

.16408 

.051 

.01518 

.104 

.04;^30 

.157 

.07898 

.21 

.11990 

.908 

.16490 

.052 

.01556 

.105 

.04391 

.158 

.07965 

.211 

.12071 

.264 

.165T8 

.068 

.01601 

.106 

.04458  1 

.169 

.08038 

.218 

.18153 

.265 

.16666 

AKBA8    OF  THE  SEGMBKT8  OF  A  CIRCLE.         Ill7 


ttrmd 

Vencd 

t     ^ 

Vened 

Vencd 

^.M. 

Am. 

StD«L 

Area. 

SilM. 

At»«. 

Sin*. 

Anm, 

Sin*. 

An*. 

JG6 

.iers6 

.813 

.»016 

.36 

.25456 

.407 

.30024 

.454 

.34676 

XT 

.16843 

.814 

.31108 

.861 

.85551 

.408 

.80122 

.455 

.84770 

Sffi 

.10K» 

.315 

.aUK)! 

.862 

.25647 

.409 

.8O.>20 

.156 

.84876 

J0» 

.17UM 

.316 

.91294 

.863 

.2574.3 

.41 

.30319 

.457 

.»1875 

J?7 

.17100 

.317 

.01.387 

.364 

.25839 

.411 

.30417 

.458 

.85076 

.n 

.17198 

.818 

.81480 

.9bC 

.25936 

418 

.80516 

.459 

.85175 

.872 

.i?«r 

.319 

.31578 

.366 

.418 

.80'-.14 

.46 

.85874 

//n 

.17376 

.88 

.31667 

.367 

.26128 

.414 

.80712 

.401 

.?5874 

.274 

.17465 

.881 

.31760 

.868 

.26:e5 

.415 

.80811 

.462 

.86474 

J873 

.I75S4 

.88:2 

.91868 

.860 

.26:ii»l 

.416 

.80910 

.463 

.35673 

.«7B 

.175*4 

.883 

.31M7 

.37 

.26418 

.417 

.31008 

.404 

.85673 

.2:7 

.17738 

.884 

.:9040 

.871 

.26514 

.418 

.81107 

.405 

.85778 

.27S 

.17828 

.885 

.8SJ84 

.878 

.96611 

.419 

.31205 

.406 

.35873 

jrrv 

.1791« 

.826 

.8^^ 

.73 

.96708 

.42 

.31.304 

.467 

.35972 

JJ9 

.18009 

.8*7 

.3S8S9 

.374 

.26805 

.421 

.31403 

.468 

.36072 

.•>1 

.180M 

.888 

.32416 

.375 

J»901 

.428 

.SLVW 

.409 

.86172 

.«J 

.18188 

.889 

.36509 

.376 

.26098 

.423 

.31600 

.47 

.36272 

JW3 

ASJ72 

.88 

.«3003 

.877 

.270a'i 

.424 

.81(599 

,471 

.86872 

.5M 

.18383 

.881 

.38697 

.378 

.27192 

.425 

.31798 

.472 

.36471 

.2S5 

.184.U 

.882 

.32799 

.879 

.a7J89 

.428 

.31597 

.473 

.36871 

.^ 

.18548 

.883 

.««» 

.88 

.87386 

.427 

.31996 

.474 

.86671 

Jf!7 

.18633 

.884 

.38980 

.881 

.27488 

.428 

.32095 

.475 

.36771 

J2» 

.I8r» 

.885 

.88074 

.382 

.27560 

.429 

.82194 

.476 

.86871 

.2» 

.18814 

.886 

.881G0 

.883 

.27878 

.43 

.88293 

.477 

.80971 

JS 

.18005 

.887 

.83308 

.384 

.27776 

.431 

.32303 

.478 

.87071 

^n 

.18896 

.888 

.88358 

.885 

.37872 

1    .488 

.32491 

.479 

.87171 

.292 

.19086 

.889 

.83468 

.386 

.87969 

.4.38 

.32590 

.48 

.37270 

;33 

.19177 

.84 

.83547 

.887 

.98067 

,    .434 

.32689 

.481 

.87870 

^4 

.19868 

.841 

.88642 

.888 

.28164 

.436 

.82788 

.482 

.3747D 

.•35 

.19860 

.848 

.83787 

.889 

.28268 

.436 

.328^7 

.488 

.87570 

•296 

.lfM51 

.343 

.83838 

.89 

.88359 

1    .4.37 

.82987 

.484 

.37670 

.387 

.1954)2 

.844 

.83987 

.891 

.884.57 

.438 

.33086 

.485 

.3'iTrO 

JS» 

.19634 

.845 

.84088 

.892 

.28554 

,   .439 

.83185 

.486 

.87870 

.2» 

.19785 

.346 

.34117 

.893 

.28652 

1   .44 

.38284 

.487 

.37970 

.3 

.10817 

.347 

.»4312 

.894 

J»750 

1    .441 

.83:^84 

.488 

.88070 

.»! 

.19908 

.848 

.84307 

.895 

.28848 

1    .448 

.33483 

.488 

.88170 

;m 

.90000 

.849 

.84408 

.896 

.28945 

.448 

.33582 

.49 

.88270 

.«3 

.90092 

.85 

.94486 

.897 

.29(M3 

.444 

.ai682 

.491 

.88370 

.304 

.90184 

.861 

.84598 

.898 

.29141 

.446 

.33781 

.498 

.88470 

^V5 

jaQS76 

.852 

.84680 

.899 

.292:» 

,   .446 

..3;^880 

.498 

.88570 

.908 

.80368 

.853 

.14781 

.4 

.298:17 

.447 

.a3980 

.494 

..38670 

^ 

J80460 

.354 

.84880 

.401 

.2W35 

1    448 

.34079 

.495 

.38770 

.365 

.84976 

.402 

.89538 

.449 

.34179 

.496 

.88870 

.«g 

.20645 

.»i6 

.85071 

.408 

Jidm 

.45 

.84278 

.497 

.38970 

;)i 

.90738 

.867 

.85167 

.404 

.89729 

j   .4.M 

.34378 

.498 

.39070 

.311 

jaoeso 

.858 

.95368 

.405 

.298-^ 

1    .4.18 

.34477 

.499 

.39170 

.Sid 

.809-^ 

.859 

.85360 

.406 

.29926 

.4.58 

.34.^77 

.5 

..39270 

For  rules  for  finding  the  area  of  a  tegment  see  Mensuration,  page  99. 


118  MAtHEMATlCAL  TABLES. 

SPHERES. 

(Some  errors  of  1  In  the  last  figure  only.    Fi-om  Tratjtwine.) 


TMam 

Sur. 

Solid- 

uiAm. 

faee. 

ity. 

1-^ 

.00807 

.00002 

1-ie 

.01287 

.00018 

8-«S 

.02761 

.00048 

^ 

.04909 

.00102 

.07670 

.00200 

8-16 

.11045 

.00845 

7-32 

.16088 

.00548 

^ 

.19685 

.00818 

.24851 

.01165 

5-16 

.80680 

.01598 

11-82 

.87128 

.02127 

isJ 

.44179 

.02761 

.51848 

.03511 

7-16 

.00182 

.04886 

15-88 

.69028 

05898 

^^ 

.78540 

!06545 

.99403 

.09319 

ii-?i 

1.2278 

.12783 

1.4849 

.17014 

IS-^ 

1.7671 

.22069 

2.0739 

.28084 

,5-?i 

2.4058 

.85077 

2.7611 

.43148 

1. 

8.1416 

.52360 

1-16 

8.5466 

.63804 

s-ll 

8.9761 

.74551 

4.4801 

.87681 

ja 

4.9068 

1 .02^i7 

5.4119 

1.1839 

T-?i 

5.9896 

1.3611 

6.4919 

1.5558 

>.\i 

7.0686 

1.7671 

7.6699 

1.9974 

itM 

8.2957 

2.2468 

8.9461 

2.5161 

li-^ 

9.6211 

2.8062 

10.321 

8.1177 

15-li 

11.044 

3.4514 

11.798 

3.8063 

t. 

12.566 

4.1868 

1-16 

18.304 

4.5939 

^11 

14.188 

5.0248 

15.083 

5.4809 

^^ 

15904 

6.9641 

16.800 

6.4751 

r-?i 

17.781 

7.0144 

18.666 

7.5829 

H 

19.635 

8.1813 

»-ltt 

20.629 

8.8108 

11-16 

21.648 

9.4706 

22.691 

10.164 

18-?^ 

28.758 

10.880 

24.890 

11.649 

15-?l 

25.967 

13.448 

27.109 

18.272 

8. 

88.274 

14.187 

1-16 

29.465 

15.080 

^11 

80.680 

15.979 

81.919 

16.957 

Diam. 


Sur- 
face. 


Solid. 

ity. 


17.974 
19.031 
20.129 
21.268 
22.449 
28.674 
24.942 
26.254 
27.611 
29.016 
80.466 
81.965 
33.510 
36.751 
40.196 
48.847 
47.718 
51.801 
56.116 
60.668 
65.450 
70.482 
75.767 
81.306 
87.118 
93.180 
99.541 
106.18 
118.10 
120.81 
127.88 
135.66 
148.79 
152.25 
161.03 
170.14 
179.59 
180.89 
199  53 
210.08 
220.89 
282.18 
348.73 
255.72 
268.08 
280.85 
294.01 
807.58 
321.56 
835.95 
350.77 
360.02 
381.70 
897.83 
414.41 
431 .44 
448.92 
466.87 
485.81 


Dlam. 


0    % 
10. 


11. 


12. 


18. 


14. 


15. 


16. 


18. 


19. 


20. 


21. 


22. 


Sur- 
face. 


306.86 
814.16 
822.06 
830.06 
838.16 
846.86 
354.66 
868.05 
871.54 
880.18 
888.83 
897.61 
406.49 
415.48 
424.50 
438.73 
448.01 
452.89 
471.44 
490  87 
510.71 
580.93 
551.55 
5TO.55 
593.05 
615.75 
637.96 
660.52 
683.49 
706  85 
730.68 
754.77 

rr9.82 

804.25 
829.57 
855.29 
881.42 
907.98 
934.88 
962.12 
989.80 
1017.9 
1046.4 
1075.2 
1104.5 
1134.1 
1164.2 
1194.6 
1225.4 
1256.7 
1288.8 
1320.3 
1852.7 
1385.5 
1418.6 
1462.2 
1486.2 
1520.5 
1655.8 


Solid- 
ity. 


501.21 
58:{.G0 
543  48 
503  m 
584.74 
606  13 
6:i8.04 
650.46 
673.42 
696.91 
7^^.95 
745.51 
770. M 
796.83 
823  58 
640.40 
8TC.79 
904  78 
962.  r.2 

iafci.7 

1085.8 
1150.3 
1218.0 
1288.8 
13G1 .2 
1486.8 
1515.1 
1596.8 
1680.8 
1767.2 
1857.0 
1949.8 
2045.7 
|2144.7 
2:246.8 
.2862.1 
2460.6 
2572.4 
12687.6 
12806.2 
2928.2 
|3a>8.6 
13182.6 
3815.8 
,3451 .5 
3591.4 
3735.0 
13882.5 
4083.7 
4188.8 
4847.8 
14510.9 
4677.9 
4849  1 
5024.8 
5208.7 
5387.4 
5575.3 
5767.6 


SPHERES. 


119 


flPU  lUftE»-<Cbnf  IniMd.) 


Diam. 

Sur- 
face. 

Solid- 
ity. 

Diam. 

Sur- 
face. 

Solid- 
ity. 

Diam. 

Sur- 
face. 

Bolid- 

tty. 

*^ 

150C.4 

6064.1 

«)   H 

5158.1 

84788 

70    H 

15G15 

183471 

1«S6.0 

6165.8 

41.'' 

5881.1 

86067 

71.  ^ 

15687 

187408 

«. 

1661. 0 

6870.6 

H 

5410.7 

87488 

H 

16061 

191880 

4 

1696.8 

6S80.6 

42.  ^ 

6541.9 

88792 

72. 

16886 

196488 

:2 

1785.0 

6796.8 

H 

5674.5 

40194 

H 

16518 

199582 

s 

1778.1 

7014.8 

43. 

5808.8 

41680 

78. 

16742 

908689 

24. 

1800.6 

7288.8 

H 

5944.7 

48099 

^ 

16978 

80790S 

t£ 

1847.5 

7466.7 

44. 

6088.1 

44608 

74." 

17804 

818175 

L 1 

1885.8 

7700.1 

K 

6S21.2 

46141 

K 

17487 

816605 

m 

1984.4 

7088.8 

45. 

6861.7 

47718 

75.  " 

17678 

880894 

». 

1968.5 

8181.8 

H 

6608.9 

40681 

^ 

17906 

225841 

'4 

900S.9 

8429.2 

46. 

6647.6 

60965 

76." 

18146 

889848 

'Hi 

2042.8 

8688.0 

H 

6792.9 

58645 

K 

18886 

284414 

iS 

8083.O 

8980.9 

47. 

6939.9 

54362 

77. 

18626 

289041 

». 

8128.7 

9d02.8 

M 

7TJ88.3 

66115 

H 

18809 

848786 

i,4 

8164.7 

9470.8 

48. 

7288.8 

57006 

78." 

19114 

848475 

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2206.2 

9744.0 

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7«9.9 

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K 

19860 

868884 

Ik 

8848.0 

looee 

49. 

7543.1 

61601 

79. 

19607 

858155 

27. 

2890.2 

10806 

H 

7697.7 

63506 

H 

19656 

868068 

M 

2838.8 

10595 

50. 

7854.0 

65450 

80. 

80106 

268068 

4 

2875.8 

10889 

K 

8011.8 

67488 

H 

80868 

278141 

H 

8419.2 

11189 

61. 

8171.2 

60456 

81. 

80618 

278868 

». 

8468.0 

11494 

» 

8882.3 

71519 

H 

80807 

288447 

iA 

2807.2 

11905 

68. 

8494.8 

78682 

88. 

81124 

888606 

!^  1 

8651.8 

12181 

H 

8658.9 

75767 

H 

81388 

894010 

i|i£ 

2596.7 

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68. 

8824.8 

77952 

88. 

81643 

899388 

». 

8642.1 

12770 

H 

8992.0 

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^ 

81904 

804881 

H 

8887.8 

18108 

64. 

9160.8 

88448 

84. 

32167 

810340 

j4 

8784.0 

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9881.2 

84760 

H 

88432 

815915 

^ 

2780.6 

18787 

66. 

9508.2 

87114 

86.  " 

88698 

881566 

8D. 

8887.4 

14187 

K 

9676.8 

89511 

H 

88966 

887864 

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56.  ^ 

9852.0 

91958 

86. 

83285 

888089 

n 

8988.5 

14866 

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10029 

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H 

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888888 

S 

2970.6 

15284 

67. 

10907 

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83779 

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SI. 

8019.1 

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850771 

8068.0 

15079 

68. 

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102161 

88. 

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£ 

8166.9 

16758 

59. 

10936 

107536 

89. 

24885 

869122 

«. 

8817.0 

17157 

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lirJ8 

110294 

H 

26165 

875878 

:^ 

ai«7.4 

17868 

60. 

11810 

118098 

90. 

25447 

381704 

"11 

8818.8 

17974 

^ 

11499 

115949 

^ 

25780 

888102 

^ 

8860.6 

18892 

61. 

11090 

118847 

91. 

26016 

804570 

as. 

3481.8 

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H 

11882 

181794 

H 

26802 

401109 

H 

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62. 

ijore 

124789 

92.  " 

86590 

407781 

-, 

8586.7 

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H 

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4071.5 

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13685 

150538 

96. 

28958 

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M 

4186.5 

85461 

H 

13893 

158980 

M 

29255 

470684 

ST. 

4800.9 

86528 

67. 

14106 

157480 

W. 

29559 

477874 

H 

4417.9 

27612 

H 

14814 

161032 

M 

89665 

485802 

38. 

4586.5 

88781 

68. 

14527 

164637 

98. 

8017^2 

492808 

H 

4656.7 

29880 

H 

14741 

1(W«95 

>li 

30481 

500888 

89. 

4778.4 

81059 

69. 

14957 

172007 

99. 

80791 

606047 

M 

4901.7 

SisSTO 

H 

15175 

1T5774 

^ 

81108 

516785 

40. 

50S6.5 

83610 

70. 

15394 

17^595 

100.  " 

81416 

828598 

120 


MATHEMATICAL  TABLES. 


contehts  in  oreio  fbet  anb  ir.  s.  oali^ons  of 

PIPKS  AND  Ciri.INDKR8  OF  VAHIOU8  DIABKSTS1K8 
ANB  ONK  FOOT  IN  liENGTH. 


1  gallon  =  231  oublo  inches.    1  cubic  foot 

=  7.4805  gaUoDS. 

For  1  Foot  in 

For  1  Foot  in 

For  1  Foot  in 

o 

Length. 

a 

Lenf?th. 

•Length. 

5*^ 

Cubic  Ft. 
also  Area 

U.S. 
Oals., 

281 
Cu.  In. 

Cubic  Ft. 
also  Area 

u.a 

Oats., 

231 
Cu,  In. 

Oublo  Ft. 
also  Area 

U.S. 
Oals.. 

231 
Cu.Id. 

in  Sq.  Ft. 

in  Sq.  Ft. 

in  Sq.  Ft. 

5-la 

.OOOB 

.0025 

en 

.2486 

1.859 

19 

1.969 

14.73 

.0005 

.004 

7 

.2878 

1.909 

19^ 

2.074 

15.51 

T?f6 

.0006 

.0067 

7U 

.28117 

2.146 

20 

2.182 

16.a2 

.001 

,0078 

TJ^i 

.8068 

2.296 

20^ 

2.292 

17.15 

H 

.0014 

.0102 

7* 

.8276 

2.45 

21 

2.406 

17.99 

9-16 

.0017 

.0120 

8 

.8491 

2.611 

21^ 

2.881 

18.86 

H 

.0031 

.0150 

^ 

.8712 

2.777 

22 

2.640 

19.7.5 

1&« 

.0036 

.0108 

* 

.8941 

2.948 

22^ 

2.761 

80.66 

,&. 

.0061 

.0280 

* 

.4176 

3.126 

28 

2.885 

81.58 

.0036 

.0269 

9 

.4418 

8.805 

88H 

8.012 

22.58 

ll^l« 

.0042 

.0312 

m 

.4667 

8.491 

94 

8.149 

23.50 

.0048 

.0850 

^y} 

.4922 

8.682 

96 

8.409 

25.50 

1 

.0066 

.0406 

m 

.5186 

8.879 

26 

8.687 

27.68 

iM 

.0066 

.0686 

10 

.5454 

4.08 

27 

3.976 

29.74 

iS 

.0128 

.0918 

io« 

.5780 

4.286 

28 

4Ji76 

81.99 

19< 

.0167 

.1240 

i^ 

.6018 

4.496 

29 

4.687 

84.81 

8 

.0918 

.1682 

.6808 

4.715 

80 

4.909 

86.78 

3^ 

.0^6 

.2068 

11 

.66 

4.937 

81 

6.841 

89.21 

S^ 

.0641 

.2550 

l1^ 

.6908 

5.164 

88 

6.585 

4I.7S 

2% 

.0412 

.3065 

.7m 

6.896 

88 

6.940 

44.48 

8 

.0491 

.8672 

ii9i 

.7580 

6.683 

84 

6.805 

47.16 

.0576 

.4809 

18^ 

.78.V4 

5.8i1( 

86 

6.681 

49.96 

3yi 

.0668 

.4996 

12^ 

.8522 

6.375 

36 

7.069 

62.88 

89i 

.0767 

.6788 

18 

.9218 

6.806 

87 

7.467 

55.86 

4 

.0878 

.6528 

18« 

.904 

7.436 

88 

7.87« 

58.92 

^ 

.0986 

.7360 

14 

1.069 

7.997 

89 

8.296 

62.06 

4t 

.1104 

.8268 

14^ 

1147 

8.578 

40 

8.727 

65.28 

^ 

.1881 

.9206 

18 

1.227 

9.180 

41 

9.168 

68.68 

r* 

.1864 

1.020 

16^ 

1.810 

9.801 

42 

9.6i1 

71.97 

5M 

.1506 

1.125 

16 

1.896 

10.44 

48 

10.066 

75.44 

^ 

.1650 

1.234 

16^ 

1.486 

11.11 

44 

10.560 

?8.99 

.1808 

1.340 

17 

1.676 

11.79 

45 

11.045 

82.68 

r 

.1968 

1.469 

\7% 

1.670 

12.49 

46 

11.541 

86.88 

§1 

.2131 

1.594 

18^ 

1.768 

18.28 

47 

18.048 

90.18 

.2804 

1.7*4 

18« 

1.867 

18.06 

48 

12.666 

94.00 

To  find  the  capacity  of  pipes  greater  than  the  largent  given  In  the  fable, 
look  in  the  table  for  a  pipe  of  one  half  the  ^iven  sixe,  and  multiply  its  capac- 
ity by  4;  or  one  of  one  third  its  siee,  and  nuiliiply  its  capacity  by  9,  etc. 

To  find  the  weight  of*water  in  any  of  the  given  sizes  multiply  the  capacity 
In  cubic  feet  by  62^  or  the  gallons  by  M^,  or,  if  a  doner  approximation  m 
required,  by  the  weight  of  a  cubic  foot  of  water  at  the  actual  temperature  in 
the  pipe. 

Oiven  the  dimensions  of  a  cylinder  in  inches,  to  find  its  capacity  in  U.  8. 
gallons:  Square  the  diameter,  multiply  by  the  length  and  by  .OOCM.  ltd  z^ 
d«  X  .7864  X  I 


diameter,  I  ^  length,  gallons  =     - 


IMl 


=  .0034dn. 


CAPACITY  OF  CYLINDRICAL  VESSELS. 


121 


CTI«IND»I€AI.  TBMBLS,  TANKS,  0I9TBBN8,  ST€« 

]HaBiet«r  in  Feet  mod  Incites,  Area  In  Square  Feet,  and 
IT.  8.  Gallons  Capacity  for  One  Foot  In  Depth* 


1  gallon  =  3Sl  cubic  inches  : 


1  ciibic  foot 
7.4805 


=  0.18868  cubic  feet. 


Diam. 

Area. 

Gals. 

DIam.  ' 

Area. 

Gals. 

DIam. 

Area. 

Gals. 

Fi.  In. 

Sq.ft. 

Ifoot 

Ft.  In. 

Sq.ft. 

Ifoot 
depth. 
1^66 

Ft.  In. 

Sq.ft. 

Ifoot 
depth. 
2120.9 

I 

.785 

5    8 

25.22 

19 

288.53 

1    1 

.g8;2 

6.89 

5    9 

25.97 

194.25 

19 

291.04 

2177.1 

1    i 

1.069 

8.00 

5  10 

26  78 

199.92 

19 

298.65 

22S4.0 

1    3 

1J887 

9.18 

5  11 

27.49 

205.67 

19 

806.86 

2291.7 

1*  4 

1.306 

10.44 

28.27 

211.51 

20 

314.16 

2360.1 

1    5 

1.576 

11.79 

6    3 

80.68 

229.50 

20 

3J2.06 

2409.2 

1    6 

1.767 

13.22 

0    6 

83.18 

248.28 

20 

330.06 

2469.1 

I    7 

1.969 

14.73 

6    9 

35.78 

267.60 

20 

88816 

2529.6 

1    8 

2.1&2 

16.32 

38.48 

287.88 

21 

:M6  36 

2591.0 

1    9 

2.405 

1799 

7    8 

41.28 

808.81 

21 

354.66 

26C3.0 

1  10 

2.640 

19.75 

7    6 

44.18 

8*).49 

21 

868.05 

2715.8 

1  U 

2.885 

21.68 

7    9 

47.17 

852.88 

21 

871.54 

-2779.3 

S 

3.14;i 

23.60 

8 

50.27 

876.01 

22 

.380.18 

2843.6 

i   i 

8.409 

25.50 

8    8 

53.46 

399.88 

22 

888.82 

2908.6 

a  2 

8.687 

27.58 

8    6 

56.75 

424.48 

22 

397.61 

a)74.3 

2    3 

8.976 

29.74 

8    9 

60.18 

449,82 
47^89 

22 

406.49 

3040.8 

2    4 

4.276 

81.99 

9 

63  62 

28 

415.48 

3J08.0 

2    5 

4387 

8181 

9    8 

67.20 

602.70 

23 

424.56 

8175.9 

3  e 

4.909 

86.72 

9    6 

70.88 

680  24 

23 

438.74 

3244.6 

2    7 

5.:»ll 

39.21 

9    9 

74.66 

558.51 

23 

448  01 

8314.0 

2    8 

5l565 

41.78 

10 

78.54 

887.52 

24 

452.89 

8884.1 

2    9 

5.940 

44.43 

10    8 

83.62 

617.26 

24 

401.86 

3455.0 

2  10 

6.305 

47.16 

10    6 

86.59 

647.74 

24 

471.44 

8626.6 

2  11 

6.081 

49.98 

10    0 

90.76 

678.95 

24 

481.11 

8598.9 

3 

7.069 

52  88 

11 

95.08 

710.90 

25 

490.87 

8672.0 

3    1 

7.467 

65.86 

11    8 

99.40 

748.58 

25 

500.74 

3745.8 

S    2 

7.876 

68.09 

11    6 

108.87 

776.90 

25 

510.71 

8820  8 

8    3 

8.296 

62.06 

11    9 

108.43 

811.14 

25 

520.77 

3895.6 

3    4 

8.727 

65.28 

12 

113.10 

846.03 

26 

580.93 

8971.6 

3    5 

9.16S 

66.58 

12    8 

117.86 

881.65 

26 

641.10 

4048.4 

3    6 

9.621 

71.97 

12    6 

122.72 

918.00 

26 

651.55 

4125.9 

8    7 

10.066 

75.44 

12    9 

127.68 

955.09 

26 

662.00 

4204.1 

3    8 

10.950 

78.99 

13 

132.73 

992.91 

27 

572.56 

4V83.0 

8    9 

11.015 

68  62 

13    8 

187.89 

1031.5 

27 

583.21 

4362.7 

3  10 

11.541 

86^ 

13    6 

143.14 

1070.8 

27 

593.96 

4448.1 

8  11 

12.WS 

90.18 

13    9 

148.49 

1110.8 

27 

604.81 

4524.3 

4 

12.566 

94,00 

14 

153.94 

1161.5 

28 

615.75 

4606.2 

4    1 

13.005 

97.96 

14    8 

159.48 

1193.0 

28 

62G.P0 

4688.8 

4    2 

18.635 

102.00 

14    6 

165.13 

1235.3 

28 

687.94 

47i;>  1 

4    8 

14.186 

106.12 

14    9 

170.87 

1278.2 

28 

649.18 

4^56  2 

4    4 

14.748 

110.82 

15 

176.71 

1321.9 

20 

660.52 

4941.0 

4    5 

15.821 

114.61 

15    8 

182.65 

1366.4 

29 

671.96 

5C26  0 

4    6 

15.90 

118.07 

15    6 

188  69 

1411.6 

29 

G88.49 

5112.9 

4    7 

16.50 

123  42 

15    9 

194.8:3 

1457.4 

29 

69r).13 

5199.U 

4    8 

17.10 

127.95 

16 

201.06 

lf04.1 

80 

7C6.8e 

5:187.7 

4    9 

17.72 

132.56 

16    8 

207.89 

1561.4 

80 

718.09 

5376.2 

4  10 

18.85 

187.25 

16    6 

213  82 

1599.5 

30 

730.62 

5465  4 

4  11 

18.99 

142  02 

16    9 

2^.35 

1648.4 

80 

742.64 

56r.5.4 

5 

19.63 

146.^ 

17 

2^6.96 

1697.9 

81 

754.77 

5646.1 

5    1 

20.29 

151.82 

17    8 

231.71 

1748.2 

31 

766.99 

5737.5 

5    2 

20.97 

156.83 

17    6 

240.53 

1799.8 

31 

779.81 

5829.7 

5    3 

21.65 

161.93 

17    9 

247.45 

1851.1 

81 

791.73 

5922.6 

5    4 

22.34 

167.12 

18 

264  47 

1903.6 

82 

804  26 

6016.2 

5    5 

23.04 

172.88 

18    8 

261.59 

1956.8 

32 

816.86 

6110.6 

5    6 

28  76 

177.72 

18    6 

268  80 

2010.8 

32 

829.58 

0e05.7 

5    7 

24.48 

188.15 

16    9 

276.  :2 

2065  5  1 

82 

842.39 

6301.5 

122  MATHEMATICAL  TABLES. 

OAIiliONS  AND  G1TBIC  FEBT. 

ITiitteil  States  Omllons  In  a  stven  Namber  of  €able  Feet* 

1  cubic  foot  =  7.480610  U.  S.  gallons;  1  gaUon  =  281  cu.  in.  =  .18868056  cu.  ft. 


Cubic  Ft. 

Gallons. 

Cubic  Ft. 

Gallons. 

Cubic  Ft. 

Gallons. 

0.1 
0.2 
0.8 
0.4 
0.5 

0.75 
1.60 
2.84 
2.99 

8.74 

60 
60 
70 
80 
90 

874.0 
448.8 
528.6 
696.4 
678.8 

8,000 
9,000 
10,000 
80,000 
80,000 

59,844.2 
67,824.7 
74,805.8 
140,6l0f4 
884,415.6 

0.6 
0.7 
0.8 
0.9 

1 

4.49 
5.24 
5.96 
6.78 
7.48 

100 
800 
800 
400 
600 

748.0 
1,496.1 
8,244.2 
2,992.2 
8,740.8 

40,000 
50,000 
60,000 
70,000 
80,000 

899,220.8 
874,025.0 
448,881.1 
588,686.8 
698,441.6 

8 

8 

4 
6 
6 

14.96 
22.44 
29.92 
87.40 
44.88 

600 
700 
800 
900 
1,000 

4,488.8 
5,286.4 
5,984.4 
6,782.5 
7,480.5 

90,000 
100,000 
200,000 
800,000 
400,000 

678,346.7 

748,051.9 

1,496,108.8 

2,-,'4l,l55.7 

2,992,207.6 

7 
8 
0 
10 
80 

52.86 
59.84 
67.82 
74.80 
149.6 

•8,000 
8,000 
4,000 
5,000 
6,000 

14,961.0 
22,441.6 
29,922.1 
87,402.6 
44,888.1 

500,000 
600,000 
700.000 
800,000 
900,000 

8.740.8S9.5 
4,488,811.4 
5,286,863  8 
5,984,415.2 
6,732,467.1 

80 
40 

2S4.4 
299.8 

7,000 

68.868.6 

1,000,000 

7,480,519.0 

Gable  Feet  In  a  stven  Namber  of  Gallons. 


Gallons. 

Cubic  Ft. 

Gallons. 

Cubic  Ft. 

Gallons. 

Cubic  Ft. 

1 
2 
3 

4 
5 

6 
7 
8 
9 
10 

.184 
JW7 
.401 
.585 
.668 

.808 

.986 

1.069 

1.808 

1.887 

1,000 
2,000 
8,000 
4,000 
5,000 

6,000 
7,000 
8,000 
9,000 
10,000 

133.681 
267.861 
401. OIJ 
534.722 
668.408 

802  088 

935.764 

1,06!).444 

1,20:5.125 

1,380.806 

1,000,000 
2,000,000 
8,00U,000 
4,000.000 
5,000,000 

6,000,000 
7,000,000 
8,000.000 
9,000,000 
10,000,000 

188,680.6 
267,861.1 
401,041.7 
684.722.2 
668,408.8 

802.088  8 

985.768.9 

1,060.444.4 

l,208,ltr,.0 

1,886,805.6 

NUMBER  OF  SQUARE  FEET  IN  PLATES. 


123 


inmBBS  OF  Sai^ABB  FBBT  IN  PI^ATBS  8  TO  92 
FBBT  I«ONG,  AND  1  INCH  DTIDB. 

For  other  widths,  multiply  by  the  width  in  inches.    1  Bq.  in.  =  .0060|  sq.  ft. 


h.  and 
In. 

Ins. 
Long. 

Square 
Feet. 

Ft.  and 
Ins. 
Long. 

Ins. 
Long. 

Square 

Ft.  and 
Ins. 
Long. 

Ins. 
Long. 

Square 

S.   0 

88 

.25 

7.10 

94 

.6628 

1«.8 

152 

1.056 

87 

.2569 

95 

.6597 

158 

1.068 

38 

.2639 

8.  0 

96 

.6667 

154 

1.069 

99 

.2708 

97 

.6736 

155 

1.076 

40 

.2778 

96 

.6806 

18.0 

156 

1.088 

41 

.2817 

99 

.6876 

157 

1.09 

42 

.2917 

100 

.6944 

158 

1.097 

43 

.2986 

101 

.7014 

159 

1.104 

44 

.3056 

102 

.7088 

160 

1.114 

45 

.8125 

103 

.7158 

161 

1.118 

10 

40 

.8194 

104 

.7822 

162 

1.125 

11 

47 

.8264 

105 

.7292 

163 

1.132 

4.   0 

48 

.3388 

106 

.7361 

164 

1.189 

49 

.8406 

107 

.7481 

165 

1.146 

50 

.3472 

9.0 

108 

.75 

166 

1.168 

51 

.8542 

100 

.7569 

167 

1.159 

53 

.3611 

no 

.7689 

14.0 

168 

1.167 

53 

.8881 

111 

.7708 

169 

1.174 

54 

.876 

112 

.7778 

170 

1.181 

55 

.3819 

113 

.7847 

171 

1.188 

06 

.8889 

114 

.7917 

173 

1.194 

57 

.8958 

115 

.7986 

173 

1.201 

10 

58 

.4028 

116 

.8066 

174 

1.208 

11 

59 

.4097 

117 

.8125 

175 

1.215 

5.    0 

60 

.4167 

118 

.8194 

178 

1.822 

61 

.4286 

119 

.8264 

177 

1.229 

9i 

.4306 

10.0 

120 

.8388 

178 

1.286 

63 

.4375 

121 

.8408 

179 

1.248 

61 

.4444 

122 

.8472 

16.0 

180 

1.25 

65 

.4614 

123 

.8542 

181 

1.257 

66 

.4583 

124 

.8611 

182 

1.264 

67 

.4668 

125 

.8681 

188 

1.271 

68 

.4782 

126 

.875 

184 

1.278 

69 

.4792 

127 

.6819 

185 

1.285 

10 

70 

.4861 

128 

.6889 

186 

1.292 

11 

71 

.4931 

129 

.8958 

187 

1.299 

«.    0 

72 

.6 

180 

.9028 

188 

1.S06 

73 

.6069 

181 

.9097 

189 

1 .313 

74 

.5189 

11.0 

182 

9167 

190 

1.319 

75 

.1^08 

183 

.9286 

191 

1.336 

76 

.5278 

184 

.9306 

16.0 

192 

1.388 

77 

.6847 

185 

.9875 

198 

1.34 

78 

.6417 

186 

.9444 

194 

1.347 

T9 

.5486 

187 

.9514 

195 

1.854 

80 

.6656 

188 

.9588 

196 

1  861 

61 

.6625 

189 

.9658 

197 

1.868 

10 

82 

.5694 

140 

.9722 

196 

1.375 

11 

83 

.5764 

141 

.9792 

199 

1.882 

1.   0 

84 

.5834 

142 

.9861 

200 

1.889 

85 

.5905 

143 

.9981 

201 

1.396 

86 

.5972 

18.0 

144 

1.000 

202 

1.408 

87 

.6042 

145 

1.007 

203 

1.41 

88 

.6111 

146 

1.014 

17.0 

201 

1.417 

89 

.6181 

147 

1.021 

1 

205 

1.424 

90 

.625 

148 

1  028 

206 

1.431 

91 

.6819 

149 

1.085 

207 

1.438 

93 

.6389 

150 

1.042 

20S 

1.444 

93 

.6458 

151 

1.049 

209 

1.461 

124  MATHEMATICAL  TABLES. 

i^tTARB  FBBT  IH  PIiATB8-(C<mfMi(ed.) 


Ft.  and 
Ins. 
Long. 

Ins. 
L«.ng. 

Square 

F66t. 

Ft.  and 
Ins. 
Long, 

Ins. 
Long. 

%■" 

Ft.  and 
Ins. 
Long. 

IllB. 

Long. 

Square 
Veet. 

17.  C 

210 

1.458 

88.6 

269 

1.868 

87.4 

828 

8.878 

7 

211 

1.465 

6 

870 

1.875 

6 

829 

2.885 

8 

2i-.a 

1.472 

r 

871 

1.882 

6 

830 

2.292 

U 

U18 

1.479 

8 

272 

1.689 

7 

881 

8.J99 

10 

214 

1.486 

9 

278 

1  696 

8 

BSi 

8.80t. 

11 

tfin 

1.498 

10 

274 

1.903 

9 

B83 

8.818 

18.0 

216 

1.5 

11 

875 

1.91 

10 

834 

8.819 

1 

217 

1.607 

118.0 

878 

1.917 

11 

835 

2.826 

a 

218 

1.514 

1 

877 

1.924 

88.0 

836 

2..^3 

3 

219 

1.521 

8 

878 

1.931 

1 

887 

2.84 

4 

220 

1.528 

8 

279 

1  988 

8 

888 

8.347 

5 

221 

1.586 

4 

880 

1.944 

8 

889 

2.854 

6 

2*12 

1.542 

6 

281 

1.951 

4 

840 

2.861 

7 

223 

1.649 

6 

882 

1.958 

6 

841 

2.868 

8 

224 

1.556 

7 

283 

1.965 

6 

848 

2  875 

9 

2-J5 

1.663 

8 

884 

1.972 

7 

843 

2  882 

0 

226 

1.669 

9 

885 

1.979 

8 

844 

2.380 

11 

2^ 

1.5T6 
1.588 

10 

280 

1.966 

9 

845 

8.896 

19.0 

228 

11 

887 

1.993 

10 

846 

2.«U3 

1 

239 

1.59 

84.0 

888 

2. 

11 

817 

8.41 

2 

230 

1.597 

1 

889 

2.007 

88.0 

848 

2.417 

3 

m 

1.604 

8 

890 

2.014 

1 

849 

2.424 

4 

232 

1.611 

8 

891 

2.0-31 

8 

frV) 

2.4n 

5 

233 

1.618 

4 

892 

2028 

8 

851 

8.438 

6 

234 

1.655 

5 

893 

2.a35 

4 

&52 

2.441 

7 

236 

1.682 

6 

294 

2.042 

6 

853 

2.451 

8 

m 

1.6:S9 

7 

895 

2.049 

6 

854 

2.458 

9 

287 

1.645 

8 

296 

2.066 

7 

8.55 

2.4es 

10 

238 

1.653 

9 

897 

20C8 

6 

856 

2.472 

11 

289 

1.659 

10 

898 

2.069 

9 

867 

2.4^9 

80.0 

240 

1.667 

11 

299 

2.076 

10 

853 

2.486 

1 

241 

1.6T4 

86.0 

800 

2.088 

11 

859 

2.41.3 

2 

242 

1.681 

1 

801 

209 

80.0 

860 

2.5 

3 

243 

1.688 

2 

802 

2.097 

1 

861 

2.607 

4 

214 

1.6W 

8 

8a3 

2.104 

8 

862 

2.614 

5 

245 

1.701 

4 

804 

2.111 

8 

863 

2.5ei 

6 

246 

1.708 

5 

8a5 

2.118 

4 

864 

2.688 

7 

247 

1.715 

6 

806 

2,125 

5 

865 

8.&S5 

8 

248 

1.722 

I 

807 

2.182 

6 

866 

2  642 

9 

249 

1.729 

803 

2.139 

7 

867 

2.649 

10 

2.'50 

1.736 

9 

809 

2.146 

8 

868 

2.556 

11 

251 

1.743 

10 

810 

2.153 

9 

869 

2.663 

21.0 

252 

1.75 

11 

811 

2.10 

10 

ro 

2.560 

1 

253 

1.757 

86.0 

812 

2.167 

11 

871 

2  578 

2 

254 

1.764 

1 

813 

2. 174 

81.0 

^ 

8.583 

3 

255 

1.771 

8 

814 

2.181 

1 

8.50 

4 

256 

1.778 

8 

815 

2.188 

8 

874 

8.597 

5 

257 

1.786 

4 

816 

2.194 

8 

875 

8.004 

6 

258 

1.792 

6 

817 

2.201 

4 

SI? 

8.611 

7 

259 

1.799 

6 

818 

2.208 

6 

2.618 

8 

260 

1.806 

I 

819 

2.215 

6 

878 

8.6i5 

9 

£61 

1.818 

8v'0 

2.222 

r 

879 

2.6.S» 

10 

262 

1.819 

9 

821 

2.229 

8 

8£0 

2.6:)9 

11 

203 

1.826 

10 

822 

2.236 

9 

881 

2  61G 

9d.o 

]»4 

1.883 

11 

823 

2.248 

10 

883 

8  c.'sa 

1 

265 

1.84 

87.0 

824 

2.26 

11 

883 

2  60 

2 

266 

1.847 

1 

825 

2.257 

88.0 

884 

2.667 

3 

267 

1.854 

2 

826 

2.264 

1 

885 

8  674 

4 

268 

1.861 

8 

827 

2.871 

8 

880 

8.681 

CAPACITY  OP  RBOTANGULAB  TAKES. 


135 


CAPACITIKS   OF  KBCTAlfGITIiAK  TAHK8  IIV   17.   8. 
GAIiIiONS,    FOB  BACH   FOOT  IK   DBPTH. 

1  cubic  foot  =  7.4806  U.  a  gallons. 


Width 

Length  of  Tank. 

of 
Tank. 

feet.  ft.  In. 

feet. 

S 

ft.  in. 
8    • 

feet. 

4 

ft.  In. 
4    6 

feet. 
6 

ft.  In. 
6    6 

88.80 
108.86 
188.43 
H4.00 
104.67 

185.14 
80.-1.71 
886.28 

feet. 
6 

ft.  In. 
6    6 

feet. 
7 

ft.  in. 
2     C 

ao.os 

37.40 
46.75 

44.88 
56.10 
67.89 

58.36 
65.46 
78.54 
01.04 

50.84 
74.80 
80.77 
104.78 
110.60 

67.38 
84.16 
100.00 

74.81 
03.51 
iia.2i 

80.T7 
112.81 
184.05 
157  00 
170.58 

801.07 
884.41 
846.86 
800.30 

07.25 
181.56 
145.87 
170,18 
194.40 

81S.80 
843.11 
867.43 
»81,74 
316.05 

104.78 
180.01 
157.00 

U     G 

117.881 180.01 

18:187 

4 
4     6 

134.65 
151.48 

149.61 

168.31 
187.01 

800.45 
835.63 

5 

861  88 

i     G 

** 

888.00 

6 

314.18 

u     6 

840.86 
366.54 

Width 

Length  of  Tank. 

of 
Tiuk. 

ft.  in. 
7      6 

feet. 
8 

ft.  In. 
8    « 

feet. 
9 

ft.  In. 
9    6 

feet. 
10 

ft.  In. 
10    6 

feft. 
11 

ft.  In. 
11    6 

feet. 
12 

fi    in. 
2 

11«.« 
140J86 
168.31 
106  80 
'tiiAl 

258.47 
280..'^ 
80H.57 
336.68 
364.67 

802.78 
480.78 

110.08 
140.01 
170.53 
800  45 
830.37 

860.30 
890.82 

820.14 
850.00 
888.98 

418.91 
448.83 
478.75 

187.17 
1.58.06 
10a75 
888.54 
854.34 

236.13 
317.92 
340.71 
381.50 
418.30 

445  00 
476.88 
508.67 
540.46 

134.65 
168.81 
208.07 
835.03 
860.80 

302.06 
330.62 
370.88 
40804 
487.60 

47187 
604.03 
588.60 
572.85 
605.02 

14813 
177.66 
213.19 
848.73 
884.86 

319.79 
355..32 
390.85 
426.89 
461.92 

497.45 
538.98 
.508.51 
604.05 
089.58 

075.11 

140.61 
187.01 
884  41 
801.88 
890.82 

336.62 
874.08 
411.43 
448.a3 
480.83 

683.64 
66104 
698.44 
6:«.&4 
678.85 

710  65 
748.06 

187.09 
196.80 
885.03 
874.90 
814.18 

858.45 
898.?^ 
438.00 
471.27 
510.54 

540.81 
580.08 
688.86 
607  6:J 
706.00 

740.17 
785.45 
884.78 

104.57 
806.71 
240.80 
288.00 
329.14 

370,88 
411.43 
452.67 
498.71 
5^.85 

67fi09 
617  14 
058.88 
690.42 
740.66 

781.71 
888.86 
804.00 
005.14 

178.05 
815.00 
258.07 
801.09 
344  10 

387.11 
4.3018 
473.14 
516.16 
650.10 

008.18 
04.5.19 
088.80 
731.21 
774  23 

817.24 
800.86 
903.86 
946.87 
060.80 

170  53 
884.41 
809.30 
814.18 
350.00 

403.04 

448.83 
403.71 
538.50 

583.47 

628  86 
673.84 
718.18 
763  00 

807.88 

852  77 

897  66 

042.56 

987.43 

1082.3 

i; 

1077.2 

126 


HATHEMATIOAL  TABLES. 


NUIIKBBB  OF  BARBEIjS  (31   1-2  GAI«I«ON8)  Ilf 
CISTERNS  AND  TANKS. 


1  Barrel  =  81^  gallons  = 


81.5X281 
1788 


=  4.21094  cubic  fpefc.   Reciprocal  =  .8S7477. 


Depth 

in 
Feet. 

Diameter  in  Feet 

6 

« 

7 

8 

9 

10 

11 

12 

IS 

14 

1 

4.663 

6.714 

9.189 

11.987 

15.108 

18.652 

22.560 

26.859 

81.522 

36.557 

6 

28.8 

83.6 

45.7 

59.7 

75.5 

98.8 

112.8 

184.3 

157.6 

183.8 

6 

88.0 

40.8 

54.8 

71.6 

90.6 

111.9 

185.4 

161.2 

189.1 

219  3 

7 

82.6 

47.0 

64.0 

88.6 

105.8 

180.6 

158.0 

188.0 

2j».7 

S55.9 

8 

87.8 

68.7 

78.1 

96.5 

120.9 

149.2 

180.6 

214.9 

2S2.2 

^»i.S 

9 

42.0 

60.4 

82.8 

107.4 

186.0 

167.9 

208.1 

241.7 

288.7 

329.0 

10 

46.6 

67.1 

91.4 

119.4 

151.1 

186.5 

228.7 

268.6 

815.2 

865.6 

11 

51.8 

78.9 

100.5 

181.8 

166.9 

205.2 

948.8 

295.4 

846.7 

402.1 

12 

66.0 

80.6 

109.7 

148.2 

181.8 

223.8 

270.8 

882.8 

878.8 

488.7 

18 

60.6 

87.8 

U8.8 

155.2 

196.4 

242.6 

298.4 

849.2 

409.8 

47B.2 

14 

65.8 

94.0 

127.9 

ler.i 

211.5 

261.1 

816.0 

8T6.0 

441.8 

SI  1.8 

16 

69.0 

100.7 

187.1 

179.1 

226.6 

289.8 

888.5 

402.9 

472.8 

548.4 

16 

74.6 

107.4 

146.2 

191.0 

241.7 

296.4 

361.1 

429.7 

504.4 

584.9 

17 

79.8 

114.1 

156,4 

202.9 

256.8 

317.1 

883.7 

456.6 

685.9 

U21.5 

18 

88.9 

180.0 

164.5 

214.9 

271.9 

386.7 

406.2 

483.5 

667.4 

058.0 

10 

88.6 

127.6 

178.6 

226.8 

287.1 

354.4 

488.8 

510.8 

606.9 

604.6 

20 

988 

184.8 

182.8 

288.7 

802.2 

878.0 

451.4 

687.2 

680.4 

731.1 

Depth 

in 
Feet. 

Diameter  in  Feet 

16 

16 

17 

18 

19 

20 

21 

82 

1 
6 
6 
7 
8 

41.966 

209.8 

251.8 

885.7 

47.748 

288.7 

286.5 

834.2 

882.0 

58.903 

269.5 

828.4 

377.8 

431.2 

60.481 
302.2 
862  6 
423.0 

483.4 

67.8S2 

836.7 

404.0 

471.8 

538.7 

74.606 

873.0 

447.6 

622.2 

596.8 

82.258 

411.8 
498.5 
575.8 
658.0 

90.«rs 

451.4 
541.6 
631.9 
722. S 

9 

10 
11 
12 
18 

8rr.7 

419.7 
461.6 
608.6 
545.6 

429.7 
477.5 
526.2 
578.0 
620.7 

4851 
539.0 
592.9 
046.8 
700.7 

543.9 
604.8 
664.7 
725.2 
785.6 

606.0 
678.3 
740.7 
806.0 
875.8 

671.5 
746.1 
830.7 
805.3 
969.9 

740.8 
822.5 
904.8 
987.0 
1069.8 

812.5 
902.7 
993.0 
1083.3 
1178.5 

14 
15 
16 

17 
18 

687.5 
629.5 
671.6 
713.4 
756.4 

668.5 
716.2 
764.0 
811.7 
859.5 

754.6 
808.5 
662.4 
916.4 
970.3 

846.0 
906.5 
966.9 
1027.8 
1087.8 

942.6 
1010.0 
1077.8 
1144.6 
1212.0 

1044.5 
1119.1 
1198.7 
1268.3 
1842.9 

1151.6 
1283.8 
1316.0 
1398.8 
1480.6 

1268.8 
1854.1 
1444.4 
1534.5 
1624.9 

19 
20 

797.4 
889.8 

907.2 
955.0 

1024.2 
1078.1 

1148.2 
1206.6 

1279.3 
1346.6 

1417.5 
1492.1 

1562.8 
1645.1 

1715.9 
1805.5 

LOOAEITHMS. 


127 


HITKBER  OP   BABRBIiS  (81   1-S  OAIitiONS)  IN 
GISTJEBN8  AND  TANKS.— Continued. 


Depth 

Diameter  in  Feet. 

in 
FeeL 

<s 

24 

25 

28 

27 

28 

29 

80 

1 
5 
0 
7 
8 

96.668 
498.8 
5»0 
090.7 
789.3 

107.488 
537.2 
344.6 
752.0 
859.5 

116.571 
582.9 
699.4 
8160 
988.6 

126.068 
680.4 
756.5 
682.6 

1006.7 

185.966 
679.8 
615.8 
951.6 

1087.7 

146.226 
781.1 
677.4 
1028.6 
1169.6 

157.658 

784.8 

941.1 
1098.0 
1264  9 

167.688 
889.8 
1007.2 
1175.0 
1342.9 

9 

10 
11 
1« 
13 

888.0 
966.7 
1065.8 
1184.0 
»82.7 

966.9 
1074.8 
1181.8 
1289.2 
1896.6 

1049.1 
1165.7 
1282.8 
1896.8 
1515.4 

1184.7 
1260.6 
1886.9 
1518.0 
1689.1 

1228.7 
1859.7 
1495.6 
1681.6 
1787.6 

1816.0 
1462.2 
1606.5 
1754.7 
1900.9 

1411.7 
1568.6 
1725.4 
1882.8 
2089.2 

1510.6 
1678.6 
1846.5 
2014.4 
2182.3 

14 

15 
]« 
17 

IS 

1881.8 
1480.0 
1578.7 
1677.8 
1776.0 

1904  0 
1611.5 
1718.9 
1826.8 
1988.8 

1682.0 
1748.6 
1665.1 
1961.7 
2096.3 

1765.2 
1891.2 
2017.8 
2148.4 
2369.5 

1908.6 
2069.5 
2176.5 
S311.5 
2447.4 

2047.2 
2196.4 
2889.6 
2485.8 
3633.0 

2106.0 
2852.9 
2509.7 
9666.6 
2828.4 

28S0.1 
2517.9 
2686.8 
2858.7 
8001.5 

19 
SO 

1874.7 
1978.8 

9041.2 
2148.6 

2214.6 
2821.4 

2895.6 
2521.7 

2588.4 
2719.4 

2778.8 
2924.5 

2960.8 
8187.2 

8189.4 
8857.8 

liOGARITSMS. 

If#KAritlims  (abbreviation  log).— The  log  of  a  number  is  the  exponent 
of  Che  power  to  which  it  is  neooonanr  to  raise  a  fixed  number  to  produce  the 
invcn  Domber.  The  fixed  number  is  called  the  base.  Thus  if  the  base  is  10. 
the  loff  of  1000  is  8,  for  10>  =  1000.  There  are  two  systems  of  logs  in  general 
OK,  the  commofiy  in  which  the  base  is  10,  and  the  Naperian,  or  hyperbolic, 
ia  which  the  base  is  2.718881838  ....  The  Kaperian  base  is  commonly  de* 
aax^  by  e»  aa  in  the  equation  e*  =  «« in  which  y  is  the  Nap.  log  of  x. 

la  any  sjsteni  of  logs,  the  log  of  1  is  0;  the  log  of  the  base,  taken  in  that 
fTHem.  is  1.  In  any  system  the  base  of  which  is  greater  tlum  1,  the  logs  of 
aQ  cambers  greater  than  1  are  positive  and  the  logs  of  all  numbers  less  than 
I  lie  negative. 

The  modulus  of  any  system  is  equal  to  the  redproeal  of  the  Naperian  log 
of  the  base  of  that  system.  The  modulus  of  the  naperian  system  is  1,  that 
^  the  common  system  is  .4842945. 

The*  lo^  of  a  number  in  anv  system  equals  the  modulus  of  that  system  x 
ib^  !9aperian  log  of  the  number. 

The^|>er6o<«;  or  .kaperian  log  of  any  number  equals  the  common  log 

ISvefy  log  consists  of  two  parts,  an  entire  part  called  the  charcuiteriatic,  or 
m^x,  and  the  decimal  part,  or  mantiasa.  The  mantissa  only  is  given  in  the 
oroal  tables  of  common  logs,  with  the  decimal  point  omitted.  The  charac- 
ttrimie  is  found  by  a  simple  rule,  vis.,  it  is  one  less  than  the  number  of 
flcores  to  the  left  of  the  decimal  point  in  the  number  whose  log  is  to  1>e 
found.  Thus  the  characteristic  of  numbers  from  1  to  9.99  +  Is  0,  from  10  to 
»J9+is  1,  from  100  to 990  +  is 2,  from  .1  to  .99  +  is  -  1,  from  .01  to  .009 -i- 
it  -  2,  etc    Thus 

log  of  IHWO  is  8.80108;  log  of       .2  is  -  1.80108; 

.P  u    jioo  ..  2.80108;  "    "       .02  **  -  2.80108; 

••   ••     20  "  1.80108;  •*   "     .008  ••  -  8.80108; 

••  ••       2  "  0.80103;  "   "  .0002  "  -  4.80108. 


128  MATHEMATICAL  TABLES. 

The  minus  lign  ii  frequently  written  a\)OTe  the  characteristic  thus: 
log  .002  s=  7.80108.  The  characteristic  only  is  negatiTd,  the  decimal  |»art,  or 
mantiasaf  being  always  positive. 

When  a  log  consists  ora  negative  index  and  a  positive  mantissa,  it  Is  usual 
to  write  the  negative  sign  over  the  Index,  or  else  to  add  10  to  the  index,  and 
to  indicate  the  subtraction  of  10  from  the  resultinsr  logarithm. 

Thus  log  .2  =  T.aolftJ,  and  this  may  be  written  9.30103  -  10. 

In  tables  of  logarithmic  sines,  etc.,  the  -  10  is  generally  omitted,  as  l>eing  : 
lin«lMn«tood. 

Rules  for  use  of  the  table  of  liOgarlthms.-  To  flna  «lie  ; 
log  of  any  ivliole  nnmber.— For  1  to  lOU  inclusive  Uie  log  is  given 
oouiplete  in  the  small  table  on  page  139. 

For  100  to  999  inclusive  the  decimal  part  of  the  log  Is  given  opposite  the  i 
given  number  In  the  column  headed  0  in  the  table  (including  the  two  fi^ires 
to  the  left,  making  six  figures).    Prefix  the  cliaracteristic,  or  index.  2. 

For  1000  to  0999  inclusive  :  The  last  four  figures  of  tho  log  are  found  i 
opposite  the  first  three  figures  of  the  given  number  and  in  the  veriical  : 
column  headed  with  the  fourth  figure  of  the  given  number ;  prefix  the  two 
figures  under  column  0,  and  the  index,  which  is  3. 

For  numbers  over  10,000  having  five  or  more  digits :  Find  the  decimal  part 
of  the  log  for  the  first  four  digits  as  above,  multiply  the  difference  figure 
in  the  last  column  by  the  remaming  digit  or  digits,  and  divide  by  10  If  there 
be  only  one  digit  more,  by  100  If  there  be  two  more,  and  so  on  ;  add  the 
quotient  to  the  log  of  the  first  four  digits  and  prefix  the  index,  which,  is  4 
Ix  there  are  five  digits,  6  if  there  are  six  digits,  and  so  on.  The  table  of  pro- 
portional parts  may  be  used,  as  shown  below. 

To  find  the  loff  of  a  deeinal  firaetlon  or  of  m  ivliole 
number  and  a  deelaial*— First  find  the  log  of  the  quantity  as  if  there 
were  no  decimal  point,  then  prefix  the  index  according  to  rule  ;  the  Index  is 
one  less  than  the  number  of  figures  to  the  left  of  the  dedmsl  point. 

Be<}uired  log  of  3.141598. 

log  of    8.141       =0.497068.  Piff.  a  188 

From  proportional  parts  B     =  690 

*•        ..     09    =  1248 

••  -  •»  003  «  041 


log    8.141593      0.4971498 

To  find  the  number  correspondins  to  a  slven  los*— l^^nd 

A)  the  table  tbe  log  nearest  to  the  decimal  part  of  the  given  log  andtake  the 
first  four  digits  of  the  required  number  from  the  column  N  and  tfie  top  or  ^ 
foot  of  the  column  containing  the  log  which  Is  the  next  less  than  the  given 
log.    To  find  the  5th  and  6th  digits  subtract  the  log  in  the  table  from  the 

given  log.  multiply  the  diffei-enoe  by  100,  and  divide  by  the  figure  in  tlie 
iff.  column  opposite  the  log ;  annex  the  quotient  to  the  four  digits  already 
found,  and  place  the  decimal  point  aocoralug  to  the  nile ;  tbe  number  oC 
figures  to  the  left  of  the  decimal  point  is  one  greater  than  the  Index. 

Find  number  corresponding  to  the  log 0.407150 

Next  lowest  log  in  table  oorresponds  to  8141 497068 

DIff.  a  89 

Tabular  diff.  =  188;  82  -•- 188  =  .59  + 

The  Index  being  0,  the  number  Is  therefore  8.14159  +. 

To  multiply  i^svo  numbers  by  tbe  use  of  loararltl&ms. 

AAd  together  the  logs  of  the  two  numbers,  and  find  the  number  whose  log   i 
1b  the  sum.  i 

To  dlTlde  ty^o  numbers.— Subtract  the  log  of  the  divisor  from  ; 
the  log  of  the  dividend,  and  find  the  number  whose  log  Is  the  differetioe. 

To  raise  a  number  to  any  ctven  poirer.— Multiply  the  log  o(  ; 
the  number  by  tbe  exponent  of  the  power,  and  find  the  number  whose  log  U 
the  product.  ' 

To  find  any  root  of  a  Klven  number.—Diyide  the  los  of  the  ' 
Dumber  by  the  index  of  the  r(X)t.    The  quotient  is  the  log  of  the  root. 

To  find  tbe  reelproeal  of  a  anmber.— Subtract  the  decimal  ^ 
part  of  the  log  of  the  number  from  0,  add  1  to  the  Index  and  change  the  sigq  ' 
of  the  index.    The  result  is  the  log  of  the  reciprocal. 


L0GARITHH6. 


12» 


Beqiiired  the  reciprocal  of  8.141603. 

Lotrof8.141S03,a8foundaboTe 0.4971406 

Subtract  decimal  part  from  0  eives 0.SO28b0i 

Add  1  to  the  Index,  and  changing  sign  of  the  Index  gives..  T.6038QQ3 
irbiefa  Is  the  loff  of  0.81W1 . 

Vo  MmA  Uia  Iburth  ttmn  of  a  vropoitlon  by  lofEaxitluns* 
—Add  the  loearithms  of  tJie  aecond  and  third  terms,  and  from  their  sum 
subtract  the  logarithm  of  tLe  first  term. 

When  one  logarithm  is  to  be  subtraoted  from  another,  it  may  be  more 
convenient  to  convert  the  subtraction  Into  an  addition,  which  may  be  done 
by  first  subtracting  tUfjgiven  logarithm  from  10.  adding  the  difference  to  the 
Of  her  losrarithm,  and  afterwards  rejecting  the  10. 

Tht»  dlflerenoe  between  a  given  logarithm  and  10  is  called  its  arWunetioal 
complement,  or  cologarithm. 

To  subtract  one  logarithm  from  another  Is  the  same  aa  to  add  its  comple- 
ment and  then  reject  10  from  the  result.    For  a  —  6  s  10  —  6  -p  «*  -  10. 

To  work  a  proportion,  then,  by  logarithms,  add  the  complement  of  the 
logarithm  of  the  first  term  to  the  logarithms  of  the  second  and  third  terms. 
The  characteriHtic  must  afterwards  be  diminished  by  10. 

Example  In  locarltlmia  nrltlt  a  nesatlve  Index. -Solve  by 

logaritiims  (^)  ^t  which  means  divide  596  by  1011  and  raise  the  quotient 

to  the  S.45  power. 

log  596  s      9.790986 
log  1011=      8.004751 


Jog  of  quotient  =  -  1.716986 
Jffitftiply  by  2.45 


-  2.561175 
-2J  64940 
-^  l.4»  2470 
-1.80  477576  =  .20178,  Ani. 


In  multiplying  -  1.7  by  5.  we  i  , 
f-  ;<  oarriea  =  —  9.    In  adding  -U4-B-\-Z-^l  carried  from  previous  oolumn, 
we  say:  1  -f  8  +  8  =:  19,  minu82  =  10.  set  down  0  and  carry  1;  14-4-2  =  & 


*y-  5  ^  I  =:  *^'  '  *9  cftiry ;  5  X  —  1  =3  —  5  less 


liOOARTTBHS  OF  N^IMBKBS  FROM  1  TO  100. 


N. 

Log. 

N. 

Log.     |!  N. 

Log. 

N. 

Log. 

N. 

Log. 

1 

o.oooooo 

21 

I.a32»9  , 

41 

1.619784 

61 

1.786880 

81 

1.906485 

2 

0.801080 

22 

1.842428 

42 

1.028949 

62 

1.792892 

82 

1.913814 

8 

0.477121 

28 

1.861796 

48 

1.638468 

68 

1.799341 

88 

1.919078 

4 

0.602060 

24 

1.880211 

44 

1.648458 

64 

1.806180 

84 

1.921279 

5 

0.098970 

25 

1.897940 

46 

1.668218 

65 

1.812918 

85 

1.929410 

6 

0.778151 

26 

1.414978 

46 

1.662758 

66 

1.819544 

86 

1.934466 

7 

0.845096 

27 

1.481864 

47 

1.679006 

67 

1.826075 

87 

1.939519 

8 

O.9O009O 

28 

1.447166 

48 

1.681241 

68 

1.882509 

88 

1.944488 

0 

0.964M3 

29 

1.462896 

40 

1.600196 

69 

1.838849 

89 

1.949390 

10 

l.OOOOOO 

80 

1.477121 

60 

1.666970 

70 

1.846096 

90 

1.954248 

11 

1.041888 

81 

1.491362 

51 

1.707670 

71 

1.851958 

91 

1.959041 

12 

1.079181 

82 

1.505160 

52 

1.716008 

72 

1.857382 

99 

1.963788 

18 

1.118948 

83 

1.618514 

58 

1.7S4276 

78 

1.868828 

98 

1.96&188 

14 

1.146198 

84 

1.581479 

54 

1.789894 

71 

1.869282 

94 

1.978198 

15 

1.176001 

85 

1.544066 

55 

1.740868 

75 

1.875061 

95 

1.977794 

16 

1.20«120 

86 

1.656806 

66 

1.748188 

78 

1.880614 

96 

1.982271 

17 

1.280449 

87 

1.668902 

57 

1.756875 

77 

1.88W91 

97 

1.086778 

18 

1.256278 

88 

1.679784 

56 

1.763498 

78 

1.892095 

98 

1.991i226 

19 

1.278754 

89 

1.601066 

50 

1.770852 

79 

1.8i)7097 

99 

1.095686 

90 

1.801090 

40 

1.6O906O  1 

60 

1.778151  , 

1  ^ 

1.908000 

100 

2.000000 

L30 


IiOGARITHMS  OF  XUHBEBS. 


Ko.  100  L.  000.] 


[No.  109  L.  (HO. 


N. 

0 

1 

2 

S 

4 

6 

6 

7 

8 

9 

Difl. 

0434 
4751 
9026 

0868 
5181 

QdAI 

ISOl 
5609 

1784 
6088 

2166 
6466 

2596 
6894 

8029 
7821 

8461 
7748 

8891 
8174 

lOU 

1 
2 

000000 

8600 

438 
436 

VMOl       ««.« 

0800 
4521 
870O 

0724 
4940 
9116 

1147  1  1570 
5860     5779 
9582  I  9947 

1998 
6197 

2415 
6616 

404 

4s» 

8 
4 

012837 
7083 

8259 
7461 

^ 

4100 
8284 

0861 
4486 
85n 

0775 
4896 
8878 

416 
41S 
408 

6 
6 

7 

021189 
5306 
9384 

1608 
5715 
9789 

2016 
6125 

2428 
6588 

2841 
6942 

8252 
7850 

3864  1  4075 
7757  1  8164 

0195 
4227 
8228 

0600 
4628 
8620 

1004 
5029 
9017 

1406 
5480 
9414 

1812 
5880 
9611 

2216 
6280 

2610 
6629 

3021 
7088 

404 

4U0 

6 
9 

osatsM 

7436 
04 

8826 
7825 

0907 

0602 

0998 

897 

Pbopobtional  Pabts. 


Diff. 

1 

2 

8 

4 

6 

6 

7 

6 

9 

484 

48.4 

86.8 

180.2 

173.6 

217.0 

260.4 

303.8 

847.2 

890.6 

48:^ 

48.8 

88.6 

129.9 

178.2 

216.5 

259.8 

803.1 

846.4 

889.7 

482 

48.2 

86.4 

129.6 

172.8 

216.0 

259.2 

802.4 

845.6 

888.8 

481 

48.1 

86.2 

129.8 

m.4 

215.6 

258.6 

801.7 

344.8 

887.9 

480 

48.0 

86.0 

129.0 

172.0 

215.0 

256.0 

801.0 

844.0 

887.0 

429 

42.9 

85.8 

128.7 

171.6 

214.6 

257.4 

800.8 

343.2 

386.1 

428 

42.S 

85.6 

128.4 

171.2 

214.0 

256.8 

299.6 

812.4 

365.2 

427 

42.7 

85.4 

128.1 

170.8 

213.6 

256.2 

298.9 

841.6 

884.8 

426 

42.6 

85.2 

127.8 

170.4 

213.0 

255.6 

29S.2 

840.8 

883.4 

425 

42.5 

65.0 

127.6 

170.0 

212.6 

255.0 

297.5 

840.0 

882.5 

424 

42.4 

84.8 

127.2 

109.6 

212.0 

854.4 

896.8 

880.2 

381.6 

423 

42.8 

84.6 

126.9 

169.2 

211.6 

258.8 

296.1 

888.4 

880.7 

422 

42.2 

84.4 

126.6 

168.8 

211.0 

258.2 

295.4 

887.6 

879.8 

421 

42.1 

84.2 

126.8 

168.4 

210.5 

252.0 

294.7 

886.8 

878.9 

420 

42.0 

84.0 

126.0 

168.0 

210.0 

252.0 

894.0 

886.0 

878.U 

419 

41.9 

83.8 

125.7 

167.0 

209.5 

251.4 

293.8 

835.2 

877.1 

418 

41.8 

83.6 

125.4 

167.2 

209.0 

250.8 

292.6 

884.4 

876.2 

417 

41.7 

83.4 

125.1 

166.8 

206.6 

260.2 

291.9 

888.6 

875.3 

416 

41.6 

83.2 

124.8 

166.4 

208.0 

219.6 

291.2 

882.8 

874.4 

416 

41.5 

88.0 

124.5 

166.0 

207.6 

M9.0 

290.5 

882.0 

878.5 

414 

41.4 

82.8 

124.2 

165.6 

207.0 

»I8.4 

289.8 

831.2 

»ra.6 

418 

41.8 

82.6 

123.9 

165.2 

206.5 

847.8 

289.1 

880.4 

871.7 

412 

41.2 

82.4 

123.6 

164.8 

206.0 

247.2 

288.4 

829.6 

870.8 

411 

41.1 

82.2 

128.8 

164.4 

205.5 

246.6 

287.7 

328.8 

809.9 

410 

41.0 

82.0 

128.0 

164.0 

205.0 

246.0 

287.0 

828.0 

869.0 

409 

40.9 

81.8 

122.7 

168.6 

2(M.5 

245.4 

286.3 

827.2 

868.1 

408 

408 

81.6 

122.4 

163.2 

204.0 

244.8 

285.6 

826,4 

867.2 

407 

40.7 

81.4 

122.1 

162.8 

208.5 

244.2 

284.9 

825.6 

866.8 

406 

40.6 

81.2 

121.8 

162.4 

208.O 

2436 

284.2 

824.8 

866.4 

406 

40.5 

81.0 

121.5 

162.0 

202.6 

248.0 

283.5 

824.0 

864.5 

404 

40.4 

80.8 

121.2 

161.6 

202.0 

242.4 

282.8 

828.2 

868.6 

403 

40.8 

80.6 

120.9 

161.2 

201.5 

241.8 

282.1 

822.4 

362.7 

402 

40.2 

80.4 

120.6 

160.8 

301.0 

211  2 

281.4 

821.6 

861.8 

401 

40.1 

80.2 

120.3 

160.4 

200.5 

210.6 

280.7 

820.6 

860.9 

400 

40.0 

800 

120.0 

160.0 

200.0 

240.0 

280.0 

820.0 

880.0 

399 

89.9 

79.8 

119.7 

159.6 

199.5 

239.4 

279.3 

819.2 

869.1 

398 

89.8 

79.6 

119.4 

159.2 

199.0 

238.8 

278.6 

318.4 

858.2 

397 

89.7 

79.4 

119.1 

l.'i8.8 

198.5 

2:w.2 

277.9 

317.6 

867.3 

896 

39.6 

79.2 

118.8 

158.4 

198.0 

287.0 

277.2 

816.8 

856.4 

896 

1  39.5 

79,0 

118.5 

158.0 

197,5 

237.0 

1    278.5 

316  0 

885.6 

LOOARITHHS  OF  XTJXBEB8. 


131 

LNo.  119  L.  (i7^  I 


No  UOLuOtL] 


N. 


041908 
5323 
S&18 


069078 
0905 


000808 
4468 
8180 


071888 
5647 


1787 
67J4 
9006 


8468 
7286 


1075 
4832 
8567 


2S60 
6012 


218S 
6105 
9993 


8846 
7066 


1452 
5a06 


8617 
6276 


6495 


0680 
4280 
8046 


5580 


6610 


6885 


0766 
461S 


5958 
9668 


70M 


8862 
7275 


1158 
4996 
8805 


6826 


8718 
7868 


87B6 
7664 


1588 
587B 
9185 


2958 


6699 


0407 
4085 
7781 


414B 
8058 


1924 
5760 
9668 


7071 


0776 
4451 
8094 


8         9       Difl. 


4540 
8442 


6142 
9942 


3709 
7448 


1145 
4816 
8457 


4932  I 
88:>0  1 


2691  I    886 


6524 


0820 
4088 
7815 


1514  870 
5182  866 
8619 


^mopoamovAi,  Pabt& 


Difl. 


805 
9M 
808 
9B8 
391 
880 
389 
388 
887 
886 
885 

381 


381 
380 

378 
377 
876 
375 

874 
373 
832 
371 
370 
369 
368 
167 
366 

364 
363 
302 
391 
360 
360 

35T 
8B6 


89.5 
89.4 
80.8 
80.2 
80.1 
80.0 
86.9 
38.8 
88.7 
88.6 
88.5 

38.4 
88.3 
88.2 
38.1 
88.0 
87.9 
87.8 
87.7 
87.6 
87.5 

87.4 
87.3 
87.2 
87.1 
87.0 
86.9 
86.8 
86.7 
36.6 
86.5 

86.4 
86.3 
86.2 
86.1 
36.0 
85.9 
85.8 
85.7 
35.0 


79.0 
78.8 
78.6 
78.4 
78.2 
78.0 
77.8 
TT.6 
77.4 
77.2 
77.0 

78.8 
76.6 
78.4 
78.3 
78.0 
75.8 
75.6 
75.4 
75.8 
75.0 

74.8 
74.6 
74.4 
74.2 
74.0 
78.8 
78.6 
78.4 
78.2 
73.0 

73.8 
78.6 
79.4 
78.3 
78.0 
71.8 
71.6 
71.4 
71.3 


118.5 
118.2 
117.9 
117.6 
117.3 
117.0 
116.7 
116.4 
116.1 
115.8 
115.5 

115.2 
114.9 
114.6 
114.3 
114.0 
118.7 
118.4 
118.1 
112.8 
112.5 

112.2 
111.9 
111.6 
111.8 
111.0 
110.7 
110.4 
110.1 
109.8 
109.5 

109.2 
108.9 
106.6 
108.8 
106.0 

iar.7 

107.4 

107.1 
106.8 


158.0 
157.6 
157.2 
166.8 
156.4 
1S6.0 
155.6 
155.2 
154.8 
164.4 
154.0 

158.6 
158.2 
152.8 
152.4 
152.0 
151.6 
151.2 
150.8 
150.4 
150.0 

149.6 
149.2 
148.8 
148.4 
148.0 
147,6 
147.2 
146.8 
146.4 
146.0 

145.6 
145.2 
144.8 
144.4 
144.0 
148.6 
148.2 
1«  8 
142.4  I 


197.5 
197.0 
196.5 
106.0 
195.5 
195.0 
194.5 
194.0 
198.5 
198.0 
192.5 

192.0 
191.5 
191.0 
190.5 
190.0 
189.5 
180.0 
188.5 
188.0 
187.5 

187.0 
186.6 
186.0 
185.5 
185.0 
184.5 
184.0 
188.5 
188.0 
182.5 

182.0 
181.5 
181.0 
180.5 
180.0 
179.5 
179.0 
-78.5 
178.0 


287.0 
286.4 
285.8 
286.2 
234.6 
234.0 
288.4 
282.8 
282.2 
281.6 
231.0 

230.4 
229.8 
229.2 
228.6 
228.0 
227.4 
226.8 
226.2 
825.6 
225.0 

224.4 
228.8 
223.2 
222.6 
222.0 
221.4 
220.8 
220.2 
219.6 
210.0 

218.4 
217.8 
217.2 
216.6 
216.0 
215.4 
214.8 
S14.2 
218.0 


276.5 
27V.8 
275.1 
274.4 
278.7 
278.0 
272.3 

2n.6 

270.9 
270.2 
269.5 

268.8 
268.1 
267.4 
286.7 
266.0 
265.8 
264.6 
268.9 
268.2 
262.5 

261.8 
261.1 
260.4 
259.7 
259.0 
258.8 
267.6 
2S6.0 
256.2 
255.7 

254.8 
254.1 
253.4 
262.7 
252.0 
251.3 
250.6 
349. 9 
249.2 


816.0 

866.5 

816.2 

854.6 

814.4 

858.7 

813.6 

8G8.8 

812.8 

851.9 

812.0 

851.0 

811.2 

850.1 

810.4 

349.2 

809.6 

848.8 

808.8 

347.4 

808.O 

846.6 

80r.2 

845.6 

806.4 

844.7 

805.6 

348.8 

804.8 

842.9 

804.0 

342.0 

808.2 

841.1 

802.4 

840.2 

801.6 

889.8 

800.8 

338.4 

800.0 

887.5 

299.2 

336.6 

206.4 

885.7 

297.6 

834.8 

206.8 

838.9 

296.0 

838.0 

205.2 

882.1 

294.4 

881.2 

203.6 

s;:o.3 

292.8 

829.4 

202.0 

U28.5 

291.2 

827.6 

200.4 

326.7 

289.6 

825.8 

288.8 

324.9 

288.0 

324.0 

287.2 

;23.1 

amy 

322.2 

2H5.0 

C21.3 

284.8 

820.4 

2Si 


UMASITHMS  OF  KUHBRBS. 


No. 

190  L.  079.) 

[No.  184  L.  1«L 

N. 

0 

1 

2 

8 

1 

6 

« 

7 

8 

9 

Diff. 

990i 

190 

07^181  1  WHO 

0966  1  0086  ! 

0067 
4576 
8186 

1847 
4984 

8490 

1707 

6291 
8815 

2007 

5W7 
9198 

M26 
00O4 
9552 

800 

1 
2 
8 

082785 
6900 
9905 

8144 
6716 

8508 
7071 

8861 
7498 

4219  ' 
7781 

887 
865 

0238     0611 
8772  1  4122 

T*>"»7      TftfU 

0003 

4471 

1315 
4^ 

1067 
5169 
86M 

2018 
5518 
8990 

2370 
5866 
9385 

2721 
6215 
9681 

8071 
6668 

862 

4 

5 

(mm 

0910 

849 

0026 
Si68 
6871 

S46 
843 

6 
7 

8 

0 
180 

2 

lOOfin     0715     1059  ,  1403 
38M     4146     4487     4S» 
TOIO     7M9     7988     8227 

1747 
5109 

2091 
5510 

2484 

6851 

2777 
6191 
9579 

8119 
6581 
9016 

0858 
8609 

6940 

838 

S35 

883 

110590 

8943 
?^71 

0926 

4277 
7003 

1263 

4611 
7931 

1509 

4944 
8265 

1984 

5278 
8595 

2270 

6611 
8926 

2605 

5948 
flG»6 

2940 

6876 
9586 

3273 

6006 
9915 

0246 
8525 
0781 

830 
825 

13a574 
3852 
7105 

13 

0003     1231 
4178     4504 
7429     ffffsi 

1560 
4830 
8076 

1888 
5156 
8899 

8S16 
fr481 
87« 

9644 

5806 
9015 

2871 
6181 
9868 

8198 
(M56 
9090 

0012 

8S3 

Pboportionai.  Farts. 


DIff. 

1 

8 

8 

4 

6 

6 

r 

8 

9 

a-is 

35.5 

71.0 

106.5 

142.0 

177.6 

218  0 

848.6 

884.0 

819.5 

354 

35.4 

70.8 

106.2 

141.6 

177.0 

212.4 

m.% 

888.8 

818.6 

fm 

35.8 

70.6 

106.9 

141.2 

176.6 

211.8 

847.1 

888.4 

817.7 

852 

35.2 

70.4 

105.0 

140.8 

178.0 

211.8 

846.4 

281.6 

816.8 

351 

35.1 

70.2 

106.8 

140.4 

175.5 

210.6 

845.7 

880.8 

816.9 

350 

a5.o 

70.0 

106.0 

140.0 

175.0 

210.0 

845.0 

280.0 

816.0 

819 

34.9 

60.8 

104.7 

189.6 

174.5 

209.4 

844.8 

879.8 

814.1 

348 

84.8 

69.6 

104.4 

189.2 

174.0 

208.8 

1M8.6 

278.4 

818.8 

847 

34,7 

69.4 

104.1 

138.8 

178.6 

206.8 

842.9 

877.6 

818.8 

846 

84.6 

69.8 

108.8 

138.4 

178.0 

807.6 

842.8 

8716.8 

SU.4 

345 

84.5 

69.0 

103.6 

188.0 

172.6 

807.0 

841.5 

876.0 

810.5 

344 

34.4 

68.8 

108.2 

137.6 

172.0 

806.4 

840.8 

87K.8 

800.6 

34.) 

84.3 

68.6 

102.9 

187.8 

m.5 

806.8 

840.1 

874.4 

808.7 

312 

84.2 

08.4 

102.6 

136.8 

171.0 

805.2 

239.4 

873.6 

807.8 

SMI 

84.1 

68.2 

102.8 

136.4 

170.5 

204.6 

838.7 

872.8 

306.9 

340 

34.0 

GK.O 

102.0 

136.0 

170.0 

801.0 

238.0 

872.0 

806.0 

330 

33.9 

67.8 

101.7 

136.6 

160.5 

808.4 

237.8 

8n.8 

aooj 

338 

33.8 

67.6 

101.4 

185.2 

100.0 

802.8 

836.6 

270.4 

804.8 

337 

88.7 

07.4 

101.1 

184.8 

168.5 

808.2 

835.9 

869.6 

806.8 

836 

33.6 

67.2 

100.8 

184.4 

108.0 

801.6 

835.8 

868.8 

808.4 

835 

33.5 

67.0 

100.5 

134.0 

167.5 

201.0 

881.5 

868.0 

801.5 

331 

:33.4 

66.8 

100.2 

138.6 

167.0 

800.4 

838.8 

867.8 

800.6 

838 

.3.3.3 

66.6 

99.9 

188. 2 

166.6 

199.8 

888.1 

866.4 

290.7 

XiJ 

3.3.2 

664 

99.6 

132.8 

166.0 

199.8 

832.4 

865.6 

298.6 

3:J1 

33.1 

66  2 

99.3 

132.4 

166.6 

198.6 

831.7 

864.8 

897.0 

830 

33.0 

66.0 

99.0 

132.0 

165.0 

198.0 

881.0 

864.0 

897.0 

3d9 

32.9 

65.3 

98.7 

131.6 

164.5 

197.4 

830.8 

868.8 

ami 

328 

32.8 

t>5.6 

98.4 

181.2 

164.0 

196.8 

8sH).6 

868.4 

896.8 

ftJ7 

38.7 

65.4 

98.1 

130.8 

168.5 

196.2 

828.9 

861.6 

894.8 

826 

32.0 

65.2 

97.8 

130.4 

168.0 

195.6 

828.2 

860.8- 

888.4 

325 

32.5 

65.0 

97,5 

180.0 

168.5 

195.0 

827.5 

860.0 

898.5 

821 

32.4 

&4.8 

97.2 

120.6 

162.0 

194.4 

226.8 

850.8 

291.6 

323 

32  3 

&4.6 

96.9 

129.2 

161.5 

198.8 

226.1 

868.4 

890.7 

822 

32.2 

64.4 

96.6 

128. h 

161.0  1 

103.2 

825.4 

SS7.6 

880.8 

LOGAUITHMS  OF  KITHBBB8* 


189 


No.  185  L.  laO.] 


[No.  149  L.  17B. 


N. 


130884 


8.^ 
9879 


143015 

8148 
flei9 


06» 
8856 

TOW 


0977 
4177 
7854 


OlM 
33S7 

6488 
9BS7 


6886 


1C1868 
43fS3 
7817 


17Q90S 
8186 


6640 
8664 


1667 
4650 
7618 


0665 

8478 


0606 
8639 

8748 


S900 

9948 
8966 


1967 
4917 
7906 


0648 
8769 


1298 
4496 

Ten 


8961 
7066 


0148 
8906 
0946 


8906 


1141 
4060 


1619 
4614 
7987 


1196 
4263 

7867 


8610 
6649 
9567 


2564 

6541 
6497 


1434 
4351 


1939 
6188 
680B 


2900 
6451 
8618 


1450 
4574 

7870 


1768 


7966 


0756 
8816 
6658 
9668 


2868 

5838 
8792 


1726 
4641 


1068 
4120 
7154 


0168 
8161 
6184 
9066 


2019 
4932 


2660 
5760 
8984 


2000 

6066 
9049 


9076 
6196 

8894 


1870 
4424 
7457 


0469 
8460 
6480 
9880 


2311 


2389 
6507 

8008 


1676 
4728 
7r69 


0769 
8766 
6796 
9674 


9608 
6612 


8819 
6406 
9664 


2702 
5618 

8911 


1962 
6082 

6061 


1068 
4066 
7098 
99G8 


2895 


PROPORTioNAii  Parts. 


DUE. 


821 
890 
319 
818 
817 
816 
815 
814 
818 
812 

811 
810 
809 
806 
807 
806 
806 
804 
806 
802 

801 
800 
299 
896 
897 
896 
296 
994 


891 
890 


287 


82.1 
82.0 
81.9 
81.8 
81.7 
81.6 
81.5 
81.4 
81.8 
81.8 

81.1 
81.0 
80.9 
80.8 
80.7 
80.6 
80.5 
80.4 
80.8 
80.2 

80.1 
80.0 
89.9 
89.8 
29.7 
89.6 
S9.5 
29.4 
89.8 
29.8 

S9.1 
89.0 
£8.9 
88.B 
28.7 
88.6 


64.2 
64.0 
68.8 
68.6 
68.4 
68.2 
68.0 
68.8 
02.6 
62.4 

68.9 
68.0 
61.8 
61.6 
61.4 
61.2 
61.0 
60.8 
60.6< 
60.4 

60.2 
60.0 
69.8 
69.6 
60.4 
69.2 
69.0 
68.8 
56.6 
68.4 

58.9 
68.0 
67.8 
OT.6 
W.4 
M,2 


8 

4 

6 

6 

7 

8 

96.8 

126.4 

160.5 

192.6 

294.7 

256.8 

96.0 

188.0 

160.0 

192.0 

294.0 

856.0 

95.7 

127.6 

159.6 

191.4 

228.8 

265.2 

95.4 

187.2 

159.0 

190.8 

222.6 

261.4 

95.1 

126.8 

156.5 

190.2 

221.9 

258.6 

94.8 

126.4 

158.0 

189.6 

221.2 

262.6 

94.5 

126.0 

157.5 

189.0 

220.5 

2S2.0 

94.2 

125.6 

157.0 

188.4 

219.8 

251.8 

98.9 

126.2 

156.6 

187.8 

219.1 

260.4 

96.0 

m.8 

166.0 

187.2 

218.4 

249.6 

96.8 

1»4.4 

166.6 

186.6 

217.7 

248.8 

96.0 

124.0 

155.0 

186.0 

217.0 

248.0 

9S.7 

128.6 

164.5 

185.4 

216.8 

247.2 

0B.4 

128.2 

154.0 

184.8 

216.6 

240.4 

96.1 

122.8 

153.6 

184.2 

214.9 

2466 

91.8 

128.4 

153.0 

188.6 

214.2 

244.8 

91.6 

182.0 

162.5 

188.0 

218.6 

244.0 

01.2 

121.6 

152.0 

183.4 

212.8 

243.2 

90.9 

121.2 

151.6 

181.8 

212.1 

242.4 

90.6 

120.8 

151.0 

181.2 

211.4 

241.6 

90.8 

120.4 

160.6 

180.6 

210.7 

240.8 

00.0 

120.0 

160.0 

180.0 

210.0 

240.0 

89.7 

119.6 

149.6 

179.4 

209.8 

289.2 

80.4 

119.2 

149.0 

178.8 

206.6 

288.4 

80.1 

118.8 

148.6 

178.2 

907.9 

287.6 

88.8 

118.4 

148.0 

177.6 

207.2 

288.8 

88.6 

118.0 

147.6 

177.0 

206.6 

286.0 

88.2 

117.6 

147.0 

176.4 

206.8 

286.2 

87.9 

117.2 

146.5 

175.8 

206.1 

2^.4 

87.6 

116.8 

146.0 

176.2 

204.4 

283.6 

87.8 

116.4 

146.5 

174.6 

208.7 

282.8 

87.0 

116.0 

145.0 

174.0 

208.0 

282.0 

86.7 

115.6 

144.6 

178.4 

202.8 

281.2 

86.4 

115.2 

144.0 

172.8 

201.6 

280.4 

86.1 

114.8 

148.5 

172.2 

200.9 

229.6 

86.6 

114.4 

148.0 

171.6 

200.2 

228.8 

.84 


lOOABITHMS  OF  KUlfBEBS. 


No.160Ll176.j 

CNo.  169L.880. 

N. 

0 

1 

f 

» 

4 

i 

• 

7 

8 

e 

Diff. 

150 

1 

178091 
8877 

6881 
9264 

6670 
9652 

6959 
0889 

7248 

7536 

7S25 

8113 

8401 

8689 

S80 

0126 
2986 
5a25 
8647 

0413 
8270 
6108 
89S8 

0099 
8555 
0391 
9209 

0966 
8839 
6674 
9490 

1272 
4128 
6056 
9771 

1668 
4407 
7239 

887 
885 
888 

2 
8 

4 

181844 
4691 
7SS1 

2129 

4975 
7808 

2415 
5259 
8064 

2700 
5542 
8366 

0051 
2846 
5028 
8882 

8S1 
871) 
878 
876 

S 
6 
7 

8 

190632 
8125 
6000 
8657 

0612 
3403 
6176 
8982 

0802 
3681 
6458 
8206 

1171 
8059 
6729 
9481 

1451 
4237 
7006 
9755 

1780 
4514 
7281 

2010 
4702 
7556 

2289 
5060 
7882 

2567 
5846 
8107 

0029 
2701 

5175 
8173 

0R53 
8518 
6166 
8798 

0806 
8088 

5746 
8441 

0577 
8805 

6016 

8no 

0850 
8577 

6286 
8979 

1124 
8848 

6566 
9247 

874 
878 

971 
880 

0 
160 

1 
2 

201897 

4120 
6820 
9515 

1670 

4891 
7096 
9788 

1943 

4663 
7365 

2210 

4934 
76M 

2188 

5204 
7904 

0061 
2720 
5378 
8010 

0619 
2986 
5638 
8273 

0586 
3252 
5002 
8536 

1121 
87^ 
6430 
9060 

1388 
4049 
6694 
9823 

1654 
4314 
0057 
9586 

1921 
4579 
7221 
9846 

867 
866 
264 
868 

8 

4 
5 

212188 
4844 
7484 

2454 
5100 
7747 

8 
7 
8 
9 

220106 
2716 
5809 
7887 

28 

0870 
2976 
5668 
8144 

0631 
8236 
5826 
8400 

0802 
3496 
6084 
8657 

1153 
8755 
6342 
8013 

1414 
4015 
6600 
9170 

1676 
4274 
6858 
9426 

1986 
4.^38 
7115 
9682 

2196 
4792 
7872 
9988 

2456 
5051 
7680 

861 
258 
8S8 

0193 

256 

PBOPORTIONAL  PARTS. 


BIfl. 

1 

8 

8 

4 

5 

6 

7 

8 

9 

286 

28.5 

57.0 

85.5 

114.0 

142.5 

171.0 

199.5 

888.0 

856.5 

284 

28.4 

56.8 

85.2 

113.6 

142.0 

170.4 

198.8 

227.2 

255.6 

288 

28.8 

56.0 

84.9 

118.2 

141.5 

169.8 

198.1 

226.4 

854.7 

282 

28.2 

56.4 

84.6 

112.8 

141.0 

169.2 

197.4 

226.0 

868.8 

281 

28.1 

66.2 

84.3 

112  4 

140.5 

168.6 

196.7 

284:8 

8S8.9 

280 

28.0 

66.0 

840 

112.0 

140.0 

168.0 

100.0 

224.0 

858.0 

279 

27.9 

55.8 

88.7 

111.6 

189.5 

lff7.4 

195.8 

228.8 

861.1 

278 

27.8 

55.6 

83.4 

111.2 

139.0 

166.8 

194.6 

222.4 

860.8 

277 

27.7 

56.4 

83.1 

110.8 

188.5 

166.2 

198.9 

281.6 

848.8 

276 

2r.6 

55.2 

82.8 

110.4 

188.0- 

165.6 

198.2 

280.8 

848.4 

275 

27.5 

56.0 

88.5 

110.0 

187.5 

166.0 

192.5 

820.0 

847.5 

274 

27.4 

64.8 

82.2 

109.6 

187.0 

164.4 

191.8 

210.8 

846.6 

278 

27.8 

54.0 

81.9 

109.2 

136.5 

168.8 

191.1 

218.4 

845.7 

272 

27.2 

64.4 

81.6 

108.8 

186.0 

168.2 

190.4 

217.6 

844.8 

271 

27.1 

54.2 

81.8 

108.4 

135.5 

102.6 

180.7 

216.8 

848.0 

270 

27.0 

54.0 

81.0 

108.0 

135.0 

168  0 

189.0 

216.0 

848.0 

269 

26.9 

58.8 

80.7 

107.6 

184.5 

161.4 

188.3 

815.8 

848.1 

288 

26.8 

58.6 

80.4 

107.2 

134.0 

160.8 

187.6 

814.4 

841.2 

867 

26.7 

58.4 

80.1 

106.8 

183.5 

160.2 

186.9 

818.6 

840.8 

866 

26.6 

53.2 

70.8 

106.4 

183.0 

159.6 

186.2 

818.8 

880.4 

865 

26.5 

53.0 

79.5 

106.0 

182.6 

159.0 

185.6 

818.0 

888.5 

264 

26.4 

52.8 

79.2 

105.6 

1S2.0 

158.4 

184.8 

811.8 

887.6 

863 

26.3 

52.0 

78.9 

105.2 

131.5 

157.8 

164.1 

810.4 

886.7 

262 

28.2 

62.4 

78.6 

104.8 

181.0 

157.2 

183.4 

809.6 

885.8 

861 

26.1 

52.2 

78.3 

104.4 

130.5 

156.6 

188.7 

808.8 

884.9 

860 

86.0 

68.0 

78.0 

104.0 

180.0 

156.0 

182.0 

808.0 

884.0 

259 

25.9 

51.8 

T7.7 

103.6 

129.5 

155.4 

181.8 

807.8 

8SS.1 

258 

25.8 

51.6 

77.4 

103.2 

129.0 

154.8 

180.6 

806.4 

888.8 

257 

25.7 

51.4 

TT.l 

102.8 

128.5 

154.2 

179.9 

806.0 

881.8 

256 

25.6 

51.2 

70.13 

102.4 

128.0 

158.6 

179.2 

804.8 

880.4 

255 

25.5 

51.0 

76.5 

102.0 

lSt7.5 

153.0 

178.6 

804.0 

889.5 

LOGABnmfS  OF  KITMBSBa 


135 


]sa.l70I^2a(Kl 


[No.  lao  L.  27a 


N. 

O 

1 

f 

s 

4 

ft 

6 

7 

8 

9 

Diff. 

170 
1 
9 
3 

Sa0449 
S906 
5528 

0704 

aaso 

6781 

0007 

0000 
8604 
e088 
8548 

1215 
8757 
6886 
8799 

1470 
4011 
6637 
9019 

1724 
4264 
6799 
9299 

1979 
4617 
7041 
9660 

2234 
4770 
7202 
9800 

2488 
6028 
7544 

2742 
6276 
7795 

256 
268 
252 

0050 
2541 
6019 
7482 
9982 

0800 
2790 
5266 
7?28 

250 
249 
248 
246 

4 
5 
G 

7 

840549      07D9 
.3088      3S85 
6518      6750 
7»;8      8219 

1<M8 
8584 

6006 
8464 

1297 
8782 
62S2 
8709 

1546 
406O 
6499 
8054 

1795 
4277 
6745 
9198 

2044 
4526 

6991 

9m 

2293 
4772 
7237 
9687 

0176 
2610 
6061 

7489 
9833 

245 
248 
242 

241 
389 

8 
9 

180 

1 

2S0i20 
£858 

5S78 
7B79 

0864 
8096 

S514 
7Vf8 

0906 
8888 

6756 
8158 

1151 
8580 

6996 

8898 

1895 
8882 

6287 
8837 

1088 
4064 

6477 
8877 

1881 
4806 

6718 
9116 

2125 
4648 

6968 
9856 

2868 
4790 

7198 
9694 

2 
3 
4 

6 

260071 
8451 
4818 
7172 
9518. 

081O 
2688 
5064 
7406 
9740 

0548 
2825 
6290 
7M1 
9980 

a?87 
816S 

7875 

1025 
3899 
6761 
8110 

1268 
8686 
6996 
8844 

1601 
8878 
6232 
8578 

1789 
4109 
G467 
8812 

1976 
4846 
6702 
9046 

2214 
4562 
6937 
9279 

288 
237 
236 
284 

0318 
2588 
4850 
7151 

0446 

27ro 

6081 
7880 

0679 
8001 
6811 
7809 

0912 
8233 
5642 
7888 

1144 
8164 
6T72 
8067 

1877 
3606 
6002 
8296 

1609 
892r 
6232 
8625 

288 
232 
280 
229 

7 

8 
9 

271842 
4158 
6402 

2074 
4889 
6692 

2306 
4620 
61ttl 

PsopomxoNAi*  Pabtb. 


Diff, 


2B5 
254 
258 
252 
261 
250 
249 
248 
2f7 
246 


944 
248 
242 
HI 
210 


296 
235 

234 


281 
280 


227 
2» 


25.6 
25.4 
25.8 
25.2 
25.1 
25  0 
24.9 
24.8 
24.7 
24.6 
24.5 

24.4 
24.8 
24.2 
24.1 
24.0 
23.9 
28.8 
28.7 
28.6 
28.6 

28.4 
28.8 
28.2 
28.1 
28.0 
22.9 
22.8 
22.7 
22.6 


62. 0 

»>.8 
«^  *5 
6<).  I 
6(»  :3 
6(1  (i 
41^^ 

4&.4 
49.2 
49.0 

4B.4 

48, S 

47,8 
47.0 
47.4 
47  2 

17  '* 

46.8 
46.6 
46.4 
46.9 
46.0 
45.8 
4S.0 

^i     I 
4S.9     I 


76.6 
76.2 
75.9 
75.6 
75.3 
75.0 
74.7 
74.4 
74.1 
73.8 
TO.6 

78.2 
72.9 
72.6 
72.8 
72.0 
71.7 
71.4 
71.1 
70.8 
70.6 

70.2 
69.9 
69.6 
69.8 
69.0 
68.7 
68.4 
68.1 
67.8 


lOS.O 
101.6 
101.2 
100.8 
100.4 
100.0 
99.6 
99.2 
96.8 
96.4 
96.0 

97.6 
97.2 
96.8 
96.4 
96.0 
96.6 
96.2 
94.8 
94.4 
94.0 

93.6 
98.2 
02.8 
92.4 
92.0 
91.6 
91.2 
90.8 
90.4 


127.5 
127.0 
1S8.5 
128.0 
125.5 
125.0 
124.6 
124.0 
123.6 
123.0 
122.6 

122.0 
121.6 
121.0 
120.6 
120.0 
119.6 
119.0 
118.5 
118.0 
117.6 

117.0 
110.6 
116.0 
116.5 
116.0 
114.6 
114.0 
113.5 
113.0 


153.0 
152.4 
151.8 
151.2 
160.6 
150.0 
149.4 
148.8 
148.2 
147.6 
147.0 

146.4 
145.8 
145.2 
144.6 
144.0 
148.4 
142.8 
142.2 
141.6 
141.0 

140.4 
139.8 
139.2 
138.6 
188.0 
187.4 
136.8 
136.2 
135.6 


175.6 
177.8 
ITT.l 
176.4 
175.7 
175.0 
174.8 
173.6 
172.9 
172.2 
171.6 

170.8 
170.1 
109.4 
168.7 
168.0 
167.8 
166.6 
165.9 
165.2 
164.6 

168.8 
168.1 
162.4 
161.7 
161.0 
160.3 
169.6 
158.9 
1582 


204.0 

203.2 
202.4 
201.6 
200.8 
200.0 
199.2 
198.4 
197.6 
196.8 
196.0 

195.2 
194.4 
196.6 
192.8 
192.0 
191.2 
190.4 
180.0 
188.8 
188.0 

187.2 
186.4 
185.6 
181.8 
184.0 
188.2 
1SJ.4 
181.6 
180.8 


L30 


LOGAUTTHMS  OF  KUMBXSa 


No.  1ML.9T8.] 

[Ko.  214  L.  aas. 

H. 

0 

1 

i 

S 

4 

h 

6 

7 

8 

9 

Diff. 

278754 

8982 

0811 

9489 

9667 

190 

9896 

0128 

fBm 

4666 
6905 
9148 

0861 
2622 
4882 

7180 
9866 

0678 
2649 
5107 
7854 
9689 

0806 

6882 

7578 
9612 

886 
827 
826 
825 
828 

1 

8 
4 

261088 
8801 
6067 
7800 

1281 
8627 
5788 
8096 

1486 
8798 
6007 
8849 

1715 
8079 
8288 
8478 

1942 
4205 
6466 
8606 

2169 
4481 
6081 
8920 

5 

? 

8 
9 

290085 

4460 
6685 
88S8 

OOBff 
2478 
4687 
6684 
9071 

0480 
26U9 
4907 
7104 
9260 

ma 
asm 

5127 
7888 
9607 

0985 
8141 
6347 
7548 

was 

1147 
8868 

6667 
7761 
9943 

1869 
8584 
57«7 
7979 

IGOl 
8804 
6007 
8108 

1818 
4025 

8416 

2084 
4246 
6446 
8085 

829 
821 
820 
810 

0181 

2881 
4491 

8^ 

08» 

0654 
8901 

QC95 

2764 
4921 
7008 
9804 

0818 

2080 
5186 
7)»« 
9417 

tl8 

217 
816 
815 
818 

200 

1 
2 
8 

4 

801080 
8198 
6851 
7498 
9680 

1847 
8412 
6068 

7710 
9848 

1484 
86tt8 
6781 
7984 

1681 
8644 
5006 
8187 

1808 
40B9 
8211 
8861 

2114 
4275 
6425 
8664 

00B6 
2177 
4280 
6800 
8481 

0268 
2868 
4499 
0909 
8080 

<VI81 
2600 
4710 
6809 
8608 

0693 
2812 
4020 
7018 
9106 

0906 
9028 
5180 
7227 
0814 

1118 
aBi84 
5840 
7488 
9688 

1880 
8445 
6551 

7648 
9780 

1548 
8666 
6760 
7854 
9986 

818 

811 
810 
800 

806 

5 

e 

7 
8 

811754 
8887 
6070 
8068 

^ 
^ 

9 
210 
1 
2 
8 

820146 

2219 
4282 
6886 
8380 

0854 

2426 

4488 
8541 
8588 

0602 

8688 

4004 
6745 
8787 

0TG9 
28m 
4899 
6050 
8901 

0977 

8046 

5105 
7155 
9194 

1184 

8868 

5310 

7X59 

!  9308 

1801 

8458 
5516 
7568 
9601 

1568 

8665 
5721 
7767 
9805 

1805 

3871 
5926 
7972 

O0G8 
2094 

2012 

4077 
6181 
8176 

207 

206 
206 
204 

^ 

903 

4 

880414 

0617 

0819 

1022 

1225 

1  1427 

1630 

1832 

802 

Pbopobtional  Parts. 


Dur. 

1 

8 

8 

4 

5 

6 

7 

8 

9 

226 

88.5 

45.0 

67.5 

90.0 

112.5 

135.0 

157.5 

180.0 

908.6 

224 

22.4 

44.8 

67.8 

69.0 

112.0 

134.4 

166.8 

179.8 

201.6 

228 

22.8 

44.6 

66.9 

69.2 

111.5 

1338 

356.1 

178.4 

200.7 

222 

22.2 

44.4 

66.6 

66.8 

111.0 

133.8 

155.4 

177.6 

199.6 

221 

82.1 

44.2 

66.8 

68.4 

110.5 

132.6 

154.7 

176,8 

198.0 

220 

82.0 

44.0 

66.0 

88.0 

110.0 

182.0 

154.0 

176.0 

198.0 

219 

21.9 

48.8 

65.7 

87.6 

109.5 

131.4 

153.3 

175.8 

197.1 

218 

81.8 

48.6 

65.4 

87.2 

109.0 

130.8 

152.6 

174.4 

196.8 

217 

81.7 

48.4 

65.1 

66.8 

106.6 

180.2 

151.9 

178.6 

195.8 

216 

21.6 

48.8 

64.8 

B6.4 

108.0 

129.6 

151.2 

172.8 

194.4 

215 

21.6 

48.0 

64.5 

86.0 

107.5 

129.0 

160.5 

178.0 

198.5 

214 

81.4 

48.8 

64.8 

85.6 

107.0 

128.4 

148.8 

171.8 

188.6 

218 

81.8 

48.0 

68.9 

85.8 

106.5 

127.8 

149.1 

170.4 

191.7 

218 

81.9 

48.4 

68.6 

84.8 

106.0 

127.2 

148.4 

169.6 

190.8 

211 

81.1 

48.8 

68.8 

84.4 

106.5 

126.6 

147.7 

168.8 

189.9 

210 

21.0 

42.0 

68.0 

84.0 

105.0 

126.0 

147.0 

168.0 

189.0 

209 

80.9 

41.8 

68.7 

88.6 

104.6 

125.4 

146.8 

197.8 

188.1 

206 

90.8 

41.6 

68.4 

88.8 

IW.O 

1248 

145.6 

166  4 

187.8 

207 

80.7 

41.4 

68.1 

82.8 

103.5 

124.8 

144.9 

165.0 

186.8 

206 

80.6 

41.8 

61.8 

82.4 

108.0 

123.6 

144.8 

164.8 

185.4 

206 

80.5 

41.0 

CI  .6 

82.0 

1025 

128  0 

143.5 

164.0 

204 

80.4 

40.8 

61  8 

81.0 

102.0 

122.4 

142.8 

168.8 

188.6 

208 

80.8 

40.0 

60.9 

81.2 

101.5 

121.8 

148.1 

108.4 

iSi 

m 

80.2 

40.4 

60.0 

'».8 

101.0 

121.2 

141.4 

161.6 

liOOABTTHHS  OF  KUMBBRS. 


No.  S15Lu  338:3 


[NaS89L.88 


K. 


215 
0 

7 
8 

9 

290 
1 

3 

4 
5 
6 
7 
8 
9 


4404 

640O 
8490 


840444 


4808 
68eS8 
8305 


2188 
4108 


3817S8 
8618 
5488 
7866 
9816 


871008 
2018 
4748 
6B77 


06«e 

9000 
^4580 
6&40 
8500 


044S 
S87& 
4801 
e817 
81)85 


loir 

8800 

6675 
7542 
04O1 


1868 


8680 


884S 
48M 

6860 


0841 

S817 
4786 
6744 
8604 


0668 


e408 

8816 


OS16 

sno6 


7729 
9687 


1487 


5115 
6048 

87B1 


8044 

8067 

Toeo 

9054 


1080 

8014 
4981 
09S0 


oeeo 

8761 
4686 
6669 
8606 


0104 


4176 
6049 
7915 
9772 


1682 
8464 


7124 
8948 


8246 
6867 
72fX> 
9868 


1287 

8212 
6173 
7186 
9068  I 


1088 
2964 

4876 
6790 
8096 


0606 


8101 
9958 


1806 
8647 
5481 
7806 
9124 


8447 
6466 
7469 
9451 


1486 

8409 
6874 
7880 
9878 


1216 
8147 
6008 

6981 
8686 


0788 

2671 
4661 
6488 
8»7 


8649 
6668 
7669 
9660 


1682 

8006 
6670 
76S5 
9472 


1410 


6260 
7172 
9076 


0972 

2859 
4739 
6610 
8478 


8860 
6869 
7868 
9849 


1880 
8809 


5766 
7J20 
9666 


1008 


6462 
7868 
9206 


1161 

8048 
4986 
6796 
8669 


0148 
1991 
8881 
6664 
7488 
9806 


2175 
4015 
6846 
7870 
9487 


0618 
2800 
4198 
6Q8Q 
iSS 
9068 


4061 

6069 
8006 


0047 
2088 

8990 

6968 
7915 
9860 


1796 
8724 
6648 
7554 
9466 


1860 


5118 
6963 
8646 


FsopoRTzoNAL  Parts. 


0098 
2644 

4888 
6812 
8084 
9640 


8900 
8867 


0846 
8886 

4196 
6167 
8110 


0064 
1989 
8916 
6884 
7744 


1589 

8424 
5801 
7169 
9060 


2788 
4565 

6894 
8816 


0080 


DIff. 

1 

» 

8 

4 

5 

S 

7 

S 

9 

aoB 

201 
200 
199 

196 
197 
198 
106 

194 

80.8 

40.^ 

60.6 

80.8 

101.0 

121.2 

141.4 

101.6 

181. 

"20.1 

40.8 

60.8 

80.4 

100.5 

120.6 

140.7 

100.8 

180. 

20  O 

40.0 

60.0 

§2-2 

100.0 

120.0 

140.0 

160.0 

180 

19.9 
19.8 
19.7 
19.6 
19.5 
19.4 

89.8 

59.7 

79.6 

99.5 

119.4 

189.8 

150.2 

179 

m.t 

59.4 
59.1 

79.2 

78.8 

99.0 
98.5 

118.8 
118.2 

188.6 
187.9 

158.4 
167.6 

178. 
177, 

ao.d 

58.8 

78.4 

98.0 

117.6 

187.2 

166.8 

176. 

ao.o 

68.5 

78.0 

97.5 

117.0 

180.6 

166.0 

175. 

88.8 

56.2 

77.0 

97.0 

116.4 

185.8 

155.2 

174. 

198 
198 
191 
190 
189 
18B 
187 
186 

19.8 
19.8 
19.1 
19.0 
18.9 
i8.S 

16.6 

80.0 

B7.9 

r7.2 

96.6 

116.8 

186.1 

164.4 

178 

S.4 

67.6 

78.8 

96.0 

115.2 

184.4 

158.6 

m 

^.S 

67.8 

76.4 

96.6 

114.0 

138.7 

152.8 

171 

as.o 

57.0 

76.0 

96.0 

114.0 

188.0 

162.0 

171 

^.8 

66.7 

76.6 

94.5 

118.4 

188.8 

161.2 

170 

97.8 

56.4 

75.2 

94.0 

118.8 

181.6 

160.4 

169, < 

S7  41 

^l 

74.8 

96.5 

112.2 

180.9 

149.6 

108  i 

87.d 

66.8 

74.4 

08.0 

111.6 

180.2 

148.8 

167.- 

18.8 

18.4 

J8.a 

18.  a 
18.1 
18.0 
17.^ 

^T.O 

86.6 

74.0 

92.5 

111.0 

129.5 

148.0 

106  1 

186 

ailB 

66.2 

78.0 

98.0 

110.4 

128.8 

147.2 

106  { 

181 

88.0 

54.9 

78.2 

91.5 

109.8 

128.1 

146.4 

104  ' 

188 

86  ^ 

54.6 

72.8 

91.0 

109.2 

127.4 

145.6 

108  1 

188 

^  - 

64.8 

72.4 

90.5 

108.6 

126.7 

144.8 

102  1 

181 
180 
179 

54.0 

72.0 

90.0 

108.0 

120.0 

144.0 

102  < 

88.7 

71.0 

89.6 

107.4 

125.8 

148.2 

101.: 

138 


IX>OARITHyS  OF  XrUMBERS. 


No.  940  L.  880.1 

[No.  868  L.  431. 

K. 

0 

1 

t 

S 

4 

ft 

6 

7 

8 

8 

DifL 

240 

S8oeii 

8017 
8815 
6606 
7390 
9166 

0898 
2197 
8995 
5785 
7568 
9843 

0578 
8877 
4174 
5964 
7746 
96ii0 

0754 
8557 
4358 
6148 

7U24 
9696 

0984 
8787 
4588 

6881 
8101 
9675 

1116 
8917 
4718 
6499 
8279 

1886 
8097 
4801 
6677 
8456 

1476 
8877 
6070 
6866 
8634 

1666 

8466 
6849 
7084 
8811 

1887 
8686 
648S 
7818 

8969 

in 

180 

ira 

178 
17« 

0061 
1817 
8675 
6826 
7071 

8808 

0288 
1993 
8751 
6601 
7845 

8881 

0105 
8169 
8086 
5676 
7419 

8154 

0688 
fBMR 
4101 
6850 
7608 

9388 

0759 
8581 
4277 
6025 
7786 
9601 

17T 

2S0 

890985 
S697 
4458 
6199 

T5M0 
9674 

1112 
8878 
4627 
6874 

8114 
9847 

1288 
8048 
4802 
6548 

8887 

1464 
8284 
4977 
6788 

8461 

1641 
8400 
5162 
6806 

8684 

176 
17« 
175 
174 
173 

0020 
1745 
8464 
6178 
6881 
8679 

0198 
1917 
8686 
5346 
7051 
8749 

0866 
8080 
.880r 
5517 
7881 
8918 

0638 
8861 
88:8 
6688 
7891 
9087 

0711 
8488 
4140 
6868 
7561 
9857 

0888 

8606 
4380 
6080 
7781 
9426 

1066 
8777 
4498 
6199 
7901 
9605 

1888 
8918 
4668 
6870 
8070 
9764 

173 
179 
171 
171 
170 
169 

401401 
8181 
4884 

6640 
8240 
9938 

1578 
3292 
6006 
6710 
8410 

0108 
1788 
8467 

5140 
680r 
8467 

0271 
1956 
8635 

5307 

69ra 

8638 

0440 
8124 
8808 

5474 
7139 
8798 

0009 
8898 
8870 

6641 
7806 
8964 

0777 
8461 
4187 
5808 

0946 
2629 
4806 

6074 
7688 
9806 

1114 
2796 
4479 

6141 
7804 
9460 

1283 
8964 
4638 

6808 
7970 
9625 

1451 
8138 

4906 

6474 
8185 
9791 

109 

S60 

411620 
8800 

4978 
6641 
6801 
qaka 

168 
167 

167 
16G 
165 

0121 
1768 
MIO 
6045 
6674 
8297 
9014 

'0286 
1938 
8574 
6806 
6886 
8459 

0451 
8097 
8737 
6371 
6999 
8621 

0616 
1^1 
8901 
6634 
7161 
8788 

0?81 
8486 
4065 
6697 
7884 
8914 

0945 
8590 
4228 
5860 
7486 
9106 

1110 
27TW 
4392 
6023 
7848 
9268 

1275 
8918 
4566 
6186 
7811 
9429 

1488 
8068 

4718 
6349 
7978 
9691 

165 
164 
104 
163 
168 
168 

8 
9 

421604 
8246 
4882 
6611 
8135 
9762 

48 

0075 

0286 

0898 

1  0560 

0720 

0881 

1048 

1808 

161 

PBopoimoNAL  Parts. 


Diff. 

1 

8 

8 

4 

5 

6 

7 

8 

9 

178 

17.8 

85.6 

63.4 

71.2 

89.0 

106.8 

184.6 

142.4 

160.2 

177 

17.7 

85.4 

53.1 

70.8 

88.5 

106.8 

123.9 

141.6 

160.8 

176 

17.6 

85.8 

52.8 

70.4 

88.0 

106.6 

128.2 

140.8 

158.4 

175 

17.5 

85.0 

52.5 

70.0 

87.5 

106.0 

122.5 

140.0 

157.5 

174 

17.4 

84.8 

62.8 

69.6 

87.0 

104.4 

121.8 

189.8 

156.6 

178 

17.8 

ai.o 

61.9 

69.8 

86.5 

106.8 

121.1 

188.4 

155.7 

172 

17.8 

84.4 

61.6 

68.8 

86.0 

103.8 

120.4 

187.6 

154.8 

171 

17.1 

84.8 

51.3 

68.4 

85.5 

102.6 

119.7 

186.8 

158.9 

170 

17.0 

84.0 

51.0 

68.0 

85.0 

102.0 

119.0 

186.0 

168.0 

169 

16.9 

88.8 

60.7 

67.6 

81.5 

101.4 

118.8 

185.8 

1S8.1 

168 

16.8 

88.6 

60.4 

67.2 

84.0 

100.8 

117.6 

184.4 

151.2 

167 

16.7 

88.4 

60.1 

66.8 

83.5 

100.8 

116.9 

183.6 

160.3 

166 

16.6 

38.8 

49.8 

66.4 

83.0 

99.6 

116.8 

188.8 

149.4 

165 

16.5 

88.0 

49.5 

66.0 

82.5 

99.0 

115.5 

188.0 

148.5 

164 

16.4 

82.8 

49.8 

65.6 

82.0 

98.4 

114.8 

181.8 

147.6 

168 

16.3 

88.6 

48.9 

65.2 

81.5 

97.8 

114.1 

180.4 

146.7 

162 

16.8 

884 

48.5 

51.8 

81.0 

97.8 

113.4 

189.6 

145.8 

161 

16.1 

82.2 

48.3 

(M.4 

80.5 

96.6 

112.7 

188.8 

144.9 

LOOAinTHHS  09  KUMBBSa 


I  No. 


S70  I^  431.] 


1846 
8450 
5048 
0640 
6896 
9606 


1881 


4518 
6071 

7088 
9170 


0711 
aS47 
8777 


9645 


1348 

2847 
4840 


7S12 
8790 


0008 
178S 
8196 
4658 
6107 


2007 
8610 
6fi07 
6790 
8884 
9964 


1588 
8106 
4660 
6886 

7778 
0894 


0666 
8400 
8980 
5454 
6073 
8487 
9996 


1499 

8997 
4490 
69T7 
7400 
8988 


0410 
1878 
8341 
4799 


2167 
8770 
5807 
69«' 

8548 


0128 
1696 


7988 
9478 


1018 


4068 
6606 
7185 


0146 
1649 

8146 
4689 
6126 

7808 
9065 


0557 
8085 


8487 
4944 
6397 


8030 
5686 

7116 
8701 


0879 
1858 
8419 
4961 
6587 

8068 

9688 


1178 
8706 
4885 
6738 
7«76 
8780 


0896 
1799 

8896 
4788 
6874 
7756 


0704 
2171 


5090 
6&t8 


2488 

4000 


7875 


0487 
8009 
8976 
5187 

8M8 

9787 


8659 
4887 
5910 
7428 
8940 


0447 
1948 

8445 
4986 
6488 
7904 
9660 


0651 
8818 
877D 
5835 
6687 


[Na  299  L.  47 
I   Dif 


8649 
4^9 
5644 
7488 
9017 


0694 
8166 
8788 
6898 
6818 


9941 


1479 
8018 
4M0 
6068 
7570 
9091 


0597 
8096 

8504 
5065 

6671 


0587 


8464 
8085 
6881 


8809 
4409 
6004 
7608 
9176 


0758 


5449 
7003 


0096 
1633 
8165 
4698 
6814 
7781 
9848 


0748 
2^ 

8744 
6884 

6719 
8800 
9675 


1145 
2610 
4071 
5586 
6970 


Pbofobtional  Parts. 


8 

4 

5 

6 

7 

8 

48.8 

64.4 

80.6 

96.6 

112.7 

128.8 

48.0 

640 

80.0 

96.0 

112.0 

128.0 

47.7 

68.6 

79.6 

95.4 

111.8 

127.2 

47.4 

68.2 

79.0 

94.8 

110.6 

128.4 

47.1 

62.8 

78.5 

94.2 

109.9 

125.6 

46.8 

02.4 

78.0 

98.6 

109.2 

124.8 

46.5 

68.0 

77.6 

98.0 

108.5 

124.0 

46.2 

61.6 

77.0 

08.4 

107.8 

123.2 

45.9 

61.2 

76.5 

91.8 

107.1 

1.22.4 

45.6 

60.8 

76.0 

91.2 

106.4 

121.6 

46.8 

60.4 

75.6 

90.6 

105.7 

180  8 

46.0 

60.0 

7B.0 

90.0 

106.0 

120.0 

44.7 

50.6 

74.5 

80.4 

104.3 

119.8 

44.4 

50.2 

74.0 

88.8 

103.6 

118.4 

44.1 

58.8 

73.5 

88.2 

102.9 

117.6 

48.8 

68.4 

78.0 

87.6 

102.2 

116.8 

48.5 

58.0 

72.6 

87.0 

101.5 

116.0 

48.8 

57.6 

72.0 

86.4 

100.8 

115.2 

42.9 

67.8 

71.6 

86.8 

100.1 

114.4 

42.6 

56.8 

71.0 

SR2 

994 

118.6 

42.8 

66.4 

70.5 

84.0 

96  t 

112.8 

42.0 

56.0 

70.0 

84.0 

96.0 

112.0 

140 

LOGARITHVS 

OF  KUMBEM. 

No,  80OL.  177.1 

[Ka339U63l.    1 

N. 

0 

1 

% 

« 

4 

ft 

• 

7 

S 

f 

DOT. 

800 

477121 

7266 

7411 

7565 

rroo 

7844 

7980 

8188 

8278     8422 

145 

1 

8566 

8711 

8655 

8909 

9148 

9287 

0481 

0675 

0710     9888 

144 

144 

480007 

0151 

0804 

0488 

0609 

0795 

0608 

1012 

1156  1  1900 

1448     1586 

1729 

18718 

2016 

2150 

9808 

d445 

2688 

9781 

148 

9674 

8016 

8150 

8800 

8445 

8587 

8780 

8872 

4015 

4167 

148 

4800 

4442 

4585 

47^ 

4869 

5011 

6158 

6295 

5487 

6679 

148 

5721 

6868 

6005 

6147 

6880 

6480 

6572 

6714 

6856 

6907 

142 

7188 

7280 

7421 

7568 

7704 

7B45 

7986 

8127 

8260 

8410 

141 

8651 

8082 

8888 

8874 

9114 

9055 

9806 

0537 

9077 

9618 

141 

9066 

0009 
1808 

0080 
1642 

0880 

17W 

0620 
1088 

0661 
2008 

0801 
2201 

0041 
0841 

1061 
2481 

1900 

2621 

140 
140 

810 

401868 

8760 

2000 

8040 

8170 

8810 

8468 

8507 

8787 

8876 

4015 

180 

41S5 

4294 

4488 

4572 

4711 

4850 

4989 

5128 

6207 

5406 

ISO 

5544 

5^8 

5882 

60G0 

6000 

6288 

6876 

6516 

6058 

6701 

189 

6960 

7068 

7906 

7844 

7488 

7621 

7759 

7807 

8085 

817^ 

188 

8811 

8448 

8586 

87^a4 

8868 

8080 

9187 

9070 

9412 

0550 

laj 

9687 

9824 

9062 

0009 
1470 

0280 
1607 

VM 

0611 

0648 
2017 

0785 
9154 

0002 
8291 

187 
187 

601080 

1106 

1888 

84S7 

2564 

2700 

2887 

2978 

8100 

8246 

8862 

8518 

8666 

186 

8791 

8087 

4068 

4100 

4885 

4471 

4607 

4748 

4878 

5014 

ISO 

820 

6150 

6286 

5421 

6657 

6698 

6828 

5064 

6099 

6284 

6870 

186 

6506 

6640 

6776 

6011 

7046 

7181 

7816 

7451 

7586 

7721 

186 

7866 

7901 

8126 

8SQ0 

8895 

8580 

8664 

8790 

f984 

9068 

185 

9908 

98S7 

9471 

9606 

9740 

9874 

0009 
1849 

0148 
1488 

0877 
1616 

0411 
1760 

in 

610545 

0670 

0818 

0047 

1081 

1215 

1668 

2017 

2151 

2284 

2418 

2551 

2084 

2818 

2851 

8084 

8818 

8851 

8484 

8617 

8750 

8888 

4016 

4140 

4282 

4415 

183 

4548 

4681 

4818 

4946 

6079 

WU 

5344 

5476 

6600 

0741 

183 

5874 

6006 

6180 

6271 

6108 

6586 

6CC8 

ot-oo 

6088 

7064 

182 

7196 

7826 

7460 

7592 

7724 

7855 

7987 

8110 

8261 

8888 

182 

880 

8514 

8646 

8777 

8909 

9010 

om 

0S03 

9434 

9666 

9097 

181 

9886 

9960 

0090 
1400 

0221 
1580 

1661 

0484 

1702 

0615 

1U28 

0745 

2058 

Of  76 
21P8 

1007 
2314 

181 
131 

621188 

1289 

2444 

»75 

2705 

2886 

2966 

8096 

3836 

8356 

8486 

8616 

180 

8746 

8878 

4006 

4186 

4266 

4396 

4526 

4656 

47W 

4015 

180 

5015 

6174 

5304 

6484 

6563 

5698 

5951 

60R1 

0210 

129 

6880 

0460 

6596 

0787 

6856 

6965 

7114 

?^48 

7872 

7601 

190 

7C80 

7780 

7888 

8016 

8145 

1  8274 

8402 

85.S1 

8660 

8768 

199 

8 

8917 

9045 

0174 

9802 

9480 

1  9560 

9687 

0H15 

9043 

0070 
1851 

128 

128 

0 

580!ii00 

QS26 

10456 

0584 

0710 

1  0640 

0968 

1096  1  1223 

Pbopobtxonai.  Parts. 

Dlif. 

1 

». 

s 

4 

a 

4 

T 

8 

9 

189 

18.9 

27.8 

41.7 

55,6 

69.5 

83.4 

97.8 

111.8 
110.4 

125.1 

188 

18.8 

«r.6 

41.4 

55.2 

60.0 

82.8 

96.6 

104.2 

187 

18.7 

27.4 

41.1 

54,8 

68.5 

82.2 

05.9 

109.6 

128.3 

186 

18.6 

97.9 

40.8 

64.4 

68.0 

81.6 

95.2 

108.0 

122.4 

185 

18.5 

27.0 

40.6 

64.0 

67.5 

81.0 

04.5 

108.0 

12?  .5 

184 

18.4 

26.8 

40.2 

68.0 

67.0 

80.4 

93.8 

107.0 

120.6 

188 

18.8 

26.6 

809 

58.2 

66.5 

79.8 

88.1 

106.4 

110.7 

188 

18.2 

26.4 

80.6 

52.8 

66.0 

79.2 

92.4 

106.6 

118.8 

181 

18.1 

S6.8 

^9.3 

62.4 

65.5 

78,6 

91.7 

104.8 

117.9 

180 

18.0 

26.0 

89.0 

62.0 

65.0 

78.0 

91.0 

104.0 

m.o 

188 

Ui 

96.8 

88.7 

61.6 

64.5 

77.4 

90.8 

106.8 

116.1 

188 

25.6 

88.4 

61.2 

64.0 

76.8 

89.0 

102.4 

116.9 

m 

W7 

96.4 

88.1 

50.8 

63.5 

76.2 

88.9 

101.6 

114.8 

XfOOAKlTHMS  OV  KTTHBSB& 


9 

8 

4 

5 

6 

7 

S5.6 

88.4 

51.8 

64.0 

76.8 

89.8 

».4. 

88.1 

60.8 

63.6 

76.8 

88.9 

W.S 

87.8 

60.4 

68.0 

76.6 

88.8 

S.o 

87.5 

60.0 

62.6 

75.0 

87.6 

M.8 

87.8 

49.0 

62.0 

74.4 

86.8 

M.e 

86.9 

«.8 

61.5 

73.8 

86.1 

M.4 

86.8 

48.8 

61.0 

78.2 

86.4 

MS 

86.8 

48.4 

60.5 

72.6 

84  7 

94.0 

86.0 

48.0 

60.0 

72.0 

81.0 

0.8 

86.7 

47.6 

69.5 

71.4 

83.3 

142 


lOaXRITRMS  OP  KtTKBBBS. 


No.  88a  um,] 

[No.  414  L.  617.  [ 

N. 

0 

1 

a 

8 

4 

i 

0 

7 

8 

0 

Diff. 

380 
1 

579784 

9806 

0012 
1158 

0126 

1267 

0041 
1881 

;  0865 

'  1496 

0460  1  0688 

0607 

1836 

0611 
19R0 

114 

fi800S25 

1030 

1606 

1723 

2 

2003 

2177 

2291 

2404 

2518 

2681 

2746 

2K58 

2972 

8085 

8 

8199 

3312 

3426 

8580 

8652 

8766 

8879 

8992 

4105 

4218 

4 

4331 

4444 

4557 

4670 

4783 

4806 

nooo 

6122 

5235 

5^48 

lie 

5 

5461 

5574 

5686 

5799 

5912 

6024 

6187 

6250 

6362 

6475 

6 

6587 

6700 

6K12 

6025 

7037 

7149 

7988 

7874 

7486 

75r.9 

7 

7711 

7823 

7935 

8047 

8160 

8272 

6884 

8496 

8G06 

87ao 

113 

8 

8838 

8044 

9056 

9167 

9279 

9891 

9508 

9015 

9726 

0838 

0 

99SO 

0061 

0178 

0284 

0806 

0507 

0610 

0780 

084S 

0953 

880 

601065 

1178 

1237 

1399 

1510 

1621 

1782 

1848 

1955 

2066 

1 

2177 

2288 

2G;>9 

2510 

262] 

2782 

2848 

2954 

8064 

8175 

111 

2 

8386 

8307 

3508 

8618 

8729 

8810 

8950 

4061 

4171 

4282 

8 

4308 

4508 

4C14 

4724 

4884 

4945 

50B6 

5165 

5276 

5386 

4 

5196 

5606 

5717 

5827 

6087 

6047 

6157 

6867 

6877 

6487 

R 

0597 

6T07 

0817 

6027 

7087 

'|-?46 

7256 

79Ba 

7476 

7586 

110 

0 

7596 

7805 

7914 

8024 

8184 

S248 

8858 

6462 

8572 

8081 

7 

mi 

8900 

0(X)9 

9110 

0228 

9387 

0446 

9556 

9065 

9774 

8 

9888 

9092 

0101 

0210 

C819 

0428 

0587 

0646 

0755 

0864 

109 

GOOOn 

106i 

U91 

1290 

1406 

1617 

1Q» 

1734 

1848 

1951 

400 

2060 

2109 

2277 

2386 

2404 

2008 

2711 

2819 

2828 

8096 

S144 

8253 

3361 

ftl09 

3577 

3C86 

8794 

8902 

4010 

4118 

108 

4296 

4384 

4442 

4550 

4656 

4706 

4874 

4962 

6069 

5197 

5305 

5113 

5521 

5G28 

5736 

6844 

5951 

6059 

6166 

6274 

6381 

6489 

6596 

6704 

6811 

6019 

7026 

7138 

7»41 

7848 

7465 

7568 

7869 

rrrr 

7884 

7991 

8098 

8206 

8312 

8419 

107 

8526 

8638 

8740 

8ft47 

8064 

9061 

9167 

9274 

0381 

0488 

9504 

9n)l 

9808 

9914 

0021 
1086 

0128 
1192 

^ 

0641 
1405 

0417 
1511 

0S54 

1617 

G10660 

07G7 

0  573 

0979 

1788 

1829 

1936 

204S 

2148 

2254 

2800 

M66 

8572 

8078 

106 

410 

2784 

2890 

2996 

8102 

8S07 

8818 

8419 

3525 

8680 

87S6 

8842 

8047 

4053 

4150 

4264 

4870 

4475 

4581 

4686 

4792 

4807 

5003 

5106 

5218 

5819 

5424 

5529 

5634 

5740 

6845 

5050 

6055 

6160 

6265 

6370 

6476 

6581 

6686 

6790 

6885 

105 

7000 

7106 

7210 

7315 

7420 

7525 

7629 

7734 

7839 

7948 

FlK>POBTZOKAl«  PaB!I& 

DU 

1 

3 

8 

4 

6 

6 

7 

8 

.    1 

118 

11.8 

23.6 

85.4 

47.2 

50.0 

70.8 

82.6 

04.4 

106.2 

117 

11.7 

23.4 

85.1 

46.8 

58.5 

70.2 

81.0 

08.6 

105.8 

116 

11.6 

23.2 

84.8 

46.4 

68.0 

60.6 

81.2 

08.6 

104.4 

115 

11.5 

28.0 

84.6 

46.0 

67.6 

68.0 

80.5 

08.0 

108.6 

lU 

Vi 

22.8 

84.2 

45.6 

W.O 

68.4 

79.8 

01.8 

102.6 

118 

11.8 

22.6 

88.0 

45.2 

56.6 

67.8 

79.1 

80.4 

101.7 

llii 

ii.a 

22.4 

88.6 

44.8 

66.0 

67.2 

78.4 

80.6 

100.6 

111 

U.l 

82.9 

88.8 

44.4 

66.6 

66.6 

77.7 

88.8 

98.0 

110 

11.0 

22.0 

83.0 

44.0 

55.0 

66.0 

77.0 

88.0 

80.0 

100 

10.9 

21.8 

82.7 

48.6 

54.6 

65.4 

70.8 

87.2 

86.1 

108 

10.8 

21.6 

82.4 

48.2 

54.0 

64.8 

76.6 

86.4 

07.2 

107 

10.7 

21.4 

82.1 

42.8 

58.5 

64.2 

74.0 

85.6 

06.8 

106 

10.6 

21.2 

81.8 

42.4 

68.0 

68.6 

74.8 

84.8 

86.4 

US 

10.6 

21.0 

.81.6 

42.0 

68.5 

68.0 

78.5 

84.0 

04.6 

104  1  10.4  1 

20.8 

81.2 

41.6 

52.0 

62.4 

72.8  1  88.2  1 

88.6 

r^OaAKITHMS  OF  KUHBEBS. 


PnrtpoRTIONAL  PaSTS. 

8 

8 

4 

5 

0 

7 

81 .0 

ai.6 

42.0 

62.6 

63.0 

73. 

1      S0.8 

81.3 

41.8 

53.0 

63.4 

721 

\      20.6 

80.9 

41.3 

61.5 

61.8 

72 

1      SO. 4 

80.6 

40.8 

61.0 

61.3 

71  ' 

1      20.3 

80.3 

40.4 

60.5 

60.8 

70' 

1      8O.0 

800 

40.0 

60.0 

60.0 

70  1 

10.8 

20.7 

80.6 

49.5 

69.4 

69.i 

LOGARITHMS  OP  NUMBIBBS 


0OL.6ae.] 


a¥a4gOL.60S. 


37B6 
4786 
6675 

oeid 

7546 
8479 
9410 


1965 

3190 
8118 
40S1 
4958 
6870 
6785 
7696 
8609 
9610 


0126 

1883 
S285 

8137 
4087 
4985 
5831 
6736 
7618 
8609 
9606 


0285 
1170 
S053 


2935 
8815 
4698 
6569 
6444 
7817 
8188 


2947 
8869 
4880 
5769 
6705 
7640 
8579 
0608 


0481 
1858 


4126 
6045 
5962 
6876 
7789 
870O 
9610 


0617 
1422 


8227 
4127 
6025 
6021 
6815 
770r 
8698 
9486 


0878 
1268 
214'^ 
802:) 
8908 
4781 
5667 
6581 
7404 
8275 


8041 


4924 


6799 
7788 
8666 
9596 


0624 
1461 

2875 
8297 
4218 
5187 
6068 
6968 
7881 
8791 
9700 


0607 

1518 
2410 
3817 
4217 
5114 
6010 
6904 
7796 
8687 
9575 


0462 

1847 
2^80 
3111 
8991 
4866 
5744 
6618 
7491 
8862 


8185 
4078 
5018 
5966 
6892 
7826 
6760 
9689 


0617 
1548 

2467 
8890 
4810 
6228 
6146 
7069 
7973 
8882 
9791 


0098 

1608 
2606 
8407 
4807 
6204 
6100 
6994 
7886 
8776 
9664 


0660 
1485 
2818 
8199 
4078 
4966 
6833 
6706 
7678 
8449 


4172 
5112 
6060 
6986 
7920 


9782 


0710 
1686 

2660 
8482 
4402 
5820 
6286 
7161 
8068 
8978 


0789 

1698 
2696 
8497 
4896 
6294 
6189 
7068 
7975 
8865 
9758 


1624 
2406 
3287 
4166 
6044 
6019 
6793 
7666 
8685 


8824 
4266 
6206 
6148 
7079 
8018 
8945 
9875 


0802 
1738 


8674 
4494 
&112 
6828 

8154 
9064 
9978 


0879 

1784 
2680 
8687 
4486 
5888 


6279 
7172 
8064 
8958 
9841 


0728 
1612 
2494 
8875 
4254 
6181 
6007 
6880 
7753 


8418 
4800 
5299 
6237 
7178 
8106 
9068 
9967 


0695 
Itfil 

2744 
8666 
4686 
5603 
6419 
7388 
8315 
9155 


0068 
0970 

1874 
2777 
8677 
4576 
6473 
6866 
7261 
8158 
9012 
9980 


0816 
17C0 
2688 
8468 
4842 
6219 
6094 
6968 
7889 
8709 


3612 
4464 

6898 
6881 
7266 
8199 
9181 


0060 
0988 
1918 

2886 
8768 
4677 
5506 
6611 
7424 


9246 


0154 
1060 

1964 
2667 
8767 
4666 
6608 
0466 
7861 
8242 
9181 


0019 

0905 
1789 
2671 
8661 
4480 
6807 
0182 
7065 
7026 
8790 


8607 
4M8 
5487 
6424 
7860 
8298 
0224 


0158 
1080 
2005 

2929 
8860 
4769 
5687 
6602 
7516 
8427 
9337 


0245 
1161 

2065 
2967 
8867 
4756 
5662 
6547 
7440 
8881 
0220 


0107 

0098 
1877 
2799 
8688 
4617 
6894 
6209 
7142 
6014 
8883 


DUE. 


n 


90 


89 


87 


rR0P0RT10NAX«  PaRTS. 


1 

2 

8 

4 

5 

« 

7 

8 

9 

9.8 

19.6 

29.4 

89.2 

40.0 

08.8 

68.6 

78.4 

88.9 

9.7 

19.4 

29.1 

88.8 

48.5 

68.2 

67.9 

77.6 

87.8 

9.6 

19.2 

28.8 

88.4 

48.0 

67.6 

67.2 

76.8 

864 

9.5 

19.0 

28.5 

88.0 

47.5 

67.0 

66.5 

76.0 

85.5 

9.4 

18.8 

28.2 

87.6 

47.0 

66.4 

65.8 

76.3 

64.6 

9.3 

18.6 

27.9 

87.2 

46.5 

66.8 

65.1 

74.4 

88.7 

9.3 

18.4 

27.6 

36.8 

46.0 

65.2 

61.4 

78.6 

82.8 

9.1 

18.2 

27.8 

30.4 

45.5 

64.6 

63.7 

73.6 

61.9 

9.0 

18.0 

37.0 

36.0 

45.0 

64.0 

63.0 

73.0 

81.0 

8.9 

17.8 

26.7 

85.6 

41.5 

58.4 

63.8 

71.2 

89.1 

8.8 

17.6 

26.4 

85.2 

44.0 

02.8 

61.6 

9D.4 

%i 

8.7 

17.4 

96.1 

84.-8 

48.B 

7S8.2 

60.9 

60.« 

8.6 

17.2 

26.8 

84.4 

48.0 

51.0 

60.2 

68.8 

77.4 

liOOARITHMS  OF  ]IUMBBB8» 


1 


^fiooi^  6^ai 

</  • 

/  ■ 

f 

8 

4 

6 

• 

7 

i 

f      ^        oesa  j  9024. 

9144 

9S81 

9817  1 

9404 

9491 

9^ 

96 

OOll 
0677 

0098 

0184 
1060 

0871 

0668 
1838 

0444 
1809 

06 
18 

$  ;  7O07O4  •  irsito 

0968 

1186 

n  /        IGOB   j    ICHVi 
^           2431    f    2517 

1741 

1887 

1018 

1999 

8086 

8178 

SS 

S608 

2689 

2775 

2861 

3947 

8038 

81 

^ 

aS91        3377 

3463 

8540 

8636 

srai 

3807 

3898 

8S 

ft 

2[di      ^isao 

4822 

4408 

4494 

4579 

4665 

4751 

4C 

0008        0004 

6179 

tti65 

5850  ' 

6430 

5532 

560r 

6( 

0BeM      0CM9 

8035 

6120 

62G6 

6891 

6876 

(M68 

66 

^B        08O3 

88oo 

0974 

7069 

7144 

7229 

7816 

74 

^^0 

7O0B 

7740 

78B6 

7911 

7996 

8061 

8166 

88 

0401 

flQOO 

8C91 

8876 

8761 

8846 

8081 

9016 

91 

9070 

9440 

9SS4 

9609 

9694 

9779 

9868 

90 

710117 
0008 

QSQS 

CS87 

0871 

0156 

0540 

0635 

0710 

07 

1048 

1132 

1217 

1301 

1386 

1470 

1554 

]( 

1807 
8650 

1B02 

1976 

2060 

2144 

2329 

8813 

3897 

S^ 

2^734 

2818 

2902 

29H6 

8070 

8154 

8338 

88 

3101 
4S30 

B167 

«57S 

3650 

3742 

8826 

8910 

8994 

4078 

41 

^4414 

4497 

4581 

4665 

4749 

4883 

4916 

6( 

SS&l 

0885 

M18 

6602 

6586 

5669 

6763 

•5fc 

ssfiao 

6008 

eoerr 

6170 

8864 

6887 

6421 

6504 

6686 

M 

OOSl 

'•004 

7088 

7171 

7854 

7888 

7421 

71 

?  '       7071 

77&4 

7887 

7900 

8008 

8086 

8169 

6888 

« 

asBo 

8668 

8751 

8884 

8917 

9000 

9068 

91 

8 

4 

osai 

04X4 

0497 

9680 

9668 

9746 

9838 

9911 

9ti 

5 

O068 

tftft 

CfiS'lS^ 

0325 

Oi07 

0490 

0578 

0656 

0788 

oe 

loeB       IIM 

1288 

1816 

1398 

1481 

1568 

16 

C 

4^S      lOTs 

9(}R8 

2140 

2322 

8305 

2887 

*M 

* 

2^    \    27ie         2798 

2881 

2968 

8046 

8137 

8209 

8S 

8 
9 

ISI    1    SM8    ^ 

8020 

8702 

8784 

8866 

8948 

4030 

41 

^    ^  1  4asB 

4440 

4588 

4604 

4686 

4767 

4849 

40 

sao 

3358 

6840 

6488 

5608 

6686 

6667 

57 

6073 
6800 

6166 
8978 

6B8U 
7068 

6880 
7184 

0401 
7316 

6488 
7297 

66 
78 

77<M 

7786 

7866 

7948 

8089 

8110 

81 

t  \        R-A   I    ^S        »16 

8597 

8678 

8759 

8841 

8923 

90 

SI    ^r4\«S 

g8l?7 

M08 

9489 

9570 

9651 

9788 

98 

•3 
1 

'               '^*        COW 

0186 

0817 
lOSM 
1880 

0208 
1106 
1911 

0878 
1186 
1991 

0459 
1366 
30?i 

0540 
1347 
3158 

06 

»  1        168©   \    186» 

0944 
1750 

14 

23 

siol      aa»4  \  »«;4 

2B65 

8685 

2715 

8796 

2878 

2956 

80 

8868 

8488 

8518 

8598 

3679 

8759 

88 

4160 

4240 

4330 

4400 

4480 

4560 

46 

4960 

6010 

5130 

5300 

5379 

5359 

54 

\  *.\  ^ 

oo  \  e«7fl 

5759 

5888 

5918 

5096 

6078 

6157 

62 

\ 

C 

Pbopoktional  Pabts. 

V\  M  • 

3 

4 

5 

6 

7 

\     «    \     UtI     17.4 

36.1 

84.8 

48.5 

53.2 

60.9 

\     »   \    ¥.6       17.2 
\    ^    1    1  5       17.0 

25.8 

84.4 

43.0 

51. C 

60.2 

26.5 

84.0 

42.5 

51. C 

59.5 

» 

1    8.4  1    16.8 

85.3 

88.6 

42.0 

50.4 

1    58.8 

146 


LOGABITHMS  OF  S^UMBEBS. 


Na  M6  L.  786.1 


N.  I 


545  i  786907  I 

6  7103  , 

7  7987  I 

8  8781  I 

9  9572 


660 
1 
2 
8 
4 
6 
6 
7 
8 
9 

660 

1 
2 

3 
4 

6 
6 
7 
8 
9 

5ro 

1 

2 
8 
4 
5 

6 

7 
8 
9 

580 

1 
2 
3 
4 


6476 
7272 
8067 
8860 
9651 


1152 
1939 
27S85 
3510 
4293 
6075 
5855 
6634 
7412 

8188 
8903 
9736 


750506 
1279 
2018 
2816 
3688 
4348 
5112 

8875 
6686 
7306 
8155 
8912 
9668 


760422 
1170 
1928 
2679 

8438 
417G 
4923 
5660 
6413 


0442 
1230 
2018 
2801 
3588 

4:m 

5158 
5933 

ona 

7489 


9614 


0686 
1356 
2125 


5189 

6951 
6712 
74« 


9743 


6556 
7352 
8146 
8039 
9781 


0621 
1800 
2096 


8667 
4449 
5281 
6011 
6790 
7567 

8843 
9118 
9691 


0496 
1251 
2003 
2751 

3508 
4251 
4998 
5743 
6487 


0063 
1433 


2970 
8736 
4501 
6266 

6027 
6788 
7548 
8300 
9063 
9819 


0573 
1326 
2078 
2829 

8678 
4326 

5072 
5818 
6562 


6685 
7481 


9018 
9810 


0600 
1888 
2175 
2961 
3745 
4528 
5309 
6060 
6868 
7645 

8421 
9195 


6715  'I  6796 

—   7590 

8384 

917r 

9968 


r511 
8305 
9097 
9889 


0740 
1510 
2279 
8017 
8813 
4678 
5841 

6103 
6864 
7624 
8382 
9139 
98&1 


0649 
1402 
2153 
2901 

8653 
4400 
5147 
5892 


0678 
1467 
2254 
3080 
3823 
4606 
5387 
6167 
6045 
7722 

8496 
9272 


0045 
0617 
1587 
2356 
3128 
S880 
4654 
5417 

6180 
6910 
7700 
8158 
9214 
99TO 


ora4 

1477 
2228 
2978 

8727 
4475 
5221 
5966 
6710 


0757 
1546 


3118 
3902 


5465 


7028 
7800 


9350 


LNo.  6841x767. 


6874 
7670 
8463 
9256 


0047 

0636 
1624 
2411 
8196 
8960 
4762 
6543 
6323 
7101 
7878 

8663 
9427 


8 


Diff. 


T749 


0126 

0016 
1703 
2489 
3275 
4058 
4810 
6621 
6401 
7170 
7965 

8781 
9504 


0000 
0971 
1741 
2509 
8277 
4042 
4807 
6570 

6332 

709S 

7851 

8533  i  8609 

i  9366 


0O15  I  0121 
0790  I  0875 


0128 
0894 
1664 


3966 
4730 
5494 

6256 
7016 
7775 


1562 
2308 
3053 

3808 


1627 
2878 
3128 

8877 


4560 
5296  I  5370 
6041  6116 
6785  6860 


0277 
1048 
1818 
2686 


4119 


5646 

6408 
7168 
7027 


9441 


0196 
0060 
1708 
2453 


8062 
4000 
5445 
6190 


70ai  i  7113 

7829  I  7908 

8622  8701 

0414  9493 


0806 

0094 
1782 
2568 


4136 
4919 
5699 
6479 
TfSbG 


8806 
0582 


0854 
1125 
1805 
2663 
3480 
4106 
4060 
6722 

6484 
7S44 
8003 
8761 
9517 


0272 
1085 
17?« 
2580 
8278 

4087 
4774 
5620 


7007 


0864 

Km 

1860 
2647 
3431 
4215 
4007 
6777 
6566 
7884 
8110 


9650 


0431 
1202 

lo;^ 

2740 
3506 
4872 
5086 

5798 

6660 
7880 
8079 
8886 

0598 


0847 
1101 
1858 
8604 
8368 


4101 
4848 
6604 
6388 
7068 


TO 


77 


76 


73 


Proportional  Vartb, 


Diff. 

1 

2 

8 

4 

5 

6 

7 

8 

0 

83 

8.3 

10. 6 

21.9 

83.2 

41.5 

49.8 

68.1 

66.4 

74.7 

82 

8.2 

16. 4 

34.6 

32.8 

41.0 

49.2 

57.4 

65.6 

ra.8 

81 

8.1 

1G.2 

24.3 

32.4 

40.5 

48.6 

56.7 

64.8 

72.9 

80 

8.0 

IG.O 

24.0 

32.0 

400 

48.0 

56.0 

64.0 

78.0 

79 

7  0 

15.8 

23.7 

31.6 

39  5 

47.4 

55.3 

68.2 

71.1 

78 

7  8 

15.6 

28.4 

31.2 

39.0 

46.8 

54.6 

02.4 

70.2 

77 

7  7 

15.4 

2;m 

30.8 

38.5 

46.2 

58.9 

61.6 

60.3 

76 

7  6 

15.2 

2iJ.8 

30.4 

38.0 

45.0 

63.2 

60.8 

68.4 

75 

7.5 

15.0 

22.5 

30.0 

37.5 

46.0 

52.5 

60.0 

67.5 

74 

7.4 

14.8 

22.2 

29.6 

37.0 

44.4 

61.8 

50.8 

06.6 

rOGABITHHS  OF  KItHBEnS. 


L 

'*b,  58S  r-. 

7B7.1 

^/  • 

J    ' 

8 

8 

4 

5 

0 

7 

r^  1  TBTlsa    1    TSaO   I    7304     7879 

7458 

!  7827 

lioF 

7675 

7 

/      S            ^»8        7»72    '    8046     8120 

8194 

8268 

8342 

8410 

£ 

/     ^           8SS8 

8ns    •    8786  :  8860 

8934 

1  9008 

9082 

9156 

G 

L 

^   ♦        03TT 

1    9451     1    9625  ;  9599 

9678 

9746 

9820 

9894 

fi 

^  ;    770115 

i  0189    :    0963 

0336 

0410 

0484 

0657 

0631 

0 

/^;        OS5S 

1   O006        O990 

1078 

1146 

1220 

1298 

1867 

1 

(         X             MtiftT 
%  /        Si3SSS 

<     1661          1734 

1806 

1881 

1966 

2028 

2102 

S 

1    :£!«»        ^$408 

8542 

2615 

2688 

276^; 

2835 

2 

t          ^   .         S05& 

31SJB      aaoi 

ai»74 

3348 

8121 

8194 

3567 

3 

r          ^   /         378a 

3860 

3933 

4006 

4079 

4152 

4225 

4298 

4 

^            4^17 

4500 

4668 

4736 

4809 

4882 

4956 

6028 

5 

^            &»46 

5319 

5392 

5466 

5638 

5610 

6683 

5756 

5 

"5-            S974 

604T 

6120 

6193 

6866 

6888 

6411 

6488 

6 

^            6701 

67T4 

6S46 

6919 

6992 

TOW 

7137 

7209 

rj 

9             74:27 

7499 

7572 

7644 

7n7 

7789 

7862 

7984 

8 

^^O^   I         81S1 

8204 

»396 

8368 

8441 

8513 

8585 

Bliss 

8 

1    i         8874 

8947 

9019 

9091 

9163 

9236 

9308     Vfm 

9 

9669 

9741 

9613 

9686 

9957 

nfk9&       f.iiM 

a 

\MCv 

wji'i 

3   "SSeir 

A   ,          ICKTT 

g    1            l-TFiS 

08B9 

0461 

0633 

0605 

0677 

0749 

OHai 

0 

1109 

1181 

1253 

1^4 

1396 

1468 

IMO 

1 

iwrr 

1809 

1971 

2042 

2114 

2186 

mB 

2. 

6 

7 

53473 

2544 

2616 

2088 

2759 

2831 

2905i 

2j?rj 

9 

31^9 

aSBGO 

3338 

»I08 

8175 

3546 

8618 

S6K9 

» 

8 
11 

3»04 

46  rr 

39^75 

4046 

4118 

4189 

4261 

4832     ^m 

4 

4689 

4760 

4831 

4902 

4974 

5045     5J16 

6 

€Srio   '         5S30 
2   i         0751 

8         74oa 

4  1         81C8 

5  887S 

S401 
6112 

5472 
6183 

5M3 
6254 

5615 
6325 

5680 
6390 

5757 
6467 

6rt2S 

5 

68BSd 

6893 

69W 

7035 

7100 

7m 

'i-Ml^ 

7 

7531 

7602 

vd'i-a 

7744 

7815 

7885 

TUTiii 

B 

8:^239 

8310 

8381 

8151 

8522 

8593 

mm 

V( 

8946 
9651 

9016 
9722 

9087 
9792 

9157 
9863 

9238 
9933 

9299     D3IJJ*  1 

fl" 

G 

©oei 

0004     i^rTA  : 

~0 
01 

7«1S85 

0356 
1059 

0426 
1129 

M96 
1199 

0567 
1269 

0637 
1810 

0707 
1410 

orrs 

14W 

S  1         1G91 

1761 

1831 

1901 

1971 

2011 

2111 

2m 

^ 

Gao           230^ 
^         1    I         3093 

>      a            4488 

1      6  ;         5880 

«S.t«>3 

S532 

2602 

2672 

2742 

2812 

3fiH2  ' 

^ 

3  n  v^ 

3281 

3301 

3871 

8141 

3511     3.Vii  j 

3( 

a^-o 

3930 

4000 

4070 

4189 

4209     4^*7\> 

4,^ 

,    4  ,',8        4627 

4697 

4767 

4836 

4906     4'.m  ' 

U 

B^^4      saw 

6393 

5463 

5532 

5602     T^\"2 

:^i 

5,*  id        6019 

6088 

6158 

6227 

6297     fl*J6     (^J 

I^VVt        6718 

6782 

6853 

6921 

6990  1  71)00  1  r 

?^^rr      7406 

7475 

7545 

7614 

7683    rrs3  i  7$ 

t    t^rJQ        80O8 

8167 

8236 

8805 

8374     »m     K 

5      wSi 

1    tTr-JO        8789 

8868 

8027 

8996 

9066     6134  1  m 

Proportional  Parts. 


d 

8 

4 

5 

6 

7 

[     i&.o 

22.5 

30.0 

87.5 

45.0 

52.5 

14-8 

22.2 

29.6 

37.0 

41.4 

51.8 

\      14.6 

21.9 

29.2 

86.6 

43.8 

51.1 

1       14.4 

21.6 

28.8 

86.0 

43.2 

50.4 

14.2 

21.8 

28.4 

85.5 

42.6 

49.7 

14.0 

21.0 

28.0 

35.0 

42.0 

49.0 

4K.^ 

18.8 

20.7 

27.6 

84.5 

41.4 

118 


XfOOARITHMS  OF  KUHBBR8. 


Ka  680  L.  TNi] 


[N<fc674L.an. 


N. 

0 

1 

8 

• 

4 

6 

6 

7 

8 

9 

Dlff. 

680 

790841 

9409 

9478 

9647 

9616 

9686 

9754 

9883 

9608 

9961 

1 

8 
4 

6 
6 
7 
8 
9 

640 
1 
8 
8 
4 
5 

800QB9 

0717 
14M 
8060 

8774 
8457 
4189 
4881 
6601 

806180 
6858 
7686 

iSi 

9660 

1478 
8168 
8818 
8088 

4808 
4889 
6669 

6848 
6086 
7608 
8879 
8068 
9687 

0167 
0664 

1541 
8806 
2910 
8604 
4876 
4967 
6687 

6816 
6904 
7670 
8846 
9081 
9694 

0886 
0088 
1609 
8885 
2979 
8668 
4844 
6085 
6706 

6884 
7061 
7788 
8414 
9088 
9708 

0606 
0908 
1678 
8868 
8M7 
8780 
4418 
5008 
6T78 

6461 
7189 
7806 
8181 
9156 
9629 

0878 
1061 
1747 
8488 
8116 
8798 
4480 
5161 
6841 

6619 
7197 
7878 
8549 
0888 
9896 

0448 
1189 
1815 
8600 
8184 
8867 
4548 
6880 
6906 

6687 
7864 
7941 
8616 
0890 
9964 

0511 
1196 
1884 
8658 
32r)2 
8865 
4616 
6897 
6978 

6656 

7838 

8006 
8684 
9868 

0680 
1866 
1968 
8687 
8881 
4006 
4686 
5865 
6044 

67S8 
7400 
8076 
8751 
9485 

064Q 
1836 
8021 
8706 
3389 
4071 
4758 
5488 
6118 

0790 
7487 
8148 
8818 
9488 

06 

0081 

oroo 

1874 
8044 
8718 

8881 
4018 
4714 
5378 
6048 
6705 
7807 
8088 
86H8 
9^16 

0006 

vno 

1441 
8111 
8780 

3448 
4114 
4780 
5446 
6109 
6771 
7488 
8094 
8784 
9418 

0166 
0687 
1606 
8178 
8617 

8514 
4181 
4847 
65U 
017S 
6888 
7499 
8160 
8880 
9478 

6 
7 

§ 

650 
1 
8 
8 

t 

6 
7 

8 
9 

810B88 
WH 
1675 
SMS 

8916 

i 

61138 

8886 
9644 

0800 
0971 
1648 
8818 

8080 
8648 
48M 
4880 
6644 
6806 
6070 

S£ 

8961 
9610 

0867 
1089 
1709 
8879 

8047 
8n4 
4881 
6046 
6711 

9017 

9m 

0484 
1106 
17?8 
8445 

8114 
8781 
4447 
6118 
67r7 
6440 
7108 
7764 
8184 
9068 

9741 

0601 
1178 
1848 
8618 

8181 
8848 
46H 

5179 
6818 

6606 
7169 
7880 
84SO 
9149 

9607 

0669 
1840 
1910 
8679 

8847 
8914 
4581 
6846 
5910 
6578 
7885 
7886 
8666 
9815 

9878 

0686 
1807 
1977 
8646 

8814 
8081 
4647 
5818 
6078 
6630 
7801 
7968 
8688 
9881 

9089 

07 
66 

660 

0004 
0661 
1817 

19:8 

8826 
8279 
8930 
4681 
6831 
6680 

6688 
7175 
78U1 
8407 
91U 

O07O 
07S7 
18W 
8087 
8691 
8344 
8986 
4646 
6896 
0945 

6698 
7840 
7886 
8681 
9176 

0186 
0798 
1448 
8106 
8786 
8400 
4061 
4711 
5861 
8010 

i 

1 
8 
8 
4 
5 
6 
7 
8 
0 

670 

1 
2 
8 

4 

880801 
0868 
1614 
8168 
8888 
8474 
4186 
4776 
6486 

6090 

o»a 

790d 
8016 
8660 

0967 
0684 
1579 

^ 

8689 
4191 
4841 
6491 

6140 

6787 
7484 
8080 

8968 
8606 
4866 
4906 

6804 
6888 
7409 
8144 
8389 

0899 
1065 
1710 
8964 
3018 
8670 
4881 
4971 
6681 

6869 
6917 

SS 

8868 

0164 
1180 
1775 
8480 
8083 
8785 
4886 
6086 

6884 

6961 

8918 

0630 
1186 
1841 
8496 
3148 
8800 
4461 
6101 
6751 

6809 

7046 
7808 
8888 

aw8 

0606 
1861 
1906 
8660 
8813 
8865 
4616 
6166 
6815 

6464 
7111 
7757 
8408 
9046 

65 

Pbopobtxohal  Pabtb. 


Dlff. 

1 

8 

S 

4 

5 

8 

7 

8 

8 

68 

18.6 

80.4 

87.8 

34.0 

40.8 

47.6 

544 

61.8 

67 

18.4 

80.1 

86.8 

88.5 

40.8 

46.0 

686 

60.8 

66 

13.8 

19.8 

86.4 

83.0 

89.6 

40.8 

688 

09.4 

65 

18.0 

19.5 

86.0 

88.5 

80.0 

45.6 

680 

06.5 

64 

U.6 

19.8 

85.8 

88.0 

38.4 

44.8 

619 

97.6 

rOGAKITHHS  OF  Km 


150 


tOGARlTHMd  Cr  KlTMBBRS^ 


No.  730  L.  857.] 

N. 


[No.  7«4  L.  J 


1 

2 

8 
4 

5 
6 
7 
8 
9 

730 
1 
2 
8 
4 
5 
6 
7 
« 
0 

-;40 

1 

2 
8 
4 

5 
6 

7 
8 
9 

730 
1 
2 
8 
4 
5 
6 


760 
1 
2 
3 
4 


7985 
8587 
9188 
9789 


0987 
1581 
2181 
2728 

8828 
8917 
4511 
5101 


6878 
7467 
8066 
8614 

9282 

9818 


870401 
0989 
1578 
2156 
2789 
8321 
8902 
44&3 

6001 
5610 
G218 
6795 
^71 
7917 
8522 
9096 


880212 

0614 
1385 
1955 
2525 
8008 


7898 
7905 
8607 
9198 
9799 


0996 
1594 
2191 
2787 


8977 
4570 
6168 
6755 
6346 
6987 
7526 
8115 
8708 

9290 
9877 


0462 
1017 
1031 
2215 
2797 
8379 
3960 
4510 

5119 
5098 
6276 
6853 
7129 

8oai 

8579 
9153 
9796 


0299 

0871 
1412 
2012 
2581 
8150 


7458 
8066 
8657 
9258 
9860 


0458 
1066 
1654 
2251 
8847 

8442 
4086 
4680 
5222 

5814 
6106 


7585 
8174 
8762 

0840 
9935 


0521 
1100 
1690 
2273 
2855 
8137 
4018 
4508 

sirr 

5736 
6338 
6910 

7187 
8062 
8637 
9211 
9784 


0356 

0928 
1499 
2069 
26:« 
82C7 


7518 
8116 
8718 
9318 
9918 


0518 
1110 
1714 
2310 
2006 

8601 
4096 
4680 
5282 
5874 
6465 
7055 
7644 
8238 
8821 

9406 
9991 


0579 
1164 
1748 
2331 
2913 
819e 
4076 
4656 

5285 
5818 
6391 
6968 
7514 
8119 
8694 
9288 
0841 


0113 

0966 
1556 
2126 
2695 
8264 


7574 
ei76 
8778 
9879 
9978 


0578 
1176 
1778 
2870 


8661 
4166 
4748 
6341 


7114 


8870 
0466 


0063 
0688 
1233 
1806 
<S89 

29ra 

8658 
4134 
4n4 

5298 
5871 
&I49 
7026 
7602 
8177 


0171 

1012 
1013 
2183 
2752 


7684 


9480 


0068 
0637 
1289 
1888 
2130 
8025 

8620 
4214 
4808 
5400 


7178 
7762 
8360 


0111 
0696 
1281 
1865 
2448 
8080 
8611 
4192 
I  4772 

5851 
5929 
6507 
7083 
7659 
8234 
8809 
9383 
9966 


1009 
1670 


2809 
8377 


7604 
8997 


0499 


0096 
0607 
1296 
1898 
»189 
8066 

8680 
4274 
4867 
5450 
6061 
G648 
7282 
7821 
8409 
8007 

0684 


0170 
0755 
1880 
1928 
2506 
8088 
8660 
4250 
4830 

5400 

5987 
6561 
7111 
7n7 


9440 


0013 
0585 

1150 
1727 

2m 

2866 
8134 


7786 

8857 


0550 


0158 
0767 
1866 
1062 
8549 
8114 

8780 


4986 
6519 
6110 
0701 
7201 
7880 
8168 
0066 

0642 


0226 
0818 
1306 
1961 
2604 
8146 
87»7 
4308 
4888 

5466 
6015 
6622 
7199 

rr74 

8319 
8924 
0497 


0070 
0642 

1218 
1784 
S354 
2923 
8401 


7815 
&117 
0018 
0619 


0218 
0817 
1416 
8018 
8606 
8204 

8799 
4882 
4086 
6578 
6160 
0760 

nso 

7080 
8627 
0114 

0701 


0287 
0678 
1456 
8040 
8628 
8201 
8786 
4366 
4945 

5501 
6102 
6680 
7256 


8407 
8981 
9655 


0127 
0609 

1271 
1841 
2411 
2980 
8648 


7875 
8477 
0078 
0070 


0278 
0677 
1476 
8078 


4468 
5(MS 


esir 

7400 
7996 


01  iB 
0760 


0646 
0080 
1515 
8008 


8844 
4434 
6006 


6100 
6737 
7814 
7860 
8464 
0080 
0612 


0185 
0756 

1828 
1806 
8468 
8087 
S606 


Diff. 


00 


W 


pROPORTioNAi.  Parts. 


DIff. 

1 

2 

8 

4 

5 

6 

7 

8 

59 

6.9 

11.8 

17.7 

23.6 

29.5 

36.4 

41.8 

47.2 

58 

5.8 

11.6 

17.4 

23.2 

29.0 

S4.8 

40.6 

46.4 

57 

5.7 

11.4 

17.1 

22.8 

28.5 

31.2 

89.9 

45.6 

56 

5.0 

11.2 

16.8 

22.4 

28.0 

88.6 

39.8 

44.8 

68.1 
68.2 
51.8 
60.4 


XiOOARITHMS  OP  K  UMBERS. 


151 


Nq.7Q5L.8B8.] 


[No.  800  L.  006. 


785 
6 

7 
8 
0 
770 
1 
2 
S 
4 
5 
6 

7 
8 
9 

1 
2 
8 
4 
5 
6 
7 
8 
0 

730 

1 
2 
3 

4 

6 
G 
7 
8 
9 

800 
1 
2 
8 
4 
£ 
6 
7 
8 
9 


888681 


4*^ 

can 


6491 
7064 
7017 
8179 
8741 
9002 
0602 


8B0«n 
0080 
1587 

2006 
2651 

an? 

8702 
4810 
4870 
5488 
5875 
6586 
7077 

7627 
8170 
8725 
9273 
96S1 


900867 

0018 
1468 
2008 

2647 

8000 
8688 

4174 
4716 
5256 
R96 
6885 
6874 
7411 
7949 


8718 

4852 
5418 
5068 

6647 
7111 
7674 
8286 
8797 
0858 
9018 


0177 
1086 
1508 

2150 
2707 


S817 
42^71 
4905 
5478 
60d0 
6581 
7182 

7682 
8291 
8780 
0828 
0875 


04S2 
0068 
1518 
20^ 
2601 

8144 
8087 
4220 
4770 
5310 
5860 
6880 
6927 
7465 
8008 


8775 
4842 
4000 
5474 
6080 

6604 
7167 

Tjao 


9414 
9974 


0533 

1001 
1649 

2206 

2762 
8318 
8878 
4427 
4080 
5633 
6065 
6686 
7187 

7787 


9680 


0476 
1032 
1567 
2112 
2065 


8199 
8741 
4288 
4824 
5364 
5904 
6448 
6981 
7519 
8066 


4800 
4066 
6531 
6006 


6660 
7223 

7?86 
8348 
8000 
9470 


0080 
0660 
1147 
1705 


2818 
3878 


4482 
5036 
5588 
6140 
6602 
7242 

7702 
8311 
8600 
9437 
9085 


058? 
1077 


2166 
2710 


8795 
4387 
4878 
5418 
6056 
6497 
7085 
7578 
8110 


4466 
5022 

5687 
6152 

6716 
7260 

7642 
6404 
6065 
9526 


0086 
0645 
1208 
1760 

2317 
2678 
3429 
3064 
4536 
5091 
5644 
6105 
6747 
7897 

7847 
8396 
6044 
9492 


0039 
0586 
1131 
1676 
2221 
2764 


8807 
8649 
4391 
4032 
M72 
6012 
6551 
7060 
7626 
6168 


8045 
4512 
5076 
5644 
6200 

6778 
7386 

7606 
6460 
0021 


0141 
0700 
1250 
1616 

2373 
2029 
3464 
4030 
4598 
6146 
5609 
6251 
6802 
7352 

7002 
&151 
6900 
0547 


0094 
0640 
1186 
1731 
2275 
2818 

8861 
8004 
4445 
4966 
5526 
6066 
6604 
7143 
7680 
8217 


4002 


5186 
5700 


7302 
7965 
8516 
0077 
0636 


0197 
0756 
1314 
1872 

2428 

2865 
8540 
4094 
4618 
5201 
57M 
6306 
6857 
7407 

7957 
6506 
9(»4 
9002 


0149 
0G95 
1240 
1785 
2329 
2878 

8416 
8956 
4499 
5010 
5580 
6119 
6656 
7196 
7784 
8270 


4059 
4625 
5102 
5757 


7449 
8011 
8573 
9134 
9604 


0612 
1370 
1026 

2484 
8040 
8505 
4160 
4704 
6257 
5809 
6361 
6912 
7402 

6012 
8661 
9109 
9(356 


0749 
1295 
1610 
2384 

2927 

8470 
4012 
4558 

5094 
5634 
6178 
6n2 
7250 
7787 


8         9      Diff. 


4115 
4682 
6246 
5613 
6378 

0912 

7605 
8067 
8629 
9190 
9750 


1426 
1068 

2540 
8006 
8651 
4206 
4750 
5312 
6864 
6416 
6967 
7517 

8067 
6615 
9164 
9711 


06O1 
1349 
1894 
2436 
2961 

8524 

4066 
4607 
5146 
5688 
6227 
6766 
7304 
7811 
6878 


4172 

4789 
5305 
5870 
6434 

6906 
7561 
8123 
8665 
0246 
9606 


0365 
0024 
1462 


2595 
8151 
87106 
4261 
4614 
53C7 
5920 
6171 
7022 
7572 

8122 
8670 
0218 
9766 


0812 
0659 
1401 
1946 
2492 
8086 

8578 
4120 
4661 


5742 
6281 
6830 
7358 
7895 
8431 


56 


53 


54 


PSOPOBTXONAL  PARTS. 


DUt 

1 

2 

8 

4 

5 

6 

7 

8 

9 

57 

5.7 

11.4 

17.1 

22.8 

28.5 

S1.2 

39.9 

45.6 

51.3 

56 

5.6 

11.2 

16.8 

22.4 

28.0 

33.6 

89.2 

44.8 

50.4 

56 

5.5 

11.0 

16.5 

22.0 

27.5 

33.0 

86.5 

44.0 

49.5 

54 

5.4 

10.8 

16.2 

21.6 

27.0 

82.4 

87.8 

48.2 

48. G 

152 


LOGARITHMS  OF  KUMBEBB. 


llo.8tOLi.Ma] 


[No.864L.9BL 


N. 


810  908486 

1  I   9091 

2  9666 


910001 
0004 
1168 
1090 

S7S8 


8814 
4848 
4878 
6400 
6027 
6464 

eoeo 

7S06 
8000 
8866 

9078 
9001 


900198 
0646 
1166 
1086 
S906 
2796 
8944 
8709 

4S79 
4796 
6818 
6888 
6848 
6887 
7870 


8908 

9410 
9080 


080440 
0019 
1466 


8688 
90r4 
9010 


0144 
0678 
1211 
1748 
2275 
8806 
8837 

S867 
4896 
4996 
5458 
5080 
0507 
7088 
7566 
8068 
8007 

0180 


0176 
0007 
1218 
1788 
2268 
2r?7 
8296 
8814 

4881 
4848 
6364 
5879 
6804 
6006 
7498 
7986 
8447 
8959 

9470 
9081 


0401 
1000 
1500 


869B 
9128 
9668 


0107 
0781 
1264 
1797 


8800 

8020 
4440 
4077 
5506 
0068 
6560 
7066 
7811 
6186 
8060 

9188 
0706 


02&8 
0740 
1270 
1790 
2810 
2829 
8348 


4888 

4800 
6116 
6081 
6446 
6059 
7478 
7086 
8t08 
0010 

0621 


0088 

0549 

1051 
1560 


8046 
9181 
9716 


0261 

0784 
1817 
1860 
2881 
2918 
8418 


8073 
4502 


5668 

0065 
6612 
7188 
7068 
8186 
8712 

9236 
9758 


0801 
1822 
1842 


8017 

4484 
4051 
5407 
5062 
0407 
7011 
7684 
8087 
8540 
0061 

9679 


0068 

0502 
1102 
1610 


8090 
9885 


0804 
0638 
1871 
1008 
2485 
2960 
8496 


4656 

6068 
5611 
0186 
0604 
7100 
TTIO 
8240 
8784 

0287 
0810 


0668 
1374 
1804 
2414 


8451 
8000 

4486 
5008 

6518 
0004 
6648 
7062 
7576 
8068 
6001 
9112 


0184 
0018 
1158 
1661 


0868 
0691 
1424 
1066 
2466 
8U19 
8549 

4070 
4008 
5186 
5004 

0191 

ffri7 

7248 
7766 
8208 
8810 

0840 
0602 


9848 

8677 


8800 
0896 
9000 


0884 
0006 
1420 
1940 
2406 
2065 
8606 


5054 

5670 
6065 
0000 
7114 
7627 
8140 
6052 
9108 


9074 


0166 
0094 
1204 
1712 


0411 
0914 
1477 
2009 
2541 
8072 
3602 

4182 
4000 
0180 
671d 
6243 
6770 
7295 
7820 
8845 
8869 

0892 
9914 


0006 
1580 
20O8 
2591 
8125 
8655 

4184 
4713 


8014 
9449 
9084 


•       ]>ifl. 


8987 


0618 
1051 
1564 
2116 
2647 
8178 
8708 

4287 
4766 


5241  5294 
5709  5882 


(822 
7848 
7878 
8397 
602t 

9444 
9907 


6875 
7400 
7925 
8450 
8078 

9490 


0486 
0956 
14;^ 
1908 
2518 
8087 
8555 
4079 

4589 
5106 
5621 
6187 
0051 
7106 
7078 
8191 
8706 
0215 

9785 


0746 
3254 
1763 


0460 
1010 
1580 
2060 
2670 
8069 
8607 
4124 

4641 

5167 
5678 
0166 
0702 
7^216 
7780 
B242 
6754 


97?6 


0019 
0641 
1062 
1562 
2102 
2622 
8140 


4176 

4098 
6209 

5785 
6240 
0764 
7266 
7781 
6206 
6605 
0817 

9627 


0067 

oon 

1104 
1087 
2109 
2700 
3281 
8701 

4200 
4819 
5847 
5875 
6401 
6027 
7458 
7078 
8608 
9026 


0287 
0796 
1305 
1814 


0847 
1366 
1865 


wn 

0608 
1114 
1634 
2104 
2074 
8192 
8710 
4226 

4744 
&961 
5778 
6291 

6606 
7819 
76» 
6845 
6667 
0906 

0679 


53 


6S 


0889 
0696 
1407 
1916 


61 


pROPORTioNAi.  Parts. 


Dili. 

1 

2 

8 

4 

6 

6 

7 

8 

9 

58 
62 
51 
60 

6.8 
5.2 
5.1 
5.0 

10.6 
10.4 
10.2 
10.0 

15.9 
15.6 
15.3 
15.0 

21.2 
20.8 
20.4 
20.0 

30.5 
2fi.O 
2f).5 
25.0 

81.8 
81.2 
3().6 
30.0 

87.1 
86.4 
85.7 
85.0 

42.4 
41.6 
40.8 
40.0 

47.7 
40.6 
45.9 
45.0 

rt>. 

roc 

^A1 

an 

rHHS 

OF   1 

^tJMB 

BES. 

i^ 

WBi:..  881.1                                                                                       1 

/^ 

;  .  /  .     . 

8 

4 

i 

• 

9 

• 

t    ^^    '  082000   /  aWT   1    9068 

8118 

8160 

8a» 

8821 

8881 

8871 

/      $ 

««rtf  /  as04      asTs 

WW 

a«7 

8797 

8778 

8aw 

887! 

9081   /  9oai      ao8s 

8188 

8188 

8884 

8886 

8886 

888f 

^ 

8497  /   >tftfW        SBSO 

8680 

8600 

8740 

8701 

8841 

880i 

«^ 

4094 

4145 

4106 

4846 

4896 

4847 

489" 

4406   /   'tfCMO 

4599 

46B0 

4700 

4761 

4801 

4868 

490i 

1 

So08   /    GO(V4 

G104 

5154 

5806 

5865 

5806 

5356 

540( 

2 

-">r  i  osfis 

6606 

5658 

5709 

6759 

5809 

5660 

591( 

8 

'^Ul 

0Ofll 

OUl 

6168 

6818 

6868 

6813 

6368 

6412 

4 

i^^I4 

Gse^ 

0614 

0665 

6715 

6765 

6815 

6665 

691( 

i              5 

7010 

7oa0 

T118 

7167 

7817 

7967 

7817 

7867 

74n 

1         e 

75 18 

7B4S8 

7816 

7868 

T718 

7780 

7819 

7860 

791t 

I    I 

hjhO 

«)O0O 

8119 

6160 

8819 

8869 

8390 

8870 

842L 

^^U0 

8fy70 

8620 

8670 

8780 

8770 

^ 

8870 

808( 

I    " 

;*.r^JO 

00^70 

O10O 

9170 

9880 

9870 

8860 

9411 

1    »70 

9510 

osae 

9619 

9680 

9719 

9760 

9819 

9669 

991f 

\           1 

7 
8 
g 

M0018 
0616 

o^^« 

0118 

0168 

0818 

(B67 

0817 

0367 

041^ 

a-  -0 

0616 

0606 

0716 

0766 

0815 

0665 

091£ 

1014 
1511 
9006 
9604 
8000 
8499 
8089 

il     1 

1114 

1163 

1818 

1868 

1813 

1368 

14U 

li     I 

1611 

1660 

1710 

1760 

1809 

1859 

190( 

0     ^ 

9107 

2157 

8907 

8866 

8806 

8855 

840e 

le     i 

9008 

8658 

8708 

8758 

2801 

8851 

8901 

»   ^^ 

8099 

8146 

8106 

8M7 

8807 

8846 

880( 

2=,  8 

8096 

8648 

8608 

8748 

8791 

8841 

889C 

2     rti 

4066 

4187 

4186 

4886 

4886 

4886 

4884 

1 
« 
8 

4 
5 
6 

7 
6 

\        9 

4488 
4078 
IV4fi9 

41      s 

C074 

4681 
5194 

4680 
5178 

4739 
5883 

4779 
6872 

4888 
6S81 

4873 
687C 

&      8 

6667 

6616 

5665 

5715 

5704 

5818 

586S 

»»     S    ? 

A^fifi    1      O           1 

6069 

6108 

6157 

6807 

6856 

6305 

6354 

6661 

6600 

6649 

6096 

6747 

6796 

684S 

•KM24  1  *:  i*^s  J  oQai 

8418        ^t»        »11 

7090 

7180 

7180 

7888 

7387 

7886 

7581 

7680 

T679 

7788 

7777 

7886 

8070 

8119 

8168 

8817 

8866 

8816 

8560 

8608 

8C57 

8706 

8755 

8804 

9048 

9097 

9146 

9196 

9844 

9898 

\J 

S2S2    5i^2 

9488 
9975 

9686 

9685 

9684 

9688 

9781 

9780 

1  J 

0B7S 

--=^ 

0084 
0611 

0078 
0660 

0121 
0608 

0170 
0657 

0219 
0706 

0887 

f 

ctfstfWIA 

0«68 

0754 

1338  I    1       g 
'.         8f7«0  \    1       « 

CM8 

0997 

1046 

1005 

1148 

1198 

1840 

4 
5 
6 
7 

1435 

1488 

1538 

1580 

1689 

1677 

1726 

IMO 

1960 

8017 

9066 

8114 

8166 

88H 

9105 

8458 

8508 

asso 

8599 

8647 

8696 

«»9 

8088 

8986 

8084 

8088 

8181 

8180 

8878 

8481 

3470 

8518 

8615 

8663 

8866 

8905 

8058 

4001 

4049 

4066 

4146 

v 

Pboportional  Parts. 

\ 

T>%ff.\      1     \        « 

8 

4 

5 

6 

7 

r 

) 

^  ^\   \  ^M  12? 

15.8 

80.4 

85.5 

30.6 

85.7 

\     «>    \     5.0        10.0 

15.0 

80.0 

25.0 

30.0 

35.0 

\  «     *?     S2 

14.7     :    19.6    1 

84.5 

20.4 

34.8 

^     48    I    4.8  1      9.6        14.4    I    19.8    I 

84.0 

28.8 

33.6 

154 


LOOAtlltttMS  OF  irtJHBEBS. 


No  900  L.  864.1 


[No.M4L.9ni 


N. 


064948 
47!ffi 

6307 
S688 
6168 
6649 
7128 
TB07 
8086 
8564 

9041 
9518 
9996 


960471 
0916 
1421 
1896 
2869 
28IS 
8816 

87B8 
4260 
4781 
5203 
6672 
6142 
6611 
7080 
7548 
8016 

8488 
8950 
9416 


970847 
0812 
1278 
1740 


8128 
8590 
4051 
4512 
4972 


4291 
4778 
5255 
6786 
6216 
6607 
7176 
7655 
8184 
8612 

9089 
9666 


0043 
0618 
0994 
1460 
1948 
2417 
2890 


4807 
4778 
5240 
6719 
6189 
6658 
7127 
7505 
8068 

8580 
8096 
9468 


0608 


1786 
2249 
2712 

8174 
8686 
4097 
4568 
5018 


4821 
5808 

6784 

6745 
7224 
Tr08 
8181 
8650 

9187 
9614 


0090 
0666 
1041 
1516 
1990 
24&I 
2987 
8410 

8882 

4854 
4825 
6296 
5766 
6286 
0706 
7178 
7642 
8109 

8576 
9M8 
9609 
9975 


0440 
0904 
1369 
1832 
2395 
2758 


4148 
4604 
5064 


4887 
4860 
6861 


6818 
8788 
7272 

rrai 

8220 
8707 

0185 
0661 


0188 
0618 
1080 
1568 
2038 
2511 
2065 
8457 


4401 
4873 
6818 
5818 
6283 
6752 
71220 
7688 
8156 

8628 

0090 
9656 


0021 
0486 
0961 
1415 
1879 
2342 
2804 

8266 
3728 
4189 
4660 
6110 


4485 
4918 
6899 

5880 
6861 
6840 
7820 
7799 
8277 
8755 


9709 


0185 
0661 
1136 
1611 
2085 


3082 
86(M 

8077 
4448 
4010 
5890 
5860 
0320 
6790 
7867 
7785 
8308 

8070 
0136 
0602 


0068 
0538 
0097 
1461 
1025 
2388 
2851 

8818 

8774 
4285 
4606 
5156 


4484 
4066 
5447 
5028 
6400 
6888 
7368 
7847 
8325 


8S80 
0757 


0238 
0700 
1184 
1668 
2188 
2606 
8070 
8552 


4024 
4405 
4066 
5487 
6007 
6876 
6845 
7814 
7782 
8240 

8716 
0188 
0640 


0114 
0579 
1014 
1508 
1071 
3484 
2807 


4281 
4742 
6308 


6014 
5485 
6076 
6457 
6086 


7416 
7804 
8878 


9804 


0756 
1281 
1706 
2180 
2668 
3126 
8500 

40n 
4542 

5018 
5484 
6064 
6428 
6803 
7861 
7880 
8306 

8768 
0220 
0696 


0161 
0626 
1090 
1554 

2018 
2481 
2948 

8405 
3866 
4827 

4788 


4680 
5068 
5548 
6024 
6605 
6964 
7464 
7942 
8421 


9675 
9668 


0804 
1279 
1768 
2227 
2701 
8174 
8646 

4118 
4500 
6061 
6631 
6001 
6470 
6060 
7408 
7875 
8848 

8810 
0276 
0742 


0307 
0673 
1187 
1601 
2064 
2527 
2060 

8451 
8018 
4874 
4884 
5204 


4828 
5110 
6682 
607S 


7082 
7512 
7000 
8468 
8046 


0676 
0661 
1826 
1801 
2275 
2748 
8221 
8608 

4165 
4687 
5108 
6578 
6048 
6517 
6066 
7454 
7828 


8866 

0828 
0780 


0264 
0710 
1188 
1647 
2110 
2678 
8065 


8407 
8050 
4420 
4880 
5840 


4677 
5158 
5640 
6120 
6601 
7080 
7550 
8088 
8516 
8004 

0471 
0947 


0428 
0600 
1874 
1848 
8822 
2796 
8268 
8741 

4212 
4684 
5155 
6625 
6096 
6564 
7088 
7801 
7969 
8486 

8906 
9860 


0800 

0765 
1899 
1698 
2167 
2619 
8082 

8548 
4005 
4466 
4086 
5886 


DifL 


47 


Peoportiomal  Pabti. 


4 

5 

1 

DIff. 

1 

3 

8 

6 

7 

8 

0 

47 
46 

4.7 
4.6 

9.4 
9.2 

14.1 
13.8 

18.8 
18.4 

23.5 
23.0 

28.2 

27.6 

82.0 
S3. 2 

87.6 
86.8 

42.8 
41.4 

X.0GAKITHM8  OF  KUXBBBS. 

15fi 

NaMfil^gVBLl                                                                               INa.fl»L.fi86.| 

H. 

0 

a 

8 

1 
69 

1 

4 

6 

• 

7 

8 

9 

Difl. 

M5 

97MK 

5478 

6804 

ro 

6010 

6062 

5707 

6768 

5799 

6846 

fi801      £987 

0068 

6089 

0076 

0121 

0107 

6212 

6258 

0804 

tfBfio    eao6 

em 

0488 

0688 

05T9 

6026 

6871 

6n7 

0763 

6M8 

0854 

6000 

0946 

0992 

7087 

7088 

7189 

7175 

7280 

7806 

7812 

7358 

7408 

7449 

7495 

7M1 

7680 

7082 

7878 

960 

7794 

7700 

7815 

7861 

7906 

7952 

7996 

8048 

8089 

8135 

8181    aseas 

8273 

8817 

8308 

8409 

8454 

8600 

8540 

8501 

86S7  ,  8688 

8728 

8774 

8810 

6665 

8911 

8050 

9002 

9047 

9003      0138 

0184 

9290 

9275 

9321 

9360 

9412 

W57 

9503 

964S      96M 

0639 

9685 

9730 

97ro 

9821 

9807 

9012 

9958 

980008      0040 

0094 

0140 

0185 

0231 

0276 

0S22 

0907 

0412 

0468      0508 

0649 

0694 

0640 

0065 

0780 

0776 

0821 

0867 

0012      0067 

lOOB 

1048 

1096 

1189 

1184 

1229 

1275 

1320 

1366      1411 

1460 

1501 

1&47 

15» 

1637 

1663 

1728 

ITTS 

1810      1804 

1909 

1954 

8000 

2045 

2090 

8186 

8181 

2220 

MO 

ssn 

2810 

2888 

8107 

2458 

8497 

2548 

2588 

8688 

8678 

2728 

2700 

2814 

2859 

2904 

2949 

2994 

8010 

8086 

8130 

8175 

8880 

3965 

8310 

8850 

8401 

8440 

8491 

8530 

8561 

3086 

8071 

3716 

8762 

3807 

8897 

3942 

8967 

4032 

4077 

4122 

4167 

4213 

4257 

4302 

4847 

4398 

4437 

4482 

4587      4578 

4617 

4662 

4707 

4758 

4797 

4848 

4887 

4932 

46 

4877 

6082 

6067 

5112 

5157 

5202 

6847 

5298 

5337 

5382 

5486 

5471 

5616 

5601 

5000 

5651 

5090 

5741 

57«0 

5830 

5875 

50B0 

6965 

6010 

6055 

0100 

6144 

6189 

6284 

6279 

0?0 

€884 

6800 

6413 

6458 

0506 

0548 

C596 

6687 

6688 

6772 

0817 

6861 

0800 

0951 

0990 

704O 

7085 

7130 

7175 

7210 

7204 

r-J09 

7S58 

7398 

7443 

7488 

7582 

7577 

7622 

7666 

7711 

7756 

7800 

7845 

7H90 

7934 

7979 

6024 

60C8 

3         8113 

8157 

8308 

8^7 

8291 

63S0 

8881 

8425 

ai70 

K514 

4         8r.59 

8604 

8CI8 

8698 

8787 

8:32 

86S6 

8871 

8016 

8(MK) 

0006 

0040 

9094 

9188 

9188 

9227 

9272 

0310 

0361 

9105 

OlSO 

OI94 

9689 

9G88 

9G28 

Hfffli 

9717 

9761 

9600 

9860 

9H06 

0030 

9988 

0028 
0478 

0072 

0117 

0161 
0605 

0200 

0850 

0204 
0TS8 

8   1   OWIMQ 

0988 

0428 

0510 

0561 

omo 

0604 

ores 

0837 

0871 

0910 

0900 

1004 

1049 

1098 

1137 

1182 

960 

1286 

1270 

1315 

1859 

1408 

1448 

1498 

1680 

1580 

1625 

1609 

1713 

1758 

1602 

IWO 

1890 

1936 

1979 

2023 

2067 

2111 

2150 

2900 

8^44 

2288 

2838 

2377 

8121 

2465 

2509 

2554 

2506 

9548 

2660 

2730 

2774 

2819 

2863 

2907 

2U51 

2006 

3080 

8068 

8127 

8172 

8316 

8260 

3904 

mis 

3302 

8486 

8480 

8684 

8568 

8013 

8657 

8701 

»r45 

3789 

3833 

8877 

8021 

8065 

4000 

4053 

4097 

4141 

4185 

4229 

4273 

4317 

4301 

4405 

4449 

4493 

4537 

4581 

4025 

4669 

4713 

44 

8 

4757 

4801 

4845 

4689 

4983 

4977 

6021 

5065 

5108 

5152 

9 

5106 

0fifi40 

6284 

6328 

5378 

5410 

5460 

5604 

5547 

5501 

VaapoKTiovAjj  Pakts. 

DUf. 

1 

2 

a 

4 

6 

0 

7 

8 

9 

46 

4.0 

9.8 

13.8 

18.4 

23.0 

27.6 

322 

3C.8 

41.4 

45 

4.5 

9.0 

18.5 

18.0 

22. 5 

27.0 

81.5 

3G.0 

40.6 

44 

4.4 

8.8 

13.2 

17.0 

22.0 

2HA 

30. H 

35.2 

39.6 

4S 

4.8 

8.e 

1S.9 

17.2 

21.5 

25.8 

30.1 

34.4 

88.7 

156 

No.  900  L.  906.] 


KATUEHATIOAL  TABLES. 


[No.  999  L.  09k 


N. 

0 

1 

a 

8 

4 

6 

6 

7 

8 

9 

Dift. 

900 

99S6SS 

6079 

6788 

5767 

6611 

6854 

6898 

SM2 

6066 

6000 

1 

9074 

6117 

6161 

0905 

6949 

6896 

6887 

6880 

6484 

6468 

44 

2 

6619 

6665 

6699 

6648 

6687 

0m 

6774 

6618 

6868 

6906 

6949 

6098 

TOB7 

7080 

7184 

7168 

7812 

7206 

7899 

7848 

7886 

7480 

7474 

7517 

7B61 

7006 

7648 

7698 

7796 

77T9 

7888 

7867 

7910 

7054 

7908 

8041 

8086 

8189 

8178 

8il6 

8269 

8808 

8847 

8890 

8484 

8477 

8081 

8564 

8608 

8668 

8605 

8780 

8788 

8826 

8860 

8918 

8956 

9000 

90«,t 

9067 

8 

9181 

9174 

9218 

9261 

9805 

9848 

9302 

9485 

9470 

9028 

9 

9065 

9609 

9668 

9000 

9789 

9788 

0686 

9870 

9918 

9967 

48 

BTPEBBOI.IC 

I.OOABITIIM8. 

No. 

Log. 

No. 
1.45 

Log. 

No. 

Log. 

No. 

Lo.. 

No. 

Log. 

1.01 

.0009 

.8?16 

1.80 

.6866 

2.88 

.8468 

2.77 

1.0188 

1.08 

.0198 

1.46 

.8784 

1.00 

.6419 

2.84 

.8002 

2.78 

1.0825 

1.08 

.0296 

1.47 

.8858 

1.91 

.6471 

2.85 

.8544 

2.79 

1.0260 

1.04 

.0308 

1.48 

.8020 

1.92 

.6628 

2.86 

.8567 

2.80 

1.0206 

1.05 

.0488 

1.49 

.8988 

1.98 

.6676 

2.87 

.8689 

2.81 

1.06S2 

1.06 

.0688 

1.50 

.4066 

1.94 

.6687 

2.88 

.86n 

2.S2 

1.0867 

1.07 

.0677 

1.51 

.4121 

1.96 

.6678 

2.89 

.8718 

2.88 

1.0408 

1.08 

.0770 

1.58 

.4187 

1.96 

.6720 

2.40 

.8706  1 

2.84 

1.0438 

1.09 

.0668 

1.58 

.4858 

1.97 

.6780 

2.41 

.8796  1 

2.86 

1.0478 

1.10 

.0058 

1.54 

.4318 

1.98 

.6831 

2.42 

.8888 

2.86 

1.0606 

1.11 

.1044 

1.56 

.4888 

1.99 

.6881 

2.48 

.8879  ! 

2.87 

1.0548 

1.18 

.1138 

1.56 

.4447 

8.00 

.6031 

2.44 

.8080  1 

2.88 

1.0578 

1.18 

.1822 

1.57 

.4511 

2.01 

.6081 

2.45 

.8961  . 

2.89 

1.0613 

1.14 

.1310 

1.56 

.4574 

2.02 

.7031 

2.46 

.0008  , 

2.90 

1.0647 

1.15 

.1396 

1.59 

.4687 

8.08 

.7080 

2.47 

.0042 

2.91 

1.068u» 

1.16 

.1484 

1.60 

.4700 

8.04 

.7120 

2.48 

.0083  ; 

2.92 

1.0716 

1.17 

.1570 

1.61 

.4768 

8.05 

.7178 

2.49 

.9123  1 

2.03 

1.0750 

1.18 

.1666 

1.68 

.4824 

2.06 

.7T227 

2.60 

.9168  < 

2.94 

1.0784 

1.19 

.1740 

1.63 

.4886 

2.07 

.7275 

2.61 

.9208  ; 

2.95 

1.0618 

1.20 

.1828 

1.64 

.4947 

2.08 

.7824 

2.52 

.9248  ' 

2.96 

1.0852 

1.21 

.1006 

1.65 

.6008 

2.09 

.7872 

2.58 

.9282 

2.97 

1.0886 

1.22 

.1088 

1.66 

.6068 

2.10 

.7419 

2.54 

.9382 

2.98 

1.0910 

1.33 

.2070 

1.67 

.5128 

8.11 

.7467 

2.55 

.9361 

2.99 

1.0963 

1.24 

.2161 

1.68 

.5188 

8.18 

.7614 

2.56 

.9400 

8.00 

1.09H6 

1.85 

.2281 

1.69 

.6247 

8.18 

.7561 

8.57 

.9489 

3.01 

1.1019 

1.26 

.8811 

1.70 

.5806 

8.14 

.7608 

2.58 

.9478 

8.09 

1.1053 

1.27 

.2300 

1.71 

.5865 

8.16 

.7655 

2.59 

.9617 

3.08 

1.1086 

1.28 

.2469 

1.78 

.5428 

8.13 

.7701 

2.60 

.9556 

8.04 

1.1119 

l.-,>9 

.2546 

1.73 

.5481 

2.17 

.7747 

2.61 

.9594 

8.05 

1.1151 

1.80 

.2624 

1.74 

.5589 

2.18 

.7793 

2.62 

.9682 

3.06 

1.1184 

1.81 

.2700 

1.75 

.6606 

8.10 

.7830 

2.63 

.9670 

8.07 

1.1817 

1.82 

.2776 

1.76 

.5653 

2.20 

.7b85 

2.64 

.9708 

8.08 

1.1249 

1.88 

.2852 

1.77 

.5710 

2.21 

.7930 

2.65 

.9746 

8.00 

1.1288 

1.34 

.2027 

1.78 

.6766 

2.22 

.7975 

2.66 

.9783 

8.10 

1.1814 

1.85 

.3001 

1.79 

.5822 

2.28 

.8020 

2.67 

.9821 

8.11 

1.1846 

1.86 

.8075 

1.80 

.5878 

8.24 

.8065 

2.68 

.9658 

8.12 

1.18:8 

1.87 

.8148 

1.81 

.5033 

2.25 

.8109 

2.69 

.9895 

8.18 

1.1410 

1.88 

.3221 

1.82 

.5088 

2.26 

.8154 

2.70 

.9933 

8.14 

1.1442 

1.80 

.8208 

1.88 

.6043 

2.27 

.8198 

2.71 

.9969 

8.15 

1.1474 

1.40 

.8865 

1.84 

.6098 

2.28 

.8242 

2.72 

1.0006 

8  16 

1.1600 

1.41 

.34.S6 

1.85 

.6162 

2.29 

.82fi6 

2.73 

1.0043 

8.17 

1.1587 

1.48 

.8607 

1.86 

.<;206 

2.30 

.8829 

2.74 

1.0080 

8.18 

1.1009 

1.43 

.8677 

1.87 

.6v'50 

2.81 

.8372 

2.75 

1.0116 

8.19 

1.1600 

1.44 

.8646 

1.88 

.6818 

2.32 

.841G 

2.76 

1.0162 

8.20 

1.1632 

HYPERBOLIC  LOGARITHMS. 


Log. 

No. 

Log. 

No. 

Log. 

l.%88 

4.58 

1.5107 

6.19 

1.6467 

1.8598 

4.54 

1.61» 

5.80 

1.6487 

1.8M4 

4.56 

1.5151 

5.81 

1.6606 

1.3610 

4M 

1.5178 

5.28 

1.6585 

l.!»35 

4.57 

1.5195 

5.83 

1.6614 

1.8661 

4.58 

1.5817 

6.24 

1.6563 

1.3686 

4.59 

1.5839 

6.85 

1.6588 

1.87W 

4.60 

1.5861 

5.96 

1.6601 

1.8737 

4.61 

1.5288 

6.87 

1.6620 

1.8768 

4.68 

1.5804 

5.88 

1.6630 

1.8788 

4.63 

1.58-J6 

5.89 

1.6658 

1.8818 

4.64 

1.5847 

5.80 

1.6677 

1.8888 

4.65 

1.5869 

6.81 

1.6606 

1.8868 

4.66 

1.5390 

5.82 

1.6716 

1.8888 

4.67 

1.5418 

5.83 

1.6734 

1.3913 

4.68 

1.5433 

5.34 

1.6758 

1.8988 

4.60 

1.5451 

5.35 

1.6771 

1.39(3 

4.70 

1.5476 

5.86 

1.6790 

1.3987 

4.71 

1.5497 

5.87 

1.6808 

1.401-^ 

4.78 

1.5518 

5.88 

1.6887 

1.4086 

4.73 

1.5589 

5.89 

1.6845 

1.4061 

4.74 

1.5560 

5.40 

1.6864 

1.4086 

4.75 

1.5581 

5.41 

1.6888 

1.4110 

4.76 

1.5808 

5.42 

1.6901 

1.4184 

4.77 

1.5683 

5.48 

1.6919 

1.4150 

4.78 

1.5644 

5.44 

1.69.« 

1.4188 

4.79 

1.5665 

5.45 

1.6956 

1.4207 

4.80 

1.5686 

5.46 

1.6974 

1.4^1 

4.81 

1.5707 

5.47 

1.6993 

1.42.Vf 

4.88 

,1.5788 

5.48 

1.7011 

1.4279 

4.83 

1.5748 

5.49 

1.7089 

1.4803 

4.84 

1.5769 

5.60 

1 .7047 

1.4887 

4.85 

1.5790 

5.51 

1.7066 

1.4351 

4.86 

1.6810 

5.52 

1.7084 

1.4875 

4.87 

1.5831 

5.54 

1.7108 

1.4398 

4.88 

1.5851 

5.54 

1.7180 

1.4488 

4.89 

1.5872 

5.55 

1.7188 

1.4446 

4.90 

1.5892 

5.66 

1.7156 

1.4469 

4.91 

1.5913 

5.57 

1.7174 

1.4193 

4.98 

1.6933 

5.58 

1.7192 

1.4516 

4.93 

1.595:^ 

5.59 

1 .7210 

1-4540 

4.94 

1.6974 

5.60 

1.7288 

1.4563 

4.95 

1.5994 

?i.61 

1.7246 

1-4586 

4.96 

1.6014 

5.68 

1.7263 

1.4609 

4.97 

1.6084 

5.68 

1.7281 

1.4683 

4.96 

1.6054 

5.64 

1.7299 

1.4656 

4.99 

1.6074 

5.65 

1.7317 

1.4679 

5.00 

1.6094 

5.66 

1.7334 

1.4708 

6.01 

1.6114 

5.67 

1.7852 

1.4785 

5.02 

1.6134 

5.68 

1.7370 

1.4748 

5.08 

1.6154 

5.69 

1.7887 

1.4770 

5.04 

1.6174 

5.70 

1.7405 

1.4793 

5.05 

1 .6194 

5.71 

1.7422 

1.4816 

5.06 

1.6214 

5.72 

1.7440 

1.4889 

5.07 

1.6283 

5.73 

1.7457 

1.4861 

5.08 

1.6253 

5.74 

1.7475 

1.4884 

5.09 

1.6278 

5.75 

1.7492 

1,4907 

5.10 

1.6292 

5.76 

1.7509 

1.4929 

5.11 

1.6312 

5.77 

1.7.527 

1.4951 

5.18 

1.6332 

5.78 

1.7544 

1.4974 

5.18 

1 .6351 

5.79 

1 .7561 

1.4996 

6.14 

1.6371 

5.80 

1.7579 

1.5019 

5.15 

1.6390 

5.81 

1.7596 

1.5041 

5.16 

1.6409 

5.82 

1.7613 

1.5068 

5.17 

1.6429 

5.83 

1.7630 

1.5085 

5.18 

1 .6448 

5.84 

1.7647 

158 


HATHEMATICAL  TABLB8. 


No. 

Lev. 

Na 

LoK. 

No. 

1 

No. 

Log. 

No. 

Log. 

6.61 

1.8783 

7.16 

1 
1.9671 

7.79 

s.osw 

8.66 

8.1687 

9.04 

8.8966 

6.52 

1.8749 

7.16 

1.9685 

7.80 

2.0641 

8.68 

8.1610 

0.06 

8.2066 

6.5S 

1.8764 

7.17 

1.9699 

7.81 

2.0654 

8.70 

8.1688 

O.OB 

8.8006 

6.54 

1.8779 

7.18 

1.9718 

7.82 

8.0567 

8.78 

2.1656 

10.00 

8.8096 

6.56 

1.8795 

7.19 

1.9727 

7.88 

2.0580 

8.74 

2.1679 

10.85 

8.8279 

6.56 

1.8810 

7.20 

1.9741 

7.84 

2.0592 

8.76 

8.1708 

10.60 

8.8513 

6.67 

1.8825 

7.21 

1.9754 

7.86 

2.0605 

8.78 

8.1786 

10.75 

8.8740 

6.68 

1.8840 

7.22 

1.0769 

7.66 

8.0618 

8.80 

8.1748 

11.00 

8.80T0 

6.59 

1.8856 

7.28 

1.9782 

7.87 

8.0631 

8.82 

2.1770 

11.25 

8.4801 

6.60 

1.8871 

7.84 

1.9796 

7.88 

2.0648 

8.84 

8.1798 

11.60 

2.44.W 

6.61 

1.8886 

7.26 

1.9810 

7.80 

8.0656 

8.86 

8.1816 

11.75 

8.4636 

6.6.2 

1.8901 

7.26 

1.9824 

7.90 

8.0669 

8.86 

2.1888 

18.00 

8.4819 

6.68 

1.8916 

7.27 

1.9638 

J.91 
102 

8.0681 

8.90 

8.1861 

18.85 

8.6062 

6.64 

1.8031 

7.28 

1.9651 

2.0694 

8.98 

8.1888 

18.60 

8.5262 

6.65 

1.8916 

7.29 

1.9865 

7.98 

2.0707 

8.94 

8.1906 

18.76 

8.6455 

6.66 

1.8961 

7.80 

1.9879 

7,94 

2.0719 

8.96 

8.1928 

18.00 

8.5649 

6.67 

1.8976 

7.81 

1.9892 

2.0782 

8.98 

8.1950 

18.25 

8.5840 

6.68 

1.8991 

7.82 

1.9906 

7.96 

8.0744 

0.00 

8.1072 

18.60 

2.6027 

6.69 

1.9006 

7.88 

1.9920 

7.97 

8.0757 

0.02 

2.1004 

18.75 

8.ti811 

6.70 

1.9021 

7.84 

1.9938 

7.{k 

2.0769 

0.04 

2.2017 

14.00 

8.6301 

6.71 

1.9086 

7.35 

1.9947 

7.90 

2.0782 

0.06 

8.2039 

14.25 

2.6567 

6.7-^ 

1.9051 

7.86 

1.9961 

8.00 

2.0794 

0.06 

8.8061 

14.60 

8.6740 

6.78 

1.9066 

7.87 

1.9974 

8.01. 

2.0607 

9  10 

8.2088 

14.76 

8.6013 

6.74 

1.9081 

7.38 

1.9988 

8.02 

2.0819 

9.12 

8.8105 

16.00 

8.7061 

6.75 

1.9095 

7.89 

2.0001 

8.03 

2.0832 

9.14 

8.2187 

15.50 

8  7408 

6.76 

1.9110 

7.40 

2.0015 

8.04 

2.0644 

9.W 

2.2148 

16.00 

8.7726 

6.77 

1.9125 

7.41 

2.0028 

8.06 

2.0857 

9.18 

2.2170 

16.60 

2.8084 

6.78 

1.9140 

7.42 

2.0041 

8.06 

2.0869 

9.80 

2.8198 

17  00 

2.8332 

6.79 

1.9155 

7.43 

2.0056 

8.07 

8.0S82 

9.22 

8.2214 

17.60 

2.662) 

6.80 

1.9169 

7.44 

2.0069 

8.08 

2.0894 

9.84 

2.2835 

18.00 

2.8904 

6.81 

1.9184 

7.45 

2.0088 

8.09 

2.0906 

9.26 

8.2857 

18.50 

2.917H 

6.K2 

1.9199 

7.46 

2.0096 

8.10 

2.0919 

9.28 

2.8U70 

10.00 

2.9144 

6.83 

1.9218 

7.47 

2.0108 

8.11 

2.0981 

9.80 

2.2800 

10.50 

2.970:1 

6.84 

1.9228 

7.48 

2.0122 

8.12 

2.0943 

9.82 

2.2322 

80.00 

2.9057 

6.85 

1.9242 

7.49 

2.0186 

8.18 

2.0956 

9.34 

2.2348 

21 

8.0445 

G.86 

1.9257 

7.60 

2.0149 

8.14 

2.0968 

9.36 

2.2364 

82 

8.0010 

6.87 

1.9272 

7.51 

2.0162 

8.16 

2.0980 

9.88 

2.2886 

83 

8.1855 

6.88 

1.9286 

7.52 

2.0176 

8.16 

2.0992 

9.40 

2.2407 

84 

8.r78l 

6.89 

1.9301 

7.53 

2.0189 

8.17 

2.1005 

0.42 

2.2428 

26 

8.8Ib0 

6.90 

1.9315 

7.54 

2.0202 

8.18 

2.1017 

0.44 

2.2450 

86 

8.2661 

6.91 

1.9330 

7.55 

2.0215 

8.19 

2.1029 

9.46 

2.2471 

87 

8.2958 

6.9-^ 

1 .9344 

7.56 

2.0220 

8.20 

2.1041 

9.48 

2.2402 

28 

8.8^22 

6.93 

1.9369 

7.57 

2.0248 

8.22 

2.1066 

9.60 

2.2518 

80 

8.86::) 

6.94 

1.9878 

7.68 

2.0256 

8.24 

2.1090 

9.62 

8.2584 

80 

8.4012 

6.95 

1.9387 

7.69 

2.0268 

8.26 

2.1114 

9.64 

2.-J665 

81 

8.4340 

6.96 

1.9402 

7.60 

2.0281 

8.28 

2.1138 

9.66 

2.2576 

88 

3.4667 

6.97 

1.9416 

7.61 

2.0295 

8.30 

2.1163 

9.58 

2.2697 

88 

8.4965 

6.98 

1.9480 

7.62 

2.0306 

8.82 

2.1187 

9.60 

2.2618 

84 

8.6263 

6.99 

1.9445 

7.63 

2.0321 

8.34 

2.1211 

9.62 

2.2638 

85 

8.5553 

7.00 

1 .9459 

7.64 

2.0384 

8.36 

2.1235 

9.64 

2.2659 

86 

8.5835 

7.01 

1.9478 

7.65 

2.0347 

8.88 

2.1268 

9.66 

2.2680 

87 

8.6109 

7.08 

1.9488 

7.66 

2.0360 

8.40 

2.1282 

0.68 

2.2701 

88 

8.0876 

7.a3 

1.9302 

7.67 

2.a373 

8.42 

8.1306 

0.70 

8.2721 

80 

8.6638 

7.W 

1.0516 

7.68 

2.0386 

8.44 

8.1330 

0.72 

2.8742 

40 

3.6889 

7.05 

1.9530 

7.69 

2.0899 

8.46 

2.1353 

0.74 

2.2762 

41 

8.7136 

7.06 

1.9544 

7.70 

2.0412 

8.48 

8.l87r 

0.76 

8.8r83 

48 

8.7377 

7.07 

1.9559 

7.71 

2.0425 

8.50 

8.1401 

0.78 

8.2808 

48 

8.7612 

7.08 

1.9573 

7.72 

2.0488 

8.52 

2.1424 

0.80 

8.8824 

44 

8.7H42 

7.09 

1.9587 

7.73 

2.0451 

8.54 

2.1448 

0.88 

8.8844 

45 

8.8067 

7.10 

1.9601 

7.74 

2.0464 

8..V) 

2.1471 

0.81 

8.8865 

46 

8.8286 

7.11 

1.9615 

7.75 

2.0477 

8.58 

2.1494 

9.86 

2.2886 

47    • 

8.8501 

7.12 

1.9629 

7.76 

2.0490 

8.60 

2.1518 

9.88 

2.2905 

48 

8.8712 

7.18 

1.964.3 

7.77 

2.0ri03 

8.62 

2.1.'S41 

9.90 

2.2925 

40 

8.8018 

7.14 

1.9657 

7.78 

2.0516 

8.64 

2.1564 

9.92 

2.2946 

60 

3.9180 

KATURAL  TBIGOKOMETRICAL  FUNCTIONS, 


159 


HATITRAIi  TRIGONOniBTBICAIi  FrNCTIONS. 


• 

M. 

SIlM. 

C«-V«n. 

Cons. 

T-». 

Cetan.    1  Bacant. 

Vpr.  8lB.    Coniu*. 

90 

*""" 

0 

1.0000 

Infinite 

.00000 

[nflnite!  1.0000 

.000001.0000 

.09000 

0 

15 

.00488 

.90664 

ifi».18 

.00486 

229.18    '  l.OOOO 

.00001    .99999 

45 

80 

.00873 

,99127 

114.59 

.00873 

114.59       1.0000 

.00004    .99996; 

80 

45 

.01809 

.96691 

76.897 

.01309 

76.390     1.0001 

.00009    .99991 

15 

0 

.01745 

.98255 

97.299 

.01745 

57.290      1.0001 

.00015    .99985   89 

0 

15 

.OseiSl 

.97819 

45.840 

.02182 

45.829  .  1.0002 

.00024    .99976 

45 

80 

.(y»\s 

.97»& 

88.202 

.02618 

38.188      1.0008 

.000:i4 

.99966 

80 

45 

.oao-Ji 

.9U946 

82.746 

.03055 

32.730  1  1.0006 

,00047 

.9995.-), 

15 

0 

.03490 

.96310 

28.054 

.03492 

28.636  ;  1.0006 

,00061 

.99939  88 

0 

15 

.08^» 

.96074 

25.471 

.06929 

25.452  1  1.0008 

.00077 

.99923 

45 

80 

.01308 

.95685 

22.926 

.04366 

22.904  ;  1.0009 

.00095 

.99905 

80 

45 

.047W 

.93202 

20.843 

.04803 

20.819     1.0011 

.00115    .99885 

15 

0 

.OTisa* 

.94766 

19.107 

.05241 

19.081      1.0014 

.00137    .99863 
.00161     .99889 

87 

0 

15 

.05609 

.948:M 

17.639 

.056« 

17.611      1.0016 
16.350      1.0019 

45 

80 

.05106 

.9S695 

16.880 

.06116 

.00187,   .99813 

30 

15 

.00510 

.98160 

15.290 

.06551 

15.257 

1.0021 

.00214    .09786 

15 

0 

.oooro 

.98024 

14.3% 

.06998 

14.801 

1.0024 

.00244    .99756 

86 

0 

15 

.omi 

.9^569 

13.494 

.07431 

IS.W 

1.0028 

.00275    .99725 

45 

80 

.07810 

.92154 

12.745 

.07870 

12.706 

1.0061 

.00308 

.99692 

80 

45 

.0*fcJI 

.91719 

12.076 

.08809 

12.035 

1.0084 

.00843 

.99656 

15 

0 

.06716 

.912S4 

11.174 

.08749 

11.430 

1.0038 

.00881 

.99619 

86 

0 

15 

.00150 

.90850 

10.929 

.09189 

10.838 

1.0042 

.00420 

.99580 

45 

80 

.09585 

.90415 

10.433 

.09629 

10.885 

1.0046 

.004601  .99540 

80 

45 

.10019 

.89961 

9.9BI2 

.10069 

9.9310 

1.0061 

.00503    .90497 

15 

0 

.10453 

.89547 

9.5668 

.10510 

9.5144 

1.0055 

.00548.  .99452 

84 

0 

15 

.ia«7 

.80118 

9.1855 

.10952 

9.1309    1.0060 

.0(1504,  .994U6 

45 

80 

.tl%i0 

.88680 

8.8387 

.11393 

8.7769    1.0065 

.00648 

.99357 

SO 

45 

.11754 

.88^46 

8.5079 

.11836 

8.4490;  1.0070 

.00693 

.99807 

15 

7       0 

.UlS? 

.87818 

8.2055 

.12278 

8.1443:   1.0075 

.00745 

.99255 

88 

0 

15 

.l^SfrJO 

.87380 

7.9210 

.12722 

7.8606;   1.0081 

,00800 

.99200 

45 

80 

.11038 

.86947 

7.6613 

.13165 

7.5958    1.0086 

.00856 

.99144 

80 

45 

.13IS5 

.86315 

7.4158 

.18609 

7.8479    1.0092 

.00013    .99086 

15 

8       0 

.13017 

.8608) 

7.1853 

.14054 

7,1154    1.0098 

.00078 

.99027 

82 

0 

15 

.14319 

.85631 

6.9690 

.14499 

6.8969|  1.0105 

.01035 

.98965 

45 

80 

.14781 

.85^19 

6.7655 

.14945 

6.69121  1.0111 

.01098 

.98902 

80 

45 

.15812 

.84788 

6.5786 

.15391 

6.4971 

1.0118 

.01164 

.98836 

15 

0 

.15618 

.84357 

6.3924 

.15883 

6.3138 

1.0125 

.01281 

.98769 

81 

0 

15 

.16074 

.839« 

6.2211 

.16286 

6.1402 

1.0132 

.01300 

.98700 

45 

80 

.16505 

.83495 

6.0589 

.16734 

6.9758 

1.0139 

.01371 

.98629 

80 

46 

.10085 

.88065 

5.90411 

.17183 

5.8197 

1.0147 

.014441   .98556 

15 

10 

0 

.17865 

.82635 

5.7568 

.17633 

5.6713 

1.0154 

.015191   .98481 

80 

0 

15 

.17794 

.82206 

6.6196 

.13083 

6.5301 

1.0162 

.01596 

.98404 

45 

80 

.18»4 

.81776 

5.4874 

.18534 

5.3955 

1.0170 

.01675 

.98326 

30 

45 

.18668 

.81848 

6.8612 

.18966 

5.2672 

1.0179 

.01755 

.98245 

15 

u 

0 

.19081 

.80919 

5.2408 

.19488 

5.1446 

1.0187 

.01887 

.98168 

79 

0 

15 

.19809 

.80491 

6.1258 

.19891 

6.0273 

1.0196 

.01021 

.9H079 

45 

80 

.19937 

.80063 

6.0158 

.20345 

4.9152 

1.0205 

.02008 

.97992 

.'JO 

45 

.:HB6I 

.79686 

4.9106 

.20800 

4.8077 

1.0214 

.02095 

.97905 

15 

IS 

0 

.:a0791 

.79209 

4.8097 

.21236 

4.7046 

1.0223 

.02185 

.97815 

78 

0 

15 

.81218 

.7878;J 

4.7180 

.21712 

4.6057 

1.0283 

.02877 

.977^-M 

45 

80 

.21644 

.78356 

4.0202 

.22169 

4.5107 

1.0243 

.02370 

.97630 

30 

45 

.2AV70 

.77900 

4.5311 

.22628 

4.4194 

1.0853 

.02466 

.97584 

15 

IS 

0 

.turn 

.77506 

4.4454 

.23087 

4.8815 

1.0263 

.02563 

.974.37 

77 

0 

15 

.229^ 

.77080 

4.3680 

.28547 

4.2468 

1.0273 

.02662 

.97838 

45 

80 

.£»45 

.76668 

4.2837 

.24008<     4.1651 

1.0284 

.02768 

.97287 

80 

45 

.tirm 

.78231 

4.2072 

•24470 

4.0667 

1.0295 

.02866 

.97184 

15 

U;    0 

.8419si 

.75808 

4.1336 

.24933 

4.0108 

1.0306 

.02970 

.97090 

76 

0 

15 

.24619 

.75380 

4.0025 

.25397 

8.9:)7S 

1.0817 

.08077 

.96928 

45 

80 

.25088 

.749QJ 

8.9989 

.25862 

8.8667 

1.0829 

.06185 

.96815 

30 

45 

.2546Q 

.7454C 

3.9277 

.26328     8.7989 

1.0341 

.03296 

.95705 

16 

tk  '    o 

.8S68il 

.741 IC 

8.8637 

.26795     8.782C 

1.0358 

.08407 

.96598 

76 

o 

0 
M. 

1 

G»lM 

V«.  Sis 

Smut. 

CoteB.  1     lanff. 

COMC 

Co-Vwt. 

Sloa. 

Vrom  76°  to  90"  vead  flrom  bottom  of  table  npivards. 


160 


ItATHSltATICAL  TABLIS. 


• 

M. 

Sloe. 

Co-Vm 

Cotee. 

TE«r 

C«tan. 

Secant. 

Vw.  »n. 

Coda*. 

16 

0 

.9669 

.74118 

8.8687 

.26705 

8.7880 

1.0358 

.08407 

.96503 

74 

0 

16 

.90808 

.78607 

8.8018 

.27868 

8.6660 

1.0866 

.06681 

.90470 

45 

ao 

.967iM 

.7W.16 

8.7420 

.277Si 

8.6060 

1.0877 

.O06S7 

.00868 

SL 

46 

.87144 

.78856 

8.6840 

.f»m 

8.6457 

1.0800 

.06754 

.00240 

15 

16 

0 

.97664 

.7^4486 

8.6280 

.28674 

3.4874 

1.0403 

.08874 

.06186 

74 

0 

15 

.27068 

.79017 

8.6736 

.20147 

8.4308 

1.0416 

.08006 

.06006 

49 

SO 

.88402 

.71508 

8.5209 

.20621 

8.37Q0 

1.0429 

•04118 

.96688 

80 

45 

.itsm 

.71180 

8.4609 

.80006 

8.8»6 

1.0448 

.04243 

.05757 

15 

17 

0 

.2W87 

.70763 

8.4208 

•80573 

8.2709 

1.0457 

.04370 

.06680 

7t 

0 

15 

.2U6d4 

.70846 

8.8722 

.81051 

8.2205 

1.0471 

.04406 

.05602 

45 

ao 

.80070 

.69029 

8.8255 

.81530 

8.1716 

1.0485 

.04628 

.05878 

80 

•16 

.80486 

.69514 

8.2801 

.82010 

8.1240 

1.0600 

.04760 

.06840 

15 

18 

0 

.aOMn2 

.69098 

8.2361 

.32402 

8.0777 

1.0615 

.04804 

.05100 

78 

0 

15 

.81316 

.68684 

3.1982 

.82975 

8.0386 

1.0630 

.06080 

.04970 

45 

ao 

.81730 

.68270 

3.1515 

.83450 

8.9887 

1.0645 

.06168 

.04688 

80 

45 

.38144 

.07856 

8.1110 

.83045 

8.9159 

1.0560 

.05807 

.94608 

15 

lf» 

0 

.82667 

.67448 

8.0715 

.34438 

8.0O42 

1.0676 

.05448 

.94558 

71 

0 

15 

.iom 

.67081 

8.0331 

.84021 

8.8686 

1.0592 

.06601 

.04400 

45 

ao 

.83881 

.66619 

8.0957 

.35412 

8.8289 

1.060S 

.05786 

.04264 

30 

45 

.88792 

.U6208 

8.0593 

.85004 

8.786fi; 

1.0625 

.068R2 

.04118 

15 

80 

0 

.8430-^ 

.66708 

2.9236 

■86897 

8.7475 

1.0642 

.06091 

.03800 

70 

0 

15 

.84618 

.66888 

8.8802 

•36808 

8.7106 

1.0669 

.06181 

.03819 

45 

80 

.86081 

.64979 

2.8554 

-87888 

8.6746 

1.0676 

.06388 

.08667 

30 

45 

.86429 

.64671 

8.8225 

.87887 

8.6305 

1.0694 

.06486 

.93614 

15 

81 

0 

.85887 

.64168 

8.7904 

.38886 

8.6051 

1.0711 

.06642 

.03868 

•9 

0 

15 

.36244 

.68756 

2.7591 

.88888 

8.6715 

1.0729 

.06700 

.OSMl 

45 

ao 

.36650 

.08360 

2.7285 

.39891 

8.5886 

1.0748 

.06068 

.08042 

80 

45 

.37056 

.62944 

2.6986 

.89696 

8.5065 

1.0766 

.07110 

.92881 

15 

82 

0 

.87461 

.62589 

2.6695 

.40408 

8.47C] 

1.0785 

.0ri68 

.02718 

68 

0 

15 

.8786ft 

.00135 

8.6410 

.40911 

84448 

1.0804 

.07446 

.08564 

46 

ao 

.88268 

.61782 

8.6181 

.41421 

8.4142 

1.0624 

.07612 

.02888 

80 

46 

.8867: 

.61829 

2.5869 

.41988 

88847 

1.0644 

.07780 

.08220 

15 

88 

0 

.89078 

.60027 

8.6593 

.42447 

88559 

1.0664 

.07050 

.08060 

67 

0 

15 

.89474 

.60526 

8.5383 

•42968 

8.8276 

1.0684 

.08121 

.91879 

46 

80 

.89875 

60185 

8.6078 

.43481 

88008 

1.0904 

.08804 

•91706 

30 

45 

.40275 

.59725 

8.4829 

.44001 

28727 

1.0995 

.06469 

•91581 

15 

84 

0 

.40674 

.69326 

8.4586 

.44528 

82460 

1.0046 

.06645 

.91856 

66 

0 

15 

.41072 

.68028 

8.4348 

.46047 

8.2109 

1.0968 

.08834 

.91176 

45 

80 

.41469 

.6853] 

2.4114 

.45678 

2.1943 

1.0989 

•00004 

.90906 

80 

46 

41866 

.68184 

8.3886 

.46101 

8.1692 

1.1011 

.00186 

.00614 

15 

85 

0 

.42262 

.67788 

8.8662 

.46631 

8.1445 

1.1034 

.09369 

.90681 

66 

0 

•  15 

.42667 

.67848 

8.8443 

•47)68 

2.1203 

1.1066 

.09564 

.00446 

45 

.  80 

.48061 

.66949 

8.8228 

.47607 

80965 

1.1079 

.09741 

.00260 

80 

46 

.48445 

.66565 

8.8018 

.48234 

8.0782 

1.1102 

.09930 

.90070 

15 

8G 

0 

.43837 

.5616:) 

2.2812 

.48778 

8.0603 

1.1120 

.10121 

.80579 

64 

0 

15 

.44-229 

.66771 

8.2610 

.40814 

8.0278 

1.11.W 

.10813 

.89087 

45 

30 

.44620 

.55380 

8.2412 

.40658 

8.0U67 

1.117^ 

.10607 

.69498 

SG 

45 

.45010 

.54990 

8.2217 

•60404 

1.9640 

1.1198 

.10702 

.80298 

16 

87 

0 

.4.'>399 

.54601 

8.2027 

.50052 

1.9026 

1.1823 

.10890 

.89101 

68 

0 

15 

,45787 

.64218 

8.1840 

.61608 

1.94ri 

1.1848 

.11098 

.88002 

45 

30 

.46175 

.58825 

2.IC67 

.69067 

1.9210 

1.1971 

.11299 

.88701 

80 

45 

.46561 

.53439 

8.1477 

.52612 

1.9007 

1.1800 

.11501 

.88499 

15 

8S 

0 

.46947 

.58058 

8.1800 

.58171 

1.8807 

1.1326 

.11705 

.88896 

68 

0 

15 

.47332 

.5206R 

2.1127 

.53782 

1.8611 

l.l85-.i 

.11911 

.88089 

45 

80 

.47716 

.52284 

2.0957 

.64205 

1.8418 

1.1379 

.12118 

.87882 

80 

45 

.48009 

.51901 

8.0790 

.54862 

1.8228 

1.1400 

.12327 

.87678 

15 

80 

0 

.48481 

.51519 

8.0627 

.55431 

1.8040 

1.1433 

.12538 

.87468 

61 

6 

1ft 

.48862 

.6113« 

2.0466 

.56003 

1.7866 

1.1461 

.12750 

.87850 

45 

ao 

.49242 

.60758 

8.0808 

.66577 

1.7675 

1.1490 

.18964 

.87036 

80 

45 

.49622 

.60876 

8.01.^8 

.67165 

1.7496 

1.1518 

.13180 

.86820 

16 

JIO 

0 

.50000 

.50000 

3.0000 

.57785 

1.7820 

1.1547 

.18897 

.86608 

JM 

_0 

C««n«. 

V«r.  Sio. 

i^Mt. 

CoUn 

Twr. 

Come. 

G>.Vm. 

8««. 

o 

M. 

From  60"  to  75"*  read  trom.  bottom  of  table  npirards* 


NATURAL  TRIGONOMETRICAL  FUNCTIONS. 


161 


e 

M. 

0 

SlM. 

Oh\tr». 

COMC 

T»g. 

1               1 
Cotaa.    ;  BmuI.   Vrr.  Sin. 

Coaisc 

SO 

.60000 

.50000 

8.0000 

.57785 

1.7890'  1.1647 

.13897 

.86603 

00 

0 

15 

.60877 

.49628 

1.9860 

.58818 

1.7147;  1.1576 

.18616 

.86884 

45 

ao 

.60754 

.40^6 

1.9703 

.68904 

1.89771  1.1606 

.18837 

.86168 

80 

45 

.511S9 

.48671 

1.9668 

.69494 

1.8606   1.10S6 

.14060 

.86M1 

15 

SI 

0 

.61504 

1.9416 

.60066 

1.6643 

1.1666 

.14388 

.86n7 

59 

0 

15 

.61877 

!481S8 

1.9276 

.60681 

1.6479 

1.1807 

.14509 

.86491 

45 

80 

.&9«0 

.47750 

1.9189 

.61280 

1.6819 

1.1788 

.14786 

.85264 

80 

45 

.5^621 

.47879 

1.9004 

.61888 

1.6160 

1.1780 

.14966 

.86035 

15 

ss 

0 

.5»08 

.47008 

1.8871 

.69487 

1.6008 

1.1792 

.15195 

.84805 

68 

0 

15 

.53861 

.46689 

1.8740 

.68096 

1.6849 

1.1824 

.15437 

.84578 

♦45 

SO 

.58780 

.46S70 

1.8618 

.68707 

1.5697 

1.1867 

.15661 

.81889 

80 

45 

.54007 

4600S 

1.8485 

.61882 

1.6547 

1.1800 

.16696 

.84104 

16 

ss 

0 

.54464 

!45586 

1.8361 

.64941 

1.S399 

1  1924 

.16188 

.88867 

67 

0 

15 

.54820 

.45171 

1.8288 

.66503 

1.5253 

1.1958 

.16371 

.88629 

45 

SO 

.55194 

.44806 

1.8118 

.66186 

1.6106 

1.1992 

.16611 

.88889 

80 

45 

.66657 

.44448 

1.7909 

.66818 

1.4966 

1.9027 

.16858 

.88147 

15 

S4 

0 

.66919 

.44061 

1.7883 

.67461 

1.4886 

1.9068 

.17096 

.82904 

66 

0 

15 

.5«a» 

.48») 

1.7768 

.68087 

1.4687 

1.9098 

.17341 

.83659 

45 

80 

.'66511 

.48859 

1.7665 

.68728 

1.4660 

1.3184 

.17587 

.82418 

80 

45 

.57000 

.48000 

1.7544 

.69S7V 

1.4415 

1.2171 

.17835 

.82165 

15 

S6 

0 

.n8&8 

.4»48 

1.7434 

.70031 

1.4281 

1.8»6 

.180S) 

.81916 

66 

0 

15 

.67715 

.42886 

1.7337 

.70673 

1.4150 

1.8245 

.18888 

.81664 

45 

80 

.68070 

.41980 

t.TWO 

.71320 

1.4019 

1.3288 

.18588 

.81413 

80 

45 

.68435 

.41575 

X.71J6 

.71990 

1.8891 

1.8322 

.18848 

.61157 

15 

S6 

0 

.68779 

.41231 

1.7013 

.72664 

1.8764 

1.2361 

.19098 

.80903 

64 

0 

15 

.60181 

.40669 

1.6912 

.78323 

1.3638 

1.2400 

.19356 

.80644 

45 

SO 

.60482 

.40518 

1.6812 

.73996 

1.8514 

1.2440 

.19614 

.80366 

80 

4^ 

.60682 

.40168 

1.6713 

.74673 

1.8892 

1.2480 

.19876 

.80126 

16 

S7 

0 

.60181 

.39619 

1.6616 

.Teaw 

1.8270 

1.2521 

.90136 

.79664 

68 

0 

15 

.60629 

.89471 

1.6021 

.78042 

1.8161 

1.2568 

.20400 

,79600 

45 

ao 

.00876 

.39m 

1.6427 

.76783 

1.8082 

1.2605 

.90665 

.79886 

80 

45 

.^ifta 

.38778 

1.6884 

.77428 

1.2916 

1.2647 

.20981 

.79069 

15 

S8 

0 

.61566 

.884:^ 

1.6248 

.78129 

1.2799 

1.2690 

.21199 

.78801 

69 

0 

15 

.61909 

.86091 

1.6153 

.78884 

1.2685 

1.2734 

.21468 

.78532 

45 

80 

.88251 

.87749 

1.6064 

.79543 

1.2572 

1.2778 

.21^739 

.78261 

8?^ 

45 

.6i59d 

.87403 

1.697G 

.802J58 

1.2460 

1.2822 

.22012 

.77988 

15 

S9 

0 

.8si9a? 

.37068 

1.689D 

.80978 

1.2349 

1.2868 

«>Qgg5 

.77715 

61 

0 

15 

.63271 

.38729 

1.6805 

.8170:^ 

1.2239 

1.2913 

122561 

.77489 

45 

80 

.64608 

.8639-J 

1.672i 

.82431 

1.2181 

1.2960 

.92688 

.77168 

80 

45 

.6:3944 

.360o6 

1.6639 

.83169 

1.9024 

1.8007 

.38116 

.76884 

15 

40 

0 

.64279 

.85721 

1.8557 

.KIRBIO 

1.1918 

1.3054 

.88396 

.76601 

60 

0 

15 

.64619 

.853S8 

1.6477 

.84656 

1.1812 

1.3102 

.88677 

.76328 

45 

30 

.64945 

.85056 

1.5398 

.85406 

1.1708 

1.3161 

.28969 

.76041 

80 

45 

.69876 

.34724 

1.5820 

.86165 

1.1606 

1.8200 

.24244 

.75756 

15 

41 

0 

.65606 

.84)94 

1.6242 

.86929 

1.1504 

1.8250 

.24529 

.76471 

49 

0 

15 

.6582)6 

.34065 

1.5166 

.87008 

1.1408 

1.3301 

.34816 

.75184 

45 

80 

.66«i 

.88738 

1  6092 

.88472 

1.1806 

1.8358 

.25104 

.74896 

80 

45 

.66588 

.38412 

1.6018 

.89258 

1.1201 

1.8404 

.35394 

.74606 

16 

42 

0 

.66918 

.33087 

1.4945 

.90040 

1.1106 

1.84.W 

.25686 

.74314 

48 

0 

15 

.67«7 

.82763 

1.4878 

.90884 

1.1009 

1.3509 

.25978 

.74022 

45 

80 

.07359 

.82441 

1.4808 

.9168:J 

1.0013 

i.sm 

.96272 

.78728 

80 

45 

.67880 

.88120 

1.4732 

.92489 

1.0818 

1.3618 

.96568 

.78482 

15 

4S 

0 

.09900 

.81800 

1.4668 

93251 

1.07*4 

1.8673 

.26865 

.78135 

47 

0 

15 

.68518 

.31482 

1.4.595 

.94071 

1.0630 

1.3?-J» 

.27163 

.?«37 

46 

80 

.68835 

.81165 

1.4597 

.94896 

1.0588 

1.8786 

.27468 

.72587 

80 

45 

.69151 

.80849 

1 .4461 

.95729 

1.0446 

1.8848 

.27764 

.72236 

15 

44 

0 

.69466 

.30684 

1.48te 

.96569 

1.08M 

1.8908 

.28066 

.71984 

46 

0 

16 

.69779 

.80221 

1.4831 

.97416 

1.026r) 

1.8961 

.28370 

.71630 

45 

80 

.70091 

.8990G 

1.4267 

.98270 

1.0176 

1.4020 

.28675 

.71825 

30 

45 

.70401 

.29509 

1.4204 

.99131 

1.U0S8 

1.4081 

.28981 

.71019 

15 

jW 

0 

.wni 

.29289 

1.4142 

1.000(j'     1.0000 

1.414;.' 

.29289 

.70711 

45 

o 

0 

Coda*. 

Ver.Sia. 

Soomt. 

CoUn. 

Tmjf. 

CoMC 

Co-Vm, 

Sine. 

M. 

From  45°  to  60«  read  ft*om  bottom  oftable  upwardii... 


162 


MATHEMATICAL  TABLES, 
I^OGARlTBiniC  8INBS,  ETC. 


Iii.Neg.  Inflnite. 
8.94186  11.76814 
8.64888  11.45718 
8.71880  11.88120 
8.84858  11.16648 


8.94080 

0.01983 

9. 

9.14856 

9.19488 

9.88967 
9.28060 
9.81788 
9.85809 
9.38868 

9.41300 
9.440S4 
9.46694 
9.48996 
9.61:;»4 

9.58406 
9.55488 
9.5786H 
9  A91H8 
9.60981 

9.64184 
9.66?m 
9.67161 
9.68567 

9.69897 
9.71184 
9.78481 
9.73611 
9.74766 

9.75859 

9.77946 
9.7Rltt4 
9.79887 

9.80807 
9.81694 
9.8;2661 
9.88878 
9.84177 

9.84949 


Cosine. 


11.06970 
10.98077 
10.91411 
10.85644 
10.8056^ 

10.76088 
10.71940 
10.68812 
10.64791 
10.61638 


Yonln. 


Tugent. 


In.Ne«:. 
G.18^1 
6.78474 
7.18687 
7.88667 

7.68089 
7.78H63 
7.87888 


8.09088 

8.18162 
8.26418 
8.83950 
8.40675 
8.47288 


10.58700  8.68848 

10.559ri6  8.58814 

10.68406  8.64048 

10.510  8  8.08969 

10.48736  8.736;!5 


10.40695 
10.44567 
10.4264:j 
10.40812 
10. 


8.78037 
8.82280 
8.86223 
8.90034 
8.93U79 


10  87405   8.97170 

lo.a^sie  9.00581 

10.84295!  9.06740 
10..S2889  9.06888 
10.81448  9.09883 


10.80106 

10.88816 

10.27679 

10.26; 

10.85844 


9.18708 
9.16483 
9.18171 
9.90771 
9.93290 


10.94141  9.96781 

10.28078  9.88099 

10.88064  9.80398 

10.81066  9.38681 

10.20113  9.84802 


10.19193 
10.18806 
10.17449 
10.16688 


10.15838  9.44818 


10.15052 


9.36918 
9.38968 
9.40969 

9.42918 


9.46671 


In. Nee. 
8.94192 
8.54308 
8.71940 
8.84464 

8.94195 
9.02168 
9.08914 
9.14780 
9.19971 

9.94638 
9  88865 
9.32747 
9.86886 
9.89677 

9.48805 
9.467.'i0 
0.48584 
9.51178 
9.&3697 

9.56107 
9.5&118 
9.60641 
9.627»5 
9.64858 

9.6C867 
9.r881R 
9.707r 
9.7256^ 
9.74375 

9.76144 
9.77877 
9.79579 
9.81952 
9.88899 

9.84583 
9.86126 
9.8771! 
9.89881 
9.908S7 

9.98381 
9.9.H916 
9.95444 
9.9f)96() 
9.96484 

10.00000 


InfiDite. 
11.75808 
11  45692 
11.88060 
11.10586 


Secant.    Corora.     Cotan.    Tangent    Yersln. 


Cotan. 


11 

10.97838 

10.91086 

10.85280 

10.80029 


10 

10.71135 

I0.672.'i8 

10.68664 

10 


10.57195 
I0.54;.»r>0 
10.5146G 
10.4t«22 
10.46:303 

10.43^93 

10.41.582 

10.89! 

10.87215 

10.85142 

lO.SSl&i 
10.31182 
10.8928:) 
10.274.3:3 
10.25625 

10.83866 
10.82123 
10.20481 
10.18748 
10.17101 

10.15477 
10.i;«74 
10.12289 
10.10713 
10.00163 

10.07619 
10.0C0S4 
10.04•^^6 
10.03aS4 
10.01516 

lO.OOOOO 


Coven. 


10.00000 
9.99285 
9.9K457 
\).97665 
9.96860 

9.90040 
9.95205 
9.94366 
9.93492 
9.98618 

9.91717 
9.90805 
9.89877 
0.88983 
9.87971 

9.8G998 
9.a'J996 
9.84061 
9.83947 
9.82891 

9.81881 
9.80729 
9.79615 
9.78481 
9.77885 

9.7614f 
9.74945 
9.73720 
9.72471 
9.71197 

9.69897 
9.68571 
9.67217 
9.65836 
9.64485 

962964 
9.61.512 
9.6(XI0H 
9.. 58471 
9.66900 

9.5.5208 
9  5:3648 
9.51966 
9.60848 
9.48479 

9  46671 


10.00000 
10.00007 
10.00086 
10.00060 
10.09106 

10.00166 
10.00839 
10.00895 
10.00426 
10.00588 

10.00665 
10.00805 
10.00960 
10.01186 
10.01310 

10.01506 
10.01716 
10.01940 
10.08179 
10.0S438 

10.02701 
10.08065 
10.03288 
10.03.597 
10.03987 

10.04879 
10.04684 
I0.0&018 
10.05407 
10.05818 

10.06947 
10  06693 
10.07158 
10.07641 
10.06148 

10.08664 
10.09804 
IO.01I765 
10.10347 
10.10960 

10.11575 
10.12829 
10.12898 
10.1.3587 
10.14807 

10.1.5062 


Coeeo. 


Dee. 


10.00000  90 
9.09998  80 
9.1*99741  88 
9.99940'  87 
9.90894.  86 

9.908341  a*) 

0.99761!  84 

9.99675f  83 

9.9057r)|  H8 

9.90468  81 

9.998351  80 
9.99105  79 
0.99040)  7B 
9.988?2,  77 
0.9h690    76 


9.9B494 
9.982841 
0.98060i 
9.9:«2I 
9.97667! 

0.97899' 
0.97T)I5I 
0.06717 
0.06408 
0.06078 

0.067881 
0.05866 
0.949W, 
9.94593 
9.94182< 


70 


65 
64 
6S 
09 
61 


9.937581  CO 

9.93807!  f>9 

9.92848  58 

9.92359  .57 

9.91857.  £6 

9  91836'  55 
9.90796  .^4 
9.90-^:35  ?A 
9.WI6.VJ  b'i 
9.89050   51 

9.88486'  50 

9  87778  49 

9.87107,  48 

9.86418  47 

9.85693  46 

9.84040   4!S 


From  45<>  to  90»  read  IVoiti  boUom  of  table  apwards. 


SPECIFIC  GRAVITY. 


168 


MATEBIAIiS. 


THK  CHEniCAIj    BliElHFNTS. 

Xha  Common  Elements  (43). 


^1 

Name. 

il 

ll 

Name. 

S  if 

it 

Name. 

II 

t^ 

<^ 

ga 

<^ 

g^ 

<^ 

Al 

Aluminum 

87.1 

P 

Fluorine 

10. 

Pd 

Palladium 

106. 

Sb 

Antimony 

l:».4 

Au 

Gold 

107.8 

P 

Phosphorus 

SI. 

As 

Arsenic 

75.1 

H 

Hydrogen 

1.01 

Pt 

PlaUnum 

ie«.o 

Ba 

Barium 

187.4 

I 

Iodine 

1S6.8 

K 

Potassium 

30.1 

Bi 

Bi«muth 

S09.1 

Ir 

Iridium 

193.1 

Si 

Silicon 

88.4 

B 

Boron 

10.9 

Fe 

Iron 

56. 

Ag 

SUver 

107.0 

Br 

Broujine 

79.0 

Pb 

Lead 

S206.9 

Ni 

Sodium 

88. 

Cd 

Cadmium 

111.9 

U 

Lithium 

7.08 

Sr 

Strontium 

87.6 

Ca 

Calcium 

40.1 

Mg 

Magnesium 

24.3 

S 

Sulphur 

98.1 

C 

Carbon 

Vi. 

Mn 

Manganese 

55. 

Sn 

Tin 

lie. 

CI 

Chlorine 

85.4 

^ 

Mei-cury 

200. 

Tl 

Titanium 

48.1 

C» 

Chromium 

6S.I 

Nickel 

68.7 

W 

Tungsten 

184.8 

Co 

Cobalt 

59. 

N 

Nitrogen 

14. 

Va 

Vanadium 

61.4 

Cu 

Copper 

63.6 

O 

Oxygen 

10. 

Zn 

Ziuc 

66.4 

The  atomic  weights  of  many  of  the  elements  vary  In  the  decimal  place  aa 
in'ven  by  different  authorities.  The  above  are  the  most  recent  valuee  re- 
fctrtsd  to  O  =  16  and  U  s  1.008.  When  H  is  taken  as  1,  O  =  16.879,  and  Uie 
other  fljrures  are  diminished  proportionately.  (See  Jour.  Ant.  Chem,  Soc.% 
liarch,  1806.) 


The  Rare  Element*  (S7)« 


Berjiliuiii,  Be. 
Cseidum,  Ob. 
C»»rium,  Ce. 
Didymium,  D. 
Erbium,  E. 
(;alUum,  Oa. 
(iermaoium,  Ge. 


Qluclnum,  G. 
Indium,  In. 
Lanthanum,  La. 
Molybdenum,  Mo. 
Niobium,  Nb. 
Osmium,  Os. 
Bhodium,  R. 


Rubidium,  Rb. 
Ruthenium,  Ru. 
Samarium,  Sm. 
Scandium,  Sc. 
Selenium,  Se. 
Tantalum,  Ta. 
Tellurium,  Te. 


Tliallium,  Tl. 
Thorium,  Th. 
Uranium,  U. 
Ytterbium,  Yr. 
Yttrium,  Y. 
Zirconium,  Zr. 


SPECIFIC   6RATITT. 


The  specific  gravity  of  a  substance  is  its  weight  as  compared  with  the 
vHsfat  of  an  equal  bulk  of  pure  water. 
To  And.  the  ■peclile  sraTtty;  of  a  ■nbstanee. 

W  s  weight  of  body  in  air;  w  =  weight  of  body  submerged  in  water. 

w 

Specific  gravity  =  ^_^. 

If  the  substance  be  lighter  than  the  water,  sink  it  by  means  of  a  heavier 
Hibstaace,  and  deduct  the  weight  of  the  heavier  substance. 

Specific-gravity  determinations  ai*e  usually  referred  to  the  standard  of  the 
wdght  of  water  at  68«  F.,  68.365  lbs.  per  cubic  foot.  Some  experiineuters 
have  used  60<*  F.  as  the  standard,  and  others  dZ^  and  89. 1<*  F.  There  is  no 
pcneral  agreement. 

Given  sp.  gr.  referred  to  water  at  89.1°  F.,  to  reduce  it  to  the  standard  of 
ei*  F.  muTuply  it  by  l.OOlld. 

Given  sp.  gr.  referred  to  water  at  62*»  F..  to  find  weight  per  cubic  foot  mul- 
tiply by  02.K6.  Given  weight  per  cubic  foot,  to  find  sp.  gr.  multiply  by 
0J)16087.    Given  sp.  gr.,  to  find  weight  per  cubic  inch  multiply  by  .036065. 


164 


MATERIALS. 


fVelgbt  and  Specific  GraTlty  of  fflleUil*. 


Aluminum 

Antimony 

Bismuth  

Brass:  Copper  +  Zinc  ^, 

TO  80  \ 

to  40 

50  60  J 

n^^^m^  i  Copper,  85  to  80 1 

BrouieJTii*^'  6to20f 

Cfulmium 

CfUcium 

Chromium 

Cobalt 

Gold,  pure 

Copper 

Iridium.....*  .. 

Iron,  Caat 

**    Wrought. 

Lead.  .  ....... 

Manganese 

Magnesium 


i  9i* 

i  60< 

212< 


Mercury -j  60« 


Nickel 

Platinum.., 
Potassium. 

Silver 

Sodium  — 

Steel 

Tin 

Titanium... 
Tungsten.., 
Zinc  


Specific  Gravity. 
Range  accord- 
ing to 
several 
Authorities. 


2.56  to  2.71 
6.M  to  6.86 
9.74    to    9.90 


7.8     to    8.6 


8.52   to   S.96 

8.6     to   8.7 
1.58 
6.0 
8.5      to    8.6 
19.245  to  19.861 
8.69    to    8.98 
to  28. 
to    7.48 
to    7.9 
to  11.44 
to    8. 
to  1.75 
to  18.62 
13..58 
to  13.38 
8.-.iT9  to    8.93 
80.88    to  82.07 

0.865 
10.474  to  10.511 

0.97 
7.69*  to    7.932^ 
7.291  to    7.409 

6.8 
17.        to  17.6 
6.86    to    7.20 


28.88 
C.85 
7.4 

11.07 
7. 
1.69 

18.60 

18.87 


Specific  Grav- 
ity.   Approx. 
Mean  Value, 

used  in 

Calculation  of 

Weight. 

Weight 

per 
Cubic 

Weight 

Cubic 

Foot, 
lbs. 

Inch, 
lbs. 

2.67 

166.5 

.0963 

6.76 

421.6 

.2139 

9.82 

612.4 

.3M4 

[8.60 

686.8 

.3108 

8.40 

628.8 

.3031 

8.86 

681.8 

.301? 

L8.80 

611.4 

.8950 

8.868 

658. 

.8195 

8.65 

539. 

.8121 

19.858 

1200.9 

.6049 

8.858 

558. 

.31% 

1896. 

.8076 

7.218 

4.V). 

.!200t 

7.70 

480. 

.2779 

11.88 

709.7 

.4106 

8. 

499. 

.2aS7 

1.75 

109. 

.0641 

13.62 

849.8 

.4915 

13.58 

846.8 

.4900 

18.38 

834.4 

.4838 

8.8 

548.7 

.3175 

81.5 

1347.0 

.7758 

10.506 

655.1 

.3791 

7.864 

489.6 

.2834 

7.350 

458.8 

.»JC52 

7.00 

486.5 

.2536 

*  Hard  and  burned. 

t  Vet'y  pure  and  soft.    The  sp.  gr.  decreases  as  the  carbon  is  increased. 

In  the  ni-st  column  of  figures  the  lowest  are  usually  those  ot  cast  metals, 
which  are  more  or  less  porous;  the  highest  are  of  metals  finely  rollecl  or 
drawn  Into  wire. 

Specific  GraTlty  ot  I^lquld*  at  eo*"  F. 


Acid,  Muriatic 1.200 

»•      Nitric  1.217 

**      Sulphuric 1.849 

Alcohol,  pure 794 

**       96  per  cent 816 

**       50    '•     "    934 

Ammonia,  87.9  per  cent 891 

Bromine 2.97 

Carbon  disulphide 1 .26 

Ether,  Sulphuric .72 

Oll.Llnseed 94 

ComprcMlon  of  tbe  followlns  Fluid*  under  a  Fressnre  of 
15  Iba.  per  Square  Inch. 

Water 0000466:^  I  Kther 00006158 

Alcohol 0000216    (Mercury 00000865 


Oil,01ive 93 

**    Palm  97 

*'    Pftroleum 78  to  .88 

**    Rape 92 

•*    Turpentine 87 

*'    Whale 98 

Tar 1. 

Vinegar 1.08 

Warer 1. 

*'    sea 1.026tol.03 


SPECIFIC  GRAVITY. 


165 


The  Hydrometer. 

The  hydrometer  is  an  instrument  for  dcterminiDg  the  density  of  liquids. 
It  is  usually  made  of  glass,  and  consfKts  of  three  parts:  (1)  the  upper  part, 
a  gradoftted  stem  or  fine  tube  of  uniforni  diameter;  (2)  a  bulb,  or  enlarge- 
m»*nt  of  the  tube,  containing  air ;  and  (3)  a  small  bulb  at  the  bottom,  con- 
raining  shot  or  mercury  which  causes  the  instrument  to  float  in  a  vertical 
position.  The  graduations  are  figures  representinrr  either  specific  gravities, 
or  the  numbers  of  an  arbitrary  scale,  as  in  Baum6's,  Ti^addell's,  Beck's, 
and  other  hydrometers. 

There  is  a  tendency  to  discard  all  hydrometers  with  arbitrary  scales  and 
u>  use  only  those  which  read  in  terms  of  the  specific  gravity  directly. 

Bmune^e  Hydrometer  and  Specific  Gravities  Compared. 

Liquids' 
Lighter 

than 
Water, 
sp.gr. 


li 

Uquida 

Uquids 

Heavier 
than 

Lighter 
than 

>c 

Water, 

Water, 

ar 

sp.  KT. 

sp.gr. 

0 

1.000 
1.007 
1.018 
l.OSSO 

T 

? 

8 

4 

1.027 
1.0S4 
1.041 

•» 

6 

~ 

1.048 
1.056 
1.06S 

8 

9 

10 

1.070 

1.000 

11 

1.07« 

.993 

13 

1.085 

.986 

n 

l.OM 

.980 

14 

1.101 

.973 

:5 

1.100 

.967 

1*5 

1.118 

.960 

17 

1.126 

.9M 

IS 

1.131 

.W8 

II 

Liquids 
Heavier 

than 
Water, 
Rp.  gr. 

19 

1.148 

20 

1.1  W 

ii 

1.160 

22 

1.169 

5J8 

1.178 

94 

1.188 

25 

1.197 

26 

1.206 

27 

1.216 

28 

1.226 

29 

1.8:^6 

30 

1.246 

81 

1.256 

32 

1.267 

33 

1.277 

34 

1.288 

&5 

1.299 

86 

1.310 

87 

1.822 

Liquids 

93     . 

Liquids 

Lighter 
tlan 

Heavier 

than 

Water, 

Is 

Water, 

»P.  JfT. 

ep.RT. 

.912 

88 

1.333 

.936 

89 

1.345 

.930 

40 

1.357 

.924 

41 

1.369 

.918 

42 

1.382 

.918 

44 

1.407 

.907 

46 

1.484 

.901 

48 

1.462 

.896 

50 

1.490 

.890 

62 

1.520 

.885 

64 

1.551 

.880 

56 

1.583 

.874 

58 

1.617 

.869 

60 

1.652 

.864 

65 

1.747 

.859 

70 

1.854 

.854 

75 

1.974 

.849 

76 

2.000 

.844 

839 
881 
810 
826 
8M 
811 
802 
794 
785 

768 
760 
7M 
745 


SpeclAc  GraTlty  and  UTelclit  or  UTood. 


W«lKht 

Welffhl 

Spcdflc  Gravity. 

C?5c 

Sp«clfic  Gnrlty. 

Cubic 

*r' 

is?- 

AMer 

Avge. 
0.56  to  0.80      768 

42 

Hornbeam. . . 

Avge. 
.76                    !76 

47 

Apple 

.73  to    .79 

.76 

47 

Juniper 

Larch 

.56 

.56 

85 

-U 

.6010    .84 

.72 

45 

.56 

.56 

35 

Bamboo..     .. 

.31  to    .40 

.85 

88 

Lignum  vitie 

.65  to  1.33 

1.00 

62 

fcrwh 

.62  to    .85 

.78 

46 

Linden 

.604 

87 

B:rch 

.58  to    .74 

.65 

41 

Locust 

.738 

40 

b-x, 

.91  to  1.83 

1.12 

70 

Mahogany... 

.56  to  1.06 

.81 

SI 

C<*lar 

.49  to    .75 

.62 

80 

Maple 

Mulberry.... 

.57  to    .79 

.68 

42 

'.berry 

.61  to    .72 

.66 

41 

.56  to    .90 

.73 

46 

'  *:««tnut  . . 

.46  to    .66 

.56 

85 

Oak,  Live... 

.96  to  1.28 

1.11 

69 

'I'tt 

.24 

.24 

15 

"     White.. 

.69  to    .86 

.<  < 

48 

'Tpress.... 

.41  to    .66 

.M 

88 

"     Red... 

.73  to    .75 

.74 

46 

I^-^wood . . . 

.76 

.7C 

47 

Pine,  White.. 

.35  to    .55 

.45 

88 

E'^oy 

1.13  to  1.83 

i.ai 

76 

*•      Yellow. 

.46  to    .76 

.61 

38 

am.' 

.65  to    .78 

.61 

88 

Poplar 

.38  to    .58 

.48 

30 

» 

.48  to    .70 

.59 

87 

Spruce, 

.40  to    .50 

.4.') 

28 

'»t.ai 

.8410  1.00 

.92 

67 

Sycamoi-e.... 

.59  to    .62 

.60 

87 

HacJnnatock 

.50 

.86  to    .41 

.59 
.38 

87 
34 

Teak 

.66  to    .98 
.50  to    .67 

.82 

.58 

51 

a-mlock    .. 

Walnut  

86 

r-ckory 

.69  to    .94 

.77 

48 

Willow 

.49  to    .59 

.54 

84 

H'llr    .... 

.76 

.76 

47 

-^ 


166 


MATERIALS. 


urelffbt  and  Specific  GraTlty  of  Stones,  Brick, 
Cement,  etc. 


Asphalium 

Brick,  Soft 

•*      Common 

"     Hard  

"     PreHsed 

•♦      Fire 

Brickwork  In  mortar 

•*  "  cement 

Cement,  Rosendale,  loose 
*'       Portland,       ** 

Clay 

Concrete    , 

Earth,  Ktose 

rammed 

Emery , 

GIosA 

♦'    flint , 

Qneiss   I 

GraniteJ 

Gravel , 

Ghrpsum 

Hornblende 

Lime,  quick,  In  bulk 

Limestone 

Magnesia,  Carbonate 

Marble 

Masonry,  dry  rubble 

••        dressed 

Mortar 

Pitch 

Plaster  of  Paris 

Quartz 

Sand 

Sandstone 

Slate 

Stone,  various 

Trap 

Tile 

Soapstone 


Pound  K  Iter 
Cubic  Foot. 


87 
100 
113 
]2r> 
185 
HO  to 
100 
IIS 

60 

78 

l^to 
1:20  to 

72  to 

00  to 
260 
IWto 
180  10 


150 


160 
140 
80 
110 

178 
196 


100  to  170 


100  to 
i;*)to 
2()(Uo 
Wto 
ITO  to 
150 
l«50tO 
140  to 
140  to 

floto 

72 

74  to 
165 

90  to 
140  to 
170  to 
1»5  to 
170  to 

no  to 

166  to 


190 
150 
tSJO 
56 
•JOO 

180 
liX) 
180 
100 

80 

110 
150 
180 
WO 
iiOO 
120 
173 


Spec'iftc 
Gravity. 


1.80 
1.6 
1.79 
2.0 
2.16 

2.34  to  2.4 
1.6 
1.70 
.96 
1.35 

1 .92  to  2.4 

1.93  to  2.24 
1.16  to  1.28 
1.44  to  1.76 
4. 

3.5  to  2.75 
2.88  to  3.14 

2.56  to  2.7S 

1.6  tol.9^ 
2.aSto2.4 
8.2   to8..^^ 

.8   to    .S8 
2.?2  to  3.a 
2.4 

2.56to2.R8 
3.24  to  2.56 
3.34  to  2.88 
1.44  to  1.6 
1.15 

1.18tol.28 
2.64 

1.44  to  1.76 
2.34  to  2.4 
2.72toS.68 
2.10  to  3.4 
2.7^3  to  3.4 
1.76  to  1.98 
3.65  to  2.8 


SpeelAo  Gravity  and  IVelsht  of  Gases  at  Atmosp]iert« 
Pressure  and  32°  Fo 

(For  other  temperatures  and  pressures  see  pp.  459,  479.) 


Air 

Oxyjfen 

H^drop:en 

Nitrogen 

Carbonic  oxide,  CO 

Carbonic  acid,  C()« 

Marsh  gns.  methane,  Cn4 
Ethylene,  C^ H4 


Density, 
Air  =  1. 


1.0(KTO 
1.1051 
0.0693 
0.9714 
0.9074 
l.r.3'.K) 
0..5.560 
0.9SI7 


Q  PR  mm  OS 
per  Uire. 


1.0931 

1 . 1390 

0.0S9S7 

1.35(51 

1.351 

1.9:7 

o.;i9 

1.373 


libs,  per 
Cu.  FU 


0.0S0738 

0.08931 

0.00561 

0.07812 

0.07810 

0.12.J43 

0.04488 

0.07949 


Cubic  Ft. 
per  Lb. 


12.387 
ll.30y 
1*^.23 
13.752 
12.801 
8.103 
83.301 
12.&80 


PROPERTIES  OF  THK  tJBBFUL  305TAtS.  167 

PROPBRTIB8  OF  THB  USBFITIi   MBTAIiS. 

Almlnuiii,  AI.— Atomic  wel^rht  27.1.  Sprciflo  Kravity  2.0  to  2.7. 
Th«*  Ufrhtt^t  of  all  the  usef al  metals  except  mafirneiiiiiin.  A  soft,  ductile, 
mall«'abl«  metal,  of  a  white  color,  approachiDft  Bilver,  but  wiUi  a  bluii^  cast. 
Very  ooa-corroeiTe.  Tenacity  about  one  third  that  of  wroueht-Iron.  For- 
meriy  a  ntre  metal,  but  since  1H90  its  production  and  une  hnve  greatlv  in- 
creased on  account  nf  the  discovery  of  cheap  proces8«'B  for  reduciufr  It  from 
the  ore.  Melts  at  about  1160<*  F.  For  further  description  see  Aluminum, 
vnAfr  Strength  of  Materials^. 

Antlmonir  (Stibium),  8b.- At.  wt.  120.4.  gp.  gr.  6.7  to  6.8.  A  brittle 
nwtal  of  a  bluish-white  color  ana  highly  crystalline  or  laminated  structure. 
Iff  Its  at  e4a°  F.  Heated  in  the  open  air  It  bums  with  a  blulsli-whlte  flame. 
Its  chief  use  is  for  the  manufacture  of  certain  allovs,  as  type-metal  (anti- 
mony ],  lead  4),  britannia  (antimony  I,  tin  9),  ana  various  anti-fricrion 
metHlft  (ffiee  Alloys).  Cubical  expansion  by  heat  from  2B?  to  212?  F.,  0.0070. 
8fw>^fk:  heat  .OAO. 

Bfnnatli,  BI.— At.  wt.  206.1.  Bismuth  Is  of  a  peculiar  Ii)?bt  reddish 
color,  highly  cryBtalline.  and  so  brittle  that  it  can  readily  be  pulverized  It 
n>elti$  at  &10*  F..  and  boils  at  about  2^i00^  F.  Sp.  gr.  9.8S3  at  54<>  P.,  and 
I0.eS5  jnst  above  the  meltincr-point.  Specific  heat  about  .0301  at  ordinanr 
temperatures.  Coelllcient  of  cubical  expansion  from  8S*  to  2I'-»®,  0  0040.  Con- 
du<-tiv1tv  for  heat  about  l/HQ  and  for  electricity  only  about  I/K)  of  that  of 
»lr(>r.  Ita  tensile  strenf^th  iH  about  G400  lljs.  per  square  ir)ch.  Bismuth  ex* 
piipds  in  cooling,  and  Tribe  has  shown  that  this  expansion  does  not  take 
iilAce  until  after  eolidification.  Bismuth  is  the  most  diamagneiic  element 
kiiowD,  a  sphere  of  ic  Ixding  repelled  by  a  mnernet. 

CmdmilEiil,  €d.— At.  wt.  lis.  Sp.  gr.  8.6  to  8.7.  A  bluish- white  metal, 
lusirtfus,  with  a  fibrous  fracture.  Melts  below  500°  F.  an<l  volatilizes  at 
aUiut  mo^  F.  It  is  used  as  an  ingredient  in  some  fusible  alloys  with  lead, 
tin.  and  •  ismutb.    Cubical  expansion  from  S^*'  to  2Vi'*  F.,  0.0004. 

Copper,  On*— At.  wt.  (HVi.  Sp.  gr.  8.81  to  8.95.  Fuses  at  about  1930o 
F.  i>ii$tinguished  from  all  oiher  metals  by  its  reddish  color.  Very  ductile 
and  malleable,  and  its  tenacity  is  next  to  iron.  Tensile  strength  20,000  to 
aO.liQO  lbs.  per  square  inch.  Heat  couductiviiy  73.0^  of  that  of  silver,  and  su- 
perior to  that  or  other  metals.  Electric  conauctivity  equal  to  that  of  gold 
and  silver.  Exfiansion  by  heat  from  92?  to  21 2®  F.,  0.0051  of  its  volume. 
Sf»^*iflc  heat  .093.    (See  Copper  under  Rtrenfcth  of  Materials:  also  Alloys.) 

Gold  (Aivum).  Aa«— At.  wt.  197.2.  Sp.  gr.,  when  pure  and  pres.Hed  in  a 
ilif,  19.81.  Melts  at  about  1915**  F.  The  most  malleable  and  ductile  of  all 
metals.  One  ounce  Troy  may  be  beaten  so  as  to  cover  itK)  sq.  ft.  of  surface. 
The  average  thickness  of  golc  leaf  is  1/2S-J000  of  an  inch,  or  100  «q.  ft.  per 
ounce.  One  grain  may  be  drawn  into  a  wire  500  ft.  in  length.  The  ductil* 
itT  i«*  destroyed  by  the  presence  of  1/2000  jwirt  of  lead,  bismuth,  or  an  imoiiy. 
<to:d  la  hardened  by  the  addition  of  silver  or  of  copper.  In  U  S.  j^old  com 
tiiere  are  90  parts  fsold  and  10  partes  of  ailo}',  which  is  chiefly  copper  with  a 
li.tle  silver.  By  jewelers  the  flueness  of  gold  is  expressed  in  carats,  pure 
gii'd  ^}n*ing  24  carats,  tliree  foiirth.s  fine  18  carats,  etc. 

Irldlam. — Iridium  Is  one  of  the  rarer  metuls.  It  has  a  white  lustre,  re- 
A*(nbling  that  of  steel:  its  hardness  Is  about  equal  to  that  of  the  ruby;  in 
th^  cold  it  is  quite  brittle,  but  at  a  white  heat  it  is  somewhat  inalleal>le.  It 
i«  one  of  the  Heaviest  of  nietals,  having  a  speciHC  gravity  ot  2-J.3a.  It  is  ex- 
tremely infusible  a:id  almost  absolutely  inoxidizable. 

For  uses  of  iridium,  methods  of  manufacturing  it,  etc.,  see  paper  by  W.  D- 
Dudley  on  the  "Iridium  Industiy."  Trans.  A.  I.  M.  E.  18«l. 

Iron  (Ferrum),  Fe.— At.  wif  56.  Sp.  gr.:  Cast,  6.rt  to  7  48;  Wrought. 
7.4  to  7.9.  Pure  Iron  is  extremely  infusible,  itK  melting  point  being  above 
3000^  F.,  but  its  fusibility  increases  with  the  addition  of  carbon,  cas^t  iron  fns' 
io? about  2900°  F.  Conductivity  for  heat  11.9,  and  for  electricity  12  to  14.8, 
Eihrer  being  lOO.  Expansion  in  bulk  bv  heat:  cast  iron  .0<V5:j,  and  wrought  iron 
0035.  from  32**  to  212^  F.  Specific  heat:  cast  iron  .1208.  wrouKht  iron  .11:38, 
stwl  .1165.  Cast  iron  exposed  to  continued  ht-at  becomes  permanently  ex- 
panded IH  to  3  per  cent  of  Its  length.  Qrate-bars  should  therefore  be 
allowed  about  4  per  cent  play.  (For  other  properties  see  Iron  and  Steel 
ander  Strength  of  xM aterlals.)  ,  ^ 

Leftd  (Plumbum),  Fb.— At.  wt.  206.**.  Sp.  gr  11.07  to  11.44  by  dUTerent 
auihorities.  Meltw  at  about  (i2r)0  F.,  softens  and  becomes  pasty  at  about 
8:t*  F.  If  broken  bv  a  sudden  blow  when  just  below  the  melting  point  it  is 
[|i.lte  brittle  and  the  fraciui-e  appears  crystalline.    l«eftd  is  very  malleable 


168  MATEKIALS. 

and  ductile,  but  its  tenadtv  la  such  Ihnt  it  can  bo  drawn  into  wire  wiih  prpat 
difficulty.  Tensile  strenj^th,  1600  to -^MitO  lbs.  per  sqimr«  inch.  Its  elast ii-ii y  15 
very  lo*v,  and  the  mntnl  flows  under  very  slight  Htralii,  Lead  diasolv^*  to 
some  extent  In  pure  water,  but  water  oontalninpr  carbonaten  or  sulphatet 
forms  over  it  a  film  of  insoluble  salt  whicli  prevents  f  uriher  action.  1 

BlasneBlum,  Mg.-At.  wt.  'J4.     Sp.  pr.  1.69  to  1.76.     Silver-white,  | 
brilliuni,  malleable,  und  ductile.  It  Ih  one  of  the  lightest  of  metals,  wei^hiDf^  1 
only  about  two  thirds  as  much  as  aluminum.    In  the  form  of  fliinfi^s,  wire. 
or  thin  ribbons  it  Is  hig^hlv  combustible,  burning?  with  a  light  of  daulinj; 
brilliancy,  useful  fur  signal-liKhU  and  for  flash-lights  for  photographers.    It 
is  nearly  non -corrosive,  a  ihin  film  of  carbonate  of  magnesia  forming^  on  ex-  i 
posure  to  damp  air,  which  protects  It  from  further  corrosion.    It  may  be 
alloyed  with  alumlrmm,  5  per  cent  Mg  added  to  Al  giving  about  as  much  in- 
crense  of  strength  and  hardness  as  10  percent  cf  copper.  Cubical  expaDsioo 
by  heat  0.0083,  from  32«»  to  ilZ^  F.    Meits  at  VXXy  F.    Si>eciflc  heat  Ji5. 

jnEanffaneBe.  Mil.— At.  wl  55.  6p.  gr.  7  to  8.  The  pure  metal  is  not 
used  in  me  aits,  out  alloys  of  manganese  and  iron,  called  spiegeleisen  when 
containing  below  ib  per  cent  of  manganese,  and  ferro-mangMuese  wb«n  o<»n- 
taiiiing  from  25  to  90  per  cent,  are  used  in  the  manuf  ctureof  steel.  Metallic 
manganem.  when  alloyed  with  iron,  oxidizes  rapidly  in  the  air,  and  Its  func- 
tion in  cteel  manufacture  is  to  remove  the  oxvgen  from  the  bath  of  sun-l 
whether  it  exists  as  oxide  of  iron  or  as  ocoluded  gas. 

Stercnry  (Hydrargyrum),  Hg.— At.  wt.  199.8.  A  silver-whit©  metal 
liquid  ai  leniperatures  above— 39'*  !•'.,  and  boils  at  660^  F.  Unchangeable  as 
gold,  silver,  and  platinum  in  the  atmosphere  at  ordinary  temperatures,  but 
oxidizes  to  the  red  oxide  when  near  its  boiling-point.  8p.  gr.:  when  liquid 
13.58  to  18.59,  when  frozen  14.4  to  14.5.  Easily  tarnished  by  sulphur  fume**, 
also  by  dust,  from  which  it  may  be  freed  by  straining  through  a  cloth.  No 
metal  except  iron  or  platinum  should  be  allowed  to  touch  mercury.  The 
smallest  portions  of  tin,  lead,  zinc,  and  even  copper  to  a  less  extents  cause  it 
to  tarnish  and  lose  its  perfect  liquidity.  Coefficient  of  cubical  ex|>all^ii>n 
from  88«»  to  5fia«  F.  .0182;  per  deg.  .000101. 

Nickel,  Nl.  -At.  wt.  58.8.  Sp.  gr.  8.37  to  8.08.  A  silvery-white  metal 
with  a  strong  lustre,  not  tarnishing  on  exposure  to  Uie  air.  Ductile,  lianl, 
and  as  tenacious  as  iron.  It  Is  attracted  to  the  maguet  and  may  be  mode 
magnetic  like  iron.  Nickel  is  very  difficult  of  fusion,  melting  at  alntut 
aoOU*  F.  Chiefly  used  In  alloys  with  copper,  as  german-sUver,  nickel  siiver, 
etc.,  and  recently  in  the  manufacture  of  steel  to  lncr(>ase  its  hardness  and 
strength,  also  for  nickel-plating.  Cubical  expansion  from  SH?  to  212^  F., 
0.0088.    Specific  heat  .109. 

Platinum,  Pt.— At.  wt.  195.  A  whitish  steel-gray  metal,  malleable. 
Tery  ductile,  and  as  unalterable  by  ordinary  agencies  as  gold.  When  fiu«ed 
ancf  refined  it  is  as  soft  as  copper.  8p.  gr.  i!1.15.  It  is  fusible  only  by  the 
oxyhydrogen  blowpipe  or  in  strong  electric  currents.  When  combined  with 
iridium  it  forms  an  alloy  of  great  hardness,  which  has  been  used  for  gun- 
vents  and  for  standard  weights  and  measures.  The  most  important  us«*s  of 
platinum  ip  the  arts  ai'e  for  vessels  for  chemical  laboratories  and  manufac- 
tories, ana  for  the  connecting  wires  in  incandesoent  ehnztric  lamps.  Cubical 
expansion  from  m*  to  *^12*  F.,  0.00S7,  less  than  that  of  any  other  metal  ex- 
cept the  rare  metals,  and  almost  the  same  as  glass. 

Silver  (Argentum),  Ag.  -At.  wt.  107.7.  Sp.  gr.  10.1  to  11.1,  according  to 
condition  and  purity.  It  is  the  whitest  of  the  metals,  very  malleable  and 
ductile,  and  in  hardness  intermediate  between  gold  and  copper.  AleltR  at 
about  1750*  F.  Specific  heat  .050.  Cubical  expansion  from  3a<»  to  81S«  F., 
0.0058.  As  a  conductor  of  electricity  it  is  equal  to  copper.  As  a  conductor 
of  heat  it  is  superior-  to  ail  other  metals. 

Tin  (Stanniun)  Sn.— At.  wt.  118.  Sp.  gr.  7.298.  White,  lustrous,  soft, 
malleable,  of  little  stivngtii,  tenacity  about  3600  lbs.  per  square  inch.  F'ui^es 
at  442®  F.  Not  sensibly  volatile  when  melted  at  onimary  heats.  Heat  con- 
ductivity 14.5,  electric  conductivity  ia.4;  silver  being  100  In  each  caF»e. 
Expansion  of  volume  by  heat  .0069  from  9^  to  2VZ?  F.  Specific  heat  .055.  Ite 
chief  uses  are  for  coating  of  sheet-iron  (called  tin  plate)  and  for  making 
alloys  with  copper  and  other  metals. 

asinc,  Zn.-At.  wt.  tt5.  Sp.  gr.  7.14.  Melts  at  780«  F.  Volatiltsee  and 
burns  in  the  air  when  melted,  with  bluish-white  fumes  of  zinc  oxide.  It  is 
ductile  and  malleable,  but  to  a  much  less  extent  than  copper,  and  its  tenacity, 
about  50UU  to  6000  ll>s.  per  s(}uare  inch,  is  about  one  tenth  that  of  wrougiit 
iron.  It  is  practically  noii  corrosive  in  the  atmosphere,  a  thin  film  of  car- 
bonate of  zinc  forming  uik>ii  it.    Cubical  expansion  between  82*  and  212**  F., 


MEASUEES  AND  WEIGHTS  OF  VARIOUS  MATERIALS,  169 


0.0088.  Specific  heat  .096.  Electric  conductivity  29,  heat  conductivity  86, 
ulver  beinj?  100.  Its  principal  uses  are  for  coating  iron  surfaces,  called 
"^  galvanizing,"  and  for  making  brass  and  other  alloys. 


MftlleablUtj. 

Gold 

SUver 

Aluminum 

Copper. 

Tin 

J^^ead 

Zinc 

Platinum 

Iron 


Table  Sboirliic  the  Order  of 


Bnetlllty. 

Tenacity. 

InmslbUUy. 

PlatiDum 

Iron 

Platinum 

Silver 

Copper 

Iron 

Iron 

Aluminum 

H^ofr 

ssrr 

Platinum 

Silver 

Silver 

Aluminum 

Zinc 

Aluminum 

Zinc 

Gold 

Zinc 

Tin 

Tin 

Lead 

Lead 

Lead 

Tin 

rOWMJJlAM    AND    TABIiK    FOB    CAI^CVLATING 

irBieHT  OP  ROD»,  BAR8,  PI4 ATBS,  TUBES,  AND 
8PSBBBS  OF   DIFFJBRENT  JHATBRlAIiS. 

Notation  :  b  =  breadth,  i  ss  thickness,  b  s  side  of  square,  d  s  external 
iiameter,  d]  =  internal  diameter,  all  in  inches. 

Sectional  areas :  of  square  bars  s=  a*;  of  flat  bars  cz  bt;  ot  round  rods  s 
:S54d«;  of  tubes  =  .7854(d'  -  d,«)  =  Z.UlfUdt  -  t*). 

Volume  of  1  foot  in  length  :  of  square  bars  =  ISfs^;  of  flat  bars  =  126^;  of 
round  bans  =  9AUiitP;  or  luueb  =  9.45J48(ct''  -  di«)  s  8T.699(dt  - /»>,  In  en.  in. 

Weight  per  foot  length  =  volume  x  weitcht  per  cubic  inch  of  the  materials 
Weight  of  a  sphere  =  diam.*  x  .&286  x  weight  per  cubic  inch. 


Cast  iron 

"^rijusht  Iron 

Steel 

Copper  A  Bronze  I 
•  j'Dpper  and  tin)f 
p-.^>  85  Chopper.. 

L«d 

Aiaminmn 

"jLaas 

Pine  Wood,  dry . . . 


7.S18460, 

7,7 

7.854 


8.855 

8.898 

11.88 
2.67 
2.62 
0.481 


I 


480. 
180.6 

55S, 


528. 

709.6 
IG6.5 
168. 4 

ao.o 


1^ 


87.6 

40. 

40.B 

4C. 


50. 
13.0 


2.5 


s^i 


^ 


833fi3 


43.6  3.G8.35' 


4.03*« 
1.16b« 


18.61.18«« 


0.21«3 


lit 


8^6/ 

3.8336/ 
3.6836/ 

A.m>t 

\AGbt 
1.186* 
0.2lbt 


III 


.2604,16-16 
.2TT9  1, 
.28331.02 

.3195|1.15 


2.464d» 
2.6l8d» 
2.670d« 

S.Ollda 


.3020'I.09  2.864d« 

.410cll.48  8.870d* 
.(WC3  0.347i0.90«d9 
.0W.')0.34  O.SOtrf' 
.01741 1-16  0.164d3 


S8 


.136Sd» 
.146fid« 
.H84d«' 

.1673d» 

.1586d« 

.2150d«- 
.06O4d>- 
.0495d» 
.0091d« 


WHebt  p»»r  cylindrical  in.,  1  in.  lone,  =  coefficient  of  d«  in  nintii  col.  -•- 12. 

For  tabes  use  the  cotrfflcieut  of  d^  in  ninth  column,  ns  for  rod».  and 
riTiitiply  it  into  (d*  —  dx*);  or  take  four  times  this  coefficient  and  multiply  it 
krofdt  —  f*). 

For  bollo-vr  spheres  use  the  coefflcient  of  d>  in  the  last  column  and 
&u.Upiy  it  into  (d«  —  d,»). 

JHEASVBBS   AND   IFEIGIIT'9   OF   VABIOUS 
MATEBIALS  (APPBOXIRKATE). 

Brlelnvor]C«— Brickwork  is  estimated  by  the  thousand,  and  for  various 
tLickneeaes  of  wall  runs  as  follows: 

K^-in.  wall,  or  1  brick  In  thickness^  14  bricks  per  superficial  Si^^'i. 
ISS m 21     ** 

SIM  "        '*     "  2M  '*     "         "  85     "         *•  "  »• 

An  ordhiary  brick  measures  about  8>^  x  4  X  2  inches,  which  is  equal  to  66 
ci;Uc  inches,  or  26.3  bricks  to  a  cubic  foot.    The  average  weight  Is  i^i  Ibe. 


170 


MATERIALS. 


Foel.^A  bushel  of  bltuminona  coal  wei^^hs  76  f>ound8  and  contains  8688 
cubic  inches  =  1.564  cubic  feet.    20.47  bushels  =  J  ^ross  ton. 

A  bueliel  of  coke  weighs  40  lbs.  (85  to  42  lbs.). 

One  acre  of  bituminous  coal  contains  lOOU  tons  of  8240  lbs.  per  foot  of 
thickness  of  coal  worked.  15  to  i^  per  cent  luust  be  deducted  for  waste  In 
minine. 

41  to  45  cubic  feet  bituminuus  coal  when  broken  down =  1  ton,  "HW  Ibe. 

d4  to  41      "       '*     anthrncite,  prepared  for  market =  1  ton,  :iii40  11^. 

123  *'       •*    of  charcoal =s  1  ton,  «f40  lbs. 

70.9  '*       *'     -coke as  1  ton,  aa40  ll**. 

1  cubic  foot  of  anthracite  coal  (see  also  page  Qi5) =  55  to  6t>  lbs. 

1      bituminous"     a60to561b6. 

1     •*       **    Cumberland  coal =531bs. 

1     "       "    Cannel  coal...  =  60.3  lb& 

1     ♦*       "    charcoal  (hardwood) =  18.6  lb«L 

1 (pine) =181bs. 

A  busbel  of  cliarcoal.— In  1881  the  American  Charcoal  Iron  Work- 
ers* AHSOciailou  adupte<l  for  use  in  its  official  publications  for  tJm  standard 
bushel  of  charcoal  2<4K  cubic  inches,  or  '20  pounds.  A  ton  of  charco>al  is  to 
be  taken  at  2000  pounds.  This  figure  of  SM)  pounds  to  the  bushel  was  taken 
as  a  fair  averago  of  different  bushels  used  throughout  the  country,  and  it 
has  since  been  established  by  law  in  some  States. 

Ores,  Bartbs,  etc, 

13  cubic  feet  of  ordinary  gold  or  silver  ore,  in  mine =  1  ton  =  SOOO  lbs. 

20     ••       "     "  broken  quartz =  1  ton  =  aoOO  Ib& 

18  feet  of  gravel  in  bank =  1  ton. 

27  cubic  feet  of  gravel  when  dry =  i  ion. 

25     **       '*     *'  sand  =  1  ton. 

18     "       *•     '*  earth  In  bank  =  1  ton. 

27     **       •*     *'      "      when  dry =  1  ntn. 

17     "       **    *'  clay =  1  ton. 

Cement.— English  Portland,  sp.  gr.  1.25  to  1.51,  per  bbl ....  400  to  430  lbs, 

Rosendale,  U.  S.,  a  struck  bushel 02  to   7ull>». 

Mme.— A  stiiick  bushel 72  to    75  lbs 

Grain*— A  struck  bushel  of  wheat  =  QO  lbs.;  of  corn  =  56  lbs.;  of  oaUi  = 
30  lbs. 

Salt.^A  struck  bushel  of  salt,  coarse,  Syracuse,  N.  Y.  =  5G  lbs. ;  Turk's 
Island  =  76  to  80  lbs. 

irelfftat  of  Barth  FllUn^. 
(From  llowe^s  **  Retaining  Walls.") 

Average  weight  in 
lbs.  ];>er  cubic  foot. 

Earth,  common  loam,  loose 72  to   HO 

**  "  '*     shaken ftij  to   93 

**  **  "     rammed  moderately 90  to  100 

Gravel 90  to  106 

Sand  90toUt6 

Soft  flowing  mud 104  to  1«) 

Sand,  perfectly  wet 118tol29 

COnmiBRCIAIi   SIZB8  OF   IRON   BAAS. 

Flats. 


Width. 


Thickness. 


^to  n 

J^  to  15/16 
y^tol 

kto  1^ 
V6toi^ 

3/10  to  1>J 


Width. 


Thickness. 


Width. 


4 


Tbickneas. 


WEIGHTS  OF  WROUGHT  IRON  BARS. 


171 


Koondfl  :  M  to  19^  inches,  advaDciog:  by  IGtbs,  and  19^  to  5  inches  by 
Squares  z  5/16  to  1^  inches,  advancing  by  lethst,  and  1^  to  8  inches  by 

Hair  ronnd«:  7/16,  ^,  %,  11/16, 94»  3.  If6^  ^H.  1H»  %  2  inches. 

Hexagons  :  9^  to  lU  iuchfs,  advancing  by  8ths. 

Ovals  I  H  X  J4.  %  X  5/16,  ^  X  ^.  %  X  7/16  inch. 

Hair  ovals:  Ji  X  J6,  %  X  5/3:.>,  94  X  3/16,  %  X  7/88,  IJi  X  «,  1«  X  5i 
l?lx  H  >nth. 

Bonnd-edse  flats:  1^  X  K.  l^  X  ^  1%  X  ^ inch. 

Bands:  Vie  to  lU  inches,  advancing  by  8tbs,  7  to  16  B.  W.  gauge. 

IH  to  5  inchtfs,  advancing  by  4ths,  7  to  16  gauge  up  to  S  inches,  4  to  14 
9&o£e,  S^  to  5  inches. 

1¥1BI6HT8   OF   SaUARE    AND   ROUNH   BARS   OF 
WROWHT    IRON   IN    POUNHS   P£R    lilNBAIi  FOOT. 


Iron  weighing  480  lbs.  per  cubic  foot. 

For  steel  add  S 

per  cent. 

c  .    . 

15^ 

-oh 

hi 

III 

-  i>5 

U3»s 

tic§2a 

•^  c^ 

tlCp  43P 

t)£3  »  C 

ftlJ 

l&5i 

13-53 

-00 

|5  = 

i=?o3 

po5 

0 

11/16 

24.06 

18.91 

t 

96.80 

75.64 

1/16 

.013 

.010 

H 

25.21 

19.80 

98.55 

77.40 

H 

.OW 

.041 

13/16 

26.37 

20.71 

100.8 

79.19 

^l« 

.117 

.092 

% 

27.55 

21.64 

V 

103.1 

81.00 

H 

.208 

.164 

15/16 

28.76 

22.59 

105.5 

82.  H3 

.VI6 

.S* 

.256 

8 

30.00 

23.56 

11/16 

107.8 

84.69 

H 

.469 

.368 

1/16 

31.26 

24.55 

94 

110.2 

86.56 

T/l« 

.638 

.501 

u 

82.55 

25.57 

13/16 

112.6 

88.45 

H 

.833 

.654 

3/16 

33.87 

26.60 

% 

115.1 

90.36 

9/16 

1.065 

.828 

k 

85.21 

27.65 

15/16 

117.5 

92.29 

^ 

i.ao-i 

1.023 

5/16 

36.58 

28.73 

6 

120.0 

94.25 

11/16 

1.576 

1.237 

k 

87.97 

29.82 

125.1 

98.23 

H 

1.875 

1.473 

7/16 

39.39 

30.91 

i2 

130.2 

102.3 

IM6 

2.201 

1.728 

% 

40.83 

3.».07 

s/ 

135.5 

100.4 

?^ 

2.^-a 

2.001 

9/lG 

42.30 

33.23 

1^ 

140.8 

110.6 

TVI6 

2.930 

2.:W1 

k 

43.80 

34.40 

76 

H6.3 

114.9 

1 

8.333 

2.618 

11/16 

45.33 

a5.60 

% 

151.9 

119.3 

1/16 

3.763 

2.9rx'S 

^ 

46.88 

36.82 

% 

157  6 

12:3.7 

H 

4.219 

3.313 

13/16 

48.45 

38.05 

7 

163.8 

128.3 

3/16 

4.701 

3.692 

% 

60.05 

3S.31 

169.2 

132.9 

^4 

5.308 

4.091 

15/16 

61.68 

40.59 

14 

175.2 

137.6 

5/16 

6.742 

4.510 

4 

53.33 

41.89 

79 

181.8 

142.4 

H 

6.302 

4.950 

1/16 

55.01 

43.21 

l2 

1S7.5 

147.3 

7716 

6.S88 

5.410 

H 

66.72 

44.55 

7H 

19:i.8 

152.2 

^ 

7.500 

5.890 

3/16 

58.45 

46.91 

&i 

200.2 

157.2 

S?16 

8.138 

6.392 

ii 

60.21 

47.29 

yk 

200.7 

162.4 

^ 

8.802 

6.913 

6/16 

61.99 

48.69 

8 

213.3 

167.6 

11/16 

9.492 

7.455 

% 

63.80 

50.11 

vc 

226.9 

178.2 

H 

10.21 

8.018 

7/16 

65.64 

61.55 

\L 

240.8 

189.2 

1-1/ 16 

10.95 

8.601 

u 

67.50 

5:1.01 

a^ 

255.2 

200.4 

Ti^ 

11.72 

9.204 

V 

69.39 

54.50 

0 

270.0 

212.1 

15716 

12.51 

9.828 

71. ;» 

60.00 

M 

285.2 

224.0 

9 

13.33 

10.47 

T 

73.21 

57.52 

i2 

300.8 

236.3 

"  1/16 

14.18 

11.14 

75.21 

59.07 

% 

816.9 

248.9 

H 

15.05 

11 .82 

13/16 

77.20 

00.63 

10' 

3:«.3 

261.8 

3/16 

15.95 

12.53 

% 

79.22 

62.22 

^ 

350.2 

275.1 

H 

16.88 

13.25 

15/16 

81.20 

63.82 

l2 

31)7.5 

288.6 

5/16 

17.  S3 

14.00 

& 

83.3:3 

65.45 

74 

385.2 

302.5 

H 

18.80 

14.77 

1/16 

85.43 

07.10 

11 

403.3 

316.8 

V16 

19.80 

15.55 

3% 

87.55 

68.76 

\/i 

421 .9 

331.3 

^ 

20.83 

16.86 

89.70 

70.45 

i2 

440.8 

346.2 

V16 

21.89 

17.19 

k 

91.88 

72.16 

9« 

460.2 

361.4 

H 

88.97 

18.04 

5/16 

94.08 

73.89 

12 

430. 

377. 

172 


MATERIALS. 


Sal 

MO    U 

fits. 
Si  I 

2  S 

fa    ^ 
fa 

H 

n 

M 


§;|iggSS35§SS^^SSSS5g.o5^?;S{:?eesss?!r:f5gS^' 


-^e*eo^rf:«t-QDao  —  "vec^towc^oDCs 


♦-iwooTTiotefXOfco  —  wec^^-oiccoi-occiOj-i 


^  i{:SS5S58SSSn:2si«V:gsa;5t:?5518?82S5fSSg$5' 


I 


r-«90^i0<Ot-l-000»O-^i?»0i?rfiCift«t-0006O^ 


s?c;^S^«S&5 


"  ©i  eo  TT  •«  irj  CD  t>^  x  os  o  (b  «'  c*  c<?  ^  lo  »r5 «"  i>I  oo  o»  o  c  -- 


SSMSS*?^^! 


^ 


^!?8r:§$;:S8fc!$SSSSSs2SS«8S,i8gS88Ss8S| 


*^c<oeo'^<vino«Dt>acxiOkOO^c)9*eoTP^io«o«0C^acaoo» 


SSc 


"  T-1 1-i  e* «  e*^'  »o  rt  to  5D  t-  db  od  »"  o"  o  »^  f-^  <?*"  eo  eo  •^  ift »«  »"  w  i>  od  oc  ci  c 


■^  r-I  (Tl  <Ji  00  "**  ^  tcj  lO  «C  d  t^  00  OD  Oi  ci  d  d  "  CJ  ©»  00  CO  3J  "^  «ft 


■'r.i**cjcoeo^"^io»rjddi-t'-odoooiddd»-'«--o»eooo'^-^ir}tr:d« 


^5*      *   *  i-i  »-^  01 7»  »  oo'  rr  ^  ^  d  d  d  c*  t*  c^  00  d  d  d  d  d  •- 1-^  M  o*  CO  00  -^  "^  rt  I 


'  T-i  t-J  o*  e»  oj  CO  d  ^  ^  d  d  d  d  d  I'  t>^  t-  X  X  d  d  d  d  d  -^  —  e*  c*  or  d  ' 


in 


i^r-ir-idoto(dd-<^-^^dddddd(.>t^xdo6dddddoi-^«^i 


;ii?R2??Sg5DS^r:8?!?S8SS3Efj2§^2S«$25 

*  ^  ^  ,J  d  ot  o<  d  eo  d '^  <«' -"i^  d  d  d  d  d  d  d  t<^  t<^  i<^  d  oc  oe  oa  o»  a»  d 


'  ^  ^  r-!  f-i  7«  ot  01  d  d  d  d  d  '^'  '^  -^  -^  d  d  d  d  d  d  d  i-^  I*  t>  c^  oc  d 


'  »-i  T-i  »-l »-  ^  d  o»  d  d  o<  d  d  d  d  d  f  •^  ^  ■^  d  d  d  d  d  d  «  d  d 


to  «o  to  o  « 


•O   O   O   CO   O   (0 


I^5-''5*.I^»«I*'5-^5  j:*5-'J«:i*5«;-«d^i 


WEIGHTS  OF    FLAT  WROUOHT  IRON. 


17S 


l> 

S8S8S8S8S8S8SSS88S8S8888 

5' 

§gj2S3S§282Bf2Sgg«S8f2SS8SSa8 

-«-'^»;:«SS28?JS8aS8fc^^5SgSg 

i 

So 

&:S8^S8'«8S8idSS8$oS8&8SSio8S3lD88 

^ 

1: 

as 

i 

^ 

i 

i 

^oied««^:o;o;;«;5j22a2«gg5gg55ggg5. 

^' 

SSi^8S2^83Sr^83Sf38S8S8S|8S8 

i 

1 

S85SS88V:«5?Si?8S28S85;SS88S 

i 

8SS8^SSr.SSS^$i;;?SS388^9SaS8 

2) 

11 

C3        (O        iD        V        0        V        to        *0 

^  ^  ii  t^  cfc  ;.  ^  -^^S^^^i^?^^ 

I 


88{28 


!    Sails 

I  sa 

I 

hS 
55 


174 


MATERIALS. 


WEIGHT  OF   IRON    AND  STEBIi   SHEETS. 

ITelKliUi  per  Sqoare  Foot. 

(For  weights  by  Decimal  Gauge,  see  page  32.) 


Thickness  by  BinniDgham  Gauge. 

Thickness  by  American  (Brown  and 
Sharpens)  Gauge. 

Thick- 

Thick- 

No.  of 

nessin 

Iron. 

Steel 

No.  of 
Gauge. 

nes8in 

Iron. 

SteeL 

Gauge. 

Inches. 

Inches. 

0000 

.454 

18.16 

18.58 

0000 

.46 

18.40 

18.77 

000 

.425 

17.00 

17.84 

000 

.4096 

16.88 

16.71 

00 

.88 

15.80 

15.50 

00 

.8648 

14.59 

14.88 

0 

.84 

18.60 

18.87 

0 

.8249 

13.00 

18.86 

1 

.8 

12.00 

18.84 

1 

.2898 

11.57 

11.80 

s 

.284 

11.36 

n.59 

8 

.2576 

10.80 

10.. M 

8 

.259 

10.86 

10.57 

8 

.2294 

9.18 

9.S8 

4 

.288 

9.52 

9.71 

4 

.2048 

8.17 

6.34 

6 

.28 

8.80 

8.98 

6 

.1819 

7.28 

7.48 

6 

.803 

8.12 

8.28 

6 

.1620 

6.48 

6.61 

7 

.18 

7.20 

7.34 

7 

.1443 

5.77 

5.89 

8 

.165 

0.60 

6.73 

8 

.1285 

6.14 

5.24 

9 

.148 

5.92 

6.04 

9 

.1144 

4.58 

4.07 

10 

.184 

5.86 

5.47 

10 

.1010 

4.08 

4.16 

11 

.18 

4.80 

4.00 

11 

.0007 

8.68 

8.70 

18 

.109 

4.86 

4.45 

18 

.0808 

8.23 

8.80 

18 

.095 

SHO 

8.88 

18 

.0780 

2.88 

2.94 

14 

.088 

8.32 

8.30 

14 

.0641 

856 

8.62 

15 

.072 

2.88 

2.04 

15 

.0571 

8.S8 

8.33 

16 

.065 

2.60 

265 

16 

.0508 

8.08 

8.07 

17 

.or>8 

282 

2.87 

17 

.0453 

1.81 

1.85 

18 

.049 

1.96 

2.00 

18 

.0^03 

1.61 

1  64 

19 

.042 

1  68 

1.71 

19 

.0359 

1.44 

1.46 

90 

.085 

1.40 

1.48 

20 

.0820 

1.28 

1.31 

21 

.032 

1.28 

1.31 

81 

.02*) 

1.14 

1.16 

S3 

.028 

1.12 

1.14 

22 

.0258 

1.01 

1.08 

28 

.025 

1.00 

1.02 

23 

.02-J6 

.004 

.922 

S4 

.028 

.88 

.808 

24 

.0201 

.804 

.820 

85 

.08 

.80 

.816 

25 

.0170 

.716 

.730 

86 

.018 

.78- 

.734 

26 

.0159 

.686 

.649 

87 

.016 

.64 

.ess 

27 

.0142 

.568 

.579 

88 

.014 

.56 

.571 

28 

.0126 

.504 

.514 

89 

.018 

.52 

.580 

29 

.0113 

.458 

.461 

80 

.018 

.48 

.490 

80 

.0100 

.400 

.408 

81 

.01 

.40 

.408 

31 

.0089 

.856 

.863 

88 

.009 

.86 

.367 

82 

.0080 

.3:20 

.826 

88 

.008 

.82 

.3-^6 

33 

.0071 

.284 

.290 

84 

.007            .28 

.286 

84 

.0063 

.358 

.257 

86 

.006            .80 

.204 

85              .0056 

.2^ 

.288 

Iron.                 SWel. 

Specfflc  graTity  . 
Wefglit  per  cubic 

ij- 

.7                  7.854 
480.6 

foot!::.'! 

::.:!;  48o 

»• 

».      tt 

Inch... 

.2778 

.2888 

As  there  are  many  gau?e8  in  use  diffi^rlng  from  eaich  other,  and  even  the 
thicknesses  of  a  certain  KptKjifled  ^auge.  aHthe  Birmingham,  are  not  assumed 
the  same  by  all  mannractiirers.  orders  for  sheets  and  wires  sliould  always 
state  the  weight  per  sauare  foot,  or  the  thickness  in  thousandths  of  an  inch. 


WEIGHT  OF  PLATE  IRON.' 


175 


- 

8S&8S&8S&8S&8S&8S&ot.c9o».»ot-e9ot-«50fc.Mo 

S3i°S8S3SoSSi?S8S^S(SS!^o».oooo««QOOe«.oooo».<» 

;se 

8SSSf2'oSS7^^i;88s8g{?'«3S!SV;o«>t.  .0  00  (MOOD  t-c>oo»o 
S3SS^9§^S18SSSS'g?i:«-|255SteS882S|{^g|§s§^ 

2 

sr 

828S8S8S8S8S8S8S8S88888ooooooooooo 

«D 

ge828fessS§82??t:8SS8?:^SSSS8fegJao^o««oo«o»« 

;i^ 

8St:SS$SSgSSS8S^SS^8&S8^SSS&Soo««»«».QDo 

1 

a 

:« 

S&S8&S8^S81»S8&88&»S8§8&8Sg8SS^8S&8S^o 
^'s:Si^S^8sSS^S?;;9^^^8SS8S8^S5S^SS8SSSS8 

i 

2 

;i! 

838i^8^S:^8'6{S^83Sr383S8S8S8S888S888S8 

2 

3? 

8SiDSI3^8SSDSS^8S&8S^8^38lDS8&S8^S8lD88 

«9 

SS23S8SSSDS?Sr2S83^SS^ie8^Si'38;SS^838:28»8 

:« 

8?S8fe8SSSr2t;SS?§S8lS$g85:8S8&SS5:8S&S??i:8 
io«rf3tD«t^t^t-<»o6o»o»ooo---2»2S2{SSS5^S28SS3iSS^ 

o 
1 

gr:SSSSeSt^??SeS5;SSSS«S$S8St-2?:S8?fSSfe$S 

99  99  oi  «0  90  09  09  09 -T  ^  ^ -^  to  lO  »6  i6  to  fO  ^  V>tAt^  I' QD^ciai  a  ^O  ^^^99 

1' 

^1 

?5S2:SS5;SSS8saaSSSSia«8SS88S^?5gl58S22S28 

176  MATERIALS. 

WEIGHTS  OF  STEEIi  BLOCKS. 

Soft  steel.    1  cubic  inch  =  0.  SSI  lb.    1  cubic  foot  =  4S0. 75  lbs. 


Sizes. 

Lengths. 

1" 

6" 
82 

18" 

164 

18" 
245 

84" 
827 

30" 
409 

86" 
491 

42" 

48" 

64" 
736 

60" 
816 

6©" 

12"  x4" 

18.63 

573 

664 

900 

11     X  6 

i8.';5 

118 

225 

388 

450 

563 

675 

788 

900 

1018 

1125 

ia*B 

X  5 

15. 6i 

94 

188 

281 

375 

469 

562 

656 

750 

843 

9:^ 

1031 

x4 

1«.60 

75 

160 

225 

800 

376 

450 

525 

600 

675 

750 

825 

10     X  7 

19.88 

120 

889 

358 

477 

596 

715 

835 

955 

iar4 

1193 

1319 

x6 

17.01 

102 

204 

807 

400 

511 

618 

716 

818 

920 

1022 

1125 

X  5 

14.*^ 

65 

170 

256 

841 

426 

511 

596 

682 

767 

852 

037 

X  4 

11.36 

68 

186 

205 

2r3 

341 

409 

477 

516 

614 

682 

780 

X  8 

8.53 

51 

102 

153 

204 

256 

806 

858 

409 

460 

511 

509 

9x7 

17.89 

107 

215 

322 

430 

537 

644 

751 

859 

966 

1078 

1181 

x6 

15.84 

92 

184 

276 

868 

460 

552 

614 

736 

838 

920 

1018 

X  5 

18.78 

77 

153 

280 

307 

888 

460 

587 

614 

690 

767 

844 

x4 

10.23 

61 

123 

184 

245 

307 

368 

429 

490 

552 

613 

674 

8x8 

18.18 

109 

218 

327 

436 

545 

656 

784 

878 

962 

1001 

1200 

X  7 

15.9 

95 

191 

286 

382 

477 

578 

668 

763 

a^9 

954 

1040 

x6 

18.68 

82 

164 

245 

327 

409 

491 

578 

654 

T36 

818 

900 

x6 

11.86 

68 

186 

205 

278 

841 

409 

477 

546 

614 

683 

750 

X  4 

9.09 

55 

109 

164 

218 

278 

327 

382 

436 

491 

545 

600 

f     x7 

13.02 

88 

167 

251 

334 

418 

801 

565 

668 

752 

886 

919 

x6 

11.93 

72 

143 

215 

286 

358 

430 

501 

573 

644 

716 

788 

X  6 

9.94 

60 

119 

179 

2:)8 

296 

358 

417 

477 

536 

596 

656 

X  4 

7.95 

48 

96 

148 

191 

239 

286 

384 

382 

429 

477 

5:25 

X  a 

5.96 

86 

72 

107 

148 

179 

214 

250 

286 

822 

858 

893 

(^x6^ 

12. 

72 

144 

216 

388 

360 

432 

504 

576 

648 

730 

798 

x4 

7.3R 

44 

89 

183 

177 

221 

266 

310 

854 

889 

443 

487 

6x6 

10.2-2 

61 

123 

184 

245 

307 

868 

429 

490 

651 

613 

674 

x6 

8.5-» 

51 

102 

153 

204 

255 

807 

858 

409 

460 

511 

569 

x4 

6.83 

41 

82 

128 

164 

304 

245 

286 

327 

368 

409 

450 

x8 

5.11 

81 

61 

92 

128 

158 

184 

214 

»I5 

276 

307 

837 

fiHx5^ 

8.59 

S2 

106 

155 

206 

258 

800 

861 

412 

464 

515 

567 

X  4 

6.25 

87 

75 

112 

150 

1H8 

235 

263 

300 

837 

375 

41 S 

6x5 

7.10 

43 

85 

128 

170 

213 

356 

298 

341 

383 

436 

469 

x4 

6.68 

84 

68 

102 

136 

170 

205 

239 

278 

307 

841 

875 

4Hx4H 

5.75 

35 

69 

104 

138 

178 

207 

242 

276 

311 

345 

380 

x4 

5.11 

31 

61 

92 

133 

153 

184 

215 

246 

278 

307 

338 

4x4 

4.54 

27 

65 

82 

109  i  186 

164 

191 

318 

246 

272 

300 

x8Hi 

3.97 

24 

48 

72 

96  1  110 

143 

167 

181 

216 

388 

262 

x3 

3.40 

20 

41 

61 

82     102 

122 

143 

IKi 

181 

304 

224 

8>ix8H 

3.48 

21 

42 

68 

84  1  104  1  125  1  146 

167 

188 

209 

2:i0 

x  8 

2.98 

18 

36 

54 

72  ^     89      107      135      14''. 

161 

179 

197 

8x8 

2.56 

15 

81 

46 

61  \ 

77 

92 

108 

138 

m 

154 

169 

L 


SIZES   AND   WEIGHTS  OF  STRUCTURAL  SHAPKS. 


SIXB8  AND  WBTOHTS  OF  8TRITCT17BAI4  8HAPB8. 

MlnlBuniB,  JVaxlmnm,   and   Intermediate   ireiffhts  and 


DlmenBlona  of  Carne^^o  Steel  I-Beama* 

Sec- 
tion 
laJex 

Depth 

of 
Beam- 

Weijfht 
l^'t. 

^fdT 

Weh 
Thick- 
ness. 

Sec- 
tion 
[ndex 

Depth 

of 
Beam- 

WeiKht 

FlanKP 
Width. 

Web 
Thick 
ness. 

ins. 

IbH. 

ios. 

ins. 

ins. 

lbs. 

ins. 

ins. 

Bl 

24 

100 

7.85 

0.76 

610 

0 

17  25 

8.58 

0.48 

»• 

05 

7.10 

0.69 

*» 

•  • 

14.75 

3.45 

0.35 

*» 

•* 

00 

7.13 

0.63 

»' 

♦• 

12.25 

8.33 

0  23 

'• 

•• 

85 

7.07 

0.57 

Bei 

5 

14.75 

8.20 

0.50 

" 

•• 

80 

7.00 

0.60 

»• 

12.26 

8.15 

0.30 

m 

90 

75 

6.40 

0.65 

*♦ 

•  ( 

0.75 

8.00 

0.21 

70 

C.8:J 

0.58 

B.J3 

4 

10.5 

2  S8 

0.41 

♦• 

•* 

65 

6.« 

0.50 

'♦ 

*• 

0.5 

2.81 

0.:M 

Bao 

18 

70 

6.26 

0.7J 

'» 

(» 

8  5 

2.73 

0  26 

** 

»* 

65 

6.18 

0.C4 

" 

'* 

7.5 

2.G0 

0.19 

•• 

•* 

60 

6.10 

0.56 

B77 

3 

7  5 

2.52 

0.36 

»• 

*• 

55 

6.00 

0  46 

C  5 

8.42 

0.26 

B7 

15 

53 

5.75 

0  CO 

'» 

»• 

6.5 

2  3^) 

0  17 

•• 

•• 

50 

5.65 

0.56 

Bi 

20 

lOU 

728 

0.88 

•• 

»* 

45 

5.55 

0.46 

" 

05 

7  21 

0.81 

** 

*t 

42 

5.50 

041 

♦* 

t« 

00 

7.14 

0.74 

B9 

IS 

35 

.5.00 

044 

•* 

tt 

85 

7,06 

0.68 

*• 

*» 

31.5 

5.00 

085 

*» 

** 

80 

7.00 

0.60 

Bll 

10 

40 

5.10 

0.75 

B4 

15 

100 

6.77 

1.18 

»• 

•' 

35 

4.05 

0.60 

»' 

•* 

05 

6.68 

1.00 

»^ 

»» 

80 

4.81 

0.46 

♦' 

" 

00 

6.58 

0.09 

•* 

»• 

liO 

4.66 

0.31 

'1 

'• 

86 

6.48 

0.80 

B13 

9 

35 

4.77 

0.73 

" 

80 

6.40 

0.81 

•♦ 

k« 

30 

4.61 

0.57 

B5 

1.5 

75 

6.20 

0  88 

»• 

•* 

25 

4.45 

0.41 

»* 

" 

70 

6.19 

0.78 

•• 

*t 

21 

4.33 

0.29 

" 

*' 

65 

6.10 

0.69 

BIS 

8 

23.5 

4.87 

0.54 

»• 

'* 

60 

6.00 

0.50 

** 

23 

4.18 

0  45 

B8 

1-2 

65 

5.61 

0.82 

•* 

•ft 

20.5 

4.00 

0.86 

" 

50 

5.40 

0.70 

" 

•» 

18 

4.00 

0  27 

" 

*' 

45 

5.37 

0.58 

Brr 

7 

SO 

3.87 

0  4G 

'* 

" 

40 

5.25 

0.46 

•» 

ft* 

«ft 

17.5 

15 

3.76 
3.66 

0..S5 
0.25 

Sections 
•'  spei'ial " 

B2,  B4.  ] 

beams, 

B5.  and  ] 
11  le  otbe 

B8  are 
rs  are 

*'8I0 

Lndard. 

Sectional  area  =  weight  in  lbs.  per  ft.  ■♦-3.4,  or  x  0.2041. 
Weigbt  ill  lbs.  per  foot  =  sectional  urea  x  3.4. 

Xaxinaiam  and  minimum  HVelgrbta   and  IMnienalona  of 
Carnegie  Steel  Heck  Bcama. 


Section 

Depth 
of 

WHpht  per 
Foot,  lbs. 

Flange  Width. 

Web 
Tliickness. 

Increase*  of 
Web  and 

Index. 

B«*atn, 
iuches 

Flange  per 

lb.  Increa.««j 

Min. 

Max. 

Min. 

Max. 

Min. 

Max. 

.63 

of  Weight. 

BlOO 

10 

27.33 

a'>.70 

5.25 

5.50 

.38 

.020 

HlOl 

9 

26.00 

30.00 

4.0i 

6.07 

.44 

57 

.im 

BlftJ 

8 

20.15 

24.48 

6.00 

5.10 

31 

.47 

.0:^7 

B'.03 

7 

18.11 

28.46 

4  87 

5  10 

31 

.54 

.042 

BIOS 

6 

15.30 

18.36 

4.y8 

4.53 

.28 

.43 

.040 

178 


MATERIALS. 


nUnlmiiiii,  Mmxtmniii,  and  Intermeillate  UTelsbt*  and 
Dimensions  of  Carnegie  Standard  Cbannela* 


|ll 

III 

8.83 

i 

^^1 
pi 

01 

15 

55 

0.82 

C5 

8 

16.25 

2.44 

0.40 

•• 

•  4 

50 

3.72 

0.72 

»» 

18.75 

2.35 

0.31 

•• 

•« 

45 

3.62 

0.62 

»» 

•  « 

11.25 

2.26 

0.22 

" 

it 

40 

8.52 

0.52 

C6 

7 

19.75 

2.61 

0.C3 

** 

'* 

35 

8.43 

0.43 

*' 

17.25 

241 

0..^8 

•' 

** 

38 

8.40 

0.40 

»* 

** 

14.75 

2.80 

0.42 

i^ 

12 

40 

8.42 

0.76 

<« 

*' 

12.25 

2-20 

O.Si 

*• 

'• 

35 

8.80 

0.64 

»« 

»* 

9.75 

2.09 

0.21 

" 

'* 

30 

8.17 

0.51 

C7 

6 

15.50 

2.28 

0.50 

i> 

*' 

A 

8.05 

0.89 

*» 

13 

2.16 

0.44 

" 

'* 

flO.5 

2.M 

0.28 

•' 

•' 

10.50 

2.04 

0..32 

C:^ 

10 

35 

3. IS 

0.82 

** 

«* 

8 

1.92 

o.ao 

tt 

tk 

30 

8.04 

0.68 

C8 

5 

11.50 

2.04 

0.48 

'* 

*' 

25 

2.89 

0.53 

9 

1.89 

0.33 

•' 

** 

20 

2.74 

0.88 

** 

" 

6.50 

1.75 

0.10 

»t 

»* 

15 

2.60 

0.24 

C9 

4 

7.25 

1.73 

0.33 

C4 

9 

25 

2.82 

0.62 

♦' 

6.25 

1.65 

O.^K 

'* 

*» 

20 

2.65 

0.45 

** 

** 

5.25 

1.58 

0.18 

" 

" 

15 

2.49 

0.29 

072 

8 

6 

1.60 

o.ae 

*• 

•• 

13  25 

2.43 

083 

t( 

5 

i.ao 

o.*-» 

ta 

8 

21.25 
18.75 

2.62 
2.53 

0.58 
0.49 

M 

4 

1.41 

0.17 

H^elshts  and  Dimensions  of  Carnegie  Steel  Z-Bars. 


Size. 

• 

Size. 

11 

15.6 

jl 

Z6 

u 

so 

c  t1 

.2^ 

3    ^ 

i 

1 

P 

Zl 

6 

H 

8  5/16 

5  1/16 

36.0 

" 

7/10 

3  9/16 

6  1/16 

18.3 

" 

13/16 

3   H 

B    >6 

28.3 

*' 

^ 

3    % 

6    H 

21.0 

Z7 

H 

3  1/16 

8.2 

Z2 

9/lC 

8    ^ 

6 

22.7 

*' 

5/16 

3  3/16 

4  1/10 

10.3 

•• 

% 

3  9/16 

6  1/16 

25.4 

** 

% 

4   H 

12.4 

'* 

U/IC 

3    % 

6    H 

28.0 

ZH 

7/16 

8  1/16 

13.8 

Z3 

Va 

3    Yi 

6 

29.8 

'* 

H 

3  8/16 

4  1/16 

15.8 

" 

13/16 

3  9/lU 

6  1/16 

32.0 

»« 

9/16 
% 

4    ^ 

17  9 

'* 

% 

8    % 

6    ^ 

84.6 

Z9 

8  1/16 

18.9 

Z4 

5/16 

3    M 

5 

11.6 

" 

11/16 

U% 

ra" 

S0.9 

'* 

% 

3  5/16 

5  1/16 

18.0 

** 

5/l6 

22.9 

'* 

7/.6 

l'^ 

5    14 

10  4 

ZIO 

2  11/16 

6.7 

Z5 

5 

17.8 

'* 

'-J  H 

3  1/16 

8.4 

*' 

X 

3  5/10 

5  1/16 

20.2 

Zll 

H 

2  11/18 

9.7 

** 

3    ^ 
3    \i 

5    >6 

22.0 

" 

7/16 

a  H 

8  1/16 

11.4 

Z6 

11/10 

5 

23.7 

Z12 

H 

2  11/16 

8 

ia.5 

D/IO 

2    « 

3  1/16 

14.2 

SIZES  AND  WEIGHTS  OF  STRUCTURAL  SHAPES.      179 


Pen 

Goyd  Steel 

Anffles. 

EVEN  Lisas. 

Approximate  Wei«:iit  in  Pounds  per  Foot  Tor  Various 

Thicknesses  in  Inches. 

Size  in 

Inches. 

j&  Win 

!i 

"ilS 

% 

% 

|]M0    % 

"/■IS 

% 

"^2 

1 
1.00 

8>  s 

3H.2 

ae.fi'ag.o 

42.4 

45.8 

49.8 

52.8 

Cxi 

I4.KI7.3 

]»  T'-.'-J.O 

'M  4 

'^.f-^^.? 

81.0 

38.4 

85.9 

5    *i 

1^.8^14^ 

;e.jj 

m.2 

aoj 

rj-O'ja.s 

25.6 

27.4 

29.4 

4     xA 

S.3 

9.«11.8rJ.H 

11.,^ 

IE?  t* 

17^  m.G 

^^^^ 

T,l 

fiSi\  1kfi\\\.l 

t'^.l 

1.1.7 

8    >% 

4.0 

fl.l 

7,y 

HX  9.\ 

10. 1 

n.& 

^  V  ia^ 

4.B 

ft.S 

B.e 

7  7 

s.d 

^-m 

SJ 

4  1 

R.O 

s.e 

eiij 

T.H 

2^4  xiZ; 

3.;i3.6 

4.5 

&.4 

2   ^a* 

a.S,3.3 

4.0 

4.e 

lH^l^ 

S.l  ii.S 

3.S 

4.1 

l^xlij 

l.S    1.8|3.4 

3.8 

S.5 

1^-T>4 

l.rt;;  i.5:iJ.O 

1     X     1 

."••i  'V'* 

UNEVEN  LEGS. 

Approximate  Weight  in  Pounds  per  Foot  for  Various 
Thicknesses  in  Inches. 

Size  in 

Inches. 

.!*» 

.1875 

1 

%1S 

^. 

^iil! 

^ 

.MS.^ 

^i 

11/16 
.6876 

M 

'.V.i§ 

^» 

Xt 

1 
1.00 

H     x8 

$3.0 

^h 

'^^^.7 

81.7 

3JI.R 

30.6 

39.  r, 

42.5 

45.6 

:   x3H 

6H*4 
6     x4 

iro 

so.o 

Jl.O 

23.0 

24.8 

28.7 

28.6 

30.5 

32.5 

12.9 

15.0 

17.0 

lt>.i> 

i^.2 

23.4 

25.6 

27.8 

29.8 

31.9 

Vi.2 

14.3 

ia.3 

3K.I 

iu.l 

22.0 

28.8 

a&.ts 

27.4 

29.4 

6     xSU 

11.6 

13.6 

l.K'. 

IT   1 

]:.o 

20.8 

22.6 

24.5 

26.5 

28.6 

54-^ 

11.0 

la.s 

]  +  .rl 

](i.'J 

]-.9 

5     x4 

11.0 

12.ti 

n.G 

10. li 

j:.9 

19.6 

21.8 

I  If" 

8.7 

10.3 

I«.0 

13.6 

15.2 

16.8 

18.4 

20.0 

8.2 

Q.7 

11.2 

12.8 

14.2 

15.7 

17.2 

18.7 

44x3 
4     «3H 
4     X.) 

T.7 

9.1 

10.5 

11.9 

13.3 

14.7 

16.0 

17.4 

7.7 

9.1 

10.5 

11.9 

13.3 

14.7 

16.0 

17.4 

7.1 

8.5 

9.8 

11.1 

12.4 

13.8 

2^x3 

34«2H 

3^x2 

3   xe^ 

6.6 

7.8 

9.1 

10.3 

11.6 

12.9 

«•? 

6.1 
5.5 

7.8 
6.6 

8.3 

9.4 

■ 

*•? 

5.5 

6.C 

7.7 

8.7 

8    xi 

^•i 

5.0 

5.9 

6.9 

7.9 

S4x2 
»4  X  IH 

2.7 

^'n 

4.5 

6.4 

6.2 

7.0 

2.8 

K 

3.7 

4.4 

2     xlS 

2.1 

'^l 

3.6 

4.3 

3     xl^ 

l.» 

2.« 

8.8 

8.9 

ANGLE-COVERS. 

SizA  in 
Izicheft. 

8/16 

M 

5/16 

% 

7/16 

H 

9/16 

H 

3     x3 

4.8 

5.9 

7.1 

8.2 

9.3 

10.4 

11.5 

8.0 

4.4 

4.0 

5.5 
5.0 

6.6 
6.0 

7.7 
7.0 

8.8 
8.1 

«^y  2W 

2.6 

8.5 

4.4 

5  3 

i     x2 

2.4 

8.3 

4.0 

4.8 

180 


MATERIALS. 


SQUARE-ROOT  ANGLES. 


Approximate  Weight  in  Pounds 
l)er  Foot  for  Various  Tbiclcnesi»es 

Approximate  Weight  to 
Poiiuda  per  Foot  for 
Various  Thiclcuesses 

Size  in 

iu  luclies. 

Size  in 

in  Inches. 

luches 

Inches. 

1 

'^^ 

If* 

7/16 

% 

9/16    % 

^ 

3/16 

H  '5/16|  H 

.4375 

,5625  .6:^5 

.1«5 

.18Y5 

.25 

.3125'  375 

4     x4 

0  8 

11.4 

18.0 

14.616.2 

2     k2 

38 

4.1 

4.9 

8V6x3»^ 

7.1 

8.5 

9.9 

11.4 

\n:\n 

2.9 

8.0 

4.4 

8     x3 

4.9 

6.1 

7.2 

8.3 

9.4 

1.80 

2.4 

8.0 

3^  x2<^ 

4.5 

5.6 

6.7 

7.8 

8.0 

1)4x14 

l.M 

2.04 

2.56 

2j^  xiJ^ 

4.1 

6.1 

C.l 

7.1 

8.:^ 

1x1 

0.82 

1.16 

1.53 

2V4  ><  -M 

8.6 

4.5 

5.4 

1 

Peneoyd  Tees. 


Section 
Number. 


Size 
iu  Indies. 


Weight 
per  Foot. 


Section 
Number. 


Size 
in  lucliea. 


Weight 
per  tooU 


EVEN  TEES. 


440T 
44  IT 
385T 
886T 

8srr 

35)OT 
83iT 
225T 
226T 
227T 
Ji22T 
223T 
220T 

iirr 

115T 
112T 

HOT 


2>,4x2^ 
2     x2 

134 « l^ 

1^4  «n4 

1      xl 


UNEVEN  TEES. 


6  IT 
C."iT 
631' 
54T 
42T 


6x4 
Cx5W 
5x3^ 
5x4 


10  9 
13.7 
7.0 
9.0 
11.0 
6.5 
7.7 
5.0 
6.8 
6.6 
4.0 
4.0 
3,5 
2.4 
2.0 
1.5 
1.0 


17.4 
:39.o 
17.0 
15.3 
6.5 


48T 
44T 
4.'>T 
88T 
89T 
»i»T 
31 T 
82T 
33T 
34T 
35T 
3CT 
28T 
SOT 
2oT 
26T 
27T 
24T 
20T 
22T 
21T 
23T 
17T 
18T 
15T 
12T 


UNEVEN  TEES. 


0.0 
10.2 
18.5 
7.0 
8.5 
4.0 
5.0 
6.0 

r.o 

8.0 
8.31 
9.5 
6  8 
7. -J 
8.3 
5.7 
6.0 

s.a 

2  0 
2  O 
2.5 
8.0 
1.9 
3.5 
1.4 


Peneoyd  Mlaeellaneous  Shapes 

Snction 
Number. 

Section. 

Size  in  Inches. 

Weight  per  Foot 
in  Pounds. 

21 7M 

210>I 

aeoM 

Hoavy  rails. 
Floor-bars. 

6 

3  1/10x4x3  l/If)xiito  Jl^ 

•46xOx2j^xUlo% 

50.0 
7.1  to  14.8 
9.8  to  14.7 

SIZES  AND  WEIGHTS  OP   ROOFING   MATERIALS.     181 

SIZES  AND  WBTGHTB  OF  ROOFING  MATKRIAIiS. 

Corr abated  Iron*    (The  Ciaciniiati  Corrugating  Co.) 

8CHKDCLB   OF    WEIGHTS. 


I 


x«.  as 

No.  26 
No.  91 
No.  2i 
No.  JO 
No.  ^^ 
No.  16 


Tlilckiiess  in 

deciiiial  parts 

of  All  inch. 

Flat. 


.015685 

.01875 

.03.1 

.0SI25 

.0673 

.05 


Weight  per 

100  sq.  ft. 

Flat,  Painted. 


75  " 

100  " 
1« 
150 

aoo  •* 

850  •• 


Weight  per 

100  sq.  ft. 

Corrugated 

and  Painted. 


70  IbR. 

84  *' 

111  •* 

i:«  *• 

1«5  " 

S«0  *» 

876  " 


Weight  per 

100  sq.  ft. 

Corrugated 

and 
Ga1vatil»>d. 


06  lbs. 

09  •* 

1«7  " 

154  '♦ 

IKS  •• 

«.%  " 

«01  *• 


Weight  in  os. 

|)«r  sq.  ft. 

Flat,  Uuiran* 

Uttfd. 


26M 


The  abOT«  table  is  on  the  basin  of  sheets  rolled  according  to  the  U.  S. 
Sundard  Sheet-metal  Gauge  of  ISM  (see  page  81).  It  is  also  ou  the  basis  of 
^X%*n.  corrugations. 

To  estimate  the  weight  per  100  sq.  ft.  on  the  roof  when  lapped  one  corru- 
gation at  aides  and  4  in.  at  ends,  add  approximately  12H<  to  the  weighto  per 
100  sq.  ft.,  respectively,  given  above. 

0>migatfons  S4  in.  wide  by  ^  or  ^  in.  deep  are  recognisced  generally  aa 
the  staiMlard  siae  for  both  rooflng  and  siding;  sheets  aie  manufactui'ed 
usually  in  lengths  6,  7,  8,  9,  and  10  ft.,  and  iiave  a  width  of  2CU  or  !36  in.  out- 
»ide  width— ten  corrugations,— and  will  cover  2  ft.  when  lapped  one  corruga- 
tion at  sides. 

Ordinary  oomigated  sheets  should  have  a  lap  of  IK  or  2  corrugations  s^lde- 
lai>  for  rooflng  in  order  to  secure  water-tight  side  seams;  if  the  roof  Is 
rather  steep  1}%  comigations  will  answer. 

Some  manufacturers  make  a  special  high-edge  corrugation  on  sides  of 
<>heeis  ( rhe  Cincinnati  Corrugating  Co.),  and  thereby  are  enabled  to  secure 
a  water-proof  side-lap  with  one  corrugation  only,  thus  saving  from  6^  to  1^ 
of  material  to  cover  a  given  area. 

The  usual  width  of  flat"  sheets  used  for  making  the  abov>e  corrugated 
matMial  is  88^  inches. 

No.  28  gauge  corrugated  iron  is  generally  used  for  applying  to  wooden 
buildiags;  but  for  applying  to  iron  framework  No.  S4  gauge  or  heavier 
should  be  adopted. 

Few  manufacturers  are  prepared  to  corrugate  heavier  than  No.  20  gauge, 
but  noma  have  facilities  for  corrugating  as  heavy  as  No.  18  gauge. 

Ten  feet  is  the  limit  in  length  of  corrugated  slieets. 

Galvanizisg  sheet  iron  adds  about  2>i  oz.  to  its  weight  per  square  foot. 

Corroffated  Arebea. 

For  corrugated  curved  sheets  for  floor  and  ceiling  construction  in  flre- 
ITiwt  buildings,  No.  16, 18,  or  80  gauge  iron  is  commonly  used,  and  sbi^ets 
inav  be  curved  from  4  to  10  in.  rise— the  higher  the  rise  the  stronger  ib« 
arrh. 

By  a  series  of  tests  It  has  been  demonstrated  that  corrugated  arches  give 
tite  moKt  satisfactorr  results  with  a  base  length  not  exceeding  6  ft.,  aiid  5 
fi.  («r  even  lens  is  prerenible  where  great  strength  is  required. 

These  corrugated  ai-ches  are  usually  made  with  2>^  X  H  ">•  corrugations, 
snd  in  same  width  of  slieet  as  above  mentioned. 

Terra-€otta« 

P^vrous  terra-cotta  roofing  3"  thick  weighs  16  lbs.  per  square  foot  and  2" 
thick.  13  lbs.  per  square  foot. 
Ceiling  maae  of  the  same  material  2''  thick  weighs  11  lbs.  per  square  foot. 

TUes. 

Flaf  files  6^"  X  t(H*'  X  %'*  weigh  from  1480  to  1850  lbs.  per  square  of 
roof  (100  square  feet),  the  lap  belnc:  one-half  the  length  of  the  tile. 
r«/M  with  grooves  atul  fillets  weij^h  from  740  to  92^}  lbs.  per  square  of  roof. 
PttnrtiUs  14Mt"  X  lOMi"  laid  10"  to  the  wcatlier  weigh  BoO  lbs,  per  square. 


182 


MATERIALS. 


Tin  PIate«yri nned  Sheet  Sloel. 

ftie  Usual  sizes  for  rooflit^  tin  are  14"  X  90"  ami  20"  x  28".  "Without 
allowance  for  lap  or  waste,  tin  rooflnK  weighs  from  50  to  62  lbs.  per  square. 

Tin  on  the  roof  weighs  from  fl*i  to  76  lbs.  per  square. 

RooflnK  plates  or  teme  plates  (8teeJ  plates  coaled  with  an  alloy  of  tin 
and  lead)  are  made  only  in  IC  and  IX  thicknesses  (S7and  20  Birinliij^ham 
gauee).  **Coke*'  and  *' charcoal'*  tin  plates,  old  names  used  when  iron 
made  with  coke  and  charcoal  was  used  for  the  tinned  nlHle,  are  still  used  in 
the  trade,  although  sleel  plates  have  been  substituted  for  iron:  a  coke  plate 
now  commonly  meaning  one  made  of  Bessemer  steel,  and  a  charcoal  plate 
one  of  open-hearth  steel.  The  thickness  of  the  tin  coating  on  the  plates 
varies  with  different  **  brands.'* 

For  valuable  information  on  Tin  Roofing,  eee  circulars  of  Merchant  &  Co.. 
Philndelpliia. 

The  thickness  and  weight  of  tin  plates  were  formerly  designated  in  tho 
•trade,  botb  in  tiie  United  States  and  England,  by  letters,  such  as  I.C\,  I>-C'., 
I.X.,  D.X.,  etc.  A  new  system  was  iniriHiuced  in  tlie  United  Statrs  in  iwu«, 
knuivn  as  the  "American  base-box  system.'*  The  base-box  is  a  puck:tKe 
•containing  3*^000  square  inches  of  plaie.  The  aciuai  boxfsutied  in  llie  trade 
•contaiu  60, 120,  or  240  sheets,  according  to  liio  size.  The  ituiuber  o:  squuro 
inc  les  in  any  given  box  divided  by  8^,000  is  known  as  liie  *'  box  ratio.*'  Tltis 
ratio  mnltiplied  by  the  weigiit  or  price  of  the  base-box  givfS  the  weight  i»r 
price  of  the  given  box.  Thus  tlie  ratio  of  a  box  of  120  sheets  14  x  20  in.  is 
83,600 -«- 82,000  =  1.0.->.  and  tlie  price  at  $;).00  base  is  $3.00  X  1.05  =  $3.15.  I  he 
following  tables  are  fumisiied  by  the  Anif  rican  Tin  Piute  Co..  Chicnj^o,  ill. 
Comparison  of  Ganfireft  and  UTeletatii  of  Ttn  Plates. 
(Butted  oil  U.  a.  oianduid  Sheei-ineial  UuuKe.) 


AMERICAN  BASE-BOX. 
(.i2,000  sq.  iu.) 
Weight.  Qau{?e. 

^51os Ko.  38.00 


00 
(«3 
70 
75 
80 
H5 
90 
i« 
100 

no 

130 

no 

160 

180 

200 

220 

240 

2(30  ' 

280 

140 

IHt) 

220 

2i0 

280 


8U.TJ 

"  35. C4 

»'  81.9;i 

"  34  20 

"  .33.4S 

••  32.70 

"  32.04 

*•  81.32 

"  80.80 

**  30.0rt 

**  28. C| 

**  27.1»;i 

'*  20.18 

"  25. 5i 

*'  24. Ho 

••  21. Os 

*'  23.30 

"  22.C4 

"  21.92 

, "  27.92 

"  2.J.5.' 

"  21.0.^ 

"  2.1. 3;i 

•»  21.92 

Amcracan  PackaKcn  Tin  Plato. 


ENGLISH  BASE-BOX. 
(31,^60  bq.  hi ) 
Gauge.  Weight. 

No.»<.00 54.4nits. 

'•  87.00 67.84  " 

*•  86.00 G1.24  ** 

"  a*). 00 08. (V)  " 

'•  34.00 74.8.-)  *» 

"  8:1.24 WVOO  " 

••  82..'V0 85.00  '* 

'*  31.77 90.00  " 

*'  81.04 1«5  tW  ** 

"  80.a5 100.00  ••   I.C.L. 

"  30.00 108.00  ••    I.e. 

"  28.74 120.00  *'    1  X  U 

••  28.00 i:«.00  ♦*    1  X. 

"  26. 4« 157. «H)  *•    l.-.:X. 

"  25.40 ]7S.0«»  •*    1..3X. 

*•  24. C8 199. tX)  "    1.  IX. 

"  23. HI 2J0.00  "    I   r^X. 

•'  23.14 241.00  '*    I.OX. 

'*  22..•^7 202.00  '*    1.7X. 

*'  21.00 28:1.00  "    1.  i<X. 

'♦  27. Sn 130  a)  •'    DC. 

'*  25. as 1<»0.00  *     D.X. 

'*  24.24 211.00  *•    D   2X. 

'•  23.12 212.00  "    1>.  "iX. 

"  22  00 273.00  *'    D.  4X. 


l4engLh. 


Inches 
Wide^ 

0  to  16?>^  S(]uare. 

17  "  2."j%  Square. 

86  '*  30     8<iiiHre. 

9  "  10%  .\11  lengths. 

n  "  1111  To  18  in   long,  incl. 

11  "  1194  I8I1J  and  longer. 

12  •*  12J^To  17  in.  loiiK,  incl. 


Sheet  > 
I)er  Hoxj] 

240 
120 
GO 
240 
240 
120 
240 


In  hfs    I 
Wi;le. 


Length. 


12941 I7V4  and  lonK«T. 

jl3   "    13»4  To  16  in.  lonjr.  InH. 
fll3  to  Vi^4  10>4and  longer. 
Dl4   '•    14514  To  1. "3  in.  long,  incl 
IJ14    •*   n->4  ir)»4  rtnd  longer. 

2:>?4  All  li*njrtlis. 
I.'O   '*  80     Alllenfirthit, 


Small  aizen  of  light  basH  weights  will  be  paclced  in  double lL>ozes. 


_  Sli»*»-ts 
'^H-r  Box 

120 
240 
IJO 
2  40 
120 
390 
60 


SIZES  AND  WEIGHTS  OF   ROOFING  MATERIALS^     183 


Slate. 

Number  and  superficial  area  of  slate  required  for  ooe  square  of  roof. 
(1  square  =  100  square  feet.) 


Dliiieiiflioiis 

in 

Inches. 

Number 

per 
Square. 

Superficial 
Area  in 
Sq.  Ft. 

Dimensions 

in 

Inches. 

Number 

per 
Square. 

Superflrial 
Area  in 
Sq.  Ft. 

6x18 
7x12 

588 
4S7 
400 
855 
874 
827 
291 
261 
277 
846 
221 
213 
192 

867 

12x18 
10x20 
11x20 
12x20 
14x20 
16x20 
12x22 
14x28 
12x24 
14x24 
16x24 
14x26 
16x26 

160 
169 
154 
141 
121 
187 
l;J6 
106 
114 
98 
86 
80 
78 

840 
285 

8x18 

9x12 
7x14 
8x14 
9x14 

254"  " 

281 

10x14 

8x18 
9x16 

846 

228 

10x16 
9x18 
10x18 

240" 

225 

An  slate  is  usually  laid,  the  number  of  square  feet  of  roof  covered  by  one 
sJate  can  be  obtained  from  the  following  formula  : 
width  xdengg.- 8  inches)  ^  ^^^  ^^^  ^^  ^^^  ^^  ^,  ^,  ^,^^ 

Weight  of  slate  of  various  lengths  and  thicknesses  required  for  one  square 
of  roof : 


Length 

in 
Inches. 

Weight  In  Pounds  per  Square  for  the  Thickness. 

«" 

3-16" 

J4" 

%" 

Ji" 

H" 

«" 

1" 

13 

483 

734 

967 

1450 

1936 

2419 

2902 

8872 

14 

460 

688 

920 

1379 

1842 

2801 

2760 

8683 

16 

445 

667 

890 

ia36 

1784 

2229 

2670 

3.^67 

18 

434 

650 

869 

l:«W 

1740 

2174 

2607 

8480 

80 

425 

637 

a*)! 

1276 

1704 

2129 

25.'i8 

3108 

28 

418 

626 

836 

1254 

1675 

2098 

2508 

88.'50 

94 

412 

617 

825 

12:38 

1653 

2(m 

2478 

8306 

26 

407 

610 

815 

1223 

1631 

2039 

2445 

3263 

Tiie  weigiita  given  above  are  based  on  the  number  of  slate  required  for  one 
square  of  roof,  taking  the  weight  of  a  cubic  foot  of  slate  at  175  pounds. 

Pine  Sblnsles. 

Number  and  weight  of  pine  shingles  required  to  cover  one  square  of 
roof: 


Xumberof 
laches 


Exposed  { 
Weather 


to  per 


4 


Number  of 

Shingles 

er  Square 

of  Roof. 


900 
800 
790 
665 
600 


Weight  in 
Pounds  of 
Shingle  on 
One-square 

of  Roofs. 


216 
192 
178 
167 
144 


Remarks. 


The  number  of  shingles  per  square  is 
for  common  gable-roofs.  For  liip- 
roofs  add  five  percent,  to  these  figures. 

The  weights  per  square  are  based  on 
the  number  per  square. 


J  84 


MATEUIALS. 


Skylislkt  GlaM. 

The  wel{i:ht8  of  various  ftizes  and  thicknesses  of  fluted  or  rough  p>a.e«^s:ias8 
required  for  one  squara  of  roof. 


DlmenKioiis  in 
Inches. 

Thickness  in 
Inches. 

Area 
In  Square  Feet. 

WeiKht  in  Lbs.  j>er 
Square  of  TUnyt. 

]Sx48 
15x00 
20x100 
04x156 

8-16 

i 

8.907 

6.246 

18.8H0 

101. T68 

350 

35C 
600 
TOO 

In  the  above  taUle  no  allowance  is  made  for  lap. 
If  oixlinary  wludow-glass  is  used,  siimle  thick  f^\a»»  (about  1-16")  will  'weSarh 
about  82  Um'.  per  square,  and  double  thick  glass  (about  %")  will  weigh  about 
164  IbK.  pel-  pquare,  no  aUotrance  being  macie  for  lap.  A  box  of  ordinary 
M'indo\v-gla«<s  contains  at*  nearly  50  vquare  feet  as  the  size  of  the  panes  wlU 
admit  of.  Panes  of  any  size  ai*e  made  to  order  by  the  manufacturers,  but  a 
great  variety  of  sizes  are  usually  kept  in  stock,  ranging  from  6x8  inches  to 
S(5  X  00  inches. 

APPROXiniATE  WBIGHT8  OF  VARIOCS  ROOF* 
COTKRINGS. 

For  preliminary  estimates  t)ie  weights  of  various  roof  coverings  mcyilOl 
taken  as  tabulated  below  (a  square  or  roof  =  10  ft.  square  =  100  sq.  ft.); 

Name.  ^fiSKe^^ir 

Cost-iron  plates  (^'' thick) IfiOO 

Copper 80-185 

Felt  and  asphalt , 100 

Felt  and  gravel  800-1000 

Iron,  corrugated  100-879 

Iron,  galvanized,  flat 100-  860 

Lath  and  plaster OOO-lOOO 

Sheathing,  pine,  V  Uiick  yellow,  northern..  800 

"    **       •'          *'      southern..  400 

Spruce,  1"  thick  90O 

Sneaihing,  chestnut  or  maple,  V  thick 400 

aKh,  hickory,  or  oak,  1"  thick....  600 

Sheet  iron  0-10"  thick) 800 

"       **          **     andhiths 500 

Shingles,  pine 200 

Slates  (J^4'^  thick)..-.  SOO 

SkylightH  (glass  8-16"  to  Ji"  thick) 265.  700 

Sheet  lead 600-  800 

Thatch 060 

Tin 70-125 

Tiles,  flat l.'iOO-aOOO 

*•      (grooves  and  fillets) TOO-lOOO 

"      pan 1000 

"      withmortar. 2000-yOOO 

ZIdc lUO- )iOO 

Approximate  Ijoad*  per  Square  Foot  for  Roofh  ot  t 
nnder  75  Feet,  Includlnar  H^elfl^tat  of  TruMU 

(Carnegie  Steel  Co.) 

Roof  covered  with  corrngated  sheets,  unboarded 8  lbs. 

Roof  covered  with  corruicated  sheets,  ou  boards 11   " 

Roof  covered  with  slate,  on  laths 18   ** 

Same,  on  boardK,  U4  in.  thick 16  " 

Roof  covered  with  shingles,  on  laths 10  ** 

Add  to  above  if  plastered  below  rafters 10  ** 

Snow,  light,  weighs  |>er  cubic  foot 6  to  12   ** 

For  spans  over  75  feet  add  4  lbs.  to  the  above  loads  per  square  foot. 

It  is  customary  to  add  80  lbs.  per  square  foot  to  the  aboTo  fore 
wind  when  separate  caloulatlous  are  not  made. 


WEIGHT  OF  CAST-IRON  PIPES  OR  COLUMNS.       185 


'WSI6HT  OF  €A8T-IRON  PIPBS  OR  COIiVniiB. 

In  I^bs.  per  I^Ineal  Foot. 

Cast  iron  =  450  Iba.  per  cubic  foot. 


;  Thick. 
Bore.       of 
Metal. 


Ins.   '     Ins. 
3 


3H 
4 

5 

6 

t 

8 

9 

10 


Weight 
per  Foot. 


Lbs. 
12.4 
17.2 
82.3 
14.3 
10.0 
S5.3 
16.1 
SW.l 
38.4 
17.9 
^.5 
31  5 
19.8 
87.0 
34.4 
31.6 
39.4 
37.0 
23.5 
81.8 
40.7 
35.3 
84.4 
43.7 
37.1 
36.8 
46  8 
39.0 
39.8 
49.9 
30.8 
41.7 
52.9 
44.3 
56.0 
68  1 
46.6 
59.1 
71.8 
49.1 
62.1 
73.5 
51.5 
65.3 


Bore  r  ^'of  •     ^'«'>»'t 


Ins. 

10 

ICW 

11 

n^ 

13 

12H 

18 

14 

15 

16 

17 

18 

19 

80 

31 

82 


Lbs. 
79.3 
54  0 
68  3 
82.8 
56.5 
71.3 
86.5 
58.9 
74.4 
90.3 
61.8 
77.5 
98.9 
68.8 
80.5 
97.6 
668 
88.6 
101.3 
71.3 
89.7 
108.6 
95.9 
116.0 
186.4 
108.0 
138.8 
145.0 
108.3 
180.7 
153.6 
114.8 
138.1 
168.1 
180.4 
145.4 
170.7 
136.6 
158.8 
179.8 
138.7 
160.1 
187.9 
i:«.8 


Bore, 


Ins. 
83 
S4 
25 
86 
87 


SO 
81 
88 
88 
34 
85 
86 


IDICK. 

of 
Meuil. 

Weight 
per  Ifool, 

Ins. 

Lbs. 

A^ 

167.5 

yk 

196.5 

a  \ 

174.9 

A  1 

305.1 

1 

23.^.6 

^ 

183.8 

818.7 

1 

845.4 

g 

189.6 

228.8 

1 

855.3 

§ 

197.0 
380.9 

1 

265.1 

^ 

204.3 

239.4 

1 

8T4.9 

^ 

211.7 
248.1 

1 

284.7 

^ 

219.1 

256.6 

1 

294.5 

% 

265.8 

1 

3W.8 

'^ 

8437 

873.8 

1 

814.3 

'^ 

a54.8 
882  4 

1 

824.0 

3C5.8 

^ 

391.0 

1 

3:«.8 

'^ 

376.9 
299.6 

1 

343.7 

'^ 

388.0 

3l)S.l 

1 

8.')3.4 

3H9.0 
310  6 

1 

363  I 

1« 

410.0 

The  weight  of  the  two  flanges  may  be  reciconed  =  weight  of  one  foot. 


186 


MATERIALS. 


WBIGHT8  OF  OJLST-IBON  PIPE  TO  I«JLT  12  FEBT 
I«ENGTH. 

Welsbts  are  Gross  yBVeigiktUf  Including  Hub. 

(Calculated  by  F.  H.  Lewis.) 


Thickness. 


i-bes.  ^!j;;;- 


7-16 
15-JJ;f 

9-16 
19-3;^ 

.% 


I 


tiials. 


.875 

.4875 

.4d«7 

.5 

.nSl25 

.56^.5 

.5JW75 

.0-25 

.0875 

.76 

.8123 

.875 

.9375 

1. 

1.125 

1.25 

i.87r> 


Inside  Diameter. 


209 
228 
217 
260 
286 
806 


304 
881 
858 
886 
414 
44-i 
470 
498 


8"   10"   12"   14"   16"   18"   20" 


400 
485 

470 
505 
541 
577 
018 
649 


581 
624 
668 
712 
756 
801 
845 

a35 

1026 


092 
744 
795 
846 
899 
951 
1U08 
3110 
1216 
1824 
1432 


804 
863 
922 
983 
1043 
1103 
1163 
1285 
1408 
1531 
16.'^ 
178:1 
1909 


1050 
1118 
1186 
1254 
1322 
1460 
lf>98 
17:i8 
1879 
iXtil 
2163 


1177 
1258 
1829 
1405 
1481 
16:tf) 
17l«9 
1945 
2101 
2259 
!»18 
2738 
806t 


1640 

1HI0 
1980 
21,52 
2»24 
2-4118 
2672 
3024 
3:iHa 


3389  I  3;  39 


Thickness. 

22" 

Inside  Diameter. 

Inches. 

Equiv. 
Decimals. 

24" 

27" 

30" 

33" 

30" 

42" 

48" 

60" 

% 

.625 

1799 

11-16 

.6875 

1985 

2160 

2422 

94 

.76 

2171 

2362 

2648 

21)84 

3221 

a507 

13-16 

.8li» 

2359 

2565 

2875 

81S« 

34WJ 

3«<-6 

4426 

H 

.875 

2:>47 

2709 

3ia3 

81i7 

3771 

4105 

4773 

6442 

I.C16 

.9375 

2737 

2975 

8832 

8690 

4048 

4406 

5122 

5839 

1. 

2927 

3180 

3562 

3942 

4325 

4708 

54?^ 

6236 

iWt 

1  125 

a3io 

3598 

4027 

4456 

4886 

5.<10 

6176 

7034 

1.25 

86y8 

4016 

4492 

4970 

5447 

.')924 

(5880 

7h33 

9r4£ 

1^2 

1.875 

4439 

4964 

5491 

(KH5 

6540 

75H1 

h640 

10740 

Jl? 

1.5 
1  625 
1.75 
1.875 
2. 

5439 

6012 
6539 

6584 
7159 
1737 

7lf)8 
77K2 
8405 

8:«3 

9022 
9742 
1()46H 
lllil7 

9447 

nweo 

11076 
11898 
12725 

117^ 

19? 

12744 

2 

13750 

14:62 

15776 

2.25 

14885 

17821 

01/ 

2  fS 
2.75 

19880 

hi 

»966 

CAST-IRON  PIPE  FITTINGS. 


187 


CAST-IRON    PIPB   FITTINGS. 

Approximate    l¥elsht. 

(Addyftton  Pipe  nnd  8t«?el  Co.,  Cincinnati,  Ohio.) 


SMze  III 
In«.-h«*. 


tin  Li)8. 


I  ROSSES. 


•> 

41 

3 

110 

3x2 

9J 

1-30 

4x3 

114 

4x4 

90 

£00 

6x4 

160 

6x8 

160 

8 

325 

8xfS 

280 

Hx4 

265 

Sx3 

2-25 

10 

575 

10x8 

4  IS 

10x6 

450 

10x4 

31K) 

10x8 

;i50 

1-2 

740 

«xTO 

6.<)0 

lix8 

6-^J 

1-2x6 

540 

1-2  X  4 

525 

12x3 

495 

14x10 

750 

lix8 

U:» 

14x6 

570 

16 

1100 

16x14 

1070 

iexi2 

1000 

16xlo 

1010 

16x8" 

825 

lGx6 

700 

lGx4 

650 

18 

1560 

ao 

1790 

•20x12 

1370 

'JOxlO 

1-225 

20x8 

1000 

a)x6 

1000 

a0x4 

1000 

24 

2400 

•24x20 

20!» 

£4  X  6 

1^0 

ajxao 

2635 

30x12 

2250 

:«x8 

1995 

TEFS. 


2 

3 

1x2 

4 

4x3 

4x2 

6 

6x4 

6x3 

6x2 

8 

8x6 


76 
100 

90 

87 
IJW 
145 
145 

75 
300 
270 


8ize  iu   |VV>iKht 
Inches.  I  III  Lbs 


TEES. 


8x4 
8x3 
Id 

10x8 
10x6 
10x4 
10x3 
1-2 

r-*xio 

1-2x8 

12x6 

12x4 

14  X  12 

14x10 

14  xS 

14x6 

lix4 

14x3 

16 

16x14 

10x12 

16x10 

16x8 

16x6 

16x4 

18 

20 

•20x16 

20x12 

20x  10 

20x8 

20x0 

20x4 

20x10 

'24 

24x12 

24x8 

24x6 

30 

30x24 

30x20 

80x12 

30x10 

80x6 

36 

36x30 

36x12 


2^i0 
2'iO 


370 

850 

810 

600 

555 

515 

550 

625 

6.-10 

650 

575 

545 

525 

490 

790 

850 

850 

H50 

765 

680 

665 

1235 

1475 

1115 

1025 

1090 

900 

875 

845 

1465 

2000 

1425 

1875 

1450 

30*25 

2640 

2:i00 

2035 

2050 

1825 

5140 

4200 

4050 


45'»  BRANCH 
PIPES. 


3 

4 

6 
6x6x4 

8 

8x6 
24 
24x24x20 
SO 
86 


90 

125 

205 

145 

8-)0 

3:^ 

2765 

2:45 

4170 

10800 


Size  iu    iWeiKliL 
Inches.  I  in  Lbs. 


SLEEVES. 


2 
3 
4 

6 
8 
10 
12 
14 
16 
18 
20 
24 
80 
86 


10 
25 
45 
65 
80 
140 
190 
208 
850 
375 
500 
710 
965 
1200 


90«   ELBOWS. 


2 

14 

3 

34 

4 

55 

6 

120 

8 

ISO 

10 

360 

12 

870 

14 

450 

16 

660 

18 

8S0 

20 

900 

24 

1400 

30 

3000 

^  or  45°  BENDS. 
3 


4 
6 
8 
10 
12 
16 
18 
20 
24 
80 


70 
95 
150 
i!00 
290 
510 
580 
780 
1425 

atoo 


1/16  or  22^0 
BENDS. 


8 
10 
12 
16 
24 
30 


15-5 
205 
260 
4.50 
1-280 
-2000 


REDUCERS. 


3x2 
4x3 
4x2 

6x4 
6x3 
8x6 

Hx4 


25 
42 
40 
95 
70 
126 
116 


Sizeiu   iWeiKht 
Inches.  I  in  Lbs. 


REDUCERS. 


8x3 
10x8 
10x0 
10x4 
12x10 
12x8 
12x6 
12x4 
14  X  12 
14  X  10 
14x8 
14x6 
16  X  12 
16x10 
20x16 
20x14 
80x12 
20x8 
24x20 
80X-24 
30x18 
86x30 


116 
212 
170 
160 
820 
250 
250 
260 
475 
440 
800 

475 
435 
690 
675 
540 
400 
990 
1305 
13S5 
1730 


ANGLE   REDUC- 
ERS FOR  UAS. 
6x4       I        95 
6x8    J^       70 

S  PIPES. 
4  I      105 


PLUGS. 


2 

3 

8 

10 

4 

10 

6 

15 

8 

80 

10 

46 

12 

66 

14 

90 

16 

100 

18 

180 

20 

150 

24 

185 

30 

370 

CAPS. 

3 

20 

4 

25 

6 

60 

8 

75 

10 

100 

12 

120 

DRIP  BOXES. 


4 
6 
8 
10 
20 


295 
330 
375 
8:5 
14-20 


188 


MATERIALS. 


WEIGHTS  OF  CAST-IRON  WATER-  AND  GAS-PIPB. 

(Addyston  Pipe  and  Steel  Co.,  Cincinnati,  Ohio.) 

I  Standard  Qos-pipe. 


Standard  Water-pipe.        | 

Per  Foot. 

Thick- 
ness. 

Per 

LeiiRth. 

2 

7    . 

5/16 

63 

3 

15 

9i 

180 

3 

ir 

1^ 

m 

4 

2i 

^ 

364 

0 

83 

\2 

396 

8 

42 

^ 

504 

8 

45 

H 

540 

10 

CO 

9/10 

7iK) 

12! 

75 

9/16 

000 

14 

117 

?4 

1400 

10 

];» 

^ 

1500 

18 

167 

U 

i?000 

20 

iiOO 

iS/lC 

2400 

Hi 

^50 

1 

aooo 

90 

350 

1% 

4','00 

80 

475 

5700 

42 

600 

]K^ 

7:J00 

48 

775 

IH 

9300 

(SO 

1330 

3 

15960 

72 

lais 

^H 

JKOJO 

9 
8 

4 

6 

8 

10 
13 
14 
16 
18 
30 
24 
30 
36 
43 
48 
6U 


Thick- 

Per 

1  Per  Foot. 

ness. 

LeiiKth. 

6 

H 

4S 

12^ 

5/16 

150 

17 

H 

2W 

80 

7/16 

860 

40 

7/16 

4b0 

50 

7/16 

600 

70 

H 

640 

84 

0/16 

1000 

100 

9/10 

13U0 

134 

11/16 

1600 

150 

11/16 

1J<00 

184 

3300 

250 

9% 

3000 

sno 

rl 

4300 

417 

15/16 

5000 

543 

]^ 

6500 

900 

1^6 

lOHX) 

1.150 

IH 

15000 

THICKNESS  OF  CAST-IRON  WATER-PIPES. 

P.  H.  Baermann,  In  a  paper  read  before  the  Enfrineers^  Club  of  Phila- 
delphia in  1H83,  {;ave  tweniy  fliffereiit  forniulag  Tor  determininK  the  thick- 
nesH  of  east-iron  pipes  under  presHure.    The  formulas  are  of  three  classes: 

1.  Depend injc  upon  the  diameter  only. 

2.  Those  dependiog  upon  tiie  diameter  and  head,  and  which  add  a  ccn* 
stant. 

3.  Those  dependinfc  upon  the  diameter  and  head,  contain  an  addlUre  .)r 
Bubtractive  term  dependinf?  upon  the  diiimeter.  and  add  a  constant. 

The  more  modern  fornmlos  are  of  tue  thiixl  class,  and  are  as  follows: 

t  =  .OOOOHAd -4- .Old  +  .36  She<ld,  No.  1. 

t  =  .00i)0G/id  -f  Oisati  +  .296 Warren  Foundry,  No.  2. 

t  =  .OOOOSH/td  4-  .0133d  -|-  .812 Francis,  No.  8. 

t=  .0000l8/id  4- .0l5d  4- .33 Dupuit,  No.  4. 

<=:  .00004ftd  +  .l  4/d-f  .15  Box,  No.  5. 

t  =  .00U135/id  +  .4-  .OOlld Whitman,  No.  6. 

t  =  .0<X)06(/i  4-  230)d 4-  .mi  -  .0038d Fanning,  No.  7. 

t  =  .000l5/»d  +  .35  -  .0053d ....Meggs,  No.  8. 

In  which  t  =  thickness  in  inches,  h  =  bead  in  feet,  d  =3  diameter  in  inches. 
Rankine,  *' Civil  Engineering,"  p.  721,  says:  **  Cast-iron  pipes  should  be 
maile  of  a  soft  and  louKh  qualitv  of  Iron.  Ureat  attention  should  l>e  paid 
to  iiiouldingthem  correctly,  BO  that  the  thick  nf^ss  may  be  exact  Ij' uniform  all 
roil  lid.  Each  pipe  should  l)e  tested  for  Jr-bub^les  and  flav  h  by  ringing  !e 
with  a  hammer,  and  for  aren^th  by  ex)X>8mg  't  to  "ou  »e  th-  iiiteiidv'd 
greatest  working  presbure.'    The  rule  for  comp..ting  the  .hickness  of  a  p:;.© 

to  resist  a  given  working  pressure  is  <  =s  ^,  where  r  Is  the  radius  In  Inch;t.i, 

p  the  pressure  in  pounds  per  square  inch,  and  /  the  tenacity  of  the  iron  iwr 
square  inch.  When/  =  IHtXX),  and  a  factor  of  safety  of  5  is  ujmkI,  the  abuvs 
expressed  in  terms  of  d  and  h  becomes 

'  =  "3600"==  16lii>8=  •^^*^^^^^^^*'*- 

"There  are  limitations,  however,  arising  from  difficulties  In  casting,  aud 
by  the  strain  produced  by  shocks,  wtiicli  couse  tlie  thickness  to  be  uiado 
greater  than  tliat  given  by  the  above  formula.** 


THICKNESS  OP  CAST-IRON   PIPE. 


189 


TIftfekneas  of  Metal  and  Weight  per  I^en^tli  for  IMIDDreiit 
Sizes  of  Cast-iron  Pipes  under  Various  Heads  of  UTater, 

(WarreD  Foundry  and  Machine  Co.) 


M 

100 

laO 

soo 

250 

soo 

Ft.  Head. 

Ft.  Hea<l. 

Ft.  Mvad. 

Ft.  J 

tad, 

Ft.  Head. 

Ft.  Head. 

8I». 

11 

en? 

P 

ll 

il 

11' 

1-3 

II 

1^ 

go 

§o 

So 

''a 

s», 

"i 

g^ 

^l 

go 

"1 

S 

.944 

144 

.858 

III) 

.fl«a 

isa 

.B71 

157 

.880 

161 

.890 

166 

4 

.861 

107 

.878 

2<U 

,26^ 

ni 

.3JI7 

318 

.409 

228 

.421 

285 

& 

.S78 

254 

.803 

»i.> 

.40t+ 

27Ji 

.4x':J 

286 

.488 

298 

.453 

.309 

6 

.803 

315 

.411 

t'A} 

.4l» 

S«i 

.-147 

;»] 

.466 

877 

.483 

393 

8 

.422 

445 

.450 

i-r> 

.474 

WIS 

41^ 

!529 

.622 

657 

.546 

684 

10 

.459 

600 

.480 

eit 

..MH*     CRi 

.hV.i 

723 

.679 

766 

.609 

808 

It 

.491 

768 

.627 

e-*; 

..^^3 

*tH-i 

.SJri) 

1M4 

.685 

1004 

.671 

1064 

U 

.BcM 

95S> 

.666 

10;n 

.mW 

un 

.fCHI 

noi 

.692 

1272 

.734 

1352 

16 

.567 

1152 

.601 

12:.:^ 

.65:2 

lae^ 

.7(^1 

1168 

.748 

1568 

.796 

1673 

18 

.560{ 

1370 

.648 

IS^Nh 

.01»7 

Tf-ftii 

.7:.  3 

1761 

.805 

1894 

.ft'iO 

2026 

iO 

.tt23{ 

1603 

.682 

17^:^ 

.74iJ 

1EW4 

.NH.^ 

.086 

.862 

2248 

.92-.> 

2412 

24 

687 

81-20 

.759 

28iLi 

.R1I 

S^'jfiO 

.tMi:i 

J  ^11 

.975 

8045 

1.047 

3379 

to 

.785 

80-JO 

.876 

8]]^'t; 

.H65 

8735 

!Jir.:. 

J')95 

1.145 

4458 

1.235 

4822 

S6 

.8^ 

4O70 

.990 

4fiM 

I  m>H 

B*M>6 

l,i.^5 

:n8 

1.814 

6188 

1.422 

6656 

4i 

.980 

&265 

1.106 

6flr.^ 

]  Si;! 

(5057il.S5K 

:m 

1.484 

8070 

I.CIO 

8804 

48 

1.078 

6616 

1.222 

75:j; 

1.366 

SI.*Jl 

1.510 

mio 

1.654 

10269 

1.798 

11105 

AH  pipe  cast  Tertlcally  In  dry  sand;  the  8  to  12  inch  in  lengths  of  12  feet, 
&li  larger  sises  in  lengths  of  12  feet  4  inches. 


talto  Pressures  and  EqulTalent  Beads  of  Water  for  Cast* 
Iron  Pipe  of  miTerent  Sizes  and  Tlilcknesses. 

(Calculated  by  F.  H.  Lewis,  from  Fanning's  Formula.) 


SlixnttlHpc 

\  ..It* 

■  it 

r 

i  1* 

4" 

«*' 

g*# 

10" 

IS" 

14" 

,«.. 

18" 

20" 

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Sf 

s  . 

II 

II 
11 

St  c 

II 

1 

5j 

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II 

ll 

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m 

li 

SJ 
Hi 

c 



aifl 

bit 
.... 

If 
IS 

13* 
iMi 

lit 

130 

Mil 

ll 

t£ 

41 

m 

Ul 

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HI 

ivi 

Sll^ 

ll 

l.-ra 
:£1<1 

74 

111 

ISi 

|l 

lis 
i:<i 
ifcji 

saft 

€81 

BSD 

190 


HATERIALS. 


Safe  PresMureii,  etc., 

for  € 

iifit-lroii 

Plp«.-<Cbn(toi<«t.) 

hijf:n  1.1  E  iiyiv. 

312" 

ti" 

87" 

30' 

»»" 

30" 

42"       48" 

or* 

Whkk^ 

1- 

5j 
II 

3 

pi 

ll 

I  5 

ti 

5  , 

is 

HI       ' 

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fill 

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E- 

£": 

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c; 

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3" 

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la 

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ll-t0 

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is 

113 

M 

(in 

u 

Fkl 

IS- 1ft 

HO 

IM 

w 

irj7 

fkU 

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Wl 

7H 

101 

403 

iW 

1BA 

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la* 

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t^ 

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3S 

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1  34 

:£H 

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4;^     183 

&CT7,  5Sii: 

fit     14A 

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*,.. 

Note.— The  absolute  safe  static  pressure  which  may  be 

put  upon  pipe  Is  Riven  by  the  formula  P  s=  ^  X  ■=-,  in 

which  formula  P  is  the  pressui-e  per  square  inch;  T.  the 
thickness  of  the  shell;  5,  the  ultimate  strentrth  per  square 
inch  of  the  metal  in  tension;  and  D,  the  inside  diameter  of 
the  pipe.  In  the  tables  S  is  taken  as  18000  pounds  per 
square  inch,  with  a  worlcinf?  strain  of  one  flfth  this  amount 
or  3600  pound*:  per  square  inch.     The  formula  for  the 

T200r 
absolute  safe  static  pressure  then  is:  P  =  . 

It  is,  however,  usual  to  allow  for  •*  water-ram  "  by  In- 
creasinjc  tho  thickness  enoueh  to  provide  for  100  pounds 
atiditional  static  pressure,  and,  to  insure  sufficient  metal  for 
good  casting,'  and  for  wear  and  tear,  a  further  increase 

equal  to  .333  (l  -  ^^). 

The  expression  for  the  thickness  then  becomes: 

and  for  safe  working  pressure 

P=^(r-.«»(t-5^))-m 

The  additional  section  provided  as  above  represents  an 
increased  value  under  static  pressure  for  the  different  sizes 
of  pi|^  as  follows  (see  table  in  margin).  So  that  to  test 
the  pipes  ud  to  one  fifth  of  the  ultimate  strength  of  the 
material,  the  pressures  in  the  marginal  table  should  be 
added  to  the  pressure- values  given  in  the  table  above. 


r  = 


Size 

of 

Lbs. 

Pipe. 

4" 

6T6 

6 

476 

8 

346 

10 

3IG 

1:3 

276 

14 

848 

16 

',>28 

18 

)a09 

SO 

396 

Si 

185 

24 

176 

27 

3  as 

80 

356 

88 

149 

80 

14.^ 

43 

J  34 

48 

128 

60 

116 

SHEET-IRON   HYDRAULIC   PIPE, 


191 


SHSBT-IBON  HTJIIRA17I«I€  PIPE* 

(Pel too  Water-Wheel  Co.) 
Weight  per  foot,  with  safe  head  for  varioas  sizes  of  double-riveted  pipe. 


z 

u 

is 

)i 

III 

ife  Head 
in  Feet  the 
Pipe  will 
stand. 

la 

ill 

ife  Head 
in  Feet  the 
Pipe  will 
stand. 

III 

< 

p  ^ 

S 

^ 

< 

3i 

15 

in. 

sq.in. 

B.W.G. 

feet. 

lbs. 

in. 

so. in. 

B.G.W. 

feet. 

lbs. 

3 

7 

18 

400 

2 

18 

854 

16 

165 

16^1 

4 

12 

18 

850 

m, 

38 

254 

14 

258 

ai? 

4 

12 

16 

685 

8 

38 

2.M 

12 

8S5 

27]^ 

5 

a> 

18 

885 

^ 

38 

254 

11 

484 

80 

5 

20 

16 

500 

38 

254 

10 

505 

34 

5 

20 

14 

675 

6 

80 

814 

36 

148 

18 

6 

88 

38 

296 

SO 

814 

14 

227 

28^ 

6 

28 

16 

4S7 

80 

814 

18 

846 

80^ 

6 

28 

14 

748 

7^ 

20 

814 

11 

880 

^ 

T 

» 

18 

251 

5^ 

20 

814 

30 

456 

!• 

W 

16 

419 

69j. 

22 

880 

36 

1.% 

80 

7 

38 

14 

640 

8U 

28 

3KG 

14 

206 

244^ 

8 

SO 

16 

867 

71^ 

28 

880 

18 

816 

82^ 

8 

50 

14 

500 

91^ 

28 

880 

11 

847 

3591 

8 

50 

12 

854 

18 

22 

380 

30 

415 

40 

9 

& 

10 

887 

8^ 

24 

458 

14 

188 

'^ 

9 

63 

14 

499 

1041 

24 

4.V2 

38 

890 

9 

GS 

12 

781 

14H 

84 

458 

13 

318 

SfT 

10 

78 

16 

895 

0^4 

24 

452 

30 

8:9 

43^ 

10 

78 

14 

450 

iis^ 

24 

452 

8 

466 

53 

10 

T8 

12 

687 

1591 

86 

580 

34 

175 

20^ 

10 

78 

11 

754 

17^ 

26 

580 

32 

267 

8H^ 

10 

78 

10 

90U 

JOW 

86 

m) 

33 

294 

42 

11 

95 

16 

869 

9^ 

26 

530 

10 

858 

47 

n 

05 

14 

418 

13 

26 

&30 

8 

432 

57W 

n 

96 

12 

686 

1^ 

88 

616 

14 

168 

31^ 

11 

95 

11 

687 

28 

615 

12 

247 

41^ 

11 

95 

10 

880 

81 

28 

615 

11 

278 

45 

li 

IW 

16 

246 

11^ 

28 

615 

30 

387 

50>4 
61^ 

12 

113 

14 

377 

14 

28 

615 

8 

400 

li 

118 

12 

674 

38W 

80 

706 

38 

231 

44 

li 

113 

11 

680 

199a 

SO 

706 

33 

254 

48 

It 

113 

10 

758 

289l 

80 

706 

30 

304 

54 

n 

\9i 

16 

288 

18 

80 

706 

8 

875 

66 

n 

138 

14 

348 

15 

80 

706 

7 

74 

u 

m 

12 

6H0 

20 

86 

1017 

31 

58 

IS 

138 

11 

688 

28 

86 

1017 

10 

6? 

u 

138 

10 

696 

84^ 

86 

1017 

8 

78 

14 

153 

16 

211 

13 

86 

1017 

7 

bS 

14 

158 

14 

884 

16 

40 

1256 

30 

71 

14 

153 

12 

494 

^ 

40 

1850 

8 

86 

11 

153 

11 

643 

40 

1256 

7 

97 

14 

163 

10 

648 

26 

40 

3256 

6 

108 

15 

176 

16 

197 

!?« 

40 

18r,6 

4 

126 

15 

178 

14 

308 

42 

1885 

10 

74>< 

15 

176 

12 

460 

23 

48 

1885 

8 

91 

15 

176 

11 

507 

24^ 

48 

13W> 

7 

108 

15 

178 

10 

006 

28 

42 

1 885 

6 

114 

I'j 

201 

16 

385 

14^ 

48 

laa-i 

4 

133 

15 

m 

14 

283 

17^ 

42 

138.') 

M 

187 

IS 

801 

12 

4S8 

84^4 

48 

188.'> 

3 

145 

15 

801 

n 

474 

.26^ 

42 

18.S5 

5-16 

177 

IS 

901 

10 

667 

m 

48 

1385 

H 

216 

193 


HATRRIALI. 


8TANBARB  PIPE  FLAIfOBS. 

Adopted  Aufcust.  1804,  at  a  conference  of  committees  of  the  American 
Society  of  Mechanical  Engineers,  and  the  Master  Steam  and  Hot  Water  Fjr- 
ters'  Association,  with  represent atives  of  leadinfc  manufacturers  and  it^rs 
of  pipe.— Trnns.  A.  S.  M.  E..  xxi.  •^.  (The  standard  dimensions  Riven  have 
not  yet,  1901,  Iwi-n  adopted  by  some  nrianufncturers  on  account  of  Uieir  un 
willingness  to  make  n  chan^^e  In  their  patterns.) 

The  list  Is  divided  into  two  grroups;  for  medium  and  hljrh  pres.«nreR,  lh€ 
first  ranfirinir  up  to  76  lbs.  per  square  incli.  and  the  second  up  to  'JOO  lt». 


s. 

2 

4 

« 

7 

8 

9 
10 
12 
14 
15 
10 
18 
JiO 
2-i 
24 
20 
28 
30 

m 

42 

48 


I 


r-f  I 


.409 
.429 
.44S 

.4G0 
.480 
.498 
.525 
.568 
.60 
.639 
.678 
.713 
.79 
.864 
.904 
.946 
1.02 
1  09 
1.18 
1.25 
1.30 
l.:« 
1.18 
1.71 
1.8? 
2.17 


2^^ 

I2H 


31  tl  3l«li24  1 

•1V4  -m  34   -  ■ 

m  ir>^  36 

47„42      429432 

r.J^  \^}i  49^  :i6  1 
h^  r^4^  56      44  I 


the 


2041)  ^^  :i6 
20iH)  14  :i8 
1920  ^4  44^ 
210»H4.')1 

z^'-^UJ^'}^  _^M[;: 

NoTKS.— Siz«^s  up  to  24  inches  are  desipjiied  for  200  Ihs.  or  less. 

Sizes  from  24  to  48  inches  are  dividetl  into  two  scales,  one  for  200  lbs, 
other  for  les.«». 

The  sizes  of  bolts  ^ven  are  for  high  pressure.  For  medium  pressures  the 
diameters  are  ^  in.  less  for  pipe.s  2  10  \H)  \n.  diameter  Inclusive,  and^  in. 
less  for  larger  hizes.  except  4H-jii.  pipe,  for  ^liich  the  size  of  bolt  is  1^  in. 

When  two  lines  of  figures  occur  under  one  hemling,  the  single  ctilumns  are 
for  both  medium  and  high  pressures.  Beginning  with  24  inches,  the  left-hand 
columns  are  for  medium  and  the  right-hand  lines  are  for  hlgli  pressures. 

The  sudden  increase  in  diameters  at  10  inches  is  due  to  the  (X)sslble  inser- 
tion of  wroiight-iron  pipe,  making  with  a  nearly  constant  width  of  g^asket  a 
greater  diameter  desirnble. 

When  wrought-iron  pipe  is  used,  if  thinner  flnnges  than  those  given  are 
surtlcient.  It  is  prop* 've*!  that  bosses  be  use«l  to  bring  the  nuts  up  to  the 
standard  lengths.    This  avoids  the  iir<"  of  a  reinforcement  around  tne  pipe. 

Figures  in  the  S*!,  4th,  5th,  and  last  columns  refer  only  to  pipe  for  high 
pressure. 

In  drilling  valve  flanges  a  vertical  line  parallel  to  the  spindles  should  be 
midway  between  two  lioles  on  the  upper  side  of  tlie  flanges. 


OAST-IROK  PIPE  AND  PIPB  PLAKGES, 


193 


TCBISNSlOIfS  OF  PIPB  FLANGES  AND  CA8T-IRON 
PIPK8« 

(J.  £.  Codman,  Engineers'  Club  of  Philadelphia,  1889.) 


2 
8 
4 
5 
6 
8 
10 
12 
14 
16 
18 
20 
22 
24 
28 
28 
30 
8^ 
81 
86 
88 
40 
42 
44 
46 
48 


PI 


15 


4 
4 
6 
6 
8 
8 
10 
12 
14 
16 
16 
18 
20 
22 
24 
24 
26 
28 
80 
82 
82 
84 
84 
86 
88 
40 


n 


H-ie 


ftae 

1 

1  1-16 
11,6 

11-16 

1  Mtf 

1  11-16 
ll8-16 

2 

2  1-16 


Thickoess 
ol  Pipe. 


Frac.  Dec. 


t-16 
7-16 
15-82 

^\fi 
19-82 
21-82 
11-16 


27-32 

?ii6 

81-82 
1 
1  1-16 

15-82 
1  8-16 

11,6 
11182 


.878 

.896 

.420 

.448 

.466 

.511 

.657 

.603 

.649 

.695 

.741 

.787 

.838 

.879 

.925 

.971 

1.017 

1.063 

1.109 

1.155 

1.201 

1.247 

1.298 

l.J 

1.885 

1.481 


|1& 


6.96 

11.16 

15.84 

21.00 

26.64 

39.86 

54.00 

70  .56 

89.04 

109.44 

131 .76 

156.00 

182  16 

210.24 

240.24 

272.16 

806.00 

841.76 

879.44 

419.04 

460.56 

604.00 

549.36 

696.64 

645.84 

696.96 


4.41 
5.96 
7.66 
9.68 
11  82 
10.91 
23.00 
80.18 
88.34 
47.70 
58.28 
70  00 
88.05 
97.42 
113.18 
180.35 
149.00 
169.17 
190.90 
214.^26 
289.27 
266.00 
294  49 
324  78 
3.^6.94 
391.00 


D  =  Diameter  of  pipe.    All  dimensions  In  inches. 
FoBMULX.— Thickness  of  flange  =  0.033D  +  0.56. 
Thiciiness  of  pipe  ==  0.023Z>  -f  0  827. 
Weight  of  pipe  per  foot  =  0.24I>2  -f  BD. 
Weight  of  flange  =  .001  Z)»  4-  0.1  D«  +  D  -f  2. 
Diameter  of  flange  =  1 .  1252)  +  4 .  25> 
Diameter  of  bolt-circle  =  1 .092D  +  2.666. 
Diameter  of  bolt  s  O.OllD  +  0.78. 
Number  of  bolts  =  0.78D  -f  266. 

PIPB  FLANGES  FOR  CIIGH  8TEAJH-PBE88CBE. 

(Oliapman  Valve  Mfg.  Co.) 


Size  of 

Diameter 

Number  of 

Diameter 

Diameter  of 

Length  of 
Pipe-Thread. 

Pipe. 

of  Flange. 

Bolts. 

of  Bolts. 

Bolt  Circle. 

Inclies. 

Inches. 

Inches. 

Inches. 

Inches. 

r 

V 

0 
6 

g 

6^ 

lit 

m 

9 

7 

,' 

7Jc 

1  7-16 

10 

8 

i 

7?2 

1  9-16 

m 

10^ 

8 

i 

^^ 

1  11>]6 

rT 

9 

\\ 

9Vi 

1  18-16 

18 

10 

^ 

10^ 

i% 

14 

12 

11^ 

1  15-16 

15 

12 

4t 

IS 

2 

16 

18 

2 

14 

2 

10 

mi 

15 

^ 

15V4 

^H 

IS 

20 

18 

^ 

i 

2^ 

14 

88 

18 

1~ 

^n 

U 

28W 

18 

1 

296 

194 


HATERIALS. 


■qooijod 
tpvdjqx 


t 
h 

il 

P 

^=- 

an 


'pvantx 

iJMJO 


i«fc?2SS2^ri^^** ******  ******** 


■adidjo 
•uoiivo 

_:8  a 


iiiiii|yillili|i§§is§igsiissii 


I  if.iuoa 


h|iJ$'4SS2 


-  *- — »"  et  a«»  oe 


^  ^  ^  «  91  e* 


§Hpil§ggS^giii!^ygi§i^i§g|g§ 


i-iMoe^c»Q»7*ioe» 


2:s2»»S5Jesasfess|gg§ 


opwno 

U*tMJ9d 
OdjdJO 

qijfiuri 

'^lovjjns 
9pi«ui 

-)J-t>MJ.)d 

adMjo 


Ui§i§lliliii§l.s§lisri§§§ga§§SS§ 


s^     

Cb  C»  I- lO '«•  00  91  M  Tt  ^  <-•  »^  o 


i5iBS|gmsp;sgss§§$ssp.gssss 


Ifc-TCi*»'9'eo*»©»i-*-i^.-0 


ii 

5  0. 


-jojiuno  ! 
•JKJIwa   I 


i?.isii5Siigii5iaigiig=ii5iigsg 


'*^»e«cieo^ietni.-c»09*^ot- 


3!:::s5:S$?i;SSS$$^SSSSc^ 


'aouajoj 

-lUn34K) 
IVIU9)UI 

JORM9U 
OPIMUI 

•uiiTia 

•PI«»jno 

•UI»|(I 

oppiui 
rroftuox 


|iiil=2SHiSpipgiiigggSggggg 


g  ^  «*>  o  oc  c5  «  e  c»  CO  «  35  (_,  «?S  c  tK  «o  «  w  »  f-  Fi  P- 

^  *     '  1-^  •-^  ^  •-•  c«  91  m '<9^ 'V  to  to  to  {<J  Qc  o»  o  •^  9f  ^  tn  «o  00  ^  or  ^ 


|3S3t3aw„s^„^„^,x 


io<ot»aDa»Oi-io>««^to 


WROUGHT-IRON   PIPE. 


195 


F6r  diflcuaslon  of  the  Brigg^  Standard  of  Wroufcht-lron  Pipe  Dimensions, 
see  Report  of  the  Committee  of  the  A.  B.  M.  E.  in  "  Standard  Pipe  and  Pipe 
Tbreads,''  1886.    Trans.,  Vol.  VIII,  p.  29.    The  diameter  of  tlte  bottom  of 

the  thread  is  derived  from  the  formula  D  —  (0.05Z>  +  1.9)  x  — ,  in  which 

X>  =  outside  diameter  of  the  tubes,  and  n  the  number  of  threads  to  the 
inch.    The  diameter  of  the  top  of  tlie  thread  is  derived  frf)m  the  formula 

0.8—  X  S  +  c2,  or  1.6 f-  d,  ia  which  d  is  the  diameter  at  the  bottom  of  the 

H  n 

thread  at  the  end  of  the  pipe. 

Morris,  Tatker  &  Ou.'s  sixes  for  the  diameters  at  the  bottom  and  top  of 
the  threiid  at  the  end  of  the  pipe  are  as  follows: 


Diam. 

DUm. 

Diam. 

Diam. 

Diam. 

Diam. 

Diam. 

Diam. 

Diam. 

of  Pipe, 

atBot- 

at  Top 

of  Pipe, 

at  Bot- 

at Top 

of  Pipe, 

at  Bot- 

at Top 

Nom- 

torn  of 

of 

Nom- 

tom of 

of 

Nom- 

tom of 

of 

ioal 

Thread. 

Thread. 

inal. 

Thread. 

Thread. 

inal. 

Thread. 

Thread. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

in. 

H 

.384 

.893 

''^^ 

2.0-iO 

2.820 

8 

8.334 

8.534 

.463 

.sa 

8 

8.841 

8.441 

9 

9.887 

9.587 

C 

.668 

.658 

^H 

8.T38 

3.938 

10 

10.445 

10.645 

^ 

.701 

.815 

4 

4.284 

4.434 

n 

11.439 

11.689 

94 

.911 

1.085 

4^ 

4.731 

4.931 

18 

18.488 

18.688 

1 

1.J44 

1.888 

6 

5.890 

5.490 

18 

13.675 

13.875 

iii 

1  488 

i.e«7 

6 

6.346 

6  546 

14 

14.669 

14.869 

IH 

1.7-27 

1.866 

7 

7.310 

7.640 

15 

15.668 

15.b68 

a 

2.£i3 

s.aw 

Having;  the  taper,  length  of  full- threaded  portion,  and  the  sizes  at  bottom 
SfKi  top  of  thread  at  the  end  of  the  pipe,  as  ffiveii  in  the  table,  uips  and  dies 
can  ite  made  to  secure  these  points  correctly,  the  length  of  the  imperfect 
threaded  portions  on  the  pipe,  and  the  length  the  tap  in  run  into  the  fittings 
bt>jrond  the  point  at  which  the  size  is  as  given,  or,  in  otlier  words,  beyond 
the  f  lid  of  the  pipe,  having  no  effect  upon  the  standard.  The  angle  or  the 
thread  is  00*.  aD<i  it  is  slightly  rounded  off  at  top  and  bottom,  so  that,  instead 
of  lU  depth  being  U.866  its  pitch,  as  is  tlie  case  with  a  full  V-t bread,  it  is 
4/5  the  pitcti^  or  equal  to  0.8  -h  n,  n  being  the  number  of  threads  per  inch. 

Ta|»er  of  oooksal  tube  ends,  1  in  88  to  axis  of  tube  =  94  inch  to  the  foot 
total  taper. 


196 


HATfiRtALS. 


WBOVGBV-ntON  WBIiABO  TVBBS,  BXTBA  SniOBrO. 

StandiiWl  IMMenslonii. 


Actual  Out- 

Thickness, 
Extra 

ThtoknesB, 

Actual  Inside 

Actual  Inside 

Nominal 

side 

Ppuble 
Extra 
Strong. 

Diameter, 

Diameter, 

Diameter. 

Diameter. 

Btrong. 

Extra 
Strong. 

Double  Extra 
Strong. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Ihclies. 

'■i  1 

0.405 

0.54 

0.075 

0.100 
O.ltt 

o.m 

0.206 
0.204 
0.421 

: 

s 

^ 

;1 

084 

0.149 

0.208 

0.549 

0.944 

^ 

1.05 

0.167 

0.814 

0.780 

0.499 

1* 

1.815 

0.18^ 

0.804 

0.961 

0.687 

iM 

l.tfO 

0  194 

0.888 

1.279 

0.8M 

iH 

1.9 

0.20.1 

0.400 

1.404 

1.068 

5 

8.875 

0  221 

0.442 

1.988 

1.401 

2^ 

2.875 

0.280 

0.500 

S.815 

1.736 

8 

8.5 

0  404 

0.608 

9.892 

9.9M 

8^ 

4.0 

0.821 

0.049 

8.858 

9  710 

4 

4.5 

0.841 

0.682 

8.818 

8.186 

STANDARD    SIZltS,    BT€«,  OF    IiAP^-WBIitlfiD    CAAB- 
COAIi-IBOlf   BOIIiBtt-TrBBS« 

(Morris,  tasker  &  Co..  Inc.,  Philadelphia,  Pa.) 


1 1.S..VH  ' 
,14.4H:> 
16.4.Vi, 

17.4101 
I1H.4M) 
l»..l«0 


v\ 

^i 

ai 

11 

rf 

r 

|S 

.11 

In. 

In. 

tn. 

.OM 

IMS 

.lus 

.ow 

3.39U 

1977 

.»& 

4.116 

*.7H 

ss 

4.B0I 

5.491 

u.m 

«.«83 

.09f) 

«.472 

7.0W 

.109 

7.I69 

7.8B4 

.109 

7.»:a 

«.S39 

IU9 

8.740 

9.42.'^ 

120 

9AiA 

10.810 

.130 

10.242 

10.99« 

l;M 

11.027 

11.781 

AM 

11.724 

l2.iiM 

.m 

13.205 

14.137 

M% 

U.77X 

l&.7i« 

.m 

17.M13 

l8.RriO 

A^ 

20.954 

21.991 

.i«r. 

24.(J'JC 

2.'5.133 

Am 

27.143 

2«.5.'74 

.'9X\ 

30.141 

31.410 

.«0 

XKAl^ 

34.,'yW 

.«« 

36.2A0 

37  699 

.2** 

».:m.'> 

40.8.1 

.2IK 

42.424 

43.982 

.i>» 

4.^497 

47.124 

.•,»7l 

48.603 

/XI.206 

.•»! 

.'il.623 

M.4(»7 

.W-! 

M.714 

iAM9 

..■WO 

hl.WXt 

.'>9.09« 

330 

B0.821 

02  8.r2 

.a»o 

IWKt: 

0:).974 

1  =  8 

^4 

n^ 

«5| 

i 

Internal 
Aruu 

External 
Are*. 

14 

^'"5 

""TtT" 

4.«7« 

I.I4« 

flq.  In. 

"iSi 

nq.  In   uq.ft, 
^  .785     0065 

IkM 

.90 

.888 

.0061 

1.227      0085 

laoi 

3.0M 

s-aio 

1.18 

1.348 

.0094 

1.707     .0128 

t.916 

8.547 

878S 

1.40 

1.911 

.0133 

«.405 

.0167 

2.448 

2.188 

«.3i6 

1.65 

<87S 

0179 

8.142 

.0218 

2.110 

1.910 

?:?« 

l.tl 

8.833 

.02:u 

8.970 

0276 

1.854 

1.698 

8.16 

4  090 

.0284 

4.909 

.0341 

1.674 

1.628 

-.601 

2.T5 

6.035 

0350 

5  940 

0412 

1.608 

1.889 

1.449 

S.04 

0.079 

.0422 

7.069 

0491 

1.878 

1.278 

1.8S8 

333 

.  7.110 

.0494 

8.290 

.0576 

1.269 

1. 176 

1.228 

:t.96 

8.347 

avto 

9.0n 

0608 

1.172 

1.091 

1.132 

4.28 

9.070 

0672 

11.045 

0767 

1.088 

1.019 

1.064 

4.60 

10  939 

OTCO 

12.500 

0872 

1.024 

.966 

.990 

5.47 

I4.0rt6 

.0977 

16.904 

1104 

.903 

.849 

.876 

6.17 

17.379 

.1207 

19.035 

.1.361 

.812 

764 

.788 

7..VI 

26.2.^ 

.1750 

28.- 74     .1962 

.674 

.087 

.660 

lO.lti 

.'U.942 

2427 

38. 485 1  .2873 

.578 

.546 

.660 

ll.OM 

40.2IH 

.I'209 

50.206,     3491 

.498 

ATI 

.488 

13.65 

58.830 

.4072 

63.617'   .4411 

.442 

.494 

.488 

16.7* 

72.292 

.50V0 

78..'>40|    5454 

.9M 

.388 

.390 

«I.Ot> 

H7.583 

.0082 

95.093,    66m 

.362 

.847 

.855 

25.0a 

104.829 

.7200 

113.0981   .7854 

831 

.318 

.825 

a-.'M 

12:5.190 

.8655 

132.7.8'   .9217 

.305 

.294 

.800 

38.06 

143.224 

.9940 

153  938  l.fl«9( 

.288 

.273 

.878 

36.0a 

104.721 

1.1439 

176.716  1.2272 

.864 

.255 

860 

40.60 

187.071 

1.30:« 

1  «)». 062, 1.390; 

.247 

.230 

.243 

4A.av 

212.000 

1.4727 

1  226.981 1 1.576; 

.232 

.225 

.829 

49.»i» 

2-18.825 

1.6.543 

251.470  1.7671 

.219 

.212 

.816 

M.t« 

28.'i.905 

1.8400 

!  283.629  1.969( 

.208 

.201 

.305 

ee.48 

294.- 75 

2.0443 

314. 159  2.1817 

.197 

.191 

.194 

66.77 

324.291 

2.2520 

;  346.301 

S.4063 

.188 

.182 

.186 

7a.4« 

In  CMtimatintr  the  effective  Ktram-heatiuff  or  boiler  sarface  of  tubes,  the  •urface  in 
contort  with  air  or  gaMe»  of  combustion  (wiielher  internal  or  external  to  the  tubes)  U  to 
be  taken 

For  heatinir  liqnidrt  by  steam.  supcrheatin(r  Ht«>ani.  or  trunsferrlncr  heat  from  one 
liquid  ur  ifOM  to  another,  the  nieun  surface  of  ibe  tubes  Is  to  be  taken. 


BITBTKI>  IBOK  PIPB. 


197 


To  find  the  square  feet  of  surfaM,  S,  tn  a  tob«  of  a  gfrai  length,  L,  in  feet, 
and  diameter,  d,  In  fitches,  multiply  the  length  in  feet  oy  the  diameter  in 

iBelieeaBdliy.Ml&    Or,  8  »  !^^^^  =  .S6l8dL.    For  (he  diameters  in  the 

table  below,  multiply  Ihe  length  in  feet  by  the  flgnres  given  o|»pOsltQ  the 
diameter. 


Inches, 
Diameierj 


Square  Feet 
p«r  Foot 
Xeiigth. 


Inches, 
Diameter. 


Square  Fleet 
TCrFoot 
Length. 


.6890 
.6645 
.7199 
.7864 
.8506 
.9163 
.9617 


Inches, 
Diameter. 


6 
6 

7 
8 
0 

1? 

19 


Square  Feet 
per  Foot 
iiength. 


1.8090 
1.6708 

i.sa^e 

t.0044 

1.6180 
S.87SB 
8.141d 


BIVETED  IRON  PIPB. 

CAbendroth  &  Boot  Mf^.  Co.) 

Sheets  pom^bed  and  rolled,  ready  for  riveting,  are  paclred  in  eonvenient 
form  for  Hliipiiient.  The  following  table  shows  the  iron  and  rivets  required 
fitr  punched  and  formed  sheets. 


Wninbrr  Square  reel  of  Iron 
rvqnlred  to  inalce  ItO  Llneai 
r«cC  PsmdMd  and  Porniod 
She«ta  when  put  tog«th6r. 


Width  of 
La»ltt 
Incfaea 


i 

4 
5 
6 
7 
8 
0 
10 

n 

It 

18 


Sgiu 
Fe< 


90 

116 
160 

Its 

£06 

m 

289 
814 
848 
809 


1,600 
1.700 
1.800 
1.900 
2.000 
2,900 
S,800 
2.400 
2.500 
2,600 
2,700 


Kamber  Square  Peel  of  Iron 
requirM  to  make  100  Lineal 
Feet  l^nohed  and  Funned 
aheeta  when  put  together. 


iMam- 
eteria 
Inches. 


14 
15 
16 
18 
20 
22 
24 
26 


Width  of 
I.Apln 
Inches. 


Sqtian 
Feet. 


807 
426 

4»J 
506 
502 
617 
670 
W5 

rro 

886 


WKIGRT  OF  ONB  $<|VARK  FOOT  OF  SStBEf-IlfcON 
FOR  RIVSTBR  PIPB. 

Thlcknesa  Jij  the  Blrmlncliaiii  TTlre-Gause. 


!to.  of 
Qauge. 

Thick- 
ness ia 
Decimals 
0f  an 
Inch. 

Weight 

Qalrati- 
ised. 

Ko.  of 
Gauge. 

Thick- 
ness hi 
Deoimala 
of  an 
Inch. 

Black. 

Weight 

in  iGs., 

Galvani. 

izc-d. 

S 

SO 

.018 
.012 
.088 
.085 

.80 
1.00 
1.25 
1.56 

.01 
1.16 
1.40 
1.67 

18 
16 
14 
U 

.049 
.065 
.083 
.109 

1.H8 
2.M) 
8.12 
i.\37 

2.1& 

2r 

8.M 

4.78 

198 


HATSBIALS. 


SPIRAIi    RITBTBD    PIPB. 

(Abendroth  &.  Boot  Mfg.  Co.) 


Thickness. 

Diam- 
eter, 
Inches. 

Approximate  Weight 

in  lbs.  per  Foot  in 

Length. 

Approximate  Burst- 
ing Pressure  in  lbs. 
per  Square  Inch. 

B.  w.  a. 

No. 

Inches. 

26 
84 

16 
14 
18 

.018 
.(ha 
.038 
.085 
.049 
.065 
.068 
.109 

8to  6 
8tol8 
8  to  14 
8to24 
8  to  21 
6to84 
8to24 
9to84 

Ib8.rs 

'*  =Hofdiam.inin8. 

"  =  .5       "           *• 

"  =  .6       " 

»*  =  .8       "           " 

"  =1.1       " 

"  =1.4       *• 

860O"   -H     " 
4800"   H-     " 
6400  "   -4-     "         " 
8000  "   ^     " 

The  above  are  black  pipes.    Galvanized  weighs  10  to  80 )( heavier. 
Double  Galvanised  Spiral  Blveted  Flanged  Pressure  Pipe,  tested  to  150  lbs. 
hydraulic  pressure. 


Inside  diameters,  inches.... 

Thickness,  B.  W.  G 

Nominal  wt.  per  foot,  lbs.. . 


81  9 
,8|,8 


13]  14115 
16  14  14 
16'80l28 


80  84 


40  50 


BinBNSIONS    OF    SPIRAL    PIPB    FITTINGS. 


Inside 
Diameter. 


ins. 

8 

4 

5 

6 

7 

8 

0 

10 

11 

18 

18 

14 

15 

16 

18 

80 

88 

24 


Outside 
Diameter 
Flanges. 


Number 
Bolt-holes. 


4 

8 

8 

8 

8 

8 

8 

8 

It 

13 

18 

18 

18 

18 

16 

16 

16 

16 


Diameter 
Bolt-holes.i 


ins. 


11/16 
11/16 


,1/16 


Diameter 
Circles  on 
which  Bolt- 
holes  are 
Drilled. 


ins. 


Sixes  of 
Bolts. 


SBAAILBSS    BRASS    TUBB.      IRON-PIPB    SIZBS. 

(For  actual  dimensions  see  tables  of  Wrought-iron  Pipe.) 


Nominal 
sue. 

Weight 
per  Foot. 

Nom. 
Size. 

Weight 
per  Foot. 

Nom. 
Sise. 

Weight 
per  Foot. 

Nom. 
Siae. 

Weight 
per  Foot. 

Ins. 

\ 

lbs. 
.85 
.48 
.68 
.00 

ins. 

lbs. 
1.85 
1.70 
8.60 
8. 

ins. 
8 

9^ 

lbs. 
4.0 
5.75 
8.80 

10.90 

ins. 
4 

6 

lbs. 

18.70 

18.90 

15.75 

18.81 

BRASS  tubing;  coiled  pipes. 


199 


SSAIHLBSS  DRADTH  BRASS  TUBING. 

(Uandolph  &  Clowes,  Waterbury,  Uonn.) 
Outside  diameter  8/16  to  TH  inches.    ThtcknesB  of  walls  8  to  85  Stubs* 
Gauge,  length  18  feet    The  following  are  the  standard  siaes: 


Lenirth 


14 

13 
13 

n 

12 

n 
u 

12 
IS 
13 
12 


or  Ol*l 
GaUfs?, 


20 
19 
19 
IB 
18 
17 
17 
IT 
17 
Ifi 
10 

la 


IMam-     F^S*"    ^^  Old 
eter.       *^^^'"     tlniige. 


t« 

14 

t« 

14 

13 

IS 

IS 

13 

w 

IS 

n 

lii 

113 

IS 

J  a 

12 

]« 

IS 

12 

12 

IS 

n 

13       J 

11 

OyUlde 
Dlum 
eter. 


Feet. 


n 

J? 

1« 

IS 

!S 

10  to  IS 
10  to  IS 
10  to  IS 
10  to  12 
10  to  IS 
Id  to  IBi 


SlubbB' 
or  Old 


It 
It 
11 
11 
11 
]1 
11 

n 

11 

n 
11 


BBNT   ANB  COILBB   PIPBS. 

(Natioual  Pipe  ijending  Co.,  New  Haren.  Conn.) 
COILS  AND  BENDS  OF  IRON  AND  STEEL  PIPE. 


Siae  of  pipe Inches 

Least   outside  diameter  of 
ooa Inches 

Siae  of  pipe Inches 

Least    outside   diameter  of 
C(^l Inches 


H 


18 


84 


8» 

4 

<H 

5 

6 

7 

8 

9 

10 

40 

48 

S3 

58 

68 

ao 

98 

lOS 

ISO 

18 
156 


Lengths  continuous  welded  up  to  Ji-iu.  pipe  or  coupled  as  desired. 
OOnJB  AND  BENDS  OF  DRAWN  BRASS  AND  COPPER  TUBING. 


Size  of  tube,  outside  diameter Inches 

Least  outside  diameter  of  coil Inches 

Siae  of  tube,  outside  diameter Inches 

Least  outside  diameter  of  coil In<^>e6 


.^ 


H 


J« 


,J« 


.?* 


16 


,^ 


Lengths  continuous  braxed,  soldered,  or  coupled  as  desired. 

90«  BENDS.    EXTRA-HEAVY  WROUGHT-IRON   PIPE. 


Diameter  of  pipe Inches 

Radius Inches 

Centre  to  end Inches 


4 

*H 

5 

6 

7 

8 

9 

10 

72 

84 

86 

80 

36 

48 

48 

60 

S6 

s^ 

31 

86 

43 

60 

37 

70 

30 


The  radii  Ri^cu  are  for  the  centre  of  the  pipe.  *'  Centre  to  end  **  means 
the  perpendicular  distance  from  the  centre  of  one  end  of  the  bent  pipe  to  a 
plane  passing  across  the  other  end.  Standard  Iron  pipes  of  sizes  4  to  8  In. 
are  bent  to  radii  8  in.  larger  than  the  radii  in  the  above  table;  siaes  9  to  18  in. 
to  radii  18  in.  larger. 

Hr elded  Solid  Brawn-sCeel  Tabes,  imported  by  P.  S.  Justice  A 
Co.,  Philadelphia,  are  made  in  sizes  from  W  to  4^  in.  external  diameter, 
Tarying  by  ^ths,  and  with  thickness  of  walls  from  1/16  to  11/16  in.  The 
msTimnm  length  is  16  feet. 


200 


MATERIALS. 


WBIG97  OV   PPASS,  COPPBB,   AND  ZINC   TITBING. 

Per  Foot. 

Thickness  bjr  Brown  &  Sliarpe's  Gauge. 


Copper, 

Brass,  Np.  17. 

Erase,  No.  90. 

LigbtDlnfc-rod  Tutie, 
No.  28. 

iDCta. 

Lbs. 

Inch. 

Lbs. 

Inch. 

Lbfl. 

.\ 

.107 
.157 

A 

.083 
.089 

^1. 

.165 
.178 

% 

.186 

^U 

.068 

% 

.186 
.ill 

7^6 

.884 

.106 

11-16 

^1. 

.906 
.818 

7?f. 

.l'.>6 
.158 

H 

.880 

.883 
.877 

^, 

.189 
.208 

Zino,  No.  30. 

' « 

.4frj 

.890 

1 

.542 
.675 

i 

.2.53 
.284 

^4 

L^ 

.161 

1; 

.740 

1 

.878 

0 

.185 

'i 

.915 

1^ 

.500 

i 

.2*1 

I'S 

.980 

.580 

.2W 

8 

1.90 

1 

811 

•iH 

1.506 

IS 

.380 

8 

2.188 

.452 

LEAP  PIP^  lOr  liBNGTHS  OF  10  FEET. 


Iq. 

8-8  Thick. 

5-18  Thick. 

M  Thick. 

3  16  Thick. 

lb.          oz, 

17             0 
20              0 
28              0 
25              0 

81               0 

lb.       oz. 

It         0 
16         0 
18         0 
21          0 

lb.       oz. 

11         0 
IS         0 

15  0 

16  0 
18         0 
80         0 

lb.       oz, 

8  0 

9  0 

9         6 

»   s  . 

I.EAD  HIFASTE^PIPB. 

l}i  in.,  8  lbs.  per  foot.  I     8Hi  In.,  4  lbs.  per  foot. 

8  "    8  and  4  lbs.  per  foot.  4      "5,  6.  and  8  lbs. 

9  *'   m  and  5  lbs.  per  foot.         f     4^  **    6  and  8  lbs. 

5  in.  8, 10,  and  IsTlbs. 

LEAI>  AND  TIN  TUBING. 

H  inch.  H  inch. 

SHEET  I4EAII. 

Weight  per  scuare  foot,  9U.  8,  8^  4.  i^,  5,  6,  8,  9, 10  lbs.  and  i]p«ttWi& 
Oihei'  weights  rolled  to  order. 

BIiO0K*TIN  PIPE. 

in.,  15,  and  18  os.  per  fool. 


( la  ,  4U,  6H>  and  8  oz.  per  foot. 

i  •*  6,  7j<.  and  10  oz.  ** 

I  ♦*  8  and  10  oz. 

I  '*  10  and  12  oz.       ** 


H4  "  11.4  UHd  lUlbq.  ** 
1^  "  aandawfbi.  ♦♦ 
2     ''   8^and81ba.       *« 


LBAO  PIPB. 


201 


I^BAD  AlfB  TIN-LINKO  liEAB  PIPK. 

(TiMhani  &  Bros.,  New  York.) 

1 

1 

Weight  per 
Foot  and  Rod, 

a  . 

1 

1 

Foot  and  Bad. 

II 

§ 

s 

|2 

3 

^7 

«in. 

£ 

7     lbs.  per  rod 

1     in. 

E 

1^  lbs.  per  foot 

10 

D 

10     oz.  per  foot 

6 

14 

D 

2      "         " 

11 

4i 

C 
B 

12     " 
1    lb.       " 

8 
12 

!! 

0 
B 

11;:    :: 

14 
17 

to 

A 

m "       ** 

16 

«4 

A 

f*  4.    4. 

21 

*• 

AA 

]L^  *i            ** 

19 

II 

AA 

m  ** 

24 

** 

AAA 

194  *'            ** 

27 

** 

AAA 

?•      *4 

30 

7-16  in. 

IS     OB.        " 

l^In. 

E 

2   •» 

10 

*' 

1      lb.         "      ^ 

D 

2K  *' 

12 

Hm. 

E 

0    lbs.  per  rod 

7 

it 

0 

3^ ;;     ;; 

14 

D 

94  lb.  per  foot 

9 

II 

B 

10 

*• 

C 

1      •* 

n 

1: 

A 

4^  **     ** 

19 

** 

B 

IW  **         " 

13 

II 

AA 

5  5 ««     ** 

85 

** 

1)4  **         ** 

14 

AAA 

89a  **          ** 

•* 

A 

1«  •* 

16 

l^in. 

£ 

8       " 

18 

•  4 

AA 

U     " 

19 

.4 

D 

?^"     " 

14 

•* 

«^  ..         - 

^ 

»» 

C 

17 

*> 

AAA 

8     " 

85 

44 

B 

5       " 

19 

Hfn. 

E 

IS      "    per  rod 

8 

»• 

A 

6«  " 

83 

»» 

D 

1     *;   per  foot 

9 

II 

AA 

s"  "        " 

87 

** 

C 

5«  " 

13 

41 

AAA 

Q       "           " 

** 

B 

2     **         »* 

16 

194  In. 

C 

4       " 

iz 

•» 

A 

M^    II                  II 

80 

"^7* 

B 

5    ;;      ;; 

17 

t* 

AA 

294    **                  " 

22 

'♦ 

A 

81 

** 

AAA 

3Vb  **             ** 

25 

«* 

AA 

qlZ  '•          *' 

87 

94  in. 

m 

1     "  perfect 

8 

2     In. 

C 

4^  "         " 

16 

•• 

fi 

1J4  **        '* 

10 

'♦ 

B 

6      *» 

18 

*4 

§ 

]9i   **        *' 

18 
16 

it 

A 
AA 

7      " 
9      " 

28 
87 

«* 

A 

8^1.         II 

80 

41 

AAA 

1194  " 

M 

AA 

8U  *•          " 

88 

M 

AAA 

SO 

WBIGttT  OF  LEAD  PIPK  WH1C0  SH017LB  BE  USED 
FOB  A  GIVEN  BEAB  OF  WATBB. 

(Tatham  &  Bros.,  New  York.) 


H«ador 

Number 

of  Feet 

FaU. 

fretfure 

per 
sq.  inch. 

Calibre  and  Weight  per  Foot. 

Letter. 

9^  Inch. 

^ Inch.  9i  Inch. 

94  inch. 

Itnch. 

lJ4in. 

30ft. 

soft. 
:5  ft. 

100  ft. 
190  ft. 
JOOffc. 

151be. 
85  lbs. 
88  lbs. 
50  lbs. 
75  lbs. 
100  Iba. 

8 

B 

A 
AA 
AAA 

10     OB. 

IS    oz. 
1     lb. 

m  lbs. 

1)2  lbs. 
194  lbs. 

94  lb.    1     lb. 
1     lb.    IHIbs. 
l^lbs.  8     lbs. 
194  lbs.  2Ulb8. 
8    lbs.'  294  lbs. 
3     lbs.  3^  lbs. 

m  lbs. 
194  lbs. 
2^ ,  lbs. 
8     lbs. 
3U  lbs. 
4«lbs. 

8     bs. 

4     lbs. 
494  lbs. 
6     lbs. 

4^rs: 

6     H>8. 
694  lbs. 

To  lliid  ili6  ttilokiiefMi  of  l«a4  pipe  required  ivlieiE  tbe 
]ie«4  or  ir*ter  Is  tfTren.    (Chadwlck  Lead  Works). 

Rtlb.— Multiply  the  head  in  feet  by  sisee  of  pipe  wanted,  expressed  deci- 
maQy,  and  diride  by  750;  the  quotient  will  give  thickness  required,  in  one- 
hunaredtbBOf  an  inch.  ,   ^^ 

IXilltfUt.--«iKa(|tUrM  tblclcneffl  of  half -inch  pipe  for  a  head  of  85  feet. 

SB  X  0.50 -i-7fiOs  0.16  inch. 


202 


MATERIALS. 


II 

I 


A< 

M    i 

^  2  I 

S  '^  ^ 

fi  I  i 

w:  id  Z 

9"! 

S:    § 
S    fe 

9 

Ed 

s 


^<5 


IS 


iJ  »-i  r-l  *       OC 


§ 


^sSisiBii^i^sss^iiiiii  s  s 


j«^„^ 


i«3ZS!§.g§iS§iSI§iiiiii  I 


J«rH«^ 


S^t-SSsS 


II 

8 


I 

6 


riS8SS!S&S«^SZSS3=SSSS8SSS9 


t7 

el 

'I 


I 


^1 


.oeoioeookoo^Q* 


9SSS93r:S9SSSSSS 


liiJ^Psiii^siigiiiiii^ 


o  3 


BOLT  COPPEB— SHEET  AND  BAB  BBASS. 


203 


IHTBIGST  OF  R0171f  B  BOIiT  COPPSB* 

Per  Foot. 


IllCl>€fr 


Pounds. 


.4125 
.7M 
1.18 
1.70 
S.81 


Inches. 


Pounds. 


8.0S 
8.88 
4.73 

6.81 


Incbes. 


Pounds. 


7.M 
9.87 
10.64 
12.10 


WBIGST 

OF    89IHBT 

ANB    BAB    BBAS0« 

Thickness, 

Sheets 

Square 

Bound 

Thickness, 

Sheets 

Square 

Bound 

aide  or 

per 

Barsl 

Barsl 

Side  or 

per 

Barsl 

Barsl 

Diam. 

sq.ft. 

ft.  long. 

ft.  long. 

Diam. 

sq.ft. 

ft  long. 

ft.  long. 

Inches. 

Inchps. 

1-16 

2.7S 

.014 

.011 

1  1-16 

46.82 

4.10 

8.82 

H 

5.45 

.066 

.045 

11,. 

40.06 

4.50 

8.61 

S-i6 

8.17 

.12S 

.100 

61.77 

5.12 

4.02 

e^l. 

10  90 

.227 

.178 

1  5-16 

54.50 

5.67 

4.45 

18.62 

.855 

.8« 

67.22 

6.86 

4.91 

7?f6 

16.85 

.510 

.401 

il... 

60.05 

6.86 

5.80 

19.07 

.096 

.645 

68.67 

7.60 

5.89 

,^6 

21.80 

.907 

.712 

It,. 

66.40 

8.16 

6.41 

24.52 

1.15 

.902 

68.12 

8.86 

6.95 

ll56 

27.25 

1.42 

l.ll 

1^ 

70.85 

9.60 

7.58 

29.97 

1.72 

1.85 

l7l-16 

78.57 

10.84 

8.18 

1^6 

82.70 

3.04 

1.60 

lis-ia 

76.80 

11.12 

8.78 

85.42 

8.40 

1.88 

79.02 

11.98 

0.86 

1536 

88.15 

3.78 

3.18 

^% 

81.75 

12.76 

10.01 

40.87 

8.19 

2.90 

1  15>16 

84.47 

18.68 

10.70 

1 

48.00 

8.68 

2.85 

2 

87,20 

14.52 

11.40 

COHPOSmOlf   OF   VABIOTT8  GBADB8  OF  BOLIiBB 
BBASS,   BTC. 


Trade  Name. 

Copper 

Zinc. 

Tin. 

Lead. 

Nickel. 

fVifnmnn  liiirh  bnuR 

61.5 
60 

60 
60 

88.5 
40 

40 
40 

Teliow  in4*Ml 

OartrMge  brass.  ................... 

Low  brass ........r......  ......rt 

Clock  brasB 

"iii" 

.«'S« 

Drill  rod.  

Spring  brass. 

18  per  cent  German  slWer 

18 

The  above  table  was  furnished  bj  the  superintendent  of  a  mill  in  Connec- 
ticut in  1894.  He  sajrs:  While  each  mill  has  Its  own  proportions  for  various 
mixtures,  depending  upon  the  purposes  for  which  the  product  is  intended, 
the  figures  gvven  are  about  the  average  standard.  Thua«  between  cartridge 
brass  with  3^  per  cent  zinc  and  common  high  brass  with  88U  per  cent 
sine,  there  are  any  number  of  different  mixtures  known  general^  as  **  high 
brass/*  or  speeiflcally  as  "spinning  brass,''  ** drawing  brass/'  etc.,  wherein 
the  amount  of  cine  Is  dependent  upon  the  amount  of  scrap  used  in  the  mix- 
ture, the  degree  of  workmg  to  which  the  metal  is  to  be  subjected,  etc. 


204 


ICATBRIALS. 


ARISBlOAlf  BTANSABll  8tSE8  #9  BROP^HOT. 


^i 

^S 

if 

Diameter. 

^1 

Diameter. 

^1 

DIam. 
«ter. 

4^ 

No.  8 

^5 

igS 

Fine  Dust. 

a-100" 

10784 

Trap  Shot 
9-100" 

471 

No.  a.... 

15-100" 

86 

Dust 

4-100 

4>(» 

"    8 

89f 

"  1..  . 

W-100 

71 

No.  IB 

5-100 

ai26 

"    7 

Trap  Mtot 

838 

"    B... 

17-100 

59 

"    11.  ... 

5-100 

Trap  Shot 
7-100" 

1H6 

••    CllO-lOiK' 

^ 

•*    BB. 

ie-100 

50 

"    10 

I'ttO 

"    6  11-100 

"    BBB 

19-100 

4i 

**    10 

848 

«•    6: 12-100 

J68 

'•    T.  . 

20-100 

96 

"     0 

Trap  Shot 

688 

"  4ia-ioo 

18-2 

"    TT.. 

21-100 

31 

"     8 

MS 

«  a  14^00 

1M 

"   P.. 

t:MOO 

27 

1 

"    FF.. 

2S-10Q 

94 

COntPRESSBD  Br€K-«ROT. 

Diameter. 

No-ofBallB 
to  the  lb. 

Diameter. 

No.  of  Balls 
to  the  lb. 

Ko.  8  ■ .-. 

"    2 

25-100" 
87-100 
:8a-l00 
i82-100 

284 

m 

Its 

140 

No  00 

"    000 

Balls 

84  100" 
C6-100 
88-100 
44.100 

•s 

•*    1 

ift 

*  a.::...:. 

50 

8CRIBW-11BBEA1M)  8ELLBRS  9U  IT.  S.  STAl|iRAlil». 

It  1804  a  comtiilttee  of  the  FrttnkliQ  Imititute  recofnmendrd  the  adca>tion 
6f  ^e  system  of  screvv-threads  and  bolts  which  was  Revised  bv  Mr.  w<niiani 
Sellers,  of  Pbiladolphia^  This  same  system  was  subseQuentW  adopted  af 
the  Btatdard  by  both  the  Army  and  Navy  Detartmenta  or  the  united  States, 
a-Dd  by  the  Master  Mechanics'  and  Master  Car  Builders*  Asseciatlona,  so 
that  it  teay  how  be  regarded,  and  ia  fact  Is  called,  the  United  States  Stan* 
dard. 

Tlie  rule  ghren  by  Mr.  Setlerti  for  proportioning  the  thread  is  as  follows : 
Divide  the  pitch,  or,  w<hat  is  the  same  thiagr*  the  side  of  the  thread,  into 
.eight  e^ual  parU;  take  off  one  part  from  the  top  and  All  in  one  part  in  thA 
bottom  of  the  thread;  then  the  flat  top  and  bottom  will  equal  one  eighth  of 
the  pitch,  the  wearing  stirface  will  be  three  qiiartei-s  of  the  pitch,  and  the 
diameter  ol  screw  at  bottom  of  -the  thivad  will  be  eKprattfd  br  Mm  /^r 
nmla 

1  299 
diameter  of  bolt  —  ; 


For  a 


no.  threads  per  inch 
V  thread  'wl«h«agle  df  00*  the  formula  is 

diameter  of  bolt  —  • 


no.  of  threads  per  inah 
The  afeigle  of  dhe  thread  in  the  Sellers  system  is  60*.    In  the  Wbitirorth  or 
English  system  it  is  56°,  and  the  point  and  root  of  tlie  tbpi»ad  ara  rounded. 
Sere w-Threaaa,  United  States  StandaHl, 


^16 


Ci« 


lT-16 


20 
18 
16 
14 
18 
12 
11 
11 


18-16 

15-16 

1 

1  1-16 

1^ 


10 
10 
0 
0 
8 
7 
7 


.s 

Q 


7 
6 
6 
6 

6 


s 

3 


15-16 


I 


2  18-16 
8 

85-18 


V.  S.  OR  SELLERS  aYSTEM  OP  SCREW-THREADS.     300 


9m 

mw«TIwmUU,  Wliltwovtb  (BiwUtll)  fiUliAlirtf 

f 

1 

1 

1 

iC 

n 
11 

10 

1 

1 

1 

1 

1 

1 

1" 

18 

8 
If 

t 
0 

5 
4 

8 
8Vi 

f 

S?1« 

13 

1?-16 

9 

li, 

5 

aU 

3^ 

BOLTS  AMD  THREADS. 


UaaT  GAU6KS  FOH  IRON  P09  9€1^|SW  TUUMA^f^. 

In  AdepliVg  (lie  9e)l«f9,  or  FrankUn  Iu«titato,  or  Uniua  States  Standard, 
w  it  ip  variOfMlT  ClMJl<9a,  a  (liffiKnilty  ai'oee  f i  ona  the  fact  that  it  is  l))e  babk 
«f  iisp  mpwx^WW^  U>  miftl^e  iron  oyer-ai^,  and  aq  th#ro  ar«  no  0¥9r-ai8a 


206 


MATERIALS. 


screws  in  the  Selleni  ssrstem,  If  Iron  is  too  lar^e  it  Is  necenary  to  cut  it  away 
with  the  dies.  So  great  is  this  diflBculty,  that  the  practice  of  making  tafx 
and  dies  over-sixe  lias  become  very  general.  If  the  Sellers  system  is  adopted 
it  is  essential  that  iron  should  be  obtained  of  the  correct  size,  or  very  nearly 
so.  Of  course  no  high  degree  of  precision  is  possible  in  rolling  iron,  and 
when  exact  sizes  were  demanded,  the  question  arose  how  much  allowable 
Tariatlonjthere  should  be  from  the  true  size.  It  was  proposed  to  make  limit- 
gauges  for  inspecting  iron  with  two  openings,  one  larger  and  the  other 
smaller  than  the  standard  size,  and  then  specify  that  the  iron  should  enter 
the  large  end  and  not  enter  the  small  one.  The  following  table  of  dimen- 
sions for  the  limit-gauges  was  recommended  by  the  Master  Car-BuUders* 
Association  and  adopted  by  letter  ballot  in  1888. 


Size  Of 

Size  of 

Size  of 

Size  of 

Size  of 

Large 

Small 

Differ- 

Size of 

Large 

Small 

Differ- 

Iron. 

End  of 

End  of 

ence. 

Iron. 

End  of 

End  of 

ence. 

Qauge. 

Gauge. 

Gauge. 

Gauge. 

^in. 

0.8550 

0.3450 

0.010 

^in. 

0.6880 

0.6170 

0.016 

6l|6 

0.8180 

0.8070 

0.011 

» 

0.7586 

0.7415 

0.017 

7?f. 

0.8810 

0.8690 

0.012 

jI 

0.8840 

0.8660 

0  018 

0.4440 

0.4810 

9.013 

1 

1.0005 

0.0905 

0.019 

^. 

0.60T0 

o.4ino 

0.014 

v.i 

1.1850 

1.1160 

o.oao 

0.6700 

0.5660 

0.015 

m 

1.2605 

1.2895 

Q.Oil 

Caliper  gauges  with  the  above  dimensions,  and  standard  reference  gauges 
for  testing  them,  are  made  by  The  Pratt  &  Whitney  Co. 

THE    nAXUHUJH    VARIATION    IN    8IZR    OF    ROUGH 
IRON  FOR  17.  S.   STANDARD  ROLTS. 

Am.  MacK,  May  IS,  1892. 

Bv  the  adoption  of  the  Sellers  or  U.  H.  Standard  thread  tapnand  dies  keep 
their  Hize  much  longer  in  use  when  flatted  in  accordance  with  this  system 
than  when  made  .sharp  "V,'*  though  it  has  been  found  advisable  in  practice 
in  most  cases  to  mnke  the  taps  of  somewhat  larger  outside  diameter  than 
the  nominal  sfz**,  thuK  carryuig  the  threads  further  towards  the  V-shape 
and  giving  corresponding  clearance  to  the  tops  of  the  threads  when  iu  the 
nuts  or  tapped  holes. 

Makers  of  taps  and  dies  often  have  calls  for  taps  and  dies,  U.  S.  Standard. 
"  for  rough  Iron." 

An  examination  of  rough  Iron  will  show  that  much  of  it  is  rolled  out  of 
round  to  an  amount  exceeding  the  limit  of  variation  in  size  allowed. 

In  view  of  this  it  may  be  desirable  to  know  what  the  extreme  variation  in 
iron  may  be,  consistent  with  the  maintenance  of  U.  S.  Standard  threads,  i.e.« 
threads  which  are  standard  when  measured  upon  the  angles,  the  only  plac«> 
where  it  seems  advisable  to  have  them  fit  closely.    Mr.  Chas.  A.  Bauer.  Uie 

general  manager  of  the  Warder.  Biishnell  A  Glessner  Co.,  at  Sprinsfleld, 
hio,  in  1884  adopted  a  plan  which  may  be  stated  as  follows:  AH  bolts, 
whether  cut  from  rough  or  finished  stock,  are  standard  size  at  the  bottom 
and  at  the  sides  or  angles  of  the  threads,  the  variation  for  flt  of  the  nut  and 
allowance  for  wear  of  taps  being  made  in  the  machine  taps.  Nuts  are 
punched  with  holes  of  such  size  as  to  give  85  per  cent  of  a  full  thread,  expe- 
rience showing  that  the  metal  of  wrought  nuts  will  then  crowd  into  the 
threads  of  the  taps  sufficiently  to  give  practically  a  full  thread,  while  if 
punched  smaller  some  of  the  metal  will  be  cut  out  bv  the  tap  at  the  bottom 
of  the  threads,  which  is  of  course  undesirable.  Machine  taps  are  made 
enough  larger  than  the  nominal  to  bring  the  tops  of  the  threads  up  sharp, 
plus  the  amount  allowed  for  flt  and  wear  of  taps.  This  allows  the  iron  to 
oe  enough  above  the  nominal  diameter  to  bring  the  threads  up  full  (sharp) 
at  top,  while  if  it  is  small  the  only  effect  is  to  give  a  flat  at  top  of  threads  ; 
neither  condition  affecting  the  actual  size  of  the  thread  at  the  point  at  which 
it  is  intended  to  bear.  Limit  gauges  are  furnished  to  the  mills,  by  which  tho 
iron  is  rolled,  the  maximum  size  being  shown  in  the  third  column  of  the 
table.  The  minimum  diameter  is  not  given,  the  tendency  in  rolling  bein|^ 
nearly  always  to  exceed  the  nominal  diameter. 

In  making  the  taps  the  threa<1ed  portion  is  turned  to  the  size  given  in  the 
eighth  column  of  the  table,  which  gives  6  to  7  thousandths  of  an  Inch  allow- 
Uice  for  fit  and  wear  of  tap.    Just  above  the  threaded  portion  of  the  tap  a 


SIZES  OP  8CRBW-THBBAD8  FOR  BOLTS  AND  TAPS.  207 

place  is  tamed  to  the  size  giveii  In  the  ninth  column,  these  sizes  befne  the 
same  as  Uioee  of  the  regular  U.  S.  Standard  bolt,  at  the  bottom  or  the 
thread,  phis  the  amount  allowed  for  fit  and  wear  of  tap  ;  or,  in  other  words, 
d'  =  U.  S.  Standard  d  +  (IX  -  D).  Gauses  like  the  one  in  the  cut.  Fig. 
7i^  are  fumlslied  for  ihis  sizing:.    In  flnlBbing  the  threads  of  the  tap  a  tool 


Fig.  7a. 
is  oaed  which  has  a  removable  cutter  finished  aocurately  togauge  bj  grind- 
ing, this  tool  being  correct  U.  8.  Standard  as  to  angle,  and  fULt  at  the  point. 
It  is  fed  <n  and  the  threads  chased  uutil  the  flat  point  just  touches  the  por- 
tion of  the  tap  which  has  been  turned  to  size  a'.  Caj*e  having  been  taken 
with  the  form  of  the  tool,  with  its  grinding  on  the  top  face  (a  fixture  being 
{HDvided  for  this  to  insure  its  being  ground  properly),  and  also  with  the  set- 
ting of  the  tool  properly  in  the  lathe,  the  result  is  that  the  threads  of  the  tap 
are  correctly  sized  without  further  attention. 

It  is  evklent  that  one  of  the  points  of  advantage  of  the  Sellers  system  Is 
sacrificed,  i.e.,  instead  of  the  taps  being  flatted  at  the  top  of  the  threads 
they  are  sharp,  and  are  consequently  not  so  durable  as  they  otherwise  would 
be ;  but  practically  this  disadvantage  is  not  found  to  be  serious,  and  is  far 
overbalanced  by  the  greater  ease  of  getting  iron  within  the  prescribed 
Umiu  ;  while  any  rough  bolt  when  reduced  in  size  at  the  top  of  the  threads, 
by  filing  or  otherwise,  will  fit  a  hole  tapped  with  the  U.  S.  Standard  hand 
taps,  thus  affording  proof  that  the  two  kinds  of  bolts  or  screws  made  for  the 
two  different  kind^  of  work  are  practically  interchangeable.  ])y  this  system 
i"  iron  can  be  .000"  smaller  or  .0106"  larger  than  the  nominal  diameter,  or, 
in  other  words.  It  may  have  a  total  variation  of  .01A8",  while  iy*  iron  can  be 
.0106"  smaller  or  .oaolK'  larger  than  nominal— a  total  variation  of  .0414"— 
and  within  these  limits  it  is  found  practicable  to  procure  the  iron. 

«TAlfl»AIt]>  SIZES  OF  SCRBIV-THBKADS  FOB  BOIiTS 
AND  TAPS. 

(Chas.  a.  Bapkr.) 


1 

8 

8 

4 

5 

0 

7 

8 

9 

10     ' 

A 

n 

D 

d 

h 

/ 

Iiches. 

D' 

d' 

H 

Inches. 

Inches 

Inches. 

Inches. 

Im*he». 

Inches. 

Inches. 

^. 

xo 

.2606 

.1855 

.0J»79 

.oo«--» 

.006 

.2668 

.1915 

.2024 

18 

.3845 

.2408 

.0421 

.0070 

.006 

.3805 

.2468 

.2589 

H 

16 

.«85 

.«9iW 

0174 

.0078 

.006 

.8945 

.2996 

.3189 

7-\6 

14 

.4.'M0 

.844? 

.0511 

.on«o 

.006 

.4590 

.8507 

.3670 

H 

13 

.51(50 

.4000 

.05W 

.0096 

.OOrt 

.6220 

.4060 

.4286 

»^« 

ite 

..•MW, 

.4518 

.Ol«Jl 

.0104 

.007 

.5875 

.4018 

.4802 

H 

11 

.0447 

.rxm 

.OrtRQ 

.0114 

.007 

.6517 

.5189 

.6846 

H 

10 

.7717 

.O-JO! 

.0:58 

.0125 

.007 

.7787 

.6871 

.6499 

9 

.8091 

.;807 

.084-i 

0180 

.007 

.9061 

.7877 

.7680 

r 

8 

1  0271 

.8:i7« 

.0047 

.0!5« 

.007 

1.0341 

.8446 

.8731 

i¥. 

7 

1.1M9 

WW* 

.lOKS 

.0179 

.007 

1.1689 

.M64 

.9789 

iS 

7 

1.2809 

1.0644 

.1088 

0179 

.007 

1.2879 

1.0714 

1.1089 

A  -  nominal  diameter  of  bolt. 

3165 

D  =  aetual  diameter  of  bolt. 

D-A+    ^^   . 

d  =  dUmeter  of  bolt  at  bottom  of 

d^A^'"^. 

thread, 
n  =  number  of  threads  per  Inch. 

.       .7577      i)  -  <f 
^-     n     -       2 
^      .125 

/=  flat  of  bottom  of  thread. 

h  =  depth  of  thread. 

^=ir- 

ld'  = 
lolei 

3  dlame 
in  nut  be 

tersofti 
>f  ore  tap 

tp. 

ping. 

H 

=  !>'- 

^- 

y-.85a 

UL) 

208 


MATERIALS. 


STANDARD  SKT-SCBBWS  AND  GAP«B€RBW8« 

Americau,  Hattford,  and  Worcester  Machine-Screw  Companies. 
(Compiled  by  W.  8.  Diz.) 


Diameter  of  ScrAW. . . . 

Threads  per  Inch 

Sisse  of  Tap  Drill* 


(A) 
No.  48 


(B) 

S4 

No.  80 


(C) 


No.  5 


(D) 
5-16 
18 

ir-w 


(E) 

!^ 

31-64 


(F) 

7-16 

14 

% 


(Q) 


Diameter  of  Sci-ew.. 
Thi-eac)8  per  Inch. .. 
Size  of  Tap  Drill*... 


(H) 

9-16 

12 

31-64 


(I) 
17-8i 


(J) 
21-32 


(K) 
49-61 


(L) 
1 
8 
% 


(M) 

'I* 

68-64 


(N) 

ij4 


Set  Screws. 


of  Hem  I  of  Head 


iC\    H 

JJ5 

(Dt  5-ia 

Ji 

It)  M 

.53 

(F>  7™tt 

,f?i 

i,Qj   ^ 

.71 

H;9^C 

M 

d>    % 

.89 

3.(« 
I  'i4 

(L}  r 

1.4> 

(M)  1^ 

!.&> 

IN)    lis 

1-77 

Round  and  Filister  Head 
Cap-screws. 


Flat  Head  Cap-screws. 


Button -head  Cap- 
screws. 


DIsm.  of 
Head. 


(A) 
(B) 
(C) 
(0) 
it) 
(F) 

(K) 


3-16 


16 
9-16 

^ 

13-16 

1^ 


Lengths 

(under 

Head). 


Diam.  of 
Head. 


K 


13-t6 


Lengths 

(including 

Head). 


biam.  of 
Head. 


7-82  (.221 
5-16 
7-16 
9-16 
% 

13^16 

15-16 

1 


Lengths 
(under 
Head). 


*  For  cast  iron.    For  numbers  of  twist-drills  see  p.  29. 

Threads  are  U.  S.  Standard.  Cap  screws  are  threaded  H  length  up  to  and 
Including  T'diam.  x  4"  long,  an»l  V6  It'ugth  above.  Lengths  increatce  by  ^" 
each  regular  size  between  tlie  limits  given.  Lengths  of  headH,  except  flat 
and  button,  equal  diam.  of  screws. 

The  angle  of  the  cone  of  the  flat  head  screw  is  76*,  the  sides  making  angleg 
of  5^  with  the  top. 


8TAKDARD  MAOHIHE  BGBEW8. 
STANDARS  9EACHINE  8CBEW8. 


209 


No. 

Threads  Der 
Inch. 

Diam.  of 
Body. 

Diam. 
of  Flat 
Head. 

Diam.  of 
Round 
Head. 

Dfam.  of 
Flllster 
Head. 

LeDgtbs. 

From 

To 

2 

66 

.0842 

.1681 

.1644 

:i^ 

8-16 

H 

8 

46 

.0078 

.1804 

.1786 

»-l6 

ll 

4 

82,86,40 

.1105 

.2158 

.2028 

.1747 

8-16 

1 

6 

»  8ft  40 

.1288 

.9421 

.2270 

.1966 

8-16 

% 

9 

30,82 

.1388 

.2684 

.2512 

.2175 

8-16 

1 

7 

80  8;) 

.ISOO 

.2047 

.trtA 

.2892 

^H 

8 

80,88 

.1631 

.8210 

.8086 

.2610 

o 

iS 

9 

S4.80.82 

.1:68 

.8474 

.8^288 

.2805 

h 

vl 

10 

24.  d0,ft( 

.1804 

.87«7 

.8480 

.8085 

h, 

'1 

12 

20,24 

.2136 

.4288 

.3928 

.8449 

1 

111 

14 

20,24 

.2421 

.4790 

.4864 

.8888 

'1 

2 

IB 

16.  18,  90 

.2684 

.5816 

.4866 

.4800 

'1 

16 

16,18 

.2047 

.584-2 

.5248 

.4710 

4 

214 

20 

16,18 

.8.il0 

.8808 

.5690 

.5900 

294 

« 

16,12 

.^H 

.0894 

.8106 

.8567 

J 

8 

24 

14.  16 

.87^ 

.7430 

.6522 

.0005 

1^ 

8 

» 

14,16 

.4000 

.74^ 

.6988 

.6425 

'  % 

8 

« 

14.16 

.4J63 

.7946 

.7854 

.6920 

12 

8 

ao 

14,  16 

.45:30 

.81^3 

.7T70 

.7240 

1 

3 

Lenirths  varj  bj  lOths  from  8>16  to  ^,  by  Sths  from  H'to  l^,  by  4ih8  from 
iHtoS. 

8ISfe£8  ANli  WJ610BTS   OF  SOlJAlftB  AND 

0E3LAGONAli   Num. 

rnltea  llMites  Stanclard  fltsea.    Gkainfereji  and  tHmmed. 

Panebed  to  salt  IT,  8.  Standard  Yap*. 


Square. 


1.04 
1.48 
1.72 
2.27 
2.94 
8.33 
4.35 
5.26 
8.83 
fl.ll 
18.64 


Hexagon. 


1" 
^1 


7615 
5200 
800O 
2000 
1430 

iioo 

740 

450 

309 

216 

148 

HI 

85 

68 

56 

40 

87 

29 

21 

16 

11 


h 


.0181 

.0192 

.0838 

.aM) 

.070 

Ml 

.135 

.222 

.324 

.468 

.676 

.901 

1.18 

1.47 

1.79 

250 

270 

3.45 

4.76 

6.67 


9.09 
11.76 


210 


MATERIALS. 


Q 


M 


0    o 


o 
o 

O 


"'   U  :  :  ;  :  ■  ■  ib--i;!tl®i:^S?g«ii^¥?|^t7^r?ll 

1" 

2^    S  ;  :  :i5lsS^esi^^S5;:^iS3itiS?^Sii=.g|^5i 

^  |i  :  :  :g|S^^iiig^iS§iiisii£i 

?SzM^i 

^  j|:HSSgSgS§l§iSISii^SSI 

MM 

1      .     ']-t:i:X}0'7'fi'tSi9t7f*^aQ'^^7'QOOOOOOOOOOQ5SO 

^'  jl  :i^gr?!g§35iE5SS=;|jlilrIiiSSi?il*^l§ 

1      .C'TliJCi^^CiT.  qirt?*K^«C4''CT>T-tP']tC:'i*^O^CCOOO 

1    ^oci"MJinii-oi^Mf»x>cJOOi»«sFn^r^3*roi<;oir:oooo 

-i  llfeg^^s5ss^t:?j:^?s^i;i;5?-^§^^siigi 

tp           .  o  O  QJ  -*  t-  O  H3  s  CI  5*  .r.  x-  ^-  .-r:  rp  r..  t  -  .     ■.  ?  -  -    -    _  =:  O  C 

^       1     ,'-r^o^ic.^7*ag!r'j'u-T*i"ClOinOiCC}*iCnrtC*^^  = 

S5SI 

- 

-:- 

- 

- 

:- 

I'll—             <-  — , — ^  —  ^  ^  ^^  . 

:  i  ; 

^       f     «  »  ®  -^  S>  Ofc  <J  1^^  C^  t  -  -T  -^  ii;  1.T  t*      _      ■      •      ;      ^      ;      ■ 

;  :  : 

«"§     =  J"    :?    J*    3!    ^    J?    LR 

J  ;  :  3 

^ 

- 1 

31 

a    j^j: 


TRACK  BOLTfl. 

'WlCb  fTnlCed  State*  Standard  0exacoii  Nuts. 


Rails  used. 


45to851b0... 


aoto 


40  lbs...  I 


aotoaoibs. 


Bolts. 


x3 


Nuts. 


No.  in  Keg, 
900  lbs. 


2S0 
240 
264 
260 
260 
268 

375 
410 
435 
466 

715 
760 
800 
8;iO 


Kegs  per  BiUe. 


6.3 

6. 

6.7 

6.5 

6.4 

5.1 

4. 

8.7 
8.8 
8.1 

2. 
2. 
8. 
2. 


KIVETS — ^TUBKBUCKLES. 


211 


€01fE-HEAI>  BOILER  RIVETS,  TITEIGHT  PER   100. 

(Hoopes  Sc  Townsend.) 


Scant. 

1/S 

9/16 
lbs. 

5/8 

11/16 

H 

18/16 

% 

1 

1^* 

IM* 

I^enRth. 

lbs. 

n>8. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

fi'mch 

8.7B 

18.7 

16.80 

,^ 

M 

0.86 
10.00 

14.4 
15.8 

17.28 
18.85 

81.70 

86.66 

^H 

•• 

10.70 

16.0 

19.88 

83.10 

88.00 

i?l 

•• 

11.40 

16.8 

90.81 

84.50 

29.45 

87.0 

46 

60 

11) 

4» 

18.10 

17.6 

21 .34 

25.90 

80.90 

88.6 

48 

68 

95 

IV. 

t< 

IS.W 

18.4 

28.87 

87.80 

82.36 

40.2 

50 

66 

08 

188 

}% 

*• 

18.50 

19.8 

88.40 

88.70 

33.80 

41.9 

62 

67 

lot 

187 

iH 

M 

14.90 

20.0 

84.48 

30.10 

85.85 

48.6 

64 

69 

104 

141 

i4 

44 

14.90 

80.8 

85.46 

31.50 

86.70 

46.8 

56 

71 

107 

145 

8 

(k 

15.60 

81.6 

86.49 

82.90 

38.15 

47.0 

68 

74 

no 

149 

•• 

16.80 

88.4 

87.58 

34.80 

80.60 

48.7 

60 

114 

158 

2^ 

(t 

17.00 

83.8 

28.56 

35.70 

41.05 

50.3 

62 

80 

118 

157 

2t2 

♦• 

17.70 

84.0 

89.58 

37.10 

48.60 

61.9 

64 

83 

121 

161 

2C4 

•• 

18.40 

84.8 

80.61 

38.60 

48.96 

63.5 

66 

86 

184 

165 

wZ 

»» 

19.10 

85.6 

31.64 

39.90 

46.40 

66.1 

68 

89 

187 

169 

S9i 

•  » 

19.80 

86.4 

88.67 

41.80 

46.85 

66.8 

70 

92 

180 

178 

2^ 

** 

ao.so 

87.8 

83.70 

48.70 

48.90 

68.4 

72 

06 

188 

177 

8^ 

*♦ 

81.90 

88.0 

84.78 

44.10 

49.75 

60.0 

74 

98 

137 

181 

•  * 

28.60 

89.7 

86.79 

46.90 

58.66 

63.8 

78 

103 

144 

189 

3^  1 

•  « 

84.00 

81  5 

88.8.') 

49.70 

65.55 

66.6 

88 

108 

151 

197 

3^ 

•• 

85.40 

83.8 

40.91 

52.50 

58.45 

69.8 

86 

118 

158 

205 

4 

•4 

86.80 

85.8 

48.97 

55.30 

61.85 

780 

90 

118 

165 

218 

4« 

88.90 

86.9 

45.08 

68.10 

64.86 

76.3 

04 

124 

178 

221 

4^ 

M 

89.60 

88.6 

47.09 

60.90 

67.15 

79.5 

98 

130 

179 

229 

^9% 

•• 

81.00 

40.8 

49.15 

63.70 

70.05 

88.8 

102 

136 

186 

237 

5 

«• 

38.40 

48.0 

51.81 

66.50 

78.95 

86.0 

106 

142 

193 

845 

5^ 

44 

ai.8o 

48.7 

53.27 

69.20 

7^.85 

89.3 

110 

148 

200 

254 

5^ 

4« 

35.90 

45.4 

55.33 

72.00 

78.75 

92.5 

114 

154 

206 

268 

fi^ 

•  • 

86.60 

47.1 

57.39 

74.80 

81.05 

96.7 

118 

160 

812 

272 

6 

*• 

8M.0O 

48.8 

59.45 

77.60 

84.56 

99.0 

122 

166 

818 

281 

«H 

** 

40.80 

58.0 

63.67 

88.30 

00.86 

105.6 

180 

177 

831 

297 

*t 

48.60 

65.8 

C7.69 

88.90 

96.15 

112.0 

138 

188 

845 

814 

Heads 

6.50 

8.40 

11.60 

18.20 

18.00 

28.0 

29.0 

88.0 

56.0 

77.5 

*  These  two  sizes  are  calculated  for  exact  diameter. 
RiTets  with  button  heads  weigh  approximately  the  same  as  cone-head 
riTets. 

TfTRNRrCKIiEl. 

(Cleveland  Citj  Forge  and  Iron  Co.) 
Standard  sizes  made  with  right  and  left  threads.    D  : 


outside  diameter 


j-B  -^ — A—^-B-^ 

Fio.  78. 


of  ncrew.    A  =  lengrth  in  clear  between  heads  =s  6  ins.  for  all  sizes, 
length  of  tapped  heads  =  ly^D  nearly.    L  =  H  ins.  +  3D  nearly. 


B  = 


318 


iJiTWIALS, 


SIXE9  OF  WXSf9VM9, 


Diameter  in 
kiclies. 


SIse  of  Hole,  in 
Incliefl. 


5-15 

i^ii 
?f.i6 

18.-16 
81-fti 


ThiokneM, 
Btrmloffbam 
Wire-gauge. 


Ko.  16 
**  16 
••  14 
"  11 
•'  11 
•*    11 


6 
6 

7 
6 


Bolt  In 
iucheg. 


No.  in  100  lbs. 


89,800 
18,000 
7,600 

iaoo 

i,180 

S.SSO 

1,680 

1,140 

680 

476 

860 

860 


TBAC^  BFIl^BS* 

BaB0  u«ed. 

Spike*. 

number  Iq  Keg, 
800  IbB. 

between  Centres. 

45  to  65 
40  •'58 
8ft'*  40 
84  "85 
84  *'  80 
18  *'  84 
16  "80 
14  "  16 
8  "  12 
8  *'  10 

880 
400 
490 
550 

880 
1850 
1850 
1550 
8:200 

80 

81! 

ai 
111 
i;i 
II 
II 
" 
6 

8TBBIBT  BAII^WAT  SPfKBS. 


Spikes. 

Number  in  Keg,  800  lbs. 

Kegs  per  MUe.  Ties  »li«. 
between  Oentrek. 

4Mixt-16 

400 
6tQ 
800 

80 
10 
18 

BOAT  0FIBBS. 


Length. 

H 

5-16. 

9^ 

H 

4  inch. 

2875 
2050 
18:i» 

1280 

1176 
900 
880 

940 
800 
650 
600 

475 

6  '* 

7  *• 

450 

875 

8     '* 

885 

9     ** 

800 

10     " 

S?5 

8PIKX8;  CUT  ITAILS. 


m 


VmOVQU-T  SPIKES. 

Bfumber  of  Nail*  in  Kee  of  15#  Pounds* 


sua. 

Min. 

5-16  In. 

«lii. 

7-16  In. 

Hin. 

a    Ib<.i«A9 

2290 
1890 
1090 
1484 
1880 
1292 
1161 

?*  -   ::;::: 

1206 
118S 
1064 
030 
868 
663 
686 
678 



t"^  "   :;•::: 



748 

070 

482 
465 
424 
891 

6        ••       

7  -        ...... 

8  -       

9  •       

It        •       —  .. 

446 
884 
800 
270 
849 
886 

ao6 

866 
840 
822 

u       ■•       

806 

18       •       

180 

DTIKB  8PIKK8. 


Sixe. 

Approx.  Size 
ofWire  Nails. 

Ap.  No. 
in  1  lb. 

60 
85 
26 
26 
16 
12 

Size. 

Approx.  Si»e 
ofWireNaiiB. 

inilb? 

Wd  Spike 

16d      "     

20d      "     

80d      ••     

40d      ••     

SOd      •*    * 

8     In.  No.  7 

?« :: ::  I 
'^ :: ::  i 

5«    "    •*   2 

aod  Spike 

fii^W    

8  "  *•  !!.."..' 

9  ••"     

6     in.  No.  J 

fi ::  r.  j 

8  "    •*   #0 

9  "    "   #0 

16 

? 

6 

I^VNCTH  AND  NtTlHRBm  OF  CUT  KAILS  TO  THB 
POUND. 


Sin. 

J3 

1 

6 
o 

-; 

i 

£ 

1 

1 

1 

i 

tic 

a 

I 

1 
1 

o 

1 

U 

800 
600 
876 
224 

180 

2  .     . 

§.:::;:::. 

fiOO 

480 

886 

200 

168 

124 

88 

70 

68 

44 

84 

23 

18 

14 

10 

8 

95 
74 
68 
53 
46 
42 
88 
88 
20 

64 
48 
86 
80 
24 
20 
16 

1100 

720 

623 

410 

268 

188 

146 

180 

102 

76 

62 

64 

1000 
760 
868 

8d 

"898 

4d. 

M 

130 
96 

68 

6d 

224 

126 
OS 
75 
65 
65 
40 
87 

7d. 

8d 

128 
110 
91 
71 
64 
40 
83 
27 

9d 

lOd 

?8 

lad 

16d 

Wl 

aod 

SOd, 

12v2 

40d 

9vl 

50d- 

8' 

eod. 



6 

214 


XATBBIAia. 


1^ 

M 

S 


a 
^  i 

K    ca 


u 

0 
0 


0) 


*1M}8 

1  iSSS  ;^SSSSSS3S|||§| 

*89qoa|  *q^a«iq 

»«„?s^»«^^«^,*«?« 

•BOJiids  wiM 

::*•:: 

i  :  i  is  :8S8=22 

•auian 

8S8  i  :  :  : 
s55  :  :  :  : 

*!i:tiz!!i:r 

'ooovqox 

:  :  :  :  !  iS^SS^S*  i  :  :  :  i  :  : 

•aianms 

!::•:::   gi^SH®  :  :  i  :  i  :  i 

*XauooH  PdqJVfl 

SI5  :S  :§?§  i  i  i  i  i  i  :  i  :  :  : 

•aapins 

:  :;  :5  :i^  i  :  i  :  :  i  :  i  i  :  :  : 

1^. 

i 

i  :  ;  :  i  ;|£|J2835S«S«SS2:S 

1 

:  :  h  i  JSISSaSfe^f^SSSUS 

•«pwa  auijooij      :::::::  :i2|S8SeS9  :  i  :  :  i 

•xoa  P«»q4tiH 
puv  qiooius 

:  ;|  "2  :2||§gSgS?JS^8  i  ' 

•iai4«a 

1500 
1000 
875 
775 
500 
890 
850 

•oaij 

"II ;  ■§ ;  H  i  n !  h  ^  n : 

•aumsiujj  paq.raa  1  :  :g  is  -SSggSfSfeSSi:  :  :  :  : 

•«»a»j  I  i  i  i  i  i  i  iggaSSSSSS  :  .  1  : 

•qoa„o   1    :  :g  iS  iggggSSSSS?  :  :  :  ; 

'uoiiiuioo  poqj«H 

:  :i  ii  :ggigaSgS?«SS  j  : 

•8p«ja  paw 
8||»ii  uomuioo 

1  il  j§  :|i§8»|te8ss655as 

•soipui  'qi3a»q 

s«_?S*^„^^,SS,f.?. 

1 

l«qS 

:  i  i  •§  i  i 

:  :  .  .5  :  : 
j  :3S8  i^S 

^gj^sdsg^ISS' 

APPROXIMATE  NUMBER  OP  WIRE  NAILS  PER  POUND.  215 


? 


;!!: 


3f 


s; 


;t? 


35 

lO  to  t«  000-4 


<Ofc«aoo»*«»ioao 


t^oooj^egjoajjjQgj 


«<*rSiSSgj88jg;;8 


•SS3i:;8S8Sg5Sg 


S;:S:5SS»5So92|g?S 


2SSSSJa88S5?2C8S:S 


;:;SS?33SS;:S2o8S8Ss^g 


'Ml 

Mis 


^ i—  63  a 
•1"  3  --fiS 


SS:S«88iSS8888§gg|§  ;  ;  ; 


8agS8!gS8t588§5|g§§gg  : 


SSSi59S8<:SSS|gg§|§g|8 


i;aS?S8.-:a8S|8|5§BJg|gg 


8a«SS8S8§teSSg||gg2|g8| 


!S5ss§S5§i55igi3||| 


§§Hiiigi^§H§|ig||||| 


gOr^M 


|g§gg§i§§SI|||||~| 


i§iisi§§|ig|||||il 


i^lliiliiliii 


oio5^<odoo>nUS 


«o^lO«^■aoo»o*«o>eo^lO<o^•aDO»os 


$s;8i 


216 


HATBBIALSi 


SIZB,  WBIGBT,  liBWOTH,  AND   STBBNGTK  OP  IBOH 
WIBB* 

(Treaton  Iron  Co.) 


DIanl. 

No.  by 

in  Deci- 

Wire 

mals  of 

aftuge. 

One 

Inch. 

00000 

.480 

0000 

.400 

000 

.860 

00 

.880 

0 

.805 

1 

.285 

8 

.965 

8 

.915 

4 

.295 

5 

.905 

6 

.190 

7 

.175 

8 

.160 

9 

.145 

10 

.180 

11 

.1175 

IS 

.106 

18 

.0995 

14 

.080 

15 

.OTO 

16 

.081 

17 

.05« 

18 

.045 

19 

.040 

90 

.035 

91 

.031 

89 

.098 

28 

.095 

94 

.09% 

95 

.090 

90 

.018 

97 

.017 

98 

.016 

29 

.015 

80 

.014 

81 

.018 

39 

.019 

88 

.011 

SI 

.010 

85 

.0093 

80 

.009 

87 

.0UH6 

88 

.OOH 

89 

.OOiA 

4i 

.wr 

Area  of 
SecUon  In 

Feet  to 

the 
Pound. 

Decimals  of 
One  Inch. 

.15904 

1.863 

.12566 

2.358 

.10179 

8.911 

.08568 

8.465 

.07306 

4.057 

.06879 

4.645 

.05515 

6.874 

.04714 

6.986 

.lWtf/6 

7.464 

.03301 

8.976 

.02885 

10.458 

.02105 

12.322 

.02011 

14.736 

.01651 

17.950 

.01327 

29.383 

.01084 

87.840 

.00^ 

84.219 

.00679 

44  099 

.00.-i08 

68.016 

.00385 

70.984 

.00999 

101.488 

.00216 

187.174 

.00159 

186.885 

.0019.560 

285.084 

.0009621 

808.079 

.0007547 

392.  na 

.0006167 

481.234 

.0001909 

003.863 

.0008976 

745.710 

.0003149 

943.806 

.0002545 

1164.680 

.0002270 

1805.670 

.0002011 

1476.869 

.0001767 

1676  969 

.0001589 

1925.321 

.0001327 

2282.658 

.0001131 

96d0.607 

.0000950 

8119.092 

.00007854 

8778.584 

.00007088 

4182.508 

.00006362 

4657.798 

.00005675 

5222.035 

.00005027 

5896.147 

.00004418 

6794.201 

.00008848 

7698.958 

Weight  of 
One  Mile 
in  pounds. 


Tennile  Strpngth  (Ap. 

proximal*')  of  Charcoal 

Iron  Wire  In  Pounds. 


TESTS  OF  TELEGRAPH  WIRE. 


21? 


GALTAN IZBD  IRON  ITIRE  FOR  TEI.EGRAPB  AND 
TEIiEPHONE  LINES, 

(Trenton  Iron  Ck).) 
Wnovr  PBB  Milb-Obv.— This  term  !« to  be  undei-stood  as  distingulBhlng 
the  mistanee  of  material  only,  and  means  the  weight  of  such  material  re- 
quired per  mile  to  giTe  the  resistance  of  one  ohm.  To  ascei'tain  the  mileage 
resistance  of  any  wire,  divide  the  '*  weight  per  mile-ohm ''  by  the  weight  of 
the  wire  per  mito.  Thus  in  a  grade  of  Extra  Best  Best,  of  wtiicb  the  weiglit 
per  mlte-obm  is  8000,  the  mllea^  resistance  of  No.  6  (weight  per  mile  fiSiS 
lbs.)  wotild  be  about  9^  ohms:  and  No.  14  steel  wire.  6A0O  lbs.  weight  per 
mile-ohm  (ftS  lbs.  weight  per  mile),  would  show  about  69  ohms. 

Sixes  of  Wire  need  In  Telecrapli  and  Teleplione  Lines* 

No.  4.  Has  not  been  much  used  until  recently;  to  now  used  on  important 
lines  where  the  multiplex  systems  are  applied. 

NOb  6.  Little  used  in  the  United  States. 

No.  C  Used  for  Important  circuits  between  oltles. 

Jfo.  8.  Medium  slxe  for  circuits  of  400  miles  or  less. 

No.  9.  For  similar  locations  to  No.  8,  but  on  somewhat  shorter  circuits ; 
until  lately  was  the  size  most  largely  used  in  this  country. 

Nos.  10.  II.  For  shorter  circuits,  railway  telegraphs,  private  lines,  police 
and  fire^lann  lines,  etc. 

No.  IS.  For  telephone  Hues,  police  and  fire-alarm  lines,  etc. 

No9. 18, 14.  For  telephone  lines  and  short  private  lines:  steel  wire  is  used 
D>o^  generally  in  these  sixes. 

The  coating  of  telegraph  wire  with  sine  as  a  protection  against  oxidation 
is  now  generally  admitted  to  be  the  most  efflcacious  method. 

The  grades  of  line  wire  are  generally  known  to  the  trade  as  "  Extra  Best 
Best "  (E.  B.  B.),  *'  Best  Best "  (B.  B.),  and  *♦  Steel." 

**  Extra  Best  Best  *'  is  made  of  the  very  best  iron,  as  nearly  pure  as  any 
commerelal  iron,  soft,  tough,  uniform,  and  of  very  high  oonauctivity,  its 
««*ii^t  per  mile-ohm  being  about  6000  lbs. 

The  **  Bemt  Best**  is  of  Iron,  showing  in  mechanical  tests  almost  as  good 
results  as  the  E.  B.  B.,  but  not  quite  as  soft,  and  being  somewhat  lower  in 
conductivity;  weight  per  mile-ohm  about  6700  lbs. 

The  Trenton  *'  Steel ^*  wire  is  well  suited  for  telephone  or  short  telegraph 
lines,  and  the  weight  per  mile-ohm  is  about  6SO0  lbs. 

The  following  are  (approximatelv)  the  weights  per  mile  of  various  sixes  of 


[appro  ^ 

gaivanixed  telegraigh  wire,  drawn  by  Trenton  Iron  Co.'s  gauge: 


No.       4,       l. 


7, 


18.      14. 


Lbs.    7;»,    610,    &25,    450,    875,    8l0,    ^,    200,    160,     1S5,    95. 

TESTS  OF  TEI.EORAPH  DTIRE. 

Ilie  following  data  are  taken  from  a  table  given  by  Mr.  Prescott  relating 
to  tests  of  E.  B.  B.  galvanized  wire  furnished  the  Western  Union  Telegrwh 
Co.:  ^  ^ 


Size 
of 

Dlam. 

Parts  of 
One 
Inch. 

Weight. 

Length. 

Feet 

I)er 

pound. 

ReslsUnce. 
Temp.  75. 8«  Fahr. 

Ratio  of 

Breaking 

Weight  to 

Weight 

per  mile. 

Wire. 

Grains, 
per  foot. 

Pounds 
per  mile. 

Feet 
per  ohm. 

per  mile. 

10 
11 
12 
14 

.888 
.2W 
.90S 
.180 
.165 
.148 
.134 
.ttO 
.100 
.063 

1048.3 
891.8 
758.9 
696.7 
501.4 
408.4 
880.7 
966.8 
818.8 
126.9 

886.6 
678.0 
57i.S 
449.9 
878.1 
804.8 
249.4 
800.0 
166.0 
95.7 

600 
7.86 
9.20 
11.70 
14.00 
17.4 
21.2 
28.4 
82.0 
55.2 

958 
727 

618 
578 
409 
828 
269 
216 
179 
104 

6.51 
7.26 
8.54 
10.86 
12.92 
16.10 
19.60 
24.42 
29.60 
51.00 

8.05 
8.40 
8.07 
8.88 
8.87 
2.97 
3.43 
8.06 

Joisrrs  IN  Tklkoraph  Wires. — ^The  fewer  the  joints  in  a  Hue  the  better. 
All  Joints  should  be  carefully  made  and  well  soldered  over,  for  a  bad  joint 
nay  cause  aa  much  resistance  to  the  electric  current  as  several  miles  of 
»ire. 


218 


KATEBIALS. 


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Dm Bl^SIONS,  WBIOHT,  RESISTANCE  OF  COPPEB  WIRE.  219 


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MATBBIALS. 


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HARD-DRAWN  COPP^ft  WIRE}    INSULATED  WIRE.    221 


lAVnt  COFPBS  TBIiBettAFli  WtBK* 

(J.  A4  Roebllng^B  Bona  Co.) 
FumMied  in  hAlf-mne  coils,  either  bare  or  insulated. 


UK.  B.  ft  6. 
Gauge* 


9 
10 
11 
18 
18 
14 
15 
16 


Reslsta&cein 

Ohms 

per  Mile. 


4.90 
0.40 
9.90 
8.TO 
10.00 
18.10 
17.40 
2^.10 


Breaklnir 
Sti-enKth. 


can 

4«) 


213 

IS! 


Weight 
per  Mile. 


ttoo 

160 
131 
104 
88 

41 


Attt>lK»±imftte 

BtfeeofB  B.B. 
Iron  Wire 
eqiial  to 
Copper. 


'I 

n(3 

If 
JO  I 


lit  haudiin^  tlii^  wire  tlie  rreatest  care  should  be  obseKed  to  avbid  Iclnlcs, 
i««fndB.  ecratches,  or  cats.  Joints  should  be  made  only  with  Mclutire  Cuu- 
nectors. 

On  account  of  ila  cendoeHvitj  being  about  fire  times  thai  of  Ex.  B.  B. 
Iron  Wire,  and  its  breaking  Strength  oter  three  times  its  weight  per  niilef 
copper  maybe  used  of  which  the  section  is  smaller  and  the  weight  less  ihnn 
an  equivaMst  if6n  wire,  allowing  a  gi^aier  number  of  wires  lo  be  strung  on 

Beaides  this  advAntage,  the  rediiotlon  of  section  materially  decreases  the 
electroetatlc  capacity^  while  its  non-magiietlc  character  lessens  the  self-in- 
duction of  the  line,  both  of  which  features  tend  to  increase  thepo.«sible 
fpeed  of  signalllitg  in  telegraphing,  and  to  give  greater  clearness  ofenuuci- 
aiioii  over  telephone  lines,  especially  Ihoee  Of  great  lengili. 

I1f917I<ATBII    COPPER    WlRB^    WfiATHEBPttOOJP 

iivscri<ATlON. 


Doable  Braid. 

Triple  Braid. 

Approziroate 
weights, 

Kum- 

henu 
B  &  B. 

Outside 

Weights, 

Outside 

Weights. 

Pounds. 

Diame- 

Pounds. 

Diattie- 

Pounds. 

Gau^. 

ters  in 
88d8 

ters  in 
ftMs 

1000 

1000 

Inch. 

Feet. 

Mile. 

Inch. 

Feet. 

Mile. 

Reel. 

Coil. 

0000 

20 

716 

8781 

24 

776 

4098 

2000 

250 

000 

18 

675 

8096 

22 

080 

8820 

2000 

2.')0 

00 

17 

46S 

a4.w 

18 

490 

2587 

500 

2.'iO 

0 

10 

875 

1980 

17 

400 

2112 

600 

250 

1 

15 

885 

1505 

10 

800 

1616 

600 

250 

2 

14 

845 

1204 

15 

268 

1415 

600 

250 

t 

13 

190 

1003 

14 

210 

1109 

600 

250 

4 

11 

15a 

808 

12 

104 

860 

250 

125 

5 

10 

m 

684 

11 

115 

700 

200 

130 

6 

9 

98 

618 

10 

112 

591 

275 

140 

8 

8 

66 

349 

9 

78 

412 

200 

100 

!0 

7 

45 

2:J8 

8 

55 

290 

200 

100 

12 

6 

80 

158 

7 

85 

186 

.... 

25 

24 

5 

20 

106 

0 

20 

U7 

25 

Id 

4 

14 

74 

5 

20 

100 

.... 

25 

»s 

8 

10 

&l 

4 

10 

85 

.... 

S5 

222 


HATBRIAL8. 


Power  Cable*.    I<e«d  Ineaeetf,  JTute  or  VwLpvr  iBsnlated* 

(John  A.  BoebliDg's  Bons  Co.) 


N08,. 

circular 
Mils. 

Outside 
Diain. 
Inches. 

Weights, 
1000  feet. 
Pounds. 

Nos.. 
B.&S.O. 

Circular 
Mils. 

Outside 
Dlam. 
Inches. 

Weights, 
1000  feet. 
Founds. 

1000000 
900000 
800000 
750000 
700000 
660000 
600000 
650000 
600000 
460000 
400000 
850000 

1  18/16 
1  88/82 
1  21/32 

1  19/82 
1  9/16 
1  17/82 

•y 

1  11/32 
1  5/16 

6685 
6228 
6778 
6543 
5316 
6088 
4857 
4630 
4278 
8928 
3619 
8410 

800000 

260000 
811600 
168100 
138835 
105625 
88581 
66564 
62441 
41616 
iJ6844 

11/.. 

1  3/38 
1  1/16 

15/16 

i/82 
lf/16 

8000 

"0606* 
CM 
00 
0 
1 
8 
8 
4 
6 

8782 
8633 

8300 

.8021 

1772 

1683 
1482 

1360 
1851 

1046 

Stranded  "Weatlter-proof  Feed  "Wire* 


Circular 

Outside 

Diam. 

Inches. 

Weighto. 
Pounds. 

CO 

ll 
Si 

m 

Circular 
Mils. 

Outside 

Diam. 

Inches. 

Weights. 
Pounds. 

5 

Mils. 

1000 
feet. 

Mile. 

1000 
feet. 

Mile. 

III 

1000000 
900000 
800000 
750000 
700000 
660000 
600000 

ll8/32 
1  11/32 
1  5/16 
1  9/82 

1  7/32 

3350 
3215 
2«80 
2718 
8545 
2378 
2210 

18744 
16975 
15206 

13438 
12.556 
11608 

800 
800 
860 
8.^) 
900 
900 
1000 

650000 
500000 

450000 
400000 
3.50000 
300000 
250000 

1  3/16 

\%^ 

1  1/16 

1 
15/16 
29/38 

2043 
1875 
1708 
1590 
1868 
1185 
1012 

10787 
9900 
8998 
8078 
7170 
6257 
5843 

1800 
1320 
1400 
1450 
1500 
1600 
1600 

The  table  Is  calculated  for  concentric  strands.     Rope-laid  strands  are 
larger. 


8TSBL  WIBE  CABLES. 


OAltTANIZED  STBBIi-lTIBE  imftAHD. 

If  or  Smokestack  Gnys,  Slffiial  Strand,  etc* 

(J.  A.  Roebling's  Sons  Co.) 
This  strand  is  composed  of  7  wires,  twisted  together  into  a  single  strand. 


i 

llf 

J  ♦ 

lit 

1 

in. 

^1 

^8 
^- 

lbs. 

Hi 

in. 

lbs. 

lbs. 

in. 

lbs. 

lbs. 

llM. 

15% 

5t 

&8-J0 

9/82 

18 

2,600 

5/8» 

tx 

700 

48 

7.500 

17/64 

15 

2,i»0 

9/64 

525 

'4' 

ST 

m 

«,000 
4.700 

7%l 

im 

1,750 
1.300 

8^ 

f^ 

875 
820 

57l« 

21 

8,aoo 

a/16 

1,000 

For  special  purposes  these  strands  can  be  made  of  50  to  100  per  cent 
f^reater  tensile  strength.  When  used  to  run  over  sheaves  or  pulleys  the  use 
of  soft-iron  stock  is  advisable. 

FI«EXIBI.E  STBBI«-WimE  CABI«E8  FOR  TBSSBI^S. 

(Trenton  Iron  Co.,  1886.) 

With  numerous  disadvantages,  the  system  of  working  ships*  anchors  with 
tiiafn  cables  is  still  in  vogue.  A  heavy  chain  cable  contributes  to  the  hold- 
ing-power of  the  anchor,  and  the  facility  of  increasing  that  resistance  by 
1)a\tng  out  the  cable  is  prized  as  an  advantage.  The  requisite  holding- 
power  is  obtained,  however,  by  the  combined  action  of  a  comparatively 
iij;ht  anchor  and  a  correspondingly  great  mass  of  chain  of  little  service  in 
proportion  to  its  weight  or  to  the  weight  of  the  anchor.  If  the  weiffbt  and 
size  of  tb«  anchor  were  increased  so  as  to  give  the  greatest  holding-power 
required,  and  it  were  attached  by  means  of  a  light  wire  cable,  Ww  combined 
wftght  of  the  cable  and  anchor  would  be  much  less  than  the  total  weight  of 
the  chain  and  anchor,  and  the  facility  of  haiidline  would  be  much  greater. 
English  shipbuilders  have  taken  the  initiative  in  this  direction,  and  many  of 
the  large«t  and  most  serviceable  vessels  afloat  are  fitted  with  steel -wire 
cables.    They  have  given  complete  satisfaction. 

The  Trenton  Iron  Co.'s  cables  are  made  of  crucible  cast-steel  wire,  nnd 
guaranteed  to  fulfil  Lloyd's  requirements.  Thev  are  composed  of  7*J  wires 
subdivided  into  six  strands  of  twelve  wires  each.  In  order  to  obtain  great 
flexibility,  hempen  centres  are  introduced  in  the  strands  as  well  as  in  the 
completed  cable. 

FI.BXIBI«B  8TBBI.-WIBE  RAWSERS. 

These  hawsers  are  extensively  used.  They  are  made  wlrh  six  strands  of 
twelve  wires  each,  hemp  centres  being  inserted  in  the  individual  strands  as 
wdl  as  In  the  completea  rope.  The  material  employed  is  crucible  cast  steel, 
galvanised,  ond  gitarantetra  to  fulfil  Lloyd's  requirements.  They  are  only 
one  ihini  the  weight  of  hempen  hawsers;  and  are  sufTlcientl  v  pliable  to  work 
ronnd  any  bitts  to  which  hempen  rope  of  eqnivalent  strength  can  be  applied. 

13-tnih  lArred  RnsKian  hemp  hawser  weighs  nbout  89  IhH.  per  fathom. 

10-inch  white  manila  hawser  weighs  about  20  lbs.  per  fathom. 

1^-inch  stud  chain  weighs  about  68  lbs.  per  fathom. 

4-Hic^  galwvuixed  ateel  hawaer  loeighs  tibont  12  Ibt.  per  faViom. 

Each  of  the  above  named  has  about  the  same  tensile  strength. 


iu 


irAtBBIALS. 


SPBOinCATIOWS  WOU  OAI^TAHimBD  IROV  «7IIiB. 

Issued  bjr  tlie  Vrtttsh  Postal  Telegrapli  Autborltles. 


WeiRht  per  Mile. 


Allowed. 


Diameter. 


Allowed. 


Teste  for  Strength  and 
Ductility. 


h5 


I 


ix 


lbs. 

dOO 
iOO 
490 
400 
200 


lbs. 

T87 
571 
494 
877 
190 


lbs. 

010 
47T 
424 
218 


mils. 

242 
SiOe 
181 
171 
121 


mils. 

237 
204 

176 

166 
118 


mils. 

247 
814 
186 

176 
125 


lbs. 

2480 
1880 
1890 
1240 


lbs. 

2550 
1910 
1425 
1270 
638 


lbs. 

20S0 
1960 
1460 
1800 
655 


ohms. 

6.75 
9.00 
12.00 
18.60 
27.00 


5400 
5100 
6400 
5400 
5400 


STRENGTH  OF  PIAN4>-1¥IRE. 

The  average  strength  of  English  piano- wire  is  given  as  follows  by  Web> 
ster,  Ho^sfals  &  Lean: 


Numbers 

Equivalents 
in  Fractions 

Ultimate 

Numbers 

Equivalents 
In  Fractions 

Ultimate. 

in  Music- 

Tensile 

in  Music. 

Tensile 

wire 

of  Inches  In 

Strength  in 

wire 

of  Inches  in 

Strength  in 

Gauge. 

Diameters. 

Pounds. 

Qauge. 

Diameters. 

Pounds. 

12 

.0«0 

286 

18 

.041 

805 

18 

.081 

260 

19 

.048 

«» 

14 

.088 

286 

20 

.045 

600 

15 

.065 

805 

21 

.047 

640 

16 

.087 

840 

28 

.052 

050 

17 

.089 

860 

These  strengths  range  from  800.000  to  340,000  lbs.  per  so.  In.  The  compo- 
sition of  this  wire  is  as  follows:  Carbon,  0.570;  silicon,  0.090;  sulphur,  0.011; 
phosphorus,  0.018;  manganese,  0.425. 

<<PI«017GH"-STBEI.  WIRE. 

The  term  "plough,"  given  in  England  to  steel  wire  of  high  quality,  was 
derived  from  the  fact  that  such  wire  is  used  for  the  coustruciion  of  ropes 
ttsed  for  ploughing  purposes.  It  is  to  be  hoped  that  the  term  will  not  be 
ised  in  this  oouutry,  as  it  tends  to  confusion  of  terms.  Plough-steel  is 
tnown  here  in  some  steel- works  as  the  quality  of  plate  steel  used  for  the 
mould-boards  of  ploughs,  for  which  a  very  ordinary  grade  is  good  enough. 

Experiments  by  Dr.  Percy  on  the  English  plough-steel  (so^Mdled)  gave  the 
following  resultji:  Specific  gravity,  7.614 ;  carbon,  0.828  per  cent;  manga- 
nese, 0.587  per  cent;  silicon,  0.143  per  cent;  sulphur,  0.009  per  cent;  phos- 
phorus, nil;  copper,  0.030  per  cent.  No  traces  of  chromium,  titaaiam,  o7 
tungsten  were  found.    The  breaking  strains  of  the  wire  were  as  follows: 

Diameter,  inch 098  .188  .159  .191 

Pounds  per  sq.  inch 814.960       237,600       224,000       201,600 

The  elongation  was  only  from  0.75  to  1.1  per  cent. 


SPECIFICATIONS  FOR  HARtMDRAWN  COPPER  WIRE.  225 


WIBBS  OP  DIFFHBBNT  nBTALS  AND  AI«I.OT8. 

(J.  Buckoall  Smith's  TreaUae  on  Wiro.) 

RnuM  Wire  to  eommonly  compoMd  of  an  alloy  of  1 8/4  to  S  parts  of 
•opper  to  1  part  of  sine.  The  tensile  strength  rangos  from  SO  to  40  tons  per 
square  inch,  increaslnjT  with  the  perceatace  of  zfno  fn  the  alloj. 

OevBUtn  or  NlcMl  Ml-ver^  an  atfojr  of  copper,  sine,  and  nickel,  is 
practically  brass  whitened  bj  the  addition  of  nickel.  It  has  been  drawn  into 
wire  as  line  as  .008"  diam. 

yiatiimm  wire  may  be  drawn  info  the  finest  sizes.  On  account  of  its 
hl^ii  price  Its  use  Is  praetieaUy  conflned  to  pedal  scientlflj  Instruments  and 
eleetrical  i^plianaes  in  which  reslstanoee  to  high  temperature,  oxygen*  and 
acids  are  easentiaL  It  expands  leas  than  other  metals  when  heated,  which 
property  permits  its  being  sealed  In  ghiss  without  fear  of  cracking.  It  is 
iharefore  used  in  Incandescent  electrio  lamps. 

FIsospMoi^broiuM  IITlre  contains  from  8  to  6  per  cent  of  tin  and 
from  l/SU  to  1/8  per  cent  of  phosphorus.  The  presence  of  pbosptioms  is 
d^rrfmental  to  electric  conductivitv. 

**  Delta«!BieCiil "  wire  Is  made  from  an  alloy  of 
Its  strength  fsnges  from  46  to  08  tons  per  84|nare  inch. 


comwr.  Iron,  and  sine. 

_  84|nare  inch.    It  Is  vied  for  some 

kinds  of  wirs  rope,  also  for  wire  gauie,    It  Is  Dot  shbJeot  to  deposits  of  Yer- 


\  great  touglmess,  even  when  Its  tensile  strength  is  over  00 
elneh. 

B  been  drawn  as  line  as  1 1 ,400  yards  to 


avity  .868.     T^'nslle  strength  only 


Sigris.    It  : 

tons  pM-  square  Inch. 

Al«SBiimBBi  tirtre*  — Speciflo 
alwai  10  tons  per  square  Inch.  It  li  ^ 
tbe  ouooe.  or  .OCajrralAs  per  yard. 

Al— irawm  mrowtrntf  W  copper,  lO  ataunlnum,  has  '  Igb  strength  and 
ddciility I  is  inozkUzablev  sonorous.  Its  eleotric  coddcKStiTit;^  Is  IS  .0  per  oent 

Hlteon  Bronze,  patented  In  1883  by  L.  Weller  of  Paris,  is  mads  n^ 
foUuws  :  Flnosilicate  or  potash,  pounded  glass,  chloride  of  sodium  and  cal- 
dom,  earbooate  of  soda  and  lime,  are  heated  in  a  plumbago  Crucible,  and 
after  the  i^eaction  takes  place  the  contents  are  thrown  Into  the  molten 
bronze  to  be  treated.  Billcon-bronce  wire  has  a  conductivity  of  from  40  to 
98  per  cent  of  that  of  copper  wire  and  four  times  more  than  that  of  iron, 
vhile  Its  tensfle  strength  is  nearir  that  of  steel,  or  80  to  55  tons  per  sqtiarO 
inch  of  SMtion.  The  conductivity  decreases  as  the  tensile  strengih  in- 
creajics.  Wire  whose  conductivity  equals  95  per  cent  of  that  of  pure  copper 
fives  a  tensile  strength  of  88  tons  per  square  inoh,  Imt  when  its  conductivity 
u  31  per  cent  of  ptire  copper,  its  strength  is  60  tons  per  square  inoh.  It  is 
bein^  largely  used  for  tel4*graf^  wires.  It  has  great  resfittAnce  to  oicldatlon. 

Ordinary  UrAurn  and  Annealed  Copper  Wire  has  a  strength 
of  from  U  to  80  tons  per  square  inch, 

nnSCIFICATIOllS  VOB  HABl»«miAWN  CO^Pttm 


Tbe  British  Post  Office  authorities  require  that  hard-drawn  copper  wire 
supplied  to  them  shall  be  of  the  lengths,  sises,  weights,  strengths,  and  Con- 
doctivities  as  set  forth  in  the  annexed  table. 


Weight  p^  Statute 

Approkimate  Squlf  a- 
lent  Diameter. 

1 

1 

is 
P 

fill 

In 

lit 

11 
11 

1 

1 

1 

1 

1 

lbs. 
100 
ISO 
»0 
460 

lbs. 
410 

158 

mils. 
78 

mils. 
80 

lbs. 
890 

490 
C'^ 
1800 

80 
85 
SO 
10 

ohmS« 
0.10 
0.06 
4.58 
8.87 

lbs. 
so 

60 

226 


MATERIALS. 


WIRE  ROPBS. 

List  adopted  by  manufacturer  in  189 J.     See   pamphlets   of  John  A. 
Boebling's  Sooa  Co.,  Trenton  Iron  Co.,  and  other  makers. 

Pliable  filoUtlns  Rope* 

With  6  strands  of  19  wires  each. 

IRON. 


1 


1 
9 
S 
4 
ft 

7 

10 

T 
\L 


I 
I 


P 


4 

m 

P 


id 


g.OO 

9.05 

1.58 
l.VD 

0.4tt 


^1 

OQS 


74 
85 
64 

44 

89 
88 
27 
80 

16 

11.50 
8.64 
5.18 
4.27 
8.48 
8.00 
2.50 


§4 
I  sal 


11 
It 

18 
12 

20 

P 


OA8T  STKBL. 


1 

8 
8 

4 
S 

7 
8 
9 
10 

lo^ 

i 

lOa 
10% 


8.00 
6.80 
6,^5 
4.10 
8.65 
8.00 
2.50 
2.00 
1.58 
1.20 
0.88 
0.60 
0.48 
0.39 
0.29 
0.23 


155 
125 
106 
86 
77 
63 
52 
42 
83 
25 
16 
12 
9 
7 


sn 


Cable-Traction  Ropes* 

According  to  English  practice,  cable  tiHcti  ^n  ropeK,  of  about  8>{  in.  in 
circumference,  are  commonly  constructed  with  six  strands  of  seven  or  fif- 
teen wires,  the  lays  in  the  strands  varying  from,  say.  8  in.  to  8H  in.,  and  the 
lays  in  the  ropes  from,  say,  7^  in.  lo  9  in.  In  the  United  States,  however, 
strands  of  nineteen  wires  are  generally  preferred  as  being  more  flexible; 
but,  on  the  other  hand,  the  smailler  external  wires  wear  out  more  rapidly. 
The  Marlcet  street  Street  Railway  Company,  Snn  Francisco,  has  used  ropes 
1^  in.  in  diameter,  composed  of  six  strands  of  nineteen  steel  wires,  weighing 
2^  lbs.  per  foot,  the  longest  continuous  length  being  24,125  ft^  The  Chicago 
City  Railroad  Company  has  employed  cables  of  i  Vntical  construction,  the 
lonxesl  length  being  27,700  ft.  On  the  New  York  and  T.  .olslyn  Bridge  cable- 
railway  steel  ropes  of  11,500  ft.  long,  containing  114  wires,  have  been  used. 


WIEE  BOPES. 


227 


Truismlsaloii  anA  Standlns  Rope. 

With  6  strandB  of  7  wires  each. 

XBON. 


a 

s 


11 

12 
IS 
14 
15 

le 

17 
18 
19 
SO 

» 

SS 
M 


IK 

Hi 


8.87 
«.77 
2.88 
1.83 
1.60 
1.18 
0.92 
0.70 
0.57 
0.41 
0.81 
O.SS 
0.21 
0.16 
0.125 


88 
80 
25 
20 
16 
12.8 
8.8 
7.6 
6.8 
4.1 
2.88 
2.18 
1.66 
1.88 
1.03 


4 
8 


Ml. 

Ijlf 

ill 


as  ^  w 


CAST  8TBKL. 


11 

iH 

^ 

8.87 

62 

18 

18 

BH 

13 

i^^i 

2.77 

52 

10 

12 

8^ 

18 

]< 

4 

2.28 

44 

0 

11 

75(, 

14 

iii 

3^  f 

1.88 

86 

7H 

10 

^ 

1ft 

1 

312 

1.50 

80 

6 

9 

S 

16 
17 

L 

2^ 

1.12 
0.92 

22 

17 

n 

8 

7 

5^ 
4^ 

18 

sS 

0.70 

14 

8 

6 

4^ 

19 
90 

1,. 

2 

0.57 
0.41 

11 

8 

^ 

?* 

21 

^.r. 

u 

0.31 

6 

]L  1 

4* 

in 

28 

1^ 

0.28 

4H 

1^ 

1 

28 
M 

t,. 

{^ 

0.21 
0.16 

4 
8 

1 

8 

96 

0-82 

» 

0.12 

2 

iS 

Plon8:h-8teel  Rope. 

Wire  ropes  of  Tery  high  tensile  strenRth,  which  are  ordinarily  called 
"Plougfa-steel  Ropes/*  are  made  of  a  high  grade  of  crucible  steel,  which, 
when  put  in  the  form  of  wire,  will  bear  a  strain  of  from  100  to  150  tons  per 
noare  indi. 

w^here  it  Is  necessary  to  use  very  long  or  very  heavy  ropes,  a  reduction  of 
the  dead  weight  of  ropes  becomes  a  matter  of  serious  consideration. 

It  is  advisable  to  reduce  all  bends  to  a  minimum,  and  to  use  somewhat 
larger  drums  or  sheaves  than  are  suitable  for  an  ordinary  crucible  rope  hav- 
ing a  strength  of  60  to  80  tons  per  square  inch.  Before  using  Plough-steel 
Hopes  it  is  oest  to  have  advice  on  the  subject  of  adaptability. 


MATERIALS. 


WItli  0  fltrands  of  19  wires  each. 


Trade 

Diameter  In 

Weight  per 
foot  ia 
pounds. 

Breaking 
Strain  in 

Proper  Work- 

Min.  Size  of 
Drum  or 

Number. 

inches. 

tons  of 

aoooibB. 

iDg  Load. 

Sheave  in 
feet. 

2H 

8.00 

240 

46 

0 

¥ 

6.ao 

189 

37 

8 

5.25 

167 

31 

7^ 

I'lg 

4.10 

128 

25 

6 

]  ^ 

8.66 

110 

22 

^ 

9H 

lis 

3.00 

90 

18 

T^H 

2.60 

75 

15 

6 

IH 

2.00 

60 

12 

41^ 

1 

1.58 

47 

9 

4i± 

l.<» 

87 

7 

2B^ 

.    1^ 

0.88 

27 

5 

8l4 

low 

tH 

0.60 

18 

8^ 

3 

10^ 

0-16 

0.44 

18 

^ 

2H 

m 

H 

0.30 

10 

r 

2 

With  7  Wires  to  the  Strand, 


15 

1 

1.80 

45 

9 

^H 

16 

L 

1.12 

83 

•H 

5 

17 

0.«2 

25 

6 

4 

18 

0.70 

21 

4 

3^ 

19 

^16 

0.57 

16 

8 

20 

0.41 

12 

212 

n 

21 

^-16 

0.81 

9 

ifft 

23 

0.23 

5 

1V6 

2 

23 

% 

0.21 

4 

1 

iH 

OalTanlzed  Iron  Wire  Rope* 

For  Ships'  Rigging  and  Quys  for  Derricks. 
CHAROOAL  ROPE. 


Circum- 
ference 
in  inches. 


6« 


4 
2« 


Weight 
per  Fath- 
om in 
pounds. 


22 
21 
19 

14^ 


ar.  of 

new 

Manila 

Rope  of 

equal 

Strength. 

11 

101^ 

10 


n 


Break- 

ifig 
Strain 
In  tons 
of  2000 
pounds 


48 

40 
35 
33 
80 
26 
23 
20 
16 
H 
IS 
10 


circum- 
ference 
f  n  inches 


Weight 

per 
Fathom 


CIr.  of 

new 
Manila 


i_      I  Hope  of 


Brwtk- 

iiig 
Strain 
in  tons 
of  2000 
pounds 


WIBE  HOPES. 


229 


Galyatoed  CMt-iitMl  Taebt 


Tjir^  'per  Path. 


Cir.  of 

new 

Vanina 

Bopeof 

equal 

Strei^h. 


Break-; 

Strain 
in  tons 
of  9000 
pounds 


18 
11 


n 


06 

49 
8t 
£7 
8S 
18 


Girram- 

farence 
kiinoiies 


Weight 
per 

Fathom 

in 
pounds. 


Cir.  of 

new 

Manilla 

Kopeof 

equal 

Strength. 


Break- 
ing 
Strain 
in  toiis 
of  2000 
pounds 


Steel  Hawsers. 

Por  Mooring,  Sea,  and  Lake  Towing. 

CircnmfBT- 
ence. 

BTCMklflff 

Strengtii. 

Size  of 
Manilla  Haw- 
ser of  eqoal 
StrengOi. 

GlreimfQr- 
eaee. 

Breaking 
Strength. 

Size  of 
Manilla  Haw- 
ser of  eqiial 
Strength. 

Inches. 

Tons. 
15 
18 

Inches. 

Inches. 

-  f" 

Tons. 
29 
85 

Inrbes. 
9 
10 

Steel  Flat  Ropes* 

(J.  A.  Boebling's  Sons  Co.) 
Steel-wire  Flat  Ropes  are  composed  of  a  number  of  strands,  aitematelf 
twisted  to  the  right  and  left,  laid  alongside  of  each  other,  and  sewed  together 
with  soft  iron  wires.  These  ropes  are  used  at  times  in  place  of  round  ropes 
Id  the  shafts  of  mines.  They  wind  upon  themselves  on  a  narrow  wiudinf;- 
dnua,  which  takes  up  less  room  than  one  necewary  for  a  round  rope.  Tiie 
softriroa  sewing-wires  wear  out  sooner  than  the  steel  strands,  and  then  it 
bfgoroes  necessary  to  sew  the  rope  with  new  iron  wires. 


Width  and 
Thickness 

^/cSi^sr 

Strength  in 
pounds. 

Width  and 
Thickness 

Weight  per 
foot  in 

Strength  hi 
pounds. 

in  Inches. 

pounds. 

in  inches. 

pounds. 

Kx> 

1.10 

85,700 

Ux8 

2.86 

71.400 

i*^ 

1.88 

55.800 

'2k3^ 

2.97 

89.000 

i^^9 

2.00 

80,000 

2x4 

8.80 

99,000 

Z^m 

S.50 

75,000 

i^*H 

4.00 

120.000 

2«4 

8.86 

85,800 

:|x6 

4.27 

128,000 

i^4H 

8.12 

88,600 

2x5^ 

4.82 

144.600 

^  x6 

8.40 

100,000 

^k6 

6.10 

153,000 

^ 

«k5« 

8.90 

110,000 

Hx7 

5.90 

177,000 

For  safe  working  load  allow  from  one  fifth  to  one  seventh  of  the  breaking 
stress. 

**  liani:  Lay  »'  Rope. 

la  wire  rope,  as  ordinarily  made,  the  component  strands  are  laid  up  Into 
rope  in  a  direction  opposite  to  that  in  which  the  wires  are  laid  into  strands; 
tiMt  is,  if  the  wires  in  the  strands  are  laid  from  right  to  left,  the  strands  are 
laid  into  rope  from  left  to  right.  In  the  **  Lang  Lay,"  sometimes  known  as 
■*  UDiTersai  Lay,**  the  wires  are  laid  into  strands  and  the  strands  into  rope 
in  the  same  db-ection;  that  is,  if  the  wire  iB  laid  in  the  strands  from  right  to 
left,  the  strands  are  also  laid  into  rope  from  right  to  left.  Its  nse  has  been 
fonnd  desirable  under  certain  conditions  and  for  certain  purposes,  mostly 
for  bauUge  plants,  inclined  planes,  and  street  railway  cables,  although  ft 
has  also  been  used  tor  Tertlcia  hoists  in  mines,  etc.    Its  advantages  are  that 


230 


MATERIALS. 


OALTANIKED  STBEIt  CABLB8. 

For  Suspension  Bridges.    (Roebling's.) 


200 

180 


I 

I 


13 

11.8 

10 


2 

1% 


155 

no 

100 


8.G4 

6.5 

6.8 


a 
a 


95 
75 
65 


t 


t 


5.6 
485 
3.7 


COniPABATITE  8TBBNGTH8  OF  FLEXIBIiE  GAI.- 
VANIZBD  STEEIi-HriBB  HADTSBRS, 

'With.  Olialn   Cable,  Tarred   Russian  Hemp,  and  DTlUte 
Manila  Ropes. 


Pftt<?iit  Flpxiblfl 

Tarred   Riib- 

White 

Sttiel-wjna    llawmerN 

Chatn  Cable 

sian   Hemp 

Blaiiilla 

mil  Ct^h}^ 

Rope. 

Ropes. 

e 
^ 

3c 

E 

g 

1 

1 

3 

i 

1 

ts 

a 

c 

IX"-^ 

« 

5 

c 

cO 

a 

t 

o" 

1 

g 

s 

II 

a.  c  ^ 

! 

5 

1 

fa 

2 

c 

& 

I 

1 

be 
c 

J 

i 

^4 

6 

It 

1 

3  . 
n 

1 

1 

1 

n 

1 

1 

!S 

1 

2" 

iH 

! 

'Hi 

7H 

>4 

H 

4HJ 

0 

3 

2m  ' 

8 

^ 

ii 

IH 

i 

» 

4 

^ 

3k! 

m 

8 

S^ 

f-H 

104 

J-tO;  ir 

A» 

7J4 

5 

6^ 

5 

4 

8 

r* 

a 

!K 

T 

13 

1 

i 

8 

7 

6 

4H 

7H 

m 

^ 

0 

1^^ 

JQ-JO 

31 

V 

0^ 

10 

9 

^ 

6 

ic^ 

m 

3^  1^  1 

15 

13 

11H 

6M 

7 

18? 

■i^ 

«j 

IS 
IS 

]S« 

11-16, 

Sfl' 

tSI 

17  8-10 

s« 

16 
10 

14 
6^ 

7 

1^ 

16^ 
18 

^ 

B 

ShJ 

J»14 

1S-1C 

s-% 

t  i^K 

10 

23 

20 

18^ 

2SIC 

0 

art 

liWtfl 

<ti 

1&8-10 

23  7-10 

11 

28 

24H 

9 

14^ 

25^ 

4^ 

ra 

3-1 

'^1 

1 

r.( 

IS 

27 

12 

33 

29 

10 

18 

1^ 

4^ 

ts 

Sfl 

o; 

IV4 

ft^,-'« 

34^ 

rr.u 

13 

89 

34 

11 

22 

f. 

■ii4  'i*     J 

sn 

t  iT-^IS* 

fr;r!7L2 

m 

Wl 

50 

1^ 

29V4 

51 

f.H 

liH 

Tl      1 

33 

m 

nn.g 

17 

C7 

GO 

85H 

62 

c 

.^1 

ftB 

M     ; 

IS 

Uki,  u 

771.^ 

'0 

m 

72 

15^ 

42 

^^ 

«H 

iJ7    \m     1 

:;:> 

I  I?uffi 

siu  b:2 

94U 

in?  1-10 

21 

106 

89 

7 

11 

116 

43 

3    l-1fl 

a^i  7.  a 

23 

123 

106 

m 

tr 

ISO 

45 

2    3-16 

i*^  ^vQ 

134^ 

24 

134 

115 

ft 

«  .»  1 

4S       ' 

a  5-;c 

yWKjJ 

25 

146 

125 

Note.— This  is  an  old  table,  and  its  authority  is  uncertain.    The  figures  In 
the  fourth  column  are  probably  much  too  small  for  durability. 


WIRB  R0P2S*  231 

It  is  somevhat  more  flexible  than  rope  of  the  same  diameter  and  composed 
of  the  same  number  of  wires  laid  up  in  the  ordinary  manner;  and  (especi- 
ally) that  owinfc  to  the  fact  that  the  whies  are  laid  more  axially  in  the  rope, 
longer  surfaces  of  the  wire  are  exposed  to  wear,  and  the  endurance  of  the 
rope  is  thereby  increased.    (Trenton  Iron  Co.) 

Note*  on  the  Vme  of  Wire  Rope. 
(J.  A.  Boeblincf's  Sons  Co.) 

SeTsral  kinds  of  wire  rope  are  manufactured.  Tlie  moftt  pliable  variety 
eontains  nineteen  wires  in  the  strand,  and  is  geuerally  used  for  liolstiug  and 
running  rope.  The  ropes  with  twelve  wires  and  seven  wires  In  the  strand 
are  stiffer,  and  are  better  adapted  for  standing  rope,  gu^'s,  nod  riguing.  Or- 
dem  should  state  the  use  of  the  rope,  and  sdvice  will  be  given.  Itopes  are 
made  up  to  three  Inches  in  diameter,  upon  application. 

For  safe  working  load,  allow  one  fifth  to  one  seventh  of  the  ultimate 
strength,  according  to  8pee<l.  so  as  lo  get  good  wear  from  the  rope.  When 
substituting  wire  rope  for  hemp  rope,  it  Is  good  economy  to  allow  for  tho 
former  the  same  weight  per  foot  which  experience  has  approved  for  tho 
latter. 

Wire  rope  is  a«(  pliable  as  new  liemp  rope  of  the  same  strength:  the  for- 
mer will  tnerefore  run  over  the  same-sized  sheaves  and  pulleys  as  the  latter. 
Bat  the  greater  the  diameter  of  tlie  sheaves,  pulleys,  or  drums,  the  longer 
wire  rope  irill  last.    The  minimum  size  of  drum  is  given  in  the  table. 

Experience  has  demonstrated  that  the  wear  incivases  with  the  t:peed.  It 
Is,  tiierefore,  better  to  increase  the  lond  tlian  the  s|»ee<l. 

Wire  rope  is  manufactured  either  with  a  wii-e  or  a  hemp  centre.  The  lat- 
ter is  more  pliable  than  the  former,  and  will  wear  better  where  there  is 
short  bending.    Orders  should  specify  what  kind  of  centre  is  wanted. 

Wire  rope  musi^  not  be  coiled  or  uncoiled  like  henip  rope. 

Milken  mounted  on  a  reel,  the  latter  should  be  mounted  on  a  Kplndle  or  flat 
turn-table  to  pay  off  the  rope.  WJien  forwarded  in  a  small  coll.  witliout  rrel. 
roll  it  over  the  ground  like  a  wheel,  and  run  off  (he  rope  in  that  way.  All 
uniwisting  or  kinking  must  be  avoided. 

To  preserve  wire  rope,  apply  raw  linseed-oil  with  a  piece  of  eheepskln, 
wool  inside;  or  mix  the  oil  with  equal  parts  of  Spanish  brown  or  lamp-black. 

To  preserve  wire  rope  under  water  or  under  jrround,  take  mineral  or  vege- 
table tar,  and  add  one  bushel  of  fresh-slacked  lime  to  one  barral  of  tar, 
which  wQl  neutralize  the  acid.  Boil  it  well,  and  saturate  the  rope  wi^  the 
hot  tar.    To  give  the  mixture  body,  add  some  Kawdust. 

The  grooves  of  cast-iron  pulleys  and  sheaves  should  be  flileil  with  well- 
sMHoned  blocks  of  hard  wood,  set  on  end,  to  be  renewed  when  worn  out. 
TTiis  end-wood  will  save  wear  and  increase  adhesion.  The  smaller  pulleys 
or  rtdlers  which  support  the  ropes  on  inclined  planes  should  be  contttrucied 
on  the  santie  plan.  When  large  sheaves  run  with  very  great  velocity,  the 
^roovea  should  be  lined  with  leather,  set  on  end,  or  with  India  rubber.  This 
IS  done  in  the  cose  of  sheaves  used  in  the  transmiaeioH  of  power  between 
distant  points  by  means  of  rope,  which  frequently  runs  at  the  rate  of  4000 
feet  per  minute. 

Steel  ropes  are  takin?  the  place  of  iron  ropes,  where  It  Is  a  special  object 
to  combine  lightness  with  strength. 

But  in  substituting  a  steel  rope  for  an  iron  running  rope,  the  object  in  view 
should  be  to  gain  an  increased  wear  from  the  rope  rather  ihau  to  reduce  the 
size. 

Locked  "Wire  Rope. 

Fig  74  ohows  what  Is  known  as  the  Patent  Locked  Wire  Rope,  made  by 
the  Trenton  Iron  Co.    It  is  chiimed  to  wear  two  to  three  times  as  long  as  an 


Fio.  74. 


ordinary  wif«  rone  of  equal  diameter  and  of  like  material.    Sizes  made  aro 
irum  ^to  1^  incmes  diameter. 


232 


HATEBIAL8. 


OBANB  GHAINS, 

(PencQyd  Iran  Works.) 


*'  D.  B.  a/*  Special  Craoe. 


Crane. 


^16 
?1C 

H 
18-16 

16<16 
1 
1  1-16 


II 

r 


25-92 

Sl-SS 
15-83 
111*88 

i2S~sa 

127-83 

181-88 

8S-88 

2  7-82 

815-82 

81<M8 

8^8-82 

8  27-82 

8  6^88 

8  7-88 

815-88 


3 

8  81-SS2 


1 

17-10 

8 

SM 

8-^10 

J« 

8 

9 

10  7-10 
118-10 

18  7-10 
16 

18  4^10 

19  7-10 
21  7-10 


1938 


89568 
89264 
87576 
41888 
46800 
00518 
66748 
60868 
66588 


I 


o 


8864 
6796 
8878 
11593 
15456 
19880 


28980 
84776 
40579 
44968 
61744 
60186 


79158 
88776 
98400 
101024 
111496 
180736 
138059 


¥ 


1988 
8790 
8864 
5188 
6440 
7948 
9660 
11598 
18594 
14989 
17848 
19718 
88176 
85060 
87995 
80800 
88674 
87165 
40245 
44858 


1680 
8500 
8640 
6040 
6790 
8400 
10660 
18600 
15180 
17640 
9044O 
88080 
86880 
80840 
84160 
88080 
42000 
45080 
50680 
64880 
60480 


8860 
6040 
7880 
10080 
18440 
160OO 
90780 


40880 
47040 
68760 
60480 
68880 
76160 
84000 
91840 
101860 
109760 
120960 


1180 
1680 
8477 
8880 

4480 
6600 
0907 
8400 
10080 
11760 
18627 
18680 
17980 
80160 
887T8 
96887 
48000 
8061S 
89787 
86687 
4O380 


The  dUtanoe  from  centre  of  one  link  to  centre  of  next  ie  equal  to  the  In- 
side length  of  link,  but  in  practice  1/82  inch  is  allowed  for  weld.  This  is  ap- 
proximate, and  where  exactness  is  required,  cliain  should  be  made  so. 

Fob  CBAiif  SBBAVB(i.»The  diameter,  if  possible,  should  be  not  lass  than 
twenty  times  the  diameter  of  chain  used. 

BxAMFLB.— For  1-inoh  chain  use  20-inch  sheaTes. 

DTBIGHTS  OF  LOGS,  liVRIBBR,  ETC. 
ITelfflit  of  Green  liOffs  to  Scale  1,000  Feet,  Board  lIlMunire* 

Yellow  pine  (Southern) 8,000  to  10.000  lbs. 

Norway  pine  (Michigan) 7,000  to  8,000   " 

whitepine(Mich.gan,]°««'i,-;>™5-:;;:;:::::;:;::::::  f^^  iz  " 

White  pine  (Pennsylvania},  bark  off 5,000  to  6,000  " 

Hemlock  (Pennsylvania),  bark  off 6.000  to  7,000  •• 

Four  acres  of  water  are  required  to  store  1,000,000  feet  of  logs. 
Wel^rbt  of  I9OOO  Feet  of  Lnmber,  Board  Rleaaare. 

Yellow  or  Norway,  pine Dry,  8.000  lbs.       Green,  5,000  lbs. 

White  pine ••     2,800"  "     4,000    " 

l¥elfflit  of  1  Cord  or  Seasoned  Wood,  188  €ttMe  Feet  per 

Cord* 

Hickory  or  sugar  maple 4,500  Ibe. 

Whiteoak 8,860    *• 

Beech,  red  oak  or  black  oak ,  a»860    ^* 

Poplar,  chestnut  or  elm 8,860    " 

Pine  (white  or  Norway) 8,000    •* 

Hemlock  bark,  dry S;K)0    " 


8IZ£S  OP  FIBE-BBICK. 


233 


\  OF  FIRB-BBICK. 

9-ineh  straight 9x4Hx3U  Incliei. 

Soap 9x8Hx2U       ** 

Jamb      \      Checker 9x8    kST      " 

2-inch 9x4Uxa  »» 

fxiUxSU     /      SpUt 9x4UxlJ4       " 

»««<«i«  /     jj;^^^ 9x42xau     •' 

No.  1  key 9  x  2^  thick  x4H  to  4  Inches 

wide. 
«.^.         \  118  bricks  to  circle  12  feet  inside  diam. 

^V__A    No.2kej 9x2^  thick  x  4H  to  S« 

f"        ik'Ue't'4^  iDches  wide. 

b  *«»«  y^^;^  03  ijricks  to  drcfe  6  ft.  inside  dIam. 

No.Skey 9  x  2^  thick  x  4H  to  8 

inches  wide. 

8S  bricks  to  circle  8  ft.  inside  diftni. 

Weds.     \  ^^'ijj^^de ^'^^  ^^^  «  <«  to  2J4 

/'•w  «tf-  imtTTTT^  25  bricks  to  circle  1 W  ft.  inside  diani. 

*  *^'^^ 'Mr  No.  1  wedge  (or  bullhead).  9x4H  wide  x  2^  to  2  in. 
thick,  tapering  lengthwise. 
A  ■  V  96  bricks  to  circle  5  ft.  inside  diam. 

/\      AKk       \    No.2wedge 9x4Wx2U  to  1^  in.  thick. 

/    y -:: \  aO  bricks  to  circle  2^  ft.  inside  dlam. 

/  A*iH*{tH:iH/   No.  larch........    ........  9x4^x2V<  to  8  in.  thick, 

V/                    /             tapering  breadthwise. 
^                 -^                             78  bricks  to  circle  4  ft.  inside  dIam. 
No.2areh 9x4^x2XtoiW. 

C\                              42  bricks  to  circl«  2  ft.  inside  diam. 
No.lBk«w\       No.  1  skew 9to7x4Hto2^. 
V               \                         Bevel  on  one  end. 
> ^    No.2Bkew 9xaUx4Uto2Ji. 
^ViiiH*S}f/                         Equal  berel  on  both  edges. 
^        No.  8skew 9x2Hx4HtolH. 

Taper  on  one  edge. 

/sr — ,   ,„,      \      24inchcircle ^to!S^x4V<xaH. 

<   \    go«8Uw\  Edjpes  curred,  9  bricks  Tine  a  2*.ineh  circle. 

\    r  7     a«-incbcircle  W to ew x 4^ x J%. 

\  /f  X  tJtx  tiiCK£i  18  bricks  line  a  Sd-inch  circle. 

\i      n  i»-«»i     4ft4ochdrcle 8^ to 7J4 x 4^ ^ 2^. 

^« »  17  bricks  Une  a  48-inch  circle. 

ISU-lnch  straight inix2Hx6. 

13>2-inch  key  No.  1 IJ^  x  2^  x  6  to  5  inch. 

.  No  s  Skew — \  *>  bricks  turn  a  12-ft.  circle. 

'  ^     IS^lncb  key  No.  2 13^x2^x0  to  49^  inch. 

/0x9UMtAU\uV  ^2  briclcs  turn  a  6-ft.  circle. 

^     ^^^*V      Bridge  wall,  No.  1 13x6^x6. 

Bridge  wall,  No.  2 18x6>i  x  3. 

38to.OI«4e  MlUtUe 18.20,  or  24x6x8. 

sV      "^        Stock-hole  tiles 18, 20, or  24x9x4, 

\       IS-inchblock  18x9x6. 

,^      •«       \     Flatback  9xQxt^, 

'       ^ ^     Flatbackarch 9x6x8«to2H. 

22-inch  radius,  66  brlcJcs  to  circle. 

Locomotive  tile 82x10x8. 

84x10x8. 
CopoU"***^  Wx  8x3. 

40x10x8. 
Tiles,  slabs,  and  blocks,  yarioita  sises  12  to  30  inches 
long,  8  to  80  Inches  wide.  2  to  6  inches  thick. 
Cupola  brick,  4  and  6  inches  high,  4  and  6  inches  radial  width,  to  line  shells 
S3  to  66  in  diameter. 

A  94ach  straight  brick  weighs  7  lbs.  and  contains  100  cubic  inches.  (=120 
lbs.  pfw  cubic  foot.    Specific  gravity  1.98.) 

One  cubic  foot  of  wall  requires  17  9>lnch  bricks,  one  cubic  yard  requires 
400.  Where  keys,  wedges,  and  other  *'  shapes  "  are  used,  add  10  per  cent  la 
ettloMttiig  the  nuoibar  required. 


234 


MATERIALS. 


One  ton  of  fire-clay  should  be  sufficient  to  \aj  8000  ordinary  bricks.  To 
secure  the  best  results,  fire-bricks  should  be  laid  in  the  same  clay  from  which 
they  are  manufactured.  It  should  be  used  as  a  thin  paste,  and  not  as  moi^ 
tar.  The  thinner  the  joint  the  better  the  furnace  walL  In  ordering  bricks 
the  service  for  which  they  are  required  should  be  stated. 


NURIBKR  OF   FIRE-BRICK   REI^ITIRED   FOB 
TARIOU8   CIRCIiES. 


KEY  BRICKS 

ARCH  BRICKS. 

WEDGE  BRICKS. 

H 

^ 

eo 

o» 

^ 

i 

ei 

-J 

•a 

o« 

- 

^ 

o 

o 

d 

o 

o 

o 

o 

c 

o 

\B, 

» 

» 

^ 

H 

SS 

SQ 

d» 

H 

sz: 

^ 

d» 

H 

ft.  in. 

1  6 

25 
17 
9 

85 
80 
84 

2    0 

18 
25 

42 

81 

42 
49 

8  6 

18 

60 

60 

8  0 

88 

88 

21 

86 

67 

48 

20 

68 

3  6 

82 

10 

42 

10 

54 

64 

86 

40 

76 

4  0 

S5 

21 

46 

72 

72 

24 

69 

83 

4  6 

19 

82 

5! 

72 

8 

80 

12 

79 

91 

6  0 

18 

42 

56 

72 

15 

87 

98 

96 

5  6 

6 

58 

69 

72 

88 

95 

96 

8 

106 

6  0 

68 

68 

72 

SO 

102 

98 

15 

118 

0  6 

58 

9 

67 

72 

88 

110 

98 

28 

121 

7  0 

52 

19 

71 

72 

45 

117 

98 

80 

128 

7  6 

47 

29 

76 

78 

58 

126 

98 

88 

186 

8  0 

42 

38 

80 

72 

60 

138 

98 

46 

144 

8  6 

87 

47 

84 

72 

68 

140 

98 

58 

161 

9  0 

81 

57 

88 

72 

75 

147 

9H 

61 

150 

9  6 

26 

66 

92 

72 

88 

155 

98 

68 

166 

10  0 

21 

76 

97 

72 

90 

182 

96 

76 

174 

10  0 

16 

85 

101 

72 

98 

170 

98 

88 

181 

11  0 

11 

94 

106 

78 

106 

177 

98 

91 

189 

11  6 

5 

104 

109 

72 

118 

186 

98 

98 

196 

12  0 

118 
118 

118 
117 

72 

121 

198 

96 

106 

20i 

12  6 

For  larf^r  circles  than  12  feet  use  113  No.  1  Key,  and  as  many  9-inch  brick 
as  may  be  needed  in  addition. 


ANAIiYSES  OF  MT.  8ATAOE  FIBE-CIiAT. 

(1)  (2)                                                     (t)  (4) 

1871  1877.                                                      187a  1885. 

Institute  of  New^lreev                                          flSrvev^  Dr.  Otto  ' 

Technology,  pj^^.  if.^^k.                                 PenS^lTanla.  ^uth. 

60.467  66.80      Silica 44.396  66.16 

86.904  80.06     Alumina 83.558  88.895 

1.15     Titanic  acid 1.680  

1.604  1.12     Peroxide  iron 1.080  0.60 

0.133  ...  .      Lime trace  0.17 

0.018              Magnesia 0.108  0.115 

trace  0 .80     PotOHh  (alkalies) 0.247  

12.744  10.50     Water  and  inors>  matter.     14.675  9.68  ; 

100.760  100.450                                                   J00.498  100.000 


MAGKE8IA  BktOItd.  <635 

KAONK8IA    BRICKS. 

**  Foreign  Abstracts  "  of  the  Institution  of  Ci^U  Engineers,  1893,  gives  a 
(taper  by  C  Btschof  on  the  production  of  magnesia  bricks.  The  material 
most  in  favor  at  present  is  the  magueslte  of  Styria,  which,  altliough  less 
pure  eonsidervd  as  a  source  of  magnesia  than  the  Greek,  has  the  property 
of  fritting  at  a  high  temperature  without  melting.  The  composition  of  the 
two  subaitances,  iu  the  natural  and  burnt  stales,  is  as  follows: 

Hagnesite.  Styrian.  Greek. 

Carbonate  of  magnesia 90.0to96.0:t  94.46)( 

"   lime 0.6  to   2.0  4.49 

"   h-on 8.0to   6.0  FeOO.OS 

Silica 1.0  0.6a 

Manganous  oxide 0.6  Water  0.54 

Burnt  Magnesite. 

Magnesia 77.6  88.46-95.86 

Lime 7.8  0.88—10.92 

Alumina  and  ferric  oxide 18.0  0.66—  8.64 

Silica 1J8  0.78—7.98 

At  a  red  heat  magnesium  carbonat-e  is  decomposed  into  carbonic  acid  and 
caustic  magnesia,  which  resembles  lime  in  becoming  hydrated  and  recar- 
bonated  when  exnosed  to  the  air,  and  possesses  a  certain  plasticity,  so  that 
it  can  be  moulded  when  subjected  to  a  heary  pressure.  By  long-continued 
or  stronger  heating  the  material  becomes  dead-burnt,  giving  a  form  of  mag- 
necua  of  high  deonity,  sp.  gr.  8.8,  as  compared  with  8.0  in  the  plastic  form, 
which  is  unalterable  in  the  air  but  devoid  of  plasticity.  A  mixture  of  two 
voiuiiies  of  dead-burnt  with  one  of  plastic  magnesia  can  be  moulded  into 
bricks  which  contract  but  little  in  firing.  Other  binding  materials  that  have 
been  used  are:  clay  up  to  10  or  )6  per  cent;  gas-tar,  perfectly  freed  from 
water,  soda,  silica,  vinegar  as  a  solution  of  magnesium  acetate  which  is 
readily  decomposed  by  heat,  and  carbolates  of  alkalies  or  lime.  Among 
magnetduin  compounds  a  weak  solution  of  magnesium  chloride  may  also  be 
used.  For  setting  the  bricks  lightly  burnt,  caustic  magnesia,  with  a  small 
proportion  of  silica  to  render  it  less  refractory,  is  recommended.  The 
strength  of  the  bricks  may  be  inci^eased  by  adding  iron,  either  as  oxide  or 
vilicate.  If  a  porous  product  is  required,  sawdust  or  starch  may  be  added 
to  the  mixture.  When  dead-burnt  magnesia  is  used  alone,  soda  is  said  to  be 
the  best  binding  material. 

See  also  papers  by  A.  £.  Hunt,  Trans.  A.  I.  M.  E.,  xvl,  7^,  and  oy  T.  Egles- 
ton.  Tran>«.  A.  I.  M.  E.,  xlv.  458. 

Asbestos.— J.  T.  Donald,  Eng.  and  M.  Jour.,  June  27, 1891. 

AHALTBIB. 

Canadian. 

Italian.  Broughton.  Templeton. 

Silica 4O.809(  40.67){          4O.S0j( 

Magnesia 48.87  41.60            42.06 

Ferrous  oxide 87  2.81              1.97 

Alumina 2.27  .90             2.10 

Water 18.72  18.65           13.46 

100.68  99.88  100.10 

Chemical  analysis  throws  light  upon  an  Important  point  in  connection 
with  asbestos,  i.e.,  the  cause  of  the  harshness  of  the  fibre  of  some  varieties. 
A««be«toe  is  piinclpally  a  hjdrouM  silicate  of  magnesia,  i.e..  silicate  of  mag- 
nesia combined  with  water.  When  harsh  fibre  is  anaijsed  it  is  found  to 
eontain  less  water  than  the  soft  fibre.  In  fibre  of  very  fine  quality  from 
BUck  Tjake  analjrsis  showed  14.88j(  of  water,  while  a  hareh-fibred  sample 
gave  only  ll.TOjt.  If  soft  fibre  be  heated  to  a  temperature  that  will  drive  off 
a  portion  of  the  combined  water,  there  results  a  substance  so  brittle  that  it 
may  be  crumbled  between  thumb  and  Anrer.  There  is  evidently  some  con- 
nection between  the  oonsistenoy  of  the  fibre  and  the  amount  of  water  in  its 
eomposition. 


236  8TBBN6TH  OF  MATEBIALS. 


8!FB£NGTH  OF  MATESEIAIiS. 

stress  an4  Straim.— There  Is  mocb  oonlusion  amouff  writers  oo 
strength  ot  msteriala  as  to  the  defloiUon  of  these  terms.  An  ezterual  force 
applied  to  a  body,  so  as  to  pull  it  apart,  is  resisted  by  an  interual  force,  or 
resists Doe,  and  the  action  of  these  forces  catises  a  displacement  of  the  mole- 
cules, or  deformation.  By  some  writers  the  external  force  is  called  a  stress, 
and  the  internal  force  a  strain;  others  call  the  external  force  a  strain,  and 
the  internal  force  a  stress:  this  confasiou  of  terms  is  not  of  importance,  as 
the  words  stress  and  strain  are  quite  commonly  used  synonymously,  but  the 
use  of  the  word  strain  to  mean  molecular  displacement,  deformation,  or  dis- 
tortion, as  is  the  custom  of  some,  Is  a  corruption  of  the  languacre.  See  JSH- 
gineeiing  Newt,  June  28, 1892.  Definitions  by  leading  authorities  are  given 
Delow. 

Stres$,—A  stress  is  a  force  which  acts  in  the  Interior  of  a  body,  and  re- 
sists the  external  forces  which  tend  to  change  its  shape.  A  deformation  is 
the  amount  of  change  of  shape  of  a  body  caused  by  the  stress.  The  word 
strain  is  often  used  as  synonymous  with  stress  and  sometimes  It  Is  also  used 
to  designate  the  deformation.    iMei'riman.) 

The  force  by  which  the  molecules  of  a  body  resist  a  strain  at  any  point  is 
called  the  stress  at  that  point. 

The  summation  of  the  displacements  of  the  motocnles  of  a  body  for  a 
given  point  is  called  the  distortion  or  strain  at  the  point  considered.    (Burr). 

Btreesee  are  the  forces  which  are  applied  to  bodies  to  bring  into  action 
their  elastic  and  cohesive  properties,  'niese  forces  causs  allerattons  of  the 
fonns  of  the  bodies  upon  which  they  set.  Strain  is  a  name  given  to  the 
kind  of  alteration  produced  by  tho  stresses.  Tiie  distinction  betwe«ni  Btn*f>« 
and  strain  Is  not  always  obeerred,  one  being  used  for  the  other.    (Wood.) 

Stresses  are  of  different  kinds,  vis. :  termie^  eomprettive,  froiwvrras,  tor- 
s/i/Mo/,  and  ahectring  stresses. 

A  tensiU  »tre»a^  or  pull,  is  a  force  tending  to  ekmgats  a  pises.  A  eorn- 
presBive  stresa^  or  pnsh,  Is  a  force  tending  to  shmten  it.  A  Irantwne  wtrem 
tends  to  bend  it.  A  torsional  atresa  tends  to  twist  it.  A  ahearinQ  ttreaa 
tends  to  foroe  one  part  of  it  to  slide  o\'er  the  adjacent  part. 

Tensile,  compressive,  and  shearing  stresses  are  called  simple  stresses. 
Transverse  stress  is  compounded  of  tensile  and  compressive  stresses,  and 
torsional  of  tensile  and  shearing  stresses. 

To  these  five  varieties  of  stresses  might  be  added  feaWno  stress,  which  Is 
either  tensile  or  shearing,  but  in  which  the  resistance  of  different  portions 
of  the  msterfsl  are  brought  into  play  in  detail,  or  one  after  the  other,  in- 
stead of  siroultaneous]3%  as  in  the  simple  stresses. 

KITects  of  fltressss.^The  following  genera)  laws  for  casss  of  simple 
tension  or  compression  have  been  established  by  experiment.    (Merritnan): 

1.  ^hen  a  small  stress  is  applied  to  a  body,  a  small  deformation  is  pro- 
duced, and  on  the  removal  of  the  stress  the  body  springs  back  to  its  original 
form.  For  small  stresses*  then,  materials  may  be  regarded  as  perfectly 
elastic. 

2.  Under  small  stresses  the  deformations  are  approximately  proportional 
to  the  foix;es  or  stresses  which  produce  them,  and  also  approximately  pix>- 
poriionai  to  tlie  length  of  the  bar  or  t>ody. 

3.  When  the  stress  is  great  enough  a  deformation  is  produced  which  is 
partly  permanent,  that  is,  the  body  does  not  spring  back  entirely  to  its 
original  form  on  removal  of  the  stress.  This  permanent  part  is  teimed  a 
set.    In  such  cases  the  deformations  are  not  proi>ortional  to  the  stress. 

4.  When  the  stress  is  greater  still  the  deformation  rapidly  increases  and 
the  body  finally  ruptures. 

5.  A  sudden  stress,  or  shook,  Is  more  hs  jurkHis  than  a  steady  stress  or  than 
s  stress  gradually  applied. 

Blastie  Limit.— The  elastic  limit  is  defined  as  that  point  at  which  the 
deformations  cease  to  be  proportional  to  the  stresses,  or,  the  point  at  which 
the  rate  of  stretch  (or  other  deformation)  begins  to  increase.  It  is  als«> 
defined  as  the  point  at  which  the  first  permanent  set  becomes  visible.  The 
last  definition  is  not  considered  as  good  as  the  first,  as  It  is  found  that  with 
some  materials  a  set  occure  with  any  load,  no  matter  how  small,  and  that 
with  others  a  set  which  might  be  called  permanent  vanlsheB  with  lapse  of 
time,  and  as  it  is  impossible  to  get  the  point  of  first  set  without  removtB^r 


8TBB88  AKD  STRAUr.  237 

Uie  whole  load  atUr  each  increMe  of  load,  wblch  hi  tnqa&uVfy  liieonf —iwit. 
Thr  eJastie  limit,  defined,  however,  as  ihe  point  at  which  the  mxtoatAoom  he* 
gin  to  increaae  at »  higher  ratio  than  the  applied  streaaea,  uauaily  comaponda 
Tery  nearly  with  thepolnt  of  first  measurable  permaneDt  aefc. 

Tl«ld*potat«— llie  term  yield-point  has  recently  been  introduoed  into 
the  literature  of  the  strength  of  materials.  It  ia  deOaed  as  that  point  a4 
which  the  rate  of  stretoh  soddenlf  Inereaaea  rapk^y.  Th9  differeoos  be* 
tween  the  elastic  limit,  strictly  defined  aa  the  point  at  which  tlw  rate  of 
stretch  begins  to  increase,  and  the  vield-point,  at  which  Ihe  rate  hiereassa 
suddealy,  may  in  some  cases  be  considerable.  This  difference,  however,  will 
not  be  (Uflcorersd  hi  short  test*pieoes  unless  the  readings  of  ehMigatioBS  an 

made  by  mn  cxeeedlBgfy  Am  instrument,  as  a  mlcroiiieter  readhig  to  t==jl 

of  aa  iaelu  In  nainf  a  coarser  Instmmeni,  such  as  oaUpen  reading  to  1/lOt 
of  aa  inch,  the  eiaaOe  Usdt  and  the  rleld'pofnt  will  appear  to  be  smiixltane* 
ousL  UaCortmiataly  for  nreeWon  of  language,  the  term  yield-point  was  not 
introduced  until  long  after  the  term  elastic  limit  had  been  almost  unirer- 
laUy  adcMted  to  ainify  the  saine  physical  fact  which  is  now  defined  by  the 
Iran  xMd-poiat,  tfaaft  ia,  not  the  point  at  which  the  first  change  In  rate^ 
obserTable  <jDly  by  a  microsoope,  occurs,  but  that  later  polDt  (pioto  or  less 
IndeOnlK*  as  to  ila  precias  positioa)  at  which  the  Increase  Is  rreat  enough  to 
be  seen  by  the  naked  eye.  A  most  oonvenlettt  method  of  deterrainitig  the 
poteS  ai  whieh  a  soddea  Increase  of  rate  of  stretch  occurs  in  atntrt  speci- 
mstm,  when  a  tesUng-machlne  in  which  the  puIHng  Is  done  by  screws  is 
uaed,  is  to  note  the  weight  on  the  beam  at  the  tnstaat  that  the  beam  **  drops.** 
DttriaiK  tbe  eartter  portioa  of  the  lest,  as  the  extension  is  steadily  increased 

2r  tka  uniform  but  slow  rotation  of  the  screws,  the  potee  is  mored  steadi]|- 
...  .    .        ...  ... 

thet 


aJoo^  the  beam  to  keep  it  in  equipoise;  suddenly  a  point  fs  reached  at  which 
the  beam  drops,  and  will  not  nae  until  the  elongation  has  been  eonslderaUy 


r  the  further  rotation  of  the  scnsws,  the  advaochig  of  the  poise 

jMng  suspended.   This  point  oorreq>onds  practical^  to  the  point 

St  wliieh  the  rate  or  eloogatlon  suddenly  Increases,  and  to  the  peint  at 
which  an  appreciable  permanent  set  is  first  found.  It  is  also  the  point  which 
haa  hltJierto  betn.  caltod  in  practioe  and  in  text-books  the  elastic  limit,  and 
it  wUl  probably  continue  to  be  so  called,  although  tbe  use  of  the  newer  term 
"yieW^oiat  *^  for  it,  and  the  restriction  of  the  term  elastic  limit  to  mean 
the  earuer  polat  at  which  the  rate  of  stret^  begins  to  Increase,  aa  determin* 


B  aaif  by  mieromelrio  measnreaoents^  Is  more  precise  and  sdentiflc. 
IB  taUea  of  strength  of  ssatsrlals  hereafter  given,  the  term  elastte  ttmit  is 
used  in  ha  easteoary  raeaatag;  the  point  at  which  the  rate  of  stress  has  be* 
gun  to  increase,  as  observable  by  ordinary  instruments  or  by  the  drop  of 
the  beam.    With  thia  definlthm  It  Is  practically  synonymous  with  yleld- 


Jit  ior  ■•Aiditt^  of  Blaatleity*— HkfB  fa  a  term  expiBss- 

lag  tbe  reladoa  between  the  amount  of  extenoion  or  cotiipressfon  of  a  mat» 
rial  aad  the  load  prodocfaiff  that  eztensioii  or  compression. 

It  ma^^  be  defined  aa  the  load  per  unit  of  sectlOD  divided  by  tlie  estcnsion 
per  unk  of  Isngth;  or  the  lecftprocal  of  the  f mclion  espresnng  the  efonga* 
tkm  per  Inch  of  length,  divided  by  the  poands  per  square  inch  of  section 
prodacfaiff  that  elongation. 

Let  P  be  the  applfed  load,  h  the  seethmal  area  of  the  piece,  I  the  length  of 
the  part  exteadad»  A  the  amoaat  of  the  extensioD,  ana  IT  the  ooefilcient  of 
elasticity.    Then 

p 

jr  B  theloadooaniiltof  sectfon; 

J  m  the  eleogation  of  a  unit  of  length. ' 
-     P       A       PJ 


The  coefilclept  of  eUutlcity  is  sometimes  defined  as  the  figure  expressina 
the  load  which  would  be  necessary  to  elongate  a  piece  of  one  iquare  inch 
seetioa  lo  double  its  original  length,  provided  Che  piece  would  not  break,  and 


the  ratio  of  extension  to  the  force  producing  it  remaiaed  ooiwtant.    This 
definitioa  follows  from  the  formula  above  given,  thus:  If  Jrasoue  squace 
Iseh,  I  and  A  each  ss  one  inch,  then  B=  P. 
WSUn  the  efawtie  limit,  when  the  deformations  are  proportional  to  thf 


238  ST&ENGTH  OF  MATERIALS. 

stresses,  the  ooefflcient  of  elasticity  Is  constant,  but  beyond  tLe  eliistic  limit 
it  decreases  rapidly. 

In  cast  iron  there  is  generally  do  apparent  limit  of  elasticity,  the  deforms^ 
Uons  increasing  at  a  faster  rate  than  the  stresses,  and  a  permanent  set  being 
produced  by  small  loads.  The  coefficient  of  elasticity  therefore  Is  not  con- 
stant during  any  portion  of  a  test,  but  grows  smaller  as  the  load  increaises. 
The  same  is  true  in  the  case  of  timber.  In  wrought  iron  and  steel,  however, 
there  is  a  well-defined  elastic  limit,  and  the  coefficient  of  elasticity  within 
that  limit  Is  nearly  constant. 

ResUlenee,  or  WorlL  of  Resistance  of  a  Material.— Within 
the  elastic  limit,  the  resistance  increasing  uniformly  from  zero  stress  to  the 
stress  at  the  elastic  limit,  the  work  done  by  a  load  applied  gniduaily  is  equal 
to  one  half  the  product  of  the  final  stress  by  the  extension  or  other  deforma- 
tion. Beyond  the  elastic  limit,  the  extensions  increasing  more  rapidly  than 
the  loads,  and  the  strain  diagram  approximating  a  parabolic  form,  the  work 
is  approximately  equal  to  two  thirds  the  product  of  the  maximum  stress  by 
the  extennion. 

The  amount  of  work  required  to  break  a  bar,  measured  usually  in  inch- 
pounds,  is  called  its  resilience;  the  work  required  to  strain  it  to  the  elastic 
limit  is  called  its  elastic  resilience. 

Under  a  load  applied  suddenly  the  momentary  elastic  distortion  is  equal 
to  twice  that  caused  by  tlie  same  load  applied  gradually. 

When  a  solid  material  is  exposed  to  percussive  streis,  as  when  a  weight 
falls  upon  a  beam  transversely,  the  work  of  resistance  is  measured  by  the 
product  of  the  weight  into  the  total  fall. 

BleTatlon  of  Ultimate  Beaiatanee  an4  Blaatio  I<lmit«— It 
was  first  observed  by  Pruf.  R.  H.  Thurston,  and  Commander  L.  ▲.  Beards- 
lee,  U.  8.  N.,  independenthr,  in  1878,  that  if  wrought  iron  be  subjected  to  a 
stress  beyond  its  elastic  limit,  but  not  beyond  its  ultimate  resistance,  and 
then  allowed  to  "  rest  ^*  for  a  definite  interval  of  time,  a  considerable  in- 
crease of  elastic  limit  and  ultimate  resistance  may  be  experienced.  In  other 
words,  the  application  of  stress  and  subsequent  **  rest "  mcreases  the  resist- 
ance of  wrought  iron. 

This  *'  rest "  may  be  an  entire  release  from  stress  or  a  simple  holding  the 
test-piece  at  a  (riven  intensity  of  stress. 

Commander  Beardslee  prepared  twelve  specimens  and  subjected  them  to 
an  Intensity  of  stress  equal  to  the  ultimate  resistance  of  the  material,  with- 
out breaking  the  specimens.  Thene  were  then  allowed  to  rest,  entirely  free 
from  stresii,  from  S4  to  SO  hours,  after  which  period  they  were  again  stressed 
until  broken.  The  gain  in  ultimate  resistance  by  the  rest  was  found  to  Taiy 
from  4.4  to  17  per  cent. 

This  elevation  of  elastic  and  ultimate  resistance  appears  to  be  peculiar  to 
iron  and  steel:  it  lias  not  been  found  in  other  metals. 

Relation  of  tl&e  Blastie  lilmit  to  Kndaranee  under  Re* 
peated  Stresses  (condensed  from  Engineering^  August  7,  10B1).~ 
When  engineers  first  began  to  test  materials.  It  was  soon  recognised  that 
if  a  specimen  was  loaded  beyond  a  certain  point  it  did  not  recover  its  origi- 
nal dimensions  on  removing  the  load,  but  took  a  permanent  set:  this  point 
was  called  the  elastic  limit.  Since  below  this  pointa  bar  appeared  to  recover 
completely  its  original  form  and  dimensions  on  removing  the  load,  it  ap* 
peared  obvious  that  it  had  not  been  injured  by  the  load,  and  hence  the  work- 
ing load  might  be  deduced  from  the  elastic  limit  by  u^g  a  small  factor  of 
safety. 

Experience  showed,  however,  that  in  many  cases  a  bar  would  not  carry 
safely  a  stress  anywhere  near  the  elastic  limit  of  the  material  as  determined 
hr  these  experiments,  and  the  whole  theoi  y  of  any  connection  between  the 
elastic  limit  of  a  bar  and  its  working  load  became  almost  discredited,  and 
engineers  employed  the  ultimate  strength  only  in  deducing  the  safe  working 
load  to  which  their  structures  might  be  subjected.  Still,  as  experience  accu- 
mulated it  was  observed  that  a  higher  factor  of  safety  was  required  for  a  live 
load  than  for  a  dead  one. 

In  1871  W5hler  published  the  results  of  a  number  of  experiments  on  bars 
of  iron  and  steel  subjected  to  live  loads.  In  these  experiments  the  stresses 
were  put  on  and  removed  from  the  specimens  without  impact,  but  it  was, 
nevertneless,  found  that  the  breaking  stress  of  the  materials  was  in  every 
case  much  below  the  statical  breaking  load.  Thus,  a  bar  of  Krupp*s  axfe 
steel  having  a  tenacity  of  49  tons  per  square  inch  broke  with  a  stress  of  88.6 
tons  per  square  inch,  when  the  load  was  completely  removed  and  replaced 
without  impact  170,0iD0  timea    These  experiments  were  made  on  a  large 


BTBE8S  AND  STBAIK.  889 

BDmber  of  different  bnnds  of  iron  and  stael,  and  the  remiltg  were  ooneor- 
dant  Id  flhowiiiff  that  a  bar  would  break  with  an  alternating  stren  of  only, 
■aj,  one  third  the  statical  breaking  strenflrtii  of  the  material,  if  the  repetitions 
of  itreea  were  sufficiently  numerous.  At  the  same  time,  howerer,  it  ap- 
peared from  the  generaltrend  of  the  experiments  that  a  bar  would  stand  an 
iDdellBite  number  of  alternations  of  stress,  prorided  the  stress  was  kept 
below  the  limit. 

Prof.  Bauflchineer  defines  the  elastic  limit  as  the  point  at  which  stress 
eeaaea  to  be  sensibly  proportional  to  strain,  the  latter  being  measured  with 

a  mirror  apparatus  reading  to  ggg^tb  of  a  millimetre,  or  about  ^jq^qq  In. 

This  limit  Is  always  below  the  yield-point,  and  may  on  occasion  be  sero.  On 
loading  a  bar  above  the  yield-point,  this  point  rises  with  the  stress,  and  the 
rise  continues  for  weeks,  months,  and  possibly  for  years  if  the  bar  Is  left  at 
rest  under  Its  load.  On  the  other  band,  when  a  bar  Is  loaded  beyond  its  true 
elastic  limit,  but  below  its  yield-point,  this  limit  rises,  but  reaches  a  maxi- 
mum as  the  yield-point,  is  approached,  and  then  falls  rapidly,  reaching  eren 
to  zero.  On  leaving  the  bar  at  rest  under  a  stress  exceeding  that  of  its 
primitive  breaking-down  point  the  elastic  limit  begins  to  rise  again,  and 
may.  If  left  a  sufficient  time,  rise  to  a  point  much  exceeding  Its  previous 
value. 

This  property  of  the  elastic  limit  of  changing  with  the  histoiy  of  a  bar  has 
done  more  to  discredit  it  than  anything  else,  nevertheless  it  now  seems  as  If 
ic«  owlDff  to  this  very  property,  were  once  more  to  take  its  former  place  in 
the  estimation  of  engineers,  and  this  time  with  fixity  of  tenure.  It  had  long 
been  known  that  th<9  limit  of  elasticity  might  be  raised,  as  we  have  said,  to 
almost  any  point  within  the  breaking  load  of  a  bar.  Thus,  in  some  experi- 
ments 1^  Professor  Styfle,  the  elastic  limit  of  a  puddled-steel  bar  was  raised 
ie,QOO  lbs.  by  subjecting  the  bar  to  a  load  exceeding  its  primitive  elastic 
Bmlt. 

A  oar  has  two  limits  of  elasticity,  one  for  tension  and  one  for  compression. 
Baiischlnger  loaded  a  number  of  oars  in  tension  until  stress  ceased  to  be 
ienslbly  proportional  to  strain.  The  load  was  then  removed  and  the  bar 
tested  in  compression  until  the  elastic  limit  In  this  direction  had  been  ex- 
ceeded. This  process  raises  the  elastic  limit  in  compression,  as  would  be 
found  on  testing  the  bar  in  compression  a  second  time.  In  place  of  this, 
however.  It  was  now  again  tested  in  tension,  when  It  was  found  that  the 
artificial  raising  of  the  limit  in  compression  had  lowered  that  in  tension  be- 
low its  previous  value.  By  repeating  the  process  of  alternately  testing  in 
tension  and  compression,  the  two  limits  took  up  points  at  equal  distances 
from  the  line  of^no  load,  both  In  tension  and  compression.  These  limits 
Baoschinger  calls  natural  elastic  limits  of  the  bar,  which  for  wrought  Iron 
correspond  to  a  stress  of  about  8^  tons  per  square  inch,  but  this  is  practically 
the  limiting  load  to  which  a  bar  of  the  same  material  can  be  strained  alter- 
mutely  In  tension  and  compression,  without  breaking  when  the  loading  is 
repeated  sufficiently  often,  as  determined  by  wahler's  method. 

As  received  from  the  rolls  the  elastic  limit  of  the  bar  in  tension  Is  above 
the  natural  elastic  limit  of  the  bar  as  defined  by  Bauschinger,  having  been 
artificially  raised  by  the  deformations  to  which  it  has  been  subjected  in  the 
process  of  manufacture.  Hence,  when  subjected  to  alternating  stresses, 
the  limit  In  tension  is  immediate^  lowered,  while  that  in  compression  Is 
raised  nntU  they  both  correspond  to  equal  loads.  Hence,  in  Wohler's  ex- 
periments, in  wnich  the  bars  broke  at  loads  nominally  below  the  elastic 
omits  of  the  material,  there  is  every  reason  for  concluding  that  the  loads 
vere  really  greater  than  true  elastic  limits  of  the  material.  This  is  con- 
firmed by  tests  on  the  connecting-rods  of  engines,  which  of  course  work 
under  alternating  stresses  of  equal  Intensity.  Careful  experiments  on  old 
rods  sliow  that  the  elastic  limit  in  compression  is  the  same  as  that  in  ten- 
sion, and  thAt  both  are  far  below  the  tension  elastic  limit  of  the  material  as 
raoeived  from  the  rolls. 

The  common  opinion  that  straining  a  metal  beyond  Its  elastic  limit  injures 
it  appears  to  be  untrue.  It  is  not  the  mere  straining  of  a  metal  beyond  one 
elastic  limit  that  Injures  It,  but  the  straining,  many  times  repeated,  beyond 
its  two  etastic  limits.  Sir  Benjamin  Baker  has  shown  that  In  bending  a  shell 
piste  for  a  boiler  the  metal  is  of  necessity  strained  beyond  its  elastic  limit, 
■othat  stresses  of  as  much  as  7  tons  to  15  tons  per  square  inch  may  obtain 
is  It  as  it  comes  from  the  rolls,  and  unless  the  plate  is  annealed,  these 
itiesses  will  still  exii^  after  it  has  been  built  Into  the  boiler.  In  such  a  case, 
hofrever,  when  exposed  t9  %^9  9<|dlt|ooal  stress  due  to  the  pressure  inskio 


240  STBBNaTH  OF  MATERIALS. 

Ihe  boJ]«r,  the  ovsntratned  poitkmft  of  the  plate  will  relieve  Chemselvee  by 
9tretchinff  and  tekinc  e  permanent  eet,  80  that  probably  after  a  Tear'ii  work- 
ing  verj  Hctle  dlflerenoe  couid  be  detected  in  (he  RtreMee  In  a  plate  built  in- 
to  the  boiler  ac  it  eame  from  tlie  bending  rolU,  and  in  one  mrhioh  had  b««fli 
aonealed.  before  rlTetloK  into  plaoe,  and  the  flrit,  la  spite  of  Ite  having  been 
strained  beyond  iU  eleetio  llnuU,  and  not  aubeequentiy  annealed,  would  be 
as  strong  as  the  other. 

Bestotanee  ot  Het«l«  to  Repeated  ffbocke* 

More  than  twelve  years  were  spent  by  WOhler  at  the  instance  of  thePrue- 
■laQ  Oovemment  In  experimenting  upon  the  resistance  of  iron  and  steel  to 
repeated  stressea  The  reeulte  of  his  experimeDts  are  expressed  in  what  is 
known  as  WOhlei^s  law,  which  le  given  in  the  following  words  In  Duboto'e 
translation  of  Weyrauch: 

"  Rupture  may  be  caused  not  only  by  a  steady  loed  which  exceeds  ib# 
carrir  ing  strength,  but  also  hf  repeated  applications  of  stresses,  none  of 
whi<$h  are  equal  to  the  carrying  strength.  The  differences  of  these  stresses 
are  measures  of  the  disturbance  of  continuity,  in  so  far  as  by  their  increase 
the  minimum  stress  which  Is  still  neoesaary  for  rupture  dinuniabes," 

▲  practical  illustration  of  the  meaning  of  the  first  portion  of  this  law  may 
tie  Ki^B  thus:  If  60,000  pounds  once  applied  will  just  break  a  bar  ot  iron  or 
steel,  a  stress  very  much  less  than  wjw  pounds  will  break  it  if  repeated 
suiUciently  often. 

This  is  fully  oonflrmed  by  the  experiments  of  Fairbaim  and  Spaogenbery. 
as  well  as  tnose  of  WOhler;  and,  as  is  remarked  by  Weyrauch,  it  may  be 
considered  as  a  long-known  result  of  common  experience.  It  parUally  ac^ 
counts  for  what  Mr.  Holley  has  called  the  *'  hitrineically  ridiculous  factor  of 
safety  of  six.*' 

Another  **  long-known  result  of  experience  ^  Is  the  fact  that  rupture  may 
be  caused  by  a  succession  of  thocka  or  impacUt  none  of  which  alone  wottkl 
be  sufficient  to  oauae  it.   Iron  axles,  the  piston-rods  of  steam  hammers,  and 

gther  pieces  of  metal  subject  to  continuously  repeated  shocks.  inTariably 
raak  after  a  oertain  leogtb  of  service.   They  have  a  "Uf^  **  which  is  lim- 
ited. 

Several  years  ago  Fairbahm  wrote:  **  We  know  that  In  some  cases  wrouirbt 
iron  subjected  to  oontbiuous  vibration  assumes  a  cnrstalline  structure,  *nd 
that  the  cohesive  powers  are  much  deteriorated,  but  we  are  ignorant  of  the 
causes  of  this  change.^'  We  are  still  ignorant,  not  only  of  the  causes  of  this 
change,  but  of  the  conditions  under  which  It  takes  place.  Who  knows 
whether  wrought  iron  subjected  to  very  slight  continuous  vibration  will  co- 
dure  forever?  or  whether  to  insure  final  rupture  each  of  the  continuous  small 
shocks  must  amount  at  least  to  a  certain  percentage  of  single  heavy  shock 
(both  measured  in  f  oot-poundK),  which  would  cause  rupture  with  one  applies^ 
tlon  ?  WOhler  found  in  testing  iron  by  repeated  stresses  (not  impacts)  tliat 
in  one  case  400,000  applications  of  a  stress  of  600  centners  to  the  square  inch 
caused  rupture,  while  a  similar  bar  remained  sound  after  48,000,000  applica- 
tions of  a  stress  of  800  centners  to  the  sauare  inch  (1  centner  =*  llO Ji  Aw.)' 

Wbo  knows  whether  or  not  a  similar  law  holda  true  in  regard  to  re|»eaiad 
shocks  7  Suppose  that  a  bar  of  iron  would  break  under  a  shigle  impact  of 
lOOO  foot-pounds,  how  many  times  would  It  be  likely  to  bear  the  repetition 
of  100  foot  pounds,  or  would  it  be  safe  to  allow  it  to  remain  for  fifty  y^Lrs 
subjected  to  a  continual  succession  of  blows  of  even  10  foot-pounds  each  r 

Mr.  WUllam  Metcalf  published  in  ibe  Metallurgical  Review,  Pea  1877,  the 
results  of  some  tests  of  the  life  of  steel  of  different  percentages  of  carbon 
under  impact.  Some  small  steel  pitmaos  were  made,  the  specifications  for 
which  required  that  the  unloaded  machine  should  run  4^  hours  at  the  rate 
of  rJOO  revolutions  per  minute  before  breaking. 

The  steel  wss  all  of  uniform  quality,  except  as  to  carbon.  Here  are  the 
results:  The 

.ao  C.  ran  1  h.  21  m.   Heated  and  bent  before  breaking. 

.49  C.    **  Ih.  88  m.,       »*        "     *•        "  ** 

.43  0.    "  4  b.  67  m.    Broke  without  heating. 

•46  a    "  <h.  90  m.    Broke  at  wekl  where  Imperfect. 

•fiOC.    '*  5h.40m. 

.84  0.    "18h. 

•87  0.    Broke  in  weld  near  the  end. 

M  0.    Ban  4.66  m.,  and  the  machine  broke  down. 

Some  other  experlmenta  by  Mr.  Metcalf  confirmed  hia  <;0D0luBion,  vis,. 


6TR£S6  AND  STRAIN.  241 

that  liigb-carbon  steel  was  better  Adapted  to  reeist  repeated  shocks  and  vi- 
brations than  low-carboD  steel. 

Tliese  results,  however,  would  scarcely  be  suiflcient  to  induce  any  eu- 
^neer  to  use  .84  carbon  steel  In  a  car-axle  or  a  bridge-rod.  Further  experi- 
ments are  needed  to  confirm  or  overthrow  them. 

(See  description  of  proposed  apparatus  for  such  an  investigation  in  the 
aiitbor*s  paper  in  Trans.  A.  I.  M.  £.,  vol.  viii ,  p.  76,  from  which  the  above 
extract  is  taken.) 

Mresfles  Prodneed  1»f  Suddenly  AppUed  Forces  and 
Sltocks* 

(Mansfield  Herriman,  B.  B.  dt  Eng.  Jour.,  Dec.  1889.) 
Let  P  be  tiie  weif?ht  which  la  dropped  from  a  height  h  upon  the  end  of  a 
bar,  and  let  y  be  the  maximum  elongation  which  is  produced.    The  work 
performed  bjr  the  falling  weight,  then,  is 

and  this  must  equal  the  internal  work  of  the  resisting  molecular  stresses. 
The  stresA  in  the  bar,  which  is  at  first  0,  increases  up  to  a  certain  limit  Q, 
which  is  greater  than  P;  and  if  the  elastic  limit  be  not  exceeded  the  elonga- 
tion increases  uniformly  with  the  stress,  so  that  the  internal  work  is  equal 
to  the  mean  stress  1/2Q  multiplied  by  the  total  elongation  y,  or 

Whence,  neglecting  the  wori^  that  may  be  dissipated  in  beat, 

if  e  be  the  elongation  due  to  the  statio  load  P,  within  the  elastic  limit 
y=  %e;  whence 


Q.p(iV»+«')' 


(t) 

which  gjkves  the  momentaiy  maximum  stress.    Substltnting  this  value  of  Q, 
there  rnnlta  

»=«(i+i^i+2^) (») 

whiefa  is  tbe  value  of  the  momentary  maximmn  elongation. 

A.  shoek  resolts  when  the  force  P,  before  its  action  on  the  bar.  Is  moving 
with  velocity,  as  is  the  case  when  a  weight  P  falls  from  a  heignt  h.  The 
above  formulas  show  that  this  height  h  may  be  small  if  e  is  a  stnall  quan- 
tity, and  yet  very  great  stresses  and  deformations  be  produced.  For  in- 
stanoe,  let  A  s  4€,  then  Q=s4P  and  tf  3  4e  ;  ahm  let  A  » iSe,  then  Q  =  8P 


steady  load  of  6000  Ikm.  tbis  will  be  compressed  about  0.018  in.,  supposfncr 
that  no  lateral  flexure  occurs;  but  if  a  weight  of  5000  lbs.  drops  upon  its  end 
from  the  amaU  height  of  0.046  in.  there  will  be  produced  the  stress  of  90,000 


A  soddeoly  applied  force  Is  one  which  acts  with  the  uniform  taCensity  P 
upon  the  end  of  the  bar,  but  which  has  no  velocity  before  acting  upon  it. 
This  corresponds  to  the  case  of  A  s  0  in  the  above  formulas,  and  gives  Q  = 
2P  and  y  s=  2e  for  the  maximum  stress  and  maximum  deformation.  Prob- 
ably the  action  of  a  rapidly-moving  train  upon  a  bridge  pivduces  stresses 
of  this  character. 

Inereaatms  tbe  Tenalle  Streng^tli  of  Iron  Bars  by  Tirlat- 
iBg:  tlaeiit«— Ernest  L.  Ransoms  of  San  Francisco  has  obtaiued  an  English 
Patenu  No.  16'<S^1  of  1888,  for  an  *'  improvement  in  strengthening  and  testing 
vrought  metal  and  steel  rods  or  bars,  consisting  in  twisting  the  same  in  a 
cold  state.  .  .  .  Any  defect  In  the  lamination  of  the  metal  which  would 
otherwiaebe  concealed  is  revealed  by  twisting,  and  imperfections  are  shown 
at  once.  The  treatment  may  be  applied  to  bolts,  suspension-rods  or  bars 
subjected  to  tensile  strength  of  any  description." 

Besnlta  of  tests  of  this  process  were  reported  by  lieutenant  F.  P.  Qilmore, 
U.  8.  v.,  in  a  paper  read  before  the  Technical  Society  of  the  Pacific  Ooast, 
published  in  the  Transactions  of  the  Society  for  the  month  of  December, 
lilSA.  The  experiments  Include  trials  with  thirty-nine  bars,  twenty-nine  of 
which  were  variously  twisted,  from  three-eighths  of  one  turn  to  six  turns  per 
loot.   Tbe  test-pieces  were  cut  from  one  and  the  same  bar,  and  accurately 


243 


STRENGTH  OF  MATERIALS. 


measured  and  numbered.  From  each  lot  two  pieces  without  twist  were 
•«8ted  for  tensile  streuKth  and  duclilit  v.  One  group  of  each  set  was  twisted 
until  the  pieces  broke,  as  a  guide  for  the  amount  of  twist  to  be  giyen  those 
to  be  tested  for  tensile  strain. 

The  following  is  the  result  of  one  set  of  Lieut.  Qilmore's  tests,  on  iron 
bars  8  in.  long,  .719  in.  diameter. 


No.  of 
Bars. 

Conditions. 

Twists 

in 
Turns. 

Twists 
per  ft. 

Tensile 
Strength. 

Tensile 
per  sq.  in. 

Gain  per 
ceoL 

Nottwisfed. 
Twisted  cold. 

««                  4» 

0 
8 

0 

SS,000 
28,900 
85,800 
86,800 
86,400 

54,180 
60,080 
68,600 
64,750 
65,000 

9 
17 
19 
20 

Tests  that  corroborated  these  results  were  made  by  the  University  of 
California  in  1889  and  by  the  Low  Moor  Iron  Works,  England,  in  1890. 

TENSIIiE  STRENGTH. 

The  following  data  are  usually  obtained  in  testing  by  tension  In  a  testing- 
machine  a  sample  of  a  material  of  construction : 

The  load  and  the  amount  of  extension  at  the  elastic  limit 

The  maximum  load  applied  before  rupture. 

The  elongation  of  the  piece,  measured  between  gauge-marks  placed  a 
stated  distance  apart  before  the  test;  and  the  reduction  of  area  at  the 
point  of  fracture. 

The  load  at  the  elastic  limit  and  the  maximum  load  are  recorded  in  pounds 
per  aquare  inch  of  the  original  area.  The  elongation  is  recorded  as  a  per- 
centage of  the  stated  length  between  the  gauge-marks,  and  the  reduction 
area  as  a  percentage  of  the  original  area.  The  coefficient  of  elasticltv  is  cal- 
culated from  the  ratio  the  extension  within  the  elastic  limit  per  inch  of 
lengfth  bears  to  the  load  per  square  inch  producing  that  extension. 

On  account  of  thedifflculty  of  making  accurate  measurements  of  the  frac- 
tured area  of  a  test-piece,  and  of  the  fact  that  elongation  is  more  valuable 
than  reduction  of  area  as  a  measure  of  ductility  and  of  redlience  or  work 
of  resistance  before  rupture,  modem  experimenters  are  abandoning  the 
custom  of  reporting  reduction  of  area.  Tne  "  strength  per  square  inch  of 
fractured  section  "  formerly  frequently  used  in  reporting  tests  is  now  almost 
entirely  abandoned.  The  data  now  calculated  from  the  results  of  a  tensile 
test  for  commercial  purposes  are:  1.  Tensile  strength  in  pounds  per  square 
inch  of  original  area.  8.  Elongation  per  cent  of  a  stated  iengu  between 
gauge-marks,  usually  8  inches.  8.  Elastic  limit  in  pounds  per  square  inch 
of  original  area. 

The  short  or  grooved  test  specimen  gives  with  most  metals,  especially 
with  wrought  iron  and  steel,  an  apparent  tensile  strength  much  higher 
than  the  real  strength.  This  form  of  test-piece  is  now  almost  entirely  aban- 
doned. 

The  following  results  of  the  tests  of  six  specimens  from  the  same  1^"  steel 
bar  illustrate  the  apparent  elevation  of  elastic  limit  and  the  changes  in 
other  properties  due  to  change  in  length  of  stems  which  were  turned  down 
in  each  specimen  to  .796''  diameter.  (Jas.  £.  Howard,  Eng.  Congress  1898^ 
Section  O.)        


Description  of  Stem. 


Elastic  Limit, 
Lbs.  per  Bq.  In. 


Tensile  Strength, 
Lbs.  per  Sq.  In. 


Contraction  of 
Area,  per  cent. 


1.00"  long 

.50     »»    

.25      "     

Semicircular  groove, 

.4"  radius 

Semicircular  groove, 

W'  radius 

V-shaped  groove 


64,900 
65,880 
68,000 

75,000 

86.000,  about 
90,000,  about 


94,400 
97,800 
108,480 

116,880 

184,960 
117,000 


49.0 
48.4 
80.6 

81.6 

S8.0 
Indeterminate. 


TEK81LB  BtRENGTH. 


243 


Teito  plate  made  by  the  author  in  1879  of  straight  and  grooved  tert-pleoes 
of  boilerplate  steel  out  from  the  same  gare  the  following  results : 
5  straight  pieces,  56,606  to  59,012  lbs.  T.  8.    Arer.  57,566  lbs. 

4  grooved     "       64,841  lo  67.400 65,450  " 

Excesi  of  the  short  or  grooved  specimen,  21  per  cent,  or  12,114  lbs. 

Heaaurement  of  Elonciitioii.— In  order  to  be  able  to  compare 
records  of  elongation,  it  is  necessary  not  only  to  have  a  uniform  length  of 
sectioo  between  gauge-marks  (say  8  inches),  but  to  adopt  a  uniform  method 
of  measuring  the  elongation  to  compensate  for  the  duferenee  between  the 
apparent  elongation  when  the  piece  breaks  near  one  of  the  sauge-marks, 
and  when  it  breaks  midway  between  them.  The  following  method  is  rec- 
ommended (Trans.  A.  8.  M .  E.,  voL  zi.,  p.  622): 

Kark  on  the  specimen  divisions  of  1/2  inch  each.  After  fracture  measure 
from  the  point  of  fracture  the  length  of  8  of  the  marked  spaces  on  each 
fractured  portion  (or  7  -f  on  one  side  and  8  +  on  the  other  if  the  fracture  is 
not  at  one  of  the  marks).  The  sum  of  these  messurements,  less  8  inches,  is 
the  elongation  of  8  inohes  of  the  original  length.  If  the  fracture  is  so 
near  one  end  of  the  specimen  that  7+ spaces  are  not  left  on  the  shorter 
portion,  then  take  the  measurement  of  as  many  spaces  (with  the  fractional 
part  next  to  the  fracture)  as  are  left,  and  for  the  spaoes  lacking  add  the 
measoreDoent  of  as  many  corresponding  spaces  of  the  longer  portion  as  are 
necessary  to  make  the  7 -f>  spaoes. 

^  apes  of  SpacimeMa  i6r  Tenalle  Taata.— The  shapes  shown 
:.  iS  were  reoommended  by  the  author  in  1883  when  he  was  connected 


No.  1.    Square  or  flat  bar,  aa 
roUed. 


No.  2.    Round  bar,  as  ndled. 


No.  8.  Standard  shape  for 
flats  or  squares.  Fillets  Vi 
inch  radius. 


No.  4.  Standard  shape  for 
rounds.  Fillets  |^  in.  radius. 

No.  5.  Government  shape  for 
marine  boiler-plates  oi:  iron. 
Not  recommended  for  other 
tests,  as  results  are  generally 
in« 


Fio.  75. 
with  the  Ptttabargfa  Testing  Laboratory.     They  are  now  in  most  general 
USB,  the  earlier  forms,  with  6  inches  or  less  in  length  between  shoulders, 
bring  almost  enUrety  abandoned. 

^nemmUonm  Baanlred  In  maklms  Tenalle  Teata*— The 
tMtine-mac^iine  itself  snould  be  tested,  to  detormine  whether  its  weighing 
spparatus  is  accurate,  and  whether  it  is  so  made  and  adjusted  that  in  the 
test  of  a  properly  maae  specimen  the  line  of  strain  of  the  testing-machine 
h  ahaolutely  in  line  with  flie  axis  of  the  specimen. 

The  specimen  should  be  so  shaped  that  It  will  not  give  an  hioorrect  record 
of  strength. 

It  should  be  of  uniform  minimum  section  for  not  less  than  five  inches  of 
its  length. 

Regard  must  be  had  to  the  time  occupied  in  making  tests  of  certain  mate- 
rials. Wrought  iron  and  soft  steel  can  be  made  to  show  a  higher  than  their 
•etoal  an*****"*'  strengdi  by  keeping  them  under  strain  for  a  great  length 

of  lime, 
la  testing  soft  alloys,  copper,  tin,  sine,  and  the  like,  which  flow  under  con- 

asat  snm  their  highesf  apparent  strength  is  obtained  by  testing  them 

raaidly.  In  reoording  teste  of  such  materials  the  length  of  time  occupied  in 

ihs  test  ahonld  be  stated. 


244  STRENGTH  OF  MATERIALS. 

For  Terv  accurate  measurements  of  eloDgatioo,  corresponding  to  Incre- 
ments of  load  during  tlte  tests,  the  electric  contact  micrometer,  described 
in  Trans.  A.  8.  M.  E.,  vol.  vl.,  p.  479,  will  be  found  coDvenient.  When  read- 
ings of  elongation  are  then  taken  during  the  test,  a  strain  diagram  may  be 
plotted  from  the  reading,  which  is  useful  in  comparing  the  qualities  of  dif- 
ferent specimens.  Such  strain  diagrams  are  made  automatically  by  the  new 
Olsen  testing-machine,  described  in  Jiimr.  Frank.  Trut  1891. 

The  coefficient  of  elasticity  shookl  be  deduced  from  measaremoiit  ob- 
served between  fixed  increments  of  load  per  nni(  section,  say  between  9000 
and  12,000  pounds  per  square  inch  or  between  1000  and  11,000  poonds  instead 
of  between  0  and  10^000  pounds. 

COMPHSSSIVB  mrBENGTtt. 

What  la  meant  by  the  term  **  compressive  strength  "  has  not  yet  been 
settled  by  the  authmities,  and  there  exists  more  confusion  in  regard  to  this 
term  than  in  regard  to  any  other  used  by  writers  on  strength  of  mnteriiUa. 
The  reason  of  this  may  be  easily  explained.  The  elfect  of  a  compresif^ 
stress  upon  a  material  varies  with  the  nature  of  the  material,  and  with  the 
shape  and  sise  of  the  madmen  tested.  While  tho  effect  of  a  tensffe  stress  la 
to  produce  rupture  or  separation  of  particles  in  the  direction  of  the  line  of 
strain,  the  effect  of  a  compressire  strsis  on  a  piece  of  material  may  be  either 
to  cause  it  to  fly  into  splinters,  to  separate  into  two  cr  more  wedge-shaped 
plecesaadfly  apart,  to  bulge,  buckle,  or  bend,  or  to  flatten  out  and  utterly  re- 
sist rupture  or  separation  of  particles.  A  piece  of  speculum  metal  nnder 
compressive  stress  will  exhibit  no  change  of  appearance  until  rupture  takes 
place,  and  then  it  will  fly  to  pieces  as  suddenly  as  If  blown  apart  by  gua- 
powder.  A  pieco  of  cast  Iron  or  of  stone  will  generally  split  into  wedifo- 
shaped  fragments.  A  piece  of  wrought  Iron  will  buckle  or  bend.  A  piece  of 
wood  or  zinc  may  bulge,  but  its  action  will  depend  upon  its  shape  and  sise. 
A  piece  of  lead  will  flatten  out  and  resist  compression  till  the  last  degree; 
that  is,  the  more  it  is  compressed  the  greater  becomes  its  resistance. 

Air  and  other  gaseous  bodies  are  compressible  to  any  extent  as  long  as 
they  retain  the  gaseous  condition.  Water  not  confined  in  a  vessel  is  com^ 
pressed  by  its  own  weight  to  the  thickness  of  a  mere  film,  while  when  con- 
fined in  a  vessel  it  is  almost  incompressible. 

It  is  probable,  although  it  has  not  been  determined  experimentally,  that 
solid  bodies  when  confined  are  at  least  as  incompressible  as  water.  Wh«*n 
they  are  not  confined,  the  effect  of  a  compressive  stress  is  not  only  to 
shorten  them,  but  also  to  increaso  their  lateral  dimenskwis  or  ba^  them. 
Lateral  strains  are  therefore  Induced  by  compressive  stresses. 

The  weight  per  square  Inch  of  original  section  required  to  produce  any 
given  amount  or  percentage  of  shortening  of  any  material  is  not  a  constant 
quantifty,  but  varies  with  Doth  the  length  and  the  sectional  area,  with  the 
stiape  of  this  secttonal  area,  and  with  the  relation  of  the  area  to  tlie  len^h. 
The  '^  compressive  strength*'  of  a  material,  if  this  term  be  sopposed  to  mean 
the  weight  in  pounds  per  square  inch  necessary  to  cause  rupture,  may  vary 
with  every  size  and  shape  of  specimen  experimented  upon.  Still  more  diffi- 
cult would  it  be  to  state  what  is  the  "  compressive  strength  "  of  a  material 
which  does  not  rupture  at  all,  but  flattens  out.  Supposa  we  are  tssiliivc  n 
cylinder  of  a  soft  metal  Ifke  lead,  two  inches  In  length  and  one  inch  in  diam- 
eter,  a  certain  weight  will  shorten  It  one  per  cent,  aiK>Cher  wedlght  ten  per 
cent,  another  fifty  ber  cent,  but  no  weight  that  we  caa  place  upon  ii  will 
rupture  it,  for  it  win  flatten  out  to  a  thin  sheet.  What,  then,  is  its  ooroprea* 
sive  strength  f  Again,  a  similar  cylinder  of  soft  wrought  iron  would  prob> 
ably  compress  a  few  per  cent,  bulging  evenly  all  arouna ;  it  would  ihea  c?odi- 
mence  to  bend,  but  at  first  the  bend  would  be  imperceptible  to  the  eje  and 
too  small  to  be  measured.  Soon  this  bend  would  be  great  enough  to  be 
noticed,  and  finally  the  piece  might  be  bent  nearly  double,  or  otherwise  dis- 
torted. What  is  the  ''  compressive  strength''  of  this  piece  of  Iron  ?  In  it 
the  weight  per  square  inch  which  compresjses  the  piece  one  per  cent  or  five 
per  cent,  that  which  causes  the  first  bending  (impossible  to  oe  discovered^, 
or  that  which  causes  a  perceptible  bend? 

As  sliowing  the  conrusion  concerning  the  definitions  of  eompreasive 
strength,  the  following  statements  from  different  authorities  on  the  strength 
of  wrought  iron  are  of  Interest. 

Wood*s  Resistance  of  Materials  states,  "  comparatively  few  ezperimenta 
have  been  made  to  determine  how  much  wrought  iron  will  sustain  at  the 
point  of  crushing.    Rodgkinson  gives  65,000,  Rondulet  7O»6O0^  Weisbach  *8«000 


COMPBESilTE  STREl^GTH.  245 

BunWim  80^000  koiOtOOO.  It  Ift  generally  aasumed  that  wrought  Iron  wiU  rerist 
about  two  thirds  as  much  crushing  as  to  tenskm,  but  the  experiments  fail 
to  give  a  twy  deOnite  ratio." 

Mr.  Whippto,  ia  his  treatise  on  bridge-buildiug,  sUtes  that  a  bar  of  good 
vrooght  iron  wiU  sustain  a  tensile  strain  of  about  (X),000  pounds  per  square 
inch,  and  a  cooapreesive  strain,  in  pieces  of  a  length  not  exceeding  twice  the 
leasK  diameter,  of  about  90,000  pounds. 

The  following  values,  said  to  be  deduced  from  the  experiments  of  Maior 
Wade,  Hodgkinson.  and  Oapb.  Meigs,  are  given  by  Hasweil : 

American  wroqght  Iron 197,720  Iba 

"  *•  (mean) 86.600  " 

™«™"  i     40,000  " 

Stooej  states  that  the  strength  of  short  pillars  of  any  given  material,  all 
having  the  same  diameter,  does  not  vary  much,  provided  the  length  of  the 
pi<^  is  not  less  than  oue  and  does  not  exceed  four  or  five  diameters,  and 
tliai  the  weight  which  win  jost  crush  a  short  prism  whoee  base  equals  one 
»qaan9  mch,  and  whose  height  is  not  less  than  1  to  IW  and  does  not  exceed 
4  or  6  diameters,  is  ealled  the  crushing  strength  of  the  material.  It  would 
be  n'ell  if  experimenters  would  all  agree  upon  some  such  definition  of  the 
term  ^*  crushing  strength,"  and  insist  that  all  experiments  which  are  made 
for  the  purpose  of  testing  the  relative  values  of  different  materials  in  com* 
prt'^sion  be  made  on  specimens  of  exactly  the  same  shape  and  size.    An 


srbitrary  siie  and  shape  should  be  assumed  and  agreed  upon  for  this  pui^ 
pORBw  The  slae  mentioned  by  8tone;r  is  definite  as  regards  area  of  section, 
vis^  ooa  square  inch,  but  is Indefiiute  as  regards  length,  vis.,  from  one  to 


five  dianteters.  In  some  metals  a  specimen  five  diameters  long  would  bend, 
and  give  a  much  lower  apparent  strength  than  a  specimen  having  a  length  of 
one  disifliet«r.  The  words  '*  will  jost  crush  "  are  fUso  indeflttit4»  for  ductile 
materialB,  in  which  the  resistance  increases  without  limit  if  the  piece  tested 
does  not  bend.  In  such  cases  the  weight  which  causes  a  certain  percentage 
Gt  compression,  as  five,  ten,  or  fifty  per  cent,  should  be  assumed  as  the 
crushing  strength. 

For  fuuire  experiments  on  crushing  strength  three  things  are  desirable  : 
First,  an  arbitrary  standard  shape  and  sixe  of  test  specimen  for  comparison 
of  ail  materials.  Secondly,  a  standard  limit  of  compression  for  ductile 
materials,' which  shall  be  considered  equivalent  to  fracture  in  brittle  mate- 
risls.  Thirdly,  an  accurate  knowledge  of  the  relation  of  the  crushing 
scrength  of  a  specimen  of  standard  shape  and  size  to  the  crushing  strength 
of  specimens  of  all  other  shapes  and  sizes.  The  latter  can  only  be 
secured  by  a  very  extensive  and  accurate  series  of  experiments  upon  all 
kinds  of  materials,  and  on  specimens  of  a  great  number  of  different  shapes 


The  anchor  proposes,  as  a  standard  shape  and  sise,  for  a  compressive  test 
ipecimcm  for  all  metiuB,  a  cylinder  one  inch  in  length,  and  one  half  square 
inch  in  sectional  area,  or  Ql798  inch  diameter:  and  for  the  limit  of  compree* 
fliCiQ  equivalent  to  flracture,  ten  per  cent  of  the  original  length.  The  term 
"oompreasive  strength,*'  or  *' compressive  strength  of  standard  specimen," 
vould  then  mean  the  weight  per  square  inch  required  to  fracture  by  com- 
pf^asive  stress  a  cylinder  one  inch  k)ng  and  0.798  inch  diameter,  or  to 
reduce  Ita  length  to  0.9  inch  if  fracture  does  not  take  place  before  that  reduc- 
tioD  in  lengthis  reached.  If  sncb  a  standard,  or  any  standard  sise  whatever, 
lisd  been  used  hy  the  earlier  authorities  on  the  strength  of  materials,  we 
never  wovdd  have  had  such  diserepancies  in  their  statements  in  regard  to 
the  oompresaive  strength  of  wrought  iron  as  those  given  above. 

Thereaaotts  why  this  particular  sise  is  recommended  are :  that  the  sectional 
trea.  one^half  square  inch.  Is  as  large  as  can  be  taken  in  the  ordinary  test- 
iog-rnachlnea  of  100,000  pounds  capadty,  to  include  all  the  ordinary  metals 
of  oonstructkm,  cast  and  wrought  iron,  and  the  softer  steels:  and  that  the 
length,  one  Inch,  Is  convenient  for  caksulatlon  of  percentage  of  oompresFion. 
If  (lie  length  were  made  two  Inches,  many  materials  would  bend  in  testing, 
•sd  give  incorrect  resoRs.  Even  in  cast  iron  Hodgkinson  f  onnd  as  the  mean 
«r  several  experiments  on  various  gradee,  tested  in  spectmens  94  inch  in 
beifht,  a  compressive  streneth  per  square  inch  of  94,730  pounds,  while  the 
aeaa  of  fbe  same  number  of  spectmens  of  the  same  irons  tested  in  pieces  1^ 
iBcfaes  in  heig:fat  was  only  88,800  pounds.  The  best  sine  and  shape  of  standard 
^Mwimen- should,  however,  be  settled  upon  only  after  oonauitation  and 
I  several  authorities. 


!i46 


S1)H£KGT&  O^  ^ATERtAtid. 


The  Oommittee  on  Standard  Tests  of  the  American  Society  of  Mechanical 
Engineers  say  (vol.  xi.,  p.  6S4) : 

'•  Although  compression  tests  hare  heretofore  been  made  on  diminutive 
sample  pieces,  it  is  highly  desirable  ihat  tests  be  also  made  on  long  pieces 
from  10  to  ISO  diameters  in  length,  corresponding  more  nearly  willi  actual 
practice,  in  order  that  elastic  strain  and  cliange  of  shape  may  be  determined 
by  usinff  proper  measuring  apparatus. 

The  elastic  limit,  modulus  ur  coefBcient  of  elasticity,  maximum  and  ulti- 
mate resistances,  should  be  determineti,  as  well  as  the  Increase  of  section  at 
various  points,  vis.,  at  bearing  surfaces  and  at  crippling  point. 

The  use  of  long  cumpressi on-test  pieces  is  i^ecomnienaed,  because  the  in- 
vestigation of  short  cubes  or  cylinders  has  led  to  no  direct  application  of 
tlie  constants  obtained  by  their  use  in  computation  of  actual  structures, 
which  have  always  been  and  are  now  designed  according  to  empirical  for 
mul89  obtained  from  a  few  tests  of  long  columns." 

COIiVllINS,  PIIiliARS,  OR  STBITTS. 

HodfslLiiisoii's  Formula  for  Columns. 

P  —  crushing  weight  in  pounds;  d  —  exterior  diameter  in  inches;  d,  =  in- 
terior diameter  in  inches;  L  =■  length  in  feet. 


Kind  of  Column. 


Both  ends  rounded,  the 
length  of  the  column 
exceeding  15  times 
its  diameter. 


Solid    cylindrical    col- ) 

umns  of  cast  iron ) 

Hollow  cylindrical  col-  } 

umns  of  cast  iron ) 

Solid    cylindrical   col- ) 

umns  of  wrought  iron.  ( 
Solid  square  pillar  of ) 

Dan  tzic  oak  (dry) ) 

Solid  square  pillar  of  \ 

red  deal  (dry) ) 


P  =  88,880 


,d»-»« 


i»-» 


P  =  29,120 


d»-'«-d^« 


IS't 


Both  ends  flat,  the 
length  of  the  column 
exceeding  80  times 
its  diameter. 

ds«ftB 
p=  98.920-^ 


P  =  24,540— 
P=  17.5101, 


The  above  formulss  apply  ouly  in  cases  in  which  the  length  is  so  great  that 
the  column  breaks  by  bending  and  not  by  simple  crushing.  If  the  column 
be  shorter  than  that  given  in  the  table,  and  more  than  four  or  five  times  its 
diameter,  the  strength  is  found  by  the  following  formula : 


Tr  = 


PCjr 
P-i-J^CiT 


L 


In  which  P  s  the  value  given  by  the  preceding  formuIcB,  K  =s  the  transverse 
^«ectlon  of  the  column  in  square  inches,  C  =:  the  ultimate  compressive  resis- 
tance of  the  material,  and  W  =  the  crushing  strength  of  the  column. 

Hodgkinson's  experiments  were  made  upon  comparatively  short  columns, 
the  greatest  length  of  cast-iron  columns  being  GO^  inches,  of  wrought  iix>a 
90^  inches. 

'Die  following  are  some  of  his  conclusions: 

1.  In  all  long  pillars  of  the  same  dimensions,  when  the  force  is  I4>plied  in 
the  direction  of  the  axis,  the  strength  of  one  which  has  flat  ends  is  about 
three  times  as  great  as  one  with  roun  led  ends. 

2.  The  strength  of  a  pillar  with  "^ne  *nd  rounded  and  the  other  flat  is  an 
arithmetical  mean  between  the  two  given  in  the  preceding  case  of  the  same 
dimensions. 

8.  The  strength  of  a  pillar  having  both  ends  firmly  fixed  is  Uie  same  as 
one  of  half  the  length  with  both  ends  rounded. 

4.  The  strenirth  of  a  pillar  is  not  increased  more  than  one  seventh  by  en- 
larging it  at  the  middle. 


XOMENT  OF  INERTIA  AND  RADIUS  OF  GYRATIOK.  247 

Ck»rAoii'fl  rormnUD  deduced  from  HodfrklnaoD^s  expert roenls  are  mora 
fimirralJj  used  than  UodfirkinflOD^s  own.    They  are: 

Colnmns  with  both  ends  fixed  or  flat,  P  =  — ^—7,; 

C6lumD8  with  one  end  flat,  the  other  end  round,  P  = — ^tt 

I  +  IA.^ 


Columns  with  both  ends  round,  or  hinged,  P  =s  — ^ p; 


l  +  ia-^ 


8  =  area  of  crofw-section  in  inches; 
P  =  ultimMte  retdfitanoe  of  odumn,  in  pounds; 
/  =  cniBhlng  strength  of  the  material  In  lbs.  per  square  inch; 
,      .      .,        -         ^111^       m      Moment  of  inertia 

r  =  least  radius  of  xyration,  in  inches,  r*  = rz—rt ; 

^-  •  area  of  section    ' 

I  =  length  of  column  in  Inches; 
a  =  a  corfncient  depending  upon  the  material; 
/and  a  are  usually  taken  as  constants:  tliey  are  really  empirical  ▼ariables, 
dependent  upon  the  dimensions  and  character  of  the  column  as  well  as  upon 
th«*  material.    (Bnrr.) 

For  solid  wroufrht-iron  columns,  values  commonly  taken  are:  /  a  86,000  to 
40,000:  a  ^  1/%,000  to  1/40.000. 
For  solid  cast-iron  columns,  /  =  80,000,  a  =  1/0400. 

For  hollow  casMron  columns,  flxed  ends,  p  = V~7i* '  ^  length  and 

d  =  diameter  in  the  rame  unit,  and  p  s  strength  in  lbs.  per  square  inch. 

The  coefflt'ient  of  f/d*  is  given  various  values,  as  1/400, 1/500.  1/UUO,  and 
y^uo.  by  fliirei-ent  writers.  The  use  of  Gordon's  formula,  with  any  coef- 
ficients derived  from  Hodt^kinnon's  experiments,  for  cast-Iron  cplumns  is  to 
be  deprecated.    See  Strength  of  Cast-iron  Columns,  pp.  250,  S51. 

Sir  Benjamin  Baker  gives. 

For  mild  steel,     /  =    07,000  ib.i.,  a  =  1/22,400. 
For  strong?  steel,/  =  114,000  lbs  ,  a  =  1/14,400 

Prof.  Burr  considers  these  only  loose  approximations  for  the  ultimate 
resintanceK.    See  his  formulas  on  p.  980. 

For  dry  timber  Runkine  givt-s/  s=  7800  lbs.,  a  =  l/SOOO. 

HOHBFfT  OP  INBRTIA  AHB  BAB1U8  OF  GTBATION, 

Tlie  momeiit  of  liierlla  of  a  section  is  the  sum  of  the  product^i  of 
each  elemental^  area  of  the  section  into  the  square  of  its  distance  from  an 
aeaiiimed  axis  of  rotation,  as  the  neutral  axis. 

The  mdliis  of  synitloit  of  the  section  equals  the  square  root  of  the 
onotieDt  of  the  moment  of  inertia  divided  by  the  area  of  the  section.  If 
B  =  Miaa  of  gyratloii.  Is  moment  of  inertia  and  A  =■  area. 

Hie  moments  of  inertia  of  various  sections  are  as  follows: 
d  =  diameter,  or  outside  diameter;  d,  =  inside  diameter;  b  s  breadth; 
k  =  depth;  b\'  ^\-  inside  breadth  and  diameter; 

Solid  rectanKle I  =  \/\2bh*\  Hollow  rectangle  7  =  1/{S(bA>  -  b./ii*); 

Solid  square     I=^/\^b*l  Hollow  square      /=  1/12(M  -  5,*); 

Solid  cylinder   /=  l/64«d<;  Hollow  cylinder    J  =  l/64»(d*  -  d,*). 

Homentfl  of  Inertia  and  Radlnw  of  Gyration  for  Tarlons 
Sections,  and  their  IJse  In  the  Formulas  lOr  Strength  of 
Girders  and  Columns*— The  strength  of  sections  to  resist  strains, 
eiciier  e^  KtrUers  or  as  columns,  depends  not  only  on  the  area  but  alno  on  the 
form  of  the  section,  and  the  property  of  the  section  which  fonns  the  basis 
of  the  constants  used  in  the  formulas  for  strength  of  fdrders  and  columns 
to  express  the  effect  of  the  form,  is  Its  moment  of  inertia  about  Its  neutral 
axis.    The  modulus  0(  resistance  of  any  section  to  transverse  bending  is  its 


248  '       STRENaXH  OF   MATERIALS. 

moment  of  Inertia  divided  by  the  distance  from  the  neutral  axis  to  tte 
fibres  farthest  removed  from  that  nxis;  or 

_     ..  ,  ,  Moment  of  inertia     ^_  Z 

Section  modulus  =  Distance  of  extreme  fibre  from  axis'       ^  '  y- 

Koment  of  resistance  s  section  modulus  X  unit  stress  on  extreme  fibre. 

BEoment  of  ImerUa  of  Compound  Shapes,  (Pencoyd  Iron 
"Worlia)— The  moment  of  inertia  of  any  section  about  any  axis  is  eaiial  to  the 
/  about  a  parallel  axis  passing  through  its  centre  of  gravity  4-  (the  area  of 
the  section  X  the  square  of  the  distance  between  the  axe^). 

By  this  rule,  the  moments  of  Inertia  or  radii  of  gyration  of  any  single  sec- 
tions being  known,  corresponding  values  may  be  obtained  for  any  combhiar 
tion  of  these  sections.  .     ^ 

Omdius  of  Gyration  of  Compound  Shapes  .--In  the  case  of  a 
pair  of  any  shape  without  a  web  the  value  of  R  can  always  be  found  with- 
out considering  the  moment  of  inertia. 

The  radius  of  gyration  for  any  section  around  an  aads  paraUel  to  another 
axis  passing  through  Its  centre  of  gravity  is  found  as  follows: 

Letr  =  radius  of  gyration  around  axis  through  centre  of  gravity;  R  = 
radius  of  gyration  around  another  axis  parallel  to  above;  d  =  distance  be- 
tween axes:  R  =  Vd*  -h  i*. 

When  r  is  small,  R  may  be  taken  as  equal  to  d  without  material  eiror. 

Oraphteal  Hethod  for  FlBdink  Badtas  of  Gyration.— Ben  J. 
F.  La  Kue,  Eng.  Neicsy  Feb.  2,  1898,  gives  a  short  graphical  method  for 
finding  the  radius  of  gyration  of  hollow,  cylindrical*  and  rectangular  col- 
umns, as  follows: 

For  cylindrical  colunms: 

Lav  off  to  a  scale  of  4  (or  40)  a  right-angled  triangle,  in  which  the  base 
equals  the  outer  diameter,  and  the  altitude  equals  the  inner  diamet^sr  of  the 
column,  or  vice  versa.  The  hypothenuse,  measured  to  a  scale  of  unl^  (or 
10).  will  be  the  radius  of  ^ration  sought. 

This  depends  upon  the  formula 

/Mom.  of  Inertia       ^D*  +  d^ 


o  =  ^- 


Area  4 

In  which  A  =  area  and  D  =  diameter  of  outer  circle,  a  =  area  and  d  a«  dia- 
meter of  inner  circle,  and  O  =  radius  of  gyration.  i^D*  +  d«  is  the  expres- 
sion for  the  hypothenuse  of  a  right-angled  triangle.  In  which  D  and  d  are  the 
base  and  altitude. 

The  sectional  area  of  a  hollow  round  column  is  .7854(D«  —  cP).  By  con- 
structing a  right-angled  triangle  in  which  2>  equals  the  hypothenme  and  d 
equals  the  altitude,  the  base  will  equsl  VD»  -  d\  Calling  the  Tolue  of  this 
expression  for  the  bsse  B^  the  area  wUl  equal  .78MB*. 

value  of  6  for  square  columns: 

Lay  off  as  before,  but  using  a  scale  of  10,  a  right-angled  triangle  of  whicL 
tlie  base  equals  Z>  or  the  side  of  the  outer  square,  and  the  altitude  equals  d, 
the  side  of  the  inner  square.  With  a  scale  of  8  measure  the  hypothenuse, 
which  will  be,  approximately,  the  radius  of  gyration. 

This  process  for  square  columns  gives  an  excess  of  slightly  more  than  4%. 
By  deducting  4%  from  the  result,  a  close  approximation  will  be  obtained. 

A  very  close  result  is  also  obtained  by  measuring  the  hypothenuse  with 
the  same  scale  by  which  the  base  and  altitude  were  laid  off,  and  multiplyiug 
by  the  decimal  0.29;  more  exactly,  the  decimal  is  0.128867. 

The  foi-mula  is 

/5  _    .  /Mom.  of  inertia  _      1       , ^  oosuvr    , • 

^      y   aSS^ 7^^^"  +  ^'»  =  0.288«7  ^TJS  +  d^ 

This  may  also  be  applied  to  any  rectangular  column  by  using  the  lesser 
diameters  of  an  unsupported  column,  and  the  greater  diimieters  If  the  col< 
umn  is  supported  in  the  direction  of  its  least  dimenKlons. 

BliKlHBNTS  OF  ITSVAL  SECTIONS.    ' 

Moments  refer  to  horufontal  axis  through  centre  of  gravity.  This  table  is 
Intended  for  convenient  application  where  extreme  accuracy  la  not  impor- 
tant. Some  of  the  terms  are  only  approximate;  those  marked  *  are  corrects 
Values  for  radius  of  gyration  in  flanged  beams  apply  to  standard  minimum 
•ections  onl> .    A  =  area  of  section ;  b  ^  k^readth;  A  =  depth;  D  =  diameter. 


ELEVBKT8  OF  CSDAL  8ECTION8. 


249 


ShAp*  of  aeeCkm. 

Moment 
of  Inertia. 

Section 
Modulus. 

Sqniareof 

Radius  of 
aeration. 

Least 
Radius  of 
Gyration. 



SoUdBect- 
angle. 

6A'  • 
12 

bh** 
6 

(Lea«t  Bide)9* 

Lea«t8ide» 

12 

8.46 

u-i-. 

H 

T 

HoUow  Beot- 
angle. 

6;i»-5,74,i* 

12 

7t4-Ai 

Hh 

4.89 

« 

ft-- 

0 

Solid  Olrole. 

16 

AD* 
8 

16 

5* 
4 

^ 

Hollow  Circle. 
A,  area  of 
large  section; 
a,  area  of 
small  section. 

Aiy-ad* 

8X> 

16 

D-f  d 

w 

Itt 

6.W 

■A^ 

Solid  Triangle. 

bh* 
30 

bh* 

Ah 
7.2 

The  least  of 
of  the  two: 

'*'  .>r  ^' 
18 '''^24 

The  least  of 
the  two: 
h           b 

P-6-A 

4.24  ^^  4.9 

- 

Q 

Bven  Angle. 

Ah* 
1C.2 

6» 
25 

6 
6 

L 

-fr-l 

p 

Uneren  Angle. 

Ah* 
9.6 

^7i 
6.5 

Oib)* 
Wi*+b*) 

Jib 

2.e(/t  4-  6) 

^ 

£f  en  Cross. 

Ah* 
19 

Ah 
9.6 

h* 
22.5 

4.74 

M 

SfenTee. 

Ah* 
11.1 

Ah 

a 

22.5 

b 
4.74 

c 

I  Beam. 

0.66 

AJi 
82 

b* 
21 

b 

4.68 

am 

ChaimeL 

Ah* 
7.34 

Ah 
3.67 

6» 
12.5 

6 
8.54 

e 

m 

Deck  Beam. 

e.o 

4 

b* 
86.6 

b 
6 

Distaace  of  base  from  centre  of  gravity,  solid  triangle,  r;  even  angle,  -^.a 
aoeven  angle,  ^ k*  ^'^^^  ^^'  fa*  ^^^  beam,  -^;  all  other  shapes  given  In 
U)etable,|or^. 


260  STRENGTH  OF  MATEHIALS. 

The  Strengtli  of  Cast-iron   Columns. 

Hodekinson's  experiments  (first  published  in  Phil.  Trans.  Roral  Socj^ 
1840,  and  condensed  in  Tred(i:old  on  Cast  Iron,  4th  ed..  1846),  and  Gordon's 
formula,  based  upon  them,  are  still  used  (189^  in  designing  cast-iron  col- 
umns. That  thej  are  entirely  inadequate  as  a  basis  of  a  practical  formula 
suitable  to  the  present  methods  of  casting  columns  will  be  evident  from 
what  follows. 

Hodgkinson's  experiments  were  made  on  nine  '*  long  **  pillars,  about  7H 
ft.  long,  whose  external  diameters  ranged  from  1.74  to  2.23  in.,  and  avei-age 
thickness  from  0.89  to  0.85  in.,  the  thickness  of  each  column  also  varying, 
and  on  18  "short  **  pillars,  0.788  ft.  to-2J251  ft.  long,  with  external  diameters 
from  1.08  to  1.26  in.,  all  of  them  less  than  ^  in.  thick.  The  iron  used  was 
Low  Moor,  Yorkshire,  No.  8,  said  to  be  a  good  iron,  not  very  hard,  earlier 
experiments  on  which  had  given  a  tennile  strength  of  14,535  and  a  crushing 
strength  of  109,801  lbs.  per  sq.  in.  The  result  of  the  experiments  on  the 
*'  long  "  pillars  were  reiluced  to  the  equivalent  breaking  weight  of  a  solid 
pillar  1  iu.  diameter  and  of  the  same  length,  7^  ft.,  which  ranged  from  2969 
to  3587  lbs.  per  sq.  in.,  a  range  of  over  13  per  cent,  although  the  pillars  were 
made  from  the  same  iron  aud  of  nearly  uniform  dimensions.  From  the  IS 
experiments  on  *' short'*  pillars  a  formula  was  derived,  and  from  it  were 
obtained  the  ''calculated"  breaking  weights,  the  actual  breaking  weights 
ranging  from  about  8  per  cent  above  to  about  8  per  cent  below  ine  calcu- 
lated weights,  a  total  range  of  about  16  per  cent.  Modern  cast-iron  columns, 
such  as  are  used  in  the  construction  of  buildings,  are  very  different  in  size, 
proportions,  and  quality  of  iron  from  the  slender ''long"  pillars  used  in 
Hoagkinson's  experiments.  There  is  uRually  no  check,  by  actual  tests  or  by 
disinterested  Inspection,  upon  the  quality  of  the  materinl.  The  tensile,  com- 
preswlve,  and  transverse  strength  of  cast  iron  varies  through  a  great  range 
(the  tensile  strength  ranging  from  less  than  10.000  to  over  40.000  lbs.  per  nq. 
In.),  with  variations  in  the  chemical  composition  of  the  Iron,  according  to 
laws  which  are  as  yet  very  imperfectly  understood,  and  with  variations  in 
the  method  of  melting  and  of  casting.  There  is  also  a  wide  variation  in  the 
strength  of  iron  of  i he  same  melt  wlien  cast  into  bars  of  different  thick- 
nesses. It  is  therefore  impossible  to  predict  even  approximately,  from  the 
data  given  by  Hodgkinson  of  the  strength  of  columns  of  Low  Moor  iit>n  in 
pillars  7yi  ft.  long,  2  In.  diam.,  and  ^  in.  ttiick,  what  will  be  the  strengtli  of 
a  column  made  of  American  cast  iron,  of  a  quality  not  stated,  in  a  crluuic 
16  ft.  long,  Vi  or  15  In.  diam.,  and  from  %  in.  to  1^  in.  thick. 

Another  difllculty  in  obtaining  a  practical  formula  for  the  strength  of  cast- 
iron  columns  is  due  to  the  uncertamty  of  the  quality  of  the  casting,  aud  the 
danger  of  hidden  defects,  such  as  internal  stresses  due  to  unequal  cooling, 
cinder  or  dirt,  blow-holes,  "  cold-shuts,"  and  cracks  on  the  inner  surfare, 
which  cannot  be  discovered  by  external  inspection.  Variation  in  thick- 
ness, due  to  rising  of  the  core  during  casting,  Is  also  a  common  defect. 

In  addition  to.',  the  above  theoretical  or  a  pnort  objections  to  the  use  of 
Gordon's  formula,  based  on  Hodgkinson's  experiments,  for  cost-iron 
columns,  we  have  the  data  of  recent  experiments  on  full-sized  columns, 
made  by  the  Building  Department  of  New  York  City  (Eng^g  Netct,  Jan.  28 
and  20,  18US).  Ten  columns  in  all  were  tested,  six  15-inch,  ]9(H  inches  long, 
two  8-inch.  160  Inches  long,  and  two  6-inch,  120  inches  long.  The  testa  were 
made  on  the  large  hydraulic  machine  of  the  Phoenix  Bridge  Co.,  of  2,000,000 
pounds  capacity,  which  was  calibrated  for  frictional  error  by  the  repeated 
testing  within  the  elastic  limit  of  a  large  Phoenix  column,  and  the  compari- 
son of  these  tCHts  with  others  made  on  ihe  government  machine  at  the 
Watertown  Arsenal.  The  average  frictional  error  was  calculated  to  be 
15.4  per  cent,  but  Engineering  Aeirs.  revising  the  data,  makes  it  17.1  per 
cent,  with  a  variation  of  3  per  cent  either  way  from  the  average  with  differ- 
ent loads.    The  results  of  the  tests  of  the  volumes  are  given  on  the  opposite 

Column  No.  6  was  not  broken  at  the  highest  load  of  the  testing  machine. 

Columns  Nos.  8  and  4  were  taken  from  the  Ireland  Building,  which  col- 
lapsed on  August  8. 1895;  the  other  four  15-inch  columns  were  made  from 
drawings  prepared  by  the  Building  Department,  as  nearly  as  possible 
duplicates  of  Nos.  3  and  4.  Nos.  1  and  2  were  made  by  a  foundry  in  New 
York  with  no  knowledge  of  their  ultimate  use.  Nos.  5  and  6  were  made  bv 
a  foundry  in  Brooklyn  with  the  knowledgfe  that  they  were  to  be  tested. 
Nos.  7  to  10  were  made  from  drawing  burnished  hy  the  Department, 


THE  8TBBK0TH  OV  CAST-IBOBT  COLUMNS. 


251 


TESTS  OF  CAST-IRON  COLUMNS. 

Thickness 

Breaking  Load. 

Number. 

DiAin. 

Inches. 

Max. 

Min. 

Averaore. 

Pounds. 

Pounds 
per  pq.  In. 

1 

1.5 

1 

1 

1,856,000 

80,880 

15 

15/16 

^i-^ 

I.8«).O00 

27,700 

15 

\i^ 

^l 

1,106.000 

24.000 

l"^ 

1:1 

1.^246,000 

25.800 

15 

1  11/16 

1    1/64 

1,642.000 

82.100 

15 

m 

'^ 

1  8/10 

8,<i8i,000  + 

40.400  -f- 

?«to8H 

1^ 

1 

(J51.(X)0 

si.guo 

H 

l?/3« 

1  8/61 

612.fl0O 

26.800 

6  1/16 

\r 

1^ 

1  9/64 

1  7/64 

400.000 

22.700 

10 

•  8/^ 

1  1/16 

466,a)0 

86,800 

Gordon's   formalu,   as   used    by    ihe   Building   Dfpailmeut, 
8  =  -^^^2222^^  to  these  columns  gives  for  the  breaking  strength  per  square 

^400d» 
Inch  of  the  15-lncb  columns  67,143  pounds,  for  the  8-inch  columns  40.000 
pounds,  and  for  Ihe  6-inch  columns  40,000.  The  strength  of  columns  Nos.  8 
nnd  4  «s  calculated  Is  128  per  cent  more  than  their  actual  strength;  their 
actual  atrength  Is  less  than  44  per  cent  of  their  caJculated  strength;  and  the 
factor  of  safety,  supposed  to  be  5  in  the  Building  Law,  is  only  2.2  for  central 
loading,  no  account  being  taken  of  the  likelihood  of  eccentric  loading. 

Prof.  Loosa,  in  his  Applied  MechanicM,  p.  972.  quotes  the  records  of  14 
tegitsi  of  cant-iron  mill  columns,  made  on  the  Wstertown  testing-machine  in 
I«^-88,  the  breaking  strength  per  square  inch  ranging  from  25.100  to  63,!J10 
pounds,  and  Khowlng  no  relation  between  the  breaking  strength  per  square 
inch  and  the  dimensions  of  the  columns.  Only  3  of  the  14  cohimns  had  a 
Btrenirth  exceeding  38,600  pounds*  per  square  inch.  The  average  strength  of 
the  other  11  was  29,600  pounds  per  square  inch.  Prof.  I^anza  says  that  it  is 
evident  that  in  the  case  of  such  columns  we  cannot  rely  upon  a  crushing 
Rtrengih  of  greater  than  25,000  or  80,000  pounds  per  square  inch  of  area  of 
section. 

He  recommends  a  factor  of  safety  of  5  or  6  with  these  figures  for  crush- 
ing strength,  or  5000  pounds  per  square  inch  of  area  of  section  as  the  highest 
altowable  safe  load,  and  in  addition  makes  the  conditions  that  the  length  of 
the  column  shall  not  be  sreatly  in  excess  of  80  times  the  diameter,  that  the 
Uiickness  of  the  metal  shall  be  such  as  to  insure  a  good  strong  casting,  and 
that  Ihe  sectional  area  should  be  increased  if  necensai-y  t<>  insure  that  the 
pxtr>  me  fibre  stress  due  to  probable  eccentric  loading  shall  not  be  greater 
Than  SOOOpounds  per  square  inch. 

Prof.  w.  H.  Burr  (Eng^g  Netos,  June  80,  1886)  gives  a  formula  derived 
frtan  plotting  the  results  of  the  Watertown  and  Fhoenixville  tests,  above 
Aftcribed,  which  represents  the  average  strength  of  the  columns  in  pounds 
per  square  Inch.  It  isp  =  80,500  -  1602/d.  It  is  to  be  noted  that  thiH  ih  hii 
average  value,  and  that  the  actual  strength  of  many  of  the  columns  was 
mach  lower.  Prof.  Burr  says:  "  If  cast-iron  columns  are  designed  with 
anything  like  a  reasonable  and  real  margin  of  safety,  the  amount  of  metal 
rnptred  dissipates  any  supposed  economy  over  cohnnns  of  mild  steel." 

Trmnswenie  Sfrenanth  of  Cast-trom  ITater-pipe.  (Tvchuology 
Qnarttrly,  Sept.  1897.>--TestH  of  81  cast-iron  pipes  by  transvei-se  stress 
Kave  a  maximum  outside  fibre  stress,  calculated  from  maximum  load. 
aaraming  each  half  of  pipe  as  a  beam  fixed  at  the  ends,  ranging  from  12,800 
a».  CO  26,800  Iha.  per  sq.  in. 

Bars  Sin.  wide  cut  from  the  pipes  gave  moduli  of  rupture  ranging  from 
^.400  to  51,400  lbs.  per  sq.  in.    Four  of  the  tests,  bars  and  pipes: 

Moduli  of  rur»ture  of  bar 28,400  34.400  40,000  51 ,400 

Fibre  stress  of  pipe 18,800  12,800  14.500  26,300 

These  figures  show  a  great  variation  in  the  strt^ngth  of  both  hnrs  and 
\iprn.  and  also  that  the  strength  of  the  bar  <ioes  not  bear  any  definite  rela- 
tion to  the  strength  of  the  pli)e. 


252 


STRENGTH  OF  VATISBTALS. 


Safe  lioad,  in  Toms  of  SOOO  libs.,  for  Round  Caat-tron 
Columnii,  ivltli  Turned  Capitals  and  Bases. 

Loads  being  not  eccentric,  and  lengrth  of  column  not  exceeding  20  times 
tfiH  diameter.  Based  on  ultiTnace  crushing  strength  of  35,000  Ibn.  per  vq.  in. 
and  a  factor  of  safety  of  6.    (For  eccentric  loads  see  page  854.) 


Thick- 

Diameter,  inches. 

inches. 

6 

7 

S 

9 

10 

11 

12 

13 

14 

16 

16 

18 

1 

si 

S6.4 
30.9 
35.8 
30.2 

31.3 
86.8 
42.1 
47.1 

48.7 

48.9 
56.0 
G0.8 

48.6 
55.8 
62.8 
69.6 
76.1 

54.5 
62.7 
70.7 
78.4 
86.9 
98.1 

60.6 
78.5 
87.8 
96.7 
166.0 

76.6 
86.4 
06.1 
106.5 
114.7 
1S3.7 

04.2 
104.9 
115.8 
1S5.6 
135.5 

102.1 
118.8 
186.8 
136.8 
147.3 
168.4 

110.0 
188.6 
135.0 
147.1 
159.0 
182.1 
804.8 

111.4 
144.8 
157.0 
170.8 
105.» 
819.0 

164.4 
170.6 
104.4 

r* 

SS8.8 

851.3 

For  lengths  greater  than  80  diameters  tlie  allowable  loads  should  be 
decreased.  How  much  they  ehouUl  be  decreased  is  uncertalu,  since  suf- 
ficient data  of  experiments  on  ftill-sised  very  long  oolumns,  from  which 
a  formula  for  tfae  strength  of  such  columns  might  be  derived,  are  as  yet 
lacking.  There  is,  however,  rarely,  if  ever,  any  need  of  proportioning  cast- 
iron  columns  with  a  length  exceeding  80  diameters. 

Safe  lioads  In  Tons  of  2000  Pounds  for  Cast-troa  Oolumns. 

(By  the  Building  Laws  of  New  York  City,  Boston,  and  Chicago,  1807.) 


New  York. 
8a 


Boston. 
5a 


I  8ct  I 

Round  columns J    -  ,    J^        -  , 


Chicago. 
6a 


6a 

800d« 


1  + 


600ef* 


a  ss  sectional  area  in  square  inches;  1 5=  unsupported  length  of  column  in 
inches;  d  =  side  of  square  column  or  diamerer  of  round  column  in  inches. 

The  safe  load  of  a  15-itich  round  column  U  inehes  diameter.  16  feet  long, 
according  to  the  lows  of  these  cities  would  be,  in  New  York,  361  tons;  m 
Boston.  864  tons;  in  Chicago,  250  tons. 

The  allowable  stress  per  square  inch  of  area  of  such  a  column  would  be, 
In  New  York,  ]l,3r;0  pounds;  in  Boston,  8300  pounds;  in  Chicago,  78S0 pounds. 
A  safe  stress  of  5000  pouuds  per  square  inch  would  give  for  tne  safe  load  oo 
the  column  150  tons. 

Strength  of  Brackets  on  Cast*lron  Colnmns.'-The  columns 
tested  by  the  New  York  Building  Department  referred  to  above  had 
brackets  cast  upon  them,  each  bracket  consiKiiiig  of  a  rectangular  shelf 
supported  by  one  or  two  triangular  ribs.  These  were  tested  after  the 
coIuniDS  luid  been  broken  in  the  prhicipal  tests.  In  17  out  of  88  oases  the 
brackets  broke  by  tearing  a  hole  in  the  body  of  the  column,  instead  of  by 
shearing  or  transvei-se  breaking  of  the  brocket  itself.  The  results  were 
surprisingly  low  and  very  iiTegular.  Reducing  them  to  strength  per  square 
inch  of  the  total  vertical  section  through  the  shelf  and  rib  or  ribs,  they 
ranged  from  3450  to  5(SO0  lbs.,  averaging  4800  lbs.,  for  a  load  concentrated 
at  the  end  of  the  shelf,  nnd  4100  to  10,900  lbs.,  averaging  8000  lbs.,  for  a  dis- 
tributed load.    {Eng'g  Neios,  Jan.  20,  15^98.) 


SAFE  LOAD  OF  OABT-IBOK  COLITUKS. 


853 


8af«  lioads, 

Im  Tons,  for  Bound  Cast  Oolnmns. 

(In  accordance  with  the  Building  Laws  of  Chicago.*) 

Dtame 
wr\n 
tncbfA 

Thick- 
tticb^ii. 

Unsupported  l^ni^th  In  F^ft* 

8 

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10 

IS 

14 

18     IH 

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From  I 


«7.) 


254  STREKGTH   OF   MATERIALS. 

BOCBNTRIC  liOABING  OF  €OI,17]IIBni. 

lo  A  given  rectaneulor  cross-section,  such  as  a  masonry  loint  und«r  |. 

ure,  the  stress  will  be  distributed  uoif  onnly  over  the  section  only  when  the 
resultant  passes  through  the  centre  of  the  section;  any  deviation  from  such 
a  central  position  will  bring  a  maximum  unit  pressure  to  one  edge  and  a 
minimum  to  the  other;  when  the  disUnce  of  the  resultant  from  one  edge  is 
one  third  of  the  entire  width  of  the  joint,  the  pressure  at  the  nearer  edge  is 
twice  the  mean  pressure,  while  that  iit  the  farther  edge  is  sero.  and  thai 
when  the  resultant  approaches  still  nearer  to  the  edge  the  pressure  at  the 
farther  edge  becomes  less  than  zero:  in  fact^  becomes  a  tension^  if  the 
material  (mortar,  etc.,  there  is  capable  of  resisting  tension.  Or,  if,  as  usual 
in  masonry  joints,  the  material  is  practically  incapable  of  resisting  tension, 
the  preasure  at  the  nearer  edge,  when  the  resultant  approaches  It  nearer 
than  one  third  of  the  wi<lth.  increases  very  rapidly  and  dangerously,  become 
iuu  tlieoreiically  influite  wlien  the  rettultant  reaches  the  edge. 

With  a  given  position  of  the  resultant  relatively  to  one  edge  of  the  Johit  or 
section,  a  similar  redistribution  of  the  pressures  throughout  Che  section  umj 
be  brought  about  by  simply  adding  to  .or  diminishing  the  width  of  the 
section. 

Let  P  =  the  total  preasure  on  any  section  of  a  bar  of  uniform  thiclcneM. 

fc  =  the  width  of  that  section  =  area  of  the  section,  when  thickness  =s  1. 

p  =  P/w  =-.  the  mean  unit  pressure  on  the  section. 

Mi  =:  the  maximum  unit  pressure  on  the  section. 

m  =  the  minimum  unit  pressure  on  the  section. 

d  =  the  eccentricity  of  the  resultant  =  its  distance  trcm  the  oeotre  of 
the  section. 

ThenJf  =  p  (l+^)andm=p  (l-^). 
When  d  =^w  then  M=s2p  and  m  =:  O. 

0 

When  d  is  greater  than  l/0i0,  the  resultant  in  that  case  being  lew  than 
one  third  of  the  width  from  one  edge,  p  becomes  negative.  (J.  0.  Traut- 
wine,  Jr..  Engiueering  Newt^  Nov.  S8, 16HL) 

Eecentrle  Iioadliiff  of  Caet-lroii  Colnmna.  —  Prof.  Lanza 
wntt'H  tlie  author  as  follows:  The  table  on  page  S5^  applies  when  the  resultant 
of  ilie  l.oKiB  upon  the  column  acts  along  its  central  axis,  i.e.,  passes  through 
the  centre  of  gravity  of  every  section.  In  buildings  and  other  construc- 
tions, however,  cases  frequently  occur  when  the  resultant  load  does  not 
pass  through  the  centre  of  gravity  of  the  section;  and  then  the  pressure  is 
not  evenly  distributed  over  the  section,  but  is  greatest  on  the  side  where 
(lie  resultant  acts.  (Examples  occur  when  the  loads  on  the  floors  are  not 
uniformlv  distributed.)  In  these  cases  the  ouUide  fibre  stresses  of  the 
column  Mhould  be  computed  as  follows,  vhE.: 
liet  P  =  total  pressure  on  the  section; 

d  3  eccentricity  of  resultant  s=  its  distance  from  the  centre  of  gravity 

of  the  section; 
A  =  area  of  the  section,  and  /its  moment  of  Inertia  about  an  axis  In  Its 
plane,  passing  through  its  centre  of  gravity,  and  perpendicular 
to  d  (Mce  page  267); 
Ci  =  distance  of  most  compressed  and  c,  r=  that  of  least  compressed 

flbre  from  above  stated  axis; 
•i  ts  maximum  and  «,  =£  minimum  pressure  per  unit  of  area.    Then 

Having  assumed  a  certain  trial  section  for  the  column  to  be  designed, «. 
should  be  computed,  and.  If  It  exceed  the  proper  safe  value,  a  difTerent 
section  should  oe  used  for  which  «x  does  not  exceed  this  value. 

The  proper  safe  value,  in  the  case  of  cast-iron  columns  whose  ratio  of 
length  to  diameter  does  not  greatly  exceed  iao.  is  5000  pounds  per  square  Inch 
when  the  eccentricity  used  in  the  computation  of  «,  is  liable  to  occur  fre- 
quently in  the  ordinary  uses  of  the  structure;  hut  when  it  is  one  whi<*h  can 
only  occur  in  rare  cases  the  value  KXX)  pounds  per  square  inch  may  be  used. 

A  long  cap  on  a  column  Is  more  conducive  to  the  production  of  eccen- 
tricity of  loading  than  a  short  one,  hence  a  long  cap  is  a  source  uf  weaklier 
in  a  column. 


ULTIMATE  STKBKGTH  OJP  WUOUGHT-IROBT  COLUMNS.     255 


ITI.TIlltATS    STRBNGTS    OF    WROUGHT-IRON 
COLVniNS. 

(PottSTille  Iron  and  Steel  Co.) 


Oompated  by  Qordon's  formula,  p  s=  • 


(^r 


1  +  C 

p  =  ultinaate  strength  in  lbs.  per  square  Inch; 

I  =  length  of  column  in  inches; 

r  =  leant  radius  of  gyration  in  inches; 

/=  40.000; 

C  =  l/iO,000  for  square  end-hearings;  1/30,000  for  one  pin  and  one  square 
bearing;  l/a),000  for  two  pin-bearings. 

For  safe  working  load  on  these  columns  use  a  factor  of  4  when  used  in 
buildings,  or  when  subjected  to  dead  load  only;  but  when  used  in  bridges 
the  teeter  should  be  6. 


WEOUOBT^IROK  OOLCMMB. 


I 

Ultimate  Strength  in  Ibe. 
per  square  inch. 

r 

Safe  Strength  in  lbs.  per 
square  inch— Factor  of  6. 

r 

^X 

Pin  and 

Pin 

Square 
Ends. 

Fin  and 
Square 
End. 

Pin 
Ends. 

10 
15 
90 
25 
30 
86 
40 
45 
SO 
55 
00 

es 

TO 

80 

85 

w 

96 
100 
Kb 

80044 
99T7B 
80004 
80884 
88118 
88810 
88480 
8807S 
87840 
87188 
88007 
88182 
85684 
88070 
84488 
88888 
88904 
S8880 
88000 
81867 

89806 

80708 
80478 
80188 
88884 
88480 
87B74 
87470 
86088 
86886 
85714 
84478 
84884 
88688 
88066 
88886 
81496 
807S0 
80000 
20850 

88800 
89664 

88788 
88878 
87000 
87086 
86888 
86&25 
84744 
88886 
880EM 
88128 
81818 
80888 
29884 
88470 
27908 

OAMM 
cOOOO 

25786 

10 
15 
» 
85 
80 

46 
50 
56 

00 
65 
70 
76 
80 
85 
90 
05 
100 
106 

7960 
7956 
7921 
7877 
7881 
7768 
7608 
7814 
7529 
7487 
7889 
7886 
7187 
7015 
6896 
6777 
6668 
6087 
6400 
6871 

7978 
7040 
7804 
7886 
7767 
7686 
7595 
7494 
7886 
7267 
7148 
6896 
6877 
6786 
6598 
6447 
6299 
6160 
6000 
5850 

7960 
7911 
7843 
7758 
7656 
7538 
7407 
7264 
7105 
6949 
6780 
6605 
6426 
6244 
6058 
58Tr 
5694 
6612 
6833 
9157 

Haxtmnm  Permlsaible  StremMS  in  columns  used  in  building 
(BaikfinsT  Ordinances  of  City  of  Chicago,  1898.)         » 
For  riveted  or  other  forms  of  wrought-iron  columns: 

I20OO0  I  -_  length  of  column  in  inches: 

2*      *         r  =  least  radius  of  gyration  in  inches; 


«  =  • 


1+; 


a  ss  area  of  column  in  square  inches. 


gy« 

I  in  f 


aoooor* 

For  riveted  or  other  steel  columns,  if  mor(>  than  60r  in  length: 

S  =  17,000-??-'. 
r 
If  leas  than  60r  in  length:     8  =  18.500a. 
For  wooden  posts: 

nc a  =  area  of  post  in  square  inches; 

o  — n — •  d  —  least  side  of  rectangular  post  in  inches; 

1  +  sscsm  '  -  length  of  post  in  inches; 

•SOti"  I  (joo  for  white  or  Norway  pine; 

c  s  -(800  for  oak; 

( 900  for  long-leaf  yellow  pine. 


256 


STBENGTH  OF  MATERIALS. 


BUILT  COLVnNS. 

From  experiments  by  T.  D.  Loveft,  discussed  by  Burr,  the  values  of /and 
a  in  several  cases  are  determined,  giving  empirical  forms  of  Goixloa''s  for- 
mula as  follows:  p  =  pouuds  crusaing  strength  per  square  loch  of  sectioDi 
2  =  length  of  column  in  inches,  r  «  raditis  of  gyration  In  inches. 


Keu9t»n0 


A.m.Br^C^ 


Flat  Knd0. 


Keystone 
Columns. 

39.fi00 


l-f 


1 
18,800  r» 


(t) 


Souare 
Columns. 

39,000 


Zi         1  + 


_J 

«,000  r* 


(4) 


Phoenix 
Culumus. 

42.000 


American  Bndgn 
Co.  Columns. 


t-f 


_1 

50,000  r« 


I  (6)        - 
1  + 


S6^000^_ 

1     n 

4«,0UU  r« 


m 


p  = 


86.000 


Flat  Bnds,  Swelled. 


1  + 


i(«) 


18,800  !■» 


Pin  Bndt. 


89.000 

" 1 — ir3 

^17,000  f» 


(5) 


42,000 


1  +  ^ 


(7) 


pss 


86,000 


»J,T00  r» 
Pin  Bnds,  Swelled. 


«.000 


(10) 


1+ 


1 

15,000  pi 


(«) 


Hound  Bnds* 


42.000 


1  + 


J 

12,500  1^ 


r<8) 


88,000 


1  + 


(11) 


11,500  r* 


With  great  variations  of  stress  a  factor  of  safety  of  as  high  as  6  or  8  may 
be  u«ied.  or  it  may  be  as  low  as  8  or  4,  if  the  condition  of  stress  is  nnfform  or 
essentiallr  so. 

Burr  gives  the  following  general  principles  whldi  govern  the  resistance  of 
built  columns  : 

The  material  should  be  disposed  as  far  as  possible  from  the  neutral  axis 
of  the  cross-section,  thereby  increasing  r; 

There  should  be  no  initial' Int'ernal  stress; 

The  Indlrldual  portions  of  the  column  should  be  mutaallr  supporting; 

The  individual  portions  of  the  column  should  be  so  firmly  8ecor<>d  to  each 
o'her  that  no  relative  motion  can  take  place,  in  order  that  the  column  may 
fail  as  a  whole,  thus  maintaining  the  original  value  of  r. 

Sconey  says:  **  When  (he  length  of  a  rectangular  wronght-iron  tubular 
column  does  not  exceed  30  times  its  least  breadth.  It  falls  by  the  biilartng  or 
buckling  of  a  short  portion  of  the  plates,  not  by  the  flexure  of  the  pillar  as  a 
whole.'* 

In  Trans.  A.  8.  0.  B.,  Oct  18S0,  are  jrlven  the  following  formulaa  for  the 
ultimate  resistance  of  wrought-iron  columns  designed  by  C.  Shaler  Smitli : 


BOTLT  COLUMKa 


267 


Plat  Bnda. 


P  = 


ColumD. 
88,800 


1  + 


P  = 


fittOSi 


88,600 

*^8000  d« 


T,(i«> 


Phoenix 
CoJuDin. 

42,800 


American  Bridge 
Co.  Column. 


1  + 


05) 


86,800 

1J-JL  H 


(18) 


4800  d> 
One  Pin  Bnd. 

40,000        ,,^,         86,800 


^  +  800  3i 


(16) 


1  IS 

14---^  — 


87,000 

1  +  JLJ? 


(W 


'TiBtro  Pin  Bnds* 

80.600        ..^  86,800 


*^1B00  d« 


(17) 


l  +  -i-^ 


(18) 


(19) 


(80) 


Common 
Column. 

86,500 


on) 


S700  ci* 


86,600 
1  +  -^    ^ 


(«) 


iite,  with  flanges 


The  **  common  "  column  consists  of  two  channels,  op 
outward,  with  a  plate  on  one  side  and  a  lattice  on  the  other. 

The  formula  for  **  square  "  columns  may  be  used  without  much  error  for 
the  common-chord  section  composed  of  two  channel-bars  and  plates,  with 
the  axis  of  the  pin  passing  through  the  centre  of  gravity  of  the  cross- 
seotioo.    (Burr). 

Compression  members  composed  of  two  channels  connected  by  zigzag 
bradnfif  may  be  treated  by  formuhe  i  and  6,  using  /  =  86,000  instead  of 
SSjOOO. 

Sxparlmants  on  full-sised  Phosniz  columns  in  1878  showed  a  close  agree- 
ment of  the  resolta  with  formulsB  6^.  Experiments  on  full-slaed  PhoBUiz 
columns  on  the  Watertown  testing-machine  in  1881  showed  considerable  dis- 
crepaocies  when  the  Talue  of  2  -i-  r  beoame  comparatively  small.  The  fol- 
lowinK  modified  form  of  Cordon^s  formula  gave  tolerable  results  through 
"   whole  r * • ^ 


ci 


)  range  of  experiments : 


PboBbbc  columns,  flat  end,  p  a 


40,000(1  +  ^) 

1  fl' 

1-1-80,000    r* 


(«4) 


PloUing  results  of  three  series  of  experiments  on  PhoBnix  cohimos,  a 
more  simple  formula  than  (Sofdon's  is  reached  as  follows  : 

PfacBolx  columna,  flat  ends,  p  =  89,640  -  46-,  when  Z  h-  r  is  from  80  to  140; 
p  s  64,700  -  4600  yi  when  I -i-r  is  less  than  80. 


IMinenalona  of  PMcenIx  Colnmna* 

(Phcsniz  Iron  Co.) 

The  dlmmisions  are  subject  to  slight  TarlatioaB,  which  are  unavoidable  in 
rollinip  iron  shapes. 

The  weii^ts  of  oolnmns  given  are  those  of  the  4. 6,  or  8  segments  of  which 
they  are  composed.  The  rivet  heads  add  from  9^  to  6)t  to  the  weights  given. 
Riveca  are  apaced  8, 4,  or  6  in.  apart  from  centre  to  centre,  and  somewhat 
more  closely  at  the  ends  than  towardn  the  centre  of  the  column. 

O  oolamne  have  8  seftments,  JS  columns  6  segments,  C,  B*,  B',  and  A  have 
I  Kgnieiita.    Laast  radiUM  of  gyration  ^  Z)  X  .8636. 

The  safe  loads  given  are  computed  as  being  one-fourth  of  the  breaking 
toad,  and  as  producing  a  mazlmum  stress,  in  an  axial  direction,  on  a  square- 
nd  eolunui  Of  not  more  than  14,000  lbs.  per  sq.  in.  for  lengths  of  90  radii 


958 


STBEKOTH  OF  MATERIALS. 


IHmeiisloiis  of  Pbttnlz  Steel  Colnmns. 

(Least  radius  of  gyration  equals  D  x  .3686.) 

One  Seiirnient. 

Diameters  in  Inches. 

One  Column. 

l« 

i 

1 

Q 

ll 

Is 

111 

*»  0 

111 

=1 

3/16 

9.7 

4 

Tl/16 

8.8 

12.9 

1.45 

18.8 

H 

12.8 

A 

4^ 

6  3/16 

4.8 

16.8 

1.60 

8:i.9 

5/16 

11.8 

8^ 

*^ 

6  5/16 

6.8 

19.7 

1.55 

30.0 

_%_ 

17.3 

6  7/16 

6.8 

28.1 

21.8 

1.69 
1.95 

85.0 

M 

"liTs" 

5B^ 

8  3/16 

6.4 

S6.4 

5/16 

19.9 

."iM 

7.8 

86.6 

8.00 

45.1 

% 

»3.5 

B.1 

4^ 

•^^ 

8  5/16 

9.8 

31.8 

8.04 

54.4 

7/16 

^7.0 

^ 

8  7/16 

10.6 

36.0 

2.09 

68.9 

H 

30.6 

8  9/16 

18.0 

40.8 

8.18 

73.8 

V 

34. « 

6 

18  4 

45.6 

8.18 

h8.2 

87.7 

«^ 

8  11/16 

14.8 

60.3 

2.83 

98.1 

Va 

"T^T 

6  9/16 

^ 

7.4 

26.2 

~2;89~ 

48.3 

5/16 

JK.O 

6  11/16 

9.0 

30  6 

2.43 

59.5 

% 

27.0 

B.8 
6  1/16 

6  13/16 

97/16 

10.6 

86.0 

2.48 

70  7 

7/16 

31.1 

6  1.VI6 

18.8 

41.5 

8  52 

88.3 

^ 

35.8 

7  1/16 

9^ 

13.8 

46.9 

8.67 

93.9 

J!_ 

393 

7  3/16 

99% 

15.4 

68.4 

861 

105  « 

43.3 

7  6/16 

9  13/16 

17.0 

67.8 

2  06 

111.9 

M 

~25^~ 

7  18/16 

11  11/16 

10.0 

84.0 

"TS" 

70.0 

5/16 

81^ 

7  16/16 

11  t8/16 

18.1 

41.8 

2.H8 

85.1 

9^ 

86 

8  1/16 

14.1 

48.0 

8.98 

968 

7/lC 

41 

8  8/16 

11  16/16 

16.0 

54.6 

2  97 

118.5 

^ 

46 

8  5/16 

18.0 

61.8 

3  01 

180.3 

V 

51 

8  7/16 

12 

19.9 

68.0 

8.06 

140.0 

56 

C 

8  9/16 

12  1/16 

81.9 

74.6 

8.11 

168.7 

11/IC 

68 

7% 

8  11/16 

12  8/16 

24. S 

886 

3.16 

170.2 

»4 

68 

8  18/16 

18  5/10 

26.6 

90.6 

8.20 

186.7 

n,  16 

7:i 

8  15/16 

18  7/16 

28.6 

97.8 

3.24 

800.3 

^ 

Hi 

9  1/18 

^HH 

30.6 

104.0 

8.80 

214.2 

1 

KO 

9  6/16 

\m 

84.8 

118.6 

8.84 

244  .S 

1V6 

09 

9  9/16 

12  13/10 

38.8 

18i.O 

8.48 

271.7 

Ik 

109 

9  13/16 
11  9/16 

13 

48.7 
16.6 

146.8 
66.0 

8.57 
4.20 

20'.i.2 

ki 

88 

116^ 
13^.8 

5/10 

88>fe 

11  11/16 

15  m 

19.1 

65.0 

4.86 

% 

37 

11  18/16 

I5|^ 

21.7 

74.0 

4.29 

1.^8.4 

7/iC 

48 

11  15/16 

i5ii 

24  7 

84.0 

4.84 

1:8  0 

^ 

47 

12  1/16 

15  15/16 

27.6 

94.0 

4.88 

193  6 

0.'1« 

.V2 

1«  8/16 

16  1/16 

80.6 

104.0 

4.48 

214.1 

r.7 

E 

18  5/16 

16  3/16 

88.5 

IH.O 

4.48 

284.7 

11/10 

68 

11  1/16 

12  7/16 

18  5/16 

38.4 

124.0 

4.52 

855.8 

*i 

68 

12  9/16 

16  7/16 

40.0 

136.0 

4.56 

2R0.O 

i-vio 

78 

18  11/16 

16  9/16 

43.0 

146.0 

4.01 

9006 

% 

78 

18  13/16 

16  11/16 

45.9 

166.0 

4.60 

881  a 

1 

88 

18  1/16 

16  13/16 

61.7 

176.0 

4.78 

868.4 

m 

98 

18  .V16 

17  1/16 

576 

196.0 

4.84 

408  G 

U4 

108 

18  9/16 

17  5/16 

63.5 

216.0 

4.B3 

444.7 

5/10 

81 

MM 

19% 

24.8 

82.6 

6.54 

170.2 

> 

36 

O 

\^% 

19^ 

28.1 

96.0 

6.69 

197  7 

7/ 16 

41 

24H 

^^ 

iel2 

38.0 

109.3 

6.64 

22R  1 

H 

46 

19  11/16 

86.0 

182.6 

6.68 

258.!-. 

TOBMVhJE   FOR   IRON   AND  STEEL   STRUTS. 


259 


Ooe  Segment. 


ti 


9/16 
% 
11/16 

1V16 
H 

1 


51 
56 
61 
66 


86 
96 
106 
116 


Diameters  in  Inches. 


I 


G 


O 


One  Column. 


IS 

"a  • 

m 


89.9 
43.8 
47.7 
51.7 
55.6 
59.6 
67.4 
75.8 
88.1 
90.9 


1^ 


136.0 
149.8 
162.6 
176.0 
189.8 
209!. 6 

256.0 
2S:J.6 
809.8 


c5 


5.78 
6.77 
5.82 
5.88 
5.91 
5.95 
6.04 
6.18 
6.27 
6.32 


Si6 


280.0 
307.4 
8849 
862.4 
389.8 
417.8 
472.1 
527.8 
.^82.0 
636.9 


Working  FonnuUD  for  Wroa^lit^roii  and  Steel  Stmte 
of  TartoMS  Forms.— Burr  gires  theJoUowing  practical  formuin,  which 


he  believes  to  poflsess  adTantages  over  Qordoirs: 


Kind  of  Stmt. 


p  =  Ultimate 

Strength, 

lbs.  per  sq.  in. 

of  Section. 


Pj  =  Working 
Strength  = 
]y5  Ultimate, 
Ids.  per  sq. 

In.  of  Section. 


Flat  and  fixed  end  iron  angles  and  tees  44000  - 140 


I 


(1) 
(8) 
(5) 
(7) 
Flat-end highsteel  angles 76OOO-29O7    (9) 


r 

Hlnged-end  iron  angles  and  tees 46000-175  — 

r 

Flat-end  ixx>n  channels  and  I  beams ....  40000—  1 10  — 

r 

Flat-end  mild-steel  angles ..BSOOO-180 -^ 


Pm-end  solid  wrought  iron  columns..  ..82000-  80 


M 


S2000-27r  -  , 


(11) 


8800-28 

0200-85-1- 

8000>28 

10400>86-^ 

10200-58 

6400-16- 

6400-55 1 
a 

I 


(4) 
<6) 
(8) 
(10) 

1(12) 


Eqoations  (1)  to  (4)  are  to  be  used  only  between  —  =  40  and  —  =  200 


(5)  and  (6) 
(7}  to  (10) 
(11)  and  (12)  < 


"  =  20  "  **  =200 
li  _  40  "  "  =  200 
"  =  20    •*    "   =200 

i=    6andi-=    65 
a  a 


Steel  columns,  properly  made,  of  steel  ranging  In  specimens  from  65,000  to 
^.000  lbs.  per  square  inch  should  give  a  resistance  25  to  33  per  cent  in  ez- 
oss  of  that  of  wrought-iron  columns  with  the  same  value  of  7  -•-  r,  provided 
ibat  ratio  does  not  exceed  140. 

The  unsupported  width  of  a  plate  In  a  compression  member  should  not 
exceed  90  times  its  thickness. 

Id  built  columns  the  transverse  distance  between  centre  lines  of  rivets 
^^euring:  plates  to  angles  or  channels,  etc.,  should  not  exceed  85  times  the 
BUte  thickm^ss.    If  this  width  la  exceeded,  longitudinal  buckling  of  the 


£60 


8XBENGTH  OF  HATBBIALS. 


Slate  takes  place,  and  the  oolumo  ceases  to  fall  as  a  whole,  but  yields  In 
euil. 

The  same  tests  show  that  the  thickness  of  the  leg  of  an  aQ^le  to  which 
latUelnff  Is  i-ivet«d  should  not  be  less  than  1/9  of  the  length  of  that  leer  or 
side  if  the  column  is  purely  and  whollv  a  compression  member.  The  above 
limit  may  be  passed  somewhat  in  atuf  ties  and  compression  members  de- 
slsrned  to  carry  transrerse  loads. 

The  panel  points  of  iattidnr  should  not  be  separated  by  a  greater  distance 
than  00  times  the  thickness  of  the  angfle-lefC  to  which  the  latticing  is  riveted, 
if  the  column  is  wholly  a  oompression  member. 

The  riret  pitch  should  never  exceed  16  times  the  thickness  of  tbe  thinnest 
metal  pierood  by  the  rivet,  and  If  the  plates  are  very  thick  it  should  never 
nearly  equal  thai  value. 

nerrliiimii's  BatloiiAl  Poramla  for  Golamna  {Eng,  Newt, 
4uly  19. 1»H). 

^°,     ^    I. ^'^ 


1  + 


(?) 


B  a  unlt.load  on  the  oolumn  s  total  load  P-»-  area  of  oron-sectlon  A\ 
C  =  maximum  compressive  uttlt-«tress  on  tbe  concave  side  of  the  oolumn; 
I  3s  length  of  the  column;  r  =  least  radius  of  gyration  of  the  cross-section 
E=i  coefficient  of  elasticity  of  tbe  material;  n  =  1  f or  both  ends  round 
n  s  4/9  for  one  end  round  and  one  flxed;  n  =  ^  for  both  ends  fixed.  This 
formula  is  for  use  with  strains  within  the  elastic  limit  only:  it  does  not 
hold  good  when  the  strain  C  exceeds  the  elastic  limit. 

Pr^.  Merriman  takes  the  mean  value  of  E  for  timber  =  1,600,000,  for  cast 
iron  =  1fi,000,000,  for  wrought-iron  s=  85,000.000,  and  for  steel  =  80,000.000, 
and  «>  s  10  as  a  close  enough  approximation.  With  these  values  he  com- 
putes the  following  tables  from  formula  (1): 


I.- 

-irroufflit-lron  Colnmna  wltb  Bound  Ends. 

Unit. 
load. 

Maximum  Compressive  Unit-stress  C. 

j„.. 

1  =  80 

r 

1  =  40 
r 

!  =  «. 

r 

i  =  80 

r 

1  =  100 

r 

i.,» 

r 

!  =  .« 

6.000 
0,000 
7,000 
8.000 
0,000 
10,000 
11.000 

6,040 
6,066 
7,080 
8.100 
9.1JJ0 
10,100 

n.aoo 

12,J40 
13,280 

M70 
0,440 
7,.330 
8,480 
9,.590 
10,680 
11,750 
18.000 

i4,mo 

6,890 
0,660 
7.780 
9,040 
10,840 
11,880 
13,070 
14.600 
15,090 

6.780 
7,090 
8,580 
10,060 
11,690 
18.440 
16.310 
17,320 
19,480 

6,260 
7.890 
9,7?0 
11,660 
14,000 
10,670 
19,640 
28.080 

0.980 
9,090 
11.610 
14,640 
18,880 
28,090 

8,220 
11,380 
16.510 
21,460 

iO.aso 

16,560 
SM,7^ 

12,000 

18.000 

STREKQTH  OF  WEOUGHT  IB017  AND  SI8B£  COLUKKS.  ^61 
II«<-l¥ro«glit*lroa  Colamtt«  wtth  Plxtt4  Bn4s« 


Unit, 
load. 

Maximum  Compressive  TTnlt-stress  Cf« 

?,«B. 

i=» 

1  =  40 

—  =s  00 

1  =  80 

1  =  100 

i=t» 

i  =  t40 

l=t« 

A 

r 

r 

r 

r 

r 

r 

r 

r 

0,000 

6,010 

6,060 

6,180 

6,940 

6,880 

a,8w 

0.800 

t,og 

7,000 

l^ 

y^ 

7,180 

7,880 

7,880 

7,780 

8»110 

8,000 

8,0« 

8,100 

8,840 

8,480 

8,700 

9,010 

9,490 

10,060 

9,000 

9,000 

0,180 

9,800 

9,860 

9,800 

10,840 

10,990 

11 090 

10,000 

10.040 

10.100 

10,370 

10,710 

11,110 

11,680 

19,440 

18440 

11,000 

11,060 

11,200 

n.480 
12,540 

11,880 

12,360 

18,070 

14,020 

18,810 

12,000 

12,060 

12,240 

18,000 

18,640 

14,510 

15,690 

17,320 

13,000 

18,070 

18,280 

13,640 

14,^0 

14,040 

15,990 

17,440 

19,480 

14,000 

14,060 

14,820 

14,740 

18,880 

16,880 

17,080 

19,290 

91,820 

III.-«4eel  Golmniis  wltli  Round  Ends. 

^. 

Maximum  Ck)mpre8Biye  Unit-strew  C 

tors. 

i=» 

r 

1  =  40 

r 

-=.60 

1  =  80 

r 

i=J00 

;-•» 

i-. 

!  =  ,« 

r 

6.000 
7.000 
8,000 
9.000 
10,000 
11,000 

6,050 
7,070 
8,090 
9,110 
10,180 
11.160 
19.900 
13,830 
14,250 

6,200 
7,270 
8.880 
9,4.')0 
10,560 
11,600 
19,820 
13.9r0 
15,130 

6.470 
7,650 
aTTO 
10.090 
11,360 
12,670 
14,090 
15,400 
16,830 

6,880 
8,280 
9,660 
11,140 
12,710 
14,870 
16,180 
18,000 
19,960 

7,500 
9,180 
10,870 
12,850 
15,000 
17,370 
90.000 
22,940 
26,250 

8,430 
10,540 
19.990 
15.860 
19,280 
28,800 
98,800 

9,870 

iIItSo 

19,800 
17,400 
94,590 

14,000 

13,000 

14,000 

IV.-«4e«l  ColQinna  wltli  Fixed  Eadf. 

Unit- 
load. 

Maximum  OompreoiiTV  Unit-atreM  a 

^orB. 

l.  =  a> 

i.40 

i-w 

i.  =  80 

i-w 

l.i» 

1.140 

i-»160 

A 

r 

r 

r 

r 

r 

r 

r 

r 

7,000 

VB 

7,070 

7,160 

7,970 

7,480 

7.660 

7,900 

8,980 

8.00O 

8.020 

8,090 

8.900 

8,880 

8,670 

8.770 

9,800 

9,660 

9;000 

9,080 

9,110 

9,2S0 

9,450 

9,780 

10,090 

10,550 

11,140 

10,000 

10,030 

10,180 

10,810 

10,560 

10,910 

11,860 

11.810 

12,710 

11,000 

^^'S!2 

11,100 

11,880 

11,600 

12,110 

18,670 

13,410 

14;870 

12,000 

19.060 

19,900 

19.480 

19,890 

18,880 

14,090 

14,080 

16,180 

18.000 

*^2S 

18,880 

18.680 

18,970 

14,680 

15,400 

16,600 

17990 

14,000 

ujm 

14,980 

14,610 

15,180 

15,860 

16,880 

18,150 

19,960 

15,000 

16,080 

16,310 

15,710 

16,810 

17,140 

18.990 

19,870 

22,060 

Tbe  design  of  the  eross-sectloo  of  a  column  to  oarry  a  given  load  with 
m^xinuun  unit-stress  C  may  be  made  by  assuming  dTmeDslona,  and  then 


S63  BTBEKQTH  OF  KATEBIALS. 

computing  C  by  formula  <1).  If  the  agreement  between  the  spedfled  and 
compated  vacdes  is  not  sufaclently  close,  new  dimensions  must  be  choaen, 
and  the  computation  be  repeated.  By  the  use  of  the  above  tables  the  work 
will  be  shortened. 

The  formula  (1)  may  be  put  in  another  form  which  in  some  cases  will  ab. 
breyiate  the  numerical  work.  For  B  substitute  its  value  P-^  A^  and  for 
Ar*  write  /» the  least  moment  of  Inertia  of  the  cross-section;  then 

^-o'-  =  V.^ ^^ 

In  which  I  and  r*  are  to  be  determined. 

For  example,  let  it  be  required  to  find  the  siase  of  a  square  oak  oolomn 
with  fixed  ends  when  loaded  with  34.000  lbs.  and  16  ft.  Ions,  so  that  the 
maximum  compressive  stress  C  shall  be  1000  lbs.  per  square  inch.  Here 
/:=  34,000.  Cs=1000,  nsM>«*  =  10,  i? a  1,000,000.  I  s  16  X  12,  and  (S)  be- 


/-84r«B  14.78. 
Now  let  :p  be  the  side  of  the  square;  then 

so  that  the  equation  reduces  to  x^  -  84«<  =  177,  from  which  sfi  is  found  to  be 
20.02  sq.  In.,  and  the  side  x  =  5.47  in.  Thus  the  unit-load  B  is  about  8QS 
lbs.  per  square  inch. 

irORKINO  STRAINS  A1.1.0WBD  IN  BRIDGE 


.  Theodore  Cooper  gives  the  following  in  his  Bridge  Speclflcatlons : 

Compression  members  shall  be  so  proportioned  that  the  maximum  load 
shall  in  no  case  cause  a  greater  strain  than  tliat  determined  by  the  follow- 
ing formula : 

8000 
P  a=  • jz —  for  square^nd  compression  members ; 

^4O,00Oi-« 

'  p  a  — Z22L —  for  comprassion  members  with  one  pin  and  one  iquare  end ; 

^'^'80,0001* 

p» ????L —  for  compression  members  with  pin-bearings; 

^"^ao,ooor« 

(These  values  may  be  increased  In  bridges  over  IfiO  ft  span.  See  Oooper*a 
Specifications.)  .     . 

p  =  the  allowed  compression  per  square  inch  of  cross-section; 
2  =  the  length  of  compression  member,  in  inches; 
r  =  the  least  radius  of  gyration  of  the  section  In  inches. 
No  compression  member,  however,  shall  have  a  length  exceeding  45  times 
its  least  width.  ,    „ ,  _..       ^ 

Tension  Members.— K\\  parts  of  the  structure  shall  be  so  proportioned 
that  the  maximum  loads  snail  in  no  case  cause  a  greater  tension  than  the 
following  (except  in  spans  exceeding  150  feet) : 

Pounds  per 
sq.  in. 

On  lateral  bracing 16,000 

On  solid  rolled  beams,  used  as  cross  floor-beams  and  stringers.    9,000 

On  bottom  chords  and  main  diagonals  (forged  eye-bars) 10,000 

On  bottom  chords  and  main  diagonals  (plates  or  shapes^  net 

section 8,000 

On  counter  rods  and  long  verticals  (forged  eye-bars) 8,000 

On  counter  and  long  verticals  (plates  or  shapes),  net  section..    6,600 

Oa  bottom  flange  of  riveted  cross-girders,  net  section  8,000 

On  bottom  flange  of  riveted  longitudinal  plate  girders  over 

20ft.  long,  netsection 8,000 


WORKIKQ  STRAINS  ALLOWED  IN  BRIDGE  MEMBERS.  263 

Ob  bottom  flange  of  riveted  longitudinal  plate  girders  under 

SO  ft.  long,  net  section  7,000 

On  floor-beam  bAugers,  and  otlier  similar  members  liable  to 

sudden  loading  (bar  iron  witb  forged  ends) 6,000 

On  floor  beam  hangers,  and  other  similar  members  liable  to 

sudden  load ing  (plates  or  shapes),  net  section 5,000 

Members  subject  to  alternate  strains  of  tension  and  compression  shall  be 
proportioiied  to  resist  each  kind  of  strain.  Both  of  the  strains  shall,  how- 
ever, be  considered  as  increased  by  an  amount  equal  to  6/10  of  the  least  of 
the  two  strains,  for  determining  the  sectional  area  by  the  above  allowed 
strains. 

The  Phoenix  Bridge  Co.  (Standard  Speciflcations,  1805)  gives  the  follow- 
inft: 

The  greatest  working  stresses  in  pounds  per  square  inch  shall  be  as  fol- 
lows: 

Tension, 
Steel.  Iron. 

f  =  ».ooor i.f"'°- '^"'"1 , ^°^"!  f=7.5(iori+"'°'*"^i 

L       Max.  stressj  forged  ends.  L       Max.  stresii  J 

p-a-50ori-4-?^-^*'???1   P'***^*""      p_7ooori4-?y5iJ^j:???l 

8.500  pounds.  Floor-beam  hangers,  forged  ends 7,000  pounds. 

7JSM        **  Floor-beam  hangers,  plates  or  shapes,  net 

section 6,000  *' 

10.000       "  Lower  tlanges  of  rolled  beams. 8,000  " 

»,000       "  Outside  fibres  of  plus 15,000  " 

30.000        "  Pins  for  wind-bracing 82,500  " 

ao,000       "  Lateral  bracing 15,000  " 

Shearing, 

B,000pound8.    Pins  and  rivets 7,500pound8. 

Hand-driven  rivets  SOjt  less  unit  stresses.     For 
bracing  increase  unit  stresses  50%. 
6,000pounds.    Webs  of  plate  girders 5,000pound8. 

Beanng. 
16,000  pounds.    Projection  semi-lntrados  pins  and  rivets.. . .  13,000  pounds. 
Hand-driven  rivets  20%  less  unit  stresses.     For 
bracing  increase  unit  stresses  bO%. 

Compression. 

Lengths  less  than  forty  times  the  least  radius  of  gyration,  P  previously 
found.    See  Tension. 

Lengths  more  than  forty  times  the  least  radius  of  gyration,  Produced  by 
foUowing  formulae: 

P 

For  both  ends  fixed,  6  =  • rj . 

^  38,000  r» 
p 
For  one  end  hinged,  6  = j5j —  • 

1-4- -— 

^24,000i« 

p 

For  both  ends  hinged,       6  = ^ . 

1  J i 

^  18,000  r« 

P=  permissible  stress  previouslv  found  (see  Tension);  5  =  allowable 
working  stress  per  square  inch:  <  =  length  of  member  in  inches;  r  =  least 
radius  of  gyration  of  section  in  inches.  No  compression  member,  how* 
erer,  shall  oave  a  length  exceeding  45  times  its  least  width. 


264  BTREKGTH  OF  MATSBIAL8. 

Poubdn  per 
•q.  in. 

In  counter  web  members • 10,600 

In  long  Terticals 10,000 

In  all  maln-web  and  lowerchord  eye-bara 18,800 

In  plate  bangers  (net  aeotion) 0.000 

In  tension  members  of  lateral  and  transverse  bracing 19.000 

In  steel-angle  lateral  ties  (net  section) 16,000 

For  spans  over  300  feet  In  length  the  greatest  allowed  working  sti  eases 
per  square  inch,  in  lower-chord  and  end  main-web  eye-bars,  shall  be  taken  •» 


io,ooo(i-f 


min.  total  stress  \ 
max.  total  stress/ 


wbeneyer  this  quantity  exceeds  18,200. 

The  greatest  allowable  stress  in  the  main-web  eye-bars  nearest  the  centre 
of  such  spans  shall  be  taken  at  18,900  pounds  per  square  inch  ;  and  those 
for  the  intermediate  eye-bars  shall  be  found  by  direct  interpolation  between 
the  preceding  values. 

The  srreatest  allowable  working  stresses  in  steel  plate  and  lattice  girders 
and  rolled  beams  shall  be  taken  as  follows : 

Pounds  per 


sq.  in. 
10,000 


tipper  flange  of  plate  girders  (gross  section) 10,000 

Lower  flange  of  plate  girders  (net  section) 10,000 

In  counters  and  long  verticals  of  lattice  girders  (net  section) . .    9,000 
In  lower  chords  and  main  diagonals  or  lattice  girders  (net 

section) 10,000 

In  bottom  flanges  of  rolled  beams 10,000 

In  top  flanges  of  rolled  beams 10,000 

BBtlSTANCB  OF  HOIiIiOW  OYIiIHBBBS  TO 
GOIiliAPSB. 

Fftirbalm^s  empirical  formula  (JPhiL  Trans.  1858)  is 

pm9,mfiO0~ (1) 

where  p  m  pressure  In  lbs.  per  square  Inch,  t  s  thickness  of  cylinder,  d  = 
diameter,  and  I  s  length,  all  in  Inches  ;  or, 

ps  806,800^,  if  I.  Is  in  feet. (S) 

He  reoonunends  the  simpler  formula 

p-9,675.600^ (^ 

as  sufficiently  aoourate  for  practical  purposes,  for  tubes  of  considerable 
diameter  ana  length. 

The  diameters  of  Fairbalm*s  experimental  tubes  were  4'\  6^',  8",  10^',  and 
i^'\  and  their  lengthsr  between  the  cast-iron  ends,  ranged  between  19  Incbe* 
and  60  inches. 

His  formula  (8)  has  been  generally  accepted  as  the  basts  of  rules  for 
ascertaining  the  strength  of  boiler-flues.  In  some  cases,  however,  limits  are 
flxed  to  ItA  application  by  a  supplementary  formula. 

Lloyd's  Register  contams  the  following  formula  for  the  strength  of  circular 
boiler-flues,  viz., 

-=^ «) 

The  English  Board  of  Trade  prescribes  the  following  formula  for  circular 
flues,  when  the  longitudinal  Joints  are  welded,  or  made  with  riveted  butt- 
straps,  viz., 

90,000f« 

^=(Zr+l)d <^ 

For  lap-joints  and  for  inferior  workmanship  the  numerical  factor  may  b« 
reduced  as  low  as  60,000. 


fflcioiit  in  M)phrliiff  Us  formula, 
g,"  by  J.  w.  Nystrom,  p.  IW.) 
ion  defect  that  tbegr  make  the 


RESISTANCE  OF  HOLLOW  GTLIN0B£8  TO  COLLAPSE.  266 

The  ruleB  of  Uoyd*8  Begister,  as  well  as  those  of  the  Board  of  Trade,  pra- 
Kribe  further,  that  In  no  case  the  value  of  P  must  exceed  the  amount  giT«n 
by  the  foUowing  equation,  via., 

^=-3- <^ 

Kb  CormolsB  (4y,  (5).  (6)  P  fa  the  highest  worUng  presBure  In  pounds  per 
square  inch,  t  and  d  are  the  thickness  and  diameter  in  Inches,  L  is  the 
kiiirth  of  the  flue  In  feet  measured  between  the  strengthening  rings.  In  case 


it  is  fitted  with  such.  Formula  (4)  is  tlie  same  as  formula  (3),  wiUi  a  factor 
of  afety  of  9.  In  formula  (6)  the  length  L  ta  increased  by  1 ;  the  influenoe 
which  this  addition  has  on  the  value  of  P  is,  of  course,  greater  for  short 
rabee  than  for  long  ones. 

Nystrom  has  deduced  from  Fairbalm*8  experiments  the  following  formula 
for  the  collapsing  strength  of  flues : 

'-I?E ("-^ 

vbere  p,  i;  and  d  have  the  same  meaning  aa  In  formula  (1),  Z^  la  the  length  in 
tift,  and  T  Is  the  tensile  strength  of  the  metal  in  pounds  per  square  inch. 

If  we  assign  to  T  the  value  fiO,000,  and  express  the  length  of  (he  floe  io 
iBchea,  equation  (7)  assumes  the  following  form,  vix.« 

'-"^5?f <» 

Njstrom  considers  a  tBCtar  of  safety  of  4  sufflcient  in  i 
(See  **  A  New  Treatise  on  Steam  Engineering,"  by  J.  ^ 

Formula  (1),  (4),  and  (8)  have  the  common  defect  that  they  make  the 
eoUapainff  pressure  decrease  indeflnitely  with  increase  of  length,  and  vice 
tursa.  H.  Ix>ve  has  deduced  from  Falrbaim*s  experiments  an  equation  of 
s  diff ereni  form,  which,  reduced  to  English  meaaures,  is  as  f oUowa,  via., 

p- 8,858,180 g+41.We^+18»|. (9) 

vbere  the  notation  Is  the  same  as  In  formula  (1). 

D.  K.  Clark,  in  his  ''  manual  of  Bules,"  etc.,  p.  806,  gives  the  dimensions  of 
»z  flues,  selected  ftnom  the  reports  of  the  Manchester  Steam-Users  Assocla- 
ti^,  1880-80,  which  collapsed  while  in  actual  use  in  boilers.  These  flues 
varied  troxa  SI  to  00  inches  in  diameter,  and  from  8-16  to  |^  Inch  in  thickness. 
Thf^j  consisted  of  rings  of  plates  riveted  together,  with  one  or  two  longitud- 
ir^  seanos,  but  all  of  them  unfortified  by  intermediate  flanges  or  strength- 
Hiing  rings.  At  theoollapstng  pressures  the  flues  experienced  compressions 
ranging  from  1.68  to  2.17  tons,  or  a  mean  compression  of  1.82  tons  per  square 
irich  M  section.  From  these  data  Clark  deduced  the  following  formula 
**for  the  average  retfstlog  force  of  common  boiler-flues,**  viz., 

p,^(«^.«o) m 

where  p  la  the  collapsing  pressure  f n  pounds  per  square  Inch,  and  d  and  t 
iTR  the  diameter  and  thickness  expressed  in  inches. 

C.  R.  Boelker,  in  Van  NoBtrana'a  Magagine^  Harch,  1681,  discussing  the 
above  and  other  formnlss,  shows  that  experimental  data  are  as  yet  Insuffl- 
a*Qt  to  determine  the  value  of  any  of  the  f  ormulsB.  He  savs  that  Nystrom^s 
formula^  (8).  gives  a  closer  agreement  of  the  calculated  with  the  actual  col- 
hpang  pressures  in  experiments  on  flues  of  every  description  than  any  of 
Uke  other  formulsB. 

CoIlapafliiiP  Preaanre  of  Plain  Iron  Tubes  or  Finos. 

(dark,  8.  B.,  vol  L  p.  648.) 

The  reaistanee  to  collapse  of  plain-riveted  flues  Is  directly  as  the  square  of 

Ute  chiekness  of  the  plate,  and  inversely  as  the  square  of  the  diameter.    The 

niiport  of  the  two  ends  of  the  flue  does  not  practically  extend  over  a  length 

^  tabe  p-eater  than  twice  or  three  times  the  diameter.    The  collapsing 

»  of  long  tubes  Is  therefore  practically  independent  of  the  length. 


BTBEKQTU  OF  HATEBIAL8. 

Insfcanoefl  of  collapfied  flues  of  ConilBh  and  Lancashire  boOerB  collated  hj 
Olark,  showed  that  the  resistance  to  collapse  of  flues  of  flinch  plates,  18  to 
48  feet  long,  and  80  to  60  inches  diamecer,  raried  as  the  i. 95  power  oC  the 
diameter.    Thus, 

for  diameters  of 80   85  40   45  SO  inches, 

the  collapsing  pressures  were 76   58  45   87  80  lbs.  per  aq.  la; 

for  7-10-inch    plates  the   collapsing 

pressures  were.. .VT.  ....  60   40  42  ••     ••       - 

For  collapsing  pressures  of  plain  iron  flue-tubes  of  Oomlih  and  Lanoft 
■hire  steam-boiiers,  Olark  giTes: 

p       MO.OOOf* 

P  m  collapsing  presMire,  to  pounds  per  square  Inckt 
1 8  thickness  of  the  plates  of  the  furnace  tube,  lit  Bchei. 
d  ss  internal  diameter  of  the  furnace  tube,  in  inches. 

For  short  lengths  the  longitudinal  tensile  resistance  may  be  effective  in 
augmenting  the  resistance  to  collapse.  Flues  efficiently  fortified  by  flange- 
lolnts  or  hoops  at  intervals  of  8  feet  may  be  enabled  to  resist  from  50  lbs. 
to  60  lbs.  or  70  lbs.  pressure  per  square  inch  more  than  plain  tubes,  accord, 
ing  to  the  thickness  of  the  plates. 

Streni^lft  of  Small  Tiib6a«->The  collapsing  mistaace  of  solid- 
drawn  tubes  of  small  diameter,  and  from  .184  inch  to  .100  inch  in  thickneas. 
Has  been  tested  experimentally  by  Messrs.  J.  Russell  A  Bona  The  results 
lor  wrought-iron  tubes  varied  from  14.88  to  20.07  tons  per  square-Inch  sec- 
tion of  the  metal,  averaging  18.20  tons,  as  against  17.57  to  24.d  tons,  averag- 
fli|r22.40  tons,  for  the  bursting  pressure. 

(For  strength  of  SegmentaiCrowns  of  Furnaces  and  Cylinders  see  Clark, 
as.,  vol.  i,  pp.  64»-661  and  pp.  027.  628.) 

Pormala  for  Corrnxmtea  Fumaeea  (Eng'g^  July  24,  1801,  p. 
102).— As  the  result  of  a  series  of  experiments  on  the  resistance  to  collapse 
of  Fox's  corrugated  furnaces,  the  Board  of  Trade  and  Lloyd's  Begiatry 
altered  their  formulas  for  these  furnaces  in  1801  as  follows: 

Board  of  Trade  formula  is  altered  from 

T  as  thickness  in  inches: 

Z>  a  mean  diameter  of  furnace; 

WP  =  working  pressure  in  pounds  per  square  inch. 

Lloyd's  formula  Is  altered  from 

iogox(rM.^^^i2tx(ra  _ ^ 

T  s  thickness  in  sixteenths  of  an  inch; 

D  =  greatest  diameter  of  furnace: 

WF  =  working  pressure  in  pounds  per  square  Inch. 

TBANSVERSB  STRENGTH. 

In  transverse  tests  the  strength  of  bars  of  rectangular  section  Is  found  to 
vary  directlv  as  the  breadth  of  the  specimen  tested,  as  the  square  of  Its 
depth,  and  inversely  as  its  length.  The  deflection  under  any  load  varies  as 
the  cube  of  the  lenfirth.  and  inversely  as  the  breadth  and  as  the  cut>e  of  the 
depth.  Represented  algebraically,  itS=  the  strength  and  D  the  deflection. 
1  the  length,  6  the  breadth,  and  d  the  depth, 

i9  varies  as  -j-  and  D  varies  as  ^. 

Fmr  the  purpose  of  reducing  the  strength  of  pieces  of  various  alaea  to 
a  oommcKi  standard,  the  term  modulus  of  rupture  (represented  by  H)  in 
uwd.    Its  value  is  obtained  by  experiment  on  a  bar  of  rectangular  section 


TBANSYEBSE  STRENGTH.  267 

supported  at  the  ends  and  loaded  In  the  middle  and  suhetltutlng  numerical 
Tajues  in  the  following:  formula  : 

in  which  P  =  the  hreaktog  load  in  pounds,  Z  s  the  length  in  inches,  h  the 
breadth,  and  d  the  depth. 

The  inodultu  of  rupture  is  sometimes  deflned  as  the  strain  at  the  instant 
of  rupture  upon  a  unii  of  the  section  which  is  most  remote  from  the  neutral 
axis  on  the  side  which  flrst  ruptures.  This  definition,  however,  is  based 
upon  a  theorjr  which  is  yet  in  dispute  among  autborities,  and  it  is  better  to 
define  it  as  a  numerical  value,  or  experimental  constant,  found  by  the  ap- 
plication of  the  formula  above  given. 

From  the  above  formula,  making  I  12  inches,  and  b  and  d  each  1  inch,  it 

follows  that  the  modulus  of  rupture  is  18  times  the  load  required  to  break  a 

bar  one  inch  square,  supported  at  two  points  one  foot  apart,  the  load  being 

applied  in  the  middle. 

rv^.^#fi..i^t:  ^*  t^^^^mu,  .*.«»<,*ii  -  span  in  feet  X  load  at  middle  in  lbs. 
OoefBctont  of  transveiBe  strength  =  ^^^^  ^  ^^^^^  ^  ^^^^  ^^  ^^^^^^^, 

=r^th  of  the  modulus  of  rapture. 


Pwndamentml  FommlsB  for  Flexvre  of  Beam*  (Iferriman). 

Kettisting  shear  =  vertical  shear; 

Resisting  moment  =  bending  moment; 

Sum  of  tensile  stresses  =  sum  of  compressive  stresses; 

Readsting  shear  s  algebraic  sum  of  all  the  vertical  components  of  the  in* 
temal  stresses  at  any  section  of  the  beam. 

If  ^  be  the  area  of  the  section  and  Si$  the  shearing  unit  stress,  then  resist* 
ing  shear  =:  ASai  and  if  the  vertical  shear  ss  F,  then  V  =  AS^. 

The  vertical  »heav  is  the  algebraic  sum  of  all  the  external  vertical  forcee 
on  one  side  of  the  section  coniddered.  It  is  equal  to  the  reaction  of  one  sup- 
port, considered  as  a  force  acting  upward,  minus  the  sum  of  ail  the  vertkal 
downward  forces  acting  between  the  support  and  the  section. 

The  resisting  moment  =  algebraic  sum  of  all  the  moments  of  the  inter- 
nal horizontal  stresses  at  any  section  with  reference  to  a  point  in  that  sec- 

sl 
tion,  =  — (in  which  8  =  the horlaontal  unit  stress,  tensile  or  compressive 

c 
as  the  case  may  be,  upon  the  fibre  most  remote  from  the  neutral  axis,  c  = 
the  shortest  distance  from  that  fibre  to  said  axis,  and  /=  the  moment  of 
inertia  of  the  cross-section  with  reference  to  that  axis. 

The  bending  moment  M  in  the  algebraic  sum  of  the  moment  of  the  ez- 
t«>mal  forces  on  one  side  of  the  section  with  reference  to  a  point  in  that  sec- 
tion =s  moment  of  the  reaction  of  one  support  minus  sum  of  moments  of 
loads  between  the  support  and  the  section  considered. 

O 

The  bending  moment  is  a  compound  quantity  =  product  of  a  force  by  the 
distance  of  Its  point  of  application  from  the  section  considered,  the  distance 
being  measured  on  a  line  drawn  from  the  section  perpendicular  to  the 
direction  of  the  action  of  the  force. 

Oonoemlng  the  above  formula.  Prof.  Merriman,  Ei%g.  Ne^m,  July  21, 1894, 
says:  The  formula  just  quoted  is  true  when  the  unit-stress  8  on  the  part  of 
the  beam  farthest  from  the  neutral  axis  is  within  the  elastic  limit  of  the 
material.  It  is  not  true  when  this  limit  is  exceeded,  because  then  the  neutral 
axis  does  not  pass  through  the  centre  of  gravity  of  the  cross-eection,  and 
because  also  the  different  longitudinal  stresses  are  not  proportional  to  their 
distances  from  tliat  axis,  these  two  requirements  lieing  involved  in  the  de- 
duction of  the  formula.  But  in  all  cases  of  design  the  permissible  unit- 
stresses  should  not  exceed  the  elantic  limit,  and  hence  the  formula  applies 
ratkmally,  without  regai-ding  the  ultimate  strength  of  the  material  or  any 
of  the  drcumstances  regarding  rupture.  Indeed  so  great  reliance  is  placed 
upon  this  formula  that  the  practice  of  testing  beams  by  rupture  has  been 
•Imost  emUrely  abandoned,  and  the  allowable  unit-stresses  are  mainly  dt»* 
rived  from  tensile  and  compressive  testji. 


SXfiBHOTH  OF  MATEEIALd. 


r 


5;-S!-5h5!-5i-5l-5N5hBI«    S> 


I 

I 


nnunnnunii 
"5  S  K  S  S  JC  c  S  C^ 

^let  •^1"*  «.oo     4-    *''<» '^••o '-IS  loj 
cewo 


itibll-Jhltlhii-ll- 


»-"l«   ^■"'    0*100    ^"^    'fl-    00   "^i    «   ftjl 

I      n      K      H      n      n      II      V 

+ 


I 


ft;! 
n 


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I  I 

£     I 


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& 


APPROXIMATE  SAFE  LOADS  IK  LBS.  OK  STEEL  BEAMS.   269 


Fonniiln  i^r  TranarerM  StMOfftli  of  Beamti*— Rfiferrlng  to 
table  oa  preceding  paxe, 

P:=:  load  at  middle; 

Wm  total  load,  distrllmted  UDtformljr: 

I  tt  leactli,  6  m  breadth,  d  «  depth,  hi  hiofaeet 

M  m  moduliia  of  elaatieity; 

B  m  modulus  Qt  rupture,  or  strees  per  square  hich  of  eztreme  fibre; 

/  m  mcNiient  of  taiertia; 

e  m  dlataiMW  between  neutral  axis  and  extreme  fibre. 

For  breaUBK  load  of  circular  section,  replace  &d*  by  0.60(2*. 

For  good  wrought  iron  the  value  of  R  is  about  80,000,  for  steel  about  180,000, 
the  percentage  of  carbon  apparently  haying  no  influence.  (Thurston,  Iron 
and  Steel,  p.  401). 

Tw  cast  iron  ttie  Talue  of  K  raries  greatly  according  to  quality.  Thurston 
found  45,740  and  87,060  in  No.  S  and  No.  4  cast  h:on,  respectlTely. 

For  beams  fixed  at  both  mds  and  loaded  in  the  middle.  Barlow,  by  experi- 
ment, found  the  maximum  moment  of  stress  =  l/6Pf  instead  of  ^H,  the 
result  giTen  by  theory.  Prof.  Wood  (Resist.  Matls.  p.  165)  says  of  tliis  case: 
The  phenomena  are  of  too  complex  a  character  to>dmit  of  a  thorough  and 
exact  analysis,  and  It  Is  probably  safer  to  aoeepC  the  results  of  Mr.  Barlow 
hi  practice  than  to  depend  upon  theoretical  results. 

approxuhatb  gbbatbst  safb  i^oabs  in  IjBS.  on 

STBEIj  BEAinS.    (Pencoyd  Iron  Works.) 

Based  on  fibre  strains  of  10,000  lbs.  for  steel.    (For  iron  the  loads  should  be 
one-eighth  less,  corresponding  to  a  fibre  strain  of  14,000  lbs.  per  square  Inch.) 
L  =  length  In  toet  between  supports;         a  =  interior  area  In  square 
A  =  sectional  area  of  beam  in  square  inches; 

Ineiiea:  d  s  interior  depth  in  hiohes. 

Das  depth  or  beam  in  inches.  «0  s  working  load  in  net  tons. 


Shape  of 
Sectkm. 

Greatest  Safe  Tioad  in  Pounds. 

DeflecUon  in  Inches. 

Load  in 
Middle. 

Load 
Distributed. 

Load  In 
Middle. 

Load 
Distributed. 

SoUd  Rect- 
angle. 

SODAD 

itWAD 
L 

Mi* 

IkADi 

f&AL^ 

HoUowRect- 

WO(^D-/irD 
L 

1780(4D-ad) 
L 

38(^D«-ail») 

U)U 

angte. 

58(AX^-ad«) 

Solid  Cylin- 
der. 

mAD 

L 

IWHAD 

L 

%^AD^ 

wL> 

Hollow 

it7(AD~ad) 

L 

13tS(^i>-a<f) 
L 

«(^D«-ad«) 

w£> 

Cylinder. 

86(^i)*-«f*) 

Angle  or 
Tee. 

666AD 
L 

irroAD 

L 

IStAIP 

tAAD^ 

Channel  or 
Zbar. 

IS^AD 
L 

9O60AD 
L 

wL' 
68^Z)» 

^AD* 

Deck  Beam. 

IdSOAD 
L 

frWAD 

L 

50^Z)« 

eOAD» 

IBsaiB. 

L 

mOAD 
L 

68^D« 

I 

11 

III 

IV 

V 

S68 


BTRBHOTB  OF  MAtBBIALS. 


e 


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O 


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IS 


e 

I 
s 

8 

s 

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IB 

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9     £ 


Sl«S!»Sh5l«5l«5l«Sh5l»5l<»    Si' 


nnuiiuflun 
»;    S    K    5  S  «:_  s;.  ^ 


ft, 


-7(0  .h7«>  - 12 


tl 

■i 


iplhplL^-Sii 


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THi«  '^"'  etioo  ^'^  'v  00  ^'eo  051 
I        II        N        M        n        tl        II        M 


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ft 


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1 


APPBOXIMATE  SAFE  LOADS  IK  LBS.  OK  STBEL  BEAMS.   209 


FonBvto  i^r  TranarerM  StMnctlft  of  Beaaiiti*--BefeiTltig  to 
table  on  precedine  paxei 
oad  at  middle; 


Wm  toua  kMul,  dtetrftmCed  unlformljr! 

I  m  laiiKih«  b  «  breadth,  d  «  depth.  In  iiicbM; 

B  m  modtihifl  oC  elutieity; 

B  m  modulus  of  rupture,  or  strees  per  square  inch  of  eztreme  fibre; 

/  m  inoment  of  inertia; 

e  ai  i**^*^"««  between  neutral  axis  and  extreme  fibre. 

For  breaklnK  load  of  circular  section,  replace  &d*  by  0.60d*. 

For  good  wrouffht  iron  the  value  of  R  is  about  80,000,  for  steel  about  190,000, 
the  percentage  of  carbon  apparently  haying  no  influence.  (Thurston,  Iron 
snd  Steel,  pTIon. 

For  cast  Iron  ttub  Talne  of  Jt  Tarles  greatly  according  to  quality.  Thurston 
found  4S^740  and  87,960  in  No.  S  and  No.  4  cast  iron,  respectively. 

Fbr  beams  fixed  at  both  ends  and  loaded  in  the  middle.  Barlow,  bv  experi^ 
meat,  found  the  maxlmom  moment  of  stress  =  l/6Pf  instead  of  ^PI,  the 
result  given  by  theory.  Prof.  Wood  (Resist.  MaUs.  p.  155)  sc^^s  of  tliis  case: 
The  phenomena  are  of  too  complex  a  character  to  admit  of  a  thorough  and 
exact  analysis,  and  It  is  probably  safer  to  aoeepC  me  results  of  Mr.  Barlow 
In  practice  than  to  depend  upon  theoretical  results. 

APPROXIBEATB  6BBATB8T  SAFB  IiOADS  IN  IjBS.  ON 
ATBEIi  BBAins.    (Pencoyd  Iron  Works.) 

Based  on  fibre  strains  of  16,000  lbs.  for  steel.    (For  iron  the  loads  should  be 
one-eightli  less,  corresponding  to  a  fibre  strain  of  14,000  lbs.  per  square  inch.) 
L  =  length  In  feet  between  supports;  a  =  Interior  area  in  square 

A  s  sectional  area  of  beam  in  square  inches; 

Indies:  d  »  interior  depth  in  inches. 

D  as  depth  of  beam  In  inches.  to  s  working  load  in  net  tons. 


Shape  of 
Section. 

Greatest  Safe  Load  In  Pounds. 

Defiectlon  hi  Inches. 

Load  in 
Middle. 

Load 
Distributed. 

Load  In 
Middle. 

Load 
Distributed. 

SoUd  Rect- 
angle. 

MAD 

L 

I'VdOAD 

L    " 

f&AD^ 

^AL^ 

HoUowRectr 

800(^D-arr) 

L 

1780(4D-a<i) 
L 

S3(AD^-ad») 

ti>L« 

angle. 

3«(AX^-«i«) 

SoUd  Qylin- 
der. 

mAD 

L 

1888^D 

toL» 
9iAD* 

Hollow 

i»7(AD^ad) 

L 

}tK{AD-wI) 

L 

tHAD^-ad^) 

w£> 

C!yllnder. 

86(^i)*-«f*) 

Even-legged 
Angle  or 
Tee. 

BBHAD 
L 

ITJUAD 

L 

wJJ 
nAD* 

wLi 
^AD* 

Channel  or 
Zbar. 

iS^AD 
L 

9O60AD 
L 

58AZ>* 

^iAD» 

Deck  Beam. 

1S90AD 

L 

^rxaAB 

L 

60i4Z)« 

BOAD» 

IBHa. 

1906  AD 

L 

mo  AD 
L 

58^2>* 

I 

U 

III 

IV 

V 

270 


8TBKNGTH  OF  MATBBULB. 


The  above  fonnul0B  for  the  etrength  and  atiffiieM  of  rolled  beams  of  ▼»> 
rious  sectionB  are  intended  for  conyenlent  applieatlon  in  cases  where 
strict  accuracy  is  not  required. 

The  rules  for  rectangular  and  circular  sections  aie  correct,  while  thoae  for 
the  flanged  sections  are  approximate,  and  limited  In  their  application  to  the 
standara  shapes  as  given  in  the  Pencoyd  tables.  When  the  section  of  any 
beam  is  increased  above  the  standard  minimum  dimensions,  the  flanges  re- 
maining unaltered,  and  the  web  alone  being  thickened,  the  tendency  will  be 
for  the  load  as  found  by  the  rules  to  be  In  excess  of  the  actual;  but  within 
the  limits  that  it  is  possible  to  vary  any  section  in  the  rolling,  the  rules 
will  apply  without  any  sorious  inaccuracy. 

The  calculated  safe  loads  will  be  approximately  one  half  of  loads  that 
would  Inlure  the  elasticity  of  tbe  materials. 

The  rules  for  deflection  apply  to  any  load  below  the  elastic  limit,  or  less 
than  double  the  greatest  safe  load  by  the  rules. 

If  the  beams  are  long  without  lateral  support,  reduce  the  loads  for  the 
ratios  of  width  to  span  as  follows : 


Length  of  Beam. 
90  times  flange  width. 
80     **        **         " 
40      **         **  ** 

00         M  M  M 

00      ••         *»  •♦ 

I^Q         it  «•  «• 


Proportion  of  Calculated  Load 
forming  Greatest  Safe  Load. 

Whole  calculated  load. 
Q-IO  "  *• 

8-10  "  •• 

7-10  "  •• 

e-10  •• 

5-10  -  " 


These  rules  apply  to  beams  supported  at  each  end.  For  beams  supported 
otherwise,  alter  the  coefBcients  of  the  table  as  described  below,  refernug  to 
the  respective  columns  indicated  by  number. 

Chance*  of  Coeflelenta  for  Special  Forma  of  Beam*. 


Kind  of  Beam. 

Coefficient  for  Safe 
Load. 

Coefficient  for  Deflec- 
Uon. 

Fixed  at  one  end,  loaded 
at  the  other. 

One  fourth  of  the  coeffi- 
cient, col.  II. 

One  sixteenth  of  the  co- 
efficient of  col.  IV. 

Fixed  at  one  ent^,  load 
evenly  distributed. 

One  fourth  of  the  coeffi- 
cient of  col.  III. 

Five  forty-eighths  of  the 
coefficient  of  col.  V. 

Both  ends  rigidly  fixed, 
or  a  continuous  beam, 
with  a  load  in  middle. 

Twice  the  coefficient  of 
col.  II. 

Four  times  the  coeffi- 
cient of  col.  IV. 

Both  ends  risidly  fixed, 
or  a  continuous  beam, 
with  load  evenly  dis- 
tributed. 

One  and  one-half  times 
the  coefficient  of  col. 

m. 

Five  times  theooefflciem 
of  col.  V. 

SliASTIC  RBSIIilBNCB. 

In  a  rectangular  beam  tested  by  transverse  stress,  supported  at  the  ends 
and  loaded  In  the  middle. 


A  = 


1     P/« 


4  Eod*  • 

In  which,  if  P  is  the  load  in  pounds  at  the  elastic  limit,  R  ss  the  modulus  of 
transverMe  strength,  or  the  strnin  on  the  extreme  fibre,  at  the  elastic  limit, 
E  s  modulus  of  elasticity,  A  =  deflection,  I.  b,  and  rf  s  length,  breadth,  and 
depth  In  hiches.    Substltutltig  for  P  iu  (2)  its  value  in  (1),  we  have 

1  m*_ 


BEAMS  OF  UNIFORM  STRENGTH  THROUGHOUT  LENGTH,  271 


The  elastic  rasllienoe  s  half  the  product  of  the  load  and  deflection  =  MPA, 
and  the  elastic  resilieDoe  per  cubic  inch 

1  PA 

"2  Ibd' 

SttbfititutiDir  the  values  of  P  and  A,  this  reduces  to  elastic  resilience  per 

cubic  inch  =  To-«.i  which  is  independent  of  the  dimensions;  and  therefore 

the  elastic  resilience  per  cubic  inch  for  transverse  strabi  may  be  used  as  * 
DiAdulua  expressing  one  valuable  quality  of  a  material. 
Similarly  for  tension: 

Let  P  =  tensile  stress  in  pounds  per  square  inch  at  the  elastic  limit; 
e_  =  eIongation_per  unit  of  lensth  at  the  elastic  limit; 

!  P+ e;  whence  e=  P-i-JBC.      \ 


E  =  modulus oielasticity  •. 
Tben  elastic  resilienoe  per  cubic  inch  r=  %Fe  = 


1P« 
8  E' 


1BEAHK8  OF  VNIFOBM  STRENGTH  TB]ft017GH017T 
THEIR  liBNGTH. 

The  section  is  supposed  in  all  cases  to  be  rectangular  throughout.  The 
beams  shown  in  plan  are  of  uniform  depth  throughout.  Those  shown  in 
elevation  are  of  uniform  breadth  throughout 

B  =  breadth  of  beam.    D  =  depth  of  beam. 

Fixed  at  one  end,  loaded  at  the  other; 
curve  parabola,  vertex  at  loaded  end;  BI^ 

Proportional  to  distance  from  loaded  end. 
he" " "  "  """^^  ""^ 


he  beam  may  be  reversed,  so  that  the  up- 
.eredge-  "     •  "    ' 

paraboii 


per  edge  is  parabolic,  or  both  edges  may  be 
JOllC. 


Fixed  at  one  end,  loaded  at  the  other; 
triaofle,  apex  at  loaded  end;  £Z>*  propor- 
tional to  the  distance  from  the  loaded  end. 

Fixed  at  one  end;  load  distributed;  tri- 
angle, apex  at  unsupported  end;  BD^  pro- 
portional to  square  of  distance  from  unsup- 
ported end. 

Fixed  atone  end:  load  distributed;  curves 
two  psrabolas,  vertices  touching  each  ot^er 
at  unnupporred  end:  Bli>*  proportional  to 
distance  rrum  unsupported  end. 

Supported  at  both  ends:  load  at  any  one 
point;  two  parabolas,  vertices  at  the  points 
of  support,  DAses  at  point  loaded ;'  BD^  pro> 
portioiial  to  distance  fmm  nearest  point  of 
support.  The  upper  edge  or  both  edges 
may  also  he  parabolic. 

Supported  at  both  ends;  load  at  anv  one 


point;  two  triangles,  apices  at  points  of  sup- 

8[)rt.  t>a8es  at  point  loaded;  BU^  proper- 
onal  to  distance  from  the  nearest  point  of 


support. 

Supported  at  both  ends;  load  distributed; 
curves  two  parabolas*  vertices  at  the  middle 
of  the  beam ;  bases  centre  line  of  beam;  BD^ 
proportional  to  product  of  distances  from 
points  of  support. 

Supported  at  both  ends;  load  distributed; 
curve  semi-ellipse;  BD*  proportional  to  the 
product  of  the  distances  from  the  points  of 
luppon. 


272  8XREKGTH  OF  KATBBIAL8. 

PBOPEBTIB8  OF  HOIiLBD  STBUGTVBAIi  fflTBBI*. 

Explanation  of  Tables  of  tbe  Properties  of  I  Beams, 
Cnannels,  Angles,  JDeck-Beams,  Bulb  Ancles,  Z  Bars, 
Tees,  Trouffh  and  Corrnsated  Plates. 

(The  Carnegie  Steel  Co.,  Limited.) 

The  tables  for  I  beams  and  channels  are  calculated  for  all  standard 
weifchta  to  which  each  pattern  Is  rolled.  The  tables  for  deck-beams  and 
angles  are  calculated  for  the  minimum  and  maximum  weiffhts  of  the 
various  shapes,  while  the  properties  of  Z  ban  are  given  for  Uiicknesses 
difTering  by  1/16  inch. 

For  tees,  each  shape  can  be  rolled  to  one  weight  only. 

Colunm  Vi  in  the  tables  for  I  beams  and  channels,  and  column  9  for 
deck-beams,  give  coefficients  by  the  help  of  which  the  safe,  unifonnly 
disiributecf  load  mny  be  readily  determined.  To  do  thl«,  divide  the  co«*ra- 
cient  given  by  the  span  or  distance  between  supports  in  feet.  If  the  weight 
of  the  deck  beams  is  intermediate  between  the  minlnmm  and  maximum 
weights  given,  add  to  tbe  coefficient  for  tbe  miiilmiun  weight  the  value  given 
for  one  pound  Increase  of  weight  multiplied  by  the  number  of  pounds 
the  section  is  heavier  than  the  minimum. 

If  a  section  is  to  be  selected  (as  will  usuall v  be  the  case),  Intended  to  carry 
a  certain  load  for  a  length  of  span  already  determined  on,  ascertain  ihe 
ooefilctent  which  this  load  and  span  will  require,  and  refer  to  the  table  for  a 
section  having  a  coefficient  of  this  value.  The  coefficient  Is  obtained  by  raul- 
tiplyiuK  the  load,  In  pounds  uniformly  distributed,  by  the  span  length  In  fett. 

In  case  tbe  load  is  not  uniformly  distributed,  but  Is  concentrated  at  the 
middle  of  the  span,  multiply  the  load  by  S,  and  then  consider  it  as  uniformly 
disLributed.    The  deflection  will  be  8/10  of  the  deflection  for  the  latter  lond. 

For  other  cases  of  loading  obtain  the  bending  moment  in  ft.-lbs.;  t-lua 
multiplied  by  8  will  give  the  coefficient  required. 

If  the  loads  are  quiescent,  the  coefficients  for  a  fibre  stress  of  16,000  lbs. 
per  Bouare  inch  for  steel  may  be  used ;  but  if  moving  loads  are  to  be  pro- 
vided for,  a  coefficient  of  12,500  lbs.  should  be  taken.  Inasmuch  ss  the  effects 
of  impact  may  be  very  considei-able  (the  stresses  produced  in  an  unyielding 
Inelastic  noaterial  by  a  load  suddenly  applied  being  double  thoMC  nroduced 
by  the  same  load  in  a  quiescent  state),  it  will  sometimes  be  advlMtole  to  use 
still  smaller  fibre  stresses  than  those  given  in  tbe  tables.  In  such  cases  the 
coefficients  may  be  determined  by  proportion.  Thus,  for  a  fibre  stress  of 
6,000  lbs.  per  squai*e  Inch  the  coelficfent  will  equal  the  coefficient  for  16,000 
lbs.  fibre  stress,  from  the  table,  divided  by  2. 

The  section  moduli,  column  11,  are  used  to  determine  the  fibre  stress  per 
square  inch  in  a  beam,  or  other  shape,  subjected  to  bending  or  transverse 
stresses,  by  simply  dividing  the  bending  moment  expressed  in  inch-poimds 
by  the  section  modulus. 

In  the  case  of  T  shapes  with  the  neutral  axis  parallel  to  the  fiange,  there 
will  be  two  section  moduli,  and  the  smaller  is  given.  The  fibre  stress  cal- 
culated from  it  win,  therefore,  give  the  largrer  of  the  two  stresses  in  the 
extreme  fibres,  since  these  stresses  are  eqiul  to  the  bending  moment  divided 
by  the  section  modulus  of  the  section. 

For  Z  bara  the  coefficients  (C)  may  be  applied  for  cases  where  the  bars  are 
subjected  to  transverse  loading,  as  in  the  case  of  roof-purlins. 

For  angles,  there  will  be  two  section  moduli  for  each  position  of  the  neutral 
axis,  since  the  distance  between  the  neutral  axis  and  the  extreme  fibres  has 
a  diflferent  value  on  one  side  o(  the  axia  from  what  it  has  on  ihe  other.  The 
section  modulus  given  in  the  table  is  the  smaller  of  these  two  values. 

Column  13  In  the  table  of  the  properties  of  standard  channels,  giving  the 
distance  of  tbe  center  of  gravity  of  channel  from  the  outside  of  web,  is  used 
to  obtain  the  radius  of  gfyratlon  for  colunms  or  struts  consisting  of  two 
channels  latticed,  for  the  case  of  the  neutral  axis  passing  through  the  centre 
of  the  cross-section  parallel  to  the  welis  of  the  channels.  This  radius  of 
gyration  Is  equal  to  the  distance  between  the  centre  of  gravity  of  the  chau- 
nel  and  the  centre  of  the  section,  i.e.,  negrlecting  the  moments  of  inertia  of 
UiH  channels  around  tiieir  own  axes,  thereby  introducing  a  slight  error  on 
the  side  of  safety. 

(For  much  other  Important  information  concerning  rolled  stniotural 
shapes,  see  tlie  "  Pocket  Companion  "  of  The  Carnegie  Steel  Co.,  Liuaited, 
Filtaburg,  Pa.,  price  $2.) 


PBOPERTIBe  OF  ROLLED  STRUCTURAL  SHAPES.     273 


Properties  of  Carnegie  Standard  I  Beams-Steel. 

1 

S 
t 

in. 

8 

* 

6 

6 

7 

« 

• 

10 

11 

18 

1 

e 

1 

1 

< 

1 
1 

i 

1  Moment    of    Inertia, 
1     Neutral   Axis    Per- 
pendicular to  Web 
1     at  Centre. 

Moment    of    Inertia, 
Neutral    Axis  Coin- 
cident with  Centre 
Line  of  Web. 

Radius    of  Gyration, 
Neutral    Axis   Per- 
1     pendicular  to  Web 
at  Centre. 

1  Radius    of  Qy ration, 
1     Neutral  Axis  Coln- 
1     cident  with  Centre 
Line  of  Web. 

Section  Modulus,  Neu- 
tral Axis  Perpendic- 
ular to  Web  at  Cen- 
tre. 

in 

iiM. 

M.  in. 

i^ 

i.. 

I 

i' 

r 

r' 

S 

c 

Bi 

84 

100 

3.41  0.75 

7.25 

S880.8 

48.56 

9.00 

1.28 

198.4 

2116800 

'* 

05 

87.94  0.69  7.10 

2809.6 

47.10 

9.09 

1.80 

192.5 

2062900 

i> 

*• 

90 

a6.47  0.fl3T.i:J 

2289.1 

46. 7U 

9.20 

1.81 

186.6 

1990300 

»» 

*• 

85 

85.00.0.67  7.07 

2168.6 

44.85 

9.81 

1.83 

180.7 

1927600 

•* 

*• 

80 

-  -^^0.50  7.00 

20679 

42.86 

9.46 

1.86 

174.0 

18&5900 

Bi 

iO 

75 

,:    jG  0.65  6.40 

1268.9 

8U.25 

7.58 

1.17 

126.9 

1^^8600 

*' 

70 

■j^f  r,'i0.6Ti6.8-2 

1219.9 

29.04 

7.70 

1.19 

182.0 

1301200 

** 

*• 

05 

]iJ()^<l  60,6.25 

1169.6 

87.86 

7.88 

1.21 

117.0 

124T600 

sao 

18 

70 

■^1  W  ).72,6  26 

981.3 

84.62 

6.69 

1.09 

102.4 

1091900 

•' 

05 

sy  TJ^*, 61  6.18 

881.5 

88.47 

6.79 

1.11 

97.9 

1044800 

41 

»i 

00 

]?  liuu  55  6.09 

841.8 

88.88 

6.91 

1.18 

93.6 

997700 

** 

** 

55 

r.  :.;^o.46  6.0() 

795.6 

81.19 

7.07 

1.15 

88.4 

943000 

B7 

lb 

56 

V)  1^iJ-66  5.75 

611.0 

17.06 

6.23 

0.06 

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L  =  safe  loads  in  lbs.,  uniformly  distributed:  2  =  span  in  feet; 
M  =  moment  of  forces  in  ft.lbs.;  C  =  coefflclent  given  above. 

L=j;      Jf=|;      C=Li  =  8Af=^;      /=  fibre  stress. 


274 


8TKENGTH   OF   MATERIALS. 


S^operltes  of  Special  I  Beams    Steel. 


1 

2 

1 

5 

8 

1 

4 

1 

1 

O 

t 

< 

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1 

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10 

11 

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Lln«  of  Web. 

s6d 

pi 

III 
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in. 

lb*. 

i*].  in. 

(R.    ' 

fn. 

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c 

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100 

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7,:fS 

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7.50 

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176C100 

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leoft  B 

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7.58 

1.85 

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1718900 

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Properties  of  Carnegie  Trough  Plates— Steel. 


Section 
Index 


Size. 

ill 

Inches. 


Weight 

Area 

FNoot. 

of  Shc- 

tioii. 

lbs. 

sq.  in. 

16. :« 

4.8 

18.02 

5.3 

19.72 

5.8 

21.42 

6.3 

23.15 

G.8 

Thick- 
ness in 
Inches. 


Moment  of 

Inertia, 

Neutral 

Axis 

Parallel  to 
Length. 


Section 
Modulus, 
Axi^tas 
before. 


Radius 
ofOyra- 

tion. 
Axis  as 
before. 


MIO 
Mil 
M12 
M!8 
Mil 


9^x.354 

nux3^ 


^16 

% 

11/16 


8.68 
4.18 
4.57 
6.02 
5.46 


S 
1.88 

1  57 
1.77 
1.96 

2  15 


0.91 
0  91 
0.90 
0.90 
0  90 


Properties  of  Carnegie  Corrugated  Plates- Steel. 


Section 
Index. 

Size, 

n 

Inches. 

Weight 
Ftiot. 

lbs 

M30 

fV^i       xlU 

8.06 

M3I 

H-Vi        xJU] 

10.10 

M3.' 

H^i        xlW 
IJ  3/10x-,''VJ 

12.04 

M3.H 

17.75 

M.H4 

12  3/lflx^^^:i 

20.71 

M:i5 

12  :i'16x2-l4 

2.1.67 

Area 
of  Sec- 
tion. 


Kq.  in. 
2.4 
3.0 
3.5 
5.2 
fi.l 
7  0 


Thick- 
ness in 
Inches. 


5/16 


r/16 


Moment  of 

Inertia. 

Neutral 

AxIh 

Parallel  to 
Length. 


/ 
0.64 
0  its 
1.2ft 
4.79 
6.81 
6.82 


Section 


Radius 
]?Sui;i8>^0>„™- 
Axis  as       ';?"• 

ht^forA       AXIS  as 
o^f<^^'     before. 


8 
0.80 
1.18 
1.42 
888 
3.90 
4.46 


0.68 
0  57 
0.62 
0.96 
0  98 
0.99 


PROPEKTIES  OP   ROLLED   STRUCTURAL  STEEL.      275 


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P&OPEBTIBS  OF  ROLLED   STRUCTURAL  STBBL.      277 


Properties  of  Standard  C1iaiiB«Li— Steel* 


1 

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t 

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9 

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15.1 

0.88 

9.21 

.584 

5.0 

53800 

.503 

M 

8. 

9.38 

0.801.92 

18.0 

0.70 

2.34 

.548 

4  3 

46200 

.517 

5 

11.5 

8.88 

0.48 

S.OI 

10.4 

0.8J 

1.76 

.493 

4.2 

44400 

.608 

9. 

9.65 

0.83 

1.8B 

8.9 

0.64 

1.83 

.493 

8.5 

87900 

.481 

•• 

6.5 

1.05 

0.19 

1.78 

7.4 

0.48 

1.95 

.498 

3.0 

81600 

,489 

4 

9.13 

0.32 

l.» 

4.6 

0.44 

1.46 

.456 

23 

84400 

.463 

tud 

1.84 

0.25 

1.36 

4.2 

0.38 

1.61 

.454 

2.1 

23800 

.458 

5!^ 

1.55 

0.18 

1.S8 

8.8 

0.32 

1.56 

.453 

1.0 

80200 

.m 

3 

e. 

1.76 

0.88 

1.60 

8.1 

0.81 

1.08 

.421 

1.4 

11700 

.459 

5. 

1.47 

0.96 

l.flO 

1.8 

0.95 

1.12 

.415 

1.8 

18100 

.443 

** 

4. 

1.19 

0.17 

1.41 

1.6 

0.20 

1.17 

.409 

1.1 

11600 

.443 

L  c=  safe  load  In  lbs.,  uniformly  distributed;  2  =  span  In  feet; 
M  as  mofneat  of  forces  in  f t.-lbs. ;  C  «  coefflcient  given  aboTe. 

i=«j;      Ifa^;       (7=Lla8if=^;      /=*  fibre itreas. 


8' 


18' 


278     PB0PERTIE8   OF   ROLLED  STRUCTURAL  STEEL. 


Cm. rnciTl e    Peek-be fttiiB, 


1 

9 

S 

4' 

fi 

fl 

1 

H 

0 

10 

11 

1 

1 
1 

1 
1 

f 

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Ibn, 

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in. 

J 

a 

r 

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45.5 

11.7 

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1§JI 

6. a 

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3  fiS 

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'S  ■*) 

1  - 

..y 

1  .It 

^'1  '^ 

"  P. 

7"  11^' 

ci  H]<r 

f>  -'' 

Add  to  coefficient  C  for  every  lb.  increase  in  weij2:ht  of  beam,  for  10-in. 
beains,  4900  lbs.;  0-ln.,  4500  lbs.;  8-in.,  4000  lbs.;  7-in.,  3400  lbs.,  6>iD.,  3000 lbs. 
Carnegie    Bulb    Anglea. 


•.'6. 50 

7.80 

.48 

3.5 

104.2 

19.9 

8.66 

211700 

21.80 

6.41 

.44 

3.5 

69.8 

14.5 

8.88 

154200 

19.23 

5.06 

.41 

8.5 

48.8 

11.7 

2.95 

124800 

18.25 

5.87 

.44 

3.0 

34.9 

9.6 

2.66 

102800 

17.20 

5.06 

.50 

8.0 

23.9 

7.6 

2.16 

80500 

18.75 

4.04 

.38 

8.0 

ao.i 

6.6 

2.21 

70400 

12.30 

3.62 

.31 

8.0 

18.0 

5.7 

2.28 

60400 

10.00 

2.04 

.81 

2.5 

10.2 

4.1 

1.86 

4^%0 

Carneicle    T 

Shapes. 

1 

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3 

4 

6 

6 

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7 

8 

9 

10 

11 

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1 

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III 

ii 

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mi 

5 

1 

o 

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ll 

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0.68 

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5290 

4    \5 

16.6 

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3.10 

1.54 

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1.41 

0.79 

24800 

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11.4 

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1.20 

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16190 

4     X4 

10.9 

8.21 

1.15 

4.7 

1.64 

1.23 

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1.09 

0.84 

13100 

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9.8 

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8TBEK0TH   OF  MATBBIAL8. 


279 


Cmmegie  T   Hhwtpem— (Continued), 


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279a 


STRENGTH  OF  MATERIALS, 


Properties  of  Standard  and  Special  Angles  of  ninlmnm 
and  naxlmnm  Tblcknesses  and  l¥eig]its« 

ANGLES  WITH  EQUAL  LEGS. 


1 

« 

S 

4 

5 

6 

7 

8 

• 

s 

1 

1 

t 

< 

P 

ifi 
III 

fA 

III 
Ills 

ill 

fill 

fill 

fln. 

in. 

fM).  In. 
9.74 

In. 

I 

8 

T 

T* 

6    xO 

^ 

83.1 

1.82 

81.02 

7.64 

1.81 

1.17 

0     xO 

7/16 

17.2 

6.06 

1.66 

17.68 

4.07 

1.87 

1.19 

•5     x5 

H 

27.2 

7.99 

1.57 

17.75 

6.17 

1.49 

0.98 

*5     x5 

^ 

12.3 

3.61 

1.80 

8.74 

2.42 

1.56 

0.99 

4     x4 

18/16 

19.9 

5.84 

1.29 

8.14 

8.01 

1.18 

0.80 

4     x4 

5/16 
18/16 

8.2 

2.40 

1.12 

8.71 

1.29 

1.24 

0.82 

SIJ«J^ 

17.1 

6.03 

1.1? 

5.25 

2.25 

1.02 

0.60 

H 

8.5 

2.48 

1.01 

2.87 

1.15 

1.07 

0.70 

8     xS 

H 

11.4 

8.86 

0.98 

2.62 

1.80 

0.88 

0.59 

8     x1 

M 

4.9 

1.44 

0.84 

1.24 

0.58 

0.98 

0.60 

^:^ 

l2 

8.5 

9.60 

0.87 

1.67 

0.89 

0.63 

0.54 

H 

4.5 

1.81 

0.78 

0.98 

0.48 

0.85 

0.65 

tt^x2U 

i 

7.7 

2.25 

0.81 

1.28 

0.78 

0.74 

0.49 

SJx^Vi 

4.1 

1.19 

0.72 

0.70 

0.40 

0.77 

0.50 

*9h  K^H 

6.8 

2.00 

0.74 

0  87 

0.58 

0.66 

0.48 

♦5m»2M 

8.7 

1.06 

0.66 

0.51 

0.82 

0.G9 

0.46 

:i    x2 

7/16 

6.3 

1.66 

0.66 

0.54 

0.40 

0.59 

0.89 

2     x2 

8/tf 

2.5 

0.72 

0.57 

0.28 

0.19 

0.62 

0.40 

7/18 

4.6 

1.80 

0.59 

0.36 

0.80 

0.51 

0.85 

3/16 

2.1 

0.62 

0.51 

0.18 

0.14 

0.54 

0.86 

iHxiH 

9<( 

8.4 

0.09 

0.51 

0.19 

0.19 

0.44 

0.31 

]^  X  1^ 

8/16 

1.8 

0.S3 

0.44 

0.11 

0.104 

0.46 

0.38 

i^xli 

'C 

2.4 

0.09 

0.42 

0.09 

0.109 

086 

0.25 

1.0 

0.80 

0.35 

0.044 

0.049 

0.88 

0.26 

liUxlt^ 

5/16 

S.l 

0.61 

0.39 

0.063 

0.067 

0.82 

0.84 

IX 

0.9 

0.27 

0.35i 

0.032 

0.039 

0.84 

0.8S 

1     xl 

Vi 

1.5 

0.44 

0.34 

0.087 

0.056 

0.29 

0.80 

1       Xl 

H 

0.8 

0.94 

0.30 

0.024 

0.031 

0.81 

0.81 

Jgx    % 

V 

1.0 

0.29 

0.29 

0.019 

0.038 

0.26 

0.18 

0.7 

0.21 

0.26 

0  014 

0028 

0.20 

0.18 

i%X     'la 

8/16 

0.8 

0.2S 

0.26 

0.012 

0.024 

0.29 

o.ie 

•S^s 

^ 

06 

0.17 

0.23 

0.009 

0.017 

0.23 

0.17 

0.5 

0.14 

0.20 

0.005 

0.011 

0.18 

O.IS 

Angles  marked  *  are  special. 


PROPERTIBS  OV   llOtLfiD   STHUOttttAL  STEEL.      270& 


Properties  of  BtandaHl  «ll4  BlMclftl  AllfflftS  of  ninlmiim 
aDd  naxlmain  Tl&lckneffs  and  Welshis. 

ANGLES  WITH  UNEQUAL  LEGS. 


1 

2 

« 

4 

^     1     8 

7          8 

9 

1     .0 

11 

' 

Mom«nt8  of 
Inertia. 

Uodulu^. 

HAdil  of  Gyration. 

1 

I 

1 

1 

8 

r 

1 

i| 

H 

H 

ii 

h 

^1 

., 

^ 

\ 

8 

{3 

il 

if 

II 

ii 

\% 

» 

a; 

* 

X, 

^ 

» 

Inoheii. 

looh. 

lbs. 

gq.tn. 

1 

^^^ 

1 

898 

7.68 

45.87 

9.96  !l0.58 

0.89 

9.19 

.88 

7/10 

16.0 

4.40 

8.95 

92.66 

1.47 

6.01 

0.93 

9.96 

.88 

•    X4 

Yk 

r.« 

7.99 

9.76 

97.73 

8.69 

7.15 

1.11 

1.86 

.88 

«    X4 

ill 

18.8 

3.61 

4.90 

13.47 

1.60 

8.89 

1.17 

1.98 

.88 

li^ 

9^  1 

86.7 

7.66 

6.66 

^:IS 

9.59 

6.98 

0.98 

l.dt 

.78 

1, 

11.7 

8.49 

8.64 

1.28 

0.99 

1.91 

.77 

•5    X4 

yi  i 

»4.d 

7.11 

9.98 

16.49 

6.31 

4.99 

1.14 

1.69 

.88 

♦5    X4 

K 

11.0 

8.23 

4.67 

8.14 

1.57 

2.34 

1.80 

1.69 

.86 

5    X^ 

g 

88.7 

6.67 

6.91 

16.67 

9.69 

4.38 

0.96 

1.58 

.77 

A    XSS 

10.4 

8.06 

8.18 

7.7B 

1.91 

9.99 

1.09 

1.60 

.76 

5    X8 

18/16 

10.9 

5.84 

8.71 

18.98 

1.74 

4.46 

0.80 

l.fiA 

.66 

B    X8 

6/16 

8.8 

8.40 

1.75 

6.96 

0.78 

1.89 

0.89 

1.61 

.66 

•4>4X3 
•4jjx3 

13/16 

16.5 

6.48 

8.60 

10.88 

1.71 

8.69 

n 

1.88 

.07 

9.1 

2.67 

1.98 

6.50 

0.88 

1.83 

1.44 

.66 

N*^^ 

18^6 

18.5 

6.48 

5.49 

7.rr 

9.80 

9.99 

1.01 

1.19 

.74 

0.1 

2.67 

2.90 

4.18 

1.16 

1.60 

1.06 

1.23 

.78 

4    X3 

18/16 

17.1 

6.08 

8.47 

7.84 

1.66 

9.87 

0.83 

1.21 

.66 

4    X8 

6/16 

7.1 

2.00 

1.86 

3.86 

0.74 

1.98 

0.38 

1.27 

.66 

^l 

18/16 

16.7 

4.69 

3.88 

4.98 

1.66 

9.90 

0.85 

1.04 

.66 

6/16 

6.6 

1.96 

1.66 

2.83 

0.79 

0.96 

0.90 

1.10 

.68 

^i^ 

11/16 

19.4 

8.66 

1.79 

4.18 

0.99 

1.86 

0.67 

1.06 

.68 

4.9 

1.44 

0.78 

1.80 

0.41 

0.76 

0.74 

1.19 

.56 

•aSxs 

y/l6 

0.0 

2.64 

0.76 

2.64 

0.68 

1.80 

0.68 

1.00 

.46 

♦82x8 

4.8 

1.96 

0.40 

1.36 

0.86 

0.63 

0.57 

1.04 

.44 

i^n 

9/16 

0.6 

8.T8 

1.42 

2.98 

0.89 

1.16 

0.79 

0.91 

.54 

M 

4.6 

].81 

0.74 

1.17 

0.40 

0.56 

0.76 

0.95 

.53 

•3    X2 

H 

7.7 

2.86 

0.67 

1.92 

0.47 

1.00 

0.56 

0.99 

.47 

•3    X« 

H 

4.0 

1.19 

0.88 

1.09 

0.26 

0.54 

0.66 

0.95 

.46 

^X*2 

M 

6.8 

2.00 

0.64 

1.14 

0.46 

0.70 

0.56 

0.75 

.44 

?»X2 

8/16 

9.8 

0.81 

0.29 

0.61 

0.20 

0.29 

0.00 

0.79 

.43 

♦^k  xm 
'MxiA 

k 

6.5 

1.68 

0.86 

0.82 

0.26 

0.59 

0.40 

0.71 

.89 

8/16 

9.8 

0.07 

0.12 

0.84 

0.11 

0.23 

0.48 

0.79 

.40 

s^ll^ 

v^. 

9.7 

O.ffl 

0.12 

0.87 

0.12 

0.58 

0.89 

0.63 

.80 

2.1 

0.60 

0  09 

0.84 

0.09 

0.18 

0.40 

0.68 

.29 

:i^x^l  1 1  'A 

0.58 

004     0.09 

0.06 

0.09 

0.87 

0.41 

.96 

0.88 

0.09     0.06     0.03  I  0.06 

0.29 

0.44 

.98 

AnglM  marked  *  are  special. 


280 


STRtlNGtH   OF  MATEMALS. 


Propertle«  of  Carnec^le  Z  Bars. 

(For  dimensions  see  table  on  page  178.) 


1 

t 

a 

4 

S 

a 

7 

8 

a 

10 

11 

12 

Si 

1= 

Pi 

^t 

«3 

13 

{ 

1 

Ill 

ill 

pi 

1 

Pi 

jli 

sit 

fl 

^.1  'k 

ml 

pq^  111. 

/ 

/ 

A^ 

.*? 

r 

1' 

T 

C 

c 

Zl 

ISO 

4.&4» 

'4^^i 

!M1 

P.  44 

2.7d 

S.STi 

1   41 

QM 

90,000 

67.500 

■' 

ia.3 

T^M 

■^AhfS 

in.&5 

U  >3 

3  :*7 

2..Vt 

1.43 

i\M 

104,800 

78.600 

" 

;il  0 

fl  10 

Z\M 

12,87 

lL2ii 

3.81 

2.% 

1.44 

0.^4 

119,700 

89,800 

7.t 

■ST 

fi.Fjt( 

MM 

13.  Ml 

11.55 

3.|>1 

2. an 

1.37 

0.81 

123,300 

92,400 

** 

i5.| 

r -ifi 

JW.FW 

14,42 

I2>i2 

4.4.H 

2, -J?* 

\M 

0.H3 

188,700 

102.600 

M 

v«  0 

S.ii'i 

43.1ti 

le.^ 

14.10 

4.08 

2.:il> 

\A\ 

0.84 

150,400 

112,800 

7r\ 

i.'fl  a 

R.O-l 

4^.12 

\TiAA 

14.01 

4,&4 

2.31 

1   34 

0.81 

149.800 

112,800 

:*'J.O 

0  40 

40.i:i 

17.1^7 

15.22 

^.47 

2.tr^ 

l.Hfi 

0  H3 

m.8O0 

121,600 

ii 

:JI,I^ 

10.17 

i^.SK 

19.18 

1G.40 

^M 

2.22 

1  a7 

0.83 

174,900 

181.200 

7A 

11, e 

3.40 

13.36 

e.iB 

5.34 

2.00 

1.98 

1.35 

0  75 

67,000 

42,700 

1.3.9 

4  30 

16  IK 

7  US 

o,ao 

2.4ft 

J.Bl* 

1.S7 

0.76 

68,200 

51.100 

** 

Efl.4 

i.m 

19.0T 

9.ao 

7.44 

2.9^ 

1.H9 

1.38 

0.77 

79,400 

59.500 

z.** 

ir.8 

r,sri 

in  1& 

fl,<B 

7  08 

3.02 

i.ni 

i.^n  ' 

0.74 

81.900 

61,400 

20.2 

^J14 

L'l.Ka 

to.^i 

8.C2 

3.47 

1.91 

KSI 

0.75 

91,900 

69.000 

tt 

iK  6 

(J.«i 

^^■l,5:» 

12. W 

9.rM 

3  9^ 

l.OU 

1.35 

0.76 

102,100 

76,600 

ZII 

Siil.T 

a.Ofi 

3?).rtfl 

n.3? 

9.47 

3.91 

1JM 

1.2K 

0.73 

101,000 

75,800 

m.(\ 

7.GI 

;!iJ  115 

v^.m 

10..1I 

4.37 

1.S5 

1.30 

0.75 

110.300 

82.700 

u 

^.3 

B,3a 

a**?*) 

H  3tf 

11.20 

4.^ 

1,S6 

1.31 

0.76 

119,500 

89,600 

Z7 

B.3 

S.4t 

fl.'ift 

4/:5i 

3.!4 

1.41 

\M 

i.aa 

0.fl7 

88,500 

25.100 

10,3 

1  03 

7  gi 

S.4fl 

3  [II 

T.»*4 

l.fc' 

1.** 

o.ea 

41,700 

81,800 

t^ 

ri.d 

^M 

tt.63 

6.77 

4.li7 

L^ae 

1.*^ 

l.&^ 

0  09 

49,800 

87.400 

zs 

la.'i 

\My 

ilJMS 

fl.T3 

4.H-1 

3.37 

1.55 

1.29 

066 

51,900 

88,600 

If^.H 

Am 

IIJH 

7  WI 

hj^ 

2  77 

1  ,^'l 

1. 31 

007 

58.700 

44,000 

■* 

17  0 

h.Z-i 

l;i-T4 

a.i^ 

6.]^ 

;i.]u 

1..'j5 

1.38 

0.60 

65,900 

49,400 

555* 

ia.9 

fnft.'i 

12.1] 

H  73 

fl.t>^ 

3.18 

1.48 

1.25 

066 

W,600 

48,400 

20  0 

flj4 

IM.a^ 

g.wfi 

6.n.i 

H.IH^ 

1.48 

1.27 

0.G7 

70,900 

58,200 

>& 

2w».a 

0.75 

H.ttT 

n.24 

7.-U 

1.00 

1  49 

1.39 

0.09 

77,400 

58,100 

ElO 

<jr 

lUT 

2.S?7 

2.m 

i.n-^ 

I.IO 

\^n 

i.in 

0..55 

20.500 

'5i!22 

8.4 

S  ■<« 

3.64 

a.&i 

2  38 

1.40 

1.21 

1.21 

0513 

25,400 

19,000 

211 

».T 

a.fta 

a.s5 

a.wy 

2,57 

1.57 

I.IG 

1   17 

0.55 

27,400 

90,600 

11. -1 

3  3ti 

4,GT 

4  ^s 

2.9H 

\.m 

1.17 

K19 

0..56 

81,800 

23,800 

zn 

ri.5 

3  aa 

4. 50 

4  85 

3.011 

\.m 

1.12 

1.15 

0  55 

Se.GOO 

24,500 

M.2 

4,1ft 

&.20 

s.ro 

3.4-1 

S.3I 

M2 

1.17 

0.56 

86,600 

27,400 

Dlnien.Miona  of  liffhtest  wt^iRht  bars  of  each  size:  Zl,  Z2,  and  Z3.  depth  of 
web  6  In.,  width  of  flange  3»^  In.,  thickness  of  meUil  »;e«pectively  %,  9/16; 
and  ai  in. :  Z4,  Z5,  Z6,  5  y  3«4  X  Vie.  ^,  and  11/16  in.;  Z7,  Z8,  Z9,  4  X  8  1/16 
X  W.  7/10.  and  %  in.;  ZIO,  Zll.  Zl2.  3x2  11/16  X  M.  %.  aud  %  in.  Each 
dimeDsion  is  increased  1/16  in.  iu  the  next  heavier  weight. 


T0B8I0NAL  STBENGTH.  281 

FliOOBUfO  MATBHIAIi. 

For  flre-proof  floorlofir*  the  space  between  the  floor-beams  may  be  spanned 
with  brick  arches,  or  with  hollow  brick  made  especially  for  the  purpose,  the 
latter  beinfc  much  lighter  than  ordinary  brick. 

Arches  4  inches  deep  of  solid  brick  weigh  about  70  lbs.  per  square  foot, 
including  the  concrete  levelling  material,  and  substantial  floors  are  thus 
made  up  to  6  feet  span  of  arch,  or  much  greater  span  if  the  skew  backs  at 
the  springing  of  the  arch  are  made  deeper,  the  rise  of  the  arch  being  prefer- 
ably not  less  than  1/10  of  the  span.  Hollow  brick  for  floors  are  usually  In 
depth  Bbout\6  of  the  span,  and  are  used  up  to,  and  eyen  exceeding,  spans 
of  10  feet.  The  weight  of  the  latter  material  will  vary  from  20  lbs.  per 
square  foot  for  Moot  spans  up  to  60  lbs.  per  square  foot  for  spans  of  10  feet. 
Pull  particulars  of  this  construction  are  given  by  the  manufacturers.  For 
supporting  brick  floors  the  beams  sliould  be  securely  tied  with  rods  to  resist 
the  uktenu  pressure. 

In  the  following  cases  the  loads,  in  addition  to  the  weight  of  the  floor 
itself,  may  be  assumed  as: 

For  street  bridges  for  general  public  traflic 80  lbs.  per  sq.  ft. 

For  floors  of  dwellings  401bs.       "     »* 

For  ehurobes,  theatres,  and  ball-rooms 80  lbs.       "    *' 

Fortaaylofts 801bs.      "    *' 

For  storage  of  grain  lOOlbs.       "    " 

For  warehouses  and  general  merchandise 850  lbs.      **    ** 

Forfaetorise 800to4001b8.       "    " 

For  snew  thirty  inches  deep 16  lbs.       "    ** 

FcM*  maximum  pressure  of  wind  fiOlbs.       **    " 

For  brick  walls Ils8  lbs.  per  cu.  ft. 

For  masonry  walls 116-]441b8.       "     ** 

Boofs,  allowing  thirty  pounds  per  square  foot  for  wind  and  snow: 
For  corrugated  iron  laid  directly  on  the  purlins. . .    87  lbs.  per  sq.  ft 

Fbr  corrugated  iron  laid  on  boards 40  lbs.       *'    '' 

For  slate  nailed  to  laths 481b8.       "    *♦ 

For  slate  nailed  on  boards 46  lbs.      **    ** 

If  plastered  below  the  rafters,  the  weight  will  be  about  ten  pounds  per 
square  foot  additional. 

TIB^RODS  FOB  BBAHS  SVPPOBTINO  BBI€K 
ABCHBA. 

The  horizontal  thrust  of  brick  arches  is  as  follows: 

'   p      =  pressure  in  pounds,  per  lineal  foot  of  arch: 

W  =  load  in  pounds,  per  square  foot; 
8  =  span  of  arch  In  feet; 
B  =  rise  in  inches. 

Place  the  tie-rods  as  low  through  the  webs  of  the  beams  as  possible  and 
epaoed  to  that  the  pressure  of  arches  as  obtained  above  will  not  produce  a 
greater  stress  than  15,000  lbs.  per  square  inch  of  the  least  section  of  the  bolt. 

TOBSIONAIi  STBBNGTH. 

T^t  a  horiaontal  shaft  of  diameter  =  d  be  fixed  at  one  end,  and  at  the 
other  or  free  end,  at  a  distance  s  I  from  the  fixed  end,  let  there  be  fixed  a 
horizontal  lever  arm  with  a  weight  =  P  acting  at  a  distance  =  a  from  the 
axis  of  the  shaft  so  as  to  twist  it;  then  Fa  =  moment  of  the  applied  force. 

Bestatln^  moment  =  twisting  moment  =  — ,  in  which  8=  unit  shearing 

resistance,  J  =:  polar  moment  of  inertia  of  the  section  with  respect  to  the 
axis,  and  e  s  distance  of  the  most  remote  fibre  from  the  axis,  in  a  cross- 
section.    For  a  circle  with  diameter  d, 


382  8TRBHQTH  OF  KATSKIALS. 

For  hollow  shafts  of  exttiBal  diftOMtar  4  ftDd  internftl  diameter  d|» 


fu^.tm^^' 


FOr  a  square  whose  side  s  d; 

For  a  rectangle  whose  sides  are  b  and  d, 

The  ahove  fonnuliB  are  based  on  the  supposltioB  that  the  shearing  resist- 
ance at  any  point  of  the  croas-Bection  to  proportional  to  Its  dtetaace  from  the 
axis;  but  this  is  tme  only  within  the  elastlo  limit.  In  materiala  oaoable  of 
flow,  while  the  oarticles  near  the  axis  are  strained  within  the  elasUc  limit 
those  at  some  distance  within  the  oircumference  may  be  strained  nearly  to 
the  ultimate  resistance,  so  that  the  total  resistance  Is  soroething  greater 
than  that  oalculated  by  the  formulsB.  (See  Thurston, ''  Matls.  of  Sag.,**  Part 
II.  p.  687.)  Saint  Tenant  finds  for  square  shafts  Fa  a  (UOM^S  (Cotterill, 
*'  Applied  Mechanics,''  pp.  848,  S55).  For  workins  strength,  however,  the 
formuUe  may  oe  used,  with  S  taken  at  the  safe  working  unit  resiftanoe. 

For  a  rectangle,  sides  6  Oonger)  and  d  (shorter)  and  area  At 

86  +  1.8d* 

The  ultimate  torsional  shearing  rsstetanoe  S  is  about  the  same  as  the  di- 
rect shearing  resistance,  and  may  be  taken  at  80,000  to  W,000  lbs.  per  square 
Inch  for  cast  iron,  4S,000  lbs.  for  wrought  Iron,  and  90,000  to  ISOJDOO  Ibe.  for 
steel,  according  to  its  carbon  and  temper.  Large  factors  of  safety  should 
be  taken,  especially  when  the  direotion  of  stress  is  reversed,  as  In  reversing 
•ngines,  and  when  the  torsional  stress  is  combined  with  other  atressea,  as  is 
tnual  in  shafting.    (See  "Shafting.'*) 

Elastic  Bealatance  to  Torston.— Let  2  =  length  of  bar  being 
twisted,  d  s=  diameter,  i*s  force  applied  at  the  extremity  of  a  lever  arm 
of  length  =  a,  JVi  =  twisting  niomenu  Q  s  torsional  modulus  of  elasticity, 
0  =  angle  through  which  the  free  end  of  the  shaft  la  twisted,  measured  In 
arc  of  radius  =  1. 

For  a  cylindrical  shaft 

OODx.1  «OZX.f 

—  =  10.180. 


Pk» 

vBGd* 

-  m  ' 

^      88PaZ 

a     88Pkil. 

92 

9 

If 

a  = 

angle  of  torsion  in  degrees, 

•'=180' 

180* 

180  X  88PM 
««d«G        " 

B88.6Akl 
d«Gf    • 

The  value  of  G  is  given  by  different  authorities  as  from  ^  to  S/5  of  JE;  the 
modulus  of  elasticity  for  tension. 

COniBINBB  8TBBa»BS« 

(From  Merriman's  '*  Strength  of  Materials.") 
Combined  Tension  and  FIexnre.~Let  .1  s  the  area  of  a  bar 

subjected  to  both  tension  and  flexure,  P=  tensile  stress  applied  at  the  ends, 
I*-*- Ass  unit  tensile  stress,  8  s  unit  stress  at  the  flbre  on  the  tensile  side  most 
remote  from  the  neutral  uis,  due  to  flexure  alone,  then  maximum  tensile 
unit  stress  =  {P-t-A)'^8.  A  beam  to  resist  combined  tension  and  flexure 
should  be  designed  so  that  (P-t-A)+S  shall  not  exceed  the  proper  allow- 
able working  unit  stress. 

Combined  Compression  and  Flexure.— If  P+ul  =  unit  stress 
due  to  compression  alone,  and  8  =  unit  compressive  stress  at  flbre  most 
remote  from  neutral  axis,  due  to  flexure  alone,  then  maximum  oompressive 
cnit  Btress  =  (P^A)4-  S. 

Combined  Tension  (or  Compression)  and  Shear.— If  ap. 


8THSNQTH  OF  FLAX  PLATES.  283 

piled  tMukm  (or  eompresskm)  unit  stress  =  p,  sppUed  sheariDg  unit  stress 
a  «,  tliao  from  the  oombined  sctlon  of  the  two  forces 

Uax.  8—±  V^  +  Wp't      Maximum  shearing  unit  stress; 

Max«  i  s  }i^  -{-  Vt>*  -H  J4p",    Maximum  tensile  (or  compressiTe)  unit  stress. 

ComMned  Flexure  mnd  Torston.— If  8  =  greatest  unit  stress 
due  to  flexure  alone,  snd  S*  =  greatest  torsional  shearmg  unit  stress  due  to 
tornoo  sJone,  then  for  the  combined  stresses 

Max.  tension  or  compression  onit  stress  t  s  M£r  +  VSt'+M^"*; 

Max.  shear  «  =  ±  V S»^ -\- li/S*. 

Formnla  for  diameter  of  a  round  shaft  subjected  to  transverse  load  while 
traosmitUog  a  given  horse-power  (see  also  Shafts  of  Engines): 


-      l«lf  ,16      /JP    . 


408,600,000fn 


where  M  =  maximum  bending  moment  of  the  transverse  forces  in  pound- 
inches,  H  —  horse-power  transmitted,  n  =  No.  of  revs,  per  minute,  and  t  = 
the  safe  allowable  tensile  or  compressive  working  strength  of  the  material. 
Combined  Oompreeelon  mnd  Tonlon.— For  a  vertical  round 
•haft  oarrying  a  load  and  also  transmitting  a  given  hoi-se-power,  the  result- 
ant maximum  compressive  unit  stress 


#=i^ 

««i« 


+  |/8a.ooo.,-^.  +  ^, 


in  which  />  Is  the  load.    From  this  the  diameter  d  may  be  found  when  t  and 
the  other  data  are  riven. 

Stresia  dne  to  Tern  pemtnre.— Let  I  s  length  of  a  bar,  ^  s  its  see- 
tional  area,  c  =  coefficient  of  linear  expansion  for  one  degree,  t  =  rise  or 
fall  in  temperature  In  degrees.  B  =  modulus  of  elasticity,  A  the  change  of 
length  due  to  the  rise  or  fall  f ;  if  the  bar  is  free  to  expand  or  oontraci,  A  .« 
ell 

If  th9  bar  Is  held  so  as  to  prevent  its  expansion  or  contraction  the  stress 
produced  by  the  change  of  temperature  =  S  =  ActE,  The  following  are 
average  values  of  the  coeflAcients  of  linear  expansion  for  a  change  in  temper- 
ature of  one  degree  Fahrenheit: 

For  brick  and  stone. . .  .a  =  0.0000060, 

For  cast  iron a  =  0.0000069, 

For  wrought  iron a  =  0.0000067, 

For  steel a  =  O.O*""*" 


The  stress  due  to  temperature  should  be  added  to  or  subtracted  from  the 
■tress  caused  by  other  external  forces  according  as  it  acts  to  increase  or  to 
relieve  the  existing  stress. 

What  stress  will  be  caused  In  a  steel  bar  1  inch  square  in  area  by  a  change 
of  temperature  of  100»  F.  f  8^  ActE  =s  1  X  .0000(966  X  100  X  80.000,000  = 
19,500  lbs.  Suppose  the  bar  Is  under  tension  of  19,500  lbs.  between  rigid  abut- 
ments before  the  change  in  temperature  takes  place,  a  cooling  of  100<*  F. 
will  double  the  tension,  and  a  heating  of  100°  will  reduce  the  tension  to  zero. 

8TBBNGTH  OF  FI^AT  PI«ATB8. 

For  a  circular  plate  supported  at  the  edge,  uniformly  loaded,  according  to 
Qrashof, 

.     6r»  .  /6^  ^       6//» 

-^=6fi'''      *  =  V-6r^       ^  =  -6,V 

For  a  divnlar  plate  fixed  at  the  edge,  uniformly  loaded, 


Ib  which  /denotes  the  working  stress;  r,  the  radius  in  inches;  <,  the  thick 
seis  In  inehes;  nod  |>,  the  pressure  in  pounds  per  square  Inch. 


284  STRENGTH  OF  MATERIALS. 

For  mathematical  dfscuaslon,  see  T^nza,  *'  Applied  Mechaiifcs,"  p.  900,  etc. 
Lanza  gives  tiie  following  table,  usin^  a  factor  of  eafetv  of  8«  with  tensile 
streDgth  of  cast  iron  90,000,  of  wrought  iron  40,000,  and  of  steel  80,000 : 

Supported.  Fixed. 

Cast  iron t  =  .0188570»- Vi^  t=  .0168800r  i'p 

Wrought  iron f  =  .OllTSSOr  V'p  t=  .0105410r  i^ 

Steel t  =  .00Q1287r  4^  t  =  .0081<M0r  fp 

For  a  cii-cular  plate  supported  at  the  edge,  and  loaded  with  a  concen- 
trated load  P  applied  at  a  circumference  the  radius  of  which  is  r,: 

for         -^=10        20        30        40        60; 


e  =  4.07     6.00      6.68     5M      0.22; 


y  wf*  c 


The  aboTe  formulas  are  deduced  from  theoretical  considerations,  and  give 
thicknesses  much  greater  than  are  generally  used  in  steam-engine  cylinder- 
heads.  (See  empirical  formulie  under  Dimensions  of  Parts  of  Engines.)  The 
theoretical  formulae  seem  to  be  baaed  on  incorrect  or  incomplete  hypoth- 
eses, but  they  err  in  the  direction  of  safety. 

Tl&e  Streniptlft  of  IJniitayed  Flat  So rfkces,— Robert  Wilson 
(Eng'g,  Sept  24, 1877)  draws  attention  to  the  apparent  discrepancy  between 
the  results  of  theoretical  iuvestigationH  and  of  actual  experiments  on  the 
strength  of  unstayed  flat  surfaces  of  boiler-plate,  such  as  the  unstayed  flat 
crowns  of  domes  and  of  vertical  boilers. 

Rankine*s  '*  Civil  Engineering'^  gives  the  following  rules  for  the  strength 
of  a  circular  plate  wpporied  all  round  the  edge,  prefaced  by  the  remaric 
that  "  the  formula  is  founded  on  a  theory  which  is  only  approximately  true, 
but  which  nevertheless  may  be  considered  to  involve  no  error  of  practical 
importance:" 

*^  ^      Wb       Pb» 

Here 

M  7  greatest  bending  moment ; 

W=  total  load  uniformly  distributed  =  ^-^; 

b  =  diameter  of  plate  in  inches  ; 
P  =  bursting  pressure  in  pounds  per  square  inch. 
Calling  t  the  thickness  iu  inches,  for  a  plate  supported  round  the  edges, 

Mz=^  43,0006<a ;  '  •    ^  =  '™^'** 

For  a  plate  flxed  round  the  edges, 

8^ft'      ..^vw.        u           «      <«X  68.000 
_  __  =  700W«;    whence  P  = . 

where  r  =  radius  of  the  plate. 
Dr.  Grashof  gives  a  formula  from  which  we  have  the  following  rule: 

<gX  72,000 
r« 

This  formula  of  Grashof's  has  been  adopted  by  Professor  Unwln  in  his 
'*EI<^roenta  of  Machine  Design."  These  formulfe  by  Rankine  and  Orashof 
may  be  ref?arded  as  being  practically  the  same. 

On  try  nig  to  make  the  rules  jriven  by  these  authorities  agree  with  the 
results  of  his  ex()et'ience  of  the  Htreiigth  of  unstaycnl  flat  ends  of  c^'lindrical 
boilers  and  domes  that  had  given  wav  after  long  use,  Mr.  Wilson  was  led  to 
believe  that  the  above  rules  give  the  broking  strength  much  lower  than  it 


BT&EiiGtfl  OF  FLAT  TLATES.  285 

adnally  is.  He  descrilies  a  number  of  experiments  made  hy  Mr.  Nichols  of 
Kirkstall.  which  gare  results  varyinfi^  widely  from  each  other,  as  the  method 
of  supportini;  the  e<lf;m  of  the  plate  was  varied,  and  also  varyinfp  widely 
from  the  calculated  burstintc  pressures,  the  actual  results  beinf?  in  all  cases 
Teiy  much  the  hisber.    borne  conclusions  drawn  from  these  results  are : 

1.  Although  the  burstinjii^  pressure  has  been  found  to  be  so  high,  boiler- 
makers  must  be  warned  af^ainst  attaching  any  importance  to  this,  since  the 
plates  dfflected  almost  as  soon  as  any  prestiure  was  put  upon  them  and 
sprang  back  again  on  the  pressure  beluK  taken  off.  This  springing  of  the 
plate  in  the  course  of  time  inevitably  results  in  grooving  or  channelling, 
which,  especially  when  aided  by  the  action  of  the  corrot&ive  acids  in  the 
water  or  steam,  w  ill  in  time  reduce  the  thickness  of  the  plate,  and  bring 
about  the  destruction  of  an  unstayed  surface  at  a  very  low  pressure. 

2.  Since  flat  plates  commence  to  deflect  at  very  low  pressures,  they  should 
nover  be  used  witlioni  stays;  but  it  is  better  to  dish  the  plates  when  they  are 
not  stayed  by  flues,  tubes,  etc. 

a.  A^nst  the  oommonly  accepted  opinion  that  the  limit  of  elasticity 
should  never  be  reached  in  testing  a  boiler  or  otlier  structure,  the^e  experi- 
ments show  that  an  exception  should  be  made  in  the  case  of  an  unstayed 
fiat  end-plate  of  a  boiler,  which  will  be  safer  when  it  has  assumed  a  perma> 
nent  set  that  will  prevent  its  becoming  grooved  by  the  continual  variation 
of  pressure  in  working.  The  hydraulic  pressure  in  this  case  simply  does 
what  ^ould  have  been  done  before  the  plate  was  fixed,  that  is,  dishes  it. 

4.  Tliese  experiments  appear  to  show  that  the  mode  of  attaching  by  flange 
or  by  on  inside  or  outside  angle-iron  exerts  an  important  Influence  on  the 
manner  in  which  the  plate  Is  strained  by  the  pressure. 

When  the  plate  is  secured  to  an  angle-iron,  the  stretching  under  pressure  is, 
to  a  eertain  extent,  concentrated  at  the  line  of  riveuholes,  and  the  plate  par- 
takes rattier  of  a  beam  supported  than  flxed  round  the  edge.  Instead  of  the 
strength  increasing  as  the  square  of  the  thickness,  when  the  plate  is  attached 
by  an  aii:£le-iron,  it  is  probable  that  the  strength  does  not  increase  even 
directly  as  the  thickness,  since  the  plate  gives  way  simply  by  stretching  at 
the  rivet-holes,  and  the  thicker  the  plate,  the  less  uniformly  is  the  strain 
borne  by  the  different  layers  of  which  the  plate  may  be  considered  to  be 
made  up.  When  the  plate  is  flanged,  the  flange  becomes  compressed  by  the 
presBurtf  agaiiist  the  body  of  the  plate,  and  near  tlie  rim,  as  shown  by  the 
contrary  flexure,  the  inside  of  the  plate  is  stretched  more  than  the  outside, 
and  it  may  be  by  a  kind  of  shearing  action  that  the  plate  gives  way  along 
the  line  where  the  crushing  and  stretehing  meet. 

5.  Tliese  tests  appear  to  show  that  the  rules  deduced  from  the  theoretical 
investigations  of  Lam^,  Rankine,  and  Qraahof  are  not  confirmed  by  experi- 
ment, and  are  therefore  not  trustworthy . 

The  rules  of  Lamd,  etc.,  apply  only  within  the  elastic  limit.  (Eng^g^  ]><;. 
13.1895.) 

Viibraeed  Wron^tkUtron  BEeAda  of  BoUers,  etc.  iThe  Loco- 
»»of'«v,  Feb.  1890). — Few  experiments  have  been  made  ou  the  strength  of 
fist  heads,  and  our  knowledge  of  them  comes  largely  from  theory.  Experi- 
ments have  been  made  on  small  plates  1-16  of  an  inch  thick,  yet  the  data  so 
obtained  cannot  be  considered  satisfactory  when  we  consider  the  far  thicker 
heads  that  are  used  in  practice,  although  the  results  agreed  well  with  Ran- 
kine's  formula.  Sir.  Nichols  has  made  experiments  on  larger  heads,  and 
from  them  he  has  deduced  the  following  rule:  *'  To  find  the  proper  thick- 
oess  for  a  flat  unstayed  head,  multiplv  the  area  of  the  head  by  the  pressure 
per  square  inch  that  it  is  to  bear  safely,  and  multiply  this  by  the  desired 
isctor  of  safety  (say  8);  tbeu  divide  tlie  product  by  ten  times  the  tensile 
strength  of  the  material  used  for  the  head."  His  rule  for  flndint?  the  burst- 
ing pressure  when  the  dimensions  of  the  head  are  given  Is:  "Multiply  the 
thickness  of  the  end-plate  in  inches  by  ten  times  the  tensile  strength  of  the 
material  used,  and  divide  the  product  by  the  area  of  the  head  in  inches." 

In  Mr.  Nichols's  experiments  the  average  tensile  strength  of  the  iron  used 
for  the  heads  was  44.800  pounds.  The  results  he  obtained  are  given  below» 
with  the  calculated  pressure,  by  his  rule,  for  comparison. 

1.  An  unstayed  flat  boiler-head  is  84Uinche8  in  diameter  and  9-16  inch 
thick.  What  is  its  bursting  pressure?  The  area  of  a  circle  34U  iitchet*  in 
diameter  Is  fOR  square  inches;  then  9-10  x  44.800  X  10  =  252,000,  and  252,000  -4- 
^  =  270  pounds,  the  calculated  bursting  pressure.  The  head  actually  burst 
at  ego  pounds. 

2.  Head  84^  inches  in  diameter  and  %  inch  thick.  The  area  =  935 
■({uare  inches;  then,  %  x  44,800  X  10  =  168.000,  and  168,000  -t-  9S5  =  180  pounds, 
calculated  bursting  pressure.    This  head  actually  burst  at  SOD  potmds. 


'dd6  .  BTRKKOT&  OF  HATlEBULfl. 

V 

^  a.  HmuI  96M  InchM  In  diameter,  and  f^  Inch  thick.  Tlie  area  541  iqtttrs 
InohM.  Then,  U  X  44,800  X  10  a  168,000;  ftod  168,000  -»-  641  a  811  pounds. 
This  head  bunt  at  370  pounds. 

4.  Bsad  88^  Inohos  tn  diameter  and  6^  Inch  thick.  The  area  s  638 
square  inchest  then,  %  x  44,800  X  10  «  168.000,  and  168,000  -«-  038  s  969 
pounds.    The  aotual  bursting;  pressure  was  800  pounds. 

In  the  third  experiment,  the  amount  the  plate  bulged  ttnder  dllferent 
presBurts  was  as  follows : 

Atpoundspersq.  In....  10  80  40  80  190  140  170  000 
Fl»t«  bulged 1/89    l/i^     H      H       H        H        %        H 

The  pressure  was  notr  reduced  to  sero,  **  and  the  end  sprang  baok  8-18 
Inch,  leaving  it  with  a  permanent  set  of  M6  inch.  The  prsssure  of  800  lbs. 
was  again  applied  on  86  separate  occasions  during  an  interval  of  five  dajra, 
the  bulging  and  permanent  set  being  noted  on  each  oooaslon,  but  without 
anr  appreciable  difference  from  that  noted  above. 

The  experiments  described  were  confined  to  plates  not  fHdsly  differsnt  in 
their  dimensions,  so  that  Mr.  Nichols's  rulo  cannot  be  relied  upon  for  heads 
ihat  depart  much  from  the  proportions  given  in  the  examples. 
_TlilekneMi  of  Flat  CMit^ron  Plftte*  to  roMat  Biiniciii« 
IPresniireii.  -Cspt.  John  Ericsson  (Church*s  Life  of  Eriosaou)  gave  the 
following  rules:  The  proper  thickness  of  a  square  oast-Iron  plate  will  be  ob- 
tained by  the  following:  Multiply  the  side  in  f^t  (or  decimals  of  a  foot)  1^ 
14  of  the  pressure  In  pounds  and  divide  by  880  times  the  side  In  Inehes;  tho 
quotient  is  the  square  of  the  thickness  tn  Inches. 

For  a  circular  plate,  multiply  11-14  of  the  diameter  In  feet  by  U  of  the 

gressure  on  the  plate  in  pounds.    Divide  by  860  times  11-14  of  the  dlansetar 
I  Inches.    [Extract  the  square  root.1 

Prof.  Wm.  Harkness,  SSig^g  lfew$j  Bept.  6, 1800,  Shows  that  these  rules  oaa 
be  put  in  a  more  convenient  form,  thus: 

For  square  platss    T^0.QfM63Vfit 
and 

For  olnmlar  plates  3*  ^  0.00480i>  v9» 

where  T  s  thickness  of  plate,  fir  at  side  of  the  square,  D  &  diameter  of  the 
circle,  and  p  »  pressure  In  lbs.  per  sq.  In.  Professor  Uarkness,  however, 
doubts  the  value  of  the  rules,  and  says  that  no  sattsteotory  theoi^oal  solu- 
tion has  yet  been  obtained. 

ttM Actli  of  Btarod  BttPthtoos.— A  flat  plato  of  thlokne«  t  Is  mp- 
ported  uniformly  by  stays  whose  distance  from  centre  to  centre  Is  a,  untfonn 
load  p  lbs.  per  square  InciL  Baoh  stay  supports  pa*  lbs.  The  greatest 
stress  on  the  plate  is 

/•=5j?P.(tynwin). 
HFKBBtOAli  SHBLIii  ANB  IHMKBB  BOKI.aB-HBAlM. 

To  And  tike  ThlekiioM  of  n  ip>iorl««l  SOioU  to  roolBt  * 
KtTOli  PreMaret^IiSt  cf  •>  diameter  in  Inches,  and  p  the  Internal  press- 
ure per  square  inch.  The  total  pressure  which  tends  to  produce  rupture 
around  the  great  circle  will  be  M<rd*p>  Let  A  »  sale  tensile  stress  per 
square  Inch,  and  t  the  thickness  of  metal  in  inches;  then  the  resistanoe  lo  the 
pressure  will  be  sdf  5.   Since  the  reslstanos  must  be  equal  to  the  preesare. 

Mird*p*«cilA   Whence! B^ 

The  same  rule  Is  used  for  flndhig  the  thickness  of  a  hemlspherloal  head 
to  a  cylinder,  as  of  a  cylindrical  boiler. 

ThleknoM  of  H  Bomod  Koftd  of  m  l^llon— If  8  m  safe  Senalle 
stress  per  square  inch,  d  ^  diameter  of  the  shell  tn  Inohss,  and  i  m  thickness 
of  the  shell,  f  as  pd  H-  85 ;  but  the  thickness  of  a  hemlspherloal  head  of  the 
tame  diameter  ht=tpd-*-iS.  Hence  If  we  make  the  radftu  of  curvature 
of  a  domed  head  equal  to  the  diameter  of  the  boiler,  we  shall  have  (  si 

^  s  ^,  or  the  thickness  of  such  a  domed  head  wUlbe  equal  to  the  Ihlok- 

Bess  of  the  shell. 


THICK  CYLINDERS  UNDER  TENSION. 


287 


in  8t««l  PlatlniC  dne  to  ^Wmter-pressnre,  oa  in 

platinff  of  vessels  and  bulkheads  {Enginetring^  May  22, 1(191.  page  QS9). 

Mr.  J.  A.  Yates  lias  made  calculations  of  the  stresses  to  which  steel  plates 
are  sabjected  by  external  water-pressure,  and  arrives  at  the  following  con- 
clustona  : 

Assume  %a  inches  to  be  the  distance  between  the  frames  or  other  rigid 
support*,  and  let  d  represent  the  depth  in  feet,  below  the  surface  of  Uie 
wat«r,  of  the  plate  under  consideration,  t  s  thickness  of  plate  in  inches, 
D  the  deflection  from  a  straight  line  under  pressure  in  inches,  and  Ps  stress 
per  square  inch  of  section. 

For  outer  bottom  and  ballast- tank  plating,  a  s  420^,  D  should  not  be 

2a  P 

greater  than  .05  --,  and  -^  not  greater  than  3  to  S  tons ;  while  for  bulkheads, 

i  8rt  P 

etc.,  a  =  ^2^^^*  J^  should  not  be  greater  than  .1~,  and  -j  not  greater  than 

7  tons.    To  illustrate  the  application  of  these  formuls  the  following  cases 
have  been  taken : 


For  Outer  Bottom,  etc. 

For  Bulkheads,  etc. 

Thick- 

D«SS    of 

Depth 
below 

Spacing  of 
Frames  should 

Thksk- 
ness  of 

Depth  of 
Water. 

Maximum  Spao 
ing  of  Rigm 

Plating. 

Water. 

not  exceed 

Plating 

Stiifeners. 

in. 

ft. 

in. 

in. 

ft. 

ft.        In. 

w 

I 

SO 

About  21 

:i 

20 

9    10 

U 

r 

10 

"      49 

M 

20 

T     4 

^H 

18 

"      18 

il 

10 

14     8 

'3 

9 

"      80 

\i. 

90 

4    10 

M 

10 

u      90 

A 

10 

9     8 

^ 

6 

"      40 

H 

10 

4    10 

It  would  appear  that  the  course  which  should  be  followed  in  stiffening 
bulkheads  is  to  fit  substantially  rigid  stiffening  frames  at  comparatively 
vide  Intervals,  and  onlv  work  such  light  angles  between  as  are  neceaaary 
fur  making  a  fair  job  of  the  bulkhead. 

THICK   HOIiliOW  GYI^INDEBS  VNBBB  TENSION. 

Burr,  **  Elasticity  and  Bealatance  of  Materials,"  p.  86,  givea 
t  ss  thickness;  r  s  interior  radius  ; 
{  /h-\-p\^        )      h  =  maximum  allowable  hoop  tension  at  the 
'  =  *■  1  ytTZr^)   ~  M  *  interior  of  the  cylinder; 

*     **     '•^  '      p  s  intensity  of  interior  pressure. 

Ucrrioian  givea 


«  =  unit  stress  at  Inner  edge  of  the  annulua; 
r  =  interior  radius ;  t  =  thickness  ; 
I  =  length. 


rl 


(1) 


The  total  stress  over  the  area  2«  =  2«Z  ^q-^ 

The  total  interior  pressure  which  tends  to  rupture  the  cylinder  is  Sri  XP* 
If  p  be  the  unit  preasure,  then  p  ^  r~xi*  ^^^^  which  one  of  the  quantities 
r,  p,  r,  or  t  can  be  found  wlien  the  other  three  are  given. 


P(r  +  t), 


.  -  c-px. 


288  STREKGTH   OF  MATERIALS. 

In  eq.  (1),  If  «  be  neglected  In  comparison  with  r,  it  reduces  to  2clt  which 
is  the  same  as  the  formula  for  thin  cylinders.  If  t  =  r.  It  becomes  «U,  or 
only  half  the  resistance  of  the  thin  cylinder. 

Tne  formul8B  given  by  Burr  and  by  Mernman  are  quite  different,  as  will 
be  seen  by  the  following  example  :  Let  maximum  unit  stress  at  the  inner 
edge  of  the  annul ns  =  8(XX)  lbs.  per  square  inch,  radius  of  cylinder  =  4  inches, 
interior  pressure  =  4000  lbs.  per  square  inch.    Required  the  thickneas. 

ByBurr,  «  =  4]  (^i^)*- 1^  =  4(V«  -  1)=  8.9S8inches. 

4   V  4000 

By  Merriman.  *  =  ^^zrmo  =  ^  *°^^«*- 

Iilmit  to  Useflil  Tl&lekness  of  HoUoir  Oyllnders  (AipV« 
Jan.  4, 1884).— Professor  Barlow  lays  down  the  law  of  the  resisting  powei-s 
of  thick  cylinders  as  follows  : 

"  In  a  homogeneous  cylinder,  if  the  metal  is  incompressible,  the  tension 
on  every  concentric  layer,  caused  by  an  internal  pressure,  varies  inversely 
as  the  square  of  its  distance  from  the  centre.^* 

Suppose  a  twelve-inch  gun  to  have  walls  15  Inches  thick. 

Pressure  on  exterior  _  0*  —  i  .  lo  25 
Pressure  on  interior  ~  «1«  ~  * 

80  that  if  the  stress  on  the  interior  is  12^  tons  per  square  inch,  the  stress 
on  the  exterior  is  only  1  ton. 

Let »  =  the  stress  on  the  Inner  layer,  and  «,  that  at  a  distance  x  from  the 
axis ;  r  =  internal  radius,  R  =  external  radius. 

«,:«::»••:  a?*,   or  «,  =  «  -j. 

The  whole  stress  on  a  section  1  inch  long,  extending  from  the  interior  to 
the  exterior  surface,  is  5=  «•  X  — ^—, 
In  a  18-inch  gun,  let «  =  40  tons,  r  =  6  in.,  22  =  21  in. 

fi=  40  X  6  X  ?^*  =  172  tons. 

Suppose  now  we  go  on  adding  metal  to  the  gun  outside:  then  R  will  be 
come  so  large  compared  with r,  that  R^r  will  approach  the  value  /?,  so 

that  the  fraction  — ^—  becomes  nearly  unity. 

Hence  for  an  Infinitely  thick  cylinder  the  useful  strength  could  never 
exceed  Sr  (in  this  case  240  tons). 
Barlow's  formula  agrees  with  the  one  givAn  by  Merriman. 
Another  statement  of  the  gun  problem  is  as  follows :  Using  the  formula 

8t 

•  =  40ton8,<=16ln..r  =  61n.,p  =  ^p?  =  28^  tons  per  sq.  in.,  88|  x 

radius  =  172  tons,  the  pressure  to  be  resisted  by  a  section  1  inch  long  of  the 
thickness  of  the  gun  on  one  side.  Suppose  thicknera  were  doubled,  making 

40  X  80 
f  =  80  in.:  p  =  — =2 —  s  88^  tons,  or  an  increase  of  only  10  per  cent. 

For  short  cast-iron  cylinders,  such  as  are  used  in  hydraulic  presses,  it  Is 
doubtful  if  the  above  formules  hold  true,  since  the  strength  of  the  cylindri- 
cal portion  is  reinforced  by  the  end.  In  that  case  the  bursting  strength 
would  be  higher  than  that  calculated  by  the  formula.  A  rule  used  in 
practice  for  such  presses  Is  to  make  the  thickness  =  1/10  of  the  inner  cir- 
cumference, for  pressures  of  8000  to  4000  lbs.  per  square  inch.  The  latter 
Pressure  would  bring  a  stress  upon  the  inner  layer  of  10,860  lbs.  per  square 
ich,  as  calculated  by  the  formula;  which  would  necessitate  the  use  c«  the 
best  charcoal-iron  to  make  the  press  reasonably  safe. 


HOLDIlifG-FOWEB  07  KAIL8^  SPIKES^  AKD  SCREWS.  289 

THIN  CTI^IMBBliB  UNIIBR  TBNBION. 

Let  p  =s  safe  working  pressure  in  lbs.  per  sq.  in. ; 
d  =  diameter  in  Inches; 

T=  tensile  strength  of  the  material,  Ibe.  per  sq.  in.; 
i  =  thickness  in  Inches; 
/  =  factor  of  safety; 
c  s  ratio  of  strength  of  riveted  johit  to  strength  of  solid  plate. 

*«'-«-  ,=^;  .  =  ^. 

If  r  =  60000,  /  =  5,  and  c  s  0.7;  then 

__MOOW.  dp 

^~     d     '  14000* 

The  above  represents  the  strength  resisting  rupture  along  a  longitudinal 

seam.    For  resistance  to  rupture  in  a  circumferential  seam,  due  to  pressure 

on  the  ends  of  the  cylinder,  we  have  ^^  =  ?^y^; 

whence  pr=i|^. 

Or  the  stTBOgth  to  resist  rupture  areund  a  draumferenee  is  twice  as  great 
as  that  to  resist  rupture  longitudinally;  hence  boilers  are  commonly  single- 
riveted  in  the  circumferential  seams  and  double-riveted  in  the  longitudinal 


KOI«I.OW  COPPBB  BAI.I«tl. 

Hollow  copper  balls  are  used  as  floats  in  boilers  or  tanks,  to  control  feed 
•ad  discharge  valves,  and  regulate  the  water-level. 

Iliey  are  spun  up  in  halves  from  sheet  copper,  and  a  rib  is  formed  on  one 
half.  Into  this  rib  the  other  half  fits,  ana  the  two  are  then  soldered  or 
brssed  together.  In  order  to  facilitate  the  brazing,  a  hole  is  left  on  one  side 
of  the  ball,  to  allow  air  to  pans  freely  in  or  out;  and  this  hole  is  made  use  of 
afterwards  to  secure  the  float  to  Its  stem.  The  original  thickness  of  the 
metal  may  be  anything  up  to  about  1-16  of  an  Inch,  If  the  spinning  is  done 
on  a  hand  lathe,  though  thicker  metal  may  be  used  when  special  machinery 
if  provldad  for  forming  it.  In  the  process  of  spinning,  the  metal  is  thinned 
down  in  places  by  stretching;  but  the  thinnest  plaee  is  neither  at  the  equator 
of  the  ball  (i.e.,  along  the  rib)  nor  at  the  poles.  The  thinnest  points  lie  along 
two  circles,  passing  around  the  ball  parallel  to  the  rib,  one  on  each  side  of  it, 
from  a  third  to  a  half  of  the  way  to  the  poles.  Along  these  lines  the  thick- 
ness may  be  10, 16.  or  20  per  cent  less  than  elsewhere,  the  reduction  depend 
ing  somewhat  on  the  skill  of  the  workman. 

f%e  Locomotive  for  October,  1801,  gives  two  empirical  rules  for  determin- 
ing the  thickness  of  a  copper  ball  which  is  to  work  under  an  external 
pressure,  as  follows: 

.  —  diameter  in  inches  x  pressure  in  pounds  per  sq.  in. 

1.  TUieknees  -  ^^  . 

8.  IliickneM  =  <Maroeter  x  ^pressure  . 

1S40 
These  rules  give  the  same  result  for  a  pressure  of  166  lbs.  only.    Example: 
Required  the  uilckness  of  a  6-inch  copper  ball  to  sustain 

Pressuresof 50     100     150     166     200     250  lbs.  per  sq.  in. 

Answer  1^  first  rule...  .0156  .0812  .0469  .0519  .0625  .0781  inch. 
Answer  by  second  rule  .0285  .0409  .0494  .0518  .0570  .0687     '' 

8CBBW8.  ^ 

(A.  W.  Wright,  Western  Society  of  Engineers,  1881.) 
SpllLMi*— Spikes  driven  into  dry  cedar  (cut  18  months): 

Size  of  spikes 6XH»n.  »q.  «XM6xJ<6xf< 

Leoeth  driven  in 4^  in.         Sin.     6in.    4Uin. 

Pounds  resistance  to  drawing.  Av'ge,  lbs.  857  881        1691      1202 

r-^ « *    a  ♦.-♦-  --^h  3  Max.  "  1169  928         2129      1556 

From  6  to  9  tests  each ^  MIn.    "  766  766        1120       687 


290  6XBBK6TH  OV  MATERIALS. 

A.  M.  WeUtacton  fauwl  the  foroa  reonlred  lo  dmv  spikas  9/18  x  0/16  in., 
driven  4^  inches  into  seasoned  oak,  to  be  4S81  lbs. ;  same  spikes,  etc.,  la  «n- 
seasoned  oak,  66S8  lbs. 

"  Professor  W.  R.  Johnson  found  that  a  plais  spike  9i  Inch  square 
driven  M^  inches  into  seasoned  Jersey  yellow  pine  or  unseasoned  chestnut 
regulrea  about  9000  lbs.  force  to  extract  it;  from  seasoned  white  oak  about 
4000  and  from  weU-seasoned  locust  «000  Iba.'* 

Experiments  In  Germany,  by  Punk,  give  from  2466  to  8940  lbs.  (mean  of 
many  experiments  about  8000  Iba)  as  the  force  neoessarv  to  extract  a  plain 
U-inch  square  iron  spike  6  inches  lonr,  wedre-pointea  for  one  inch  and 
driven  4H  inches  into  white  or  yellow  pine.  When  driven  5  Inches  the  force 
requlrea  was  about  1/10  put  greater.  Similar  spikes  9/16  hichee  square,  7 
incnes  long,  driven  6  incnes  doep,  required  from  8700  to  6745  lbs.  to  extract 
them  from  pine:  the  mean  of  tne  results  being  4878  lbs.  In  all  cases  about 
twice  as  much  force  was  required  to  extract  them  from  oak.  The  spikes 
were  all  driven  across  the  grain  of  the  wood.  When  driven  with  the  grain, 
spikes  or  nails  do  not  boki  with  more  than  half  as  much  force. 

Boards  of  oak  or  pine  nailed  together  by  fxx>m  4  to  16  tenuenny  oommoB  cut 
nails  and  then  puUed  apart  in  a  direction  lengthwise  of  the  boards,  and 
across  the  nails,  tending  to  break  the  latter  in  two  by  a  shearing  action, 
averaged  about  800  to  400  lbs.  per  nail  to  separate  them,  as  the  result  of 
many  trials. 

mewimimmem  of  Urtlft-lbttlto  in  Tlflib6r«*TMts  made  by  Rust  and 
OooUdge,  in  187& 


1st  Test.  1  in.  square -iron  drove  80  In.  in  white  pine,  15/16-ln.  hole. S6,400 

Sd  "  1  In.  round  "  "  84"  "       "       "      18/l6-in.  **   16.80ft 

8d  "  1  in.  square  "  •*  IS"  "       "       "     lB/16-in.  "   14,000 

4th  "  1  in.  round  "  "  M"  "       ••       •'     18/16.in.  "   ia,«O0 

Bth  "  1  in.  round  "  "  84"  ''Norw'ypine,18/l6.in.  "   18.7«« 

6th  ♦•  1  In.  square  ••  "  80  "  "       "       "     lV16.1n.  '•   l»,aoo 

7th  "  ]  in.  square  "  "  18"  "       "       "     18/16.in.  "   15,600 

8th  "  1  In.  round  "  ••  «  "  "       ♦•       "     18/16.in.  "  14,406 

Nora.— In  test  No.  6  drift-bolts  were  not  driven  properly,  holes  not  being 

In  line,  and  a  piece  of  timber  split  out  in  driving. 
Force  required  to  draiv  Screiv*  out  of  Norway  Pine* 

W'  diaro.  drive  screw  4  in.  in  wood.  Power  required,  average  MM  Ib^ 

''       *'      4  threads  per  in.  6  in.  in  wood.       "  *'  "        8748   " 

•'       "      D'blethr*d,8perln.,4in.in"  "  •*  "        8780   " 

•*       "      Lag-screw,  7  per  in.,  lU  *'    '♦  "  ••  ••        1465   - 

4»        *«  iT       li       Q    M    it  gfz  tt    «»  M  »«  ••         8086    ** 

MinchR.R8pike B     **    *♦  ••  "  "        a»l    " 

Force  required  to  draw  \rood  Screw*  out  of  Arjr  DTood* 

-^TeaU  made  oy  Mr.  Bevan.  The  screws  were  about  two  inches  in  length, 
.28  diameter  at  the  exterior  of  the  threads,  .15  diameter  at  the  bottom,  the 
depth  of  the  worm  or  thread  being  .085  and  the  number  of  threads  in  one 
inch  equal  18.  They  were  passed  through  pieces  of  wood  half  an  Inch  in 
thickness  and  drawn  out  by  the  weights  stated:  Beech,  460  lbs.:  ash,  790 
lb». :  oak,  760  lbs. ;  mahogany,  770  lbs. ;  elm,  665  lbs. ;  sycamore,  880  lbs. 

Teata  of  liac-acrews  In  Varionii  Wood*  were  mada  by  A.  J. 
Cox,  University  of  Iowa,  1891: 

Kind  of  Wood.  gStoB^        H  Je    %J°^,?  fe    T?s'tk 

Seasoned  white  oak ^in*        Hln.   4Min.     8087  8 


^in.        Uin.   4M  in.     8087  8 

>/16"       7/16"     8      "      6480  1 


„         4H  "      8780  2 

Yellow-pine  stick S"         JJ  *'     4     "      8800  8 

White  cedar,  unseasoned 96  '*         H  "     ^     "      8406  8 

In  figuring  area  for  lag-screws,  the  surface  of  a  cylinder  whose  diameter  is 
equal  to  that  of  the  screw  was  taken.  The  length  of  the  screw  part  In  each 
case  was  4  inch^B.^ KnaineeiHng  Newg,  1891. 

Cat  versus  Wire  Nalla.-^Experiments  were  made  at  the  Watertown 
Arsenal  in  1898  on  the  comparative  direct  tensile  adhesion,  in  pine  and 
spruce,  of  cut  and  wire  nails.  The  results  are  stated  by  Prof.  W.  H.  Burr 
as  follows: 


HOLDINQ-POWBB  OF  NAILS,  BPIKS8>  AJTP  SCREWS.  291 


There  w6J«MMria8  of  taats,  ttn  Mfraof  nails  (•  out  Md*  wire  oall  ineach) 
bfjDfi:  used,  makiDf?  a  total  of  1160  nails  drawn.  The  testa  were  made  In 
spruce  wood  in  most  Instances,  but  some  extra  ones  were  made  in  white 
pine,  with  '*  box  nails. ''  The  nails  were  of  all  sizes,  varying  from  1^  inches  to 
6  inclies  in  lensrth.  In  every  case  the  cut  nails  showed  the  superior  holding 
strenj^  bv  a  Targe  percentajre.  In  spruce,  in  nine  different  sisee  of  nails, 
both  standard  and  light  weight,  the  ratio  of  tenacity  of  cut  to  wire  nail 
was  about  8  to  2,  or,  as  he  terms  it,  "  a  superiority  of  47.45K  of  the  former.** 
With  the  "  finishing  '*  nails  the  ratio  was  roughly  9.5  to  9;  superioritv  72j(. 
With  box  nails  (1>4  to  4  inches  long)  the  ratio  was  roughly  8  to  9;  supeilority 
51%,  The  mean  superiority  in  spruce  wood  was  t\%.  In  white  pine,  cqt  nails, 
driTen  with  taper  along  the  grain,  showed  a  superioritj  of  lOQjt,  and  with 
taper  across  the  grain  of  13Sj{.  Also  when  the  nails  were  driTon  in  the  end 
of  the  stick,  i.a,  along  the  grain,  the  superiority  of  cut  nails  was  lOQ^,  or  the 
ratio  of  cut  to  wire  was  8  to  1.  The  total  of  the  results  showed  the  ratio  of 
tenacity  to  be  about  6.2  to  8  for  the  harder  wood,  and  about  2  to  1  for  the 
softer,  and  for  the  whole  taken  together  the  ratio  was  8.6  to  2.  We  are 
led  to  oonolude  that  under  these  circumstances  toe  out  nail  is  superior  to 
the  wire  nail  in  direct  tensile  holding-power  by  72.7411, 

Nall-lftoldlnip  Power  of  Varloo*  Wood*. 
(Watertown  Bzperiments.) 

Holding-power  per  square  inch  of 
Kind  of  Wood.  Sine  of  Nan.  Surface  in  Wood.  lbs. 


White  pine 

r     M     ] 

9" 

20" 
50" 

Wire  Nail 
167 

Cut  NaU. 

f         450       1 

iS 

840 

Mean. 

-      405 

60  •• 

r        8"       1 

r         606       1 

Yellow  pina.... i 

10" 

818 

756 

662 

60" 
00" 

696 
W4 

White  oak  

8** 

■     •"    1 

1340 
12W 
1018 

-    1216 

Chestnut 

.     60" 
60" 

664 
702 

688 

Uurel 

9" 
20" 

f     «>    \ 

1179 
12;» 

1200 

N»ll-lioldlns  Power  of  Various  Woods. 

(F.  W.  Clay's  ExperimenU.    JBng'g  New§,  Jan.  11. 1891.) 

w/w^/i  ' Tenacity  of  6i1  nails 

Wood.  p,j^j„    ^    .    ,    -..     .      . 

White  pine 106 

Yellow  pine 100 

Basswood 78 

White  oak 220 

Hemlock 141 


Barbed.  Blued.  Mean. 
94          185  111 

180         270         loa 
182  210  148 

800  665  860 

201  819  220 


Tests  made  at  the  Unlveraity  of  Illinois  gave  the  resistance  of  a  Mn.  round 


rod  in  a  15/16-inch  hole  perpendicular  to  the  grain,  as  6000  lbs.  per  lin.  ft.  in 
pine  and  15.600  lbs.  in  oak.  Experiments  made  at  the  East  River  Bridge 
Kave  reaistances  of  12,000  and  15,000  lbs.  per  lln.  ft.  for  a  Mn.  round  rod  in 


pine  and 

Rave  reaisL , .^  

holes  15/10-in.  and  14/16-in.  diameter,  respectively,  in  Georgia  pine. 

Holdtnff^power  of  Bolts  In  Wlilte  Pine. 

iEng'g  N€to$t  September  26, 1801.) 

Round.  Square. 

Lbs.  Lbs. 

Avemgeof  all  plain  Mn.  bolts 8294  8300 

AveitSeof  all  plain  bolts,  H  to  IH in 7806  8110 

ATerage  of  4U  bolts 8888  6688 

Bound  drift-bolts  should  be  drlTsn  In  holes  18/16  of  their  diameter,  and 
square  drlf|-bQ|ts  in  holee  w)|o6e  diameter  is  14/16  of  the  side  of  the  square. 


292 


STRENGTH  OF  MATERIALS. 


STRENGTH  OF  WROIJOHT  IRON  ROLT8. 


o  8 

4,1-* 


9-16 


6 

5 
5 

4 
4 


.44 

.49 

.60 

.71 

.81 

.91 

1.04 

1.12 

1  .'ib 

1..% 

1.45 

1.57 

1.66 

1.92 

2.1J 

2.. 37 

2.57 

8.01 

8.50 


(Computed  by  A.  F.  Nagle.) 


.12 

.15 

;19 

.28 

.39 

.52 

.65 

.84 

1.00 

1.23 

1.44 

1.65 

1.95 

2.18 

2.88 

3..\5 

4.43 

5.20 

7.26 

9.02 


is* 

Ib8. 


Stress  upon  Bolt  upou  Basis  of 


350 
450 
560 
750 
1180 
1550 
1950 
2520 
.TOOO 
8680 
4:^00 
4950 
5840 
6540 
8650 
10640 
13290 
15580 
217(K) 
28860 


OB 

lbs. 


460 

600 

750 

li:» 

1570 

2070 

26(H) 

8360 

4000 

4910 

5740 

6600 

7800 

8720 

115:^0 

14200 

17720 

20770 

290(X) 

88500 


Ib8. 


580 
750 
930 
1410 
1970 
2(500 
32:)0 
4200 
5000 
6140 
7180 
8250 
9800 
KKJOO 
14400 
17T30 
221N) 
26000 
36260 
48100 


810 
1050 
1310 
1980 
2760 
3630 
4560 
5900 
7000 
8600 
10000 
11.560 
13610 
15260 
20180 
24H30 
310(H) 
36.')60 
50760 
67350 


u 

ia 

11^ 

jO  «  Q 

11^ 

lbs. 

lbs. 

1160 

5800 

1500 

750»l 

1870 

9000 

i8S0 

14000 

3940 

1901)0 

5180 

2rAH) 

6510 

30000 

8410 

30000 

10000 

46000 

12280 

56000 

14360 

65000 

1&510 

740UO 

19.'.00 

85000 

21HtX) 

9.5000 

28.S00 

125000 

3.'>5(X) 

150000 

44.300 

l«i0i>0 

52000 

213000 

72500 

200000 

96200 

385000 

When  it  is  known  M-hat  load  is  to  be  put  upon  n  bolt,  and  the  jud{(ment  of 
the  engineer  has  determined  what  stress  is  safe  to  put  upon  iliito  Iron,  look 
down  in  the  proper  colunm  of  said  stress  until  the  required  load  is  found. 
The  area  at  the  bottom  of  the  thread  will  give  the  equivalent  area  of  a  flat 
bar  to  that  of  the  Imlt. 

EflTect  of  Initial  Strain  In  Rolts.— SupTK>se  that  bolts  are  U8e<l 
to  connect  two  parts  of  a  machine  and  that  (hey  are  screwed  up  riehtly  be- 
fore tlie  effective  load  comes  on  the  connected  parts.  Let  Pj  =  the  initial 
tension  on  a  bolt  due  to  screwing  up.  and  P^  =  the  load  afterwards  added. 
The  greatest  load  may  vary  but  little  from  i*,  or  Pj.  accord Insf  as  the 
former  or  the  latter  is  greater,  or  it  may  approach  the  value  P^  ■+-  P^,  de- 
pending upon  the  relative  rigidity  of  the  bolts  and  of  the  part«  connect*^!. 
Where  I'igid  flanges  are  bolted  together,  metal  to  metal,  it  is  probable  that 
the  extension  of  the  bolts  with  any  additional  tension  relieves  the  iniilal 
tension,  and  that  the  total  tension  is  Pi  or  P^.  but  in  cases  where  ela.Ntic 
packing,  as  India  rubber,  is  interposed,  the  ext^-nsion  of  the  l)olts  may  very 
liMle  affect  the  initial  tension,  and  the  total  strain  mav  be  nearly  P^  -f-  p,. 
Since  the  latter  atstsumption  is  more  unfavorable  to  the  resistance  or  the 
bolt,  I  his  contingency  should  usually  be  provided  for.  (See  Unwin,  "Ele- 
ments of  Machine  Design  "  for  demonstraiioo.) 

STAND-PIPES  AND  THEIR  DESIGN. 

(Freeman  C.  CoflBn.  New  England  Water  Works  Assoc.,  Eng.  NeiM.  March 
16.  1893  )  See  also  papers  by  A.  H.  Howlaud,  Eiig.  Club  (»f  Phil.  1887;  B.  F. 
Stephens,  Amer.  Water  Works  Assoc,  Eug.  News,  Oct.  6  and  13,  IftsB:  W. 
Kiersted,  Rensselaer  Soc.  of  Civil  Eng.,  Entf'fi  Record,  April  25  and  May  2, 
1891.  and  W.  D.  Pence,  Enq.  AVira,  April  and  May,  1894. 

The  question  of  diameter  is  almost  entirely  independent  of  that  of  height. 
The  efflcient  capacity  must  be  measured  by  the  length  from  the  high-water 
line  to  a  point  below  which  it  is  unde.Kirat)le  to  draw  the  water  on  account  of 
loHS  of  pressure  for  Are  supply,  whether  that  point  is  the  actual  bottom  of 
the  stand-pipe  or  above  it.  This  allowable  fluctuation  ought  not  to  exceed 
50  (t.,  in  most  cases.    This  makes  tlie  diameter  de^>endent  upon  two  eondi- 


StAl^D-PiPteS  ANt)  THtllR  DESIGN.  ,293 

tlons,  the  first  of  which  is  the  amount  of  the  consumption  durliur  the  ordi- 
nary interral  between  the  stopping  and  starting  of  the  pumps.  This  should 
never  draw  the  water  below  a  point  that  will  give  a  good  Are  stream  and 
leaire  a  margin  for  still  further  draught  for  flres.  The  second  condition  Is 
the  maximum  number  of  Are  streams  and  their  Hise  which  it  is  considered 
necessary  to  provide  for,  and  the  maximum  length  of  time  which  they  are 
liable  to  have  to  run  before  the  pumps  can  be  relied  upon  to  reinforce 
them. 

Another  reason  for  making  the  diameter  large  is  to  provide  for  stability 
against  wind -pressure  when  empty. 

The  following  table  gives  the  height  of  stand-pipes  beyond  which  they  are 
not  safe  against  wind-pi'es8ures  of  40  and  60  lbs.  per  square  foot.  The  area 
of  surface  taken  is  the  height  multiplied  by  one  half  the  diameter. 


HfOiEtktm  of  SCand^lpe  tlimt  wUl  Resist  Wind* 
by  Its  Welfflit  alone,  vrhen  Empty* 


•pressure 


Diameter,  Wind,  40  lbs.      Wind,  50  lbs. 

feet.  per  sq.  ft.  per  sq.  ft. 

aO 46  85^ 

25 70  65 

ao 150  80 

35 160 

To  have  the  above  degree  of  stability  the  stand-pipes  must  be  designed 
with  the  outside  angle-iron  at  the  bottom  connection. 

Any  form  of  anchorage  that  depends  upon  connections  with  the  Bid3 
plates  near  the  bottvom  Is  unsafe.  By  suitable  gtiys  the  wind-pressure  is  re- 
siKttMl  by  tenKion  in  the  guys,  and  the  stand-pipe  is  relieved  from  wind 
strains  that  tend  to  overthrow  it.  The  guys  should  be  attached  to  a  band 
of  angle  or  other  shaped  Iron  that  completely  encircles  the  tank,  and  rests 
upon  some  sort  of  bracket  or  projection,  and  not  l)e  riveted  to  the  tank. 
They  should  be  anchored  at  a  distance  from  the  base  equal  to  the  height  of 
tii«  point  at  which  they  are  attached,  if  possible. 

The  best  plan  is  to  build  the  stand-pipe  of  such  diameter  that  it  will  resist 
the  wind  by  its  own  stability. 

Tlalckness  of  tlie  Side  Plates. 

The  pressure  on  the  sides  is  outward,  and  due  alone  to  the  weight  of  the 
water,  or  pressure  per  .•square  inch,' and  Increases  In  direct  ratio  to  the 
hei^t,  and  also  to  the  diameter.  The  strain  upon  a  section  1  inch  in  height 
at  any  point  is  the  total  strain  at  that  point  divided  by  two— for  each  side  is 
supposed  to  bear  the  strain  equallv.  The  total  pressure  at  any  point  is 
equal  to  the  diameter  In  inches,  multiplied  by  the  pressure  per  square  inch, 
due  to  the  height  at  that  point.    It  may  be  expressed  as  follows: 

H  =  height  in  feet,  and  /  =  factor  of  safety; 

d  =  diameter  in  inches; 

p  =  pressure  in  lbs.  per  square  inch; 
.434  =:  p  for  1  ft.  in  height; 

g  =  tensile  strength  of  material  per  square  Inch; 

T  =  thickness  of  plate. 

Then  the  total  strain  on  each  side  per  vertical  inch 

-       2       -2*  2s    '  "    2s  ' 

Mr.  Oofiln  takes /=  5,  not  counting  reduction  of  strength  of  joint,  equiv- 
alent to  an  actual  factor  of  safety  of  8  if  the  strength  of  the  riveted  joint  Is 
taken  as  00  per  cent  of  that  of  the  plate. 

The  amount  of  the  wind  strain  per  square  Inch  of  metal  at  any  joint  can 
be  found  by  the  following  formula,  in  which 

H  =  height  of  stand-pipe  In  feet  above  joint; 

T  =  thickness  of  plate  in  inches; 

p  =  wind  pressure  per  square  foot: 
W  —  wind-pressure  per  foot  in  height  above  joint; 
W  s=  Dp  wliere  D  Is  the  diameter  in  feet; 
m  =  average  leverage  or  movement  about  neutral  axis 

or  central  points  In  the  circumference;  or, 
m  ss  able  of  45<»,  or  .707  times  the  radius  in  feet. 


294 


8TREKGTH  OF  MATERIALS. 


Then  the  strain  per  square  inch  of  plate 


{Hw) 


clrc.  in  ft.  X  mT 


Mr.  Ck>flfln  (^fves  a  number  of  diafrrams  useful  In  the  Jesiflrn  of  stand-pipes, 
together  with  a  number  of  instances  of  failures,  with  discussion  of  their 
probable  causes. 

Mr.  Kiersted's  paper  contains  the  following: :  Among  the  most  prominent 
strains  a  stand-pipe  has  to  bear  are:  that  due  to  the  static  pressure  of  the 
water,  that  due  to  the  overturnlnf  effect  of  the  wind  on  an  emptv  stand- 
pipe,  and  that  due  to  the  collapsing  effect,  on  the  upper  rings,  of  Tiolent 
wind  storms. 

For  the  thickness  of  metal  to  withstand  safely  the  static  pressure  of 
water,  let 

t  s=  thickness  of  the  plate  iron  in  inches; 
U  =  height  of  stand-pipe  in  feet; 
D  s  diameter  of  stand-pipe  in  feet 

Then,  assuming  a  tensile  strength  of  48,000  lbs.  per  square  inch,  a  factor 
of  safety  of  4,  and  efficiency  of  double-riveted  lap-Joint  equalling  0.6  of  the 
strength  of  the  solid  plate. 


which  will  give  safe  heights  for  thicknesses  up  to  ^  to  I 
for  greater  heights  and  tn 


,i  of  an  inch.  The 
same  formula  may  also  apply  for  greater  heights  and  thicknesses  within 
practical  limits,  if  the  joint  efficiency  be  increased  by  triple  riveting. 

The  conditions  for  the  severest  overturning  wind  strains  exist  when  the 
stand-pipe  is  empty.  • 

Formula  for  wind-pressure  of  60  pounds  per  square  foot,  when 

d  =■  diameter  of  stand-pipe  In  Inches; 
X  =  any  unknown  height  of  stand-pipe; 
X  =  imndt  =  15.85  Vdt. 

The  following  table  Is  calculated  by  these  formuIsB.  The  stand-pipe  is 
Intended  to  be  self-sustainmg;  that  is,  without  guys  or  stiffeners. 

Helfflita  of  Stand-plpea  for  Tarlona  IMameters  mnd 
TlUckneaaea  of  Plates* 


Thickness  of 

Diameters  in  Feet. 

Plate  in  Frac- 
tions of  an  Inch. 

6 

50 
55 

60 
TO 
75 
80 
86 

6 

"55" 

7 

"eo" 

8 
65 

9 
BA 

m 

11. 
lar. 
13i] 

ID 

TO 
W 
100 

mi 

n 

36 
50 

55 

H6 
VX) 
115 

i;« 
1*5 
ir« 

105 

14 

40 
50 
GO 
75 
85 
100 
110 
120 
185 
146 
160 

15 

*  40 
46 
65 
TO 
80 
90 
100 
115 
125 
185 
160 
160 

16 

18 

20 

25 

8-16 

7«.32          

... 

4-16 .* 

65 
75 
80 
90 
95 

70 
80 
DO 
95 
100 

75 
85 
95 
100 
110 
115 

40 
60 
66 

75 
86 
95 
105 
180 
180 
140 
160 
160 

85 
45 
65 
65 
75 
85 
95 
105 
115 
1S5 
186 
146 
155 

85 

40 

60 

60 

70 

80 

86 

95 

106 

110 

190 

180 

140 

2R 

5-16 

85 

6-16 

40 

7-16 

8-16  

45 

9-16 

60 

10-16 

65 

11-16 

75 

18-16        

m 

18-16 

90 

14-16        

95 

15-16  

inn 

16-16 

— 

.... 

no 

Heights  to  nearest  5  feet.    Rings  are  to  build  5  feet  vertically. 


Fallnrea  of  Stand*pipea  have  been  numerous  in  rscent  years.    A 
list  showing  23  important  failures  inside  of  nine  years  is  given  in  a  paper 
Prof.  W.  D.  Pence,  Eng'g.  iVetct,  April  6,  18, 19  and  96,  May  8. 10  and  94,  and 


er  by 


June  7, 1894.    His  discussion  of  the  probable  causes  of  the  failures  is  most 
valuable. 


WROUGHT-IRON  AND  STEEL  WATER-PIPES.        295 

Kenneth  Allen,  Engineers  Club  of  Philadelphia,  1886,  giyec  the  following 
rules  for  thickness  of  plates  for  stand  pipes. 

Assume:  Wrourht  iron  plate  T.  8.  48,000  pounds  In  direction  of  fibre,  and 
T.  8.  45.000  pounds  across  the  fibre.  Strength  of  single  riveted  Joint  .4  that 
of  the  plate,  and  of  double  riveted  Joint,  .7  that  of  the  plate  ;  wind  pressure 
=  50  pounds  per  square  foot ;  safety  factor  =  8. 

Let  h  =  total  height  in  feet ;  r  =  outer  radius  In  feet ;  r*  =  Inner  radius 
in  feet ;  p  =  pressure  per  square  inch  ;  t  =  thickness  In  inches  ;  d  =  outer 
diameter  in  feet. 

Then  for  pipe  filled  and  longitudinal  seams  double  riveted 


«s 


pr  X  18 


hd 


48,000  X  .7  X  H  ""  480r 


and  for  pipe  empty  and  lateral  seams,  single  riveted,  we  hare  by  equating 
momenta  : 

60  X  ar  (|)«  =  144  X  eOOO  (H  -  r**}  •^,  whence  r^^r'*^  ~j^. 
Table  ■bowlnc  required  TMekneM  of  Bottom  Plate. 


Height  in 

Diameter. 

Feet. 

5  feet. 

10  feet 

15  feet 

20  feet 

25  feet 

80  feet 

/. 

// 

// 

ft 

ff 

ff 

•    60 

t  7-H* 

^: 

11-64* 

15-64 

19-64 

28.M 

60 

tn-64« 

7-82 

9-82 

23-61 

27-64 

70 

t  7-82 

11-4J4* 

A 

21-64 

18-82 

81-64 

80 

n9-ti 

3-16 

15-82 

]5-82 

9-16 

90 
100 

tA 

7-52 

tl&<«4 

5-16 
28-64 

17-^ 
87-64 

4^ 

195 

t8S-64 

7-16 

87-64 

47-64 

rA 

150 

t33-64 

17-82 

45-64 

,?^ 

175 

tn-16 

89-64 

13.16 

1    7-82 

200 

t»-8« 

46-64 

15-16 

111-64 

125-64 

*  The  minimum  thickness  should  =  8-16". 

N.B.— Dimensions  marked  t  determined  by  wlnd^pressure. 

^Water  Tower  at  Tonkers,  If.  T«— This  tower,  with  a  pipe  122  feet 
bttii  and  20  feet  diameter,  is  described  In  Bngineering  News,  May  18, 1892. 

The  thickness  of  the  lower  rings  is  11-16  of  an  Inch,  based  on  a  tensile 
strength  of  60,000  lbs.  per  square  inch  of  metal,  allowing  65)(  for  the  strength 
of  riveted  Joints,  using  a  factor  of  safety  of  8^  and  adding  a  constant  of 
^  inch.  The  plates  diminish  in  thickness  by  1-16  inch  to  the  last  four 
plates  at  the  top,  which  are  )4  inch  thick. 

The  contract  for  steel  requires  an  elastic  limit  of  at  least  88,000  lbs.  per 
square  Inch  ;  an  ultimate  tensile  strength  of  from  56.000  to  66.000  lbs.  per 
sqoare  inch  ;  an  elongation  in  8  inches  of  at  least  20j(,  and  a  reduction  of 
area  of  at  least  ASH.  The  inspection  of  the  work  was  made  by  the  Pittsburgh 
Ttratine  Laboratory-  According  to  their  report  the  actual  conditions  dt*- 
▼eloped  were  as  follows :  Elastic  limit  from  34,020  to  89,420 ;  the  tenRile 
strength  from  66.880  to  65,800  ;  the  elongation  In  8  inches  from  22^  to  8^  ; 
reduction  in  area  from  62.78  to  71.82j( ;  17  plates  out  of  141  were  rejected  in 
tlie  inspection. 

irROUeHT-mON  Attn  STSEIi  ITATBR-PIPES. 

Rlweted  Steel  Water-pipes  {EngineeHng  News,  Oct.  11, 1890,  and 
Aug.  1,  ItlOl.)— The  use  of  riveted  wrought-iron  pipe  has  been  common  in 
tlie  Paeifle  States  for  many  years,  the  largest  being  a  44-inch  conduit  in 
coanection  with  the  works  of  the  Spring  valley  Water  Co.,  which  supplies 
San  Francisco.  The  use  of  wrought  iron  and  steel  pipe  has  been  neces- 
wuy  In  the  West,  owing  to  the  extremely  high  pressures  to  be  withstood 
•od  the  difficulties  of  transportation.    As  an  example  :  In  connection  with 


296  STBEKOTH  OF  MATERIALS. 


¥15 


the  water  supply  of  Virginia  Clt^  and  Gold  HIH,  Not.,  there  waa  laid  in 
1872  an  llj^-lnch  riveted  wrougbt-iron  pipe,  a  part  of  which  is  under  a  head 
of  IT^iO  feet. 

In  the  East,  the  moat  im]x>rtant  example  of  the  use  of  riveted  steel  water 

Ipe  is  that  of  the  East  Jersey  Water  Co.,  which  supplies  the  city  of  Newark, 
'he  contract  provided  for  a  maximum  high  servic«^  supply  of  25.000,000  gal- 
lons daily.  In  this  case  il  m  lies  of  48-inch  pipe  was  laid,  8ome  of  It  under  S40 
feet  head.  The  plates  from  which  tlie  pipe  is  made  are  about  13  feet  long 
by  7  feet  wide,  open-hearth  steel.  Four  plates  are  uf<ed  tK)  make  one  section 
of  pipe  about  27  feet  long.  The  pii>e  is  meted  longitudinally  with  a  double 
row,  and  at  the  end  joints  with  a  single  row  of  rivets  of  varying  diameter, 
corresponding  to  the  thickness  of  the  steel  plates.  Before  lieing  rolled  into 
the  trench,  two  of  the  iiST-feet  lengths  are  riveted  together,  thus  diminisliing 
still  further  the  number  of  joints  to  be  made  in  the  trencli  and  the  extra 
excavation  to  give  room  for  jointing.  All  changes  in  the  grade  of  the  pii^e- 
line  are  made  by  10*>  curves  and  all  changes  in  line  by  2^,  5,  7^  ana  10° 
curves.  To  lay  on  curved  lines  a  standard  bevel  was  used,  and  the  different 
curves  are  secured  by  varying  the  number  of  beveled  joints  used  on  a 
certain  length  of  pipe. 

The  thickness  of  the  nlates  varies  with  the  pressure,  but  only  three  thick- 
nesses are  used,  ^,  5-16,  and  %  inches,  the  pipe  made  of  these  thicknesses 
having  a  weight  of  160, 18S,  and  %i&  lbs.  per  foot,  respectively.  At  the  works 
all  the  pipe  was  tested  to  pressure  1^  times  that  to  which  it  is  to  be  sub- 
jected  when  in  place. 

BImnnesmmnn  Tabes  for  BElsli  Pressures.— At  the  Mannes- 
mann  Works  at  Koniotau.  Hungary,  more  than  600  tons  or  25  miles  of  8-Inch 
and  4-inch  tubes  averaging  ^  inch  in  thickness  have  been  successfully 
tested  to  a  pressure  of  2000  lbs.  per  smiare  inch.  The^e  tub»>s  were  intended 
for  a  high-pressure  water-msin  in  a  Chilian  nitrate  district. 

This  great  tensile  strength  is  probably  due  to  the  fact  that,  in  additlnn  to 
being  much  more  worked  than  most  metal,  the  fibres  of  the  meial  run 
spirally,  as  has  been  proved  by  microscopic  examination.  While  cast-Iron 
tubes  wHl  hardly  stand  more  than  200  lbs.  per  square  inch,  and  welded  tub(« 
are  not  safe  above  1000  lbs.  per  square  inch,  the  Mannesmann  tube  easilv 
wlthstands  2000  lbs.  per  square  Inch.  The  length  up  to  which  they  can 
be  readily  made  is  shown  by  the  fact  that  a  coil  of  3-inch  tube  70  feet  long 
was  made  recently. 

For  description  of  the  process  of  making  Mannesmann  tubes  see  Trans. 
A.  I.  M.  E  ,  vol.  xlx.,  884. 

STRENGTH  OF  VARIOUS  MATER  lAIiS.    EXTRACTS 
FROM  KIRKAIiDY'S  TESTS. 

The  recent  publication.  In  a  book  by  W.  O.  Kirkaldv,  of  the  results  of  many 
thousand  tests  made  during  a  quarter  of  a  century  ov  his  father,  David  Kir- 
kaldy,  has  made  an  important  contribution  to  our  knowledge  concerning 
the  range  of  variation  In  strength  of  numerous  materials.  A  condensed 
abstract  of  these  results  was  publislied  in' the  Americ'in  Machinist^  May  II 
and  18, 1893,  from  which  the  following  still  further  condensed  extracts  are 
\aken: 

The  figures  for  tensile  and  comprc*ssive  strength,  or,  as  KIrkaldy  calls 
them,  pulling  and  thrusting  stress,  are  given  in  pounds  per  square  inch  of 
original  section,  and  for  bending  sti-ength  in  pounds  of  actual  stress  or 
pounds  per  BD^  (breadth  X  souare  of  depth)  for  length  of  36  inches  between 
supports.  The  contraction  of  area  is  given  as  a  percentage  of  the  original 
area,  and  the  extension  as  a  i)ertrentage  in  a  length  of  10  inches,  except  when 
otherwise  stated.  The  abbreviations  T.  S.,  E.  h.,  Contr.,  and  Ext.  are  used 
for  the  sake  of  brevity,  to  represent  tensile  strength,  elastic  limit,  and  per- 
centasres  of  contraction  of  area,  a?)d  elongation,  respectively. 

Cast  Iron.— 44  tests:  T.  K.  15.468  to  28,7<)0  })ounds;  17  of  these  were  un- 
sound, the  strength  ranging  from  16,468  to  24,357  pounds.  Average  of  all, 
28.805  pounds. 

Thrusting  stress,  specimens  2  inches  long,  1.34  to  1.5  In.  diameter:  48  tests, 
all  sound,  {M,352  to  131,01i{;  one,  unsound.  93,759;  average  of  all,  113.8S5. 

Bending  streKs,  bars  about  1  in.  wide  by  2  in  deep,  cast  on  edge.  Ulti- 
mate stress  2876  to  8854;  stresvs  per  BI>^  ~  725  to  892;  average,  830.  Average 
mo<iulu8  of  rupture,  H,  =  stress  per  BD^  X  length,  ~  29,520.  Ultimate  de- 
tleiaion,  .29  to  .40  in.;  average  .31  inch. 

Other  tests  of  cast  iron,  460  tests,  16  lots  from  various  sources,  grave  re- 


EXTRACTS  FROM  KIRKALBY'S  TESTS.  297 

■ults  with  total  range  as  followB:  Pulling  gtreas,  13,688  to  88.616  ponnds; 

thrusting  stress,  66,36:)  to  175.950  pounds;  bending  stress,  per  BD^.  505  to 

11<S  pounds;  modulus  of  rupture,  R,  18,180  to  40,008.    Ultiniato  deflection, 

.21  to  .45  inch. 

Tlie  specimen  which  was  the  highest  in  thrusting  strcra  was  also  the  high- 
est in  bending,  and  showed  the  greatest  deflection,  but  its  tensile  strength 

was  only  28,502. 
The  specimen  with  the  highest  tensile  strength  had  a  thrusting  stress  of 

143,SKI9,  and  a  bending  strength,  per  BD^,  of  979  pounds  with  0.41  deflection. 

The  specimen  lowest  in  T.  S.  was  also  lowest  in  thrusting  and  bending,  but 

gave  .38  deflection.  The  specimen  which  gave  j21  deflection  had  T.  S.,  19,188: 

thrusting.  10l.2»tl;  and  bending,  561. 
Iron  CmsUns**— <^9  tests;  tensile  strength,  10,416  to  81,602;  thrusting 

streKs,  ultimate  per  square  inch.  58,50S  to  132,031. 
€laaiinel  Irons.— Tests  of  18  pieces  cut  from  channel  irons.    T.  S. 

40.093  to  5^,1 41  pounds  per  square  inch;  contr.  of  area  from  8.9  to  83.5  %. 

Evt.  in  10  in.  from  2.1  to  23.5  %,    The  fractures  ranged  all  the  way  from  100  % 

fibrous  to  100^  crystalline.  The  highest  T.  S..  63,141.  with  8.1  %  contr.  and 
5.3  %  ezt..  was  100  %  crystalline;  the  lowest  T.  8.,  40,693,  with  3.9  contr.  and 
3.1  iKext.,  was  75 )( crystalline.  All  the  fibrous  irons  showed  from  13.3  to 
33.5  jC  ext.,  17.3  to  33.5  contr..  and  T.  S.  from  48.426  to  49.615.  The  fibrous 
inms  are  therefore  of  medium  tonsile  strength  and  high  ductility.  The 
crystalline  irons  are  of  variable  T.  S.,  highest  to  lowest,  and  low  ductility. 

liOKVntoor  Iron  Bars.— Three  rolJed  bars  2U  inches  diameter;  ten- 
fiile  tests:  elastic,  33.300  to  -J4,300;  ultimate,  50.875  to  51,905:  contraction,  44.4 
to  4^5;  extension,  S9.3  to  34..3.  Three  hammered  bars,  4Vi  inches  diameter, 
elasUc  325,100  to  34.300;  ultimate,  46,810  to  49,223;  contraction,  20.7  to  4G.5; 
extension.  10.8  to  31.6.  Fractures  of  all,  100  percent  fibrous.  In  the  ham- 
m**red  bars  the  lowest  T.  S.  was  accompanied  by  lowest  ductility. 

Iron  Bars,  Various.— Of  a  lot  of  80  bars  of  various  sizes,  some  rolled 
an«l  some  liamtnered  (tiie  above  Lowmoor  bars  included)  tlie  lowest  T.  S. 
(except  one)  40,8(M  pounds  per  square  inch,  was  shown  by  the  Swedish 
^'hoop  L^'bar  3V^  inclies  diameter,  rolled.  Its  elastic  limit  was  19,150 
pounds;  contraction  68.7  %  and  extension  37.7  %  in  10  inches.  It  was  also 
the  most  ductile  of  all  the  bars  tested,  and  was  100  %  fibrous.  The  highest 
T.  S..  60,780  pounds,  with  elastic  limit,  39,400:  coutr..  86.6;  and  ext..  24.3  %, 
was  shown  by  a  ^'  Farnley  '^  2-inch  bar,  rolled.  It  was  also  100  %  fibrous. 
The  lowest  ductilitv  2.6^  contr.,  and  4.1  %  ext.,  was  shown  by  a  89:^-inch 
hammered  bar,  witiiout  brand.  It  also  had  the  low^est  T.  8..  40.278  pounds, 
but  rather  high  elastic  limit,  25,700  pounds.  Its  fracture  was  95  %  crystal- 
line. Tlius  of  the  two  bars  showing  the  lowest  T.  S.,  one  was  the  most  duc- 
tile and  the  other  the  least  ductile  in  the  whole  series  of  80  bars. 

Generally,  high  ductility  is  accompanied  by  low  tensile  strength,  as  In  the 
Swedish  bars,  but  the  Parnley  bars  showed  a  combination  of  high  ductility 
and  hifrh  tensile  str«>n8rth. 

liOeomotlTe  Forglnars,  Iron.  —17  tests:  average,  E.  L.,  80,420;  T.  8., 
SO.S^n:  contr,  86.5:  ext.  m  lu  in<^hes,  2:{.8. 

Broken  Anelior  Forsf  nfi^s,  Iron.— 4  tests:  average.  E.  L.,  23,835; 
T.  8  .  40,0*J;  contr.,  8.0;  ext. In  lu  inches,  8.K. 

Kirkaldy  places  these  two  irons  in  conrrast  to  show  the  difference  between 
good  and  bad  work.  The  brolcen  anchor  material,  he  says,  is  of  a  most 
treacherous  character,  and  a  disgrace  to  anv  manufacturer. 

Iron  Plate  Girder*— Tensile  tests  of  pieces  cut  from  a  riveted  iron 
girder  after  twenty  years'  service  in  a  railway  bridge.  Top  plate,  average 
of  3  tests.  K.  L..  36,600;  T.  8.,  40,806;  contr.  16  1;  ext.  in  10  inches,  7.8. 
Bottom  plato,  average  of  3  tests,  E.  li.,  81,300;  T.  S.,  44,288;  contr.,  13.3;  ext. 
in  10  incnes,  6.3.  Web-plate,  average  of  8  tests.  E.  L..  28.000;  T.  S  ,  45,002; 
contr..  15  9;  ext.  in  10  inches,  8.9.  Fractures  all  flbmu3.  The  results  of  30 
Vsts  from  different  parts  of  the  girder  prove  that  the  iron  has  undergone 
*o  ciiange  during  twenty  years  of  use. 

8teel  Plates.— Six  plates  100  inches  long,  2  inches  wide,  thickness  vari- 
ous, .m  to  .97  inch  T.  8..  55,485  to  60,805;  E.  L  .  29,600  to  33,300;  contr.,  53.9 
to  59.5;  ext..  17.06  to  18.57. 

Steel  Brldco  IilnlLS.— 40  links  from  Hammersmith  Bridge,  1886. 


298 


8TRENQTB  OF  MATERIAtS. 


»4 

a 

a 

g 

5 

& 

Fracture. 

1 

Average  of  all 

67,8M 
60,758 

64,<V44 
68,745 

68,960 

88.904 
36,080 
44J06 
88,441 
88,118 
86,70S 
89,017 

84.B)C 
80.1 
81.8 
84.7 
W.8 
40.8 
6.0 

u.u% 

15.51 
19.49 

18.48 
15.46 
17.78 
6.68 

80jt 
15 
80 
100 

1 

Lowest  T.S 

Tdi 

Highest  T.S.  And  E.L 

Lowest  £.L 

Greatest  Contraction 

Greatest  Extension 

heast  Contr.  and  Ext 

86 
70 
0 
86 
100 

The  ratio  of  elastic  to  ultimate  strength  ranged  from  60.6  to  66.8  per  eent; 
average,  56.9  per  cent. 

Extension  in  lengths  of  100  inches.  At  10,000  lbs.  per  sq.  in.,  .018  to  .084; 
mean,  .O'iO  Inch;  at  siO.OOO  lbs.  per  sq.  In.  .049  to  .068:  mean,  .066  Inch;  at 
80.000  lbs.  per  sq.  in.,  .088  to  .100;  mean,  .090;  set  at  90,000  potmds  per  sq.  In., 
0  to  .008;  mean,  0. 

The  mean  extension  between  10,000  to  80,000  lbs.  per  sq.  in  increased  retni- 
larly  at  the  rate  of  .007  inch  for  each  9000  lbs.  per  sq.  In.  Increment  of  strmin. 
This  corresponds  to  a  modulus  of  elasticity  of  fi8,6i  1,4W.  The  least  Increase 
of  extension  for  an  Increase  of  load  of  80,000  lbs.  per  sq.  in.,  .Odii  Inch,  cor- 
responds to  a  modulus  of  elasticity  of  80,769,881,  and  the  greatest,  .078  Inch, 
to  a  modulus  of  96,815,789. 

S8eel  Bsdla.— Bending  tests.  5  feet  between  supports,  11  teats  of  flange 
rails  Ti  pounds  per  yard,  iJSS  Inches  high. 

Elastic  stress.  Ultimate  stress.  Deflection  at  60,000  Ultimate 

Pounds.              Founds.  Pounds.  DellecU<Mi. 

Hardest...         84,900                   60,900  8.sd4  ins.  8  ins. 

Softest....         89,000                    56,740  8.70   "  8  *' 

Mean »2,768                    68,900  8.68   "  8  " 

All  uncracked  at  8  inches  deflection. 

Pulling  tests  of  pieces  cut  from  same  rails.  Mean  results. 

Elastic  Ultimate  Contraction  of 

Stress.          Pounds.  area  of  f  rao-  BxtenaioB 

per  sq.  In.  per  sq.  in.  ture.  in  10  insL 

Top  of  rails 44,900             88.110  19.9f                   18.(W 

Botton  of  rails 40,900             77,890  80.9)(                   89.8S( 

Steel  Tires*— Tensile  tests  of  specimens  cut  from  steel  tires. 

Krupp  &nBL.~4M9  Tests. 

Ext.  In 
E.  L.  T.  8.  Oontr.  6  Incbea. 

Highest 09,990  119,079  81.9  lai 

Mean 69,800  104,119  89.6  10.7 

Lowest 41,700  90.588  45.6  2&.7 

ViCKSBS,  Bona  &  Ca— 70  Tests. 

Ext.  In 
E.  L.  T.  8.  Oontr.  6  inches. 

Highest 68,600  190,788  11.8  8.4 

Mean 61.068  101,964  17.6  1SL4 

Lowest 48,700  87,697  S4.7  110 

Note  the  correspondence  between  Krupp*s  and  Tickers^  steels  as  to  te»- 
sile  strength  and  elastic  limit,  and  their  great  difference  in  contraction  and 
elongation.  The  fractures  of  the  Krupp  steel  averaged  99  per  cent  silky, 
78  per  cent  granular;  of  the  Vicker  steel,  7  per  cent  silky,  98  per  cent  granu- 
lar. 


EXTRACTS  FROM  KIRKALDY^S  TESTS. 


29* 


Steel  Axles.— Tensile  tests  of  specimens  eat  from  flteel  axles. 
Patent  Shaft  and  Axle  Taek  Co.— 157  Tests. 

EjeL  In 
E. !«.  T.  a  OoAtr.  6  Inches. 

Highest. 49,800  »,€00  Sl.l  16.0 

Mean 86,967  73,000  83.0  S8.6 

Lowest M^aOO  61,888  84.8  S5.8 

ViCKKBS,  SoMS  &  Co.— 125  Tests. 

Sst  in 
S.L.  T.  8.  Contr.  6  inches. 

Highest 4S!.600  83,701  18.8  J8.S 

Mean 87,618  70.692  41j6  87.6 

I>jwest SO.S&O  56,888  40.0  87.8 

The  average  fracture  of  Patent  Shaft  and  Axle  Tree  Co.  steel  was  83  per 
opnt  silk  J,  87  per  cent  granalar. 

The  average  fracture  of  Vickers'  steel  was  88  per  cent  ^ky,  ISpereent 
granular. 

Tleoaile  teats  -of  specimens  cut  from  looomotiw  crsak  axles. 

VicKaKS*.— 89  Tests,  1878. 

Ext.  is 

E.  L.                  T.  8.                 Contr.  5  inches. 

Hvfaeat. 96,700                  68,067                   88.8  18.4 

Neaa 84,146                  67,023                   82.9  81.0 

Uwest 21,700                 60,106                  S3.7  86JI 

yiCKBia\-78  Teats,  1884. 

E.  L.  T.  8.  Oontr.  5  inches. 

HigheeL 87,600  64,878  2TjO  9a8 

Mean 88,578  06,807  82.7  25.0 

lowest 17,060  47,605  85.«  27.8 

Fbibd.  KR1TPP.--48  Tests,  1888. 

Ext.  in 
E.  L.  T.  S.  Contr.  5  inches. 

Highest 81,668  66,866  48.8  85.6 

■eaa 89,401  61,774  47.7  88.8 

Lowest 81,060  d6,i;s  6C.8  85.8 

Steel  Propeller  ffibmite.— Tensfle  tests  of  pieces  cut  from  two  shafts, 
mean  of  four  tests  each.  Hollow  shaft,  Whitworth.  T.  S.,  61,290;  E.  L., 
10,&75;  contr.,  62.8;  ext.  in  10  Inches,  28.6.  Solid  Shaft,  Yfckers*,  T.  8., 
C6.870;  E.  L.  86,425 ^eontr.,  44.4;  ext.  in  W  inches,  80.7. 

Thrusting  testa,  \¥hitworth,  ultimate,  56,201 ;  elastic,  20,800;  set  at  88,860 
lbs.,  8Jfi  per  cent;  set  at  40,000  lbs.,  2.04  per  cent;  set  at  90,808  Ibe^  3.88  per 
£ent. 

Thrurttag  tests.  Tickers*,  uHlmate,  44,60?;  elastic,  88,250;  set  at  89,608  lbs., 
129  per  cent;  set  at  40,000  lbs.,  4.00  per  cent. 

Shearing  strength  of  the  Whitworth  shaft,  mean  of  four  tests,  was  40,684 
lbs.  persqiupe  Inch,  or  66.8  per  cent  of  the  pulling  stress.  SpecMe  gravity 
of  the  Whitworth  steel,  7.867:  of  the  Vi(Aer8\  7.856. 

Sprlnc  Steel.— Untempered,  6  tests,  average,  E.  L.,  67,016;  T.  8., 
115,688;  contr.,  87.8;  ext.  In  10  hiches,  16.6.  Sprmg  sted  tmtempered,  16 
tests,  average,  E.  L.,  88,785;  T.  8.,  68,406;  cootr.,  19.1;  ext.  in  n  hic^es,  29  8. 
These  two  lots  were  shipped  for  the  same  purpose,  viz.,  railway  carriage 
leaf  springs. 

Steel  Cmattags.— 44  tests,  E.  L.,  81415  to  85,567;  T.  S.,  54,928  to  (RMO; 
coocr.,  1.67  to  15.8;  ext.,  1.45  to  15.1.  Note  the  great  variation  in  ductOity. 
the  steel  of  the  highest  strength  was  also  the  most  dnctfle. 

Blweted  Jotete,  PvUiac  T^mtm  ef  WUwet^d.  Steel  Plmtea, 

Sttyle  Blveted  Kiap  Joints.  Mmelilne  Blwetod. 

Soles  Drilled* 

Plates,  width  and  tftrfdEneBS,  inches  : 

18-50  X  .25       18.00  X  .51        11.75  X  .78       18.85  X  1.91       14.00  X  .77 
PlatesL  grom  secttonal  area  sqnare  inches : 

8.8^^  6.68  9.166  18.878  10.780 

,  total,  poonds  : 
188,880  888,640  488,180  588t860  4a6)8lt 


300  BTRENQTH  OF  HATEBIALS.    - 

Straw  per  sqoKre  inch  of  gro«  area,  Joint : 

69%  50«m  46.178  48,600  O^ 

Stren  per  square  inch  of  plates,  solid  : 

70,765  65,300  64,060  68,280  68,045 

Ratio  of  strength  of  Joint  to  solid  plate  : 

83.46  76.83  713.00  66.66  63.06 

Ratio  net  area  of  plate  to  gross : 

73.4  66.6  68.7  64.7  78.9 

Where  fractured : 

plate  at  plate  at  plate  at  plate  at  rivets 

holes.  holes.  holes.  holes.  sheared. 

Rivets,  diameter,  area  and  number : 

.46,  .189, 84        .64,  .881,  isSl       .06,  .706, 13        1.06,  .916, 18      .96,  .706, 18 
Rivets,  total  area : 

8.816  6.741  8.496  10.998  &496 

Strenstli  of  WeliU«~Temiile  teste  to  determine  ratio  of  strength  of 
weld  to  solid  bar. 

Irok  Tib  Babs.— 88  Tests. 

Strength  of  solid  bars  varied  from 48,801  to  67,066  lbs. 

Strenth  of  welded  bars  varied  from 17,816  to  44,686  lbs. 

Ratio  of  weld  to  solid  varied  from 87.0to  79.1)11 

Iron  Plates.— 7  Tests. 

Strength  of  solid  plate  from 44,861  to  47,481  lbs. 

Strength  of  welded  plate  from 86,448  to  88,931  lbs. 

RaUo  of  weld  to  solid 67.7to88.99( 

Craik  Links.— 816  Tests. 

Strength  of  solid  bar  from 49,198  to  67,875  lbs. 

Strength  of  welded  bar  from 89,675  to  48,884  lbs. 

Ratio  of  weld  to  solid 78.1to96.4^ 

Iron  Bars.— Hand  and  Electric  Machine  Welded. 

88  tests,  solid  iron,  average 68,444 

17     *'     electri    welded,  average 46,886  ratio  89.1 )( 

19     *•     hand  "  *»       46.899    "    89.8)( 

Stbsl  Bars  and  Platbs.— 14  Tests. 

Strength  of  solid 54,896  to  64,580 

Strength  of  weld 88,558  to  46,019 

Ratio  weld  to  solid 58.6to88.U 

The  ratio  of  weld  to  solid  In  all  the  tests  rangiog  from  87.0  to  96.4  is  proof 
of  the  great  variation  of  workniannhip  In  welding. 

Cmaf  Copper.— 4  tests,  average,  E.  L.,  5900;  T.  8.,  24,781;  contr.,  84.5; 
est.,  81.8. 

Copper  Plmtea.— As  rolled,  28  tests,  .26  to  .75  in.  thick;  E.  L.,9766  to 
18,660;  T.  S.,  80.994  to  84.881 ;  contr,  81.1  to  57.6;  ext.,  39.9  to  58.8.  The  va- 
riation In  elastic  limit  is  due  t<)  difference  in  the  heat  at  which  the  plates 
were  finished.  Annealing  reduces  the  T.  S.  only  about  1000  pounds,  but  the 
E.  L.  from  8000  to  7000  pounds. 

Another  series,  .88  to  .52  thick;  148  tests,  T.  S.,  29,099  to  81,924;  oontr..  88.7 
to  56.7:  est.  in  10  inches,  28.1  to  41.8.  Note  the  uniformity  in  tensile 
strength. 

Brmwn  Copper.— 74  tests  (0.88  to  1.08  inch  diameter);  T.  S.,  81,634  to 
40A'>7;  contr.,  8<.5  to  64.1;  ext.  in  10  inches.  5.6  to  48.8. 

Bronme  fk^in  a  Propeller  BImde.— Means  of  two  tests  each  from 
centre  and  edge.  Central  portion  (sp.  gr.  8.320).  E.  L.,  7550;  T.  8..  86i812; 
contr.,  85.4;  ext.  in  10  hiohes,  88.&  Edge  portion  (sp.  gr.  8560).  K  L.,  8860; 
T.  8.,  85,960;  contr.,  87.8;  ext.  In  10  inches,  47.9. 

Cast  German  SUver.-lO  tests:  E.  L.,  18,400  to  89,100;  T.  S.,  28,714  to 
46,510;  contr.,  3.2  to  81.5;  ext  in  10  inch-J,  0.6  to  10.8. 

Tliln  Sbeet  metal.— Tensile  Strength. 

Germ  an  silver,  8  lots 75.616  to  87, 1 89 

Bronze,  4  lots 78,880  to  98,066 

Brass,  8  lots  44,898  to  66,188 

Copper,  91ots 80,470  to  48,450 

Iron,  18  lots,  lengthway 44,881  to  69,484 

Iron,  18  lots,  crossway 89388  to  67,860 

Steel,  61ots 49,858  to  78,851 

Steel,  6  lots,  oroBsway. 66,948  to  80,799 


XZIBACTS  PfiOK  KISCALDY'S  TESTS. 


301 


IFire*— Tensile  Strength. 

German  illTier,  5  lots 81,786  to  C 

Bronze,  1  lot 78,040 

Braes,  as  drawn,  4  lots 81,114  to  98,578 

Copper,  as  drawn,  8  lots 37,607  to  46,494 

Copper  annealed,  8  lots 84,986  to  45,210 

Copper  (another  lot),  4  lots  85,05S  to  62,190 

Copper  (extension  86.4  to  0.6J0. 

IronTsiots 69.846  to  97.908 

Iron  (extension  16.1  to  0.7j0. 

Steel,  8  lots 108.272  to  818,888 

The  Steel  of  818.828  T.  S.  was  .047  Inch  diani.,  and  had  an  extension  of  only 
0.3  per  cent;  that  of  106,272  T.  8.  was  .107  inch  dlam.  and  had  an  extension 
of  £2  per  cent.   One  lot  of  .044  inch  diam.  had  267.114  T.  S.,  and  6.2  per  cent 


iriTe  Bopee. 

Selected  Tests  Showing  Bange  of  Variation. 


DeserlptiOD. 


Strands. 


U 


Hemp  Core. 


OalTanised 

UngaWanlzed. 
UngalTaniaed.... 

GiOVanlxed 

Ungatranised... 
UngalTanized... 

Gahranlxed 

QslTanlaed 

Galvanised 

Ungalvanized... 
Ungalyanized... 
Ungalranfaed... 

GalVaniaed 

GalTaniaed 

Ungalvanixed... 

Ungalvanized.... 

GalVaniaed..... 

Galvanised 

Uogalvanfaed.. 

Ga^anixed 

Galvanized 


7.70 
7.00 
6.88 
7.10 
6.18 
6.19 
4.02 
6.86 
4.82 
8.65 
8.50 
Z.»i 
4.11 
8.81 
8.02 
2.68 
2.87 
2.46 
1.76 
2.04 
1.76 


58.00 

58.10 

42.90 

87.57 

40.46 

40.88 

80.86 

18.94 

«.50 

r^.21 

12.65 

14.12 

11.85 

7.27 

8.62 

6.26 

5.48 

8.85 

2.80 

2.72 

1.86 


.1563 

.1496 

.1847 

.1004 

.1903 

.1816 

.0728 

.1104 

.1698 

.0756 

.128 

.186 

.080 

.068 

.106 

.0968 

.0660 

.0472 

.0619 

.0378 

.0305 


Main  and  Strands 

Wire  Core 

Main  and  Strands 

Wire  Core 

Wire  Core 

Main  and  Strands 

Main  and  Strands 

Main 

Main 

Wire  Core 

Main 

Main  and  Strands 

Main  and  Strands 

Main 
Main  and  Strands 
Main  and  Strands 
Main  and  Strands 

Main 

Main  and  Strands 

Main 


880,780 

814,860 

206,920 

278,760 

268.470 

^880 

190,890 

186,560 

190,710 

110.180 

101,440 

98,670 

75,110 

66,096 

40,666 

41,206 

88,666 

88,075 

24,552 

20,416 

14.684 


Hemp  Bopee.  tlnterred*— 16  tests  of  ropes  from  1.58  to  6.90  Inches 
drcumferenoe,  weighing  0.42  to  7.77  pounds  per  fathom,  showed  an  ultim- 
ate  strength  of  from  16^  to  33,808  pounds,  the  strength  per  fathom  weight 
varyinfr  from  2872  to  6534  pounds. 

Hemp  B4>pee,  Tmrred* -16  tests  of  ropes  from  1.44  to  7.12  inches 
drcumference,  weighing  from  0.88  to  10.30  pounds  per  fathom,  showed  au 
ultimate  strength  of  from  1046  to  31,540  pounds,  the  strength  per  fathom 
wHirht  varying  from  1767  to  5140  pounds. 

Cotton  Bopee.— 6  ropes,  2.48  to  6.61  Inches  circumference,  1.08  to  8.17 
pounds  per  fathom.  Strength  8080  to  23,258  pounds,  or  2474  to  8346  pounds 
per  fathom  weight. 

is^MJim  Bopea.— 36  tests:  1.10  to  8.00  Inches  circumference,  0.20  to 
11.40  pounds  per  fathom.  Strength  1280  to  65,550  pounds,  or  3008  to  7304 
pouiufai  per  fathom  weight. 


302 


filBEKGTH  OF  HATEBIAL8. 


Belttnc. 

No.  of  Tensile  strength 

lots.  per  square  Indi. 

11  Leather,  singrle,  ordinary  tanned {B48to4834 

4  Leather,  Single,  Helvetia &6S1  to«M4 

7  Leather,  double,  ordinary  tanned 31fiOto3578 

8  Leather,  double  Helvetia.... 4078to5412 

6  Cotton,  solid  woven fiMStoSeOO 

14  Cotton,  folded,  stitched  4570to77S0 

1  Flax,  solid,  woven • 1)046 

1  Flax,  folded,  stitched 68R0 

6  Hair,  solid,  woven 8888  to  5180 

t  Rubber,  solid,  woven 437Ito434S 

€mnTa««— 85  lots:  Strength,  lengthwise,  118  to  406  pounds  per  inch; 
orossways,  191  to  488  pounds  per  inch. 

The  grades  are  numbered  1  to  6,  but  the  weights  are  not  given.  The 
strenguis  vary  considerably,  even  in  the  same  number. 

marbles.— Crushing  strength  of  various  marbles.  88  tests,  8  kinds. 
Specimena  were  6-inch  cubes,  or  columns  4  to  6  inches  diameter,  and  6  and 
i2  inches  high.  Range  7549  to  18,720  pounds  per  square  inch. 
.  Climillte*~Cru8hing  strength,  17  tests;  square  columns  4x4  and  6x4, 
4  to  24  inches  high,  8  kinds.  Crushing  strength  ranges  10,088  to  iMn 
pounds  per  square  inch.    (Very  uniform.) 

StoneSc— (Probably  sandstone,  local  names  only  given.)  11  kinds,  49 
tests,  6  X  6t  columns  12, 18  and  84  inches  high.  CruBhing  strength  ranges 
from  S106  to  12,122.  The  strength  of  the  column  24  inches  long  is  generally 
from  10  to  20  per  cent  less  than  that  of  the  6-lnoh  cube. 

Stones*— (Probably  sandstone)  tested  for  London  &  Northwestern  Rail- 
way. 16  lots,  8  to  6  tests  in  a  lot.  Mean  results  of  each  lot  ranged  from 
878o  to  11.966  pounds.  The  variation  is  chiefly  due  to  the  stones  being  from 
different  lots.  The  different  specimens  in  each  lot  gave  results  which  gen- 
erally agreed  within  80  per  cent. 

KiiCKS*— Crushing  strength,  8  lots;  6  tests  in  each  lot;  mean  results 
ranged  from  1885  to  9209  pounds  per  square  inch.  The  maximum  variation 
in  the  specimens  of  one  lot  was  over  luO  per  cent  of  the  lowest.  In  the  most 
uniform  lot  the  variation  was  less  than  20  per  cent. 


"Wood.— Transverse  and  Thrusting  Tests. 

1 

Siie8abt.in 
square. 

Span, 
inches. 

Ultimate 
Stress. 

LW 
4BD» 

Thrust- 
ing 
Stress 
per-,. 

Pitch  pine 

10 
12 
8 
5 

llKtol2« 
12    to  18 
4«X12 
4H  X  12 

144 
144 

120 
120 

45,856 

to 
80,580 
87.948 

to 
64,152 
82,856 

to 
89.084 
23,624 

to 
26,962 

1096 

to 
1408 

657 

to 

790 
1506 

to 
1779 
1190 
to 
1872 

8586 
to 

Dantzicflr 

EngUKhoak 

American  white 
oak 

548S 

2478 

to 

842S 

2473 

to 
4437 
X656 

to 
8899 

Demerara  greeoheart,  9  tests  (thrusting) 8169  to  10,785 

Oregon  pine,  2 tests... 5888and728l 

Honduras  mahogany,  1  test 6769 

Tobasco  mahogany,  1  test 5078 

Norway  spruce,  2  tests 6650  and  5494 

American  yellow  pine,  2  tests 8875and)008 

English  ash,  1  test afti5 

Portland  Cement*— (Austrian.)   Cross-sections  of  specimens  ^9  X  2^ 
inches  for  pulling  tests  only ;  cubes,  8x8  inches  for  thrusting  tests;  weight, 


HISGELLiJ^EOUS  TESTS  OF  MATERIALS. 


303 


96.8  pounds  per  Imperial  bushel:  residue,  0.7  per  cent  with  sieve  8500  meshes 
per  s()uare  Jnch;  88.8  per  cent  by  volume  of  water  required  for  mixing;  time 


of  setting,  7  days;  10  tests  to  each  lot. 
were  as  follows: 

Cement  Cement 

alone,  alone. 

Age.              Pulling.  Thrusting. 

10  days                 378  2010 

20  days                 420  8843 

80  days                 451  8724 


The  mean  results  in  lbs.  per  aq.  in. 

1  Cement,     1  Cement,  1  Cement, 

2  Sand.         8  Sand,  4  Sand, 

Thrusting.    Thrusting.  Thrusting. 

898                 407  228 

1028                 404  275 

1172                 694  888 
Portlmnd  Cement. —Various  samples  pulling  tests,  2x2^  Inches 
cross-section,  all  aged  10  days,  180  tests;  ranges  87  to  648  pounds  per  square 
loch.                                                    • 

TENSIIiB  8TRBNGTH  OF  iriBE. 
(From  J.  Buckuall  Smithes  Treatise  on  Wire.) 

Tons  per  sq.  Pounds  per 
in.  sectional  aq.  in.  sec- 
area,  tional  area. 

Stack  or  annealed  iron  wire 25  56,000 

Bright  bard  drawn 85  78,400 

Bessemer,  steel  wire 40  89,600 

Mild  Siemens-Martin  steel  wire 60  134,000 

BifSti  carbon  ditto  (or  ''  improved  '*) 80  170,200 

Cruciblecast-steel  "improved'*  wire 100  224,000 

-  Improved  "cast-steeP*  plough" 120  268,800 

Special  qiualities  of  tempered  and  improved  cast- 
steel  wire  may  att^n ]50tol70    886,000  to  880,800 

BHSCEIiliANEOUS  TESTS   OF  IHATERIAIiS. 
Reports  of  l¥ork  of  tlie  l¥aiertovirii  Testlns-nimclilne  In 

1883. 

TEgTS  OF  HlVFrTED  JOINTS,  IRON  AND  STEEL  PLATES. 


i 

f 

ill 

^8 

1 

s 

i 

Tensile  Strength 
Joint  in  Net  Sec- 
tion of  Plate  per 
square  inch, 
pounds. 

ill 

H 

11  r^'. 

P. 

is^ 

6 

^H 

89,800 

47,180 

47.0  t 

K 

11- 1^^ 

6 

m 

41,000 

47,180 

49.0  ± 

V2 

2t 

13116 

10^ 

6 

85,650 

44,615 

45.6  t 

H 

il 

18-16 

10 

5 

85,150 

44,615 

44.9  t 

12 

11   K. 

8 

10 

5 

46,860 

47.180 

59.9  « 

S 

ll-:ii 

10 

5 

46,875 

47,180 

60.5  « 

H 

4,^ 

18-16 

10 

6 

46,400 

44,615 

50.4  1 

v2 

h 

13-16 

10 

5 

2 

46,140 

44,615 

59.2  § 

'    ^ 

1 

1  1-16 

s 

4 

^gk^ 

44,260 

44,685 

57.2  § 

'  s 

1 

1  1-16 

4 

2^ 

42,^50 

44,6a5 

54.9  § 

•    g 

1^ 

1  8-16 

4 

2  9 

42,310 

46.590 

52.1  § 

1^  i 

1  8-16 

11.9 

4 

2!9 

41,920 

46,590 

51.7  § 

•     £  1 

t2 

18-16 

10^ 

io>2 

6 

\H 

61,270 

53.330 

59.5  1 

f  1    i2 

T 

18-16 

6 

m 

60,830 

53,330 

59.1  I 

+  1  s 

15-16 

1 

10 

5 

2 

47,580 

57,215 

40.2  i 

^     }i 

15-16 

1 

10 

6 

2 

49,840 

57,215 

42.8  X 

^     n 

11-16 

^ 

10 

5 

2 

62,770 

68,830 

71.7  § 

t    H 

11-16 

10 

5 

2 

61,210 

53,330 

69.8  f 

^ '  H 

15-16 

1 

10 

5 

2 

68,920 

57,215 

57.1  ■» 

^    » 

15-16 

1 

10 

5 

2 

66,710 

67.215 

55.0  « 

^'  K 

1 

1  1-16 

sit 

4 

2^ 

62.180 

52,445 

63.4  f 

^>  K 

1 

1  1-16 

4 

«^ 

62.590 

52,445 

63.8$ 

^    H 

1^ 

1  8-16 

10^ 

4 

J^ 

5i,650 

51,545 

54.0  § 

t    « 

1  8-16 

10 

4 

54,200 

61,545 

53.4  § 

•Iron. 


t  Steel. 


$  Lap-joint. 


i  Butt-Joint. 


304 


STRENGTH  07  KATERIAL8. 


The  efficiency  of  the  joints  Is  found  by  dividing  the  mazlmmii  tenillB 
stress  on  the  gross  sectional  area  of  plate  by  the  tensile  strength  of  the 
material. 

OOMPKIE8SION  TESTS  OF  8  X  8  INCH  WBOUGHT-IBON  BARS. 


Tested  with  Two  Pin  Ends,  Pins 
1H(  Inch  in  Diameter. 

Tested  with  One 
Flat  and  One  Pin 

Length,  inches. 

TTltimate  Oom- 

pressive  Strength 

pounds  per  square 

taich. 

Tested  with -Two 
•  Flat  Ends,  Ulti- 
mate CompresBive 
Strength,  pounds 
per  square  inch. 

End,  UlUmate 

Comprefwire 

Strength,  pounds 

per  square  inch. 

80 

(88,860 
181,990 
j  86,810 
186,640 
(84,080 
185,880 
(80,660 
80,800 
16,580 
117,840 
( 13,010 
115,700 

60 

90 

180...  

jab^Tao 

185.580 
(88,010 
122,460 

' 

85,180 
85,190 
82,450 
21,830 

150 

180 

Tested  with  two 
ends.  Length 
iSOinchea. 


UlL  Oomp.  Str., 
I>er  sq.  in.,  lbs. 

16,880 

17,740 

21,400 

22,210 


TENSILE  TEST  OF  SIX  STEEL  EYE-BARS. 

COMPARBD  WITH  SMALL  TSST  INOOTS. 

The  steel  was  made  by  the  Cambria  Iron  Company,  and  the  eye-bar  beads 
made  by  Keystone  Bridge  Company  by  upsetting  and  hammering.  All  the 
bars  were  made  from  one  ingot.  Two  test  pieces,  ^-Inch  round,  rolled  from 
a  teat-ingot,  gave  elastic  limit  48,010  and  48.210  pounds;  tensile  strength, 
78,150  and  09,470  pounds,  and  elon^fatlon  In  8  inches,  28.4  and  25.6  per  cent. 
respectively.  The  ingot  from  which  the  eye-bars  were  made  was  14  inches 
square,  rolled  to  billet,  7x6  inches.  The  eye-bars  were  rolled  to  6U  x  1  inch. 
Cnemical  tests  gave  carbon  .87  to  .80;  manganese,  .64  to  .78;  phosphorus, 
.074  to  .096. 


Gauged 
Length, 
inches. 

160 

160 

160 

800 

800 

200 

800 


Elastic 

limit,  lbs. 

persq.  in. 

87.480 

80,650 

87.666 
85,810 
88,880 
87,640 


Tensile 

strength  per 
sq.  in.,  lbs. 

per  cent,  in 

Gauged  Length. 

67,800 

15.8' 

64,000 

6.96 

71,560 

8.0 

68,780 

12.8 

65,850 

12.0 

64,410 

16.4 

68,890 

18.2 

The  aTerage  tensile  strength  of  the  9^.inch  test  pieces  was  71,810  lbs.,  that 
of  the  eye-bars  67,880  lbs.,  a  decrease  of  5.1%.  The  average  elastic  limit  of 
the  test  pieces  was  45,150  lbs.,  that  of  the  eye-bars  86,408  lbs.,  a  decrease  of 
19. 4i.  The  elastic  limit  of  the  test  pieces  was  68.89(  of  the  ultimate  strength, 
that  of  the  eye-bars  54.8g(  of  the  ultimate  strength. 


MISCELLAKEOUS  TE8TS  OF  MATHRIALS. 


305 


COMPRESSION  OF  WROUOHT-IRON  COLUMNS,  LATTICED  BOX 
AND  SOLID  WEB. 


ALL  TESTED  WITH  PIN  ENDS. 


Colomns  made  of 


6  inch  channel,  solid  web. 

6  • 
8  ' 


8-iDch  channels,  with  5-ld-iD.  continuous 


5-16-inch  continuous  plates  and  angles. 

Width  of  plates,  12  in.,  1  in.  and  7.&  in. 
7-16-inch  continuous  plates  and  angles. 

Plates  12  in.  wide 

8-inch  channels,  latticed 

8  *♦  •*  •'      

8  *•  ••  ••      

8-lDch  channels,  latticed,  swelleid  sides.. 

^       M  «t  It  ««  it 

g       U  ••  tt  ft  tt        " 

10 "         **  "    !! 

10  "         ••  "    .,..'. 

10-inch  channels,  latticed,  swelled  sides. 
«•  »»  it  it  tt 

*  10- inch  channels,  latticed  one  side;  con- 
tinuous plate  one  side 

1 10  inch  channels,  latticed  one  side;  con- 
tinuous  plate  one  side 


^ 

«   . 

tp» 

1 

<1 

JS    - 
4=^ 

.4 

c  ^ 

^^1 

1 

sn 

F 

■0 

10.0 

9.881 

482 

150 

9.977 

602 

20.0 

9.762 

755 

20.0 

16.281 

1,200 

26.8 

16.141 

1.645 

26.8 

19.417 

1,940 

26.8 

16.168 

1,765 

26.8 

20.954 

2,242 

18.8 

7.628 

679 

20.0 

7.621 

024 

26.8 

7.678 

1,255 

18.4 

7.624 

684 

200 

7.617 

921 

26.8 

7.702 

1,280 

16.8 

11.944 

1,470 

25.0 

12.175 

1,926 

16.7 

12.366 

1.549 

25.0 

11.932 

i;962 

85.0 

17.682 

1,848 

25.0 

17.721 

1,827 

80,220 
21,060 
16,220 
22,540 
17,570 

25.290 


25,770 
88,910 
84,120 
89,870 
88,530 
88,890 
80,7it) 
88,':40 
82,440 
31,180 
82,740 

86,190 

17,270 


*  Pins  in  centre  of  gravity  of  channel  bars  and  continuous  plate,  1.68 
inches  from  centre  line  of  channel  bars. 
i  Pins  placed  in  centre  of  gravity  of  channel  bars. 

EFFECT  OF  COLD-DRAWING  ON  STEEL. 
Three  pieces  cut  from  the  same  bar  of  hot -rolled  steel: 
1.  Original  bar,  2.08  in.  diam..  gauged  length  80  in.,  tensile  strength  65,400 

Ibe.  per  square  in.;  elongation  2!i.9%. 
1  Diameter  reduced  in  compression  dies  (one  pass)  .094  in.;  T.  S.  70,420;  el. 

2.7j(  in  20  in. 
3.         "  •*         *•  *'  "        '*       "      .222  in.;  T.S.  81,890;  el. 

0.(y:b%  in  20  in. 
Compression  test  of  cold-drawn  bar  (same  as  No.  8),  length  4  In.,  dIam. 
1J06  in.:  CompreKslTe  strength  per  sq.  in.,  75,000  lbs.;  amount  of  compres- 
sion .057  in.;  set  .04  in.    Diameter  increased  by  compression  to  1.821  in.  In 
ibe  middle;  to  1.813  in.  at  the  ends. 

Tests  or  Cold-rolled  and  Cold-drawn  Steel,  made  by  the 
Cambria  Iron  Co.  in  1897,  gave  the  following  results  (averages  of  12  tests  of 
each) 


Before  cold-roUing,  E.  L.  86,890 
After  •'  **  ,  "  72,580 
After  cold-drawing,     "     76,850 


T.  S.  59,980 
"  79,&S0 
'*     83,860 


El.  in  8  in.  28.3^ 
"  it  9.0. t 
..      .t       8.9" 


Red.  58.5  j( 
"  34  9" 
•*     34.2" 


The  original  bars  were  2  in.  and  %  in.  diameter.  The  test  pieces  cut  from 
the  bars  were  9^  in.  diam.,  18  in.  long.  The  reduction  in  diameter  from  the 
hot-rolled  to  the  cold-rolled  or  cold-drawn  bar  was  1/16  in.  in  each  case. 


306 


STEBKaTH  OF  MATERIALS. 


TESTS  OF  AMERICAN  WOODS.    (See  also  page  809.) 
In  all  cases  a  large  number  of  tests  were  made  of  each  wood.    Minimum 
and  maximum  results  only  are  glFen.    All  of  the  test  specimens  had  a  sec- 
tional area  of  1.575  X  1.575  inches.   The  transverse  test  specimens  were  89un 
inches  between  supports,  and  the  compressive  test  specimens  were  13.68 

inched  long.    Modulus  of  rupture  calculated  from  formula  R  =  5^^;  P  3 
load  in  pouttdB  at  the  middle,  I  =  length  in  inches,  b  =  breadUi,  d  =  depth: 


Name  of  Wood. 


Cucamber  tree  (Mafrnolia  acuminata).. 

Tellow  poplar  white  wood  {Lirioden- 
dron  tultpifera) 

White  wood,  Bass  wood  (Tilia  Ameri- 
cana)  

Sugar-maple,  Rock-maple  (Acer  sac- 
charimim 

Kdd  m&ple (Acenttbrum) ..... 

Locust  {Robinia  pseudacacia) 

Wild  cherry  (Prunut  nerotina) 

Sweet  gum  {Liquidamiiar  styraclfina) . . 

Dogwood  iCormisflorida) 

Sour  gum,  Peppendge  (Ngssa  siflvaiica), 

Persimmon  {Diospyros  Vtrginiana).  . . . 

White  ash  (S^raxunis  Amtiicana) 

Sassafras  (Sassafras  oJIHcinale) 

Slippery  elm  (I7init«y^/txi) 

White  elm  (Ulmus  Americana) 

Sycamore;  Buttonwood  (Ptoteni«  occi- 
dentalis) 

Butternut;  white  walnut  (Juglans  cl 
nevea) 

Black  waltrat  (Juglans  niffia) 

Shellbark  hickory  (Carya  alba) ... 

Pignut  (Carya  poi-cina) 

While  oak  (Quercus  alba) 

Red  oak  (Qnereus  rubra) 

Black  oak  (Quercus  tinctoria) 

Chestnut  (Castanea  vulgaris) 

Beech  (Fhgua  fentiginea) 

Canoe-birch,  paper-birch  (BeUilapapy' 
i-acea) 

Cottonwood  {Populus  monilifera). . . . 

White  cedar  (Tht^J'a  occidentalis) 

Red  cedar  (Junipems  Virginiana). . 

Cypress  (Saxodium  Distichum) 

White  pine  (Pinus  strobus) , 

Spruce  pine  {Pinus  ghibra) 

Liong-leaved  pine.  Southern  pine  (Pitius 

W9(dvstris)    
hite  spruce  (Ptoea  aZ6a,^ 

HemlocK  (Tsuga  Canadensis) 

Rt5d  flr,  yellow  flr  (Pseiulotsuga  Doug- 

lasii) 

Tamarack  (Larix  Americana)  


Transverse  Tests. 

Modulus  of 

Rupture. 


Mln.        Max. 


7,440 
6,600 

«,7ao 

9,080 
«,610 

12,«0 
8,310 
7.470 

10,190 
9.830 

io,a» 

5,950 
6,180 
10,220 
8,250 

«,?«) 

4.700 
8,400 
14,870 
11,500 
7.010 
9.760 
7,900 
5,950 
18,830 

n,7M 
8.S90 
6,310 
6,640 


5,610 
8,780 

9,220 

9,900 
7,590 


10,080 


12,050 

11,756 

11,590 

20,190 
18,450 
21,790 
16,800 
ll,r90 
14.560 
14,300 
18,500 
15,800 
10,150 
13,953 
15,070 

11,900 

11,740 
I6,3i» 
20,710 
19,490 
18,360 
18,870 
18.420 
12,870 
18,840 

17,610 
13«430 
9,530 
15,100 
10,080 
11,580 
10,980 

21,060 

11,660 
14,680 

17,990 
16.770 


Compresaion 

Parallel  to 

Grain,  pouTids 

per  square  inch. 


Min. 


4,560 

4,150 

8,810 

7,460 
6,010 
8,890 
5,890 
5,690 
6,250 
6,240 
6,650 
4,520 
4,0S0 
6,980 
4,M0 

4.900 

6,480 
6,940 
7,630 
7,460 
5,810 
4,960 
4.540 
3,680 
5,770 

6,770 
8,790 
2,660 
4,100 
5,060 
8,750 
2,580 

4,010 
4,t50 

4,500 

4,880 
6,610 


Max. 


7,410 

6,790 

6,4fi0 

9.940 
7,300 
11.940 
9,120 
7,«0 
9,400 
7,480 
8,080 
8.830 
6,970 
8,790 
8,010 

7.S40 

«,.S10 
8,850 
10,280 
8,470 
9,070 
8,970 
8,590 
6,650 
7,840 

8,5«N) 
6,510 
5,810 
7,040 
7,140 
6,000 
4,680 

10,860 
A,80O 
7,490 

9,800 

10.700 


8IIEARIN4»  STRBNOTII  OF  IRON  ANR  STSBI^ 

H.  Y.  Loss  In  American  Engineer  and  Railroad  Journal^  March  and  April, 
1893,  describes  an  extensive  series  of  experiinentj)  on  the  shearing  of  Iron 
and  steel  bars  in  shearing  machines.    Some  of  his  results  ore : 


CfiAIKS. 


307 


Depth  of  penetmtioii  at  point  of  roazlmnm  reslstanoe  for  ioft  steel  Mrs 
i»  ttidepeiideiifrof  the  width,  but  Taries  with  the  thickoeeB.  If  d  =  deptli  of 
peoetrati<»and  t  =  thickness,  d  =  M  for  a  flat  knife,  d  =  .25  t  for  ai"  bevel 
knifp.  and  d  =  .16  V^for  an  8*"  bevel  knife.  The  ultimate  pretsure  per  inch 
of  width  in  flat  steel  hare  is  approxinwtely  50,000  lbs.  X  t  The  energy  con- 
sQiiied  in  foot  pounds  per  inch  width  of  steel  bars  Is,  approximately:  1" 
thick,  laoo  fL-lbs.;  1^",  IKOO;  l^'\  8700;  1%",  4500;  the  enerfor  increasing 
at  a  slower  rate  than  the  square  of  the  tliickneas.  TrcMi  angles  require  more 
euergj  than  steel  angles  or  the  same  size;  steel  breaks  while  iron  has  to  be 
cut  off.  For  hot-roUed  steel  the  resistance  per  square  inch  for  rectan- 
gular sections  varies  from  4400  lb».  to  20,600  lbs.,  depending  nartly  upon  its 
hardness  and  partly  upon  the  size  of  its  cross-area,  which  latter  element 
indirectly  but  greatly  indicates  the  temperature,  as  the  smaller  dimensions 
require  a  considerably  longer  time  to  reduce  them  down  to  size,  which  Ume 
again  roeana  loss  of  heat. 

It  is  not  probable  that  the  resistance  in  practice  can  be  brought  very 
much  below  the  lowest  figures  here  given— viz.,  4400  lbs.  per  square  Inch- 
as  a  decrease  of  1000  lbs.  will  henceioi*th  mean  a  considerable  increase  In 
cruB8-«ectlon  and  temperature. 

HOI.]»ING«POWBB  OP  BOIIiBR-TITBBS  BXPANBEB 

iivro  TiJBB-sHBinrs. 

Experinaents  by  Chief  Engineer  W.  H.  Shock,  U.  S.  N.,  on  brass  tubes,  8^ 
inches  diameter,  expanded  into  plates  ^-inch  thick,  gave  results  ranging 
from  5B90  to  46.000  lbs.  Out  of  48  tests  5  gave  figures  under  10,000  lbs.,  13 
liKween  lO.OOO  and  90,000  lbs.,  18  between  20,000  and  80,000  lbs.,  10  between 
91.000  and  40,000  lbs.,  and  3  over  40,000  lbs. 

Experiments  bv  Yarrow  &  Co.,  on  steel  tubes,  8  to  2f4  inches  diameter, 
gave  results  similarly  varying,  ranging  from  7900  to  41,715  lbs.,  the  majority 
-atiging  from  2O.CO0  to  90,000  lbs.  In  15  experiments  on  4  and  5  inch  tubes 
the  strain  ranged  from  20,^20  to  68,OiO  lbs.  Beading  the  tube  does  not  neces- 
sarily give  increased  resistance,  as  some  of  the  lower  figures  were  obtained 
«ith  beaded  tubes.  (See  paper  on  Rules  Governing  the  Construction  of 
istetaa  Boilers,  Trans.  Engineering  Congress,  Section  Q,  Chicago,  1803.) 

CHAINS. 
'Weight  ]»er  Foot,  Proof  Ifest  and  Breaklne  l¥»lelit. 

(Pennsylvania  Railroad  Specifications.) 


Nominal 

Description. 

Specifications. 

Ihameter 
of  Wire, 
inches. 

Weight  per 
foot,  lbs. 

Proof  Test, 
lbs. 

Breaking 

Weight. 

lbs. 

6/39 
8/18 

Lock-chain 

0.9» 

0.35 
O.TO 
l.IO 
1.50 
1.50 
1.90 
1.90 
2.50 
3.50 
4.00 
4.00 
6.50 
5.50 
7.40 
9.50 
12.00 
15.00 
21.00 

Fire-door  chain 

Crossing-gate  chain 

Sprocket-wheel  chain 

Brake-chain   

55l6 

J500 

3000 

8500 

4000 

5000 

5500 

7000 

7500 

11,000 

11,000 

16,000 

16,()00 

2y,ooo 

30,000 
40,000 
50.000 
70,000 

.3000 
6500 
7000 

Crane-chain    

7500 

Drop-bottom  branch  chain. 

Oane-chain  

Drop-bottom  main  chain.. . . 
Crane-chaiu 

9500 
10.000 
12,500 
13  000 

t 

Safety    **     

20,000 

l\ 

Crane     "     

20  (X)0 

11 

Log        •*     

29  000 

1 

Crane    "     

29  000 

% 

^  ».        .»     

40,000 

1 

•(            at 

55.000 

«*                 44 

66  000 

1*5 

.»            It                                     ** 

^.000 

i2 

M              iff 

116,000 

Ekm^tioD  of  all  sizes,  10  per  cent.    All  chain  must  stand  the  prescribed 
liToof  test  without  deformation. 


STBENGTH  OF  MATERIALS. 


BritUlft  Admiralty  FroTtiur  Tests  of  Clialn  Cables.-S^tiid- 
links.    Minimum  size  in  Inchea  and  loths.    Proving^  test  in  tons  of  ^40  Itw. 

TtSi,  tora:  8^  1^^  "ll  l^S  15H  18  90^  2§|  sSJa,  Sft>A  'si  S  37^! 
MIn.  Size:  !•  !•  1^*  1"  1»"  1"  1»*  1"  2  2«  S«  2«. 
Test,  tons:      «H«  4H%   4r*g   61*   S5A   59*   ^h},  ^hh   «    764J   81*  91,V 

Wroiislit-lron  Cbaln  Cables.— The  strenfcth  of  a  chain  link  is 
lesM  Lhan  twice  that  of  a  straight  bar  of  a  sectional  area  equal  to  that  of  one 
side  of  the  link.  A  weld  exists  at  one  end  and  a  bend  at  the  other,  eacli  re-  I 
quiring  at  least  one  heat,  which  produces  a  decrease  in  the  strength.  The 
report  of  the  committee  of  the  U.  S.  Testing  Board,  on  tests  of  wrought-iron  I 
and  chain  cables  contains  the  following  conclusions.  That  beyona  doubt, 
when  made  of  American  bar  iron,  with  cast-iron  studs,  the  studded  link  is 
inferior  in  strength  to  the  unstudded  one. 

**  Tliat  when  proper  care  is  exercised  in  the  selection  of  material,  a  Taria-  i 
tlon  of  5  to  17  per  cent  of  the  strongest  may  be  expected  in  the  resistance  | 
of  cables.    Without  this  care,  the  variation  may  rise  to  35  per  cent. 

*'  That  with  proper  material  and  construction  the  ultimate  resistance  of 
the  chain  may  be  expected  to  vary  from  155  to  170  per  cent  of  that  of  the 
bar  used  in  making  the  links,  and  show  an  average  of  about  ]64  per  cent. 

''  That  the  proof  test  of  a  chain  cable  should  be  about  50  per  cent  of  tiie  i 
ultimate  resistance  of  the  weakest  link.*'  I 

The  decrease  of  the  resistance  of  the  studded  below  the  unstudded  cable 
is  probably  due  to  the  fact  that  in  the  former  the  sides  of  the  link  do  not 
remain  parallel  to  each  other  up  to  failure,  as  they  do  in  the  latter.  The  re- 
sult is  an  increase  of  stress  in  the  studded  link  over  the  unstudded  in  the 
proportion  of  unity,  to  the  secant  of  half  the  inclination  of  the  sides  of  Uie 
former  to  each  other. 

From  a  great  number  of  tests  of  bars  and  unfinished  cables,  the  commit- 
tee considered  that  the  average  ultimate  resistance,  and  proof  tests  of  cliain 
cables  made  of  the  bars,  whose  diameters  are  given,  should  be  such  as  are 
shown  in  the  accompanying  table. 


ULTIMATS  RBSISTANCB  AND  PROOF  TESTS  OF  CBAIN  CABLKS. 

Diam. 
of 
Bar. 

Average  resist. 
=  \mot  Bar. 

Proof  Test. 

Diam. 

of 

Bar. 

Average  resist. 
=  168)(of  Bar. 

Proof  Test. 

Inches. 

Pounds. 

Pounds. 

Inches. 

Pounds. 

Pounds. 

1  1/16 

71,178 

83,840 

1  9/a6 

162.283 

77.159 

1  1/16 

79.544 

87,820 

m 

174,475 

82.d56 

11/,. 

88.445 

42.053 

1  11/16 

187,075 

8S,947 

97,781 

46,468 

m 

200.074 

95,12S 

1  5/16 

107,440 

51,084 

1  13/16 

213.475 

101.499 

117.677 

55,903 

1  15/16 

227,271 

lOS.aVi 

11/16 

128,129 

60,920 

SM1,468 

114,806 

]:«,103 

66,138 

S 

256,040 

121,737 

IVi 

150,485 

71.650 

STBENGTH  OF  GLASS. 

(Falrbaim's  "  Useful  iuformaiiuu  for  Engineers,''  Second  Series.) 

Best         Commun    Extra  Whu^* 
Flint  (llasfl.  Ore«n(}liu«.  Crown  UU^a. 


Mean  specific  gravity  3.078 

Mean  tensile  strength,  lbs.  per  sq.  in.,  bars. .  2,413 

do.                           thin  plates.  4.900 

Mean  crush'g  strength,  lbs.  p.  sq.  in.,  cy I'drs.  27,-582 

do.                                   cubes.  13,180 


1.528 


S.4fiO 

2,516 

6.000 

81,0113 

21,867 

The  crushing  t<M«t3 


4,800 
89.876 
20,206 


The  bars  in  tensile  tests  were  about  X^  incli  diameter, 
were  made  on  cylindeix  al)oiit  ^4  inch  diameter  and  from  1  to  2  inches  lii^b. 
and  on  cul>es  approximately  1  inch  on  a  side.  The  mean  transverse  sti^ngth 
of  glass,  as  calculated  by  Fair  bairn  from  a  mean  tensile  strength  of  ;*i5tiO 
lbs.  and  a  mean  compressive  strength  of  30,150  lbs.  per  sq.  in.,  is,  for  a  bar 
supported  at  the  ends  and  loaded  in  the  middle, 

w  =  3140—-, 


BTBEKOTH  OF  TIMBEB. 


309 


In  which  to  s  breaking  weight  In  ibe.,  b  =  breadth,  d  s  depth,  and  2  a  length, 
in  Inches.  Actuai  tests  will  probably  show  wide  variauona  in  both  dlrec- 
lions  from  the  mean  calculated  strength. 

STREN GTBt  OF  COPPBB  AT  HIGH  TBREPBBATVRBflU 

The  British  Admiralty  conducted  some  experiments  at  Portsmouth  Dock- 
yard in  1877,  on  the  effect  of  increase  of  temperature  on  the  tensile  strength 
of  oc^>per  and  ▼arioua  bronaee.  The  copper  experimented  upon  was  in  rods 
.T^iu.  diameter. 

The  following  table  shows  some  of  the  results: 


Temperature 
Fahr. 

Tensile  Strength 
in  lbs.  per  sq.  in. 

Temperature 
Fahr. 

Tensile  Strength 
in  lbs.  per  sq.  in. 

Atma«plieric. 
200» 

98,115 
23,366 
23,110 

aoo" 

400° 
600« 

21,607 
21,105 
19.597 

Up  to  a  temperature  of  400<>  F.  the  loss  of  strength  was  only  about  10  per 
cent,  and  at  500"  F.  the  loss  was  16  per  cent.  The  temperature  of  steam  at 
8U0  lbs.  pressure  is  882"  F.,  so  that  according  to  these  experiments  the  loss 
or  strength  at  this  point  would  not  be  a  serious  matter.  Above  a  tempera- 
ture of  500"  the  strength  is  seriously  affected. 


STRENGTH    OF 

StrenCtlK  of  I<oiiK*]emf  Pine  (Yellow  Pine,  Pinua  Ftihutria)  from 
Alabama  (Bulletin  No.  8,  Forestry  Div.,  Dept.  of  Agriculture,  1888.  Tests 
by  Prof.  J.  B.  Johnson.) 

The  following  Is  a  condensed  table  of  the  range  of  results  of  mechanical 
tests  of  OTer  2000  specimens,  from  26  trees  from  four  different  sites  in 
Alabama ;  reduced  to  15  per  cent  moisture  : 


Speciflc  gravity  •  •  •  • 
Transversestrength,-  -^ 

do  do.  at  elast.  limit 
Mod.  of  elast.,  thous.  lbs. 
Belative  elast.  resilience. 

Inch-pounds  per  cub.  in. 
Crashing  endwise,  str.  per 

sq.  in.-lbs 

Crushing    across    grain, 

strength  per  sq.  in.,lbs. 
Tensile  strength  per  sq.  in. 
Shearing  strength   (with 

grain),  mean  per  sq.  in. 


Butt  Logs. 


0.449  to  1.089 

•1,762  to  16,200 

4,930  to  18,110 
1,119  to  3,ir 

0.28  to  4.60 

4,781  to   9,850 

675  to  2,094 
8,600  to  81,890 

464  to   1,299 


Middle  Logs.    Top  Logs. 


AvVof 

allBuU 

Logs. 


0.575  to  0.859  ,0.484 

7,640  to 

5,540  to 
1,180  to 


17,1284,268 

11,790  2,558 
2,982,    842 


1.84  to 

5,030  to 

656  to 
6,330  to 


4.21 

9,800 

1,445 
29,600 


too. 907 

to  15,554 

to  11,950 
to   2,697 

to  4.65 


09 
4,587  to  9,100 


584 
4,170 


to  1,766 
to  28,280 


589  to    1,280    484  to    1156 


0.767 

12,614 

9,460 
1,926 

2.96 


1,596 
17,859 

866 


Some  of  the  deductions  from  the  tests  were  as  follows  : 

1.  With  the  exception  of  tensile  strength  a  reduction  of  moisture  Is  ac- 
companied by  an  increase  in  ntrength,  stiffness,  and  toughness. 

2.  variation  In  st^rength  goes  generally  hand-in*hand  with  speciflc  gravity. 

3.  In  tlie  first  20  or  80  feet  in  height  the  values  remain  constant ;  then 
occurs  a  decrease  of  strength  whicli  amounts  at  70  feet  to  20  to  40  per  cent 
of  that  of  the  butt-log. 

4.  In  shearing  parallel  with  the  grain  and  crushing  across  and  parallel 
vith  the  grain,  practically  no  difference  was  found. 

5.  lATge  beams  appear  10  to  20  per  cent  weaker  than  small  pieces. 

6.  Compression  tests  endwise  seem  to  furnish  the  best  average  statement 
of  the  value  of  wood,  and  If  one  test  only  can  be  made,  this  is  tlie  safest,  as 
was  also  recognized  by  Bauschinger. 

7.  Bled  timber  is  in  no  respect  inferior  to  unbled  timber. 


310 


STRENGTH  OF  MATERIALS. 


The  fl^rea  for  cniahlnf?  across  the  fiT&lQ  represent  the  losd  required  to 
cause  a  compressiou  of  15  per  ceut.  Tne  relative  elaRtic  reRillence.  in  Inch- 
pouuds  per  cubic  iuch  of  the  material,  i»  obtained  by  measuring  the  area 
of  the  plotted-strain  diaif^ram  of  the  transvei-se  test  from  tlie  oilfdn  to  the 
poiut  in  the  curve  at  which  the  rate  of  deflection  is  fiO  per  cent  greater  tliao 
the  rate  in  the  earlier  part  of  the  test  where  the  diagram  is  a  straight  line. 
This  point  is  arbitraril}'  chosen  since  there  is  no  deflnite  "elastic  limit  **  in 
timber  as  there  is  in  iron.  The  '* strength  at  the  elastic  limit*'  is  the 
srrenf^h  taken  at  this  same  point.  Timber  is  not  perfectly  elastic  for  any 
load  if  left  on  any  great  length  of  time. 

The  long-leaf  pine  is  found  in  all  the  Southern  coast  states  from  North 
Carolina  to  Texas.  Prof.  Johnson  says  it  is  probably  the  strongest  timber 
in  large  sizes  to  be  had  in  the  United  States.  In  small  selected  specimens, 
other  species,  as  oak  and  hickory,  may  exceed  it  in  strength  and  tough- 
ness. The  other  Southei-n  yellow  pines,  viz.,  the  Cuban,  short-leaf  and 
the  loblolly  pines  are  inferior  to  the  long-leaf  about  in  the  ratios  of  their 
speciflc  gravities;  the  long-leaf  being  the  heaviest  of  all  the  pinee.  It 
averages  (kiln-dried)  48  pounds  per  cubic  foot,  the  Cuban  47,  the  short-leaf 
40,  and  the  loblolly  84  pounds. 

Strenstli  of  Sprnce  Timber.— The  modulus  of  rupture  of  spruce 
is  given  as  follows  by  different  authoi's :  Hatfield,  0900  lbs.  per  square  Inch  ; 
Rankine,  11,100 ;  Laslett,  U045 ;  Trautwiiie,  8100  ;  Rodman,  6168.  Traut- 
wine  advises  for  use  to  deduct  one- third  In  the  case  of  knotty  and  poor 
timber. 

Prof.  Lanza,  in  25  tests  of  large  spruce  beams,  found  a  modulus  of 
rupture  from  2995  to  5666  lbs.;  the  average  being  4618  lbs.  These  were 
average  beams,  ordered  from  dealers  of  good  repute.  Two  beams  of 
selected  stock,  seasoned  four  years,  gave  7662  and  8i48  lbs.  The  modulus 
of  elasticity  ranged  from  897,000  to  1,588,000,  averaging  1.'<MM,000. 

Time  tests  show  much  smaller  values  for  both  modulus  of  rupture  and 
modulus  of  elasticity.  A  beam  tested  to  5800  lbs.  in  a  screw  machine  was 
left  over  night,  and  the  resistance  was  found  next  morning  to  have  dropped 
to  about  SOOO,  and  it  broke  at  3500. 

Prof.  Lanza  remarks  that  while  it  was  necessary  to  use  larger  factors  of 
safety,  when  the  moduli  of  rupture  were  determined  from  tests  with  smaller 
pieces,  it  will  be  sufficient  for  most  timber  constructions,  except  in  factoriea, 
to  use  a  factor  of  four.  For  breaking  strains  of  beams,  he  states  that  it  Is 
better  engineering  to  determine  as  the  safe  load  of  a  timber  beam  the  load 
that  will  not  deflect  it  more  than  a  certain  fraction  of  its  span,  say  about 
1/800  to  1/400  of  its  length. 

Properties  of  Timber. 

(N.  J.  Steel  &  Iron  Co.'s  Book.) 


Description. 


Ash 

Beech 

Cedar 

Cherry 

Chestnut , 

Elm 

Hemlock 

Hiclcory , 

Locust 

Maple  

Oak,  White..,. 

Oak,  Live  

Pine,  White..., 
Pine,  Yellow.., 

Spruce 

Walnut,  Black 


48  to  55.8 
43  to  53.4 
50  to  56.8 


Weight 

per 

cubic 

foot,  in 
lbs. 


88 
84  to  36.7 


44 

49 
45  to  64.6 

70 

30 
28.8  to  33 


42 


Tensile 

Strength 

per  sq.  inch, 

in  lbs. 


11.000  to  17,207 
11,500  to  18,000 
10,300  to  11,400 


10,500 
13,400  to  13,489 

8.700 
12,800  to  18,000 
•20,.'500  to  24,800 
10,500  to  10.5vM4 
10,233  to  19,500 


10,000  to  19,000 
12.600  to  19,200 
10,000  to  19,500 
0.286  to  16.000 


Cnishing 

Strength  per 

sq.  inch, 

in  lbs. 


4,400  to  0,363 
5.K)0to  9,:«i3 
5,000  to  6,000 


5,350  to  5,600 
6,831  to  10,381 

5,700 

8,925 
9,113  to  11,700 

8,150 
4,684  to  9,609 

6,850 
5.000  to  6.650 
.5.400  to  9,500 
5,050  to  7,850 

7,500 


Relative 
Strength 
for  Cross 
Breaking. 

White 
Pine  =100. 


130  to  180 
100  to  144 
55  to  63 

180 
96  to  128 

96 
88  to  95 
150  to  210 
182  to  297 
122  to  220 
180  to  177 
165  to  189 
100 

98  torn 

86  to  110 


Shearing 
Strength 
with  the 
Grain, 
Ibe.  per 
sq.  inch 


458  to  TOO 


867  to  047 
759  to  960 

«»to42S 
886  to  415 
858  to  374 


8T&SKGTH  OF  tIMSES. 


311 


The  AbOT6  table  should  be  taken  vlth  caution.  The  range  of  Tariation  fn 
the  species  is  apt  to  be  much  greatBr  than  the  flfciires  indicate.  See  Johnson's 
xesU  on  lonff-leaC  pine,  and  Lanza's  on  spruce,  above.  The  weiffht  of  yellow 
pine  In  the  table  is  much  less  than  that  given  by  Johnnon.    (W.  K.) 

CompresalTe  Strength*  of  American  l¥oodS9  when  slowly 
and  carefully  «ecwon<?d.— Approximate  averaj^es,  deduced  from  many  exper- 
iments made  with  the  U.  8.  Government  testine- machine  at  Watertown, 
Mass..  by  Mr.  8.  P.  8harpless,  for  the  Census  of  1880.  Heasoned  woods  resist 
crushing:  much  better  than  green  ones;  in  many  cases,  twice  as  well.  DifTer- 
ent  specimens  of  the  same  wood  vai7  greatly.  The  strengths  may  readily 
UTj  as  much  as  one-third  part  more  or  less  from  the  average. 


AA.  red  and  white 
A^p^n.., ..«...«. 

Hefch 

Birch 

B^eteffe , 

Butternut 

^t^onwood 

(sycamore) 

Cctiar,  r«d 

C«dar,white  (arbor- 

vit«) 

Catalpa  (Ind.  bean) 
CAerry,  wild.... 

Ottuinut 

CoffteArte^  Ky. 
CypretB,  bald . . . 
Elm^  Am.  or  white 

*     red 

Hemlock 

Hickory 

lAgMoiuviicB 

litidfft,  American. 

Mack  and  yellow. 

honey. 

Jtohogany ... 

MapU: 

broad-leafed.  Ore. 


End- 
wise,* 
lbs.  per 
sq.  In. 


6800 
4400 
7000 
8000 
4400 
MOO 

6000 
6000 

4400 
SOOO 
8000 
5800 
5800 
6000 
6800 
770D 
6800 
8000 
10000 
SOOO 

S)800 
7000 
9000 

6800 


Side- 

wlse,+ 

lbs.  per 

sq.  m. 


.01   .1 


1300 
800 
1100 
1800 
600 
700 

1800 
700 

500 

700 
1700 

000 
1300 

500 
1800 
1800 

600 
2000 
1600 

500 

1000 
1600 
1700 

1400 


3000 
1400 
1000 
3600 
1400 
1600 

2600 
1000 

900 
1800 
2600 
1600 
2600 
1900 
2600 
2600 
1100 
4000 
13000 

000 

4400 
2600 
5300 

2600 


End- 
wise,* 
lbs.  per 
sq.  In. 


Maple : 

sugar  and  black. 

white  and  red.... 
Oak: 

white,  post  (or 
iron),  swamp 
white,  red,  and 
black... 

scrub  and  basket. 

chestnut  and  live 

pin 

Pme: 

white 

red  or  Norway... 

pitch  and  Jersey 
scrub 

Georgia 

Poplar 

SaMofras 

Spnicej  black... 
white.... 
Sycamore    (button* 

wood) 

Walnut : 

black 

white  tbutternut). 
Willow 


8000 
6800 


7000 
6000 
7600 
6600 

5400 
6800 

5000 
8500 
5000 
5000 
5700 
4500 

6000 

8000 
5400 
4400 


8tde. 

wise,+ 

lbs.  per 

sq.  in. 


.01 


1000  4800 
1800,2000 


1600  4000 
1700'4«)0 
1600  4.'')00 
1300  3000 


»600 
600 

1000 
1800 
600 
1800 
700 
600 

1300 

1800 
700 
700 


1200 
1400 

8000 
2600 
1100 
2100 
1800 
1200 

2600 

9600 
1600 
1400 


*  Specimens  1.57  ins.  square  X  19.6  ins.  long. 

t  Spenimena  1.57  ins.  square  X  6.3 ins.  long.  Pressure  applied  at  mid-length 
by  a  punch  covering  one-fourth  of  the  length.  The  fli-st  column  gives  llie 
loads  producing  an  indentation  of  .01  inch,  the  second  those  producing  un 
Ifldentation  of  .1  inch.    (See  also  page  306>. 

Krpmiurtoii  of  Ttmber  Hue  to  tlie  Absorption  of  'Wmter. 

(De  Volson  Wood,  A.  8.  M.  E.,  vol.  x.) 
Pieces  86  X  5  in.,  of  pine,  oak.  and  chestnut,  were  dried  thoroughly,  and 
thm  immersed  in  water  for  87  days. 
The  mean  per  cent  of  elongation  and  lateral  expansion  were: 

Pine,  Oak.  Chestnut. 

Elongration,  per  cent 0.065  0.085  0.165  ' 

liateral  expansion,  percent..  .  2.6  3.5  8.65 

Bxpansion  of  Wood  by  Heat.— Traut  wine  gives  for  the  expansion 
^*  white  pine  for  1  degree  Fahr.  1  part  in  440,580,  or  for  180  degrees  1  part  in 
2i{7,  or  a!bout  one-third  of  the  expansion  of  iron. 


813 


8TBBKGT&  OF  HAtfettlALS. 


Sheaiiiiff  Mrenfftb  of  American  irood«»  adapted  for 
Pins  or  Treenails, 

J.  C  Trautwlne  (Jour,  FrankUn  Inat),    (Shearing  across  the  grain.) 


per  sq.  in. 

Ash 6880 

Beech 6228 

Birch B695 

Cedar  (white) 1879 

"     1519 

Cedar  (Central  American) 8410 

Cherry 2945 

Chestnut 1586 

Dogwood 6510 

Ebony 7750 

Gum 6890 

Hemlock 2760 

Locust 7176 


per  sq.  in. 
Hickory «)45 

Maple.. .W.'.V'.. V.V .*.'.'." *.'*".".'.*. '.  6355 

Oak 4425 

Oak  (liTe) 8*90 

Pine  (white) 2480 

Pine  (Northern  yellow 4JM0 

Pine  (Southern  yeiiow)  ......  5735 

Pine  (very  resinous  yellow) 6068 

Poplar 4418 

Spruce 8255 

Walnut  (black) 4728 

Walnut  (common) S680 


THE  STRENGTH  OF  BRICK,  STONE,  ETC, 

A  great  advance  has  recently  been  made  in  the  manufacture  of  brick,  in 
the  direction  of  inci'easing  their  strength.  Chas.  P.  Chase,  in  Engineering 
Netos,  says:  ** Taking  the  tests  as  given  in  standard  engineering  books  eight 
or  ten  years  ago,  we  find  in  Tiuutwine  the  strength  of  brick  given  as  600  to 
4200  lbs.  per  sq.  in.  Now,  talcing  recent  tests  in  experiments  made  at 
Watertown  Arsenal,  the  strength  ran  from  6000  to  22,000  lbs.  per  sq.  in.  In 
the  tests  on  Illinois  paving  brick,  by  Prof.  I.  O.  Baker,  we  find  an  average 
strength  in  hard  paving  brick  of  over  6000  lbs.  per  square  inch.  The  average 
crushing  strength  of  ten  varieties  of  paving-brick  much  used  in  the  West,  I 
find  to  be  7150  lbs.  to  the  square  inch/' 

A  recent  test  of  brick  made  by  the  dry-clay  process  at  Watertown  Arsenal, 
according  to  Faving,  showed  an  average  compressive  strength  of  897i2  lbs. 
per  sq.  in.  In  one  instance  it  reached  4978  lbs.  per  !K].  in.  A  t«>8t  wa»  made 
at  the  same  place  on  a  ''fancy  pressed  brick."  The  first  crack  developed 
at  a  pressure  of  805.(K)0  lbs.,  and  the  brick  crushed  ai  864.300  lbs.,  or  11. ISO 
\b8.  per  sq.  in.  This  indicates  almost  as  great  cotnpressive  strength  as 
granite  paving-blocks,  which  is  from  12,000  lo  80,000  lbs.  |>er  sq.  in. 

The  following  notes  on  bricks  are  from  Trautwine*s  Engineer's  Pocket' 
book : 

Sfrengtln  of  Briek*— 40  to  800  tons  per  sq.  ft.,  622  to  4668  lbs.  per  sq.  in. 
A  soft  brick  will  crush  under  450  to  600  lbs.  per  sq.  in.,  or  80  to  40  tons  per 
square  foot,  but  a  first-rate  machine-pi-essed  brick  will  stand  200  to  400  tons 
per  sq.  ft.  (8112  to  6224  lbs.  per  sq.  in.). 

Iireiiclit  of  Bricks*— Per  cubic  foot,  best  pressed  brick,  150  lbs.:  (rood 

Fressed  brick,  181  lbs.;  common  hard  brick,  125  11m.;  good  common  brick. 
18  lbs.;  soft  inferior  brick,  100  lbs. 

Absorption  of  l¥ater«— A  brick  will  in  a  tftvr  minutes  abeorb  }4  to 
^  lb.  of  water,  the  last  being  1/7  of  the  weight  of  a  liand-moulded  one,  or  ^ 
of  its  bulk. 

Tests  of  Bricks,  tall  size,  on  flat  side*  (Tests  made  at  Water- 
town  Arsenal  in  1888.)— The  bricks  were  tested  betw^Nsn  flat  steel  buttress^es. 
Compressed  surfaces  (the  largest  surface)  ground  approximately  flat.  Tlie 
bricks  were  all  about  2  to  2.1  inches  thick,  7.5  to  8.1  inches  long,  and  8.5  to 
8.76  inches  wide.  Crushing  streng^th  per  square  inch:  One  lot  ranged  from 
1 1 ,056  to  16,784  lbs. :  a  second,  12,995  to  22,851 ;  a  third,  10,890  to  12,709.  Other 
testa  gave  results  from  5960  to  10.2.'50  lbs.  per  sq.  in. 

Crusliliur  Strenstk  of  Masonry  InateHals.  (From  Howe^s 
*'Betaining^all8."> 

tons  per  sq.  ft.  tons  per  sq.  ft. 

Brick,  best  pressed. .    40  to  800       Limestones  and  marbles.  250  to  1000 

Chalk 20to     30       Sandstone ISOto   550 

Granite 800tol200       Boapstone 400to   800 

Strenstk  of  Grmnlte*— The  crushing  strength  of  granite  Is  commonly 
rated  at  12,000  to  15,000  lbs.  per  sq.  in.  when  tested  in  two-inch  cubes,  and 
only  the  hardest  and  toughest  of  the  commonly  used  varieties  reacH  a 
strength  above  20,000  lbs.   samples  of  granite  from  a  quarry  on  the  Cox^ 


8TBEK0TH  OB  LIHE  AND  CEKENT  HOBTAB.       313 


D«etieat  River,  tested  at  the  Watertown  Arsenal,  have  shown  a  strength  oC 
K,983 lbs.  per sq.  in.  (EngineeringNews^  Jan.  13,  1808). 

Strenetli  of  ATondale.  P««,  lAtwaentone—(Engineei'ing  Netes^ 
»b.  9,  iai8>.— Crushing  strength  of  2-in.  cubes:  light  stone  18,112,  gray  stone 
1S.(M0.  Ibs.per8q.to.  -i      .r    j  ^ 

Transverse  test  of  lintels,  tool-dressed,  42  in.  between  knife-^ge  bear- 
ings, load  with  knife-edge  brought  upon  the  middle  between  bearings: 
Gray  stone,  section  6  In.  wide  X  10  in.  high,  broke  under  a  load  of  20,8S0  lbs. 

If  odulus  of  rupture 2,200    *• 

U^t  stone,  section  8^  in.  wide  X  10  in.  high,  broke  under 14,720    '* 

Modulus  of  rupture 1,170    " 

A.b8orption.->Oray  stone 051  of  lj( 

Light  stone 052  of  1^ 

Transrerse  Strengtli  of  Flacstns. 

(N.  J.  Steel  &  Iron  Co/s  Book.) 
EzpBRtnim  itADB  BT  R.  O.  Hatticld  uro  Others. 
h  =  width  of  the  stone  in  Inches;  d  =  its  thickness  in  inches;  I  s  distance 
between  bearings  In  inches. 

The  breakingloadM  in  tons  of  2000  lbs.,  for  a  weight  placed  at  the  centre 
of  the  space,  will  be  as  follows: 

6d«. 


Bliiestone  flagging 744 

Quincy  granite 6^4 

Little  Falls  freestone 57V 

BeUeTille,  N.  J.,  freestone 480 

< jranite  (another  quarry) 432 

Connecticut  freestone 313 

Thus  a  block  of  Qulncy  granite  80  inches  wide  and  6  Inches  thick,  resting 
on  beams  06  inches  in  the  clear,  would  be  broken  by  a  load  resting  midway 


Dorchester  freestone .*.....    J264 

Aubigny  freestone 210 

Caeu  freestone 144 

Glass 1.000 

Slate 1.2  to  2.7 


between  the  beams  = 


80X30 
86 


X  .834  =  40.02  tons. 


STRENGTH  OF  IiUITB  AN1»  CBmXKT  MOBTAB. 
(Engineering^  October  2, 1891.) 
Tests  made  at  the  University  of  Illinois  on  the  effects  of  adding  cement  to 
lime  mortar.  In  all  the  tests  a  good  quality  of  ordinary  fat  lime  was  used, 
slaked  for  two  days  in  an  earthenware  jar,  adding  two  parts  by  weight  of 
water  to  one  of  lime,  the  loss  by  evaporation  being  made  up  by  fresh  add!- 
lions  of  water.  The  cements  used  were  a  German  Portland,  Black  Diamond 
il»uisville),  and  Bosendale.  As  regards  fineness  of  grinding,  85  per  cent  of 
tbur  Piortlaiid  passed  through  a  No.  100  sieve,  as  did  72  per  cent  of  the  Bosen- 
dale. A  fairly  sharp  sand,  thoroughly  washed  and  dried,  passing  through  a 
No.  18  sieve  and  caught  on  a  No.  80,  was  used.  The  mortar  In  all  cases  con- 
listed  of  two  volumes  of  sand  to  one  of  lime  paste.  The  following  results 
vcre  obtained  on  adding  various  percentages  of  cement  to  the  mortar: 


Tensile  Strenfftb 

,  poanda  per  square  Incb. 

Age - 

4 

7 

14 

21 

28 

60 

84 

Days. 

Days. 

Days. 

Days. 

Days. 

Days. 

Days. 

L'me  mortar 

4 

8 

10 

13 

18 

21 

26 

3>n*»r 

cent  Bosendale.. 

6. 

^ 

OH 

12 

17 

17 

18 

2D    - 

"     Portland.... 

5 

14^ 

20 

25 

24 

26 

an  »* 

**     Bosendale.. 

7 

11 

18 

18^ 

21 

22^ 

28 

»  '• 

'•     Portland.... 

8 

16 

18 

22 

25 

28 

27 

«  *• 

••      Bosendale.. 

10 

12 

10^ 

21^ 

22^ 

24 

86 

40    '• 

"      Portland..  . 

27 

89 

88 

48 

47 

59 

57 

«)    ** 

**      Bosendale.. 

9 

18 

20 

16 

2i 

^i^ 

28 

60    " 

'•      Portland.... 

45 

56 

55 

68 

67 

102'^ 

78 

iO   •• 

**      Bosendale.. 

12 

im 

22H 

27 

29 

81H 

as 

80    " 

••     Portland.... 

87 

91 

103 

124 

94 

210 

145 

W   - 

•*      Bosendale.. 

18 

28 

26 

81 

34 

46 

48 

W   - 

'•      Portland.... 

00 

120 

146 

152 

m 

205 

202 

314  8TBBXOTH  OF  KATERIAL8.  > 

MOBUIiI  0F  BIiASTICITT  OF  VAlftlOVS  MATBMIJLMA 

The  modulus  of  elasticity  detennineil  from  a  tensile  test  of  »  bar  of  any 
material  is  the  quotient  obtained  by  dividing  the  tensile  streas  in  pounds  per 
flquare  inch  at  any  point  of  the  (est  by  the  elongation  per  inch  of  length 

Sroduced  by  that  stress  ;  or  if  P  c=  pounds  of  stress  applied,  K  =  the  sec* 
onal  area,  I  =  length  of  the  portion  of  the  bar  in  Avhich  the  meaaure- 
ment  is  made,  and  A  =  the  elongation   in  that  length,  the  modulus  of 

P      ii      PI 
elasticity  ^=  i^  +  r  =  Yk'    "^^  modulus  is  generally  measured  withtb  the 

elastic  limit  only,  in  materials  that  have  a  well-defined  elastic  limit,  such  as 
iron  and  steel,  and  when  not  otherwise  stated  the  modulus  is  understoud  to 
be  the  modulus  within  the  elastic  limit.  Within  this  limit,  for  such  materials 
the  modulus  is  practically  constant  for  anv  given  bar,  the  elongation  being 
directly  proportional  to  the  stress.  In  other  materials,  such  as  <sast  iron, 
which  have  no  well-deflned  elastic  limit,  the  elongations  from  the  befclnning 
of  a  test  increase  in  a  greater  ratio  than  the  stresses,  and  the  modulus  is 
therefore  at  its  maximum  near  the  beginning  of  the  test,  and  continually 
decreases.  The  moduli  of  elasticity  of  various  materials  have  already  been 
given  above  in  treating  of  these  materials,  but  the  following  table  gives 
home  additional  values  selected  from  different  sources : 

Brass,ca8t 9,170.000 

"   wire 14,230,000 

er 15,000,000  to  18,000,000 

1,000,000 

Tin.  cast 4,800,000 

Iron,  cast 18.000.000  to  87.000.000(f) 

Iron,  wrought. fi^\000,000  to  20,000,000  (n 

Steel ;..... 88,000.000  to  82,000,000  (see  below) 

Marble 85,000,000 

Slate. 14,500,000 

Glass 8,000.000 

Ash. l.COO.OOO 

Beech 1,300,000 

Birch 1,850,000  to    1,600,000 

Fir 869,000  to    8,101,000 

Oak  074,000  to    2,288,000 

Teak 3,414,000 

Wahiut 806,000 

Pine. long-leaf  (butt-lo«8)...  1,119,000  to  8,117,000  Avge.  l,flMk,0QO 
The  maximum  figures  given  by  many  writers  for  iron  and  stecL  Tis^ 
40,000,000  and  42,000,090,  are  undoubtedly  erroneous.  The  modulus  of  elas- 
ticity of  steel  (within  the  elastic  limit)  is  remarkably  constant,  notwithstand- 
ing great  variations  in  chemical  analysis,  temper,  etc.  It  rately  Is  found 
below  29,000,000  or  above  31,000,000.  It  is  generally  taken  at  80,000,000  in 
engineeiing  calculations.  Prof.  J.  B.  Johnson,  in  his  report  on  Long-leaf 
Pine,  1893,  says :  **  The  modulus  of  elasticity  is  the  most  constant  and  reliable 
property  of  all  engineering  materials.  The  wide  range  of  value  of  the 
modulus  of  elasticity  of  the  various  metals  found  in  public  records  must  bo 
explained  by  erroneous  methods  of  testing.'* 

In  a.tf  nslie  test  of  cast  iron  by  the  author  (Van  Nostrand*s  Science  Series, 
Ko.  41,  page  45),  in  which  the  ultimate  strength  was  24,285  lbs.  per  sq.  in., 
the  meanurements  of  elongation  were  made  to  .0001  inch,  and  the  modulus 
of  elasticity  was  found  to  liecrease  from  the  beginning  of  the  test,  as 
follows:  At  1000  lbs.  per  sq.  in.,  25.000,000;  at  2000  lbs..  ]i5,666,000 ;  at  4000 
Hm.,  15.381,000  ;  at  COUO  lbs.,  18,686,000  ;  at  HOOO  lbs.,  12.500.000;  at  12,000  lbs.. 
11,250,000 ;  at  15,000  lbs.,  10,000,000;  at  20,000  lbs.,  8,000,000 :  at  88,000  Ibs^ 
•.140.000. 

FACTORS  OP  SAFETY. 
A  factor  of  safety  is  the  ratio  in  which  the  load  that  is  just  sufBcient  to 
overcome  Instantly  the  strength  of  a  piece  of  material  is  greater  than  the 
greatest  safe  ordinary  working  load.    ( Rantdne. ) 

Rankine  gives  the  following  *'  examples  of  the  values  of  those  faetons 
which  occur  in  machines  ": 

r\^^A  T  r^^A      Live  Load,        Uve  Load, 
Dead  Load.       (jreatST  MeanT^ 

Iron  and  steel  3  0  from  6  to  40 

Timber 4to5  8tolO 

Masonry 4  8  l-  ••#•     -^ 


PACTOBS  OF  safety;  815 

The  great  factor  of  safety,  40,  Is  for  sbafU  i&  mUIwoxic  which  traDsrait 
rery  variable  efforts. 

Lnvrin  gives  the  foUowIng  "  factors  of  safety  which  have  been  adopted  in 
certain  cases  for  different  materials.^'  They  "  Include  an  allowance  for 
ordinary  contingencies.*^ 


Dead 


-Live  Load.' 


tTtJi  In  Temporary  In  Permanent    In  Structures 

*^*^"*  Structures.  Structures,     nibl.  to  Shocks. 

Wrought  Iron  and  steel.     8  4  4  to  5  10 

Castiron...  8  4  6  10 

Timber. 4  10 

Brickwork ....  6  .... 

Masonry. 90  ....  SOtoSO 

Unwin  says  says  that  *'  these  numbers  fairly  represent  practice  based  on 
experience  In  many  actual  cases,  but  tliey  are  not  very  trustworthy.'* 

Prof.  Wood  in  his  *' Resistance  of  Materials*'  says:  **In  regard  to  the 
marzin  that  should  be  left  for  safety,  much  depends  upon  the  character  of 
the  loading.  Xf  the  load  is  siiuply  a  dead  weight,  the  margin  may  be  com- 
paratively small;  but  if  the  structure  is  to  be  subjected  to  percussive  forces 
or  shoelcs,  the  margin  should  be  comparatively  large  on  account  of  the 
indeterminate  effect  produced  by  the  force.  In  machines  which  are  sub- 
)ected  to  a  constant  jar  while  in  use,  it  la  veiy  difficult  to  determine  the 
proper  margin  which  is  consistent  with  economy  and  safety.  Indeed,  in 
such  eases,  economy  as  well  as  safety  generally  consists  in  making  them 
excesUveiy  strong,  as  a  single  brealcage  may  cost  much  more  than  the  extra 
msterial  neoessaiy  to  fully  insure  safety." 

For  discussion  of  the  resistance  of  materials  to  repeated  stresses  and 
ibocks,  see  pages  888  to  24a 

Instead  of  using  factors  of  safety  it  is  becoming  customary  In  designing 
to  fix  a  certain  number  of  pounds  per  square  inch  as  the  maximum  stress 
which  will  be  allowed  on  a  piece.  Thus,  hi  designing  a  boiler,  instead  of 
samlng  a  factor  of  safety  of  6  for  the  plates  and  10  for  the  stay-bolts,  the 
ultimate  tensile  strength  of  the  steel  being  from  S0,000  to  80,000  lbs.  per  sq.  in., 
an  allowable  working  stress  of  10,000  lbs.  per  sq.  In.  on  the  plates  ana  6000 
lbs.  per  sq.  In.  on  the  stay-bolts  may  be  specified  instead.  So  also  in 
Merriman's  formula  for  columns  (see  page  200)  the  dimensions  of  a  column 
are  calculated  after  assuming  a  maximum  allowable  compressive  stress  per 
square  Inoh  on  the  concave  side  of  the  column. 

The  factors  for  masonry  under  dead  load  as  given  by  Rankine  and  by  Un  win. 
Til.,  4  and  20,  show  a  remarkable  difference,  which  may  possibly  be  explained 
as  follows :  If  the  actual  crushing  strength  of  a  pier  of  masonry  is  known 
from  direet  experiment,  then  a  factor  of  safety  of  4  is  sufficient  for  a  pier  of 
tiie  same  aixe  and  quality  under  a  steady  load;  but  if  the  crushing  strength 
is  merely  assumed  from  figures  given  by  the  authorities  (such  as  the  cnmh- 
iag  strength  of  pressed  brick,  quoted  above  from  Howe^s  Retaining  Walls,  40 
to  800  tons  per  square  foot,  average  170  tons),  then  a  factor  of  safety  of  20 
Biay  be  none  too  great.  In  this  case  the  factor  of  safety  is  really  a  "  factor 
of  ignoraaoe.** 

The  selection  of  the  proper  factor  of  safety  or  the  proper  maximum  unit 
ftress  for  any  given  case  is  a  matter  to  be  largely  determined  by  the  judg> 
ment  of  the  engineer  and  by  experience.  No  definite  rules  can  be  given. 
The  customary  or  advisable  factors  in  many  particular  cases  will  be  found 
nhere  these  eases  are  considered  throughout  this  book.  In  general  the 
fallowing  circumstances  are  to  be  taken  into  account  in  the  selection  of 
a  factor: 

1.  When  the  ultimate  strength  of  the  material  is  known  within  narrow 
Kmita,  as  in  the  case  of  structural  steel  when  tests  of  samples  have  been 
made,  when  the  load  is  entirely  a  steady  one  of  a  known  amount,  and  there 
i«iio  reason  to  fear  the  deterioration  of  the  metal  by  corrosion,  the  lowest 
fictar  that  should  be  adopted  is  8. 

1  When  the  circumstances  of  1  are  modified  by  a  portion  of  the  load  being 
Tuii^le,  as  in  floors  of  warehouses,  the  factor  should  be  not  less  than  4. 

3.  When  the  whole  load,  or  nearly  the  whole,  is  apt  to  be  alternately  out 
tm  and  taken  off,  as  In  suspension  rods  of  floors  of  bridges,  the  factor  should 
beSorS. 

1  When  the  stresses  are  reversed  in  direction  from  tension  to  compres- 
BGo,  as  in  some  bridge  diagonals  and  parts  of  machines,  the  factor  aliould 
te  not  toss  than  8. 


816  STRENGTH  OP  MATERIALS. 

B.  When  the  piece  is  subjected  to  repeated  shocks,  the  factor  should  be 
not  less  than  10. 

0.  When  the  piece  Is  subject  to  deterioration  from  corrosion  the  section 
should  be  sufficiently  increased  to  allow  for  a  definite  amouni  of  oorroelon 
before  the  piece  be  so  far  wealcened  by  it  as  to  require  removal. 

7.  When  the  strength  of  the  material,  or  the  amount  of  the  load,  or  bolh 
are  uncertain,  the  factor  should  be  increased  by  an  allowance  sufficient  to 
coyer  the  amount  of  the  uncertainty. 

8.  W^hen  the  strains  are  of  a  complex  character  and  of  uncertain  amount, 
such  as  those  in  the  crank-shaft  of  a  reversing  eni^ne.  a  very  hii?h  factor  is 
necessary,  possibly  even  as  high  as  40,  the  figure  given  by  Rankine  for  shafts 
in  mUlwork. 

TH£  MECHANICAIj  PROPERTIB8  OF  CORK. 

Cork  possesses  qualities  which  distinguish  it  from  all  other  solid  or  liquid 
bodies,  namely,  its  power  of  altering  its  volume  in  a  very  marked  degree  in 
consecmDce  of  change  of  pressure.  It  consists,  practically,  of  an  aggreara- 
tion  of  minute  air-vessels,  having  thin,  water-tight,  and  very  strong  walls, 
and  hence,  if  compressed,  the  resistance  to  compression  rises  in  a  manner 
more  like  the  resistance  of  gases  than  the  resistance  of  an  elastic  solid  such 
as  a  spring.  In  a  spring  the  pressure  increases  in  proportion  to  the  dis- 
tance to  which  the  spring  is  compressed,  but  with  gases  the  pressure  In- 
creases in  a  much  more  rapid  manner;  that  Is,  inversely  as  the  volume 
which  the  gas  is  made  to  occupy.  But  from  the  permeability  of  cork  to 
air,  it  is  evident  that,  if  subjected  to  pressure  in  one  direction  only,  it  will 
gradually  part  with  its  occluded  air  by  effusion,  that  is,  by  its  passage 
through  the  porous  walls  of  the  cells  in  which  it  is  contained.  The  gaseous 
part  of  cork  constitutes  6»%  of  its  bulk.  Its  elasticity  has  not  only  a  very- 
considerable  range,  but  it  in  very  pensistent.  Thus  in  the  better  Mod  of  corks 
used  in  bottling  the  corks  expand  the  instant  thev  escape  from  the  bottles. 
This  expansion  may  amount  to  an  increase  of  volume  of  75j(,  even  after  the 
corks  have  been  kept  in  a  state  of  compression  in  the  bottles  for  ten  years. 
If  the  cork  be  steeped  in  hot  water,  the  volume  continues  to  Increase  till 
It  attains  nearly  three  times  that  which  It  occupied  in  the  neck  of  the  bottle. 

When  cork  is  subjected  to  pressure  a  certain  amount  of  permanent  defor- 
mation or  **  permanent  set ''  takes  place  very  quicklv.  This  property  Is 
common  to  all  solid  elastic  substances  when  strained  beyond  tneir  elastic 
limits,  but  with  cork  the  limits  are  comparatively  low.  Besides  the  perma-> 
nent  set.  there  is  a  certain  amount  of  sluggish  elasticity— that  is,  cork  on 
being  released  from  pressure  springs  baclc  a  certain  amount  at  once,  btic 
the  complete  recovery  takes  an  appreciable  time. 

Cork  which  had  been  compressed  and  released  in  water  many  thousand 
times  had  not  changed  its  molecular  structure  in  the  least,  and  had  contin- 
ued perfectly  serviceable.  Cork  which  has  been  kept  under  a  pressure  of 
three  atmospheres  for  many  weeks  appears  to  have  shrunk  to  from  80je  to 
85)t  of  its  original  volume.— Finn  Noatrand^s  Eng'g  Mag.  1880,  xxxv.  a07. 
TB8T8  OF  VUIiCANiaEED  INBIA-SrBBEB. 

Lieutenant  L.  Yladomiroff,  a  Russian  naval  officer,  has  recently  carried 
out  a  series  of  tests  at  the  St.  Petersburg  Technical  Institute  with  a  view  to 
establishing  rules  for  estimating  the  quality  of  vulcanized  india-rubber. 
The  following,  in  brief,  are  the  conclusions  arrived  at,  recourse  being  had 
to  physical  properties,  since  chemical  analysis  did  not  give  any  reliable  re- 
sult: 1.  India- rubl>er  should  not  give  the  least  sign  of  superficial  crackln^c 
when  bent  to  an  angle  of  180  degrees  after  five  hours  of  exposure  in  a  closed 
air-bath  to  a  temperature  of  125°  C.  The  test-pieces  should  be  2.4  inches 
iJ^ck.  2.  Rubber  that  does  not  contain  more  than  half  its  weight  of  metaU 
lie  oxides  should  strt^tch  to  five  times  its  length  without  breaking.  3.  Rub. 
ber  free  from  all  foreign  matter,  except  the  sulphur  used  in  vuIcanhdnK  it, 
should  stretch  to  at  least  seven  times  its  length  without  rupture.  4.  The 
extension  measured  immediately  after  rupture  should  not  exceed  189(  of  the 
original  length,  with  given  dimensions.  5.  Suppleness  may  be  determined 
by  measuring  the  percentage  of  ash  formed  in  incineration.  This  may  form 
tne  basis  for  deciding  between  different  grades  of  rubber  for  certain  pur- 
poses.  6.  Vulcanized  rubber  should  not  harden  under  cold.  These  rules 
have  been  adopted  for  the  Russian  navy.— Iron  Age^  June  15,  18S>3. 

XYIiOIilTH,  OB  WOOBSTONB 
is  a  material  invented  in  1883,  but  only  lately  Introduced  to  the  trade  by 
Qtto  Serrig  ^  Co.,  of  Pottscbappel,  near  Dresden.    It  is  made  of  magnesia 


ALUMIKUK— ITS  PB0PERTIE8  AND  USES.  317 

eement,  or  cftlcined  magnesite,  mixed  with  tawduBt  and  saturated  with  a 
solation  of  chloride  of  calcium.  This  pastv  ixiaas  is  spread  out  into  sheets 
and  submitted  to  a  pressure  of  about  1000  lbs.  to  the  square  inch,  and  then 
simply  dried  in  the  air.  Specific  fcravity  1.558.  The  fractured  surface  shows 
a  uniform  close  grain  of  a  yellow  color.  It  has  a  tensional  resistance  when 
dry  of  100  Iba.  per  square  inch,  and  when  wet  about  66  lbs.  When  immersed 
in  water  for  IS  hours  it  talcee  up  2.1](  of  its  weight,  and  S.9%  when  Immersed 
216  hours. 

When  treated  for  several  davs  with  hydrochloric  add  it  loses  2.Z%  in 
weight,  and  shows  no  loss  of  weight  under  boiling  in  water,  brine,  soda-lye, 
and  solution  of  sulphates  of  iron,  of  copper,  and  of  ammonium.  In  hardness 
the  material  stands  between  feldspar  and  quarts,  and  as  a  non-conductor  of 
heat  it  ranks  between  asbestos  and  cork. 

It  stand;;  Are  well,  and  at  a  red  heat  it  is  rendered  brittle  and  crumbles  at 
the  edgea.  but  retains  its  general  form  and  cohesion.    This  zylolith  is  sup- 


plied  in  siieets  from  ^  in.  to  lU  in.  thick,  and  up  to  one  metro  square.  It 
B  eztensiTely  used  in  Germany  for  floors  in  railway  stations,  hospitals,  etc., 
and  for  decks  of  Teasels.  It  can  be  sawed,  bored,  and  shaped  witn  ordinary 
woodworking  tools.  Putty  in  the  joints  and  a  good  coat  of  paint  make  ft 
eoUrely  water-proof.  It  is  sold  in  Germany  for  flooring  at  about  7  cents  per 
square  foot,  and  the  cost  of  laying  adds  about  4  cents  more.— JEVij/'o  New». 
July  28.  1802,  and  July  87, 1808. 

AI«IT1IIINITBI-IT8    PROPEHTIE8    ANB  USES. 
(By  Alfred  £.  Hunt,  Pres't  of  the  Pittsburgh  Reduction  Co.) 

The  ftpeciflo  gravity  of  pure  aluminum  in  a  cast  state  is  2.58  :  in  rolled 
bars  of  large  section  it  is  2  6 ;  in  very  thin  sheets  subjected  to  high  com- 
pression under  chilled  rolls,  it  is  as  much  as  2.7.  Talcing  the  weight  of  a 
l^Ten  bulk  of  cast  aluminum  as  1,  wrought  iron  is  2.00  times  heavier ;  struc- 
Tural  steel,  2.95  times ;  copper,  8.00  ;  ordinary  high  brass.  8.45.  Most  wood 
suitable  for  use  in  structures  has  about  one  third  the  weight  of  aluminum, 
which  weighs  0.002  lb.  to  the  cubic  inch. 

Pure  aluminum  Is  practically  not  acted  upon  by  boiling  water  or  steam. 
Carbonic  oxide  or  hydrogen  sulphide  does  not  act  upon  it  at  any  tempera- 
lore  under  OOO"  F.    It  is  not  acted  upon  by  most  organic  secretions. 

Hydrochloric  acid  is  the  best  solvent  for  aluminum,  and  strong  solutions 
of  caustic  alkalies  readily  dissolve  it.  Ammonia  has  a  slight  solvent  action, 
and  concentrated  sulphuric  acid  dissolves  aluminum  upon  heating,  with 
erolntion  of  sulphurous  acid  gas.  Dilute  sulphuric  acid  acts  but  slowly  on 
the  metal,  though  the  presence  of  any  chlorides  in  the  solution  allow  rapid 
d<vompoeition.  Nitric  acid,  either  concentrated  or  dilute,  has  very  little 
action  upon  the  metal,  and  sulphur  has  no  action  unless  the  metal  is  at  a  red 
l>9it.  8ea-water  has  very  little  effect  on  aluminum.  Strips  of  the  metal 
idaced  on  the  sides  of  a  wooden  ship  corroded  less  than  1/1000  inch  after  six 
months*  exposure  to  sea-water,  corroding  less  than  copper  sheets  similarly 
pi%ced. 

In  malleabnity  pure  aluminum  is  only  exceeded  by  gold  and  silver.  In 
ductility  it  stands  seventh  in  the  series,  being  exceeded  by  gold,  silver, 
piatmnm.  Iron,  very  soft  steel,  and  copper.  Sheets  of  aluminum  have  been 
roiled  down  to  a  thickness  of  0.0006  inch,  and  beaten  into  leaf  nearly  as 
tbin  as  gold  leaf.  The  metal  is  most  malleable  at  a  temperature  of  between 
490*  and  000^  F.,  and  at  this  temperature  it  can  be  drawn  down  between 
rolls  with  nearly  as  much  draught  upon  it  as  with  heated  steel.  It  has  also 
been  drawn  down  into  the  verr  flnest  wire.  By  the  Mannesmann  process 
alunimim  tubes  have  been  made  in  Germany. 

Aluminum  stands  very  high  in  the  series  as  an  electro-positive  metal,  and 
eiwtact  with  other  metals  should  be  avoided,  as  it  would  establish  a  galvanic 

Theelectrfcal  conductivity  of  aluminum  is  only  surpassed  by  pure  copper, 
^ver,  mnd  gold.  With  silver  taken  at  100  the  electrical  conductivity  of 
tfaiminnni  fa  64.90 ;  that  of  gold  on  the  same  scale  is  78;  zinc  is  29.90;  iron  is 
c'ttly  16,  and  platinum  10.60.  Pure  aluminum  has  no  polarity,  and  the 
cwtal  in  the  market  is  absolutely  non-magnetic. 

Sound  castings  can  be  made  of  aluminum  in  either  dry  or  "  green  "  sand 
inoQlda,  or  In  metal  **  chills.''  It  must  not  be  heated  much  beyond  its 
i^fidng-pofnt,  and  must  be  poured  with  care,  owing  to  the  ready  absorption 
fi  occluded  leases  and  air.  The  shrinkage  in  cooling  is  17/64  inch  per  fooC, 
T  a  little  more  than  ordinary  brass.  It  should  be  melted  in  plumbago 
cmdbles,  and  the  metal  becomes  molten  at  a  temperature  of  llsO"  F.  ac« 
eording  to  Professor  Boberts- Austen,  or  at  i:X)0<*  F.  according  to  Richards. 


318  '  STREKGTH   OP  JiATKRTALS. 

The  coefRcIent  of  linear  expansion,  as  teBted  on  ^-fnch  ronnd  &1uBibiim^ 
rods,  Is  O.OOOOiHOR  per  degree  centigrade  between  tiie  freezing  and  boiling 
point  of  water.  Tlie  mean  specific  neat  of  aluminum  is  higher  than  that  ot 
any  other  metal,  excepting  only  magnesium  and  the  alkali  metals.  From 
zero  to  the  melting-point  le  is  0.2185;  water  being  taken  as  1,  and  the  latent 
heat  of  fusion  at  28.5  heat  units.  The  coeilicient  of  thermal  conductivity  of 
unannealed  aluminum  is  87.96;  of  annealed  alnminum,  88.87.  As  a  conductor 
of  heat  aluminum  ranks  fourth,  being  exceeded  only  by  silver,  copper,  and 
gold. 

Aluminum,  under  tension,  and  section  for  section,  is  about  as  stroni?  afi 
cost  iron.  The  tensile  strength  of  aluminum  is  increased  by  cold  rolling:  or 
cold  forging,  and  there  are  alloys  which  add  considerably  to  the  tensile 
strength  without  increasing  the  specific  gravity  to  over  8  or  8.25. 

The  strength  of  commercial  aluminum  is  given  in  the  following  table  as 
the  result  of  many  tests : 

Elastic  Limit        XTItimate  Strength     Percentage 
per  sq.  in.  in  per  sq.  in.  in  of  Reduct'n 

Form.  Tension,  Tension,  of  Area  in 

lbs.  lbs.  Tension. 

Castings fi,600  15,000  15 

Sheet 12,000  24,000  S5 

Wire. 16.000-80.000  80,000-65,000  ISO 

Bars.  14,000  88,000  40 

The  elastic  limit  per  square  inch  under  compression  in  cylinders,  with 
length  twice  the  diameter,  is  3500.  The  ultimate  strength  per  square  inch 
under  compression  in  cylinders  of  same  form  is  12,000.  The  modulus;  of 
elasticity  of  cost  aluminum  is  about  11 ,000,000.  It  is  rather  an  open  metal  in 
its  texture,  and  for  cylinders  to  stand  pressure  an  increase  in  thickness  must 
be  given  to  allow  for  this  porosity.  Its  maximum  shearing  stress  in  caatiogs 
Is  about  12,000,  and  in  forgings  about  16,000,  or  about  that  of  pure  copper. 

Pure  aluminum  is  too  soft  and  lacking  in  tensile  strength  and  rigidity  for 
many  purposes.  Valuable  alloys  are  now  being  made  which  seem  to  Rive 
great  promise  for  the  future.  They  are  alloys  containing  from  2j(  to  7}(  or  8< 
of  copper,  manganese,  iron,  and  nickel.  As  nickel  is  one  of  the  principal 
constituents,  these  alloys  have  the  trade  name  of  **  Nickel-aluminum.^' 

Plates  and  bars  of  this  nickel  alloy  have  a  tensile  strength  of  from  40,000  to 
50,000  pounds  per  square  inch,  an  elastic  limit  of  55jC  to  60%  of  the  ultimate  ten- 
sile strength,  an  elongation  of  20^  In  2  inches,  and  a  reduction  of  area  of  ^SjC. 

This  metal  is  especially  capable  of  withstanding  the  punishment  and 
distortion  to  which  structural  material  is  ordinarily  subjected.  Nickel- 
aluminum  alloys  have  as  much  resilience  and  spring  as  the  veiy  hardest  of 
hard-drawn  brass. 

Their  speciflo  gravity  Is  about  2.80  to  2.85,  where  pure  aluminum  bas  a 
specific  gravity  of  2.72. 

In  castings,  more  of  the  hardening  elements  are  necessary  In  order  to  criv-e 
the  maximum  stiffness  and  rigidity,  together  with  the  strength  and  ductultr 
of  the  metal;  the  favorite  alloy  material  being  zinc.  Iron,  manganese,  and 
copper.  Tin  added  to  the  alloy  reduces  the  shrinkage,  and  alloys  of  alumi« 
num  and  tin  can  be  made  which  have  less  shrinkage  than  cast  iron. 

The  tensile  strength  of  hardened  aluminum-alloy  castings  Is  from  20,000 
to  25.000  pounds  per  square  inch. 

Alloys  of  aluminum  and  copper  form  two  series,  both  valuable.  The 
first  Is  aluminum  bronze,  containing  from  5^  to  IIU^  of  aluminum;  and  the 
second  is  copper-hardened  aluminum,  containing  from  2^  to  15^  or  copper 
Aluminum-bronze  is  a  very  dense,  line-gi-ainedj_aud  strong  alloy,  havinir  Rood 
ductility  as  compared  with  tensile  strength.  The  \Q%  bronze  in  forged  barn 
will  give  100,000  lbs.  tensile  strength  per  square  inch,  with  60.000  lbs.  elAatic 
limit  per  square  inch,  and  lOjl  elongation  in  8  Inches.  The  ^  to  7y0L  bronze 
has  a  speciAc  gravity  of  8  to  8.30.  as  compared  with  7.50  for  the  iO%  to  11|4< 
bronze,  a  tensile  strength  of  70,000  to  80,000  lbs.,  an  elastic  limit  of  40,WO 
lbs.  per  square  inch,  and  an  elongation  of  80^  In  8  Inches. 

Aluminum  is  used  by  steel  manufacturers  to  prevent  the  retention  of  the 
occluded  gases  in  the  steel,  and  thereby  produce  a  solid  Ingot.  The  propor* 
tlons  of  the  dose  ranire  from  k|  lb.  to  several  pounds  of  aluminum  per  ton  of 
steel.  Aluminum  is  also  used  in  giving  extra  fiuid ity  to  steel  used  In csstlnmu 
making  them  sharper  and  sounder.  Added  to  cast  iron,  aluminum  cau^M 
the  iron  to  be  softer,  free  from  shrinkage,  and  lessens  the  tendency  to  * '  oliiU  ^* 

With  the  exception  of  lead  and  mercury,  aluminum  unites  with  all  "»**^ala 


iXLOTS. 


319 


Uioogrh  It  nnltes  with  antimony  with  great  dlAcolty.  A  nsall  percentage 
of  silver  whitens  and  hardens  the  metal,  and  rives  It  added  strength;  and 
this  alloy  is  especially  appllcabln  to  the  roanufacture  of  fine  Instruments 
and  apparatus.  The  lollowlng  alloys  have  been  found  recent^  to  be  useful 
in  the  arts:  Nickel-aluminum,  composed  of  20  paru  nickel  to  80  of  aluminum : 
rosine,  made  of  40  parts  nickel,  10  parts  silver,  80  parts  aluminum,  and  99 
parts  tin,  for  jewellers*  work;  mettallne,  made  of  il5  parts  cobalt,  w  parts 
aluminum,  10  ports  iron,  and  80  parts  copper.  The  aluminum^bonrbouns 
metal,  shown  at  the  Paris  Exposition  of  1^,  has  a  speciflo  (rravity  of  S.9  to 
2.M,  and  can  be  cast  In  very  solid  shapes,  as  it  has  very  little  shrlnkacre. 
From  Moalysistfae  following  composition  is  deduced:  Aluminum,  85.74)C;  un, 
12.949(;  silicon,  1.89;  iron,  none. 

The  metal  can  be  readily  electrically  welded,  but  soldering  is  still  not  sat* 
tafaetory.  The  high  heat  conductivity  of  the  aluminum  withdraws  the  heat 
of  the  molten  soloer  so  rapidly  that  It  ^  f  reeees  ^*  before  it  can  flow  suffi- 
ciently. A  German  solder  said  to  give  good  results  Is  made  of  809(  tin  to  90jt 
dnc,  nslBg  a  flux  composed  of  80  parts  stearic  add,  10  parts  chloride  of 
zioc,  and  10  parts  of  chloride  of  tin.  Pure  tin,  fusing  at  SSO*  C,  has  also 
been  used  as  a  solder.  The  use  of  chloride  of  silver  as  a  flux  has  been 
patented,  and  need  with  ordinary  soft  solder  has  given  some  success.  A 
pare  nickel  soldering^biC  should  be  used,  as  it  does  not  discolor  aluminum 
ss  copper  bits  da 

AIXOYS. 
AI^LOTS  OF  COPPKR  AND  TIN. 
(Bxtract  from  Report  of  U.  B.  Test  Board.*) 


Mean  Com* 

position  by 

Analysis. 


OB  Jt. 

ii 


27,800 
12,700 
M.580 
82,000 


8fl,.%40 
90,660 


29,480 


82,980 


8,010 


5,585 


2,901 
1.456 
8.010 
8,371 
fl,77B 


0,890 

MS 

4,780 
8,505 


14.000 
11,000 
10,000 
16,000 


19.000 
15,750 


20,000 


22,010 


5,566 


2,201 
1,455 
8.010 
8,871 
6,T75 


8,500 
8,900 
2,750 


ll 


6.47 
0.47 
18.83 
14.29 


6.58 
8.66 


8.88 


0.04 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

0. 


4.10 
6.87 
12.82 
85.51 


lis 

h 


29,848 
21,251 


n 

i^  ■ 


bent, 
2.81 


83.282 

88,659 
48,781 
49,400 
60,408 
34,.'»1 
67,980 
56,715 
29,936 
82.210 
9.512 
12,076 
9,152 
9,477 
4,776 
2,126 
4,776 
5,884 
12,408 
9.068 
10,706 
5,805 
6,926 
3,740 


bent. 


4.00 
0.68 
0.49 
0.16 
0.19 
0.05 
0.06 
0.04 
0.09 
0.02 
0.02 
0.08 
0.04 
0.27 
0.66 
5.85 
bent. 


42.000 
89,000 
84,000 
42,048 


42,000 
88,000 


58,000 
78',666 


114,000 
147,666 


84,TW 


85,800 
19,600 


6,500 
10,100 
9.800 
9,800 
6,400! 


Torsion 
Tests. 


148 
65 
150 
157 


160 
175 


190 


122 

'is* 


16 


23 

12 


153 
40 
817 
247 


126 
114 


100 


16 
"i'.6 


1 


25 
62 
182 
220 

597 


*  The  teats  of  the  alloys  of  copper  and  tin  and  of  copper  and  sine,  the  re- 
mits c/t  which  are  published  in  the  Report  of  the  U.  S.  Board  appointed  to 
tnt  Iron,  Steel,  and  other  Metahi,  Vols.  I  and  II,  1879  and  1881,  were  made 
'  the  author  under  direction  of  Prof.  R.  H.  Thurston,  chairman  of  the 
on  Alloys.    Bee  preface  to  the  report  of  the  Committee,  in  YoLL 


allots; 

Nob.  la  and  8  were  full  of  blow-holes. 

Testfl  Nos.  1  and  la  show  the  Tariation  io  cast  cooper  due  to  rarying  con* 
ditioiis  of  castlnfp.  In  the  crushing  tests  Nos.  12  to  &i,  ioclusive,  crushed  and 
broke  uoder  the  strain,  but  all  the  others  bulfced  and  flattened  out.  Io  th«iie 
cases  the  crushing:  strength  Is  taken  to  be  that  which  caused  a  decrease  of 
iO%  in  the  length.  The  test-pieces  were  8  in.  long  and  H  in.  diameter.  The 
torsional  tests  were  made  in  Thurston's  torsion-machine,  on  pieces  ^  in. 
diameter  and  1  in.  long  between  heads. 

Speelflc  OntTlt/  of  ibe  €opper*tin  AUots.— The  specific 
gravity  of  copper,  as  found  in  these  tests,  is  8.874  (tested  in  turnings  from 
the  ingot,  and  reduped  to  89.1*  F.).  The  alloy  of  maximum  sp.  srr.  8.966 
contained  0^.43  copper,  87.48  tin,  and  all  the  alloys  containing  less  than  ^% 
tin  varied  irregularly  in  sp.  gr.  between  8.65  and  8.98,  the  density  depending 
not  on  the  composition,  but  on  the  porosity  of  the  casting.  It  is  probable 
that  the  actual  sp.  g^r.  of  all  these  alloys  containing  less  than  87](  tin  is  About 
8.95,  and  any  smaller  figure  indicates  porosity  in  the  specimen. 

From  97%  to  ]00j(  tin,  the  sp.  gr.  decreases  regularly  from  the  maximmn  of 
8.056  to  that  of  pure  tin,  7.3vd. 

Note  on  the  Strenctli  of  the  Copper-iln  Alloys. 

The  bars  containing  from  2%  to  9i%  tin,  inclusive,  have  considerable 
strength,  and  all  the  rest  are  practically  worthless  for  purposes  in  which 
s^.rength  is  required.  The  dividing  line  between  the  strong  and  brittle  alloys 
is  precisely  that  at  which  the  color  changes  from  golden  yellow  to  silver- 
white,  viz.,  at  a  composition  containing  between  84]f  and  90%  of  Un. 

It  appears  that  the  tensile  and  compressive  strengths  of  these  allovn  are 
in  no  wav  related  to  each  other,  that  the  torsional  strength  iff  cloeely  pro- 
portional to  the  tensile  strength,  and  that  the  transverse  strength  may  de- 
p*'nd  in  some  degree  upon  the  compressive  strength,  but  it  is  much  ii>ore 
nearly  related  to  the  tensile  strength.  The  modulus  of  rupture,  as  obtained 
by  the  transverse  tests,  is,  in  general,  a  figure  between  those  of  tensile  aD<^ 
compressive  strengths  per  square  inch,  but  there  are  a  few  exceptions  io 
which  it  is  larger  than  either. 

The  strengths  of  tlie  alloys  at  the  copper  end  of  the  series  increase  r^idl> 
with  the  addition  of  tin  till  about  4%  of  tin  is  reached.  The  transverse 
strength  continues  regularly  to  increase  to  the  maximum,  till  the  alloy  con- 
taining about  17>^  of  tin  is  reached,  while  the  tensile  and  torstonaJ 
strengths  also  Increase,  but  irregularly,  to  the  same  point.  This  irregularity 
is  piobably  due  to  porosity  of  the  metal,  and  might  possibly  be  removed  by 
any  means  which  would  make  the  castings  more  compact.  The  niaxloiuiu 
is  reached  at  the  alloy  containing  83.70  copper,  17.34  tin,  the  transverse 
strength,  however,  being  very  much  greater  at  this  point  than  the  tensile 
or  torsional  strength.  From  the  point  of  maximum  strength  the  flgurefi 
drop  rapidly  to  the  alloys  containing  about  27.6]f  of  tin,  and  then  more  slowly 
to  37.5J(,  at  which  point  the  minimum  (or  nearly  the  minimum)  strength,  by 
all  three  methods  of  test,  is  reached.  The  alloys  of  minimum  strength  are 
found  from  87.0j(  tin  to  62.6^  tin.  The  absolute  minhuum  is  probably  about 
46%  of  tin. 

From  &i,b%  of  tin  to  about  77.5)(  tin  there  is  a  rather  slow  and  irrsRular  in- 
crease  in  strength.  From  Tt.6%  tin  to  the  end  of  the  series,  or  all  tin,  the 
strengths  slowlv  and  somewhat  irregularly  decrease. 

The  results  of  these  tests  do  not  seem  to  corroborate  the  theorr  given  by 
some  writers,  that  peculiar  properties  are  possessed  by  the  alloys  which 
are  compounded  of  simple  multiples  of  their  atomic  weights  or  chemical 
equivalents,  and  that  these  properties  are  lost  as  the  compositions  vary 
more  or  less  from  tliis  definite  constitution.  It  does  appear  that  a  certain 
percentege  composition  gives  a  maximum  strength  and  another  certain 
percentage  a  minimum,  but  neither  of  these  compositions  is  represented  by- 
si  mpie  multiples  of  the  atomic  weights. 

Tnere  appears  to  be  a  regular  law  of  decrease  from  the  maximum  to  the 
minimum  strength  which  does  not  seem  to  have  any  relation  to  the  atomic 
proportions,  but  only  to  the  percentage  compositions. 

Hardneaa*— The  pieces  containing  less  than  M%ot  tin  were  turned  In 
the  lathe  without  difficulty,  a  gradually  increasing  hardness  beino:  notic«*d, 
the  last  named  giving  a  very  short  chip,  and  requiring  frequent  sharpeninjc 
of  tlie  tool. 

With  the  most  brittle  alloys  it  was  found  impossible  to  turn  the  test-piecv-s 
in  the  lathe  to  a  smooth  surface.  No.  13  to  No.  17  (28.85  to  84.47  tin)  could 
not  be  cut  with  a  tool  at  alL   Chips  would  fly  off  in  advance  of  the  tod  and 


ALLOYS  OP  COPPEB  AND  ZIKO. 


321 


ben^rh  It,  leaving  a  rough  surface:  or  the  tool  would  sometimes,  apparently, 
crush  off  portions  of  the  metal,  gilnding  it  to  powder.  Beyond  w%  tin  the 
hardness  decreased  so  that  the  bars  oould  be  easily  turned. 


AI^I^OYS  OF  COPPER  ANB  ZINC.    (U.  S.  Test  Board). 

Elastic 

v^  . 

Trans- 
yerse 

^ 

Torsional 

Mean  Com- 

Limit 

gS 

in 

Crush- 

Teats. 

No. 

position  by 
Analysis. 

Tensile 

Strength, 

lbs.  per 

sq.  in. 

%ot 
Break- 
ing 

lbs.  per 
sq.  in. 

So 

Test 
Modu- 
lus of 
Rup- 
ture. 

Strgth 
per  sq. 
In.,  l3. 

hi 

Cop- 
per. 

Zinc. 

III 

1 

gfr.83 

82.98 

1.88 
16.98 

27,240 
82,600 

180 
155 

357 

s 

26.1 

26.7 

28.197 

Bent 

829 

3 

81.91 

17.99 

82,670 

80.6 

31.4 

21.198 

*• 

166 

845 

4 

77.80 

22.45 

85,630 

20.0 

35.5 

25.874 

It 

169 

811 

5 

76.66 

28.08 

80,520 

24.6 

36.8 

22,825 

*• 

42.000 

165 

267 

6 

73.20 

26.47 

81,580 

28.7 

38.5 

25,894 

u 

168 

298 

t 

71.20 

28.54 

80,510 

29.5 

29.2 

24,468 

** 

164 

269 

8 

69.74 

80.06 

28,120 

28.7 

20.7 

26,930 

tt 

148 

202 

9 

66.27 

88.50 

87,800 

26.1 

87.7 

28,469 

M 

176 

2.'^7 

10 

63.44 

86.86 

48,300 

32.8 

CI. 7 

43,216 

(t 

202 

230 

11 

60.94 

88.65 

41,065 

40.1 

20.7 

88.968 

«« 

75,000 

194 

202 

•2 

58.49 

41.10 

60,450 

54.4 

10.1 

68,:04 

t* 

227 

93 

:s 

55.15 

44.44 

44,280 

44.0 

15.3 

42.468 

tl 

78.000 

209 

109 

A 

54.86 

44.78 

46,400 

68.9 

8.0 

47,955 

tl 

223 

72 

15 

49.6C 

50.14 

80,990 

54.5 

5.0 

88,467 

1.26 

117,400 

172 

88 

16 

48.99 

80.82 

26,050 

100. 

0.8 

40,189 

0.61 



176 

16 

17 

47.56 

62.28 

24,150 

100. 

0.8 

48,471 

1.17 

121.000 

165 

18 

18 

43.86 

66.22 

9,170 

100. 

•  • .. 

17,691 

0.10 

88 

19 

41.80 

58.12 

8,727 

100. 

•  ... 

7,761 

0.04 

18 

20 

32.94 

66.28 

1,774 

100. 

.«•• 

8,290 

0.04 

29 

« 

29.20 

70.17 

6,414 

100. 

.... 

16,579 

0.04 

...  .... 

40 

a 

20.81 

77.63 

9,000 

100. 

0.2 

22.972 

0.13 

52,152 

65 

23 

12.12 

86.67 

12,418 

100. 

04 

85,026 

0.31 

82 

u 

4.85 

94.59 

18.065 

100. 

0.5 

26,162 

0.46 

81 

22 

25 

Cast 

Zinc. 

6.400 

75. 

0.7 

7.539  1  0.12 

22.000 

87 

142 

Varlmtlon  In  Strength  of  Oan-bronze,  and  Meana  of 
laiprovln^  ilie  Strenstlt*— The  figures  obtained  for  alloys  of  from 
'M  to  12.7jf  lui,  viz..  from  26,860  to  20,430  pounds,  are  much  leHS  than  are 
iwuaUy  fifiyen  as  the  strength  of  gun-metal.  Bronze  guns  are  usually  cast 
under  the  pressure  of  a  h^ad  of  metal,  which  tends  to  increase  the  strength 
aod  density.  The  strength  of  the  upper  part  of  a  gun  casting,  or  sinking 
Wad,  is  not  greater  than  that  of  the  small  bars  which  have  been  tested  in 
ibese  experiinents.  The  following  Is  an  extract  from  the  report  of  Major 
Wade  concerning  the  strength  and  density  of  gun-bronze  (1650):— Extreme 
Tuiation  of  six  samples  from  different  parts  of  the  same  gun  (a  82-pounder 
bowitaer):  Specific  gravity,  8.487  to  8.835;  tenacity,  26,428  to  52,192.  Extreme 
variation  of  all  the  samples  tested:  Specific  gravity.  8.308  to  8.850;  tenacity, 
S3. 108  to  54.531.  Extreme  variation  oc  all  the  samples  from  the  gim  heads: 
Sprciflc  gravity.  8.808  to  8.756;  tenacity,  23.529  to  85,484. 

Major  Wade  says:  The  general  results  on  the  quality  of  bronze  as  it  is 
fi^ind  in  guns  are  mostly  of  a  negative  character.  They  expose  defects  in 
iiensiry  and  strength,  develop  the  neterogeneous  texture  of  the  metal  in  dif- 
firent  parts  of  the  same  gun.  and  show  the  irregularity  and  uncertainty  of 
quality  which  attend  the  castibg  of  all  guns,  although  made  from  s  milar 
materials,  treated  in  like  manner. 

Kavv  ordnance  bronze  containing  9  parts  copper  and  1  part  tin,  tested  at 
WashingtoD,  D.  C,  in  1875-6,  showed  a  variation  in  tensile  strength  from 
SJOO  to  51,400  lbs.  per  square  inch,  in  elongation  frcm  S%  to  bOji^  and  in  spe- 
cAcgravity  from 8.39 to 8.88. 

That  a  great  improvement  may  be  made  in  the  density  and  tenacity  of 
nm-brooxe  by  compression  has  been  shown  by  the  experiments  of  Mr.  S.  B. 
I>ean  in  Boston.  Mass.,  in  1869,  and  by  those  of  General  Uchatius  in  Austria 
in  ISTSJ.  Th«  former  increased  the  density  of  the  metal  next  the  bore  of  the 
CxiB  from  HJ8rZl  to  8.875,  and  the  tenacity  from  27,238  to  41,471  pounds  per 


39? 


AiiLOTS. 


§ai|§re  ii}cb.  The  |A.ttor,  by  a  sijxtPar  prppatff,  pl)taif>e4  Uip  f^IUNrlnflr  ftsiWM 

PpuQfls  nor  04*  liLi 

Bronze  with  1W  tin ,..,  72,068 

Bronxa  with  8](  tin : ?ft,M 

Bronse  wfth  6)(  Un T7,666 


Ai«l«air|s»  op  coppp^, 

TIN,  A99  IBilWC, 

(Report  of  U.  8.  Te»t  poar4,  YpL  11, 1881.) 

No. 

in 

Report. 

Origin^  Mixture. 

Strength. 

BtrpiL|;Lli  p«»r 
^qiitue  inch. 

Elpqg^ipn 

Kodulns 

Deflec. 

Cu. 

8n. 

Zn, 

RojpAifne 

tion, 
in^. 

A 

a 

A. 

^. 

ft 

TO 

P8.14 

66 

6 

1.86 
6 

6 
10 
10 

11 

1^ 
2.86 

P 

13'^^^ 

g-SI 
17.6 
6.80 

9.68 
J9.5 
B.8B 

n 

1 

12.6 

6 
2.6 

h 

86,680 
84,500 

» 

h 

2.26 

88 

82.5 

12.11 

5 

11 

86  000 

34,000 

.86 

77 

8-2.5 

16 

2.6 

69;o« 

83,600 

33,800 

........ 

.66 

d7 

80 

6 

15 

67.117 
64,476 

Pr,560 

82  800 

IIIB 

3:50 

SI 

P5 

10 
15 

10 
6 

2.46 

§i880 
P,850 

31050 
30  760 

1.6 
t4 

10 

12.6 

63,849 

1.19 

i'^ 

$$^ 

9!6d 

i!a 

87 
63 

r 

10 
??.5 

-1:706 
56,te6 

2.9 
1.89 

Hi 

i 

.50 

S.18 

85 

1 

7.5 

62,807 

1.S3 

64 

10 

15 

56,346 

.n 

84000 

1.28 

05 
66 

16 
2P 

't 

51,109 
40,285 

.8 
.21 

iiil440 

Si  0 

P;S8 

:63 
.43 

.54 

83 

9.5 

20 

51,839 

2.86 

i;87 

ffl7(0 

ao,o(o 

34  800 

8.78 

"3:78" 

84 

72.5 

le 

ir.5 

58,280 

^n 

.48 

.49 

69 

?5 

6 

25 

57.349 

48,886 
36,620 
37.924 
1.'),126 

38,000 

2.06 

.99 

8d 

7.5 

22.5 

.36 

38,000 

82.400 

.84 

.40 

62 

?3 

70 

10 

20 
15 
10 

1 

17,000 

li 

.81 

81 

07.6 

2.5 

ao 

58,34G 
55.976 

^'01 

34  720 

tS 

7.27 

"iioo  * 

74 

67.5 

6 

27.5 

■.i 

84;000 

1.06 

.48 

AS 

57 

67.5 

7.5 

25 

46,875 

^,^ 

l.Bl 
.16 

.96 

65 

65 
65 

20 
2.5 

IS' 

16 
85 

11,932 
69,255 

.06 

61,400 

li 

7,281 
62,000 

8.02 
.61 
.10 

58 

........ 

79 

"i'.ii* 

"i'M" 

78 

2.5 

37.5 

69,508 

4.87 

3.02 

5-3 

GO 

5 

35 

46,076 
24,699 

.28 

41,160 
i5l780 

iA,p20 

66,500 

86.880 

.89 

.4C 

53 

60 

10 

80 

J 

^''^itS 

.16 

61 

60 
58.2;.' 

2.80 

25 
3d.48 

18,248 
95,623 

I'i 

"i'.ii" 

"a'is  * 

3 

58.75 

8.7.')   B^i.i 

35,752 

.18 

Broke 

tjeforet 

e6t;Ter 

rtiHttle 

4 

ip 

2]f.2."i 

21.25 
44.5 

2,752 

.02 

735 

1,300 

73 

0.5 

72:308 

8.05 

68,900 

68.900 

"9.43* 

"8.88* 

50 

.•V5 

,3 

6 

40 

88.174 
28.258 
20,814 

.28 

27,400 

30,600 

.46 

.4S 

51 
40 

55 
50 

35 
45 

,14 
.11 

25,460 
d8.000 

Jt'wS 

:S! 

.10 
.46 

'fhe  tiangverse  tests  were  nm<1e  In  bar«  1  In^pqUAre,  22  In.  between  sup- 
ports, f  he  tensile  tests  were  made  op  Ijars  0.788  jn.  dlam.  turne4  ffom  the 
two  h|ilvt»  of  t-he  trapsrerse-tetjt  har,  ope  )ia2f  belpg  ip(^rlfpa  A  and  ^o 
Other  #. 


ALLOTS  OJf  GOPPSBy  TIN,  AND  ZIKa  823 

< 

-inctowf  An^BSMUv-TlM  usual ^ooipoiiHioA  of  juiclapt  broace  wmb  Um 
«ame  aa  tb&t  of  modern  gun-metal— 90  copper,  10  tlii:  but  the  proportUm  ot 
tinrafieafjipmAt  toS£^aiidJUispm  Botoean- 

,   .  •HieaUojaoootoiDlnirleai 

-  aeaerally  dfifectiva.    Tba  bars 

were  f  uU  of  bloW'-faoles,  and  the  metal  abowad  «igiw  of  oxidation.  To  lasum 
irood  castings  it  appears  that  copper-zinc  alloys  diould  contain  more  than 
ibji  of  zinc. 

From  No.  2  to  Ko.  8  Inclusive,  16.M  to  fOMji  zinc  the  ban  show  a  remark* 
able  aimilarity  in  all  their  properties.  Tliey  have  all  nearly  the  same 
strength  and  ductilitv,  tlie  latter  decreasijig  slightly  as  dao  increases,  and 
are  nearly  alilce  in  color  and  appearance.  Ebetwean  Kos.  8  and  10,  90.06  and 
a6.S6)(  jEinc,  the  atrengtb  by  all  methods  of  test  rapidly  increases.  Between 
No.  10  and  No.  V^  MM  and  60.14^  zinc,  th?re  is  another  croup,  distinguished 
by  high  stranglii  and  diminisbad  ductility.  The  alloy  of  maximum  tonsile, 
transverse  «od  torsional  strength  contains  about  A\%  ot  sine. 

The  alloTs  containing  less  than  S6^  of  zinc  are  r,U  yellow  metals.  Beyond 
55^  the  color  efaanges  to  vhica,  and  the  alloy  becomes  weak  and  brittle.  Be- 
tween TOjt  and  pure  sine  the  rotor  is  biuisn  gray,  the  brittleness  decreases 
and  the  strength  iacreaaes,  but  not  to  such  a  d^ree  as  to  make  them  useful 
for  oonstructiTe  purposes. 

IMlTereiiee  b«iweea  Com^oaltloB  br  Klxtnre  and  1>y 
Analyafl*,— There  is  in  every  esse  a  smaller  percentage  of  zinc  in  the 
averag^e  analysis  than  in  the  original  miztun,  aad  a  larger  percentage  of 
copper.    The  loss  of  zinc  is  variable,  but  in  goneral  averages  from  1  to  2j(. 

U^vaUon  or  Separattoa  of  tlie  BEotm]«.^In  several  of  the 
bars  a  considerable  amount  of  liquation  took  place,  analysis  showing  a 
difference  in  composition  of  the  two  ends  of  the  bar.  In  such  cases  the 
change  in  composition  was  gradual  from  one  end  of  the  bar  to  the  other, 
the  upper  end  in  general  containing  the  higher  percentage  of  copper.  A 
notable  instance  was  bar  No.  13,  in  the  above  table,  turnings  from  the  upper 
end  containing  40.86j(  of  zinc,  and  from  the  lower  end  48.523(. 

Speelllc  OraTliy*— The  specific  gravity  follows  a  definite  law.  varying 
vitta  the  composition,  and  decreasing  with  the  addition  of  zinc.  From  the 
plotted  curve  of  specific  gravities  the  following  mean  values  are  taken: 

Feroentzinc 0      10     20     80     40     60     60     70     80     90    loa 

Specific  gravity. 8.80  8.72  8.60  8.40  8.86  8.20  8.00  7.72  7.40  7.20  7.14. 

Gimpliflc  Representation  of  tke  liair  of  Variation  of 
Streni^k  of  Copper-Tln-Zlnc  A11osra.->In  an  equilateral  triangle 
the  Slim  of  tlie  perpendicular  distances  from  any  point  witnin  It  to  the  thiee 
Bidea  ia  equal  to  (he  altitude.  Such  a  triangle  can  therefore  be  used  to 
siiow  graphically  the  percentage  com  position  of  any  compound  of  three 
narts,  such  as  a  triple  alloy.  Let  one  side  represent  0  copper,  a  second 
0  tin,  aiul  the  thlrU  0  zinc,  the  vertex  oppo&ite  eaoh  of  these  sides  repre- 
ttoting  300  of  each  element  respectively.  On  points  In  a  triangle  of  wood 
representing  dlfiTerent  allo3's  tested,  wires  were  erected  of  letipths  proper* 
tional  to  the  tensile  strengths,  and  the  triangle  then  built  up  with  plaster  to 
the  height  of  the  wires.  The  surfaoe  thus  formed  has  a  characteristic 
topograpby  represenUng  the  variations  of  strength  with  variations  of 
composition.  The  out  shows  the  surface  thus  made.  The  vertical  section 
to  the  left  represents  the  law  of  tensile  strength  of  the  copper-tin  alloys, 
the  one  to  the  right  that  of  tin-zinc  alloys,  and  the  one  at  the  rear  that  of 
tiie  copper-zinc  alloys.  The  high  point  represents  the  strongest  possible 
alloys  of  the  three  metals.  Its  composition  is  copper  55,  einc  48,  tin  2,  and  Its 
Ktr^gth  about  70,000  lbs.  The  hign  ridge  from  this  point  to  the  point  of 
maximum  height  of  the  section  on  the  left  Is  the  line  of  the  strongest  alloys, 
represented  by  the  formula  zinc  +  (3  X  tin)  =:  55. 

All  alloys  lying  to  the  rear  of  the  ridge,  containing  more  copper  and  less 
tin  or  sino  are  allovs  of  greater  ductility  than  thope  on  the  line  of  maximum 
strength,  and  are  the  valuable  commercial  alloys;  those  in  fronton  the  decliv- 
ity toward  the  central  valley  are  brittle,  and  those  In  the  Talley  are  both  brl&- 
tfe  and  weak.  Paeaing  from  ihe  valley  toward  the  section  at  the  right  the 
•Iknrs  loee  tbefr  brittleness  and  become  soft,  the  maximum  softness  being 
at  tin  as  100,  but  tbey  remain  weak,  as  is  shown  by  the  low  elevation  of  the 
iurface.  This  model  was  planned  and  constructed  by  Prof.  Thurston  In 
ItfTT.    (Bee  Trans.  A.  a  C.  £.  1881,  Report  of  the  U.  S.  Board  appointed  to 


824 


ALLOYS. 


test  Iron,  Steel,  etc.,  Tot.  H.,  Washington,  1881,  and  Thurston^  UdfeHdti 
of  Enaineering,  vol.  til.) 

The  best  alloy  obtained  In  Thnrston^  research  for  the  U.  S.Testlni^  Board 
has  the  oomposltiun.  Copper  55,  Tin  0.6,  Zinc  44.5.  The  tensile  stren^h  in  a 
cast  bar  was  68,900  lbs.  per  sq.  in.,  two  specimens  givinfi:  the  same  result;  the 
elongation  was  47  to  51  per  cent  in  5  inches.  Thurston^s  formula  for  copper- 
tin-mc  alloys  of  maximum  strength  (Trans.  A.  S.  0.  £^  1881)  is  «+  8<  »  S8* 


Alloys  proportioned 
of  about  40,000  Ibe. 


no.  77. 

In  which  g  Is  the  peroentase  of  sine  and  f  that  of  tin. 

according  to  this  formula  should  have  a  strength  _ 

per  sq.  in.  4-  QOOz,    The  formula  fails  with  alloys  containing  less  than  1  per 

cent  of  tin. 

The  followinf?  would  be  the  percentage  composition  of  a  number  of  alloys 
made  according  to  this  formula,  and  their  corresponding  tensile  strength  in 
castings : 


Tin.      Zino.    Copper. 


fid 

47 

49 

49 

40 

61 

48 

68 

40 

60 

87 

67 

84 

69 

Tensile 
Strength, 

lbs.  per 

sq.  in. 

66,000 

<M,.V)0 

68,000 

61,500 

60,000 

68.500 

67,000 


Tensile 
Tin,  Zinc.  Copper,  ^ig^p^ 
sq.  In. 
66,800 
64,000 
68,500 
49,600 
40,600 
48,500 


8 
9 
10 
12 
14 
16 
18 


81 
28 
85 

19 
18 
7 

1 


61 
68 
65 
69 
78 
77 
81 


These  alloys,  while  poKs**s8ini?  maximum  tensile  streng^th,  would  in  general 
be  loo  hard  for  easy  working  by  luachiuu  tools.  Another  series  made  on 
the  formula  z  4-  4  t  =  50  would  have  i^reater  ductility,  together  with  con- 
slilnrabltf  slreiij^th,  as  follows,  ilie  strength  being  calculated  as  before, 
tensile  strength  in  lbs.  per  sq.  In.  =  10,000  4<  500^. 


lliOTS  OF  COPPBB,  TIK,  XSD  ZISC. 


838 


TensUe 

Tensne 

IlL 

Zino. 

Copper. 

StrenRth, 
lbs.  per 
eq.  In. 

Tin. 

Zinc. 

Ciopper. 

Strength, 

48 

88 

88,000 

f 

£9 

71 

61,000 

4» 

M 

81,000 

8 

18 

74 

40.000 

» 

80 

60,000 

8 

14 

77 

47,000 

84 

88 

67,000 

10 

10 

80 

46,000 

80 

65 

66,000 

11 

8 

88 

43,000 

SO 

88 

68,000 

18 

8 

86 

41,000 

Coi 


iposttion  of  Alloys  In  STory-Aay  Ume  In  Bfmm 
Foundries.    (American  MachinUi.) 


CJop- 
per. 


Zinc.    Tin.  Lead. 


TbS: 


Admiralty  metal. 

Bell  metal........ 

Braas  (yellow).... 


Bush  metal., 
Gun  metal.... 


Steam  metaL. 


Bard  gun  metal., 
Muntz  metal 


Fliosphor  bronse. 


Bnidng  metal.. 
••      solder. 


lbs. 
87 


ao 


Ibe. 
6 


lbs. 
8 


40 


4 
8 

2^ 


4 
1 


8  phos.  tin 
10    •• 


For  parts  of  engines  on  board 

naval  veeaels. 
Bells  for  ships  and  factories. 
For  plumbers,  ship  and  house 

brass  worlc. 
For  bearing  busbesf or  shafting. 
For  pumps  and  other  hydraulic 

purposes. 
Castings   subjected  to  steam 

pressure. 
For  heavy  bearings. 
Metal  from  which  bolts  and  nuts 

are  forged.Talve  spindles,  etc. 
For  valves,  pumps  and  general 

work. 
For  cog   and   worm  wheels, 

bushes,  axle  bearings,  slide 

valves,  etc. 
Flanges  for  copper  pipes. 
Solder  for  the  above  flanges. 


OnrloT^a  Bronae*— 18  parts  copper,  1  tin,  1  zinc,  ^  lead,  uaied  by 
W.  &  L.  £.  Gurley  of  Troy  for  the  framework  of  their  engineer's  transits; 
Tensile  strength  41,114  lbs.  per  sq.  in.,  elongation  87;^  in  1  inch,  sp.  gr.  8.690. 
(W.  J.  Keep,  Trans.  A.  I.  M.  E.  1800.) 

Vttal  Alloys  of  Copper,  Tin,  and  Zlno, 

(Selected  from  numerous  sources.) 
Copper.  Tin.       Zlno. 
v.  S.  Kavy  I>epi.  Journal  boxes  I  ^  j  o 

and  g:iiide-grb8 ("{82.8 

Tobin  bronse. 68.23 


Kaval  bn 

Composition,  U.  S.  Navy.. 

Brass  bearings  (J.  Boss).. 

GnnmstaL 


ToQgh  brass  for  engines 

Brooae  for  rod-boxes  (Laf ond) 

**   pieces  subject  to  shock.. 

&ed  brass  parts 

••       '*     percent 

Bhmze  for  pump  casings  (Lafond)... 
••  eccentric  straps.       •• 

••      ••  shrill  whisUes 

«      «•  iow-tonsd  whistles 


68 

88 
i64 
187.7 

02.6 

91 

87.75 

85 

83 
jl3 
176.5 


20 
87 
88 
84 
80 
81 


1  hi  parts. 

13.8  &4  percent. 

2.80  89.48   "      " 

1  87  ••  - 
10           2  •*      •• 

8  1  parts. 

11.0        1.8  percent. 

6  2.5  •*      •♦ 

7  8  •*  • 
9.75  2.5  ••  •• 
6  10  •*      •• 

2  16  ••  •• 
2  2  parts. 

11.8  11.7  percent 

16  8  slightly  malleable 

16  1.60  0.^  lead. 
1           11" 
4.4        4.8  4.8      •• 

10  S 

14  8 

18  ....  2.0 antimony. 

17  ....  8.0       " 


326 


ALLOT& 


BearinirtneUil  !!!*.!!.  !!!..!!r.II 

00^.  m     m. 
....     8d.5     8.1       6.0  16  lead. 

....      80         8           8 

»«»^l    «UtOk«M 

u           u 

::::  IS    i?<    ^. 

M               ••         

::::  %^  if^    ! 

...79        18           9U  V^Iead. 

M               M 

....74          OU        Oi2  Ylead. 

Edglfah  brass  of  A.D.  1504 

Copper-Zflekel 

Ofwtnim  silver. 

....      04         8         SD^S^lead. 
Jklloymf  G«rmaii  SIlTer* 

Copper.         KIckeL            Tin. 
..       61^            «.8             a.6 
..        60.8              14.8                8.1 

61.1          13.8           as 

..    68to65       18to85          

.      76toe6       S5toa8          

Sdne. 

tt            t» 

81.9 

U                  M 

81.9 

•1                   It 

90  to  80 

Nickel        "    

A  refined  copper-nfclrel  alloy  contalninj?  S0%  copper  and  49f  nickel,  with 
very  small  amounts  of  iron,  silicon  and  carbon.  Is  prodaoed  direct  from 
Bessemer  matte  in  the  Sudbury  (Canada)  Nickel  works.  German  silver 
manufacturers  purchase  a  ready-made  alloy,  which  melts  at  a  low  heat  and 
requires  simple  addition  of  zinc,  Instead  of  buying  the  nickel  and  copper 
separately.  This  alloy,  **S0-50*'  as  it  is  called,  is  almost  indiffrlnfrulshaDle 
from  pure  nickel.  Its  cost  is  less  than  nickel,  its  melting  point  much  lower, 
it  can  06  cast  rolld  In  any  form  desired,  and  furnishes  a  casting  which  works 
easily  in  the  lathe  or  planer,  yielding  a  silvery  white  surface  unchanged  by 
air  or  moisture.  For  bullet  casings  now  used  in  various  British  and  conti- 
nental rifles,  a  special  alloy  of  W  copper  and  80it  nickel  is  made. 


Special  Alloys. 

Japanesb  Allots  for  art  work  : 

(Sngin^er 

March  84,1808.) 

Copper. 

Silver. 

Gold. 

Lead. 

Zina 

Iron. 

6haku-do 

Shibu-icbl 

94.60 
67.81 

1.66 
8e.07 

8.78 
traces. 

0.11 

trace. 

trace. 

GiLBBBT^s  Alloy  for  eera-perduia  process,  for  casting  in  p!aater-of-paris  * 
Copper  01.4         Tin  6.7         Lead  2.9      Very  fusible. 

COPPSR-ZINC-IBON  ALLOTfl* 

(7.  L.  Garrison,  Jour,  Frank.  /n<(.,  June  and  July,  1601.> 
Delta  Metal,— This  alloy,  which  was  formerly  known  as  sferro-mefaK, 
Is  composed  of  about  60  copper,  from  84  to  44  aina,  3  to  4  Iron,  and  1  to  8  tin. 
The  peculiarity  of  all  these  alloys  is  the  content  of  Iron,  whioh  appears  to 
have  tne  property  of  increasing  their  strength  to  an  unusual  dcf^rao.  In 
making  delta  metal  the  iron  is  previously  alloyed  with  elnc  In  knows  and 
deflnite  proportions.  When  ordinary  wrought-iron  Is  introduced  Into 
molten  zinc,  the  latter  readily  dissolves  or  absorbs  the  former,  and  will  *&ke 
it  up  to  the  extent  of  about  o%  or  more.  By  adding  the  einc-Iron  alloy  thus 
obtained  to  the  requisite  amount  of  copper,  it  is  possible  to  introduce  any 
deflnite  quantity  of  iron  up  to  6jt  Into  the  copper  alloy.  Garrison  gives  th^ 
following  as  the  range  of  composition  of  copper-sino-iron,  and  copper-zliic- 
tln-iron  alloys :  ^ 

L  tL 

Per  cent.  Per  cent. 

Iron 0.1  to6  Iron 0.1  to  5 

Copper. 60to05  Tin .....O.ltolO 

Zinc 1 49.9to80  Zinc 1.8to46 

Copper 98to40 

The  advantages  claimed  for  delta  mefal  are  great  strength  and  toughness. 
It  produces  sound  castings  of  cIom*.  ^rain.    It  can  be  rolled  and  forged  hot 
and  can  stand  a  certain  amount  of  drawing  and  hammering  when  cold.     It 
takes  a  high  polish,  and  when  exposed  to  the  atmosphere  Camlshes  less  thao 
brass. 


PHOSPHOB-BBONZE  A^D  OTHEB  SPECIAL  BBOKZES.  827 

When  cast  in  sand  delta  metal  has  a  tensile  strength  of  about  45,000  poondi 
par  pqnare  Inch,  and  about  \0%  elooeatlon  ;  when  rolled,  tensile  strength  of 
90,000  to  75,000  pounds  per  square  incn,  elongation  from  9%  to  17%  on  bars  l.isi^ 
inch  in  diameter  and  1  inch  area. 

Wallace  glTes  the  ultimate  tensile  strength  88,600  to  61,590  pounds  per 
square  inch,  with  from  10tU)20fi  elongation. 

Delta  metal  can  be  forged,  stamped  and  rolled  hot  It  must  be  forged  at 
a  dark  cherry«red  heat,  and  care  taken  to  avoid  sulking  when  at  a  olack 
heat. 

Aooording  to  JAoiyd'9  Proving  House  tests,  made  at  Cardiff,  December  20, 
18S7,  a  half-inch  delta  metal-roUed  bar  gave  a  tensile  strength  of  88,4M 
pounds  per  square  inch,  with  an  elongation  of  90%  In  three  inches. 

Tokus  lironae.— This  alloy  is  practically  a  sterro  or  delta  metal  with 
(he  addition  of  a  small  amount  of  lead,  which  tends  to  render  copjper  softer 
sod  more  ductile. 

The  following  analyses  of  Tobin  bronse  were  made  by  Dr.  Chas.  B.  Dudley; 

Pig  Metal,       Test  Bar  (Boiled), 
per  cent.  per  cent. 

Gbpper 59.00  ^1.20 

2Sa»c^. 88.40  87.14 

Tin 8.18  0.80 

Iron 0.11  0.18 

liead 0.81  0.85 

Dr.  Dudley  writes,  **  We  tested  the  test  bars  and  found  78,500  tensile 
ttrength  with  ISiji  elongation  In  two  inches,  and  40V^  in  eight  Inches.  This 
high  tensile  strength  can  only  be  obtained  when  tne  metal  is  manipulated. 
Such  high  results  could  hardly  be  expected  with  cast  metal. ^^ 

The  original  Tobin  bronze  in  1875.  as  described  bv  Thurston.  Trans. 
A  S.  C.  E  1S81,  had.  composition  of  copper  58.22,  tin  2.80,  zinc  88.48.  As 
east  it  bad  a  tenacity  of  66,000  lbs.  per  sq.  in.,  and  as  rolled  70,000  lbs. ;  oold 
rolled  it  gave  104,000  lbs. 

A  circular  of  Ansonia  Brass  &  Copper  Co.  gives  the  following :— The  tensile 
strength  of  six  Tobin  bronze  one-inch  round  rolled  rods,  turned  down  to  a 
diameter  of  H  o'  &"  Incb.  tested  by  Fairbanks,  averaged  79.600  lbs.  per  sq. 
in.,  and  the  elastic  limit  obtained  on  three  specimens  averaged  64,257  lbs.  per 
■q.  In. 

At  a  cherry-red  heat  Tobin  bronze  can  be  foived  and  stamped  as  readily 
w  steeL  Bolts  and  nuts  can  be  forged  from  it,  either  by  hand  or  by  ma- 
chinery, with  a  marked  degree  of  economy.  Its  great  tensile  strength,  and 
resistance  to  the  corrosive  action  of  sea-water,  render  it  a  most  suitable 
metal  for  condenser  plates,  steam-launch  shafting,  ship  sheathing  and 
fastenings,  nails,  hull  plates  for  steam  yachts,  torpedo  and  life  boats,  and 
ship-dMsk  flttings. 

The  Navy  Department  has  specified  its  use  for  certain  purposes  in  the 
machinery  of  the  new  cruisers.  Its  specific  gravity  is  8.071.  The  weight  of 
a  cubk:  inch  Is  .881  lb. 

PHOSraOB-BBOBraEB  ANB  OTHKB  SPBCIAI* 
BBOBTZBS, 

F1i4Mspl&or«1nronze,— In  the  year  ISCS,  Montefiore  A  Kunzel  of  LIdge. 
BiflgTura.  found  by  adding  small  proportions  of  phosphorus  or  "  phosphorec 
of  tin  or  copper"  to  copper  that  the  oxides  of  that  metal,  nearly  always 
presffot  as  an  impurity,  more  or  less,  were  deoxidized  and  the  copper  much 
improved  in  strength  and  ductility,  the  grain  of  the  fracture  beoime  finer, 
the  color  brighter,  and  a  greater  flnidlty  was  attained. 
Three  samples  of  phospnor-bronze  tested  by  KIrkaldy  gave : 

EUstic  limit,  lbs.  per  sq.  .In  1^,800       24,7tK)       16,100 

Tensilestrength,  lbs.per8q.  in. ...    62,695       46,100       44.448 
Elongation,  per  cent 8.40  1.50  88.40 

The  strength  of  phosphor-bronze  varies  like  that  of  ordinary  bronze 
iooordinir  to  the  percentages  of  copper,  tin,  zinc,  lead,  etc,  in  the  alloy. 

Beou411xod  Bronxe*— This  alloy  resembles  phosphor  bronse  some, 
vbac  in  composition  and  also  delta  metal.  In  containing  zinc  and  iron.  The 
foUowinj^  analysis  gives  its  aversge  composition: 


Copper.,.. &.67 

Tin 18.40 

Ztac 8.23 

8.14 


Iron 0.10 

Silver 0.07 

Phosphorus 0.006 

100.615 


328 


Comparison  of  €o- 


AIiLOTS. 


bronze 


!opper«  Slllcon-bronze,  and  1 
Wlrea.     (Engineering,  Nov.  88, 1888.) 


and  Pbosplior" 


Description  of  Wire. 

Tensile  Strength. 

Relative  ConductiTltr. 

Pure  copper 

Silicon  bronze  (teleicraph) 

•♦           "      (telephone) 

Phosphor  bronze  (telephone). . 

89,8«nbB.perBq.ln. 

41,89« * 

108,080  ♦*  •*  *•  ** 
10-2,S90  "       "    "    " 

100  per  cent. 
96    "       '* 
84    •'      ** 
26    "       •• 

Silicon  Bronze,    {Aluminum  Worid.  Maj,  1887.) 

The  moRt  useful  of  the  silicon  bronzes  are  the  9^  (97j(  copper,  9^  KlHcon) 
and  the  b%  i9h%  copper,  6%  silicon),  althouich  the  hardness  and  strength  of 
the  alloy  can  be  increased  or  decreased  at  will  by  Increasing  or  decreasing 
silicon.  A  9%  silicon  bronze  has  a  tensile  stren^h,  in  a  casting,  of  about 
55,000  lbs.  per  sq.  in.,  and  from  BOji  to  90%  elongatiou.  The  6%  bronae  has  a 
*teiisile  strength  of  about  75,000  lbs.  and  about  89^  elongation.  More  than  Si% 
or  h^  of  silicon  in  copper  makes  a  brittle  alloy.  In  using  silicon,  either  as 
A  flux  or  for  making  silicon  bronze,  the  rich  alloy  of  silicon  and  copper 
which  is  now  on  the  market  should  be  used.  It  should  be  free  from  iron 
and  other  metals  if  the  best  results  are  to  be  obtained.  Ferro^lUcon  is  not 
suitable  for  use  in  copper  or  bronze  nilrtures. 

AliVmiWnE  ALLOTS. 
Alnmlnnm  Bronze*   (Co wles  Electric  t^melt  ing  and  At.  Co.*s  circular.) 

The  standard  A  No.  2  grade  of  aluminum  bronze,  containing  lOjK  of  alumi- 
num and  90j(  of  copper,  has  many  remarkable  characteristics  which  dis- 
tinguish it  from  all  other  metals. 

The  tenacity  of  castings  of  A  No.  S  grade  metal  varies  between  75,000  and 
90,000  lbs.  to  the  square  inch,  with  from  4%  to  14j{  elongation. 

Increasing  the  proportion  of  aluminum  In  bronze  beyond  U%  produces  a 
brittle  alloy;  therefore  nothing  liigher  than  the  A  No.  1,  which  contains  ]  1%, 
is  made. 

The  B,  C,  D,  and  E  grades,  containing  7Kj(,  5<,  2}^,  and  l}i%  of  slumiDum, 
respectively,  decrease  in  tenacity  in  the  onier  named,  that  of  the  former 
being  about  65,000  pounds,  while  the  latter  is  25,000  pounds.  While  there  is 
also  a  proportionate  decrease  in  transverse  and  torsional  strengths,  elastic 
limit,  and  resistance  to  compression  as  the  percentsge  of  aluminum  is  low- 
ered  and  that  of  copper  raised,  the  ductility  on  the  other  band  increases  in 
the  same  proportion.    The  specific  gravity  of  the  A  No.  1  grade  is  7.56. 

Bell  Bros.,  Newcastle,  gave  the  specific  gravity  of  the  aluminum  bronzes 
as  follows: 

SjK,  8.G0I;  4;^.  8.C21;  6)(,  8.860;  10^,7.689. 

Oaatlnfl:.— The  melting  point  of  aluminum  bronae  varies  slightly  wfth 
the  amount  of  aluminum  contained,  the  higher  grades  melting  at  a  some*. 
what  lower  teniperature  than  the  lower  grades.  The  A  No.  1  grades  in«fU 
at  about  1700*>  F.,  a  little  higher  than  ordinary  bronze  or  brass. 

Aluminum  bronze  shrinks  more  than  ordinary  bi-ass.  As  the  metal  solidi- 
fies rapidly  ft  is  necessary  to  pour  it  quickly  and  to  make  the  feeders  amply 
large,  so  that  there  will  be  no  *'  freezing  **  in  them  before  the  casUng  is 
properly  fed.  Baked-sand  moulds  arepi-eferable  to  green  sand,  except  for 
small  castiTigs,  and  when  fine  skin  colore*  are  desired  In  the  castings.  (See 
paper  by  Thos.  D.  West,  Trans.  A-  8.  M.  E.  1886,  voL  vili.) 

All  grades  of  aluminum  bronze  can  be  rolled,  swedged,  spun,  or  drawn 
cold  except  A  1  and  A  2.    They  can  all  be  worked  at  a  bright  red  heat. 

In  rolling,  swedeing,  or  spinning  cold,  it  should  be  annealed  very  often,  and 
at  a  brielit4>r  red  neat  than  Is  used  for  annealing  brass. 

Brazing.— Aluminum  bronze  will  braze  as  well  as  any  other  metal, 
using  one  quarter  brass  solder  (zinc  500,  copper  500  (and  three  quarters 
borax.  r>r,  better,  three  quart  era  cryolite. 

Soldering.— To  solder  aluminum  bronze  with  ordhiary  soft  fpewter) 
solder:  CHeanse  well  the  parts  to  be  Joined  free  from  grease  and  dirt.  Then 
place  the  parts  to  be  soldered  In  a  strong  solution  of  sulphate  of  copper  and 
place  In  the  bath  a  rod  of  soft  iron  touching  the  parts  to  be  Joined.  After 
a  while  a  coppery-like  surface  will  he  seen  on  the  metal.  Remove  from 
bath,  rin<e  quite  clean,  and  brighten  the  surfaces.  These  surfaces  can  then 
be  tinneil  by  UKlnfir  a  fluid  consisting  of  zinc  dissolved  in  hydrochloric  acid.  In 
the  ordinary  way,  with  common  soft  solder. 

Miet*zinskl  recommends  oniinary  hard  solder,  and  says  that  Hnlot  usea 
an  alloy  of  the  usual  halfood-lialf  leod-tiu  solder,  with  12.Sj(,  f&%  or  S0%  of 
sine  amalgam. 


ALUMIKUM  BBONZE. 


329 


T«atoof  Ala 

(By  John  R.  J.  Dac^iper,  in  a  paper 

read  before  the  British  Association.  1889.) 

Bercent 

Tensile  Strength. 

Elonga- 
tion, 
per  cent. 

Specific 
Qravity. 

of 
Aluminum. 

Tons  per 
square  inch. 

Pounds  per 
square  inch. 

11^ 

40  to  45 
88**  40 
85"  80 
15  ••  18 
18  •*  16 
11  "  18 

89,600  to  100,800 
78,930  *»    89,600 
56,000  "    67,800 
88,600  ♦»    40,890 
89,120"    88,600 
84,640  "    89,190 

8 
14 
40 
40 
50 
66 

7.28 

10^ 

754 

7.60 
8.00 

5^i       ...... 

8.87 

%=.-■.:: 

8.00 

Both 


tphyidoal 


,  and  chemical  tests  made  of  samples  out  from  Tarious  sec  - 
tions  of  Mj(«  5)(,  THJi,  or  lOjf  aluminixed  copper  castings  tend  to  prove  that 
the  aluminum  unites  itself  with  each  particle  of  copper  with  uniform  pro- 
portion in  each  case,  so  that  we  hare  a  product  that  is  free  from  liquation 
and  hifirhlT  homogeneous.    (R.  C.  Cole,  Iron  Age,  Jan.  16, 1890.) 

Aluiiiiniii-lirmM  (E.  H.  Oowles,  Trans.  A.  L  M.  E.,  toI.  xriii.h- 
Oowies  aluminum-brass  Is  made  by  fusing  together  equal  weights  of  A  1 
aluminum-bronxe,  copper,  and  zinc  The  copper  and  bronze  are  first  thor- 
oughly melted  and  mixed,  and  the  sine  is  finally  added.  The  material  is  left 
in  the  furnace  until  small  test-bars  are  taken  from  it  and  broken.  When 
these  bars  show  a  tensile  strength  of  80,000  pounds  or  over,  with  8  or  8  per 
cent  dnctility,  the  metal  is  ready  to  be  poured.  Tests  of  this  brass,  on  small 
bars,  have  at  times  shown  as  high  as  100,000  pounds  tensile  strength. 

The  screw  of  the  United  States  gunboat  Petrel  is  cast  from  this  brass, 
nixed  with  a  trifle  less  zinc  in  order  t^  increase  its  ductility. 
Teats  of  Almnlmmi-Bram. 
(Cowles  £.  8.  &  Al.  Co.) 


Specimen  (Castings.) 

Diameter 

of  Piece. 

Inch. 

Area. 
sq.in. 

Tensile 

Strength, 

lbs.  per 

sq.ln. 

Elastic 
Umit, 
lbs.  per 
sq.  in. 

Elonga- 
tion, 
perct. 

Remarks. 

]59(  A  grade  Bronze. 
ITyZinc 

.465 
.465 
.460 

.1698 
.1096 
.1661 

41,825 
78,887 
72.846 

17,668 

nil 
IP' 

•W  Copper. . . .  ^ 

lpart.1  Bronse.... 

1  part  Zinc 

1  part  Copper 

Ipartv4  Bronae.... 

Ipart  Zhic } 

1  part  Copper 

The  first  brass  on  the  above  list  Is  an  extremely  tough  metal  with  low 
elastic  limit,  made  purposely  so  as  to  '*  upset "  ea.sUy.  The  other,  which  Is 
cailed  Aluminum-brass  No.  8,  is  very  hard. 

We  have  not  in  this  country  or  in  England  any  official  standard  by  which 
to  Judge  of  the  physical  characteristics  of  cast  metals.  There  are  two  con- 
ditions that  are  absolutely  necessary  to  be  known  before  we  can  make  a 
fair  comparison  of  different  materials:  namely,  whether  the  caating  was 
made  io  dry  or  green  sand  or  in  a  chill,  and  whether  it  was  attached  to  a 
larger  casting  or  cast  by  Itself.  It  has  also  been  found  that  chill-castings 
Rive  higher  results  than  sand-castings,  and  that  bars  cast  by  themwlves 
purposely  for  testing  almost  invariably  run  higher  than  test-bars  attached 
to  caatingB.  It  is  also  a  fact  that  bars  cut  out  from  castings  are  generally 
weaker  than  bars  cast  alone.    (E.  H.  Cnwies.) 

Cantlom  as  to  Reported  Strenfctlt  of  Alloya.— The  same 
variation  in  strength  which  has  been  found  in  tests  of  gun-metal  (copper 
and  tin)  noted  above,  must  be  expected  in  te^ts  of  aluminum  bronze  and  in 
fact  of  all  alloys.  They  are  exceedingly  subject  to  variation  In  density  and 
fai  grain,  caused  by  differences  In  method  of  molding  and  casting,  tempera- 
ture of  pouring,  size  and  shape  of  casting,  depth  of  ^*  sinking  head,*^  eto. 


836 


ALLOT&i 


Alnmlnnm  nar#eiilMl  hj  A#dltttfii  •€  €«pper  Rolled 


Sheeto  .114  liieli  Tiilelc* 


(The  Engineer,  J«a  3,  tflOl.) 

Tensile  Strength 


AI. 

Ctt. 

Sp.  Qr. 

Sp.  Gr. 

in  pounds  per 

Per  cent. 

Per  eentj 

Caieulated. 

Determined. 

Bcfoare  Inch. 

joa 

,    , 

8.87 

8ftj6Q5 

98 

8 

2.78 

2.71 

48,563 

96 

4 

8.90 

8.77 

441SD 

M 

0 

9.M 

2.tt 

54,778 

90 

8 

9.14 

8.86 

C0.S74 

Tesfo  of  Aleninam  AUot*. 

(Engirieer  Halrrte,  T7.  8.  N.,  Triins.  A.  I.  M.  EJ.,  vol. 

XTlll.) 

OotopwUiim, 

Tensile 

Elostle 

Ihs.p&t 
flq.  Id. 

fi1on«»- 

tlon. 

perct. 

Reduo. 
tkmdfi 

Cop- 

Aloml- 
nuta. 

ailicOD. 

2ino. 

Iron. 

8trenf(th, 
persq.  in. 

61.SW 
88.«r 
91.(0 
90.00 

9.W 
9.88 
6.50 

IS 

6.50 
9.00 
0.33 
6.50 

1.73 
1.90 
0.88 
0.88 
1.78 
0.90 
1.69 
0.19 



9.W 

0.50 

0.85 

90,790 
66,900 
97,600 
79,8*) 
89,300 
70,400 
50,100 
69,000 
69,980 
46,539 

18,009 
27,009 
M.dOO 
88,000 
60,609 
86,900 
19,009 
19,(100 
88,000 
17,000 

89.8 

8.8 

% 
IT 

15.1 
6.9 

1.89 

7.8 

39.7 

7.9 
81.98 

6.79 

98.00 
69.09 
91.50 

88.88^ 
88.88 

■  9!89" 

9.89 
4.88 

89.59 
19.5 

88.50 
9S.00 

0.50 

8.89 

19  19 

For  eoBipariflon  with  the  above  6  tests  of  "  Navy  Yard  Broase/'  Cu  SS^ 
8d  10,  Zd  8,  are  gi^tn  In  which  the  T.  8.  ranges  from  18,000  to  84,500,  E.  L. 
from  10.000  to  18,000.  £1. 1^.5  to  5w89(.  Red.  4.7  to  10.89. 

Allot*  or  AlmtotAuiiiy  Sflleoa  mnd  Itoik. 

M.  and  E.  Bernard  hate  succeeded  in  obtaloinje:  through  electrolysis,  by 
treating  directly  and  without  previous  purtflcatfon,  the  alumluum  ewtfas 
(red  and  white  bfluxites)lhe  following : 

Alloys  such  as  ferro-aluniiBum.ferr<Hsilicon-aluniio(ifli  Atid  sIHcdil-ftlttinl- 
mim,  where  the  proportion  of  silicon  may  exceed  10^  Which  are  employed 
in  the  m^allurgy  or  Iron  for  refining  steel  and  cast-iron. 

Also  silicoB-aluniinum,  where  the  proportieo  of  silicon  does  Aot  etce^ 
tOi^  Which  may  be  employed  in  mechanical  cobstnictions  in  a  rolled  or 
hammered  condition,  in  place  of  steel,  on  account  of  their  great  resistance, 
especially  where  the  lightness  of  the  piece  in  oonstfuction  constiiuteA  one 
of  the  main  conditions  of  success. 

The  following  analyses  are  given: 

1.  Alloys  applied  to  the  metallurgy  of  Iron,  the  reflolng  of  steel  and  cast 
Iron:  No.  1.  aI  70jr;  Pe,  25j^;  Si,  H.  No.  2.  A1,  70;  li-e,  20;  RI,  10.  5o.  8.  Al, 
70;  Fe,  15;  81.  15.  No.  4.  Al,  70;  Fb,  10;  SI.  20.  No.  5.  Al,  70;  Fe,  10;  81,  10; 
Mn,  10.    No.  6.  Al.  70;  Fe,  trace;  SI,  30;  Mn,  10. 

8.  M<tHiAniCfl)  alloys:  No.  1.  Al,  09;  8i,  6.75;  Fe,  1.86.  No.  2.  AT,  90;  SI, 
9;25;  Fe,  0.75.  No.  3.  Al,  90;  81,  10;  Fe,  trace.  T^ie  best  results  were  vrtth 
alK^s  whei-e  tbe  proportion  of  Iron  was  very  low,  and  the  proportion  of 
silicon  in  tlie  neighborhood  of  ^0%.  Above  that  proportion  the  alloy  be- 
eomeiv  crystalline  and  can  no  longer  be  employed.  Tlie  density  of  the  alloys 
of  silicon  Is  approximately  the  same  as  that  of  aluminum.— L«t  MetaMurgie, 
18W. 

TtiM9#eii  mtkA  Altmifli tilted— Mr.  L^Inhardt  Mannesmann  says  thAt 
th<$  adduion  of  a  little  tungsten  to  pure  aluminum  or  its  alloys  commutrl- 
cates  a  remarkable  resistance  to  the  Action  of  cold  and  hot  water,  salt 
ifrater  and  other  reagents.  When  the  proportion  of  tungsten  Is  sufflclent 
the  alloys  offer  great  resistance  to  tensile  strains. 

AltnftHlltittt,  €oj|»pei*,  and  Tin.— Prof.  R.  C.  Carpenter,  I'raiiB. 
A.  H,  M.  E.,  vol.  xix.,  finds  the  foliowiiig  alloyR  of  maximum  strength  tn  a 
series  in  which  two  of  the  three  metals  are  in  equal  propoi'tlons: 


ALLOYS  OF  MANGAirriflB  AND  COPPEB.  331 


(*trt«rttlffctfi 
-    EI,  18; 


__, .-irpelitef  fltid«  tfiarthe  «trWii?w:| 

tllov  of  ttie«e  thef aix  cotiRlfiig  of  <Wd  parts  of  flluinlnnm  aikI  nne  pAH  Of  tU\ii. 
Its  (ttmm  Mt^heth  te  ^i.m  t  liB,000  \m.  pet  fa.  th.;  has  hut  )iit>  ductnify, 
i«  rejidlly  ciii  with  rilflchliie-tooU,  4iid  Is  Ik  gdod  feubstitut«  foi-  Mid  cm 
brftM. 

Atitmintim  and  ^H.— M.  fiotirbmiz^  faati  (lomtioutided  an  lilloy  t>t 


num  is,  luHl  It  can  alao  be  worked  more  readily.  Another  adTantaiire  is  that 
it  can  be  BOidered  as  easily  as  bronze,  without  further  preliminai'y  prepara- 
tions. 

AIwiiiliiiini-Antliiioiiy-  Alloys.— t>r.  0.  U.  Alder  Wright  describes 
tome  aluminum-antiiiionyaUoys  in  a  communication  read  before  tho  Society 
of  Chflmfteal  Industry,  jhp  results  of  his  researches  do  hot  disclose  the 
rxisteuce  of  a  commerciafly  useful  alloy  of  these  two  metals,  and '  have 
t^nmver  aeidntiflc  than  practical  interest.  A  remarkable  point  Is  that  the 
alloy  with  the  chemical  composition  Al  Sb  has  a  higher  meltinfi:  point  than 
Htber  almntniiiti  dr  atitJilumjr  alone,  and  Ihat  when  alumlinith  is  added  to 
pure  antimony  the  melting-point  goes  up  from  that  of  antlmonj  (450^  0<) 
to  a  etttain  Mtti^raturb  nithel'  above  that  of  silver  (1000"  C). 

ALLdlrft  OP  ttAifdAftfiittB  Aifn  corPKAi 

raM«p«li  ISMkikgtkmBmii  Alloy**~-Bi  H.  Cowles,  la  Trane.  A.  h  M .  E., 
Vol.  z'Vll},  p.  496,  States  that  as  the  reeult  of  numerous  experiments  on 
tnixtnr^  of  the  several  itletals,  cdpper,  sine,  tin,  lead,  aluminutn,  Irdn,  and 
manganese,  and  the  netallbld  eillcoii,  and  eJfcperlHieiits  npoti  the  same  In 
ascertaining  tensile  strength,  ductilitv,  color,  etc.,  the  most  important 
deief ililitmbM  atiFpear  to  Be  Itbout  as  fSlldiVs  i 

1.  That  pure  metallic  manganese  exerts  a  bleaching  effect  upon  copper 
more  radlo^  In  its  OctlOtt  even  than  rilckel.  In  other  words,  it  was  found 
that  18^;^  or  manganese  t>re8ent  hi  (topper  produces  as  white  a  tiolbh  Ih  the 
reaultinR  Alloy  as  8&)(  (tf  nickel  wqiild  do,  this  being  the  amotint  of  each 
required  to  remove  the  last  trace  of  red. 

i.  That  Upwards  of  SOK  or  S5j(  of  Qi|knni|}e8e  may  be  lidded  to  copper  with- 
oat  redadhg  its  ductility,  although  doubling  its  tenklle  stMiigrth  and  chang- 
iofc  its  color. 

a.  Thaa  maasaneae, « 
iafeo  moulds  beliave  verj 
prodMclBg  ao  ingot  whie 
above  tfie  modld  before  cooling. 

4.  Thai  the  alloy  of  manganese  and  copper  bgr  itself  is  very  easily 
oxMbed.  u    .      ■         . 

5.  Tha4  the  addition,  of  i.2Si%  of  aluminum  to  a  manganese-copper  allojr 
eoBverte  it  fmin  one  of  the  most  refraptory  of  metals  in  tlie  casting  process 
into  a  metai  of  soperior  easting  qualities,  and  the  non-corrodibility  or  wliicH 
it  In  aiany  instahces  greater  than  tbHt  of  either  Qertdan  or  nickel  silver. 

A**silTer-broh9e"  allor  especially  designed  for  rods,  sheets,  and  ^ire 
ha«  the  following  eompqsitlon  :  Manganese,  18;  aluminum,  ).:20;  silicon,  0.5 ; 
ajoe,  13;  and  copper,  07.5j{.  It  has  a  tensile  strength  of  about  57,000  t>ound^ 
on  small  bars,  and  2Q3t  elongation.  It  has  been  rolled  into  thin  plate  and 
drawn  into  wire  .006  inch  in  diameter.  A  test  of  the  electrical  conductivity 
of  lliis  win  M  etee  Kd.  CBI)  Mioivs  Its  resistant^  to  be  41.44  times  that  of  pure 
eopder.    Urn  Is  far  lower  eoadUetlvlty  than  that  of  German  silver, 

Jrail^lieM  BroilCtot  (F.  L.  Oarrisoii,  Jour.  F.  I.,  I891.)-Thls  alloy 
bas  been  liaed  emtehslveiy  for  casting  propeller-blades.  Tests  of  some  made 
by  Bw  H.  Cramp  A  Co..  of  Philadelphia,  gave  an  average  elostlt  Uialt  o< 
W,O0O  pottUda  per  aq[tiate  Itioh,  tensile  strength  of  about  60,000  pounds  per 
noMv  finch,  with  an  eUySgatlon  of  9%  to  10^  in  sand  enatings.  When  rolled^ 
tbe  elaatic  limit  is  abont  80,000  pounds  per  square  ineh,  tPSRile  strength 
fe.OW  to  108,^09  poands  per  squate  ineh,  with  an  elongation  of  12^  to  l^* 

Compression  tests  made  at  Ufiited  States  Navy  Dc'partment  from  the 
DMKal  tn  tbe  pouring-gate  of  propeller-hub  of  U.  S.  S.  Maine  gave  in  two  tests 
A  eroihiiijr  stress  of  120,450  and  135,750  lbs.  per  so.  in.  The  specimens  were 
1  iach  b^  by  0.7  X  0.7  inch  in  cross-section  =  0.48  square  inch.    Both  specl- 


332  ALLOYS. 

mens  gave  w»y  by  shearing,  on  a  plane  making  an  angle  of  neariy  45*  wiUi 
the  direction  of  stress. 

A  test  on  a  specimen  1  X  1  X  1  inch  was  made  from  a  piece  of  the  same 
pouring-gate.  Under  streiss  of  ]50,U00  pounds  it  was  flattened  to  0.72  inch 
hiKb  by  about  U4  X  lU  inches,  but  without  rupture  or  any  sign  of  distress. 

One  of  the  great  objections  to  the  use  of  manganese  bronze,  or  in  fact 
any  alloy  except  iron  or  steel,  for  the  propellers  of  iron  ships  is  on  account 
of  the  galvanic  action  set  up  between  the  propeller  and  the  stern-post». 
This  difficulty  has  in  great  measure  been  overcome  by  putting  strips  of 
rolled  Hue  around  the  propeller  apertures  in  the  stern-frames.  i 

The  following  analysis  of  Parsons*  manganese  bronze  No.  2  was  made    ' 
from  a  chip  from  the  propeller  of  Mr.  W.  K.  Vanderbilt's  yacht  Alva. 

Copper 88.644 

Zinc  1570 

Tin 8.700 

Iron 0.780 

Lead 0.3895 

.    Phosphorus trace 

It  will  be  observed  thera  is  no  manganese  present  and  the  amount  of  zinc 
is  very  small. 

K.  H.  Ck>wle8.  Trans.  A.  I.  M .  E.,  vol.  xviii,  says  :  Manganese  bronze,  so 
called,  is  in  reality  a  manganese  brass,  for  zinc  Instead  of  tin  Is  the  chief 
element  added  to  the  copper.  Mr.  P.  M.  Parsons,  the  proprietor  of  this 
brand  of  metal,  has  claimed  for  it  a  tensile  strength  of  from  94  to  :£  tous  on 
small  bars  when  cast  in  sand.  Mr.  W.  C.  Wallace  states  that  brass-founders 
of  high  repute  in  England  will  not  admit  that  manganese  bronze  has  more 
than  from  13  to  17  tons  tensile  strength.  Mr.  Horace  See  found  tensile 
strength  of  46,000  pounds,  and  from  ^%  to  IS)^  elongation. 

GEBMAN-SILTKR  AND  OTHBB  NICKKI.  AIiI.OTS. 

Copper.  Nickel.  Zinc. 

Chinese  packfong 40.4              81.0  0.5  parts, 

**       tutenag 8                   8  0.5  ** 

German  silver 2                   1                      1  ** 

"          "     (cheaper) 8                   9  8.5  *• 

*'          **     (closely  resembles  sU).    8                   8  8.5  " 

For  analyses  of  some  German-silvers  see  page  886. 

German  Stiver. —The  composition  of  German  silver  Is  a  very  uncertain 
thing  and  depends  largely  on  the  honesty  of  the  manufacturer  and  the 
price  the  purchaser  is  willing  to  pay.  It  is  composed  of  copper,  aine.  and 
nickel  in  varying  proportions.  The  best  varieties  contain  from  IHJS  to  25%  of 
nickel  and  from  'w%iodO%ot  zinc,  the  remainder  being  copper.  The  more 
expensive  nickel  silver  contains  from  2i%  to  33%  of  nickel  and  from  75%  to  60% 
of  copper.  Tlie  nickel  is  used  as  a  whitening  element;  It  also  strengthens 
tlie  fuloy  and  renders  it  harder  and  more  non-corrodible  than  the  brass 
made  without  it,  of  copper  and  zinc.  Of  all  troublesome  alloys  to  handle  in 
the  foundry  or  rolling-mill,  German  silver  is  the  worst.  It  is  unmanageable 
and  refractory  at  every  step  In  its  transition  from  the  crude  elementa  into 
rode,  sheeta,  or  wire.    (E.  H.  Cowles,  Trans.  A.  I.  M.  £.,  vol.  xviii.  p.  4M.) 

AliliOTS  OF  BISMUTH. 

By  adding  a  small  amount  of  bismuth  to  lead  that  metal  may  be  hard- 
ened and  toughened.  An  alloy  consisting  of  three  parts  of  lead  and  two  of 
bismuth  has  ten  times  the  hardness  and  twenty  times  the  tenacity  of  lead. 
The  alloys  of  bismuth  with  both  tin  and  lead  are  extremely  fusible,  aitd 
take  fine  impre«<sions  of  casts  and  moulds.  An  alloy  of  one  part  blamuih, 
two  parts  tin,  and  one  part  lead  is  used  by  pewter-workers  as  a  soft  solder, 
and  by  soap-makers  for  moulds.  An  alloy  of  five  parts  bismuth,  two  parte 
tin,  and  three  parts  lead  melts  at  199*  F.,  and  is  somewhat  used  for  ater- 
eotyping,  and  for  metallic  writing-pencils.  Thorpe  gives  the  following 
proportions  for  the  better^known  fusible  metals: 


BEABINQ-HETAL  ALLOTS. 


333 


Name  of  Alloy. 

Bismuth. 

Lead. 

Tin. 

Cad- 
mium 

Mer- 
cury. 

Melting, 
point. 

Newton*8 

60 
50 
50 
50 
50 
50 
50 

81  .S5 
28.10 
25.00 
25.00 
25.00 
26.00 
20.55 

18.76 
24.10 
26.00 
25.00 
12.50 
12.78 
21.10 

902»   F. 

Rose's 

D'Arcet's 

201*    •• 

Wood's 

iiiso 

10.40 
14.0« 

2500 

11S«    " 
149*    " 

Upowitz*s 

Gathrie's  ** Entectic '*.. . 

1490    " 
"Veiylow." 

The  action  of  heat  upon  some  of  these  alloys  is  remarkable.  Thus,  Lipo- 
vitz's  alloy,  which  Rolidifles  at  149^  Fah.,  contracts  ?ery  rapidiv  at  first,  as 
it  cools  from  this  point.  As  the  cooling  goes  on  the  coti traction  becomes 
slower  and  slower,  until  the  temperature  falls  to  101.8'  Fall.  From  this 
point  the  alloy  expands  as  it  cools,  until  the  temperature  falls  to  about  77^ 
rah.,  after  which  it  again  contracts,  so  that  at  82*  F.  a  bar  of  the  alloy  has 
the  same  l«*ngth  as  at  1 15*  F. 

Alloys  of  bismuth  have  been  used  for  makln:;  fusible  plugs  for  boilers,  but 
it  is  found  that  they  are  lUtered  by  the  continued  action  of  heat,  so  that  otie 
cannot  rely  upon  them  to  melt  at  the  proper  temperature.  Pure  Banca  tin 
is  used  by  the  U.  8.  OoTemment  foi'  fusible  plugs. 

FIJSIBIiB  AIjIiOTA.    (From  various  sources.) 

Sir  Isaac  Kewton's.  bismutli  5.  lead  8,  tin  2,  melts  at 212*  F. 

R^>8e's,  bismuth  2,  lead  1,  tin  1,  melts  at 200  " 

Wood's,  cadmium  1,  bismuth  4,  lead  2.  tin  1.  melts  at 166  " 

Guthrie's,  cadmium  18.29,  bismuth  47.88,  lead  19.80,  tin  19.97,  melts  at.  160  " 

Lead  8,  tin  5,  bismuth  8,  melu  at 208  ** 

Lead  1,  tin  a,  bismuth  5,  melts  at 212  '* 

Lead  1.  tin  4,  bismuth  5,  melts  at 240  " 

Tin  1,  bismuth  1,  melts  at 286  '* 

I.ead  8,  tin  8.  melU  at 884  '• 

Tfn  2.  bismuth  1,  melts  at 8:i6  " 

Lead  1,  tin  2,  melts  at 860  " 

Tln8.  bismuth  1,  melts  at 892  " 

Lead  «,  tin  1,  melts  at 475  ** 

Lead  1.  tin  1,  melts  at  466  " 

Lead  1.  tin  3,  melts  at 884  " 

Tin  8,  Usmuth  1,  melts  at. 892  '* 

Lead  1,  bismuth  1,  melts  at 257  »* 

Lead  1.  Tin  1.  bismuth  4,  melts  at 201  ** 

Leads,  tins,  bismuths,  melts  at 202  '' 

Tin  8,  bismuth  5.  melts  at , 202  ** 

BEARING-.nBTAL  AI.I.OTS. 

(C.  B.  Dudley,  Jour.  F.  /.,  Feb.  and  March,  1892.) 

Allosrs  are  nse«I  hh  b«'artnirs  in  place  of  wrought  iron,  cast  iron,  or  steel, 
partly  becaune  wear  and  f  i-i<*tion  are  believed  to  be  more  rapid  when  two 
metala  of  t  e  same  kind  work  together,  partly  because  the  soft  metals  are 
more  easily  worked  nnd  got.  into  proper  shape,  and  partly  l)ecanse  it  is  de- 
rirable  to' use  a  soft  metal  which  will  take  the  wear  rather  than  a  hard 
metal,  which  will  wear  the  J'>urnal  more  rapidly. 

A  gOfMl  bearing-metal  inuKt  have  five  characteristics:  (1)  It  must  be  strong 
enough  to  carry  the  load  without  di.«ttortion.  Pressures  on  car- journals  are 
frequeotly  as  high  aM  dHO  to  400  lbs.  per  square  inch. 

rt}  A.  good  bearing-metal  should  not  heat  readily.  The  old  copper-tin 
Iwtsiing,  made  of  seven  parts  copper  to  one  part  tin,  is  more  apt  to  heat 
than  uome  other  alloys.  In  general,  reHearch  seems  to  sliow  that  the  harder 
tntf  bearing-metal,  the  more  likely  it  is  to  heat. 

3)  Good  beariiiK-uietal  should  work  well  in  the  foundry.  Oxidation  while 
iii«*lting  caufles  spongy  castings.  It  can  he  prevented  by  a  liberal  use  of 
powdered  charcoal  while  melting.  The  addition  of  1%  to  2%  of  zinc  or  a 
■mail  amount  of  phosphorus  greiitiv  aids  in  the  production  of  sound  cast- 
ings.   Tbls  is  a  principal  element  of  value  in  phosphor-brouie. 


834 


ALLOTS. 


(4)  Good  bearlDg-metalfl  should  show  small  friction.  It  is  true  that  frietlos 
is  almost  wholly  a  question  of  the  lubricant  used;  but  the  metal  of  the  bear- 
ing: has  certainly  some  influence. 

(5)  Other  things  being  equal,  the  best  bearing-metal  is  that  which  wears 
slowest. 

The  princlfial  constituents  of  bearing-metal  allojs  are  copper,  tin,  lead. 
sine,  antimony,  iron,  and  aluminum.  The  following  table  gives  the  constitu- 
ents of  most  of  the  prominent  beering-metals  as  analyzed  at  the  Peniieyl' 
▼aula  Railroad  laboratory  at  Altoona. 

Analyses  of  Beartiur-inetal  Alloys. 


MetaL 


Camelia  metal 

Aiiti'friction  uiebU. 

White  metal 

CHP-brase  lining 

Bulge**  anti-f rietion 

Orapbite  bearing-metal 

Anlimonial  lead 

Carbon  bronze 

Cornish  bronze 

D«>lta  metal 

*Mainiolia  metal 

American  anti-friction  metal.. 

Tobin  bronze 

Qraney  bronze 

Damascus  bronze. 

Idanganese  bronze 

AJax  metal 

Anti-friction  metal 

Harrington  bronze 

Car-box  metal 

Hard  lead 

rhosplior-bronse 

Kjc.B.  metal 


Cop- 
per. 


7D.90 
1.60 

'4!6i 


75.47 

77.88 
iW.39 
trace 


M.OO 
75.80 
78.41 
0O.&a 
81  .S4 


66. 78 


TD.17 
78.80 


Tin. 


4.86 
08.18 


trace 

0  01 

"oItj 

0.60 


9.16 
080 
10.80 

e.c8 

10.08 


0.07 


lO.SS 
6.00 


14.75 


87.02 
84.87 

1.15 
67.78 
80.80 
14.6 
U.40 

5.10 
83.56 
78.44 

0.81 
16.06 
12.6;! 


7.87 
88.8S 

84.88 
04.40 
0.81 
16.00 


Zinc. 


10.90 


86.6'; 


(race 

0.06 
88.40 


49.87 
trace 


Anti- 
mony. 


12.06 
15.10 


10.78 
1S.88 


16  46 
10.60 


11.08 


14.88 
8.06 


Iron. 


0.65 


f   (1) 


trace(8) 

0.07 
traced) 

0.66 

0.11 


.(5) 
.(8) 


0.86 
O.Cl 


.(71 


Other  constituents: 

(1)  No  graphite.  r6)Noi       ^, 

(9)  Possible  trace  of  carbon.  (0)  Phosphorus  or  arsenic,  0.87. 

(8)  Trace  of  phoftphorus.  (7)  Phosphoruis  0.04. 

(4)  Possible  trace  of  bismuth.         (8)  Phosphorus,  0.90. 

*Dr.  H.  C.  Torrey  says  this  analysis  is  erroneous  and  that  Magnolia 
metal  always  contains  tin. 

Aa  an  example  of  the  influence  of  minute  changes  in  an  alloy,  the  Har- 
rington bronze,  which  conxIstH  of  a  minute  proportion  of  iron  in  a  copper- 
zinc  alliiy,  Bhowed  after  rolling  a  tensile  strength  of  75,000  lbs.  and  S0%  elon- 
gation In  9  inches. 

In  experimenting  on  this  subject  on  the  Pennsylvania  Railroad,  a  certain 
number  of  the  bearings  were  made  of  a  standard  bearinsr-mrtai.  and  the 
same  number  were  made  of  the  metal  to  be  tt'sted.  Tiiese  bearinrs  w«»re 
placed  on  opposite  ends  of  the  same  axle,  one  side  of  the  oar  having  the 
standard  bearings,  the  oUier  the  experimental.  Before  iroing  into  service 
the  bearings  were  carefully  weighed,  and  after  a  sufficient  time  they  were 
again  weighty). 

The.  Ktaiulard  bearing-metal  used  is  the  "  8  bearing^metal**  of  the  Phoa- 
phor-bronze  SmeltiuK  Co.  It  contains  about  79.70^  copp«*r,  9.f>Q%  lead.  U)% 
tin,  and  O.HO-C  phoBplu»rtis.  A  large  number  of  evperimentM  liaveslipwn  that 
th«*  loMi  of  wfi»rhf  of  a  b«*aring  of  thiB  metal  Ik  1  lU.  to  each  I8.0U0  to  96.00U 
miles  travelled.  Be««i«les  the  meaHurenn»nt  of  wear.  olMiervations  were  matde 
on  the  frequency  of  "  hot  boxew  "  with  tiie  diflferent  metals. 

The  reMiiUs  of  the  tests  for  wear,  so  far  as  given,  are  condensed  into  the 
following  table : 


BBARINQ-MSTAL  ALLOYS.  8S5 

CompodtloD.  Rate 

Metal.  4 ' ,     of 

Copper.        Tin.  liead.      Fhoe.      Araenio.  Wear. 

Standard 79.70  10.00  9.50  0.80  100 

Copper-Un 87.60  13.50  148 

Oopper<tln,  second  experiment,  same  metal 158 

Copper-tin.  third  experiment,  same  meial 147 

Areenic-bronze 89.20  10.00  ....  ..•.  0.80         149 

Anenic-bronze 79.80  10.00  7.00  ....  0.80        115 

Ameoic-bronse 79.70  10.00  9.50  ....  0.80        101 

**K"bronze 77.00  10.60  «.60  98 

''K**  bronze,  second  experiment,  same  metal 03.7 

Alloy  "B" 77.00  8.00  15.00  86.5 

Tbe  old  copper-tin  alloy  of  7  to  1  has  repeatedly  proved  Its  inferiority  to  the 
phosphor-bronze  metal.  Many  more  of  the  copper-tin  bearings  heated 
than  of  the  phosphor-bronze.  The  showing  of  these  tests  was  so  satisf  ac- 
toiy  that  phosphor-bronze  was  adopted  as  the  standard  bearlDK-metal  of 
the  Ponnsylvania  R.R,  and  was  used  for  a  long  time. 

Tbe  experimeats,  however,  were  continued.  It  was  found  that  arsenic 
praeiieally  takes  the  place  of  phosphorus  in  a  copper-tin  alloy,  and  three 
teeta  were  made  with  arsenic- bronzes  as  noted  aboTe.  As  the  proportion 
lo  lead  is  increased  to  correspond  with  the  standard,  the  durability  increases 
sa  well.  In  view  of  these  results  the  "  K  **  bronze  wae  tried.  In  which  neither 
phosphoniB  nor  arseniewore  used,  and  in  which  the  lead  was  increased 
above  (he  proportion  in  the  standard  phosphor-bronze.  The  result  was  that 
the  metal  wore  7.20i%  slower  than  the  phosphor-bronze.  No  trouble  from 
beating  was  experienced  with  the  **  K  ** bronze  more  than  with  the  standard. 
Dr.  Dudley  continues: 

At  about  this  time  we  began  to  find  evidences  that  wear  of  bearing-metal 
ailoye  varied  in  accordance  with  the  following  law:  **That  alloy  which  has 
the  greatest  power  of  distortion  without  rupture  (i^eslllence),  will  best  resist 
wear.'*  It  was  now  attempted  to  d«|gn  an  alloy  in  accordance  with  this 
law,  taking  first  the  proportions  of  c<Kper  and  tin,  OU  parts  copper  to  1  of 
tan  was  settled  on  by  experiment  as  the  standard,  altnough  some  evidence 
since  that  time  tends  to  show  that  18  or  possibly  15  parts  copper  to  1  of  tin 
might  have  been  better.  The  influenoe  of  lead  on  this  copper-tin  alloy  seems 
to  be  Duicb  the  same  as  a  still  further  diminution  of  tin.  However,  the 
tendency  of  the  metal  to  yield  under  pressure  increases  as  the  amount  of 
Un  is  diminished,  and  the  amount  of  the  lead  increased,  so  a  limit  is  set  to 
the  use  of  lead.  A  certain  amount  of  tin  Is  also  necessary  to  keep  the  lead 
alloyed  with  the  copper. 

Reelings  were  cast  of  the  metal  noted  In  the  tabI6  as  alloy  **  B,'^  and  it 
wore  18.fij(  slower  than  the  standard  phosphor-bronze.  This  metal  is  now 
the  standard  bearing-metal  of  the  rennsylvanla  Railroad,  being  slightly 
chaaged  in  composition  to  allow  the  use  of  phosphor-bronze  scrap.  The 
formula  adopted  Is:  Ck>pper,  105  lbs.;  phosphor-bronze,  60  lbs.;  tin,  ^  lbs.: 
lead,  9B^  lbs.  By  using  ordinary  care  in  the  foundry,  keeping  the  metal 
well  covered  with  charcoal  during  the  melting,  no  trouble  is  found  in  casting 
good  bearings  with  this  metal.  Ttie  copper  and  the  ^osphor^bronse  can  be 
pot  fa  the  pot  before  putting  it  in  the  melting-hole.  The  tin  and  lead  should 
be  added  after  the  pot  is  taken  from  the  fire. 

It  is  not  known  whether  the  use  of  a  little  zinc,  or  possibly  some  other 
eooibinAtion,  might  not  give  still  better  results.  For  tiie  present,  however, 
this  alloy  is  considered  to  fulfil  the  various  conditions  required  for  good 
b$«riog-metal  better  than  any  other  alloy.  The  phodphor-bronse  had  an 
nttimate  tensile  strength  of  80.000  lbs.,  with  6jf  elongation,  whereas  the  alloy 
"  B  **  had  84,000  IbsL  tensile  strength  and  1 M  elongation. 

(For  oChsr  bearlqg^iiietals,  see  Alloys  containing  antimony,  on  next  page, 


336  ALLOYS. 

AIiI.OTS  CONTAINING  ANTIIHONT'. 

VABXODB  AMALT8S8  OF  BaBBITT  MbtAL  AND  OTBER  ALLOTS  COMTAUriKO 

Antimony. 


Tin. 

Copper 

Antimony. 

Zinc. 

Lead. 

Bismuth. 

Babbitt  metal    ) 
for  lifrht  duty  1 

60 

=89.3 
96 

=88.9 
85.7 
81.9 
81.0 
70.6 
29 
45  5 
89.8 
85 

1 

1.8 

4 

8.7 

1.0 

■*2'"" 

4 
10 

1.6 

1.8 

6 

6  parts 
8.9  per  ct. 
8  imrts 
7.4perct. 

10.1 

16.2 

16. 

25.5 

62. 

18. 
7.1 

10. 

Harder  Babbitt » 
for  bearings*  f 

Britannia 

2.9 
1.9 
1. 

H 

*k 

«c 

6. 

"Babbitt"  .... 

40.0 

Plate  pewter.. 

t  ft 

White  metal... 

Bearinfcs 

on  Qer.  locomotiTes. 

*  It  Is  mlx(>d  as  follows:  Twelve  parts  of  copper  are  first  melted  and  then 
86  parts  of  tin  are  added;  24  parts  of  antimony  are  put  in,  and  then  .36  parts 
of  tin,  the  temperature  bein|(  lowered  as  soon  as  the  copper  is  melted  in 
order  not  to  oxidize  the  tin  and  antimony « the  surface  of  the  bath  beinf? 
protected  from  contact  with  the  air.  The  alloy  thus  made  is  sulisequently 
rem«>ltf d  in  the  proportion  of  60  parts  of  alloy  to  100  tin.    (Joshua  Rose.) 

llTlilte-iiietal  Alloys*— Tiie  following  alloys  are  used  as  lining  meuds 
by  the  Eastern  Kailroad  of  France  (1890): 


Number. 

Lead. 

An  tl  moor. 

1 

65 

25 

2 

0 

11.12 

8 

TO 

90 

4 

80 

8 

Tin. 
0 

Copyer. 

88.88 

6.66 

10 

0 

12 

0 

No.  1  is  used  for  lining  cross-head  slides,  rod-brasses  and  axle-bearings: 
No.  2  for  lining  axle-bearings  and  connecting-rod  brasses  of  heavv  engines; 
No.  8  for  lining  eccentric  straps  and  for  bronse  slide-Talves;  ana  No.  4  for 
metallic  rod-packing. 

Some  of  the  best-known  white-metal  alloys  are  the  following  (Circular 
of  Hoveler  &  Dieckbaus,  London,  1893): 

Tin.      Antimony. 

1.  Parsons'  86  1 

2.  Richards' 70  15 

8.  Babbitt's 66  18 

4.  Fentons' 16  0 

6.  French  Navy 7M  0 


Lead. 
0 


Copoer. 


6.  Geriiiau  Navy 86 


7« 


7H 


Zinc 
27 

0 

0 
79 
87H 

0 


**  There  are  engineers  who  object  to  white  metal  containing  lead  or  sine. 
Tills  is.  however,  a  prejudice  quite  unfounded,  inasmuch  as  lead  and  sico 
often  have  properties  of  great  use  in  white  allovs." 

It  Ih  a  further  fact  that  an  *'ea8y  liquid'*  alloy  must  not  contain  more 
than  \S%  of  antimony,  which  Is  an  Invaluable  ingredient  of  white  metal  for 
improving  its  hardness;  but  In  no  case  must  it  exceed  that  margin,  as  this 
would  r<»duce  the  plasticity  of  the  compound  and  make  it  brittle. 

Hardettt  alloy  of  tin  and  lead:  6  tin,  4  lead.  Hardest  of  all  tin  alloys  (?):  74 
Un,  18  antimony,  8  copper. 

Alloy  for  thin  open-work,  ornamental  castings:  Lead  2,  antimony  1. 
White  metal  for  patterns:  Lead  10,  bisnmth  0,  antimony  2,  common  brass  8» 
tin  10. 

Type-metal  Is  made  of  various  proportions  of  lead  and  antimony,  from 
17%  to  20^  antifiiony  aooording  to  the  hardness  desired. 

Babbitt  mtetals.    (C.  R.  Tompkins,  Mecfianical  News,  Jan.  1801.) 
The  practice  of  lining  Journal-boxes  with  a  metal  that  is  sufficiently  fusi- 
ble to  be  melted  In  a  common  ladle  is  not  always  so  much  for  the  purpoee 
of  securing  anii-frlction  properties  as  for  the  convenience  and  cheHpness  of 
forming  a  perfect  bearing  in  line  with  the  shaft  without  the  necessity  of 


ALLOYS  CONTAINING  ANTIMONY.  837 

Dorinsr  them.    Boxes  that  Are  bored,  oo  matter  how  accurate,  require  Rreat 
care  in  fltting  and  attaching  thetu  to  the  frame  or  other  parts  of  a  iiiachiue. 

It  iff  not  f^ood  practice,  however,  to  use  the  shaft  for  the  purpose  of  cast- 
ing the  bearings,  etipecially  if  ttie  phaf c  be  steel,  for  the  reason  that  the  hot 
metal  is  apt  to  sprlnK  it;  the  better  plan  is  to  use  a  mandrel  of  the  same 
size  or  a  trifl '  larger  for  this  purpose.  For  slow-running  Journals,  where 
the  load  is  moderate,  aim  st  any  metal  that  may  be  conveniently  melted 
and  will  run  free  will  answer  the  purpose.  For  wearing  properties,  with  a 
moderate  speed,  there  is  probably  nothing  superior  to  pure  zinc,  but  when 
not  combined  with  some  other  metul  it  shrinks  so  much  in  cooling  that  it 
caooot  be  held  flrmlv  in  the  recess,  and  soon  works  loose;  and  it  lacks  those 
anti-friciion  properties  which  are  necessary  in  order  to  stand  high  speed. 

For  Une-«haf ling,  and  all  work  where  the  speed  is  not  over  800  or  400  r.  p. 
iR.,  an  alloy  of  8  parts  zinc  and  2  parts  block-tin  will  not  only  wear  longer 
than  any  composition  of  this  class,  but  will  successfully  resist  the  force  of 
a  heary  load.  The  tin  counteracts  the  shrinkage,  so  that  the  metal,  if  not 
overheated,  will  firmly  adhere  to  the  box  until  it  Is  worn  out  But  tbla 
mixture  does  not  possess  sufficient  anti-friction  properties  to  warrant  its  use 
in  faat-ranning  journals. 

Among  all  tfie  soft  metals  in  use  there  are  none  that  possess  greater  anU- 
friciion  properties  than  pure  lead;  but  lead  alone  is  impracticable,  for  it  is  so 
soft  that  It  cannot  be  retained  In  the  recess.  But  when  by  any  process  lead 
can  be  sufllcientlr  hardened  to  be  retained  in  the  boxes  without  materially 
injuring  Its  anti-friction  properties,  there  Is  no  metal  that  will  wear  longer 
in  lirht  fast-running  journals.  With  most  of  the  best  and  most  popular 
aoti- friction  metals  in  use  and  sold  under  the  name  of  the  Babbitt  metal, 
the  basis  is  lead. 

Lead  and  antimony  have  the  property  of  combining  with  each  other  in 
all  proportions  without  impairing  the  anti- friction  properties  of  either.  The 
antimony  hardens  the  lead,  and  when  mixed  id  tne  proportion  of  80  parts 
lead  by  weight  with  20  parts  antimony,  no  other  known  composition  of 
metala  possesses  greater  anti-friction  or  wearing  properties,  or  will  stand  a 
higher  speed  without  heat  or  abrasion.  It  runs  free  in  its  melted  state,  has 
no  shrinkage,  and  is  better  adapted  to  light  high-speeded  machinery  than 
anr  other  known  metal.  Care,  however,  should  be  manifested  in  uning  it, 
and  it  should  never  be  heated  beyond  a  temperature  that  will  scorch  a  dry 
pine  stick. 

Many  different  compositions  are  sold  under  the  name  of  Babbitt  metal. 
Some  are  good,  but  more  are  worthless;  whil^  but  very  little  genuine  Babbitt 
metal  is  sold  that  is  made  strictly  according  to  the  original  formula.  Most 
of  the  metals  sold  under  that  name  are  the  refuse  of  type-foundries  and 
other  smelting-works,  melted  and  cast  into  fancy  ingots  with  special  brands, 
and  aold  under  the  name  of  Babbitt  metal. 

It  Is  difficult  at  the  present  time  to  determine  the  exact  formulas  used  by 
the  original  Babbitt,  tne  inventor  of  the  recessed  box,  as  a  number  of  differ. 
ent  formulas  are  given  for  that  composition.  Tin,  copoer,  and  antimony 
were  the  ingredients,  and  from  the  best  sources  of  information  the  original 
propcdrtiona  were  as  follows : 

Another  writer  gives: 

SOpartstln  =>  80.8<  BS.9i 

2parts  copper =    Z.QjC  S.H 

4  parts  antimony s    T.ljt  8.^ 

The  copper  was  first  melted,  and  the  antimony  added  first  and  then  about 
ten  or  fifteen  pounds  of  tin,  the  whole  kept  at  a  dull-red  heat  and  constantly 
Btirrad  until  the  metals  were  thoroughly  incorporated,  after  which  the 
balance  of  the  tin  was  added,  and  after  being  thoroughly  stirred  again  it 
was*  then  cast  into  ingots.  When  the  copper  is  thoroughly  melted,  and 
before  the  antimony  is  added,  a  handful  of  powdered  charcoal  should  he 
thrown  into  the  crucible  to  form  a  flux,  in  ortier  to  exclude  the  nir  and  pre- 
vent the  autimony  from  vaporizing;  otherwise  much  of  it  will  H$wrape  in  the 
form  of  a  vapor  and  conseouently  be  wasted.  This  metnl.  when  carefully 
prepared,  is  probably  one  of  the  best  metals  in  use  for  lininpr  boxes  that  are 
vihjfcted  to  a  heavv  weight  and  wear;  but  for  light  fast-running  ioumals 
the  copper  renders  ft  more  susceptible  to  friction,  and  it  in  more  liable  to 
farat  (ban  the  metal  composed  of  lead  and  antimony  in  the  proportiODa  just 
giveii* 


S3S 


StKKi^CKrfi  01*  MJjtmULiA, 


(^6THmoti  soldets,  equlU  purU  tin  and  lead :  fine  solder,  2  tin  to  1  lead ;  chea^ 
«o!der,2lead.ltln.  t~  ,  , 

Fu6tiig.tk>lnt  of  tin- lead  Alloys: 


"  1 


1   ' 


OoiMttR>n 


Tift  1^  to  lead 
«*  <^     **     *^ 

«•    9  M         «» 

«•    ^  ««         •« 

*•  6      •*     •• 

**  a     *'    ** 


.894»F. 
.840 
.  8641 

..806 
..878 

..8n 


0<M  iold«r  fof  14-carat 


^in}tolead86......566"Fj 

6i.....»tl 

8...;. .489 

9....i.441 

1....W.890 

^      ^      kffcont*l«4l*iidtcrftfft. 

QoM  sofaer:  M  Mlrts  rold^  6  ftflver,  4  copper. 

I^ld:  88  pdHft  ^Id^  89  8l^r«ir,  Itt^  brass,  1  zinc. 

fsmtf  solder:  Teflo#  brass  Wp&TtB,  ri&c  7,  tte  11^    Another:  Silt«r  145 
^rfs,  bras*  (8  efopper,  1  tihc)  78,  sfne  4. 
Oemiito-rtlter'  »o!dei*:  Copper  86,  zliid  54,  tfrleltel  8. 
NoteFtf  MttdeM  toif  MumiiittMi: 

Tin  100  parts,  lead  5;  melts  at  68(«  to  67)»  F. 

"   IW^*     atueH;  "       688  to  618 

•MOW     ••     copper  10  ttf  15;        "       Wto84« 
<MODO     "     nlclcel  10  to  16;        **       663  to  848 
Notel^H  solder  for  ahimlaiim  broBae?  TU  860  parta^  copper  100,  bismuth  8 
to  8.    K  is  olaifned  that  this  Solder  Is  iri*>  suitable  for  joining  ahimiDiim  ta 
•oppor«  brasa,  lifR;,  iroB,  or  niftkeL 

BOPBB  AH D  CABZfB8« 

I^TltBlli>ar»  OF  R€i!frBS^ 

(A  S.  Itenr<m  A  Co,,  Birkenhead.    Kleln*S  Tt-avslatian  (ft  Wd^tiacli,  ^ol.  Iff. 
part  1,  sec.  2.) 


Hemp. 


Glfth. 

Inches. 

% 

*^ 

6» 

6 

6H 

7 

8 
if" 

n 

18 


Weisrht 


afb! 


Falboiti. 


Founds. 
8 

4 

8 

7 

9 
10 
18 
14 
10 
18 

88 

96 
80 

84 


Iron. 


GWrth. 


tncheS. 


FAthom. 


i^oundsj 

1 

fi 

?< 
i« 
1? 

18 
18 
14 
15 
16 
18 
SO 


Steel. 


Girth. 


Inches. 

1 

m 

2 


^4 


Weight 

per 
Fathom. 


Pounds. 
1 

IM 
8 


6^ 

8 

8 

10 
18 


Tensile 
8treB|(tli. 


Ghrosstonsb 
8 
8 

4 
5 
8 
7 
8 
9 

1? 
il 

14 

15 

a 

28 
89 
88 
80 
40 


dsd 


Hemp. 


Girth. 


per 
Fathom, 


Iron, 


GHrih. 


Weight. 

per 
Fathdm. 


8toel. 


Girth. 


Weight 
Fathom, 


tensito   , 
St^M^th* 


Inch< 


Founts. 
11 
18 
15 
16 
18 
20 
S3 
25 
28 
82 
84 


ZMIMb. 


l^oitndB. 


1? 

Ifll 
19 


18 

18 


90 


28 
88 
» 
40 


60 


irorlUii 


liOMl«_llianieter.  und  ITelslit  of  Hopes  and 

(Klein'8  Weisbachf  vol.  Ul«  |«ri  1,  sec  2,  p.  561.) 


Hemp  ropes:  d  =  diam.  of  rope.  Wire  rope?  d  =i  dlam.  of  wire,  n  s 
number  of  wlree,  O  =  wel^t  per  running  foot^  k  =  permLBsible  kmS  M 
poundi  per  square  Inch  of  eection,  P=  permissible  ltm4  on  rope  or  chain. 

Oval  ehaf ns :  d  :*  dlam.  of  Iron  uset :  inside  dInaentioDB  of  oval  1.5d  and 
2.9d.  Cach  link  is  a  piece  of  diain  2.6c2  lone.  O*  »  wetf^ht  of  a  single  IMV  oiF 
2.10d»  ]b&  }  0  =  weight  per  running  foot  =  9.7Sd«  " 


Hba 


Bettfien  Rope. 

Wire  Rope. 

Dry  and  Untarlre<l. 

Wdt  or  Tarred. 

tab«.)  = 

cf  (Ins.)s 

P<lb8.)=: 

fi^(lbe)  =  . 

1480 

0.08  KP 

llaOd*  s  885S6i 
1.28d*»8.00e05P 

IHQ 

0.088  fP 

»t6d»  =  HTSflf 
1.54d«±i0.0006P 

19880   _ 

d.OOBT-Zf 

tSfyfhtd*  s  45000 
2.«1nd*  c«0XK)O218P 

Open-fhik  Chain. 

Stutlink  Chain. 

4  (ioft)  - 

,      0.0 

13850(P 

0.78d» 

8M0 
987  4^ 
=:  1860(7 
.0.000787P 

114019 

8.0076  4/? 

17800d«  «  168W7 

18.66cis  s  0.0808P 

Stud  ChaliM  4/8  times  as  siroiiff  as  open-Uak  variety.  [This  is  contrary  to 
the  statements  of  Capt.  6eardslee<  U.  S.  N.,  In  the  report  of  the  U/  8.  Teat 
Board.  He  holds  that  the  open  link  Is  stronger  than  the  studded  Uiyi*  See 
p.806a»to]. 


840 


STBENaXH  OF  UATERIAIS. 


BTRENQTH  AND  WEIGHT  OF  WIRE  ROPE,  HEMPEN  ROPE,  ANB 
CHAIN  CABLES.    (Klein's  WeiBbach.) 


Breaking  T.oad 
in  tons  of 

saioibs. 

Kind  of  Cable. 

Girth  of  Wire  Rope 

and  of  Hemp  Rope 

Diameter  of  Iron 

of  Chain,  inches. 

Weight  of  One 

Foot  In  leng:th. 

Pounds. 

ITon 

(Wire  Rope 

<  Hemp  Rope 
Chain 
Wire  Rope 

<  Hemp  Rope 
Chain 
Wire  Rope 

•  Hemp  Rope 
Chain 
Wire  Rope 

<  Hemp  Rope 
Chain 
Wire  Rope 

•<  Hemp  Rope 

Chain 

Wire  Rope 
•<  Hemp  Rope 

Chain 

Wire  Rope 

•  Hemp  Rope 
Chain 
Wire  Rope 

<  Hemp  Rope 
Chain 

( Wire  Rope 
■<  Hemp  Rope 

Chain 

Wire  Rope 
-{ Hemp  Rope 

Chain 

1.0 
8.0 

6.0 

7.0 

11/16 

8.0 

8.0 
18/16 

8.6 

9.0 
29/32 

4.0 
10.0 
81/88 

4.5 
11.0 

1.1/16 

6.0 
14.5 

1.8/16 

5.5 
14.0 

1.5/16 

6.0 
16.0 

1.7/16 

0.126 
0.177 

STong 

0.500 
0.488 
0.078 

12Ton8 

2.667 
0.758 
2.086 

16 Tons.. . ■ .-«.  •• 

4.508 
1.186 
2.866 

aOTons 

21  Tons 

6.109 
1.646 
8.836 
7.674 
2.048 
4.166 

aOTons, 

86  Tons* 

8.886 
2.725 
6.000 
10.885 
8.728 
6.940 

44  Tons....  

61  Tons 

18.01 
4.50 
6.94 

16.00 
5.67 
7.92 

19.16 

Length  sufficient  to  provide  the  maximum  working  stress : 

Hempen  rope,  dry  and  untarred 8055  feet. 

**  '•     wetortarred 1975    " 

Wirerope 4590    " 

Open  link  chain 1860    «• 

Studchain 1660    " 

Sometimes,  when  the  depths  are  very  great,  ropes  are  given  approximately 
the  form  of  a  body  of  uniform  strength,  by  making  them  of  separate  pieces, 
whose  diameters  diminish  towards  the  lower  end.  It  is  evident  that  by  this 
means  the  tensions  In  the  fibres  caused  by  the  rope*s  own  weight  can  be 
considerably  diminished. 

Hop«  tor  Holatlns  or  Trannitlsalon.  Manila  Kopa- 
(C.  W.  Hunt  Company,  New  York. >— Rope  used  for  hoisting  or  for  trana- 
mission  of  power  is  subjected  to  a  rerv  severe  test.  Ordinary  rope  chafes 
and  grinds  to  powder  in  the  centre,  while  the  exterior  may  look  as  though 
It  was  little  woi-n. 

In  bending  a  rope  over  a  sheave,  the  strands  and  the  yams  of  these  strands 
slide  a  small  distance  upon  eacli  other,  causing  friction,  and  wear  the  rope 
internally. 

The  *'  Stevedore  "  rope  used  by  the  C.  W.  Hunt  Co.  Is  made  by  lubricating 
the  fibres  with  plumbago,  mixed  with  sufficient  tallow  to  hold  it  in  position. 
This  lubricates  the  yams  of  the  rope,  and  prevents  internal  chsmng  and 
wear.  After  running  a  short  time  the  exterior  of  the  rope  gets  compressed 
and  coated  with  the  lubricant. 

In  manufacturing  rope,  the  fibres  are  first  spun  into  ayaro.  this  Tarn 
being  twisted  in  a  direction  called  "right  hand.^*  From  20  to  80 of  Uteiie 
Tarns,  depending  on  the  size  of  the  rope,  are  then  put  together  and  twisted 
In  the  opposite  direction,  or  "left  hand,*' into  a  strand.   Three  of  these 


8TBEKGTH  OF  ROPBS.  341 

stnnds,  for  a  S«tnuid,  or  four  for  a  4-straiid  rope,  are  then  twisted 
together,  the  twiat  being  again  in  the  '*  right  hand  '^  direction.  When  the 
strand  is  twisted.  It  untwists  each  of  the  threads,  and  when  the  three 
strands  are  twisted  together  into  rope,  it  untwists  the  strands,  but  again 
twists  up  the  threads.  It  is  this  opposite  twist  that  keeps  the  rope  in  its 
proper  form.  When  a  weight  is  hung  on  tlie  end  of  a  rope,  the  tendsncjr  is 
for  the  rope  to  untwist,  and  become  longer.  In  untwisting  the  rope,  it 
would  twi«t  the  threads  up,  and  the  weight  will  re?olve  uniifthe  strain  of 
tlie  untwisting  strands  just  equate  the  strain  of  the  threads  being  twisted 
tighter.  In  malting  a  rope  it  is  impossible  to  malce  these  strains  exactly 
hslanoe  each  other.  It  is  this  fact  that  makes  it  necessary  to  take  out  the 
"turns"  in  a  new  rope,  that  Is,  untwist  It  when  It  is  put  at  work.  The 
proper  twist  that  shouM  be  put  in  the  threads  has  been  ascertained  approx- 
unstely  by  experience. 

Tha  amount  of  work  that  the  rope  will  do  ▼aries  greatly.  It  depends  not 
only  on  the  quality  of  the  fibre  and  the  method  oflaving  up  the  rope,  but 
also  on  the  kind  of  weather  when  the  rope  is  used,  the  blocks  or  sheaves 
over  which  it  is  run,  and  the  strain  In  proportion  to  the  strain  put  upon  the 
rope.  The  principal  wear  comes  in  practice  from  defective  or  badly  set 
sheaves,  from  excess  of  load  and  exposure  to  storms. 

The  loads  put  upon  the  rope  should  not  exceed  those  given  In  the  tables, 
for  the  most  economical  wear.  The  Indications  of  excessive  load  will  be  the 
twist  coming  out  of  the  rope,  or  one  of  the  strands  slipping  out  of  its  proper 


p^jsitlon.  A  certain  amount  of  twist  comes  out  In  using  it  the  first  day  or 
two,  bat  after  that  the  rope  should  remain  substantially  the  same.  If  it 
does  not,  the  load  Is  too  great  for  the  durability  of  the  rope.  If  the  rope 
wears  on  the  outside,  and  is  good  on  the  Inside,  it  shows  that  it  has  been 
chafed  In  running  over  the  pullejrs  or  sheaves.  If  the  blocks  are  very  small. 
It  will  increase  the  sliding  of  the  strands  and  threads,  and  result  in  a  more 
rapid  Internal  wear.  Rope  made  for  hoisting  and  for  rope  transmission  is 
nsoally  made  with  four  strands,  as  experience  nas  shown  tnis  to  be  the  most 
a»^loeable. 
The  strength  and  weight  of  **  stevedore  *'  rope  is  estimated  as  follows: 

Breaking  strength  in  pounds  =  780  (circumference  In  Inches)*; 
Weight  in  pounds  per  foot     =  .062  (circumference  in  Inches)*. 

The  Teelmlcal  UToriU  relating  to  Cordage  most  frequently 
heard  are: 

Tabic.— Fibres  twisted  together. 

Thxkad.— Two  or  more  amcUl  yams  twisted  together. 

SnuNO.— The  same  as  a  thread  but  a  little  larger  yams. 

Stband.— Two  or  more  large  yaniM  twisted  together. 

OoRD.— Several  threads  twisted  together. 

BopK.— Several  atranda  twisted  together. 

Haw8BR.~A  rope  of  three  atraruU. 

Shroud-Laio.— A  rope  of  four  atranda, 

Cablb.— Three  hawsers  twisted  together. 

Tarks  are  laid  up  left-handed  into  atranda, 

Sraaims  are  laid  up  right-handed  Into  rope. 

Hawbbrs  are  laid  up  left-handed  into  a  cable. 
A  rope  is : 

Laid  by  twisting  strands  together  In  making  the  rope. 

SrucBD  by  Joining  to  another  rope  by  Interweaving  the  strands. 

Wbippbd.— By  winding  a  string  around  the  end  to  prevent  untwisting. 

Sbbvbd. — When  covered  by  winding  a  yam  continuously  and  tightly 
around  it. 

Pabcblbd.— By  wrapping  v^ith  canvas. 

SaizBD. — ^When  two  parts  are  bound  together  by  a  yam,  thread  or  string. 

Patbd.— Whan  painted,  tsrred  or  greased  to  resist  wet. 

Haui-.— To  pull  on  a  rope. 

Taut. — Drawn  tight  or  strained. 

ilctnff  of  RopeB.— The  splice  in  a  transmission  rope  is  not  only  the 
part  of  the  rope  but  Is  the  first  part  to  fail  when  the  rope  Is  worn 


Spile 

veakest 


oat  If  the  rope  is  larger  at  the  splice,  the  projecting  part  will  wear  on  the 
pulleys  and  the  rope  fail  from  the  cutting  off  of  the  strands.  The  following 
alrecUona  are  given  for  splicing  a  4-8trand  rope. 

The  engravings  show  each  successive  operation  in  splicing  a  1^  Inch 
manOa  rope.    Each  engraving  was  made  from  a  f ull-sl2e  specimen. 


342 


8Tfi£17QTH  OF  HATEBIALS. 


Fia.  81. 
Spucixg  or  RoPM, 


SPUCtHQ  09  fiOPSd. 


843 


Tie  a  piece  of  twine,  9  and  10,  around  the  rope  to  be  spliced,  about  6  feet 
from  each  end.    Then  unlay  the  strands  of  each  end  back  to  the  twine. 

Batt  the  ropes  together  and  twist  each  corresponding  pair  of  strands 
loosely,  to  Iceep  them  from  being  tangled,  as  shown  In  Fig.  78. 

The  twine  10  is  now  cut,  and  the  strand  8  unlaid  and  strand  Tcarefutly  laid 
In  its  place  for  a  distance  of  four  and  a  half  feet  from  the  Junction. 

The  strand  6  is  next  unlaid  about  one  and  a  half  feet  aud  strand  5  laid  In 
tts  place. 

The  ends  of  the  cores  are  now  cut  off  so  they  just  meet. 

Unlay  strand  1  four  and  a  half  feet,  laying  strand  d  in  its  place. 

Unlay  strand  8  one  and  a  half  feet,  laying  in  strand  4. 

Cut  all  the  strands  off  to  a  length  of  about  twenty  Inches,  for  convenience 
in  manipulation. 

The  rope  now  assumes  the  form  shown  In  Fig.  79  with  the  meeting  polnti 
of  the  strands  three  feet  apart. 

Each  pair  of  strands  is  successively  subjected  to  the  following  operation: 

From  the  point  of  meeting  of  the  strands  8  and  7.  unlay  each  one  thi-ee 
turns;  split  both  the  strand  8  and  the  strand  7  in  halves  as  far  back  as  they 
are  now  unlaid  and  "  whip  *'  the  end  of  each  half  strand  with  a  small 
piece  of  twine. 

The  half  of  the  strand  7  is  now  laid  In  three  turns  and  the  half  of  8  also 
laid  in  three  turns.  The  half  strands  now  meet  and  are  tied  in  a  simple 
knot,  11,  Fig.  80,  makhig  the  rope  at  this  point  Its  original  size. 

The  rope  is  now  opened  with  a  marlin  spike  and  the  half  strand  of  7 
worked  around  the  half  strand  of  8  by  passing  the  end  of  the  half  strand  7 
through  the  rope,  as  shown  in  the  engraving,  drawn  taut  and  again  worked 
around  this  half  strand  until  It  reaches  the  half  strand  18  that  was  not  laJd 
in.  This  half  strand  18  is  now  split,  and  the  half  strand  7  drawn  through 
ihe  opening:  thus  made,  and  Chen  tucked  under  the  two  adjacent  strands,  as 
shown  in  Fig.  61.  The  other  half  of  the  strand  8  is  now  wound  around  the 
other  half  strand  7  In  the  same  manner.  After  each  pair  of  strands  has 
been  treated  In  this  manner,  the  ends  are  cut  off  at  12,  leaving  them  about 
four  inches  long.  After  a  few  days*  wear  they  will  draw  into  the  body  of  the 
rope  or  wear  off.  so  that  the  locality  of  the  splice  can  scarcely  be  dt«tected. 

Coal  HIolctiiiK*  (0.  W.  Hunt  Oo.).— The  amount  of  coal  that  can  be 
hoisted  with  a  rope  varies  greatly.  Under  the  ordinary  conditions  of  use 
a  rope  hoists  from  fiOOO  to  8000  tons.  Where  the  circumstances  are  more 
favorable,  the  amounts  run  up  frequently  to  12,000  or  15,000  tons,  occasion- 
ally to  20,000  and  in  one  case  32,400  tons  to  a  single  fall. 

when  a  hoisting  rope  Is  first  put  in  use.  it  Is  likely  from  the  strain  put  upon 
It  to  twist  up  when  the  block  Is  loosened  from  the  tub.  This  occurs  in  the 
first  day  or  two  only.  The  rope  should  then  be  taken  down  and  the 
''turns  ^  taken  out  of  the  rope.  When  put  up  again  the  rope  should  give 
DO  further  trouble  until  worn  out. 

It  is  necessary  that  the  rope  should  be  much  larger  than  Is  needed  to  bear 
the  strain  from  the  load. 

Practical  experience  for  many  years  has  substantially  settled  the  most 
ecx>nomScal  size  of  rope  to  be  used  which  is  given  in  the  table  below. 

Hoisting  ropes  are  not  spliced,  as  it  is  difficult  to  make  a  splice  that  will 
not  pull  out  while  running  over  the  sheaves,  and  the  increased  wear  to  be 
obtained  in  this  way  is  very  small 

Coal  is  usually  hoisted  with  what  is  commonly  called  a  **  double  whip;  *' 
that  ia,  with  a  running  block  that  Is  attached  to  the  tub  which  reduces  the 
strain  on  the  rope  to  approximately  one  half  the  weight  of  the  load  hoisted. 
The  following  table  gives  the  usual  sizes  of  hoisting  rope  and  the  proper 
working  strain: 

SCeT64ore  Holatlnsr-rope. 
C.  W.  Hunt  Co. 


CSrcamfereace  of 
the  rope  in  ing. 


8 


Proper  Working 

Strain  on  the  Hope 

in  lbs. 


8S0 
600 
650 
800 
1000 


Nominal  slse  of 

Coal  tubs.    Double 

whip. 


1/6  to  1/5  tons. 
1/5--- 


Approximate 

Weight  of  a  Coll, 

inlba 


860 
480 
650 
880 
MO 


Hoisting  rope  is  ordered  by  circumference,  transmission  rope  by  diameter. 


344 


8TREH0TH   OF  MATERIALS. 


Welclit  and  ^trenctli  of  IHanlla  Bop«« 

Spencer  Miller  iEng^g  Neivs,  Dec.  6, 1800)  gives  a  table  of  breaking  strength 
of  maiiila  rope,  which  he  considers  more  reliable  than  the  strength  computed 
bv  Mr.  Huni^s  fonnula:  Breaking  strength=7:20x(circuniference  in  inchtMi)*. 
Mr.  Miller^s  formula  Is:  Breaking  weight  11)8.  =  circumference* x a  coefflcient 
which  varies  from  900  for  ^"  to  700  for  2*'  diameter  rope,  as  below: 

Circumference    ..,  l\i     2     2^9^     8     8H    894    4W    4H     &     ^     ^ 
Coefficient    900    845    8a0    790    780    765    760    745    785    T25    718    700 

The  following  table  gives  the  breaking  strength  of  manlla  rope  as  cal- 
culated by  Mr.  Hunt's  formula,  and  also  by  Mr.  Miller^s,  using  in  the  latter 
the  coefflcieni  900  for  sizes b^Iow  lU  in.  circumference  and  700  for  sizes  above 
6  in.  The  differences  between  the  figures  for  any  given  size  are  probably 
not  greater  than  the  difference  in  actual  strength  of  samples  from  different 
makers.  Both  sets  of  figures  are  considerably  lower  than  those  given  in 
tables  published  by  some  makers  of  rope,  but  they  are  believed  to  be  more 
reliable.    The  figures  for  weight  per  100  ft.  are  from  manufacturers*  tables. 


B 

L 

1  Weight    of    1 
1      ](XJ    Feet 
of    Rope 
1      In  lbs. 

Ultimate 

fl 

Ultimate 

5'" 

5 

Stren 
Rope 

gthof 
in  lbs. 

11 

Strength  of 
Rope  in  lbs. 

Hunt. 

Miller. 

5 

|S?5 

Hunt. 

Miller. 

s 

9/16 

2 

230 

S80 

1  5/16 

4 

52 

n,600 

12,000 

H 

8 

400 

500 

^% 

4^4 

58 

18,000 

13,500 

1 

4 

680 

790 

iR 

4zV 

66 

14,600 

14.900 

n 

Iki 

5 

900 

1,140 

1  9/16 

4?4 

72« 

16,«00 

16.500 

7/16 

1^4 

6 

1,240 

1,550 

1^ 

5 

80 

16,000 

18,100 

lA 

iH 

^ 

1,620 

2,05?0 

5H 

97 

21,800 

21,600 

9/16 
13  Az 

m 

11 

2,050 

2,480 

2 

6 

118 

25,900 

25,200 

2 

13H 

2,880 

3.880 

2%^ 

^H 

188 

80,400 

29.600 

2W 

m 

3.610 

4.150 

2w 

7 

153 

35.800 

34.800 

20 

4,.')00 

6,030 

2v2 

7M 

184 

40,500 

89,400 

2^ 

23^ 

5,440 

5.970 

2^ 

8 

211 

46,100 

44,800 

1 

3 

2HVf» 

6,480 

7,020 

-m 

6H 

287 

52,000 

50.600 

1  1/16 

3V4 

»3Hi 

7.600 

8,160 

3 

9 

262 

58.800 

56.700 

m 

8V^ 

38 

8,820 

9,87t) 

^ 

9H 

298 

66,000 

68.200 

m 

m 

45 

10.120 

10.U90 

10 

S2S 

72,000 

70,000 

For  rope-driving  Mr.  Hunt  recommends  that  the  working  strain  should 
not  exceed  1/20  of  the  ultimate  breaking  strain.  For  further  data  on  ropes 
see  "  Rope-d living.'* 

Knots*— A  gi*eat  number  of  knots  have  been  devised  of  which  a  few 
only  are  illustrated,  but  those  selected  are  the  most  frequently  used.  In 
the  cuts.  Fig.  82.  they  are  shown  open,  or  before  being  drawn  taut,  in  order 
to  show  the  position  of  the  parts.    The  names  usually  given  to  them  are: 


A.  Bight  of  a  rope. 

B.  Simple  or  Overhand  knot. 

C.  Figure  8  knot. 

D.  Double  knot. 

E.  Boat  knot. 

F.  Bowline,  first  step. 
Q.  Bowline,  second  step. 
H.  Bowline  completed. 
I.  Square  or  reef  knot. 

J.  Sheet  bend  or  weaver's  knot. 

K.  Sheet  bend  with  a  toggle. 

L.  Carrick  bend. 

M.  Stevedore  knot  completed. 

N.  Stevedore  knot  commenced. 

O.  SUpknot. 


P.  Flemish  loop. 

§.  Chain  knot  with  tosKlei 

.  Hair-hitch. 

S.  Timber-hlrch. 

T.  Clove  hitch. 

U.  Rolling-hitch. 

V.  Timber-hitch  and  half-hitch. 

W.  Blaekwall-hltch. 

Z.  Fisherman's  bend. 

Y.  Round  turn  and  half -hitch. 

Z.  Wall  knot  commenced. 
A  A.       "       '*    completed.. 

B  B.  Wall  knot  crown  oomroenoed. 

CC.       • oompleCed. 


KKOn. 


845 


'Rte  principle  of  a  knot  Is  that  no  two  parts,  which  wonid  moTe  in  the 
same  (urection  if  the  rope  were  to  slip,  should  lay  along  side  of  and  touch- 
iDfT  each  other. 

The  howline  is  one  of  the  meet  useful  knots,  it  will  not  slip,  and  after 
being  strained  Is  easily  untied.  Oommence  by  making  a  bight  in  the  rope, 
then  put  the  end  through  the  bight  and  under  the  standing  part  as  shown  in 
0,  then  pass  the  end  again  through  the  bight,  and  haul  tight. 

The  square  or  reef  knot  must  not  be  mistaken  for  the  *'  granny  '*  knot 
that  slips  under  a  strain.  Knots  IT,  K  and  M  are  easily  untied  after  being 
under  strain.  The  knot  M  to  useful  when  the  rope  passes  through  an  eye 
azxi  is  held  fay  the  knot,  as  It  wHl  not  slip  and  is  esJBily  untied  after  being 
strained. 

ABO  0  E 


Flo.  8{.~Knotb. 

The  timber  hitch  8  looks  as  though  it  would  gi^e  way,  but  it  will  not:  the 
gnmter  the  strain  the  tighter  it  willhold.  The  wall  knot  looks  complicated, 
but  ia  easily  made  by  proceeding  as  follows:  Form  a  bight  with  strand  1 
and  paae  the  strand  2  around  the  end  of  it,  and  the  strand  8  round  the  end 
of  Sand  then  tlu-ough  the  bight  of  1  as  shown  in  the  cut  Z.  Haul  the  ends 
taut  when  the  appearance  is  as  shown  in  AA.  The  end  of  the  strand  1  ii* 
DOW  laid  over  the  centre  of  the  knot,  strand  2  laid  over  1  and  8  over  2,  when 
tlie  end  of  3  is  passed  through  the  bight  of  1  as  shown  in  BB,  Haul  all  the 
~  I  taut  as  shown  in  CC 


940  8TBENGTH  QW  VATEBIALS. 


^b9ft«iia«H0iariiBe 


Ta  M$ff  m  Wlr»  *i>»*f-Tlje  tool»  raqnimdr  Itt  b#  « 
fpike.  mppivg  GtiUen,  aii4  «i(oer  damps  or  a  «^Q#jl  hemp-rops  sfJos  viUi 
which  16  wrap  around  and  untwist  the  rope.    If  a  bench-vi8«  is  JiooQWihto 
It  jvy  1  be  toif$i4  QOfyvmiieui. 

jua  3plicitt«[  nopo.  a  /certain  length  la  used  «p  to  maklofs  tlM  spUo^-  Aji 
allowanoe  pf  oot  le«s  than  16  f^et  for  ^  inch  rope,  am  proportlooatelj 
lonRor  for  larf^ar  »izies»  m^  be  added  to  the  Jenc^Qi  of  m»  efoditiai  nope  ui 


ving  oiMMued,  «arefMl}7.  the  Iwirth  th«  rope  ehoujd  be  after  spliO' 
..■iw.Trrr...  _-._._  «,'__.  w,  *,._  ».     -f^-Ttj,e«ti»nd»  from  each 

tfaqdjr.afidt^iep: 

each  end  alternately  and  diaw 
them  together  so  that  the  points  Af  and  M*  meet,  as  in  Fig-  84- 

(2).  Unl4f  a  strand  from  one  end,  aod  following  the  unlay  closely,  lay  Into 
the  sesm  or  groove  it  Qpens,  the  strand  opposite  it  b^opging  to  the  other 


having  messurea,  earerMiiy,  tiM  length  U)»  rope  st 
UpiL  an<rin»rkAd  Uie  poioU  M  and  W,  Fig,  SB,  palay  U 
end  If  and  fy  to  Jtf  and  M'  »nd  cut  off  the  centre  at  Mi  i 

(1).  Interlock  the  six  unlaid  strands  of  each  end  £ 


end  of  the  rcme,  imtM  within  a  ipnerth  eqaaTto  three  or  four  times  the  length 
of  one  lay  of  the  rope,  and  out  the  other  strand  to  about  the  same  length 
from  the  point  of  meeting  as  at  ^,  Fig.  85, 

(8).  Unlay  tbo  adjacent  strand  in  tbe  opposite  dlrectien,  and  foNowing  the 
unlay  closely,  lay  ip  lU  place  tlie  correspondlpg  oppofftte  t^ngko,  cutting  the 
ends  i»s  described  before  at  B,  Ffg.  K.  • 

There  ara  bow  four  strands  laid  in  place  terminating  at  A  and  B,  with  the 
eight  remaining  at  M  M\  as  in  Fig.  85. 

It  will  be  well  aft^r  laying  eocb  pair  of  strands  to  tie  them  temporarily  at 
the  points  A  and  B. 

Pursue  theaa«M  eo^ne  with  the  remaining  tour  pnir»  of  opponite  stnutds^ 


no.  88. 


ITm*  04.  Fio*  V. 

Fe«K  80.  Fi9.  07. 

SVUOINO  WiBB  BOPB. 

stopping  each  pair  about  eight  or  ton  turns  of  the  rope  short  of  the  preced- 
ing pair,  and  cutting  the  ends  as  before.  ,    ,    . 

We  now  have  all  the  strands  laid  in  their  proper  places  with  their  roepect' 
ive  ends  passing  each  other,  as  in  Fig.  86.  .        .         .    ,  . 

All  methods  of  rope-splicing  are  identical  to  this  point:  their  variety  con- 
sists in  the  method  of  tucking  the  ends.  The  one  given  below  in  the  one 
most  generally  prant}eed.  .    ,  ^     ^  .  ^    ^ 

Clamp  the  rope  either  in  a  vlpe  at  a  point  to  the  left  of  A,  Fig.  U,  and  by  a 
hand-olamp  applied  noar  A,  open  up  the  rope  by  untwisting  sufflclently  to 
cut  the  core  at  A,  and  seising  it  with  the  nippero.  let  an  assistant  draw  it 
out  slowly,  you  following  it  olonely,  crowding  the  strand  in  its  olace  until  it 
is  all  laid  in.  Cut  the  core  where  the  strand  ends,  and  push  the  end  back 
into  its  place.  Remove  the  olamps  and  let  the  rope  close  together  around  it. 
Draw  out  the  core  in  the  opposite  direction  and  fay  the  other  strand  in  thf 
centre  of  the  rope,  In  the  same  manner.  Repeat  the  operation  at  the  five 
remaining  poinu,  and  hammer  the  rope  lightly  at  the  points  where  the  ends 
pass  each  other  at  A,  A,  B,  B,  etc.,  with  small  wooden  mallets,  and  the 
ipHoe  is  eomplete,  as  shown  in  Fig.  ST.  .    .^     ^  . 

U  a  elamp  and  vise  are  not  obtainable,  two  rope  slings  and  short  wooden 
BeveM  may  be  used  to  untwist  and  open  up  the  rope. 

▲  rope  spliced  as  above  will  be  nearly  as  strong  as  the  original  rope  and 
■mootn  everywhere.  After  running  a  few  days,  the  spltoe,  if  well  made, 
oanno%  be  found  except  by  close  examination.       .... 

The  above  instructions  fia^o  been  adopted  by  the  leading  rope  manufae* 
tnPBPB  of  Amerioa. 


HBLIOAL  9im^  SPRINGS.  347 

Deflnlttoiis.— A  spiral  spring  is  one  which  is  wound  Mound  a  fixed 
poiqt  or  centre,  and  coptinually  receding  from  i(  Hlpi  a  watch  spHng.  A 
nelical  aprins:  is  one  wkicli  Is  wound  ajroimd  an  ariMr,  and  ac  the  s^e  time 
adTaqcfns:  li^®  ^he  thread  qt  a  screw.  An  elliptical  or  lamina^  spring  is 
made  orVat  bars,  plates,  or  •*'  laavas,"  of  regtilarly  vai^iiig  lengths,  super- 
posed one  upon  the  other. 

the  KMowingfrom  M9  vof*  QU^Uioay  MqJhfnfnft  w; 

A  s=  elastlcitj,  or  deflection,  in  sixteen^  of  an  inch  per  ton  of  load. 


A  s=  elasdcitj,  or  deflection,  in  sixteenths  of  an  in 
»  =  working  strength,  or  load,  in  toim  <S^  iba.), 
L  =  span,  when  loaded,  in  inches, 
b  =  breadth  of  plates.  In  inches,  taken  t^  uniform, 
t  s  thiclcness  of  pl^pes,  in  a^t^epths  of  an  ino)!, 
n  =  number  of  putes. 


n  =  number  of  pll 
Mots.— The  span  and  the  elasticity  are  those  due  to  the  spring  when 


br  an  equivaleirt  number  of  plates  of  the  ruling  thickness,  prior  to  the  em- 
ployment of' the  ^rs't  two  formnisB.  fThia  is  round  b^'  militiplying  the  num- 
ber of  extra  thick  plates  by  the  cube  of  their  thicknespiy  and  dividing  by  the 
cnbe  of  the  ruling  thicknesfi.  Oonravwlr,  (Iw  nippiber  of  plates  of  the  rulios 
thickness  given  by  the  third  formula,  required  to  be  deducted  and  replaced 
by  4  fiiyen  wwtMf  of  a^tra  t^ilajc  plat#«,  ara  feuiid  by  the  niaie  caUiuiati9n. 

a.  |t  iff  iMBiimed  tM  tha  plates  are  similArly  and  regularly  /prmao,  M94 
that  they  aro  of  imiform  bFeAdtb.  and  bpt  slightly  tapet  at  M^eaada. 

QaMleMiz*^  O0ii8^r||ator  gi? as  tor  sami-^lliptic  /ipringst 

9  s  max.  direet  fll^rerstrftin  in  pUil9;        b  s  width  Qf  platest 
n  =  number  of  plates  in  spring;  k  =  thid^Qesa  of  pjfttesj 

I  =  opie  i»alf  lengtb  pf  spring;  /  =  da0eoUoi)  of  end  of  spring; 

P  =  load  on  ope  end  ot  sprfpg;  JO  =  modulus  of  direct  el^icity. 

The  above  formula  for  deAeotioa  ean  be  relied  upon  where  all  the  plates 
of  tha  spring  are  regularlv  shortened;  but  in  semi-elliptio  springs,  as  used, 
thare  are  generally  several  plates  extending  the  full  length  of  the  spring, 
aad  the  proportion  of  these  long  plates  to  the  whole  number  is  usually  about 


onefooith.    In  such  cases /=  ^^-^,.   (Q.  R.  Saoderson,  Tmns,  A.  Sit  K.  P., 

vol.  xvi.) 

In  order  to  conpase  tha  formulas  of  Reuleaux  and  Clark  we  may  make 
the  following  silbstitfitiona  In  the  lapter:  f  in  tons  =?  P  in  lbs.  -*-  IV^i  l8  = 

^*=^y=4096XliaOxn6M'       '^"^      -^^^S^f.m' 


correspond 


takeJr=:»,1tti,n6. 

^^  *"J1«)"}UX«*      '^'*'***      ^^  i         » 

which  corresponds  with  Beuleaux's  formula  for  working  load  when  ^In  the 
latter  is  taken  at  78,120. 

The  value  of  J?  is  usually  taken  fit  80,000,000  and  8  at  80,000,  in  which  case 
Beuleaux*8  formulsa  beoome 

i  »"u        /        5.000,000»iWi»' 

Melleal  Steel  Sprlncf*— Clark  quotes  the  following  from  the  report 
on  Safety  Vftlves  (Trans.  Inst.  Engrs.  and  Shipbuilders  in  Scotland,  1874-5): 
„  _  rf«  X  w 


348  BPBiiros. 

E  =s  comprefwion  or  extension  of  one  coil  In  inches, 

d  8  diameter  from  centre  to  centre  of  steel  bar  constituting  the  spring, 

ill  inches, 
to  =  weight  applied,  in  pounds, 
D  =  diameter,  or  side  of  the  square,  of  the  steel  bar,  in  sixteenths  of  an 

inch, 
Css  a.  constant,  which  may  be  taken  as  fSt  for  round  steel  and  SO  for 

square  steel. 

Note.— Tlie  deflection  J?  for  one  coil  is  to  be  multiplied  by  the  number  of 
free  coils,  to  obtain  the  total  deflection  for  a  given  spring. 

The  relation  between  the  safe  load,  size  of  steel,  and  diameter  of  coil,  may 
be  taken  for  practical  purposes  as  follows: 

^^  ,  for  round  steel; 


ywd 


— — ,  for  square  steeL 
4.S9 

Raukine*s  Machinery  and  Millwork,  p.  300,  gives  the  following: 
W         cd*    .        .-        .196/dV  ^        18.Be6tt/r«. 

VfT 

-—i  =  greatest  safe  sudden  load. 

In  which  d  is  the  diameter  of  wire  in  inches;  c  a  co-efilclent  of  transverse 
elasticity  of  wire,  say  10,500,000  to  18,000.000  for  charcoal  iron  wire  and  steel; 
r  radius  to  centre  of^wire  in  coil;  n  effective  number  of  colls;  / greatest  safe 
shearing  stress,  say  80,000;  H^any  load  not  exceeding  greatest  safe  load; 
V  corresponding  extension  or  compreKsion;  TT,  greatest  safe  load;  and  t?] 
greatest  safe  steady  extension  or  compression. 

If  the  wire  Is  square,  of  the  dimensions  d  x  d,  the  load  for  a  given  deflec- 
tion is  greater  ihun  for  a  round  wire  of  the  diameter  d  in  the  ratio  of  2.81  to 
1.96  or  of  1 .48  to  1,  or  of  10  to  7,  nearly. 

Wilson  Hartnell  (Proc.  Inst.  M.  E.,  1888,  p.  4S6),  says:  The  sise  of  a  spiral 
spring  may  be  calculated  from  the  formula  on  page  304  of  ''  Rankine^s  Use- 
ful Rules  and  Tables";  but  the  experience  with  Salter's  springs  has  shown 
that  the  safe  limit  of  stress  is  more  than  twice  as  great  as  there  giv«'u. 
namely  60,000  to  70,000  lbs.  per  square  iuch  of  section  with  %  inch  wire,  mkI 
about  60,000  with  %  inch  wire.  Hence  the  work  that  can  be  done  by 
springA  of  wire  is  four  or  five  times  as  great  as  Rankine  allows. 

For  96  inch  wire  and  under, 

^     ,  I     ^ .    IV-       ^2,000  X  (diam.  of  wire)* 

Maximum  load  in  lbs.  =  — ; ^, ^ — '- ; 

Mean  radius  of  springs  ' 

Weight  hi  lbs.  to  deflect  spring  1  in.  =        ^f '^/ jf  *°^;>\  ,.. 
*  f      B  Number  of  coils  X  (rad.)» 

The  work  in  foot-pounds  that  can  be  stored  up  in  a  spiral  spring  would 
lift  it  above  60  ft. 

In  a  few  rough  experiments  made  with  Salter's  springs  the  coefficient  of 
rigidity  wan  noticed  to  be  12.600,000  to  13,700,000  with  Jd  inch  wire;  11,000,000 
for  U/fi'i  inch :  and  10,600,000  to  10,900.000  for  %  inch  wire. 

Helleal  SprlnM,— J.  Begtrup,  in  the  American  MachiniMt  of  Aug. 
18,  189-^,  gives  rormuTas  for  the  deflection  and  carrying  capacity  of  helical 
springs  of  round  and  square  steel,  as  follow: 


Sd* 


for  round  steeL 


for  square  steel. 


HELICAL  SPBIKGS. 


849 


ITb  eUTjbig  cafMuHty  In  pounds, 
8  B  frreatest  teoBile  strees  per  oquare  inch  of  matoriA], 
d  =  diameter  of  steel, 
D  =  outside  diameter  of  coil, 
JP*  s  deflection  of  one  coil, 
E  =  torsional  modulus  of  elasticity, 
P  =  load  in  pounds. 

From  these  formulas  the  following  table  has  been  calculated  bv  Mr.  Beg- 
tnip.  A  ftprlng  being  made  of  an  elastic  material,  and  of  such  shape  as  to 
allow  a  pneat  amount  of  deflection,  will  not  be  affected  bv  sudden  sliocks  or 
blows  to  the  same  extent  as  a  rigid  body,  and  a  factor  of  safety  very  much 
488  than  for  rigid  constructions  may  be  used. 

HOW  TO  USE  THE  TABLE. 

When  designing  a  spring  for  continuous  work,  as  a  car  spring,  use  a 
(greater  factor  of  safety  than  in  the  table;  for  intermittent  working,  as  in 
a  steam-engine  governor  or  safety  valve,  use  figures  given  in  table;  for 
square  steelmultiply  line  TT  by  1.2  and  line  F  by  .59. 

Example  ].— How  much  will  a  spring  of  9^"  round  steel  and  8"  outside 
diameter  carry  with  safety  ?  In  the  line  headed  D  we  And  S,  and  right  un- 
derneath 478,  which  is  the  weight  it  will  carry  with  safety.  How  many  coils 
must  this  spring  have  so  as  to  deflect  9'*  with  a  load  of  400  pounds  ?  Assum- 
ing a  modulus  of  elasticity  of  U  millions  we  find  in  the  centre  line  headed 
F  the  flgure  .0610;  this  is  deflection  of  one  coil  for  a  load  of  100  pounds; 
therefore  .001  x  4  =  .844"  is  deflection  of  one  coil  for  400  pounds  load,  and  8 
-t-  .341  =  VZyi  is  the  number  of  coils  wanted.  This  spring  will  therefore  be 
4^"  long  when  closed,  counting  working  coils  only,  and  stretch  to  7^". 

Example  2. —A  spring  8^"  outside  diameter  of  7/16"  steel  is  wound  close; 
bow  much  can  it  be  extended  without  exceeding  the  limit  of  safety  ?  We 
find  maximum  safe  load  for  this  spring  to  be  702  pounds,  and  deflection  of 
one  coil  for  100  pounds  load  .0406  inches;  therefore  7.02  x  .0406  =  .284"  is  the 
greatest  admissible  opening  between  coils.  We  may  thus,  without  know- 
mg  the  load,  ascertain  whether  a  spring  la  overloaded  or  not. 

Carrjlnc  Capaeltr  and  Deflection  of  Helical  Sprlnc*  of 
Bound  Steel. 

d  s=  diamerer  of  steel.  D  =  outside  diameter  of  coil.  W  =  safe  working 
load  in  pounds— tensile  stress  not  exceeding  60,000  pounds  per  square  inch. 
F  =  deflection  by  a  load  of  100  pounds  of  one  coil,  and  a  modulus  of  elasti- 
city of  10,  12  and  14  millions  respectively.  The  ultimate  carrying  capacity 
wiil  be  about  twice  the  safe  load. 


N'^ 

.25 

.60 

.75 

1.00 

1.25 

1.50 

1.75 

2.00 

85 

15 

0 

7 

5 

4.5 

8.8 

3.8 

ti 

.0278 

.8568 

1.483 

8.862 

7.250 

12.88 

20.85 

81.57 

F- 

.0286 

.8075 

1.228 

8.053 

6.214 

11.04 

17.87 

27.06 

tj 

.0197 

.2502 

1.023 

2.544 

5.178 

9.200 

14.89 

22.5.5 

r. 

D 

.50 

.75 

1.00 

1.25 

1.60 

1.75 

200 

2.25 

2.50 

W 

107 

65 

46 

86 

29 

25 

23 

19 

17 

^.'^ 

4 

.0206 

.0887 

.2566 

.5412 

.9856 

1.624 

2.492 

S.62.5 

5.056 

«:? 

^\ 

.0176 

.0604 

.2191 

.4689 

.8418 

1.39-.; 

2.136 

3.107 

4.884 

^Z 

\ 

.0147 

.0670 

.182 

.8866 

.7010 

1.160 

1.780 

2.589|3.612 

I.-- 

D 

75 

1.00 

1.25 

1.60 

1.75 

2.00 

2.25 

Tm 

2.75 

8.00 

"^"^ 

W 

Ml 

167 

128 

104 

88 

75 

66 

59 

58 

49 

*  o 

( 

.01«7 

.0406 

.0907 

.1703 

.2866 

.4466 

.6571 

.9249 

1.256 

1.660 

i^r< 

.0118 

.0830 

.0778 

.1460 

.2457 

.3828 

.fi632 

.7928  1.077 

1.428 

"« 

« 

.0008 

.0202 

.0648 

.1217 

.2018 

.3190 

.4693 

.6607 

.8975 

1.186 
3. .50 

* 

D 

1.25 

1.50 

1.75 

2.00 

2.25 

2.. 50 

2.75 

3.00 

3.25 

* 

2f 

W 

868 

294 

245 

210 

184 

104 

147 

134 

123 

113 

1 

.0199 

.0660 

.0672 

.1067 

.1598 

.2270 

.8109 

.4139 

.587.5 

.6H35 

F- 

.0171 

.0888 

.0570 

.0914 

.1865 

.1944 

.2665 

.8548 

.4607 

..5859 

.0142 

.0278 

.0480 

.0768 

.1187 

.1610 

.2221 

.2967 

.8889 

.4883 

S50 


SPRIKGS. 


Carrylnff  Capacitr  and  Befleetton  of  Helleal  Sf  Hii£ft  of 
Bound  9im9U-HConUnued), 


%> 

D 

1.60 

1.75 

2.00 

2.26 

2.80 

2.75 

8.00 

3.26 

8.60 

8.75 

4.O0 

s 

W 

006 

600 

426 

871 

829 

295 

207 

245 

226 

209 

195 

\ 

.0136 

.0842 

.0892 

.0698 

.0864 

.1187 

.15«! 

.2066 

.2640 

.881S 

.4089 

II 

f\ 

.0117 

.0207 

.0386 

.0508 

.0782 

.1012 

.1867 

.1771 

.22081.2889 

.8605 

•« 

< 

.00»7 

.0178 

.0280 

.0424 

.0610 

.0868 

.1181 

.1476 

.1886 
4.00 

.2866 

.2981 

» 

D 

2.00 

2.26 

2.50 

2.76 

8.00 

8.25 

8.60 

8.75 

4.25 

4.50 

II 

TV 

766 

668 

689 

628 

478 

488 

896 

868 

848 

821 

BOI 

.0169 

.0269 

.0877 

.0628 

.0711 

.0985 

.1200 

.1613 

.1874 

.2290 

.9761 

F- 

.0145 

.02« 

.032.3 

.045-2 

.0610 

.0801 

.1029 

.1297 

.1006:  1968 

.2367 

•0 

.0120 

.0185 

.0269 

.0870 

.0506 

.0668 
8.25 

.0858 

.1081 

.1838.1635 

.1972 

^ 

s 

D 

S.OO 

2.26 

2.60 

2.76 

8.00 

8.50 

8.76 

4.00 

4.60 

5.00 

W 

1968 

1089 

967 

868 

770 

702 

644 

600 

644 

480 

432 

\ 

.OOBl 

.0126 

.0186 

.0262 

.0857 

.0472 

.0617 

.0772 

.0960 

.1428 

.2016 

II 

f\ 

.0069 

.0108 

.0160 

.0226 

.0606 

.0405 

.0529 

.0601 

.0828 

.1220 

.1728 

•« 

1 

.0066 

.0090 

.0183 

.0187 

.0255 

.0887 

.0441 

.0661 

.0686 

.1017 

.1440 

> 

D 

2.00 

2.25 

2.60 

2.76 

3.00 

325 

3.50 

3.75 

4.00  4.50 

5.00 

II 

W 

1968 

1688 

1472 

1809 

1178 

1071 

082 

900 

811 

788 

654 

.0042 

.0067 

.0099 

.0141 

.0194 

.026fl 

.0380 

.0427 

.0614 

.0796 

.1184 

F- 

.0086 

.0067 

.0085 

.0121 

.0167 

.0222 

.0288 

.0306 

.0157 

.0088 

.0072 

"8 

.0060 

.0048 

.0071 

.0101 

.0189 

.0185 

.0240 

.0906 

.0381 

.0600 

.0610 

1, 

D 

2.60 

2.75 

8.00 

8.26 

3.50 

8.75 

4.00 

4.2S 

4.50 

5.00 

6.50 

W 

2168 

1916 

1720 

1660 

1427 

1815 

1220 

1187 

1066 

046 

849 

.0066 

.0081 

.0112 

.0151 

.0197 

.0262 

.0816 

.0890 

.0474 

.0079 

.0085 

n 

F- 

.0048 

.0070 

.0096 

.0129 

.0109 

.0210 

.0271 

.0884 

.0406 

.0682 

.0801 

•« 

.0040 

.0058 

.0080 

.0106 

.0141 

.0180 

.0226 

.0278 

.0889 

.0486 
6.00 

,0608 

D 

2.50 

2.76 

8.00 

8.26 

8.50 

8.76 

4.00 

4.26 

4.50 

&.60 

R 

W 

8068 

2707 

2422 

2191 

2001 

1841 

1704 

1587 

1484 

1815 

1180 

.0034 

.0049 

.0068 

.0092 

.0121 

.0156 

.0190 

.0248 

.0297 

.0427 

.0691 

f\ 

.OOiM 

.0042 

.0058 

.0079 

.0104 

.0188 

.0168,  .0206 

.0254.0886 

.0506 

ts 

.0024 

.0085 

.0049 

.0066 

.OObC 

.0111 

.0140 

.0173 

.0212  .0805 

.0422 

D 

8.00 

8.26 

8.60 

8.75 

4.00 

4.26 

4.60 

4.75 

6.00  6..V) 

0.00 

s' 

W 

8811 

29H8 

2728 

2600 

2311 

2161 

2009 

1885 

1776  1601 

1441 

( 

.0048 

.0058 

.0077 

.0100 

.0127 

.0167 

.0198 

.0288 

.Ot79 

.0888 

.0Q« 

tt.-' 

f\ 

.0037 

.0050 

.0066 

.0086 

.0108 

.0185 

.0166 

.0200 

.0280 

.0883 

.0447 

1 

.0080 

.0042 

.0055 

.0071 

.0090 

.0112 

.0188 

.0167 

.0199 

.0277 
6.60 

.0873 

D 

8.00 

8.25 

8.60 

8.75 

4.00 

4.25 

4.60  i  4  7S 

6.00 

0.00 

II 

W 

4418 

3976 

8616 

8818 

8058 

2810 

2651  1  2486 

2880 

2098 

1808 

( 

.0028 

.0038 

.0051 

.0066 

.0084 

.0106 

.0129  .0167 

.0189 

.0904 

.0860 

f\ 

.0024 

0038 

.0044 

.0057 

.0072 

.0090 

.0111 

.0185 

.0162 

oem 

.0906 

IS 

( 

-.0020 

.0027 

.0006 

.0M7 

.0060 

.0075 

.0098 

.0118 

.0186 

.0188 

.0254 

D 

8.50 

8.75 

4.00 

4.25 

4.60 

4.75 

6.00 

6.25 

6.60  6.00 

0  50 

II 

W 

6018 

5490 

6061 

4676 

4864 

4078 

8826 

8607 

8418.  8080 

2800 

( 

.0041 

.0037 

.0086 

.0046 

.0056 

.0067 

.0081 

.0097 

.0115 

.0160 

.021^ 

f\ 

.0018 

.0024 

.0080  .0088 

.0047 

.0068 

.0070 

.0068 

.OOM 

.0194 

.0177 

•0 

1 

.0015 

.0020 

.0026 

.0082 

.0089 

.0048 

.0058|  .0069 

.000 

.0112 

.0148 

T) 

8.60 

8.76 

4.00 

4.25 

4.60 

4.75 

6.00  1  5.25 

6.50 

6.00 

0  no 

^ 

W 

9425 

8568 

7854 

7250 

6732 

62S8 

5890  >  6644 

6286 

4712 

4284 

(1 

.0018 

.0016 

.0021 

.0020 

.0083 

.0041 

.0049  .0069 

.0071 

.0007 

.0129 

f- 

.0010 

.0014 

.0018 

.0028 

.0028 

.0085 

.0043!  .0061 

.0001 

.0088 

0111 

.0008 

.0011 

.0016 

.0019 

.0023 

.0029 

.0085  .0048 

.0061  [.0009 

.0092 

The  formulflB  for  deflection  or  compresgion  given  by  Clark,  Hartneh.  and 
Begtrup.  although  very  differeot  In  form,  show  a  subfttant4al  aareement 
when  reduced  to  the  same  fonn.  Let  d  s  diameter  of  wire  in  inches,  i>,  » 
mean  diameter  of  coil,  n  the  Dumber  of  coila,  v?  the  applied  weight  1q 
pounds,  aud  C  a  coefllclent,  then 


HELICAL  SPRINQS.  851 

Oompresaion  or  extension  of  one  coll  =  -;rn-; 

CO* 

Cd* 
Weight  in  pounds  to  cause  comp.  or  ext.  of  1  In.  b:  -g-^. 

The  coeflQcIent  C  reduced  from  Hartneirs  formula  is  8  X  180,000  ^  1,440,000; 
acoordituc  to  Clark,  16*  x  22  =  1,441,799,  and  aocordinir  to  Begtrup  (using 
];!,000,000  for  the  torsional  modulus  of  elasticity)  =  12,000,000-1-8  =  1,500,000. 

RanUoe*8  formula  for  greatest  safe  extension,  v.  ss -j^ — may  take 

Ca 

the  form  Vi  »  '^^^'*  i'  ^«  ^^  80,000  and  12,000,000  as  the  values  for/ 

and  c  respectively. 

The  several  formulse  for  safe  load  given  above  may  be  thus  compared, 
letting  d  —  diameter  of  wire,  and  Z>,  s  mean  diameter  of  coil,  Itankine, 

jr  =  mr^;  Clark.  W,^^^^  ;  Begtrup/IT^  '^^^  ;     H^tndl, 

I2000rf* 

W  =  ^—^ — .    Substituting  for  /  the  value  80,000  given  by  Rankine,  and  for 
8, 80,000  aagiven  by  Begtrup,  we  have  W  a  11,780  4r  Ra&kine  ;  19,288  -^ 

Clark;  38,M3  ~  Begtrup;  24,000  ^  Hartnell. 

Takinir  from  the  Pennsylvania  Railroad  speclflcatfons  the  capacitv  when 
closed  of  the  following  springs,  in  which  d  =  diameter  of  wire,  D  diameter 
outtdde  of  coil.  i>i  =  D  —  d,  e  capacity,  H  height  when  free,  and  h  height 
when  cloaedt  all  in  inches. 

!•    \     r  * 

d  1^  4^  Ss 


Cr=400 

B=  9   A=.6 

1,000 

8            6 

2,100 

r        4H 

8,100 

10«        8_ 

10.000 

9            69^ 
4M         m 

16,000 

and  substituting  the  values  of  c  in  the  formula  c  =  TV  =  xjr-  we  find  z,  the 

ooefflclcnt  of  ^  to  be  respecUvely  32,000;    88,000;   82,400;  24,888;  84,560; 
42.140.  average  il,000. 
Taking  12,000  as  the  coefndent  of  -^  according  to  Rankine  and  Clark  fof 

safe  load,  and  24,000  as  the  coefficient  according  to  Begtrup  and  Hartnell, 
we  have  for  the  safe  load  on  these  springs,  as  we  take  one  or  the  other  co« 
efficient, 

T  8  1C  D  I  C 

Rankine  and  Clark ISO        600     1,012     3.000     8,750     5.400  lbs. 

Hartnel 800      1.200     2,024     6,000      7,600*  10,800  *» 

Capacity  when  closed,  as  above    400      1,000     2.100     8,100    10,000    16,000   ** 
J.  W.  Cloud  (Trans.  A.  B.  M.  E.,  v.  178)  gives  the  following: 
^      Sfwd«  ,      ^        38PA«1 

^=-165-       -"^^     f=-Q^'^ 

P  =r  load  on  spring; 

S  =r  maximum  shearing  fibre-strain  in  bar; 

d  s  diameter  of  steel  of  which  spring  is  made; 

R  zz  radius  of  centre  of  coil : 

I  =  length  of  bar  before  coiling: 

O  ss  modulus  of  shearing  elasticity: 

/  =  defiectlon  of  spring  under  load. 
Mr.  Otoud  takes  8  »  80,000  and  G  e=  19,600,000. 

The  streas  in  a  helical  npHng  is  almost  wholly  one  of  torsion.  For  method 
of  deriving  the  formulae  for  springs  from  torsional  formula  see  Mr.  Cioud*8 
paper,  above  quoted. 


352 


SPBIKOS. 


BLLIPTICAL   SPBIlfOS,    SiaSES,   AND  PROOF  TBSTS. 

Pennsylvania  Railroad  Speciflcations,  1869. 


-5d 

5 

1 

TesU. 

P 

f 

III 

ClaM. 

With  Load 
of  lbs. 

m  between  bands. 

480O 

-^.Trtple 

40 

"94 

8 

*% 

J3*       « 
2           **             ** 
394       " 

6600 

C,  Quadruple.. 

40 

15H 

s 

^H 

J  J"*         u 

8000 

A  Triple 

86 

n« 

8 

xM 

2           " 

4            «<             II 

8           "             " 
6  bet.  centre  of  eye 

8000 

».  Single 

40 

■in. 

8 

x« 

8x11/82 

and  top  of  leaf. 
2U  between  bands. 

Whenfkve 
2850 
11.800 
When  free 
80OO 

J\  Triple 

^.Double 

88 
88 

8 
3 

8x11/82 

H,  Double 

86 

»« 

8 

x« 

\f*  :     « 

5400 
8000 

r. 

Double,  ) 
6  plates  f 

22 

low 

3«xH 

4^x11/32 

1S/1«    " 

18,800 

A. 

Double,   1 
7DUte8r 

28 

10^ 

J^xW 

4^x11/82 

IJA«  "          " 

15,600 

jr.  Quadruple.. 

40 

1B« 

8 

x« 

8 

A                   U                       •« 

8 

2           II             II 

10,000 
A.  p.  t.* 

*  A.  p.  t.,  auxiliary  plates  touching. 

PM08PH0B-BB0NZB  8PBINCI8. 

Wilfred  Lewis  (Engineers*  Club,  Philadelphia,  1887)  made  some  tests  with 
phosphor-bronse  wire,  .12  in.  diameter,  coiled  In  the  form  of  a  sphral  spring, 
IMJo*  diameter  from  centre  to  centre,  making  62  coils. 

Tbte  spring  was  loaded  gradually  up  to  a  tension  of  80  lbs.,  but  as  the  load 
was  remoTed  it  became  evident  that  a  permanent  set  had  taken  place. 
Buch  a  spring  of  steel,  according  to  the  practice  of  the  P.  R.  R.,  mi  At  be 
used  for  40  lbs.  A  weight  of  21  lbs.  was  then  suspended  so  as  to  aflow  a 
small  amount  of  vibration,  and  the  length  measured  from  day  to  day.  In  80 
hours  the  spring  lengthened  from  20^4  inches  to  21^  inches,  and  in  200  hours 
to  fSXH  inches.  It  wasconcluded  that  21  lbs.  was  too  great  for  durability,  and 
that  probably  10  lbs.  was  as  much  as  could  be  depended  upon  with  safety. 

For  a  given  load  the  extension  of  the  bronze  spring  was  Just  double  the 
extension  of  a  similar  steel  spring,  that  is,  for  the  same  extension  the  steel 
spring  is  twioe  as  strong. 

8PBIN68  TO  BB8IST  TOB8IONAI1   POBCB. 

(Reuleaux*s  Constructor.) 

pj^ 


Flat  spiral  or  helical  spring...  P=  f  ^; 

0    A 

Bound  helical  spring ^^%%'' 

Sird* 

Bound  bar,  in  torsion P=-^  -^'^ 

10    K 


/  =  £«  =  12 


Ebh*' 


•^  [w  E  d* 


Flat  bar,  in  torsion ^=90 


b*h^      .  ^      r,j»      8PJyi  1>«  +  A« 


6»M 


P  =  force  applied  at  end  of  radius  or  lever-arm  A;  d  =  angular  motion  at 
end  of  radius  m;  8  ^  permissible  maximum  stress,  =  4/6  of  permissible 
stress  in  flexure;  E  =  modulus  of  elasticity  in  tension;  O  »  torsional  modu- 
lus, =  2/6  JC;  <  =  developed  length  of  spiral,  or  length  of  bar;  d  s 
U  wire;  5  s  breadth  of  flat  bar;  h  =  thickness. 


HELICAL  SPRINGS  FOR  CARS  AKD  LOCOMOTIVES.    363 


B 

s 

0 


Ms 

<  : 

c 

hi 

SI 

iB' 

4 


as 


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361  BIYETEP  JOINTS. 


BIVETED  JOINTS. 

Palrbairn's  Experiments.    (From  Report  of  Committee  on 
Riveted  Joints,  Proc.  Jnit.  M.  i?..  April,  1881.) 

The  earliest  published  experiments  on  riveted  joints  are  contained  in  the 
memoir  by  Sir  W.  Fairbairn  in  the  Transactions  of  the  Royal  Society. 
Making  certain  empirical  allowances,  he  adopted  the  following  ratios  as  ex- 
pressing the  relative  strengtli  of  riveted  Joints  : 

Solid  plate 100 

Double-riveted  joint. 70 

Single-riveted  joint 68 

These  well-known  ratios  are  quoted  in  most  treatises  on  riveting,  and  are 
•till  sometimes  referred  to  as  having  a  considerable  authority.  It  is  singular, 
however,  that  Sir  W.  Fairbairn  does  not  appear  to  have  been  aware  that  the 

1>roportion  of  metal  punched  out  in  the  line  of  fracture  ought  to  be  different 
n  properly  designed  double  and  single  liveted  joints.  These  celebrated 
ratios  would  therefore  appear  to  rest  on  a  very  imsatisfactory  analysis  of 
the  experiments  on  which  theywere  based. 

I«osa  of  Strenfftli  In  Pnnelied  Flat0s«~A  report  by  Mr.  W. 
Parker  and  Mr.  John,  made  in  1878  to  Lloyd's  Committee,  on  the  effect  of 
punching  and  drilling,  showed  that  thin  steel  plates  lost  comparatively  little 
from  punching,  but  that  in  tliick  plates  the  loss  was  very  considerable. 
Tho  following  table  gives  the  results  for  plates  pimched  and  not  annealed 
or  reamed : 

Thickness  of  Material  of  Loss  of  Tenacity, 

Plates.  Plates.  per  cent. 

M  Steel  8 . 

n  "  J8 

U  *'  96  *  A 

g  '•  88  • 

12  Iron  18  to  88 

The  effect  of  increasing  the  size  of  the  hole  in  the  die-block  Is  shown  in 
the  following  table : 

Total  Taper  of  Hole  Material  of  Loss  of  Tenacity  due  to 

in  Plate,  inches.  Plates.  Punching,  per  cent. 

1-16  Steel  17.8 

M  "  18.3 

M  •*  (Hole  ragged)  24.6 

The  plates  were  from  0.675  to  0.713  inch  thick.  When  ^In.  punched  holes 
were  reamed  out  to  \%  in.  diameter,  the  loss  of  tenacity  disappeared,  and 
the  plates  carried  as  high  a  stress  as  drilled  plates.  Annealing  also  restores 
to  punched  plates  their  original  tenacity. 

Strenfftli  of  Performted  Plates. 

(P.  D.  Bennett,  Eng'g,  Feb.  12, 1886,  p.  166.) 

Tests  were  made  to  determine  the  relative  effect  produced  upon  tensile 
sireiiKth  of  a  flat  bar  of  iron  or  steel :  1.  By  a  ^-inch  hole  drillea  to  the  re- 
quired size  ;  :2.  by  a  hole  punched  ^  inch  smaller  and  then  drilled  to  the 
8ize  of  the  flrst  hole ;  and,  8,  by  a  hole  punched  in  the  bar  to  the  size  of  the 
lirilled  bur.  The  relative  results  in  strength  per  square  inch  of  original  area 
were  as  follows : 

1.  2.  8.  4. 

Iron.       Iron.     Steel.       Steel. 

Unperforated  bar 1.000       l.OOO       1.000       1.000 

Perforated  by  drilUng 1 .089       1 .012       1 .068       1 .  108 

''  puuching  and  drilling.  1 .080       1.008       1.059       1.110 

"  *•  punching  only 0.79S       0.894       0.986       0.907 

In  tests  2  and  4  the  holes  were  filled  with  rivets  driven  by  hydraulic  pres- 
sure. The  increase  of  strength  per  square  inch  caused  by  drilling  is  a  phe- 
nomenon of  similar  nature  to  that  of  the  increased  strength  of  a  grooved  bar 
over  that  of  a  straight  bar  of  sectional  area  equal  to  the  amallest  section  of 
the  grooved  bar.    Mr.  Bennett's  tests  on  an  iron  bar  0.84  in.  diameter,  10  in. 


EFFICIENCY  OF  BIVETUSTG  BT  DIFFBBBNT  METHODS.  855 


loDir,  and  a  similar  bar  turned  to  0.84  In.  diameter  at  one  point  only,  ehowed 
that  the  relative  strong^  of  the  latter  to  the  former  was  1.8S8  to  1.000. 

BlTeted  JTolnia.— l^rllliiiff  verana  Fanehtns  of  Soles. 

The  Report  of  the  Research  Committee  of  the  Instlmtlon  of  Mechanical 
EnKioeerH,  on  Riveted  Joints  (1881),  and  records  of  InveetlKatlons  by  Prof. 
A.  B.  W.  Kennedy  (1861, 1882,  and  1886),  summarize  the  existing  Information 
refiFC^rding  the  comparative  eifects  of  punching  and  drilling  upon  iron  and 
steel  plates.  From  an  examination  or  the  voluminous  tables  given  In  Pro- 
fessor Unwin's  Report,  the  results  of  the  greatest  number  of  the  experi- 
ments made  on  iron  and  steel  plates  lead  to  the  general  conclusion  that, 
while  thio  plates,  even  of  steel,  do  not  suffer  vezy  much  from  punching,  yec 
in  those  of  Winch  thickness  and  upwards  the  loss  of  tenacity  due  to  punch- 
ing ranges  from  10%  to  *a%  in  iron  plates,  and  from  11  ](  to  38%  in  the  case  ct 
mild  steel.  In  drilled  plates  there  is  no  appreciable  loss  of  strength.  It  is 
possible  to  remove  the  bad  effects  Of  punching  by  subsequent  reaming  or 
annealing:  but  the  speed  at  which  work  is  turned  out  In  these  days  is  not 
favorable  to  muliiplied  operations,  and  such  additional  treatment  is  seldom 
practised.  The  introduction  of  a  practicable  method  of  drilling  the  plating 
of  ships  and  other  structures,  after  it  has  been  bent  and  shaped,  is  a  matter 
of  great  importance.  If  even  a  portion  of  the  deterioration  of  tenacity  can 
be  prevented,  a  mu<di  stronger  structure  results  from  the  same  material  and 
the  same  scantling.  This  has  been  fully  recognized  in  the  modem  English 
praetJoe  (1887)  of  the  construction  of  steam-boilers  with  steel  plates;  punch- 
ing in  sttch  cases  being  almost  entirely  abolished,  and  all  rivet-holes  being 
drilled  after  the  plates  have  been  bent  to  the  desired  form. 


CompanttlTe 


ieieneyof  BiTeilnff  Aone  hf  IMmrent 
iHetliods. 


Ihe  Reports  of  Professors  Unwin  and  Kennedy  to  the  Institution  of  Me- 
chanical Engineers  {Proc,  1881, 188^  and  1885)  tend  to  establish  the  four  fol- 
lowing points: 

1.  Thai  tlie  shearing  resistance  of  rivets  is  not  highest  in  joints  riveted  by 
means  of  the  greatest  pressure; 

8.  That  the  ultimate  strength  of  Joints  is  not  affected  to  an  appreciable 
extent  by  the  mode  of  riveting;  and,  therefore, 

S.  That  very  great  pressure  upon  the  rivets  in  riveting  is  not  the  Indispen- 
sable requirement  that  it  has  been  soroectmes  supposedi  to  be; 

4.  That  the  most  serious  defect  of  hand-riveted  as  compared  with  maohlno- 
riveted  work  consists  in  the  fact  that  in  hand-riveted  Joints  visible  slip 
commences  at  a  comparatively  small  load,  thus  giving  such  joints  a  low 
value  as  regards  tightness,  and  possibly  also  renderiMg  tiiem  liable  to  failure 
under  sudden  strains  after  slip  has  once  commenced. 

The  following  figures  of  mean  results,  token  from  Prof.  Kennedy's  tables 
(ProceedinQt  188R,  pp.  216-225),  give  a  comparative  view  of  hand  and  hy- 
draulic riveting,  as  regards  their  ultimate  strengths  In  joints,  and  the  periods 
at  which  in  both  c»aes  visible  slip  commenced. 


Total  Breaking  Load. 

Load  at  which  Visible  Slip  began. 

Hand-riveting. 

hydraulic  Rivet- 
ing. 

Hand-riveting. 

Hydraulic  Rivet- 
ing, 

Tons. 
86.01 

ui'.i' 
iii.i' 

Tons. 
86.75 
77.00 
8d.70 
78.68 
145.6 
140.8 
188.1 
183.7 

Tons. 
$1.7 

8i:7 
25:6 

Tons. 
47.5 
85.0 
68.7 
64.0 
49.7 
46.7 
66.0 

In  these  flgiires  hand-riveting  appears  to  be  rnther  better  than  hydraulic 
riveting,  as  far  as  regards  ultimate  strength  of  Joint;  but  is  very  much  in- 
ferior to  hydraulic  work,  in  view  of  the  small  proportion  of  load  borne  by 
k  before  visible  slip  commepcecU 


356 


BITETED  JOIinS. 


Some  of  tlie  Coneliisloiis  of  tlie  Oommittee  of  Re«e«reh 
on  JBlTeted  JTolnts. 

CProc.  Inst  M.  E.,  Apl.  1885.) 

Tbe  conelustons  all  refer  to  joints  made  in  soft  steel  plate  with  steel 
rivets,  the  holes  all  drilled,  and  the  plates  in  their  natural  state  (unannealed). 
In  every  case  the  rivet  or  shearing  area  has  been  assumed  to  be  that  of  the 
holes,  not  the  nominal  (or  real)  ai'ea  of  the  rivets  themselves.  Also,  the 
strength  of  tlie  metal  in  the  Joint  has  been  compared  with  that  of  strips 
cut  from  the  same  plates,  and  not  merely  with  nominally  similar  material. 

The  metal  between  the  rivet -holes  has  a  considerablyjTeater  tensile  re- 
sistance  per  square  inch  than  the  unperforated  metal.  This  excess  tenacity 
amounted  to  more  than  20j(,  both  in  ^-inch  and  ^-ioch  plates,  when  the 
pitch  of  the  rivet  was  about  1.9  diameters.  In  other  cases  9|-inch  plate  gave 
an  excess  of  l^  at  fracture  with  a  pitch  of  2  diameters,  of  lOK  with  a  pitch 
of  8.6  diameters,  and  of  6.6)(,  with  a  pitch  of  8.9  diameters;  and  9^-lnch  plate 
gave  7.9%  excess  with  a  pitch  of  2.8  diameters. 

In  single-riveted  Joints  it  may  be  taken  that  about  22  tons  per  square  inch 
is  the  shearing  resistance  of  rivet  steel,  when  the  pressure  on  the  rivets  does 
not  exceed  about  40  tons  per  square  inch.  In  double-riveted  Joints,  with 
rivets  of  about  %  inch  diameter,  most  of  the  experiments  gave  about  24  tons 
per  square  inch  as  the  shearing  resistance,  but  the  Joints  in  one  series  went 
at  22  tons. 

The  ratio  of  shearing  resistance  to  tenacitv  is  not  constant,  but  diminishes 
verv  markedly  and  not  very  Irr^pilarly  as  the  tenacitv  increases. 

The  size  of  the  rivet  heads  and  ends  plays  a  most  important  part  in  the 
strength  of  the  Joints— At  any  rate  in  the  case  of  single-riveted  Joints.  An 
increase  of  about  one  third  in  the  weight  of  the  rivets  (all  this  increase,  of 
course,  going  to  the  heads  and  ends)  was  found  to  add  about  fij^  to  the 
resistance  of  the  Joint,  the  plates  remaining  unbroken  at  the  full  shearing 
resistance  of  22  tons  per  square  inch,  instead  of  tearing  at  a  shearing  stress 
of  only  a  little  over  20  tons.  The  additional  strength  is  probably  due  to  the 
prevention  of  the  distortion  of  the  plates  by  the  great  tensile  stress  in  the 
rivets. 

The  intensity  of  bearing  pressure  on  the  rivet  exercises,  with  joints  propor> 
tioned  in  the  ordinary  way,  a  very  important  influence  on  their  strength. 
So  long  as  it  does  not  <«oeed  40  tons  per  square  inch  (measured  on  the  pro- 
jected area  of  the  rivets),  it  does  not  seem  to  affect  their  strength  ;  but  pres- 
sures of  50  to  55  tons  per  square  inch  seem  to  cause  the  rivets  to  shear  to 
most  cases  at  stresses  varying  from  16  to  18  tons  per  square  inch.  For  or- 
dinary Joints,  which  are  to  be  made  equally  strong  in  plate  and  in  rivets, 
the  bearing  pressure  should  therefore  probably  not  exceed  42  or  48  tons  per 
square  inch.  For  double-riveted  butt-joints  perhaps,  as  will  be  noted  later, 
a  nigher  pressure  may  be  allowed,  as  the  shearing  stress  may  probably  not 
be  more  than  10  or  18  tons  per  square  inch  when  the  plate  tears. 

A  margin  (or  net  distance  from  outside  of  holes  to  edge  of  plate)  equal  to  the 
diameter  of  the  drilled  hole  has  been  found  suffleient  in  all  cases  hitherto  tried. 

To  attain  the  maximum  strength  of  a  Joint,  the  breadth  of  lap  must  be 
such  as  to  prevent  it  from  breaking  sigzag.  It  has  been  found  that  the  net 
metal  measured  zigzag  should  be  from  SOJit  to  85}(  In  excess  of  that  measured 
straight  across,  in  order  to  injure  a  straight  fracture.  Th\m  corresponds  to 
a  diagonal  pitch  of  2/8  p  -f-  d/8,  if  p  be  the  straight  pitch  and  d  the  diam- 
eter of  the  rt vet-hole. 

Visible  slip  or  *'g{ve**  occurs  always  in  a  riveted  joint  at  a  point  verr 
much  below  its  breaking  load,  and  by  no  means  proportional  to  that  lo&dL 
A  collation  of  the  results  obtained  in  measuring  the  slip  indicates  that  it  de- 
pends upon  the  number  and  size  of  the  rivets  in  the  Jomt,  rather  tiian  npon 
anything  else  ;  and  that  it  Is  tolerablv  constant  for  a  given  size  of  rivet  In  a 
given  type  of  joint.  The  loads  per  rivet  at  which  a  joint  will  commence  to 
slip  visibly  are  approximately  as  followB  t 


Diameter  of  Rivet. 

Type  of  Joint. 

RiveUng. 

Slipping  Load  per 
Rivet. 

glneh 

0  ** 
llnch 

1  " 
1    " 

Single-riveted 
Double-riveted 
Double- riveted 
Single-riveted 
DouDle- riveted 
Double-riveted 

Hand 
Hand 

Machine 
Hand 
Hand 

Machine 

8.5  tons 
8.0  to  8.5  tons 

7  tons 

8.2  tons 

4.8  tons 
8  to  10  tons 

DOUBLB-SITETED  lAP-JOINTS. 


867 


To  find  the  probable  load  at  which  a  Joint  of  an  j  breadth  will  commenoe 
to  slip,  Riulttply  the  number  of  rlTets  in  the  {^ven  breadth  by  the  proper 
flffure  taken  from  the  last  colonin  of  the  table  above.  It  will  be  understood 
that  the  above  figures  are  not  given  as  exact;  but  they  represent  very  well 
the  results  of  the  experiments. 

The  experiments  point  to  simple  rules  for  the  proportioning  of  Joints  of 
maximum  strength.  Assuming  that  a  bearing  pressure  of  48  tons  per  square 
inch  mar  be  allowed  on  tlie  rivet,  and  that  the  excess  tenacity  of  the  plate 
is  W%  of  Its  original  strength,  the  following  table  gives  the  values  of  the  ratios 
of  diameter  d  of  bole  to  thiclcnees  t  of  plate  (d  •*■  f),  and  of  pitch  p  to  diam- 
eter of  hole  (p  -«-  d)  in  joints  of  maximum  strength  in  ^^-inch  plate. 

For  Slncle-rlTeted  Plates* 


Original  Tenacity  of 
PUte. 

ShearingResIstance  of 

Ratio. 
d-*-t 

Ratio, 
p-i-d 

Ratio. 
PUte  Area 

Lbs.  per 
sq.  in. 

Tons  per 
sq.  in. 

Lbs.  per 
sq.  in. 

Tons  per 
sq.  in. 

Rivet  Area 

80 
28 
80 
S8 

87,800 
88,720 
87,00 
02.7t» 

22 
22 
84 
24 

49,900 
49,200 
63,780 
6S,';60 

8.48 
8.48 
8.28 
2.28 

8.80 
2.40 
8.87 
8.88 

0.G87 
0.786 
0.718 
0.690 

This  table  shows  that  the  diameter  of  the  hole  (not  the  diameter  of  the 
rivet)  should  be  ^  times  the  thickness  of  the  plate,  and  the  pitch  of  the 
riveto  296  times  the  diameter  of  the  hole.  Also,  it  makes  the  mean  plate  area 
Tit  of  the  rivet  area. 

If  a  smaller  rivet  be  used  than  that  here  specified,  the  Joint  will  not  be  of 
uniform,  and  therefore  not  of  maximum,  strength;  but  with  any  other  size 
of  rivet  the  best  result  will  be  got  by  use  of  the  pitch  obtained  from  the 
limple  formula 

p  =  aj-  +  <<t 

where,  as  before,  d  is  the  diameter  of  the  hole. 
The  value  of  the  constant  a  in  this  equation  is  as  follows: 

For  8(^ton  plate  and  88-ton  rivets,  a  =  0.504 
"88  "  22         **  •*    0.B68 

"80  -  24         ••  "    0.670 

-    88  ••  24         "  -    0.806 


Or,  In  the 


the  pitch  p=  0.66  ~^+c2. 


It  should  be  noticed  that  with  too  small  rivets  this  gives  pitches  often  con- 
siderablv  smaller  in  proportion  than  9%  times  the  diameter. 

For  iloable-rlweted  lap*Jolnta  a  similar  calculation  to  that  given 
above,  but  with  a  somewhat  smaller  allowance  for  excess  tenacity,  on 
soootint  of  the  large  distance  between  the  rivet-boles,  shows  that  for  joints 
of  maximum  strength  the  ratio  of  diameter  to  thickness  should  remain  pre- 
cisely  as  In  singk»>n voted  joints;  while  the  ratio  of  pitch  to  diameter  of  hole 
should  be  8.64  for  dO-ton  plates  and  22  or  84  ton  rivets,  and  8.88  for  28-ton 
piatee  with  the  same  i  ivets. 

Here,  still  more  than  in  the  former  case,  it  is  likely  that  the  prescribed 
size  of  rivet  mar  often  be  inconveniently  large.  In  this  case  tlie  diameter 
of  rivet  ahoukl  be  taken  as  large  as  possible;  and  the  strongest  Joint  for  a 

Even  thickness  of  plate  and  diameter  of  hole  can  then  be  obtained  by  using 
e  pitch  given  by  the  equation 

psOy-f  d, 

where  the  values  of  the  constant  a  for  different  strengths  of  plates  and 
rivets  maj  be  taken  as  follows: 


368  RIVETED  JOINTS. 

TmMe  of  Proportions  of  Bon1>le*rlTeted  Eiap*Joliita, 

(fa 
In  which  p  =s  o  -T-  -f-  d« 


Original  tonacity 

Shearinii:  Resist-     \ 
ance  of  Rivets. 

^alue  of  Con- 

Thickneatf  of 

of  Plate, 

stant. 

PUte. 

Tons  per  iq. 

in. 

Tons 

persq. 

in. 

a 

Hinoh 

80 

88 

84 
84 

1.15 
1.88 

i2    " 

80 
28 

ao 

28 
80 
28 

88 

88 
M 

84 
82 
2:3 

1.05 
1.13 
1.17 
1.25 
1.07 
1.14 

L 


PrROtically,  haTine  assumed  the  rivet  diameter  as  larffe  as  possible,  we 
can  fix  ihe  pitcli  as  Follows,  for  anj  tlilckness  of  plate  from  H^H  ioch: 

For  80-ton  plate  and  24*  ton  rivets?  «  —  iis^-Lrf. 
•♦    2S    **      "       "    28   '*       *•     >*'—*••*'   I  ^**. 

»    80    "      "       ••    88   ••       "        p  =  1.06  J  +  d; 

"    88    "       "        "    84    "        "        p=1.24y  +  cl. 

In  don1>le»rlTeted  bntt^Jolnts  it  is  Impossible  to  develop  the  full 
shearing  renlstance  of  ttie  Joint  witiiout  getting  excessive  bearing  prBmiure, 
because  the  shearing  area  is  doubled  without  Increasing  the  area  on  whick 
the  pressure  acts.  Coiisideiing  only  the  plate  resistance  and  the  bearing 
pressure,  and  taking  this  latter  as  45  tons  per  square  Inch,  the  bent  pitch 
would  be  about  4  times  the  diameter  of  the  hole.  We  may  probably  say 
with  some  certainty  that  a  pressure  of  from  46  to  60  tons  per  square  Inch  on 
the  rivets  will  cause  shearing  to  take  place  at  from  16  to  18  tons  per  square 
Inch.  Working  out  the  equations  as  Isefore,  but  allowing  excess  strength  of 
only  6^  on  account  of  the  large  pitch,  we  find  tliat  the  proportions  of  double- 
riveted  butt-ioints  of  maximum  strength,  under  given  conditions,  are  those 
of  the  following  tabta: 

Donble-HTetod  Bntt-Jolnts. 

OriginiaTen.  Shearing  Re-  Bearing 

acity  sistance  Pres-  Hjitin  i>.fi/« 

of  Plate.  ofRlvete,  sure,  ^"®  ^^ 

Tons  per  Tons  per  Tons  per              -r-  S 

sq.  in.  sq.  in.  sq.  in.                  *  d 

30  16  45                     1.80  8.86 

38  16  46                     1.80  4.00 

80  18  48                     1.70  4.08 

88  18  48                    1.70  4.87 

80  16  60  8.00  4.90 

88  16  60  8.00  4.48 

Practically,  therefore,  it  may  be  said  that  we  get  a  double-riveted  butt-joint 
of  maximufn  strength  by  making  the  diameter  of  hole  about  1.8  times  the 
thickness  of  the  place,  and  making  the  pitch  4.1  times  the  diameter  of  the 
hole. 

The  proportions  just  given  belong  to  joints  of  maximum  strength.  But  in 
a  boiler  the  one  part  of  the  joint,  the  plate,  is  much  more  affected  by  time 
than  the  other  part,  the  rivets.  It  is  therefore  not  unreasonable  to  estimate 
the  percentage  by  which  the  plates  might  be  weakened  by  corrosion,  etc., 
before  tbe  boiler  would  be  unfit  for  use  at  its  proper  steam-pressure,  and  to 
add  correspondingly  to  the  plate  area.  Probably  the  best  thing  to  do  in  thifi 
case  is  to  proportion  the  joint,  not  for  the  actual  tlilckness  of  plate,  but  for 
a  nominal  thickneHS  less  than  the  actual  by  the  assumed  percentage.  In 
this  cane  the  joint  will  be  approximately  one  of  uniform  strength  by  the 
time  it  has  reached  its  fitial  workable  condition ;  up  to  which  time  the  joint 
as  a  whole  will  not  really  have  been  weakened,  the  corrosion  only  gradually 
bringing  the  strength  of  the  plates  down  to  that  of  riveta 


BIYEIBD  JOINTS. 


8S9 


Billeienciea  of  JTointfl* 

The  averaffe  results  of  experiments  by  the  committee  gave:  For  double- 
riveted  lap- joints  In  ^4Bch  plates,  eflOciendes  ranging  from  Vr.1%  to  B1.2ji. 
Far  doiible-rlTeted  butt-joints  (in  double  shear)  6\A%  to  71.8j{.  These  low  re- 
sulu  were  probably  due  to  the  use  of  very  soft  steel  in  the  rivets.  For  single- 
riveted  lap-joints  of  various  dimensions  the  efficiencies  varied  from  54.^  to 
60.83t. 

The  experiments  showed  that  the  shearing  resistance  of  steel  did  not  In* 
crease  nearly  so  fast  as  its  tensile  resistance.  With  Teiy  soft  steel,  for 
ioiitanee,  of  only  26  tons  tenacity,  the  shearing  resistance  was  about  80^  of 
the  tensile  r«'si8tance,  whert>aM  with  very  hard  steel  of  5£  tons  tenacity  tHe 
shearing  resistance  was  only  somewhere  about  W  of  the  tensile  resistance. 

Proportions  of  Pitch  «nd  OTerlap  of  Plates  to  Blfuneter 
of  RlTot-Mole  and  ThleKneBa  of  Plate. 

(Prof.  A.  B.  W.  Kennedy.  fVoc.  Jn»t.  M.  E„  AprU,  1886.) 
t  =:  thickness  of  plate; 

d  =  diameter  of  rivet  (actual)  In  parallel  hole; 
p  =  pitch  of  rivets,  centre  to  centre; 
8  =  space  between  lines  of  rivets; 
[I  =  overlap  of  plate. 
The  pitch  Is  as  wide  as  is  allowable  without  bnparing  the  tightness  of  the 
joint  under  steam. 

For  single-riveted  lap-joints  In  the  circular  seams  of  boilers  which  hava 
double-riveted  longitudinal  lap  joints, 
d  s  r  X  2.85; 

p  =  d  X  8.85  s  <  X  5  (neoclr); 
i  =  t  X  6. 
For  double-riveted  lap-jointa: 

B  =  4.5f ; 
I  =  10.5«. 


Single-riveted  Jointo. 

Double-riveted  Joints. 

t 

d 

P 

I 

t 

d 

p 

$ 

1 

S-16 
5-1. 

^1. 

7-16 
9-16 
11-16 
18-16 

16-16 

8« 

S-16 
^16 

r?^6 

9^6 

7-16 
9-16 
11-16 
13-16 

s 

With  them  proportions  and  good  workmanship  there  need  be  no  fear  of 
leakage  of  steam  through  the  riveted  joint. 

Th«»  net  diagonal  area,  or  an>a  of  plate,  along  a  sigsag  line  of  fracture 
should  not  be  less  than  SOjt  In  excess  of  the  net  area  straight  across  the 
joint,  and  a&i  Is  better. 

Mr.  Theodore  Cooper  (R.  R.  Qazette,  Aug.  22,  1890}  referring  to  Prof.  Ken- 
iiedy*s  statement  quoted  above,  gives  as  a  dufflcientlv  approximate  rule  for 
the  proper  pitch  between  the  rows  in  staggered  riveting,  one  half  of  the 
pitch  of  the  rivets  In  a  row  plus  one  quarter  the  diameter  of  a  rivet-liole. 

Apparent  ExcoM  In  Strenctb  of  Perforated  over  Unper* 
'^^^  rorated  Plates.  (Proc.  Inst.  H.  E.,  October,  1888.) 
The  metal  between  the  rivet-holes  has  a  considerably  greater  tensile  re- 
nstance  per  squara  inch  than  the  unperforated  metal.  This  excess  tenacity 
smouDted  to  more  than  S0)(,  both  in  9^lnch  and  ^-inch  plates,  when  the 
pitch  of  the  rivets  was  about  1.9  diameterH.  In  otiier  cases  ^-Inch  plate 
eav«>  an  exoeM  of  injK  at  fracture  with  a  pitch  of  2  diameters,  of  \Q%  with  a 
pitch  of  8.6  diameters,  and  of  6.6j(  with  a  pitch  of  s.9  diameters;  and  ^-inch 
plate  $»^e  iM  es^oew  with  a  pitch  of  2.8  diametei'a. 


360 


BIVETBD  JOINTS. 


(1)  The  **  excess  strength  due  to  perforation  **  Is  increased  bj  anrthing 
which  tends  to  make  the  stress  in  the  plate  uniform,  and  to  diminteh  the 
effect  of  the  narrow  Rtrip  of  metal  at  the  edge  of  the  specimen. 

(3)  It  is  diminished  by  increase  in  the  ratio  of  p/d,  of  pitch  to  diameter  of 
hole,  so  that  in  this  respect  it  becomes  less  as  the  efficiency  of  the  joint 
increases. 

(3)  It  is  diminished  by  any  increase  in  hardness  of  the  plate. 

(4)  For  a  given  ratio  ji/d,  of  pitch  to  diameter  of  hole,  it  is  also  apparently 
diminished  as  the  tliickness  of  the  plate  is  increased.  The  ratio  of  pitch  to 
thickness  of  plate  does  not  seem  to  affect  this  matter  directly,  at  least 
within  the  limits  of  the  experiments. 

Teat  of  povlile-rlTeted  Lap  and  BnU  JTolnte. 
(Proc.  Inst.  M.  E.,  October,  1888.) 
Steel  plates  of  25  to  26  tons  per  square  inch  T.  8.,  steel  riyets  of  S4.6  tons 
shearing-strength  per  square  inch. 


vi«H  ftf  Tr»i«i-    Thickness  of     Diameter  of  Ratio  of  Pitch 


Plate, 


to  Diameter. 


ComparaUre 
Efficiency 


Lap. 
Butt. 
Lap.. 

Butt' 
»( 

Lap. 
Butt 


8.62 
3.93 
2.fiS 
3.41 
4.00 
3.94 
8.49 
8.00 
8.92 


iency  of 
Joint. 
75.2 
76.5 
68.0 
78.6 
7«.4 
76.1 
68.0 
70.2 
76.1 


Rivet-holes. 
0.8" 

?:I 

1.6 

l.t 

1.6 

1.3 

1.75 

1.8 

Some  Rnlea  ^vliicli  have  been  Proposed  A>r  tlie  IMnnieter 
of  tbe  Rivet  in  Single  Shear.    (Iron^  June  18,  1880.) 

Browne d  =  2Mwith  double  covers  mo  (D 

Fairbaim ri  =  2t  for  plates  less  than  9^  in.  (2) 

"        d  =  mt  for  plates  greater  than  %  in.  (8) 

Lemaitre d  =  1.5^  +  0.16  (4) 

Antoine d  =  1.1  V^  (5> 

Pohllg d  =  2t  for  boiler  riveting  (6) 

"         d  =  8<  for  extra  strong  riveting  (7) 

Redtenbacher d  =  1.5^  to  n  (8) 

Unwin d  =  %t  +  ^mto%t'\-%  (9) 

*•     d=rl.2Vl  (10) 

The  following  table  contains  some  data  ot  the  sizes  of  rivets  used  In 
practice,  and  the  corresponding  sizes  given  by  some  of  these  rules. 
Diameter  of  Riveta  for  PiflTerent  Tliirkneaaea  of  Platea» 


Thick- 
ness of 
plate. 
Inches. 


6/16 
?^16 

9/16 
1?^16 


18/16 

15/16 

1 


Diameter  of  Rivets,  in  inches. 


3« 


% 


«  s 

a" 


15/16 


1 
1I/I6 


II 


^ 


Va 


18/16 


1  1/16 


a* 


% 


21/82 


27/32 

15/16 

1  1/88 


1  7/32 


28/32 

18/16 
15/16 


1  3/16 
IM 


1« 


S, 


716 


18/16 

15/16 
15,16 


1 

1 

1  1/16 

Hi— 


11/16 

13/16 


15/16 
1 
1  1/16 


1  8/82 
18/16 


a 


n/16 


K 


MTETED  JOINTS. 


361 


Strenstlft  of  BottMe*  riveted  Seams,  €a1enl«ted«  —  W.  B. 

RufEKles.  Jr.,  in  i'otrer  for  June,  18W,  gives  tableR  of  relative  Birengrth  of 
riveis  and  parts  of  sheet  between  rivets  in  double-riveted  seams,  compared 
Willi  strenfHh  of  shell,  based  on  the  assumption  that  the  shearing  strength 
of  rivets  and  the  tensile  strength  of  steel  are  equal.  The  following  figures 
show  the  sizes  in  his  tables  which  show  the  nearest  approximation  to  equal- 
itj  of  strength  of  rivets  and  parts  of  plates  between  the  rivets,  together 
with  the  percentage  of  each  relative  to  the  strength  of  the  solid  plate. 


Size  of 
Rivet- 
holes, 

inches. 


9/16 


n 


lf/16 
9/16 


% 


11/16 


II/IC 
lJ/16 
lf/16 


Percentage  of 

Strength  of 

Plate. 


Rivets.  Plate. 


.789 
.795 
.785 
.810 
.749 
.748 
.761 
.780 
.727 
.756 
.754 
.762 
.777 
.714 


.766 
.775 
.800 
.810 
.785 
.762 
.780 
.793 
.728 
.738 
.760 
.776 
.788 
.711 


Pitch 

of 
Rivets, 
inches. 


Size  of 
Rivet- 
holes. 
Inches, 


18/16 

% 
15/16 

H 
18/10 

1.5/16 

13/16 

15/16 

1  1/16 


Percentage  of 

Strength  of 

Plate. 


Rivets.   Plate. 


.784 
.768 
,7^8 
.765 
.707 
.721 
.740 
.7:^6 
.761 
.701 
.714 
.727 
.745 
.742 


.740 
.750 
.773 
.700 
.718 
.781 
.750 
.758 
.690 
.708 
.722 
.788 
.750 


H.  De  B.  Parsons  {Am.  Engr.  db  R.  B.  Jour.^  1898)  holds  that  It  is  an  error  to 
assame  that  the  shearing  strength  of  the  rivet  is  equal  to  the  tensile  strength. 
Also,  referring  to  the  apparent  excess  in  strength  of  perforated  over  unper- 
ftirated  plates,  he  claims  that  on  account  of  the  difficulty  in  properly  match- 
ing the  holes,  and  of  the  stress  caused  by  forcing,  as  is  too  often  the  case 
in  practice,  this  additional  strength  cannot  be  trusted  much  more  than 
that  of  friction. 

Adopting  the  sizes  of  iron  rivets  a.<«  generally  used  in  American  practice 
for  steel  plates  from  ^  to  1  Inch  thick:  the  tensile  strength  of  the  plates  as 
60.000  lbs.;  the  shearing  strength  of  the  rivets  as  40.000  for  single-shear  and 
35,500  for  double  -  shear,  Mr.  Parsons  calculates  the  following  table  of 
pitches,  so  that  the  strength  of  the  rivets  against  shearing  will  be  approxi- 
mately equal  to  that  of  the  plate  to  tear  between  rivet-holes.  The  diameter 
of  the  rivets  has  in  all  cases  been  taken  at  1/16  in.  larger  than  the  uorainaL 
size,  as  the  rivet  is  assumed  to  All  the  bole  under  the  power  riveter. 

Riveted  Joints* 

Lap  OB  Burr  with  Sxhoub  Wslt— Stbbl  Platbs  and  Iron  Rivets. 


Thickness 

Diameter 

of 

Rivets. 

Pitch. 

Efficiency. 

of 
Plates. 

Single. 

Double. 

Single. 

Double. 

in. 

f 

In. 

1 
1 
1  1/8 

ill. 
1  3/10 

1  11/16 

1  11/10 
2^/16 

in. 

r^i/16 
r^/16 

rf/16 
2« 

55.rj< 

52.7 
49.0 
43.6 
42.0 
38.6 
88.1 

TO.Ojf 

68.0 

66.9 

C0.4 

59.5 

55.4 

54.9 

J 


862 


RIVETED  JOINTS. 


Calculated  Bttclencies-Steel  Plates  and  Steel  KtTeta.— 

The  differences  between  ihe  calculaie<l  efilciencieK  given  in  the  two  tables 
above  are  notable.  Those  Riven  by  Mr.  Ru^g^les  are  pi-obably  too  IiiKh,  Bince 
be  assumes  the  shearing  strenfrth  of  the  rivets  equal  to  the  tensiie  strenicth 
of  the  plates.  Those  given  by  Mr.  Parsons  are  probably  lower  than  will  be 
obtained  In  practice,  since  the  figure  be  adopts  for  shearing  sti-en^th  is 
rather  low,  and  he  maken  no  allowance  for  excess  of  strength  of  the  perfo- 
rated over  the  unperforated  plate.  The  following  table  baa  l>een  calculated 
by  the  author  on  the  assumptions  that  the  ezcesn  strength  of  ihe  perforated 
plate  is  \0%y  and  that  the  shearing  strength  of  the  rivets  per  f:quan*  inch  is 
four  fifths  of  the  tensile  strength  of  the  plate.  If  f  =  tliickness  of  plate, 
d  =  diameter  of  rivet -hole,  p  =  pitch,  and  T  =  tensile  strength  per  square 
Inch,  then  for  slngle-riveteu  plates 


(p-d)txUlOT-- 


T^'Xg^' 


whence  p  •■ 


:.5Tlf  +  4 


,«d» 


For  double  riveted  plates,  p  =  ^-^^^  +  ^ 

The  coefncients  .571  and  1.142  a^irree  closely  with  the  averages  of  those 
given  in  the  report  of  the  committee  of  the  Institution  of  Mechanical  En- 
gineers, quoted  on  pa^es  897  and  358,  ante. 


,i 

Diam. 

Pitch. 

Efficiency. 

1 

Diam. 

PItdL 

1 

a 

. 

of 
Rivet- 
bole. 

I| 

if 

4 

«5 

of 
Rivet- 
hole. 

i 

i 

in. 

In. 

in. 

in. 

% 

% 

In. 

in. 

in. 

In. 

% 

% 

8/16 

7/16 

1.020 

1.608 

67.1 

72.7 

J< 

^ 

1.892 

2.085 

46.1 

63.1 

1^ 

1.261 

2.038 

60.5 

76.8 

1.749 

2.624 

60.0 

66.6 

M 

12 

1.071 

1.642 

63.3 

69.6 

•' 

1 

3.142 

8.281 

58.3 

70.0 

9/16 

1.285 

2.006 

56.2 

«.o 

•* 

2. 570   4.016 

66.2 

78.0 

6/16 

9/16 

1.187 

1.712 

50.5 

67.1 

»/16 

ij 

1  321|  1.802 

43.2 

60.3 

». 

% 

1.389 

2.a'i3 

58.3 

69.5 

'* 

A\ 

1.652!  2.429 

47.0 

64.0 

■* 

11/16 

1.551 

2.415 

65.7 

71.6 

«< 

1 

2.015!  S-ffiK) 

60.4 

67.0 

% 

Vi 

1.218 

1.810 

48.7 

66.5 

M 

2.410   8.694 

58.8 

69.5 

\? 

» 

1.607 

2.4C3 

58.8 

69.6 

t( 

]C 

3.836 

4.422 

66.9 

71.6 

(« 

XrZ 

2.011 

8.206 

67.1 

72.7 

% 

8^ 

1.264 

1.778 

40.7 

67.8 

7/16 

78 

1.186 

1.647 

45.0 

62.0 

% 

1.576 

2.274 

44.4 

61.9 

4» 

^ 

1.484 

2.218 

49.6 

66.2 

•• 

1 

1.914 

2.827 

47.7 

64.6 

*» 

z2 

1.869 

2.864 

68.2 

69.4 

** 

1^ 

2.281 

3.488 

50.7 

67.8 

»4 

1 

2.305 

8.610 

66.6 

72.8 

ti 

2.678 

4.106 

53.3 

60.6 

RlTetlns  Pressure  Required  for  Bridge  and  BoUer 
ITork. 

(Wilfred  Lewis,  Engineers'  Club  of  Philadelphia,  Nov.,  1893.) 

A  number  of  l^-inch  rivets  were  subjected  to  pressures  between  10.000  and 
60.000  Iba  At  10,900  lbs.  the  rivet  swelled  &nd  fuled  the  hole  without  forming 
a  head.  At  20,000  lbs.  the  head  was  formed  and  the  plates  were  sliffhtly 
pinched.  At  30.000  lbs.  the  rivet  was  well  set.  At  40,000  lbs.  the  metal  in  the 
plate  surrounding  the  rivet  began  to  stretch,  and  the  stretching  became 
more  and  more  apparent  as  the  pressure  was  increased  to  60,000  and  60,000 
lbs.  From  these  experiments  the  conclusion  might  be  drawn  that  the  pres- 
sure required  for  cold  riveting  was  about  300,000  lbs.  per  squarelnch  of  rivet 
section.  In  hot  riveting,  until  recently  thei-e  was  never  any  call  for  &  pres- 
sure exceeding  60,000  lbs.,  but  now  pressures  as  high  as  150,000  lbs.  are  not 
uncommon,  and  even  800,000  lbs.  have  been  contemplated  «s  desirable. 


6HEAHING   RESISTANCE  07  BIVET  IRON  AKD  STEEL.   363 


App*reot  SbeariiiS  Resistance  of  RiTeC  Iron  mnd  Steel* 

iProc.  Inst.  M.  E„  18T9,  Engineering,  Feb.  80, 1880.) 

The  true  ahearing  resistance  of  the  rivets  cannot  be  ascertaiiied  from 
experimeuts  on  riveted  Joints  (1)  because  the  uniform  distribution  of  the 
load  to  all  the  rivets  cannot  be  insured:  (-J)  because  of  the  friction  of  the 
plates,  which  has  the  effect  of  increasing  the  apparent  resistance  to  shear- 
ing in  an  element  uncertain  in  amount.  Probably  in  the  case  of  single* 
riveted  joints  the  shearing  resistance  is  not  much  affected  by  the  friction. 

Ultimate  Shearing  Stress 
Tons  per  sq.  in.  Lba  per  sq.  In. 
Iron,  single  shear  (12  bars)..  84.15  C^096t^.^.^  . 

"    double  shear  (8  bars)..  K.IO  49.504  f  ^^"*^*' 

^*  ..  28.68  60.660    Barnalqr. 

82.80  49.058    Ranklne.  > 

"     l^-in.  Hvets. 23.05  to  25.57   51.682  to  57.277  ) 

"     ^in.  rivets 24.82  to  27.94   54.477  to  62.868  V Riley. 

"    mean  value    25.0  66.000) 

"    ^in.  rivets.  19.01  42JSBi    Greig  and  E^yth. 

St<t>l 17to26        88.080 to 68.240    Parker. 

Landore  steel,  t^-in.  rivets. .   81.67  to  88.09   70.941  to  75.466 ) 

"      ft.in.rtvete..  80.4510  85.73   68.208  to  80.035  V Riley. 
<*     mean  value..  88.8  74.598) 

Brown's  steel 82.18  49.688    Qreig  and  Eyth. 

Fairbsim>  experiments  nhow  that  a  rivet  is  6^<  weaker  In  a  drilled  than 
In  a  punched  hole.  By  rounding  the  edjre  of  the  rivet-hole  the  a}>parent 
shearing  resistance  is  increased  ISjK.  Mr.  Maynard  found  the  nvets  A% 
weaker  In  drilled  holes  than  in  punched  holes.  But  these  results  were 
obtained  with  riveted  Joints,  and  not  by  direct  experimeuts  on  shearing. 
There  is  a  good  deal  of  difficulty  in  determining  the  true  diameter  oia 
punched  hole,  and  it  is  doubtful  whether  in  these  experiments  Uie  diameter 
was  -verr  accurately  ascertained.  Messrs.  Oreig  and  Eyth's  experiments 
also  indicate  a  greater  resistance  of  the  rivets  in  punched  holes  than  In 
drilled  holes. 

If.  as  appears  above,  the  apparent  shearing  resistance  Is  less  for  doubts 
than  for  single  shear,  it  is  probably  due  to  unequal  distribution  of  the  stress 
on  the  two  rivet  sections. 

The  shearing  resistance  of  a  bar,  when  sheared  in  circumstances  which 
prevent  friction.  Is  usually  less  than  the  tenacity  of  the  bar.  The  following 
results  show  the  decrease  : 


Tenacity  of 
Bar. 

Shearing 
Resistance. 

Ratio. 

Harkcwl.  Iron..... 

26.4 
26.4 
82.8 

28.8 

16.6 
20.2 
19.0 
22.1 

0.62 

Lavalley .  iron 

Greig  and  ItytUi,  iron... 

0.79 
0.85 
0.77 

In  WShler's  researches  (in  1870)  the  shearing  strength  of  iron  was  found 
to  be  foar-flf  ths  of  the  tenacity.  Later  researches  of  Bauschinger  confirm 
this  result  generally,  but  they  show  that  for  iron  the  ratio  of  the  shearing 
resistance  and  tenacity  depends  on  the  direction  of  the  stress  relatively  to 
the  direction  of  rolling.  The  above  ratio  Is  valid  only  if  the  shear  is  in  a 
plane  perpendicular  to  the  direction  of  rolling,  and  if  the  tension  is  applied 
parallel  to  the  direction  of  rolling.  The  shearing  resistance  in  a  plane 
parallel  to  the  direction  of  rolling  is  different  from  that  in  a  plane  perpen> 
dicular  to  that  direction,  and  again  differs  according  as  the  plane  of  shear  is 
perpendicular  or  parall^  to  the  breadth  of  the  bar.  In  the  former  case  the 
rpsQtance  is  18  to  809t  greater  than  in  a  plane  perpendicular  to  the  fibres,  or 
is  equal  to  the  tenacity.  In  the  latter  case  it  is  only  half  as  great  as  In  a 
plane  perpendlciilar  to  the  fibres. 


964 


IBOK  AND  STEEL. 


tBON  AND  STEEL. 

(CLASSIFICATION  OP  IRON  AND  STEEL. 


^ 

<  I 

a| 

*  t 
•I 


si 


t 

•o 

I 

o 


I 

08 

1 

3 


l!l! 


ill 'I 


a  s 


jiiijifi 

i5-«  ISSN'S 

^  CO  yJS  9<C  * 

«s*^     o  S  5    -o 


■Silos' 
I  .61 


b 

B 


^7  i  ri^i 

u  »  u^-i      '"  L.  K  C 


"?-"  tip. 


^  .3    E  £ 

?  J  u  tj 


s^  i^li 


iil-5  Jill 


g   »   «   C    =   £i   S   i   ■   * 


CAST  IBOK.  •  8e& 

^  oAflrr  iBON.  ^ 

Gfa^Uhc  of  Pic  Iron*— Pfff  iron  is  commonlr  gntded  aooordinsr  to  its 
fracture,  the  number  of  grades  IvArying  in  different  districts.  In  Eastern 
PeonsylTania  the  principal  jrrades  recognised  are  known  as  No.  1  and  S 
foundry,  gray  forge  or  No.  s,  mottled  or  No.  4fand  white  or  No.  6.  Inter- 
mediate fprades  are  sometimes  made,  as  No.  S  X.  between  No.  1  and  No.  3, 
tnd  special  names  are  given  to  irons  more  higblv  siliclzed  than  No.  1,  as 
No.  1  X  Bilver-gray,  and  soft.  Charcoal  foundry  pig  iron  Is  graded  by  num- 
bers 1  to  5,  but  the  quality  is  very  different  from  the  corresponding  num- 
bers in  anthracite  and  coke  pig.  Southern  coke  pig  iron  is  graded  into  ten 
or  more  grades.  Grading  bV  fracture  is  a  fairly  satisfactory  method  of 
grading  irons  made  from  uniform  ore  mixtures  and  fuel,  but  is  unreliable  as 
a  means  of  determining  quality  of  irons  produced  In  different  sections  or 
from  different  ores.  Grading  bV  chemical  analysis,  in  the  latter  case,  is  the 
only  satisfactory  method.  The  following  analyses  of  the  five  standard 
crades  of  northern  foundry  and  mill  pig  irons  are  giTSn  by  J.  M.  Hartman 
{BulL  Lit  8.  A.,  Feb..  1898) : 

No.  1.  No.S.  No.  8.  No. 4.  No.  4  B.  No.  5. 

Iron 08.97  98.81  94.M  94.48  94.06  iM.68 

Gimphltic  carbon..      8.SS  8.99  8.M  8.08  8.08       

Oombined  carbon..       .18  .87  1.G8  1.96  1.48  8.88 

Silicon 8.44  8.58  .78  .56  .98  .41 

Phosphorus 1.86  1.06  .86  .19  .04  .04 

Sulpbur 08  .08  trace  .06  .04  .08 

ICanganese S»  .78  .84  .67  8.08  .96      ' 

CHiJUcnBRisncs  or  Thssb  Iboms. 

No.  1.  Oray.^A  laige,  dark,  open-grain  Iron,  softest  of  all  the  numbers 
and  used  ezdusiyely  in  the  foundry.  Tensile  strength  low.  Elastic  limit 
low.    Fracture  rough.    Turns  soft  and  tough. 

No.  S.  Oray.—A  mixed  large  and  small  dark  grain,  harder  than  No.  1  iron, 
and  used  exclusively  In  the  foundry.  Tensile  strength  and  elastic  limit 
higher  than  No.  1.  Fracture  less  rough  than  No.  1.  Turns  harder,  less 
tough,  and  more  brittle  than  No.  1. 

No.  8.  Oray.^SmaU,  gray,  close  grain,  harder  than  No.  8  Iron,  used  either 
in  the  rolling-mill  or  foundry.  Tensile  strength  and  elastic  limit  higher  than 
No.  8.    Toms  hardfless  tough,  and  more  brittle  than  No.  8. 

No.  4.  Mottied.—White  background,  dotted  closely  with  small  black  spots 
of  graphitic  carbon ;  little  or  no  grain.  Used  exclusively  in  the  roUing-milL 
Tensile  strength  and  elastic  limit  lower  than  No.  8.  Turns  with  dilmnilty; 
leas  tough  and  more  brittle  than  No.  3.  The  manganese  In  the  B  pig  iron 
replaces  part  of  the  combined  carbon,  making  the  iron  harder  ana  closing 
the  grain,  notwithstanding  the  lower  combined  carbon. 

So.  a.  White.— Smooth^  white  fracture,  no  grain,  used  exclusively  In  the 
rolling  mill.  Tensile  strength  and  elastic  limit  much  lower  than  No.  4.  Too 
hard  to  torn  and  more  brittle  than  No.  4. 

Southern  pig  Irons  are  graded  as  follows,  befrinning  with  the  highest  in 
siUoon:  Nos.  1  and  8  silvery,  Nos.  1  and  8  soft,  all  containing  over  8)(  of 
silicon;  Noa.  1,  8,  and  8  foundry,  respectively  about  8.76j(,  2.6ii  and  2%  silteon; 
No.  1  mill,  or  *' foundry  forge;**  No.  8  mill,  or  gray  forge;  mottled;  white. 

Good  charcoal  chilling  Iron  for  car  wheels  contains,  as  a  rule.  0.56  to  0.95 
aliooo,  0.06  to  0.90  manganese,  0.06  to  0.75  phosphorus.  The  following  Is  an 
analyiis  of  a  remarkably  strong  car  wheel:  SI,  0.784;  Mn,  0.488;  P.  0.486, 
S, 0.OB:  Graphitic  C,  8.068;  Combined  C,  1JM7;  Copper.  0.089.  The  chill  was 
Tery  bard--|4  'd*  <1®^P  At  root  of  flange,  M_in.  deep  on  tread.  A  good 
ordnanoe  Iron  analysed:  Si,  0.80;  Graphitic  C.  8.80;  Combined  C.  1.70:  P, 
0.44;  Mn,  8.55  (f).  lU  spedflc  gravity  was  7.2<  and  tenacity  81,784  lbs. 
IM^rsq.  in. 

Influence  of  Mlleon,  Plioeptaornei  Snlplmr,  and  Man- 
nineee  iii»oii  Cmmt  Iron*~W.  J.  Keep,  or  Detroit,  in  several  papers 
nrrans.  A.  ITH.  IL,  1889  to  1808),  discusses  the  influence  of  various  chemical 
elements  on  the  quality  of  cast  hron.  From  these  the  following  notes  have 
been  condensed: 

SiuooH.— Pig  iron  contains  all  the  carbon  that  it  could  absorb  during  its 
ndnctton  In  ube  blast-furnace.  Carbon  exists  in  cast  iron  in  two  distinct 
forms.  In  chemi<^  union,  as  "  combined  "  carbon.  It  cannot  be  discerned, 
except  as  It  may  Increase  the  whiteness  of  the  fracture,  in  so-called  white 


36S    »  •  IRON  AKD  STEEL, 

'  ^  i 

Iron.  Carbon  mechanically  mixed  with  the  Iron  as  nn'aphlte  la  ylslble,  Taij* 
ins  In  color  from  eray  to  black,  while  the  fracture  of  the  Iron  raogoa  from  a 
llfbt  to  a  very  dark  gray. 

Silicon  wlU  expel  curboo.  if  the  iron,  when  melted,  contains  all  the  oarboi 
that  it  can  hold  and  a  portion  of  silicon  be  added. 

Prof.  Turner  concludes  from  his  tests  that  the  amount  of  silicon  producing 
the  maximum  strength  is  about  l.SOji.  But  this  is  onlv  true  when  a  white 
base  is  used.  If  au  iron  is  used  as  a  base  which  will  produce  a  sound  casUni; 
to  begin  with,  each  additioQ  of  silicon  will  deoreasa  strength.  Bilicon  itself 
is  a  weakening  agent.  Variations  in  the  percentage  of  silicon  added  to  a  pig 
iron  will  pot  insure  a  given  strength  or  physical  structure,  but  theae  reaulU 
will  depend  upon  the  physical  properties  of  the  original  iron. 

ilfter  enough  silicon  has  been  added  to  cause  solid  castings,  anv  further 
addition  and  consequent  increase  of  graphite  weakens  the  casting.  The 
softness  and  strength  given  to  castings  by  a  suitable  addition  of  siiloon  is, 
by  a  further  increase  of  silicon,  changed  to  stilfness,  brittleneas,  and  weak- 
ness. 

As  strength  decreases  from  increase  of  graphite  and  decrease  of  combined 
carbon,  deflection  increases ;  or,  in  other  words,  bending  Is  Increased  by 

graphite.  When  no  moie  graphite  can  foi*m  and  ailicou  still  increasefl,  de- 
ectfon  diminishes,  showing  that  high  sHIcon  not  only  weakens  iron,  but 
makes  it  stiff.  This  stiffness  is  not  the  same  strengthrstiffness  which  is 
caused  by  compact  iron  and  combined  carbon.    It  is  a  brittle-stiffneu. 

In  pig  irons  which  received  their  silicon  while  in  the  blaat-furnaoe  the 
graphite  more  easily  separates,  aud  the  shrinkage  is  less  than  in  any  mix- 
ture. As  silicon  increases,  shrinkage  also  increases.  Silicon  of  iuelf  in- 
creases shrinkage,  though  by  reason  of  its  action  upon  the  carbon  in  ordi- 
nary practice  it  is  truly  said  that  silicon  **  takes  the  shrinkage  out  of  cast- 
iron."  The  slower  a  casting  crystallises,  the  greater  will  be  the  quantity  of 
graphite  formed  within  It 

Bilicon  of  itself,  however  small  the  quantity  present,  hardens  cast-iron; 
but  the  decrease  of  hardness  from  the  change  of  the  combined  carbon  to 
graphite,  caused  by  the  silicon,  is  so  much  more  rapid  than  the  hardening 
produced  by  the  increase  of  silicon,  that  the  total  effect  is  to  decrease  hard- 
ness, until  the  silicon  reaches  from  8  to  fijC. 

As  practical  foundry- work  does  not  call  for  more  than  2i%  of  silicon,  the 
ordinary  use  of  silicon  does  reduce  the  hardness  of  castings;  but  this  is  pro- 
duced through  its  influence  on  the  carbon,  and  not  Its  direct  influenca  on  the 
Iron. 

When  the  change  from  combined  to  eraphfte  carbon  has  ceased  to  dimin- 
ish hardness,  say  at  from  fi%Xxih%ot  silicon,  the  hardening  by  the  silicon  it- 
self becomes  more  and  more  apparent  as  the  silicon  increases. 

Shrinkage  and  hardness  are  almost  exactly  proportional.  When  silicon 
varies,  and  other  elements  do  not  vary  maleriHlVy,  castings  with  low  shrink- 


age are  soft :  as  shrinkage  Increases,  the  castings  grow  hard  in  almost,  if 
not  exactly,  the  same  proportion.  For  ordinary  foundry-praotiee  the  scale 
of  shrinkage  may  be  made  also  the  scale  of  hardness,  provided  variations  in 


sulphur,  and  phosphorus  especially,  are  not  present  to  complicate  the  re- 
sult. 

The  term  "•chilling**  irons  Is  generally  applied  to  such  as,  cooled  slowly, 
would  be  gray,  but  cooled  suddenly,  become  white  either  to  a  depth  suffi- 
cient for  practical  utilization  (e.gr.,  In  car-wheels)  or  so  far  as  to  be  detrimen- 
tal. Many  irons  chill  more  or  less  in  contact  with  the  cold  surface  of  the 
mould  in  which  they  are  cast,  especially  if  they  are  thin.  Sometimes  this  is 
a  valuable  quality,  but  for  general  foundry  purposes  it  is  desirable  to  have 
all  parts  of  a  casting  an  even  gray. 

Silicon  exerts  a  powerful  influence  upon  this  property  of  irons,  partially 
or  entirely  removing  their  capacity  of  chilling. 

When  silicon  is  mixed  with  irons  previously  low  In  silicon  the  fluidity  is 
Increased. 

It  is  not  the  percentage  of  silicon,  but  the  state  of  the  carbon  and  the 
action  of  silicon  through  other  elements,  which  causes  the  Iron  to  be  fluid. 

Silicon  irons  have  always  had  the  I'eputation  of  Imparting  fluidity  to  other 
irons.  This  comes,  no  doubt,  from  the  fact  that  up  Ui%%ori%  they  increase 
the  quantity  of  graphite  in  the  resulting  casting. 

From  the  statement  of  Prof.  Turner,  that  the  maximum  strength  occurs 
with  just  such  a  percentage  of  silicon,  and  his  statement  that  a  founder  can, 
with  silicon,  produce  Just  the  quality  of  iron  that  he  may  need,  and  from 
his  naming  the  composition  of  what  he  calls  a  typical  foundiy-lron,  some 


iroi 


INFLUENCE  OF  SILICON,  ETC.,  UPON  CAST  IRON.    367 

foaoders  baTe  inferred  that  if  they  knew  the  percentages  of  silicon  In  thetr 
irons  and  in  their  ferro-dlicon,  they  need  only  mix  so  as  to  get  9%  of  silicon 
in  order  to  obtain,  always  and  with  certainty,  the  maximum  strength.  The 
solution  of  the  problem  is  not  so  Rimple.  Each  of  the  Irons  which  the  foun- 
der uses  will  have  peculiar  tendencies,  given  them  in  die  blast-furnace, 
which  will  exert  theur  influence  in  the  most  unexpected  ways.  However,  a 
white  iron  which  will  invariably  give  porous  and  brittle  castings  can  be 
made  solid  and  strong  by  the  addition  of  silicon;  a  further  addition  of  sili- 
con will  turn  the  iron  gray;  and  as  the  grayness  increases  the  iron  will  grow 
weaker.  Excessive  silicon  will  again  lighten  the  grain  and  cause  a  hard  and 
brltile  as  well  as  a  very  weak  iron.  The  onlv  softening  and  shriukage-les- 
senioK  influence  of  silicon  is  exerted  during  the  time  when  graphite  is  oeing 
produced,  and  silicon  of  itself  is  not  a  softener  or  a  lessener  of  shrinkage; 
Diit  through  its  influence  on  carbon,  and  only  during  a  certain  stage,  does  it 
produce  these  effects. 

PHoePBOBDa— While  phosphorus  of  itself,  In  whatever  quantity  present, 
weakens  oast-iron,  yet  m  quantities  less  than  \.9%  its  influence  Is  not  sufli- 
ciently  great  to  overbalance  other  beneflcial  effects,  which  are  exerted 
before  the  percentage  reaches  1%.  Probably  no  element  of  itself  weakens 
cast  iron  as  much  as  phosphorus,  especially  when  present  in  large  quantities. 
Shrinkage  is  decreased  when  phosphorus  is  Increased.  All  high-pnoHphorus 
»ig  irons  have  low  shrinkage.  Phosphorus  does  not  ordinarily  harden  cast 
on,  probably  for  the  reason  that  it  does  not  increase  combined  carbon. 
The  fluidity  of  the  metal  is  slightly  increased  by  phosphorus,  but  not  to 
any  such  great  extent  as  has  been  ascribed  to  it. 

The  property  of  remaining  long  in  the  fluid  state  must  not  be  confounded 
with  fluidity,  for  it  is  not  the  measure  of  its  ability  to  make  sharp  castings, 
or  to  run  into  the  veiy  thiu  parts  of  a  mould.  Generally  speaking,  the  state- 
ment is  Justified  that,  to  some  extent,  phosphorus  prolongs  the  fluidity  of 
the  iron  while  It  is  filling  the  mould. 

The  old  Scotch  irons  contained  about  1%  of  phosphorus.  The  foundry -irons 
which  are  most  sought  for  for  small  and  thin  castings  in  the  Eastern  States 
contain,  as  s  genenu  thing,  over  1%  of  phosphorus. 

Certain  irons  which  contain  from  4%  to  7%  silicon  have  been  so  much  used 
on  aooount  of  their  ability  to  soften  other  irons  that  they  hare  come  to  be 
known  as  **  softeners  "  and  as  lesaeners  of  shrinkage.  These  irons  are  valu- 
able as  carriers  of  silicon  ;  but  the  irons  which  are  sold  most  as  softenei'S 
and  shrlnkage-lesseners  are  thode  containing  from  1)(  to  aj(  of  phnnphorus. 
We  must  therefore  ascribe  the  reputation  of  some  of  them  largely  to  the 
pliosphorus  and  not  wholly  to  the  silicon  which  tliey  contain. 

From  ^  to  1%  of  phosphorus  will  do  all  that  can  be  done  In  a  beneflcial 
way,  and  all  above  that  amount  weakens  the  Iron,  without  corresponding 
benefit.  It  is  not  necessary  to  search  for  phosphorus-irons.  Most  irons 
contain  more  than  is  needed,  and  the  care  should  be  to  keep  it  within  limits. 
8ru*BUR.— Only  a  small  percentage  of  sulphur  can  be  made  to  remain 
in  carbonised  iron,  and  it  is  difficult  to  introduce  sulphur  into  gray  cast  iron 
or  into  any  carbonized  iron,  although  gray  cast  iron  oft**n  takes  from  the 
fuel  as  much  more  sulphur  as  the  iron  originally  contained.  Percentages 
of  sulphur  that  could  be  retained  by  gray  cast  iron  cannot  materially  Injure 
the  iron  except  through  an  increase  of  shrinkage.  Tiie  higher  the  carbon, 
or  the  hifirher  the  sllieon,  the  smaller  will  be  the  influence  exerted  by 
solphnr. 

TlM»  influence  of  sulphur  on  all  cast  iron  is  to  drive  out  carbon  and 
silfcon  and  to  increase  chill,  to  Increase  shrinkage,  and,  as  a  general  thing,  to 
decrease  strength  ;  but  if  in  practice  sulphur  will  not  enter  such  iron,  we 
•hall  not  have  any  cause  to  fear  this  tendency.  In  every-day  work,  however, 
it  is  found  at  times  that  Iron  which  was  gray  when  put  into  the  cupola  comes 
oat  white,  with  increased  shrinkage  and  chill,  and  often  with  decreased 
•trength.  This  Is  caused  by  decreased  silicon,  and  can  be  remedied  by  an 
increase  of  silicon.  ...  ^  ^    i.         i 

Mr.  Keep's  opinion  concerning  the  influence  of  sulphur,  quoted  above,  is 
dijugreed  withhy  J.  B.  Nau  {Iron  Aife.  March  89,  1804).    He  says: 

"Sulphur,  in  whatever  shape  It  mi|y  be  present,  has  a  deleterious  influence 
OD  the  iron.  It  has  the  tendency  to  render  the  iron  white  by  the  influence 
it  exercises  on  the  combination  between  carbon  and  iron.  Fig  imn  coutain- 
teg  a  certain  percentage  of  it  becomes  porous  and  full  of  holes,  and  castings 
made  from  sidphurous  iron  are  of  inferior  quality.  This  happens  especially 
when  the  element  is  present  in  notable  quantities.  With  foundry-iron  con- 
tabiifiy  ss  high  as  QA%  of  sulphur,  castings  of  greater  strength  may  be  oh* 


L 


368  IROK  AKD  STEEL.' 

tained  than  when  no  sulphur  Is  present.  Thus,  in  some  tests  on  tblseleRienl 
quoted  bv  R.  Akerman,  it  is  stated  that  in  the  foundrv-iron  from  Flnsnong. 
used  in  the  manufacture  of  cannons,  a  peroentage  of  0.1  j(  to  0.1 4](  of  sulphur 
in  the  iron  increased  its  strength  to  a  considerable  extent.  The  peroentag« 
of  sulphur  found  orlKioally  in  the  iron  put  in  the  cupola  is  liable  to  be 
further  increased  by  part  of  the  sulphur  that  is  invariably  found  in  the  coke 
used.  It  is  seldom  that  a  coke  with  a  small  percentage  of  sulphur  is  found, 
whereas  coke  containing  i%  of  it  and  over  is  very  common.  With  such  a 
fuel  In  the  cupola,  if  no  special  precautions  are  resorted  to,  the  percentage 
of  sulphur  in  the  metal  will  in  most  cases  be  Increased." 

That  the  sulphur  contents  of  pig  iron  may  be  increased  by  the  sulphur 
contained  in  the  coke  used,  is  shown  by  some  experiments  in  the  cupola, 
reported  by  Mr.  Nau.    Seven  consecutive  heats  were  made. 

The  sulphur  content  of  the  coke  was  1^,  and  11.7j(  of  fuel  was  added  to  the 
charge. 

Before  melting,  the  silicon  ranged  from  0.990  to  0.880  in  the  seven  heats  : 
after  melting,  it  was  from  0.110  to  0.684,  the  loss  in  melting  being  from  .100 
to  .87&  The  sulphur  before  melting  was  from  .076  to  .000,  and  after  melting 
from  .183  to  .174,  a  gain  from  .044  to  .096. 

From  the  results  the  following  conclusions  were  drawn : 

1.  lu  all  the  charges,  without  exception,  sulphur  increased  in  the  pifl^  iH>n 
after  its  passage  through  the  cupola.  In  some  cases  this  increaae  more 
than  doubled  the  original  amount  of  sulphur  found  in  the  pig  iron. 

2.  The  increase  of  the  sulphur  contents  in  the  iron  follows  the  elimination 
of  a  greater  amount  of  silicon  from  that  same  iron.  A  larger  amount  of 
limestone  added  to  these  charges  would  have  produced  a  more  basic  cinder, 
and  undoubtedly  lees  sulplmr  would  have  been  incorporated  in  the  iron. 

8.  This  coke  contained  1%  of  sulphur,  and  if  all  its  sulphur  had  passed  into 
the  iron  there  would  have  been  an  average  increase  or  0.12  of  sulphur  for 
the  seven  charges,  while  the  real  increase  in  the  pig  iron  amounted  to  only 
O.OSl.  This  shows  that  two  thirds  of  the  sulphur  of  the  coke  was  taken  up 
by  the  iron  in  Its  passage  through  the  cupola. 

MANGANESE.— Manganese  is  a  nearly  white  metal,  having  about  the  same 
appearance  when  fractured  as  white  cast  iron.  Its  specific  gravity  is 
about  8,  while  that  of  white  cast  iron,  reasonably  free  from  Impurities,  is 
but  a  little  above  7.6.  As  produced  commercially,  it  is  combined  with  iron, 
and  with  small  percentages  of  silioon,  phosphorus,  and  sulphur. 

It  is  generally  produced  in  the  blast-furnace.  If  the  manganese  Is  under 
40^,  with  the  remainder  mostly  iron,  and  silicon  not  over  OMU^  the  alloy  is 
called  splegelelsen,  and  the  fracture  will  show  flat  reflecting  suifaoes^  frui^ 
which  it  takes  its  name. 

With  manganese  above  60)(,  the  iron  alloy  is  called  ferro-manganeee. 

As  manganese  increases  beyond  60%,  the  mass  cracks  in  cooling,  and  when 
it  approaches  9Bi%  the  mass  crumbles  or  falls  in  small  pieces. 

Manganese  combines  with  iron  in  almost  any  proportion,  but  If  an  Iron 
containing  manganese  is  remelted,  more  or  less  of  the  manganese  will  escape 
bv  volatilization,  and  by  oxidation  with  other  elements  present  in  the  iron. 
If  sulphur  be  present,  some  of  the  manganese  will  be  likely  to  unite  with  it 
and  escape,  thus  reducing  the  amount  of  botli  elements  in  the  casting. 

Cast  iron,  when  free  from  manganese,  cannot  hold  more  than  i.SO%  of  car- 
bon, and  8.80^  is  as  much  as  is  generally  present ;  but  as  manganese  increases, 
carbon  also  increases,  until  we  often  find  it  In  spifsgel  as  high  as  b%,  and  in 
ferro-manganese  as  high  as  fist.  This  effect  on  capacity  to  hold  carbon  ia 
peculiar  to  manganese. 

Manganese  renders  cast  iron  less  plastic  and  more  brittle. 

Manganese  increases  the  shrinkage  of  cast  iron.  An  increaae  of  1%  raised 
the  shrinkage  2Bi%.  Judging  from  some  test  records,  manganese  does  not 
influence  chill  at  ail;  but  other  tests  show  that  with  a  given  percentage  of 
silioon  the  carbon  may  be  a  little  more  inclined  to  remain  in  the  combined 
form,  and  therefore  the  chill  may  be  a  little  deeper.  Hence,  to  cause  the 
chill  to  be  the  same,  it  would  seem  that  the  percentage  of  silioon  should  be 
a  little  higher  with  manganese  than  without  it. 

An  increase  of  i%  of  manganese  increased  the  hardness  40jC.  If  a  hard 
chill  is  required,  manganese  gives  it  bv  adding  hardness  to  the  whole  casting. 

J.  B.  Nau  {Iron  Age,  March  20, 1804),  discussing  the  influence  of  manga* 
nese  on  cast  iron,  says: 

Manganese  favors  the  combination  between  carbon  and  iron.  Its  influ* 
ence,  when  present  in  sufficiently  large  quantities,  is  even  great  enough  not 
only  to  keep  the  carbon  which  would  be  naturally  found  In  pig  Iron  coii»* 


'  TESTS  OF  CAST  IBON.  869 

Miwd,  bnt  It  Incroaocfl  the  capacity  of  Iron  to  retaiD  lai^er  amounts  of  car- 
boo  and  to  retain  it  all  in  the  combined  state. 

Mangaaeae  iron  is  often  used  for  foundry  purposes  when  some  chill  and 
hardness  of  surface  Is  required  In  the  casting.  For  the  rolls  of  steel-rail 
mills  we  always  put  into  the  mixture  a  large  amount  of  manraniferous  iron, 
and  the  rolls  so  obtained  always  presented  the  desired  hardnero  of  surface 
and  in  general  a  mottled  structure  on  the  outside.  The  inside,  which  al- 
ways cooled  much  slower,  was  gray  iron.  One  of  the  standard  mixtures  that 
inTariably  gave  good  results  was  the  following: 

eOf  of  foundry  iron  with  t.9%  silicon  and  1.5jt  manganese; 
8!^  of  foundry  iron  with  i%  silicon  and  1.5]t  manganese; 
IbH  steel  (rail  ends)  with  about  O.SSjt  to  0.4(^  carbon. 

The  roll  resulting  from  this  mixture  contained  about  1%  of  silicon  and  1% 
of  manganese. 

Anotber  mixture,  which  diifered  but  little  from  the  preceding,  was  as 
follows: 

45%  toandry  iron  with  about  1.8^  silicon  and  l.fi^  manganese; 

W  foandry  iron  with  about  1%  silicon  and  1.6i  manganese; 

10^  white  or  mottted  iron  with  about  O.SjC  to  0.6j(  Si.  and  1.2)(  Mn. 

IH  Bessemer  steel-rail  ends  with  about  0.86)(  to  0.40)(  C.  and  O.djC  to  i%  Mn. 

The  piic  iron  used  in  the  preceding  mixtures  contained  also  invariably 
from  M^tolM  of  phosphorus,  so  that  the  rolls  obtained  therefrom  carried 
about  l.fljjC  to  1.4)(or  that  element.  The  last  mixture  used  produced  rolls 
coptolning  on  the  average  O.Bji  to  1}(  of  silicon  and  1%  of  manganese.  When- 
ever we  tried  to  make  those  rolls  from  a  mixture  containing  but  O.Sj(  to  0.9% 
manganese  our  rolls  were  invariably  of  inferior  quality,  grayer,  and  con- 
sequently softer.  Manganese  iron  cannot  be  used  inaiscriminately  for 
foundry  purposes.  When  greater  softness  Is  required  in  the  castings  man- 
faoese  has  to  be  avoided,  but  when  hardness  to  a  certain  extent  has  to  be 
obtained  manganese  iron  can  be  used  with  advantage. 
»decreaa * '  " 


lecreases  the  magnetism  of  the  iron.    This  characteristic  in- 

with  the  percentage  of  manganese  that  enters  into  the  composition 
of  the  iron.  The  Iron  loses  all  its  magnetism  when  manganese  reaches  fUi% 
of  its  composition.    This  peculiarity  has  been  made  use  of  by  French 


this  reason  manganese  iron  has  to  be  avoided  in  castings  of  dynamo  fields 
and  other  pieces  belonging  to  electric  machinery,  where  magnetic  conduc- 
tibai^  is  one  of  the  first  considerations. 

Irresvlmr  IMstrllmfloii  of  Sllieon  in  Pig  Iron.— J.  W. 
Tbomaa  (Ir<m  Age^  Nov.  18, 1891)  finds  In  analyzing  samples  taken  from  every 
other  bed  of  a  cast  of  pig  iron  that  the  silicon  varies  considerably,  the  iron 
eoming  first  from  the  furnace  having  generally  the  highest  percentage.  In 
one  series  of  tests  the  silicon  decreased  from  8.040  to  1.718  from  the  first  bed 
to  the  eleventh.  In  another  case  the  third  bed  had  1.860Si..  the  seventh  1.718, 
sod  the  elerventh  1.101.  He  also  finds  that  the  silicon  varies  in  each  pig.  be- 
ing higlier  at  the  point  than  at  the  butt.  Some  of  his  figures  are:  point  of 
piK8L888  Si..  buU  of  same  8.167;  point  of  pig  1.834,  butt  of  same  1.78f. 

Sonao  T^sta  of  Cast  Iron.  (O.  Lanza,  Tran9.  A.  S,  M.  B.,  x.,  187.>- 
The  chemical  analyses  were  as  follows: 

Qun  Iron,       Common  Iron,  • 

per  cent.  per  cent. 

Totalcarfoon 8.61  

Graphite S.80  

Sulphur 0.1S8  0.178 

Phosphorus 0.1S5  0.418 

Silicon 1.140  1.89 

The  test  specimens  were  88  Inches  long  and  square  in  section;  those  tested 
ivith  the  skm  on  being  very  nearly  one  inch  square,  and  those  tested  with 
the  sUn  removed  being  cast  nearly  one  and  one  quarter  Inches  square,  and 
afterwards  planed  down  to  one  inch  square. 

Tensile  Elastic  «,^l!l?? 

Strength.  Limit,  yS^ 

TJnplaned  common.  80,900  to  88,000  T.  S.  Av.  =  88,066  6,500  18,194,888 

Planed  oommon....  80,800  to 90,800    **     "      =80,580  6,888  11,948,058 

Unplaned  gun 87,000  to  88,775    "     *"     =38.176  11,000  16,180,800 

Raaadgim 99,000  to  81,000   '*     **      m  80,600  8^600  16.988,880 


370  IRON   AKB  STEEL. 

The  elastic  limit  is  not  clearly  defined  in  cast  Iron,  the  elongations  increas- 
infc  faster  than  the  increase  of  the  loads  from  the  begianliifc  of  the  test. 
The  modulus  of  elasticity  ia  therefore  variable,  decreasluf?  as  the  loads  in- 
crease.   For  example,  see  the  results  of  test  of  a  cast-iron  bar  on  p.  314. 

Tlie  Strength  of  C«st  Iron  depends  on  nianv  oiher  tliin;;s  besides 
its  chemical  composition.  Amonf!^  tliem  are  the  size  and  shape  of  the 
casting:,  the  temperature  at  which  the  metal  is  poured,  and  the  rapidity  of 
coolinff.  Internal  stresses  are  apt  to  be  induced  by  rapid  cooling,  and  slow 
cooling  tends  to  cause  segregation  of  the  chemical  constituents  and  op>ening 
of  the  grain  of  the  metal,  making  it  weak.  The  relation  of  these  variable 
conditions  to  the  strength  of  cast  iron  is  a  complex  one  and  as  yet  but  im- 
perfectly  understood.    (See  **  Cast-iron  Columns,"  p.  SJiO.) 

The  author  recommends  that  in  making  expe rlments  on  the  strength  of 
cast  iron,  bars  of  several  different  sizes,  such  as  V^,  1, 1%,  and  2  in.  square  (or 
round),  should  bo  taken,  and  the  results  compared.  Tests  of  bars  of  one 
size  only  do  not  furnish  a  satisfactory  criterion  of  the  quality  of  the  Iron  of 
which  they  are  made.    See  Trans.  A.  I.  M.  E.,  xxvi.,  10I7. 

CHEIHISTRT  OF  FOUNDRY  IRONS. 

(C.  A.  Meissner,  Columbia  College  Q'ly^  1690 ;  7ron  Age,  1890.) 

Silicon  is  a  very  important  element  in  foundry  irons.  Its  tendency  when 
not  above  '2y^  is  to  cause  the  carbon  to  separate  out  as  graphite,  giving  the 
casting  the  desired  benefits  of  graphitic  iron.  Between  8^9  and  SV^  silicon 
is  best  adapted  for  iron  carrying  a  fair  proportion  of  low  silicon  scrap  and 
close  iron,  for  ordinarily  no  mixture  should  run  below  1^  silicon  to  get 
good  castings. 

From  ^%  to  5%  silicon,  as  occurs  in  silvery  iron,  will  carry  heavy  amounts 
of  scrap.  Castings  are  liable  to  be  brittle,  however,  if  not  handled  carefully 
as  regards  proportion  of  scrap  used. 

From  1\^  to  2%  silicon  is  best  adapted  for  machine  work ;  will  give  strong 
clean  casUngs  if  not  much  scrap  is  ustnl  with  it. 

Below  1%  silicon  seems  suited  for  drills  and  castings  that  have  to  stand 
great  variations  in  temperature. 

Silicon  has  the  effect  of  making  castings  fluid,  strong,  and  open-grained  ; 
also  sound,  by  its  tendency  to  separate  the  graphite  from  the  totalcarbon. 
and  consequent  slight  expansion  of  tlie  iron  on  cooling,  causing  it  to  All  out 
thoroughly.  Phosphorus,  when  high,  has  a  tendency  to  make  iron  fluid, 
retain  its  heat  longer,  thereby  helping  to  All  out  all  small  spaces  in  castinir. 
It  makes  iron  brittle,  however,  when  above  ^%  in  castings.  It  is  excellent 
when  high  to  use  in  a  mixture  of  low-phosphorus  irons,  up  to  l\i%  giving 
good  results,  but,  as  said  before,  the  casting  should  be  bi*luw  ^%.  It  has  a 
strong  tendency  when  above  1%  in  pig  to  make  the  iron  less  graphitic,  pre- 
venting the  separation  of  graphite. 

Sulphur  in  open  iron  seldom  bothers  the  founder,  as  it  is  seldom  present 
to  any  extent.  The  conditions  causing  open  iron  in  the  furnace  cause  low 
sulphur.  A  little  manganese  is  an  excellent  antidote  against  sulphur  in  the 
furnace.  Irons  above  \%  manganese  seldom  have  any  sulphur  of  any  con. 
sequence. 

Uranhite  is  the  all-important  factor  in  foundry  irons :  unlesa  this  fs  present 
in  sumcient  amoimt  in  the  casting,  the  latter  will  be  liable  to  be  poor. 
Gsaphite  causes  iron  to  slightly  expand  on  cooling,  makes  it  soft,  tough  and 
fluio.    (The  statement  an  to  expansion  on  cooliner  is  denied  by  W.  J.  Keep.) 

Relation  of  the  AppemranLce  of  Frmctnre  to  tlie  Clieiulcal 
Composition.— S.  H.  Chauvenet  says  when  run  [from  the  blast-fur- 
nacej  the  lower  bed  is  almost  always  close  grain,  but  snows  practically  the 
same  analysis  as  the  large  grain  in  the  rest  of  the  cast.  If  the  iron  runs 
rapidly,  the  lower  l>ed  may  have  as  large  grain  as  any  in  the  cast.  If  the 
iron  runs  rapidly,  for,  say  six  betls  and  some  obstruction  in  the  tap-hole 
causes  the  seventh  bed  to  fill  up  slowly  and  sluggishly,  this  bed  nuky  he 
close-grain,  although  the  eighth  bed,  if  the  obstruction  is  removed  will  be 
open-grain.  Neither  the  granhiiic  carbon  nor  the  silicon  seems  to  have  any 
iuMuenceon  the  fracture  in  these  cases,  since  bj*  analysis  the  graphite  and 
siiicou  is  the  same  In  each.  Ttie  question  naturally  arises  whether  it  would 
not  be  better  to  be  guided  by  the  analysis  than  by  the  fracture.  The  frac- 
ture is  a  guide,  but  it  is  not  an  infallible  guide.  Should  not  the  open-  and 
the  close-grain  iron  of  the  same  cast  be  numbered  under  the  same  ^rade 
when  they  have  the  same  analysis  ? 
Mr.  Melssner  bad  many  analyses  nuide  for  the  comparison  of  fracturs 


CHEHISTBT  OF  FOUNDRY  IRONS. 


371 


with  analysis,  and  nnless  the  condition  of  furnace,  whether  the  iron  ran 
fast  or  alow,  and  from  what  part  of  pig  bed  the  sample  is  taken,  are  known, 
the  fracture  is  often  very  misleading.    Take  the  following  analyses : 


A. 

B. 

C. 

D. 

E. 

P. 

Silicon 

Sulphur 

(iraphiticcar. . 
Comb,  carbon . 

4.315 
0.008 
8.010 

4. 818 
0.008 
2.757 

4.270 
0.007 
2.680 

3.3S8 
0.088 
2.\M8 

3.8C9 
0.006 
8.0:0 

o.ioe 

8.861 
0.006 
8.100 
0.096 

A.  Very  dose-grain  iron,  dark  color,  by  fracture,  gray  forge. 

B.  Open-grain,  dark  color,  by  fracture.  No.  1. 

C.  Very  close-grain,  by  fracture,  gray  forge. 

D.  Bledium -grain,  by  fracture,  No.  2,  but  much  brighter  and  more  open 
than  A,  C,  or  F. 

E.  Very  large,  open-grain,  dark  color,  by  fracture,  No.  1. 

F.  Very  close-grain,  by  fracture,  gray  forge. 

By  comparing  analyses  A  and  B,  or  B  and  F,  it  appears  that  the  close- 
(rrain  iron  is  In  each  case  the  highest  in  graphitic  carbon.  Comparing  A 
and  E,  the  graphite  is  about  the  same,  but  the  close-grain  is  highest  in 
uiioon. 

Anmljmem  of  Fonndry  Irons.    (0.  A.  Meissner.) 
Scotch  Irons. 


Nome. 


Summerlee 

RglioUm 

Coltnesa 

C^rnbroe 

ifiengamock  .... 

(ilengamock  said 

10  carry  5i  scrap 


Grade. 


Silicon. 

Phos- 
phorus. 

2.70 

0.545 

2.47 

0.7ti0 

8.44 

1.000 

2.70 

0.810 

2.15 

0.G18 

n.m 

0.840 

1.70 

1.100 

8.03 

1.200 

4.00 

0.900 

Manga- 
nese. 


1.80 
2.51 
1.70 
2.90 
2.80 
1.70 
1.83 
2.85 

3.41 


Sul- 

Graph- 

Com. 

phur. 

it^. 

Carbon. 

0.01 

3.09 

0.35 

0.015 

0.015 

0.02 

2.00 

0.80 

0.0i5 

8.76 

0.21 

O.OiO 

3.75 

8.75 

0.008 

8. 50 

0.40 

0.010 

1.78 

0.90" 

American  Scotch  Irons. 

No. 
Grade. 

No. 
Sample 

Silicon. 

Phos- 
phorus. 

Manganese 

Sulphur. 

1 

6.00 
1.67 
2.40 
1.28 
8.50 
2.90 
8.41 
3.35 
S.OS 

0.430 
1.920 
1.000 
0.690 
0.613 
0.733 
1.000 
1.300 
0.503 

1.00 
1.90 
1.70 
1.40 
2.31 
1.40 
1.70 
1.50 
2.96 

1 

:; 

casting. 

8 

2 
2 

1 

4 

Sa 

hb 

casting. 

6a 

0.015 
0.012 

i 

1 
1 

r,b 

I>EscRiPTiON  OF  Saxplks.— No.  1.  Well  known  Ohio  Scotch  iron,  almost 
Mlrery,  but  carries  two-thirds  scrap  ;  made  from  part  black-band  ore.  Very 
*ucce«5fui  brand.    The  high  silicon  gives  it  its  scrap-carrying  capacity. 

No.  2.  Brier  Hill  Scotch  castings,  made  at  scale  works  ;  castings  demand- 
iag  more  fluidity  than  strength. 


S72 


IKON  AND  STEEL. 


No.  8.  Formerly  a  famous  Ohio  Scotch  brand,  not  now  in  the  market 
Made  mainly  from  black-band  ore. 

No.  4«  A  good  Ohio  Scotch,  very  soft  and  fluid;  made  from  black-band 
ore-mixture. 

N06.  6a  and  66.  Brier  Hill  Scotch  iron  and  casting;  made  for  stove  pur- 
poses; 850  lbs.  of  Iron  used  to  150  Ibe.  scrap  gave  very  soft  fluid  iron;  worked 
well. 

No.  6a.  Shows  comparison  between  Summerlee  (Scotch)  (6a)  and  Brier  Hill 
Scotch  (06).  Dnllings  came  from  a  Cleveland  foundry,  which  found  both 
irons  closely  alike  in  physical  and  worlcing  quality.  ' 

No.  7.  One  of  the  best  southern  brands,  verv  hard  to  compete  with,  owing 
to  its  general  qualities  and  great  regularity  of  grade  and  general  working. 

Machinb  Irons. 


Sample 
No. 

Silicon. 

Phos- 
phorus. 

Manga- 
nese. 

Sulphur. 

Graphite. 

Comb. 
Carbon. 

Goule 
No. 

8 

2.80 
1.80 
2.66 
8.68 
2.10 
1.87 
8.10 
2.12 
1.70 
1.46 
1.40 
8.86 
0.80 

0.402 
0.268 
0.770 
0.411 
0.415 
0.294 
0.124 
0.610 
0632 
0.470 
0.816 
0.4S6 
0.104 

0.61 

0.70 

1.20 

1.25 

0.60 

1.61 

trace 

0.80 

1.60 

1.25 

1.37 

0.25 

0.00 

0.015 
0.080 
0.020 
0.014 
0.050 
0.080 
0.021 

1 

9 

8 

10a 

2.51 
8.05 

2 

10b 

1 

11 

2 

IS 
13 

8.81 

0.78 

8 
2 

14 

16 
16a 

'oooi  ■ 

0.008 

"2" 

19b 

17 

1 

16 

0.016 

1 

Dkscriftion  or  Samples. ^No.  8.  A  famous  Southern  brand  noted  for  fine 
machine  castings. 

No.  9.  Also  a  Southern  brand,  a  very  good  machine  iron. 

Nos.  10a  and  106.  Formerly  one  of  the  best  known  Ohio  brands.  Does  not 
shrink;  is  very  fluid  and  strong.  Foundries  having  used  this  have  reported 
very  favorably  on  it. 

Ko.  11.  Iron  from  Brier  Hill  Co.,  made  to  Imitate  No.  8  ;  was  stronger 
than  No.  8;  did  not  pull  castings:  was  fluid  and  soft. 

No.  12.  CJopy  of  a  very  strong  English  machine  iron. 

No.  18.  A  Pennsylvania  iron,  very  tough  and  soft.  This  is  partially  Bease- 
mer  iron,  which  accounts  for  strength,  while  high  silicon  makes  it  soft. 

No.  14.  Castings  made  from  Brier  Hni  Co.*s  machine  brand  for  scale  works, 
Teiy  satisfactory,  strong,  soft  and  fluid. 

No.  15.  Castings  made  from  Brier  Hill  Co.^s  one  half  machine  brand,  one 
half  Scotch  brand,  for  scale  works,  castings  desired  to  be  of  fair  stren^^, 
but  very  fluid  and  soft. 

No.  16a.  Brier  Hill  machine  brand  made  to  compete  with  No.  8. 

No.  166.  Ctatings  (clothes-hooks)  from  same,  said  to  have  worked  badly, 
castings  being  white  and  Irregular.  Analjrsis  proved  that  some  other  iron 
too  high  in  manganese  had  been  used,  and  probabiv  not  weii  mixed. 

No.  17.  A  Pennsylvania  iron,  no  shrinkage,  excellent  machine  iron,  soft 
and  strong. 

No.  18.  A  very  good  quality  Northern  charcoal  iron. 

<< Standard    Grades')  of  ibe    Brier  HIU  Iron  and  Coal 
Company, 

Brter  Hill  ScotcJi  Iron.^Standard  Analyais^  Grade  Nba.  1  and  9. 

Silicon 8.00  to  8.00 

Phosphorus 0.60  to  0.75 

Manganese 8.00  to  8.60 

Used  successfully  for  scales,  mowing-machines,  agricultural  implements, 
novelty  hardware,  sounding-boards,  stoves,  and  heavy  work  requiring  no 
special  strength. 


CHEUI8TBY  OP  FOUNDET  IS0N8. 


873 


Brier  Bill  Silvery  Iron.—Standard  Analiftit,  Grade  No.  1. 

Stlioon 8.60to5.50 

Phosphorus 1.00  to  1.60 

Manganese  S.OOtoS.SS 

Used  successfully  for  hollow-ware,  car-wheels,  etc.,  stoves,  bumpers,  and 
siiDilar  work,  with  heavy  amounts  of  scrap  in  all  cases.  Should  be  mainly 
used  where  fluidity  and  no  great  strength  is  required,  especially  for  heavy 
work.  When  used  with  scrap  or  close  pig  low  in  phosphorus,  castings  of 
considerable  strength  and  great  fluidity  can  be  made 

Fctirly  Beavy  Machine  Iron,— Standard  AnalyMte,  Grade  No.  1. 

Silicon 1.75  to  8.60 

Phosphorus 0.60  to  0.00  ' 

Manganese 1.90  to  1.40 

The  best  Iron  for  madiinery,  wagon-boxes,  agricultural  implements, 
pump- works,  hardware  specialties,  lathes,  stoves,  etc.,  where  no  large 
amounts  of  scrap  are  to  be  carried,  and  where  strength,  combined  with 
neat  fluidity  and  softness,  are  desired.    Should  not  have  much  scrap  with 

Segrular  Machine  Iron.Standard  AntUyBitt  Grade  Noe.  1  and  8. 

Silicon 1.50to2.00 

Phosphorus 0.80toO.&0 

Manganese O.SOtol.OO 

Used  for  hardware,  lawn-mowers,  mower  and  reaper  works,  oil-well 
machinery,  drills,  fine  machinery,  stoves,  etc.  Excellent  for  all  small  flne 
castings  requiring  fair  fluidity,  softness,  and  mainly  strength.  Cannot  be 
frell  used  alone  for  large  castings,  but  gives  good  results  on  same  when  used 
with  above-mentioned  heavv  nuichine  grade:  also  when  used  with  the 
Scotch  in  right  proportion,  will  carry  but  little  scrap,  and  should  be  used 
alone  for  good  strong  castings. 

Jbr  Axles  and  Material*  Beguinng  Great  Strength^  Grade  No.  8. 

Silicon 1.60 

Phosphorus O.SOOandleas. 

Manganese 0.80 

This  gave  excellent  results. 

A  good  neutral  iron  for  guns,  etc.,  will  run  about  as  follows : 

Silicon 1.00 

Phoq>boru8 0.26 

Sulphur 0.80 

Manganese none. 

It  shoiutd  be  open  No.  1  iron. 

This  gives  a  very  tough,  eUstio  metal.  More  sulphur  would  make  tough 
bat  decrease  elasticity. 

For  flne  castings  demanding  elegance  of  design  but  no  strength,  phos- 
phorus to  8.00)(  is  good.    Can  also  stand  1  .BOf  to  2.00)(  manganese.    For  work 
of  a  hard,  abrasive  character  manganese  can  run  2.00j(  in  casting. 
Analyses  of  CasUnss. 


Sample 
No. 

Silicon. 

Phos- 
phorus. 

Manganese 

Sulphur. 

Graphite. 

Comb. 
Carbon. 

81 

8.60 
0.85 
1.68 
1.84 
8.20 
2.80 
2.80 
8.10 
8.80 
2.88 
4.60 
8.48 
2.68 
1.90 

1.400 
0.361 
0.827 
0.577 
0.748 
1.808 
0.416 
1.880 
0.87» 
0.408 
0.660 
1.480 
0.000 
0.060 

8.80 
0.98 
1.08 
1.04 
1.10 
1.16 
0.54 
1.14 
0.80 
1.10 
0.78 
0.90 
1.80 
1.20 

82 

0.080 
0.040 

84a 

8.10 

0.68 

845 
84e 

85a 

866 

85r 

asd 

85e 

86 

0.085 

STa 

9tb 

I 

L 


374  IBON  AKD  STEEL. 

No.  81.  Sewing-machine  casttnsr,  said  to  be  yery  fluid  and  good  casting. 
This  Is  an  odd  analysis.  I  should  say  it  would  have  been  too  bard  and  brit- 
tle, yet  no  complaint  was  made. 

No.  32.  Very  good  machine  casting,  strong,  soft,  no  shrinkage. 

No.  38.  Drlrtiiigs  from  an  annealer-bor  that  stood  the  heat  very  well. 

No.  84a.  Drillings  from  door-hinge,  very  strong  and  soft. 

No.  846.  DriUiugs  from  clothes-hooks,  tough  and  soft,  stood  severe  ham- 
mering. 

No.  34c.  Drillings  from  window-blind  hinge,  broke  off  suddenly  at  light 
strain.    Too  high  phosphorus. 

No.  35rt.  Castmg  for  heavy  ladle  support,  very  strong. 

Nos  856  and  85e.  Broke  after  short  usage.  Phosphorus  too  high.  Car- 
bumpers. 

No.  add.  Elbow  for  steam  heater,  very  tough  and  strong. 

No.  86.  Cog-wheels,  very  good,  shows  abBolutelv  no  shrinkage. 

No.  87.  Heater  top  network,  requiring  fluidity  but  no  strength. 

No.  87a.  Gray  part  of  above. 

No.  876.  White,  honeycombed  part  of  above.  Probably  bad  mixing  and 
got  chilled  suddenly. 

STBBNGXn    OF    CAST    IRON. 

Rankine  gives  the  following  figures: 

Various  qualities,  T.  S 13,400  to       99,000,  average       16.900 

Compress! ve  strength 82,000  to      145,000,       **  1 18,000 

Modulus  of  elasticity 14,000,000  to  28,900,000,       "        17,000.000 

speelllc  Grairlty  and  Strenertli.    (Major  Wade,  1856.) 

Third-class  guns:  Sp.  Gr.  7.0b7.  T.  S.  :)K),148.  Another  lot:  least  Bp.  Gr.  7.16& 
T.  S.  82,402. 

Second-class  guns:  8p.  Or.  7.154,  T.  8.  S4,767.  Another  lot :  mean  8p.  Gr. 
7.802,  T.  8.  27,2©. 

First  olass  guns:  Sp.  Or.  7.904,  T.  8.  28,805.  Another  lolK  greatest  Sp.  Gr. 
7.402,  T.  8.  81,027. 

Strenstli  of  Cimreoal  Pig  Iron. -Pig  iron  made  from  Salisbury 
ores,  in  furnaces  at  Wassaic  and  Millerton,  N.  Y.,  has  shown  over  40,000  lbs. 
T.  8.  per  square  inch,  one  sample  giving  42,281  lbs.  Muirkirk,  Md.,  iron 
tested  at  the  Washington  Navy  Yard  showed:  average  for  No.  2  Iron,  21,601 
lbs. ;  No.  8, 28,959  lbs. ;  No.  4, 41 ,820  lbs. ;  average  density  of  No.  4, 7.886  (J.  C. 
L  W.,  v.  p.  44.) 

Nos.  8  and  4  charcoal  pig  Iron  from  Chapinville,  Conn.,  showed  a  tensile 
strength  per  square  inch  of  from  84,761  lbs.  to  41.882  lbs.  Charcoal  pig  iron 
from  (Shelby,  Ala.  (tests  made  in  Auirust,  1891),  showed  a  strength  of 
84.800  lbs.  for  No.  8;  No.  4, 89,675  lbs.;  No.  5,  46,450  lbs.;  and  a  mtxture  of 
«qual  parts  of  Nos.  B,  8,  4.  and  5,  41.470  lbs.    {Bull,  I.  dt  S.  A.) 

vartailon  of  Ilenslty  and  Tenacltj  of  Gnn-f roiM«w.An  in- 
crease of  density  invariably  follows  the  rapid  cooling  of  caat  Iron,  and  as  a 
general  rule  the  tenacity  is  increased  by  the  same  means.  The  tenacity 
generally  increases  quite  uniformly  with  the  density,  until  the  latter  ascends 
to  some  given  point;  after  which  an  increased  density  is  accompanied  by  a 
diminished  tenacity. 

Tile  turning-point  of  density  at  which  the  best  qualities  of  gun-Iron  attain 
their  maximum  tenacity  appears  to  be  about  7.3().  At  this  point  of  denMty, 
or  near  it.  whether  in  proof-bars  or  gun-heads,  the  tenacity  Is  greatest. 

As  the  density  of  iron  is  increased  its  liouidity  when  melted  is  diminished. 
This  causes  it  to  congeal  quickly,  and  to  rorm  cavities  in  the  interior  of  the 
casting.    (Pamphlet  of  Builders'  Iron  Foundry,  1898.) 

8peclflcatlon«  for  Cast  Iron  for  tlie  "World's  Fair  Build* 
Ing^s,  1 8 94t«— Except  where  chilled  iron  is  specified,  all  castings  shall  be 
of  tough  gray  iron,  free  from  injurious  cold-shuts  or  blow^boles,  true  to 

Sittern,  and  of  a  workmanlike  finish.  Sample  pieces  1  in.  square,  cast  from 
e  same  heat  of  metal  in  sand  moulds,  shall  be  capable  of  sustaining  on  a 
Clear  span  of  4  feet  6  Inches  a  central  load  of  500  lbs.  when  tested  In  the 
rouim  oar. 

Speclflcattona  for  Tests  ofCast  Iron  In  1^"  B.  I««  Mortera. 
(Pamphlet  of  Builders  Iron  Foundry,  1893.)— C/iarcoa<  Oun  /ron.— The  tensile 
strength  of  the  metal  must  average  at  each  end  at  least  80,000  lbs.  per 
square  inch  :  no  specimen  to  be  over  37,000  lbs.  per  square  inch  ;  but  one 
specimen  from  each  end  may  be  as  low  as  as.OOO  lbs.  per  square  inch.    The 


MALLEABLE  CAST  IROK.  375 

loDfir  extension  specimens  will  not  be  considered  In  making  up  these  ATer- 
ages,  bui  inuHt  snow  a  good  eloneation  and  an  ultimate  strength,  for  each 
specimen,  of  not  less  than  34.000  lbs.  The  density  of  the  metal  must  be  such 
as  to  mdicate  that  the  metal  has  oeen  sufficiently  refined,  bub  not  carried  so 
hi?h  as  t  >  impair  the  other  qualities. 

SpeelilcmUoiiB  fbr  Oradlnie  Pig  Iron  for  Car  DTlieels  by 
Chill  Tests  made  at  tlie  Furnace.  (Penna.  R.  R.  Specifications, 
18Sii{.)— The  chili  cup  is  to  be  filled,  even  full,  at  about  the  middle  of  every 
cast  from  the  furnace.  The  test-piece  so  made  will  be  7^  inches  long,  Sy(^ 
inches  wide,  and  1^  Inches  thick,  and  is  to  be  broken  across  the  centre  when 
entirely  cold.  The  depth  of  chill  will  be  shown  on  the  bottom  of  the  test- 
piece,  and  Is  to  be  measured  by  the  clean  white  portion  to  the  point  where 
KTAT  specks  begin  to  show  in  the  white.  The  grades  are  to  be  by  eighths  of 
an  inch,  viz..  H,  )4,  %,  V^,  %,  %,  %,  etc.,  until  the  Iron  is  mottled  ;  the  lowest 
grade  being  ^  of  an  inch  in  depth  of  chili.  The  pigs  of  each  cast  are  to  be 
marked  with  the  depth  of  chill  shown  by  its  test-piece,  and  each  grade  is  to 
be  kept  by  ttseif  at  the  furnace  and  In  forwarding. 

IHlJrtare  of  Cast  Iron  wltli  Steel.— Car  wheels  are  sometimes 
made  from  a  mixture  of  charcoal  iron,  anthracite  iron,  and  Bessemer 
steel.  The  following  shows  the  tensile  strength  of  a  number  of  tests  of 
wheel  mixtures,  the  average  tensile  strength  of  the  charcoal  Iron  used  being 
«2,0001b8.: 

lbs.  per  sq.  in. 

Charcoal  Iroti  with  2^jt  steel s«.467 

**    3^J<8teel 26,78S 

"  "       "   CMjt  steel  and  6^j(  anthracite 24,400 

M  .4       *»   ;^ijj  ^jp^l  ^„jj  ;^jg  anthracite 88,150 

••  "       "   2^6  steel,  2^j(  wrot  iron,  and  C^jt  anth...  25,560 

•*  ••       *•  6    J<  steel,  b%  wro*t  iron,  and  iO%  anth 26.600 

(Jour.  C.  J.  TT.,  iii.  p.  184.) 

Cast  Iron  Partially  Bcssemerlzed*— Oar  wheels  made  of  par- 
tially Bestsemerized  iron  (blown  in  a  Bessemer  converter  for  8U  minutes), 
chilled  in  a  chill  test  mould  over  an  inch  deen.  Just  as  a  test  of  cold  blast 
charcoal  Iron  for  car  wheels  would  chill.  Oar  wheels  made  of  this  blown 
iron  have  run  250,000  miles.    (Jour.C.  I.  W.,  vl.  p.  77.) 

Bad  Cast  Iron.—On  October  15, 1891,  the  cast-iron  fly-wheel  of  a  large 
pair  of  Corliss  engines  belonging  to  the  Amoskeag  Mfg.  Co.,  of  Manchester, 
N.  H.,  exploded  from  centrifugal  force.  The  fly-wheel  was  80  feet  diam- 
eter and  110  Inches  face,  with  one  set  of  12  arms,  and  weif^hed  116,000  lbs. 
After  the  accident,  the  rim  castings,  as  well  as  the  ends  of  the  arms,  were 
found  to  be  full  of  flaws,  caused  chiefly  by  the  drawing  and  shrinking  of  the 
metal.  Specimens  of  the  metal  were  tested  for  tensile  streDetli,  and  varied 
from  1S,000  Ibe.  per  square  inch  in  sound  pieces  to  1000  lbs.  in  spongy  ones. 
None  of  these  flaws  showed  on  the  surface,  and  a  rigid  examination  of  the 
parts  before  they  were  erected  failed  to  give  any  cause  to  suspect  their  true 
nature.  Experiments  were  carried  on  for  some  time  after  tne  accident  In 
Che  Amoskeag  Company's  foundry  in  attempting  to  duplicate  the  flaw8«  but 
with  no  success  in  approaching  the  badness  of  these  castings. 

MAIiliKABIiB  CAST  IRON. 

Halleablelzed  cast  iron,  or  malleable  Iron  castings,  are  castings  made 
of  ordinary  cast  iron  which  have  been  subjected  to  a  process  of  deearboni- 
zation,  which  results  in  the  production  of  a  crude  wrought  iron.  Handles, 
latches,  and  other  similar  articles,  cheap  harness  moimtlngs,  plowshares. 
Iron  bADdles  for  tools,  wheels,  and  pinions,  and  many  small  parts  of  ma- 
chinery, are  made  of  malleable  cast  iron.  For  such  pieces  charcoal  cast  iron 
of  the  best  qiiality  (or  other  iron  of  similar  chemical  composition),  should 
be  selected.  Coke  irons  low  In  silicon  and  sulphur  have  been  used  in  place 
of  charcoal  irons.  The  castings  are  made  in  the  usual  way,  and  are  then 
imbedded  in  oxide  of  ircn,  in  the  form,  usually,  of  hematite  ore,  or  in  per- 
oxide of  manganese,  and  exposed  to  a  full  i-ed-heat  for  a  sufflcietit  length  of 
time,  to  insure  the  nearly  complete  removal  of  the  carbon.  Tliisdecarboniza- 
tion  is  conducted  In  cast-iron  Ijoxes,  in  which  the  articles,  if  Rmall,  are 
packed  In  alternate  layers  with  the  decarl>onlzing  material.  Tiie  largest 
pieces  require  the  longest  time.  The  fire  is  quickly  raised  to  the  maximum 
temperature,  but  at  the  close  of  the  process  the  ftnnace  is  cooled  verv 
slowly.  The  operation  requires  from  three  to  five  days  with  ordinary  small 
castings,  and  may  take  two  weeks  for  large  pieces. 


876 


lEOK  AKD  STEBL.    ^ 


Bales  A>r  Use  of  Malleable  CastingSf  by  Oommlttee  of  Uasier 
Garbuilden'  Assn,  1890. 

1.  Never  run  abruptly  from  a  heavy  to  a  light  section. 

2.  Ab  the  strength  of  malleable  cast  iron  lies  in  the  skin,  expose  as  much 
surface  as  possible.  A  star-shaped  section  is  the  strongest  possible  from 
which  a  casting  can  be  made.  For  brackets  use  a  number  of  thin  ribs  inatead 
of  one  thick  one. 

8.  Avoid  aU  round  sections;  practice  haa  demonstrated  this  to  be  the 
weakest  form.  Avoid  sharp  angles. 
4.  Shrinkage  generally  in  castings  will  be  8/16  in.  per  foot 
Strenffth  of  Malleable  Cant  Iron^—Experiments  on  the  strength 
of  malleable  cast  iron,  made  in  1801  by  a  committee  of  the  Master  Car* 
builders'  Association.  The  strength  of  this  metal  varies  with  the  thickness, 
as  the  following  results  on  specimens  from  ^  in.  to  1%  in.  In  thickness  show: 


Dimensions. 

Tensile  Strength. 

Elongation. 

Elastic  Limit. 

in.          in. 

lb.^r^.ln. 

percent  In 4  in. 

'^•je®''-59-  ^• 

1.52  by    .26 
1.52  '^     .89 

21,100 

88,700 

15,200 

1.58  "      .5 

82,800 

17,000 

1.68  "      .M 

82,100 

19,400 

8.      "      .78 

25,100 

¥\ 

15,400 

1.54  "      .88 

88,600 

i-i 

10.800 

1.06  "    1.02 

80,600 

17,600 

1.88  "    1.8 

27,400 

1.52"    1.54 

28,200 

iH 

The  low  ductility  of  the  metal  Is  worthy  of  notice.  The  committee  gives 
the  following  table  of  the  comparative  tensile  resistance  and  ductility  of 
malleable  cast  iron,  as  compared  with  other  materials: 


Cast  iron 

Malleable  cast  iron, 

Wrought  Iron 

Steel  castings 


Ultimate 

Strength, 

lb.  per  sq.  in 


Comparative 

Strength ; 

Cast  Iron 

=  1. 


20,000 
82,000 
60,000 
60,000 


1 

1.6 
2.5 
8 


Elongation 
Percent 
in  4  in. 


0.86 

2.00 

20.00 

10.00 


Comparative 

Ductiyty; 

Malleable 

Cast  Iron 

=  1. 


0.17 

1 

10 
5 


Another  series  of  tests,  reported  to  the  Association  in  1802,  gave  the 
following: 

Thick, 
ness. 

Width. 

Area. 

Elastic 
Limit. 

UlUmate 
Strength. 

^IS!" 

in. 

in. 

sq.  in. 

'"■^'s^- 

n.^r^g..n. 

percent. 

.271 

2.81 

.7615 

1.5 

.298 

2.78 

.8145 

88.660 

88,100 

.0 

.89 

2.82 

1.098 

20,595 

82,080 

1.5 

.41 

8.79 

1.144 

20,2S0 

28,860 

1.(1 

.539 

2.76 

1.46 

19.520 

27,875 

1.1 

.661 

2.81 

1.857 

18.840 

25,700 

.7 

.8 

2.76 

2.208 

18.890 

85,180 

1.1 

1.025 

2.82 

2.890 

18.220 

28,780 

1.5 

1.117 

8.81 

8.188 

17,060 

85,510 

l.« 

1.021 

8.82 

8.879 

18.410 

86,060 

1^ 

WROUGHT  IROlSr. 


377 


WHOVGHT  IRON. 

Inflaenee  of  Chemieal  Oomposltioii  on  the  Properties 
or  IV'roncht  Iron.  (Beardslee  on  Wrought  Iron  and  Ohaln  Cables. 
Abridgement  by  W.  Kent.  Wiley  &,  Sons,  1879.)— A  series  of  itOOO  tests  of 
specimens  from  14  brands  of  wrought  iron,  most  of  tbem  of  liljrh  repute, 
was  made  in  1877  by  Capt.  L.  A.  Beai-dslee,  n.S.NM  of  the  United  States 
Testing  Board.  Forty-two  chemical  analyses  were  made  of  these  Irons, 
with  a  view  to  determine  what  influence  tlie  chemical  composition  had 
upon  the  strenfcth,  ductility,  and  welding  ^wer.  From  the  report  of  these 
tefcts  by  A.  L.  Holley  the  foUowing  figures  ^re  taken : 


Average 

Tensile 

Streugth. 

Chemical  Composition. 

Brand. 

8. 

p. 

8i. 

C. 

Mn. 

Mag. 

L 

P 
B 
J 
O 
C 

06,506 

U,883 
53,764 

51,754 

51,1S4 
50,765 

\ 
\ 

trace 

0.009 
0.001 

o.ooe 

O.OOS 
0.005 
0.004 
0.005 

o.oor 

j  0.065 
10.064 
0.260 
0.005 
0.S81 
0.140 
O.iiOl 
0.067 
0.078 
0.109 

0.080 
0.105 
0.183 
0.028 
0.156 
0.189 
0.821 
0.065 
0.078 
0.154 

0.318 
0.518 
0.088 
0.066 
0.015 
0.0*7 
0.051 
0.045 
0.042 
0.048 

0.006 

o.oao 

0.088 
0.000 

o.oir 

trace 
0.058 
0.007 
0.005 
0.081 

0.198 
0.468 
0.848 
1.814 

"o,m 

1.784 
1.168 
0.974 

Where  two  analyses  are  given  they  are  the  extremes  of  two  or  more  ana- 
lyses of  the  brand.  Where  one  is  given  it  is  the  only  analysis.  Brand  L 
should  be  classed  as  a  puddled  steel. 


Order  or  Qualitiks  Qradbd  from  No.  1  to  No.  10. 


Brand. 

L 
P 
B 
J 
O 
O 


8S."nX        ^T^       Elongation.     Welding  Power. 

1  18  10  most  imperfect. 

6  6  8  badly. 

18  16  15  best. 

16  19  18  rather  badly. 

18  1  4  very  good. 

19  18  16                


The  reduction  of  area  varied  from  54.2  to  8S.9  per  cent,  and  the  elonga- 
tion from  29.9  to  8.8  per  cent. 

Brand  O,  the  purest  iron  of  the  series,  ranked  No.  16  in  tensile  strength, 
bat  was  one  of  the  most  ducrile;  brand  B,  (quite  impure,  was  below  the 
average  both  in  strength  and  ductility,  but  was  the  best  in  welding  power; 
P.  also  quite  impure,  was  one  of  the  best  in  every  respect  except  welding, 
while  L,  the  highest  In  strength,  was  not  the  most  pure,  it  had  the  least 
ductility,  and  its  welding  power  was  most  imperfect.  The  evidence  of  the 
Influence  of  chemical  composition  upon  quality,  therefore,  is  quite  contra- 
dictory and  confusing.  The  irons  dlliering  remarkably  in  their  mechanical 
properties,  it  was  found  that  a  much  more  marked  influence  upon  their 
quaJities  waa  caused  by  different  treatment  in  rolling  than  by  differences  in 
composition. 

In  regard  to  slag  Mr.  Holley  says :  "  It  appears  that  the  smallest  and 
most  worked  Iron  often  has  the  most  slag.  It  Is  hence  reasonable  to  con- 
clude that  an  iron  may  be  dirty  and  yet  thoroughly  condensed.** 

In  his  summary  of  **  What  is  learned  from  chemical  analysis,**  he  says : 
**  So  far.  It  may  appear  that  little  of  use  to  the  makers  or  users  of  wrought 
Iron  has  been  learned.  .  .  .  The  character  of  steel  can  be  surely  pred- 
icated on  the  analyses  of  the  materials;  that  of  wrought  iron  is  altered  by 
subtle  and  unobserved  causes.** 

Inflaonoe  of  Bedvetlon  In  BolUniT  ft^m  PUe  to  Bar  on 
Cbe  Strenctli  of  UTronglit  Iron.— The  teusile  strength  of  the  irons 
owd  in  Buara8lee*8  tests  ranged  from  46,000  to  02,700  lbs.  per  sq.  in.,  brand 
L.  which  was  really  a  steel,  not  being  considered.  Some  specimens  of  L 
rive  figures  as  high  as  TO.QOO  lbs.    The  amount  of  reduction  of  sectionill 


378 


IBOK   AKD  STEEL. 


area  In  roUiog  the  bars  has  a  notable  Influence  on  the  strength  and  e1asU« 
limit;  the  greater  the  reduction  from  pile  lo  bar  the  higher  the  strengih. 
The  following  ai-e  a  few  figures  from  tests  of  one  of  the  brands: 


Size  of  bar,  in.  diam. 
Area  of  pile,  ra.  in.: 
Bar  per  cent  of  pile: 
Tetisile  strength,  lb.: 
Elastic  limit,  lb.: 


4 

3 

2 

1 

H 

80 

80 

n 

S5 

? 

15.7 

8.83 

4.3G 

8.14 

2.17 

46.323 

47,781 

48,:»0 

61,128 

6d,875 

23,480 

|6,400 

81,898 

86,467 

89,1S8 

1.6 
60,&85 


Sped  flea tlona  for  UTromrbt  Iron  (F.  H.  Lewis,  Engineers'  Club 
of  Pliiladelphia,  1891).—!.  All  wrought  iron  must  be  tough,  ductile,  fibrous, 
and  of  u o if orm  quality  for  each  class,  straight,  smooth,  free  from  cinder- 
poclcets,  flaws,  buckles,  blisters,  and  injurious  cracks  along  the  edges,  and 
must  have  a  workmanlike  finish.  No  epeciflc  process  or  proviaion  of 
manufacture  will  be  demanded,  provided  the  material  fulfils  the  require- 
ments of  these  specifications. 

2.  The  tensile  strength,  limit  of  elasticity,  and  ductilitv  shall  be  deter- 
mined from  a  btaiidard  teat-piece  not  less  ihan  V4  ^"ch  thick,  cut  from  the 
f  iill-Hized  bar,  and  planed  or  turned  parallel.  The  area  of  cross-section  shall 
not  be  less  than  ^square  inch.  The  elongation  shall  be  measured  after 
bi*enking  on  an  original  length  of  8  inches. 

S.  Tlie  tests  shall  show  not  leas  than  the  following  results: 


For  bar  iron  in  tension 

For  shape  iron 

For  plates  under  36  in.  wide. 
For  plates  over  86  in.  wide . . 


Ultimate 

Strenifth, 

lbs.  per  sq. 

inch. 


50,000 
48,(X)0 
48.0»K) 
46,000 


Limit  of 

Elasticity, 

lbs.  per  sq. 

inch. 


26,000 
26,000 
36,000 
25.000 


Elongation  in 
8  inches, 
per  cent. 


18 
15 
12 
10 


4.  When  full-sized  tension  niemberK  are  tested  to  prove  the  strength  of 
their  connections,  a  reduction  in  their  ultimate  strength  of  (500  X  width  of 
bar)  pounds  per  square  inch  will  be  allowed. 

5.  All  iron  shall  bend,  cold,  180  degrees  around  a  curve  whose  diameter 
is  twice  the  thickness  of  piece  for  bar  iron,  and  three  times  the  thickness 
for  plates  and  shapes. 

6.  Iron  which  is  to  be  worked  hot  in  the  manufacture  must  be  capable 
of  bending  sharply  to  a  light  angle  at  a  working  heat  without  sign  of 
fracture. 

7.  Specimens  of  tensile  iron  upon  being  nicked  on  one  side  and  bent  shall 
show  a  fracture  nearly  all  flbrous. 

8.  All  rivet  iron  must  be  tough  and  soft,  and  be  capable  of  bending  cold 
until  the  sides  are  in  close  contact  without  sign  of  fracture  on  the  convex 
side  of  the  curve. 

Pennayl  vanla  Railroad  SpeclflcaUonn  for  Merebant  Bar 
Iron  or  steel.— Miscellaneous  merchant  bar  iron  or  steel  for  which  no 
special  speciilcaiions  defining  shapes  and  use.s  are  issued,  should  have  a 
tensile  strength  of  50,000  to  55,000  lbs.  per  square  inch  and  an  elongation  of 
20%  in  a  section  originally  2  inches  long. 

No  iron  or  steel  will  be  accepted  under  Uils  specification  if  tensile  strength 
falls  below  48,000  lbs.  or  goes  above  60.000  lbs.  per  square  inch,  nor  if  eion- 
gation  is  less  than  V)%  in  2  inches,  nor  if  it  shows  a  granular  fracture  cover- 
ing more  than  50;(  of  the  fractured  surface,  nor  if  it  shows  any  difllculty  in 
welding. 

In  preparing  test-pieces  from  round  or  rectangular  bars,  they  will  be 
turned  or  shaped  so  that  the  tested  sections  may  be  the  central  portion  of 
the  bar,  in  all  sizes  un  to  1%  inches  in  any  diametrical  or  side  measurement. 
In  larger  sizes  test-pieces  will  be  mode  to  fall  about  half-way  from  centre  to 
circumference. 

Bars  of  iron  J^  in.  thick  or  less,  or  tortured  forms  of  iron,  such  as  angle,  tee 
or  channel  burs,  will  be  accepted  if  tensile  strength  is  above  45.000  lbs.  and 
elongation  above  12j(;  but  the  testing  of  such  sizes  and  sections  is  optional. 


FORMULA   FOB  UNIT  STRAINS  FOB  IBON  AND  STEEL.   379 


Speclfleatlons  for  'Wroai^t  Iron  for  ibe  'World'v  Fair 
Halldlne*.  {l£ug*g  JVetr«,  Marcii  26,  1»9S.)— All  Iron  to  bo  used  In  tbo 
leosiie  iiieiubers  of  open  trusses,  laterals,  pins  and  bolts,  except  plate  iron 
over  8  inches  wide,  and  shaped  iron,  must  show  by  the  standam  test-pieces 
a  tensile  strength  in  lbs.  per  square  inch  of  : 

SQQQQ  ^       7,000  X  area  of  original  bar  in  sq.  in. 

circumference  of  original  bar  in  inches  * 
with  an  elastic  limit  not  less  than  half  the  strength  given  by  tliis  formula^ 
and  an  elongation  of  20^  in  8  in. 

Plate  iron  24  inches  wide  and  under,  and  more  than  8  inches  wide,  must 
show  by  the  standard  test-pieces  a  tensile  strength  of  48,000  lbs.  per  sq.  In. 
with  an  elastic  limit  not  less  than  26,000  lbs.  per  square  inch,  and  an  elon- 
gation of  not  less  than  V^.  All  plates  over  24  inches  in  width  must  have  a 
tensile  strength  not  less  than  46,000  lbs.  with  an  elastic  limit  not  less  than 
a*,(MO  lbs.  per  square  inch.  Flates  from  24  luclius  to  36  inches  in  width  must 
bcve  an  elongation  of  not  less  than  10%;  those  from  36  inches  to  48  inches  in 
width,  89(;  over  48  inches  in  width.  6%, 

All  shaped  iron,  flanges  of  beams  and  channels,  and  other  iron  not  herein- 
before specified,  must  show  by  the  standard  test-pieces  a  tensile  strength  Jo 
lbs.  per  square  inch  of : 

fiO  OOP        ^'^^  ^  *''^*  ^^  original  bar 
'      "  circumference  of  original  bar' 
with  an  elastic  limit  of  not  less  than  half  the  strength  given  by  this  formula, 
and  an  elongation  of  16%  for  bars  %  Inch  and  less  in  thickness,  and  of  ]2%  for 
bars  of  greater  thickness.    For  webs  of  beams  and  channels,  speclflcaliona 
for  plates  will  apply. 

All  rivet  iron  must  be  tough  and  soft,  and  pieces  of  the  full  diameter  of 
the  rivet  must  be  capable  of  oending  cold,  until  (he  sides  are  in  close  contact, 
without  sign  of  fracture  on  the  convex  side  of  the  curve. 

8tay*l^oU  Iroii«~Hr.  Vauclain,  of  the  Baldwin  Locomotive  Works, 
at  a  meeting  of  the  American  Bailway  Master  Mechanics*  Association,  in 
1882,  says:  Many  advocate  the  softest  iron  in  the  market  as  the  best  for 
stay-bolts.  He  believed  in  an  iron  as  hard  as  was  consistent  with  heading 
the  holt  nicely.  The  higher  the  tensile  strength  of  the  iron,  the  more  vibra- 
tions ft  will  stand,  for  it  is  not  so  easily  strained  beyond  the  yield-point. 
The  Baldwin  specifications  for  stay-bolt  iron  call  for  a  tensile  strength  of 
fiO,000  to  52,000  lbs.  per  square  Inch,  the  upper  figure  being  preferred,  and 
the  lower  being  insisted  upon  as  the  minimum. 

FOBBIIJI^iE  FOB  UNIT  STRAINS  FOB  IBON  AND 

STBBIi  IN  STBUCTURBS. 

(F.  H.  Lewis,  Engineers'  Club  of  Philadelpliia,  1891.) 

The  following  formulis  for  unit  strains  per  square  inch  of  net  sectional 
area  shall  be  used  in  determining  the  allowable  working  stress  In  each  mem- 
ber of  the  structure.  (For  definitions  of  soft  and  medium  steel  see  Specifi- 
cations for  Steel.) 

Tension  IVIembem. 


Wrought  Iron. 


Soft  Steel. 


Medium  Steel. 


Floor-beam  hanj 
suspenders, 
bars 

Connter-tles.. 

Suspenders,  hangers 
and  counters,  riveted 
members,  net  sec- 
tion  

BoHd  rolled  beams.. 

Riveted  truss  members 
and  tension  flanges 
of  girders,  net  sec- 
tion   


Forged  ^yebars 

Lateral   or   cross  scc« 
tion  rods 


Will  not  be  used 
6000 


6000 
8000 


7000(l  +  ~~) 
V     '  mar./ 

Will  not  be  used 
15,000 


Will  not  be  used 


5S00 
8000 


&%  greater  than 
iron 


Will  not  be  used 
16.000 


7000 
7000 


7000 
Will  not  be  used 


900oCl  +  -^i5:) 

V        inaxy 

/        jnluX 

V.        niax.>' 

For    eyebarsX 

only,  17.000  / 


380 


IRON  AND  STEEL. 


Sliemiiiiic, 


On  pins  and  shop  rivets 

On  field  rivets 

In  webs  of  girders.. 


Wrought  Iron.        Soft  SteeL 


6000 

4800 

Will  not  be  used 


6600 
6000 
5000 


Medium  SteeL 


7800 

Will  not  be  used 

6000 


Bearings 


Wrought  Iron. 


Soft  Steel. 


Medium  SteeL 


On  projected  semi- 
intrados  of  main-plu 
holes 

On  projected  seml-ln- 
trades  of  riyec-holes* 

On  lateral  pins 

Of  bed-plates  on  ma- 
soiiry .. 


18,000 

12,000 
15,000 


18,800 

18,900 
16,600 


14,600 

14.500 
18,000 


2501b8.per8q.  in. 


*  Excepting  that  in  pin-connected  members  taking  alternate  stresses,  the 
bearing  stress  must  not  exceed  9000  lbs.  for  iron  or  steel. 
Bending, 
On  extreme  fibres  of  pins  when  centres  of  bearings  are  considered  as 
points  of  application  of  strains: 

Wrought  Iron,  15,000.       Soft  Steel,  16,000.       Medium  Steel,  17,000. 
Compre— Ion  Membeni,  


Wrought  Iron. 


Soft  SteeL 


Medium 
Steel. 


Chord  sections : 

Flat  ends 

One  flat  and  one  pin  end . . 

Chords  with  pin  ends  and 
all  end-posts 

All  trestle-posts 

Intermediate  posts 

Lateral  struts,  and  com- 
pression in  collision 
struts,  stiff  suspenders 
and  stiff  chords 


V  '  max./         r 

7000(1+™*"-)- 85-' 

V  '  max./         r 


7500-40- 


10,600  -  50  - 


109^ 

greater 

than 

iron 


90i 

greater 

than 

iron 


In  which  formulas  I  =  length  of  compression  member  in  inches,  and  r  ^ 
least  radius  of  gvration  of  member  in  inches.  No  compression  member 
shall  have  a  length  exceeding  45  times  its  least  width,  and  no  post  should  be 
used  in  which  l-t-r  exceeds  185. 


Membeni  Subject  to  Alternate  Tension  and  Compre— lon» 

Wrought  Iron. 

Soft  Steel. 

Medium 
SteeL 

For  compression  only. . . 
For  the  greatest  stress. . 

Use  the  formulss  above 

Wl  -     "*^-  ^^^"^    ) 
\       2  max.  greater/ 

8jt  greater 
than  iron 

mi  greater 
than  iron 

Use  the  formula  giving  the  greatest  area  of  section. 
The  compression  flanges  of  beams  and  plate  girders  shsU  have  the  same 
cross-section  as  the  tension  flanges. 


FOBMULiE  FOB  TJKIT  STEAINS  FOR  I&ON  AND  BTBBL.  381 

W.  H.  Borr,  dteeinsing  the  formuln  proposed  by  Mr.  Lewis,  says:  **  Taking 
the  remilts  of  experiments  as  a  whole,  I  am  constrained  to  believe  that  they 
indicate  at  least  15jt  increase  of  resistance  for  sof t-steel  columns  oyer  those 
of  wrought  iron,  with  from  ilO%  to  2Bi%  tor  medium  steel,  rather  than  lOfl  and 
m  respectively. 

**Tbe  high  capacity  of  soft  steel  for  enduring  torture  fits  it  eminentlv  for 
alteniate  and  combined  stresses,  and  for  that  reason  I  would  give  it  W 
inoreaae  over  iron,  with  about  22%  for  medium  steel. 

"Shfearing  tests  on  steel  seem  to  show  that  16%  and  fBi%  increases,  for  the 
two  grades  respectively,  are  amply  Justifled. 

**  Ishould  not  hesitate  to  assign  15)(  and  22%  increases  over  values  for  iron 
for  bearing  and  bending  of  soft  and  medium  steel  as  being  within  the  safe 
Umita  of  experience.  Provision  should  also  be  made  for  increasing  pin- 
shearing,  bending  and  bearing  stressee  for  increasing  ratios  of  fixed  to  mov- 
ing loads.'* 

HaadBtam  Permiwrtble  StrenMs  In  Mraetural  IKiitetials 
used,  lo  Iliilldliiffs.    nsuilding  Ordinances  of  the  City  of  Chicago,  18B8.) 


Cast  iron,  crushing  stress:  For  plates,  15,000  lbs.  per  square  Inch ;  for  lintels, 
brackets,  or  corbels,  compression  18,&00  lbs.  per  square  inch,  and  tension 
80QO  lbs.  per  square  inch.   For  girders,  beams,  corbels,  brackets,  and  trusses, 


16.000  lbs.  per  square  Inch  for  steel  and  12,000  lbs.  for  iron. 
For  plate  girders : 

— .  maximum  bending  moment  in  ft.-lbe. 

jTiange  area  -  ^^ 

D  =  distance  between  centre  of  gravity  of  flanges  in  feet. 

^  _  1 1S,800  for  steel. 

^  -  1 10,000  for  Iron. 

xB  %.    ^        maximum  shear     _     J  10,000  for  steel, 
Web  area  =  ^ .   C  =  \  6,000  for  iron. 

For  rivets  In  single  shear  per  square  Inch  of  rivet  area : 

Steel.  Iron. 

If  shop-driven 90001bs.        75001bs. 

If  fleld-driven 7500  '•  MOO  ** 

For  timber  girders :  ^ 

b  =  breadth  of  beam  in  inches, 
d  =  depth  of  beam  in  inches. 
-     c&d*  1=  length  of  beam  in  feet. 

*  =  ~r '  i  100  for  long-leaf  yellow  pine, 

c=s  <  120  for  oak, 

( 100  for  white  or  Norway  pine. 
Pvopoittonlnir  of  Materials  In  the  Memplils  Bridge  (Geo. 
8.  If  orison,  Trant,  A.  8,  C.  E.,  1886).— The  entire  superstructure  of  the  Mem- 
phis bridge  is  of  steel  and  It  was  sll  worked  as  steel,  the  rivet-holes  being 
drilled  in  all  principal  members  and  punched  and  reamed  in  the  lighter 
members. 


The  tension  members  were  proportioned  on  the  basis  of  allowing  the  dead 
toad  to  produce  a  strain  of  SO,OOU  lbs.  per  square  inch,  and  the  live  load  a 
strain  of  10,000  lbs.  per  square  inch.    In  the  case  of  the  central  span,  where 


the  dead  load  was  twice  the  live  load,  this  corresponded  to  15,000  lbs.  total 
■train  per  square  inch,  this  being  the  greatest  tensile  strain. 

The  coroprsssion  members  were  proportioned  on  a  somewhat  arbitrary 
baste.  No  distinction  was  made  between  live  and  dead  loads.  A  maximum 
■train  of  14,000  lbs.  per  square  inch  was  allowed  on  the  chords  and  other 
Isrge  oomprseslon  members  where  the  length  did  not  exceed  16  times  the 
lewt  transverse  dimension,  this  strain  being  reduced  7S0  lbs.  for  each  addi- 
tional unit  of  length.  In  long  compression  members  the  maximum  length 
was  limited  to  80  times  the  least  transverse  dimension,  and  the  strains 
limited  to  6,000  lbs.  per  square  inch,  this  amount  being  increased  by  900  lbs. 
for  each  unit  by  which  the  length  Is  decreased. 

Wherever  ravertals  of  strains  occur  the  member  was  proportioned  to  re- 
list the  sum  of  compression  and  tension  on  whichever  basis  (tension  or 
compression)  there  would  be  the  greatest  strain  per  square  inch ;  and,  in 
■ddltlon,  the  net  section  was  proportioned  to  resist  the  maximum  tension, 
and  the  gross  section  to  resist  the  maximum  compression. 

TTie  floor  beams  and  girders  were  calculated  on  the  strain  being  limited  to 
10,000  Iba.  per  square  inch  in  extreme  fibres.  Rivet-holes  in  cover-plates  and 
idadooted. 


882 


IROK  AND  STEEL. 


The  rivets  of  steel  in  drilled  or  reamed  holes  were  proportioned  on  the 
basis  of  a  bearing  strain  of  15,000  lbs.  per  square  inch  and  a  shearinK  strain 
of  7600  lbs.  per  fiquare  inch,  and  special  pains  were  taken  to  get  the  double 
shear  in  as  many  riyets  as  jpossiole.  This  was  the  requirement  for  shop 
rivets.    In  the  case  of  field  nvets,  the  number  was  increased  one>half. 

The  pins  were  proportioned  on  the  basis  of  a  bearing  strain  of  18,000  lbs. 
per  square  inch  and  a  bending  strain  of  80,000  lbs.  per  square  inch  in  ex- 
treme fibre,  the  diameters  of  the  pins  being  never  made  more  than  one  inch 
less  than  the  width  of  the  largest  eye-bar  attaching  to  them. 

The  weight  on  the  rollers  or  the  expansion  joint  on  Pier  II  is  40,000  IH. 
per  linear  foot  of  roller,  or  8,SS8  lbs.  per  linear  inch,  the  rollers  being  15  ins. 
in  diameter. 

As  the  sections  of  the  supf^rstructure  were  unusuallv  heavy,  and  the  strains 
from  dead  load  greatly  in  excess  of  those  from  moving  load,  it  was  thought 
best  to  use  a  slightly  higher  steel  than  is  now  generally  used  for  lighter 
structures,  and  to  work  this  steel  without  punching,  all  holes  being  dnlled. 
A  somewhat  softer  steel  was  used  in  the  floor-system  and  other  lighter 
partst 

The  principal  requirements  which  were  to  be  obtained  as  the  results  of 
tests  on  eamples  cut  from  finished  material  were  as  follows: 


Max. 

Ultimate 

Strength, 

lbs.  per 

sq.  inch. 

High-grade  steel. 

78,500 

Eye-bar  Rteel  — 
Itedium  steel... 

76,000 

72,500 

Soft  steel 

68.000 

Min. 

Ultimate 

Min.ElaatIc 

Strength, 

Limit,  lbs. 

lbs.  per 

pcrsq.  In. 

sq.  inch. 

69,000 

40,000 

66,000 

88.000 

64.000 

87,000 

65.000 

80,000 

Min.  per^ 
centage  of 
Elongation 
in  8  inches. 


Min.  Per- 
centage  of 
BeductloD 
at  Fracture 


18 
80 
28 
98 


88 

40 
44 

60 


TENACITY  OF  KETAI^S  AT  VARIOUS 
TBlltPJBBATUBBS. 

The  British  Admiralty  made  a  series  of  experiments  to  ascertain  what  loss 
of  strength  and  ductility  takes  place  in  gun-metal  compositions  when  raii«ed 
to  high  temi^eraiures.  It  was  found  that  all  the  varieties  of  gun-metal 
suffer  a  gradual  but  not  serious  loss  of  sli'ength  and  ductility  up  to  a  certain 
temperaiui'e,  at  which,  within  a  few  degrees,  a  great  change  takes  place, 
the  strength  falls  to  about  one  half  the  original,  and  the  ductility  is  wholly 

f:one.  At  temperatures  above  this  point,  up  to  600,  there  is  little,  if  any. 
urther  loss  of  strength;  the  temperature  at  which  this  great  change  and 
loss  of  strength  takes  place,  although  uniform  in  the  specimens  oast  from 
the  same  pot,  varies  about  lOO"  in  uie  same  composition  cast  at  different 
temiMtratures,  or  with  some  varying  conditions  In  the  foundry  process. 
The  temperature  at  which  tlie  oliange  toolc  place  in  No.  1  series  was  asoer> 
tained  to  be  about  STO«,  and  in  that  of  No.  8,  at  a  little  over  850".  Whatever 
may  be  the  cause  of  this  important  difference  in  the  same  composition,  the 
fact  stated  may  be  taken  as  certain.  Rolled  Munta  metsl  and  copper  are 
BAtiHfactory  up  to  600®,  and  may  be  used  as  securing-bolts  with  safety. 
Wroui(lit  Iron,  Yorkshire  and  remanufactured,  increase  in  strength  up  to 
600<*,  but  lose  slightly  in  ductility  up  to  &00«,  where  an  increase  begins  and 
continues  up  to  500«,  where  it  is  still  less  than  at  the  ordinary  temperature 
of  the  atmosphere.  The  strength  of  Landore  steel  is  not  affected  by  temper- 
ature  up  to  600<>,  but  its  ductility  is  reduced  more  than  one  half,  (/rois  Oct. 
6,  1877.) 

Tensile  Strengrtli  of  Iron  and  Steel  mt  Slffb  Tempem* 
tares.— James  £.  Howard^  tests  (Iron  Age,  April  10,  ltWi»)  show  that  the 
tensile  strength  of  steel  diniiuishes  as  the  temperatui'e  increases  from  0* 
until  a  minimum  is  reached  between  800^  and  800*  F..the  total  decrease 
being  about  4000  lbs.  pt^r  square  hich  in  the  softer  steels,  and  from  8000  to 
8000  lbs.  in  steols  of  over  80.000  lbs.  tensile  strength.  From  this  minimum  point 
the  strength  increases  up  to  a  temperature  of  400*>  to  650*  F.,  the  maximum 
bein^  reached  earlier  in  the  liarder  Kteels,  the  increase  amonnting  to  from 
10,000  to  SO.OOO  lbs.  per  square  inch  above  the  minimum  strength  at  from  800" 


TENACITY  OF  METALS  AT  VARIOUS  TEMPERATUBES.   383 

to  300°.  From  this  maximum,  the  stren«:th  of  all  the  steel  decreages  steadil:^ 
at  a  rate  approximating  10,000  lbs.  decrease  per  100*  Increase  of  tempera- 
ture. A  strength  of  20,000  lbs.  per  squai-e  inch  is  still  sliown  bj  .10  C.  steel 
at  about  mKr*  F.,  and  by  .60  to  1.00  C.  steel  at  about  IfXXy*  F. 

The  streng^  of  wrought  iron  increases  with  temperature  from  G°  up  to  a 
maximum  at  from  400  to  600*  F.,  tlie  increase  being  from  8000  to  10,000  lbs. 
per  square  inch,  and  then  decreases  steadily  till  a  strength  of  only  6000  Iba 
per  square  inch  is  shown  at  1500*  F. 

Oast  iron  appears  to  maintain  its  strength,  with  a  tendency  to  increase, 
not-l  900*  is  reached,  beyond  which  temperature  the  strength  gradually 
diminishes.  Under  the  liighest  temperatures,  1500*  to  1600*  F.,  numerous 
eraclcs  on  the  cylindrical  surface  of  the  specimen  were  developed  prior  to 
rapture.  It  is  remarkable  that  cast  iron,  so  much  inferior  in  strengtn  to  the 
steels  at  atmospheric  temperature,  under  the  highest  temperatures  has 
nearlj  the  same  strength  the  high-temper  steels  then  have. 

Strenstli  of  Iron  and  Steel  Boiler-plate  at  Klcli  Tem* 
peratnres.    (Chas.  Huston,  Jour,  F.  /.,  1877.) 

AVKRAGB  OF  THBU  TbSTS  OF  EaCH. 

Temperature  F.  68*  675*  925* 

Charooal  iron  plate,  tensile  strength,  lbs 56,866  68,080  65,848 

•*  '*        "      contr.  of  area )( 26  28  21 

Soft  open-hearth  steel,  tensile  strength,  lbs 54,600  66,063  64.350 

"      contr.jf 47  M  S3      • 

*"   Crucible  steel,  tensile  strength,  lbs 64,000  69.266  68,600 

'*      contr.jt 86  80  21 

Strenctli  of  'Wronglit  Iron  and  Steel  at  Klslft  Temper- 
atarea*  (Jour.  F,  /.,  cxii.,  1881,  p.  241.)  Kollmann's  experiments  at  Ober- 
bausen  included  tests  of  the  tensile  strength  of  iron  ana  steel  at  tempera- 
tures ranging  between  70*  and  2000*  F.  Three  kinds  of  metal  were  tested, 
viz.,  fibrous  iron  having  an  ultimate  tensile  strength  of  52.464  lbs.,  an  elastic 
strength  of  88,280  lbs.,  and  an  elongatiou  of  17,t%;  fine-grained  iron  having 
for  the  same  elements  values  of  56.892  lbs.,  89,118  lbs.,  and  20^;  <uid  Bes- 
semer steel  having  values  of  84,826  lbs..  .^5.029  lbs.,  and  14.5^.  The  mean 
ultimate  tensile  strength  of  each  muteiial  expressed  in  per  cent  of  that  at 
ordinary  atmospheric  temperature  is  given  in  the  following  table,  the  flfih 
column  of  whicn  exhibits,  for  purposes  of  comparison,  the  results  of  experi- 
ments carried  on  by  a  committee  of  the  Franklin  Institute  in  the  years 


Fibrous        Fine-grained  Bessemer       Franklin 

Temperature     Wrought             Iron,  Steel,          Institute, 

Degrees  F.      Iron,  p.  c.         per  cent.  per  cent.        per  cent. 

0                 100.0                 100.0  100.0                  96.0 

100                 100.0                 100.0  100.0                102.0 

900                 100.0                100.0  100.0                105.0 

800                   ir7.0                 100.0  100.0                 106.0 

400                   95.5                 100.0  100.0                 106.0 

600                   92.6                   98.5  96.5                 104.0 

600                  88.5                  95.5  02.0                  99.6 

700                   81.5                   90.0  68.0                   02.5 

800                   67.6                   77.5  44.0                   75.5 

900                   44.5                   51.5  36.5                   68.5 

1000                  20.0                  86.0  31.0                  86.0 

1100                   20.0                   30.5  26.5                 

1200                   18.0                   28.0  22.0                 

1800                  16.5                  28.0  18.0                 

1400                   18.5                   19.0  15.0                 

1900                   10.0                   15.5  12.0                 

1600                   7.0                   12.5  10.0                  

1700                   6.6                    10.5  8.5                  

J800                   4.5                     8,5  7.5                  

1900                   8.5                     7.0  6.5                  

»000                   8.5                     5.0  5.0                  

Tbe  SSTeet  of  Cold  on  tbe  Strength  of  Iron  and  Steel.— 

Th«-  followinir  concluKions  were  arrived  at  h>  Mr.  Styffe  iu  1805  : 

(I)  Tiiat  the  absolute  strength  of  iron  and  Kteei  is  not  diminished  by 
eon.  but  that  even  at  tlie  lowest  teinperatui-e  wltich  ever  occurs  in  Sweden 
It  is  at  least  aa  great  as  at  the  ordinary  temperature  (about  00*  F.). 


384  IROK  ANIi  STEEL. 

(2)  That  neither  la  steel  nor  in  iron  Is  the  extensibility  less  in  serere  cold 
than  at  the  ordinary  temperature. 
(8)  That  the  Huiit  of  elasticity  in  both  steel  and  iron  lies  higher  in  severe 

(4)  That  the  modulus  of  elasticity  in  both  steel  and  iron  is  increased  on 
reduction  of  temperature,  and  diminished  on  elevation  of  temperature  ;  but 
that  these  variations  never  exceed  0.05  %  for  a  change  of  temperature  of  1.8* 
F.,  and  therefore  Fuch  variations,  at  least  for  ordinary  purposes,  are  of  do 
special  importance. 

Mr.  C.  P.  Sandber^  made  in  1867  a  number  of  tests  of  iron  rails  at  various 
temperatures  by  means  of  a  falliiiK  weight,  since  he  was  of  opinion  that, 
although  Mr.  StyfPe's  conclusions  were  perfectly  correct  as  regards  tensile 
strength,  they  miglit  not  apply  to  tlie  resistance  of  iron  to  impact  at  low 
temperatures.  Mr.  Sandberg  convinced  himself  that  "  the  breaking  strain  " 
of  iron,  such  as  was  usuallv  employed  for  rails,  **  as  tested  by  sudden  blows 
or  shocks,  is  considerably  influenced  by  cold ;  such  iron  exhibiting  at  10*  I> . 
only  from  one  third  to  one  fourth  of  the  strength  which  it  possesses  at 
84°  F.**  Mr.  J.  J.  Webster  (Inst.  C.  E..  1880)  giveH  reasons  for  doubting 
the  accuracy  of  Mr.  8andberg*s  deductions,  since  the  tests  at  the  lower 
temperature  were  nearly  all  made  with  21 -ft.  lengths  of  ralL  while  those  at 
the  higher  temperatures  were  mode  with  abort  lengths,  the  supports  in 
every  case  being  the  same  distance  apart. 

W.  U.  Barlow  (Proc.  Inst.  C.  E.)  made  experiments  on  bars  of  wrought 
iron,  cast  iron,  malleable  cast  iron,  Bessemer  steel,  and  tool  steel.  The  bars 
were  tested  with  tensile  and  transverse  strains,  and  also  by  impact ;  one 
half  of  them  at  a  temperature  of  60^  F.,  and  the  other  half  at  6^  P.  The 
lower  temperature  was  obtained  by  placing  the  bars  in  a  freezing  mixture, 
care  being  taken  to  keep  the  bars  covered  with  it  during  the  whole  time  of 
the  experiments. 

The  results  of  the  experiments  were  summarised  as  follows : 

1.  When  bars  of  wrought  iron  or  steel  were  submitted  to  a  tensile  strain 
and  broken,  their  strength  was  not  affected  by  severe  cold  (5°  F.),  but  their 
ductility  was  increased  about  1%  in  iron  and  S%  in  steel. 

2.  When  bars  of  cast  iron  were  submitted  to  a  transverse  stnUn  at  a  low 
temperature,  their  strength  was  diminished  about  8^  and  their  flexibility 
about  19%. 

8.  When  bars  of  wrought  iron,  malleable  cast  iron,  steel,  and  ordinary 
cast  iron  were  subjected  to  impact  at  a  temperature  of  5°  F.,  the  force  re- 
quired to  break  them,  and  the  extent  of  their  flexibility,  were  reduced  as 
follows,  viz.: 

Reduction  of  Force         Reduction  of  Flexl- 
of  Impact,  per  cent.  bility,  per  cent. 

Wrou«rht  iron,  about 8  10 

Steel  (best  cast  tool),  about 9U  17 

Malleible  cast  iron,  about 4^  15 

Cast  iron,  about 81  not  taken 

The  experience  of  railways  in  Russia,  Canada,  and  other  countries  where 
the  winter  is  severe  is  that  the  breakages  of  rails  and  tires  are  far  more 
numerous  in  the  cold  weather  than  in  the  summer.  On  this  account  a 
softer  class  of  ste^l  is  employed  in  Russia  for  rails  than  is  usual  In  more 
temperate  climates. 

The  evidence  extant  in  relation  to  this  matter  leaves  no  doubt  that  the 
capability  of  wrought  iron  or  steel  to  resist  impact  is  reduced  by  cold.  On 
the  other  hand,  its  Ptntlc  strength  is  not  impaired  by  low  temperature*. 

BflTect  of  liow  TempentturM  on  Streniptli  of  lUOlroad 
Axles,  (Thos.  Andrews,  Proc.  Inst.  C.  E.,  ]891.)^Axles  6  ft.  6  in.  Ions 
between  centres  of  ioumals,  total  length  7  ft.  8^  in.,  diameter  at  middle  4^ 
in.,  at  wheel-sets  5Vft  <n  ,  journals  Sfti  X  7  in.  were  tested  by  impact  at  temper- 
atures of  0**  and  100<*  F.  Between  the  blows  each  axle  was  half  turned  over, 
and  was  also  replaced  for  16  minutes  in  the  water-bath. 

The  mean  force  of  concussion  resulting  from  each  impact  was  ascertained 
08 follows:  . 

Jj9i  hsK  height  of  free  fall  In  feet,  to  s  weight  of  test  ball,  liw  =  TT  = 
**  energy,**  or  work  in  foot-tons,  x  =  extent  of  deflections  between  bearings, 

then  F  (meaa  force)  =  -r  «  ■— •. 

X       m 


DURABILITY  OF  IRON,  CORROSION,  ETC. 


385 


The  resaltB  of  these  experiments  show  that  whereas  at  a  temperature  of 
0»  F.  a  total  averafre  mean  force  of  170  tons  was  sufficient  to  cause  the 
breaking  of  the  axles,  at  a  temperature  of  100«  F.  a  ti>tal  a^erige  mean 
foroe  of  4:28  tons  was  rvouislte  to  produce  fracture.  In  other  words,  the  re- 
sistance to  concussion  of  the  axles  at  a  t*'mperature  of  0*  F.  was  only  about 
i-i%  of  what  it  was  at  a  temperature  of  iW*  F. 

The  average  total  dellection  at  a  temperature  of  0«  F.  was  6.48  in.,  as 
against  15.06  hi.  with  the  axles  at  100«  F.  under  the  conditions  staied;  this 
represents  an  ultimate  reduction  of  flexibility,  imder  the  test  of  impact,  of 
about  67%  for  the  cold  axles  at  0"  F.,  compared  with  the  warm  axles  at 
1(W  F.  »         .— 

EJUPANSION  OF  IRON  AND  STEEI.  BT  BEAT. 

James  K  Howard,  engineer  in  charge  of  the  U.  8.  testing- machine  at  Wa- 
tertowu,  Mass.,  gives  the  following  results  of  tests  made  on  bars  35  inches 
long  (Iron  Age,  April  10,  1890): 


Marka 

Chemical  composition. 

Coefficient  of 
Expansion. 

Metal. 

C. 

Mn. 

Si. 

Feby 
difference. 

Per  degree 
F.  per  unit 
oflength. 

Wrought  iron 

.0000067302 

Steel 

la 
8a 
8a 
4a 

5a 
0a 
7a 
8a 
9a 
10a 

.00 
.80 
.81 

.5J7 

.61 
.57 
.71 
.81 
.89 
.97 

.11 
.45 
.57 
.70 
.58 
.9S 
.58 
.56 
.57 
.80 

".09" 
.07 
.06 
.17 
.19 
.28 

99.80 
99.85 
99.12 
96.98 
96.89 
98.48 
96.68 
98.46 
98.85 
97.95 

.0000067561 
.0000066259 

»» 

.0000065149 

•4 

.0000066597 
.0000066202 

ti 

.0000068801 

»k 

.O0OOOC4716 

t( 

.0000062167 

!• 

0000062885 

i« 

.00011061700 

Cast  (din)  iron .... 

00000.59261 

Drawn  copper 

.0000091286 

. 

DVBABIIilTY  OF  IRON,  COBBOfiflON,  ETC. 

Bvrft1»llltj  of  Cast  Iron.— Frederick  O  raff,  in  an  article  on  the 
Philadelphia  water-supply,  says  that  the  first  cast-iron  pipe  used  tliere  was 
laid  In  1^.  These  pipes  were  made  of  charcoal  iron,  ana  were  in  constant 
use  for  53  years.  They  were  uncoated,  and  the  inside  was  well  fllled  with 
toberclea.  In  salt  water  good  cast  iron,  even  uncoated,  will  last  for  a  cen- 
tury at  least;  but  It  often  becomes  soft  enough  to  be  cut  by  a  knife,  as  is 
shown  in  iron  cannon  taken  up  from  the  bottom  of  harbors  after  long  sub- 
mersion. Close-grained,  hard  white  metal  lasts  the  longest  in  sea  water.— 
Efui'g  New,  April  23.  1867,  and  March  26.  l89-i. 

Ttotfto  of  Iron  alter  Forty  TearsC  Service.— A  square  link  12 
inches  broad.  1  inch  thick  and  about  12  feet  long  was  taken  from  the  Kieff 
bridge,  then  40  yearn  old,  and  tested  in  comparison  with  a  similar  link  which 
bad  been  presenred  in  tlie  stock-house  since  the  bridge  was  built.  The  fol- 
lowing Is  the  record  of  a  mean  of  four  longitudinal  test-pieces,  1  X  1^  X  6 
inches,  takon  from  each  link  (StaJd  und  Eiaen,  1890): 

Old  Link  taken  New  TJnk  from 

from  Bridge.  Store-house. 

Tensile  strength  per  square  inch,  tons 21.8  22.2 

Elaatic  limit                "               '*        11.1  11.9 

Elongation,  per  cent 14.05  18.42 

CoDtraction,  percent 17.35  18.75 

IHira1»lllt7  of  Iron  In  Bridges.  (Q.  Lindenthal,  Eng^g.  May  8, 
18M,  p.  189.) — ^The  Old  Monongahela  BUt»(>eii8ion  bridge  in  Pittaburgn,  built 
in  184.5,  waa  taken  down  in  1«2.  The  wires  of  the  cables  were  frequently 
•trained  to  half  of  their  ultimate  strength,  yet  on  testing  them  after  37  years' 


386  IRON  AND  STEEL. 

tue  they  showed  a  teoBile  strength  of  from  72,700  to  100,000  lbs.  per  squars 
inch.  The  el.i8tic  limit  was  from  67,100  to  78,600  lbs.  per  square  inch.  Re« 
duct  Ion  at  point  of  fracture,  S5%  to  75%.    Their  diameter  was  0.13  inch. 

A  new  ordinary  telej^raph  wire  of  same  gauge  tested  for  comparison 
showed:  T.  S.,  of  100,000  lbs.:  E.  L.,  81,650  lbs.;  reduction,  67%.  Iron  rods 
used  as  stays  or  suspenders  showed:  T.  S.,  48,770  to  49,?iiO  lbs.  per  square 
Inch;  E.  L.,  20,880  to  ii9,ii00.  Mr.  Lindenthal  draws  these  conclusions  from 
his  tests: 

*"  The  above  tests  Indicate  that  iron  highly  strained  for  a  long  number  of 
yean:,  but  still  within  the  elastic  limit,  and  exposed  to  slight  vibration,  will 
not  deteriorate  in  quality. 

*'  That  if  subiected  lo  only  one  kind  of  strain  it  will  not  change  its  texture, 
even  if  strained  beyond  its  elastic  limit,  for  many  years.  It  will  stretch  and 
behave  much  as  in  a  testing-machine  during  a  long  test. 

''  That  ii-on  will  change  its  texture  only  when  exposed  to  alternate  severe 
straining,  as  in  bending  in  different  directions.  If  the  bending  is  slight  but 
very  rapid,  as  in  violent  vibrations,  the  effect  is  the  same.** 

Corrosion  of  Iron  Bolts.— On  bridges  over  the  Thames  in  London, 
bolts  exposed  to  the  action  of  the  atmosphere  and  rain-water  were  eaten 
away  in  :;:5  years  from  a  diameter  of  %  in.  to  )^  in.,  and  from  ^  In.  diameter 
to  5/16  inch. 

Wire  ropes  exposed  to  drip  in  colliery  shafts  are  very  liable  to  corrosion. 

Corrosion  of  Iron  and  Steel.— Experiments  made  at  the  Riverside 
Iron  Works,  Wlieeling,  W.  Va.,  on  the  comparative  liability  to  rust  of  iron 
and  soft  Bessemer  steel:  A  piece  of  iron  plate  and  a  similar  piece  of  steel, 
both  cleau  and  bright,  were  placed  4n  a  mixture  of  yellow  loam  and  sand, 
with  which  had  been  thoroughly  incorporated  some  carbonate  of  soda,  nitrate 
of  soda,  ammonium  chloride,  and  chloride  of  magnesium.  The  earth  as 
prepared  was  kept  moist.  At  the  end  of  33  days  the  pieces  of  metal  were 
taken  out,  cleaned,  and  weighed,  when  the  iron  was  found  to  have  lost  0.^% 
of  its  weight  and  the  steel  0.7:2^.  The  pieces  were  replaced  and  after  28  days 
weighed  again,  when  the  iron  was  found  to  have  lost  2.06)(  of  its  original 
weight  and  the  steel  1.7W.    (Eiig'g,  June  26,  1891.) 

Corrosive  Asenis  In  llie  Aimospliere.— The  experiments  of  F. 
Crace  Calvert  (Cliemical  News,  March  8,  1^71)  show  that  carbonic  acid,  in 
the  presence  of  moisture,  is  the  agent  which  determines  the  oxidation  of 
iron  in  the  atmosphere.  He  subjected  .'perfectly  cleaned  blades  of  iron  and 
steel  to  the  action  of  different  gases  for  a  period  of  four  months,  with 
results  as  follows: 

Dry  oxygen,  dry  carbonic  acid,  a  mixture  of  both  gases,  dry  and  damp 
oxygen  and  ammonia:  no  oxidation.  Damp  oxygen:  in  three  experiments 
one  blade  only  was  slightly  oxidized. 

Damp  carbonic  acid:  slight  appearance  of  a  white  precipitate  upon  the 
Iron,  found  to  be  carbonate  of  iron.  Damp  carbonic  acid  and  oxygen: 
oxidation  very  rapid.  Iron  immersed  in  water  containing  carbonic  acid 
oxidized  rapidly. 

Iron  immersed  in  distilled  water  deprived  of  its  gases  by  boiling  rusted 
the  iron  in  spots  that  were  found  to  contain  Impurities. 

Galvanic  Action  is  a  most  active  agent  of  corrosion.  It  takes  place 
when  two  metals,  one  electro-negative  to  the  other,  are  placed  in  contact 
and  exposed  to  dampness. 

Sulphurous  acid  (the  product  of  the  combustion  of  the  sulphur  In  ooal)  is 
an  exceedingly  active  corrosive  agent,  especially  when  the  exposed  iron  Is 
coated  with  soot.  This  accounts  for  the  rapid  corrosion  of  iron  in  railway 
briilges  exposed  to  the  smoke  from  locomotives.  (See  account  of  escpert' 
men  is  by  the  author  on  action  of  suluhurous  acid  in  Jotir  Frank  /n^t..  June, 
1875,  p.  437.)  An  analvsis  of  sooty  iron  rust  from  a  rallwav  bridge  snowed 
the  presence  of  sulphurous,  sulphuric,  and  carbonic  acids,  chlorine,  and 
ammonia.  Bloxnm  states  that  ammonia  Is  formed  from  the  nitrogen  of  the 
air  during  tl  e  ])roccss  of  rusting. 

Corrosloo  In  Steani-bolleni.->Intemal  corrosion  may  be  due 
either  to  the  use  of  water  containing  free  acid,  or  water  containing  sulphate 
or  chloride  of  magnesium,  which  decompose  when  heated,  liberating  the 
acid,  or  to  water  containing  air  or  carbonic  acid  in  solution.  External 
corrosion  rarely  takes  place  when  a  l>oiler  is  kept  hot,  but  when  cold  it  is 
apt  to  corrode  rapidly  in  those  portions  where  it  adjoins  the  brickwork  or 
where  it  may  be  covered  by  dust  or  ashes,  or  wherever  dampness  may 
lodge.  (See  Impurities  of  Water,  p.  551,  and  Incrustatioa  and  Oorrosloo, 
p.  710.) 


PRESEBVATIVE  COATIKQS.  38T 


PBESERVATIVB    COATINGS, 

(The  following  notes  have  been  furnished  to  the  author  by  Prof. 
A.  H.  Sabln.) 

Cement^—Iron-work  is  sometimes  protected  by  beddingr  in  concrete, 
in  wliich  case  it  is  first  cleaned  and  then  washed  with  neat  cement  before 
beiu?  imbedded. 

Aspltaltimi.— This  Is  applied  hot  either  bv  dippine  (as  water-pipe)  or 
by  pouring  it  on  (as  bridge  floors).  The  asphalt  should  be  slightly  elastic 
when  cold,  with  a  high  melting-point,  not  softening  much  at  lOO'  F.«  applied 
at  aoO"  to  400":  surface  must  be  dry  and  should  be  not;  coating  shoula  be  of 
considerable  thickness. 

Paint*— Composed  of  a  vehicle  or  binder,  usually  linseed  oil  or  some 
Inferior  substitute,  or  varnish  (enamel  paints):  and  a  pigment  which  is  a 
more  or  less  inert  solid  In  the  form  of  powder,  either  mixed  or  ground 
together.  The  piiuclpal  pigments  are  white  lead  (carbons  te)  and  white 
zinc  (oxide),  red  lead  (peroxide),  oxides  of  iron,  bydrated  and  delivdrated, 
graphite,  lamp-black,  chrome  yellow,  ultramarine  and  Prussian  blue,  and 
various  tinting  colors.  White  l<Mid  has  the  greatest  body  or  opacity  of  white 
pigments:  three  coats  of  it  equal  five  of  wliite  zinc;  zinc  is  more  brilliant 
and  pennanent,  but  it  is  liable  to  peel,  and  it  is  customary  to  mix  the  two. 
These  are  the  standard  wliite  paints  for  all  uses  and  the  basis  of  all  light- 
colored  paints.  Anhydrous  Iron  oxides  are  brown  and  purplish  brown, 
hydrated  iron  oxides  are  yellowish  red  to  reddish  yellow,  with  more  or  less 
brown;  most  iron  oxides  are  mixtures  of  both  sorts.  They  also  contain 
frequently  nuutganese  and  clay.    They  are  cheap,  and   are  serviceable 

^1^8  for  wood,  and  are  often  used  on  iron,  but  for  the  latter  use  are 
lling  into  disrepute.  Qraphite  used  for  painting  iron  contcdns  from  10 
to  90%  foreign  matter,  usually  siUcates  and  Iron  oxides.  It  is  very  opaque, 
hence  has  great  covering  power,  and  may  be  appii<Kl  in  a  very  thin  coat 
which  should  be  avoided.  It  retards  the  drying  of  oil,  hence  the  necessity 
of  using  dryers;  these  are  lead  and  manganese  compounds  dissolved  in  oil 
and  turpentine  or  benzine,  and  act  as  carries  of  oxygen;  they  are  necessary 
in  most  paints,  but  should  be  used  as  little  as  possible.  There  are  many 
grades  of  lamp-black;  as  a  rule  the  cheaper  sorts  contain  oily  matter  and 
are  especially  hard  to  dry;  all  lamp-black  is  slow  to  dry  in  oil.  It  is  the 
principal  black  on  wood,  and  is  used  some  on  iron,  usually  in  combination 
with  varnish  or  vamisnUke  compounds.  It  is  very  permanent  on  wood. 
A  gallon  of  oil  takes  only  a  pound  of  lamp-black  to  make  a  paint,  while 
tlie  same  amount  of  oil  requires  alxxit  -40  lbs.  of  red  lead.  On  this  account 
red-lead  paint,  which  weighs  about  30  lbs.  per  gallon,  is  the  most  expensive 
of  all  comon  paints.  It  does  not  dry  slowly  like  other  oil  paints,  but  com* 
bines  with  the  oil  to  make  a  sort  of  cement;  on  this  account  it  is  used  on 
the  joints  of  steam-pipes,  etc.  To  prevent  the  mixture  of  red  lead  and  oil 
settmg  into  a  cake,  and  also  to  cheapfu  it,  it  is  often  adulterated  with 
whiting  or  sometimes  with  white  zinc,  the  proportion  of  adulterant  being 
sometimes  double  the  lead.  Red  lead  lias  long  had  a  high  reputation  as  a 
paint  for  Iron  and  steel  and  Is  still  used  very  extensively;  but  of  late  vears 
some  of  the  new  paints  and  varnijiih-like  preparations  have  displaced  it  to 
some  extent  even  on  the  most  important  work. 

VmmiaheB.— These  are  made  by  melting  fossil  resin,  to  which  is  then 
added  from  half  its  weight  to  three  times  its  weight  of  refined  linseed  oil, 
and  the  compound  is  thinned  witli  turpentine;  they  usually  contain  a  little 
dryer.  They  are  chiefly  used  on  wood,  being  more  durable  and  more 
bnlliant  than  oil,  and  are  often  used  over  paint  to  preserve  it.  Asphaltum 
is  sometimes  snbstituted  in  part  or  in  whole  for  the  fossil  resin,  and  in  this 
way  are  made  varnishes  which  have  been  applied  to  iron  and  steel  with 
good  results.  Asphaltum  and  animal  nnd  vege  able  tar  and  pitch  have  also 
been  simply  dissolved  in  solvents,  as  benzine  or  carbon  disulphide,  and  used 
for  the  same  purpose. 

All  these  preservative  coatings  are  supposed  to  form  impervious  films, 
keeping  out  air  and  moisture;  but  in  fact  all  are  somewhat  porous.  On  this 
account  it  is  necessary  to  have  a  film  of  appre<'iablc  thicknesH,  best  formed 
by  successive  coats,  so  that  the  pores  of  one  u  ill  be  closed  by  the  next.  The 
pigment  is  used  to  give  an  agreeable  color,  to  help  fill  the  pores  of  the  oil 
film,  to  make  the  paint  harder  so  tiiat  it  will  resist  abrasion,  and  to  make  a 
thicicer  film.  In  varnishes  these  results  are  sought  to  be  attained  by  the 
re»in  which  is  dissolved  in  the  oil.    There  is  no  sort  of  agreement  among 


388  ntOK  AKD  STEEL. 

pnctieal  m«n  as  to  wliieb  Is  the  best  coating  for  any  partienlar  case;  this  is 
probably  because  so  much  depends  on  the  preparation  of  the  surface  and 
the  care  with  which  the  coating  Is  applied,  and  also  because  the  conditions 
of  exposure  vary  so  gr-eatly. 

Methods  of  Application*— Too  much  care  cannot  be  given  to  the 
preparation  of  the  surface,  if  it  is  wood,  it  should  be  dry,  and  the  surface 
of  knots  should  be  coated  with  some  preparation  which  will  keep  tlie  tarry 
matter  In  the  wood  from  the  coating.  Ail  old  paint  or  Taruitih  should  be 
removed  by  burning  and  scraping.  Metallic  surfaces  should  be  cleaned  br 
wire  brushes  and  scrapers,  and  if  the  permanence  of  the  work  Is  of  much 
importance  the  scale  and  oxide  should  be  completely  removed  by  acid 
pickling  or  by  the  sand-blast  or  some  equally  efficient  means.  Pickling  Is 
usually  done  with  a  \0%  solution  of  sulphuric  acid;  as  the  solution  becomes 
exhausted  it  may  be  made  more  active  by  heating.  All  traces  of  acid  must 
be  removed  by  washing  and  the  metal  must  be  rapidly  dried  and  painted 
before  it  becomes  in  the  slightest  degree  oxidized.  Tne  pand-blastl  which 
has  been  applied  to  large  work  recently  and  for  many  years  to  small  work 
with  good  results,  leaves  the  surface  perfectly  clean  and  dry:  the  paint 
must  be  applied  immediately.  Plenty  of  lime  should  always  be  allowed, 
usually  about  a  week,  for  each  coat  of  paint  to  dry  before  tlie  next  coat  is 
applied;  less  than  two  coats  should  never  be  used.  Two  will  last  tliree 
tinies  as  lonir  as  one  coat.  Benzine  should  not  be  an  ingredient  in  coatings 
for  iron-work,  because  its  rapid  evaporation  lowers  the  temperature  of  <ne 
iron  and  may  cau.se  formation  of  dew  on  the  surface  adjacent  to  the  paint 
which  is  immediately  to  be  painted. 

Cast-iron  water-pipes  are  usually  coated  by  dipping  in  a  hot  mixture  of 
ooal-tar  and  coal-tar  pitch;  riveted  steel  pipes  by  dipping  in  hot  asphalt  or 
by  a  Japan  enamel  which  is  baked  on  at  about  400*  F.  Ships*  bottoms  are 
iisuaUv  coated  with  some  sort  of  paint  to  prevent  rusting,  over  which  is 
spread,  hot,  a  poisonous,  slowly  soluble  compound,  usually  a  copper  soap, 
to  prevent  adhesion  of  marine  growths. 

Galvanized-iron  and  tin  surfaces  should  be  thoroughly  cleaned  with 
benzine  and  scrubbed  before  painting.  When  new  they  are  covered  with 
grease  and  chemicals  used  in  coating  the  plates,  and  these  must  be  removed 
or  the  paint  will  be  destroyed. 

Aaaiitlt|r  of  Paint  for  a  Gl^en  Snrflaoe*— One  gallon  of  paint 
will  cover  850  to  350  sq.  ft.  as  a  first  coat,  dependmg  on  the  character  of  the 
surface,  and  from  850  to  450  sq.  ft.  as  a  second  coat. 

Qualities  of  Paints.— T^o  BaUroad  and  Engineering  Joumai,  toIs. 

Uv  and  Iv,  1890  and  1891.  has  a  series  of  articles  on  paint  as  applied  tofcoocien 
ttructurea^  its  chemicai  nature,  application,  adulteration,  etc.,  by  Dr.  C.  B. 
Dudley,  chemist,  and  F.  N.  Pease,  assistant  chemist,  of  the  Penna.  R.  R. 
They  give  the  results  of  a  long  series  of  experiments  on  paint  as  applied  to 
railway  purpoRes. 

RnsttesB  Coating*  for  Iron  and  Steel.— Tinning,  enamelling, 
lacquering,  galvanizing,  electro-chemical  painting,  and  other  preservative 
methods  are  discussed  in  two  important  papers  by  M.  P.  Wood,  in  Trans. 
A.  8.  M.  E..  volf*.  XV  and  xvi. 

A  Metlftod  of  Prodnelnc  An  Inozldlxable  Snrflice  on 
iron  and  steel  by  means  of  electricity  has  been  developed  by  M.  A.  de  Meri- 
tens  (Engineering),  The  article  to  be  protected  is  placed  in  a  baih  of  ordi- 
nary or  distilled  water,  at  a  tenoperature  of  from  158®  to  176*  F.,  and  an 
electric  current  is  sent  through.  The  water  Is  decomposed  Into  its  elements, 
oxygen  and  hydrogen,  and  the  oxygen  is  deposited  on  the  metal,  while  the 
hydrogen  appears  at  the  other  pole,  which  may  either  be  the  tank  in  which 
the  operation  in  conducted  or  a  plate  of  carbon  or  metal.  The  current  has 
only  sufficient  electromotive  force  to  overcome  the  resintance  of  the  circuit 
and  to  decompose  the  water;  for  if  it  be  stronger  than  this,  the  oxygen  com« 
bines  with  the  iron  to  produce  a  pulverulent  oxide,  which  has  no  adherence. 
If  the  conditions  are  as  th«y  should  be.  it  is  only  a  few  minutes  after  the 
oxygen  appears  at  the  metal  before  the  darkening  of  the  surface  shows 
that  the  gas  has  united  wiih  the  iron  to  form  the  magnetic  oxide  Fe«04, 
which  will  resist  the  action  of  the  air  and  protect  the  metal  beneath  it. 
After  the  action  has  continued  an  hour  or  two  the  coating  is  sufficiently 
solid  to  resiflt  the  scratch -bruAh,  and  it  will  then  take  a  brilliant  polish. 

It  a  piece  of  thickly  ruHltxl  Iron  be  placed  in  the  tmth.  its  eesquioxide 
(Fe«Ot)  is  rapidly  iraudfonued  into  tho  magnetic  oxide.    This  outer  ii^er 


CHEMICAL  COMPOSITION  AKD  PHYSICAL  CHARACTER,  389 

has  no  adbesion.  but  beneath  it  there  wlU  be  found  a  coatini;  7hioh  to 
actually  a  part  of  the  metal  Itself. 

In  the  early  experiments  M.  de  Meritens  employed  pieces  of  steel  only« 
bat  in  vrrougrht  and  cast  iron  he  was  not  successful,  for  the  coatinji^  came  off 
with  the  sliKhtest  friction.  He  then  placed  the  iron  at  the  negative  pole  of 
the  apparatus,  after  it  had  been  already  applied  to  the  positive  pole.  Here 
the  oxide  was  reduced,  and  hydrogen  was  accumulated  in  the  pores  of  the 
metal.  The  specimens  were  then  returned  to  the  anode,  when  it  was  found 
that  the  oxide  appeared  quite  readily  and  was  very  solid.  But  the  result 
was  not  quite  perfect,  and  It  was  not  until  the  bath  was  filled  with  distilled 
water,  in  place  of  that  from  the  public  supply,  that  a  perfectly  satisfactory 
rpsolt  was  attained. 

Mmngmneme  Platlns  of  Iron  ma  a  Protection  firom  WLumt* 
—According  to  the  Italian  Progreao,  articles  of  iron  can  be  protected  againsc 
rust  by  sinking  them  near  the  negative  pole  of  an  electric  bath  composed  of 
10  litres  of  water,  60  grammes  of  chloride  of  manganese,  and  200  grammes 
of  n{l3*ate  of  ammonium.  Under  the  influence  of  the  current  the  l>ath 
deposits  on  the  articles  a  protecting  film  of  metallic  manganese. 


A  Noii«ozl4tziDsr  Process  of  Annealing  is  described  by  H.  P. 
Jones,  in  Eng^g  Ifeicg.jBn.  %  189^.  The  new  process  uses  a  non-oxidizing 
gas,  and  is  the  inrention  of  Mr.  Horace  K.  Jones,  of  Hartford,  Conn.    Its 


principal  feature  consists  in  keeping  the  annealing  retort  in  communication 
with  the  gas-holderor  gas-main  during  the  entire  process  of  heating  and 
cooling,  the  gas  thus  being  allowed  to  expand  back  into  the  main,  and  being, 
therefore,  kept  at  a  practically  constant  pressure. 

The  retorts  are  made  from  wrought-iron  tubes.  The  gas  Is  taken  directir 
from  the  mains  supplying  the  city  with  illuminating  gas.  If  metal  which 
has  been  blued  or  sliglitly  oxidized  is  subjected  to  the  annealing  process  it 
comes  out  bright,  the  oxide  being  reducea  by  the  action  of  the  gas, 

OomparatiTe  tests  were  made  of  specimens  of  steel  wire  annealed  in 
illuminating  gas,  in  nitrogen,  and  in  an  open  fire  and  cooled  in  ashes,  and  of 
specimens  of  the  unannealed  metal.  The  wires  were  .188  in.  in  diameter 
and  were  turned  down  to  .150  in. 

The  average  results  were  as  follows: 

Unannealed,  two  lots,  6  pieces  each,  tensile  strength  av.  97,120  and  80,790 
lbs.  per  sg.  in.,  elongation  7.12^  and  8.80^.  Annealed  in  open  fire,  8  tests,  av. 
t.  s.  88,090.  el.  25.7^.  Annealed  in  nitrogen,  av.  of  3  lots,  IS  pieces,  t.  s, 
50,8*20,  el.  89.81K.  Annealed  in  illuminating  gas,  av.  of  3  lots.  IS  pieces,  t.  s. 
60,180,  eL  iSJMjt.  The  elongations  are  referred  to  an  original  length  of 
1.15  ins. 

STEEL. 

BEI.ATIOH    BETWRBN    THB    CMKMICAIa    COIHPOSI- 
TION  AND  PHYSICAL  CHABACTBR  OF  STBBIi. 

W.  R.  Webster  (see  Trans.  A.  I.  M.  E.,  vols,  xxi  and  xxii,  1893-4)  gives  re- 
sults of  several  hundred  analyses  and  tensile  tests  of  basic  Bessemer  steel 
plates,  and  from  a  study  of  them  draws  conclusions  as  to  the  relation  of 
chemical  composition  to  strength,  the  chief  of  which  are  condensed  as 
follows : 

The  indications  are  that  a  pure  iron,  without  carbon,  phosphonis,  man- 
gaoeste,  silicon,  or  sulphur,  if  it  could  be  obtained,  would  have  a  tensile 
strength  of  84,750  lbs.  per  square  inch,  if  tested  In  a  9^-inch  plate.  With 
this  as  a  base,  a  table  Is  constructed  by  adding  the  following  hardening 
effects,  as  sdbown  by  Increase  of  tensile  strength,  for  the  several  elements 
named. 

Carbon,  a  constant  effect  of  800  lbs.  for  each  O.OIjC. 

Sulphur,        •*  "  600       "        "      O.OljC. 

Mioephoms,  the  effect  is  higher  in  high-carbon  than  In  low-carbon  steels. 

With  carbon  hundreths )( 9      10     11      12     18     14      16      16      17 

Each  .0I](P  has  an  effect  of  lbs.  90Q  1000  1100  1200  1300  1400  1500  1600  150^ 

Manganese,  the  effect  decreases  as  the  per  cent  of  manganese  increases. 
(    .00    .16    .20    .25    .80    .35    .40    .45     .50       .55 

Mn  being  per  cent •<     to    to     to     to     to     to     to     to      to       to 

(    .15    .20    .25    .30    .35    .40    .45    .50      .55       .65 

8tr*gih  Increases  for  .01](  240  240  2^  300   180   160   140   120     100     100  lbs. 

Total  fncr.  from  0  Mn . ..  8600  4800  5900  6900  7800  8G00  9:300  9900  10,400  11,400 


390 


STEEL. 


Silicon  ts  80  low  in  this  steel  that  its  hardeniofl:  effect  has  not  been  cod- 
Bidered. 
With  the  above  additions  fcr  carbon  and  phosphorus  the  followinf^ table 


by  Mr.  Webster). 


'%^ 


the 


has  been  constructed  (abridj^ed  from  the  orl„ „ ,.     

flfi^res  fi^lven  the  additions  for  sulphur  and  manganese  should  be  made  as 
above. 

Bstlmated  Ultimate  StrenetliB  of  Basic  BeMemer  St«c] 
Plates. 

For  Carbon,  .06  to  .24;  Phosphorus,  .00  to  .10;  Manganese  and  Sulphur,  .00  in 
all  cases. 


Carbon. 

M 

.06 

Phos.  .006 

m,mi 

41„Vi0 

'*      .01 

40,3:j« 

\vm 

"      .08 

4K1N" 

ri:^ 

"      .08 

4i,tirH) 

i:j,:^ 

"      .04 

i-ll^^ 

;  1.^50 

•*      .05 

i:5AV) 

VkIT^ 

"      .06 

4  L^i 

\Kim 

"      .07 

4jJ..VJ 

|i:.:50 

"      .08 

4"i.U.» 

1^350 

"      .09 

4'',:'^ti 

114-rrfi 

♦•      .10 

i.  ■■"■ 

;-  -A-) 

.001  Phos  r- 

8 

.i5u»    I    .24 


sajoo 

St,s60 

S8,:^60 
&0,S5O 

fli;i50 

G^,h50 
64,'^ 
ft."i.^60 

•'?    BO 

....Ibl 


54,700 
55,450 
66.050 
58.450 
50,950 
61.450 
6:^.950 
64.450 
65.950 
67.450 
68.950 
1501b 


III  all  rolled  steel  the  quality  depends  on  the  size  of  the  bloom  or  ingot 
from  which  it  is  rolled,  the  work  put  on  it,  and  the  temperature  at  which  it 
is  finished,  as  well  as  the  chemical  composition. 

The  above  table  is  based  on  tests  of  plates  %  inch  thick  and  under  TO 
inches  wide;  for  other  plates  Mr.  Webster  gives  the  following  corrections 
for  thickness  and  width.  They  are  made  necessary  only  by  the  effect  of 
thickness  and  width  on  thd  finishing  temperature  in  ordinary  practioa 
Steel  is  frequently  spoiled  by  being  finished  at  too  high  a  temperature. 
Gorrectiona  for  Size  of  Plates* 


"3« 


Plates. 
Inches  thick, 
and  over 


Up  to  70  ins.  wide.  Oter  70  Ins.  wid& 


Lbs. 
-2000 

—  1750 

—  1500 

—  ISSO 

—  1000 

—  500 

0 
+  3000 


Lbs. 

—  1000 

—  7W 

—  500 

—  »0 

—  0 
±  600 
•4-1000 
+  5000 


Comparing  the  actual  result  of  tests  of  408  plates  with  the  calculated 
results,  MrTwebster  found  the  variation  to  range  as  In  the  table  below. 
Aummary  of  the  IMflTerences  Between  Calculated  and 
Actual  Results  In  408  Tests  of  Plate  Steel. 

In  the  first  three  columns  the  effects  of  sulphur  were  not  considered;  In 
the  last  three  columns  the  effect  of  sulphur  was  estimated  at  600  Iba  for 
each  .Oljt  of  S. 


t*^ 

i 

.2 

h 

1 

S3 

ill 

r,^ 

« 

.d 

•5^ 

A 

l^«? 

p 

« 

& 

P 

" 

& 

^61 

Per  cent 

within  1000  lbs.. 

23.4 

.".2.1 

28.4 

24.6 

r.o 

26.0 

28.4 

iJOiK)  ••  .. 

40.9 

4S.') 

45.6 

48.5 

64.9 

.V2.8 

55.1 

«•        It 

♦'        3(K10   "  .. 

«2  5 

7i.:i 

07.6 

67.8 

73.0 

70.8 

74.7 

ti        t» 

"        4000   ".. 

T5  .') 

81.0 

78.7 

82.5 

85.8 

84. 1 

89.9 

i«       II 

"       6000  *'  .. 

83. 5 

91.1 

90.4 

93.0 

92.8 

99.9 

94.9 

STRENGTH  OF  BESSEMER  AND  OPEN-HEARTH  STEELS.   391 


The  last  fig:ure  In  the  table  would  indicate  that  if  specifications  were  drawn 
calling  for  steel  plates  not  to  vary  more  than  5000  lbs.  T.  S.  from  a  specified 
figure  (equal  to  a  total  raii^e  of  10,000  lbs.),  there  would  be  a  probability  of 
the  rejection  of  ^fi  of  the  blooms  rolled,  even  if  the  whole  lot  was  made  from, 
steel  of  identical  chemical  analysis.  In  1000  heats  only  *^  of  the  heats  failed 
to  meet  the  requirements  of  the  orders  on  which  they  were  graded:  the  loss 
of  plates  was  much  less  than  1^,  as  one  plate  was  rolled  from  each  neat  and 
tested  before  rolling  the  remainder  of  the  heat. 

R.  A.  Hadfleld  {Jour,  Iron  and  Steel  Inst.,  No.  1, 1894)  gives  the  strength  of 
very  pur©  Swedish  iron,  remelted  and  tested  as  cast,  20.1  tons  (45,0^  lbs.) 
per  sq.  in.;  remelted  and  forged,  SI  tons  (47,040  lbs.).  The  analysis  of  the 
cast  har  was:  C.  0  08:  8i,  O.Ol;  S,  0  02;  P,  0.02;  Mn.  0.01 ;  Fe,  99.82. 

KflTect  of  Oxygen  upon  Strengtlft  of  Steel.— A.  Lantz,  of  the 
Peine  works,  Germany,  in  a  letter  to  Mr.  Webster,  says  that  oxygen  plays 
an  important  role — such  that,  given  a  like  content  of  carbon,  phosphorus, 
and  manganese,  a  blow  with  greater  oxygen  content  gives  a  greater  hard- 
ness and  less  ductility  than  a  blow  with  less  oxygen  content.  The  method 
used  for  determining  oxyeren  is  that  of  Prof.  Ledebur,  given  in  StcUtl  und 
Kiaeit,^  May,  1893,  p.  19').  The  variation  in  oxygen  may  make  a  difference  in 
strength  of  nearly  ^  ton  per  sq.  in.  (Joitr.  Iron  and  Steel  In»t.,  No.  1,  ISd-l.) 
BANCB  OF  TABIATION  IN  8TBENf7TH  OF  BESSEMER 
AND  OPEN-HEABT0  STEEIiS. 

The  Carnegie  Steel  Co.  iu  1888  published  a  Ust  of  1057  tests  of  Bessemer 
^nd  open>hearth  steel,  from  which  the  following  figures  are  selected  : 


Kind  of  Steel. 

V4 

o 

Elastic  Umit. 

[Ultimate 
Strength. 

Elongation 

per  cent 
in  8  inches. 

HighH. 

Lowest 

High't. 

Lowest 

High't. 

Lowest 

(ra)  Bess. structural... 

(b)  ♦' 

(c)  Bess,  angles 

(dj  O.  H.  flre-box.... 
(e)  O.  H.  bridge 

100 
ITO 
7-2 
25 
20 

46,570 
47,690 
41,890 

89,230 
89,970 
82,630 

71,800 
73,540 
63,450 
6-J.790 
69.940 

61,450 
65,200 
56,1 ;« 
50,350 
63.970 

88.00 
30.25 
84.80 

36.00 
30.00 

28.75 
23.15 
26.25 
25.62 
22.75 

RBqniRCMENTS  OF  SrECIFICATIOKS. 

<a)  Elastic  limit,  85.000;  tensile  strength,  62.000  to  70,000;  elong.  73%  in  8  in. 

(6)  Elastic  limit,  40,000;  tensile  strength,  C7.000  to  75,000. 

(c)  Elastic  limit,  80.000;  tensile  stiength,  56,000  to  64.000;  elong.  20^  in  8  in. 

id}  Tensile  strength  50,000  to  62,000;  elong.  26^  in  4  in. 

(tf)  Tensile  strength.  64,000  to  70,000;  elong.  20^  in  8  In. 

Strensfh  of  Open-beartli  Structural  Steel.  (Pencoyd  Iron 
Works.)— As  a  general  iiile,  ihe  peixientage  of  carbon  in  steel  determines  its 
hardness  and  strength.  The  higher  the  carbon  the  harder  the  steel,  the 
higher  the  tenacity,  and  the  lower  the  ductility  will  be.  The  following  list 
exhibits  the  average  physical  properties  of  good  open-hearth  basic  st*^el ; 


If 

lastic 
Lhnir, 
lbs.  per 
sq.  in. 

» 

vt 

1< 

If 

Itimate 
Strength, 
lbs.  per 
sq.  iu. 

lastic 
Limit, 
lbs.  per 
sq.  in. 

P 

» 

m 

tf 

£ 

D 

M 

C£ 

« 

.06 

54000 

82600 

82 

60 

.17 

61600 

87000 

27 

50 

.09 

64fl00 

88000 

31 

58 

.18 

62500 

37500 

27 

40 

.10 

55700 

88500 

81 

57 

.19 

63300 

38000 

26 

48 

.11 

56500 

84000 

80 

56 

.20 

64200 

38500 

26 

47  ' 

.12 

57400 

34500 

80 

55 

.21 

65000 

39000 

25 

46 

.18 

58»0 

85000 

20 

54 

.22 

65800 

89500 

25 

45 

.14 

69100 

85500 

29 

53 

.23 

66600 

40000 

24 

44 

.16 

60000 

86000 

28 

52 

.24 

67400 

40500 

24 

43 

.16 

60800 

36600       28 

51 

.25 

6SJ00 

41000 

23 

42 

The  coefficient  of  elasticity  is  practically  uniform  for  all  grades,  and  is 
the  seme  as  for  iron,  viz.,  29.000.000  lbs.  These  figures  form  the  average  of 
a  mmerous  aeries  of  tests  from  rolled  bars,  and  can  only  serve  as  an  ap- 


392 


STEEL. 


grozlmatlon  In  single  InstanceA,  when  the  Taiiation  from  the  avemse  may 
e  considerable.  Steel  below  .10  carbon  should  be  capable  of  doublloe  flat 
without  fracture,  after  being  chilled  from  a  red  heat  in  cold  water.  Steel 
of  .15  carbon  will  occasionally  submit  to  the  same  treatment,  but  will 
usually  bend  around  a  curve  whose  radius  Is  equal  to  the  thickness  of 
the  specimen  ;  about  00^  of  specimens  stand  the  latter  bending  test  without 
fracture.  As  the  steel  becomes  harder  its  ability  to  endure  this  bending 
test  becomes  more  exceptional,  and  when  the  carbon  ratio  becomes  .Hff^ 
little  over  25^  of  specimens  will  stand  the  last-described  bending  test.  Steel 
having  about  A0%  carbon  will  usually  harden  sufficiently  to  cut  soft  iron 
and  maintain  an  edge. 

Mehrtens  gives  the  following  tables  in  Stahl  und  EUen  {Iron  Age,  April  SO, 
1898): 


Basle  Bessemer  Steel* 
680  Charges. 

Elastic  Limit,  Charges  within 

pounds  per  Range,  per  cent 

sq.  in.  of  total  number. 

85,600  to  88,400 16.0 

38,400  to  89,800 81.6 

:i9,800  to  41,200 87.6 

41,200  to  42,700 16.0 

42,700  to  46,400 9.9 

Tensile  Strength,      Charges  within 

pounds  per  Range,  per  cent 

sq.  in.  of  total  number. 

65,600  to  56,900 18.67 

66,900  to  58,300 88.67 

68,800  to  59,700 88.63 

69,700  to  61, 800 15.60 

61,800  to  6^800 8.53 

Stbuctural  SriEii. 

Charges  within 
Elongation.  Range,  per  cent 

per  cent.  of  totai  number. 

81to85 8.65 

25toa6... 8.58 

26to87 17.85 

87  to  28 26.7C 

88  to  89...   83.68 

29to30 14.41 

80to32.5 6.68 

RnrsT  Stbbl. 

25.8  to86 80.0 

86    to87 15.0 

27  to28 25.0 

28  to89 25.0 

83     to89,8 15.0 


Basle  Open-lfteartli  Strne« 

taral  Steel. 

489  CliarKes. 

Elastic  Limit,  Changes  within 

pounds  per  Range,  per  cent 

sq.  in.  of  total  charges 

84,400  to  37,000 18.8 

87,000  to  88,400 15.6 

88,400  to  89,800 20.3 

89,800  to  41 ,200 17.4 

41,800  to  42,700 18.8 

42,700  to  44,100 11  4 

44,100  to  48,400 8.5 

Tensile  Strength. 

55,800  to  66,900 8.0 

56,900  to  58,800 26.4 

68,30010  59,700 25.4 

59,700  to  61,800 19.6 

61,200  to  62,600 11.2 

68,600 to  66,100 9.04 

Elongation, 
per  cent. 

80  to  85 21.7 

85to86 7.7 

28  to  87 10.0 

87to28   11.0 

28to29 12.0 

89  to  30 13  8 

30to87.1 84.8 

RrvBT  Stbel,  19  Charobs. 
Tensile  Strength. 

61,800 5.8 

51,900  to  68,800 ..  26.8 

63,800  to  54.900 21.0 

64,900  to  66,300 21.0 

66i:«)0  to  66.900 26.4 

£longaiion  all  above  25  percent. 


In  the  basic  Bessemer  steel  over  90)(  was  below  0.06  phosphorus,  and  all 
were  below  0.10;  manganese  was  below  0.6  in  over  90^,  and  below  0.9  in  all ; 
sulphur  was  below  0.05  in  84)t,  the  maximum  being  0.071;  carbon  was  below 
0.10,  and  silicon  below  0.01  in  all.  In  the  basic  open-hearth  steel  phosphorus 
was  below  0.06  in  96jt.  the  maximum  being  0.08;  manganese  below  0.50  in  OTjt: 
sulphur  below  0.07  in  883(,  the  maximum  being  0.18.  The  carbon  ranged 
from  0.09  to  0.14. 

Iioir  Tensile  Strenctli  of  TeiT  Pure  Steel*— Swedish  nail-rod 
open-hearth  steel,  tested  by  the  author  in  1881,  showed  a  tensile  strength  of 
only  48,591  lbs.  per  sq.  in.  A  piece  of  American  nail-rod  steel  showed  46,081 
lbs.  per  sq.  in.  Both  steels  coutained  about  .10  carbon  and  .015  phosphorus, 
and  were  very  low  in  sulphur,  manganese,  and  silicon.  The  pieces  tested 
were  bars  about  2  x  ^  in.  section. 

lioyKT  Strenstli  Dae  to  Insnlllclent  HVork.  (A.  E.  Hunt, 
Trans.  A.  I.  M.  £7,  1886.)— Soft  steel  ingots,  made  in  the  ordinary  way  for 
boiler  plates,  have  only  from  10,UOO  to  20,000  lbs.  tensile  strength  per  eq.  in., 
an  elongation  of  only  about  10^  in  8  in.,  and  a  reduction  of  area  of  less  than 
20$,    Such  ingots,  properly  heated  and  rolled  down  from  10  In.  to  J^  in. 


STRENGTH  OF  BESSEMER  AND  OPEN-HEARTH  STEELS.  398 


Qomcation 

Reduction 

in  8  in. 

of  Area. 

Per  cent 

Per  cent. 

27 

62 

86 

50 

22 

4a 

f» 

49 

thickness,  will  f^ve  from  S5,000  to  65,000  lbs.  tensile  strengrth,  an  elongation 
in  8  in.  of  from  23jC  to  88j(,  and  a  reduction  of  area  of  from  65j<  to  10%.  Any 
work  stopping  short  of  the  above  reduction  in  thickness  ordinarily  yields  in* 
termediate  results  in  its  tenRile  tests. 

flardeiitiui:  of  Soft  Steel.— A.  E.  Hunt  (Trans.  A.  I.  M.  ^.,  1883,  vol. 
zii),  says  that  soft  8teel,  no  niatt«>r  how  low  in  carbon,  will  harden  to  a  cer- 
tain extent  upon  being  heated  red-hot  and  plunged  into  water,  and  that  it 
hardens  more  when  plunged  into  brine  and  less  when  quenched  in  oiL 

An  illustration  was  a  heat  of  open-hearth  steel  of  O.IS^  carbon  and  0.29jC  of 
manganese,  which  gave  the  following  results  upon  test-pieces  from  the  same 
^  in.  thick  plate. 

Maximum 

Load. 

lbs.  per  so.  in. 

Unhardened 55,000 

Hardened  in  water 74,000 

Hardened  in  brine 84,000 

Hardened  in  oil 67,700 

While  the  ductility  of  such  hardened  steel  does  hot  decrease  to  the  extent 
that  the  increased  tenacity  would  indicate,  and  is  much  superior  to  that  of 
normal  steel  of  the  high  tenacity,  still  the  greatly  increased  tenacity  after 
hardening  indicates  that  there  must  be  a  considerable  molecular  change  ih 
the  steel  thus  hardened,  and  that  if  such  a  hardening  should  be  created 
locallv  in  a  steel  plate,  there  must  be  very  dangerous  internal  strains  caused 
thereby. 

KITeei  of  €old  Rolllnfl:.— Ck>ld  rolling  of  iron  and  steel  increases  the 
elastic  limit  and  the  ultimate  strength,  and  decreases  the  ductility.  Major 
Wade*s  experiments  on  bars  rolled  and  polished  cold  by  Lauth^s  process 
showed  an  average  increase  of  load  required  to  give  a  slight  permanent  set 
as  follows :  Transverse,  16Sj(;  torsion,  130^;  compression,  \%\%  on  short 
columns  l\i  in.  long,  and  6l)(  on  columns  8  in.  long;  tension,  05j(.  The  hard- 
ness, as  measured  by  Ihe  weight  required  to  produce  equal  indentations, 
was  increased  503(;  and  it  was  found  that  the  hardness  was  as  great  in  the 
centre  of  the  bars  as  elsewhere.  Sir  W.  Falrbairn's  experiments  showed  an 
increase  in  ultimate  tensile  strength  of  50j(,  and  a  reduction  in  the  elongation 
in  10  in.  of  from  2  in.  or  20^,  to  0.i9  in.  or  7.9^. 

Comparlnon  of  Tests  of  Fall-size   Bye-lMirs  and  Sample 

Test-pleees  of  Same  Steel  Used  In  tbe  Memplils  Brldse. 

(Geo.  8.  Morison,  Trans.  A.  8.  C.  E.,  1898.) 


Full-Sized  Eyebars, 

Sample  Bars  from  Same  Melts, 

Sections  10"  wide  X 1  to  2  8/16" 

thick. 

about  1  in.  area. 

Reduc- 

Elongation. 

Max. 

Reduc- 

Elon- 

Elastic 

Max. 

tion  of 

Limit, 

Load, 

tion, 

gation, 

Limit, 

Load, 

Area, 

p.c. 

Inches. 

p.c. 

lbs.  per 

sq.  in. 

p.c. 

p.c. 

lbs.  per 

sq.  in. 

89.6 

20.2 

16.8 

85.100 

67,490 

47.5 

27.5 

\\-m 

78,050 

ae.T 

26.6 

8.2 

87,680 

70,160 

52.6 

24.4 

■i-v'fiO 

75.6-^ 

44.4 

86.8 

11.8 

89,700 

65,500 

47.9 

28.8 

3i.^.'J80 

70.280 

88.5 

88.5 

17.8 

88,140 

65,060 

47.5 

27.5 

^l.r«0 

78.050 

40.0 

82.5 

18.5 

82,860 

a^eoo 

44.5 

20.0 

M.750 

75.000 

88.4 

86.8 

15.8 

81,110 

61.060 

42.7 

28.8 

n:.J10 

69.730 

M.8 

82.9 

18.? 

33,990 

68,220 

52.2 

28.1 

^li-BO 

69,720 

82.6 

13.0 

13.5 

29,330 

63,100 

48.3 

28.8 

:!S.,)90 

71,300 

7.8 

208 

6.9 

28,080 

65,160 

432 

24.2 

2^,m 

70.220 

88.1 

28.9 

14.1 

29,670 

62,140 

69.6 

28.8 

40,aoo 

71,080 

31.8 

24.0 

11.8 

32.700 

65.400 

40.8 

25.0 

39,360 

69,360 

48.0 

39.4 

19.8 

80.500 

58,870 

40.8 

25.0 

40,910 

70,360 

10.8 

11.8 

12.8 

3:1360 

73,.^^ 

51.5 

25.5 

40,410 

69,900 

44.0 

82.0 

15.7 

82,520 

60,710 

43.6 

270 

40,400 

70.490 

46.0 

86.8 

14.0 

28.000 

68,7-^0 

44.4 

29.5 

40,000 

66,800 

41.8 

28.6 

18.1 

82,290 

6-,>,-,»T0 

42.8 

21  8 

40,530 

72,240 

41  « 

47.1 

16.1 

29,970 

5S,680 

45.7 

27.0 

40,610 

70,480 

The  average  strength  of  the  full-sized  eye- 
In.,  or  about]29t,  less  than  that  of  the  sample 


bai-8  was  about  8000  lbs.  per  sq. 
test-pieces. 


394  STEEL. 

TREATimBNT  OF  STRUCTURAIi  STBEI<« 

(James  Christie,  Trans.  A.  S.  C.  E.,  1893.) 

Effect  of  Panchlng  and  Sbearln^.—Tliere  is  no  doubt  that  steel 
of  higher  tensile  strength  than  is  now  accepted  for  structural  purpo««! 
should  not  be  punched  or  sheared,  or  that  the  softer  material  may  contain 
elements  prejudicial  to  its  use  however  treated,  but  especially  if  punched. 
But  extensive  evidence  is  on  record  indicating  that  steel  of  good  Quality,  in 
bars  of  moderate  thickness  and  below  or  not  much  exceeding  80.000  lbs. 
tensile  strength,  is  not  any  more,  and  frequently  not  as  much,  injured  as 
wrought  iron  by  ihe  process  of  punching  or  shearing. 

The  physlcil  effects  of  punching  and  shearing  as  denoted  by  tensile  test 
are  for  iron  or  steel: 

Reduction  of  ductility:  elevation  of  tensile  strength  at  elastic  limit;  reduc- 
tion of  ultimate  (ensile  strength. 

In  very  thin  material  the  superficial  disturbance  described  is  less  than  in 
thick;  in  fact,  a  degree  of  thinness  is  reached  where  this  disturbance  prac- 
tically ceases.  On  the  contrary,  as  thickness  is  increased  the  injury 
becomes  more  evident. 

The  effects  described  do  nor  invariably  ensue;  for  unknown  reasons  there 
are  sometimes  marked  deviations  from  wliat  seems  to  be  a  general  result. 

By  tho»*oughly  annealing  sheared  or  punch<>d  steels  the  ductility  is  to  a 
large  extent  restored  and  the  exaggerated  elastic  limit  reduced,  the  change 
being  modified  by  the  temperature  of  reheating  and  the  method  of  cooling. 

It  is  probable  that  the  best  results  combined  with  least  expenditure  can 
be  obtained  by  punching  all  holes  where  vital  strains  ai*e  not  transferred  by 
the  rivets;  and  by  reaming  for  important  joints  whei-e  strains  on  riveted 
Joints  are  vital,  or  wherever  perforation  may  reduce  sections  to  a  minimum. 
The  reaming  should  be  sufficient  to  thoroughly  remove  the  material  dfs- 
turbed  by  punching;  to  accomplish  this  it  isbest  to  enlarge  punched  holes 
at  least  >4m.  diameter  with  the  reamer. 

Rive  tins:*— It  is  the  current  practice  to  perforate  holes  1/16  in.  larger 
than  the  rivet  diameter.  For  work  to  be  reamed  it  is  also  a  usual  require- 
ment to  punch  the  holes  from  ^  to  8/16  in.  less  than  the  finished  diameter, 
the  boles  being  reamed  to  the  proper  size  after  the  various  parts  are 
assembled. 

It  is  also  excellent  practice  to  remove  the  sharp  corner  at  both  ends  of 
the  reamed  holes,  so  that  a  fillet  will  be  formed  at  the  junction  of  the  bodr 
and  head  of  the  finished  rivets. 

The  rivets  of  either  iron  or  mild  steel  should  be  heated  to  a  bright  red  or 
yellow  heat  and  subjected  to  a  pressure  of  not  less  than  50  tons  per  sauara 
Inch  of  sectional  area. 

For  rivets  of  ordinary  length  this  pressure  has  been  found  sufficient  to 
completely  fill  the  hole.  If,  however,  ti^e  holes  and  the  rivets  are  excep- 
tionally long,  a  greater  pressure  and  a  slower  movement  of  the  closing  txml 
than  is  used  for  shorter  rivets  has  been  found  advantageous  in  compelling 
the  more  sluggish  flow  of  the  metal  throughout  the  longer  hole. 

UTeldlnffa^No  welding  should  be  allowed  on  any  steel  that  enters  Into 
structures. 

Upsettlnit*— Enlarged  ends  on  tension  bars  for  screw-threads,  eyeCkars. 
etc.,  are  formed  by  upsetting  the  material.  With  proper  treatment  and  a 
sufficient  increment  of  enlarged  sectional  area  over  the  bodv  of  the  bar  the 
result  is  entirely  satisfactory.  The  upsetting  process  should  be  performed 
so  that  the  properly  heated  metal  is  compelled  to  flow  without  folding  or 
lapping. 

Anneallns:*— The  object  of  annealing  structural  steel  is  for  the  purpose 
of  securing  homogeneity  of  structure  that  is  supposed  to  be  impaired  by  un- 
equal heating,  or  by  the  manipulation  necessarily  attendant  on  certain  pro. 
cesses.  Tlie  objects  to  be  annealed  should  be  heated  throughout  to  a 
uniform  temperature  and  uniformly  cooled. 

The  physical  effects  of  annealing,  as  indicated  by  tensile  tests,  depend  on 
the  grade  of  steel,  or  the  amount  of  hardening  elements  associated  with  it; 
also  on  the  temperature  to  which  the  steel  is  raised,  and  the  method  or  rate 
of  cooling  the  heated  material. 

The  physical  effects  of  annealing  medium-grade  steel,  as  Indicated  by  ten- 
sile test,  are  reported  verv  differently  bv  different  observers,  some  claiming 
directlv  opposite  results  from  others.  It  is  evident,  when  all  the  attendant 
conditions  are  considei*ed,  that  the  obtained  results  must  vaiy  both  in  Idnd 
and  degree. 


TREATMENT  OF  STRUCTURAL  STEEL.  395 

The  temperatures  employed  will  vary  from  1000*  to  IGOO*  F. :  possibly  even 
a  wider  range  is  used,  in  some  cases  the  heated  steel  is  withdrawn  at  full 
temperature  from  the  furnace  and  allowed  to  cool  in  the  atmosphere  ;  in 
others  the  mass  is  removed  trom  the  furnace,  but  covered  under  a  muffle, 
to  lessen  the  free  radiation;  or.  again,  the  charge  is  retained  in  the  furnace, 
and  the  whole  mass  cooled  with  the  furnace,  and  more  slowly  than  by  either 
of  the  other  methods. 

The  best  general  results  from  annealing  will  probably  be  obtained  by  in- 
troducing the  material  into  a  uniformly-heated  oven  in  which  the  tempera- 
ture is  not  so  high  as  to  cause  a  possibility  of  cracking  by  sudden  and 
uoeqaal  changing  of  temperatui^e,  then  gradually  raising  the  temperature 
of  the  material  until  it  is  uniformly  about  ISOu*  F..  then  withdrawing  the 
material  after  the  temperature  is  somewhat  i*educed  and  cooling  under 
shelter  of  a  muffle,  sufficiently  to  prevent  too  free  and  unequal  cooling  ou 
tile  one  hand  or  excessively  slow  cooling  on  the  other. 

O.  6.  Mehrtens,  Trans.  A.  S.  C.  £.  ISaf,  says :  **  Annealing  is  of  advantage 
to  all  steel  above  64,000  lbs.  strength  per  square  inch,  but  it  is  questionable 
whether  It  is  necessary  in  softer  steels.  The  distortions  due  to  heating 
cause  trouble  in  subsequent  straightening,  especially  of  thin  plates. 

**  In  a  general  way  all  uoannealed  mild  steel  for  a  strength  of  56.000  to 
64,000  lbs.  majT  be  worked  in  the  same  way  as  wrought  iron.  Rough  treat- 
ment or  working  at  a  blue  heat  must,  however,  be  prohibited.  Shearing  is 
to  be  avoided,  except  to  prepare  rough  plates,  which  should  afterwards  be 
smoothed  by  machine  tools  or  files  oerore  using.  Drifting  is  also  to  be 
avriided,  because  the  edges  of  the  holes  are  thereby  strained  beyond  the 
yield  point.  Reaming  drilled  holes  is  not  necessary,  particularly  when 
sharp  drills  are  used  and  neat  work  is  done.  A  slight  countersinking  of  the 
e«lges  of  drilled  holes  is  all  that  is  necessary.  Working  the  material  while 
heated  should  be  avoided  as  far  as  possible,  and  the  engineer  should  bear 
this  in  mind  when  designing  structures.  Upsetting,  cranking,  and  bending 
ought  to  be  avoided,  but  wnen  necessary  the  material  should  be  annealed 
after  completion. 

"The  riveting  of  a  mild-steel  nvet  should  be  finished  as  quickly  as  pos- 
sible, befoi'e  It  cools  to  the  dangerous  heat.  For  this  reason  machine  work 
is  the  best.  There  is  a  special  advantage  In  machine  work  from  the  fact 
that  the  pressure  can  be  retained  upon  the  rivet  until  it  has  cooled  suffi- 
ciently to  prevent  elongation  and  the  consequent  loosening  of  the  rivet.'* 

Pmielftliis  and  Drilling  of  Steel  Plates.  (Froc.  Inst.  M.  E., 
Aug.  1887,  p.  3v'6.)— In  Prof.  Unwin's  report  the  results  of  the  greater  num- 
ber of  the  experiments  made  on  iron  and  steel  plates  lead  to  the  general 
conclusion  that,  while  thin  plates,  even  of  steel,  do  not  suffer  very  much 
from  punching,  yet  in  those  of  ^  in.  thickness  and  upwards  tbe  loss  of  te- 
nacity due  to  punching  ranges  from  10](  to  23%  in  iron  plates  and  from  1\%  to 
9i%  ill  the  case  of  mild  steel.  Mr.  Parker  found  the  loss  of  tenacity  in  steel 
plates  to  be  as  high  as  fully  one  third  of  the  original  strength  of  the  plate. 
In  drilled  plates,  on  the  contrary,  there  is  no  appreciable  loss  of  strength. 
It  is  even  possible  to  remove  the  bad  effects  of  punching  by  subsequent 
reaming  or  annealing. 

HForlLiiiic  Steel  at  a  Blae  Heat.— ^Not  only  are  wrought  iron  and 
steel  much  more  brittle  at  a  blue  heat  (i.e.,  the  heat  that  would  produce  an 
oxide  coating  ranging  from  light  straw  to  blue  on  bright  steel,  430*>  to  600<* 
F.),  but  while  they  are  probably  not  seriously  affected  by  simple  exposure 
to  blneness,  even  if  prolonged,  vet  if  they  be  worked  in  this  range  of  tern- 
perature  they  remain  extremely  brittle  after  cooling,  and  may  indeed  be 
more  brittle  than  when  at  blueness  :  this  last  point,  however,  is  not  certain. 
(Howe,  *•  Metallurgy  of  Steel,"  p.  634.) 

Tests  by  Prof.  iLrohn,  for  the  German  State  Railways,  show  that  working 
at  blue  heat  has  a  decided  influence  on  all  materials  tested,  the  injury  done 
being  greater  on  wrought  iron  and  harder  steel  than  on  the  softer  steel. 
The  fact  that  wrought  iron  is  injured  by  working  at  a  blue  heat  was  reported 
by  Stromeyer.    {Enqineering  New8^  Jan.  9,  W^i.) 

A  practice  among  boiler-makers  for  guarding  against  failures  due  to  work- 
ing at  a  blue  heat  consists  in  the  cessation  of  work  as  soon  as  a  plate  which 
had  been  red-hot  becomes  so  cool  that  the  mark  produced  by  rubbing  a 
hammer-handle  or  other  piece  of  wood  will  not  glow.  A  plate  which  is  not 
hot  enough  to  produce  this  effect,  yet  too  hot  to  be  touched  by  the  hand,  is 
most  probably  blue  hot,  and  should  under  no  circumstances  oe  hammered 
or  bent.    (C.  S.  Btromeyer,  Proc.  Inst.  C.  E.  1886.) 

Weldlns  of  Steel.^A.  E.  Hunt  (A.  I.  M.  £.,  1892)  says :  I  have  never 
aeen  ao-called  **  welded  "  pieces  of  steel  pulled  apart  in  a  testing-machine  or 


396 


STEEL. 


othenrlse  broken  at  the  joint  which  have  not  ehown  a  smooth  cleavage- 
plane,  as  it  were,  Ruch  as  in  iron  would  be  condemned  as  an  imperfect 
weld.  My  experience  iti  this  matter  leads  me  to  a^ree  with  the  position 
taken  by  Mr.  William  Metcalf  in  his  paper  upon  Steel  in  the  Trans.  A.  8. 
C.  B.,  vol.  zvi.,  p.  801.  Mr.  Metcalf  says,  *'  I  do  not  believe  steel  can  be 
welded." 

OH-temperiiifl:  and  Anneallnjc  of  Ste«l  Forsinca*— H.  F.  J. 
Porter  says  (isy7)tiiat  all  steel  fonj^ings  above  0.1%  carbon  nhould  be  an- 
nealed, to  relieve  them  of  forging;  and  annealing  strains,  and  that  the 
Srocess  of  annealing  reduces  the  elastic  limit  to  47jt  of  the  ultimate  strength. 
11  tempering  should  only  be  practised  on  thin  sections,  and  large  forgings 
should  be  hollow  for  the  purpose.  This  process  raises  the  elastic  limit 
above  iOi  of  the  ultimate  tensile  strength,  and  in  some  alloys  of  steel, 
notably  nickel  sreel.  will  bring  ir  up  to  00%  of  the  ultimate. 

Sydranllc  Forffinir  of  Steel.    (See  pages  618  and  610.) 

INFL17KNGB   OF  ANNBALINO   UPON   MAGNBTIO 
CAPACITY. 

Prof.  D.  E.  Hughes  (Eng'g,  Feb.  8, 1884,  p.  180)  has  invented  a  •*  Magnetic 
Balance,"  for  test^ig  the  condition  of  Iron  and  steel,  which  consists  chiefly  of 
a  delicate  magnetic  needle  suspended  over  a  graduated  circular  index,  and 
a  magnet  coil  for  magnetizing  the  bar  to  be  tested.  He  finds  that  the  fol- 
lowing laws  hold  with  every  variety  of  iron  and  steel : 

1.  The  majcnetic  capacity  is  directly  proportional  to  the  softness,  or  mo- 
lecular f  reeoom, 

S.  The  resistance  to  a  feeble  external  magnetizing  force  is  directly  as  the 
hardness,  or  molecular  rigidity. 

The  magnetic  balance  diows  that  annealing  not  only  produces  softness  in 
iron,  and  consequent  molecular  freedom,  but  it  entirely  frees  it  from  all 
strains  previously  introduced  by  drawing  or  hammering.  Thus  a  bar  of 
iron  drawn  or  hammered  has  a  peculiar  structure,  say  a  fibrous  one,  which 

eves  a  greater  mechanical  strength  in  one  direction  than  another.  This 
kr,  if  thoroughly  annealed  at  high  temperatures,  becomes  homogeneous  in 
all  directions,  and  has  no  longer  even  traces  of  its  previous  strains,  provided 
that  there  has  been  no  actual  separation  into  a  distinct  series  of  fibres. 

BflTect  of  Anneallns  upon  tike  Masnettc  Capacity  of 
IHAnsrent  Wlrea;  Teats  by  tbe  Ma^^netlc  Balance. 


Description. 

MagneUc  Capacity. 

Bright  as  sent. 

Annealed. 

Best  Swedish  charcoal  Iron,  first  variety. 
**          "            **          **      second    " 
••          ««            i»          u     tiiird      •' 

deg.  on  scale. 
S30 
2S6 
279 
165 
813 
IGO 
115 
50 

deg.  on  scale. 
525 
510 
503 
490 

Pudd  1  ed  Iron ,  best  beet 

840 

Bessemer  steel,  soft 

"     hard 

Crucible  fine  cast  steel 

891 

m 

84 

Crucible  Fine  Steel.  Temoered. 


Bright-yellow  heat,  cooled  comoletely  In  cold  water. 
Tellow-red  heat,  cooled  comDletely  in  cold  water. . . . 
Bright  yellow,  let  down  in  cold  water  to  straw  color. 

"  "        ♦»       "  «*        ••  blue 

"  *•       cooled  completely  In  on 

•»  "       let  down  in  water  to  wnue 

Reheat,  cooled  completely  m  water 

•'  "  "         ,"ou 

Annealed,    ** "  «*  ofl 


Magnetic 
Capacity. 


83 
43 
51 
58 
66 
7% 
84 


SPEOIFICATIONS  FOR  STEEL.  S97 

8PSIOIFICATIONS   FOR  STEBIi. 

Struct arml  fitteel*— There  has  been  a  cbanKe  during:  Uie  ten  years  from 
1880  to  1890,  in  the  opinions  of  engineers,  as  to  the  requirements  in  specifica* 
tions  for  structural  steel,  in  the  direction  of  &  prefen^nce  for  metal  of  low 
tensile  streufcth  and  great  ductility.  The  following  specifications  of  differ- 
ent dates  are  given  by  A.  E.  Hunt  and  G.  H.  Clapp,  Trans.  A.  I.  H.  E.  1890, 

TursioH  MBKBBB8.        1870.         1881.        1883.     1886.        1887.  1888. 

Elastic  limit 50,000  40(^45,000  40.000  40,000      40,000         88.000 

Tensile  strength 80.000  TOS^.OOO  70.000  70,000  07^75,000  63^70,000 

Elongation  in  8  in VH  i9%  1^       m  :iOfi  Otfi 

ReducUon  area S0j(  aO](  45^       429(  42]t  46% 

Kind  of  steel O.H.  O.H.  or  B.  O.H.    Not   O.H.  or  B.  O.H.or  B. 

OOKPRKSSIOM   MXHBESS:  ^^' 

fiiastio  limit Same  50^56,000  60,000  80,000  Same  as  tension 

Tensile  strength as  80^90,000  80,000  80.0^0  members. 

Elongation  in  8  in ten-  iftji  15%       1R%  '* 

Reduction  area sion.        W  SSjt       85j( 

F.  H.  Lewis  (Iron  Age,  Nov.  8, 1892)  says:  Regarding  steel  to  be  used  under 
the  same  conditions  as  wrought  iron,  that  is,  to  be  punched  without  ream- 
ing, there  seems  to  be  a  decided  opinion  (and  a  growing  one)  among  engi- 
neers, that  it  Is  not  safe  to  use  steel  in  this  wav,  when  the  ultimate  tensile 
8iren^:th  is  above  65,000  lbs.  The  reason  for  tnis  is,  not  so  much  because 
there  is  any  marlced  change  in  the  material  of  this  grade,  but  because  all 
steel,  especially  Bessemer  steel,  has  a  tendency  to  segregations  of  carbon 
and  phosphorus,  producing  places  in  the  metal  which  are  narder  than  they 
normally  should  be.  As  long  as  the  percentages  of  carbon  and  phosphorus 
are  kept  low,  the  effect  of  tnese  segregations  is  inconsiderable;  but  when 
these  percentages  are  increased,  the  existence  of  these  hard  spots  in  the 
metal  oecomes  more  marked,  and  it  is  therefore  less  adapted  to  the  treat- 
ment to  which  wrought  iron  is  subjected. 

There  is  a  wide  consensus  of  opinion  that  at  an  ultimate  of  04,000  to  65,000 
lbs.  the  percentages  of  carbon  and  phosphorus  (which  are  the  two  harden- 
ing elements)  reach  a  point  where  the  steel  has  a  tendency  to  become  tender, 
and  to  crack  when  subjected  to  rough  treatment. 

A  grade  of  steel,  therefore,  running  in  ultimate  strength  from  64,000  to 
63,000  lbs.,  or  in  some  cases  to  64.000  lbs.,  is  now  generally  considered  a 
proper  material  for  this  class  of  work. 

Millard  Hunsicker,  engineer  nf  testts  of  Carnegie,  Phipps  &  Co.,  writes  as 
follows  concerning  grades  of  structural  steel  (Ent/'g  Neioa^  June  2,  180'if): 

Grade  of  Steel.— ^teel  shall  be  of  three  gi  aden— xof  t,  medium,  high. 

Soft  Steel.— Hp**<^meus  from  finished  materiul  fui- tent;,  cut  to  size  speci- 
fied above,  shall  have  an  ultimate  streugtli  of  from  64,000  to  6-2.000  lbs.  per 
sq.  in.;  elastic  limit  one  half  the  ultimate  strength:  minimum  elongation  of 
d^  in  8  in.;  minimum  reduction  o(  area  at  fracture  50%.  This  grade  of 
steel  to  bend  cold  180°  flat  on  itself,  without  sign  of  fracture  on  the  outside 
of  the  bent  portion. 

Medium  5(e<rZ.— Spedinens  from  finished  material  for  test,  cut  to  size 
specified  above,  shall  have  an  ultimate  strength  of  60,000  to  68,000  lbs.  per 
sq.  in.:  elastic  limit  one  half  the  ultimat*^  strength;  minimum  elongation  20% 
in  8  in.;  minimum  reduction  of  area  at  fracture.  40)(.  This  grade  of  steel 
to  bend  cold  180<*  Co  a  diameter  equal  to  the  thickness  of  the  piece  tested, 
without  crack  or  flaw  on  the  outHide  of  the  bent  portion. 

Hu/h  SteW.— Specimens  from  finished  marerfaf  for  test,  cut  to  sise  speci- 
fied above,  shall  have  hu  ultimate  strength  of  66  000  to  74.000  lbs.  per  sq.  in.: 
elastic  limit  one  half  the  ultimate  ntreogth;  minimum  elongation.  18%  In  8 
in.;  minimum  reduction  of  area  at  fracture,  86^.  This  grade  of  steel  to  bend 
cold  iSXy*  to  a  diameter  equal  to  three  times  the  thickness  of  the  test-piece, 
without  crack  or  flaw  on  th**  outside  of  the  bent  portion. 

F.  H.  Lewis,  Engineers*  Club  of  Phila.,  1891,  gives  specifications  for  stnic- 
toral  steel  as  follows:  Tlie  phosphorus  in  acid  open-hearth  steel  must  be 
leas  than  0A0%.  and  in  all  Bessemer  or  basic  steel  must  be  less  than  O.QS%. 

The  material  will  be  tested  in  specimens  of  at  least  one  half  square  inch 
section,  cut  from  the  finished  material.  Each  melt  of  steel  will  be  tested 
and  each  section  rolled,  and  also  widely  differing  gauges  of  the  same  section. 


398  STEEL. 

Bequlrements.  Soft  Steel.  Medium  Steel 

Elastic  limit,  lbs.  per  sq.  In. ,  at  least 82.000  85,000 

TJitimate  strent^th,  lbs.  per  sq.  in 64,000  to  82,000  60,000  to  70,000 

Elonfiration  in  8  in.,  at  least 25j(  iO% 

Reduction  of  area,  per  cent,  at  least 45%  40% 

In  soft  steel  for  web-plates  over  86  in.  wide  the  elongation  will  be  reducea 
to  90%  and  tlie  reduction  of  area  to  40%. 

It  must  bend  cold  180  degrees  and  close  down  on  itself  without  cracking 
on  the  outside. 

^inch  holes  pitched  9i  inch  from  a  roll-finished  or  machined  edge  and  S 
inches  between  centres  must  not  crack  the  metal;  and  ^-inch  holes  pitched 
1^  inches  between  centres  and  1^  inches  from  the  edge  must  not  split  the 
metal  between  the  holes. 

Medium  steel  must  bend  180  degrees  on  itself  around  a  lU-inch  round  bar. 

Full-sized  eye-bni-8,  when  tested  to  destruction,  must  show  an  ultimate 
strength  of  at  least.  56,000  lbs.,  and  stretch  at  least  \0%  in  a  length  of  10  feet. 

A.  E.  Hunt,  in  discussing  Mr.  Lewis's  specifications,  advises  a  requirement 
as  to  the  character  of  the  fracture  of  tensile  tests  being  eoiirely  silky  in 
sections  of  less  than  7fiquare  inches,  and  in  larger  sections  the  test  specimen 
not  to  contain  over  26%  crystalline  or  granular  fracture.  He  also  advises 
the  drifting  test  as  a  requirement  of  both  soft  and  medium  steel;  the  require- 
ment being  worded  about  as  follows:  **  Steel  to  be  capable  of  having  a  nole. 
punched  for  a  ^"  rivet,  enlarged  by  blows  of  a  sledge  upon  a  drift-pin 
until  the  hole  (which  in  the  fintt  case  should  be  punched  lU'' from  the  roll- 
finish  or  machined  edge)  is  1^'*  diameter  in  the  case  of  soft  steel,  and  1^" 
diameter  in  the  case  of  medium  steel,  without  fracture.'*  This  drifting  test 
is  an  excellent  requirement,  not  only  as  a  matter  of  record,  but  as  a  mea» 
ure  of  the  ductility  of  the  steel. 

H.  H.  Campbell,  Trans.  A.  I.  M.  E.  1808,  says:  In  adhering  to  the  safest 
course,  engineers  are  continually  calling  for  a  metal  with  lower  phosphorus 
The  limit  has  been  0.10^;  it  is  now  0.0B%\  soon  it  will  be  O.OBi%;  it  should  he 
0.01^. 

A.  B.  Hunt,  Trans.  A.  I.  M.  E.  1893,  says:  Why  should  the  tests  for  steel 
be  so  much  more  rigid  than  for  iron  destined  for  the  same  purpoee  f  Sonit* 
of  the  reasons  are  as  follows:  Experience  shows  that  the  acceptable  quali- 
ties of  one  melt  of  steel  offer  no  absolute  guarantee  that  the  next  melt  to  it, 
even  though  made  of  the  same  stock,  will  be  equally  satisfactory. 

Again,  good  wrought  iron,  in  plates  and  angles,  has  a  narrow  range  (from 
85,000  to  37,000  lbs.)  in  elastic  limit  per  square  inch,  and  a  tensile  strenftth  of 
from  46,000  to  5^,000  lbs.  per  squara  inch;  whereas  for  steel  the  range  in 
elastic  limit  is  from  27,000  to  80,000  lbs.,  and  in  tensile  strength  from  48,000  to 
120,000  lbs.  per  square  inch,  with  corresponding  variations  in  ductility. 
Moreover,  steel  is  much  more  susceptible  than  wrought  iron  to  widely  vary- 
ing effects  of  treatment,  by  hardening,  cold  rolling,  or  overheating. 

It  is  now  almost  universally  recognised  that  soft  steel,  if  properly  made 
and  of  good  quality,  is  for  many  purposes  a  safe  and  satisfactory  substitute 
for  wrought  Iron,  being  capable  of  standing  the  same  shop-treatment  as 
wrought  iron.  But  the  conviction  is  equally  general,  that  poor  steel,  or  an 
unsuitable  grade  of  steel,  is  a  very  dangerous  substitute  for  wrought  iron 
even  under  the  same  unit  strains. 

For  tills  reason  it  is  advisable  to  make  more  rigid  requirements  in  select- 
ing material  which  may  range  between  the  brittleness  of  glass  and  a  due- 
tilitv  ffre«ter  than  that  of  wrought  iron. 

Speelflcatlons  for  Steel  for  tlie  HVorld's  Fair  lialldlns*« 
Clfticasro,  1898.— No  steel  shall  contain  more  than  .09%  of  phosphorus. 
From  three  separate  ingots  of  each  cast  a  round  sample  bar,  not  less  than 

?$  in.  in  diameter,  and  having  a  length  not  less  than  twelve  diameters  be- 
ween  jaws  of  testing  machine,  shall  be  furnished  and  tested  by  the  manu- 
facturer. From  these  test-pieces  alone  the  quality  of  the  material  in  the 
steel  works  shall  be  determined  as  follows: 

AW  the  test-bars  must  have  a  renKUe  strength  of  from  60.000  to 68, (XX>Ih8.  per 
square  inch,  an  elastic  limit  of  not  less  than  half  the  tensile  strength  of  the 
test-bar.  an  elongation  of  not  less  than  24^,  and  a  reduction  of  area  of  not 
less  than  403<  at  the  point  of  frartui-e.  In  determining  the  ductilltv.  the  elon- 
gation shall  h*»  measured  after  breaking  on  an  original  length  of  ten  times 
th*»  shortest  dimension  of  the  test-piece. 

Rivet  steel  shall  have  a  tensile  strength  of  from  52.000  to  68,000  lbs.  per 
square  hich,  and  an  elastic  limit,  elongation,  and  reduction  of  Area  at  the 


SPECIFICATIOXS  POB  STEEL. 


899 


poiiit  of  fracture  as  stated  above  for  test-bars,  abd  be  capable  of  bending 
double  flat,  without  sign  of  f ractura  oa  the  convex  surface  of  the  bend. 

Boiler,  Slilp,  and  Tank  Plates*  W.  F.  Mattes  (Iron  Ape,  Jul7 
9, 1898)  recommends  that  the  different  qualities  of  steel  plates  be  cuissifled 
as  follows : 


Tensile  test,  loni^tudinal 

coupon , 

Elongation  in  8-in.  lon^tu 

dinal  coupon,  percent.. .. 
Bending   test,  longitudinal 

coupon 

Bending  test,  transverse 

coupon 

Phosphorus  limit 

Sulphur  limit 

Surface  Inspection 


Tank. 


Limit, 
75,000 


0.15 
Easy. 


Ship. 


j     56.000 
1  to  65,000 

90 

Flat. 
( Over  1  in. 
{     diam. 

0.10 

{  Careful. 


Shell. 


j     55,000 
1  to  65,000 

Flat 

(OverHiu. 

1     diam. 
0.06 
0.065 
Close. 


Fire-box. 


J     55.000 
1  to  60,000 

25 

Flat. 

}■    FI»t. 

0045 
O.O) 
Rigid. 


A  steel-manufacturing  firm  in  Pittsbui-gh  adveKises  six  different  grades 
of  steel  as  foUovrs  : 
Extra  fire-box.       Fire-box.       Extra  flange.       Flange.       Shell.       Tanlt. 

The  probable  average  phosphorus  content  in  these  grades  is,  respectively: 

Different  speciflcatloiis  for  steel  plates  are  the  following  0888) : 

United  States  .yavy.—Shell :  Tensile  strength,  68,000  to  67,000  lbs.  per  sq. 
in.;  elongation,  ^S%  in 8-in.  transvei-se section, 85^  in  8-in.  longitudinalseetion. 

Flange :  Tensile  strength,  50,000  to  58,000  lbs. ;  elongation.  86)(  in  8  inches. 

Chemical  requirements :  P.  not  over  .035j£ ;  S.  not  over  .040^. 

Cold-bending  test :  Specimen  to  stand  being  bent  flat  on  itself. 

Qnenching  test :  Steel  heated  to  cherry-red.  plunged  in  water  83«  F.,  and 
to  be  bent  around  curve  1^  times  thick uess  of  the  plate. 

BritUti  Admiralty.^TenaAle  strength,  58,240  to  67,900  lbs.;  elongation  in 
8  In.,  20%  ;  same  cold-bending  and  quenching  tests  as  U.  S.  Navy. 

Amet-ican  Boiler-makerg^  AaaoctcUion.—TensUQ  stren|»th,  55.000  to  65,000 
lbs.;  elongation  in  8  in.,  20%  for  plates  %  in.  thick  and  under  ;  2i6%  for  plates 
9^  in.  to  9^  in. ;  26%  for  plates  H  in.  and  over. 

Cold-bending  test :  For  plates  ^  in.  thick  and  under,  ppeciraen  must  bend 
back  on  itself  without  fracture  ;  for  plates  over  ^  in.  thick.  Bpecimen  must 
withstand  bending  180^  around  a  mandril,  1^  times  the  tnickness  of  the 
plate. 

Chemical  requirements  :  P.  not  over  .040^ ;  8.  not  over  .080^. 

American  Shipmastere^  .^uociafton.—Tensile  strength,  6:^,000  to  79,000 
lbs.;  elongation,  16^  on  pieces  9  in.  long. 

^rips  cut  from  plates,  heated  to  a  low  red  and  cooled  in  water  the  tem- 
perature  of  which  is  89**  F.,  to  undergo  without  crack  or  fracture  being 
doubled  over  a  curve  the  diameter  of  which  does  not  exceed  three  times 
the  thickness  of  the  piece  tested. 

Boiler  8hell«platea«  Front  Tube-plate,  and  Butl-atrlpa* 
(Penna.  R.  B.,  1899.)— The  metal  desired  is  a  homogeneous  steel  having  a 
tensile  strength  of  60,000  lbs.  per  sq.  in.,  and  an  elongation  of  95^  in  a 
section  originally  8  in.  long.  These  plates  will  not  be  accepted  if  the  test- 
piece  shows— 

1.  A  tensile  strength  of  less  than  55,000  Ibn.  per  sq.  in.-;  9.  An  elongation 
in  section  originally  8  in.  long  less  tlian  90% ;  8.  A  tensile  strength  over 
6.000  lbs.  per  sq.  in. :  should,  however,  the  elongation  be  27%  or  over,  plates 
will  not  he  rej»'cted  for  hi(rh  strength. 

Inaide    Fire«-1>ox   Plates,    Inclndlns  Back    Tube-plate* 
(Penna.  R.  R..  18i».)— The  metal  should  show  a  tensile  strength  of  t)0,000  lbs. 
persq.  in.,  and  an  elongation  of  28%  in  a  test  section  originally  8  in.  long. 
Chemical  Composition.  Desired.  Will  be  Rejected. 

Carbon 0.18  per  cent.       pver  0.95,  below  0.15 

Phosphorus,  not  above 0.03       **  over  0.0 1 

Manganeso.  not  above 0. 10       "  over  0.55 

Silicon,  not  above 0.02       "  over  0.04 

Sulphur,  not  above 0.09       ' '  over  0  05 

Copper,  not  above 0.03       "  over0.06 


400  STEEL. 

These  plates  will  not  be  accepted  If  the  test-piece  shows :  1.  A  tensile 
fltrenKth  of  less  than  55.000  lbs.  per  sq.  In.;  2.  An  elongation  in  section 
originally  8  in.  loni?,  JesM  tliati  2:i%  {iO%  In  plates  ^  inch  thick) ;  S.  A  teDs«ile 
stranicth  over  05,000  lbs.  per  sq.  in.  (68,000  for  plates  ^  in.  thick);  slinuld, 
however,  the  elimination  bv  iV)%  or  over,  plates  will  not  be  rejected  for  hi^h 
strenf^th  ;  4.  Any  single  Keani  or  cavity  more  than  ^  in.  long  In  either  of  the 
three  fractures  obtained  on  lest  for  liomogeneity,  as  described  below. 

Homogeneity  test :  A  portion  of  the  test-piece  is  nicked  with  a  chisel,  or 
grooved  on  a  machine,  transversely  about  a  sixteenth  of  an  Inch  deep,  in 
three  places  about  1>4  in.  apart.  The  first  groove  should  be  madn  on  one 
side,  U4  In.  from  the  squara  end  of  the  piece;  the  second,  1^  in.  from 
it  on  the  opposite  side;  and  the  third,  m  in.  from  the  last,  and  on  the 
opposite  side  from  it.  The  test-piece  is  then  put  in  a  vise,  with  the  first 
groove  about  ^  in.  above  the  jaw,  care  being  taken  to  hold  it  flrnily. 
'I^e  projecting  end  of  the  test-piece  is  then  broken  oflT  by  means  of  a  ham- 
mer, a  number  of  light  bloivs  being  used,  and  the  bending  being  away 
from  the  groove.  The  piece  is  broken  at  the  other  two  grooves  In  the  xaroe 
way.  The  object  of  this  treatment  is  to  open  and  render  visible  to  the  eye 
any  seams  due  to  failure  to  weld  up,  or  to  foreign  interposed  matter,  or 
cavities)  due  to  gas  bubbles  in  the  ingot.  After  rupture,  one  side  of  each 
fracture  Is  examined,  a  pocket  lens  being  used  if  necessary,  and  the  length 
of  the  seams  and  cavities  Is  determined.  The  length  of  the  longest  seam  or 
cavity  determines  the  acceptance  or  rejection  of  the  plate. 

Dr.  C.  B.  Dudley,  chemist  of  the  Penna.  R.  R.  (Trans.  A.  I.  M.  E.  18W,  vol. 
XX.  p.  709),  gives  as  an  example  of  the  progressive  Improvement  in  spedfl- 
cations  the  following :  In  the  early  days  of  Rteel  boilers  the  specification  in 
force  called  for  steel  of  not  lefw  than  50,000  lbs.  tensile  strength  and  not  less 
than  85^  elongation.  Some  metal  was  received  having  75.000  lbs.  tensile 
strength,  and  aa  the  elongation  was  all  right  it  was  accepted ;  but  when  those 
plates  were  being  flanged  in  the  holleivshon  they  cracked  and  went  to 
pieces.  As  a  result,  an  upper  limit  of  65,(100  lbs.  tensile  strength  was 
established. 

Am.  Ry.  Master  Mechanics''  Absiv.,  189l.~45ame  as  Penna.  R.  R.  Spedflca- 
tions  of  1892,  including  homogeneity  test. 

Plate,  Tank,  and  Sbect  Steel.  (Penna.  R.  R.,  1888.*)— A  test  strip 
taken  lengthwise  of  each  plate,  %  in.  thick  and  over,  without  annealing, 
should  have  a  tensfle  strength  of  60,000  lbs.  per  sq.  in.,  and  an  elongation  of 
25jt  in  a  section  originally  Sin.  long. 

Sheets  will  not  be  accepted  if  the  tests  show  the  tensile  strength  less  than 
55.000  ll)S.  or  greater  than  70,000  lbs.  per  sq.  in.,  nor  if  the  elongation  fails 
below  an^.  . 

Steel  Billets  for  Main  and  Parallel  Kods.  (Penna.  R.  R.,  1884.) 
^One  billei  from  each  lot  of  '^  billettt  or  smaller  Khipment  of  steel  for  main 
or  parallel  rods  for  locomotives  will  have  a  niece  drawn  from  it  under  the 
hammer  and  a  test-section  will  be  turned  down  on  this  piece  to  H  !"•  in 
diameter  and  2  in.  long.  Such  test-piece  should  show  a  tensile  strength  of 
&5,000  lbs.  and  an  elongation  of  \:y%. 

No  lot  win  be  acceptable  if  the  test  shows  less  than  80,000  lbs.  tensile 
strength  nrlit;  e  ongatinn  in  2  in. 

Ijoromotlve  Spring  Steel.  (Penna.  R.  R.,  1887.)— Bars  which  vary 
ni'  rn  thnn  0.01  in.  in  thickness,  or  more  than  0  02  in.  in  width,  from  the  slsa 
ordered,  or  which  break  where  they  are  not  nicked,  or  which,  when  properly 
rirke<l  and  held,  fail  to  break  square  across  where  they  are  nicked,  will  he 
returned.  The  metal  desired  has  the  following  composition:  Carbon,  l.OOjJ; 
manganese,  0.25^;  phosphorus,  not  over  0.03^;  silicon,  not  over  O.ISJC;  sul- 
phur, not  over  0M%\  copper,  not  over  O.WJjC. 

Siiipinents  will  not  be  accepted  which  show  on  analysis  less  than  0  90^  or 
over  1.10:<  of  carbon,  or  over  0.50;^  of  manganese,  O.OPjC  of  phosphorus,  0.25^ 
of  silicon.  O.O.'jg  of  sulphur,  and  0.0,")?^  of  copper. 

Steel  for  Locomotive  OriTlne^axIes.  (Penna.  R.  R.,  1888.)— 
Steel  for  driving-axles  sbouUl  have  a  lensile  strengih  of  85,000  lbs.  per  sq.  in. 
and  an  elongation  of  \^i%  in  section  originally  2  in.  long  and  %  in.  diameter, 
taken  midway  between  centre  and  circumference  of  the  axle. 

Axles  will  not  be  accepted  if  tensile  strength  is  less  than  80,000  lbs.,  nor  if 
elontratlon  Is  below  Vii, 

Steel  for  Crank-plnii.    (Penna.  R.  R.,  1886.)— 8t«>el  ingots  for  crank- 

*  The  Penna.  R.  R.  specifications  of  the  several  dates  given  are  still  In  force. 


SPECIFICATIONS  FOR  STEEL.  401 

fdiis  must  be  swaged  as  per  drawiogn.  For  each  lot  of  60  ingots  ordered,  51 
must  be  furnished,  from  which  one  will  be  taken  at  random,  and  two  pieces, 
with  test  sections  ^  in.  diameter  and  2  in.  long,  will  be  cut  from  any  part  of 
it,  provided  that  centre  line  of  test-pieoes  falls  I^  in.  from  centre  line  of  in- 
got. Such  test-pieces  should  have  a  tensile  strength  of  86,000  lbs.  per  sq.  in. 
and  an  elongation  of  lb%.  Ingots  will  not  be  accepted  if  the  tensile  strength 
is  le»  than  60,000  lbs.  nor  if  the  elongation  is  below  Vif. 

Dr.  Chas.  B.  Dudler,  Chemist  of  the  P.  R.  R.  (Trans.  A.  I.  M.  E.  1802).  re- 
ferring to  this  SDeclflcatlon,  says :  In  testing  a  recent  shipment,  the  piece 
from  one  side  of  the  phi  showed  88,000  lbs.  strength  and  itzi  elongation,  and 
the  piece  from  the  opposite  side  showed  106,000  lbs.  strength  and  \4%  elonga- 
tion. Each  piece  was  above  the  specified  strength  and  ductility,  but  the 
lack  of  uniformity  between  the  two  sides  of  the  pin  was  so  marked  that  it 
was  flnallT  determined  not  to  put  the  lot  of  50  pins  in  use.  To  guard  against 
trouble  of  this  sort  in  future,  the  specifications  are  to  be  amended  to  require 
that  the  dilTerence  in  ultimate  strength  of  the  two  specimens  shall  not  be 
more  than  DOOO  lbs. 

Steel  Car^mxles*  (Penna.  R.  R.,  1801 )— For  each  100  axles  ordered  101 
must  be  furnished,  from  which  one  will  be  taken  at  random,  and  subjected 
to  tests  prescribed. 

Axles  for  passenger  cars  and  passenger  locomotive  and  tender  tnicks 
must  be  made  of  steel  and  be  rough  turned  throughout.  Two  test-pieces 
will  be  cut  from  an  axle,  and  the  test  sections  of  %  in.  diameter  by  2  in.  long 
may  fall  at  any  part  of  the  axle  provided  that  the  centre  line  of  the  test- 
section  is  1  In.  from  the  centre  line  of  the  axle.  Such  test-pieces  should  have 
a  tensile  strength  of  80,000  lbs.  per  sq.  in.  and  an  elongation  of  20%.  Axles 
will  not  be  accepted  if  the  tensile  strength  is  less  than  75,000  lbs.  or  the 
elongation  below  16j(,  nor  if  the  fractures  arc  irregular. 

Axles  for  freight  cars  and  freight-locomotive  tender  tnicks  must  be  made 
of  steel,  and  will  be  subjected  to  the  following  test,  which  they  must  stand 
without  fracture : 

AxuB  4  IN.  DiAM CTKB  AT  CKNTBB  —  Five  blows  at  20  ft.  of  a  1640-Ib.  weight, 
striking  midway  between  supports  8  ft.  apart;  axle  to  be  turned  over  after 
each  blow. 

AZLBs49^iN.  DiAMBTKR  AT  CBKTRE— Five  blows  at  25  ft.  of  a  1640-lb.  weight, 
striking  midway  between  supports  8  ft.  apart:  axles  to  be  turned  over  after 
each  blow. 

Steel  ror  Ral1««— P.  H.  Dudley  (Trans.  A.  S.T?.  E.  1898)  recommends 
the  following  chemical  composition  for  I'ails  of  the  weights  specified  : 

Weights  per  yard 60,  65,  and  70  lbs.       75  and  80  lbs.     100  lbs. 

Carbon 45  to  .55)(  .60  to  .60j(         .66  to  .75^ 

For  all  weights:  Manganese,  .90%  to  1.00%;  silicon,  .lOjl  to  .16^;  phos- 
phoru8»  not  over  .0G%\  sulphur,  not  over  .07jt. 

Carbon  by  itself  up  to  or  over  1%  increases  the  hardness  and  tensile  strength 
of  the  Iron  rapidly,  and  at  the  same  time  decreases  the  elongation.  The 
amount  of  carbon  in  the  early  rails  ranged  from  0.26  to  0.6  of  1^.  while  in 
recent  rails  and  very  heavy  sections  it  has  been  increased  to  0.6,  0.6,  and  0.76 
of  1%.  With  good  irons  and  suitable  sections  it  can  run  from  0.65  to  0.75  of 
1%,  according  to  the  section,  and  obtain  flne-graiu  tough  rails  with  low 
phosphorus. 

Manganese  is  a  necessary  ingredient  in  the  first  place  to  take  up  the  oxide 
of  Iron  formed  in  the  bath  of  molten  metal  during  the  blow.  It  also  is  of  great 
assistance  to  check  red  shortness  of  the  ingots  during  the  first  passes  in 
the  blooming  train.  In  the  early  rails  0.4  to  0.6  of  1%  was  sufHcient  when 
the  ingots  were  hammered  or  the  reductions  in  the  passes  in  the  trains  were 
very  much  lighter  than  to  day.  With  the  more  rapid  rolling  of  recent  years 
the  manganese  is  very  often  increased  to  1.25^  to  1.5j(.  It  makes  the  rails 
hard  with  a  coarse  crystallization  and  with  a  decided  tendency  to  brittleness 
Rails  high  in  manganese  seem  to  flow  quite  easily,  esT>ecially  under  severe 
service  or  the  use  of  sand,  and  oxidize  rapidly  in  tunnels.  From  0.80  to  l.OOjC 
seems  to  he  all  that  is  necessary  for  good  rolling  at  the  present  time. 

Steel  BiTets*  (H.  C.  Torrance,  Amer.  Boiler  Mfrs.  Assn.,  1890.)— The 
Government  requirements  for  the  rivets  used  in  l)oilerR  of  the  cruisers  built 
hi  1800  are :  For  longitudinal  seams,  68,000  to  67.000  lbs.  tensile  strength; 
elongation,  not  less  than  20^  in  8  in.,  and  all  others  a  tensslle  strength  of 
60,000  to  66,000  lbs.,  with  an  elongation  of  not  less  than  80^.  They  shall  lie 
capable  of  being  fbittened  out  cold  under  the  hammer  to  a  thickness  of  one 
bfllf  tike  diameter,  and  of  being  flattened  out  hot  to  a  thkskness  of  one  third 


402  STEEL. 

the  diameter  without  uliowine  cracks  or  flawft.    The  steel  must  not  contain 
more  than  .035  of  1%  of  phospnonis,  nor  more  than  .04  of  i%  of  sulphrr. 

A  lot  of  20  successive  tests  of  rivet  steel  of  the  low  tensile  s trench  quality 
and  12  tests  of  the  higher  tensile  strength  gave  the  following  results : 

Low  Steel.  Higher. 

Tensile  strength,  lbs.  per  sq.  in . . .    51,830  to  54,100       69.100  to  Gl  ,850 

Elastic  limit,  lbs.  per  sq.  in 31,050  to  83,190       33,060  to  83,070 

Elongation  in  8  in.,  per  cent 80.5  to  85.^  28.5  to  81.75 

Carbon,  per  cent 11  to  .14  .l6to.l8 

Phosphorus 0*^7  to  .029  .08 

Sulphur ai8to.036  .068  to  .085 

The  safest  steel  rivets  are  those  of  the  lowest  tensile  strength,  since  they 
are  the  least  liable  to  become  hardened  and  fractura  by  hammeriuf?.  or  to 
break  from  repeated  concussive  and  vibratory  strains  to  which  they  are 
subjected  in  practice.  For  calculations  of  the  strength  of  riveted  joints  the 
tensile  strength  may  be  taken  as  the  average  of  the  figures  above  giveu,  or 
62,665  lbs.,  and  the  shearing  strength  at  45,000  lbs.  per  sq.  in. 

MISCELLANBOIJS  NOTB8  ON  STBBIi. 

May  Carbon  be  Burned  Ont  of  Steel  ?— Experiments  made  at 
the  Laboratory  of  the  Penna.  Railroad  Co.  (Specifications  for  Springs,  1888) 
with  the  steel  of  spiral  springs,  show  that  the  place  from  which  the  borings 
are  taken  for  analysis  has  a  very  important  influence  on  the  amount  of  car- 
bon found.  If  the  sample  is  a  piece  of  the  round  bar,  and  the  borings  are 
taken  from  the  end  of  this  piece,  the  carbon  is  always  higher  than  if  the 
borings  are  taken  from  the  side  of  the  piece.  It  is  common  to  find  a  differ* 
ence  of  0.10^  between  the  centre  and  side  of  the  bar,  and  in  some  cases  the 
difference  is  as  high  as  O.S9%.  Furthermore,  expei-inients  made  with  samples 
taken  from  the  drawn  out  end  of  the  bar  show,  usually,  less  carbon  tnau 
samples  taken  from  the  round  part  of  the  bar,  even  though  the  borings  may 
be  taken  out  of  the  side  in  both  cases. 

Apparently  during  the  process  of  reducing  the  meial  from  the  ingots  to  the 
round  bar,  with  successive  heatings,  the  carbon  in  the  outside  of  the  bar  is 
burned  out. 

*^  Recalescence  "  of  Steel.—If  we  heat  a  bar  of  copper  by  a  flame 
of  constant  strength,  and  note  carefully  the  interval  of  time  occupied  in 
passing  from  each  degree  to  the  next  higher  degree,  we  And  that  ihese  in- 
tervals increase  regularly,  i  e.,  that  the  bar  heats  more  and  more  slowly,  as 
its  temperature  approaches  that  of  the  flame.  If  we  substitute  a  bar  of 
steel  for  one  of  copper,  we  And  that  these  intervals  increase  regularly  up  to 
a  certain  point,  when  the  rise  of  temperature  is  suddenly  and  in  most  caaea 
greatly  retarded  or  even  completely  arrested.  After  this  the  regular  rise  of 
temperature  ix  resumed,  though  other  like  retardations  may  recur  as  the 
temperature  rises  farther.  So  if  we  cool  a  bar  of  steel  slowly  the  fall  of 
tempeniture  is  greatly  retarded  when  Jt  reaches  a  certain  point  In  doll  red- 
ness. If  the  steel  contains  much  carbon,  and  if  certain  favoring  conditions 
be  maintained,  the  temperature,  after  descending  regularly,  suddenly  rises 
spontaneously  very  abruptly.,  remains  stationary  a  while,  and  then  rede- 
Bcends,    This  spontaneous  reheating  is  known  as  "  recalescence.'* 

These  retardations  indicate  that  some  change  which  absorbs  or  evolves 
heat  occurs  within  the  metal.  A  retardation  while  the  temperature  Is  rising 
pomts  to  a  change  which  absorbs  heat;  a  retardation  during  cooling  points 
to  some  change  which  evolves  heat.  (Henry  M.  Howe,  on  **  Heat  Treauuent 
of  Steel,"  Trans.  A.  I.  M.  K.  vol.  xxii.) 

BflTect  of  Nlcklns  a  Steel  Bar*— The  statement  is  sometimes  made 
that,  owing  to  the  homogeneity  of  steel,  a  bar  with  a  surface  crack  or  nick 
in  one  of  its  edges  is  liable  to  fail  by  the  gradual  spreading  of  the  nick,  and 
thus  break  under  a  very  much  smaller  load  than  a  sound  bar.  With  iron  it 
is  contended  this  does  not  occur,  as  this  metal  has  a  fibrous  structure.  Sir 
Benlamin  Baker  has,  however,  shown  that  this  theory,  at  least  so  far  as 
statical  stress  is  concerned,  is  opposed  to  the  fact.s.  as  he  purposely  made 
nicks  in  specimens  of  the  mild  steel  used  at  the  Forth  Bridge,  but  found 
that  the  tensile  strength  of  the  whole  was  thus  reduced  by  only  about  one 
ton  per  square  inch  of  section.  In  an  experiment  by  the  Union  Bridge  Com' 
pany  a  full-sized  steel  counter-bar,  with  a  screw-turned  buckle  connection, 
was  tested  under  a  heavy  statical  stress,  and  at  the  same  time  a  weight 
weighing  1040  lbs.  was  allowed  to  drop  on  it  from  various  heights.  The  bar 
wasflfiBt  broken  by  ordinary  statical  strain,  and  showed  a  breaking  stress  ot 


MISCELLANEOUS  NOTES  ON"  STEEL. 


403 


njBOO  lbs.  per  square  inch.    The  loneer  of  the  broken  parts  was  then  placed 
to  the  machine  and  put  under  the  following  loads,  whilst  a  weight,  an  already 

arToi 


mentioned,  was  dropped  on  it  from  varTous  helf^hts  at  a  distanoe  of  five 
feet  from  tlie  sleeTe-nut  of  the  turn-buckle,  as  shown  below: 

Stress  in  pounds  per  sq.  in 60,000       55,000       60,000       63,000       66,000 

ft.  in.      ft.  in.      ft.  in.      ft.  in.      ft.  in. 
Heicrht  of  fall 31  26  80  40  50 

The  weii^ht  was  then  shifted  so  as  to  fall  directly  on  the  sleeve-nut,  and 
the  test  proceeded  as  follows : 

Stress  on  specimen  in  lbs.  per  square  inch 65,360  66,850  68,800 

Height  of  foil,  feet 8  6  6 

It  will  be  seen  thai  under  this  trial  the  bar  carried  more  than  when  origi- 
nally tested  statically,  showing  that  the  nicking  of  the  bar  by  screwing 
had  not  appreciably  weakened  its  power  of  resisting  shocks.— J^yV  NetD$, 

Bl«ctrlc  CondnctlTlty  of  Steel.— Louis  Campredon  reports  in  Le 
Ginie  Civil  the  results  of  experiments  on  the  electric  resistance  of  steel 
wires  of  diiTerent  composition.  The  wires  were  8  mm.  diameter.  The 
results  are  given  below,  the  resistance  being  that  of  1  kilometre  of  wire  1 
square  mm.  in  section. 


Car- 
bon. 

Silicon. 

Sulphur. 

Phos- 
phorus. 

Manga- 
nese. 

Total. 

Electric 
Resist- 
ance, 
Ohms. 

0.090 

0.020 

0.050 

0.030 

0.210 

0.410 

137.7 

2 

0.100 

0.0«0 

0.050 

0.040 

0.240 

0.450 

133.0 

0.100 

0.020 

0.060 

0.040 

0.260 

0.480 

137.5 

0.100 

0.020 

O.OTiO 

0.050 

0.310 

0.530 

140.8 

0.120 

0.030 

O.OTO 

0.050 

0.830 

0.600 

142.7 

0.110 

0.030 

0.060 

0.060 

0.850 

0.610 

144.5 

0.100 

0.090 

0.070 

0.010 

0.400 

o.m 

149.0 

8 

0.120 

O.OSO 

O.OTO 

0.070 

0.400 

0.680 

150.8 

9 

0.110 

0.030 

0.060 

0.060 

0.490 

0.750 

156.0 

10 

0.140 

0.030 

0.060 

0.080 

0.540 

0.850 

178.0 

An  examination  of  these  series  of  figures  shows  tliat  the  purer  and  softer 
steel  the  belter  is  its  electric  conductivity,  and,  furthermore,  that  manga- 
nese ifi  the  element  which  most  influences  the  conductivity. 

Speelfle  Cravlty  of  Soft  Steel.  (W.  Kent,  Trans.  A.  L  M.  E.,  ziv. 
583.>— Five  specimens  of  boiler-plate  of  C.  0.14,  P.  0.03  gave  an  average  sp. 
gr.  of  7.082,  maximum  variation  0.008.  The  pieces  were  first  planed  to  re- 
move all  possible  scale  indentations,  then  filed  smooth,  then  cleaned  in 
dilute  sulphuric  acid,  and  then  boiled  in  distilled  water,  to  remove  all  traces 
of  air  from  tho  surface. 

The  figures  of  speciflc  gravity  thus  obtained  by  careful  experiment  on 
bright,  smooth  pieces  of  steel  are,  however,  too  high  for  use  in  determining 
the  weights  of  rolled  plates  for  commercial  purposes.  The  actual  average 
thickness  of  these  plates  is  always  a  little  less  than  is  shown  by  the  calipers, 
on  account  of  the  oxide  of  iron  on  the  surface,  and  because  tho  surface  is 
not  perfectly  smooth  and  regular.  A  number  of  experiments  on  commercial 
plates,  and  comparison  of  other  authorities,  led  to  the  ficrure  7.854  as  the 
average  speciflc  gravity  of  open-hearth  boiler-plate  steel.  This  figure  Is 
easily  remember€»d  as  being  the  same  figure  with  change  of  position  of  the 
decimal  point  (.7854)  which  expresses  the  relation  of  the  area  of  a  circle  to 
that  of  its  circumscribed  square.  Taking  the  weight  of  a  cubic  foot  of  water 
at  62**  F.  as  62.36 11)8.  (avera^^e  of  several  authorities),  this  figure  gives  489.775 
lbs.  as  the  weight  of  a  cubic  foot  of  steel,  or  the  even  flgm-e,  400  lbs.,  may  be 
taken  as  a  convenient  figure,  and  accurate  within  the  hmits  of  tlie  error  of 
observation. 

A  common  method  of  approximating  the  weight  of  iron  plates  is  to  con- 
sider them  to  weigh  40  lbs.  per  square  foot  one  inch  thick.  Taking  this 
weight  and  adding  2%  gives  almost  exactly  the  weight  of  steel  boiler-plate 
given  above  (40  x  12  X  1.03  =  489.6  lbs.  per  cubic  foot). 

Occasional  Failures  of  Bessemer  Steel.— G.  H.  Clapp  and  A. 
£.  Hunt|  in  their  paper  on  **Tne  Inspectiuu  o£  Materials  of  Construction  in 


404  STEEL. 

the  United  States  "  (Tiuns.  A.  I.  M.  E.,  vol.  six),  say:  Numeroas  tnstanoee 
could  be  cited  to  show  the  unreliability  of  Bessemer  steel  for  structural  pui^ 
poses.  One  of  the  most  marked,  however,  was  the  followiof?:  A  ]2*iD.  I-beam 
weifi^binj^  80  lbs.  to  the  foot,  20  feet  long,  on  being  unloaded  from  a  car 
broke  in  two  about  6  feet  from  one  end. 

The  analyses  and  tensile  tests  made  do  not  show  any  cause  for  the  failure. 

The  cold  and  quench  bending  tests  of  both  the  original  9^-in.  round  test- 
pieces,  and  of  pieces  cut  from  the  finished  material,  gave  satisfactory  re- 
sults; the  cold>bendlng  tests  dosing  down  on  themsalres  without  sign  of 
fracture. 

Numerous  other  cases  of  angles  and  plates  that  were  so  ^lord  In  peaces  as 
to  break  off  short  in  punching,  or,  what  was  worse,  to  break  the  punches, 
have  come  under  our  observation,  and  although  makers  of  Bessemer  steel 
claim  that  this  is  just  as  likely  to  occur  in  open-hearth  as  in  Beeseme:  steel, 
we  have  as  yet  nerer  seen  an  instance  of  failure  of  this  kind  in  open-hearth 
steel  having  a  composition  such  as  C  O.S5^,  Mn  O.TOjt,  P  O.QOjl, 

J.  W.  Wailes,  in  a  paper  read  before  the  Chemical  Section  of  the  British 
Association  for  the  Advancement  of  Science,  in  speaking  of  mysterious 
failures  of  steel,  states  that  investigation  shows  that  **  these  failures  occur 
in  steel  of  one  class,  viz.,  soft  steel  made  by  the  Bessemer  process.** 

Seffremtlon  In  Steel  Iiiffo$a«  (A.  Pourcel,  Trans.  A.  L  M.  E.  180S.) 
— H.  H.  Iiowe,  in  his  **  Metallurgy  of  Steel,"  gives  a  r4sum4  of  observations, 
with  the  results  of  numerous  analyses,  bearing  upon  the  phenomena  o^  seg- 
regation. 

In  188!  Mr.  Stubbs,  of  Manchester,  showed  the  heterogeneous  results  of 
analyses  made  upon  different  parts  of  an  ingot  of  large  section. 

A  test-piece  taken  d4  inches  from  the  head  of  the  ingot  7.5  feet  in  length 
gave  by  analysis  very  different  results  from  those  of  a  test-piece  taken  80 
inches  frOiii  the  bottom. 

C.  Mn.  Si.  8.  P. 

Top 0.92  0.686  0.048  0.161  0.«1 

Bottom 0.87  0.498  0.006  0.085  0.096 

Windsor  Richards  says  he  had  often  observed  in  tes^pieces  taken  from 
different  points  of  one  plate  variations  of  0.06%  of  carbon.  Segregation  Is 
specially  pronounced  in  an  ingot  in  its  central  portion,  and  around  the 
space  of  the  piping. 

It  is  most  observable  in  large  ingots,  but  in  blocks  of  smaller  weight  and 
limited  dimensions,  subjected  to  the  influence  of  solidification  as  rapid  as 
casting  within  thick  walls  will  permit,  it  noay  still  be  observed  distinctly. 
An  ingot  of  Martin  steel,  weighing  about  1000  lbs.,  and  having  a  height  of 
1.10  feet  and  a  section  of  10. !M  inches  square,  gave  the  following: 

1.  Upper  section:  C.  S.  P.  Mn. 

Border 0.880  0.040  0.088  0.420 

Centre 0.580  0.077  0.067  0.430 

2.  Lower  section:  C.  S.  P.  Mn.       t 

Border 0.280  O.O-^O  0.016  0.890 

Centre 0.890  0.080  0.038  0.890 

S.  Middle  section:  C.  S.  P.  Mn. 

Border 0.390  0.025  0.086  O.40O     ' 

Centre 0.830  0.048  0.048  0.4^ 

Segregation  is  less  marked  in  ingots  of  extra-soft  metal  cast  in  cast-iron 
raonldH  of  considerable  thickness.  It  is,  however,  still  important,  and  ex- 
plains the  difference  often  shown  bv  the  results  of  tests  on  pieces  taken 
from  different  portions  of  a  plate.  Two  samples,  taken  from  the  sound  part 
of  a  flat  ingot,  one  on  the  outside  and  the  other  in  the  centre,  7.9  Inches  from 
the  upper  edge,  gave: 

0.  8.  P.  Mil 

Centre 0.i4  0.058  0.073  0.676 

Exterior 0.11  0.086  O.OW  0.610 

Manganese  is  the  element  most  uniformly  disseminated  in  hard  or  aoft 
steel. 

For  cannon  of  large  calibre,  if  we  reject,  in  addition  to  the  part  cast  in 
sand  and  calletl  the  maaselotte  (sinking-head),  one  third  of  the  upper  |tart 
of  the  ingot,  we  can  obtain  a  tube  practically  homogeneous  in  composition, 
because  the  central  part  is  naturally  removed  by  the  boring  of  tne  tuh<». 
"With  extra  soft  steels,  destined  for  ship- or  boiler-plates,  the  solution  for 
practically  perfect  homogeneity  lies  in  the  obtaining  of  a  metal  more  closely 
deserving  its  name  of  extra-Boft  metal. 


BTEEL  CASTIKGS,  405 

The  Id  juriouB  congequences  of  seffregaUon  must  be  suppressed  by  reduo- 
iDfT.  fts  far  a«  possible,  the  elements  subject  to  liquation. 
Earllevt  JJmem  or  Steel   for  Strnetnral  Purnoseit*    (Q.  G. 

Mefartens,  Trans.  A.  S.  C.  E.  1893).— The  Pennsylvania  Kaflroad  Company 
first  introduced  Bessemer  steel  in  America  In  locomotive  boilers  in  thevear 
1868,  but  the  steel  was  too  hard  and  brittle  for  such  use.  The  first  plates 
made  for  steel  boilers  had  a  tenacity  of  66,000  to  93,000  lbs.  and  an  elonf^ation 
of  but  7j(  to  103(.  The  results  were  not  favorable,  and  the  steel  works  were 
soon  forced  to  offer  a  material  of  lees  tenacity  and  more  ductility.  The  re- 
quirements  were  therefore  reduced  to  a  tenacity  of  78.000  lbs.  or  less,  and 
the  elon^ration  was  increased  to  15)(  or  more.  Even  with  this,  between  the 
years  1870  and  1880,  many  explosions  occurred  and  many  careful  examina- 
tions were  made  to  determine  their  cause.  It  was  found  on  examining  the 
rivet-boles  that  there  were  incipient  changes  In  the  metal,  many  cracks 
around  them,  and  points  near  them  were  corroded  with  rust,  all  caused  by 
the  shock  of  tools  in  manufacturing;.  It  was  evident  that  the  material 
was  unsuitable,  and  that  the  treatment  must  be  chanf^ed.  In  the  beginning 
of  1878,  Mr.  Parker,  chief  engineer  of  the  Lloyds,  stated  that  there  was  then 
but  one  English  steamer  in  possession  of  a  steel  boiler;  a  year  later  there 
were  120.  In  1878  there  were  but  five  large  English  steamers  built  of  steel, 
while  in  1883  there  were  116  building.  The  use  of  Bessemer  steel  In  bridge- 
building  was  tried  first  on  the  Dutch  State  railways  in  186&-61,  then  in  Eng. 
land  and  Austria.  In  1874  a  bridge  was  built  of  Bessemer  steel  in  Austria. 
The  first  use  of  cast  steel  for  bridges  was  in  America,  for  the  St.  Louis  Arch 
Bridge  and  for  the  wire  of  the  East  River  Bridge.  These  gave  an  impetus 
to  the  use  of  Ingot  metal,  and  before  1880  the  Glasgow  and  Plattsmouth 
Bridges  over  the  Missouri  River  were  also  built  of  ingot  metal.  Steel  eye- 
bars  were  applied  for  the  first  time  in  the  Glasgow  Bridge.  Since  1880  the 
introduction  of  mild  steel  in  all  kinds  of  engineering  structures  has  steadily 
increased. 

stbeij  castings. 

(E.  S.  Cramp,  Engineering  Congress,  Dept.  of  Marine  Eng^g,  Chicago,  1898.) 

In  1891  American  stef  1-founders  had  successfully  produced  a  considerable 
variety  of  heavy  and  difficult  castings,  of  which  the  following  are  ihe  most 
noteworthy  specimens: 

Bed-plates  up  to  d4,000  lbs.;  stem-poRts  up  to  54,000  lbs.;  stems  up  to 
21,000  lbs. ;  hydraulic  cylinders  up  to  11,000  lbs. :  shaft-struts  up  to  82,000  lbs. ; 
hawse-pipes  up  to  7500  lbs. ;  stem-pipes  up  to  8000  lbs. 

The  percentage  of  success  in  these  classes  of  castings  since  1890  has  ranged 
from  fSH  in  the  more  difficult  forms  to  90^  in  the  simpler  ones:  the  tensile 
strength  has  been  from  6^^,000  to  78,000  lbs.,  elongation  from  ISjt  to  25jt.  The 
best  performance  recorded  is  that  of  a  guide,  cast  in  January,  1893,  which 
developed  84,000  lbs.  tensile  strength  and  16.6%  elongation. 

The  first  steel  castings  of  which  anything  is  generally  known  were 
crossing-frogs  made  for  the  Philadelphia  &  Reading  R.  R.  in  July,  1867,  by 
the  William  Butcher  Steel  Works,  now  the  Midvale  Steel  Co.  The  moulds 
were  made  of  a  mixture  of  ground  fire-brick,  black-lead  cruclble-pois 
ground  fine,  and  fire-clay,  and  washed  w^ith  a  black-lead  wash.  The  steel 
was  melted  in  crucibles,  and  was  about  as  hard  as  tool  steel.  The  surface 
of  these  castings  was  very  smooth,  but  the  interior  was  very  much  honey- 
combed. This  was  before  the  days  when  the  use  of  silicon  was  known  for 
solidifying  steel.  The  sponginess,  which  was  almost  universal,  was  a  great 
obstacle  to  their  general  adoption. 

The  next  step  was  to  lea\e  the  ground  pots  out  of  the  moulding  mixture 
and  to  wash  the  mould  with  finely  ground  fire-brick.  This  was  a  great  im- 
provement, especially  in  very  heavy  castings:  but  this  mixture  still  clung  so 
strongly  to  the  casting  that  only  comparatively  simple  shapes  could  be  made 
with  certainty.  A  mould  made  of  such  a  mixture  became  almost  as  hard  as 
fire-brick,  and  was  such  an  obstacle  to  the  proper  shrinkage  of  castings, 
that,  when  at  all  complicated  in  shape,  they  had  so  great  a  tendency  to 
crack  as  to  make  their  successful  manufacture  almost  impossible.  By  this 
time  the  use  of  silicon  had  been  discovered,  and  the  only  obstacle  in  the  way 
of  making  good  castings  was  a  suitable  moulding  mixture.  This  was  ulti- 
mately found  in  mixtures  having  the  various  kinds  of  silica  sand  as  the 
prindpal  constituent. 

One  of  the  most  fertile  sources  of  defects  in  castings  is  a  bad  design. 
Very  intricate  shapes  can  be  cast  successfully  if  they  are  so  designed  as  to 


406 


STEEL. 


cool  uniformly.  Mr.  Cramp  says  whne  he  Is  not  yet  prepared  to  state  that 
anytbinfif  that  can  be  cast  succes.«ifully  in  iron  can  be  cast  in  steel,  indica- 
tions seem  to  point  that  way  in  all  cases  where  it  is  possible  to  put  on  suit- 
able  sinkinf^-heads  for  feeding  the  caRting. 

H.  L.  Gantt  (Trans.  A.  S.  M.  E.,  xii.  710)  says :  Steel  castings  not  only 
shrink  much  more  than  iron  ones,  but  with  less  regularity.  The  amount  of 
shrinkage  varies  with  the  composition  and  the  heat  of  the  metal;  the  hotter 
the  metal  the  greater  the  shrinkage;  and,  as  we  get  smoother  castings  from 
hot  metal,  it  is  better  to  make  alloM-ance  for  large  shrinkage  aud  pour  tlie 
metal  as  hot  as  possible.  Allow  S/16  or  yi  in.  per  ft.  in  length 
for  shrinkage,  and  H  in-  for  finish  on  machined  surfaces,  except  such  as  are 
cast  **up."  Cope  surfaces  which  are  to  be  machined  should,  in  large  or 
hard  castings,  have  an  allowance  of  from  9^  to  ^  in.  for  finish,  as  a  large 
mass  of  metal  slowly  rising  in  a  mould  is  apt  to  become  crusty  on  the  sur- 
face, and  such  a  crust  is  sure  to  be  full  of  imperfections.  On  small,  soft 
castings  f^  in.  on  drag  side  and  ^  in.  on  cope  side  will  be  sufficient.  No  core 
shoula  have  less  than  ^  in.  finish  on  a  side  and  very  large  ones  should  have 
as  much  as  ^  in.  on  a  side.  Blow- holes  can  be  eutireljr  prevented  in  cast- 
ings by  the  addition  uf  manganet«H  and  tiilicou  in  sufficient  quantities;  but 
both  of  these  cause  brittieness,  and  it  is  the  object  of  the  conscientious  stt^el- 
maker  to  put  no  more  manganese  and  silicon  in  his  steel  than  is  just  suffi 
cient  to  make  it  solid.  The  b«*8t  results  are  arrived  at  when  all  portioos  of 
the  castings  are  of  a  uniform  thickness,  or  very  nearly  so. 

The   following  table  w^ili   illustrate  the  eliect  of  annealing  on  tensile 
strength  and  elongation  of  steel  castings : 


Carbon. 

Unannealed. 

Annealed. 

Tensile  Strength. 

Elongation. 

Tensile  Strength. 

Elongation. 

.87 
.58 

68,788 
86,540 
90,121 

22.40)e 
8.20 
2.35 

67,210 
82,228 
106,415 

81.40:( 
21.80 
0.80 

The  proper  annealing  of  large  castings  takes  nearly  a  week. 

The  proper  steel  for  roll  pinion^',  hammer  dies,  etc.,  seems  to  be  that  con- 
taining  about  .G0<  of  carbon.  Such  castings,  properly  annealed,  have  worn 
well  and  seldom  broken.  Miscellaneous  gearing  should  contain  carbon  .40)e 
to  60^,  gears  larger  in  diameter  being  softest.  General  machinery  castings 
should,  as  a  rule,  contain  less  than  .403(  of  carbon,  those  exposed  to  great 
shocks  containing  as  low  at  .20^  of  carbon.  Such  castings  will  give  a  tensile 
strength  of  from  60,000  to  80,000  lbs.  per  sq.  in.  and  at  least  16%  extension  in 
a  2  in.  long  specimen.  Machinery  and  hull  castings  for  war-vessels  for  the 
United  States  Navy,  as  well  as  carriages  for  naval  guns,  contain  from  JSO%  to 
.3()j(  of  carbon. 

The  following  is  a  partial  list  of  castings  in  which  steel  seems  to  be 
rapidly  taking  the  place  of  iron:  Hydraulic  cylinders,  crossheadsand  pistons 
for  large  engines,  roughing  rolls,  rolling-mill  spindles,  coupling-boxes,  roll 
pinions,  geanng,  hammer-heads  and  dies,  riveter  stakes,  castings  for  ships, 
car  couplers,  etc. 

For  description  of  methods  of  manufacture  of  steel  castings  by  the  Besse- 
mer, open-hearth,  and  crucible  processes,  see  paper  by  P.  Q.  Salom,  Trans. 
A.  I.  M.  E.  xiv,  118. 

Specifications  for  steel  castings  issued  by  the  U.  S.  Navy  Department,  18S9 
(abridged) :  Steel  for  castings  must  be  made  by  either  the  open-hearth  or 
the  crucible  process,  and  must  not  show  more  than  .06%  of  phosphorus.  All 
castings  must  be  annealed,  unless  otherwise  directed.  The  tensile  strength 
of  steel  castings  shall  be  at  least  60,000  lbs.,  with  an  elongation  of  at  least 
lti%  in  8  in.  for  all  castings  for  moving  parts  of  the  machinery,  and  at  least 
1(^  in  8  in.  for  other  castings.  Bars  1  in.  so.  shall  be  capeible  of  bending 
cold,  without  fracture,  through  an  angle  of  90'',  over  a  radius  not  greater 
than  1%  in.  All  castings  must  be  sound,  free  from  injurious  loughneea, 
sponginess,  pitting,  slirinkage,  or  other  cracks,  cavities,  etc. 

Pennsylvania  Railroad  specifications,  1888:  Steel  castings  should  have  a 
tensile  strength  of  70,000  lbs.  per  sq.  in.  and  an  elongation  of  lb%  in  section 
originally  2  in.  long.    Steel  castings  will  not  be  accepted  if  tensile  strength 


MANGANESE,  NICKEL,  AND  OTHER  **  ALLOY"  STEELS.  40? 

falls  below  fiO,000  lb&,  nor  if  the  eloiifration  is  leas  than  12%,  nor  if  cast- 
iDf^  have  biow-hoIeB  and  Rhrinkafce  cracks.  Castings  welRhing  80  lbs.  or 
more  must  have  east  with  them  a  strip  to  be  used  as  a  tesUpiece.  The  di- 
mensions of  this  strip  must  be  9i  in.  sq.  by  12  in.  long. 

IHANCANESE,  NICKEIi,  ANB  OTMBR  <<ALIiOT»' 
8TKELS. 

Mmnsanese  Steel,  (H.  M.  Howe,  Trans.  A.  8.  M.  B..  vol.  zil.)— ^Man- 
ganeae  steel  is  an  alloy  of  iron  and  manganese,  incidentally,  and  probably 
unavoidably,  containing  a  considerable  proportion  of  carbon. 

The  (rffect  of  small  proportions  of  manganese  on  the  hardness,  strength, 
and  ductility  cf  iron  is  probably  slight.  The  point  at  which  manganese 
begins  to  have  a  predominant  effect  is  not  known :  it  may  be  somewhere 
about  2.5%.  As  the  proportion  of  manganese  rises  above  2.6$(  the  strength 
and  ductility  diminish,  while  the  hardness  increases.  This  effect  reaches  a 
maximum  with  somewhere  about  (i%  of  manganese.  When  the  proportion 
of  this  element  rises  be^^ond  e%  the  strength  and  ductility  both  increase. 
«bile  tlie  hardness  diminishes  slightly,  the  maximum  of  both  strength  and 
ductility  being  reached  with  about  14i(  of  manganese.  With  this  proportion 
the  metal  is  still  so  hard  that  it  is  very  difficult  to  cut  it  with  steel  tools.  As 
the  proportion  of  manganese  rises  above  15)(  the  ductility  falls  off  abruptly, 
the  strength  remaining  nearly  constant  till  the  manganese  passes  1B%,  when 
it  in  turn  diminishes  suddenly. 

Steel  containing  from  4%  to  6.6%  of  manganese,  even  if  it  have  but  0.2^%  of 
carbon,  is  reported  to  be  so  extremely  brittle  that  it  can  be  powdered  under 
a  hand-hammer  when  cold  ;  yet  it  is  ductile  when  hot. 

Manganese  steel  is  very  free  from  blow-holes  ;  it  welds  with  great  diffi- 
culty; its  toughness  is  increased  by  quenching  from  a  3'ellow  heat ;  its  elec- 
tric resistance  Is  enormous,  and  very  constant  with  changing  temperature ; 
il  is  low  in  thermal  conductivity.  Its  remarkable  combination  of  great  haixl- 
uess.  which  cannot  be  materially  lessened  by  annealing,  and  great  tensile 
strength,  with  astonishing  toughness  and  ductility,  at  once  creates  and 
limits  its  usefulness.  The  fact  that  manganese  steel  cannot  be  softened, 
that  it  ever  remains  so  hard  that  it  can  be  machined  only  with  great  diffi- 
rulty,  sets  up  a  barrier  to  its  usefulness. 

The  following  comparative  results  of  abrasion  tests  of  manganese  and 
ether  steel  were  reported  by  T.  T.  Morrell : 

ABSAeioN  BT  Pbjesscrb  Aoaikst  A  RsToiiViKo  Hardkkkd-Stkkl  Shaft. 

Loss  of  weight  of  manganese  steel 1.0 

**  blue-tempered  hard  tool  steel 0.4 

**  annealed  hard  tool  steel 7.5 

**  hardeneil  Otis  boiler-pUte  steel 7.0 

"  annealed      **  *'  "  14.0 

Abrasion  bt  an  Emert-Wbkbl. 

Loss  of  weight  of  hard  manganese-steel  wheels 1 .00 

**  softer  "  »*     M8 

"  liardest  carbon-steel  wheels 1 .  88 

*•  soft  "  •'     2.86 

The  hardness  of  manganese  steel  seems  to  be  of  an  anomalous  kind.  The 
alloy  is  hard,  but  under  somo  conditions  not  rigid.  It  is  very  hard  in  its 
rvsistance  to  abrasion  ;  it  is.not  always  hard  in  its  resistance  to  impact. 

Blanganese  steel  forges  readily  at  a  yellow  heat,  though  at  a  bright  white 
heat  it  crumbles  under  the  hammer.  But  it  offers  greater  resistance  to 
deformation,  i.e.,  it  is  harder  when  hot,  than  carbon  steel. 

The  most  important  single  use  for  manganese-steel  is  for  the  pins  which 
hold  the  buckeu  of  elevator  dredges.      Here  abrasion  chiefly  is  to  be 
resisted. 
Another  important  use  is  for  the  links  of  common  chahi-elevators. 
As  a  material  for  stamp-shoes,  for  horse-shoes,  for  the  knuckles  of  an 
automatic  car-coupler,  manganese  steel  has  not  met  .expectation r. 

Manganese  steel  has  been  regularly  adopted  for  the  blacies  of  the  Cyclone 
pnlverizer.  Some  manganese-steel  wheels  are  reported  to  have  run.  over 
aOO.OOO  miles  each  without  turning,  on  a  New  England  railroad. 

IVlcfeLel  Steel.— The  remarkable  tensile  strength  and  ductility  of  nickel 
fteel,  as  shown  by  the  test-bars  and  the  behavior  of  nickel-steel  annor- 
plate  under  shot  tests,  are  witness  of  the  valuable  qualities  conferred  upon 
steel  hy  the  addition  of  a  few  per  cent  of  nickel.  , 


408 


8tBEL« 


The  following  tests  were  made  on  nickel  steels  by  Mr.  Maunsel  White  of 
the  Bethlehem  Iron  Company  (Eng.  <t  M.  Jour.,  Sept.  16, 1898.) : 


r 

^ 

Tensile 

Elastic 

Elonga- 
tion, 

Reduc> 

Specimen 

*c— • 

Str^gth, 

Limit, 

tion  of 

from— 

f 

lbs.  per 
sq.  in. 

lbs.  per 
sq.  in. 

Area, 

Forged 

.625 

4 

276,800 

2.75 

*  *6.*0f 

Special 

~ 

"     !! 

•* 

246.596 

4.26 

treatment. 

1 

bars.* 

** 

106,900 

19.25 

56.0 

Annealed. 

"Jo 

'.m 

4 

142,800 

'74.066' 

18.0 

28.2 

% 

»i 

143.800 

74,000 

12.82 

27.6 

M  , 

IM-in 

round 

rolled  bar.t 

«t 

«* 

117.600 

04,000 

17.0 

46.0 

"5 

.4 

** 

119,800 

65,000 

16.66 

42.1 

ti 

91,600 
91,200 

61,000 
51,000 

22.25 
21.62 

58.2 
68.4 

CO 

»« 

t» 

85.200 

58,000 

21.82 

49.5 

■s 

*' 

*♦ 

86,000 

48,000 

21.26 

47.4 

.798 

8 

115,464 

61,8«) 

86  25 

66.28 

s 

IK  in.  sq. 
bar,  rolled4 

♦• 

** 

112,600 

60.000 

37.87 

68.82 

K 

ti 

t« 

102,010 

89,180 

41.87 

60.59 

Annealed. 

*© 

*t 

«t 

102,510 

40,200 

44.00 

68.84 

*• 

.g  ■ 

.600 

2 

114,590 

56,020 

47.26 

68.4 

•g 

1-in.  round 

'* 

4t 

115.610 

69,080 

45.25 

62.8 

VI 

bar,  roUedl 

»* 

»t 

105,240 

45,170 

49.65 

72.8 

Annealed. 

1^ 

»» 

** 

106,780 

45,170 

56.50 

68.6 

'• 

*  Forged  from  6-in.  ingot  to  %  in.  diam.,  with  conical  heads  for  holding. 
t  Showing  the  effect  of  varying  carbon. 

t  Rolled  down  from  14-in.  ingot  to  IH-in.  square  billet,  and  turned  to  siae. 
I  Rolled  down  from  14-in.  ingot  to  1-in.  round,  and  turned  to  size. 
Nickel  steel  has  shown  itself  to  be  possessed  of  some  exceedingly  valuable 
properties:  these  are,  resistance  to  cracking,  high  elastic  limit,  and  homo- 

geneitv.  Resistance  to  cracking,  a  property  to  which  the  name  of  non  flssi- 
iltty  has  been  given,  is  shown  more  remarkably  as  the  percentage  of  nickel 
increases.  Bars  of  27j(  nickel  illustrate  this  propertv.  A  l^-in.  square  bar 
was  nicked  V^  in.  deep  and  bent  double  on  Itself  without  furtlier  fracture 
than  the  splintering  off,  as  it  were,  of  the  nicked  portion.  Sudden  failure  or 
rupture  of  this  steel  would  be  impossible  :  it  seems  to  possess  the  toughness 
of  rawhide  with  the  strength  of  steel.  With  this  percentnge  of  nickel  the 
steel  is  practically  non  corrodible  and  non-magnetio.  The  resistance  to 
cracking  shown  by  the  lower  percentages  of  nickel  is  best  illustrated  in  the 
many  trials  of  nickel-steel  armor. 

The  elastic  limit  rises  in  a  very  marked  degree  with  the  addition  of  about 
Ji%  of  nickel,  the  other  physical  properties  of  the  steel  remaining  unchanged 
or  perhaps  slightly  increased. 

In  such  places  (shafts,  axles,  etc.)  where  failure  is  the  result  of  the  fatigue 
of  the  metal  this  higher  elastic  limit  of  nickel  steel  will  tend  to  prolong  in- 
definitely the  life  of  the  piece,  and  at  the  same  time,  through  Its  superior 
toughness,  offer  greater  resistance  to  the  sudden  strains  of  shock. 

Howe  states  that  the  hardness  of  nickel  steel  depends  on  the  proportion 
of  nickel  and  carbon  jointly,  nickel  up  to  a  certain  percentage  increasinjr 
the  hardness,  beyond  this  lessening  it.  Thus  while  steel  with  9%  of  nickel 
and  0.90^  of  carbon  cannot  be  machined,  with  less  than  Bi%  nickel  It  can  be 
worked  cold  readily,  provided  the  proportion  of  carbon  be  low.  As  the 
proportion  of  nickel  rises  higher,  cold-working  becomes  less  ea^y.  It  forges 
easuy  whether  it  contain  much  or  little  nickeL 

The  presence  of  manganese  in  nickel  steel  is  most  important,  as  It  appears 
that  without  the  aid  of  manganese  in  proper  proportions,  the  conditions  of 
treatment  would  not  be  successful. 

Teats  of  Nickel  Steel.— Two  heats  of  open  hearth  steel  were  made  by 
the  Cleveland  Rolling  Mill  Co..  one  ordinary  steel  made  with  9000  lbs.  each 
scrap  and  pig,  and  165  lbs.  ferro-manganese,  the  other  the  same  with  the 
addition  of  8^,  or  540  lbs.  of  nickel.  Tests  of  six  plates  rolled  from  each 
heat.,  0.24  to  0.8  In.  thick,  gave  results  as  follows  : 

Ordinary  steel,  T.  S.  62,500  to  56,500 ;  E.  L.  32,800  to  87,900 ;  elong,  26     to  82j(. 
Nickel  steel.         "     68.370  to  67,100 ;    **     47,100  to  48^000;      '*      88)4to863{. 


JCAKGANESE,  NICKEL,  AND  OTHER  '' ALLOY"  STEELS.  409 

The  nickel  steel  averages  3\%  higher  in  elastic  limit,  90%  higher  in  ultimate 
tensUe  strength,  with  but  slight  leductioc  in  ductility.  (Sng,  it  M.  J<mr., 
Feh.25,  1893.)  ^      x     •» 

Alaminam  Steel.— R.  A.  Hadfleld  rTrant*.  A.  T.  M.  K  1890)  says: 
Aluiiunutii  app«!arH  lo  l>e  of  service  asan  addition  to  baths  of  molten  iron  or 
steel  unduly  saturated  with  oxides,  and  this  in  properly  regulated  steel 
manufacture  should  not  often  occur.  Speaking  generally,  its  role  appears 
to  be  similar  to  that  of  silicon,  though  acting  more  powerfully.  The  state- 
ment that  aluminum  lowers  the  li.elting-point  of  iron  seems  to  have  no 
foundation  in  fact.  If  any  increase  of  heat  or  fluidity  takes  place  by  the 
addition  of  small  amounts  of  aluminum,  it  may  be  due  to  evolution  of  neat, 
owing  to  oxidation  of  the  aluminum,  as  the  calorific  value  of  this  metal  is 
v«y  high — in  fact,  higher  than  silicon.  Accoiding  to  Berthollet,  the  con- 
veniioD  of  aluminum  to  Al^f  )|  eauals  7900  cal . ;  silicon  to  SiOa  is  staled  as  7800. 

The  action  of  aluminum  may  Declassed  along  with  that  of  silicon,  sulphur, 
phosphorus,  arsenic,  and  copper,  as  giving  no  increase  of  hardness  to  iron, 
In  contradistinction  to  carbon,  manganese,  chromium,  tungsten,  and  nickel. 
Therefore,  whilst  for  some  special  purposes  aluminum  may  be  employed  in 
I  be  manufacture  of  iron,  at  any  rate  with  our  present  knowledge  of  its 
properties,  this  use  cannot  be  large,  especially  when  taking  into  considera- 
tion the  fact  of  its  comparatively  high  price.  Its  special  advantage  seems  to 
be  that  it  combines  in  liself  the  advantages  of  both  silicon  and  manganese  ; 
but  so  long  as  alloys  containing  these  metals  are  so  cheap  and  aluminum 
dear«  its  extensive  use  seems  hardly  probable. 

J.  E.  Stead,  in  discussion  of  Mr.  Hadfleld's  paper,  said  t  Everv  one  of  our 
trials  has  Indicated  that  aluminum  can  kill  tlie  most  fiery  steel,  providing, 
of  course,  that  it  is  added  In  sufficient  quantity  to  combine  with  all  the  oxy- 
gen which  the  steel  contains.  The  metal  will  then  be  absolutely  dead,  and 
will  pour  like  dead-melted  silicon  steel.  If  the  aluminum  is  added  as  metal- 
Ik;  ammiuum,  and  not  as  a  compound,  and  if  the  addition  is  made  just  be- 
fore the  steel  is  cast,  ]/IOj(  is  smple  to  obtain  p«*rfect  solidity  in  tiie  steel. 

Clirome  Steel*  (F.  L.  Garrison,  Jour.  F.  /.,  Sept.  1891.)— Chromium 
increases  the  hardness  of  iron,  perhaps  also  the  tensile  strength  and  elastic 
limit,  but  it  lessens  its  weldibility. 

Ferro  chrome,  according  to  Berth ier,  is  made  by  strongly  heating  the 
mixed  oxides  of  iron  and  chromium  in  brasqued  crucibles,  auoiing  powdered 
charcoal  if  the  oxide  of  chromium  Is  in  excels,  and  finxes  to  scorify  the 
earthy  matter  and  prevent  oxidation.  Chromium  does  not  appear  to  give 
steel  the  power  of  becoming  harder  when  quenched  or  ciililed.  Howe  states 
that  chrome  steels  forge  more  readily  than  tungsten  steels,  and  when  not 
«>ntaining  over  0.5  of  chromium  nearly  as  well  as  ordinary  carbon  steels  of 
like  percentage  of  carbon.  On  the  whole  the  status  of  chrome  steel  is  not 
satinactory.  There  are  other  steel  alloys  coming  into  use,  which  are  so 
much  better,  that  it  would  seem  to  be  only  a  question  of  time  when  it  will 
drop  entirely  out  of  the  race.  Howe  states  that  many  experienced  chemists 
have  found  no  chromium,  or  but  the  merest  traces,  in  chrome  steel  sold  in 
the  markets. 

J.  W.  Langley  (Trans.  A.  S.  C.  E.  1802)  says :  Chromium,  like  manganese. 
M  a  true  hardener  of  iron  even  in  the  absence  of  carbon.  The  addition  of  \% 
or  S<  of  chromium  to  a  carbon  steel  will  make  a  aietal  which  gets  exces- 
streiy  hard.  Hitherto  its  principal  employment  has  been  in  the  production 
of  chiOed  shot  and  shell.  Powerful  molecular  stresses  result  d  uring  cooling, 
and  the  shells  frequently  break  spcmtaneously  months  after  they  are  made. 

Tunssten  Mteel— Ilaiiliet  Steel.  (J.  B.  Nau,  Iron  Age,  Feb.  11, 1892.) 
—By  incorporating  slmnltaueously  carbon  and  tungsten  in  iron,  it  is  poFsI- 
hlc  to  obtain  a  much  harder  steel  than  with  carbon  iilone,  without  danger  of 
an  extraordinary  brittleness  in  the  cold  metal  or  an  increased  difllculty  in 
the  working  of  the  heated  metal. 

When  a  special  grade  of  hardness  is  required,  it  is  frequently  the  custom 
to  use  a  high  tungsten  steel,  known  In  England  as  special  steel.  A  specimen 
from  Sheffield,  used  for  chisels,  contained  9.9l%  of  tungsten,  0.7j(  of  silver, 
asd  O.H  of  carbon.  This  steel,  thougli  used  with  advantage  in  its  untem- 
pered  state  to  turn  chilled  rolls,  was  not  brittle  ;  nevertheless  it  was  hard 
enough  to  scratch  glass. 

A  sample  of  Mushet^s  special  steel  contained  ^M  of  tungsten  and  1.78j(  of 
manganese.  The  hardness  of  tungsten  steel  cannot  be  increased  by  the  or- 
dinary process  of  hardening. 

The  only  operation  that  it  can  be  submitted  to  when  cold  is  grinding.  It 
bas  to  be  given  its  final  shape  through  hammering  at  a  red  heat,  and  even 


410  STEEL. 

then,  when  the  percentage  of  tungsten  is  high,  it  has  to  be  treated  Tcry 
carefully ;  and  in  order  to  avoid  brealcing  it,  not  only  is  it  necessary  to  reheat 
it  several  times  while  it  is  being  hammered,  but  when  the  tool  has  acquired 
the  desired  shape  hammering  must  still  be  continued  gently  and  with  nu- 
merous blows  until  it  becomes  nearly  cold.  Then  only  can  it  be  cooled  en- 
tirely. 

Tungsten  is  not  only  employed  to  produce  steel  of  an  extraordinary  hard- 
ness, but  more  especially  to  obtain  a  steel  which,  with  a  moderate  hardness, 
allies  great  toughness,  resistance,  and  ductility.  Steel  from  Asaailly,  used 
lor  this  purpose,  contained  carbon,  0.5*^;  silicon,  0.04^;  tungsten,  O.St; 
phosphorus,  0.01%;  sulphur,  0.00!^. 

Mechanical  testa  made  by  Styffe  gave  the  following  results : 

Breaking  load  per  square  inch  of  original  area,  pounds. .  172,424 

Reduction  of  area,  per  cent  0.54 

Average  elongation  after  fracture,  per  cent  18 

According  to  analyses  made  by  the  Due  de  Luynes  of  ten  specimens  of  the 
celebrated  Oriental  damasked  steel,  eight  contained  tungsten,  two  of  Uiem 
in  notable  ouantities  (0.518j(  to  1%),  while  in  all  of  the  samples  analyzed 
nickel  was  discovered  ranging  from  traces  to  nearly  4%, 

Stein  &  Schwartz  of  Philadelphia,  in  a  circular  sav :  It  Is  stated  that 
tungsten  steel  is  suitable  for  the  manufacture  of  steel  magnets,  since  it  re- 
tains its  magnetism  longer  than  ordinary  steel.  Mr.  Kuiesche  has  made 
tungsten  up  to  9S%  fine  a  specialty.  Dr.  Heppe.  of  Leipsig,  has  written  a 
number  of  articles  in  German  publications  on  the  subject.  The  following 
instructions  are  given  concerning  the  use  of  tungsten:  In  order  to  produce 
cast  iron  possessing  great  liardness  aii  addition  of  one  half  to  one  and  one 
half  of  tungsten  is  all  that  Is  needed.  For  bar  iron  it  must  be  carried  up  to 
1%  to  2jt,  but  should  not  exceed  2^.  For  puddled  steel  tlie  range  is  larger, 
but  an  addition  beyond  8Uj(  only  increases  the  hardness,  so  that  ft  is  brouglit 
up  to  IW  only  for  special  tools,  cuiniige  dies,  drills,  etc.  For  tires  S^J^  to  S% 
have  proved  best,  and  for  axles  ^  to  l^.  Cast  steel  to  which  tungsten  has 
been  added  needs  a  higlier  temperature  for  temuering  than  ordinary  steel, 
and  should  be  hardened  only  between  yellow,  led,  and  white.  Cliisels  made 
of  tungsten  steel  should  be  drawn  between  cherry-red  and  blue,  and  stand 
well  on  iron  and  steel.  Tempering  is  best  done  in  a  mixture  of  6  parts  of 
yellow  rosin,  S  parts  of  tar,  and  2  parts  of  tallow,  and  tlien  the  article  ic 
once  more  heated  and  then  tempered  as  usual  in  water  of  about  15*  C 

Fluld-coinpreMed  iSteel  by  tlie  ^*  "WliUivortli  Procf.w 
(Proc.  Inst.  M.  E.,  May,  1887,  p.  1U7.)— In  this  system  a  gradually  increasinir 
pressure  up  to  6  or  8  tons  per  square  inch  is  applied  to  the  fluid  ingot,  and 
within  half  an  hour  or  lesp  after  .the  application  of  the  pressure  the  column 
of  fluid  steel  is  shortened  1^  inch  per  foot  or  oiie-eiglith  of  its  length;  the 

gressure  is  then  kept  on  for  several  hours,  the  result  being  that  the  metal 
I  compressed  into  a  perfectly  solid  and  homogeneous  material,  free  from 
blow-holes. 

In  large  gun-ring  ingots  during  cooling  the  carbon  is  driven  to  the  centre, 
the  centre  contaimng  0.8  carbon  and  the  outer  ring  0.8.  The  centre  is  bored 
out  until  a  test  shows  that  the  inside  of  the  ring  contains  the  same  percent- 
age of  carbon  as  the  outside 

Fluid -compressed  steel  is  made  by  the  Bethlehem  Iron  Co.  for  gon  and 
other  heavy  forgiugs. 

CRITCIBIiE  STEEL. 

Selection  of  Grades  by  tbe  Eye.  and  Effect  of  Heat  Treat- 
ment. (J.  W.  Langley,  Amer.  Chemiat,  November,  1876.)— In  1874,  Miller, 
Metcair  &  Parkin,  of  Pittsburgh,  selected  eight  samples  of  steel  which  were 
believed  to  form  a  set  of  graded  specimens,  the  order  being  based  on  the 
quantity  of  carbon  which  they  were  supposed  to  contain.  They  were  num- 
bered from  one  to  eight.  On  analysis,  the  quantity  of  carbon  was  found  to 
follow  the  order  of  the  numbers,  while  the  other  elements  present— ail  icon, 
pho8{>horus,  and  sulphur— did  not  do  so.  The  method  of  selection  la 
described  as  follows  : 

The  steel  is  melted  in  black-lead  crucibles  capable  of  holding  about  elglity 
pounds;  when  thoroughly  fluid  it  is  poured  into  cast-iron  moulds,  and  when 
cold  the  top  of  the  ingot  is  broken  oiT,  exposing  a  freshly-fractured  surface, 
'ilie  appearance  presented  is  that  of  confused  groups  of  crystals,  all  appear- 
ing to  have  started  from  the  outside  and  to  have  met  in  the  centre;  this 
general  form  is  common  to  all  ingots  of  whatever  composition,  but  to  the 
trained  eye,  and  only  to  one  long  and  critically  exercised,  a  minute  but  in- 


CBUCIBLE  STBEL. 


411 


deacribable  difference  is  perceived  between  varylns  samples  of  steel,  and 
this  difference  is  now  known  to  be  owiag  almost  wholly  to  variations  in  the 
amount  of  combined  carbon,  as  tiie  following  table  wiil  show.  Twelve  sam- 
ples selected  by  the  eve  alone,  and  analyses  of  drillings  taken  direct  from 
the  ingot  before  it  had  been  heated  or  hammered,  gave  results  as  below: 


Ingot 
Nos. 

Iron  by 
Diff. 

Carbon. 

Diff.  of 
Carbon. 

Silicon. 

Phos. 

Sulph. 

1 

99.614 
99.455 

.808 
.490 

.019 
.034 

.047 
.005 

.018 

8 

.188 

.016 

8 

99.368 

.529 

.089 

.043 

.047 

.018 

4 

99.270 

.649 

.180 

.039 

.030 

.012 

5 

99.119 

.801 

.163 

.029 

.085 

.016 

6 

99.066 

.841 

.040 

.a39 

.084 

.010 

7 

99.041 

.887 

.086 

.057 

.014 

.018 

8 

99.040 

.871 

.004 

.054 

.024 

.018 

9 

98.900 

.955 

.084 

.059 

.070 

.016 

10 

98.861 

1.005 

.050 

.068 

.084 

.018 

11 

96.762 

i.as8 

.058 

.190 

.064 

.006 

12 

98.884 

1.079 

.021 

.039 

.044 

.004 

Here  the  carbon  is  seen  to  increase  in  quantity  in  the  order  of  the  num- 
bers, while  the  other  elements,  with  the  exception  of  total  iron,  bear  no  rela- 
tion to  tlie  numbers  on  the  samples.    The  mean  difference  of  carbon  is  .071. 

In  mild  steels  the  discrimination  is  less  perfect. 

The  appearance  of  the  fracture  by  which  the  above  twelve  selections 
mere  made  can  only  be  seen  in  the  cold  ingot  before  any  operation,  except 
the  original  one  of  casting,  has  been  performed  upon  It.  As  soon  as  it  is 
hammered,  the  structure  changes  in  a  remarkable  manner,  so  that  all  trace 
of  the  primitive  condition  appears  to  be  lost. 

Another  method  of  rendering  visible  to  the  eye  the  molecular  and  chemi- 
cal changes  which  go  on  in  steel  is  by  the  process  of  hardening  or  temper- 
ing. Wlien  the  metal  is  heated  and  plunged  into  water  it  acquires  an 
increase  of  hardness,  but  a  loss  of  ductility.  If  the  heat  to  which  the  steel 
has  been  i*ai8ed  just  before  plunging  is  too  high,  the  metal  acquires  intense 
hardness,  but  it  is  so  brittle  as  to  l>e  worthless*,  the  fi'acture  is  of  a  bright, 
granular,  or  sandy  character.  In  this  state  it  is  said  to  be  burned,  and  it 
cannot  again  be  restored  to  its  former  strength  and  ductility  by  annealing; 
it  is  ruined  for  all  practical  purposes,  but  m  ^ust  this  state  it  again  shows 
differences  of  structure  corresponding  with  its  content  in  carbon.  The 
nature  of  these  chansres  can  be  illustrated  by  plunging  a  bar  highly  heated 
at  one  end  and  cold  at  the  other  into  water,  and  then  breaking  it  off  in 
pieces  of  equal  length,  when  the  fractures  will  be  found  to  show  appear- 
ances characteristic  of  the  temperature  to  which  the  sample  was  raised. 

The  specific  gravity  of  steel  is  influenced  not  only  by  its  chemical  analj''- 
SM.  but  by  the  heat  to  which  it  is  subjected,  as  is  shown  by  the  following 
table  (densities  referred  to  60°  F.): 

Specific  gravitiea  of  twelve  samples  of  steel  from  the  ingot;  also  of  six 
hammeied  bars,  each  tar  being  overheated  at  one  end  and  cold  at  the 
other,  in  this  state  plunged  into  toater^  and  then  broketi  into  pieces  of 
equal  length. 


1 

2 

3 

7.841 
7.818 

4 
7.791 

6 

i\838 

6 
7.834 

7.789 

7.784 
7.780 
7.808 
7.8ia 
7.889 

7 

8 

7.818 

7.7.58 
7.755 
7.7.58 
7.773 
7.790 
7.8-25 

9 

7.813 

10 



7.807 

7.744 
7.749 
7.755 
7.789 
7.812 
7.826 

11 
7.803 

12 

Ingot 

Barr 
*Bamed  I. 

7.819 

7.805 
7.690 

2. 

7.814  7.811 
7.82;J'7.Pao 

7.741 

3. 

7.769 

4. 

5 

7.826 
7  831 

7.849 
7.806 
7.824 

7.798 
7.811 

Cold  6. 

7.844 

7.825 

*  Qrd^r  of  samples  from  b^r. 


412 


8TEEL. 


^ITeet  of  Heat  on  tlie  Grain  of  St«el«  (W.  Metcalf,— Jeanti  on 
8teel«  p.  64tS.)— A  simple  experiment  will  show  the  alteration  produced  in  a 
bigh-earbon  steel  by  different  methods  of  hardening:.  If  a  bar  of  such  st«el 
be  niclced  at  about  9  or  10  places,  and  about  half  an  inch  apart,  a  suitable 
specimen  is  obtained  for  the  experiment.  Place  one  end  of  the  bar  in  a 
good  Are,  so  that  the  flrst  nicked  piece  is  heated  to  whiteness,  while  the  rest 
of  the  bar,  being  out  of  the  fire,  is  heated  up  less  and  less  as  we  approach 
the  other  end.  As  soon  as  the  first  piece  is  at  a  good  white  heat,  which  of 
course  burns  a  high  carbon  steel,  and  the  temperature  of  the  rest  of  the  bar 

Sadually  passes  down  to  a  very  dull  red,  the  metal  should  be  taken  out  of 
e  fire  and  suddenly  plunged  in  cold  water,  in  which  It  should  be  left  till 
quite  cold.  It  should  then  be  talcen  out  and  carefully  dried.  An  examina- 
tion with  a  file  will  show  that  the  flrst  piece  has  the  greatest  hardness, 
while  the  last  piece  is  the  softest,  the  Intermediate  pieces  gradually  passing 
from  one  condition  to  the  other.  On  now  breaking  off  the  pieces  at  each 
nick  it  will  be  seen  that  very  considerable  and  characteristic  changes  have 
been  produced  in  the  appearance  of  the  metal.  The  flrst  burnt  piece  is  veiy 
open  or  crystalline  in  fracture;  the  succeeding  pieces  become  closer  and 
closer  in  the  graiu  until  one  piece  is  found  to  possess  that  perfectly 
even  grain  and  velvet-like  appearance  which  is  so  much  prized  by  experi- 
enced steel  users.  The  flrst  pieces  also,  which  have  been  too  much  hard- 
ened, will  probably  be  cracked ;  those  at  the  other  end  will  not  be  hardened 
through.  Hence  if  it  be  desired  to  make  the  steel  hard  and  strong,  the 
temperature  used  must  be  high  enough  to  harden  the  metal  through,  bat 
not  sufficient  to  open  the  grnin. 

€liang:es  In  intimate  Strenfptli  and  Elastlcltr  dne  to 
Bammerlns:.  Annealing,  and  Temperinc*  (J-  w.  Langley, 
Trans.  A.  S.  C.  K  1882.)— The  following  tablA  gives  the  result  of  tests  made 
on  some  round  steel  bars,  all  from  the  same  ingot,  which  were  tested  by 
tensile  stresses,  and  also  by  bending  till  fracture  took  place: 


Treatment. 

Carbon. 

1^1 
ill 

III 

It 
1.^ 

ii 

IS 

i 

B 

1 

it 

1 

2 

3 

4 

Cold-hammered  bar 
Bar  drawn  black.... 

Bar  annealed  

Bar    hardened   and 
drawn  black 

153 

75 
175 

30 

1  25 
1.25 
1.81 

1.09 

.47 
.47 
.70 

.86 

.575 
.577 
.580 

.678 

9-^,420 
114,700 

88,  no 

152,800 

141,500 
188,400 
96,410 

248,700 

8.00 
6.00 
10.00 

8.88 

8.42 

12.45 
11.69 

17.9 

The  total  carbon  given  in  the  table  was  found  by  the  color  test,  which  is 
affected,  not  only  by  the  total  carbon,  but  by  the  condition  of  the  carbon. 

The  analysis  of  the  steel  was: 

Silicon  242       Manganese 94 

Phosphorus 02        Carbon    (true   total  carbon,   by 

Sulphur 009  combustion) 1.81 

Heatlna;  Tool  Steel.  (Crescent  Steet  Co..  Pittsburg,  Pa.>~There are 
three  distinct  stages  or  times  of  heating:  First,  for  forging;  second,  for 
hardening;  third,  for  tempering. 

The  flrst  requisite  for  a  good  rieat  for  forging  is  a  clean  flre  and  plenty  of 
fuel,  so  that  jets  of  hot  air  will  not  strike  the  corners  of  the  piece;  next,  the 
flre  should  be  regular,  and  give  a  good  uniform  heat  to  the  whole  part  to  be 
forged.  It  should  be  keen  enough  to  heat  the  piece  as  rapidly  as  may  be, 
and  allow  it  to  be  thoroughly  heated  through,  without  being  so  fierce  as  to 
overheat  the  corners. 

Steel  should  not  be  left  in  the  flre  any  longer  than  is  necessary  to  heat  it 
clear  through,  as  *'  soaking  '^  in  flre  Is  very  injurious;  and,  on  the  other  hand, 
it  is  necessary  that  it  should  be  hot  through,  to  prevent  surface  cracks. 

By  observing  these  precautions  a  piece  of  steel  may  alwa/s  be  heated 
safely,  up  to  even  a  bright  yellow  heat,  whea  there  is  much  forging  to  be 
done  on  it. 


CRUCIBLE  STEEL.  ^  413 

The  best  and  most  economical  of  welding  fluxes  fs  clean,  crude  boras, 
vhich  should  be  flrst  thoroiifrhly  melted  and  then  fcrouod  to  fine  powder. 

After  the  steel  is  properly  heated,  it  should  be  forged  to  shape  as  quickly 
as  posidble;  and  just  as  the  red  heat  Is  leaving  the  partn  intended  for  cuttitie 
edKes.  these  parts  should  be  reflned  by  rapid,  light  blows,  continued  until 
the  red  disappears. 

For  tlie  second  stage  of  heating,  for  hardeniuRr,  great  care  should  1)6  used: 
first,  to  protect  the  cutting  edges  and  working  parts  from  heating  more 
rapidly  than  the  body  of  the  piece:  next,  that  the  whole  part  to  be  hardened 
be  heated  uniformly  through,  without  any  part  becoming;  visibly  hotter 
than  the  other.  A  uniform  heat,  as  low  as  will  give  the  required  hardness, 
is  the  best  for  hardening. 

For  every  variation  of  heat,  which  Is  great  enough  to  be  seen,  there  will 
result  a  variation  Ingrain,  which  maybe  seen  by  brealciiig  the  piece:  and 
for  every  such  variation  In  temperature,  there  Is  a  very  good  chance  for  a 
crack  to  be  aeen.    Many  a  costly  tool  is  ruined  by  inattention  to  this  point. 

The  effef't  of  too  high  heat  Is  to  open  the  grain;  to  make  the  steel  coarse. 
The  effect  of  an  irregular  heat  Is  to  cause  Irregular  grain,  irregular  strains, 
and  craclis. 

As  soon  as  the  piece  is  properly  heated  for  hardening,  it  should  bo 
pr>frnptly  and  thoroughly  quenched  in  plenty  of  the  cooling  medium,  water, 
brine,  or  oil.  as  the  case  may  be. 

An  abundance  of  the  cooling  bath,  to  do  the  work  quickly  and  uniformly 
an  over^  is  very  necessaiy  to  pood  and  safe  work. 

To  liarden  a  large  piece  safely  a  running  stream  should  be  used. 
Much  uneren  hardening  is  caused  by  the  use  of  too  small  baths. 
For  the  third  stage  of  heating,  to  temper,  the  flrst  important  requisite  is 
airain  uniformity.    The  next  is  time;  the  more  slowly  a  piece  is  brought 
dowD  to  its  temper,  the  better  and  safer  is  the  operation. 

When  expensive  tools  are  to  be  made  it  is  a  wise  precaution  to  try  small 
pieces  of  the  sted  at  different  temperatures,  so  as  to  And  out  how  low  a  heat 
will  frive  the  necensary  hardneas.  The  lowest  heat  Is  the  best  for  any  steel. 
Heatlnflf  to  Poree*— The  trouble  in  the  forge  flre  is  usually  uneven 
heat,  and  not  too  high  heat.  Suppose  the  piece  to  be  forced  has  been  put 
into  a  very  hot  flre,  and  forced  as  quickly  as  possible  to  a  high  yellow  beat, 
so  that  it  is  almost  up  to  the  scintillating  pomt.  Tf  this  be  done,  in  a  few 
minutes  the  outside  will  be  quite  soft  and  In  a  nice  condition  for  forging, 
while  the  middle  parts  will  not  be  more  than  red-hot.  Now  let  the  piece  be 
placed  under  the  hammer  and  forged,  and  the  soft  outside  will  yield  so 
much  moi«  readily  than  the  hard  inside,  that  the  outer  particles  will  be  tern 
aatinder.  while  the  inside  will  remain  sound. 

Suppose  the  case  to  be  reversed  and  the  inside  to  be  much  hotter  than  the 
oaraide;  that  is,  that  the  inside  shall  be  in  a  state  of  semi-fusion,  while  the 
outside  is  hard  and  firm.  Now  let  the  piece  be  forged,  and  the  outside  will 
be  all  sound  and  the  whole  piece  will  appear  perfectly  good  until  it  is 
cropped,  and  then  it  is  found  to  be  hollow  Inside 

In  either  case,  if  the  piece  had  been  heated  soft  all  through,  or  if  it  had  been 
only  red-hot  all  through,  it  would  have  f orgred  perfectly  sound. 

In  some  cases  a  high  heat  is  more  desirable  to  save  heavy  labor  but  in 
every  case  where  a  fine  steel  is  to  be  used  for  cutting  purposes  It  must  be 

bonie  In  mind  that  very  heavy  forging  refines  the  bars  as  they  slowly  cool, 
and  if  the  smith  heats  such  reflned  bars  until  they  are  soft,  he  raises  the 
grain,  makes  them  coarse,  and  he  cannot  get  them  fine  tig&\n  unless  he  has 
a  very  heavy  steam-hammer  at  command  and  knows  how  to  use  it  well. 

Aiuiealliifl:.  (Crescent  Steel  Co.)— Annealing  or  softening  is  accom- 
pljahed  by  heating  steel  to  a  red  heat  and  then  cooling  it  very  slowly, 

tojpreTent  It  from  getting  hard  again. 
The  higher  the  decree  of  heat,  the  more  will  steel  be  softened,  until  the 

limit  of  softness  is  reached,  when  the  steel  is  melted. 
It  does  not  follow  that  the  higher  a  piece  of  steel  is  heated  the  softer  It 

will  he  when  cooled,  no  matter  how  slowly  It  may  be  cooled:  this  Is  proved 

by  the  fact  that  an  ingot  is  always  harder  than  a  rolled  or  hammered  bar 

mad«*  from  It 
Therefore  there  is  nothing  gained  by  heating  a  piece  of  steel  hotter  than 

a  good,  bright,  cherry-red:  on  the  contrary,  a  higher  heat  has  several  dis- 

advasta^es:  First.  If  carried  too  far.  It  may  leave  the  steel  actually  harder 

than  a  good  red  heat  would  leave  it.    Second.  If  a  scale  is  raised  on  tlie 

steel,  this  scale  will  be  harsh,  granular  oxide  of  Iron,  and  will  spoil  the  tools 

used  to  cut  it.    Third.  A  high  scaling  heat  continued  for  a  little  time 


4U 


STEEL. 


changes  the  struotare  of  the  steel,  makes  It  brittle,  liable  to  crack  in  hard- 
ening«  and  impossible  to  reflne. 

To  anneal  any  piece  of  steel,  heat  it  red-hot ;  heat  it  uniformly  and  heat  it 
through,  taking  care  not  to  let  the  ends  and  corners  get  too  hot. 

Aa  soon  as  it  is  hot.  take  it  out  of  the  Are,  the  sooner  the  better,  and  coo! 
It  as  slowly  as  possible.  A  good  rule  for  heating  is  to  heat  it  at  so  low  a  red 
that  when  the  piece  is  cold  it  wilt  still  show  the  blue  gloss  of  the  oxide  that 
was  put  there  by  the  hammer  or  the  rolls.  ' 

Steel  annealed  in  this  way  will  cut  very  soft ;  it  will  harden  very  bard, 
without  cracking;  and  when  tempered  it  will  be  v^y  strong,  nicely  refined, 
and  will  hold  a  keen,  strong  edge. 

Temperliis.—Teinpering  steel  is  the  act  of  giving  it,  after  it  has  been 
shaped,  the  hardness  necessary  for  the  work  it  has  to  do.  This  is  done  by 
flrsc  hardening  the  piece,  generally  a  good  deal'  harder  than  is  necessary, 
and  then  toughening  it  by  slow  heating  and  gradual  softening  until  it  is  Just 
right  for  work. 

A  piece  of  steel  properly  tempered  should  always  be  finer  in  grain  than 
the  bar  from  which  it  is  made.  If  it  is  necessary,  in  order  to  make  the  piece 
as  hard  as  is  required,  to  heat  it  so  hot  that  after  being  hardened  the  grain 
will  be  as  coarse  as  or  coarser  than  the  grain  in  the  original  bar,  then  the 
steel  itself  is  of  too  low  carbon  for  the  desired  work. 

If  a  great  degree  of  hardness  is  not  desired,  as  in  the  case  of  taps,  and 
most  tools  of  complicated  form,  and  it  is  found  that  at  a  moderate  heat  the 
tools  are  too  hard  and  are  liable  to  crack,  the  smitli  should  first  use  a  lower 
heat  In  order  to  save  the  tools  already  made,  and  then  notify  the  steelmaker 
that  his  steel  is  too  high,  so  as  to  prevent  a  recurrence  of  thA  trouble. 

For  descriptions  of  various  methods  of  tempering  steel,  see  "  Tempering 
of  Metals,'*  by  Joshua  Rose,  in  App.  Cyc  Mech.,  vol.  ii.  p.  868 ;  also, 
*'  Wrinkles  and  Recipes,"  from  the  Scientific  American.  In  both  of  these 
works  Mr.  Rose  gives  a  "  color  scale,"  lithographed  in  colors,  by  which  the 
following  is  a  list  of  the  tools  in  their  order  on  the  color  scale,  together  with 
the  approximate  color  and  the  temperature  at  which  the  color  appears  on 
brightened  steel  when  heated  in  the  air : 


Scrapers  for  brass  ;  very  pale  yeU 
iSw,  4«0*  F.  '  ^     " 

Steel-engraving  tools. 

Slight  turning  tools,  j 

Hammer  faces. 

Planer  tools  for  steel. 

Ivory-cutting  tools. 

Planer  tools  for  iron. 

Paper-cutters. 

Wood-engraving  tools. 

Bone  cutting  tools. 

MillinK-cutters:  9t%'aw  yellow^  460*  F. 

Wire-drawing  dies. 

Boring^utters. 

4/eather-cutting  dies. 

Screw-cutting  dies. 

Inserted  saw-teeth. 

Taps. 

Rock^l  rills. 

Chasers. 

Punches  and  dies. 

Penknives. 

Reamers. 

Half-round  bits. 

Planing  and  moulding  cutters. 

Stone-cutting  tools  ;  brovm  yellow^ 
SOO-F. 

Gouges. 


Hand-plane  irons. 

Twist-drills. 

Flat  drills  for  brass. 

Wood-boring  cutters. 

Drifts. 

Coopers*  tools. 

Edging  cutters;  light pw'pU^  630*  F. 

Augers. 

Dental  and  surgical  Instnimenta. 

Cold  chisels  for  steel. 

Axes  ;  dark  purple,  560*  F. 

Gimlets. 

Cold  chisels  for  cast  iron. 

Saws  for  bone  and  Ivorr. 

Needles. 

Firmer-chisels. 

Hack-saws. 

Framing-chisels. 

Cold  chisels  for  wrought  Iron. 

Moulding  and  planing  cutters  to  b« 

filed. 
Circular  saws  for  metal. 
Screw-drivers. 
Springs. 
Saws  for  wood. 

Dark  blue,  670*  F. 

FaU  blue,  610*. 

Blue  tinfftd  toiih  green,  680". 


FOECS,  STATICAL  MOMENT^  BQUILIBRIU.M,  STO.    416 


MECHANICS. 

FOBOBi  STATIOAIi  nOHIENT,  E<|I^II'IBBIU]II,  BTC. 

Umcbamiob  is  the  scteQce  kbat  treats  of  the  action  of  force  upon  bodies. 

A  Vore«  is  any  thins  that  tends  to  change  the  state  of  a  body  with  respect 
to  rest  or  uiotion.  If  a  body  Is  at.rest,  anything  that  tends  to  put  it  in  mo- 
tion is  a  force;  if  a  body  is  in  motion,  anything  that  tends  to  change  either 
its  direction  or  its  rate  of  motion  is  a  force. 

A  force  should  always  mean  the  pull,  pressure,  rub,  attraction  (or  rspul- 
Bioii)  of  one  body  upon  another,  and  always  implies  the  existence  of  a  simul- 
taneous equal  and  opposite  force  exerted  by  that  other  body  on  the  first  body, 
Le.,  the  reaction.  In  no  case  should  we  call  anything  a  force  unless  we  can 
conceive  of  It  as  capable  of  meavurement  by  a  spring-balance,  and  are  able 
til  say  from  what  other  body  Ic  comes.    (I.  P.  Church.) 

Forces  may  be  divided  into  two  classes,  extraneous  and  molecular:  extra- 
neous forces  act  on  bodies  from  without;  molecular  forces  are  exerted  be- 
tween the  neighboring  particles  of  bodies. 

Kagtraneout  foixe»  are  of  two  kinds,  pressures  and  moving  forces:  pres- 
sures simply  tend  to  produce  motion;  rooYing  forces  actually  produce 
motion.  Thus,  If  gravity  act  on  a  fixed  body,  it  creates  pressure;  if  on  a  free 
body,  it  produces  motion. 

MoUctUar  /ofxea  are  of  two  kinds,  attractive  and  repellent:  attractive 
forces  tend  to  bind  the  i>articles  of  a  body  together;  repellent  forces  tend 
to  thrust  them  asunder.  Both  kinds  of  molecular  forces  are  continually 
exerted  between  the  molecules  of  bodies,  and  on  the  predominance  of  one 
or  the  other  depends  the  physical  state  of  a  body,  as  solid,  liquid,  or  gaseous. 

The  ITiilf  of  Force  used  in  engineering,  by  English  writers,  is  the 
nound  avoirdupois.  (For  some  scientific  purposes,  as  in  electro-dynamics, 
forces  are  sometimes  expressed  in  '*  absolute  units."  The  absolute  unit  of 
force  is  that  force  which  acting  on  a  unit  of  mass  during  a  unit  of  time  pro- 
duces  a  unit  of  velocity;  in  English  measures,  that  force  whteh  acting  on 
the  mass  whose  weight  is  one  pound  in  London  will  in  one  second  produce  a 
velocity  of  one  foot  per  second  »  ]  -»•  89.167  of  the  weight  of  the  standard 
pound  avoirdupois  at  London.  In  the  French  C.  Q.  8.  or  centimetre-gramme 
second  system  it  is  the  force  which  acting  on  the  mass  whose  weight  Is  one 
gramme  at  Paris  will  produce  in  one  second  a  velocity  of  one  centimetre  per 
second.    This  unit  is  called  a  *'  dyne ''  s  1/981  gramme  at  Paris.) 

Inertia  is  that  property  of  a  body  hy  virtue  of  which  it  tends  to  continue 
in  the  state  of  rest  or  motion  in  whksh  ft  may  be  placed,  until  acted  on  by 
some  force. 

H eivton'9  I<aw»  of  Motton.— Ist  Law,  If  a  body  be  at  rest.  It  will 
remain  at  rest;  or  if  in  motion,  it  will  move  uniformly  in  a  stralc^t  line  till 
acted  on  by  some  force. 

9d  Law.  If  a  body  be  acted  on  by  several  forces,  it  will  obey  each  as 
thotigh  the  others  did  not  exist,  and  this  whether  the  body  be  at  rest  or  in 
motion. 

8d  Law.  If  a  force  act  to  change  the  state  of  a  body  with  respect  to  rest 
or  motion,  the  body  will  offer  a  resistance  equal  and  directly  opposed  to  the 
force.    Or.  to  every  action  there  is  opposed  an  equal  and  opposite  reoctfon. 

dmplile  Bepreeentatlon  of  a  Force.— Forces  may  be  repre- 
sented geometrically  by  straight  lines,  proportional  to  the  forces.  A  force 
is  given  when  we  know  its  intensity.  Its  point  of  application,  and  the  direc- 
tion In  which  it  acts.  When  a  force  Is  represented  by  a  line,  the  length  of  the 
line  represents  its  intensity;  one  extremity  represents  the  point  of  applies^ 
tjon;  and  an  arrow-head  at  the  other  extremity  shows  the  direction  of  the 
fovce. 

Compoeltioii  of  Forces  is  the  operation  of  finding  a  single  force 
vhoee  effect  is  the  same  as  that  of  two  or  more  given  forces.  The  required 
force  Is  calledthe  resultant  of  the  given  forces. 

Beeolatlon  of  Forces  Is  the  operation  of  finding  two  or  more  forces 
whose  combined  effect  Is  equivalent  to  that  of  a  given  force.  The  required 
forces  are  called  components  of  the  given  force. 

Tile  resultant  of  two  forces  kpplied  at  a  point,  and  acting  in  the  same  di- 
rectioiif  is  equal  to  the  sum  of  the  forces.  If  two  forces  act  in  opposite 
directions,  their  resultant  Is  equal  to  their  difference,  and  it  acts  in  the 
directioa  of  the  greater. 


416 


MECHANICS. 


If  any  number  of  forces  be  applied  at  a  point,  some  In  one  direction  aod 
others  in  a  contrary  direction,  their  resultant  is  equal  to  the  sura  of  those 
that  act  in  one  direction,  diminished  by  the  sum  of  those  that  act  in  the  op- 
posite direction;  or,  the  resultant  is  equal  to  the  algebraic  sum  of  the  com- 
ponents. 

Parallelogram  of  Foreea*— If  two  forces  acting  on  a  point  be  rep- 
resented in  direction  and  intensity  by  adjacent  sides  of  a  parallelogram, 
their  resultant  will  be  represented  by  that  diagonal  of  the  parallelogram 
which  passes  through  the  point.  Thus  OR,  Fig. 
88,  is  the  resultant  of  OQand  OP. 

Polygfon  of  Forces.— If  several  forces  are 
applied  at  a  point  and  act  in  a  single  plane,  their 
resultant  is  found  as  follows: 

Through  the  point  draw  a  line  representing  the 
first  force ;  through  the  extremity  of  this  draw 
a  line  representing  the  second  force;  and  so  on, 
-.      QQ  throughout  the  system ;  finally,  draw  a  line  from 

Fia.  w.  ^e  starting-point  to  the  extremity  of  the  last  line 

drawn,  and  this  will  be  the  resultant  required. 

Suppose  the  body  A,  Fig.  89.  to  be  urged  in  the  directions  A1,  Ai^  A^,  A4^ 
and  ^oby  forces  which  are  to  each  other  as  the  lengths  of  those  lines. 

take  it 

^^^^ ...       Ithefifih 

to  6''  ^The Tine  /15' represents  in  magnitude  and  direction  the  i-esultant  of 
all  the  forces  considered.  If  there  had 
been  an  additional  force,  Ax,  in  the  group, 
the  body  would  be  returned  by  that  force 
to  its  original  position,  «UPP<»«»K  ^^e 
forces  to  act  successively,  but  If  they  had 
acted  simultaneously  i  he  body  would  never  : 
have  moved  at  all;  the  tendencies  to  mo- 
tion balancing  each  oth«*r. 

It  follows,  thffrefore,  that  if  the  several 
forces  which  tend  to  move  a  bodv  can  be 
represented  in  magnitude  and  direction 
by  the  sides  of  a  closed  polygon  taken  In 
order,  the  bedy  will  remain  at  rest;  but  if 
the  forces  are  represented  by  the  sides  of 
an  open  polvgonT  the  body  wiU  move  and  the  direction  will  be  repreamted 
by  the  straight  line  which  doses  the  polygon.  «    ,^   * 

Tl^sted  PolysfOii.— The  mle  of  the  polygon  of  forces  holds  true  even 
when  the  forces  are  not  in  one  plane.  In  this  case  the  lines  ^1,  1-^'  rsj', 
etc    form  a  twisted  polygon,  that  is.  one  whose  sides  are  not  In  one  plane. 

Paralleloplpedon  of  Forces.- If  three  forces  acting  on  a  point  be 
represented  by  three  edges  of  a  paralleloplpedon  which  meet  In  a  common 
point,  their  resultant  will  be  represented  by  the  diagonal  of  the  parallelo- 
nloedon  that  nasses  through  their  common  point. 

'^^fhSs  O^l^T^  l«  th?  resultant  of  OQIOS,  and  OP.    OJf  Isthe  result 
ant  of  OjPand  OQ,  and  OR  is  the  resultant  of  03f  and  OS, 

Moment  of  a  Force.— The  mo- 
ment of  a  force  (sometimes  called  stat- 
ical moment),  with  respect  to  a  point. 
Is  the  product  of  the  force  by  the  per- 
pendicular distance  from  the  point  to 
the  direction  of  the  force.  The  fixed 
point  Is  called  the  centre  of  mo- 
S 


FSO.  961 


Fio.  91. 


FORCE,  STATICAL  MOMENT,  EQUILIBRIUM,  ETC.    417 

menta  ;  theperpeudieulAr  dfstaoce  Is  the  loTer-arm  of  the  force;  and  the 
moment  itself  measuren  the  tendency  of  the  force  to  produce  rotation  about 
the  centre  of  moments. 

If  the  force  is  expressed  in  pounds  and  the  distance  in  feet,  the  moment 
is  expresaed  in  foot-pounds,  it  is  necessaiy  to  observe  the  distinction  be- 
tween foot-pounds  of  statical  moment  and  foot- pounds  of  work  or  energy. 
(See  Woiic.) 

In  the  bent  lever,  Fig.  Ql  (from  Trautwine),  if  the  weights  n  and  m  repre- 
sent forces,  their  moments  about  the  point  /  are  respectively  nXa/  and 
mx/c  If  instead  of  the  weight  m  a  pulling  force  to  balance  the  weight 
n  is  applied  in  the  direction  te,  or  by  or  od,  «,  y,  and  d  being  the  amounts  of 
these  loroes,  their  respective  moments  are  »  X  ft,  y  X/b,  dxfh. 

If  the  forces  acting  on  the  lever  are  in  equilibrium  it  remains  at  rest,  and 
the  moments  on  each  side  of/  are  equal,  that  is,  n  X  a/=  m  X  /c,  or  «  x  /If, 
or  »  x  /&,  or  d  X  hf. 

The  moment  of  the  resultant  of  any  number  of  forces  acting  together  in 
the  same  plane  Is  equal  to  the  algebraic  sum  of  the  moments  of  the  forces 
taken  separately. 

StAtlcml  Moment.  Stability.— The  statical  moment  of  a  body  is 
the  product  of  its  weight  bv  the  distance  of  its  line  of  gravity  from  some 
assumed  line  of  rotation.  The  line  of  gravity  Is  a  vertical  line  drawn  from 
iu  centre  of  gravity  through  the  body.  The  stability  of  a  body  is  that  re- 
aistaDce  which  its  weight  alone  enables  it  to  oppose  against  forces  tending 
to  overturn  it  or  to  slrae  It  along  its  foundation. 

To  be  safe  against  turning  on  an  edge  the  moment  of  the  forces  tending  to 
overturn  It,  taken  with  reference  to  that  edge,  must  be  less  than  the  stati- 
cal moment.  When  a  body  rests  on  an  inclined  plane,  the  line  of  gravity 
being  vertical,  falls  toward  the  lower  edge  of  the  body,  and  the  condition  of 
its  not  being  overturned  by  its  own  weight  is  that  the  line  of  gravity  must 
fall  within  this  edge.  In  the  case  of  an  inclined  tower  resting  on  a  plane 
the  same  condition  holdsr— the  line  of  gravity  must  fall  within  the  base.  The 
condition  of  stability  against  sliding  along  a  horisontal  plane  is  that  the  hor- 
izontal component  of  the  force  exerted  tending  to  cause  it  to  slide  shall  be 
less  than  the  product  of  the  weight  of  the  body  into  the  coefficient  of  fric- 
tion between  the  base  of  the  body  and  its  supporting  plane.  This  coefficient 
of  friction  Is  the  tangent  of  the  angle  of  repose,  or  the  maximum  angle  at 


which  the  supporting  plane  might  be  raised  from  the  horizontal  before  the 
body  would  begin  to  slide.    (See  Friction.) 

Tlhe  Stability  of  a  Ilam  against  overturning  about  Its  lower  edge 
is  calculated  by  comparing  its  statical  moment  referred  to  that  edge  with 
the  resultant  pressure  of  the  water  against  its  upper  side.  The  horizontal 
presBuie  on  a  square  foot  at  the  bottom  of  the  dam  is  equal  to  the  weight  of 
a  column  of  water  of  one  square  foot  In  section,  and  of  a  height  equal  to  the 
dtttauoe  of  the  bottom  below  water-level :  or,  if  H  is  the  height,  the  pressure 
at  the  bottom  per  square  foot  =  68.4  x  JET  lbs.  At  the  water-level  tJie  pres- 
sure te  zero,  and  it  increases  uniformly  to  the  bottom,  so  that  the  sum  of  the 
pressures  on  a  vertical  strip  one  foot  in  breadth  may  be  represented  by  the 
area  of  a  triangle  whose  base  is  6S.4  x  H  and  whose  altitude  is  H,  or  69  4H>-«-2. 
The  centre  of  gravity  of  a  triangle  being  %  of  its  altitude,  the  resultant  of 
all  the  horisontal  pressures  m^v  be  taken  as  equivalent  to  the  sum  of  the 
preasnres  acting  at  f^H,  and  the  moment  of  the  sum  of  the  pressures  is 
therefore  62.4  x  H*  -h  6. 

Parallel  Forces.— If  two  forces  are  paraUel  and  act  in  the  same  direc- 
tion, their  resultant  Is  parallel  to  both,  and  lies  Itetween  them,  and  the  Inten- 
sity of  the  resultant  is  equal  to  the  sum  of  the  intensities  of  the  two  forces. 
Itans  In  Fig.  91  the  resultant  of  the  forces  n  and  m  acts  vertically  down- 
ward at/,  and  is  equal  to  n  -f  m. 

If  two  parallel  forces  act  at  the  extremities  of  a  straight  line  and  in  the 
same  direction,  the  resultant  divides  the  line  joining  the  points  of  application 
of  the  components,  inversely  as  the  components.  Thus  in  Fig.  91,  mm:: 
afife\  and  InFlg.  98,P:  Q::  8N  i  SM.  m,  ^   ^ 

The  resultant  of  two  parallel  forces  A  ^ 

acting  in  opposite  directions  is  parallel  y     > 

to  tioth,  lies  without  both,  on  the  side  ?^^      C  r  n 


and  In  the  dtrectloQ  of  the  greater,  /         i 

and  its  faitenalty  is  equal  to  the  differ-  «  y            \         ^  ^ 

enoe  of  the  Intensities  of  the  two  ""                L            ^ 

forces.  Fxo.  99, 


418  KECHAKIOS. 

Thnstbeniiilteiit  of  the  two  foroes  Oand  P,  F\g,  ML  is  equal  to  Q-  Pe 

B.    Of  any  two  parallel  f oroea  and  their 

N  resultant  each  Is  proportional  to  the  dls- 

Q<  '   '^  tuuse  between  the  other  two;  thua  in  both 

/{  Fifn.  ttaad  98,  Pi  Q  tRiiSNt  SMt  MN. 

fA-jS    I  ■  » p         Oovplea*— IfPandQbeequalandaot 

/       I  in  opposite  directions,  R  =  0:  that  li,  ther 

/         I  haTB  no  reaultant.    Two  such  Coroea  con- 

J .^|{  atltiite  wliat  is  called  a  couple* 


Qt 


^  G  The  tendency  of  a  ooaple  ia  to  produce 

no.  ML  rotation;  the  meaaure  of  thia  tendency, 

called  tke  moment  of  the  couplt,  is  the 
prodaot  of  one  of  the  forces  by  the  distance  between  the  two. 

Since  a  couple  has  no  single  resultant,  no  single  force  can  balance  a 
couple.  To  prevent  the  rotation  of  a  body  acted  on  by  a  couple  the  applica- 
tion of  two  other  forces  is  required,  forminn:  a  second  couple.  Thus  In  Fig. 
M,  Pand  Q  formlnfj^  a  couple,  may  be  balanced 
by  a  second  couple  formed  by  R  and  S.    The  IR 

point  of  application  of  either  RorS  may  be  a 
fixed  pivot  or  axis. 

Moment  of  the  couple  PQ  s  P(c  +  6  -f  a)  =< 
moment  of  R3  =*  Rb,    Also,  P  4- «  =*  Q  +  ». 

Th«  forces  R  and  8  need  not  be  parallel  to  P 
and  Q.  but  if  not,  then  their  components  parallel 
to  iv  Are  to  be  taken  Instead  of  the  forces 
themHftlTfts. 

Eqnlllbrltiai  of  Foreec.—A  system  of 
forces  applied  at  points  of  a  solid  body  will  be 
In  equilibrium  when  they  have  no  tendency  to  yS 

produce  motion,  either  of  translation  or  of  rota-  Fio.  iM. 

The  conditions  of  equilibrium  are :  1.  The  algebraio  sum  of  the  compo- 
nents of  the  forces  In  the  direction  of  any  three  rectangular  axes  must  be 
separately  equal  to  0. 

2.  The  algebraic  sum  of  the  moments  of  the  forces,  with  respect  to  any 
three  rectangular  axes,  must  be  separately  equal  to  0. 

If  the  forces  lie  in  a  plane :  1.  The  algebraic  sum  of  the  oomponenta  of  the 
forces,  in  the  direction  of  any  two  rectangular  axes,  must  be  separately 
equal  to  0. 

t.  The  algebraic  sum  of  the  moments  of  the  forces,  with  respect  to  any 
point  in  the  plane,  must  be  equal  to  0. 

If  a  body  is  restrained  by  a  fixed  axis,  as  in  ease  of  a  pulley,  or  wheel  and 
axle,  the  foi*ces  will  be  in  a  equilibrium  when  the  algebraic  sum  of  the  mo- 
ments of  the  forces  with  respect  to  the  axis  is  equal  to  0. 

CENTBB  OF  GBAVITT. 

The  centre  of  gravity  of  a  body,  or  of  a  system  of  bodies  rigidly  connected 
together,  is  that  point  about  which,  if  suspended,  all  the  parts  will  be  In 
equilibrium,  that  is,  there  will  be  no  tendency  to  rotation.  It  is  the  point 
through  which  passes  the  resultant  of  the  efforts  of  gravitation  on  each  of 
the  elementary  particles  of  a  body.  In  bodies  of  equal  heavineea  through- 
out, the  centre  of  gravity  is  the  centre  of  mognitude. 

(The  centra  of  magnitude  of  a  figure  is  anoint  such  that  if  the  flgnre  be 
divided  into  equal  parts  the  diKtance  of  the  centre  of  magnitude  of  tJie 
whole  figure  from  any  given  plane  is  the  mean  of  the  distances  of  theoentres 
of  magnitude  of  the  several  equal  paru  from  that  plane.) 

If  a  body  be  suspended  at  its  centre  of  gravity,  It  will  be  in  equilibrium  in 
all  positions.  If  It  be  suspended  at  a  point  out  of  its  centre  of  graTlty,  it 
will  swing  Into  a  position  such  that  its  centre  of  gravity  is  ▼ertlcally  beneath 
itspolnt  of  suspension. 

To  And  the  centre  of  gravity  of  any  plane  figure  mechanically,  suspend 
tbe  figure  by  any  point  near  its  edge,  and  mark  on  It  the  direction  of  a 
plumb-line  hung  from  that  point :  then  suspend  it  from  some  other  point, 
and  again  mark  the  direction  of  the  plumb-line  in  like  manner.  Than  the 
centre  of  gravity  of  the  surface  will  be  at  the  point  of  interseclton  oC  the 
two  marks  of  the  plnmb-line. 

Tlie  Centre  of  Grairity  of  Resalar  Fl^iirea,  whether  plane  or 
■olid,  is  the  same  as  their  geometrical  centre  ;  for  instance,  a  straight  line, 
a 


MoiTEirT  ot  tst&ruu  419 

|MtfB]le1oin«in,  regular  polygon,  etrole,  circular  ring,  prism,  c)rttiider, 
sphere,  spheroid,  middle  fnistutns  of  spheroid,  etc. 

Of  a  triangle :  On  a  line  draws  from  aay  angle  to  Um  middle  of  the  op- 
posite side,  at  a  distance  of  oue  thitti  of  the  line  from  the  side;  or  at  the 
lotersection  of  such  lines  drawn  from  any  two  anKles, 

Of  a  trapexium  or  trapezoid :  Draw  a  diagonal,  dtvidlnflr  it  Into  two  tri- 
angles. Draw  a  line  Joiniag  thtir  centres  of  f^rarlty.  Draw  the  other 
diagonal,  malring  two  other  triangles,  and  a  line  joining  their  centres.  The 
interaection  of  the  two  lines  is  Che  centre  of  gravity  required. 

Of  a  metttor  of  a  eirtle :  On  the  JUdiUH  which  lilaects  the  arc,  Scr  •«-  8/  from 
the  centre,  e  being  the  chordi  r  the  radius,  and  I  the  arc 

O/a  •mucirefo.'  On  the  oiiddto  raoiusi  MUr  from  the  centre. 

W  a  quadrant :  On  the  middte  radius,  .(WKhir  from  tlie  centre. 

Of  a  aeffment  of  a  cirde ;  c*  h-  14a  f  itMu  the  centre,    c  =  chord,  a  =  area. 

Of  a  poroboUc  9m-fiJLct :  In  the  axle,  a/S  of  its  lenglh  from  the  vertex. 

Of  a  aemi-fjariMboia  {turf ace) :  fl/6  length  of  the  axis  from  the  vertex,  iuid 
^  of  ihe  aeim*base  from  the  axia 

Of  a  emis  or  pwramid :  In  tiie  axis,  |4  o^  ^ts  length  from  the  base. 

Of  a  pM-ahoiold  ;  In  the  axis,  ^  of  its  length  from  the  vertex. 

Of  a  cylinder^  or  regular  pritm  :  In  the  nuddle  point  of  the  axis. 

Of  a  frustum  of  a  ctme  or  pyramid  :  Let  a  =  length  of  a  line  drawn  from 
the  vertex  of  tlM  M&a  Wfasn  oomolete  to  die  ovntre  of  gravity  of  the  base,  and 
a'  that  portion  of  it  between  the  vertex  and  the  top  of  the  frustum;  then 
distance  of  centre  of  giiivity  of  the  ftvitum  f ktim  centre  of  gravity  of  its 

fktr  two  hodiMM,  fixed  one  at  each  end  of  a  Straight  Mtr,  the  common 
centre  of  gravity  is  in  the  bar,  at  that  poinc  which  divides  the  distance 
between  ttieir  respective  centres  of  gravity  in  the  Inverse  t-atio  of  the 
weights.  In  this  solution  the  weight  of  the  bar  is  neglected.  But  It  may 
be  taken  as  a  third  body,  and  allowed  fbr  as  In  the  following  directions  : 

For  more  than  two  bodies  connected  in  one  system:  Find  the  common 
centre  of  gravity  of  two  ot  them  ;  sndfind  the  common  centre  of  these  two 
jointly  with  a  third  body,  and  to  on  to  the  last  body  of  the  group. 

Another  method,  by  the  principle  of  moments :  To  find  the  centre  of 
Kravfty  Of  a  system  of  bodMS,  or  a  body  oonsietiog  of  several  parts,  whoi« 
several  centres  are  known.  If  the  bodies  are  in  a  plane,  refer  their  several 
centres  to  two  rectangular  eo<»rdinate  axes.  MnlUpIv  each  weight  by  its 
distance  from  one  of  the  axes,  add  the  prodUctsi  and  divide  the  sum  by  the 
sum  of  the  weights:  the  result  Is  the  distance  of  the  centre  of  gravity  from 
that  axis.  Do  the  same  with  regard  to  the  other  axis.  If  the  bodies  are 
not  In  a  plane,  refer  them  to  three  planes  at  right  angles  to  each  other,  and 
determine  the  meiia  distance  of  th«  sum  of  the  weights  f  i^om  eaoh  of  ihe 
three  planes. 

MOMBNV  OF  in IBRTIA. 


moment  of  Inei*t4a  with  respect  to  any  axis  =  J,  the  weight  of  any  element 
of  the  body  =  io,  and  its  distance  from  tbe  axis  s  r,  we  nave  /  >=  %{wr*). 

The  moment  of  Inertia  vAries,  in  the  Satne  body,  according  to  the  position 
of  tlie  axis.  It  is  the  least  possible  wheh  the  axis  passes  through  the  centre 
of  gravity.  To  find  the  moment  of  inertia  of  a  body,  referred  to  a  given 
axis,  divide  the  body  into  small  parts  of  regular  figure.  Multiply  the  Weight 
of  each  part  by  the  square  of  tht  distance  of  its  centre  of  gravity  from  the 
axis.  The  sum  of  the  products  Is  the  moment  of  inertia.  The  value  of  the 
moment  of  inertia  thtis  obtained  will  be  more  nearly  exact,  the  smaller  and 
more  numerous  the  parts  into  Which  the  body  is  divided. 

MoMXNTs  or  Inertia  of  tlKoniJkg  Solids.— Rod,  or  bnr,  of  utilforili  thick- 
,  with  respect  to  an  axis  perpendicular  to  the  length  of  the  rod. 


W^  weight  of  rod,  iU  =  length,  d  s  distance  of  centre  of  gravity  from  axis. 

slrcular  plate,  axis  in  its!  ,     ivf^  am\,  /m 

pUne.  \I=W[j^^d»);   .    , <?) 


Thin  circular 

own 
rs  radius  of  plate. 


420  HBCHAKICS. 

r 

Circular  plate,azi8  perpendicular )  ,      nrt'"^  i  ^\  <« 

tothepUte.  f/«»rVY+<t*) « 

Circular  ring,  axis  perpendicular  )  _      mt  ^•"^  +  »*'•    ,  m\  mm>, 

to  its  own  plane,  \'^^^\ — s +"  /•      •    •    •    -    W 

r  and  r*  are  the  exterior  and  interior  radii  of  the  ring. 

Cylinder,  axis  penaendicular  to?  ,      fw/**'  ,    ^    j  j.^  /n 

the  axis  of  the  cylinder,  f  '  =  ^\7  +  T  "^  ^'^Z ^ 

r  =  radius  of  base,  21  =  length  of  the  cylinder. 

By  making  d  =  0  in  any  of  the  above  formuln  we  find  the  moment  of 
inertia  for  a  parallel  axis  through  the  centre  of  gravity. 

The  moment  of  inertia.  Sirr*,  numerically  equals  the  weight  of  a  body 
which,  if  concentrated  at  the  distance  unity  Irom  the  axis  of  rotation,  would 
require  t  he  same  work  to  produce  a  given  increase  of  angrular  velncity  iliat  the 
actual  body  requires.  It  bears  the  same  relation  to  angular  aoc«>leratloii 
which  weight  does  to  linear  acceleration  (Rankine).  The  term  moment  of 
inertia  is  also  used  In  regard  to  areas,  as  the  cross-sections  of  beams  under 
strain.  In  this  case  J=  2ar*,  In  which  a  is  any  elementary  area,  and  r  lu 
distance  from  the  centre.  (See  Moment  of  Inertia,  under  Strength  of  Ma- 
terials, p.  247.) 

OBlfTRB  AND  RADIUS  OF  GYRATION. 

The  centre  of  gyration,  with  reference  to  an  axis,  is  a  point  at  which,  if 
the  entire  weight  of  a  body  be  concentrated,  its  moment  of  inertia  will  re- 
main unchanged;  or,  in  a  revolving  body,  the  point  in  which  the  whole 
weight  of  the  body  may  be  conceived  to  be  concentrated,  as  If  a  p«iund  nf 
platinum  were  substituted  for  a  pound  nf  revolving  feathers,  the  angular 
velocity  and  the  accumulated  work  remaining  the  name.  The  distance  of 
this  point  from  the  axis  Is  the  radiiu  of  gyi-ation.  It  W  =  the  weight  of  a 
body,  /  =  ZuT*  =  Its  moment  of  Inertia,  and  k  =  its  radius  of  gyration. 


i  =  TTib*  =:  Ztor«;    k 


y    w 


The  moment  of  inertia  s  the  weight  x  the  square  of  the  radius  of  gyration. 

To  find  the  radius  of  gyration  divide  the  body  into  a  considerable  number 
of  equal  small  parts— the  more  numerous  the  more  nearly  exsct  is  the  r«»> 
suit.— then  take  the  mean  of  all  the  squares  of  the  distances  of  the  parts 
from  the  axis  of  rev«)lutlon,  and  find  the  square  root  of  the  mean  square. 
Or,  if  the  moment  of  inertia  is  known,  divide  it  by  the  weight  and  extmct 
the  square  root.  For  radius  of  gyration  of  an  area,  as  a  cross^sectton  of  a 
beam,  divide  the  moment  of  Inertia  of  the  area  by  the  area  and  extract  the 
square  root. 

The  radius  of  gyration  Is  the  least  possible  when  the  axis  passes  through 
the  centre  of  gravity.  This  minimum  radius  is  called  the  principal  radius 
of  gyration.  If  we  denote  It  by  h  and  any  other  radius  of  K-ration  by  ft', 
we  have  for  the  Ave  cases  given  under  the  head  of  moment  of  inertia  abovo 
the  following  values : 

(8)  Circular  plate,  axis  It,.-./^.  w--  /*•  i  Ji 
perpen. to plani,       \'""^y%'  *^-|/  -g"*"    ' 

(4)  arcular  ring,  axis)  .  ^    /r«-»-r^*.   w.      /,*  +  i-i 
perpen.  to  plane.      I  *      y  — s — »  *^«  |/  — g —  +  «"• 

(5)  Cylinder,  axis  per-  J  j.  .  ^  /»^^T*^ .    w  - .  /r»       l»  .  ^ 
pen.  to  length,  J*      J/T  +  T'    *'-|/7  +  y+^ 


OESrXRES  OF  08CILLATI0K  AKD  OF  PERdTSSIOK.  421 


Principal  Iftadll  of  Gyration  and  Square*  of  Badll  of 
Gyration* 

(For  radii  of  gyration  of  sections  of  columns,  see  pai^e  849.) 


Surface  or  Solid. 


Bad.  of  Gyration.      ^J^^y'S^^fo^* 


faralleloeram: )  axis  at  its  base 

beffEhtK  §    '*    inid-height 

^*|?i  ^i  thin  I"*''  ^L^- 

recuauT.  plate  f  mid-length. . 
ftectangular  prism: 

axes  ia^  2&,  2c,  referred  to  axis  2a.,, 
Parallelopiped:  leuKth  Z,  tMMe  6,  axis  ) 

at  one  end,  at  raid-breadth f 

Hollow  square  tube: 

out.  side  A,  inn'r  V,  axis  mid-leogth . . 

▼ery  thin,  sides  A, '* 

Thin  rectangular  tube:  sides  fr,  hy  [ 
axis  mid-length f 

Thincircplate:  rad.r,diam.A,ax.  diam. 

Flat  circ.  ring:  diams.  ft,  h',  axis  dIam. 

Solid   circular  cylinder:    length  L  r 
axis  diameter  at  mid-length 

Circular  plate:  solid  wheel  of  uni- 
form thickness,  or  cylinder  of  any 
length,  referred  to  axis  of  cyl 

Hollow  circ.  cylinder,  or  flat  ling: 
{,  length;  R^  r,  outer  and  inner 
radii.  Axis,  1,  longitudinal  axis; 
2,  diam.  at  mid-length. 

Same:  very  thin,  axis  Its  diameter. . . . 

'*     radius  r;  axis,  longitudM  axis. . 

Circumf .  of  circle,  axis  its  centre 

*     *♦  diam 

Sphere:  radius  r.  axis  its  diam 

S|>her«>ld :   equatorial  radius  r,  re- ) 

solving  polar  axis  a ) 

Paraboloid :  r  =  rad.  of  base,  rev.  \ 

oil  axis f 

Ellipsoid:  semi-axes  a,  2>,  c;  revolv-  ( 

Ingonaxisto ) 

Spherical  shell:  radii  H,  r,  reTolving  i 
on  its  diam ) 

Same:  very  thin,  radius  r 

Solid  cone:  r  =  rad.  of  base,  rev.  on  I 
axis I 


.5778^ 
,2a9dh 

.67T8i 


.577V5«-fc« 


.289  V4i«  -f  6« 


.289  Vh*  -f  /*'» 
.406A 


.289  Vn-f8r« 
.7071r 


.W71  V«'4-»» 
9  V«'  +  8(H*-t-r«) 

.289  VI*  +  GRi 

r 

r 

.7071r 


.e825r 
.5773r 


.4472  Vfc»-f  c« 


^  /JB«  -  ri 

.8165r 
5477r 


«ft« 

1/I2ft« 

l/12/« 

(6«-|-c«)H-8 

41*  -\-  ft* 

12 

(ft«-|-ft'«)-i-18 

M    ft -f  8ft 

12*  ft-Hft 

J4)-«  =  ft«-+-16 

(/i«-fft'«)-+-16 

12^  4 

(R«  +  r«)-».2 

12"^        4 

12"^  2 
r« 
r* 

2/5i» 

fta  +  c« 

5 

2  g»  ~  r* 

6  «>  -  r> 

0.8r« 


CKlfTRBS  OF  OSCililiATION  AND  OF  PERCUSSION. 

Centre  of  Osclllatloii.— If  a  body  oscillate  about  a  fixed  horizontal 
axis,  not  passing  through  it.s  centre  of  gravity,  there  is  a  point  in  the  line 
drawn  from  the  centre  of  gravity  perpendicular  to  the  axis  whose  motion 
is  the  same  as  it  would  be  If  the  whole  mass  were  collected  at  that  point 
and  allowed  to  vibrate  as  a  pendulum  about  the  fixed  axis.  This  pomt  is 
called  Uie  centre  of  oscillation. 

Tlie  Badlas  of  Oscillation,  or  distance  of  the  centre  of  oscillation 
from  the  point  of  suspension  =  the  square  of  the  radius  of  gyration  -+-  dis- 
tance of  Uie  centre  of  gravity  fmm  the  point  of  suspension  or  axis.  The 
centres  of  oscillation  and  sunpencion  are  convertible. 

If  a  straight  line,  or  uniform  thin  t)ar  or  cylinder,  be  suspended  at  one  end, 
oscillating  about  it  as  an  axis,  the  oettre  of  oscillation  is  at  H  the  length  of 


422  IIECHAKIOS. 

the  rod  from  the  asb.  If  the  point  of  fiuM)«Dsioo  is  At  W  the  ktifftb  from 
the  end,  the  centre  of  oscillation  is  also  at  fi  the  length  from  the  axis,  that 
iR.  it  is  at  the  other  end.  In  both  cases  the  oscillation  will  be  performed  in 
the  name  time.  If  the  point  of  suspension  is  at  the  centre  of  gravity,  the 
length  of  the  equivalent  simple  pendulum  is  Infinite,  and  therefore  the  time 
of  vibration  isfnflnite. 

For  a  sphere  suspended  by  a  cord,  r=  radius,  h  =  distance  of  axis  of 
motion  from  the  centre  of  the  sphere,  A'  ss  distance  of  centre  of  oscillation 

9  |>9 

from  centre  of  the  sphere,  I  =  radius  of  oscillation  =3^  +  ^85^  +  -  X"' 

o  n 

If  the  sphere  vibrate  about  an  axis  tangent  to  its  surface,  A  =  r,  and  I  ss  r 
+  2/6r.    If  fc-clOr,  I=10r+^- 

Lengths  of  the  radius  of  oscillation  of  a  few  regular  plane  figures  or  thin 
plates,  suspended  by  the  vertex  or  uppermost  point. 

1st  When  the  vibrations  are  flatwl8e>  or  perpendicular  to  the  plane  of  the 
figure: 

In  an  isosceles  triangle  the  radius  of  oscillation  is  equal  to  9i  of  the  height 
of  the  triangle. 

In  a  circle,  %  of  the  diameter. 

In  a  parabola,  5/7  of  the  height. 

ad.  When  the  vibrations  are  edgewise,  or  In  the  plane  of  the  figure: 

In  a  circle  the  radius  of  oscillation  is  9i  of  the  diameter. 

In  a  rectangle  suspended  by  one  angle,  H  of  the  diagonal. 

In  a  parabola,  suspended  by  the  vertex,  5/7  of  the  height,  plus  ^  of  the 
parameter. 

In  a  parabola,  suspended  by  the  middle  of  the  base,  4/7  of  the  height  plus 
^  the  parameter. 

Centre  of  Percuaaloii.— The  centre  of  percussion  of  a  body  oecillat- 
Ing  about  a  fixed  axis  is  the  point  at  which,  If  a  blow  is  struck  by  the  body, 
the  percussive  action  is  the  same  as  if  the  whole  mass  of  the  body  were  con- 
centrated  at  the  point.  This  point  is  Identical  with  the  centre  of  oscillation. 

THIS  VWmBMJlsVJfK. 

A  body  of  any  form  suspended  from  a  fixed  axis  about  which  it  oeclllates 
by  the  force  of  gravity  is  called  a  compound  pendnlum.  The  ideal  body 
concentrated  ai  the  centre  of  oscillation,  suspended  from  the  centre  of  sus- 
pen.sion  by  a  string  without  weight,  is  called  a  simple  pendulum.  This  equi- 
valent simple  pendulum  has  the  same  weight  as  the  given  body,  and  aino 
the  same  moment  of  Inertia,  referred  to  an  axis  passing  through  the  point 
of  Ruspenfilon,  and  It  oscillates  in  the  same  time. 

The  ordinary  pendulum  of  a  given  length  vibrates  In  equal  times  when  the 
angle  of  the  vibrations  does  not  exceed  4  or  6  degixies,  that  Is,  S*  or  S>^«  each 
side  of  the  vertical.    This  property  of  a  pendulum  is  called  its  isochronlsm. 

The  time  of  vibration  of  a  pendulum  varies  directly  as  the  square  root  of 
the  length,  and  Inversely  as  the  square  root  of  the  acceleration  due  to  grar- 
ity  at  the  given  latitude  and  elevation  above  the  earth ^s  surfbce. 

If  T  =  tiie  time  of  vibration,  I  =  length  of  the  simple  pendulum,  g  =  accel- 
eration =  32.16,  r  =  »  4/ -;  since  » Is  constant,  Too  Jl..    At  a  given  loca- 

tion  9  is  constant  and  Ttc  fT.   If  I  be  constant,  then  for  any  location 

r«  — .  If  The  constant,  gT*  s=  ir«/;  I  atg;  fr  =  ^-    Prom  this  equation 

Vg  ^ 

the  force  of  gravity  at  any  place  may  be  determined  if  the  length  of  the 
simple  penduhim.  vibrating  seconds,  at  that  place  Is  known.  At  new  York 
this  length  Is  89.1017  Inches  =  3.3586  ft.,  whence  g  =  32.16  ft.  At  London  the 
length  is  89.1393  Inches.  At  the  equator  89.015S  or  30.0168  Inches,  according 
to  different  authorities. 
Time  of  vibration  of  a  pendulum  of  a  firi^en  length  at  New  York 


/CZZ       "^ 

'  * "  y  89.1017  *  6jaS 


£58* 

t  being  In  seconds  and  I  in  inches.    Length  of  a  pendulum  ha? inff  ii  Klveo 
lime  of  vibration,  lmi*x  89.1017  inches. 


VELOCITY,  ACCELBRATION,  FALLING  BODIES.      423 

The  time  of  vibration  of  a  pendulum  may  be  varied  bv  the  additioD  of  a 
weight  at  a  point  above  the  centre  of  suspension,  which  counteracts  the 
lower  weight,  and  leoKihens  the  period  of  vibration.  By  varying  the  height 
of  the  upper  weight  the  time  is  varied. 

To  find  the  weight  of  t)ie  upper  bob  of  a  compound  penduiimi.  vibrating 
seconds,  when  the  weight  of  the  lower  bob,  and  the  distances  of  the  weights 
from  the  jwint  of  suspension  are  given: 

W sa  the  weight  of  the  lower  bob.  to  s  the  weight  of  the  upper  bob;  Z)  =3 
the  distance  of  the  lower  bob  and  d  s  the  distance  of  the  upper  bob  from 
the  point  of  suspension,  in  inches. 

Thus,  by  means  of  a  second  bob.  short  pendulums  msy  be  constructed  to 
vibrate  as  slowly  as  longer  pendulums. 

By  Increasing  w  or  d  until  the  lower  weight  Is  entirely  counterbalanced, 
the  time  of  vibration  may  be  made  Infinite. 

Conlesil  Pendnlam.—A  weight  suspended  by  a  cord  and  revolving 
at  a  uniform  speed  in  the  circumference  of  a  circular  horizontal  plane 
whose  radius  is  r,  the  distance  of  the  plane  below  the  point  of  suspension  be- 
ing K  is  held  in  equilibrium  by  three  forces— the  tension  in  the  cord,  the  cen- 
Krif ugal  force,  which  tends  to  increase  the  radius  r,  and  the  force  of  gravity 
acting  downward.  If  v  c  the  velocity  in  feet  pen*  second,  the  centre  of 
gravity  of  the  weight,  as  it  describes  the  circumference,  gm  iM.lB,  and  r 
and  h  are  taken  in  feet,  the  time  in  seconds  of  performing  one  revoiuUon  Is 


*-^-«.|/^;  »-g:-JiM«.. 


If  f  a  1  second,  h  a  .8146  foot  m,  9.775  inches. 

The  principle  of  the  conical  pendulum  Is  used  in  the  ordinary  fly-ball 
governor  for  steam-engines.   (See  Govemort.) 

OBNTRIFVOAIi  FORCB* 

A  body  revolving  in  a  curved  path  of  radius  =  A  in  feet  exerts  a  force, 
called  centrifugal  force,  F,  upon  the  arm  or  cord  which  restrains  it  from 
moving  in  a  straight  line,  or  '*  flying  off  St  a  tangent."  It  W  ss  weight  of 
the  body  in  pounds,  N  a  number  of  revolutions  per  minute,  v  s  linear 
velocity  of  tne  centre  of  gravity  of  the  body,  in  feet  per  second,  g  ^92.1% 
then 

If  n  s  number  of  revolutions  per  second,  F  =  1 .3276 TTRn'. 
(For  centrlfu^  force  in  fly-wheels,  see  Fly-wheels.) 

TBIiO€ITT,  ACCBI.BKATION,  FAIililBfO  BODtBS. 

Telocity  is  the  rate  of  motion,  or  the  distance  passed  orer  by  a  body  in 
a  given  time. 

If  «  a  space  in  feet  passed  over  In  ( seconds,  and  v  m  velocity  in  feet  per 
second.  If  the  velocity  is  uniform, 

•  =  !;    .  =  v«;    tm!. 

If  the  velocity  varies  uniformly,  the  mean  velocity  v«  a  -'  "^  ^^,  in  which 
V,  is  the  velocity  at  the  beghming  and  v^  the  velocity  at  the  end  of  the  time  t, 

.-ais*. 0) 

Aeael«railOM  is  the  change  In  velocity  which  takes  place  In  a  unit  of 
time.  0nlt  of  acceleration  x=  a  =  1  foot  per  second  in  one  second.  For 
QQifomily  varying  velocity,  the  acceleration  is  a  constant  quantity,  and 


a: 


~^;   «i«:v»  +  a<;  t;»«v,-af;    f  =  ^*  ^ \   •   .   •  (9 


424  MECHANICS. 

If  the  body  start  from  rest,  v^  ss  0;  then 

Combining  (1)  and  (2),  we  have 

If  «»aO,»»^«. 

Retarded  Motion.— If  the  body  start  with  a  velocity  Vi  and  coma  to 
rest,  t>,  ss  0;  then  a  =  -^*. 
In  any  case,  if  the  change  in  velocity  Is  v, 

•=«"  —si'  •=§'•• 

For  a  body  starting  from  or  ending  at  rest,  we  have  the  equations 

V  s  at;   «  =  2<;   •  ■  "g"  * 

Falllne  Bodlea.— In  the  case  of  falling  bodies  the  acceleration  due 

to  gravity  Ta  82.16  feet  per  second  In  one  second,  sr  g.    Then  If  v  s  velocity 
quired  at  the  end  of  t  seconds,  or  f     '      '    '"     --^*      ^..  .  ^ 
feet  passed  over  in  the  same  time, 


acquired  at  the  end  of  t  seconds,  or  final  velocity,  and  h  s  heighe  or  space 
infei " '-^* ^' — 


2^ 

vsgt   ^  8S.16t   s  V^h  s  &09  i^  a  -jl 

y      "88.16    "y     g  ""4.01  "v' 

1*  s  space  fallen  through  in  the  7th  second  ss  giT-^  10. 


During  the  flrst  second  the  body  starting  from  a  Ktate  of  rest  (resistance 
of  the  aJr  neglected)  falls  y  -h  2  s  16.08  feet ;  the  acquired  velocity  is  g  = 

32.16  ft.  per  sec.;  the  distance  fallen  in  two  seconds  is  /(  =  -^  =  16  06  x  4  = 

64.82  ft. ;  and  the  acquired  velocity  \avssgt  =  64.32  ft.  The  acceleration,  or 
increase  of  velocit  v  in  each  second,  is  constant,  and  Is  82.16  ft.  per  aec.  Solv- 
ing the  equutions  for  dlilerent  times,  we  find  for 

Seconds,  t 12       8       4       5        6 

Acceleration,  p 82.16     X    1       1       1       1       1         i 

Velocity  acquired  at  end  of  time,  v....  82.16     X    1       2      8       4       5        6 

Height  of  fall  m  each  second,  ti ^^     X    1       8      6      7      9       n 

Total  height  of  fall.  A ^^     XI       4       0      16     25      38 

Valve  of  g.— The  value  of  g  Increases  with  the  latitude,  and  decreasea 
wiih  the  elevation.  At  the  latitude  of  PhiUdelphla,  40o,  its  ?alue  Is  82. 16.  AC 
the  sea-level.  Everett  gives  g  =  82.178  -  .062  cos  2  lat.  -.000008  height  in 
fe*»t.    At  Paris,  lat.  48* 7,0'  N.,  g  =■  0f0.R7  cm.  =  33.181  ft. 

Values  of  4^,  calculated  by  an  equation  given  by  C.  8.  Pierce,  are  given 
la  a  table  in  Smlih's  Hydranlics,  from  which  we  take  the  following : 
Latitude...^..       0«  lO*"  20«  80*  40*  60*  60» 

Value  of  V20..   a0112      8.0118      8.0187      8.0166      8.0189      8.0235      8.0269 

The  value  of  Vig  decreases  about  .0004  for  every  1000  feet  increase  in  ele- 
vation above  the  sea-level. 

For  all  ordinary  calculations  for  the  United  States,  g  is  generally  takeo  at 
82.16,  and  V2g  at  8.02.  In  England  g  ^  35f.2.  i^2g  s  8.085.  Practical  limit. 
Ing  values  of  g  for  the  United  States,  according  to  Pierce,  ai'e : 

Latitude  49"  at  sea-level 0a88.]86 

*"       25«  10,000  feet  above  the  sea ya^oSS 


VELOCITY,  ACCELERATION,  FALLING  BODIES.      426 


Fig.  95  represents  graphically  the  velocity,  space,  etc.,  of  a  body  falling  for 


fux  seconds^  Tlie  vertical  line  at  the  left  is 
the  time  in  eecondfl,  the  horizontal  lines 
represent  the  acquired  velocities  at  the 
euU  of  each  second  =  82.16/.  The  area  of 
the  small  triangle  at  the  top  represents 
the  height  fallen  throng.,  in  the  first 
second  =  ^g  =  16.06  feet,  and  each  of  the 
other  triangles  is  an  equai  space.  The 
number  of  triangles  between  each  pair  of 
horizootal  lines  represents  the  height  of 
fall  in  each  second,  and  the  number  of 
triangles  between  any  horizontal  line  and 
the  top  is  the  total  neight  fallen  during  16 
the  time.     The  figures  under  /i,  u.  and  v 


4     8 


9     5 


adjoining  the  cut  are  to  be  multiplied  by 

i«.oe  U     ' 


25     9 


KlG.  Jfe. 


.  to  obtain  the  actual  velocities  snd 
beiehts  for  the  giv«>n  times. 
ABsnlar  and  Mnear  Telocity 

of  a  Turning  Body  .•Let  r  =  radius  of  a  86    12 
turning  tK>dy  In  feet,  n  =  number  of  revo- 
lutions per  minute,  v  ss  linear  velocity  of 
a  point  OD  the  chrcumference  in  feet  per  second,  and  60v  s  velocity  in  feet 
per  minute. 

v=~^.  60u  =  an7i. 

Angnlar  velocity  Is  a  term  used  to  denote  the  angle  through  which  anv 
radius  of  a  body  turns  in  a  second,  or  the  rate  at  which  any  point  in  it 
having  a  radius  equal  to  unity  is  moving,  expressed  in  feet  per  second.  The 
unit  of  angular  velocity  is  the  angle  which  at  a  distance  =  radius  from  the 

180 
centre  is  subtended  by  an  arc  equal  to  the  radius.    This  unit  angle  k  — 

degrees  ss  57.8*.    Sv  X  574)f  a  880*,  or  the  drcumferenoe.    If  ^  «  angular 

velocity,  v  =s  Ar^  A  =  '  =t  -^.    The  unit  angle  —  is  called  a  radian. 


Helfflii  Correapondlns 

to  a  GlTen  Acqalred  Telocity* 

1    "  ' 

i 

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feet. 

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feet. 

feet 

feet. 

feet 

feet 

feet 

feet. 

feet 

feet. 

p.Hec 

?.8ec. 

3.  sec. 

p.  sec. 

p.sec. 

p.sec. 

*^.» 

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2.62 

84 

17.9 

55 

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76 

89.8 

97 

146 

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86 

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77 

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98 

149 

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8.49 

36 

20.1 

57 

50.5 

78 

94.6 

99 

152 

1.00 

.016 

8.96 

87 

21.8 

68 

52.8 

79 

97.0 

100 

155 

1.25 

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4.49 

88 

22.4 

50 

54.1 

80 

99.5 

105 

171 

1.50 

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18 

5.08 

89 

28.6 

60 

56.0 

81 

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110 

188 

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82 

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27.4 

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8 

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Pavallelocviun  •t  Veltteltie«*-<nie  prinpiole  of  the  composition 
An<l  resolutioit  of  rorcee  mey  also  be  applied  to  Telociilea  or  to  dietancee 
moved  io  yiTeu  intervals  of  tiiue.  RaferHnfc  to  Vik-  80,  pase  416,  if  a  body 
at  0  hBM  a  f orae  applied  to  it  which  acting  alone  would  gfre  it  a  Telocity 
repreaented  by  OQ  per  second,  and  at  the  8ame  time  U  to  Ofitad  on  li 


VELOCITY,  AOCBLXBATIOK,  FALLIKG  BODIES.     427 

another  force  which  ftotin^  alone  would  give  It  a  Telocity  OP  per  Beoond, 
the  resvultoC  the  two  forces  acting  together  for  one  second  will  carry  it  to 
/?,  OR  being  the  difigonal  of  the  paraUeloeram  of  OQ  and  Of^,  and  the 
resultant  Telocity.  If  the  two  component  Telocities  are  uniform,  the  result- 
ant will  be  uniform  and  the  line  OR  will  be  a  straight  line;  but  if  either 
Telocity  Is  a  Tarylng  one,  the  line  will  be  a  Qqrvo;  Fi^.  M  shows  the 
resultant  Telocities,  also  the  path  traversed 
by  a  body  acted  on  by  two  forces,  one  of 
which  would  carry  it  at  a  uniform  velocity 
OTer  the  intervals  1,  2,  %  B,  and  the  other  of 
which  would  carry  it  by  an  accelerated  mo- 
tion over  the  intervals  a,  6,  c.  D  in  the  same 
times.  At  the  end  of  the  respective  infcer- 
Tals  the  body  will  be  found  at  C,,  Cj.  C,,  C, 
and  the  mean  Telocity  during  each  interval 
is  represented  by  the  distances  between 
these  points.  Such  a  curved  pathistraT* 
ersed  by  a  shot,  the  impelling  force  from 
the  gun  giving  It  a  uniform  velocity  in  the 
direction  tho  gun  is  aimed,  and  gravity  giv-  '      «_    •« 

inr  it  an  accelerated  velocity  downward,  Fm.M. 

Tm  path  of  a  projectile  i»  a  pcarabcia.    The 

distance  it  will  travel  is  greatest  when  its  Initial  direction  !s  at  an  angle  40* 
above  the  horizon  tal. 

Haas  -Force  of  Aeeeleratlon.— 7%e  mass  of  a  body,  or  the  quantity 
of  matter  it  oontaina«  is  a  oonstant  quantity,  while  the  weigh  t  varies  aooording 
to  the  Tariation  in  the  force  of  gravity  at  difTerent  places.    If  g  s  the  acceler- 


ation due  to  graWty,  and  if  n  weighty  then  the  mass  mm^^w^  w*9-   Weight 

here  means  the  resultant  of  the  force  of  graTlty  on  the  particles  of  a  body, 
inch  as  may  be  measured  by  a  springp-balance,  or  by  the  extension  or 
deflection  of  a  rod  of  metal  loaded  with  the  given  weight. 

Force  has  been  defined  as  that  which  causes,  or  tends  to  cause,  or  to 
destroy,  motion.  It  may  also  be  defined  (Kennedy ^s  Mechanics  of  Ma- 
chinery^ as  the  cause  of  acceleration;  and  the  unit  of  force  as  the  force 
required  to  produce  unit  acceleration  In  a  unit  of  free  mass. 

i  nrce  equals  the  product  of  the  mass  by  the  acceleration,  or/  a  ma. 

Also,  if  i>  =  the  Telocity  acquired  In  the  time  <,  ft  =s  mv;  fssmv-^ti  the 
acceleration  being  uniform. 

The  force  required  to  produce  an  acceleration  of  g  (that  is,  82.16  ft.  per 

MecO  In  one  second  \s/ssmgm  —g  a  to,  or  the  weight  of  the  body,  Also« 

9 

fm  ma  n  m^  "T  ^',  in  which  r,  is  the  veloel^  at  the  end,  and  «itfaa 
velocity  at  the  beginning  of  the  time  I,  and /=  my  a  —  ft^  J  ^'^^  Ha; 
•^  =s  -;  or,  the  force  required  to  give  any  acceleration  to  a  hody  la  to  the 

V         Q 

weight  of  the  body  as  that  acceleration  Is  to  the  acceleration  produced  by 
gravitT.    (I'he  weight  w  is  the  weight  where  g  is  measured.) 

EsLUIFUK.— Tension  in  a  cord  lifting  a  weight.  A  vsUr^t  of  100  Iba.  Is 
nrted  vertically  Inr  a  cord  a  distance  of  80  feet  in  4  seconds,  the  Telocity 
uttlfoniily  iaereasiDg  from  0  to  the  end  of  the  time.  What  tension  must  he 
maintained  In  the  oocdr  Mean  velocity  a  «^  x=  j»  ft.  par  see.;  final  Telocity 

*«ia2t;,=  40;accele'^tlono5s^  »  ^  «  JO.    Force/s;  ma  a  '-^  -^Je^ 

30  cs  81.1  lbs.  This  is  the  force  required  to  produce  the  acceleration  only; 
to  It  must  be  added  the  force  requh^d  to  lift  the  weight  without  accelera- 
tion, or  100  lbs.,  making  a  total  of  181.1  lbs. 

The  Resistance  to  Acceleration  is  the  same  as  the  force  reqolTed  to  pro- 
doee  the  aocelenitlon  »  H.  <?iz!!2>. 

FonnnlSD  for  Aecelerafed  notion  •—For  cases  ef  unitormly 
seoelerated  motion  other  titan  those  of  falling  bodies,  we  haTS  the  f  ovmnlfB 

already  giTen,/0^a,  B  ^^^^.   If  the  body  starts  from  test,  vt«<l«^ 


428  HECHAKICS. 

■B«,  and/-  ~  p  fgt  «  tcv.    We  also  have  <  e  --.  Tran^fonnlogaiidsub- 
gtitutlng  for  q  its  value  8S.10,  we  obtain 

ttw*  tco  tg<  82.16/it      64.82/* 

^  ■"  MIk*  ■  88.16<  ■"  16.08(»  '    "^  "        V       ■     »«      ' 

1     -/^ 


«-5oi37-4:oiy  / 


For  any  change  In  velocity/  as  «;(  ^^^^  /* 

(See  al«lo  Work  of  Acceleration,  under  Work.) 

IHotloii  on  Inclined  Planes.— The  velocity  acquired  by  a  body 
desceudini;  an  inclined  plane  by  the  force  of  gravity  (friction  neglected)  n 
<*aual  to  that  acquired  by  a  body  fallins  freely  from  the  height  of  the  plane. 

The  times  of  descent  down  different  inclined  planes  of  the  same  height 
▼ary  as  the  length  of  the  planes. 

The  rules  for  uniformly  accelerated  motion  apply  to  inclined  planes.  If  a 
Is  tlie  angle  of  tiie  plane  with  the  horizontal,  sin  a  =  the  ratio  of  the  height 

to  the  length  s  j,  and  the  constant  accelerating  force  is  (^  sin  a.    The  final 

Telocity  at  the  end  of  i  seconds  is  v  =  j/f  sin  a.    The  distance  passed  over  in 
t  MOODds  is  <  V  H  y<'  "hi  a*   The  time  of  descent  is 


fif  Bin  a        4.01  Vh 

mOMENTVlir,  TIS-VITA. 

Atomontam.  or  quantity  of  motion  in  a  body,  is  the  product  of  the  i 

V) 

by  the  velocity  at  any  instant  =  «ir  =  — r. 

Since  the  moving  force  =  product  of  mass  by  acceleration,  /  s  nia\  and  if 

the  velocity  acquired  in  i  seconds  =  v,  or  a  =  t,  /  =  -7- ;  /<  =  »«;;  that  ia, 

the  product  of  a  constant  force  into  the  time  in  which  it  acts  equals  namer 
ically  the  momentum. 

Since /<  =  mv,  if  <  ss  1  second  tut;  =-  /.  whence  momentum  might  be  de- 
fined as  numerically  equivalent  to  the  number  of  pounds  of  force  that  will 
stop  a  moving  body  in  1  second,  or  the  number  of  pounds  of  force  which 
acting  during  1  second  will  give  it  the  given  velocity. 

Tla-irlFa)  or  living  force,  is  a  term  used  by  early  writers  on  Mechanics 
to  denote  the  energy  stored  in  a  moving  body.    Some  defined  it  as  the  pro- 

duct  of  the  mass  into  the  square  of  the  velocity,  mv*,  =?  —  v*  others  as  one 

half  of  this  quantity  or  V^mv*,  or  the  same  as  what  is  now  known  as  enei^y. 
The  term  is  now  practically  obsolete,  its  place  being  taken  by  the  word 
energy. 

l¥ORK,   ENERGT9  POUTER. 

Work  is  the  overcoming  of  resistance  through  a  certain  distance.  It  is 
measured  by  the  product  of  the  resistance  Into  the  space  through  which  it 
is  overcome.  It  is  also  measured  by  the  product  of  the  moving  force  Into 
the  distance  through  which  the  force  acts  in  overcoming  the  resistance. 
Thus  in  lifting  a  body  from  the  earth  against  the  attraction  of  gravity,  the 
resistance  is  the  weight  of  the  body,  and  the  product  of  this  weight  into  the 
height  the  body  Is  lifted  Is  the  work  done. 

Tbe  17nlf  of  Work^  in  British  measures.  Is  the  fcoUpoyLnd^  or  the 
amount  of  work  done  in  ovei'coming  a  pressure  or  weight  equal  to  one 
pound  through  one  foot  of  space. 


WOBK,  SKBBGT,  POWER.  429 

Tbe  wotk  perf oimed  by  a  pbton  In  driTliiflr  a  fluid  before  It,  or  by  a  fluid 
In  drtyinir  &  piston  before  It,  may  be  ezpreased  in  either  of  the  following 

W^JBI 

Besistanoe  X  distance  trarereed 
m  intensi^  of  pressure  X  area  x  distance  traTersed  ; 
m  intensity  of  pressure  X  Tolume  traversed. 

The  work  performed  in  Uf  tins'  a  body  is  the  product  of  the  weight  of  the 
body  huto  the  height  through  which  its  centre  of  graTity  is  lifted. 

If  a  machine  lifts  the  centres  of  gravity  of  several  bodies  at  once  to  heights 
either  the  same  or  different,  the  whole  quantity  of  work  performed  in  so 
doing  te  the  sum  of  the  several  products  of  the  weights  and  heights  ;  but 
that  quantity  can  also  be  computed  by  multiplying  the  sum  of  all  the 
weights  Into  the  height  thrcmgh  which  their  common  oentre  of  gravity  is 
lifted.    Otanklne.) 

Powrer  is  the  rate  at  which  work  Is  done,  and  Is  expressed  by  the  quo- 
tient of  the  work  divided  by  the  time  in  which  it  is  done,  or  by  units  of  work 
per  second,  per  minute,  etc,  as  foot-pounds  per  second.  The  most  common 
nnit  of  power  is  the  horge^wwer^  established  by  James  Watt  as  the  power  of 
a  stronsr  London  draught- horse  to  do  work  during  a  short  interval,  and  used 
by  him  to  measure  the  power  of  his  steam-engines.  This  unit  Is  28,000  foot- 
pounds per  minute  b  660  foot-pounds  per  second  a  1,960,000  foot-pounds  per 
hour. 

BxpreMioBS  for  Force,  ITorlc,  Poinrer,  efe* 

The  fundamental  conceptions  In  Dynamics  are: 

Mwum^  Force,  Time,  Space,  represented  by  the  letters  3f,  F,  7,  8. 

WLmmm  =  weight  -f-  g.  Ii  the  weight  of  a  body  is  determined  by  a  spring 
balance  standardisied  at  London  It  will  varv  with  the  latitude,  and  the  value 
of  g  to  be  taken  in  order  to  find  the  mass  is  that  of  the  latitude  where  the 
welghlnic  is  done.  If  the  weight  is  determined  by  a  balance  or  by  a  plat- 
form  scale,  as  Is  customary  in  engineering  and  in  commerce,  the  London 
value  of  g.  =  82:2,  is  to  be  taken. 

Telocity  s  space  divided  by  time,  V=  8 -%- T.it  Vhe  uniform. 

l¥orlL  =  force  multiplied  by  space  z=FS=:  W3f  F*  =  FVT.  (F uniform.) 

Poirer  =  rate  of  work  =  work  divided  by  time  =  FS-*-T  =  P=  prod- 
uct of  force  into  velocity  =  Fl''.  

Power  exerted  for  a  certain  time  produces  work;  PT  ss  FS  =:  FVT. 

EflTort  is  a  force  which  acts  on  a  body  In  the  direction  of  Its  motion. 

Hertrtance  is  that  which  Is  opposed  to  a  muying  force.  It  is  equal  and 
oppmrite  force. 

Horse-poirer  Honm*  an  expression  for  work  measured  as  the 

Eroduct  of  a  power  Into  the  time  during  which  It  acts  a  PT,  Sometimes  it 
I  the  summation  of  a  variable  power  for  a  given  time,  or  the  average  power 
mnltiptled  by  the  time. 

Kacrinr«  or  stored  work,  Is  the  capacity  for  performing  work.  It  Is 
measnred  by  the  same  unit  as  work,  that  is.  In  foot-pounds.  It  may  be 
either  potential,  as  in  the  case  of  a  body  of  water  stored  In  a  reservoir, 
capable  of  doing  work  by  means  of  a  water-wheel,  or  actual,  sometimes 
called  hinetie^  whksh  is  the  energy  of  a  moving  body.  Potential  energy  is 
measured  by  the  product  of  the  weight  of  the  stored  body  Into  the  distance 
through  which  it  Is  capable  of  acting,  or  by  the  product  of  the  pressure  It 
exerts  Into  the  distance  through  which  t^%  pressure  is  capable  of  acting. 
Poteotial  energy  may  also  extol  as  stored  heat,  or  as  stored  chemical  energy, 
as  in  fuel,  gunpowder,  etc.,  or  as  electrical  energy,  the  measure  of  these 
energies  being  the  amount  of  work  that  they  are  capable  of  performing. 
Aecoal  energy  of  a  moving  body  te  the  work  which  It  Is  capable  of  performing 
against  a  retarding  resistance  before  being  brought  to  rest,  and  Is  equal  to 
the  work  which  must  be  done  upon  it  to  bring  It  from  a  state  of  rest  to  Its 
actual  velocity. 

The  measure  of  actual  energy  Is  the  product  of  the  weight  of  the  body 
into  tne  height  from  which  it  must  fall  to  acquire  its  actual  velocity.  If  v  s 
the  velocity  In  feet  per  second,  according  to  the  principle  of  falling  bodies, 

K  tbe  height  doe  to  the  velocity  m  ^,  and  If  to  ■  the  weight,  the  energy  m 

^intr*  =  wtfl  -4-  ^  =r  wh.  Since  energy  Is  the  capacity  for  performing 
work,  the  units  of  work  and  energy  are  equivalent,  or  FS  =  ^mv*  =  w/i. 
Energy  exerted  =  work  done. 


430  hechaihics. 

Hie  actual  energy  of  a  rotatlnf^  body  whose  ang^nlar  velocity  is  A  and 

moment  of  Inertia  Sun**  b  /  is  -— ,  that  Is,  the  product  of  the  moment  of 

Inertia  Into  the  height  due  to  the  velocity,  A^  of  a  point  whose  distance  from 

the  axis  of  rotation  Is  unity;  or  it  is  equal  to  -;j— ,  in  which  to  is  the  weight  of 

the  body  and  v  Is  the  v«»1ocfty  of  the  centre  of  gyration. 

"Work  of  Acceleration.  -The  work  done  in  giving  acceleration  to  a 
body  is  equal  to  the  product  of  the  force  producing  the  acceleration,  or  of 
the  resistance  to  acceleration.  Into  the  distance  moved  in  a  given  time.  This 
force,  as  already  stated  equals  the  product  of  the  mass  into  the  acceleration, 

or/  SB  ma  M  ~  ^^  T"  ^^   If  the  distance  traversed  in  the  time  <  £=  «,  then 
work-/t-l^SLr^i,. 


BxAKPUC^what  work  is  required  to  move  a  body  weighing  100  lbs.  bori- 
Bontally  a  distance  of  80  ft.  in  4  seconds,  the  velocity  uniformly  increasing, 
friction  neglected  t 

Mean  velocity  Vo  "  20  ft.  per  second;  final  velocity  =s  «,  =s  Sv^  ss  40;  initial 

velocity  Vj  as  0;  acceleration,  a  =  ^^  7  ^'  =  —  =  10;  force  =  ~a  =  r^-r^  x 

»  4  g  Se.lo 

10  B  81.1  lbs. :  distance  80  ft. ;  work  s  /t  a  81.1  x  80  a  M88  foot-pounds. 

The  energy  stored  in  the  body  moving  at  the  final  velocity  of  40  ft.  pe» 
second  is 

Hmv«  -  ^  ^t;«  «  ^^  :=  2488  foot-pounds, 
which  equals  the  work  of  acceleration. 

If  a  body  of  the  weight  W  falls  from  a  height  H;  the  work  of  acceleration 
Is  simply  WH^  or  the  same  as  the  work  required  to  raise  the  body  to  the 
same  height. 

l¥ork  ot  Accelerated  Rotation.— Let  A  s=  angular  velocity  of  a 
solid  body  rotating  about  an  axis,  that  Is.  the  velocity  of  a  particle  whose 
radius  is  unity.  Then  the  velocity  of  a  particle  whose  radius  is  r  is  v  =  Ar. 
It  the  angular  velocity  Is  accelerated  from  ^,  to^ti  the  increase  of  the 
velocity  of  the  particle  is  v,  -  v,  =s  r(Ai  -  ^j),  and  the  work  of  accelerating 
it  is 

in  which  V)  is  the  weight  of  the  parttole. 
The  work  of  acceleration  of  the  whole  body  is 


21^^.JL^^^J^ 


Tbe  tftrm  2wr*  Is  the  moment  of  inertia  of  the  body. 

*<  Force  of  the  Blour  99  of  a  Steam  Hammer  or  Otbor  Fall* 
Inff  Welffht.— The  question  is  often  aslced:  ''With  what  force  does  a 
falliog  hauimer  strike  ?**  The  question  cannot  be  answered  directly,  and 
it  is  based  upon  a  misconception  or  ignorance  ot  fundamental  mechanical 
laws.  The  energy,  or  capacity  of  doing  work,  of  a  body  raised  to  a  given 
height  and  let  fall  cannot  be  expressed  in  pounds,  simply,  but  only  in  foot- 
rmnnrlB,  whlcV  '^  t}i»*  product  of  the  weight  Into  the  height  through  which 
)t  fm)!^.  f>r  Uny  (Uuthi<  t  Of  its  weight  -«-  04.88  into  the  square  of  the  velocity, 
ill  feet  per  Beei>Tiil,  which  it  acquires  after  falling  through  the  given  heiiEhU 
If  F  m  ivelichc  of  tho  body.  M  its  mass,  g  the  acceleration  due  to  gravity, 
S  the  hetfftit  of  fall,  raid  v  the  velocity  at  the  end  of  the  fall,  the  energy  In 
the  body  In^t  lH*fui->  striking,  H  FS  =  HMp«  =  Wt/*  •«-  8&m  TTv* -•- 64.82, 
whtch  Is  tiie  j:;Hnf4ru4  equation  of  energy  of  a  moving  body.  Just  as  the 
f^n^i'^  of  thti  body  ts  a  product  of  a  force  Into  a  distance,  so  the  work  it 
c^Of'K  wht^n  it  Rtrikr^  Is  not  the  manifestation  of  a  force,  which  can  be  ex- 
prt'«iAiA  J  iinipLy  in  pounds,  but  it  is  the  overcoming  of  a  resistance  through 
a  c«rtALti  dlstauciBi  ^thich  is  expressed  as  the  product  of  the  average  reaisir 


WORK,  ENEROT,  POWER.  431 

anee  Into  the  distance  throuiph  which  it  ia  exerted.  If  a  hammer  weighing 
100  Ibe.  falls  10  ft.,  its  energy  is  1000  foot-poundii.  Before  being  brou^t  to 
rest  it  must  do  1000  foot-pounds  of  work  against  one  or  more  resistances. 
These  are  of  various  kinds,  such  as  tliat  due  to  motion  imparted  to  the  body 
struck,  penetration  against  friction,  or  against  resistance  to  shearing  or 
other  deformation,  and  crushing  and  heating  of  both  the  falling  body  and  the 
body  struck.  The  distance  through  which  these  resisting  forces  act  is  gen- 
erally  indeterminate,  and  therefore  the  average  of  the  resisting  forces, 
which  themselves  generally  vary  with  the  distance,  is  also  indeterminate. 
ImjMMt  of  Ilodles«~If  two  inelastic  bodies  collide,  they  will  move  on 
together  as  one  mass,  with  a  common  velocity.  The  momentum  of  the  com- 
bined mass  is  equal  to  tlie  sum  of  the  momeuta  of  the  two  bodies  before  im- 
pact. If  ni^  ana  m,  are  the  masses  of  the  two  bodies  and  i;.  and  v,  their  re- 
spective velocities  before  impact,  and  i;  their  common  velocity  after  impact, 
(Wi  +  m^  SB  mxVi  X  »4t^ , 

^     ffitVi  -f  tntVt  ^ 

If  the  bodies  move  In  opposite  directtons  v  s  ^^^^'~^^\  or,  the  velocity 

W»j  -J-  tW| 

of  two  inelastic  bodies  after  impact  is  equal  to  the  algebraic  sum  of  their 
momenta  before  impact,  divided  by  the  sum  of  their  masses. 
If  two  inelastic  bodies  of  equal  momenta  impinge  directly  upon  one  an- 


other  from  opposite  directions  they  will  be  brought  to  rest. 
Impmet  or  Inelastic  Bodlea  Cause*  «  IjOso  of  Enenrr, 

this  loss  is  equal  to  the  sum  of  the  energies  due  to  the  velocities  Tost  and 


Impmet  or  Inelastic  Bodies  Causes  «  IjOss  of  Knenrf  ^nc^ 
his  loss  is  equal  to  the  sum  of  the  energies  due  to  the  velocities  Tc  ^ 
gained  by  the  bodies,  respectively. 

In  which  t7|  —  « is  the  velocity  lost  by  m|  and  v  —  vw  the  velocity  gained  by  m^ 
Example^Jjet  mj  ss  ]0,  nif  s  8,  Vi  ss  18,  v,  ts  15. 

If  the  bodies  collide  they  wiU  come  to  rest,  for  v  a  ^^^|q7|^^^  «  0. 

The  energy  loss  Is 
H^O  X  144-f  ^  X  225-  H18X  Oct  H10(18  -  0)«+ H8(  15-0)*  =  1690ft lbs. 

What  becomes  of  the  energy  lost  ?  Ans.  It  is  used  doing  internal  work 
on  the  bodies  themselves,  changing  their  shape  and  heatine  them. 

fbr  imperfecfly  elcutic  bodies^  let  «  c=  the  elasticity,  that  is,  the  ratio 
which  the  force  of  restitution,  or  the  internal  force  tending  to  restore  the 
shape  of  a  body  after  it  has  been  compressed,  bears  to  the  force  of  compres- 
sioo;  and  let  m^  and  m,  be  the  masses,  iii  and  Vf  their  velocities  before  im- 
pact, and  Vi'Vs'  their  velocities  after  impact:  then 

,  _  m|V,  -f  mtVt  ^  mae(p,  ~  t>t), 
*  m,  -J-  nij      ""     Wi  -+■  m,    * 

If  the  bodies  are  perfectly  elastic,  their  relative  velocities  before  and  after 
impact  are  the  same.    That  is :  Vx'  —  v^'  =  Vt  —  Vi. 

In  the  Impact  of  bodies,  the  sum  of  their  momenta  after  impact  is  the 
same  as  the  sum  of  their  momenta  before  impact. 

For  demonstration  of  these  and  other  laws  of  impact,  see  Smithes  Me- 
chanics; also.  Weisbach's  Mechanics. 
Bnervy  of  Reeoll  of  Clnns.— (^tg*sr«  Jan.  S6, 1864,  p.  79.) 
Let  W  =  the  weight  of  the  gun  and  carriage; 

V  =  the  maximum  velocity  of  recoil; 
tt;  =3  the  weight  of  the  projectile; 

V  s  the  muzzle  velocity  of  the  projectile. 

Then,  since  the  momentum  of  the  gun  and  carriage  Is  equal  to  the  momen- 
tum of  the  projectile,  we  have  Wvzs  tiw,  or  r  =  ici>  -♦-  w. 

•The  statement  by  Prof.  W.  D.  Marks,  in  Nystrom^a  Mechanics,  SOtb  edi' 
tk>n,  p.  4:^  that  thi0  formula  is  in  error  is  itself  erroneous. 


432  MECHANICS. 

Tatdog  the  case  of  a  lO-loch  gixn  flrinfr  a  400-1b.  projectile  with  a  mtixile 
Telocity  of  1400  feet  per  second,  the  weight  of  the  fi^un  aod  carriage  being  Si 
ions  8  49,280  lbs.,  we  find  the  velocity  of  recoil  s 

_     1400  X  400       ,,  -    ^  . 

"49280      =  ^^  '**'  P®**  second. 

Now  the  energy  of  a  body  in  motion  is  WV^  -t-  2g, 

Therefore  the  energy  of  recoil  =  ^-^g^^"*  =  ^^^  foot-ponnda. 

The  energy  of  the  projectile  is    ^  ^  iTZ  *=  19,178.018  foot-pounds. 

«  X  OSS.* 

Gonaerration  of  Mnergfm—No  form  of  energy  can  ever  be  pra 
diioed  except  by  the  expenditure  of  some  other  form,  nor  annihilated  ex- 
cept by  being  reproduce  in  another  form.  Consequently  the  sum  total  of 
energy  in  the  universe,  like  the  sum  total  of  matter,  must  always  remain 
the  Mune.  (S.  Newcouib.)  Energy  can  never  be  destroyed  or  lost;  it  can 
be  transformed,  can  be  transferred  from  one  body  to  another,  but  no 
matter  what  ti*anpformation8  are  undergone,  when  the  total  effects  of  the 
exertion  of  a  given  amount  of  energy  are  summed  up  the  result  will  be 
exactly  equal  to  the  amount  originally  expended  from  the  source.  This  law 
is  called  the  Conservation  of  Energy.    (CotterUl  and  Blade.) 

A  heavy  body  sustained  at  an  elevated  position  has  potential  energy. 
When  it  falls,  just  before  it  reaches  the  earth's  surface  it  has  actual  or 
kinetic  energy*  <iue  to  its  velocity.  When  it  strikes  it  may  penetrate  the 
earth  a  certain  distance  or  may  be  crushed.  In  either  case  fnction  resulta 
by  which  the  eneigy  Is  converted  into  heat,  which  is  gradually  radiated 
into  the  earth  or  into  the  atmosphere,  or  both.  Mechanical  energy  and  beat 
are  mutually  convertible.  Electric  eneigy  Is  also  convertible  into  heat  or 
mechanical  energy,  and  either  kind  of  energy  may  be  converted  into  the 
other. 

Source*  of  Knernr*— The  principal  sources  of  eneivy  on  the  earth's 
surface  are  the  musciuar  energy  of  men  and  animals,  me  energy  of  the 
wind,  of  flowing  water,  and  of  fuel.  These  sources  derive  their  energ/ 
from  the  rays  of  the  sun.  Under  the  influence  of  the  sun's  rays  vegeiatiod 
grows  and  wood  is  formed.  The  wood  may  be  used  as  fuel  under  a  steam 
boiler,  its  carbon  being  burned  to  carbonic  acid.  Three  tenths  of  its  heat 
energy  escapes  in  the  chimney  and  by  radiation*  and  seven  tenths  appeam 
as  potential  energy  in  the  steam.  In  the  steam-engine,  of  this  seven  tenths 
six  parts  are  dissipated  in  heating  the  condensing  water  and  are  wasted; 
the  remaining  one  tenth  of  the  original  heat  energy  of  the  wood  is  con- 
verted  into  mechanical  work  in  the  steam-engine,  which  may  be  used  to 
drive  machinery.  This  work  is  finally,  by  frtouon  of  various  kinds,  or  pos- 
sibly after  transformation  into  electric  currents,  transformed  into  heat, 
which  is  radiated  into  the  atmosphere,  Increasing  its  temperature.  Thus 
all  the  potential  heat  energy  of  the  wood  is,  after  various  transformations, 
converted  into  heat,  which,  mingling  with  the  store  of  heat  in  the  atnnoe- 
piiere,  apparently  is  lost.  But  the  carbonic  acid  generated  by  the  combus- 
tion of  the  wood  is,  again,  under  the  influence  of  the  sun's  rays,  absorbed 
by  vegetation,  and  more  wood  may  thus  be  formed  having  potential  energy 
equal  to  the  original. 

Perpetual  IIIotloii«~The  law  of  the  conservation  of  energy,  than 
which  no  law  of  mechanics  is  more  firmly  establislied,  is  an  absolute  barrier 
to  all  schemes  for  obtaining  by  mechanical  means  what  is  called  **  perpetual 
motton,"  or  a  machine  which  will  do  an  amount  of  work  greater  than  the 
equivalent  of  the  energy,  whether  of  heat,  of  chemical  combination,  of  elec- 
tricity, or  mechanical  energy,  that  is  put  Into  it.  Such  a  result  would  be 
the  creation  of  an  additional  Ktore  of  energy  in  the  universe,  which  is  not 
possible  by  any  human  agency. 

Tlie  Elllciency  of  a  Rlacblne  is  a  fraction  expressing  the  ratio  of 
the  useful  work  to  the  whole  work  performed,  which  is  equal  to  the  energy 
expended.  The  limit  to  the  efficiency  of  a  machine  is  unity,  denoting  the 
efficiency  of  a  perfect  machine  in  which  no  work  is  lost.  The  difference 
between  the  energy  expended  and  the  useful  work  done,  or  the  loss.  Is 
usually  expended  either  in  overcoming  friction  or  in  doing  work  on  bodies 
surrounding  the  machine  from  which  no  useful  work  is  received.  Thus  In 
an  engine  propelling  a  vessel  part  of  the  energy  exerted  in  the  cylinder 


AimtAL  POWBK. 


433 


does  the  uaehil  Work  6t  fdTln^  motion  to  tbe  reaael,  and  the  remaftider  to 
spent  in  OTeroominfi^  the  friction  of  the  machinery  and  in  maldng  cmrento 
aad  eddies  in  the  smrounding  water. 

ANIHIAI^  POWER, 

WoriL  of  a  Man  against  Known  Rosistanees.   (Rankine.) 


lbs. 

V, 

8600 

BF, 

BVT. 

Kind  of  Exertion. 

ft.  per 

(hours 

ft.-Ib8. 

ft-Ibe. 

sec. 

<S^x 

per  sec. 

per  day. 

1.  RalsiDK  his  own  weight  up 

g(fif  i-  fyf  ladder 

148 

0.6 

8 

98.5 

8.088,000 

8.  Hauling  up  weights  with  rope. 

loaded 

40 

0.78 

6 

80 

648,000 
688,780 

4.  Carrying    weights  up-stalrs 

44 

0.65 

6 

84.8 

and  returning  unloaded .... 

148 

0.18 

6 

18.6 

800,600 

5.  Shovelling    up    earth    to  a 
height  of  5  ft.  8  in 

e 

1.8 

10 

7.8 

880,800 

6.  Wheeling  earth  in  barrow  up 

slope  of  1  in  18,  H  horta. 

Teloc.  0.0  ft.  per  sec.  and  re- 

turning  unloaded.......  ... 

188 

0.075 

10 

9.9 

866,400 

7.  Pushing  or  pulUng  honaon- 
tally  (cMMtan  or  oar) 

86.5 

8.0 

8 

68 

1,686,400 

18.5 

•     18.0 

80.0 

6.0 

? 

68.6 

&  Turning  a  crank  or  winch  .  . 

8.6 
14.4 

8 
8mln. 

46 

888 

1,896,000 

9.  Working  pump 

10.  Hfunmennflr. 

18.8 
16 

8.5 

? 

10 

8? 

88 

f 

1,188,000 
480,000 

ESzpiJJiATiON.— ii,  resistance:  F,  eiTective  velocity  =  distance  through 
which  R  is  overcome  h-  total  time  occupied,  including  the  time  of  moving 
unloaded,  if  any;  V,  time  of  working,  in  seconds  per  day;  3*'  h-  8600,  same 
time,  in  hours  per  day;  BV,  effective  power,  in  foot-pounds  i>er  second; 
BFT,  daUy  work. 

leo  of  a  nan  In  Transportlnff  Loads 
JHoriaontaUy.   (RankiJe.) 


Bnd  of  BxartloiL 


& 


ft. 


f; 


3800 

(hours 

er 


LF, 
lbs. 
con- 
veyed 
Ifoot. 


LVT, 
lbs.  con- 
veyed 
1  foot. 


II  Walking  unloaded,  transport- 
ing hw  own  weight 

181  Wheeling  load  L  in  8-whld. 
barrow,  return  unloaded.. 

13L  DiUo  in  1-wb.  barrow,  ditto.. 

14.  Travelling  with  burden. 

15.  OarryinflT  burden,  returning 

unloaded 


ML  Carrying  buzden,  for808ec- 
ondaon' 


sonly. 


140 

894 
188 
90 

140 
1858 
-{186 
I     0 


10 
10 
7 


700 

878 
880 
885 

888 
0 

1474.8 
0 


85,800,0(K) 

18,488,000 
7.9^,000 
6,670,000 

5,088300 


EzpLAiCATXON.— £,  load;  F,  effective  velocity,  computed  as  before;  I*', 
time  of  working,  in  seconds  per  day;  r'  -h  8600,  same  time  In  hours  per  day; 
LV,  transport  per  second,  hi  lbs.  conveyed  one  foot;  LVT,  daily  transport. 


434 


ME0HAKJG8, 


In  the  flnt  line  only  of  eaob  of  ibe  two  tables  abo?e  la  tbe  wdgbt  of  the 
man  taken  into  aooount  in  oouiputinz  the  work  done. 
Clark  says  that  the  average  net  daily  work  of  an  ordinary  laborer  at  a 

pump,  a  winch,  or  a  crane  may  be 
taken  at  8800  foot-pounds  per  minute, 
or  one* tenth  of  a  borse-powar,  for  8 
hours  a  day;  but  for  shorter  periods 
from  four  to  five  times  this  rate  may 
be  e^certed. 

Mr,  Glynn  says  that  a  man  may 
exert  a  force  of  85  lbs.  at  the  handle 
of  a  erane  for  short  periods;  but  that 
for  continuous  work  a  force  of  15  lb«. 
Is  all  that  should  be  assumed,  moving 
through  280  feet  per  minute. 

miitt-iirheel.— Fig.  97  is  a  sketch 
of  a  very  efficient  man-power  hoist- 
ing-maohine  which  the  author  saw  in 
Berne,  Switzerland,  in  18S9.  The  face 
of  the  wheel  was  wide  enough  for 

three  men  to  walk  abreast,  so  thai 

Fio.  97.  nine  men  oould  work  in  It  at  one  time. 

UTork  of  a  Ifonie  axalnst  a  Known  Reststane^.    (Rankine.) 


Kind  of  Exertion. 


1.  Cantering  and  trotting,  draw- 
ing a  light  railway  carriage 
(thoroughbred) 

8.  Rorse  drawing  cart  or  boat, 
walking  (draught-horse). . . . 

8.  Horse  drawing  a  gin  or  mill, 
walking   

4.  Ditto,  troiting 


R. 


raln.2«J- 
mean  80^ 
max.  66 

100 
06 


V. 

T. 

SOOO 

RV. 

U^H 

4 

i^m 

3.6 

8 

438 

8.0 
0.5 

8 

800 
489 

RVT, 


6,444,000 


18,441,000 

a.840,000 
6.960,000 


BxnjiNATioii.— R,  resiatanoe,  in  Iba;  T,  valocitv,  in  feet  per  second;  T' 
•*-  8000,  hours  work  per  day;  JiK,  work  per  seooad;  RVT,  work  per  day. 

The  average  power  of  a  draught^horse.  as  given  In  line  8  of  the  above  table, 
being  438  foot-pounds  per  second,  is  488/560  =  0.T65  of  the  conventional  value 
assigned  by  watt  to  the  ordinary  unit  of  the  rate  of  work  of  prime  movers. 
It  is  the  mean  of  several  results  of  experiments,  and  may  be  eomifdered  the 
average  of  ordinary  performance  under  favorable  circumstances. 

Per|6vii»aiice  of  a  Honse  In  Tranaportf  nff  Loads 
Kortxontally*    (kankine.) 


Kind  of  Exertion. 

L. 

r. 

T. 

LV. 

LVT. 

6.  Walkhig  with  cart,   always 

'S8 

1600 

870 

180 

8.6 
T.2 

9.0 

8.6 
T.8 

10 
4» 

10 
10 
7 

6100 
5400 

3000 

979 
1896 

1M,400.0QO 

6.  Trotting,  ditto 

7,  Walking  with  cart,  going  load- 

ed,   returning    empty;  T, 
mean  velocity 

87,480,000 
108,000,000 

8.  Carrying  burden,  walking... 
a  Ditto,  trotting 

84,908,099 
88,089,909 

Explanation.— Zr,  load  In  Ibe.;  F,  velocity  hi  feet  per  second;  r-t-8600^ 
working  hours  per  day;  LV,  transport  per  second;  LkT,  transport  per  day. 

This  table  has  reference  to  conveyance  on  common  roads  only,  and  those 
evidently  in  bad  order  as  respects  the  resistance  to  traction  upon  them. 

001*119  Gtn*— In  this  machine  a  horse  works  less  aovantageouelv 
than  in  drawing  a  carriage  along  a  straight  track.    In  order  that  the  beal 


ELEMENTS  OF  HAOUINES.  435 

poaalble  ratidta  vwy  b«  rallied  with  a  honie-gia,  the  diametor  of  tlie  oiis 
eiilar  track  In  which  the  horse  walks  should  not  be  Jess  than  aboqt  foi^y 

Oxen,  Miilesy  Aaaeo.— Authorities  differ  ooosiderablf  at  to  the  power 
of  tbe««  animals.  The  following  may  be  taken  as  an  approximative  oooi- 
parison  between  them  and  drauffht-horses  (Kanktne): 

Or^'Load,  the  same  as  that  w  average  draught-horae;  best  Telocity  and 
work,  two  thirds  of  horae. 

Jfa^-^lJoRd,  one  half  of  that  of  average  draugbt-horset  best  Tekxslty, 
the  same  with  horse;  work  one  half. 

^Mu— Uwd,  one  quarter  that  gf  average  draught-horae;  best  velocity  the 
same:  work  one  quarter. 

V^^vetton  of  nmnglit  of  Horae«  1i j  Inere««e  of  firmde 
of  Ilo«4lo«  (Eimineeriug  H^cwd^  Prise  JCuHays  cm  Roads.  I8e9.)~-£xpert- 
Bi«*q(s  on  EugllMh  roads  by  Gay  flier  &  Famell: 

Gallinjc  load  that  <3an  be  drawn  on  a  level  100: 

On  a  rise  of 1  in  100. 1  in  50. 1  in  40. 1  in  80.  1  in  M.  llnM.  IfnlO. 

A  horse  can  draw  only       00.  81.         TJ.  04.         54.         40.  95. 

The  HestoUmce  of  C^rriBuem  on  Roa4«  Is  (according  to  Gen. 
Iforin}  given  approxiniaiely  by  Uie  following  empirical  formula: 

i?«^[o  +  b(tt-8.»)l. 

In  this  formula  R  m  total  reeistance;  r  «•  radius  of  wheal  In  inehea;  W  ■ 
groas  load ;  n  is  velocity  in  feet  per  second ;  while  a  and  b  are  constants, 
vhoee  valuea  are:  For  good  broken-stone  road,  a  <b  .4  to  .5&,  <^  s  .084  to  .099; 
for  i>aved  roads,  n  »  .27,  ^  a  .0084. 

Rankine  states  that  on  gravel  the  resistance  is  about  double,  and  on 
sand  ftTO  times,  the  reaistanoe  on  good  brokeu-atone  roada 

Kl4K]IKBNTS  OF  MACVmUBB. 

The  object  of  a  jnachiue  is  usually  to  transform  the  work  or  mechanical 
energy  everted  at  the  point  where  the  machine  reoeirea  ite  motion  into 
work  at  the  point  where  the  final  resistance 
is  overcome.  The  speoitlo  end  may  be  to 
change  the  character  or  direction  of  mo- 
tion, as  fnun  circular  to  rectilinmr,  or  vice 
versa,  to  change  the  vei'H'ity,  or  to  overcome 
a  grvat  reaistanae  by  the  application  of  a 
moderate  force.  In  all  caaee  the  total  energy 
exerted  equaU  the  total  work  done,  the  latter  _.      ^ 

including  the  overcoming  of  all  the  f  riciional  FlO.  9B, 

reststaiures  of  the  macliine  as  well  as  the  u8o< 
ful  work  performed.  No  increase  of  power 
can  be  obtained  from  sny  machine,  since  this 
is  impoesible  aooording  to  the  law  of  oonser^ 

vatton  of  energy.  In  a  frictioiUess  machine  the        _[ B 

product  of  the  force  exei'tHl  at  the  driving- 
point  into  the  velocity  of  the  driving-point. 
or  the  distance  it  moves  In  a  given  mrervai 
of  lime,  equals  the  product  of  tlie  resistance 
into  the  distance  through  wli'ch  the  resist- 
ance ie  overcome  in  the  same  vime.  pio.  qqi. 

The  most  simple  machines,  or  elementaiy 
machines,  are  reducible  to  three  classes,  viz., 
the  Lever,  tne  Cord,  and  the  IncUnfd  Plane. 

The  flrsi  olass  includes  every  machine  con- 
sisting of  a  solid  body  capable  of  revolving  q 
on  an  axis,  as  the  Wheel  and  Axle. 

The  eeoond  class  includes  every  machine  in 


whiuh  force  is  transmitted  hy  meaiiH  of  flexi-  JL 


A O  B 

Ow 

rio.0 

1 


hie  threads,  ropea,  etc.,  as  the  Pulley.  ^^  _ 

The  third  class  includes  every  machine  in  jsq  im 

which  a  bard  surface  inclined  to  the  direc- 
tion of  motion  is  introduced,  as  the  Wedge  and  the  Screw. 

A  l40Yer  is  an  inflexible  rod  capable  of  motion  about  a  fixed  point, 

calieU  a  fulcrum.    The  rod  may  be  Kiraight  or  bent  at  any  angle,  or  curved. 

U  is  generally  regarded,  at  orst,  as  without  weight,  but  ita  weight  may  ho 


436  h:bchanics. 

ooiuldered  as  another  force  applied  fn  a  vertical  directlOD  at  Ito  centre  of 
gravity. 

The  arms  of  a  lever  are  the  portions  of  it  Intercepted  between  the  force, 
P,  and  fulcrum,  C,  and  between  the  weiglit,  W,  and  fulcrum. 

Levers  are  divided  into  three  kinds  or  orders,  according:  to  the  relative 
positions  of  the  applied  foi-oe,  weight,  and  fulcrum. 

In  a  lever  of  the  flrat  ord«r,  the  fulcrum  lies  between  the  points  at  which 
the  force  and  weight  act.    (Fig.  08.) 

In  a  lever  of  the  second  order,  the  weight  acts  at  a  point  between  the 
fulcrum  and  the  point  of  action  of  the  force.    (Fig.  09.) 

In  a  lever  of  the  third  order,  the  point  of  action  of  the  force  is  between 
that  of  the  weight  and  the  fulcrum.    (Fig.  1(X).) 

In  all  cases  of  levers  the  relation  between  the  force  exerted  or  the  pull, 
P,  and  the  weight  lifted,  or  resistance  overcome,  W,  is  expressed  by  the 
equation  P  X  AG  ==  WX  BC,  in  which  AC  is  the  lever-arm  of  P,  and  BC 
is  the  lever-arm  of  TT,  or  moment  of  the  force  s=  the  moment  of  the  resist- 
ance.  (See  Moment.) 

In  cases  in  which  the  direction  of  the  force  (or  of  the  resistance)  is  not  at 
right  angles  to  the  arm  of  the  lever  on  which  it  acts,  the  '*  lever-ami"  is  the 
length  of  a  perpendicular  from  the  fulcrum  to  thellneof  direction  of  the 
force  (or  of  the  resistance).  WtP::  AC:  BC,  or,  the  ratio  of  the  resistance  to 
the  applied  foix»  is  the  inverse  ratio  of  their  lever-arms.  Also,  if  Tw  is  the 
velocity  of  W,  and  Vp  is  the  velocity  of  P,  TTi  P:  :  Fj»  i  Fte^  and  Px  Tp 
=  Wx  Vuf. 

If  S»  Is  the  distance  through  which  the  applied  force  acts,  and  3w  is  the 
distance  the  weight  is  lifted  or  through  which  the  resistance  is  overcome, 
W  t  P ::  Sp  t  a*o:  W  X  Sw-  PX  SiP.or  the  weifcht  into  the  distance  it  is  llfiei 
equals  the  force  into  the  distance  through  which  It  Is  exerted. 

These  equations  are  general  for  all  classes  of  machines  as  well  as  for 
levers,  it  t>eing  understood  that  friction,  which  in  actual  machines  increasej 
the  resistance,  is  not  at  present  considered. 

Tlie  Bent  IjeTer.— lu  the  bent  lever  (see  Fig.  91,  page  416)  the  lever- 
arm  of  the  weight  m  is  cf  instead  of  bf.  The  lever  is  in  equilibrium  when 
nXaf=mx  cfy  but  it  is  to  be  observed  that  the  action  of  a  bent  lever  may 
be  very  different  from  that  of  a  straight  le^er.  In  the  latter,  so  long  as  the 
force  and  the  resistance  act  in  lines  parallel  to  each  other,  the  ratio  of  the 
lever-arms  remains  constant,  although  the  lever  itself  changes  its  inclina- 
tion with  the  horizontal.  In  the  bent  lever,  however,  this  ratio  changes: 
thus,  in  the  cut,  if  the  arm  hf  is  depressed  to  a  horizontal  dii*ectIon,  the  dis- 
tance ct  lengtliens  while  the  horizontal  projection  of  af  shortens,  the  latter 
becoming  zero  when  the  direction  of  a/  becomes  vertical.  As  the  arm  a/ 
approaches  the  vertical,  the  welirfat  m  which  may  be  lifted  with  a  given 
force  «  is  very  great,  but  the  distance  through  which  it  may  be  lifted  is 
very  small.  In  aU  cases  the  ratio  of  the  weight  m  to  the  weight  n  is  the  in- 
verHe  latio  of  the  horizontal  projection  of  their  respective  lever-arms. 

Tlie  ntovlng  Strut  (Fig.  lOl)  is  similar  to  the  bent  lever,  except  that 
one  of  the  arms  is  missing,  and  that  the  force  and  the  resistance  to   be 

overcome  act  at  the  same  end  of  the 
single  arm.  The  resistance  in  the 
case  shown  in  the  cut  is  not  the 
weight  IT,  but  its  resistance  to 
being  moved,  A,  which  may  be  sim- 
ply that  due  to  its  friction  on  the 
horizontal  plane,  or  some  other  op- 
posing force.  When  the  angle  be- 
tween the  strut  and  the  horizontal 
plane  changes,  the  ratio  of  the 
resistance  to  the  applied  force 
changes.  When  the  angle  becomes 
very  small,  a  moderate  force  will 
Fio.  101.  overcome  a  very  great  resistance, 

which  tends  to  become  infinite  as 
the  angle  approaches  zero.  If  a  =  the  angle,  Pxcosas/^xsina.  If 
a  =  6  degrees,  cos  a  =  .90619,  sin  a  =  .06716,7?  =  11.44  P. 

The  stone-crusher  (Fig.  V^l)  shows  a  practical  example  of  the  use  of  twc> 
moving  struts. 

Tlie  TOKffl«*Jolnt  is  an  elbow  or  knee-joint  consisting  of  two  bars  sci 
connected  that  they  may  be  brought  into  a  straight  line  and  made  to  pro- 
duce great  endwise  pressure  when  a  force  is  applied  to  bring  them  Into  tUtt 


ELEHElirTS  OF  HACHINES. 


437 


position.  It  Is  a  case  of  two  movlDg  struts  placed  end  to  end,  the  movlofif 
force  b«>inK  appilcnl  at  their  point  of  junction,  in  a  direction  at  right  angrles 
to  the  direction  of  the  resistance,  the  other  end  of  one  of  the  struts  restin^f 
a^irainstt  a  fixed  abutment,  and  that  of  the  other  ag^ainst  the  body  to  be 
moved.  If  a  =  the  angle  each  strut  makes  with  the  straight  line  joining  the 
points  about  which  their  outer  ends  rotate,  the  ratio  of  the  resistance 
to  the  applied  force  is  i?  :  P::  cosa:  Ssin  a;   2J?8in  a  =  Pcosa.     The 


Fio.  loe. 


Fio.  108. 


Fio.lOl 


ratio  Tarles  when  the  angle  varies,  becoming  infinite  when  the  angle 
beoomes  sero. 

The  toggle-joint  is  used  where  great  resistances  are  to  be  overcome 
through  verv  small  distances,  as  In  stone-crushers  (Fig.  103). 

Ttee  Inclined  Plane,  as  a  mechanical  element,  is  supposed  perfectly 
liard  and  smooth,  unless  friction  be  considered.  It  assists  m  sustaining  a 
heavy  body  by  Its  reaction.  This  reaction,  however,  being  normal  to  the 
plane,  cannot  entirely  counteract  the  weight  of  the  body,  which  acts  verti- 
cally  downward  Some  other  force  must  therefore 
be  made  to  act  upon  the  body,  in  order  that  it  may 
be  sustained. 

If  the  sustaining  force  act  parallel  to  the  plane 
(Fig.  104).  the  force  is  to  the  weight  as  the  height  of 
the  plane  is  to  its  lentrth,  measured  on  the  incline. 

If  the  force  act  parallel  to  the  base  of  the  plane, 
the  power  is  to  the  weight  as  the  height  is  to  the 
base. 

If  the  force  act  at  any  other  angle,  let  i  =  the 
angle  of  the  plane  with  the  horizon,  and  e  =  the 
angle  of  the  direction  of  the  applied  force  with  the 
anffle  of  the  plane.    P  i  IT  ::  sin  »  »  cos  e;  P  X  cos  c  =  IT  sin  f 

Problems  of  the  inclined  plane  may  be  solved  by  the  parallelogram  of 
forces  thus : 

Let  the  weight  W  be  kept  at  rest  on  the  incline  by  the  force  P,  acting  in 
the  line  6P',  parallel  to  the  plane.  Draw  the  vertical  line  ba  to  represent 
the  weight :  also  bb'  perpendicular  to  the  plane,  and  complete  the  parallelo- 
gram b'e.  Then  the  vertical  weight  ba  is  the  resultant  of  66',  the  measure  of 
support  fdven  by  the  plane  to  the  weight,  and  6c,  the  force  of  gravity  tend- 
ing to  draw  the  weiglit  down  the  plane.  The  force  required  to  maintain 
the  weight  in  equilibrium  is  represented  by  this  force  6c.  Thus  the  force 
and  the  weight  are  in  the  ratio  of  6c  to  6a.  Since  the  triangle  of  forces  a6c 
is  similar  to  the  triangle  of  the  incline  ABC,  the  latter  may  be  substituted 
for  the  former  in  determining  the  relative  magnitude  of  the  forces,  and 

PiW::bc:ab::BC'.  AB. 

The  IVedffe  is  a  pair  of  inclined  planes  united  by  their  bases.  In  the 
application  of  pressure  to  the  head  or  butt  end  of  the  wedge,  to  cause  it  to 
penetrate  a  resistinflr  body,  the  applied  force  Is  to  the  resistance  as  the 
thickness  of  the  wedge  is  to  its  length.  Let  t  be  the  thickness,  I  the  length, 
Wttoo  resistance,  and  Pthe  applied  force  or  pressure  on  tlie  head  of  the 

Wt  PI 

wedge.    Tlien,  friction  neglected,  P:  IT::  f:I;  P=  —1;      W^=  j- 

Tiie  SereiBir  is  an  inclined  plane  wrapped  around  a  cylinder  in  such  a 
vay  that  the  height  of  the  plane  is  parallel  to  the  axis  of  the  cylinder  If 
the  screw  is  formed  upon  the  internal  surface  of  a  hullo w  cylinder,  it  is 
usually  called  a  nut.  when  force  is  applied  to  raise  a  weight  or  overcome 
a  resMance  by  means  of  a  screw  and  nut,  either  the  screw  or  the  nut  may 


438 


HECHA17IC8. 


be  fixed,  the  other  beloft  movable.  The  force  to  (renerally  applied  at  ihn  end 
of  a  wrench  or  leTer-arm,  or  at  the  circumference  of  a  wheel.  If  r  =  radius 
of  the  wheel  or  lever  arm,  and  p  =  pitch  of  the  screw,  or  distance  between 
threads,  that  is,  the  heif?ht  of  uie  inclined  plane 
for  one  revolution  of  the  screw,  P  s  the  applied 
force,  and  Wes  the  resistance  overcome,  then,  neg- 
lecting resistance  due  to  friction,  itn-  xP  =  H"p ; 
W=z  6.:«8fV-Hp.  The  ratio  of  Pto  Wis  thus 
independent  of  the  diameter  of  the  screw.  In 
actual  screws,  much  of  the  power  transmitted  is 
lost  through  friction. 

The  Cam  is  a  revolv- 
iu|^  iiicliued  plane.  It  maj 
be  either  an  inclined  plane 
wrapped  around  a  cylin- 
der in  such  a  way  thai  the 
height  of  the  plane  Is  ra- 
dial to  the  cylinder,  such 


-V-o-A-- 


Fio.  106. 


the    ordinaiy  lifting- 
cam,  used  in  stamp-mills 


FiG.  106. 


(Fig.  106),  or  it  may  be  an  inclined  plane  curved  edgew'se,  and  rotating  in  a 
plane  parallel  to  its  base  (Fig.  106).    The  relation  of  the  weight  t     ' 


plane  parallel  to  its  base  (rig.  lOO).    xne  relation  or  tne  weignt  to  the  applied 
force  is  calculated  in  the  same  manner  as  in  the  case  of  the  screw. 


f^ 


CJw 


A.. 


Pnlleya  or  Blocks.— F  ==  force  applied,  or  pull ;  W  s  weight  lifted 
or  resisiance.  In  the  simple  pulley  A  (Fig.  107)  the  point  Pon  the  pulling 
rope  descendR  the  same  amount  t)mt  ttie  weis^ht  is  lifted,  therefore  F  s=  wi 
In  B  and  Cthe  point  P  moves  twice  as  far  as  the  weight  Is  lifted,  there- 
fore W  ss  2l\  In  B  and  C  there  is  one  movable  block,  and  two  plies  of  tbe 
rope  engage  with  it.  In  1)  there  are  three  sheaves  in  the  movable  block, 
each  with  two  plies  engaged,  or  six  in  all.  Six  plies  of  ihe  rope  are  there- 
fore shortened  by  the  same  amount  that  the  weight  is  lifted,  and  the  point 
P  moves  six  times  as  far  as  the  weight,  conKequenily  W  =  6P.  In  general, 
the  ratio  of  IT  to  P  is  equal  to  the  number  of  pllt»8  of  the  rop^  that  are 
shortened,  iind  also  is  equal  to  the  number  of  plies  that  engage  the  lower 
block.  If  the  lower  block  has  2  sheaves  and  the  upper  8,  the  end  of  the  rope 
is  fastened  to  a  hook  in  the  top  of  the  lower  block,  and  then  there  are  6 
plies  shortened  instead  of  6.  and  W  =t  5P.  If  K  =  velocity  of  W.  and  v  = 
velocity  of  P.  then  in  all  cases  V\V  =  t>P,  whatever  the  number  of  sheaves 
or  their  arrangement.  If  the  hauling  i*ope,  at  the  pulling  end.  passes  first 
around  a  sheave  in  the  upper  or  stationary  block,  it  makes  no  difference  In 
what  direction  the  ro{>e  is  led  from  this  block  to  the  point  at  which  the  nuU 
on  the  rope  is  applied  ;  but  if  it  first  passes  around  the  movable  block,  it  Is 
necessary  that  the  pull  be  exerted  In  a  direction  parallel  to  the  line  of  action 
of  the  resistance,  or  a  line  Joining  the  centres  of  the  two  blocks.  In  order  to 
obtain  the  maximum  effect.  If  the  rope  pulls  on  the  lower  block  at  an 
angle,  the  block  will  be  pulled  out  of  the  line  drawn  between  the  weight 
and  the  upper  block,  and  the  effective  pull  will  be  less  than  the  actual  pull 


ELEUEKT3  OF  MACBIK£8. 


i39 


on  the  rope  ia  the  ratio  of  the  cogine  of  the  antcle  the  puUiag  rope  makef 
with  the  Tertical,  or  line  of  action  of  the  resistance,  to  unity. 

IHflrerentUa  Pnllejr*  (Fij?.  108.)— Two  pulleys.  Band  C,  of  different 
radii,  rotate  as  one  piMje  about  a  fixed  axis,  A,  An  end* 
less  chain.  BDECLKH,  passes  over  both  pulleys.  The 
rims  of  the  pulleys  are  shaped  so  as  to  hold  (he  chain  and 
prevent  it  from  slipping.  One  of  the  bights  or  loops  in 
which  the  chain  han^,  DE,  posses  under  and  supports  the 
runninsf  block  F.  The  otlier  loop  or  bighr,  HKL,  hangs 
freely,  and  is  called  the  hauling  part,  ft  is  evident  that 
the  velocity  of  the  hauling  pan  is  equal  to  Chat  of  the 
pitch-circle  of  the  pultey  B. 

In  order  that  the  velocity-ratio  may  be  exactly  uniform, 
the  radius  of  the  sheave  J^  should  be  an  exact  mean  be- 
tween the  radii  of  B  and  (7. 

Conaider  that  the  point  B  of  the  cord  BD  moves  through 
an  arc  whose  length  s  AB,  during  the  same  time  the 
point  C  or  the  oora  CE  will  move  downward  a  distance  =3 
AC.  The  length  of  the  bight  or  loop  BDEC  will  be 
shortened  by  AB  ^  ACy  which  will  cause  the  pulley  F  to 
be  I'aised  half  of  this  amount.  If  P  =r  the  pulling  force  on 
the  cord  HK^  and  W  the  weight  lifted  at  F,  then  P  X 
AB  =  Wy.}^{AB-AO, 

To  calculatethe  length  of  chain  required  for  a  differential 
puller,  take  the  following  sum:  Half  the  circumference  of 
A  -^  half  the  circumference  of  B  -^  half  the  circumference 
ot  F  +  twice  the  greatest  distance  of  F  from  A  -f  the 
least  length  of  loop  HKL.  The  last  quantity  is  fixed 
according  to  convenience. 
TI&0  miTereiitlal  WIndlaM  (Fig.  109)  is  identical  in  principle 
with  the  differential  pulley,  the  difference  In  con- 
struction being  that  in  the  differential  windlass  the 
running  block  hangs  in  the  bight  of  a  rope  whose  two 
parts  are  wound  round,  and  have  their  ends  respec- 
tivelv  made  fast  to  two  barrels  of  different  radii, 
wliieu  rotate  as  one  piece  about  the  axis  A.  The  dif- 
ferential windlass  is  little  used  iu  practice,  because 
of  the  great  length  of  rope  which  it  requires. 

Tbe  Differential  Screw  (Fig.  llO)  is  a  com- 
pound screw  of  different  pitches.  In  which  the 
threads  wind  the  same  way.  Ni  and  JV,  are  the  two 
nuts;  SiSi^  the  longer-pitched  threaa;  S^S^,  the 
shorter-pitched  thread:  in  the  figure  botn  these 
threads  are  left-handed.  At  each  turn  of  the  screw 
the  nut  Nt  advances  relatively  to  N^  through  a  dis- 
tance equal  to  the  difference  of  the  pitch.  The  use 
of  the  differential  screw  is  to  combine  the  slowness 
of  advance  due  to  a  fine  pitch  with  the  strength  of  thread  which  can  be 
obtahied  by  means  of  a  coarse  pitch  only. 

A  Wkeel  and  Axle,  or  Windlass,  resembles  two  pulleys  on  one  axis, 
haviug  different  diameters.  If  a  weight  be  lifted  by  means  of  a  rope  wound 
over  the  axle,  the  force  being  applied  at  the 
rim  of  the  wheel,  the  action  is  like  that  of  a 
lever  of  which  the  shorter  arm  is  equal  to 
the  radius  of  the  axle  plus  half  the  thick- 
ness of  the  rope,  and  the  longer  arm  is 
eqaal  to  the  radius  of  the  wheel.  A  wheel 
and  axle  is  therefore  sometimes  classed 
ss  a  perpetual  lever.    If  P  £=  the  applied  force,  D 


Fio.  100. 


FiQ.  110. 
diameter  of  the  wheel. 


W  8  the  weight  lifted,  and  d  the  diameter  of  the  axie  4-  the  diameter  of 
the  rope,  PD  ^  Wd. 

Tootbed-^wlieel  Gearing:  is  a  combination  of  two  or  more  wheels 
and  axles  (Fig.  11  li.  If  a  series  of  wheels  and  pinions  gear  into  each  other, 
as  in  the  cut,  friction  neglected,  the  weight  lifted,  or  resistance  over> 
oome,  is  to  the  force  applied  inversely  as  the  distances  through  which 
they  act  in  a  given  time.  If  R,  R^^  R^be  the  radii  of  the  successive  wheels, 
measured  to  the  pitch-line  of  the  teeth,  and  r,  ?*,.  r,  the  radii  of  the  cor- 
responding pinions,  Pthe  applied  force,  and  W  the  weight  lifted*  Px 


440  MECHAKICS. 

J^  X  R,  X  R,  =  TV  X  r  X  r,  X  rj,  or  the  applied  force  is  to  the  weight 
as  the  product  of  the  radii  of  the  pinions  is  to  the  product  of  the  radii  of 
the  wheels;  or,  as  the  product  of  the  numbers  expressini?  the  teeth  in 
each  pinion  Is  to  the  product  of  the  numbers  expressing  the  teeth  In  each 
wheel. 

EndleM  Screw,  or  Worm-Kear.   (Fir.  112.)~This  gear  is  com- 
monly used  to  convert  motion  at  high  speed  into  motion  at  ^erj  slow 


Pio.  111.  Tio.  U9, 

speed.  When  the  handle  P  describes  a  complete  circumference,  the  -pitch- 
line  of  the  cog-wheel  moves  through  a  distance  equal  to  the  pitch  of  the 
screw,  and  the  weight  Win  lifted  a  distance  equal  to  the  pitch  of  the  screw 
multiplied  by  the  ratio  of  the  diameter  of  the  axle  to  the  diameter  of  the 

{litch-circle  of  the  wheel.  The  ratio  of  the  applied  force  to  the  weight 
ifted  Is  inversely  as  their  Telodtiee,  friction  not  being  considered;  but  the 
friction  in  the  worm-gear  Is  usuallv  very  great,  amounting  sometimes  to 
three  or  four  times  the  useful  work  done. 

If  V  =  the  dintance  through  which  the  force  Pacts  In  a  given  time,  say  1 
second,  and  Vss  distance  the  weight  W  is  lifted  in  the  same  time,  r  = 
radius  of  the  cranlc  or  wheel  through  which  Facts,  t  s  pitch  of  the  screw, 
and  also  of  the  teeth  on   the  cog-wheel,   d  =  diameter  of  the   axle. 

and  D  a  diameter  of  the  pitch-line  of  the  cog-wheel,  v  as      't^  **  -^ 

XT;  FssvXfdH- 6.288rd.    Pu  =  WV+  friction. 

8TRB88E8  IN   FRAMEB   STB17CTITBB8. 

Framed  structures  in  general  consist  of  one  or  more  triangles,  for  the 
reason  that  the  triangle  is  the  one  polygonal  form  whose  shape  cannot  be 
changed  without  distorting  one  of  its  sides.  Problems  in  stresses  of  simple 
framed  structures  may  generally  be  solved  either  by  the  application  of  the 
triangle,  paralellogram,  or  polygon  of  forces,  by  the  principle  of  the  lever, 
or  by  the  method  of  moments.  We  shall  give  a  few  examples,  referring  the 
student  to  the  works  of  Burr,  Dubois,  Johnson,  and  others  for  more  elabo- 
rate trentrnent  of  the  subject 

1 .  A  Simple  Crane.  (Figs.  1 18  and  114.)—^  is  a  fixed  mast,  B  a  brace  or 
boom,  T  a  tie,  and  P  the  load.  Required  the  strains  in  B  and  T.  The  weight 
P,  considered  as  acting  at  the  end  of  the  boom.  Is  held  in  equilibrium  by 
three  forces:  first,  gravity  acting  downwards:  second,  the  tension  in  7*:  and 
third,  the  thrust  of  B.  Lot  the  length  of  the  line  p  represent  the  magnitutie 
of  the  downward  force  exerted  liy  the  load,  and  draw  a  parallelogram  with 
sides  bt  parallel,  respectively,  to  B  and  T,  such  that  p  is  the  diagonal  of  the 
parallelogram.  Then  6  and  t  are  the  components  drawn  to  the  same  scale 
as  p,  p  being  the  resultant.  Then  if  the  length  p  represents  the  load,  t  Is 
the  tension  in  the  tie,  and  b  is  the  compression  in  the  brace. 

Or,  more  simply,  7',  B,  and  that  portion  of  the  mast  included  between  them 
or  A'  may  represent  a  triangle  of  forces,  and  the  forces  are  proporUooal  to 
the  length  of  the  sides  of  the  triangle:  that  is,  if  the  height  of  the  triangle  A* 
s=  the  load,  then  B  a  the  compression  in  the  brace,  and  r  =  the  tension  Tu  the 

tie;  or  if  P  s  the  load  in  pounds,  the  tension  iuTmPx^,t  and  the  oona- 


8TBESSES  IN  FOAMED  BTBUCTUBES. 


441 


pnaslon  \nB  =  Px 


Also,  if  a  s  the  angle  the  Inclined  member  makei 


vith  the  roast,  the  other  member  being  horizontal,  and  the  triangle  beinf^ 
right->aiigl«$d,  then  the  length  of  the  inclined  member  ss  height  of  the  tri- 
angle X  secant  a,  and  the  strain  in  the  inclined  member  =  P  secant  a.  Also, 
the  strain  in  the  horizontal  member  =;  P  tan  a. 

The  solution  by  the  triangle  or  parallelogram  of  forces,  and  the  equations 
TeiisiuD  in  T=:  Px  T/A\  and  Compression  inB^Px  B/A\  hold  true  even 
if  the  triangle  is  not  right-angled,  as  in  Fig.  115;  but  the  trigonometrical  rtda- 


Fio.  118. 


Fia.  114. 


Fio.  115. 


tions  aboTe  given  do  not  hold,  except  in  the  case  of  a  right-angled  triangle. 
H  is  evident  that  as  A'  decreases,  the  strain  in  both  Tand  B  Increases,  tend- 
ing to  become  infinite  as  A*  approaches  zero.  If  the  tie  TIs  not  attached  to 
ihe  mast,  but  is  extended  to  the  ground,  as  shown  in  the  dotted  line,  the 
tensinn  in  it  remains  the  same. 

2.  A  Gnyed  Crane  or  Herrlek*  (Fig.  110.)— The  strain  in  B  is,  as 
before,  Px  B/A\  A'  being  that  portion  of  the  vertical  included  between  B  and 
T,  wherever  Tmay  be  attached  to  A.  If,  however,  the  tie  Tib  attached  to  B 
beneath  its  extremitv.  there  may  be  in  addition  a  bending  strain  in  B  due  to 
a  tendency  to  turn  about  the  point  of  attachment  of  7  as  a  fulcrum. 

The  ntrain  in  T  may  be  calculated  by  the  principle  of  moments.  The  mo* 
nient  of  P  is  fV,  that  is,  its  weight  X  its  perpendicular  distance  from  the 
point  of  rotation  of  B  on  the  mast.  The  moment  of  the  strain  on  T  is  the 
product  of  the  strain  into  the  perpendicular  distance  from  the  line  of  its 


direction  to  the  same  point  of  rotation  of  B,  or  Td.  The  strain  in  T  there- 
fore ^  Pc-t-d.  As  d  decreases  the  strain  on  7*  increases,  tending  to  infin- 
ity as  d  approaches  zero. 

The  stram  on  the  guy-rope  is  also  calculated  by  the  method  of  moments. 
The  moment  of  the  load  about  the  bottom  of  the  mast  O  is,  ss  before,  Po. 
If  the  guy  is  horizontal  the  strain  in  it  is  F  and  its  moment  is  FY,  and  F  =3 
Pc-*-/.  If  it  is  inclined,  the  moment  is  the  strain  O  X  the  perpendicular 
distance  of  the  line  of  its  direction  from  O,  or  Gg,  and  &  =s  Pc-*-g. 

The  guy-rope  having  the  least  strain  is  the  horizontal  one  F^  and  the  straio 


442 


HBCBAKICS. 


in  &  =  the  strain  In Fx  ttte  afr 
cant  of  the  angle  between  I*koA 
(7.  An  OIb  made  more  nearly 
vertical  g  decreases,  and  tlui 
strain  increases^  becomingr  infW 
nite  when  g  ^  0. 

Ouya.  (Fijf.  117.)— Fir«t  assume 
that  the  two  masts  act  as  one 
placed  at  BD^  and  the  two  f^iivs 
08  one  at  AB.  Calculate  the 
strain  in  BD  and  AB  aa  in  Fig. 
115.  Multiply  hair  the  strain  in 
BD  (or  AB)  by  the  secant  of  linlf 
Fig.  117.  the  an^le    the   two  masis   (or 

guvs)  make  with  each  other  to  find  the  strain  tii  each  mast  (or  guy). 

fwo  Diagonal  Braces  and  a  Tie-rod.  (Fifr.  1 18.)— Suppose  the  braces 
are  used  to  sustain  a  single  load  JP.  Compressive  stress  on  AD  ==  yiP  X  AD-+- 
AB  ;  on  Oil  B  J^i»  X  CA-*-  AB,  This  is  true  only  if  CB  and  BDnre  of  equal 
length.  In  which  case  ^  of  P  is  supported  by  each  abutment  C  and  D,  If 
thev  are  unequal  In  length  (Fig.  119),  then, 
by  the  principle  of  the  lever.  And  the  re- 
actions of  the  abutments  Ri  and  lU.  If  P 
is  the  load  applied  at  the  point  Bon  the 
lever  CZ)»  the  fulcrum  being  D,  then  R,  X 
CD  =  P  X  BD  and  P,  X  CD  ss  P  X  PC; 
Pj  =  PX  PD  -I-  CD;  R^  =  FXBO'*'  CD, 
•the  strain  on  AC  =  P.  X  AC-*-  ABy  and 
on  itD  «  P,  X  -4D  t-  AB. 

The  strain  on  the  tie  t=  Pj  x  CP  •♦■  .4P 
=s  P,  X  PD  +  -4P.  _  ^^,^^^  CB=BD,  Rx^R^.    The  stitUn 

on  CB  and  PD  is  the  same,  whether 
the  braces  are  of  equal  length  or 
not,  and  is  equal  to  }iP  X  ^CD  -%-AB. 
If  the  braces  support  a  uniform  load, 
as  a  pair  of  rafters,  the  straina  caused 
by  such  a  load  are  equivalent  to  that 
caused  by  one  half  of  the  load  applied 
at  the  centre.  The  hoiisonutl  thni&t 
of  the  braces  against  each  other  at  the 
apex  equals  the  tensile  strain  In  the  tie. 

Kins-post  Trnsa  or  Bridge.  (Fig.  l^.y-lt  the  load  is  distributed 
over  tiie  whole  lengtli  of  the  truss,  tiie  effect  is  the  same  as  if  half  the  load 
were  placed  at  the  centre,  the  other  half  being  carried  by  the  abutmeuts.  Let 
P  =  one  half  the  load  on  the  truss,  then 
tension  in  the  vertical  tie  ^P  s  P.  Com- 
pression in  each  of  the  inclined  braces  a 
HP  XAD-t-AB.  Tension  In  the  tie  CD 
=  HPX  BD-t-AB.  Horizontal  thrust  of 
inclined  brace  ^D  at  D  =  the  tension  in 
the  tie.  If  fT  =  the  total  load  on  one  truss 
uniformly  distributed,  i  ss  Its  length  and 
d  =  its  depth,  then  the  tension  on  the  hor- 

iTOntal  tie  =  ^. 

on 

Inverted  Klns-post  Trnss*  (Fig.  131.>— If  P  s  a  load  applied  al 
P,  or  one  half  of  a  uniformly  dit<irtbuted  load,  then  compression  on  AB  =  F 
(the  floor-beam  CD  not  being  considered 
to  have  any  resistance  to  a  rtight  benditig^. 
Tension  on  ^C Or  i4D  ==  UP  X  XD  -*-  AB. 
Coninression  on  CD  =  HP  X  PD  ■•-  -«IP. 

<|ueen-po0t  Truss.  (Fig.  1S3.>~lf 
uniformly  loaded,  and  the  queen«poa*R  dl- 
vldt^  the  length  into  three  equal  bays,  the 
load  may  be  considered  to  be  divided  Into 
three  equal  parts,  two  parts  of  which,  Pj 
SDd  Pt,  are  concenlratedat  the  panel  Joints 


Fro,  110. 


FI0.1SOL 


8TBESSES  IN  FRAMED  BTBUCTUBES. 


443 


and  the  reoialnder  fa  equally  divided  between  the  abiitmeotfl  and  gupported 
\gy  tlMm  direotljr.   The  two  parte  P^  and  P,  only  are  coDsidered  to  afftet 

the  members  of  the  truss.  Strain  in 
the  vertical  ties  BE  and  CF  each 
aguals  Pi  or  P,.  Strain  on  AB  and 
CD  each  =  P,  X  CD  •¥  CF,  Btrain 
on  the  tie  AE  or  EF or  ED  =  P|  X 
FD  -H  OF.  Thrust  oaBOm  tension 
on  EF. 

For  stability  to  resist  heavy  un- 
equal loads  the  queen-post  truss 
should  have  dis^ooal  braces  ftoiu 
B  to  Fasd  from  CtoE. 

InTerted  (| ii « e n-post 
TruM.  (Fie^_  128.)^  Compression 
on  EB  and  FC  eaoh «  p,  or  P,. 
Compression  on  ^B  or  BC  or  CD  = 
P,  X  -4a-*-l?B.  Tension  on  ^jP  or 
Fl):aPiXAE-t- EB.  Tension  on 
EFnz  compression  on  BQ,  For  sta- 
bility to  resist  unequal  loads,  ties 
should  be  run  from  OXoE  and  from 
BtoP. 


Fro.  128. 


Burr  VroM  of  Five  Panels.  (FiR.  1«4.>— Four  fifths  of  the  load  may 
be  taken  as  concentrated  at  the  points  B^JCfL  and  F^  the  other  fifth  being 


snpporled  directly  by  the  two  abutmenls.  For  the  strelns  In  BA  and  CD 
the  truss  may  be  considered  as  a  queen-post  truss,  M-ith  the  loads  Pj ,  P^ 
concentrated  at  IT  and  the  loads  P. ,  P.  concentrated  at  F.  Then,  oompres* 
Siva  strain  on  AB  s  (P|  +  P,)  x  AB  '+-BE,  The  strain  on  CD  is  the  same  if 
the  loads  and  panel  lenfcths  are  equal.  The  tensile  strain  onf^or  CFs= 
Pi  -f  P..  That  portion  of  tlie  truss  oetween  E  and  F  may  be  considered  as 
a  smaller  queen-post  truss,  supporting  rhe  loads  P, ,  Pj  at  f  and  L.  The 
strain  on  £&  or  mF  =3  P,  x  ECf-h  OK,  The  dlaiconals  G^I;  and  KH  receive  no 
strain  unless  the  truss  Is  unequally  loaded.  The  verticals  OKaxuX  HL  each 
receive  a  tensile  strain  equal  to  P.  or  P|. 

For  the  strain  In  the  horisontal  members:  BO  and  CB  receive  a  thrust 
equal  to  the  horizontal  component  of  the  thrust  in  ^B  or  CD,  =  (Pi  +  J^) 
X  tan  aiiffle  ABE,  or  (P,  +  P«)  X  AS-*-  BE.  Off  receives  this  thrust  and 
also,  in  aadittoe,  a  thmst  equal  to  the  horizontal  component  of  the  thrust  in 
EOerHF,  or,  In  all,  (P.-T^.  +  p,)  x  AE-*-BE. 

The  tension  in  ^£  or  FD  equals  the  thrust  In  BO  or  HC,  and  the  tension 
in  SK.  KL,  and  LF-  equals  the  thrust  in  OH. 

Pratt  or  Wblpple  Tmes*  (Fig.  125.)— In  this  truss  the  diagonals  are 
ties,  and  the  verticalu  are  struts  or  columns. 

Calculation  by  the  method  of  distribution  of  strains:  Consider  firat  the 
load  Px.  The  truss  having  six  bays  or  panels,  5/6  of  the  load  is  transmitted 
to  the  abutment  H,  and  1/6  to  the  abutment  O,  on  the  principle  of  the  lever. 
As  the  five  sixths  must  be  transmitted  through  JA  and  AIu  write  on  these 
HH^mberH  the  figure  6.  The  one  sixth  is  transmitted  successively  through 
JC^  CK,  KD,  DC,  etc.,  passing  alternately  through  a  tie  and  a  strut.  Write 
on  these  members,  up  to  the  strut  OO  inclusive,  the  figure  1.  Then  consider 
th«*  Utad  P, ,  of  which  4/6  goes  to  AH  and  8/6  to  OO,  Write  on  KB,  BJ,  JA^ 
and  AH  the  figure  4,  and  on  KD,  DL,  LE,  etc.,  the  figure  2.    The  load  P, 


444 


MECHANICS. 


timnsmlt  8/S  In  each  direction;  write  8  on  eacb  of  the  members  tbroucfa 
which  this  BtnMM  paaeee,  and  so  on  for  all  the  loads,  when  the  flg^ures  oo  ^e 
several  members  will  appear  as  on  the  cut.  Adding  them  up,  we  have  the 
following  totals : 

Tfinidon  on  dla«i«hii  ^-^  ^^  ^^  CJ  CL  DK  DM  EL  EN  FM  FO  G29 
Tension  on  diagonals  {  j5      o      10     1       6     8      8      6      1     10     0      15 


Oompreaskm  on  Tertlcals  j 


AH 

15 


BJ 
10 


CK  DL 

7       6 


EM 

7 


FN 
10 


GO 

15 


Each  of  the  flgures  in  the  first  line  is  to  be  multiplied  bv  1/dPx  secant  of 
angle  HAJ^  or  1/6/"  xAJ-¥-  AH^  to  obtain  the  tension,  and  each  figure  In  the 
lower  line  Is  to  be  multiplied  by  1/6P  to  obtain  the  oompresricm.  Tlie  diag* 
coals  HB  and  j^  zeoelTe  no  strain. 


O     O     O     O     Q 

P,  P«  Pt  P4  P5 


Fia.  125. 

It  Is  common  to  build  this  truss  with  a  diagonal  stmt  at  BB  Instead  of  the 
post  HA  and  the  diagonal  AJ\  in  which  case  R/6  of  the  load  Pis  carried 
through  JB  and  the  strut  BH^  which  latter  then  reoelTes  a  strain  s  15/OP  x 
secant  of  HBJ. 

The  strains  In  the  upper  and  lower  horizontal  members  or  chords  increase 
from  the  ends  to  the  centre,  as  shown  in  the  case  of  the  Burr  truss.  AV 
recelTes  a  thrust  equal  to  the  horizontal  component  of  the  tension  in  AJ^  or 
15/6PX  tan  AJB.  BC  receives  the  same  thrust  +  the  horizontal  component 
of  the  tension  in  BK,  and  so  on.  The  tension  in  the  lower  chord  of  each  panel 
is  the  same  as  the  thrust  in  the  upper  chord  of  the  same  panel.  (For  calcu 
lation  of  the  chord  strains  by  the  method  of  moments,  see  below.) 

The  maximum  thrust  or  tension  is  at  the  centre  of  the  chords  and  is  equib 

to  ~,  in  which  IF  Is  the  total  load  supported  by  the  truss,  L  Is  the  length, 

and  D  the  depth.    This  Is  the  formula  for  maximum  stress  In  the  chords 
of  a  truss  of  any  form  whatever. 

The  above  calculation  is  based  on  the  assumption  that  all  the  loads  P^.  I\, 
etc.,  are  equal.  If  they  are  unequal  the  value  of  each  has  to  be  taken  Into 
account  in  distributing  the  strains.  Thus  the  tension  in  A  J,  with  unequal 
loads,  instead  of  being  15  X  VO  P  secant  $  would  be  sec  #  X  (5/IBP,  +  4/0  P,  4- 
3/5  P|  +  2/6  Pa  4- 1/6  P«.)  Each  panel  load,  P|  eto..  Includes  its  fraction  of 
th(>  weight  of  toe  truss. 

General  Formula  for  Strains  In  mayonals  and  TerCleala. 
— I^i  n=  total  number  of  panels,  x  =  number  of  auy  vertical  considered 
from  the  nearest  end,  counting  the  end  as  1,  r  s  rolling  load  for  eacdii  panel, 
P  =  total  load  for  each  panel, 

StnUn  on  yerttcU.  =  l(»=S^}+(n=^)l-(>'-l>+<'-lr>^P.tix-t)+<^~l)* 

2n  '  8a 

For  a  uniformly  distributed  load,  leave  out  the  last  term, 
[r(«-l)4-(aj-l)«]^8,i. 

Stndn  on  principal  diagonals  ss  strain  on  verticals  x  secant  #,  that  la 
secant  of  the  angle  the  diagonal  makes  with  the  vertical. 

Strain  on  the  count«rbraces :  The  strain  on  the  counterbraoe  in  the  first 
panel  is  0,  if  the  load  is  uniform.    On  the  9d,  8d,  4th,  eta,  it  is  P  secant  # 

X  J,  ^—-^  -J^tl±^,  etc.,  P  being  the  total  toad  to  one  panel 


STRESSES  IK  FRAMED  STRUCTURES. 


445 


MnUB  In  the  €1ioWU-RIetbod  of  RIomeiito.-L6t  the  truu  be 
nniformlv  loaded,  the  totnl  load  acting  on  it  =  W.  Weight  supported  at 
each  end,  or  reaction  of  the  abutment  =  W/2.  Length  of  the  truss  s  L. 
Weight  on  a  unit  of  length  -  W/L.  Horizontal  distance  from  the  nearest 
abutment  to  the  point  (aay  Af  in  Fig.  125j  In  the  chord  where  the  strain  is  to 
be  determined  s  x.  Rorisontal  strain  at  ttiat  point  (tension  on  the  lower 
chord,  compression  in  th<  upper)  =  H.  Depth  of  the  truss  =  D.  By  the 
meihod  of  momenCe  we  talce  the  difference  of  the  moments,  about  the  point 
Jf.  of  the  reaction  of  the  abutment  and  of  the  load  betwet'n  M  and  the  abut- 
ments, and  equate  that  difference  with  the  moment  of  the  resistance,  or  of 
the  strain  in  the  horlaontal  chord,  considered  with  reference  to  a  point  in 
the  oppoeftte  chord,  about  which  the  truss  would  turn  if  the  first  chord  were 
severed  at  M. 

The  naoineDt  of  tlie  reaction  of  the  abutment  is  Wx/2.  The  moment  of 
the  load  from  the  abutment  to  if  is  W/Lce  X  the  distance  of  its  centre  of 
gravity  from  M,  which  is  ^/8*or  moment »  Wx^-t-UL.  Moment  of  the  stress 

hi  the  chord  =:fli)  =  ^_^,  whence  fl=^/«-jY   lfa;  =  OorL. 

H  =  0.    IfxsLAHss  j^,  which  is  the  horizontal  strain  at  the  middle 

of  the  chords,  as  before  given. 
Tlie  Kowe  Tthm,    (Fig.  126^In  the  Howe  truss  the  diagonals  are 


strata,  and  the  vertioals  are  I 


Tbe  calculation  of  strains  may  be  made 


te  tbe  same  nnethod  as  described  above  for  the  Pratt  tram. 

Tlte  ITarren  Olrdler.   (Fig.  1)27.)— In  the  Warren  girder,  or  triangular 
truaa,  there  are  no  vertical  struts,  and  the  diagonals  may  transmit  either 


Fla.  187. 

tanaloii  or  compression.  The  strains  in  the  diagonals  may  be  calculated  by 
the  method  of  distribution  of  strains  as  in  the  case  of  the  rectanerular  truss. 
On  the  principle  of  the  lever,  the  load  P]  being  1/10  of  the  length  of  the 
span  from  the  line  of  the  nearest  support  a,  transmits  9/10  of  its  weight  to  a 
sod  1/10  to  g.  Write  9  on  the  right  hand  of  the  strut  la.  to  represent  the 
eompreasion,  and  1  on  the  right  hand  of  lb.  2c,  3d,  etc.,  to  represent  com- 
pression, and  on  the  left  hand  of  62,  c3,  etc. ,  to  represent  tension .  The  load  P^ 
truismits  7/10  of  its  weight  to  a  and  3/10  to  g.  write  7  on  each  member  from 
S  to  a  and  8  on  each  member  from  2  to  gi,  placing  the  figures  representing 

ession  on  the  right  hand  of  the  member,  and  those  representing 

I  on  the  left.    Proceed  in  the  same  manner  with  all  the  loads,  then 


448 


HECHAKICS. 


■um  np  th«  flgnrM  6a  Moh  tide  of  each  diagonal,  and  write  the  difference 
of  each  sum  beneath,  and  on  the  side  of  the  (greater  aum,  to  ahow  whether 
the  difference  repreaeota  tenaion  or  compression.  The  reaulta  are  as  follows: 
Oompreasion,  la,  96;  86,  15;  Sc,  6;  8d,  5;  4«,  15;  6o,  95.  Tension,  16,  15;  So, 
6:  4a,  5;  fie,  16.  Bach  of  these  flKures  la  to  be  multiplied  by  1/10  of  one  of 
the  loads  as  Pi ,  and  by  the  secant  of  the  angle  the  diagonals  make  with  a 
Tertical  line. 

The  strains  in  the  horlxontal  chords  may  be  determined  by  the  method  of 
moments  as  In  the  case  of  rectangular  tnisaea. 

Roof<itniss«*-ar>/u<ion  by  Method  of  Momenta.-^The  calculation  of 
atratns  In  structures  by  the  method  of  statical  moments  oonsista  in  taking  a 
eroa8*seotion  of  the  stnioture  at  a  point  where  there  are  not  more  thaa 
three  members  (struts^  braces,  or  chords). 

To  And  the  strain  In  eitlier  one  of  these  members  take  the  moment  about 
the  intersection  of  the  other  two  as  an  axis  of  rotation.  The  sum  of  the 
moments  of  these  members  must  be  0  if  the  structure  is  in  equilibrium^ 
But  the  moments  of  the  two  members  that  pass  throu;;h  the  point  of  refer- 
ence or  axis  are  both  0,  hence  one  equation  containing  one  unknown  quan* 
tity  can  be  found  for  each  cross-section. 


^^^^ 


rxa.  188. 


In  the  traaa  shown  In  Fig.  198  take  a  oross-eectloo  at  /«,  and  detartnlne  the 
strain  In  the  three  members  cut  by  it,  viz.,  CB,  ED,  and  DF.  Let  X  b  force 
exerted  in  direction  CB,  Y  s  force  exerted  in  direction  DE^  Z  s  force  ex- 
erted in  direction  FD. 

For  X  take  its  moment  about  the  intersection  of  Fand  Z  at  D  s  Xx.  For 
Y  take  its  moment  about  the  interaection  of  Xand  Z  at  ^4  =  Fy.  For  Z  take 
its  moment  about  the  intersection  of  X  and  F  at  /?  ss  Zz.  het  2  s  16, «  a 
18.6,  y  s  88  4.  ^D  =3  50,  C/)  s  20  ft.  Let  P,.  P.,  P„  P4  be  equal  loads,  as 
shown,  and  8^  P  the  reaction  of  the  abutment  A. 

The  sum  of  all  the  moments  taken  about  D  or  A  or  It!  will  be  0  when  the 
structure  is  at  reat.  Then  -  Xr  -f  8.6P  X  00  -  P,  X  1S8.6  -  P.  X  «  -  P,  x 
87.5  =  0.  ' 

The  -(-.signs  are  for  moments  in  the  direction  of  the  hands  of  a  watch  or 
**  clockwise  **  and  —  signs  for  the  reverse  direction  or  anti-clockwise.  Since 
P^Pi-P^^Pt,    -l8.6X+175P-76Ps=0;  -18.6X=-100P:    X  = 

li0P-H'l8.Cs5.8T8P. 
-  Fy  +  i^87.6-f-P,  X28  f  P,  X  W.5ss0;  8a4F=  75P;  F=76P-t-8e.4 

-Zi-f  8.*5PX87.8-P,  Xfl6-  P,Xia.5-P,X0=:0;  lfilf  =  98.78P;  Z  = 

In  the  same  manner  the  forces  exerted  in  the  other  members  hare  been 
found  as  follows:  SO  =  0.73P;  GJ  =  8.07P;  J  A  =  9.4«P;  JH  a  1 .88P:  GF  « 
1.69P;  AH  =  8.75 P;  HF  =  7.50P. 

Tbe  Fink  Boof-tmaa.  (Fig.  120.)— An  analysis  by  Frot  P.  fl.  Ftii|< 
brick  {Van  N,  Mag.»  Aug.  1880)  irivea  the  following  resulta; 


8T&BSSES  IN  FBAHBD  8TBU0TUBB&  447 

C 


Fio.  129, 
W  =s  total  load  on  roof; 
N  s  No.  of  panels  on  l>oth  rafters  i 
W/N  «  F  «  load  at  each  J<3int  6,  d.  /,  etc.; 
V  =a  reaction  at  ^  =  ^JT  =  i^NI* »  AF% 
AOm8\    AC^Lx   CD=iD; 
ft*  ^1  ^t  »  tension  on  i>e,  eu^gA,  respeotively; 
^xt  <?«•  Cm*  c«  b  compression  on  C6,  M,  c(/,  aod/^. 


Strains  in 

1,  orD«  ss  fj-8P«^D; 

2,  •*  ^0  s  r.  s  8/»S  ^  /); 

4.    •*  4/'«C4  =  7/2PZ»-«-D; 


dbme^m  7/iPL/D  ^StPD/L; 


7.  or  60  =  c,  =7/8  PZ;/D  w  8  PD/Ll 

0,  "  de  B  «PS  -•-  Z; 

JO,  "  od  or  dy  a  HPa-*-  D; 

il.  "  ee  aPS^D; 

12,  •♦  c(7  «8/BP5-»-D. 


£rampZe.— Given  a  Fink  roof -truss  of  span  04  ft ,  depth  16  ft.,  with  four 
panels  on  each  vide,  as  in  the  cut;  total  load  BH  tone,  or  4  tons  each  at  tlio 
pblnts  /,  d,  6,  C»  etc.  (and  S  tons  each  at  A  and  B^  which  transmit  no  strain 
to  ihe  truss  members).  Here  1^=  82  tons,  P  =  4  tons,  5  s  88  ft.,  D  «  10 
ft.,  L  «  VS*  +  D»  «  «.«88  X  D.  L  -».  D  »  8.888,  D*  L  =  .4472,  8  ■*- D  =  ii, 
H-*-  L»  .8044.    The  strains  on  the  numbered  members  then  are  as  follows: 


1,  8X4X9  «18  tons; 
t,  SX4XS  »»4  ** 
8,  7/8X4X8  "88  •• 
4,  7/8  X4X8.888.  81.8  " 
9!81.8~4X  .447  «  88.68  •« 
8^  tl.8-6X  .447  ■  37.7a  «• 


7,  81.8  -  12  X  .447    =  29.04  tons. 

8,  4  X  .$044  =    8.58    " 
0,  8x  .8044  «    7.16   " 

10,  BX    2       s   4 

11,  4X    8      «   8 

1%  ex   9     mti      " 


Tbe  Bconomlcal  Angle.— A  structure  of  tri 
angular  form,  Kik.  IJto,  in  supported  at  a  and  b.  It 
sustains  any  load  L,  the  elenienu  cc  being:  in  coinpres- 
Rion  and  tin  tension.  Required  the  angle  9  so  that 
the  total  weiffhr  of  the  structure  shall  be  a  minimum. 
F.  R.  Honey  {8cl.  Am.  Supp.y  Jan.  17, 1896)  giveaattolu- 

tkm  of  this  problem,  with  the  result  tan  e 

in  which  C  and  Troprssent  ibe  crushing  and  the  ten- 
sile strength  resp*H;tively  of  the  material  employed. 
It  is  applicable  to  iiny  material.    For  0»  T,  tan  #  = 
64J».    For  C  =  0.4r  (yellow  pine),  tan  9  s  4»|».    For  O: 
tan  8  as  Mi*.    For  C  «  62*  (oast  iron),  tan  8  s  60i«. 


"7       T    ' 


Fio.  ISOa. 
:0.8r(i3oft  steel> 


448  HEAT. 


HEAT. 

THERlVfOnffETBRS. 

The  Fahrenheit  thermometer  is  generally  used  in  EngliRh-Bpeakinf?  coun- 
tries, and  the  Centi{?rade,  or  Celsius  thermometer,  in  countries  that  uw  the 
metric  system.  In  many  scientiflc  treatises  in  English,  however,  the  Centi- 
grade temperatures  are  also  used,  either  with  or  without  their  Fahrenlieit 
equivalents.  The  R6aumur  thermometer  is  used  to  some  extent  on  the 
Continent  of  Europe. 

In  the  Fahrenheit  thermometer  the  freezing-point  of  water  is  taken  at  32^, 
and  the  hoiling-point  of  water  at  mean  atmospheric  pressure  at  the  sea- 
level,  14.7  lbs.  per  sq.  in.,  is  taken  at  '^12^,  the  distance  between  these  two 
points  being  divided  into  18(P.  In  the  Centigrade  and  Reaumur  thermomet««ra 
the  freezing-^M>int  is  taken  at  O^*.  The  boilmg-point  is  100*  in  the  Centigrade 
scale,  and  W"  in  the  R6aumur. 

I  Fahrenheit  degree         =  5/0  deg.  Centigrade    s  4/0  deg.  R^umur. 

1  Centigrade  degree         =  0/5  deg.  Fahrenheit    s  4/5  deg.  R6aumur. 

1  Reaumur  degree  =  0/4  deg.  Fahrenheit    e  5/4  deg.  Centigrade. 

Temperature  Fahrenheit  =  0/5  X  temp.  C.  -f  32«  =  0/4  R.  -|-  82?. 

Temperature  Centigrade  =  6,^  (temp.  F.  —  8S»)    =  5/4  R. 

Temperature  Reaumur    =  4/5  temp.  C.  =  4/0  (F.  ^  82*). 

2IIercarial  Tbermometer.  (Ranklne,  S.  E.,  p.  884.)— The  rate  of 
expansion  of  mercury  with  rise  of  temperature  increasesas  the  temperature 
becomes  higher  ;  from  which  it  follows,  that  if  a  thermometer  showing  the 
dilatation  or  mercury  simply  were  made  to  agree  with  an  air  thermometer 
at  82?  and  il2?,  the  mercurial  thermometer  would  show  lower  temperaturea 
than  the  air  thermometer  between  those  standard  points,  and  higher  tem- 
peratures l>eyond  them. 

For  example,  according  to  Regnanit,  when  th**  air  thermometer  marked 
aSO**  C.  (-  6W?  F.),  the  mercurial  thermometer  would  mark  802.16*  C.  (a 
888.80«  F.),  the  error  of  the  latter  being  in  excess  1S.16*  C.  (=  81.S0«  F.). 

Actual  mercurial  thermometers  indicate  intervals  of  temperature  propor- 
tional to  the  difference  between  the  expansion  of  mercury  and  that  of  glasn. 

The  inequalities  in  the  rate  of  expansion  of  the  glass  (which  are  very 
different  for  difTerent  kinds  of  glass)  correct,  to  a  greater  or  less  extent,  the 
errors  arising  from  the  inequalities  in  the  rate  of  expansion  of  the  mercury. 

For  practical  purposes  connected  with  heat  engines,  the  mercurial  ther- 
mometer made  of  common  glass  may  be  considered  as  sensibly  coinciding 
with  the  air-thermometer  at  all  temperatures  not  exceeding  600^  F. 

Prlnelples  Used  In  Various  Pyrometeni*— Contraction  of  day 

U  heat,  as  in  the  Wedgwood  pyrometer  used  bv  f  '" —     ^'-' '     - 

the  contraction  varies  with  the  quality  of  the  clay 


by  heat,  as  in  the  Wedgwood  pyrometer  used  bv  potters.  Not  accurate,  as 
he  contraction  varies  with  the  quality  of  the  clay. 

Expansion  of  air,  as  in  the  air-thermometers,  Wiboigh*s  pyrometer,  Ueh* 
ling  and  Steinbart*s  pyrometer,  etc. 

Specific  heat  of  solids,  as  in  the  copper-ball,  platinum^ball,  and  fire-clay 
pyrometers. 

Relative  expansion  of  two  metals  or  other  substances,  as  copper  and  Iron, 
as  in  Brown's  and  Bulkley's  pyrometers,  etc. 

Melting-points  of  metals,  or  other  substances,  as  in  approximate  deters 
minations  of  temperature  by  melting  pieces  of  zinc,  lead,  etc. 

Measurement  of  strength  of  a  thermo-electric  current  produced  by  heat- 
ing the  Junction  of  two  metals,  as  in  Le  Ch atelier's  pyrometer. 

Changes  in  electric  resistance  of  platinum,  as  in  tue  Siemens  pyrometer. 

Mixture  of  hot  and  cold  air,  as  in  Hobson's  hot-blast  pyrometer. 

Time  requirtnl  to  heat  a  weighed  quantity  of  water  enclosed  in  a  vessel, 
as  in  the  water  pyrometer. 

Tltermoiiieter  for  Temporatnres  up  to  950*  F«— Mercury 
with  compreKHCHt  nitrogen  in  the  tube  above  the  mercury.  Made  by  Queen 
&  Co.,  Philadelphia. 


TBnPBBATURBS,  €BNTIGBADE  AND 

liQ 

FAHRJBNHEIT. 

c. 

F, 

36 

F. 

c. 

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108.6 

983 

649 

176.1 

960 

510. 

W 

—  6.7 

86 

80. 

159 

66.7 

218 

108.8 

884 

14a 

860 

176.7 

960 

515.8 

91 

-6.1 

87 

80.6 

158 

67.9 

210 

106.9    986 

140.6    8611 

m.8 

97d 

B81.1 

9* 

-  5.6 

88 

81.1 

154 

67.8 

220 

104.4    986 

141.1    868 

m.8    980 

686.7 

98 

-6. 

80 

81  7 

155 

68.3 

2-.>l 

106.      987 

141.7    668 

6828 

»4 

-4.4 

90 

82.2 

156 

68.0 

222 

105.6    288 

148.8    864 

i^i&i 

95 

—  3.9 

0! 

82.8 

157 

60.4 

223 

106.1    989 

14a8   886 

PYBOMEIBT.  451 

PtaUMtttti  OF  Oopp*r  Biai  PFrolB«t«r,-^A  welglMd  titooe  of 
plAtlBiiin,  copper,  or  Iron  is  fttlowod  to  remain  In  the  furtimce  or  heeled 
ohember  till  ft  bee  attained  the  temperature  of  ifce  BurrottndlnirL  It  ie  theft 
suddenly  taken  oat  and  dropped  Into  a  veiftel  containlnff  water  of  a  known 
weight  and  temperature.  Tiw  water  to  etlrred  rapidly  and  Its  maidmum 
temperature  taken.  Let  W  =3  weight  of  the  water,  w  the  weigh!  of  the  balL 
t  s  the  original  and  T  the  final  heat  of  the  water,  and  a  the  mcilto  beat  off 
the  metal;  then  the  temperature  of  fire  may  be  found  from  t&e  formula 

Th*  mean  speclflc  heat  of  platinum  between  88«  and  446*  F.  to  .08888  or 
1/90  that  of  water,  and  it  Increoaee  with  the  temperature  about  .000809  for 
each  100"  F.  For  a  fuller  description,  by  J.  0.  Boadiey ,  see  Trans.  A.  8.  M.  S., 
▼i.  708.    Compare  also  Henry  M.  Bowe,  Trani.  A.  L  M.  £.,  icTlii.  938. 

For  aocuracnr  oorreotionB  are  required  for  variations  in  the  specific  heat  of 
the  water  ana  of  the  metal  at  different  temperatures,  for  loss  of  heat  by 
radiation  from  the  metal  during  the  transfer  from  the  rumaoe  to  the  water, 
aiid  from  the  apparatus  during  the  heating  of  the  water;  also  for  the  heafr* 
absorbing  capacity  of  the  vessel  containing  the  water. 

Fire-clay  or  flre^brick  may  be  used  instead  of  the  metal  boll. 

!«•  CliateUer'a  Xlienao-oleetrle  PFrom«ter»->For  a  very  fall 
deecription  see  paper  by  Joseph  Btrutbers,  School  of  Minn  QuaWerty,  toI, 
xii,  18B1 ;  also,  paper  read  by  Prof.  Roberts-Austen  before  the  Iron  and  Bteel 
Institute,  May  7, 1801. 

The  principle  upon  which  thto  pyrometer  Is  oonstructed  Is  the  measure- 
ment of  a  current  of  electricity  produced  by  heating  a  couple  composed  of 
two  wires,  one  platinum  and  the  other  platinum  with  I0j(  rhodium— the  cur- 
rent produced  being  measured  by  a  gal'rauometer. 

The  composition  of  the  gas  which  surrounds  the  couple  has  no  influence 
Oil  the  indications. 

When  temperatures  above  S500"  F.  are  to  be  studied,  the  wires  must  have 
an  Isolating  support  and  must  be  of  good  length,  so  that  all  ports  of  a  fur- 
nace can  be  reached. 

For  a  Siemens  furnace,  about  11U  feet  Is  the  general  length.  The  wlrei 
are  supported  In  an  iron  tube,  ^  incn  interior  dtometer  and  held  lb  place  by 
a  cylinder  of  refractory  clay  having  two  holes  bored  through.  In  which  tha 
wires  are  placed.  The  shortness  of  time  (five  seconds)  allows  the  tempera- 
ture to  be  taken  without  deteriorating  the  tube. 

Tests  made  by  this  pyrometer  iu  measuring  furnace  temperatures  under 
a  great  varietT of  conditions  show  that  the  readings  of  the  scale  uncorreoted 
are  always  within  4S<'  F.  of  the  correct  temperature,  and  In  the  majority  of 
industrial  measurements  this  Is  sufficiently  accurate.  Le  Chatelfer^s  py- 
rometer to  sold  by  Queen  &  Co.,  of  Philadelphia. 

Gimdaatloii  of  I<e  Cliatelloi^a  Fjrromet«r.— W.  0.  Roberti- 
Austen  in  his  Researches  on  the  Properties  of  Alloys.  Proc.  Inst.  M.  IB.  1808, 
says :  The  electromotive  force  produced  by  heating  the  thermo-Junctlon 
to  any  given  temperature  is  measured  by  the  movement  of  the  spot  of  light 
on  the  scale  graduated  In  millimetres.  A  formula  for  converting  the  divi- 
sions of  the  scale  into  thermometric  degrees  to  given  by  M.  Le  Chateller;  but 
it  to  better  to  calibrate  the  scale  by  heating  the  thermo-Junctlon  to  temper* 
aturee  which  have  been  very  carefully  determined  by  the  aid  of  the  air- 
thermometer,  and  then  to  plot  the  ourve  from  the  data  so  obtained.  Many 
fusion  and  boiling-points  have  been  established  by  concurrent  evidence  of 
various  kinds,  and  are  now  f^ty  generally  accepted.  The  following  table 
contains  certain  of  these  : 

Deg.  F.  Deg.  C. 
1733  045    Silver  melts. 

lafiO        1016   Potassium  sul- 
phate melts. 
1018        1048    Gold  melts. 
1080        1094   Copper  melts. 
<789        1000   Palladium  melts. 
8227        1776    Platinum  melts. 


Mi  iSio  Water  boito. 

618  836  Lead  melts. 

676  398  Mercury  boils. 

779  419  Zinc  melts. 

88B  448  Sulphur  boils. 

1167  686  Aluminum  melts. 

1880  666  Selenium  bolls. 


Tlie  Temp«mtarea  Deweloped  In  Induatrial  Fnrnacea.— 

M.  Le  Chateller  states  that  by  means  of  his  pyrometer  he  has  dlsoorered 
that  the  temperatures  which  occur  in  melting  steel  and  in  other  industrial 
operations  have  been  hitherto  overestimated. 


453  HEAT. 

M.  Le  Chateller  flndH  the  melting  beat  of  white  oast  Iron  1185*  <S095*  F.). 
and  that  of  gray  cast  iron  \&a»  {2Sr»^  F.).  Mild  steel  melts  at  1475*  (8687* 
F.),  semi.mild  at  14fi6»  (2661*  F.),  and  hard  steel  at  14I0*  (2570*  F.).  The 
furnace  for  hard  porcelain  at  the  end  of  the  baking  has  a  heat  of  1370* 
(3496*  F.).  The  heat  of  a  normal  incandescent  lampls  1800*  (837)$*  F.).  but 
It  may  be  pushed  to  beyond  2100*  (88  K>*  F.). 

Prof.  R<>oerts- Austen  (Recent  Advances  in  Pyrometry.  Trans.  A.  I.  M.  B., 
C!hica«^>  Meetinflr»  l^M)  gives  an  excellent  description  of  modem  forms  of 
pyrometers.    The  following  are  some  of  his  temperature  determinatioDs. 

GOLD-MKLTIKO,  ROTAL  MlMT. 

Degrees.  Degrees. 
Centigrade.       Fahr. 
Temperature  of  standard  alloy,  pouring  Into  moulds.  ...  1180  S156 

Temperature  of  standard  alloy,  pouring  into  moulds  (on 

a  previous  occasion,  by  thermo-couple) 1 147  9007 

ADneal|^Dg  blanks  for  coinage,  temperature  of  chamber..    890  1684 

SlLVBR-MKLTINO,  ROTAL  MlMT. 

Temperature  of  standard  alloy,  pouring  into  mould 960  1796 

Ten-ton  Opbn-hbarth  Furnace,  Woolwich  Arsenal. 

Temperature  of  steel,  O.B%  carbon,  pouring  into  ladle 1045  8908 

Steel,  0.9%  carbon,  pouring  into  large  mould 1 580  8878 

Reheating  furnace,  interior 930  1706 

Cupola  furnace.  No.  'J  cost  iron,  pouring  into  ladle 1600  2918 

The  following  determhiations  have  been  effected  by  M.  Le  Chatelier: 

Bessemer  Process. 

Six-ton   Converter. 

Degrees.  Degrees 

Centigrade  Fahr. 

A.  Bathofslag im  2876 

B.  Metal  in  ladle 1640  2984 

C.  Metal  in  ingot  mould 1580  2876 

P.  Ingot  in  reheating  furnace 1200  8108 

E.  Ingot  under  the  hammer 1060  1978 

Opbn>h  EARTH  FuRNACE  (Slomens). 
Semi-Mild  Steel. 

A.  Fuel  gas  near  gas  generator 720  JS28 

B.  Fuel  gas  entering  into  bottom  of  regenerator  chamber    400  758 

C.  Fuel  gas  Issuing  from  regenerator  chamber 1200  8192 

Air  issuing  from  regenerator  Cham  her 1000  1888 

Chimney  gases.    Furnace  in  perfect  condition 800  590 

End  of  the  melting  of  pig  charge 1420  2588 

Completion  of  conversion 1500  278i 

Molten  steel.    In  the  ladle— Commenceiueut  of  casting. .  1580  2H7tt 

Endof  casting 1400  8714 

Intliemoulds 1520  8768 

For  very  mild  (soft)  steel  the  temperatures  are  higher  by  50*  GL 

Siemens  Crucible  or  Pot  Furnace. 
1600*  a,  2912*  F, 

ROTART  PUDDLXNO  FURNACE. 

Degrees  C.  Degrees  F 

Furnace 1840-1280  2444-8846 

Puddled  ball— End  of  operation 1880  8486 

Blast-furnace  (Gray -Bessemer  Pig). 

Opening  in  face  of  tuyere 1980  8906 

Molten  metal— Commencement  of  fusion 1400  8538 

End,  or  prior  to  tapping 1570  8866 

HomiAN  Red-brick  Kiur. 

Burning  temperatures 1100  8018 


PYROMETRY.  453 

BolMM^n's  Bot«1»last  PTrometer  conalttB  of  a  brasa  chamber 
barinfp  three  hollow  arms  and  a  handle.  The  hot  blast  enters  one  of  the 
arras  and  induces  a  mirrent  of  atmospheric  air  to  flow  Into  the  second  arm. 
The  two  corrents  mix  In  the  chamber  and  flow  out  through  the  third  arm, 
ia  which  the  temperature  of  the  mixture  is  taken  by  a  mercury  thermom' 
eter.  The  openings  in  the  arms  are  adjusted  so  that  the  proportion  of  hot 
blast  to  the  atmospheric  air  remains  the  same. 

T^e  iriborsli  Air-pyrometer*  (B.  Trotz,  Trans.  A.LM.E. 
1S9^) — The  inventor  using  ilie  expansion-coeflflctent  of  air,  as  determined 
by  Gay-Lussac,  Dulon,  Rudberg,  and  Regnault,  bases  his  construction  on 
the  following  theory :  If  an  air-yolume,  K,  enclosed  in  a  porcelain  globe 
and  connected  through  a  capillary  pipe  with  the  outside  air,  be  heated  to 
the  temperature  2"  (which  is  to  be  determined)  and  thereupon  the  connection 
be  discontinued,  and  there  be  then  forced  Into  the  globe  containing  V 
another  volume  of  air  V  of  known  temperature  t,  which  was  prevlouslv 
under  atmospheric  pressure  H^  the  add  itioual  pressure  h,  due  to  the  addi- 
tion of  the  alr-Yolume  V*  to  the  air-volume  v,  can  be  measured  by  a  ma- 
nometer. But  this  pressure  is  of  course  a  function  of  the  temperature  T, 
Before  thelntroduction  of  V\  we  have  the  two  senorate  air- volumes.  Vat 
the  temperature  Tand  V  at  the  temperature  f,  both  under  the  atmospheric 
pressure  H.  After  the  forcing  in  of  V*  Into  the  globe,  we  have,  on  the 
contrary,  only  the  volume  Vol  the  temperature  T,  but  under  the  pressure 
Ja -f"  A. 

"Die  Wiborgh  Air-pyrometer  is  adapted  for  use  at  blast-furnaces,  smelting- 
works,  hardening  and  tempering  f umaoes.  etc,  where  determinations  of 
temperature  from  0*  to  8400°  F.  are  required. 

Seder's  Flre-claj  Pyrometer*  (H.  M.  Howe,  Eng.  and  Mining 
Jour,,  June  7,  18IX).)— Proftvsor  Seger  uses  a  series  of  slender  triangular 
lire-clay  pyramids,  about  S  inches  nigh  and  %  inch  wide  at  the  base,  and 
each  a  little  less  fusible  than  the  next :  these  he  calls  **  normal  pyramids  " 
C'  Dormal-kegel  *^).  When  the  series  is  placed  in  a  furnace  whose  temper- 
ature is  graduallv  raised,  one  after  another  will  bend  over  as  its  range  of 
plasticity  is  reached ;  and  the  temperature  at  which  it  has  bent,  or  *'  wept,** 
so  far  that  its  apex  touches  the  hearth  of  the  furnace  or  other  level  surface 
on  which  it  is  standing,  is  selected  as  a  point  on  Seger's  scale.  These  points 
may  be  accurately  determined  by  some  absolute  method,  or  they  may 
merely  serve  to  give  comparative  results.  Unfortunately,  these  pyramids 
aCrora  no  indications  when  the  temperature  is  stationary  or  falling. 

Meenr^  and  Novel's  Pyrometrf e  Telescope*  (Ibid.)— "Meear^ 
and  Nouers  pyrometric  telescope  gives  us  an  immediate  determination  of 
the  temperature  of  incandescent  bodies,  and  is  therefore  much  better 
adapted  to  cases  where  a  great  number  of  observations  are  to  be  made,  and 
at  short  Intervals,  than  Beer's.  Such  cases  arise  in  the  careful  heating  of 
steel.  The  little  telescope,  carried  in  the  pocket  or  hung  from  the  neck,  can 
be  used  by  foreman  or  heater  at  any  moment. 

It  is  based  on  the  fact  that  a  plate  of  quartz,  cut  at  right  angles  to  the 
axis,  rotates  the  plane  of  polarization  of  polarized  light  to  a  degree  nearl/ 
Inversely  proportional  to  the  square  of  the  length  of  the  waves ;  ana, 
further,  on  tlie  fact  that  while  a  body  at  dull  redness  merely  emits  red 
light,  as  the  temperature  rises,  the  orange,  yellow,  green,  and  blue  waves 
successively  appear. 

If,  now,  such  a  plate  of  quarts  is  placed  between  two  Niool  pHSms  at 
right  angles,  **a  ray  of  monochromatic  light  which  passes  the  flrst,  or 
polarizer,  and  is  watched  through  the  second,  or  analyzer,  is  not  extin- 
guished as  it  was  before  Interposing  the  quaru.  Part  of  the  light  passes 
the  analyzer,  and,  to  again  extinguish  it,  we  must  turn  one  of  the  Kicols  a 
certain  angle,''*  depending  on  the  length  of  the  waves  of  light,  and  hence  on 
the  temperature  of  the  Incandescent  object  which  emits  this  light.  Hence 
the  angle  through  which  we  must  turn  the  analyzer  to  extinguish  the  light 
is  a  measure  of  the  temperature  of  the  object  observed. 

For  illustrated  descriptions  of  different  kinds  of  pyrometers  see  circular 
issued  by  Queen  &  Co.,  Philadelphia. 

The  Uelilliis  and  Stelnbmrt  Pyrometer.  (For  illustrated  descrip- 
tion see  Singineerina^  Aug.  34,  l8U4j— Tlie  action  of  the  pyrometer  is  based 
on  a  principle  which  involves  the  law  of  the  flow  of  gas  through  minute 
apertures  in  the  following  manner  :  If  a  closed  tube  or  chamber  be  supplied 
with  a  minute  Inlet  and  a  minute  outlet  aperture  and  air  be  caused  by  a 
constant  suction  to  flow  in  through  one  and  out  through  the  other  of  these 
apertures,  the  tension  in  the  chamber  between  the  apertures  will  vary  with 


454 


HBAT. 


the  diffarenoe  of  tempemture  between  t-h^  Inflowfoir  Bn6  otitflowf ufp  air.  If 
the  intlowinflr  a<r  be  made  to  vary  with  (be  temperature  to  be  meaeured, 
and  the  ontflowlDf;  air  Im  Icept  at  a  certain  ooQHtaot  tempera  Hire,  then  the 
t«*naion  in  the  epaoe  or  chamber  between  the  two  apertnitm  wUi  be  ao  exact 
measure  of  the  temperature  of  the  faifloviring  air,  and  henoe  of  the  tern, 
perature  to  be  measured. 

In  operation  it  is  necessar}-  that  the  air  be  sucked  into  it  through  the  firgt 
minute  aperture  at  the  temperature  to  be  measured,  through  the  second 
aperture  at  a  lower  but  conKtant  temperature,  and  that  the  suction  be  of  a 
constant  tension.  The  first  aperture  is  therefore  located  In  the  end  of  a 
platinum  tube  in  the  bulb  or  a  porc**laiii  tube  over  which  the  hot  blast 
sweeps,  or  inserted  into  the  pipe  or  chamber  containing  the  gas  whose  tem- 
perature Is  to  be  ascertained. 

The  second  aperture  is  located  In  a  coupling,  surrounded  by  boiling  water, 
and  the  suction  is  obtained  by  an  aspirator  and  regulated  by  a  column  of 
water  of  constant  height. 

The  tension  in  the  chamber  between  the  apertures  is  Indicated  by  a 
manometer. 

The  Alr-flfteniiometer«  (Prof.  R.  C.  Carpenter.  jEVt^V  Ifeum^  Jan.  5, 
18Ki.>— Air  is  a  Perfect  thermonietric  substance,  and  if  a  giTen  mass  of  air 
be  considered,  tne  product  of  its  pressure  and  volume  divided  by  lis 
absolute  temperature  Is  in  every  case  constant.  If  the  volume  of  air 
remain  constant,  the  temperature  will  vary  with  the  pressure;  if  tlM 

Bressure  remain  constant  tue  temperature  will  vary  with  the  volume.  As 
ie  former  condition  is  more  ea8f^  attained  air-thermometers  are  usually 
constructed  of  constant  volume,  In  which  case  the  absolute  temperature 
will  vary  with  the  pressure. 

If  we  denote  pressure  by  p  and  j/,  thp  corre8poiidi:*g  absolute  temper^ 
stares  1^  T  and  T\  we  ahouid  have 


P'.p'iiT'.T*  anfi   T' 


"f 


The  absolute  tmnperature  718  to  be  considered  in  every  oase  400  highes 
than  the  tbermometer>reading  expressed  in  Fahrenheit  degrees.  From  tlie 
form  of  the  above  equation,  if  the  pressure  p  correspoDdlng  to  a  known 
absolute  temperature  T  be  known,  T'  can  be  fouud.  The  quotient  T/p  Is  a 
constant  wiiich  may  be  used  in  all  determinations  with  the  instrument.  The 
pressure  on  the  instrument  can  be  expressed  in  inches  of  mercury,  and  is 
evidently  the  atmospheric  pressure  b  as  shown  by  a  barometer,  plus  or 
minus  an  additional  amount  h  ahown  by  a  manometer  attached  to  the  air 
thermometer.    That  is.  In  general,  pxh±h. 

The  temperature  of  SS**  F.  la  fixed  as  the  point  of  melting  Ice.  in  which 
caiie  7*  s  460  +  32  =  493*  F.  This  temperature  can  be  produced  hy  sur- 
rounding  the  bulb  in  melting  !oe  and  leaving  several  minutes,  so  that  the 
temperature  of  the  confined  air  sluill  acquire  that  of  the  surrounding  loe. 
Wiien  the  air  is  at  that  temperature,  note  the  reading  of  the  attached 
manometer  h,  and  that  of  a  barometer;  the  sum  will  be  the  value  of  p  cor- 
responding to  the  absolute  temperature  of  492o  F.  The  constant  of  the 
Instrument,  IT  s  493  -♦-  p,  once  obtained,  can  be  used  In  all  future  detennina> 
tions. 


W^  Tcntpenttaren  Ja< 

body  jan  be  approximately  Jiidj,  -     .  .  -  .     , 

M.  roultlet  has  constructed  a  table,  which  has  been  generally  accepted, 

giving  the  colors  and  their  corresponding  temperature  as  below: 


d  by  <k»lor«— The  temperature  of  a 
by  the  experienced  eye  unaided,  and 


Incipient  red  heat. 
"  ilfrei 


Dulfred  heat  ......    700 

Incipient  chernr-red 

heat SOO 

Cherry-red  heat WO 

Clear  cherrj-red 

heat 1000 


9T7 
1292 

1479 
1053 

1882 


Deep  orange  heat . .    1 100  eSst 

Clear  orange  heat..    }200  2192 

White  heat 1800  8972 

Bright  white  heat..    1400  2S52 

11600  2?«t 

Dazzling  white  heat  y  to  to 

( 1000  2012 


The  results  obtained,  however,  are  unsatisfactory,  as  much  depends  en 
the  susceptibility  tif  the  retina  of  the  observer  to  light  as  well  as  tlM  degrsa 
of  illumination  under  which  the  observation  is  madiiB. 


QUANTITATIVE  MEA8UBEMEKT  OF  HEAT.  455 

A  bright  bar  of  iron,  dowly  faeated  in  contaot  with  «lr,  mmnxam  tha  fol- 
lowing  tints  at  annexed  temperaturoB  (Ciaudel): 

Cent.       Fabr. 


Tellovat 

Cent. 

,....  as 

Fahr. 
437 

Oranse  at 

MS 

47S 

R3hS.rr..v.... 

986 

fi09 

Viotetat 

277 

051 

Indigo  at...., S8B  560 

Blueat 298  6M 

Greenat 8N  680 

"Oxide-gmy" 400  TBfi 

BOII.INO  POINTS  AT  ATnOSPHBRIO  FSB89I7]ftB. 

14.7  lbs.  per  square  incb. 

Etber,  aulpburlo 10D«F.      Average tes^water sn8.S*F. 

Qtrbon  bisulphide 118  Saturated  brine 886 

Ammonia 140  Nltrieacld M8 

Chloroform 140  Oil  of  turpentine 815 

Bromine 146  Phosphorus 664 

Woodmlrit ICO  Sulphur »70 

Alcohol. ITS  Sulphuric  tcid fiSO 

Beoxhie 176  Linseed  oO 097 

Water 212  Mercury UTS 

The  boiling  points  of  liquids  increase  as  the  pressure  inoreasss.  The  boil- 
ing point  of  water  at  any  given  pressure  is  the  same  as  the  temperature  of 
saturated  steam  of  the  same  pressure.    (See  Steam.) 

HBIiTING-PI^IHTS  OP  VARIOUS  S17BSTANCES. 

The  following  figures  are  given  by  Clark  (on  the  authority  of  Pouillet, 
Claudel,  and  Wilson),  ezoepi  those  marked  *,  which  are  given  by  Prof.  Rob- 
erts-Austen in  his  deHcriptfon  of  the  Le  Cbatelier  pyrometer.  These  latter 
are  probably  the  most  reliable  figures. 

Sulphurous  add -  148«F.  Alloy,  1  tin,  1  lead..    370  to   460*  F. 

Garbonlcacid -106  Tin  442to    446 

Mercury ^    80  Cadmium.. 442 

Bromhie +     0.5  Bismuth 504to    507 

Turpentine 14  Lead O06to   618* 

Hyponitric  acid 16  Ztaic    680to   77i»» 

Ice 62  Antimony 810  to  1160 

Nitro-glycerine 46  Aluminum 1167* 

Tallow 9:8  Magnesium 1200 

Phosphorus 113  Calcium FuUredheat. 

Acetic  acid 118  Bronxe 1692 

Stearine 109  to  1^  Silver ,...  1788*  to  187S 

Spermaceti 190  Potassium  sulphate 1850* 

Margaricacid 181  to  140  Qoid  1918*  to  a»2 

Potassinm 186  to  144  (Topper 1929*  to  1906 

Wax 142tol54  Csstiroa,  white...  1982  to  207«^ 

Stearicacid 1S6  *'        gray  2012  to 2780  SUH* 

Sodium 194to206  Steel 2372  to  2582 


AlIoy,81ead,  2  tin,5bismuth  199  *"    haiM 2070*:  mild,  swi- 

Iodine 225  Wrougbtiron ftm  to  2912 

Sniphur 299  Palladium 273a* 

AUoy,  1^  Un,  1  lead 8^  Platinum 8il27* 

For  melting-point  of  fusible  alloys,  see  Alloys. 

Cobalt,  nickel,  aad  manganese,  fusible  In  higheflt  heat  Of  4  forge.  Tung- 
sten and  chromium,  not  fusible  In  forge,  but  soften  and  agglomerate.  Plati- 
num  and  iridium,  fusible  only  before  the  oxyhydrogen  blowpipe. 

aVANTITATIVB  HBASURBIKKlIT  OF  SDBAT* 

VuH  or  Heat,— Tlie  British  unit  of  heat,  or  British  thermal  unit 
(B.  T.  U.),  is  that  quantity  of  beAt  which  is  required  to  raise  ttte  temperature 
of  1  lb.  of  pure  water  l®  Fahr.,  at  or  near  88<>.l  F.,  the  temperature  of  maxi- 
mum density  of  water. 

Tiie  French  thermal  unit,  or  calorie,  is  that  quantity  of  heat  which  is  re- 
quired to  raise  the  temperature  of  1  kilogramme  of  pure  water  1«  Cent.,  at  or 
about  4*  C,  which  is  equivalent  to  89*.l  F. 

I  French  catorie  =  8.968  British  thermal  units:  1  B.T.  U.  ^  .2B2  calorie. 
The  "  pound  calorie  "  is  sometimes  used  by  English  wilten;  it  is  the  qoaO'' 


456 


HEAT. 


UtT  of  heat  required  to  ralfte  the  temperature  of  1  lb.  of  water  1*  O.  1  Ih. 
calorie  =  9/5  B.T.U.  ss  0.4596  calorie.  The  heat  of  combustion  of  carbon,  to 
COa,  is  said  to  be  8080  calories.  This  figure  is  used  either  for  French  calories  or 
for  pound  calories,  as  it  is  the  number  of  pounds  of  water  that  can  be  raised 
l"  C.  by  the  complete  combustion  of  1  lb.  of  carbon,  or  the  number  of 
kilogrammes  of  water  tliat  can  be  raised  1«  C.  by  the  combustion  of  1  kilo, 
of  carbon;  assuming  in  each  case  that  all  the  heat  generated  is  transferred 
to  the  water. 

Tlie  neelianleal  EqnlTalent  of  Heat  is  the  number  of  foot- 
pounds of  mechanical  energy  equivalent  to  one  British  tliermal  unit,  heat 
^ .-_._.  ^t « _,^..     '•  'a experiments, 

ent.    More  re- 
I  and  ScienceM^ 

„    „ „ ,  and  the  most 

probable  average  is  now  considered  to  be  778. 

1  heat-unit  is  equivalent  to  778  ft.-lbs.  of  energy.  1  ft.  lb.  =a  1/778  =.0012858 
heat-uniU.  1  horse-power  =  88,000  ft. -lbs.  per  minute  =  2545  heat^uuits  per 
hour  =  42.416  +  per  minute  =  .706M  per  second.  1  lb.  carbon  burned  to  CO* 
=  14,544  hea^un^ts.  1  lb.  C.  per  H.P.  per  hour  =  2545  •«-114544  =  17)j(  efficiency 
(.174986). 

Heat  of  Comliuetlon  of  Various  Sabeiancee  In  Oxycen* 


Hydrogen  to  liquid  water  at  0«  C . . . . 

"         to  steam  at  100*  C. 

Carbon  (wood  charcoal)  to  carbonic 
acid,  (X>ti  ordinary  temperatures. 

Carbon,  diamond  to  CO^ 

'*        black  diamond  lo  CO^ 

"        graphite  to  COj 

Carbon  to  carbonic  oxide,  CO 

Carbonic  oxide  to  CO,,  per  unit  of  CO 

CO  to  CO,  per  unit  of  C  =  2^^  X  2403 

Marsh-gas,  Methane,  CH4  to  water 
and  CO, 

Oleflant    gas.    Ethylene,    C,H4    to 
water  and  CO, 

Benzole  gas,  CflH«  to  water  and  (X>, 


Heat-units. 


Cent.    Fahr. 


[  84,462 
83,808 
34,342 


8,080 
7,900 
8,187 
7,859 
7,861 
7,901 
2,478 
2,403 
2,431 
2,385 
5.607 

-^18,108 
1 13,063 
11,858 
11,942 
11,957 
10,102 
9,915 


60,&M 
61,816 
61,71 
14,544 
14,220 
14,647 
14,146 
14.150 
14,222 
4,451 
4,S:» 
4,876 
4,:;98 
10,093 
23,616 
23,594 
23,513 
21,844 
21,496 
21,533 
18,184 
17.847 


Favre  and  Silbennann. 

Andrews. 

Thomsen. 

Favre  and  Silbermann. 

«l  u 

Andrews. 
Berthelot. 


Authority. 


Favre  and  Silbermann. 

Andrews. 

Thomsen. 

Favre  and  Silbermann. 

Thomson. 

Andrews. 

Favre  and  Silbermann. 

Andrews. 
Thomsen. 

Favre  and  Silbermann. 


L 


In  burning  1  pound  of  hydrogen  with  8  pounds  of  oxygen  to  form  9  pounds 
of  water,  the  unils  of  heat  evolved  are  02,082  (Favre  and  8.);  but  If  the 
resulting  product  is  not  cooled  to  the  initial  temperature  of  the  gases, 
part  of  me  heat  is  rendered  latent  in  the  steam.  The  total  heat  of  I  lb. 
of  steam  at  2\2?  F.  is  1146.1  heat-units  above  that  of  water  at  32*,  and 
9  X  1146  1  =  10,315  heat-units,  which  deducted  from  62,032  gives  61,717  as  the 
heat  evolved  by  the  combustion  of  1  lb.  of  hydrogen  and  8  lbs.  of  oxygen  at 
82*  F.  to  form  steam  at  2I2*>  F. 

By  the  decomposition  of  a  chemical  compound  as  much  heat  is  absorbed 
or  rendered  latent  as  was  evolved  when  the  compound  was  formed.  If  1  lb. 
of  carbon  is  burned  to  CO,,  generating  14,544  B.T.U.,  and  the  (X),  thus  formed 
is  immediately  reduced  to  (X>  in  the  presence  of  glowing  carbon,  by  the 
reaction  CO,  4*  O  =  200,  the  result  is  the  same  as  if  the  2  lbs.  C  had  been 
burned  directly  to  2CO,  generating  2  X  4451  =  8902  heat-units;  consequently 
14,544  -  8902  =:  5642  heatrunits  have  disappeared  or  become  latent,  and  th9 


SPECIFIC  HEAT.  457 

* unburnfns:  **  of  CO,  to  CO  is  thus  &  cooling  operatioD .    (For  heats  of  oom- 
bustion  of  various  fuelSi  see  Fuel.) 

SPBCIFIC  HBAT. 

Therma]  Capacity*— The  thermal  capacity  of  a  body  la  the  quantity 
of  heat  required  to  raise  its  temperature  one  degree.  The  ratio  of  the  heat 
required  to  raise  the  temperature  of  a  givea  substance  one  degree  to  that 
required  to  raise  the  temperature  of  water  one  degree  from  the  temperature 
of  maximum  density  89.1  Is  commonly  called  the  specific  heat  of  the  sub- 
stance. Some  writers  object  to  the  terra  as  being  an  inaccurate  use  of  the 
words  '*  specific  "  and  "  heat."  A  more  correct  name  would  be  **  coefficient 
of  thermal  capacity." 

Betenninatloift  ot  Speelfle  Heat*— lfe<Aod  hy  Mixture.— Th^ 
body  whose  specific  beat  Ib  to  be  determined  is  raised  to  a  known  tempera- 
ture, and  is  then  immersed  in  a  mass  of  liquid  of  which  the  weij^ht.  specific 
beat,  and  temperature  are  known.  When  both  the  body  and  the  liquid 
bare  attained  the  same  temperature,  this  is  carefully  ascertained. 

Now  the  quantity  of  heat  lost  by  the  body  is  the  same  as  the  quantity  Of 
heat  absorbed  by  the  liquid. 

Let  c,  to,  and  I  be  the  specific  heat,  weight,  and  temperature  of  the  hot 
body,  and  &,  «/,  and  i'  of  the  liquid.  Let  T  be  the  temperature  the  mix- 
ture assumes. 

Then,  by  the  definition  ofspeciflc  heat,  e  X  w  X  (f  -  7)  =s  heat-units  lost 
by  the  hot  body,  and  c'  X  tc'  X  (T  -  f)  —  heat-units  gained  by  the  cold 
liquid.  If  there  is  no  heat  lost  by  radiation  or  conduction,  these  must  be 
equal,  and 

cicKr-r)  =  cw(r-«')  or  c=  l^^lj^  - 

Speelflc  Heats  of  Various  Snbatancea. 

The  specific  heats  of  substances,  as  given  by  different  authorities,  show 
considerable  lack  of  agreement,  especially  in  the  case  of  gams. 

The  following  tables  give  the  mean  specific  heats  of  the  substances  named 
according  to  Regnault.  (From  Rontgen's  Thermodynamics,  p.  184.)  These 
speelflc  heats  are  average  values,  taken  at  temperatures  which  usually  come 
under  observation  in  te^nical  application.  The  actual  speelflc  heats  of  all 
substances,  in  the  solid  or  liquid  state,  increase  slowly  as  the  body  expands 
or  as  the  temperature  rises.  It  is  probable  that  the  specific  heat  of  a  body 
when  liquid  is  greater  than  when  solid.  For  many  oodles  this  has  been 
verified  by  experiment 

SOUDB. 

Steel  (soft) 0.1186 

Steel  (hai-d) 0  117« 

Zinc. 0.0986 

Brass 0.0IW9 

Ice... 0.5040 

Sulphur 02086 

Charcoal 0.2410 

Alumina 0.1970 

Phosphorus 0.1887 


Antimony 0.0608 

Copper 0.0951 

Qold. 0.0824 

Wroughtiron 0.1188 

Glass 0.1937 

Cast  iron 0.129S 

Lead  0.0814 

Platinum 0.0834 

Silver 0.0670 

Tin  0.066a 


Water 1.0000 

Lead  (melted) 0.040S 

Sulphur    '•      0.2340 

Bismuth    **      0.0808 

Tin  " 0.0687 

fiulpfauric  add 08860 


LiquiDS. 


Mercury 0.0888 

Alcohol  (absolute) 0.70M 

Fusel  oil 0..%40 

Benzine  0.4.500 

Ether 0.5084 


458  HBAT. 

Qammm, 

Constant  Pressure.    Constant  Volume. 

Air a.8WBl  0.16847 

Oxygen 0.21751  0.16607 

Hrdrogm 9.40900  9.41»6 

KUrofraa 0JMS80  OlITSTS 

Superheated  steam 0.4806  aMO 

CarbonJcacid 0.817  ai68» 

Oleflant  Qat  (OH,) 0.404  O.m 

CarboalcozUie 0.8479  0.1968 

Aimnonia 0.606  0.800 

Ether 0.4797  0.3411 

Alcohol 0.4534  aWW 

Acetioacid 0.4185  

Chloroform 0.1587  

In*  additloa  to  the  above,  the  (folIowlDg>  are  given  by  other  authorities. 
(Selected  Crom  various  souroee.) 

MmiB, 

Wrought  Iron  (Petit  &  DuIongX 

38»t<j212» 1096 

"  58»to888« 115 

"  88«to6:8* 1218 

*•  82*  to  MS* 1866 

Wrought  iron  (J.  C.  Hoadley, 
ATS.  M.  E..  vI.  718), 

Wrought  iron,  82*  to  800* IISO 

"  «««to  600* 1827 

"  82«toa000» 8619 


Platinum,  32*  to  446*  P. 0688 

(Increased  .000606  for  each  100*  F.) 

Cadmium 0667 

Brass 0039 

Copper,  82*  to  818*F 094 

*•        a8»toW«»F 1018 

Sine       88»tofl2»F 0927 

a8*to67a»F..., 1015 

Nickel 1066 

Aluminum,  0*  F.  to  melting- 
point  (A.  £.  Hunt) 0.2185  I 

Othkr  Solids. 
Brlckvork  and  masonry,  about.  JW 

Marble JUO 

Chalk JM5 

Quicklime 817 

Sagnedan  limestone 817 

SUksa 191 

Corundum 196 

Stones  generally • .8  to  88 


Ck>al J»to841 

Coke .803 

Graphite .aO-J 

Sulphate  of  lime 197 

Ifagnesia. • Jtt2 

Soda Ml 

QuarU 168 

River  sand 195 


Woods. 

Pine  (turpentine) 467  I  Oak 570 

Fir .V. 666      Ptear 500 


Lk^uids. 


OMveoU JIO 

Bensine SOB 

Turpentine,  density  «a72 .4n 

Bromine Llll 


Aloobol,  density  .793 

fiiilpburic  acid,  density  1.87 885 

'»  •»       1.80 ,661 

Hydrochloric  add 600 

Oasis. 

At  Constant  At  Constant 

Pressure.  Volume. 

Sulphurous  acid 1553.  .1246 

Light  carburetted  hydrogen,  ouffth  gas  (CH4).  .5929  .4688 

Blast-furnace  gases 2277  

i^pMlfleBMt  ofSftlt  flolufioB*    (Sdinller.) 
Percent  salt  in  solution........      6  10  15  90  8S 

Bpectfloheat 9306       .8909       .8606    « .8490       .80» 

Specille  Beat  of  Atr.-Regnanlt  gives  for  the  mean  vahw 

Between  — 80»C.  and +  10*  0 0.887n 

»*  0«C.    "        100»0 0.88741 

"  0*0.    "       800»C 0.88761 


I  uses  0.1686  for  the  specific  heat  of  air  at  constant  volume.    The 

value  of  this  constant  has  never  been  found  to  any  degree  of  accuracy  by 
direct  experiment.    Prof.  Wood  gives  0.2875  -«- 1.406  =  0.1680.    The  ratio  of 


BXPAHSIOK  BY  HEAT. 


459 


the  specific  heat  of  a  fbted  ms  ftt  constant  prpasnm  to  the  up.  ht.  at  oon- 

Btact  volume  is  given  as  foliovrs  bv  different  writers  {Eng^g^  July  18,  18H9): 
K'Kuault,  1.8963;  Moll  and  Beck,  1.4086;  Szathmari,  1.4027;  J.  Macfarlaiie 
Gray,  1 .4.  The  fli'st  three  are  obtained  from  the  velocity  of  sound  in  air.  The 
fourth  is  derived  from  theory.  Prof.  Wood  sayv:  The  value  of  the  ratio  for 
air,  as  found  in  the  days  of  La  Place,  was  1.41,  and  we  have  0.2877  -i-  1.41 
=:  O.I4S8S,  the  value  lised  by  Clausius,  Hanssen,  and  many  others.  But  this 
ratio  is  not  definitely  Icnown.  Rankine  in  his  later  writiiifps  used  1.406,  and 
Tait  in  a  recent  work  gives  1.40i,  while  some  experiments  gives  less  than 
1.4  and  othem  more  than  1.41.    Prof.  Wood  uses  1.406. 

9|^cUle  0e*t  of  Gases.— Experiments  by  Mallard  and  Le  Chatelier 
indicate  a  continuous  increase  in  the  specific  heal  at  constant  volume  of 
steam.  CX)a.  and  even  of  the  perfect  gases,  with  rise  of  temperature.  The 
variation  is  inappreciable  at  100*  O.,  but  increases  rapidly  at  the  high  tem- 

e^raturt^  of  the  gas-engine   cylinder.     (Robinson's  Gas  and  Petroleum 
nginefi.) 

apeelAe  Heat  and  Latent  Heat  of  Fusion  of  Iron  anA 
Steel.    (H.  H.  Campbell,  Trans.  A.  I.  M.  E.,  xiz.  181.) 

Akerman.    Ttoilius. 

Specfflc  heat  pig  Iron,      0to1900«C 0.16 

»*       1300tol800«C 0.«l 

"         "  •*  OtolflOO»C 0.18 

••       lS00to1800»C o.ao 

Calculating  by  both  sets  of  data  we  have  : 

Akerman.    Troilius. 

Heating  from  0  to  1800*  0 816  830  calories  per  kilo. 

Hence  probable  value  Is  about. ..... 825  calories  per  kilo. 

Sped  Ac  heat,  steel  (probably  high  carbon). . . .  <TroUiu8) 1 175 

-         **     soft  iron "       1061 

Henoe  probable  value  solid  rail  steel lliiS 

••    melted  raU  steel law 

• 

Akerman.     Troilius. 
Latent  heat  of  fusion,  pig  iron,  calories  per  kilo.  .46 

"      grmvftig 83 

••      whitepig »8 

From  which  we  may  anume  that  the  truth  is  about :  Steel,  20  ;  pig  iron,  SQL 

BXPANSION  BY  HBAT. 

In  the  centigrade  scale  the  coefficient  of  expansion  of  air  per  degree  Is 
O.OCEJfXiS  =  l/:i{i8;  that  Is,  the  pressure  being  constant,  the  volume  of  a  pei^eci 
gas  increaees  1/378  of  ita  volume  at  0°  C.  for  every  increase  in  tempeittture 
of  1°  C.  In  Fal-renheit  units  it  Increases  1/491.2  =  .002036  of  its  volume  at 
&«•  F.  for  every  increase  of  1®  P. 

Bvpansion  of  Oases  by  Heat  ftom  32*  to  313*  F.  (Regnault.) 


Hydrogen 

Atmospheric  air. 

Nitrogen    

Carbonic  oxide... 
Carbonic  acid  . . . . 
Biitpburous  acid 


Increase  In  Volume, 
Pressure  Constant. 
Volume  at  32oFahr. 
e  1.0,  for 


100«C. 


0.8661 
0.8670 
0.8670 
0.8669 
0.3710 
0.8908 


1»F. 


0.002084 
0.00>.'089 
0.00'A)89 
0.002^188 
0.0020CI 
0.002168 


Increase  in  Pressure, 
Volume  Constant. 
Pressure  at 82* 
Falir.  =  1.0,  for 


100*0. 


0.8667 
0.8665 
0.3668 
0.8667 
0.3688 
0.8815 


!•?. 


0.008087 
0.002086 
0.002089 
0.002037 
0.00208» 
0.002186 


If  tlie  ▼olume  is  kept  constant,  the  pressure  varies  directly  as  the  absolute 
temperature. 


460 


HEAT. 


lilneal  Expansion  of  Solids  at  Ordinary  T^nlpelwtnres. 

(British  Board  of  Trade;  from  Clark.) 


1). 


Aluminum  (cast). .  

Antimony  (cryst.) , 

Brass,  cast 

**       plate 

Brick 

Bronze  (CJopper,  17;  Tin,  2^;  Zinc 

Bismuth 

Cement.  Portland  (mixed),  pure  . . 
Concrete: cement,  mortar, and  pebbles 

Copper 

Elionite 

Glass,  Enj^lish  flint. 

"       thermometer 

"      hard 

Granite,  ^ray,  dry. . 
"       red,  dry... 

Gold,  pure 

Iridium,  pure 

Iron,  wrought 

'*     cast 

Lead 

Magnesium 


Marbles,  various  \  fj^"" 


Masonry,  brick  ]f^™ 


Mercury  (cubic  expansion) 

Nickel 

Pewter 

Plaster,  white 

Platinum 

Platinum,  85  per  cent  ( 

Iridium,     15    "      "    S 

Porcelam 

Quartz,  parallel  to  major  axis,  t  0"  to 

40*'C 

Quarts,  perpendicular  to  major  axis, 

/0*'to40«C 

Silver,  pure  

Blate 

Steel,  cast 

**     tem^>ered 

Stone  (sandstone),  dry  .     

Riiuville . 

Tin 

We<igwood  ware 

Wood,  pine 

Zinc 

Zinc,  8 1 

Tin,l    f     • 


For 
»  Fahr. 


For 
V  Cent. 


Length  «1  Length=i 


.0(X)0rJ84 
.00(XK)0;27 
.00000»57 
.(K)0010.'i2 
(KXKWSOe 
.00000986 
.00000975 
.00000.'}94 
.00000795 
.00000t<87 
.00004278 
.00000451 
.00000499 
.00000397 
.00000438 
.00000498 
.00000786 
.00000856 
.00000648 
.00000550 
.00001571 


.00000808 
.00000786 
.00000256 
.00000494 
.00009984 
.00000695 
.00001129 
.00000922 
.00000479 

.00000453 

.00000vH)0 

.00000434 

.00000788 
.00001079 
.00tXXtt77 
.00000636 
000006S9 
.00000652 
.(XHKX>417 
.(X)00nt« 
.00000 »H9 
.00(KM>.>76 
.00001 107 

.00001196 


.00002221 
.00001129 
.00001722 
.00iX)1894 
.00000550 
.00001774 
.00001755 
.00001070 
.00001480 
.00001590 
.00007700 
.00000812 
.00000897 
.00000714 
.00000789 
.00000897 
.00001415 
.00000641 
.00001166 
.00001001 


.00000554 
.00001415 
.00000460 
.00000890 
.00017971 
.00001251 
.00002083 
.00001660 
.00000863 

.00000815 

.00000860 

.00000781 

.00001419 
.00001943 
.001)01088 
.00001144 
.00001940 
.00001174 
.00000750 
.00002094 
.00000881 
.00000496 
.00002532 

.00002692 


Coef- 
fl^*^°^  Uccord- 

Expan- 
sion 
from 

82<>to 

212*  F. 


.002221 
.001129 
.001782 
.001894 
.000550 
.001774 
.001756 
.001070 
.001430 
.001596 
007700 
.000H12 
.000897 
.000714 
.000789 
.000897 
.001415 
.000641 
.001166 
.001001 
.002828 

066554 
.001415 
.000460 
.000890 
.017971 
.001251 
.002083 
.001660 
.000868 

.000615 

.000360 

.000781 

.001419 
.001948 
.001088 
.001144 
.001240 
.001174 
.000750 
.002094 
.000H81 
.000496 
.002532 

.002692 


Cubical  expansion,  or  expansion  of  volume  =  linear  expansion  x  8. 


LATENT  HEATS  OP  FUSIOK.  461 

AlMM»liite  Temperature— A bflolate  Zero.— The  absolute  zero  of  a 
exui  is  a  tlteoretical  consequence  of  the  law  of  expansion  by  heat,  assuming: 
UiaL  ii  in  possible  to  continue  the  cooling  of  a  perfect  gas  until  its  volume  is 
din-inished  to  nothing. 

If  the  volume  of  a  perfect  gas  increases  1/273  of  its  volume  at  0°  C.  for 
every  increase  of  temperature  of  !•  C,  and  deci*ease8  1/873  of  its  volume  for 
every  decrease  of  temperature  of  1®  C,  then  at  -  878«»  C.  the  volume  of  the 
imi^inary  gas  would  be  reduced  to  nothing.  This  point  —  TTS**  C,  or  491/J" 
F.  below  the  melting-point  of  ice  on  the  air  thermometer,  or  49*2.66'*  F.  be- 
low on  a  perfect  gas  thermometer  =  —  459.2*  F.  (or  —  460.66*),  is  called  the 
absolute  zero:  and  absolute  temperatures  are  temperatures  measured,  on 
«itber  the  Kanrenheit  or  centigrade  scale,  from  tjiis  zero.  The  freezing 
foiiit,  9£*  F..  corresponds  to  491.^*  F.  absolute.  If  Po  be  the  pressure  and 
f ,  the  volume  of  a  gas  at  the  temperature  of  32*  F.  =  491. '2*  on  the  absolute 
a»le  =  T«,  and  p  the  pressure,  and  v  the  volume  of  the  same  quantity  of 
gas  at  any  other  absolute  temperature  7',  then 

pv  _  r_  _   1 4-  459.8  ^     pv  _  j?ot?o 

Po^o  ~  To  "       491 .8     *      r   ~    To  * 
The  value  of  PoVq  ■*■  To  for  air  is  58.87,  and  pv  =  58.37T,  calculated  as  fol- 
lows bv  Prof.  Wood: 
A  cubic  foot  of  dry  air  at  82^  F.  at  theeea-level  welglia  0.060788  lb.    The 

volume  of  one  pound  is  Vo  =  '  Qopyos  =  12-887  cubic  feet.  Tiie  pressure  per 

square  foot  is  2116.2  lbs. 

PbUq  _   2116.2  X  12.887         26214  _^„ 
To    "  491.18  *  491.13^ 

The  figure  491.13  is  the  number  of  degrees  that  the  absolute  zero  is  below 
ttie  melting-point  of  ice,  by  the  air  thermometer.  On  the  absolute  scale, 
whose  divisions  would  be  indicated  by  a  perfect  gas  thermometer,  the  cal* 
eulated  value  approximately  is  492.66,  which  would  malce  pv  =  53.;ilT.  Prof. 
Thomson  considers  that  -  273.1*  C.  =  —  459.4*  F.,  is  the  most  probable  value 
of  the  absolute  zero.    See  Heat  in  Ency.  Brit. 

Expansion  of  Liquids  flrom  32*  to  312*  F.— Apparent  ex- 
Vansiou  in  glass  (Clark).    Volume  at  222*,  volume  at  3'i2*  being  1: 

Water 1.0466       Nitricacid ...  1.11 

Water  saturated  with  salt. ...  1 .05  Olive  and  linseed  oils 1 .06 

Mercury 1.0188       Turpentine  and  ether 1.07 

Alcohol 1.11  Hydroehlor.  and  sulphuric  acids  1.06 

For  water  at  various  temperatures,  see  Water. 

For  air  at  various  temperatures,  see  Air. 

ImAvknv  heats  of  fvsion  anb  evaporation. 

I^ntent  Hent  means  a  quantity  of  heat  which  has  disappeared,  having 
oeeu  employed  to  produce  some  change  other  than  elevation  of  temperature. 
By  exactly  reversing  that  change,  the  quantity  of  hear  which  has  dis- 
appeared IS  reproduced.  Maxwell  deflnen  it  as  the  quantity  of  heat  which 
must  be  communicated  to  a  body  in  a  »fiven  state  in  order  to  convert  it  into 
another  ntate  without  chan?iiK  its  letriperatura. 

Itntent  Hent  of  Fusion.— When  a  body  passes  from  the  solid  to  the 
liquid  Htate.  its  temperature  remains  stationary,  or  nearly  stationary,  at  a 
certain  melting  point  during  (he  whole  operation  of  meltmg;  and  in  order 
to  make  that  opeiaiiou  go  on.  a  C|uaniity  of  heat  must  be  transferred  to  the 
sutisiance  melted,  beint;  a  certam  amount  for  each  unit  of  weight  of  the 
substance.    This  qunntity  is  calleil  ihe  latent  heat  of  fusion. 

When  a  body  passes  fnmi  tlie  liquid  to  the  solid  state,  its  temperature 
remains  siationaij  or  nenrly  stationaiy  during  the  whole  operation  of  freez- 
ing: a  quantity  of  heat  equal  to  the  latent  heat  of  fusion  Is  produced  in  the 
body  and  rejected  rato  the  armospliere  or  other  surrounding  oodles. 

The  foHowinfCH'e  exam  pies  in  British  thermal  units  per  pouqd,  as  giveo 
in  Landolt  &  Bornstein's  Physiknli'gche-Chenusche  Tabellen  (Berlin,  1894). 

S"'«—-    ';?/Y'.l«!:,u."  Substancs.     'TfL^^^ 

Rismnili J-J.To  Sliver 87.93 

Cast  Iron,  gray.. .       .  41.4  lieeswax 76.14 

Vtist  Iron,  while 59.4  Parafflne 6:j.'^ 

I-ead 9.nfi  Kp*»rniaceti b6.ft6 

Tin  ijneft  Pliosphorus 9.06 

Zinc  50.t>8  Sulphur 10.86 


462  .  HEAT. 

Prof.  Wood  considers  144  heftt  uniU  as  th«>»  most  reliable  value  for  the 
latent  heat  of  fiision  of  ice.    Person  gives  14S  65. 

lifttent  Heat  of  BTaporatlon*— When  a  bodjr  passes  from  the 
solid  or  liquid  to  the  graseoiiM  state,  its  temperature  durioK  the  operatios 
remains  stationary  ataoertain  boiling  point,  depending  on  the  prcMsure  ol 
the  vapor  produced;  and  in  order  to  make  the  evaporations  on,  a  quantity 
of  heat  must  be  transferred  to  the  substance  evaporated,  whose  amount  for 
each  unit  of  weight  of  the  substance  evaporated  depends  on  t)te  temperature. 
That  heat  does  not  raise  tlie  temperature  of  the  substance,  but  disappt'ars 
in  causing  it  to  assume  the  gaseous  state,  and  it  is  called  the  latent  beat  of 
evaporation. 

when  a  l)ody  pasfses  from  the  gaseous  state  to  the  liquid  or  solid  state.  Ita 
temperature  remains  stationary,  during  that  operation,  at  the  boiling-point 
corresnondiog  to  the  pressure  of  the  vapor:  a  quantity  of  heat  equal  to  the 
latent  neat  of  evaporation  st  that  tenH>erature  is  produced  in  the  body;  and 
in  order  that  the  operation  of  condensation  may  go  on.  that  heat  must  be 
transferred  from  the  body  condensed  to  some  other  body. 

The  following  are  examples  of  the  latent  heat  of  evaporation  In  British 
theniial  units,  of  one  pound  of  certain  substances,  when  the  pressure  of  the 
vapor  is  one  atmosphere  of  H.t  lbs.  on  the  square  Inch: 

finKa4^«««  BolUng-poiotunder  Latent  Heat  In 

Substance.  ^^^  J^»^  P^,,^  B^Hj^t^  ^^^^ 

Water £18.0  966.7  (Regnault) 

Alcohol    l«.a  864.8  (Andrews.) 

Ether 95.0  16«.8 

Bisulphide  of  carbon 114.8  156.0 

The  latent  heat  of  evaporation  of  wat4'r  at  a  series  of  boiling-points  eie 

tending  from  a  few  degrees  below  its  fk^ezing-point  np  to  about  875  degr^er 

Fahrenheit  has  been  determined  expeiimentally  by  N.  Regnanlt.    The  n« 

suits  of  those  experiments  are  represented  approximately  by  the  formula 

In  British  themoal  units  per  pounds 

I  nearly  =  1091.7  -  0.7(f  -  88o)  =  966.7  -  0.7(«  -  218«»). 

The  Total  Memt  of  BTapomtlon  is  the  sum  of  the  heat  whk«i 
disappears  In  evaporating  one  pound  of  a  given  substance  at  a  given  tem- 
perature (or  latent  heat  of  evaporation)  and  of  the  heat  required  to  raise  Ua 
temperature,  before  evaporation,  from  some  fixed  temperature  up  to  the 
temperature  of  evaporation.  The  latter  part  of  the  total  heat  la  called  the 
sensible  heat. 

In  the  case  of  water,  the  experiments  of  M.  Regnault  show  that  the  tot.il 
beat  of  steam  from  the  temperature  of  melting  toe  increases  at  a  onlfonii 
rate  as  the  temperature  of  evaporation  rises.  The  following  is  the  formub* 
in  British  thermal  units  per  pound: 

fc=:  1091.7 +0.805(^-a8«). 

For  the  total  heat,  latent  heat,  etc.,  of  steam  at  different  pfMsures,  see 
table  of  the  Properties  of  Saturated  Steam.  For  tables  of  total  heat,  hitent 
heat,  and  other  properties  of  steams  of  ether,  alcohol,  acetone,  chloroform, 
chloride  of  carbon,  and  bisulphide  of  carbon,  see  Rontgen*s  Thermodynam- 
ics (Dubois's  translation.)  For  ammonia  and  sulphur  dioxide,  see  wood's 
Thermodynamics;  also,  tables  under  Refrigerating  Machinery,  In  this  book. 

BVAPOBATION  ATVB  BRTING. 

In  evaporation,  the  formation  of  vapor  takes  place  on. the  surface;  In  boil- 
ing, within  the  liquid:  the  former  is  a  slow,  the  latter  a  quick,  method  of 
evaporation. 

K  we  bring  an  open  vessel  with  water  under  the  receiver  of  an  air-pump 
and  exhaust  the  air  the  water  in  the  vessel  will  commence  to  boil,  and  if  we 
keep  up  the  vacuum  the  water  will  actually  bofl  near  Its  freezing  point.  The 
formation  of  steam  in  (his  case  is  due  to  the  hent  which  the  water  takes  ont 
of  the  surroundings. 

Steam  form*»d  under  pre»sui'e  has  the  same  tempernture  as  the  liqulfl  in 
which  It  was  formed,  provided  the  steam  Is  kept  under  the  same  prewine. 

By  properly  cooling  the  rising  steam  from  bailing  wat>er,  as  in  the  nuiliiple* 
efr**ob  evsporatinfr  i*ystenm,  we  can  regulate  the  pressure  so  that  tl.'*  water 
b  Us  at  low  temperatures. 


BVAPORATIOK.  463 

ETftp^mtloii  Of  'Water  %m  Kefterrolrs.— EzperimflBts  at  the 

Mount  Hope  Keservoir,  Rochester,  N.  Y.,  in  It^l*  Rave  the  following  results: 

July.  Aug.  Sept.  Oct. 

Mean  temperature  of  Air  in  shade 70.6  70.8  flS.7  68.8 

*•  water  In  reservoir. 68.2  70.2  66.1  54.4 

"     humidity  of  air,  percent 67.0  74.6  75.«  74.7 

ETaporatlon  in  Inches  QUrlne  month 5.60  4.06  4.05        8.28 

Rainfall  in  inches  during  month 8.41  2.06  1.44        2.16 

Krapomtton  of  "Water  tronk  Open  Cliaiiiiel**  (Fljnn's 
Irrigation  Canals  and  Flow  of  Water.)— Experimeuts  from  1H81  to  18B5  in 
Tulare  County,  Callfomta.  showed  an  evaporation  from  a  pan  in  the  river 
equal  to  an  average  depth  of  one  eighth  of  an  inch  per  day  throughout  the 
year. 

When  the  pan  was  in  the  air  the  average  evaporation  waa  less  than  3/16 
of  an  inch  per  day.  The  average  for  the  month  of  August  was  1/3  inch  per 
day,  and  for  March  and  April  1/12  of  an  Inch  per  day.  Exi)eriments  in 
Colorado  show  that  evaporatinu  i*ange8  from  .Obs  to  .10  of  an  inch  per  day 
during  the  irrigating  season. 

In  Northern  Italy  the  evaporation  was  from  1/12  to  1/0  Inch  per  day,  while 
in  the  sonth,  under  Ihe  induenoe  of  hot  winda,  it  waa  from  1/6  to  1/6  inch 
per  day. 

In  the  hot  aeaaon  in  Northern  India,  with  a  decidedly  hot  wind  blowing, 
the  average  evaporation  was  ^  inch  per  day.  The  evaporation  increaaea 
with  the  temperature  of  the  water. 

Evaporation  by  the  Mnltlple  8j«tem«—A  multiple  efTeet  is  a 
series  ox  evaporating  vessels  each  having  a  steam  chamber,  so  connected 
that  the  heat  of  the  steam  or  vapor  produoed  in  the  flmt  vessel  heats  the 
second,  the  vapor  or  steam  pixxluced  in  the  second  heats  the  third,  and  so 
oil.  The  vapor  from  the  last  vessel  is  condensed  in  a  condenser.  Three 
vcwsfln  are  generally  used,  in  which  case  the  apparatus  ia  called  a  TripU 
^tci.  In  evaporating  In  a  triple  effect  the  vacuum  Is  graduated  so  that  the 
liquid  Is  boiled  at  a  constant  and  low  temperature. 

Bealatanee  to  Boiling.— Brine*  (Ranldne.)— The  nresence  in  a 
liquid  of  a  substance  dissolved  in  it  (as  salt  In  water)  resists  ebullition,  and 
ranea  the  temperature  at  which  the  liquid  bolls,  under  a  given  pressure;  but 
unleM  the  dissolved  substance  enters  into  the  composition  of  tne  vapor,  the 
relation  between  the  temperature  and  pressure  of  saturation  of  the  vapor 
remains  unchanged.  A  resistance  to  ebullition  ia  also  offered  by  a  vessel  of 
a  material  which  attracts  the  liquid  (as  when  water  bolls  in  a  glass  vessel), 
and  the  boiling  take  place  by  starts.  To  avoid  the  errors  which  causes  of 
this  kind  produce  in  the  measurement  of  boiling-poinia,  it  is  advisable  to 
place  the  thermometer,  not  in  the  liquid,  but  In  ttie  vapor,  which  shows  the 
true  boiling-point,  freed  from  the  disturbing  effect  of  the  attractive  nature 
of  the  vessel.  The  boUifig-point  of  saturated  brine  under  one  atmosphere 
is  226*  Pahr.,  and  that  of  weaker  brine  is  higher  than  the  boiling-pomt  of 
pure  water  by  1.2o  Fahr.,  for  each  1/32  of  salt  that  the  water  contains. 
Average  sea- water  contains  1/33;  and  the  brine  hi  marine  boilers  is  not  suf- 
fered tr»  contain  more  than  from  2/'32  to  8/32. 

Ket^oda  of  Braporatlon  Kmployed  In  tbe  Manufacture 
of  Salt*  (F.  B.  £ngeihardt,  Chemist  Onondaga  Salt  Springs;  Report  for 
18B9.)— 1.  Solar  heat— solar  evaporation.  2.  Direct  Are,  applied  to  the  hi>at' 
ing  surface  of  the  vessels  containhig  brine— kettle  aud  pan  methods.  3.  Tne 
steam-gralner  system— steam-pans,  steam-kettles,  etc  4.  Use  of  steam  and 
a  reduction  of  the  atmospheric  pressure  over  tbe  boiling  brine— vacuum 
^stttn. 

When  a  saturated  salt  solution  bolls.  It  is  immaterial  whether  it  is  done 
under  ordlnuy  atmospheric  pressure  at  2*^**  F.,  or  under  four  atmospheres 
with  a  temperature  of  SCO**  F.,  or  In  a  vacuum  under  1/10  atmosphere,  the 
result  will  always  be  a  fine-grained  salt. 

The  fttd  consumption  Is  stated  to  be  as  follows:  By  the  kettle  method,  40 
to  46  bu.  of  salt  evaporated  per  ton  of  fuel,  anthracite  dust  burned  on  per- 
forated grates;  evaporutiou,  6.53  lbs,  of  water  per  pound  of  coal.  By  the 
pan  method,  <U  to  76  bu.  per  ton  of  fuel.  By  vacuum  pans,  single  effect,  b6 
bu.  per  ton  of  anthracite  dust  (2000  lbs.).  With  a  double  effect  nearly 
double  that  amount  can  be  produced. 


^6^ 


HEAT. 


flalnbUltj  of  Con 


(Aadren.) 


Temp,  of  brine,  F 88        60        M         104       140       178 

100  parts  water  dissolve  parts....  8S.68   85.60   86.03    96  8S   87.06    88.00 
100  parts  brine  contain  salt 26.27   S6.30   86.49   26.64   27.04   27.54 

According  to  Pogglal,  100  parts  of  water  dissolve  at  220.66^  F.,  40.85  parts 
of  salt,  or  In  per  cent  of  brine.  28.749.  Gay  Lussac  found  that  at  !&!9.7^  F., 
lUO  parts  of  pure  water  would  dissolve  40.88  parte  of  salt,  in  per  c^it  uf 
brine,  28.764  parts. 

Tlie  solubilitv  of  salt  at  229*  F.  is  only  fLS/jt  greater  than  at  82*.  Hence  ws 
cannot,  as  in  the  case  of  alum,  separate  the  salt  from  the  water  by  allou  ing 
a  saturated  solution  at  the  boiling  point  to  cool  to  a  lower  temperature. 

Solubility  of  Sulplutte  of  I«lme  In  Pure  'Water.  (Uarignac) 
Temperature  F.  degrees.  82     64.5    89.6   100.4    105.8     127.4    186.8    212 

^^'■i^jr^ifL^PJ"^*'''^        415     886     8n      868       870       875       417     450 


1  part  gypsum  ) 

Parts  water  to  dissolve  1 1 

part  anhydrous  Ca804 ) 


470     466       468       474       528     572 


In  salt  brine  sulphate  of  lime  Is  much  more  soluble  than  in  pure  water. 
In  the  evaporation  of  salt  brine  the  accumulation  of  sulphate  of  lime  t«*ud9 
to  Slop  the  operation,  and  it  must  be  removed  from  the  pans  to  avoid  waste 
of  fuel. 

The  average  strength  of  brine  In  the  Mew  York  salt  districts  in  1889  was 
69.H8  decrees  of  the  sallnometer. 

Stronstli  of  Salt  lliines,— The  following  table  is  condensed  from 
one  given  in  U.  S.  Mineral  Resources  for  1888,  on  the  authority  of  Dr. 
Englehardt. 

Belatlotao  between  Sallnometer  Strenortli,  Speeifle  GraTtty« 
Solid  Contents,  etc.,  of  Brines  of  IHirerent  Strenctba* 


i 

a 
1_ 

1 

2 

4 

6 

8 

10 

12 

14 

IG 

18.. 

20 

80 

40 

60 

60 

70 

80 

90 

100 


'flT 

i 

i 
1 

1 

1 

Jl 
P 

i8 

c—. 
5  1^^ 

5"" 

.26 

1.002 

JK5 

8.347 

.022 

2.581 

21.076 

8,518 

.52 

1.008 

.580 

8.356 

.044 

1,204 

10,510 

1,752 

1.04 

1.007 

1.060 

8.889 

.088 

629.7 

5,227 

871.2 

1.56 

1.010 

1.590 

8.414 

.183 

418.6 

8.466 

577.7 

2.08 

1.014 

2.1S0 

8.447 

.179 

812.7 

2,586 

430.9 

2.60 

1.017 

2  6.^ 

8.472 

.224 

249.4 

2,057 

842.9 

8.12 

1.021 

8.180 

8.506 

.270 

207.0 

1,705 

284.2 

8W 

l.O-tt 

8.710 

8.589 

.816 

176.8 

1,458 

242.2 

4.16 

102H 

4.240 

8.564 

.864 

154.2 

1,265 

2IU.8 

4.68 

1.0« 

4.770 

8.597 

.410 

186.5 

1,118 

186.8 

6  20 

i.oas 

6.300 

8  622 

.457 

122.5 

1,001 

178.8 

7.H0 

1.054 

7.950 

8.781 

.696 

80.21 

648.4 

108.1 

10  40 

1.078 

10.600 

8.939 

.947 

59.09 

472.8 

78.71 

18(H) 

i.WM 

13.250 

9.105 

1.206 

46.41 

866.6 

61.10 

15  00 

i.in 

1.V900 

9.280 

1.475 

87.94 

296.2 

49.86 

IH-JO 

l.i:«> 

18.550 

9.4W 

1.755 

81.89 

245.9 

40.98 

20  N) 

1.158 

•21.200 

9.647 

2.045 

27.38 

208.1 

84.G9 

2.'J.40 

l.lK*,' 

28.8:)0 

9  847 

2.348 

23.84 

178.8 

29.80 

26.00 

1.205 

26  500 

.0.089 

2.660 

21.04 

155.3 

25.88 

SSI 
^  «  o 

til 


.569 
1.141 
2.295 
8.462 
4.641 
5838 
7.088 
S.256 
9.488 
10.78 
11.09 
18.51 
25.41 
3278 
40.51 
48.80 
67.65 
6711 
77.28 


EVAPORATION.  465 

Coii««iitmttoii  of  Svflpar  Sol  atlonii.*  (From  '*  treating:  and  Gon- 
eentraling:  Liquids  by  8teara, '  by  Joliu  G.  Hudson;  The  Shigineer^  June  18, 
1890.)— In  the  early  stagres  of  tlie  process,  when  the  liquor  in  or  low  density,  the 
evapioraUre  duty  will  be  hlfch,  say  two  to  three  (British)  ^llons  per  square 
foot  of  heatlnfp  surface  with  10  lbs.  steam  pressure,  but  will  gradually  fall  to 
an  almost  nominal  amount  as  the  final  suige  is  approached.  As  a  generally 
safe  basis  for  designing,  Mr.  Hudson  takes  an  eTaporation  of  one  gallon  per 
hour  for  each  squnre  foot  of  gross  healing  surface,  with  steam  of  the  pres- 
sure of  about  10  lbs. 

As  examples  of  the  evaporative  duty  of  a  vacuum  pan  when  performing 
the  earlier  stages  of  concentration,  during  which  all  the  heating  surface 
can  be  employed,  he  gives  the  follow ingr 

Con.  Vacuuv  Pan.— 49^  in.  copper  coils,  528  square  feet  of  surface; 
steam  in  coils,  15  lbs.;  temperature  in  pan,  ]41<*  to  148^;  density  of  feed,  85* 
Beaum6,  and  concentrated  to  81^  Beauind. 

First  3^-ia{.~Evaporation  at  the  rate  of  2000  gallons  per  hour  a  8.8  gallons 
per  square  foot;  transmission,  870  units  per  degree  of  difference  of  tem- 
perature. 

Second  IViVir— Evaporation  at  the  rate  of  1508  gallons  per  hour  s  2.8  gal- 
lons per  square  foot;  tran.Hmi88ion,  265  units  per  degree. 

As  regards  the  total  time  needed  to  work  up  a  charge  of  massecuite  from 
liquor  of  a  given  density,  the  following  figures,  obtained  by  plotting  the 
results  from  a  large  number  of  psns.  form  a  guide  to  practical  working. 
The  pans  were  all  of  the  coil  type,  some  with  and  some  without  jackets, 
the  gross  heating  surface  pmbably  averaging,  and  not  greatly  differing 
from,  .25  square  foot  per  gallon  capacity,  and  the  steam  pressure  10  lbs.  per 
square  incn.  Both  plantation  and  refining  pans  are  included,  making 
various  grades  of  sugar: 

Density  of  Feed  (degs.  Beaumfi). 
10*       15»        20*        250       80* 

evaporation  required  per  gallon  masse- 
cuite  discharged 6.123    8.6         S.26       1.5         .97 

Average  working  hours  required  per 
charge 18.         0.  6^       6,         4. 

Equivalent  average  evaporation  per  hour 
per  square  foot  of  gross  surface,  as- 
suming .25  sq.  ft.  per  gallon  capacity..      S.04       1.6         1.39      1J8         .97 

fa««test  working  hours  required  per 
charge ^5        6.5         8.8        2.75      2.0 

Equivalent  average  evaporation  per 
hour  per  square  foot 2.88      2.6         2.38      2.18       1.9 

The  quantity  of  heating  steam  needed  is  practically  the  same  in  vacuum 
as  in  open  pans.  The  advantages  pro|)er  to  the  vacuum  system  are  pri- 
marily the  reduced  temperature  of  boiling,  and  incidentally  the  possibility 
of  using  heating  steam  of  low  pressure. 

In  a  solution  of  sugar  in  water,  each  pound  of  sugar  adds  to  the  volume 
of  the  water  to  the  extent  of  .061  gaUon  at  a  low  density  to  .0638  gallon  at 
hi^h  dpnMties. 

A  Metliod  of  STmpomtliig  by  Exlianst  Steam  is  described 
by  Albert  Siearua  in  Trans.  A.  8.  M.  E.,  vol.  viii.  A  pan  17'  6"  x  11'  x  1'  6", 
fitted  with  cast-iron  condensing  pipes  of  about  250  so.  ft.  of  surface,  evapo- 
rated ViO  gallons  per  hour  from  clear  water,  condensing  only  about  one  half 
of  the  steam  supplied  by  a  plain  slide-valve  enfrine  of  14"  x  82"  cylinder, 
making  6B  revs,  per  min.,  cutting  off  about  two  thirds  stroke,  with  steam  at 
75  Iba.  boiler  pressure. 

It  was  found  that  keeping  the  pan-room  warm  and  letting  only  suflHcient 
air  in  to  carry  the  vapor  up  out  of  a  ventilator  adds  to  its  efflclencv,  as  the 
avera'-e  temperature  of  the  water  in  the  pan  was  only  about  165»  F. 

Experiments  were  made  with  coils  of  pipe  in  a  small  pan,  first  with  no 
aidtator,  then  with  one  having  straight  blades,  and  lastly  with  troughed 
blades;  the  evaporative  results  being  about  the  proportions  of  one,  two,  and 
three  respectively. 

In  evaporating  liquors  whose  bolliTig  point  is  220«  F..  or  much  above  that 
of  water,  it  fs  found  that  exhaust  steam  can  do  but  little  more  than  bring 
them  up  to  saturation  strength,  but  on  weak  liquors,  syrups,  glues,  etc.,  it 
should  nc  very  useful. 

*  For  other  sugar  data  see  Bagasse  aa  Fuel,  under  Fuel^ 


466  HEAT. 


le  three  eMsential  requirements  for  a  succe&sf  I  and  eco- 

of  drying  are:    1.  Cheap  evaporation-  of  the  moisture; 

Bit  a  low  temperature;  H.  lArge  capacity  of  the  apparatus 


DrjrlBir  In  Taeanni.— An  apparatus  for  drying  grain  and  other  sub- 
stances ill  vacuum  is  described  by  Mr.  Emil  Passbiirg  in  Pro-J.  Inst.  Mech. 
Engrs.i  1880.    The  three  essential  requirements  for  a  successf  I  and  eco- 
nomicsl  process  of  *     " 
£l  Quick  drying  at  c 
employed. 

The  removal  of  the  moisture  can  be  effected  in  either  of  two  ways:  either 
tor  slow  evaporation,  or  by  quicic  evaporation—tliat  is,  by  boiling. 

Slow  Evaporation.— The  principal  idea  carried  into  practice  in  machines 
•cling  by  slow  evaporation  is  to  brine  the  wet  substance  repeatedly  Into 
contact  with  the  inner  surfaces  of  tne  apparatus,  which  are  heated  by 
steam,  while  at  the  same  time  a  current  of  not  air  is  also  passing  through 
the  suostances  for  carrying  off  the  moisture.  This  method  requires  much 
heats  because  the  hot-air  current  has  to  move  at  a  consideraole  speed  in 
order  to  shorten  the  drying  process  as  much  as  possible;  consequently  a 
great  qaantity  of  heated  air  passes  through  and  escapes  unused.  As  a  car- 
rier of  moisture  hot  ajr  cannot  in  practice  be  charged  beyond  half  its  full 
saturation;  and  It  is  in  fact  considered  a  satisfactory  result  if  even  this 
proportion  be  attained.  A  great  amount  of  heat  is  here  produced  which  is 
not  used ;  while,  with  scarcely  half  the  cost  for  fuel,  a  much  quicker  re- 
moval of  the  water  is  obtained  by  heating  it  to  the  boiling  point. 

Quick  Evapotatiot^  by  Boiling.-^TUU  does  not  take  place  until  the  water 
is  brought  up  to  the  boiling  point  and  kept  there,  namely,  212^  F..  under 
atmospheric  pressure.  The  vapor  generated  then  escapes  freely.  Liquids 
araeasiiv  evaporated  in  this  way,  because  by  their  motion  conHequent  on 
boiling  the  heat  is  continuously  convoyed  from  the  heating  surfaces  tlirough 
the  liquid,  but  it  is  different  with  solid  substances,  and  many  more  difficul- 
ties have  to  be  overcome,  because  convection  of  the  heat  ceases  entirely  In 
solids.  The  substance  remains  motionless,  and  consequently  a  much 
greater  quantity  of  heat  is  required  than  with  liquids  for  obtaining  the 
same  results. 

Evaporation  in  Vacuum.-^ All  the  foregoing  disadvantages  are  aToided  it 
the  boiling-pohit  of  water  Is  lowered,  that  is,  if  the  evaporation  Is  carried 
out  under  vacuum. 

This  plan  has  been  successfully  applied  In  Mr.  Passburg's  vacuum  drying 
apparatus,  which  is  designed  to  evaporate  large  quantities  of  water  con- 
tained in  solid  substances. 

The  drying  apparatus  consists  of  a  top  horizontal  c>ilnder,  surmounted 

Jr  a  cha[rging  vessel  at  one  end,  and  a  bottom  horisontal  cylinder  with  e 
scharging  vessel  beneath  it  at  the  same  end.  Both  cylinders  are  encased 
in  steam-jackets  heated  by  exhaust  steam.  In  the  top  cylinder  worlcs  a  re- 
volving cast-iron  screw  with  hollow  blades,  which  is  also  heated  by  exhaust 
steam.  The  bottom  cylinder  contains  a  revolving  drum  of  tubes,  consisting 
of  one  large  central  tube  surrounded  by  24  smaller  ones,  all  fixed  In  tube- 
plates  at  both  ends;  this  drum  is  heated  by  live  steam  direct  from  the  boiler. 
The  substance  to  be  dried  is  fed  into  the  charging  vessel  through  two  man- 
holes, and  is  carried  ak>ng  the  top  cylinder  by  the  screw  crseper  to  the  back 
end,  where  it  drops  through  a  valve  into  the  oottom  cylinder,  in  which  It  is 
lifted  by  blades  attached  to  the  drum  and  travels  forwards  in  the  reverse 
direction:  frcnn  the  front  end  of  the  bottom  cylinder  it  falls  into  a  discharg- 
ing vessel  through  another  valve,  having  by  this  time  become  dried.  Ilie 
vapor  arising  daring  the  process  is  carried  off  by  an  air-pump,  through  a 
dome  and  air-valve  on  the  top  of  the  upper  cylinder,  and  also  through 
a  throttle- valve  on  the  top  of  the  lower  cylinder;  both  of  these  valves  are 
supplied  with  strainers. 

As  soon  as  the  diBcbarglng  vessel  is  flhed  with  dried  material  the  valve 
connecting  it  with  the  bottom  cylinder  is  shut,  and  the  dried  charge  taken 
out  without  impairing  the  vacuum  in  the  apparatus.  When  the  charging 
vessel  requires  replenishing,  the  intermediate  valve  between  the  two  cylhi. 
ders  is  shut,  and  tbe  charging  vessel  filled  with  a  fresh  supply  of  wet  mate- 
rial; tiie  vacuum  still  remains  unimpaired  in  tbe  bottom  cylinder,  and  has 
to  be  restored  only  in  tlte  top  cylinder  after  the  charging  vessel  has  been 
closed  again. 

In  this  vacuum  the  boiling-point  of  the  water  contained  in  the  wet  mate- 
rial is  brought  down  as  low  as  llO*  F.  The  difference  between  this  tempera- 
ture and  that  of  the  heating  siirfaces  is  amply  sufHcient  for  obtaining  good 
results  from  the  employment  of  e.\haiist  steam  for  heating  all  the  surfaces 
except  the  revolving  drum  of  tubes.  The  water  contained  in  the  solid  sub- 
stance to  be  dried  evaporates  as  soou  as  the  latter  is  heated  to  about  110^  t^ 


dfs 


RADIATION  OP  HEAT.  467 


ftttd  M  lomr  M  tlMTt  if  Aor  moislure  U>  be  ranovvd  (iieiolld 

not  heated  above  tliis  temperature. 

Wet  Rrainft  from  a  brewery  or  distillery,  ooDtaining:  from  76jt  to  789t  of 
water,  have  by  this  dr^'ing:  process  been  converteil  in  some  localities  from 
a  wortlilero  incumbrance  into  a  valuable  food-stuff.  The  water  i?  removed 
by  evaporation  only,  no  previous  meeiianloal  pressing  being  resorted  to. 

AtMcssm.  Guinness's  brewery  in  Dublin  two  of  Uiese  machines  nre  em- 
ployed. In  each  of  these  the  top  cylinder  Is  ffy  4"  long  and  2'  %"  diam.,  and 
the  screw  working  inside  it  makes  7  revs,  per  min.;  the  bottom  cylinder  itf 
19'  2"  long  and  5'  4"  diam.,  and  the  drum  of  the  tubes  Inside  it  makes  6  revs, 
per  min.  The  drying  surfaces  of  the  two  cylinders  amount  together  to  a 
total  area  of  about  lOOO  so.  ft.,  of  whksh  about  Hi%  b  heated  by  ezhanst  0tcam 
dii^ect  from  the  boiler.  There  is  only  one  aJr-pump,  which  is  made  large 
enough  for  three  machines;  it  Is  horizontal,  and  has  only  o«ie  alr-eylliider, 
which  Is  double-acting,  17%  in.  diam.  and  1794  in.  stroke;  aud  It  la  driven  at 
about  45  revs,  per  mlo.  As  the  reeult  of  about  eight  months*  experience,  the 
two  machines  nave  been  drying  the  wet  grains  from  about  MO  cwt.  o(  malt 
per  day  of  t4  hours. 

Rou|[hly  speaking,  8  ewt.  of  malt  gave  4  cwt.  of  wet  grains,  and  the  latter 
yMd  1  cwt  of  dried  grains;  800 cwt.  of  malt  will  therefors  yleki  about  670 
cwt  ot  wet  grains,  or  MO  cwt.  per  machine.  The  quantity  of  water  to  he 
evaporated  from  the  wet  graius  is  f lom  75](  to  WH  of  their  total  weight,  or 
say  about  612  cwt  altogethtfr,  being  tX  cwt.  per  machine. 

KABIATION  OF  HBAT. 

Radiation  of  heat  takes  place  between  bodies  at  all  distances  apart,  and 
fbllovi  8  the  laws  for  the  radiation  of  light. 

The  heat  rays  proceed  in  straight  lines,  and  the  Intensity  of  the  rays 
radiated  from  any  one  sonroe  varies  inversely  aa  the  square  of  their  distance 
from  the  source. 

This  statement  has  been  erroneously  interpreted  by  some  writers,  who 
have  assumed  from  It  that  a  boiler  placed  two  feet  above  a  fire  would  re- 
ceive by  radiation  onlr  one  fourth  «a  much  heat  as  if  it  were  only  one  foot 
abore.  In  the  case  of  holler  furnaces  the  siUe  walls  reflect  those  rays  tiiat 
are  received  at  an  angle— following  the  law  of  optics,  that  the  angle  of  Inci- 
dence is  equal  to  the  anf^le  of  reflection,— with  the  result  that  ttie  intensity 
of  heat  two  feet  above  the  fire  is  practically  the  same  as  at  one  foot  above, 
instead  of  only  one-fourth  as  muou. 

The  rate  at  Which  a  hotter  body  radiates  heat,  and  a  colder  body  absorbs 
heat,  depends  upon  the  state  of  the  surfaces  of  the  bodies  as  well  as  on  their 
temperatures.  The  rate  of  radiation  and  of  absorption  are  increased  bj 
darkness  and  roogbness  of  the  surfaces  of  the  bodies,  and  dhnluished  hy 
smoothness  and  polL<UL  For  this  reason  the  oovertng  of  sCeam  pipes  and 
boilt-m  should  be  smooth  and  of  a  light  oolor;  uncovered  pipes  and  steam- 
Qrlinder  covers  should  be  polished. 

Tfie  quantity  of  heat  radiated  by  a  body  to  also  a  mesatwettf  Its  heat- 
absorblog  power,  under  the  same  circumstances.  When  a  polished  body  is 
stmck  I7  a  ray  of  heat,  it  absorbs  part  of  the  heat  and  refleecs  the  rest. 
The  reflecting  power  of  a  body  is  therefore  the  complement  of  Its  absorbing 
power,  which  utter  Is  the  same  as  Its  radiating  power. 

The  relative  radiating  and  reflecting  power  of  different  bodies  has  been 
determined  by  experiment,  as  shown  in  the  table  below,  but  aa  far  aa  quan- 
tities of  heat  are  concerned,  says  Prof.  Trowliridge  (Jolinson's  CycIofiSBdia, 
art.  Rent),  It  is  doubtftil  whether  anything  further  than  the  said  relative 
determinations  can,  hi  the  present  state  of  oar  knowledge,  be  depended 
upon,  the  actual  or  abrotnte  quantities  for  different  tenrperatttres  being  still 
uncertain.  The  authorities  do  not  even  agree  on  the  rvlatlve  radiiirhig 
powers.  Thns,  Leslie  gives  for  tin  plate,  gold,  silver,  and  copper  the  flgiiro 
li,  which  differs  considerably  from  the  flgnres  in  the  table  below,  given  by 
Clark,  stated  to  be  on  the  authority  of  Leslie,  De  La  Provostaye  and  De- 
sains,  and  Mollooi, 


468 


fiEAT. 


KelAtlTe  BadlAtlnff  And  B«flectlnff  Po^grer  of  IMfl^rent 
Snbstanees. 


s 

III 

t. 
P 

Lampblack 

100 
100 
100 

98 
98  to  98 

90 

85 

72 

87 

S5 
28 

23 

0 

0 

0 

2 
7to2 
10 
15 
28 
78 

re 

77 

77 

Zincpolished 

Steel,  polished 

Platinum,  polished., 
in  sheet.. 

Tin 

Brass,     cast,    dead 
polished 

19 
17 
24 

17 
16 

11 

7 
14 
7 
6 

8 

8 

81 

Water 

Carbonate  of  lead... 

Writine-paper 

Ivory,  j«t,  marble. . . 

Ordinary  glaw 

Ice 

83 
76 
83 
85 

89 

Gum  lac 

Brass,    bright    pol- 
ished  

Copper,  ▼amlshed  . . 

Gold,  plated 

•'    on  polished 
steel 

Silver,    polished 
bright 

SilTer-leaf  onfflaaa.. 
Cast  iron,  bright  pol- 
ished  

93 
86 
98 

Mercury,  about 

Wroight    iron,   pol- 

96 
97 

97 

Experiments  of  Dr.  A.  M.  Mayer  give  the  following:  The  relative  radia- 
tions from  a  cube  of  cast  iron,  having  faces  rough,  as  from  the  foundry, 
planed,  *'  drawflled,^*  and  polished,  and  from  the  same  surfaces  oiled,  are  as 
below  (Prof.  Thurston,  iu  Trans.  A.  S.  M.  E.,  vol.  xvi.) : 


Surface. 

Oiled. 

Dry. 

Itough 

100 
60 
49 
45 

100 

Planed 

82 

Drawflled  

20 

Polished 

18 

It  here  appears  that  the  oiling  of  smoothly  polished  castings,  as  of  cylin- 
der-heads of  steam-engines,  more  than  doubles  the  loss  of  heat  by  radiation, 
while  it  does  not  seriously  affect  rough  castings. 

CONDUCTION  AND  CONVBCTION  OF  HBAT. 

Conduetlon  is  the  transfer  of  heat  between  two  bodies  or  parts  of  a 
body  which  touch  each  other.  Internal  conduction  takes  place  between  the 
parts  of  one  continuous  body,  and  external  conduction  through  the  surface 
of  contact  of  a  pair  of  distinct  bodies. 

The  rate  at  which  conduction,  whether  Internal  or  ozternal.  goes  on, 
being  proportional  to  the  area  of  the  section  or  surface  through  which  it 
takes  place,  may  be  expressed  in  thermal  units  per  square  foot  of  area  p-w*r 
liniir 

Internal  Conduction  varies  with  the  heat  conductivity,  which  de- 
pends upon  the  nature  of  the  substance,  and  is  directly  proportional  to  the 
diflference  between  the  temperatures  of  the  two  faces  of  a  layer,  and  in- 
versely as  its  thickness.  The  reciprocal  of  the  conductivity  is  called  the 
internal  thermal  rcMtstatice  of  the  substance.  If  r  represents  this  resistances 
X  the  thickness  of  the  layer  in  inches,  7*  and  Tthe  temperatureo  on  the  two 
faces,  and  q  the  quautity  in  thermal  units  transmitted  per  hour  per  square 


foot  of  area,  q  = 


T'  -  T 


(Rankine.) 


P6clet  gives  the  following  values  of  r : 


Gold,  platinum,  silver. . ......  0.0016 

Copper 0.0018 

Iron 0 .0048 

Zinc 0.0045 


Lead 0.0090 

Marble 0.0716 

Brick 0.1500 


COKDUCTIOK  AND  CONVECTION  OF  HEAT.         469 

Belatlve   Heat-eondnctliiff  Poorer  of  Rletals, 

(*  Calvert  &  Johnson  ;  t  Weidemana  &  Franz.) 


Metok.         •C.  &  J.  tW.  Si  F. 

RiWer 1000  1000 

Qold U81  saii 

(iiAd,  with  1%  ot  Kilver  840 

Copper,  rolled  ftl5  736 

Cupper,  casL 811  .... 

Mercury 677  .... 

Mercury,    with    UiSf 

of  Un 412 

Aluminum. 666  .... 

Zinc : 

cast  vertically 6J!8  .... 

cast  horizontally...  608  .... 

rolled 641 

hfPLITBMCE  OF  ▲  NON-HBTALUC  SUBSTANCE  IN  COMBINATION  ON  THE 
CONDUOITNa  POWEB  OF  A  MSTAL. 


Metals.        •C.&J.  tW.&F. 

Cadmium 577  .... 

Wrought  iron 486  119 

Tin 438  145 

Steel 897  116 

Platinum ShO  84 

Sodium 865 

Castiron 850 

Lead 287  85 

Antimony : 

cast  horizontally..  215  .... 

cast  vertically....  192 

Bismuth 61  18 


Influence  of  carbon  on  Iron  : 

Wrought  iron 436 

Steel 897 

Cast  Iron 859 


Cast  copper 811 

Copper  with  1%  of  arsenic 570 

with  .hi  of  arsenic C69 

"       with  .**S>%  of  ai-aenic 771 


Tlie  Rmte  of  External  Conduction  through  the  bounding:  surface 
bftweeu  a  solid  body  and  a  fluid  is  approximately  proportional  to  the 
difTerence  of  temperature,  when  that  is  small ;  but  when  tnat  difference  is 
considerable  the  rate  of  conduction  increases  faster  than  the  simple  ratio  of 
that  difTerence.    (Rankine.) 

If  r,  as  before,  is  the  coefBclent  of  internal  thermal  resistance,  e  and  ef  the 
coel&ci«nt  of  external  resistance  of  the  two  surfaces,  x  the  thickness  of  the 
plate,  and  T  and  Tthe  temperatures  of  the  two  fluids  in  contact  with  the 

I*  —  r 

two  surfaces,  the  rate  of  conduction  in  q  =  — ; — ^—, .  According  to 

e-f-e  -i-rx 

Fsdet,  e  +  e'  =  ^       ,  In  which  the  constants  A  and  B  have 

the  following  values : 

B  for  polished  metallic  surfaces 0028 

B  for  rough  metallic  surfaces  and  for  non-metallic  surfaces. .    .0037 

A  for  polished  metals,  about 90 

^  for  glassy  and  varnished  surfaces 1.84 

.^  for  dull  metallic  surfaces 1.58 

A  for  lamp-black 1.78 

When  a  metal  plate  has  a  liquid  at  each  side  of  it,  it  appears  from  ezperi- 

menu  by  Peclet  that  B  =  .068.  A  =  8.8. 
The  results  of  experiments  on  the  evaporative  power  of  boilers  agree  very 

well  with  the  following  approximate  formula  for  the  thermal  resistance  of 

boiler  plates  and  tubes : 

«  +  «'  =  (r-T)' 
which  gives  for  the  rate  of  conduction,  per  square  foot  of  surface  per  Lour, 

(T-Ti* 
«= a • 

This  formit%  is  proposed  by  Rankine  as  a  rough  approximation,  near 
enough  to  the  truth  for  its  purpose.  The  value  of  a  lies  between  160  and  200. 

OoDTOCtloil)  or  carrying  of  beat,  means  the  transfer  and  diffusion  of 
the  heat  in  a  fluid  mass  by  means  of  the  motion  of  the  particles  of  that 
If  ass. 

The  conduction,  properly  so  called,  of  heat  through  a  stagnant  mass  of 
Ihiid  Is  very  slow  in  liquids,  and  almost,  if  not  wnolly,  Inappreciable  In 
gHse&  It  is  only  bv  the  continual  circulation  and  mixture  of  the  particles  of 
tlie  fluid  that  uniformity  of  temperature  can  be  maintained  in  the  fluid 
mass,  or  heat  transferred  between  the  fluid  mass  and  a  solid  body. 

The  free  circulation  of  each  of  the  fluids  which  touch  the  side  of  a  solid 
f  lite  is  a  necessary  condition  of  the  correctness  of  Bankliie*8  formulee  for 
tbe  conduction  of  heat  through  that  plate;  and  in  these  formulas  it  is  im- 


470 


HEAT. 


plied  that  the  drcuUtion  of  Mch  of  the  fluldn  by  currents  and  eddleft  la 
such  as  to  prevent  any  considerable  difference  of  temperature  between  the 
fluid  particles  in  contact  with  one  side  of  the  solid  plate  and  those  at  con- 
siderable distances  from  it. 

When  heat  is  to  be  transferred  by  convection  from  one  fluid  to  another, 
throuKh  an  in i  erven infc  layer  of  metal,  the  motions  of  the  two  fluid  manses 
should,  if  possible,  l)e  in  opposite  directions,  in  order  that  the  hottest  paN 
tides  of  each  fluid  may  be  in  communication  witli  the  hottest  particles  of 
the  other,  and  chat  the  minimum  difference  of  temperature  between  the 
adiaoent  particles  of  the  two  fluids  may  be  the  greatest  possible. 

Thus,  in  the  surface  condensation  of  steam,  by  passing  it  through  metal 
tubes  immersed  in  a  current  of  cold  water  or  air,  the  cooling  fluid  shouJd 
be  made  to  move  in  tlie  opposite  direction  to  the  condensing  steam. 

St«Aiii«plpe  OoTerlngs« 

(Experiments  by  Prof.  Ordway,  Trans.  A.  S.  M.  E.,  vl.  ICft;  also  Circular  No. 
n7  of  Boston  Mf rs.  Mutual  Fire  Ins.  Co..  1800.) 


Substance  1  inch  thick, 
applied,  310<>  F. 


Heat 


1.  Loose  wool 

2.  Live-geese  feathers .... 

8.  Carded  cotton  toooJ 

4.  Hairfelt 

6.  .Loo«e  lampblack 

0.  Compressed  lampblack. 

7.  Cork  charcoal 

8.  White-pine  charcoal 

9.  Anthracite-coal  potpder 

10.  Loose  calcined  magnesia 

11.  Compressed  calcined  magnesia. . 

12.  Light  carbonate  of  magm^sia.. . . 

13.  Compressed  carb.  of  magnesia.. 

14.  Loose  fossil-meal 

15.  Crowded  fossil-meal 

16.  Ground  chalk  (Paris  white) 

17.  Dry  plaster  of  Paris 

18.  Fine  asbestos • 

19.  Air  alone 

20.  Sand 

31.  Best  slag'wool.. 

22.  FSifyer 

23.  Blotting-paper  wowid  t igh t 

24.  Asbestos  paper  xoound  tight 

25.  Cork  strips  bound  on 

2fl.  Straw  rope  f pound  spirally 

27.  Loose  rice  chaff. 

28.  Ptiste  of  fosHll -meal  with  hair... . 

29.  Paste  of  fcMsil-meal  with  asbestos 
3u.  Loose  bituminous-coal  ashes . 
81.  Ijoose  anthracite-coal  ashes . . 
88.  Paste  of  clay  and  vegetable  flhre 


Pounds  of 

Water 

heated 

10«  F.,  per 

hour, 
through 
1  sq.  ft. 


8.1 
9.6 
10.4 
10.3 
9.8 
lO.G 
11.9 
13  9 
86.7 
12.4 
42.6 
13.7 
15.4 
14. B 
15.7 
20.6 
80.9 
49.0 
48.0 
62.1 
18. 
14. 
21. 
21.7 
14.6 
18. 
18.7 
16.7 
22. 
21. 
27. 
SO. 9 


British 
Thermal 

Units 
per  sq.  ft. 


hute. 


J  pel 
nu 


1.86 
1.60 
1.78 
1.72 
1.68 
1.77 
1.98 
2.3S 
5.96 
2.07 
7.10 
2.28 
2.57 
2.42 
2.62 
8.48 
5.19 
8.17 
8.00 

10.80 
2.17 
2.88 
8.50 
8.62 
2.48 

•8. 
3.12 
2.78 
3.67 
8.50 
4.&0 
5.16 


Solid 

Matter  In 

Isq  ft. 

1  inch 

thick, 

paruin 

1000. 


56 

50 

20 
185 

66 
844 

53 
119 
606 

88 
285 

60 
160 

60 
112 
258 
868 

81 
0 


-I 

944 
SSO 
980 
815 
944 
766 
947 
881 
494 
977 
715 
940 
859 
94C 
888 
747 
682 
919 
1000 
471 


It  will  be  observed  that  several  of  the  incombustible  materials  are  nearly 
as  efficient  as  wool,  cotton,  and  feathers,  with  which  they  may  be  compared 
in  the  preceding  table.  The  materials  which  may  be  considered  wholly  fre« 
from  the  danger  of  being  carbonized  or  ignited  by  slow  contact  with  pipea 
or  boilers  are  printed  in  Roman  type.  Those  which  are  more  or  lesa  liable 
to  be  carbonized  are  pilnted  in  italics. 

Tlie  results  Nog.  1  to  20  Inclusive  were  from  experlmeult  with  the 
various  non-conductors  each  used  in  a  mass  one  inch  thick,  placed  on  a  flat 
■nrfaoe  of  Iron  kept  heated  by  steam  to  810*  F.    Hie  substances  Nos.  81  to 


COKDtJCTlON  AKD  COKVKCTIOK  O*'   HfiAT.        47X 


83  wero  tried  M  ooveringa  for  tiro>iocb  steam  pipe;  UftB  remlte  being  re- 
duced to  (be  lame  termii  lui  the  others  for  oouvenieooa  of  oompiU'teoD. 

Experimente  on  BtiU  air  gave  results  which  differ  little  from  those  of  Noe. 
a,  4,  and  6.  The  bulk  of  matter  in  (he  best  non-ooDduotorB  is  relatlTely  too 
•mall  to  have  any  speciflo  eif eot  except  to  trap  the  fiir  and  keep  it  stagnant. 
TItieae  subetanoes  keep  the  air  ttiU  by  virtae  of  the  roughnen  of  their  flbrea 
or  particles.  The  asbestos,  No.  16,  had  smooth  Abides.  Asbestos  with  ex- 
ceedingly fine  fibre  made  a  somewhat  better  showing,  but  asbestos  is  really 
one  of  the  poorest  non-conductors.  It  may  be  need  advantageously  to  hold 
togtftiier  other  Incombustible  subetances,  but  tlie  less  of  it  the  better.  A 
**m«gDeaia"  covering,  made  of  carbonate  of  magnesia  with  a  small  per- 
centage of  good  asbestos  fibre  and  containing  OJi&  of  solid  matter,  trans- 
mitted 2J>  B.  T.  U.  por  equare  foot  per  minute,  and  one  eoptaining  0.806  of 
solid  matcttr  transmitted  9JS»  B.  T.  if. 

Any  suitable  substance  which  Is  used  to  prevent  the  eecape  of  steam  heat 
•faouid  not  be  less  than  one  Inch  thick. 

Any  covering  should  be  kept  perfectly  diy,  for  not  only  Is  water  a  good 
carrier  of  heat,  but  it  has  been  louud  tnat  still  water  conducts  heat  about 
ciifht  times  as  rapidly  as  stUl  air. 

Testa  of  Commeirolal  CoTerlniT"  ^^i^  made  by  >Ir.  Geo,  U.  Brill 
and  reported  in  Trams.  A-  S.  M.  £.,  xvi,  ijei7.  A  length  of  00  feet  of  8-incii 
steam- pipe  was  used  in  the  tests,  and  the  heat  loss  was  determined  by  the 
condensation.  The  steam  pressure  was  from  100  to  117  lb%,  gaugei  and  the 
temperature  of  the  air  from  58**  to  Si <*  F.  The  diflCerence  between  the  tem- 
perature of  steam  and  air  ranged  from  263*  to  itSt^",  averaging  27:2*. 

The  following  are  the  principal  results  : 


Kind  of  Ck>veriDg. 


Bare  pipe 

MajcneHia 

Rock  wool 

Mineral  wool 

Fire-felt 

Man  villa  sectional ..... 
Manv.  sect.  &  hairfelr. 
Kin  vine  wool -cement. 
Cliampionmineral  wool 

Hair-ffelt 

Riley  cement 

Fossil-meal 


6 


1.23 
1.80 
1.30 
1.30 
1.70 
2.40 
2.30 
1.44 

.75 


it 

jj I  « 


.846 
.120 
.080 
.089 

.\h7 

.109 
.060 
.108 
.099 
.18-3 
.298 
.'275 


12.2T 
1.74 
1.16 
1.291 
2.2« 
1.59 
0.06 
1..56 
1.44 
1.91 

3.99 


2.706 
•  .384 
.256 
.285 
.502 
.360 
.212 
.345 
.117 
.422 
.058 
.879 


II. 

fl 

100. 

.7>6 

14.2 

.766 

9.5 

.757 

10.6 

.G89 

18.6 

.737 

12  9 

.780 

7.8 

.■iss 

12.7 

.747 

11.7 

.714 

15.6 

.548 

85.8 

.571 

82.6 

IP 


2.619 
.400 
.«67 
.897 
.623 
.564 
.221 
.359 
.880 
.439 
.906 
.916 


aDsmleflloii  of  0eat«  tbroiyrli  Solid  Plates,  trowut 
Water  to  Water*  (Clark,  S.E.).~M.  I%clet  found,  from  ezperimenta 
made  with  plates  of  wrought  iron,  cast  iron,  copper,  lead,  ziuc,  and  tin, 
tluit  when  the  fluid  in  contact  with  the  surface  of  the  plate  was  not  circu- 
lated by  artificial  means,  the  rate  of  conduction  was  the  same  for  different 
metals  and  for  platee  of  the  same  metal  of  different  thicknesses.  But 
when  the  water  was  thoroughly  circulated  over  the  surfaces,  and  when 
these  were  perfectly  clean,  the  quantity  of  transmitted  heat  was  inversely 
proportloiMU  to  the  thickness,  and  directly  as  the  difference  in  temperature 
of  the  two  faces  of  the  plate.  When  the  metal  surface  became  dull,  the 
rate  of  transmfssion  of  heat  through  all  the  metals  was  very  nearly  the 
same.  .    . 

It  follows,  sa^  Clark,  that  the  absorption  of  heat  through  metal  plates  to 
more  active  whilst  evaporation  is  in  progress— when  the  circulation  of  the 
water  is  more  active— than  while  the  water  is  being  heated  up  to  the  boiling 
pohit. 


472 


fifiAT. 


TmnamlMrton  from  Stemm  to  WAter.— M.  Ptelet^s  principle  is 
supported  bv  the  results  of  experiments  made  in  1867  b/  Mr.  Isherwood  on 
the  conductivity  of  different  metals.  Cylindrical  pots,  10  inches  in  diameter, 
8t^  inches  deep  inside,  and  %  inch,  ^  inch,  and  %  inch  thick,  turned  and 
bored,  were  formed  of  pure  copper,  brass  (60  copper  and  40  zinc),  rolled 
wrougrbt  iron,  and  remelted  cast  iron.  They  were  immersed  in  a  steam 
bath,  which  was  varied  from  2-JO*  to  8a0<*  F.  water  at  2]x«  was  supplied  to 
the  pots,  which  were  kept  filled.  It  was  ascertained  that  the  rate  of  evapora- 
tion was  in  the  direct  ratio  of  the  difference  of  the  temperatures  inside  and 
outside  ot  the  pots;  that  is.  that  the  rate  of  evaporation  per  deeree  of 
difference  of  temperatures  was  the  same  for  all  temperatures;  and  that  the 
rate  of  evaporation  was  exactly  the  same  for  diffei-ent  thicknesses  of  the 
metal.  The  respective  rates  of  conductivity  of  the  several  metals  were  as 
follows,  expressed  in  weight  of  water  evaporated  from  and  at  212*  F.  per 
square  foot  of  the  interior  surface  of  the  pots  per  defn'ee  of  difference  of 
temperature  per  hour,  together  with  the  equivalent  quantities  of  heat-units: 
Water  at  212?,       Heat-units.       Ratio. 

Copper 66filb.  642.5  1.00 

Brass 677  *•  566.8  .87 

Wroughtiron 887"  878.6  .68 

Castiron 827"  815.7  .40 

Whitham,  "Steam  Engine  Design,"  p.  288,  also  Trans.  A.  8.  M.  E  ix.  4S5,  in 
using  these  data  in  deriving  a  formula  for  surface  condensers  calls  these 
figures  those  of  perfect  conductivity,  and  multiplies  them  by  a  coefficient 
C  which  he  takes  at  0.828,  to  obtain  the  efficiency  of  condenser  surface  in 
ordinary  use.  i.e.,  coated  with  saline  and  greasy  deposits. 

TransmlBsloii  of  Heat  fi-om  Steam  to  Water  tltronsli 
Colls  of  Iron  Pipe.— H.  Q.  C.  Kopp  and  F.  J.  Meystre  iStevena  Indi- 
cator^ Jan.,  1B94),  give  an  account  of  some  experiments  on  transmission  of 
heat  through  coils  of  pipe.  They  collate  the  results  of  earlier  experiments 
as  follows,  for  comparison: 


1 

1 

Steam  Con- 
densed per 
Square  foot  per 
degree  differ- 
ence of  temper- 
ature per  hour. 

Heat  trans- 
mitted per 
square  foot  per 
degree  differ- 
ence of  temper- 
ature per  hour. 

Remarks. 

•c 

S. 

M 

1! 

ill 

1^ 

S2n 

Laurens 

Havrez.. 
Perkins. 

Box 

Havrez.. 

Copper  colls... 
2  Copper  coils. 
Copper  coil . . . 

Iron  coil 

Iron  tube .... 

Cast-iron  boil- 
er  

.292 
.268 

.235 
.196 
.206 

.077 

.981 
1.20 
1.26 

.24 
.22 

.106 

816 

'280 

280 

207 
210 

82 

974 
1120 
1200 

215 
208.2 

100 

(Steam  pressure 

=  lOtT 
Steam  pressure 
=  10. 

From  the  above  It  would  appear  that  the  efficiency  of  iron  surfaces  is  le«s 
than  that  of  copper  coils,  plate  surfaces  being  far  inferior. 

In  ail  experiments  made  up  to  the  present  time,  it  appears  that  the  tem- 
perature of  the  condensing  water  was  allowed  to  rise,  a  mean  between  tlra 
initial  and  final  temperatures  being  accepted  as  the  effective  tempermture. 
But  as  water  becomes  wanner  it  circulaies  more  rapidly,  thereby  causing 
the  water  surrounding  the  coil  to  become  agitated  and  replaced  b3  cooler 
water,  which  allows  more  heat  to  be  transmitted. 


CONDUCnOK  AKD  CONVECTIOlf  OF  HEAT.        473 


Ai^ln.  in  acceptlDfi:  the  mean  temperature  as  that  of  the  eonaenslDK  me- 
dium, the  amumption  is  made  that  the  rate  of  condeDsatlon  is  Id  direct  pro- 
portion to  the  temperature  of  the  condensing  water. 

In  order  to  correct  and  avoid  any  error  arising  from  these  assumptions 
and  approximations,  experiments  were  undertaken,  in  wliich  all  the  coudi- 
tlons  were  constant  during  each  test. 

The  prmsure  was  maintained  uniform  throughout  the  coil,  and  provision 
was  made  for  the  free  outflow  of  the  condensed  steam,  in  order  to  obtain 
at  ail  times  the  full  efficiency  of  the  condensing  surface.  The  condensing 
water  was  continually  stirred  to  secure  unlformltv  of  temperature,  which 
was  regulated  by  means  of  a  steam-pipe  and  a  cold-water  pipe  entering  the 
tank  in  which  the  coil  was  placed. 

The  following  Is  a  condensed  statement  of  the  resolta 

IlKAT    TRAICSHOTTSO    PER    BqUARB    FoOT    OF    COOUKO  SURFACC,  PER  HoUR, 

pxa  Deorxk  or  Diptkbicnce  or  Txmpcraturk.    (British  Thermal  Units.) 


Temperature 
of  (xmdens- 
ing  Water. 

1-in.  Iron  Pipe; 

Sieam  inside, 

60  lbs.  Gauge 

Pressure. 

Steam  inside, 

10  lbs. 

Pressure. 

IH  in.  Pipe; 

Steam  outside, 

10  lbs. 

Pressure. 

1^  in.  Pipe; 

Bteam  inside, 

60  lbs. 

Pressure. 

80 
100 
ISO 
140 
100 
180 
900 

265 
969 
97« 
277 
881 
290 
818 

128 
180 
187 
.     149 
158 
174 

200 
980 
260 
267 
271 
270 

'280 
847 
276 
806 
849 
419 

The  results  indicate  that  the  heat  transmitted  per  degree  of  difference  of 
temperature  in  general  Increases  as  the  temperature  of  the  condensing 
water  is  increased. 

The  amount  transmitted  is  much  larger  with  the  steam  on  the  outside  of 
the  coil  than  with  the  steam  inside  the  coil.  This  may  be  explained  in  part  by 
the  fact  that  the  condensing  water  when  inside  the  coil  flows  over  the  sur^ 
face  of  conduction  very  rapidly,  and  is  more  efficient  for  cooling  than  when 
eontained  In  a  tank  outside  of  the  coil. 

This  result  is  in  accordance  with  that  found  by  Mr.  Thomas  Craddock, 
which  indicated  that  the  rate  of  cooling  by  transmission  of  heat  through 
metallk:  smrfaoes  was  almost  wholly  dependent  on  the  rate  of  circulation  of 
the  cooling  medium  over  the  surface  to  oe  cooled. 

TnuamiftMton  of  Heat  In  €k>ndeiieer  Tabee.  {Eng^g,  Dec. 
10, 1875,  p.  449.).— In  1874  B.  C.  Nichol  made  experiments  for  determining  the 
rate  at  which  heat  was  transmitted  through  a  condenser  tube.  The  results 
wrait  to  show  that  the  amount  of  heat  transmitted  through  the  walls  of  the 
tube  per  estimated  degree  of  mean  difference  of  temperature  increased 
considerably  with  this  difference.  For  example: 
Estimated    mean    difference    of      Vertical  Tube.  Horizontal  Tube 


temperature  between  inside  and 
outside  of  tube,  degrees  Fahr.  . 
Heat-units  transmitted  per  hour 
per  square  foot  of  surface  per 
degree  of  mean  diff.  of  temp. 


128     161.0     162.9       111.6     146.2     190.4 


610       787 


422     581        6C1 

These  resulte  seem  to  throw  doubt  upon  Mr.  Isherwood's  statement  that 
the  rate  of  evaporation  per  degree  of  difference  of  temperature  Is  the  same 
for  all  temperatures. 

Mr.  Thomas  Craddock  found  that  water  was  enormously  more  efficient 
than  air  for  the  abstraction  of  heat  through  metallic  surfaces  in  the  process 
of  cooling.  He  proved  that  the  rate  of  cooling  by  transmission  of  heat 
through  metallic  surfaces  depends  upon  the  rate  of  circulation  of  the  cool- 
ing medium  over  the  surface  to  be  cooled.  A  tube  filled  with  hot  water, 
moved  by  rapid  rotation  at  the  rate  of  59  ft.  per  second,  through  air,  lost  as 
much  h«U  in  one  minute  as  it  did  in  still  air  in  12  minutes.  In  water,  at  a 
velocity  of  8  ft.  per  second,  as  much  heat  was  abstracted  in  half  a  minute  as 
wss  abetracted  In  one  minute  when  it  was  at  rest  in  the  water.  Mr.  Crad- 
dock concluded,  further,  that  the  circulation  of  the  cooling  fluid  became  of 


474 


HEAT. 


flrreator  imtx>rtaiioe  m  the  differenoe  of  temp«ratar«  on  the  two  sidM  of  tbe 
plato  became  lees.    (Clark,  R  T.  D.,  p.  461.) 

0eat  Transmission  ttaroaffli  Cast^ron  Plates  Ptckled  lit 
Nltrle  Add.— Bxperiments  btr  R.  c.  Oarpeater  (Trans.  A.  8.  M.  £.,  zii 
179)  elK>w  a  marked  change  in  the  conduetinfr  power  of  the  plates  (from 
steam  to  water),  due  to  prolonged  treatment  with  dilute  nitric  acid. 

The  action  of  the  nitric  add,  07  dissolving  the  free  iron  and  not  attacking 
the  carbon,  forms  a  protecting  surteoe  to  the  iron,  which  is  largely  com- 
posed of  carbon.    The  following  is  a  summary  of  results: 


Character  of  Plates,  each  plate  8.4  in. 
by  5.4  in.,  exposed  surfAce  37  sq.  ft. 


Increase  in 
Tempera^ 

ture  of 

3.185  lbs.  of 

Water 

each 

Minute. 


Oast   Iron— untreated    skin   on,  but 

clean,  free  from  rust 

l^t  iron— nitric  acid,  \%  sol.,  9  days. . 

"  *  1%  sol.,  18  days. 

"  "  U  sol.,  40  days. 

5j<sol.,9day8.. 

"  "  5)(  sol.,  40  days. 

Plate  of  pine  wood,  same  dimensions 

sa  the  plate  of  cast  iron 


Proportionate 
Thermal  Units 
Transmitted  for 
each  Degree  of 

Dijferenoe  of 

Temperature  per 

Square  Foot  per 

Hour. 


18.90 
U.5 
9.7 
9.6 
9.96 
10.6 

0.88 


113.9 
97.7 
60.06 
77.8 
87.0 
77.4 

1.9 


Rela- 
tive 
Trans' 
mission 

of 
Heat. 


100.0 
86.8 
70.7 
68.7 
78.8 
68.5 

1.6 


The  effect  of  covering  cast-iron  surfaces  with  varnish  has  been  investi- 
gated by  P.  M.  Cliamberlain.  He  subjected  the  plate  to  the  action  of  strong 
acid  for  a  few  hours,  and  then  applied  a  non-conducting  varnish.  One  sui^ 
face  only  was  treated.    Some  of  his  results  are  as  follows: 

170.  As  finished— greasy. 
152.   "      '*         washed  with  benzine  and  dried. 
160.  Oiled  with  lubrtoatlng  oil. 
to  nltrl 


ilirlc  acid  sixteen  hours,  then  oiled  (lin- 

166  After  exposure  to  hydrochloric  acid  twelve  hours,  tlien  oiled 
iseed  oil.) 


16R.  After  exposure 
seed  oil.) 


(Iin8< 

^^^'  /After  exposure  to  sulphuric  add  1,  water  8,  for  48  hours, 
]]^    r  then  oiled,  varnished,  and  allowed  to  dry  for  94  hoars. 

Transmission  of  H«at  tbroajtlt  SoHA  Plates  Arou  Air 
or  other  Dry  Oases  to  ITater.  (From  Clark  on  the  Steam  Engine.) 
*»The  law  of  the  transmission  of  heat  from  hot  air  or  other  gases  to  water, 
through  metallic  plates,  has  not  been  exactly  determined  uy  experiment. 
The  general  results  of  experiments  on  the  evaporative  action  of  different 
portions  of  the  heating  surface  of  a  steam-boiler  point  to  the  general  law 
that  the  quantity  of  heat  transmitted  per  degree  difference  of  temperature 
is  practically  uniform  for  various  differences  of  temperature. 

The  communication  of  heat  from  the  gas  to  the  plate  surface  is  much 
acoelerated  by  mechanical  impingement  of  tlie  gaseous  products  upon  the 
surfAce. 

Clarlr  says  that  when  the  surfaces  are  perfectly  clean,  the  rate  of  tmns- 
mission  of  heat  through  plates  of  metal  from  air  or  gas  to  water  is  greater 
for  copper,  next  for  brass,  and  next  for  wrought  iron.  But  when  the  sur- 
faces tare  dimmed  or  coated,  the  rate  is  the  same  for  the  different  metals. 

With  respect  to  tfie  Influence  of  the  conductivity  of  metals  and  of  the 
thickness  of  the  plate  on  the  transmission  of  heat  from  burnt  gases  to 
water.  Mr.  Napier  made  experiments  with  small  boilers  of  iron  and  copper 

{>laced  over  a  gas-flame.  The  vessels  were  6  Inches  in  diameter  ann  tf^ 
nches  deep.  From  three  ve.ssels,  one  of  Iron,  one  of  copper,  and  one  of  Iron 
sides  and  copper  bottom,  each  of  them  1/80  Inch  in  thickness,  equal  quanti- 
ties of  water  were  evaporated  to  di-yness,  in  the  times  as  follows : 


OOl^DUCTION  AND  CONVECTION   OF  HEAT.         475 

Water.  Iron  VesseL         Copper  VeaseL     ^'^^  vwsSl*'^^^ 

4  ounoes  19  minutes  18.5  minutes  

11        ••  88        "  80.76        *•  

4^    **  85.7    "  86.88  minutes. 

Two  oilier  Tessels  of  iron  Rides  1/80  Inch  thick,  one  hftvins  a  ^-inch  copper 
oottom  and  the  other  a  ^-inch  lead  bottom,  were  tested  artist  the  iron 
and  copper  vessel,  1/80  inch  thick.  Equal  quantities  of  water  were  evapo- 
rated in  54,  56,  and  53)^  minutes  respectively.  Taken  genei-alty,  the  results 
of  these  experiments  snow  that  there  are  practically  but  slight  differences 
between  iron,  copper,  and  lead  in  evaporative  activity,  and  that  the  activity 
is  not  affected  by  the  thickness  of  the  bottom. 

Mr.  W.  B.  Johnson  formed  a  like  conclusion  from  the  results  of  his  obser- 
vations  of  two  boilers  of  160  horse-power  each,  made  exactly  alike,  ex- 
cept that  one  had  iron  flue-tubes  and  the  other  copper  flue-tubes.  No  dif- 
ference could  be  detected  between  the  performances  of  these  boilers. 

Divergencies  between  the  results  of  different  experimenters  are  attribut- 
able probably  to  the  difference  of  conditions  under  which  the  heat  was 
transmitted,  as  between  water  or  steam  and  water,  and  between  gaseous 
matter  and  water.  On  one  point  the  divei^enoe  is  extreme:  the  rate  of 
transmission  of  heat  per  degree  of  difference  of  temperature.  'Whilst  from 
400  to  600  units  of  heat  are  transmitted  from  water  to  water  through  iron 

|>lat««,  per  degree  of  difference  per  square  foot  per  hour,  the  quantity  of 
leat  transmitted  between  water  and  air,  or  other  dry  gas,  is  only  about 
from  9  to  6  units,  according  as  the  surrounding  air  is  at  rest  or  in  movement. 
In  a  looomotlve  boiler,  where  radiant  heat  was  brought  Into  play,  17  units 
of  heat  were  transmitted  through  the  places  of  the  fire-box  per  degree  of 
difference  of  temperature  per  square  foot  per  hour. 

Transmission  of  Heat  thronen  Plates  and  Tabes  ft^m 
Steam  or  Hot  Water  to  Alr«-~The  transfer  of  heat  from  steam  or 
wAter  through  a  plate  or  tube  into  the  surrounding  air  is  a  complex  opera- 
tion. In  which  the  internal  and  external  conductivity  of  the  metal,  the  radi- 
ating power  of  the  surface,  and  the  convection  of  neat  in  the  surrounding 
air  are  all  concerned.  Since  the  quantity  of  heat  radiated  from  a  surface 
varies  with  the  condition  of  the  surface  and  with  the  surroundings,  according 
to  laws  not  yet  determined,  and  since  the  heat  carried  away  by  convection 
varies  with  the  rate  of  the  flow  of  the  air  over  tlie  surface,  it  is  evident  that 
no  general  law  can  be  laid  down  for  the  total  quantity  of  heat  emitted. 

The  following  Is  condensed  from  an  article  on  Loss  of  Heat  from  Steam- 
plpea,  in  The  Loco7notivt\  Sept.  and  Oct.,  1802. 

A  hot  steam  pipe  is  radiating  heat  constantly  off  into  space,  but  at  the 
same  time  it  is  cooling  also  by  convection.  Experimental  data  on  which  to 
base  calculations  of  the  heat  radiated  and  otherwise  lust  by  steam-pipes  are 
neither  numerous  nor  satisfactory. 

In  Box*s  Practical  Treatise  on  Heat  a  number  of  results  are  given  for  the 
amount  of  heat  radiated  by  different  substances  when  the  temperature  of 
the  air  Is  I*'  Fahr.  lower  than  the  temperature  of  the  radiating  body.  A 
yortion  of  this  table  is  given  below.  It  is  said  to  be  based  on  P^clet^s  ex- 
periments. 

Hbat  Units  Radiated  per  Hoor,  fir  Squarb  Foot  or  Surface,  for 
l^'  Fahrenheit  Excess  in  Temperature. 


Copper,  polished 0327 

Tin,  polished  0440 

Zine  and  brass,  polished 0491 

Tinned  iron,  polished 0858 

Sheet -Iron,  polished 0920 

Sheet  lead 1829 


Sheet-iron,  oixiinary 5603 

Glass 6948 

Cast  Iron,  new 6480 

Ctommon  steam-pipe.  Inferred..  .6400 

Cast  and  sheet  iron,  rusted 6668 

Wood,  building  stone,  and  brick  .7358 
When  the  temperature  of  the  air  is  about  50<>  or  60^*  Fahr.,  and  the  radiat- 
ing bodT  is  not  more  than  about  30**  hotter  than  the  air,  we  may  calculate 
the  radiation  of  a  given  surface  by  assuming  the  amount  of  heat  given  off 
by  it  iu  a  given  time  to  be  proportional  to  the  difference  in  temperature  5e- 
tsrren  the  radiating  bodt/  and  the  air.  This  is  ''Newton's  law  of  cooling.''* 
But  when  the  difference  In  temperature  is  great,  Newton's  law  does  not  hold 
gvx>d;  the  radiation  is  no  longer  proportional  to  the  difference  in  tempera- 
ture, but  must  be  calculated  by  a  complex  formula  established  experiment, 
ally  by  Dulong  and  Petit.  Box  has  computed  a  table  from  this  formula, 
which  greatly  facilitates  its  application,  and  which  is  given  below  : 


476  HEAT. 

Faoi^rs  roB  Reduction  to  Dulong^s  Law  op  Radiation. 


Differences  in  Tem- 

Temperature of  the  Air  on  the  Fahrenheit  Scale. 

perature  between 

RadiaUuK  Body 

f 

, 

and  the  Air. 

3- 

r^ 

t^ 

C«i° 

86° 

104" 

122^ 

140* 

158* 

I76« 

194' 

21;.»* 

Deg.  Fahr. 

18 

1  ^X)  1.07 

M^ 

Lift 

Lia 

1  3fi;i.^r 

l.fji^ 

1.7D 

1.85 

1.99 

2.15 

36 

1   IW 

I.OHIJC 

iM 

I  ;^ 

1,40  L52 

1  G8 

1  71^.912.06 

2.;J3 

54 

j.o; 

Kiti  \  *^) 

u-i^ 

i.^'i 

i.irj  i.&*J 

l.TO 

l.M-^  J  992.14 

2.31 

72 

i.j:: 

1.21J  l.aS 

I  :Hi 

1.40 

i.r^e  i.tii 

l-7ti 

l.at^^  07,2.23 

2.40 

90 

IJO 

Mi5  ,l,3t 

\r-iii 

K4*i 

1.58  K7i 

l.SW 

1..JH  J  15  2.33 

2.51 

106 

i/ij 

l.^il  l.^Jli 

I .  li 

1  ^ 

1.U.M.7B 

I  tft; 

■4.07  -  2812.42 

2.62 

136 

i.iSJ 

J.3fi  14^ 

K4M 

1  riO 

K70  1.04 

^J  OU 

^](^:  84  2.52 

2.72 

144 

i.a-j 

1  4>M.IS 

1  ru 

|.<35 

J.  OS 

i  *d4  ■:  44  2.64 

2.83 

162 

l.ffT 

1.^8  1^ 

i.i^} 

i.::j 

ijm.Hri 

e.]^ 

e.:M  J  54  2.74 

2.96 

180 

1.44 

L.Vll.BJ 

l.GH 

1hK[ 

1.SK.;,Mi1j,l';1;J  -J!;-  66  2.87 

8.10 

198 

K50 

l.tiill.tiy 

].75 

IhU 

^  aj  -.'ii 

■i..''^-:  .r.     r8  3.00 

8.24 

216 

1.5« 

i.ttyi  7U 

rtti 

I    !^7 

-J,IH-. 

B13.18 

3.38 

234 

L64 

l,77,l.H 

IJ*0 

'J.  Oil 

■J.*J^ 

03  3.'^ 

8.46 

252 

1. 71 

l.K.'il  0:i 

tJ.lW 

2  ir> 

,*  aa  : 

18  3.48 

8.70 

270 

l.7» 

I.»:ir^.O] 

J  OS 

■i.i"> 

3.44  J  ti^ 

i;.H4|;i.Oii.i.32  8.58 

3.87 

288 

1,80 

'i.mlt.  V2 

-  lJII 

:;.;i7 

J.5(PJ  7K 

■i9£*j3,i.^'J.S  50  3.77 

4.07 

806 

urn 

1'  Jji';!.-^:! 

■J  31 

2Aii 

li  tiU.J.SO 

A.  v^  :l  :r  ■;  66  3.95 

4.'X 

324 

2.07 

2.iiii,;;.33 

:i.42 

iixi 

J.HI  a  01 

•i  ■                 M;4.14 

4.46 

342 

3.17 

d.3J  2M 

i.t^ 

a.73 

2  1^5  3  10 

[h.»i4.34 

4.68 

360 

2.W7 

a,43*J,:^ 

'4M 

^.^Ij 

-t.raa  a-'i 

■  Jj     .     -   ,82  4.55 

4.91 

378 

2M 

a  &;*.^c^' 

2.70 

3  tii> 

i.'JI  ^.51 

:i;>  *a>s  !  42  4.77 

5.15 

886 

2  m 

;-'.75t'J  Kl 

;i  !« 

a.i:> 

ri4(i  ;i.{)k 

ij; 

4  X*H  1  64  5.01 

5.40 

414 

2.^n 

'i,H4^  1*5 

3.07 

3.ai 

:i.M>3.h7 

4.1;i 

1.4.S  4  87  5.26 

5.67 

482 

.,. 

2m  ^.  iQ 

ii.ya 

3,« 

H.7ti4.l0 

4.3,^ 

1.01  C.  18  5.88  6.01 

The  loss  of  heat  by  convection  appears  to  be  independent  of  the  nature  of 
the  surface,  that  is,  it  is  the  same  for  iron,  stone,  wood,  and  other  materials. 
It  is  different  for  Ixxiies  of  different  shape,  iiowever.  and  it  varies  with  the 

(Mjsition  of  the  body.  Thus  a  vertical  stenm-pipe  will  not  lose  so  much  beat 
>y  convection  as  a  horizontal  one  will;  for  rhe  air  heated  at  the  lower  part 
of  the  vertical  pipe  will  ri«e  alon^  the  surface  of  the  pipe,  protecting;  it  to 
some  extent  from  the  chilling  action  of  the  surrounding  cooler  air.  For  a 
similar  reason  the  shape  of  a  body  has  an  important  influence  on  the  result, 
those  bo<lles  losing  most  heat  whose  forms  are  such  as  to  allow  the  cool  air 
free  access  to  every  part  of  their  surface.  The  following  table  from  B«>x 
gives  the  number  of  heat  units  that  hoiizontal  cylinders  or  pipes  lose  by 
convection  per  square  foot  of  surface  per  hour,  for  one  degree  difference  in 
temperature  between  the  pipe  and  the  air. 

Hkat  Units  Lost  by  Convection  from  ITortzontal  Pipes,  per  Square 

Foot  of  Surk-acr  pkk  Hour,  for  a  Temperature 

Difference  op  1®  Fahr. 


External 

External 

External 

Dii  meter  of 

Heat  Units 

Diameter 

Heat  Unite 

Diameter 

Heat  Units 

ri\w 

Lost. 

of  Pipe 

Lost. 

of  Pipe 
In  inches. 

Lost. 

in  inches. 

in  indies. 

0.728 

7 

0.509 

18 

0.455 

0.6SJ6 

8 

0.498 

24 

0.447 

0.574 

9 

0.489 

86 

0.439 

0.544 

10 

0.482 

48 

0.484 

0.523 

12 

0.472 

•• 

The  loss  of  heat  by  convection  is  nearly  proportional  to  the  difference  in 
temperature  between  the  hut  body  and  the  air;  but  the  experiments  of 


CONDUCTIOK  AND  COKVECTION  OF  HEAT.        477 


Dnlong  and  P6clet  show  that  this  is  not  exactly  true,  and  we  mav  here  also 
resort  to  a  table  of  factors  for  correcting  the  results  obtaiued  by  simple 
proportion. 

Factobs  fob  Rkduction  to  Dulong's  Law  of  Conybotion. 


DiCTerence 

Difference 

Difference 

in  Temp, 
between  Hot 

in  Temp, 
between  Hot 

in  Temp. 

Factor. 

Factor. 

between 

Factor. 

Bodv  and 

Body  and 

Hot  Body 

Air. 

and  Air. 

18»F. 

0.94 

180»F. 

1.62 

842°  F. 

1.87 

»• 

1.11 

198« 

1.65 

860» 

1.90 

64» 

1.23 

216' 

1.68 

8780 

1.98 

7^^ 

1.80 

884* 

1.78 

896« 

1.94 

90O 

1.87 

262« 

1.74 

414» 

1.96 

loe* 

1.43 

270«» 

1.77 

4sa^ 

1.98 

126» 

1.49 

288«» 

1.80 

460° 

2.00 

144» 

1.58 

SOti' 

1.88 

468« 

2.02 

1<W« 

1.58 

824» 

1.86 

.... 

ExAXPLc  nf  THS  UsB  OF  THK  TABLES.— Reoalred  the  total  loss  of  heat  by 
both  radiation  and  conTection«  per  foot  of  length  of  a  steam-pipe  2  ll/$3 
in.  external  diameter,  steam  pressure  60  lbs.,  temperature  of  the  air  in  the 
room  68»  Fahr. 

Temperature  corresponding  to  00  lbs.  equals  807*:  temperature  difference 
=  307  -  68  =  239«. 

Area  of  one  foot  length  of  steam-pipe  =  2  11/82  X  3.1416  -h  12  =  0.614  sq. 
ft. 

Heat  radiated  per  hour  per  square  foot  per  decree  of  difference,  from 
table,  0.64. 

Badiation  loss  per  hour  by  Newton's  law  =  239o  X  .614  ft.  X  .64  =  93.9 
heat  units.  Same  reduced  to  conform  with  Duloni^'s  law  of  radiation:  factor 
from  table  for  lemi^erature  difference  of  239<*  and  temperature  of  air  06"  = 
1.93.    93.9  X  1.98  =  181.2  heat  units,  total  loss  by  radiation. 

Convection  loss  per  square  foot  per  hour  from  a  2  ll/S2-inch  pipe:  by  in* 
terpolation  from  tabic,  2"  =  .728.  8"  =  .0'J6,  2  11/32''  =  .693. 

Arva,  .614  X  .698  X289o  =  101.7  heat  units.  Same  reduced  to  conform  with 
Dulong's  law  of  couTection:  101.7  X  1-73  (from  table)  =  175.9  heat  units  per 
hour.  Total  loss  by  radiation  and  convection  =  181.2  -f  176.9  =  357.1  heat 
units  per  hour.  IjOrs  per  degree  of  difference  of  temperature  per  linear 
f<H»t  of  pipe  per  hour  =  357.1  -»-  239  =  1.494  heat  units  =  2.433  per  sq.  ft. 

It  is  nut  claimtKl,  says  The  Locomotive,  that  the  results  obtained  by  this 
method  of  calculation  are  strictly  accurate.  The  experimental  data  are  not 
sufficient  to  allow  us  to  compute  the  heat-loss  from  steam-pipes  with  any 
great  desrree  of  refinement:  yet  it  is  believed  that  the  results  obtained  as 
indicated  above  will  be  sufficiently  near  the  truth  for  most  purposes.  An 
experiment  by  Prof.  Ordway,  in  a  pipe  2  11/32  in.  diam.  under  the  above 
conditions  (Trans.  A.  S.  M.  E  ,  v.  73),  showed  a  condensation  of  steam  of  181 
grammes  per  hour,  which  is  equivalent  to  a  loss  of  heat  of  358.7  heat  units 
per  hour,  or  within  half  of  one  per  cent  of  that  given  by  the  above  calcula- 

According  to  different  authorities,  the  quantity  of  heat  given  off  by  steam 
and  hot-water  radiators  in  ordinary  practice  of  heating  of  buildings  by 
direct  radiation  varies  from  1.8  to  about  3  heat  units  per  hour  per  square 
foot  per  degree  of  difference  of  temperature. 

The  lowest  figure  is  calculated  from  the  following  statement  by  Robert 
Briggs  in  hl»  paper  on  ''American  Practice  in  Warming  Buildings  by 
Steam  "  (Proc.  Inst.  C.  E.,  1882,  vol.  Ixxf):  "  Each  100  sq.  ft.  of  radiating 
surface  will  give  off  3  Fahr.  heat  units  per  minute  for  each  degree  P.  of  dif- 
ference in  temperature  between  the  radiating  surface  and  the  air  in  which 
it  Ir  fxposeil." 

The  figure  8  1/2  heat  units  is  given  by  the  Nason  Manufacturing  Company 
in  their  catalogue,  and  2  to  2  1/4  ar»»  given  by  many  recent  writers. 

For  the  ordinanr  temperature  difference  in  low-pressure  steam- heating, 
say  212»  -  70*'  =  142'  F.,  1  lb.  steam  condensed  from  212°  to  water  at  the 


478  HEAT. 

same  temperature  Rfres  up  M8.7  heat  units.  A  Ions  of  H  heat  unite  per  «q. 
ft.  per  hour  per  desrree  of  difference,  under  thene  conditions,  is  equivalent 
to  2  X  142-+-905  =  0.8  lbs.  of  steam  condensed  per  hour  per  sq.  ft.  or  heating 
surface.    (See  also  Heatjnff  and  Veatilatioii .  > 

TfrnnamlMilon  of  Heat  tbroutfli  l¥alla,  ate.,  of  BuUdlnoa 
(Nason  Manufacturing  Co.).  (See  also  Heating  and  Ventilation.)— Heat 
has  the  remarkable  property  of  passing  through  moderate  thicknesses  of  air 
and  gases  without  appreciable  loss,  so  that  air  Is  not  warmed  by  radiant 
heat,  but  by  contact  with  surfaces  that  have  absorbed  the  radiation. 

PowKRs  or  DirrgREKT  Substamcbb  fob  TBAMsmmNa  Heat. 

Window-glass 1000       Bricks,  rough SOOto  8S0 

Oak  or  walnut 66       Bricks,  whitewashed....  900 

'Whitepine 80       Granite  or  slate 2S0 

Pitch-pine 100       Sheet  iron lOSOtolllO 

Lath  or  plaster ,     75  to   100 

A  square  foot  of  glass  will  cool  l.$70  cubic  feet  of  air  from  the  tempera- 
ture inside  to  that  outside  per  minute,  and  outride  wail  surface  is  generally 
estimated  at  one  fifth  of  the  rate  of  elass  In  cooling  eflfect. 

Box,  in  his  "  Practical  Treatise  on  Heat,"  gives  a  table  of  the  conducting 
powers  of  materials  prepared  from  the  experiments  of  P6clet.  It  given  the 
quantity  of  heat  in  units  transmitted  per  square  foot  per  hour  by  a  plate  1 
inch  in  thickness,  the  two  surfaces  differing  in  temperature  1  degree: 

Fine-grained  gray  marble 88.00 

Coarse-grained  white  marble.. 88.4 

Stone,  calcareous,  fine ...<..  16.7 

Stone,  calcareous,  ordinary 18.68 

Baked  olay,  brickwork  4.88 

Brick-dust,  sifted 1.88 

Hood,  in  his  '*  Warming  and  Ventilating  of  Buildings."  p.  848,  ffivea  the 
results  of  M.  Pepretz,  which,  placing  the  conducting  power  of  marble  at  1.00, 
give  .468  as  the  value  for  firebrick. 

THEBnODTNAniCS. 

Tbennodynamlea,  the  science  of  heat  considered  aa  a  form  of 
energy,  is  useful  in  advanced  studies  of  the  theory  of  stesm,  gas,  and  air 
•ngtnes,  refrigerating  machines,  compressed  air.  etc.  The  method  of  treat- 
ment adopted  by  the  standard  writers  Is  severely  mathematical,  involvinfc 
constant  application  of  the  calculus.  The  stunent  will  find  the  subject 
thorougly  treated  in  the  recent  works  by  Rontgen  (Dubois^s  tmnelatioo). 
Wood,  and  Peabody. 

First  liftiv  ofTlieniiodjrnaiiilea.— Heatand  mechanical  energy 
are  mutually  convertible  in  the  ratio  of  about  778  foot-pounds  f or  the  Britiith 
thermal  unit.  (Wood.)  Heat  is  the  living  force  or  vu  i;<vodue  to  certain 
molecular  motions  of  the  molecules  of  bodies,  and  this  living  force  may  be 
stated  or  measured  in  units  of  heat  or  In  foot-pounds,  a  unit  of  heat  in 
British  measures  being  equivalent  to  77iS  [778]  foot-pounds.  (Trowbridge, 
Trana.  A.  S.  M.  E.,  vii.  727.) 

8«eond  liftw  of  Tliennodyitaiiiflca.— The  second  law  has  by  dif- 
ferent writers  been  stated  in  a  variety  of  ways,  and  apparently  with  Ideas 
so  diverse  as  not  to  cover  a  common  principle.    (Wood,  Therm.,  p.  888.) 

It  Is  impossible  for  a  self-acting  maonlne,  unaided  by  any  external  agency 
to  convert  heat  from  one  body  to  another  at  a  higher  temperature.  (Ciau- 
aius.) 

If  all  the  heat  absorbed  be  at  one  temperature,  and  that  rejected  be  at 
one  lower  temperature,  then  will  the  heat  which  is  transmuted  into  work  be 
to  the  entire  heat  absorbed  in  the  same  ratio  as  the  difference  between  the 
absolute  temnerature  of  the  source  and  refrigerator  Is  to  the  absolute  tem- 
perature of  tiie  source.  In  other  words,  the  second  law  is  an  exprsasion  for 
the  effloienoy  of  the  perfect  elementary  engine.    (Wood.) 

The  living  force,  or  vis  viva,  of  a  booy  (called  heat)  is  always  proportional 
to  the  absolute  temperature  of  the  body.    (Trowbridge.) 
O   —  O         T  —  T 

The  expression  -'^^-^  =  — ^  «. — ~  may  be  called  the  symbolical  or  al- 
gebraic enimclation  or  the  secona  law,— the  law  which  limits  the  efflclency 
of  heat  engines,  and  which  does  not  depend  on  the  nature  of  the  working 
medium  employed.    (Trowbridge.)      Qi  and  Ti  s  quantity  and  absolute 


PHYSICAL  PROPERTIES  01  GASB&  479 

tempermtore  of  the  heat  rsoelTed,  Q^  and  T^  »  quantity  and  abaolate  tai»> 
peratore  of  tlw  heat  nejeoted. 

The  expression  -^-^, — '  represents  the  efBciencj  of  a  perfect  beat  engine 
•I  I 
which  receives  all  its  heat  at  the  absolute  temperature  Ti,  and  rejects  heat 
at  the  temperature  T^,  converting  into  worlc  the  difference  between  the 
quantity  received  and  rejected. 

ExAMPLB.— What  is  the  efficiency  of  a  perfect  heat  engine  which  receives 
heat  at  888*  F.  (the  temperature  of  steam  of  900  lbs.  gauge  pressure)  and 
rejects  heat  at  100*  F.  (temperature  of  a  condenser,  pressure  X  lb.  above 
vacuum). 


+  459.g-(100-f4«)Jg)  .  g.^  _^rt_ 
888  +  490:8  ~  "*•  neany. 

lis  efflolency  can  oevar  be  attftlned, 

^ of  heat  received  Into  the  cylinder  l  , . 

}Dto  the  condenser  is  not  all  converted  into  work,  much  of  it  being  Inst  by 
radiation,  leakage,  etc.  In  the  steam  engine  the  phenomenon  of  cylinder 
condensation  also  tends  to  reduce  the  efficiency. 


In  the  aotual  engine  this  efflolency  can  oevar  be  attained,  for  the  difference 
between  the  quantity  of  heat  received  into  the  cylinder  and  thai  rejected 


FHYBICAIi  PROPBBTJE8  OF  GABBS. 


(Addltkmal  matter  on  this  subject  will  be  found  under  Heat,  Mr,  Gas,  and 
St«>am.) 

When  a  mass  of  gas  is  enclosed  in  a  vessel  it  exerts  a  pressure  against  tba 
walla.  This  pressure  is  uniform  on  every  square  inch  of  the  surface  of  the 
vessel;  aUo,  at  any  point  In  the  fluki  mass  Uie  prsssure  lathe  same  in  every 
direotion. 

In  small  vessels  contalnining  gases  the  increase  of  pressure  due  to  weight 
may  be  neglected,  since  all  gases  are  w^xj  light;  but  where  liquids  are  coup- 
neriied,  the  increase  in  pressure  due  to  their  weight  must  always  be  taken 
Into  account. 

Sxpanalon  of  GAaea,  JRIanrlotte'a  IfAiv.— The  volume  of  a  gas 
diuiiuwbes  in  the  same  ratio  as  the  pressure  upon  it  is  increased. 

This  law  is  by  experiment  found  to  be  very  nearly  true  for  all  gases,  and 
is  known  as  Boyle*s  or  Mariotte's  law. 

If  P  0  pressure  at  a  voluma  v,  and  pi  «>  pressure  ftt  a  volume  «i,  p^Vi  m 

pp;  Pi  =  — p;  pv  =  ft  constant. 

The  constant,  (7,  varies  with  the  temperature,  everything  else  remaininip 
Utesamo.' 

Air  oomprsesed  by  a  pressure  of  seventy-flve  atmospheres  has  a  volume 
about  SjC  less  than  that  computed  from  Boyle*8  law,  but  this  is  the  greatest 
diverxenee  that  is  found  below  180  atmospheres  pressure. 

liftvr  of  Charles.— The  volume  of  a  perfect  gas  at  a  constant  pressure 
is  proportional  to  its  absolute  temperature.  If  v^  be  the  volume  of  a  gas 
at  s2*  r.,  and  Vx  the  volume  at  any  other  temperature,  t^  then 

''^  =^  ^'V     401.4     J '       «i  =  M  +  19iTJ^ 
or       «»  =  [!  +  O.flO0O86(f g  -  92?)]v^ 
If  the  pressure  also  ohangs-  frompo  to  pt, 


p,/^+45M\ 
•px^    401.8     /• 


Vx  s=    „ 

"Pi 

The  Oenaltlea  of  the  elementary  gases  are  simply  proportional  to 
their  atomic  weifrhTs.  The  density  of  a  compound  gas,  referred  to  hydrogen 
ssi,  is  one-half  its  moleculsr  weight ;  thus  the  relative  density  of  CO.  is 

Aroipadro'a  I^a^r.— Equal  volumes  of  all  gases,  under  the  same  oouo 
ditions  of  temperature  and  pri^sure.  contain  the  same  number  of  molecules. 

To  find  the  weight  of  a  gas  In  pounds  per  cubic  foot  at  3;2*>  F..  multiply  half 
the  molecular  weight  of  the  gas  by  .00550.    Thus  1  cu.  ft.  marsh-gas,  CH^ , 
«"  M(ia  +  4)  X  .OOUO  9  .0447  lb. 


480  PHYSICAL  PROPERTIES  OF  GASES. 

Wlien  a  certain  volume  of  hydrogen  combines  with  one  lialf  its  yolume  of 
oxygen,  there  is  produced  an  amount  of  water  vapor  which  will  occupy  the 
same  volume  as  that  which  was  occupied  by  the  hydrogen  gas  when  at  the 
same  temperature  and  pressure. 

SatUimtfon-polni  of  Vftpom.— A  vapor  that  is  not  near  the  satura- 
tion-point behaves  like  a  gas  under  changes  of  temperature  and  pressure; 
but  if  it  is  sufflcientiy  compressed  or  cooled,  it  reaches  a  point  where  it  be- 
gins to  condense:  it  then  no  longer  obeys  the  same  laws  as  a  gas,  but  its 
f>re8sure  cannot  be  increased  by  diminishing  the  size  of  the  vessercontainiug 
t,  but  remains  constant,  except  when  the  temperature  is  changed.  The 
only  gas  that  can  prevent  a  liquid  evaporating  seems  to  be  its  own  vapor. 

iMlton's  M^rnvr  ofOftseona  Pressures*— Every  portion  of  a  mass 
of  gas  incloMcd  in  a  vessel  contributes  to  the  pressure  against  the  sides  of 
the  vessel  the  same  amount  that  it  would  have  exerted  by  itself  had  no 
other  gas  been  present. 

niztures  of  Tftpors  and  Gases*— The  pressure  exerted  against 
the  Interior  of  a  vessel  by  a  given  quantity  of  a  perfect  gas  enclosed  in  it 
is  the  sum  of  the  pressures  which  any  number  of  parts  into  which  such  quan- 
tity might  be  divided  would  exert  separately,  if  each  were  encloited  in  a 
vessel  of  the  same  bulk  alone,  at  the  same  temperature.  Although  this  law 
is  not  exactly  true  for  any  actual  gas,  it  is  very  nearly  true  for  many.  Thus 
if  0.0607%  lb.  of  air  at  SS"  F.,  being  enclosed  in  a  vessel  of  one  cubic  foot 
capacity,  exerts  a  pressure  of  one  atmosphere  or  14.7  pounds,  on  each  square 
inch  of  the  interior  of  the  vessel,  then  will  each  additional  0.060728  lb.  of  air 
which  is  enclosed,  at  32**,  in  the  same  vessel,  produce  very  nearly  an  addi- 
tional atmoibphere  of  pressure.  The  same  law  Is  applicable  to  mixtures  of 
gases  of  different  kinds.  For  example,  0,12344  lb.  of  carbonic-acid  gas,  at 
iS",  being  enclosed  in  a  vessel  of  one  cubic  foot  in  capacity,  exerts  a  pressure 


of  one  atmosphere;  consequently,  if  0.080788  lb.  of  air  and  0.12344  lb.  of 
lie  acid,  mixed,  be  enclosed  at  the  temperature  of  88°,  in  a  Tessel  of 


carbonic  a 


one  cubic  foot  of  capacity,  the  mixture  will  exert  a  pressure  of  two  atmo» 
pheres.    As  a  seoona  example:  Let  0.0807V8  lb.  of  air,  at  SIS",  be  endosed  in 
a  vessel  of  one  cubic  foot;  it  will  exert  a  pressure  of 
S12  +  459.2     ,«^    , 

32  ■!■  459.2  =  '-^  atmospheres. 

LetO.08797  lb.  of  steam,  at  S12«,  be  enclosed  in  a  vessel  of  onectibio  foot;  it 
will  exert  a  pressure  of  one  atmosphere.  Consequently,  if  0.080788  lb.  of  air 
and  0.08797  lb.  of  steam  be  mixed  and  enclosed  together:  at  218^,  in  a  vessel  of 
one  cubic  foot,  the  mixture  will  exert  a  prrasure  of  2.806  atmospheres.  It  is 
a  common  but  erroneous  practice,  in  elementary  books  on  physics,  to  de. 
scribe  this  law  as  constituting  a  difference  between  mixed  and  homogeneous 
gases;  whei'eas  it  is  obvious  that  for  mixed  and  homogeneous  gases  the  Utw 
of  pressure  is  exactly  the  same,  viz.,  that  the  pressure  of  the  whole  of  a 
gaseous  mass  is  the  sum  of  the  pressures  of  all  Us  parts  This  is  one  of  thfi 
bkws  of  mixture  of  gases  and  vapors. 

A  second  law  is  that  the  presence  of  a  foreign  gaseous  substance  in  con 
tact  with  the  surface  of  a  solid  or  liquid  does  not  affect  the  density  of  the 
vapor  of  that  solid  or  liquid  unless  there  is  a  tendency  to  chemical  com- 
bination between  the  two  substancea  in  which  case  the  density  of  the 
vapor  is  slifrhtly  increased.    (Rankine,  S.  E.,  p.  280.) 

Vlovr  of  Gases*— By  the  principle  of  the  conservation  of  energy.  It  may 
be  shown  that  the  velocity  with  which  a  gas  under  pressure  will  escape  into 
a  vacuum  is  inversely  proportional  to  the  square  root  of  it.8  density;  that  is, 
oxygen,  which  is  sixteen  times  as  heavy  aa  nydrogen,  would,  under  exactly 
the  same  circumstances,  escape  through  an  opeuing  only  one  fourth  as  Cast 
as  the  latter  gas. 

Absorption  of  Gases  by  liflqulds*— Many  gases  are  readily  ab- 
sorbed by  water.  Other  liquids  also  possess  this  power  in  a  greater  or  less 
d^ree.  Water  will  for  example,  absorb  its  own  volume  of  carbonic-acid 
gas,  480  times  its  volume  of  ammonia.  2^  times  its  volume  of  chloriue,  and 
only  about  1/80  of  its  volume  of  oxygen. 

liie  weight  of  gas  that  is  al)Borb€Kl  by  a  given  volume  of  liquid  is  propor- 
tional to  the  pressure.  But  as  the  voluma  of  a  mass  of  eas  is  less  as  the 
pressure  is  greater,  the  volume  which  a  given  amount  of  liquid  can  absorb 
at  a  certain  temperature  will  l)e  constant,  whatever  the  pressure.  Water, 
for  example,  can  absorb  its  own  volume  of  carbonic-acid  gas  at  atmospheric 
pressure;  it  will  also  diKsolvu  its  own  volume  if  the  pressure  is  twice  as 
great,  but  in  that  case  the  gas  will  be  twice  as  dense,  and  consequently  twice 
the  weight  of  gas  is  dissolved. 


FBESSURE  OF  THE   ATMOSPHERE. 


481 


AIB. 

Propertlea  of  Alr.>-Alr  Is  a  mechanical  mlxtare  of  the  gaaes  oxygen 
and  nitro|?en ;  :i0.7  parts  O  and  T0.3  parts  N  by  Tolume,  88  parts  O  and  77  parts 

ne  weurht  of  pure  air  at  32"  F.  and  a  barometric  pressure  of  29.99  inches 
of  mercury,  or  14.0968  lbs.  per  so.  in.,  or  3116.8  lbs.  per  sq.  ft.,  is  .OBff728  lb.  per 
cubic  foot.    Volume  of  1  lb.  =s  1S.387  en.  ft.    At  any  other  temperature  and 

barometric  pressure  ito  weight  in  lbs.  per  cubic  foot  is  IT  =  ?j^L£-^, 

where  B  =  heiirht  of  the  barometer.  Tss  temperature  Fahr.,  and  1.8868  3 
weiffbt  in  lbs.  of  450.3  c.  ft.  of  air  at  0"  F.  and  one  inch  barometric  pressars^ 
Air  expands  1/491.2  of  its  volume  at  8a<»  P.  for  every  increase  of  1»  F.,  and 
its  volume  varies  inversely  as  the  pressure. 


▼olnM,  Henplfr,  and  PreMOM  of  Air  at  Yartoiui 

Temperatnres,    (D.  K.  Clark.) 

Volume  at  Atmos. 

Pressure  at  Constant 

Pressure. 

Density,  lbs. 
per  Cubic  Foot  at 

Volume. 

Fishr. 

Cable  Feet 
in  1  lb. 

Compara- 
tlve  Vol. 

Lbfl.  per 
Sq.K. 

Compara- 
tive Pres. 

0 

11.588 

.881 

.066881 

12.96 

.881 

82 

12.887 

.048 

.080728 

13.86 

.943 

40 

12.686 

.968 

.079439 

14.06 

.958 

60 

13.840 

.977 

.077884 

14.86 

.977 

es 

18.141 

1.000 

.076097 

14.70 

1.000 

w 

18.842 

1.015 

.074960 

14.92 

1.015 

80 

13.508 

1.084 

.073565 

15.21 

1.034 

90 

18.845 

1.064 

.O7%280 

15.49 

1.054 

100 

14.096 

1.073 

.070942 

15.77 

1.073 

110 

14.844 

1.092 

.009721 

16.06 

1.092 

120 

14.602 

1.111 

.068500 

16.33 

1.111 

180 

14.840 

1.180 

.067361 

16.61 

1.130 

140 

15.100 

1.149 

.066221 

16.89 

1.149 

ISO 

15.861 

1.168 

.065155 

17.19 

1.168 

100 

15.608 

1.187 

.064088 

17.50 

1.187 

170 

15.864 

1.206 

.068089 

17.76 

1.206 

180 

16.106 

1.226 

.062090 

18.02 

1.226 

900 

16.606 

1.264 

.oeoaio 

18.58 

1.264 

SIO 

16.860 

1.883 

.059818 

18.86 

1.283 

»9 

16.010 

1.287 

.060135 

16.02 

1.887 

Tlio  Aix^maJiomeCer  consists  of  a  long  vertical  i^lass  tube,  closed  at 
the  upp^r  end,  open  at  the  lower  end,  containing^  air,  provided  with  a  scale, 
and  immersed,  moug  with  a  thermometer,  in  a  transparent  liquid,  such  as 
water  or  oil,  contained  iu  a  strong  cylinder  of  glass,  which  communicatee 
with  the  vessel  in  which  the  pressure  is  to  be  ascertained.  The  scale  shows 
the  volume  occupied  by  the  air  in  the  tube. 

JjBt  v«  be  that  volume,  at  the  temperature  of  32«  Fahrenheit,  and  mean 
pressure  of  the  atmosphere,  p«;  let  Vj  be  the  volume  of  the  air  at  the  tem- 
perature f,  and  under  the  absolute  pressure  to  be  measured  pi ;  then 

(f4-459.g')Poiy, 
491. «•  t>, 

Pressure  of  the  Atmospbere  mt  Dilftorent  AlUtade«« 

At  the  sea-level  Uie  pressure  of  the  air  is  14.7  pounds  per  square  inch;  at 
S4  of  a  mile  above  the  sea-level  it  is  14.02  pounds;  at  H  mile,  13.33;  ati£ 
--     19.66;  at  t  mile,  12.0b{;  at  IM  mile,  1142;  at  IH  mile,  10.68;  aod  atl 


Pi' 


482 


AIB. 


miles,  0.80  pounds  per  square  Inch.  For  a  rougrh  approximation  we  may 
assume  that  the  pressure  decreases  ^  pound  per  square  inch  for  everj  1000 
feet  of  ascent. 

It  is  calculated  that  at  a  height  of  about  8U  miles  above  the  sea-level  the 
weight  of  a  cubic  foot  of  air  is  only  one  half  what  it  is  at  the  surface  of  the 
•arta,  ai  aoveii  miles  only  on*  fourth,  at  fourteen  nfles  only  one  aizteemh, 
at  4wenty>one  miles  only  onn  siztr.fourih«  and  at  a  height  of  over  forty- 
flve  miles  it  becomes  so  attenuated  as  to  have  no  appreciable  welgbi. 

The  preasore  of  the  aUnospbera  increases  with  the  depth  of  iiiafts,  eqnal 
to  about  one  Inch  rise  in  the  barometer  for  each  000  feet  Increase  la  depth: 
this  migr  be  taicen  as  a  rough-and-ready  rule  for  asoertaining  the  depta  of 
sliafts. 

Praaanre  of  tlie  AtmoapMare  par  Square  Incb  and  per 
8%  wra  Foot  at  Varlana  Beadlnsa  of  the  Barametar. 

RnuB.— Barometer  in  inches  x  .4006  s  pressure  per  square  inch;  pnBssure 
per  square  inch  x  144  a  pressure  per  square  foot. 


Barometer. 

Pressure 

PraiBiWB 

Pressura 

Pleasure 

per  Sq.  In. 

perSq.Ft. 

per  Sq.  In. 

per  Sq.  Ft. 

In. 

lbs. 

lbs.* 

In. 

lbs. 

lbs.* 

88.00 

18.74 

1978 

90.75 

14.00 

9109 

98.95 

18.80 

1006 

80.00 

14.79 

9110 

98.60 

18.06 

9018 

80.95 

14.64 

9186 

98.79 

I4.n 

9031 

80.50 

14.06 

9154 

90.00 

14.38 

9040 

80.75 

15.00 

8179 

90.95 

14.85 

9060 

81.00 

15.91 

9100 

90.60 

14.47 

9068 

*  Decimals  omitted. 
For  lower  pressures  see  table  of  the  Properties  of  Steam. 

roaietrle  Raadlnga  eorreapondlng  "with  miTaraat 
Aliliadaa,  tn  Francb  and  EntfUan  Meaaarea. 


Read- 

Reading 

Reading 

Beading 

Altl- 
tude. 

ing  of 
Earom^ 

Altitude. 

of 
Barom- 

Alti. 
tude. 

of 
Barom- 

AlUtude. 

of 
Barom- 

eter. 

eter. 

eter. 

eter. 

meters. 

mm. 

feet 

inches. 

meters. 

mm. 

feet. 

Inches. 

0 

769 

0. 

80. 

1147 

660 

8768.9 

95.06 

91 

760 

68.0 

90.09 

1260 

650 

4168.8 

25.59 

197 

750 

416.7 

90.68 

1393 

640 

4868.8 

95.10 

984 

740 

90.13 

1519 

630 

4088.1 

94.80 

34a 

780 

1122.1 

88.74 

1647 

690 

5406.9 

84.41 

453 

790 

1486.2 

28.85 

1777 

610 

5830.9 

94.01 

564 

710 

1850.4 

97.05 

1009 

600 

6943. 

88.68 

678 

700 

ae24.5 

27.55 

2048 

590 

6702.0 

88.28 

708 

600 

9599.7 

27.16 

2180 

580 

7159.4 

89.8S 

900 

680 

2062.1 

26.77 

2318 

570 

7605.1 

89.44 

1027 

670 

8360.5 

96.38 

9460 

660 

8071. 

88.04 

Ijaralllnfl:  by  tbe   Barometer  and   by  BoUlnir  ITater. 

(TrAiitwine.)->Maiiy  circuniKtanoes  combine  to  render  the  results  of  tliis 
kind  of  levelling  unreliable  whore  great  accuracy  is  required.  It  Is  dlfflcult 
to  read  off  from  an  aneroid  (the  kind  of  barometer  usually  employed  for 
engineering  purposeR)  to  within  from  two  to  five  or  six  feet,  depending  on 
its  size.  The  moisture  or  dryness  of  the  air  affects  the  results;  also  wuids, 
the  vicinity  of  mountains,  and  the  daily  atmospheric  tides,  which  oause 
incessant  and  irregnlai-  fluctuations  in  the  barometer.  A  barometer  hang- 
ing quietly  in  a  room  will  often  vary  1/4  of  an  inch  within  a  few  hours,  cor- 
reiiponding  to  a  difference  of  elevation  of  nearly  100  feet.  No  formula  can 
possibly  be  devised  that  shall  embraoe  these  sources  of  error. 


MOISTURE  IN  THE  ATMOSPHERE. 


488 


T«  Find  the  lHll^reii«e  In  Altltade  of  Two  Plaees*— Take 

from  the  table  the  aliltudee  opMeite  to  Uie  iwo  builiiie  temperatures,  or  to 
the  two  barometei  readinKS.  Bobtraot  the  one  oppoute  the  lower  readiii|r 
from  that  opposite  the  upper  rsadlnjr.  The  remainder  will  be  the  required 
height,  ns  a  rough  approximation.  To  oorrect  this,  add  together  the  two 
thermoro*'(er  readinKS,  and  divide  the  sum  by  2,  for  their  mean.  From 
table  of  corrections  for  temperature,  take  out  the  number  under  this  mean. 
Multiply  the  approximate  height  just  found  by  this  uumber. 

At  iV*  P.  pure  water  will  boil  at  1*  lees  of  temperature  for  an  average  of 
abriiit  KO  feet  of  elevation  above  sea-level,  up  to  a  height  of  1/9  a  mile.  At 
the  height  of  1  mile,  1*  of  bulling  temperature  will  correepond  to  aiKHit  MX) 
feel  of  elevation.  In  the  table  the  mean  of  the  temperatures  at  the  two 
staiioiia  is  assumed  to  be  SS^F.,  at  which  no  correction  for  temperature  is 
necesHary  In  using  the  table. 


liii 

h 

w 

m 

1^ 

lil< 
ih^ 

its 

1^ 

w 

IW 

18.79 

i5,sn 

196 

81.71 

8,481 

906 

27.78 

2,068 

IS5 

17.16 

14,649 

197 

28.17 

7.988 

908.5 

28.00 

1,809 

186 

17.54 

14,075 

196 

28.64 

7.881 

809 

28.29 

1,689 

187 

17.« 

18,498 

199 

88.11 

6.848 

909.5- 

28.66 

1,890 

188 

18.83 

19,984 

900 

88-.9 

6.804 

810 

28.86 

1,085 

189 

18.« 

18,887 

801 

8<.()R 

6,764 

810.5 

29.16 

764 

190 

19.18 

11,799 

808 

81.58 

6,885 

811 

29.48 

618 

191 

19.54 

11.848 

803 

25.08 

4,69r 

811.5 

29.71 

855 

199 

1996 

10,685 

904 

28.59 

4,109 

218 

30.00 

8.L.«0 

198 

S0.89 

10,187 

805 

26.11 

8.648 

21J?.5 

S0.80 

-861 

191 

«0M 

9,679 

806 

26.64 

8,115 

813 

80.69 

-611 

195 

81.90 

9,061 

207 

27.18 

8,689 

OORRBCnONS  FOB  TUfPXEATUIUi. 


Mean  temp.  F.  in  Shade.  01  10-  80*1  80«»    4'  ^     60«  I  60«  |  7U«  leO*    jOO»    I  100»| 
Mnliiply  by ^938  1.954  .975  .996  1.016  1.0^!l.058|l.079!l.l00ll.l2l|l.l4g| 


Hoflvture  in  th.e  Atmoapliere*— Atmospherio  air  always  contains 
a  small  quantity  of  carbonic  aciil  (see  Ventilation,  p.  b&<)  and  a  vai-vfng 
quantity  of  aqueous  vapor  or  moisture.  The  relalive  humidity  of  tiie  air  at 
aiiy  time  is  the  percentage  of  moisture  contained  In  it  as  coinpai-ed  with  ihe 
amount  it  is  capable  of  holding  at  the  same  temperature. 

The  degree  of  saturation  or  relative  humidity  of  the  air  la  detei-ralned  by 
the  use  of  the  dry  and  wet  bulb  thermometer.  The  degree  of  sai  urntion  for 
a  number  of  different  readings  of  the  thermometer  I.s  given  in  the  following 
table,  condensed  from  one  published  by  the  U.  S.  Weather  Bureau,  1^97: 

RSULTXVB  HUMIDITT,  I*BR  CeKT. 


11^ 


40 


DtfTenfuee  between  the  Dry  and  Wt*t  Thermomolers,  I>Hf»,  F. 


IS 


1^14 


I5|iri,.7ll»|  lo|2(lj'Jl|i^-Jt!»[:ij|'.'c[i.>^i  m 


B^latlve  Humtdft^H  gfvturatioa  Lt- latf  IIX). 


0-*  fH;:tj|«g| 


m 

iO 

m 


S;i*>74 
DOiWiBI 


S7  in ' 

:;ii6H' 


Sf  94!  90 1 86 

97  viiv^m 


75- 
7S 

HO' 


solti 

4i'M 


45  38 

,^15  SO 

7-J.I» 
7:i  7T  m 
777^171 

lT8'7fll77i 

'rtft|r?Tn'7 

I8^l7fl|77|7:> 


S7|'^.;  iflU 

57Mrn  K  *^ 

rtTft.'iuvi|(ii)fi7 
Tti  +J7  tiri  rt^  (lit 
rH,ri:*wlflii  M 


i-  1.' 


ivu\ 


I 


13!1'V 


P   8 
17  13 

?ioa7 

i^j  Si 


484 


AIB. 


l¥elshtB  of  Air,  Tapor  of  VTrnter,  and  8atarat«d  BElxtvrea 

of  Air  and  Vapor  at  Different  Temperatures,  under 

tbe  Ordinary  Atmospheric  Prewinre  of  39.931 

Incite*  of  iVIercary. 


11^ 

HI 

^ 

Mixtures  of  Aib  Saturatbo  with  Vapor. 

>9 

W*>iKht  of  Cubic  Foot  of  the 

L 

FiTijiy  of 
tli^  Air  in 

of  Air  and 

Vapor, 
Inches  of 
Mercury. 

Sllxture  of  Air  and  Vapor. 

weight 

Weljfht 

of  the 

Air,  lbs. 

Weight 
of  the 
Vapor, 
pounds. 

Total 
WVhtof 
Mixture, 
pounds. 

Vapor 
mixed 
witfa  1  lb. 
of  Air. 
pounds. 

o* 

.0664 

.044 

29.8T7 

.0668 

.000079 

.088879 

.00092 

12 

.0842 

.074 

29  849 

.0840 

.000130 

.084180 

.00155 

22 

.0624 

.118 

29.803 

.08J1 

.000202 

.082802 

.00246 

32 

.0807 

.181 

29.740 

.0802 

.000304 

.080504 

.00379 

42 

.0791 

.267 

29.654 

.0784 

.000440 

.078840 

.00561 

62 

.0776 

.888 

29.583 

.0766 

.000627 

.077227 

.00619 

«2 

.0761 

.566 

29.865 

.0747 

.000681 

.075581 

.01179 

72 

.0747 

.785 

29.136 

.QTsnr 

.001221 

.073921 

.01680 

82 

.0788 

1.092 

28.829 

.0706 

.001667 

.072267 

.02861 

»2 

.07iO 

1.501 

28.420 

.0684 

.002250 

.O"!  0*1 17 

.08289 

102 

.0707 

2.086 

27.885 

.0659 

.002997 

.068897 

.04547 

112 

.0604 

a.781 

27.190 

.0631 

.008946 

.067046 

.06253 

122 

.06»i 

8.621 

26.300 

.0599 

.005142 

.065042 

.08684 

182 

.0671 

4.752 

25.169 

.0664 

.006639 

.068039 

.11771 

142 

.0660 

6.166 

28.756 

.0524 

.008478 

.060873 

.16170 

162 

.0649 

7.980 

21.991 

.0477 

.010716 

.068416 

.22465 

162 

.0688 

10.099 

19.822 

.0428 

.018415 

.066716 

.31713 

172 

.0688 

12.758 

17.163 

.0860 

.016682 

.062689 

.46388 

182 

.0618 

15.960 

13.961 

.0288 

.020686 

.049336 

.n80O 

192 

.0609 

19.828 

10.098 

.0206 

.025142 

.046642 

1.22648 

202 

.0600 

24.450 

5.471 

.0109 

.080545 

.041446 

2.80230 

212 

.0591 

29  921 

0.000 

.0000 

.036820 

.086820 

Infinite. 

The  weiglit  in  lbs.  of  the  vapor  mixed  with  100  lbs.  of  pura  air  at  any 
given  temperature  and  pressure  is  given  by  the  formula 

62.8  X  E       29.98 
29.92- jB  ^      p  • 

where  E  =s  elastic  force  of  the  vapor  at  the  given  temperature.  In  Inches  of 
mercury;  p  s=  ab.^tolute  pressure  in  inches  of  mercury,  =  29.92  for  ordinary 
at  m ospheric  pressu re . 
8peclflc  Heat  of  Air  at  Constant  Volume  and  at  Constant 

PsesBU  re.— Volume  of  1  lb.  of  air  at  32®  b\  and  pieKsure  of  14  7  lbs.  per  nq. 
in.  =  ]2.3tj7  cu.  ft.  =  a  column  1  sq.  ft.  area  X  12.38t  ft.  high,  fiaising  temper- 
ature 1«  F.  expands  it  rr^,  or  to  12.4122  ft.  high— a  rise  of  .02522  foot. 

Woric  done  s  8116  lbs.  per  sq.  ft.  X  .02382  =  68.87  foot-pounds,  or  5S.S7-«-778 
B  .0686  heat  units. 

The  specific  heat  of  air  at  constant  pressure,  according  to  Regnault,  Is 
0  2'175;  but  this  includes  the  wortc  of  expansion,  or  .0686  heat  units;  hence 
the  speciflc  heat  at  constant  volume  =s  0.2375  —  .0686  =  0.1689. 

Ratio  of  speciflc  heat  at  constant  pressure  to  speciflc  heat  at  constant 
volume  =  .237.'i  -i-  .1689  =  1.406.    (Ree  Speciflc  Heat,  p.  458.) 

Floir  of  Air  thronffli  OHflces*— The  theoretical  velocity  In  feet 
per  second  of  flow  of  any  fluid,  liquid,  or  gas  through  an  oriflce  is  o  ss 
f^2gh  =  8.02  i/h,  in  which  h  =  the  ''  head  *'  or  height  of  the  fluid  in  feet 
required  to  produce  the  pi'essure  of  the  fluid  at  the  level  of  tbe  orifice. 
(t«V)r  gase<<  tlie  formula  holds  good  only  for  small  difTerences  of  pressure  on 
the  two  siilea  of  tl^e  orlfle#»,)    The  quantity  of  flow  in  cubic  feet  per  seeopd 


FLOW  OP  AIB  IN   PIPES.  486 

Is  equal  to  the  product  of  this  TelocitT  by  the  area  of  the  orifice,  in  square 
feet,  multiplied  by  a  "ooefBcient  of  flow/' which  takes  into  account  the 
contraction  of  tlie  vein  or  fiowlnff  stream,  the  friction  of  the  oriflce,  etc. 

For  air  flowing^  through  an  oriflce  or  snort  tube,  from  a  reservoir  of  the 
pmwure  j9i  into  a  reseryoir  of  the  pressure  p^,  Weisbacfa  gives  the  follow- 
log  yalues  for  the  coefficient  of  flow,  obtained  from  his  experiments. 

Flow  of  Aib  through  as  Orifice. 

Coeflicient  c  in  formula  v  =  e  i^^gh, 
IMameter      )  Ratio  of  pressures pj-«-pi  1.0&    1.09    1.48    I.e.*)    l.gQ    2.15 

1  centimetre.    (Coefficient 565    .5S9    .6»i!    .7)24    .754    .788 

I>iameter       [  Ratio  of  pressures 1.05    1.00    IM    1.67    SOI     .... 

IL14 centimetres iCoefficieut 558    .573    .684    .678    .7^  .... 

Flow  of  Air  through  a  Short  Tubs. 

Diam.  1  cm.,     )  Ratio  of  pressures  Pi-+*pa  1.05    1.10    1.80    

Leiigth3cm.  {Coefficient 780    .771    .880 

DiJim.  1.414 cm.,  (Ratio  of  pressures 1.41    1.60     

Leiigih4  24^cm.>  Coefficient. 818    .822     

lEI^hlft^m    (.Ratio  of  pressures 1.24    1.38    1.50    1.85    2.14    .... 

o'riSS''ri«n5Si.fCoefflcieft. 079    .986    .965    .971    .978.... 

FUBOKxa's  Equations  for  Flow  of  Air  from  a  Resbrtoir  through  ah 
Orifiok.    tPeabody's  Thermodynamics,  p.  185.) 

Forp,  >  2p„    G  =  OJSaor-^; 


Pi  <  2p„    G  =  1.060  F 


^PcAP\  -Pa). 

'1\     * 


29.03 


O  =  flow  of  air  through  the  oriflce  in  lbs.  per  sec.,  F  =  area  of  oriflce  in  Fq. 
in.,  pi  =  absolute  pressure  in  reservoir  In  lbs.  per  sq.  in.,  pa  -  pressure  of 
atmosphere,  T\  =  alM«olute  temperature,  Fahr..  of  air  In  reservoir. 

Clark  (Rules.  Tables,  and  Data,  p.  891)  gives,  for  the  velocity  of  flow  of  air 
through  an  oriflce  due  to  small  dilrerenoes  of  pressure, 

OP,  slmplifled, 

r  =  862  C  a/(i  +  .00208(t  -  82^-; 

In  which  V=  velocity  in  feet  per  second ;  2g  =  64.4;  h  =  height  of  the  column 
of  water  in  inches,  measuring  the  difference  of  pressure;  t  =  tiie  tempera- 
ture Fahr.;  and  p  =  barometric  pressure  in  inches  of  mercury.  riS.'J  is  the 
volume  of  air  at  32«  under  a  pressure  of  29.92  inches  of  mercury  when  tliat  of 
an  equal  weight  of  ^-ater  is  taken  as  1. 

For  62«  F.,  the  formula  becomes  V  =  868C  a/-,  and  if  p  s  29.92  inches r= 

66.85CfX 

The  coefficient  of  efflux  C,  according  to  Weisbach,  is: 
For  cotioldal  mouthpiece,  of  form  of  the  contracted  vein, 

with  pre»<sui*es  of  from  .28  to  1.1  atmospheres C  =  .97  to  .99 

Circular  oriflces  in  thin  plates C  =  .66  to  .79 

Short  cylindrical  mouthpieces C  =  .81  to  .M 

The  same  rounded  at  the  inner  end C=  .92  to  .98 

C'lnical  converging  mouthpieces  C  —  .90  to  .99 

Flow  Of  AlF  In  Plpoa.— Hawlcsley  (Proc.   Inst.  C.  E^  xxxlii,  «) 

states  that  his  formula  for  flow  of  water  in  pipes  v  =  48  A/  ~j—  niay  also 

be  employed  for  flow  of  air.  In  this  case  H  =  height  in  feet  of  a  column  of 
air  required  to  produce  the  pressure  causing  the  flow,  or  the  loss  of  head 


486 


AIR. 


for  a  id^en  flow;  v  s  velocity  Id  feet  per  second,  D  =  diameter  In  feet,  L  9 
length  in  feet. 

If  the  head  Is  expressed  In  Inches  of  water,  h,  the  air  befnsr  taken  at 
0:2*  F  ,  its  weight  per  cubic  foot  at  atmospheric  pressure  zs  .OTQflb.    Then 

H  »  ^^'^  ^^  a  08.8ft.    If  d  a  diameter  in  inches,  I> «  ^.  Md  the  formula 
becomes  v  =  114.5  i/  7 ,  in  which  h  ■>  fnehes  of  water  column,  d  a  diam- 


eter in  inches  and  L  s  length  in  feet;  h : 
The  quantity  in  cubic  feet  per  second  is 


ISllOd 


\d^ 


<i  =  .n^i^v. 


■««/?.  -;/!=  *=:^. 


Th«>  horse-power  required  to  drive  air  through  a  pipe  is  the  volume  O  in 
cubic  feet  per  second  multiplied  by  the  pi'assure  In  pounds  per  iiquare  root 
and  divided  by  660.  Pressure  in  pounds  per  square  foot  s  P  »  loobes  of 
water  column  X  5.190,  whence  horse-power  = 

HP  -  2?  -     ^^    -    ^^ 
560  "  106.9  ~  41.3d»' 

If  the  head  or  pressure  oausing  the  flow  is  expressed  In  pounds  pnr  square 
inch  m  p,  then  h  a  27.71p,  and  tiie  above  formuliB  become 


>  602.7 


Vt-> 


lAfl 


L^ 


^  ""  308,800d*       *"  8O8.SO0!p* 


,...«r/f;,  =  -^,  .»^^ 


.  y^ 


HP, 


gll44p 
550 


»  .8018^  a  .094^ 


Yolmiie  of  Air  Trstnamltled  In  CvMe  Feet  per  ntniite  In 
Plpea  of  Tiuiona  Dl»me$enu 


Formula  Q  = 

r44-d»«  X  60. 

>>^ 

1= 

Actual  Diameter  of  Pipe  in  Inches. 

f« 

II 

1 

S 

8 

4 

5 

0 

8 

10 

19 

10 

90 

84 

1    ,  .8?7 

1.81 

2.95 

5.94 

8.18 

11.78 

90.94 

82.78 

47.19 

88.77 

180.9 

188.5 

2       .656 

2.6fi 

5.89 

10.47 

18.80 

28.50 

4189 

05.45 

94.85 

107.6 

901.8 

877 

8       .9»{ 

3.9S 

8.84 

15.7 

24.6 

85.8 

62.8 

96.2 

141.4 

261.8 

882.7 

665.5 

4     1.31 

5,94 

11.78 

90.9 

8SJ.7 

47.1 

88.8 

181 

188 

885 

698 

754 

5      1.64 

6.54 

14.7 

26.2 

41 

60 

104 

108 

tt& 

410 

664 

Ma 

6    !l.96 

7.85 

17.7 

81.4 

49.1 

70.7 

V4& 

190 

988 

609 

7» 

1181 

7     |«.«9 

9.10 

900 

80.0 

57.8 

89.4 

140 

899 

880 

588 

016 

1810 

S    HM 

103 

28.5 

41.9 

65.4 

94 

107 

869 

877 

070 

1047 

1606 

9    ;«.96 

11J8 

20.5 

47 

78 

100 

188 

994 

4«4 

754 

IS 

1086 

10    J8.S7 

14.1 

90.4 

ti 

89 

118 

J09 

327 

471 

838 

1886 

19     8.98 

16.7 

85.8 

08 

96 

141 

251 

898 

505 

1006 

1871 

16    j4.91 

19.6 

44.2 

W 

1&> 

1T7 

314 

491 

707 

1260 

1908 

Sra 

18    15.89 

28.5 

58 

94 

147 

312 

877 

580 

848 

1506 

29M 

90     6.54 

S6.9 

59 

105 

104 

Zi& 

419 

054 

942 

1075 

9818 

6770 

S4     7.85 

31.4 

71 

1S6 

190 

•m 

W-l 

T85 

1181 

2010 

8141 

4684 

25     8.18 

&i.7 

78 

131 

204 

204 

aas 

818 

1178 

S» 

8978 

4718 

f»     9.16 

86.6 

89 

140 

229 

880 

580 

918 

1819 

8886 

8818 

80    <0.8     89.8 

88 

157 

946 

858 

098 

989 

1414 

8618 

8685 

FLOW  OF  Am  IK  PIPES.  487 

In  Hawlnley*i  formula  and  its  deriratlTes  the  numerical  coefBdentB  are 
eonstant.  It  Is  scaroely  poeslble,  however,  that  they  can  be  accurate  esce|>t 
within  a  limited  range  of  coiiditiohs.  In  the  case  of  water  it  is  found  that 
the  coefficient  of  friction,  on  which  the  Ices  of  head  depends,  varies  with  the 
length  and  diameter  of  the  pipe,  and  with  the  Telocity,  ai  well  as  with  the 
condition  of  the  interior  surface.  In  the  case  of  air  and  other  gases  We 
have,  in  addition,  the  decrease  in  density  and  consequent  Increase  In  volume 
and  in  velocity  due  to  the  prograsetve  loM  of  head  from  one  end  of  the  pipe 
to  the  other, 

Clark  states  that  according  to  the  experiments  of  D^Aubulsson  and  those  of 
%  flardltilan  commlMlon  on  the  reslfetance  of  air  through  long  conduits  or 
plpea,  the  diminution  of  pressure  Is  yet*  nearl/  directly  as  the  length,  end 
as  the  square  of  th«  velocity  and  Ihtersely  as  toe  diameter.  The  resistance 
ii  not  varied  bjr  the  density. 

If  these  statements  ari  correct,  th«n  Oie formttlsBfc  a  —■  imd  h  &=  ^i 

and  their  derivatives  are  correct  in  form,  Mid  they  may  be  used  when  the 
Bum«4cal  coefficients  c  and  c'  are  obtained  by  ejcperiment« 

If  we  take  the  forms  of  the  above  formiiHS  as  oorrect.  and  let  C  be  a  vari- 
able coefficient,  depending  upon  the  length,  diameter,  and  condition  of  sur- 
face of  the  pipe,  and  poesibly  also  upon  the  velocity,  the  temperature  and 
the  densitv.  to  be  determined  by  future  experiments,  then  for  A  =  head  In 
in^es  of  water,  d  ss  diameter  In  inches,  L  s  length  In  feet,  «  s  velocity  in 
feet  per  second,  and  Q  a  quantity  in  cubic  feet  per  second: 

ttor  difference  or  ioM  ot  pratautej*  In  ptniitdi  per  «inue  taeb, 

(Fbr  oOidr  fonmilfl»  ffof  flow  ofitfa>«  «ee  Mine  Ventllfttiott.) 

IKMM  or  PreMnre  Ift  OuttMs  per  square  Knelu-^B,  F.  St«rte« 
vaa&  Oompttoy  uses  the  foUowlng  fonuulss : 


^?L.   «^./^^:    d^J^ 


iMOOd  ^ 


-/^ 


;  — i/i^=9^i    "-s^crJ 


te  whleh  pi  «■  loss  of  pressure  In  oonoes  per  square  Inch,  y  1 
la  feet  per  second,  and  L  s  length  of  pipe  in  feet,  if  p  is  1 
per  squaie  Inch,  these  formute  reduce  to 


i  In  oonoes  per  square  Inch,  y  m  velocity  of  air 

ength  of  pipe  in  feet,    if  p  Is  taken  In  pounds 

persqcuuel 

p  to  .000000-^  i     «  =  «S2.B4/   jr.  .     "-  p — • 

t  t>* 
These  are  dedticed  from  the  common  formula  (Welsbach*s),  P  »  /j  §;:*  '<■ 

which /»  .0001  OiM« 

The  following  table  Is  condensed  from  one  given  In  the  catalogue  of  B.  F« 
■turterafit  Company*  .    ^     ^ 

Loss  of  prsssnre  in  pipes  100  feet  long,  in  ounces  per  iquare  inch.  For 
any  iMlM»r  wagth,  the  loss  Is  proportioiial  to  the  length. 


488 


An. 


11 

Diameter  of  Pipe  in  Inches. 

1 

2 

8 

4 

5 

6 

7 

8 

9 

10 

11 

12 

|J 

Loss  of  Pressure  in  Ounces. 

AOO 

.400 

.800 

.183 

.100 

.080|     .067 

.057 

.050 

.044 

.040 

.a36 

.088 

1800 

1.600 

.800 

.688 

.400 

.880 

.867 

.889 

.800 

.178 

.160 

.145 

.188 

1800 

8.600 

1.80C 

1.800 

.900 

.780 

.600 

.514 

.450 

.400 

.860 

.887 

.800 

2400 

6.400 

8.800 

8.188 

1.600 

l.»» 

1.067 

.914 

.800 

.711 

.640 

.688 

.538 

8(MM) 

10. 

5. 

8.833 

8.6 

8. 

1.667 

1  489 

1.850 

1.111 

l.OUO 

.909 

.883 

3mo 

14.4 

7.8 

4.8 

8.6 

8.88 

2.4 

8.067 

1.8 

1.6 

1.44 

1.800 

1.20O 

4200 

9.8 

6.663 

4.9 

8.98 

8.867 

8.8 

8.45 

8.178 

1.96 

1.788 

1.688 

4800 

18.8 

8.683 

6.4 

6.13 

4.267 

8.667 

8.8 

2.844 

8.56 

8.827 

8.138 

0000 

80. 

18.833 

10.0 

8.0 

6.667 

5.714 

5.0 

4.444 

4.0 

8  686 

8.SS8 

Diameter  of  Pipe  in  Inches. 

U 

16 

18 

20 

23 

84 

28; 

88 

86 

40 

44 

48 

Loss  of  Pressure  in  Ounces. 

600 

.029 

086 

.088 

.080 

.018 

.017 

.014 

.012 

.011 

.010 

.009 

.008 

1800 

.114 

.100 

.089 

.080 

.078 

.067 

.067 

.050 

.044 

.040 

.086 

.Offl 

1800 

.857 

.800 

.180 

.164 

.166 

.189 

.112 

.100 

.090 

.088 

.075 

MOO 

.457 

400 

.856 

.880 

.891 

.867 

.889 

.200 

.178 

.160 

.145 

.188 

flflOO 

1.0Bi9 

.900 

.800 

.WO 

.(Ob 

.600 

.614 

.450 

.400    .860 

.827 

.800 

4200 

1.400 

1.885 

1.089 

.980 

.891 

.817 

.700 

.618 

.644    .490 

.446 

.408 

4800 

1.889 

1.600 

1.482 

1.280 

1.164 

1.067 

.914 

.800 

.711'    640 

.588 

.688 

6000 

8.857 

2.500 

8.888 

8.000 

1.818 

1.667 

1.429 

1.250 

1.111  1.000 

.909 

.i«3 

BITeet  of  Bends  In  Pipes.    (Norwallc  Iron  Worlcs  Go.) 
Radius  of  elbow,  in  diameter  of  pipe  =  5     8      2     lU    1^     1       H     H 
Equivalent  Iffths.  of  straight  pipe,  diams  7.86  8.24  0.08  lO.ft  18.7217.61 86.09 121.2 

Compreased-ftlr  Tranamleelon*  (Frank  Richards,  Am.  Jiturfc., 
March  8, 1804  )— Tkie  volume  of  free  air  iraiismitted  may  be  assumed  to  be 
directly  as  the  number  of  atmospheres  to  which  the  air  is  compressed. 
Thus,  If  the  air  transmitted  be  at  75  pounds  ffauge-pressure,  or  six  atmos- 
pheres, the  volume  of  free  air  will  be  six  times  the  amount  f^ven  In  the 
table  (pafre  486).  It  is  generally  considered  that  for  economical  transmission 
the  velocity  in  main  pipes  should  not  exceed  80  feet  per  second.  In  the 
smaller  distributing  pipes  the  velocity  should  be  decldedlv  less  than  this. 

The  loss  of  power  in  the  transmission  of  compressed  air  In  general  is  not 
a  serious  one,  or  at  all  to  be  compared  with  the  losses  of  power  in  the  opera- 
tion of  compression  and  in  the  re-expansion  or  final  application  of  the  air. 

The  formulas  for  lotw  bv  friction  are  all  unsatisfactory.  The  statements 
of  observed  facts  in  this  line  are  in  a  more  or  less  chaotic  state,  and  self- 
evidently  unreliable. 

A  statement  of  the  friction  of  air  flowing  through  a  pipe  tnyolves  at  least 
all  the  following  factors:  Unit  of  time,  volume  of  air,  pressure  of  air,  diam- 
eter of  pipe,  length  of  pipe,  and  the  difference  of  pressure  at  the  ends  ol 
the  pipe  or  the  head  required  to  maintain  the  flow.  Neither  of  these  factors 
can  he  allowed  its  independent  and  absolute  value,  but  is  subject  to  modifl- 
cations  in  deference  to  its  aiwociates.  The  flow  of  air  being  assumed  to  be 
uniform  at  the  entrance  to  the  pipe,  the  volume  and  flow  are  not  uniform 
after  that.  The  air  is  consrantly  losing  some  of  its  pressure  and  its  volume 
is  constantly  increasing.  The  velocity  of  flow  is  therefore  also  somewhat 
accelerated  continually.  This  also  modlfles  the  use  of  the  length  of  the 
pipe  as  a  constant  factor. 

Then,  besides  the  fluctuating  values  of  these  factors,  there  Is  the  oondltioa 
of  the  pipe  itself.  The  actual  diameter  of  the  pipe,  especlmlly  in  the 
smaller  sixes,  is  different  from  the  nominal  diameter.  The  pipe  may  be 
straight,  or  it  may  be  crooked  and  have  numerons  elbows.  Mr.  Richards 
oonsiders  one  elbow  as  equivalent  to  a  length  of  pipe. 


PLOW  OF   COMPRESSED   AIR  IK   PIPES. 


489 


Formnlae  for  Flow  of  Compremied  Air  In  Plpes.-Tlie  for- 
mutee  on  p^gw  4isii  and  487  are  for  air  at  or  near  atniospheriu  pressure.  For 
compressed  air  the  density  has  to  be  taken  into  account.  A  commoD 
formula  for  the  flow  of  air,  gas,  or  steam  in  pipes  is 


Q=CA 


in  which  Q  =■  volume  In  cubic  feet  per  minute,  p  =  difference  of  pressure 
ill  lbs.  per  itq.  in.  causiuff  the  flow,  d  =  diameter  of  pipe  in  in.,  L  =:  length 
of  pipe  in  ft..  117  =  density  of  the  entering  gas  or  steam  In  lbs  per  cu.  ft., 
and  c  ^  a  coefficient  found  by  experim<'nt.  Mr.  F.  A.  Halsey  in  calculating 
a  table  for  the  Rand  Drill  Co.'s  Catalogue  talies  the  value  of  c  at  58,  basing 
it  upon  the  experiments  made  by  order  of  the  Italian  government  prelim- 
inary lo  boring  ihe  Mt.  Cenis  tunnel.  These  experiments  were  made  with 
?ipe8  of  3-^1  feet  in  length  and  of  approximately  4,  8,  and  14  in.  diameter, 
he  volumes  of  compressed  air  jiassed  ranged  between  16.64  and  ISUO  cu.  ft. 
per  minute.  The  value  of  c  is  quite  constant  throughout  the  range  and 
shows  little  disposition  to  change  with  the  varying  diameter  of  the  pipe.  It 
is  of  course  probable,  says  Mr.  Halsey,  that  c  would  be  f^maller  if  determined 
for  smaller  sizes  of  pi|:)e.  but  to  offset  that  the  actual  sizes  of  small  com- 
mercial pipe  are  considerably  larger  than  the  nominal  sizes,  and  as  these 
calculations  are  commonly  made  for  the  nominal  diameters  it  is  probable 
that  in  those  small  sizes  the  loss  would  really  be  less  than  shown  by  the 
table.  The  formula  is  of  course  strictly  applicable  to  fluids  which  do  not 
change  their  density,  but  within  the  change  of  density  admissible  in  the 
transmission  of  air  for  power  purposes  it  is  probable  that  the  erroi*s  intro- 
duced by  this  change  are  less  than  those  due  to  errors  of  observation  in  the 
E resent  state  of  knowledge  of  the  subject.  Mr.  Halsey 's  table  is  condensed 
elow. 


i 

Cubic  feet  of  free  air  compressed  to  a  gauge-pressure 
and  passing  through  the  pipe  each  minute. 

of  80  lbs. 

o  « 

50 

100 

aoo 

400 

800 

1000 

1500 

9000 

3000 

4000 

5000 

Loss  of  pressure  in  lbs.  per  square  inch  for  each  1000  ft. 
of  straight  pipe. 

8.61 
1.45 

o.ao 

0.18 

5.8 
1.05 
0.S5 
0.14 

4.80 
1.41 
0.57 
0.26 
0.14 

5.80 
2.28 
1.06 
0.54 
0.18 

4.16 
2.12 
0.08 
0.28 
0.07 

6.4 

8.27 

1.08 

0.43 

0.10 

7.60 
2.43 
1.00 
0.24 
0.08 

4.32 
1.75 
0.42 
0.14 

9.6 

3.91 

0.93 

0.30 

0.12 

7.10 
1.68 
0.55 
0.22 
O.IO 

5 

0 

10.7 

8 

2  59 

10 

0  84 

]'.! 

0  34 

14 







0.16 

To  apply  the  formula  given  above  to  air  of  different  pressures  it  may  be 
given  otner  forms,  as  follows: 

Let  Q  =s  the  volume  in  cubic  feet  per  minute  of  the  compressed  air;  Q,  = 
the  volume  before  compression,  or  "*  free  air,"  both  being  takt^n  at  mean 
atmospheric  temperature  of  62"  F.;  Wj  =•.  weight  per  cubic  foot  of  <?,  = 
0.0761  lb.;  r  =  atmospheres,  or  ratio  of  absolute  pressures,  =^  (gauge-pres- 
sure -f  14.7)  -•-  14.7;  w  =  weight  per  cu.  ft.  of  ^;  p  =  difference  of  pressure, 
in  lbs.  per  sq.  in.,  causing  the  flow;  d  =  diam.  of  pipe  in  in.;  L  =  length  of 
pipe  in  ft.;  c  =  ezi>erimental  constant.    Then 


4d0 


AIR. 


Q  *s  ci/ A  ^ ;       Qj  A  1 Q;       wts  n©,  =1  .0T61r; 


-  =  for«^'=a»r^^=^.«„^-. 


0.fi07, 


c*pr 


p  =  .«,.^'=.07.X^!. 


The  value  of  c  aocordinpr  to  the  Mi.  Oeais  ezpertmentg  Is  about  58  for  pipes 
i,  8.  auU  14  io.  diameter,  «il81  ft.  loug.  In  the  St.  Qothard  experfmtrDtM  It 
raiiK«Hl  from  iKi  8  to  73.2  (wse  Uble  below)  for  pipeii  6.01  aud  7.87  io.  diameter. 
1714  and  16,0118  ft.  long,  values  derived  from  D^Arcy's  formula  fur  flow  of 
water  in  pipes,  ran^tiug  from  46.8  for  1  lu.  diameter  to  dS  ^  for  2*  in.,  are  given 
under  *'  Fluw  of  8ceam,*'  p.  071.  For  approximate  calculations  the  Tulue  00 
may  be  used  for  all  pipes  of  4  In.  diameter  and  upwards.  Using  c  =  OO^  the 
above  formulfe  become 


Q  sz  817, 


V^' 


Qi  «  317.6, 


/¥' 


[d  =  0.11014*/^^^  =  0.1101 

r     V 


r     pr 


p  =  0.0000ill4-^'  =  0.00008114-5;^. 

Loss  of  Preaaore  In  Compressed  Air  Pipe-main, 
St.  Golhard  Tunnel. 

(B.  Stockalper.) 


at 


No. 


in. 
7.87 
5.«1 

87 
6.91 

.87 
5.91 


t  U  O  4»«« 

o  o  ^  «  • 


cu.ft, 
[ss.OSej 

[88.008] 

[i8a04J 


15^ 


en.  ft 
0.534 
7.008 
6600 
5.808 
6.8<» 
6.580 


O  08 

Hi. 

V  k  !r 

■oe.| 

B 


den. 
.00050 
.00009 
.00614 
.00J88 
.00449 
.00128 


n 

•gbC 


lbs. 
8.000 
8000 
1.770 
1.770 
1.4R8 
1.488 


lu 

IS. 


feet. 
10.88 
87.14 
16.90 

i5.'68 
89.84 


Observed  Preosures. 


at. 
6.00 
6.84 
4.86 
4.1S 
8.84 
8.0S 


at. 
6.84 
6.G0 
4.18 

8.06 
8.M 


Loesof 
Pressure. 


lbs. 
per 
BQ.tn. 
6.888 
8.638 
8.884 

8.788 
1.01T 


lli'^ 


71.8 
Gi.9 
TO. 7 

«7;« 

04.8 


The  lenicth  of  the  pipe  7.67  in  diameter  was  16.098  ft.,  and  of  the  smaller 
pipe  1712.0  ft.  The  mean  temperature  of  the  air  in  tbe  Uuse  p^ie  was  90*  F. 
and  In  the  small  pipe  80*  F. 


MEASURKMEKT  OF  VELOCITY  OF  AIIU 


'491 


K4«ft*t«ii  mf  n9M.^It  is  fk*eqiMDtif  dMirad  to  know  trlMit  ttvmber 
of  pipes  of  n  giv^n  sin  ftre  equal  in  cKnying  oft|iaclty  to  one  vipt  of  » larfpir 
9tm.    At  the  aame  velocity  of  flow  ths  ▼olume  deliTertxl  by  two  vkpm  of 


different  sizes  is 


to  the  aquareB  of  tlieir  diMMten:  tbes,  on^ 


4-ixich  pipe  will  deliyer  the  same  volume  as  four  2-iuch  pipes.  With  the  same 
liead,  however,  tlie  velooitj  is  iessin  tiie  soudler  ralpe,  and  the  volume  de- 
livered varies  about  as  ihe  square  root  of  the  fifth  power  (I.e.,  as  the  ie.S 
power).  The  f[)llowlnK  table  has  been  calculated  on  this  iMttls.  The  figures 
opposite  the  intersection  of  any  two  sizes  is  the  number  of  the  snialler-Bize<t 
pipes  required  to  equal  one  of  the  larger.  Tbus,  one  4-inok  pine  Is  equal  U» 
5.7  2-incfi  pipes. 


So 

1 

8 

8 

4 

6 

6 

7 

8 

9 

10 

18 

14 

16 

16 

20 

H 

2 
8 

6.7 
15.6 

2.8 

1 

4 

8S 

6.7 

2.1 

1 

5 

56.9 

9.9 

8.6 

1.7 

1 

6 

88.2 

15.6 

6T 

2.8 

1.6 

1 

7 

lao 

22.9 

83 

4.1 

2.8 

1.6 

8 

181 

32 

11.7 

6.7 

8.2 

2.1 

1 

9 

«8 

48. 

15.6 

7.6 

4.8 

2.8 

1.8 

1 

10 

216 

55.9 

20.8 

9.9 

5.7 

8.6 

1.7 

1.8 

n 

401 

70.9 

26.7 

12.6 

7.2 

4.6 

2.2 

1.7 

1.3 

K 

499 

88.2 

88 

16.6 

8.9 

6.7 

2.8 

2.1 

1 

18 

609 

106 

39.1 

19 

10.9 

7.1 

8.4 

2.5 

1.2 

14 

788 

180 

47 

22.9 

18.1 

8.8 

4.1 

8.0 

1.0 

35 

871 

154 

96.9 

27.2 

16.6 

9.9 

4.8 

8.6 

1.7 

1« 

181 

66.7 

32 

16.8 

11.7 

5.7 

4.2 

2.1 

1 

17 

211 

76.4 

37.2 

21.3 

18.6 

6.6 

4.9 

2.4 

1.2 

18 

248 

88.2 

48 

24.6 

16.6 

I0!fl 

7.8 

6.7 

2.8 

1.8 

1 

19 

278 

101 

49.1 

28.1 

17.8 

12.1 

8.7 

6.6 

8.2 

1.6 

1.1 

20 

816 

115 

66.9 

32 

90.8 

18.8 

9.9 

7.4 

8.6 

1.7 

1.8 

1 

\ 

22 

401 

146 

70.9 

40.6 

28.7 

17.6 

12.8 

9.8 

7.8 

4.6 

2.2 

i.r 

1.8 

\ 

24 

199 

181 

88.2 

50.8 

82 

21.8 

15.6 

11.6 

6.7 

2.8 

2.1 

1.6 

1 

26 

009 

221 

108 

61.7 

89.1 

26.6 

19. 

14.2 

io!fl 

7.1 

8.4 

2.8 

1.9 

l.» 

28 

raj 

886 

180 

74.2 

47  182 

22.9 

17.1 

18.1 

8.8 

4.1 

8 

2.8 

1.8 

80 

971 

«16 

164 

88.2 

5S.9 

88 

«7.2 

20.9 

16.6 

9.9 

4.8 

8.6 

2.8 

1.? 

88 

199 

243 

180 

88.2 

60 

43 

82 

24.6 

15.6 

io!6 

7.6 

8.7 

4.3 

2.» 

42 

738 

367 

806 

180 

88.2 

68.2  47 

86.2 

19 

16.6 

11.2 

8.8 

6.4 

4.1 

48 

499 

286 

181 

128 

88.262.7 

50.5 

82 

21.8 

15.6 

11.6 

8.9 

5.1 

54 

670 

388 

243 

166 

118  88.2 
154  Jjl5 

07.8 

48 

23.2 

20.9 

15.6;12 

7.S 

€0 

Bfri 

499 

316 

215 

88.2 

56.9 

38 

27.2 

80.8;ia.6'  9.9 

If  easvi^ment  of  the  TelooltT  of  A.lr  In  Pipes  hr  an  Aii«* 
■lOBieter*— Tests  were  made  by  B.  Don  kin.  Jr.  {InsU  Civil  Enffv§.  1892). 
to  compare  the  velocity  of  air  in  pipes  from  8  in.  to  24  in.  diam.,  as  shown  bj- 
an  anemometer  2^  in.  diam.  with  the  true  velocity  as  measured  by  the  timo 
of  descent  of  a  gas-holder  holding  1622  cubic  feet.  A  table  of  the  results 
with  discussion  is  given  in  Enay  Nete$,  Dec.  22, 1892.  In  pipes  from  8  in.  to  2d 
in.  diam.  with  air  velocities  of  from  140  to  690  feet  per  minute  the  anemome* 
ter  showed  errors  varying  from  I4.5)(  fast  to  10j(  slow.  With  a  24-IdcIi  pip* 
and  a  velocity  of  73  ft.  per  minute,  the  anemometer  gave  from  44  to  63  feet» 
or  from  18.6  to  39.6)(  alow.  The  practical  concliution  drawn  from  these  ex- 
periments is  that  anemometers  for  the  measurement  of  velocities  of  air  In 
pipes  of  these  dianietera  should  he  used  with  great  caution.  The  percentage 
of  error  is  not  constant,  nnd  varies  considerably  with  the  diameter  of  the 
pip(«  and  tlie  speeds  of  air.  The  une  of  a  baffle,  consisting  of  a  perforated 
plate,  whlub  tended  to  equalise  the  velocity  in  the  centre  and  at  the  sides  in 
diminished  tlie  error. 


492 


AIR. 


Th6  imp086ibllity  of  measurine  the  true  qUantitv  of  air  by  an  anemometer 
held  stationarv  in  one  position  is  shown  by  the  following  figures,  given  by 
Wm.  Daniel  (Proc.  Inst.  M.  £.,  1875).  of  the  velocities  of  air  found  at BifTerent 
points  in  the  oross-sections  of  two  diiferent  airways  in  a  mine. 

DiFFBRKNCBS  OF  AlfBHOlCBTBB  BkAOINOS  IN  AlRWATB. 

8 ft.  square.        6x8ft. 


1712 

1795 

1859 

1829 

IttSS 

16S6 

1788 

1091 

1477 

1844 

1524 

1049 

186a 

1856 

1293 

19SA 

1170 

1209 

1988 

948 

1104 

1177 

1134 

1049 

1106 

Average  1469. 


Average  1132. 


WIND. 

F«#rce   of  the  l¥liid.— Smeaton  iii  1750  published  a  table  of  the 

velocity  aii«i  pietsi.re  of  wind,  as  follows: 

Velocity  and  Forcb  of  Wind,  in  Pounds  pkr  SquARg  Inch. 


ic 

^1 

hi 

ii 

IS 

Itl 

S 

fe* 

Cb 

1 

1.47 

0.006 

2 

2.93 

0.020 

3 

4.4 

0.014 

4 

6.87 

0.079 

5 

7.3:i 

0.1 2:i 

6 

R.8 

0.177 

7 

10.25 

0.241 

8 

11.75 

0.315 

9 

18.2 

0.400 

10 

14.67 

0.49i 

13 

17.6 

0.708 

14 

20.6 

0.964 

15 

22.00 

1.107 

16 

28.45 

1.25 

Common    Appella 

tion  of  the 

Force  of  Wind. 


I  Hardly  percepti- 
^     hie. 

Just  perceptible, 

Gentle  pleasant 
^     wind. 


Pleasant  brisk 
gale. 


IS 


;S"a 


1.55 
1.968 
3.076 
4.429 
6.027 
7.878 
9.968 
12.80 
14.9 
17.71 
20.85 
24.1 
27.7 
81.49 
49.2 


Common  Appella- 
tion of  the 
Force  of  Wind. 


Verybrislt. 
High  wind. 

Veiy  high  storm. 

Great  Storm. 

Hurricane. 
Immense  huiri- 


The  pressures  pf>r  square  foot  in  the  above  table  correspond  to  the 
formula  P  =  0.0Or>F«,  in  which  V  is  the  velocity  in  miles  per  hour.  Eng^g 
MitM,  Feb.  9,  1893,  says  that  the  formula  was  never  well  established,  and 
has  floated  chiefly  on  Smeaton^s  name  and  for  lack  of  a  bett«*r.  It  was  put 
forward  only  for  surfaces  for  use  in  windniill  practice.  The  trend  of 
modem  evidence  is  that  it  is  appruzimately  correct  only  for  such  surfaces, 
and  that  for  large  solid  bodies  it  often  gives  greatly  too  large  reeulta. 
Observations  by  others  are  thus  compared  wlih  Smeaton's  formula: 

Old  Rmeaton  formula Pss    .OOSFS 

As  determined  by  Prof.  Martin P=    .OOiV* 

Whipple  and  Dines Pss  MS»V* 


WIND.  493 

At  00  miles  per  hour  tbeBe  formulas  ^ive  for  the  pressure  per  square  fool, 
18,  14.4  and  10.44  lbs.,  respectively,  the  pressure  ▼ar.finff  by  all  of  them  as 
the  square  of  the  velocity.  Lieut.  Crosby's  experiments  iEiig''g,  June  18. 
1890),  claiminjr  to  prove  that  P=i/V  lustead  of  F  =  /r>,  are  discredited. 

A.  R.  Wolff  (The  Wiodmill  as  a  Prime  Mover,  p.  0)  gives  as  the  theoretical 

pressure  per  sq.  ft.  of  surface,  P  =  -^,  in  which  d  =  density  of  air  in  pounds 
per  cu.  ft.  =  ■ — ^     ^"^  " ;  p  being  the  barometric  pressure  per  square 

foot  at  any  level,  and  temperature  of  W*  F.,  i  any  absolute  temperature, 
g  =  volume  of  air  carried  along  per  square  foot  in  one  second,  v  =  velocltv 

of  the  wind  hi  feet  per  sec.,  g  =  82.16.   Since  Q  s  v  cu.  f  i.  per  sec.,  P=  ^. 

Multiplying  this  by  a  coefficient  0.96  found  by  experiment,  and  substituting 

the  above  value  of  d,  he  obtains  P  =   .  J'^lf^  ^  ^ ,   and    when    p 

'  ^  r**"  -  .018748 
s  2116.6  Ibflkper  sq.  ft.  or  average  atmospheric  pressure  at  the  sea^level, 

P=7 — =-7s « *■!  expression  in  which  the  pressure  is  shown  to  vary 

12^^-018748 

with  the  temperature;  and  he  gives  a  table  showing  the  relation  between 
velocity  and  pressure  fur  temperatures  from  0*  to  100*  F.,  and  velocities 
from  1  to  80  miles  per  hour.  For  a  temperature  of  46*  F.  the  pressures  agree 
with  those  in  Smeaton's  table,  for  0^  P.  they  are  about  10  per  cent  greater, 
and  for  lOO*'  10  per  cent  less.  Prof.  H.  Allen  Hazen,  Wng'^g  Neu>9^  July  6, 
180O.  says  that  experiments  with  whirling  arms,  by  exposing  plates  t^  direct 
wind,  and  on  locomotives  with  velocities  running  up  to  40  miles  per  hour, 
have  invariably  shown  the  resistance  to  vary  with  F*.  In  the  formula 
F  ■=  .006SF*,  in  which  F  ■=  pressure  in  pounds,  ^  =  surface  in  square  feet, 
V  =  velocity  in  miles  per  hour,  the  doubtful  question  is  that  regarding 
the  accuracy  of  the  first  two  factors  in  the  second  member  of  this  equation. 
The  first  factor  has  been  variously  determined  from  .008  to  .005  [it  has  been 
determined  as  low  as  .0014.— Ed.  Enay  Newt], 

The  second  factor  has  been  found  in  some  experiments  with  very  short 
whirling  arms  and  low  velocities  to  vary  with  tne  perimeter  of  the  plate, 
but  this  entirely  difappears  with  longer  arms  or  straight  line  motion,  and 
the  only  question  now  to  be  determined  is  the  value  of  the  coefficient.  Per- 
haps some  of  the  best  experiments  for  determining  this  value  were  tried  in 
France  in  1886  by  carrying  flat  boards  on  trains.  The  resulting  formula  in 
this  case  was,  for  44.6  miles  per  hour,  p  =  .00685SF*. 

Mr.  Crosby's  whirling  experiments  were  made  with  an  arm  6.5  ft.  long. 
It  Is  certain  that  mont  serious  effects  from  centrifugal  action  would  be  set 
up  by  using  such  a  short  arm,  and  nothing  satisfactory  can  be  learned  with 
arms  less  than  90  or  80  ft.  long  at  velocities  above  6  miles  per  hour. 

Prof.  Kemot,  of  Melbourne  (Engineering  Record^  Feb.  20, 1804),  states  that 
experiments  at  the  Forih  Bridge  showed  that  the  average  pressure  on  sur- 
faces as  large  as  railway  carriages,  houses,  or  bridges  never  exceeded  two 
thirds  of  that  upon  small  surfaces  of  one  or  two  square  feet,  such  as  have 
been  used  at  observatories,  and  also  that  an  inertia  effect,  which  Is  frequently 
overlooked,  may  cause  some  forms  of  anemometer  to  give  false  results 
enormously  exceeding  the  correct  indication.  Experiments  of  Mr.  O.  T. 
Crosby  showed  that  the  pressure  varied  directly  as  the  velocity,  whereas  all 
the  early  Investigators,  from  the  time  of  Smeaton  onwards,  made  it  vary  as 
the  square  of  the  velocity.  Experiments  made  by  Prof.  Kemot  at  speeds 
varying  from  8  to  15  miles  per  hour  agreed  with  the  earlier  authorities,  and 
tended  to  negative  Crosby's  results.  The  pressure  upon  one  side  of  a  cube, 
or  of  a  block  proportioned  like  an  ordinary  carriage,  was  found  to  be  .9  of 
that  upon  a  thin  plato  of  the  same  area.  The  same  result  was  obtained  for 
a  square  tower.  A  square  pyramid,  whose  height  was  three  times  its  base, 
experienced  .8  of  the  pressure  upon  a  thin  plato  equal  to  one  of  its  sides,  but 
if  an  angle  was  turned  to  the  wind  the  pressure  was  increased  by  fully  20%. 
A  bridge  consisting  of  two  plate-girders  connected  by  a  deck  at  the  top  was 
found  to  experience  .9  of  the  pressure  on  a  thin  plato  equal  in  size  to  one 
Kirder,  when  the  distance  between  the  girders  was  equal  to  their  depth,  and 
tills  was  increased  by  one  fifth  when  the  distance  between  the  girders  was 


494  Aliu 

double  ilM  d«pth.  A  Uttio6*work  in  which  the  area  of  the  openings  wat^  S69 
of  the  whole  are*  eKperienoed  a  preeeure  otWof  tliat  upon  a  plate  of  tb« 
■ame  area.  The  praeeure  upon  cylindera  and  ooues  was  proved  to  be  equai 
to  half  that  upon  the  diametral  planes,  aud  that  upon  an  octaironal  priem  te 


be  $M  greater  than  upon  the  cireumBOribing  cylinder.  A  sphere  was  sttb- 
JfKst  to  a  pressure  of  .86  of  that  upon  a  thin  circular  plate  of  equal  diameter. 
A  hemlMpherioal  cup  ipave  the  same  reeult  as  the  sphere;  when  its  ooncaTity 


was  turned  to  the  wind  the  pressure  was  1.15  of  that  on  a  flat  plate  of  equal 
dtameter4  When  a  plaue  surfaee  parallel  to  the  direction  of  the  wind  was 
brought  nearly  into  contact  with  a  cylinder  or  sphere,  the  pressure  on  the 
latter  bodies  was  augmented  by  about  flOjt,  owing  to  the  lateral  escape  of  the 
air  being  cheeked.  Thus  it  is  possible  for  the  Monrity  of  a  tower  or  ohlmney 
to  be  impaired  by  the  erection  of  a  building  nearly  touching  it  on  one  side. 

Prenaares  ^r  Wind  tt^glntered  In  Storms.— Mr.  Frtzell  has 
examined  the  published  recordu  of  Greenwich  Observatory  from  1649  to  1868, 
and  reports  that  the  highest  pressure  of  wind  he  finds  recorded  is  41  lU*. 
per  sq.  ft.,  and  there  are  numerous  instances  in  which  it  was  between  BO  and 
40  lbs.  per  sq.  ft.  Prof.  Henry  says  that  on  Mount  Washington.  N.  H.,  a  ve- 
lo<-ity  of  150  miles  per  hour  has  been  observed,  and  at  New  York  City  60 
miles  an  hour,  aud  that  the  highest  winds  observed  In  1870  were  of  12  and  66 
miles  per  hour,  respectively. 

Lieut.  Dunwoody,  U.  0.  A*,  says,  In  substanoa,  that  the  New  Enghud  coast 
is  exposed  to  storms  which  produce  a  pressure  of  60  Iba.  per  sq.  ft  Xngi- 
neering  XeufM,  Aug.  20, 1880. 

wiNimiiiiiS. 

Pow«r  and  mSkttenef  of  WindmllUu— Rankine^  8.  B.,  p.  91&. 
gives  the  following:  Let  Q  :=  volume  of  air  which  aots  on  the  tall,  or  part 
of  a  sail,  in  cubic  feet  per  second,  v  «  velocity  of  the  wind  in  feet  per 
second,  s  »  sectional  area  of  the  cylinder,  or  annular  cylinder  of  wind, 
through  which  the  sail,  or  part  of  the  sail,  sweeps  in  one  revolution,  o  b  a 
coefRcient  to  be  found  by  eJcperience:  then  Q  »  ct».  RanUne,  from  experi- 
mental data  given  by  Smeaton,  and  taking  0  to  include  an  allowance  for 
friction,  gives  for  a  wheel  with  four  sails,  proportioned  In  the  best  manner, 
.  e  «  0.75.  Let  ift  =  weather  angle  of  the  sail  at  any  distance  from  the  axis. 
I.e..  the  angle  the  portion  of  the  sail  considered  makes  with  its  plane  of 
revcilution.  This  angle  gradually  diminishes  from  the  Inner  end  of  cha  sail 
to  the  tip:  u  s  the  velocttv  of  the  same  portion  of  the  sail,  and  IP  =  the  effl' 
ciency.  The  efficiency  Is  the  ratio  of  ihe  useful  work  performed  to  whole 
energy  of  the  stream  of  wind  acting  on  the  surface  s  of  the  wheel,  which 

energy  is  ~^,  D  being  the  weight  of  a  cubic  foot  of  air.  Itankine*s  formula 

for  efficiency  Is 

In  which  c  £s  0.75  and  /  is  a  coefficient  of  friction  found  fh>m 
data  e  0.016.    Banklne  gives  the  following  from  6meaton*s  data: 

^■weather-angle :»  7*  19"  19* 

F^  V  a  ratio  of  speed  of  greatest  effl- 
oienoy,  for  a  given  weather* 

angl^  to  that  of  the  wind a  S.68  1.86   .       1.41 

JTttaffieiency e  O.M         0.89         OJI 

Rankina  gives  the  following  as  the  best  rallies  for  the  angle  of  weather  at 
different  distanoea  from  the  aids: 

Distance  In  sixths  of  total  radius...     18        8        4       6        6 
Weatheraagle ...    18*     !••     18»     16«     IJJ^*   ?• 

But  Wolff  (p.  186)  shows  that  Smeaton  did  not  tern  these  the  best  angles, 
but  simply  says  they  '*  answer  aa  well  as  any,**  possibly  any  that  were  In  ex- 
istence In  his  time.  Wolff  says  that  they  **  cannot  In  the  nature  of  tbliign 
be  the  most  desirable  angles.**  Mathematical  oonskleratJons,  he  says,  con- 
clusively show  that  the  angle  of  impulse  depends  on  the  relative  velocity  of 
each  point  of  the  sail  and  the  wind,  the  angle  growing  larger  aa  the  ratio  be- 
comes greater.   8msatou*8  angles  do  not  fttlfll  this  oonditkm*    Wtflffdevet 


WINDMILLS. 


495 


ops  a  tliAoreilcAl  formulA  for  the  beat  aiirle  of  WMther,  fttid  from  it 
calculatrs  a  table  for  different  relative  ▼elocities  of  the  blades  (at  a  distance 
of  one  seventh  of  Uie  total  lenirtb  from  the  centr*  of  the  abaft)  and  the  wind, 
from  wbicb  the  following  is  condensed: 


Disunee  from  the  axis  of  the  wheel  in  sevenths  of  radiua. 

Ratio  of  the 

Speed  of  Blade 

* 

at  I A  of  Radius 

1 

2    . 

8 

4             5             6 

7 

to  Velocity  of 

Wind. 

Beet  angles  of  weather. 

0.10 

42*    0' 

89*  sr 

86«  89^ 

S4»    y 

81«48' 

29«31' 

«7»  80* 

0.16 

40    44 

88    39 

82    53 

29    81 

26    84 

24     0 

21    48 

O.SO 

89   n 

34     0 

89    81 

96    40 

Vi    80 

19    64 

17    40 

0.25 

97    50 

88    48 

90    84 

88    80 

19    90 

10    51 

14    58 

0.80 

»    89 

89    81 

94     0 

19    54 

10    51 

14    88 

18    44 

0.85 

35    »1 

97    80 

81    48 

17    40 

14    08 

m    44 

11      0 

0.40 

44      6 

85    40 

19    54 

10     0 

18    17 

11    19 

9    60 

0.46 

:«2    53 

94      0 

18    16 

14    32 

11    59 

10    10 

8    48 

0.50 

81    48 

«9    30 

10    51 

18    IT 

10    64 

0    18 

7    56 

The  effective  power  of  a  windmill,  as  Smeaton  ascertained  by  experiment, 
Tariea  as  »,  the  sectional  area  of  the  acting  stream  of  wind;  that  is,  for  simi- 
lar wheels,  as  the  squares  of  the  radii 

The  value  0.75,  assigned  to  the  multiplier  o  in  tbe  formula  Q  s  eva,  is 
founded  on  the  factf  ascertained  by  Smeaton,  that  the  effective  power  of  a 
windmill  with  sails  of  the  best  form,  and  about  15M  ft.  radius,  with  a  breete 
of  18  ft.  per  second,  is  about  1  horse*power.  In  the  computations  founded 
on  that  fact,  the  mean  angle  of  weather  is  made  =:  18^.  Tbe  efficiency  of 
this  wheel,  according  to  the  formula  and  table  given,  is  0.29,  at  its  nest 
speed,  when  the  Ups  Of  the  laito  move  at  a  teloolty  of  2.6  times  that  of  the 
wind. 

Merlvale  (Xotes  and  FormulsB  for  Mining  Students),  using  Smeaton*s  co* 
efficient  of  efficiency,  0.29,  gives  the  following: 

V  =  units  of  work  In  f  ooMbs.  per  see. ; 

W  ss  weight,  in  pounds,  of  tbe  cylinder  of  wind  psssing  the  sails  each 
second,  the  diameter  of  the  cylinder  being  equal  to  the  diameter 
of  the  sails; 

V  =s  Telocity  of  wind  in  feet  per  second; 
HJ?.  e  effective  horse-power; 

^-^T'    ^•^- *=  64X580- 
A.  R.  Wolff,  in  an  article  in  the  American  Bngineet,  gives  the  following 
iwe  also  his  treatise  on  Windmills): 
Let  c  B  velocity  of  wind  in  feet  per  second; 

n  =3  number  of  revolutions  or  the  windmill  per  minute; 

^•«  ^1*  ^st  bgg  be  the  breadth  of  the  sail  or  blade  at  distances  /«,  li,  /ft 

If.  and  U  respectively,  from  the  axis  of  the  shaft; 
|«  =s  distance  from  axis  of  shaft  to  beginning  of  sail  or  blade  proper; 
1  =  distance  from  axle  of  shaft  to  extremltv  of  sail  proper; 
v^  Vit  V,.  tf|,  Vjg  =  the  velocity  of  the  sail  in  feet  per  second  at  dis- 
tances lo.  li,  l^„  I,  respectively,  from  the  4Xis  of  the  shaft; 
o«,  Ot,  Of,  Of,  a^g  e  the  angles  of  impulse  for  maximiffn  effect  at  dis- 
tances !•«  If  I9.  U,  I  respectively  from  the  axis  of  the  shaft; 
a  s  the  angle  of  Impulse  when  the  sails  or  blocks  are  plane  surfaoeo, 

so  that  there  is  but  one  angle  to  be  considered; 
N  ss  mimber  of  sails  or  blades  of  windmill; 
jr=.98. 
d  =  density  of  wind  (weight  of  a  cubic  foot  of  air  at  average  temper»> 

ture  and  barometric  pressure  where  mill  is  erected); 
TTs  weight  of  wind-wheel  in  pounds; 
/  «s  coefficient  of  friction  of  nhaf t  and  bearings; 
D  s  diameter  of  bearing  of  windmill  in  feet. 


496 


▲IB. 


[  Hie  effectlTA  borae-power  of  a  windmiU  with  plane  sails  win  equal 
2 ^- X  mean  or^v,(sin  a  -  -=  cos  a)6t  cos  a 


Va;  (sin  a  -  -^  cos  a)  b^  cos  a^-  < ^ . 

'  The  effective  horse-power  of  a  windmill  of  shape  of  sail  for  mazimnm 
effect  equals 


Nil  -  lo)Kdc»  p 8lD« g, -.  1  2sin«a,-l 

—  fflOCS X  mean  of  I     ^^,^^    6..  dn'a.      ^^ 


sin. 


fW  X  .0588CnD 
560 


The  mean  value  of  quantities  iu  brackets  is  to  be  found  according  to 
Simpson's  rule.  Dividincr  I  into  7  parts,  flndinjc  the  angles  and  breadths 
correspondinic  to  these  divisions  by  substituting  them  in  quantities  within 
brackets  will  be  found  satisfactory.  Comparison  of  these  formulas  with  the 
only  fairly  reliable  experiments  in  windmills  (Coulomb^s)  showed  a  dose 
agreement  of  results. 

Approximate  formulsa  of  simpler  form  for  windmills  of  present  construc- 
tion can  be  based  upon  the  above,  substituting  actual  average  values  for  a, 
c,  d,  and  «.  but  since  improvement  in  the  present  angles  is  possible,  it  is 
better  to  give  theformulfe  in  their  general  and  accurate  form. 

Wolff  gives  the  following  table  based  on  the  practice  of  an  American 
manufacturer.  Since  its  preparation,  he  says,  over  1800  windmills  have  been 
sold  on  Its  guaranty  (1865),  and  in  all  cases  the  results  obtained  did  not  vary 
sufficiently  from  those  presented  to  cause  any  complaint.  The  actual  re- 
sults obtained  are  in  close  agreement  with  those  ontained  by  theoretical 
analysis  of  the  impulse  of  wind  upon  windmill  blades. 


Capacity  ofibe  Windmill. 

G3 

1^ 

ill 

E 

^^ 

6=,: 

OaJLod^  of  Water  raided  pmr  Minute  to 

-si; 

a^i 

g 

3% 

■BK 

IS. 

o 

an  Elt!?iitlou  uf-^ 

it 

1 

as 

M 

Tfl 

100 

150 

SQO 

III  Mil 

1 

& 

f«t. 

• 

fwt. 

feet. 

feist. 

feet. 

feeL 

I^S 

y^s 

w>iHel 

m  f  ^^ 

TOtoTS 

e.113 

3^6 

...  * 

0.04 

ly  - 

ootoffii 

lfl,l7S> 

9^m 

fl<wa 

4.750 

, .  I 

0.12 

lu  '* 

WtoM 

33.  Wl 

17.5»>! 

lltel 

W,<B& 

5.6*1 

0.S1 

14    ■* 

BatoM 

45.m 

i^.!^ 

15  304,  U  -4fi 

7,S«7 

4996 

0.^ 

Ifi    *' 

«to50 

«i«oa 

UM*i 

JS.^il 

i6J5a 

11.771 

S.075 

0,41 

m  *' 

40bo4fi 

97.fiftJ 

!ii^m\H2,hW 

QiMi 

17  485 

n.m 

aei 

»  '* 

M 

sato^oiaJiiw 

mrm-wmo 

ai  LMH 

1%/^i 

n.m 

0.78 

«S    " 

it 

iWtoS.'i'ai^.wi 

1W.36I  71  AM 

4y  rJ.'S  37  .^M 

a5,7ii 

LSI       a 

These  windmills  are  made  in  regular  sizes,  as  high  as  sixty  feet  diameter  of 
wheel:  but  the  experience  with  the  larger  olafs  of  mills  is  too  limited  to 
enable  the  presentation  of  precise  data  as  to  their  performance. 

If  the  wind  can  be  relied  upon  in  exceptional  localities  to  average  a  higher 
velocity  for  eight  hours  a  day  than  that  stated  in  the  above  table,  the  per- 
formance  or  horse  power  of  the  mill  will  he  increased,  and  can  be  obtained 
by  multiplying  the  ngures  in  the  table  bv  the  ratio  of  the  cube  of  the  higher 
average  velocity  of  wind  to  the  cube  of  the  velocity  above  recorded 

He  also  gives  the  following  table  showing  the  economy  of  the  wlndmilL 
All  the  items  of  expense,  including  both  interest  and  repairs,  are  reduced  to 
the  hour  by  dividing  the  costs  per  annum  by  365  x8  =  S920;  the  interest. 


WINDMILLS. 


497 


etc.  for  the  twenty-four  hours  being  chareed  to  the  eight  hours  of  actual 
work.  By  multiplying  the  figures  in  the  6tn  column  by  584,  the  first  cost  of 
the  windmill,  in  dollara,  is  obtained. 


Eeonomy  of  ibe  irindmlll. 

1 

II 

t^    igQO'i 

Expanse  of  Aelunl  UBeful  Power 

iJeir*^ loped ^  IQ  cents^  pf  r  hour. 

DHiiRHBlifm 
of  MILL 

a 

< 

0 

5 

III 

o 

^ 

^ 

S 

Ei. 

!«< 

t^ 

'^ 

n^n.whe^^i 

3:0 

0.04 

8 

D.2ft 

o,a.^ 

0,06 

O.OJ 

0.60 

J  5.0 

lO*  *•        " 

1151 

0J2 

a 

o.ao 

o.ai 

o.oe 

0.0)  0,70 

5.8 

IS      *'        **     ' 

aogfl 

o.ai 

8 

o,;i6 

0.3*j 

o.tw 

O.OJ  10.82 

3.9 

14      "        *» 

?ros 

0,28 

6 

0.7S 

0.75 

0.00 

0.07 

i.ca. 

5.9 

Ifi      "        " 

3676 

0  41 

8 

1.1& 

1.15 

0,0Q 

0.0: 

aj3 

B.II 

IS      "        " 

5t?6l 

O.fil 

8 

i.aa 

1.35 

0.06 

0.0: 

a.Ba 

4.6 

to     "      " 

74m 

O.TD 

8 

1.70 

3-70 

OM 

0.10 

3.M 

4  5 

s&     ■*       ^' 

1^743 

1.34 

s 

S.05 

2.05 

OM 

O.Kt 

AJta 

3.*J 

Lieut.  L  N.  Lewis  (Eni^'y  if<ip.,  Dec.  1894)  gives  a  table  of  results  of  ex* 
periments  with  wooden  wheels,  from  which  the  following  is  taken : 


Diameter 

of  wheel. 

Feet. 


IS 
16 
90 
95 
80 


Velocity  of  Wind,  miles  per  hour. 


10 


12       I       16       I       20       I       S5       I     90 


Actual  Useful  Horse-power  developed. 


.^ 


SI 


1 

2M 

4 

6 

7 


3 

4 
7 
10 
12 


The  wheels  were  tested  by  driving  a  differentially  wound  dynamo.  The 
**  useful  horse-power  "  was  measured  bv  a  voltmeter  and  ammeter,  allow- 
ing 500  watts  per  horse-power.  Details  of  the  experiments,  including  the 
means  used  for  obtaining  the  velocity  of  the  wind,  are  not  given.  The  re- 
sults are  so  far  in  excess  of  the  capacity  claimed  by  responsible  manufactu- 
rers that  they  should  not  be  given  credence  until  established  by  further 
experiments. 

A  recent  article  on  windmills  in  the  Iron  Age  contains  the  following:  Ac- 
cording to  observations  of  the  United  States  Signal  Service,  the  average 
velocity  of  the  wind  within  the  range  of  its  record  is  9  miles  per  hour  for 
tlie  year  along  the  North  Atlantic  border  and  Northwestern  States,  10  miles 
00  the  plains  of  the  West,  and  6  miles  in  the  Gulf  States. 

The  horse-powers  of  windmills  of  the  best  construction  are  proportional 
to  the  squares  of  their  diameters  and  inversely  as  their  velocities;  for  ex- 
ample, a  10-ft  mill  in  a  16-mile  breeze  will  develop  0.16  horse-power  at  66 
revolutioDS  per  minute;  and  with  the  same  breeze 

A  90-ft.  mill,  40  revolutions.  1  horse-power. 

A  26-ft.  mill,  85  revolutions,  194  horse-power. 

A  80-ft  mill,  28  revolutions,  2^  horse-power. 

A  40-ft.  mill,  22  revolutions,  Tyi  horse-power. 

A  60-f  U  mill,  18  revolutions,  12  horse-power. 

The  increase  in  power  from  increase  in  velocity  of  the  wind  is  equal  to  the 

square  of  its  proportional  velocity;  as  for  example,  the  25-ft.  mill  rateA 


L 


498  AIR. 

above  tor  a  16-inile  wind  will,  with  a  3:2*mile  wlud.  have  its  hors6-power  iik 
creased  to  i  X  191  =  7  horse-power,  a  iOtt.  mill  in  a  3i!-itiil6  wtiul  will  run 
up  to  80  horse-power,  aud  a  SO-ft.  mill  to  48  horae-power,  with  a  small  de 
duction  for  increased  friction  of  air  on  the  wheel  aud  the  machiuery. 

The  modern  mill  of  niediuui  and  larce  else  will  ran  and  produce  work  in  a 
4-mile  breeze,  becomluf^  very  effloient  in  an  8  to  16-miIe  breese.  and  Imnrase 
its  power  with  safety  to  the  running-gear  up  to  a  gale  of  46  miles  per  hour. 

Prof.  Thurston,  in  an  article  on  modem  uses  of  the  wimlmill.  Engineer'- 
ing  Magazine^  Feb.  1893,  says :  The  best  mills  cost  from  about  $600  for  the 
10-ft.  wheel  of  ^  horse-power  to  $1200  for  the  85-f t.  wheel  of  lU  horse-power 
or  less.  In  the  estimates  a  working-day  of  8  hours  is  assumed:  but  the  ma> 
chine,  when  used  for  pumping,  its  most  common  application,  may  actually 
do  Its  work  94  hours  a  day  for  days,  weeks,  and  even  months  together, 
whenever  the  wind  is  '*  stiff  '*  enough  to  turn  it.  It  costs,  for  work  done  in 
situations  in  which  its  irregularity  of  action  is  no  objection,  only  one  half  or 
one  third  as  much  as  steam,  hot-air,  and  gas  engines  of  similar  power.  At 
Faversham.  it  is  said,  a  Ift-hoi'se-power  mlU  raises  8,000,000  gallons  a  roonUi 
from  a  depth  of  100  ft,  saving  10  tons  of  coal  a  month,  which  would  other- 
wise be  expended  in  doing  the  work  by  steam. 

Electric  storage  and  lighting  from  the  power  of  a  windmill  has  been  tested 
on  a  large  scale  for  several  years  bv  Charles  F.  Brush,  at  Cleveland,  Ohio. 
In  1887  he  erected  on  the  grounds  or  his  dwelling  a  windmill  56  ft.  in  diam- 
eter, that  operates  with  ordinaiy  wind  a  dynamo  at  SOO  revolutions  per 
minute,  wlin  an  output  of  12,000  watt»-^]6  electric  horse-power-rchargitic; 
a  storage  system  thatgives  a  constant  lighting  capacity  of  100  16  to  90 
candle-power  lamps.  The  current  from  the  dynamo  is  automatically  regu- 
lated to  commence  charging  at  830  revolutions  and  70  volts,  and  cutting  Oie 
circuit  at  75  volts.  Thus,  by  its  SI  hours*  work,  the  storage  system  oC  406 
cells  in  12  parallel  series,  each  cell  having  a  capacity  of  100  ampdre  hours,  is 
kept  In  constant  readiness  for  all  the  requirements  of  the  establishment,  it 
being  fitted  up  with  SfiO  incandescent  lamps,  about  100  being  in  use  each 
evening.  The  plant  runs  at  a  mere  nominal  expense  for  oil,  repairs,  and  At' 
tentlon.  (For  a  fuller  description  of  this  plant,  and  of  a  more  recent  one  at 
Marblehead  Neck,  Mass.,  see  JLieut.  Lewises  paper  in  Engineeritig  Magazine^ 
Dec.  1894,  p.  475.) 

COMPBES8EB  AIB. 

Keatlnffof  Air  1^7  ComprMMton*— Kimball,  in  his  treatise  on  Phrsi* 
cai  Properties  of  Gases,  says:  When  air  is  compressed,  all  the  work  which  is 
done  hi  the  compression  Is  converted  into  heat,  and  shows  itself  In  the  rise  in 
temperature  of  r ho  comprefwed  gas.  In  practicomany  <levices  are  eniployt»d 
to  carry  olT  the  heat  ah  fattt  rk  it  is  developed,  and  keep  the  temperature  down. 
But  it  fs  not  possible  in  any  way  to  totally  remove  this  difficulty.  But,  it  may 
be  objected,  if  all  tlie  work  done  in  compression  is  converted  into  heat,  and 
if  this  heat  is  got  rid  of  as  soon  as  possible,  then  the  work  may  be  virtually 
thrown  away,  and  the  compressed  air  can  have  no  more  energy  than  it  haid 
before  compression.  It  is  true  that  the  compressed  gas  has  no  more  energy 
than  the  gas  had  before  compression,  if  lis  temperature  is  no  higher,  but 
the  advantage  of  the  compression  lies  in  bringing  its  energy  Uito  more  avail- 
able form. 

The  total  energy  of  the  compressed  and  uncompressed  gas  Is  the  same  at 
the  same  temperature,  but  the  available  energy  is  much  greater  in  the  former. 

When  tlie  compressed  air  is  used  in  driving  a  rock-driU,  or  any  other  piece 
of  machinery,  it  gives  up  energy  eoual  in  amount  to  the  work  it  does,  and 
its  temperature  is  accordingly  greatly  reduced, 

Gftuaes  of  liOns  of  Ener|nr  In  l^ao  of  CompresfteA  Alr« 
(Zahner,  on  Transmission  of  Power  by  Compressed  Air.)~l.  The  compreasioo 
of  air  always  develops  heat,  and  as  the  compressed  air  always  cools  down  to 
the  temperature  of  the  surrounding  atmosphere  liefore  it  is  used,  the  me- 
chantoal  equivalent  of  this  dissipated  heat  is  work  lost. 

2.  The  heat  of  compression  increases  the  volume  of  the  air,  and  hence  It 
is  necessary  to  carry  the  air  to  a  higher  pressure  in  the  compressor  In  order 
that  we  may  finally  have  a  given  volume  of  air  at  a  given  pressure,  and  at 
the  temperature  of  the  surrounding  atmosphere.  The  work  spent  in  effect* 
ing  this  excess  of  pressure  \&  work  tost. 

S.  Friction  of  the  air  in  the  pipea  leakage,  dead  spaces,  the  resistance  of> 
fered  by  the  valves,  insufficiency  of  valve-area,  infHrior  workmanship,  and 
slovenly  attendance,  are  all  more  or  less  serious  causes  of  loss  of  power. 


COMPRBSSSn  AIR. 


499 


The  first  eauM  of  Iom  of  work,  namely,  the  heat  developed  hr  oompres- 
non.  Is  enilrelj  unavoidable.  The  whole  of  the  mechanical  energy  whksh 
the  oompraHor-piaton  spends  upon  the  air  is  converted  into  heat.  This  heat 
■  dissipated  by  conduction  and  radiation,  and  its  mechanical  equivalent  Is 
vork  kist.  The  compressed  air,  having:  afcain  reached  thermal  equilibrium 
viih  Uie  surrounding  atmosphere,  expands  and  does  work  in  virtue  of  its 
btriitsic  energy. 

The  inuiaste  energy  of  a  fluid  is  the  energy  which  it  is  capable  of  exert- 
ine  agaimt  a  pinion  in  changing  from  a  given  state  as  to  temperHture  and 
Tolume  to  a  totnl  privation  of  heat  And  Indefinite  expansion. 

A€llml»tttie  and  laoihennal  Compresalon.— Air  msy  be  com- 
pressed either  adiitbaticttUy,  in  which  all  the  ht^at  rfsultlog  from  com* 
pressioD  is  retained  in  the  air  compressed,  or  iMthennallff,  in  which  the 
heat  is  removed  as  rapidly  as  produced,  by  means  of  8on?e  form  of  refrig. 
eraior. 

TolHHteis  Mean  PraMares  per  OCrakA,  Temperaiarea,  ete*, 
in  the  Operation  of  Alr-compresalon  fi-om  1  Atmoapliere 
and  eo*  valir.    (F.  Richards,  .4m.  Mach.,  March  SO,  1893.) 


r 

n 

I 


It 


1 

1.008 


5'1.84 


1  08 
2.02 
^.36 

n.stfi 


♦3  3.W1 


1.061 
1.401 

flO|5.08J 

70  5. 


.1 


1 

MS 

.88DB 
.8809 
.7881 
.74« 

.sgse 

.495 
.4S37 
.JK08 
8869 


.a68r 

.S4«2 

.2109 
.1968 
.1844 
.17«S 
.1«89 


1 

.95 
.91 
.878 
.84 
.81 
.89 
.806 
.548 
.494 

.45in 

.43 

.896 

.87 

.» 

.881 

.8144 

.801 

8R8 

,276 


0 

.96 

1.87 

3.74 

8.58 

4.8 

7.62 

10.83 

12.6: 

14.09 

16.84 

17.92 

19.83 

90.57 

21.69 

28.76 

83.78 

94.75 

S5  67 

36.85 


<1 

V 

I 


60« 

71 

80.' 

88. S 

96 
106 
145 
178 
207 


381 
803 
831 


867 
875 
889 
406 


37  480 


I! 
1 


80   6.443 
85*  6.783 
90.  7.122 
96   7.462 
1001  7.802 
lOS;  8.143 
110   8.488; 
ll.*^   8  823! 
120,  9.163] 
135,  9.r«6 
180.  9.843 
18510.188 
140  10.523< 
145  10.864 
15011.204 
16011.88 
ITO  12.56 
180  18.34 
190  18.98 
900  14.61 
I 


Column  8  gives  the  volume  of  air  after  compression  to  the  given  pressure 
and  after  it  is  cooled  to  its  initial  temperature.  After  compression  air  loses 
it.s  beat  very  rapidly,  and  this  column  may  be  taken  to  represent  the  volume 
of  air  after  compression  available  for  the  purpose  for  which  the  air  has 
beeo  compressed. 

Column  4  gives  the  volume  of  air  more  ni^arly  as  the  compressor  has  to 
deal  with  it.  In  any  compressor  the  air  will  lose  some  of  its  heat  during 
eomproMion.  The  slower  the  compressor  runs  the  cooler  the  air  and  the 
cnaiiar  the  volume. 

Column  6  gives  the  mean  effective  resistance  to  be  overcome  by  the  air- 
cylinder  piston  in  the  stroke  of  compression,  supposing  the  air  to  remain 
constantly  at  its  initial  temperature.  Of  course  it  will  not  so  remain,  but 
tiiis  column  is  the  ideal  to  be  kept  in  view  in  economical  air-compression. 


500 


AIB. 


Goliunn  6  B\ren  the  mean  effective  resisUnce  to  be  overcome  by  the  pis* 
ton,  supposing^  that  there  is  no  coollne  of  the  air.  The  actual  mean  effec- 
tive pressure  will  be  somewhat  less  than  as  given  in  this  column ;  but  for 
computing  the  actual  power  required  for  operating  air-coinpreflsor  cylinders 
the  fiicures  in  this  column  may  be  taken  and  a  certain  percentage  added — 
say  10  per  cent— and  the  result  will  represent  very  doeely  the  power  required 
by  the  compressor. 

The  mean  pressures  given  being  for  compression  from  one  atmosphere 
upward,  they  will  not  be  correct  for  computations  in  compound  compression 
or  for  any  other  initial  pressure. 

IjOm  Due  to  BxceMi  of  Pressure  caused  by  WKemttwktg  in 
the  CompreBSloii-cyllnder*— If  the  air  during  conipres^on  were 
kept  at  a  constant  temperature,  the  compression-curve  of  an  indicator-dia- 
gram taken  from  the  cylinder  would  be  an  isothermal  curve,  and  would  fol- 
low the  law  of  Boyle  and  Marriotte,  pv  =  a  constant,  or  piv,  =p«tro,  or 

Pi  =l>o^«  P«  &nd  v«  being  the  pressure  and  volume  at  the  bet^nning  of 

Vi 

compression,  and  p^Vi  the  pressure  and  volume  at  the  end,  or  at  any  inter- 
mediate point.  But  as  the  air  is  heated  during  compreRsion  the  pressure 
increases  faster  than  the  volume  decreases,  caubing  the  work  required  for 
any  given  pressure  to  be  increased.  If  none  of  the  heat  were  alxBtracte<l 
by  radiation  or  by  Injection  of  water,  the  curve  of  the  diagram  would  be  an 

adiabatic  curve,  with  the  equation  p,  =  P9\^J  Cooling  the  air  dur- 

ing compression,  or  compressing  it  tn  two  cylinders,  called  compounding, 
and  cooling  the  air  as  it  passes  from  one  cylinder  to  the  other,  reduces  the 
exponent  of  this  equation,  and  reduces  the  quantity  of  work  necessary  to 
effect  a  given  compression.  F.  T.  Gause  {Am.  Mach.^  Oct  90, 189S),  describ- 
ing the  operations  of  the  Popp  alr-coni pressors  in  Paris,  says :  The  greatest 
saving  realized  in  compressing  in  a  single  cylinder  was  88  percent  of  that 
theoretically  possible.  In  cards  taken  from  the  :2000  H.P.  compound  com- 
pressor at  Quai  De  La  Gare.  Paris,  the  saving  realised  is  85  per  cen»  of  the 
theoretical  amount.  Of  this  amount  only  8  per  cent  is  due  to  cooling  dur- 
ing compression,  so  that  the  increase  or  economy  In  the  compound  com- 
pressor is  mainly  due  to  cooling  the  air  between  the  two  stages  of  compres- 
sion. A  compression-curve  with  exponent  1.25  is  the  best  result  that  was 
obtained  for  compression  In  a  single  cylinder  and  cooling  with  a  very  fine 
spray.  The  curve  with  exponent  1.15  is  that  which  must  be  realized  in  a 
single  cylinder  to  equal  the  present  economy  of  the  compound  compressor 
at  Quai  De  La  Gare. 


Horse"poiver  required  to 
compress  and  deliver  one 
cubic  foot   of  Free  Air  per 

niniuie  tu  ugixeu  preMsure  with  no 
coiding  of  the  air  during  the  com- 
piesbiun;  also  the  horse-power  re- 
qinre<l,  supposing  the  air  to  be  main- 
lained  at  constant  temperature 
during  the  compreslon. 


Horse"poiver  required  to 
compress  and  deliver  one 
cubic  foot  of   CompreicMrd 

Air  per  minute  ai  a  given  i>i*-»^iiiv 
with  no  coohng  of  ilie  aii  (Jimug 
the  coniprHKsion;  also  the  liuist>> 
power  required,  supposing  ihenir  tu 
be  uiaimuined  at  countant  teniptrrA 
ture  during  the  couipiesslon 


GauKe- 

Air  not 

Air  constant 

Gauge- 

Air  not 

Aircorstnnc 

pressure. 

cooled. 

temperature. 

pressure. 

cooled. 

temperature. 

5 

.0196 

.0I8H 

5 

.0*J68 

.Offil 

10 

.0861 

.0388 

10 

.0606 

.0659 

20 

.06.a 

.0551 

20 

.1483 

.1800 

30 

.0846 

.0718 

80 

.8578 

jtim 

40 

.1038 

.0848 

40 

.884« 

.8188 

50 

.1195 

.0946 

50 

.5361 

.4166 

60 

.1813 

A(m 

60 

.6818 

.ft»K 

70 

.1476 

.11*20 

70 

.8508 

.8456 

80 

.1599 

.1196 

80 

1.080« 

.rroo 

90 

.1710 

Aim 

90 

l.«177 

.89:s 

100 

.1815 

.1318 

100 

1.4171 

1.0291 

The  horse-power  given  above  is  the  theoretical  power,  no  allowance  being 
made  for  friction  of  the  compressor  or  other  losses,  which  may  amount  to 
10  per  cent  or  more. 


COMPRESSED  AIR.  501 

FormmUB  fi»r  Adlmbatlc  CompreMlon  or  BxpanflloB  of 
Air  (or  oiber  sensibly  perfeci  gm»U 

I>t  air  at  an  absolute  temperature  7*],  alwolute  pressure  p.,  and  volume 
Vi  be  compressed  to  an  absolute  pressure  p,  and  correspoDdlnfc  volume  v« 
and  absolute  temperature  T^;  or  let  compressed  air  of  an  Initial  pressure, 
volume,  and  temperature  p,,  v,,  and  T,  be  expanded  topi,  v,,  and  T,,  there 
beiDfr  no  transmission  of  heat  from  or  into  tlie  air  during  the  operation.  Then 
the  fol lowing  equations  express  the  relations  between  pressure,  volume, 
and  temperature  (see  works  on  Thermodynamics): 


The  sxiMnents  are  derived  from  the  ratio  cp  -#-  cp  =  ft  of  the  speclflc  heats 
of  air  at  constant  pressure  and  constant  volume.  Taking  A;  =  1.406,  l-^k  = 
aril  ;  *  -  1  =  0.4011 ;  1  •«.  (fc  -  1)  =  «.4«;  *  h-(*  -  1)  =  8.4«8;  (A  -  1)  -i-  it  = 

'ITork  of  Adlabatlc  Compression  of  Air. -If  air  is  com. 
pressed  in  a  cylinder  without  clearance  from  a  vulume  t*.  and  pressure  P| 
to  a  smaller  volume  v.  and  higher  pressure  p^,  work  equal  to  P|V,  is  done  by 
the  external  air  on  the  piston  while  the  air  is  drawn  into  the  cylinder. 
Work  is  then  done  by  the  piston  on  the  air,  flrgt.  in  compressing  it  to  the 
pressure  p,  and  volume  «««  ad<1  ^^^o  i°  expelling  the  volume  Va  from  the 
cylinder  against  the  pressure  p,.  If  the  compression  is  adlabatlc,  PiVt*  ^ 
p,r9^  =  constant,    ft  =  1.41. 

The  work  of  compression  of  1  pound  of  air  Is 


!!n]a;r'-'f  =ii^]o*"^'-4 


The  work  of  expulsion  is  p^v,  =  p,i',  (^  ^  ^ 

The  total  work  is  the  sum  of  the  work  of  compression  and  expulsion  less 
the  work  done  on  the  pisioii  during  admission,  and  it  equals 


mean  eflfective  pressure  during  the  stroke  is 


p,  and  ps  are  absolute  pressures  above  a  vacuum  in  atmospheres  or  in 
pounds  per  squai-e  inch  or  per  square  foot. 

ExAKPLB.— Required  the  work  done  in  compressing  1  cubic  foot  of  air  per 
second  from  1  to  6  atmospheres,  including  the  work  of  expulsion  from  the 
ej'llnder. 

P« -*-  Pi  =  «;  «•'••  -  1  =  0.681;  8.468  X  0.681  =  8.358  atmospheres,  X  14.7  = 
34.06  Itw.  per  sq.  in.  mean  eflTeotive  prettsure.  X  144  =  4991  lbs.  per  sq.  ft.,  X  1 
ft.  stroke  =  mi  ft.-lb8.,  -«-  550  ft.  lbs.  per  second  :=  9.Uti  U.P. 


501a  AIB. 

It  Jl  at  ratio  of  preMur«i  «3  ps  •«-  pp  and  if  tij  s  1  oubtc  foot,  the  work  done 
la  compressing  1  oubio  foot  from  pi  to  i)|  is  in  foot-pouuds 

8.46api(i?«  "  -  1), 

Pi  being  taken  In  lbs.  per  sq.  ft.  For  eompretislon  at  tbe  Ma-level  p,  may  be 
taken  at  14  lbs.  per  sq.  in.  ^  3016  lbs.  per  sq.  ft.,  as  there  is  noine  loas  of 
pressure  due  to  friction  of  valyes  and  passatres. 

Indicator-cards  from  compressors  in  good  condition  and  under  working- 
speeds  usually  follow  the  adlabatlc  line  closely.  A  low  curve  itidlcaies 
piston  leakage.  Such  cooling  as  there  may  be  from  the  oylinder-jacket  and 
the  re-expansion  of  the  air  in  clearance-spaces  tends  to  reduce  the  mean 
effective  pressure,  while  the  "camel-backs'*  in  tbe  expulsion -line,  due  to 
resistance  to  opening  of  the  discharge- valve,  tend  to  increase  It. 

Work  of  one  stroke  of  a  compressor,  with  adiabatic  compression,  in  foot- 
pounds, 

W  ^  8.463F,  r,(H««*  -  1), 

in  which  Pj  =  Initial  absolute  pressure  in  lbs.  per  sq.  ft.  and  Vi  =  volume 
traversed  by  piston  In  cubic  feet. 

The  work  done  during  adiabatic  oompresslon  (or  expansion)  of  1  pound  of 
air  from  a  volume  v,  and  pressure  p|  to  another  volume  ««  and  prea«ure  », 
is  equal  to  the  mechanical  equIvHient  of  the  heating  (or  cooling).  If  /,  is  tin; 
higher  and  i^  the  lower  temperature,  Fatir.,  the  work  done  is  c^(<,  -  /,) 
foot-pounds,  c^  being  the  speciflo  heat  of  air  at  constant  volume  =  O.lOBQaad 
Jzr  778,  c^=  181.4. 

The  work  during  compression  also  equals 

Ra  being  the  value  of  pv  -4-  absolute  temperature  for  1  pound  of  air  r=  BS.87. 
The  work  during  expansion  is 

in  which  Pi  V|  are  the  initial  and  p,v,  the  final  pressures  and  volumes. 
Compressed-air    Bnfflnes,     Adiabatic    Expansion.  —  Le( 

the  iniiial  pressure  and  voiuiiie  taken  iitio  the  cyliuder  be  P|  lbs.  pei 
sq.  ft.  and  V|  cubic  feet;  let  expansion  take  place  to  p«  and  v^  according  to 
the  adiabatic  law  piVji*^*  =  p^v^*^*;  then  at  the  end  of  the  stroke  let  tbt» 
pressure  drop  to  tiie  back-pressure  p,,  at  which  the  air  Is  exhausted. 
Assuming  no  clearance,  the  work  done  by  one  pound  of  air  during  ad- 
mission, measured  above  vacuum,  is  P|V„  the  work  during  expausloa   ij 


2.463  pit»,  r  I  —  ^  "  V     n ,  and  the  negative  or  back  pressure  work  is  -  p,t?,. 
Thetotal  work  ispiW, -| -2.463^,1;, f  I  -  (^*y  "  J-p,»t,aadthenieaneff»*> 

tive  pressure  is  the  total  work  divided  by  v^. 
If  tlie  all'  is  expanded  down  to  the  back-pressure  pa  the  total  work  is 

or.  In  terms  of  the  final  pressure  and  volume, 

and  the  mean  effective  pressure  is 

The  actual  work  Is  reduced  by  clearance.  When  this  is  considered,  the 
product  of  the  initial  pressui-ep,  by  the  clearance  volume  is  to  be  subtracted 
from  the  total  work  calculated  from  the  initial  volume  V|  including  clearanos. 
(jSee  p.  744,  under  *'  Steam-eogiiie/') 


COMPRBfiSEt)  AtR. 


501& 


HMin  Kfir<M>tl««PreM«i>efl  ofAlv  CompreMed  Adlabaiieally. 

(F,  A 

.  Halsey,  Am. 

JfacA.,  M»r.  10, 1898.) 

MEP  from 

MEP  from 

R 

J?"'** 

14  lb».  iDitia). 

JJ 

2J0.af 

14  lbs,  Initial. 

].» 

1.067 

8.24 

4.75 

1.570 

27.5 

l.fiO 

i.m 

6.04 

6. 

l.MM 
l.«7 

28.7 

1.76 

1.170 

8.61 

5.25 

29.8 

2. 

i:^ 

10.8 

6.6 

1.089 

8U.8 

8.W 

i2:b 

6.75 

1.660 

81.8 

S.K 

i.aw 

14.7 

6. 

1.681 

8^.8 

2.T5 

1.841 

16.4 

6.i» 

1.701 

83.8 

a. 

1.875 

18.1 

0.5 

1.720 

84.7 

8,35 

1.407 

19.6 

6.76 

l.>6r 

35.6 

S.6 

1.488 

2t.l 

7, 

86.5 

S.75 

1.467 

22.5 

7.86 

1.77» 

87.4 

4. 

1.405 

)».9 

7.6 

1.798 

88.8 

4.t& 

l.Ml 

25.2 

8. 

1.8i7 

89.9 

4.5 

1.B46 

26.4 

B=  flual  -*-  Initial  absolute  prossure. 

MEP=  mtiaii  effective  presaure,  lbs.  per  sq.  ih.,  based  on  14  lbs.  initial. 

Gompound  C^mpreMlon*  with.  Air  CooI«d  between  the 
T^ro  CjllndeF*.  (Am.  Much.,  March  lO  and  31, 18»j.>— Worn  in  low-prea- 
fiun)  eyiiuder  =  If  2,  In  high- pressure  ayliuder  W^.    Total  voric 


W^+Wt  =  8.46P,rj[r,«»  +  i?'"ri 


-8]. 


r,  =  ratio  of_preHures  in  1.  p.  cjl.,  r,  =  ratio  in  h.  p.  cyl.,  R  =  viv^.  When 
r,  =3  tb  =  VR,  the  sum  TT,  -f-  IT,  Is  a  minimum.  Hence  for  a  Riven  total  ratio 
of  preasures,  A,  the  work  of  compression  will  be  lefut  when  the  ratios  of  the 
pressures  in  each  of  the  two  cylinders  are  equal^ 

The  equation  may  be  simplified,  when  rj  =  fi?,  to  the  following: 
TT,  +  ir,  =  6.92P,  V^IR^  •"*  -  1]. 
Dividing  bv  F.  gives  the  mean  effective  pressure  reduced  to  the  low-pressure 
cjlinder  lf^=  fl.WP,[i2«"»  ~  1]. 

Id  the  above  equation  the  compression  in  each  cylinder  is  supposed  to  be 
adiabatic,  bub  the  Intercooler  is  supposed  to  reduce  the  temperature  of  the 
air  to  that  at  which  oompresnlon  began. 

SleAii  BITectlTe  Preaaures  of  Air  CompreMied  In  Two 
Stacea,  aaamnlns  tlie  Intercooler  to  Reduce  tlie  Teni« 
parfitnro  to  Tbat  »t  wbtcl^  Comprasalon  BeirAa-    (F>  •^• 

Hai»ey»  Am,  MacK,  Mar.  81,  I89B.)        


^fffP 

Ultimate 

MSP 

Ultimate 

from  14 

Saving 

from 

Saving 

R 

2J0.1W 

lbs 

by  Com- 

R 

RO-li» 

14  lbs. 

by  Com- 

Initial. 

pound- 

Initial. 

pound- 
ing. K 

5.0 

1.263 

V5.4 

11.5 

9.0 

l..'J75 

36.3 

5.5 

1.280 

12  8 

9.5 

l.:^86 

87.3 

6.0 

1.296 

28.6 

12.8 

10 

1.396 

38.3 

e.5 

1.812 

80  1 

18.2 

11 

1.410 

40.2 

7.0 

1.826 

81.5 

18.7 

18 

1.484 

41.9 

7.5 

1.836 

8v».8 

14.8 

18 

1.4.M 

43.5 

8.0 

1.852 

84.0 

14.8 

14 

1.466 

45.0 

8.6 

1.864 

85.8 

15 

1.481 

46.4 

R  =  final  -¥■  initial  absolute  pressure. 
M(PP=  mean  effective  pressure  lbs.  per  aq.  in.  based  oq  14  lbs.  absolute 
initial  pressure  reduced  to  the  low-pressure  cylinder. 
To  Find  tbe  Index  of  the  Onrre  of  an  Alr-dlaiTi'oni.— 

If  Pi  Pj  be  preeinre  and  volume  at  one  point  on  the  curve,  and  ^y  ihe  prea. 

SUB  and  volume  at  another  point,  then  j^  =  (l^)*'  *°  which  x  is  tlie  index 
to  be  found.  Let  P -h  P,  =  «,  and  Fi  -*-  ^  =  r ;  then  iJ  =s  r*  log  U  =  «  log  r, 
"       9Xs»]oeR-*-logr, 


502 


AlU. 


Table  Ibr  Adlabatle  Compremilon  or  Expaiislon  of  Air. 

(Proc.  Inst.  M.E.,  Jan.  1881,  p.  1S3.) 


Absolute  Pressure. 

Absolute  Temperature. 

Volume. 

Ratio  of 

Ratio  of 

Ratio  of 

Ratio  of 

RaUo  of 

Ratio  of 

Greater 

Less  to 

Greater 

Less  to 

Greater 

Lees  to 

to  Less. 

Greater. 

to  Less. 

Greater. 

to  Less. 

Greater. 

(Expan- 

(Compres- 

(Expan- 

(Compres- 

(Compres- 

(Expan- 

sion.) 

sion.) 

sion.) 

sion.) 

doo.) 

Mon.) 

1.8 

.888 

1.054 

.948 

1.188 

.W9 

1.4 

.714 

1.102 

.907 

1.870 

.788 

1.6 

.685 

1.146 

.878 

1.896 

.716 

1.8 

.650 

1.180 

.848 

1.518 

.650 

8.0 

.500 

1.888 

.818 

1.686 

.€11 

8.8 

.454 

1.857 

.796 

1.760 

.571 

8.4 

.417 

2.889 
1.810 

.776 

1.868 

5S7 

8.e 

.885 

.758 

1.971 

.607 

8.8 

.867 

1.848 

.748 

8.077 

.481 

3.0 

.888 

1.875 

.787 

8.188 

.458 

8.8 

.818 

1.401 

.714 

8.884 

.438 

8.4 

.804 

1.486 

.701 

8.884 

.419 

8.6 

.878 

1.450 

.690 

8.488 

.4418 

8.8 

.868 

1.478 

.679 

8.580 

.888 

4.0 

.850 

1.406 

.660 

8.676 

.874 

4.8 

.888 

1.616 

.660 

8.770 

.861 

4.4 

.887 

1.587 

.651 

8.868 

.849 

4.6 

.817 

1.557 

.648 

8.055 

.888 

4.8 

.808 

1.576 

.»85 

8.046 

.828 

5.0 

.900 

1.596 

.687 

8.185 

.819 

6.0 

.167 

1.681 

.505 

8669 

.880 

7.0 

.148 

1.758 

.569 

8.981 

-»1 

8.0 

.185 

1.898 

..M7 

4.877 

.898 

0.0 

.111 

1.891 

.589 

4.759 

.810 

10.0 

.100 

1.950 

.518 

6.189 

.105 

mean  BflTectlTe  Presenrea  for  the  Compremlon  Part  only 


Sle  Cylinder.    (K. 

Richards,  Am.  Mack,,  Dec.  14, 1898.) 

Gauge- 

Adiabatic 

Isothermal 

Gaufre- 

Adiabatic 

Isothermal 

pressure. 

Compression 

Compression. 

pressure. 

Compression. 

Compreasicin. 

1 

.44 

.48 

46 

18.95 

18.68 

8 

.96 

.95 

50 

15.05 

18.48 

8 

1.41 

1.4 

fA 

15.98 

14.8 

4 

1.86 

1.84 

60 

16.89 

15.05 

5 

8.86 

8.88 

65 

17.88 

15.76 

10 

4.86 

4.14 

70 

18.74 

16  48 

16 

6.99 

6.77 

75 

19.54 

17.09 

80 

7.58 

7.8 

80 

90.6 

177 

85 

9.05 

8.49 

9S 

81.88 

18.8 

30 

10.89 

9.66 

90 

88. 

18.87 

85 

11.59 

10.78 

95 

88.77 

19.4 

40 

18.8 

11.7 

100 

88.48 

19.08 

The  mean  effective  pressure  for  compression  only  is  always  lower 
the  mean  effective  pressure  for  the  whole  worlc 


COMPRESSED  AIB. 


503 


mean  and  TemUnal  Pressnre*  of  ComfreMied  Air  used 
KxpanalTely  for  Gaase-presflare*  fi-om  60  io  100  Ibii* 

(Frank  Richards,  Am.  Much.,  April  18, 1»08.) 


The  preraures  in  the  table  are  all  firauge-pressures  except  thoee  in 
rV.Lh  are  absolute  pressures  (above  a  yacaum). 

BKovntaln  or  BUgli-altititde  Compressors* 

(Nor walk  Iron  WorkR  Co.i 


At  Sea- 

At  2000 

At  6000 

At  10.000 

II 

1^ 

level. 

feet. 

feet. 

feet. 

1^ 

jli 

ll 

i? 

dl 

ll 

5 

ti 

C 

Q 

A 

o 

m 

5 

» 

« 

12 

\i 

7 

10 

190 

29S 

85 

280 

84 

244 

8;i 

214 

80 

16 

19 

9LZ 

14 

150 

558 

70 

624 

68 

462 

04 

405 

60 

20 

20 

]^ 

18 

1:20 

H72 

110 

819 

107 

7-22 

100 

684 

94 

9i 

24 

1^^ 

20 

110 

1160 

146 

1090 

140 

960 

132 

843 

124 

26 

ao 

17H 

24 

90 

1059 

216 

1A60 

207 

1878 

165 

1200 

184 

As  tb«  capaelty  decreases  in  a  greater  ratio  than  the  power  necessary  to 
compress,  it  follows  that  operations  at  a  high  altitude  are  more  expensive 
ilian  at  sea- level.    At  10,000  feet  this  extra  expense  amounts  to  over  20  per 

Cr*llt. 

Compressors  at  High  AlUtpdea.    (Ingersoll-Sergeant  Drill  Co.) 

Alt.  above  sea-level,  ft. ..     0    1000  SOOOJ^IOOO  4000  5000  6000:7000  HOOO  9000  10000 

Barometer,  in.  mercury.  80.0:28.9 '^7.8^0.8  25.8  24.8  24.9  23.0  23.1  21.3  20.5 

lb8.persq.in.  14.7  14.2  18.7  13.2  12.7  12.2  11.7  11.8  10.9  10.5  10.1 

Air  delivered,  je 100    97     98     90     87     84     81     78      76     78  70 

Liiss  of  capacity,  ^ 0       8       7      10     13     16     19     22      24      27  30 

Decreased      power     re- 

qmr»Kl,jr 0     1.8   3.5    5.2    6.9    8.5  10.111.6  13.1  14.6  16.1 


504 


AIR. 


Air-eompressoni.     Band 

Drill 

04> 

RAND-CORLISS,  CLASS  "BB-:}"  (COMPOUND 

CLASS  "  E  "  (STRAIGHT- 

STEAM,  CONDENSING;  COMPOUND  AIR). 

LINE,  BELT-DRIVEN). 

FOB  8TKAM-PRBSSURB  OF  1^  LBS.   AMD  TRRMINAU 

rOR   TERMINAL    PBBSSURIS 

AIR-PRK8SURKS  OP  80  AND  100 

LBS. 

1 

OF  80  AND  100  LB8.PBK  0^  IM. 

6< . 

_  «  4> 

Cylinder  Diaroetera,  Ins. 

t. 

* 

"1" 

Alr-Cjl- 
iiider, 

1 

Indi- 
cated 

6^1 

s 

1| 

-Is 

in 

Incb«*8. 

H.P. 
Air- 
pws- 

Steam, 
h.  p.  1  1.  p. 

Air. 

» 

1 

E 

i 

«} 

h.p. 

l.p. 

sure 
80  lbs. 

670 

10 

18 

104 

17 

30 

86 

102 

97 

8 

IS 

140 

17 

1196 

12 

8« 

13 

21 

86 

88 

182 

165 

10 

14 

180 

29 

156i 

14 

26 

15 

24 

36 

88 

288 

851 

12 

16 

120 

45 

16S0 

14 

26 

15 

24 

42 

76 

252 

892 

14 

ti 

100 

69 

T9iO 

16 

ao 

IT* 

28 

86 

75 

298 

687 

16 

24 

05 

94 

«J4i 

16 

80 

17* 

28 

42 

75 

842 

688 

174 

SM 

96 

112 

OT95 

16 

80 

I7l 

28 

48 

70 

865 

85--W 

18 

84 

20 

89 

86 

75 

884 

8897 

18 

84 

90 

82 

42 

75 

442 

81]» 

18 

84 

20 

82 

48 

70 

476 

8060 

SO 

88 

22i 

86 

48 

70 

604 

4100 

as 

40 

24 

88 

48 

65 

625 

4R80 

2i 

42 

25 

40 

48 

65 

690 

5000 

84 

44 

264 

49 

48 

65 

768 

6000 

26 

48 

29 

46 

48 

65 

915 

6820 

28 

52 

80 

48 

48 

05 

1040 

In  the  first  four  sizes  (Class  '*  BB-3 '')  the  air-cylinders  have  poppet  inlet 
and  outlet  valves;  in  the  next  six  the  low-pressure  air-cylinders  have  me- 
chanical inlet-valves  and  poppet  outlet-valves;  and  iu  the  last  six  the  low- 
pressure  air-cylinders  have  Corliss  inlet- valves  and  poppet  out  let- valves. 
AU  hiRh-presBure  air-cylinders  have  poppet  Inlet  and  outlet  valves. 

^  Terminal  air-pressure  at  80  pounds. 

CLASS  "  B-2  "  (DUPLEX  STEAM,  NON-1  CLASS  "C'MSTRAiaHT-LINE." 

_.  STEAM-DRIVEN). 

I  FOR  BTKAM-  AND  TBRMIIfAL   AIR- 
PRESSURES  OF  100  LBS.  PKR  M)    IK. 


CONDENSING, 

COMPOUND  AIU).       ; 

FOR  STEAM-  AND  TERMINAL  AIR-PRESBURKSI 

OF   80  AND  100  LBS 

5h 

Cylinder  Diam- 
eters, Inches. 

a 

u 

i 

1 

I 

Hh 

Alr-cyls. 

h.  p.  1  I.  p. 

t 

35 

820 

8 

74       12 

12 

140 

35 

800 

9 

9 

14 

12 

140 

47 

898 

10 

94 

15 

16 

120 

62 

565 

12 

11 

18 

16 

120 

89 

770 

14 

18 

21 

16 

120 

121 

882 

14 

18 

21 

22 

100 

189 

1152 

16 

15 

2t 

22 

100 

182 

1812 

18 

174 

28 

80 

86 

',•85 

8085 

20 

19 

30 

80 

85 

8« 

23.56 

20 

10 

30 

48 

60 

870 

2848 

22 

21 

33 

48 

60 

446 

lis 

Cyl 

Diatn., 

Ins. 

i 

a 

i 
1 

i 

•^8 

PI 

i 

N 
< 

=  1 

97 

8 

8 

18 

140 

90 

1C5 

10 

10 

14 

130 

as 

251 

18 

18 

16 

180 

52 

89* 

14 

14 

82 

100 

82 

5i7 

16 

16 

24 

95 

110 

071 

18 

18 

84 

05 

140 

950 

20 

20 

80 

87 

2O0 

18% 

24 

24 

80 

85 

880 

I     All  air-cylindt*rs  have  poppet 
I  inlet  and  outlet  valves. 


The  first  six  sizes  (Class  "  B-2")  have  both  air-cylinders  fitted  with  popi)ei- 
valves  (inlet  and  discharge).    The  last  four  have  low-pressure  air-cyiiiider.s 


fitted  with  mechanical  in  let- valve; 
poppet  inlet  and  discbai-ge  valves. 


hif^h-pressure  air^ylindera  0tted  with 


STANDARD  AIR  COMPBBSSOBS. 

(The  Ingersoll-Ser^ant  Drill  Co.,  New  York  City.) 


5(5 


DI 

am. 

of  Cyl. 

=  l-i,    .2 



=  ^'^E     ^1 

Space 

[ 

Class 

Steam. 

Air. 

1  lesj  1 

Occupied. 

and 

10 

Type. 

Length. 

Width. 

ion!  177 

50-100 

lO'  a" 

8'  0" 

25-85 

A* 
Straight- 
line, 
Steam- 
driven. 

18 

. .  • . 

Vi]^ 

, 

M 

\:^  *285 

50-100 

12    6 

8    9 

40^ 

14 

\m 

1ft 

1-J11    M82 

60-100 

15    3 

4    8 

S0-7» 

16 

•  •  •  • 

16M 

, 

IH 

rii>   498 

60-100 

15    S 

4    3 

««-100 

18 

18^ 

24 

SI    057 

50-100 

19    1 

5    3 

86-131 

2r> 

Sq 

S^i 

«*    809 

60-100 

19    1 

5    8 

n3-l60 

2-3 

tM 

IH    ^«0 

60-100 

19    1 

5    3 

126-192 

24 

34^ 

80 

R0]Ji5   fiO-100 

22    0 

8    0 

160-245 

B.    Straighi-Iiue,  belt-diiven.    Same  as  A  in  sizes  up  to  16  x  16M  x  18  ins. 


at 

Skipl«^ 

CoHiH 

Buplc'z  air. 


CompouTifl 
OrtlJM 

Conipotmd 


|0!4 

16 

«0 

n 

no 

101^ 

N 

16 

\% 


Soutl 

■tralf^t^ 

Htie. 


90|  riTO: 
8-^  k^6 

7?^  ■mo 

6L*fin7 

ml  Gi5 

m\r.m 

7:*'^'S15 
TOpHflfiO 


101) 

hX7 
100 
100 
100 

too 


10) 

IflO 
lOt} 

lot* 
too 

100 


frfl-80 

m  m 

IMQ 


81 '   0^" 

10'    6'^ 

36    6 

VJ    6 

41     0 

13    0 

4S    a 

H    C 

4!     0 

16    6 

6U    0 

]»    fi 

m    tt 

H    0 

4.1    0 

!l     fl 

40    6 

IS    fl 

&S    G 

IS    U 

Sfi    6 

IH    C 

:ih    0 

l!J    e 

5    ^ 

as 

€    » 

ii& 

7  ta 

ao 

H    fi 

30 

KJ  li> 

3S 

llfi 

2V4 
4  4 

ion 
isr5 


97 

367 
«>4 
661 

^  ^!4 

18^-25 
S3^-t| 
a4f4-W) 


J£L    Beit^riveo.    Same  as  i^in  sizes  up  to  14^  diam.  by  10  ins.  stroke. 


o. 

10 

...10^4 

13 

160 

854 

100 

14'   6" 

V  0" 

Steam- 

12 

:.::?^ 

14 

ir>5 

5T0 

100 

16    6 

9    0 

actuated, 

.... 

14 

18 

120 

764 

100 

20    0 

10    0 

duplex 
orVialf 

16 

::::'!S^ 

18 

120 

996 

100 

80    0 

10    0 

18 

24 

94 

1314 

100 

26    6 

11    6 

duplex. 

20 

...jaoM 

24 

M 

1618 

100 

25    6 

12    0 

O. 

10 

LT} 

....llo^ 

12 

160 

446 

80-100 

16    8 

7    3 

Duplex  St., 

16 

....  1 5^1 

18 

120 

1130 

80-100 

23    0 

10    0 

com  p.  air. 

20 

30^ 

....  18>J 

24 

100 

1963 

100 

30    0 

12    0 

O. 

10 

17 

14m  »M 

22^114^ 

12 

160 

344 

80-100 

16    8 

7    6 

0«>mp.  St., 

16 

26 

18 

120 

950 

80-100 

23    0 

10    0 

cum  p.  air. 

20 

38 

28M 

17>4 

24 

100 

1710 

80^100 

30    0 
~8"6~ 

12    0 

H. 

8 

.... 

8 

8 

150 

138 

60-100 

4    6 

Duplex  St., 

10 

10 

10 

150 

268 

70-100 

10    0 

4    9 

duplex  air. 

.... 

12 

.... 

12 

12 

150 

474 

80-100 

11    8 

5  10 

H. 

8 

14 

9 

8 

150 

210 

80-100 

8    6 

6    3 

Duplex  St., 

10 

16 

10 

10 

150 

342 

80-100 

10    2 

5    9 

com  p.  nir. 

12 

18 

12 

12 

150 

hU\ 

80-1011 

Jl  10 

6    9 

75 
181 

163 
212 
280 
814 

71-80 

lyO  208 

353 

55-62 
152-171 
274-308 

20-28 
43  54 
83-96 

32-36 
52-58 

7K-88_ 

J,    Belted  duplex  or  compound.    8  to  98  H.P.;  50  to  1059  cu.  ft.  per  m. 

*  Classes  A.  C,  G,  and  H  are  also  built  in  intermediate  sixes  for  lower 
pressures,  t  Furnished  either  duplex  or  half  duplex,  t  Most  economical 
form  of  compressor.  Compound  air-cylinders  in-e  two-stage,  f  Self  con  - 
taiaed  steam-compressor. 


505a 


AIR. 


Coble  Feet  of  Free  Air  Required  to  Run  from  One  to 
Forty  IHacblnes  wltli  60  1d«.  Pressure.  (lugereolUHergeant 
Drill  Co.) 


For  75  lbs.  Pressure  add  1/5 

For  90  lbs. 

add  2A 

OOAIi- 

ROCK-DRIUjB. 

CDTTERS. 

No.  of 

A 

B 

C 

D 

E 

F 

G 

H 

Machfues 

2  in. 

iHln. 

««in. 

8  III. 

3^  in. 

S^in. 

4kiii>. 

5  in. 

8Hln. 

4  in. 

G5 

70 

93 

110 

115 

135 

140 

165 

TO 

93 

no 

120 

160 

190 

800 

880 

260 

280 

140 

186 

150 

174 

834 

879 

294 

888 

860 

405 

210 

871) 

196 

220 

804 

856 

872 

428 

460 

624 

880 

87:; 

iMO 

860 

870 

425 

445 

510 

555 

686 

850 

466 

864 

294 

426 

486 

616 

588 

643 

738 

420 

S58 

29^1 

8:!9 

476 

616 

581 

668 

721 

886 

490 

651 

320 

860 

580 

600 

640 

790 

800 

9^ 

560 

744 

860 

405 

685 

675 

720 

810 

000 

1085 

680 

8S7 

10 

400 

450 

650 

760 

800 

900 

1000 

1150 

700 

880 

18 

480 

540 

780 

900 

900 

1080 

1200 

1880 

840 

1116 

16     • 

675 

975 

1125 

1200 

1350 

1500 

1725 

1060 

1996 

80 

. . .  • 

1800 

1500 

1600 

1800 

8000 

2800 

1400 

1860 

SiS 

10. '5 
1U50 

1875 
2250 

2000 
2400 

2850 
8700 

2500 
8000 

2775 
8450 

1750 
8100 

28^ 

80 

2790 

40 

2600 

8000 

8200 

8600 

4000 

4600 

2800 

8720 

Ooiiipresse4«alr  Table  for  Pumplnc  Pluits. 

(lugersoll-Sergeant  DriU  Co.) 
For  the  convenience  of  engineers  and  others  flfcurlof?  on  pumptnf?  plants 
to  be  operated  by  compressed  air,  we  subjoin  a  table  by  which  the  pressure 
and  ▼oluiiie  of  air  required  for  any  size  pump  can  be  readily  ascertained. 
Iteasonable  allowances  have  been  made  for  loss  due  to  clearances  in  pump 
and  friction  in  pipe. 


Ratio  of 
Diam- 
eters. 


1  *oH!b 
lWtoll|^ 
1«  to  1 1  I  fj 
«  tolj  j^ 
2MtolJ  ^ 
2«tol{^ 


Perpendicular  Heic^ht.  In  Feet,  to  which  the  Water  Is  to  be 
Pumped. 


13.75 
0.21 


»7.5 
0.45 
12.82 
0.65 


55.0 

0.76 
24.44 

0.95 
19.8 

1.14 
13.75 

1.83 


0.89 

.%.:« 

1.09 
22.8 

1.84 
17.19 

1.37 
13.75 

l.M.'} 


82.5 

1.04 
36.06 

1.24 
27.5 

1.30 
80.63 

1.58 
16.5 

1.C8 
18.2 

1.79 


176 

200 

260 

soo 

96.25  110.0 

1.801     1.84 

4.J.78   48.88 

61.11 

73.88 

1.80 

1.53 

1.88 

2.18 

82.1 

86.66 

45.88 

55.0 

1.54 

1.60 

1.99 

8.39 

84.06,  87.5 

84.38 

41.85 

1.661     1.81 

8.11 

2.40 

19.25   28.0 

27.6 

8i.O 

1.83     1.97 

8.86 

8.56 

15.4     17.6 

28.0 

86.4 

1.98 

8.06 

8.84 

2.62 

97  66 

8.70 
78  J3 

2.88 
65.0 

£.98 
44  0 

8.15 
S6.8 

8.18 


A  s  air-pressure  at  pump.  B  —  cubic  feet  of  free  air  per  gallon  of  water. 
To  And  the  amount  of  air  and  pressure  required  to  pump  a  given  quantity 
of  water  a  given  height,  And  the  ratio  of  diameters  between  water  and  air 
cylinders,  and  multiply  the  number  of  gallons  of  water  by  the  figure  found 
in  th»*  column  for  the  required  lift.  The  result  is  the  number  of  cttbic  ftti 
of  free  air.  The  pressure  required  on  the  pump  will  be  found  directly  above 
In  the  same  column.  For  example:  The  ratio  between  cylinders  being  2  tn 
1,  required  to  pump  100  gallons,  height  of  lift  850  feet.  We  find  under  850 
feet  at  ratio  2  to  1  the  figures  2.11 ;  2.11  x  100  :;i  811  cubic  feet  of  free  air. 
The  pressMre  required  is  84,38  pounds, 


COMPRESSED   AIR. 


5055 


Compre«sed-alr  Table  for  IEolsttnv-eii|;ines. 

(Ingersoll-Sers^eant  Drill  Co.) 
The  following  table  gives  an  approximate  idea  of  the  volume  of  free  air 
required  for  operating  hoisting-engines,  the  air  being  delivered  at  60  lbs. 
gauge-pressure.  There  are  so  many  variable  conditions  to  the  operation  of 
hoisting-engines  iu  common  use  that  accurate  computations  can  only  be 
c^ered  when  fixed  data  are  given.  In  the  table  the  engine  is  assumed  to 
aclually  run  but  one-half  of  the  time  for  hoisting,  while  the  compressor,  of 
course,  runs  continuously.  If  the  engine  runs  less  than  one-half  the  time, 
as  it  usually  does,  the  volume  of  air  required  will  be  proportionately  less, 
and  vice  versa.  The  table  is  computed  for  maximum  loads,  which  also  in 
practice  may  vary  widely.  From  the  intermittent  character  of  the  work  of 
a  hoisting-engine  the  parts  are  able  to  resume  their  normal  temperature 
between  the  hoists,  and  there  is  little  probability  of  the  annoyance  of  freez- 
ing up  the  exhaust-passages. 

VOLUME  OF  FREE  AIR  REQUIRED  FOR  OPERATING  HOISTING- 
ENGINES,  THE  AIR  COMPRESSED  TO  60  POUNDS  GAUGE- 
PRESSURE. 

SlMOt,Si^3TUMDBR  HoiSTIKO-BNOINB. 


Diara.  of 

Stroke. 
Inches. 

Revolu- 

Normal 

Actual 

CN^linder, 
iDcfaes. 

tions  per 
Minute. 

Horse- 
power. 

Horse- 
power. 

5 

6 

aoo 

8 

5.9 

5 

8 

160 

4 

6.8 

^ 

8 

160 

6 

0.9 

7 

10 

185 

10 

18.1 

^ 

10 

m 

15 

16.8 

18 

110 

20 

18.9 

10^ 

13 

110 

85 

86.8 

Weight 
Urted, 
Single 
Rope. 


600 
1,000 
1,600 
8,000 
8,000 
5,000 
6,000 


Cubic  Ft. 
of  Free  Air 
Required. 


75 
80 
126 
151 
170 
838 
330 


DOUBLB-OYLINDER  HoimNO-EMOTNB. 


5 

6 

800 

6 

11.8 

1,000 

150 

5 

8 

160 

8 

18.6 

1.650 

160 

6M 

8 

160 

18 

19.8 

8,500 

250 

7 

10 

185 

80 

84.8 

8.500 

308 

^ 

10 

VA 

30 

8.1.6 

6,000 

340 

18 

no 

40 

37.8 

8,000 

476 

10^ 

18 

110 

60 

58.4 

10,000 

660 

18M 

15 

100 

75 

80.2 

1,185 

14 

18 

90 

100 

185. 

1,687 

Prmctlcal  Results  -wttb  Compressed  Air.— Comprested-air 
8u»tem  at  the  Chnpin  Mtnen.  Iron  Mountain^  A/irA.— These  mines  are  three 
miles  from  the  falls  which  supply  the  power.  There  are  four  turbines  at  the 
falls,  one  of  1000  horse-power  and  three  of  900  horse-power  each.  T)je  press- 
ure is  60  pounds  at  60^  Fahr.  Each  turbine  runs  a  pair  of  compressoi-s. 
The  pipe  to  the  mines  is  84  ins.  diameter.  The  power  is  applied  at  ine  mines 
to  Corliss  engines,  running  pumpn.  hoists,  etc.,  and  direct  lo  rock-drillfi. 

A  test  made  in  1888  gave  1480.87  H.P.  at  the  compressors,  and  890.17  H  P. 
as  the  sum  of  the  horse-power  of  the  engines  at  the  mines.  Therefore,  only 
87jf  of  the  power  generated  was  recovered  at  the  mines.  This  includes  the 
loss  doe  to  leakage  and  the  loss  of  energy  in  heat,  but  not  the  friction  In  the 
engines  or  compressors.    (F.  A.  Pocock,  Trans.  A.  I.  M.  E.,  1890.) 

W.  L.  Saunders  {Jour.  F.  1. 1893)  says:  "There  is  not  a  properly  designed 
oomprcesed-air  installation  in  operation  to-day  that  loses  over  f4  by  trans^ 
mission  alone.  The  question  is  altogether  one  of  the  size  of  pipe;  and  If  the 
pipe  is  large  enough,  the  friction  loss  is  a  small  item. 

••  The  loss  of  power  In  common  practice,  where  compressed  air  is  used  to 
drive  machinei^  in  mines  and  tunneln,  is  about  70)(.  In  the  beat  practice, 
with  the  best  air-compressors,  and  without  reheatiner,  the  loss  Is  about  60^. 
These  losses  may  be  reduced  to  a  point  as  low  as  80^  by  combining  the  best 
ayitems  of  rebeatiog  with  tbe  beat  air-conipressors." 


606  AIB. 

Gain  4m%  i»  Balieatliiff*— Prof.  Ceonedy  uyt  oompreased-alr 
traDBinifwion  sysUsm  is  now  being  carried  on.  on  a  larse  commercial  ncale, 
Ip  such  a  fashion  that  a  small  motor  four  miles  away  from  the  central  sta- 
tion can  Indicate  in  round  numbers  10  horse-power,  for  90  borse-power  at 
Che  station  itself,  ailowinf?  for  the  value  of  the  coke  used  In  heating  the  air. 

The  limit  to  successful  reheating  lies  in  the  fact  that  air-engineB  osBAOt 
work  to  advantage  at  temperaturt^s  over  S50". 

The  effleiency  of  the  common  system  of  reheating  is  shown  by  the  re- 
sults obtained  with  the  Popp  system  in  Paris.  Air  is  admitted  to  the  re- 
beater  at  about  88*,  and  paioes  to  the  engine  at  about  Si 5*,  thus  being  lo- 
cr«Mwed  in  volume  about  49%.  The  air  used  in  Paris  is  about  11  cubic  feet  of 
free  air  per  minute  per  horse-power.  The  ordinary  practice  in  America 
with  cold  air  is  from  15  to  tf  cubic  feet  per  minuto  per  horse-power.  When 
the  Paris  engines  were  worked  without  reheating  the  air  consumption  was 
increased  to  about  16  cubic  feet  per  horse-power  per  minute.  The  amount 
of  fuel  consumed  during  reheating  Is  trifling. 

KiBtftenej  of  OompreMwd-atr  BiKglneii.— The  efUciency  of  an 
air-engine,  that  is,  the  percentage  which  the  power  given  out  by  the  air-en- 
gine bears  to  that  required  to  compress  the  air  in  the  compressor,  depends 
on  the  loss  by  friction  in  the  pipes,  valves,  etc.,  as  well  as  in  the  engine  itself. 
This  question  is  treated  at  length  in  the  catalogue  of  the  Norwaik  Iron  Wcirks 
Ck>M  from  which  the  following  is  condensed.  As  the  friction  increases  the 
most  economioal  pressure  increases.  In  fact,  for  any  siven  friction  In  a 
pipe,  the  pressure  at  the  compressor  must  not  be  earned  below  a  ceruin 
limit.  The  following  table  gives  the  lowest  pressures  which  should  be  used 
at  the  compressor  with  varying  amounts  of  friction  in  the  pipe: 

Friction,  lbs. 8.0     6.8     8.8    11.7    14.7    17.6    a0..5    83.5    28.4    89.4 

Lbs,atOompreMor...  20.5   80.4    83.8   47.     62.8    61.7    70.5    76.4    83.8    S8.8 
ElQclency^ 70.0    61.5    60  6    57.0    55.7    54.0    52.5    51.8    50.8    40.8 

An  Increase  of  pressure  vriU  decrease  the  bulk  of  air  passing  the  pipe  and 
Its  velocity.  This  will  decrease  the  loss  bv  friction,  but  we  subject  ourselves 
to  a  new  lots,  t,e.  the  diminishing  eflUciencies  of  increasing  pressures.  Yet  as 
each  cubic  foot  of  air  is  at  a  higher  pressure  and  therefore  carries  more 
power,  we  will  not  need  as  many  cubic  feet  as  before,  for  tlie  same  work. 
With  so  many  sources  of  gain  or  loss,  the  question  of  selecting  the  proper 
pressure  is  not  to  be  dHcided  iiastily. 

The  losses  are,  first,  friction  of  the  compressor.  This  will  amonnt  ordinarily 
to  16  or  80  per  cent,  and  cannot  probably  be  reduced  below  10  per  rent. 
Seoond,  the  losa  oocosionsd  by  pumping  the  air  of  the  engine-room,  rather 
than  the  air  drawn  from  a  cooler  place.  This  losa  varies  with  the  season  and 
amounts  from  8  to  10  per  cent.  This  can  all  be  saved.  The  third  loss,  or  aeries 
of  losses,  arises  in  the  compressing  cylinder,  viz.,  insufflcient  supply,  difflcult 
discharge,  defective  cooliiur  arrangements,  poor  lubrication,  etc  The  fourth 
loss  is  found  in  the  pipe.  This  loss  varies  with  the  situation,  and  is  subject 
to  somewhat  complex  influences.  The  fifth  loss  Is  chargeable  to  fall  of 
temperature  in  the  cylinder  of  the  air-engine.  Losses  anslng  from  leaks 
are  often  serious. 

BflTect  of  Temperature  oflntafce  upon  tbe  IMacbars^  ofm 
Coiiipresaor«— Air  should  be  drawn  f  ram  outside  the  engine>rooin,  and 
from  as  cool  a  place  as  possible.  The  gain  amounts  to  one  per  cent  for  every 
five  degrees  that  the  air  is  taken  in  lower  than  the  temperature  of  the  engine 
room.  The  inlet  conduit  should  have  an  area  at  least  50jK  of  the  area  or  the 
air-piston,  and  should  be  made  of  wood,  brick,  or  other  non-conductor  of 
heat. 

Discharge  of  a  compressor  having  an  intakn  capacity  of  1000  cubic  fe«i 
per  minute,  and  volumes  of  the  discharge  reduoea  to  cubic  feet  at  atmos- 
pheric pressure  and  at  temperature  of  68 degrees  Fahrenheit: 

Temperature  of  Intake,  F 0»    «•    68«»  75«  80»  00»  100«    110* 

Relative  volume  discharged,  cubic  ft...  1185  1060  1000  075  006  048    888   Old 

Bequlrementa  of  Hock-drtUa  BrlTen  by  CompresaeA 
Atr«  (Norwaik  Iron  Works  Co.)— Tiia  speed  of  the  drul,  the  pressure  of 
air,  and  the  nature  of  the  rock  affect  the  conRumptlon  of  power  of  drills. 

A  three-Inch  drill  using  air  at  80  lbs.  pressure  mode  800  blows  per  minute 
and  consumed  the  equivalent  of  64  t-ubic  fei't  of  free  air  per  minute.  The 
same  drill,  with  air  of  68  lbs.  prej^uiire,  niatle  450  blows  per  minute  and 
consiimeil  160  cubic  feet  of  free  air  X)cr  minute.    At  Hell  Gate  different 


COMPRESSED   A  IK. 


507 


BOkchinta  doing  the  same  wotk  used  from  80  to  160  cubio  feet  free  air  pef 
minut4'. 
An  averafre  comtiimptlon  may  be  taken  firenerally  from  80  to  100  cubic  feet 

i  Parls*<«A  most  exten- 

^ ^  „  '  uoiiipreeeed  air  is  that  of 

H.  Popp.  In  Paris.  One  of  the  central  stations  is  laid  out  for  JM^OOO  horse* 
poirer.  For  a  very  complete  description  of  the  system,  see  Engineering^ 
Feb.  15.  June  7,  21.  and  Vi,  1880,  and  March  13  and  M,  April  10,  and  May  1. 
1891.  Also  Proc.  Inst.  M.  E.,  July,  1889.  A  condensed  description  will  be 
found  in  Modern  Mechapisra.  p.  12. 

ITttltaatlon  of  Compr— <d  Air  in  ftonall  lloton.»ln  the 
earliest  siacres  of  the  Popp  svstem  in  Paris  It  was  recofcnised  that  no  f^ood 
results  oould  be  obtaineu  if  the  air  were  allowed  to  expand  direct  into  the 
motor;  not  only  did  the  formation  of  ice  due  to  the  expansion  of  the  air 
rapidly  aocomulate  and  choke  the  exhaust,  but  the  percentaij^e  of  userul 
wurx  obtained,  compared  with  that  put  into  the  air  at  the  central  station, 
was  so  small  as  to  render  commercial  results  hopeless. 

After  a  number  of  experiments  M.  Popp  adopted  a  simple  form  of  cast- 
iron  stove  Imed  with  flreday,  heated  either  by  a  ^as  jet  nr  by  a  smsli  coke 
fire.  This  apparatus  answered  the  desired  purpose  until  some  better  ar- 
ranfcement  was  perfected,  and  tlie  type  was  accordingly  adopted  througrh* 
out  the  whole  system.  The  economy  resultinjr  from  the  use  of  an  improved 
form  was  Tery  marked,  as  will  be  seen  from  the  following  table. 

EFncixwcT  or  Air-heatino  Stoves. 


CasMron  Box 

Stoves. 

14 

14 

S0.34» 

11,054 

45 

45 

215 

364 

17,000 

17,200 

1,278 

1,228 

2,032 

2.058 

Wrouifht. 

iron  Coiled 

Tubes. 

40.3 

38,4'J8 

41 

847 

30,^200 

830 

2,545 


Heatinf^surface,  sq.  ft, 

.Air  hesat«'d  iter  hour,  cu.  ft 

Temp,  of  air  admitted  to  oven,  deg.  F 

"  '•   at  exit.  dt»K.  F 

Touil  hent  absorbed  per  hour,  calories 

Do.  per  M|.  ft.  of  heating  surface  per  hour,  culs 
Do.  per  lb.  of  coke 

The  results  given  in  this  table  were  obtained  from  a  large  number  of 
trials.  From  these  trials  it  was  found  that  more  than  70%  of  the  total  num- 
ber of  calories  in  the  fuel  employed  was  absorbed  by  the  air  and  trans- 
formed into  useful  work.  Whether  gas  or  coal  be  employed  as  the  fuel,  the 
amount  n*quired  Is  so  small  as  to  be  scarcely  worth  consideration;  accord- 
ing to  the  experiments  carried  out  it  does  not  exceed  0.2  lb.  per 
horse-power  per  hour,  but  it  is  scarcely  to  be  expected  tluit  in  regular  prac- 
tice this  quantity  is  not  laraely  exceeded.  The  efficiency  of  f  uelconsumed 
in  this  way  is  at  least  six  tunes  greater  than  whea  utilized  In  a  boiler  and 
steam-engine. 

According  to  Prof.  Riedler,  from  15)(  to  2<^  above  the  power  at  the  central 
station  oan  be  obtained  by  means  at  the  disposal  of  the  power  users,  and  it 
has  been  shown  by  experiment  that  by  heating  the  air  to  480<*  F.  an  1D' 
creased  efficiency  of  90%  can  be  obtained. 

A  large  number  of  motors  in  use  among  the  subscribers  to  the  Compressed 
Air  Company  of  Paris  are  rotary  engines  developing  1  horse- power  and 
less,  and  these  in  the  early  times  of  the  industry  were  very  extravagant  in 
iheir  consumption.  Small  rotary  engines,  working  cold  air  without  expan- 
sion, used  as  high  as  X330  cu.  ft.  of  air  per  brake  horse-power  per 
hour,  and  with  heated  air  1624  cu.  ft.  Working  expansively,  a  1  horse- 
power rotary  engine  used  1469  cu.  ft.  of  cold  air,  or  960  cu.  ft.  of  heated  afr, 
and  a  2- horse-power  rotary  engine  1059  cu.  ft.  of  cold  air,  or  847  cu.  ft.  of  air, 
heated  to  about  60«  C. 

The  efficiency  of  this  type  of  rotary  motors,  with  air  heated  to  50*  C,  may 
now  be  assimied  at  43](.  With  such  an  efficiency  the  use  of  small  motors  In 
many  industries  becomes  possible,  while  in  cases  where  It  is  necessary  to 
have  a  constant  supply  of  cold  air  economy  ceases  to  be  a  matter  of  the  first 
importance. 

Tests  of  a  small  Riedinger  rotary  engine,  iiueU  for  driving  sewing-machines 
and  indicating  about  0.1  U.P.  showed  an  air-cousumptlou  of  1377  cu.  ft.  per 


508  AIB. 

HP.  per  hour  when  the  Initial  pressure  of  the  air  was  86  lbs.  per  bq.  in.  and 
its  temperature  54«  P.,  and  988  cu.  ft.  when  the  air  was  heated  to  898*  F.,  its 
pressure  being  72°  Ibt*.  With  a  one-haif  horse-power  Tariable^zpansion 
rotary  enfi:iiie  tlie  air-consumption  was  from  800  to  900  cu.  ft.  per  H.P.  per 
hour  for  initial  pressures  of  64  to  85  lbs.  per  sq.  in.  with  the  air  neated  from 
336«  to  888°  F.«  and  1148  cu.  ft.  with  cold  air,  4G«  F.,  and  an  initial  pressure 
of  78  lbs.    The  ▼olumee  of  air  were  all  talcen  at  atmospheric  pressure. 

Trials  made  with  an  oid  slngle-cyUnder  80-hor8e-power  Farcot  steam-en 
gine,  indicatinK  7^  horae«power,  rave  a  consumption  of  air  per  brake  horse- 
power as  low  as  465  cu.  ft.  Der  hour.  Tlie  temperature  of  admission  was 
fe0«  F.,  and  of  vxliaust  95«  ¥. 

Prof.  Elliott  fciTes  the  followinfr  as  typical  results  of  efiSclency  for  various 
systems  of  compressors  and  air-motors : 

Simple  compressor  and  simple  motor,  efBciency  9dA% 

Compound  compressor  and  simple  motor,    **      44.9 

*•  "    compound  motor,  eflBciency 80.7 

Triple  compressor  and  triple  motor,  " 65.8 

The  efflciencv  Is  the  ratio  of  the  Indicated  horse-power  In  the  motor  cylln 
ders  to  the  indicated  horse-power  in  the  steam-cyliuders  of  the  compressor. 
The  pressure  assumed  is  6  atmospheres  absolute,  and  the  losses  are  equal 
to  those  found  in  Paris  over  a  distance  of  4  miles. 

BuminaiT  of  Bfflelencleii  of  €oiiipresfled««ir  TrmnsmlsaAoii 
Bt  Paris,  between  tlie  Central  Station  at  St.  Fargean  and 
a  lO-liorse-povrer  Motor  l¥orkinir  ivltb  Pressnre  Me- 
dnced  to  4yk  Atniosplieres. 

(The  flffures  below  correspond  co  mean  results  of  two  experiments  cold  and 

two  heated.) 
1  indicated  horse-power  at  central  station  gives  0.846  indicated  horse-power 
In  compressors,  and  corresponds  to  the  compression  of  848  cubic  feet  of  air 
per  hour  from  atmospheric  pressure  to  6  atmospheres  absolute.    (The  weight 
of  this  air  is  about  So  pounds.) 

0.845  indicated  horse-power  In  compressors  delivers  as  much  air  as  will  do 
0.52  Indicated  horse-power  in  adiabatic  expansion  after  it  has  fallen  iu  tem- 
perature to  the  normal  temperature  of  the  mains. 

The  fall  of  pressure  in  mams  between  central  station  and  Paris  (say  5  kilo- 
metres) reduces  the  possibility  of  work  from  0.5:i  to  0.51  indicated  horse- 
power. 

The  further  fall  of  pressure  through  the  reducing  valve  to  4Haimospheres 
(absolute)  reduces  the  possibility  of  work  from  0.51  to  0.50. 

Incomplete  expansion,  wire-drawing,  and  other  such  causes  reduce  the 
actual  indicated  horse-power  of  the  motor  from  0.50  to  0.89. 

By  heating  the  air  before  it  enters  the  motor  to  about  Stiff*  F.,  the  actual 
indicated  horsepower  at  the  motor  is,  however,  increased  to  0.54.  The  ratio 
of  pnlu  by  healing  the  nlr  is,  therefore.  0..M  -*-  0.80  =  1.8S. 

In  this  process  additional  heat  Is  supplied  by  the  combustion  of  about  0.39 
pounds  of  coke  per  Indioated  horse-power  per  hour,  and  If  this  be  taken  into 
account,  the  real  indicated  efficiency  of  the  whole  process  becomes  0.47 
instead  of  0.54. 

Working  with  cold  air  the  work  spent  in  driving  the  motor  itself  reduces 
the  avHilable  horse-power  from  0.89  to  0.80. 

Working  with  heated  air  the  work  spent  in  driving  the  motor  itself  reduces 
the  available  horne-power  from  0.54  to  0.44. 

A  summary  of  the  efficiencies  is  as  follows : 

Efficiency  of  main  engines  0.845. 

Efficiency  of  compressors  0.52  -•-  0.845  s  0.61. 

Efficiency  of  transmission  through  mains  O.i^l  •+■  0.68  ss  0.96L 

Efficiency  of  reducing  valve  O.SO-i-  0.51  s=  0.96. 

The  combined  efficiency  of  the  mains  and  reducing  valve  between  B  and 
4U  atmospheres  is  thus  0.98  X  0.9S  =  0.96.  If  the  reduction  had  been  to  4. 
8)4  or  8  atmospheres,  the  corresponding  efficiencies  would  have  been  0.90, 
O.W),  and  0.85  respectively. 

Indicated  efficiency  of  motor  0.39  -«-  0.50  =  0.78. 

Indicated  efficiency  of  whole  process  with  cold  air  0.80.  Apparent  indl 
csat4^  efficiency  of  whole  proces-s  with  heated  air  0.54. 

Real  indicated  efficiency  of  whole  process  with  healed  air  0.47. 

Mechanical  efficiency  of  motor,  cold,  0.67. 

Mechanical  efficiency  of  motor,  hot,  0.81. 


COMPRESSED   AIR.  609 

Most  of  the  compressed  air  In  Pftris  is  used  for  driviDK  motors,  but  the 
work  done  by  th^se  is  of  the  most  varied  kind.  A  list  of  motors  driven  from 
St.  Farvreau  station  shows  2S6  installations,  nearly  all  motors  working  at 
from  ^  horse>power  to  50  horse-power,  and  the  i^reat  majority  of  them  more 
than  two  miles  away  from  the  station.  The  new  station  at  Quai  de  la  (iare 
is  much  larger  than  the  one  at  St.  Fargeau.  Experiments  on  the  RIedler 
air-compressors  at  Paris,  made  in  December,  1891,  to  determine  the  ratio 
between  the  indicated  work  done  by  the  air-pistons  and  the  indicated  work 
in  the  steam-cylinders,  showed  a  ratio  of  0.8097.  The  compressors  are  driven 
by  four  triple-expansion  Corliss  engines  of  2000  horse-power  each. 

Shops  Operated  by  Compressed  Air.— The  Iron  Age,  March  2, 
1H93,  dencribes  the  shops  o(  ihe  Wuerpei  Switch  and  Signal  Co..  East  St.  Louis, 
tiie  machine  tools  of  which  are  operated  by  compressed  air,  each  of  the 
l&reer  tools  having  its  own  air  engine,  and  the  smaller  tools  being  belted 
from  shafting  dtiven  by  an  air  engine.  Power  is  supplied  by  a  conipound 
eompreasor  rated  at  55  horse-power.  The  air  engines  are  of  the  Kriebel 
mnke,  rated  from  2  to  8  horse-power. 

PnevniaUe  Postal  Transmission.— A  paper  by  A.  Falkenau. 
Eiig  ra  Club  of  Philadelphia,  April  1894,  entitled  the  **  First  United  SUires 
Pneumatic  Postal  System,'' gives  a  description  of  the  system  used  in  London 
atid  Paris,  and  that  recently  introduced  in  Philadelphia  between  the  main 
postroffloe  and  a  substation.  In  London  the  tubes  ara  2^  and  8  inch  lead 
pipes  laid  in  cast-iron  pipes  for  protection.  The  carriers  used  in  2J4-inch 
tubes  are  but  1^  inches  diameter,  the  remaining  space  being  taken  up  by 
packing.  Carriers  are  despatched  singly.  First,  vacuum  alone  was  used; 
htffv,  vacuum  and  compressed  air.  The  tubes  used  in  the  Continental  cities 
in  Europe  are  wrought  iron,  the  Paris  tubes  being  2^  inches  diameter. 
There  tne  carriers  are  despatched  in  trains  of  six  to  ten,  propelled  by  a 
piston.  In  Philadelphia  the  size  of  tube  adopted  is  6%  incnes,  the  tubes 
being  of  cast  iron  bored  to  size.  The  lengths  of  the  outgoing  and  return 
tubes  are  2928  feet  each.  The  pressure  at  the  main  station  is  7  lbs.,  at  the 
■ubstation  4  lbs.,  and  at  the  end  of  the  return  pipe  atmospheric  pressure. 
The  compressor  has  two  air-cylinders  18  X  24  in.  Each  carrier  holds  about 
200  leCters,  but  100  to  150  are  taken  as  an  average.  Eight  carriers  may  be 
despatched  in  a  minute,  giving  a  delivery  of  48,005  to  72,000  letters  per  hour. 
The  time  required  in  transmission  is  about  57  seconds. 

Pneumatic  postal  transmission  tubes  were  laid  in  1898  by  the  Batcheller 
Pneumatic  Tube  Co.  between  the  general  post- offices  in  New  York  and 
Brooklyn,  crossing  the  East  River  on  the  bridge.  The  tubes  are  cast  iron, 
Vi-tu  leusrths,  bored  to  8f^  in.  diameter.  The  joints  are  bells,  calked  with 
\e&ti  and  yarn.  There  are  two  tubes,  one  operating  in  each  direction.  Both 
lines  ate  op«*rated  by  air-pressure  above  the  atmospheric  pressure.  One 
tube  is  operated  by  an  air-compressor  in  the  New  York  office  and  the  other 
by  oite  located  in  the  Brooklyn  office. 

The  carriers  are  24  in.  long,  in  the  form  of  a  cylinder  7  in.  in  diameter, 
and  are  made  of  steel,  with  fibrous  bearing-rings  which  fit  tlie  tube.  Each 
carrier  will  contain  about  600  ordinary  letters,  and  they  are  despatched  at 
intervals  of  10  seconds  in  each  direction,  the  time  of  transit  between  the  two 
offices  being  3^  minutes,  the  carriers  travelling  at  a  speed  of  from  30  to  35 
miles  per  iiour. 

Tlie  air-compressors  were  built  by  the  Rand  Drill  Co.  and  the  Ingersoll- 
Sergeant  Drill  Co.  The  Rand  Drill  Co.  compressor  is  of  the  duplex  type 
and  has  two  steam-cylinders  10  x  20  in.  and  two  air-cylinders  -^4  X  20  in., 
df liveriug  1570  cu.  ft.  of  free  air  per  minute,  at  75  revolutions,  the  power 
b(*ing  about  50  H.P.  Corliss  valve-gear  is  on  the  steam  cylinders  and  the 
Rand  mechanical  valve-gear  on  the  air-cylinders. 

The  IngersoU -Sergeant  Drill  Co.  furnished  two  duplex  Corliss  air-com- 
pressors, with  mechanically  moved  valves  on  air-cylinders.  The  steam- 
c^'linders  are  14  X  18  in.  and  the  air-cylinders  26^  X  18  In.  They  are  de- 
signed for  80  to  1»  revs,  per  min.  and  to  compress  to  20  lbs.  per  sq.  in. 

Another  double  line  of  pneumatic  tubes  has  been  laid  between  the  main 
office  and  Postal  Station  H.  Lexington  Ave.  and  44th  St.,  in  New  York  City. 
This  line  is  about  8^  miles  in  length.  There  are  three  intermediate  stations: 
Third  Ave.  and  8th  St..  Madison  Square,  and  Third  Ave.  and  28th  St.  The 
carriers  can  be  so  adjusted  when  they  are  put  into  the  tube  tliat  they  will 
traverse  the  line  and  be  discharged  automatically  from  the  tube  at  the  sta- 
tion for  which  they  are  intended.  The  tubes  are  of  the  same  size  as  those 
of  the  Brooklyn  line  and  are  operated  in  a  similar  manner.  The  Initial  air- 
compreasiou  is  about  12  to  15  lbs.    On  the  Brooklyu  line  it  is  about  7  )I)S. 


610  AIB. 

There  is  also  a  tube  syvtem  between  the  New  York  Poft-offlee  and  the 
Produce  Exchancre.  For  a  very  complete  description  of  the  »y«t«m  and  its 
macblneiT  see  "The  Pneumatfc  Despatch  Tube  Syetem/'  by  B.  C.  BatchH- 
ler  J.  B.  tippincott  Co.,  Philadelphia,  18»7. 

Tbe  niekfirsfcl  Co]iiprcased"«lr  Tntmira/  at  Berne. 
Burltserland.  UCng'g  Ifeivs,  April  9M),  IBSSO'-The  Blekareki  aystem  hM 
been  iulroUuced  in  Berne,  Bwiuerland,  on  a  line  about  two  milea  lonir,  with 
grades  of  OMji  to  3.7^  and  b.2i.  The  air  ig  heated  by  paaainfr  it  through 
superheated  water  at  3$0<*  F.  It  thus  beoomes  saturated  with  steam,  which 
subsequently  partly  condenses,  its  larent  heat  being  absorbed  by  the  es:> 
panding  air.    The  pressure  in  the  oar  reservoirs  is  440  lbs.  per  eq.  in. 

The  engine  is  constructed  like  an  ordinary  9tearo  tramway  locomotive, 
and  drives  two  coupled  axles,  the  wheel-base  being  5.3  ft.  It  has  a  pair  of 
outside  boricontal  cylinders,  5.1  x  8.6  io.;  four  coupled  wheels,  V7.S  in. 
diameter.  The  total  weight  of  the  car  including  compressed  air  is  7.S5  ions, 
and  with  30  passengers,  including  the  driver  and  conductor,  about  9.5  tons. 

The  authorized  speed  is  about  7  miles  per  hour.  Taking  the  raeiatanoe 
due  to  the  grooved  rails  and  to  curves  under  unfavorable  conditions  at  80 
11)8.  per  ton  of  car  weight,  the  engine  baa  to  overcome  on  the  steepest  grade, 
5jf,  a  total  resistance  of  about  0.63  ton,  and  has  to  develop  35  H.P.  At  tho 
maximum  authorised  working  pressure  incylindersof  170 the.  persq.  in.  tho 
motors  can  develop  a  tractive  force  of  0.64  ton.  This  maximum  ia,  there* 
fore,  just  suflicient  to  take  the  car  up  the  6.^  grade,  while  on  the  flatter 
sections  of  the  line  the  working  pressure  does  not  exceed  78  to  147  lbs.  per 

31.  ill.   Sand  has  to  be  frequently  used  to  increase  the  adheaion  on  the  Sst  to 
grades. 

Between  the  two  car  frames  are  suspended  ten  borisontal  eompraased-alr 
storage-cylinders,  varying  in  length  according  to  the  available  space,  but  of 
uniform  inside  diameter  of  17.7  in.,  composed  of  rtveted  0.87»ln.  Hheet  iron, 
and  tested  up  to  588  lbs.  per  sq.  in.  These  cylinders  b«Te  a  collective 
capacity  of  04.35  cu.  ft.,  which,  according  to  Mr.  Mekarski's  estimate, 
should  have  been  sufficient  for  a  double  trip,  i9i  miles.  Ttie  trial  trips, 
however,  showed  this  estimate  to  be  inadequate,  and  two  further  aniall 
storage-cyllndei-s  had  therefore  to  be  added  of  5.3  cu.  ft.  capacity  each. 


bringing  tbe  total  cubic  contents  of  tbe  12  storage-cylinders  per  oar  np  to 

76  cu.  ft,  divided  into  two  groups«  the  working  and  "" " —  •^-—  -      ■ 

former  of  49  cu.  ft.  the  latter  of  Sti  cu.  ft.  capacity. 


From  tbe  results  of  six  official  trips,  the  pressure  and  the  mean  consump- 
tion of  air  during  a  double  journey  per  motor  oar  are  as  follows: 

Pressure  of  air  in  storage-cylinders  at  starting  440  lbs.  per  sq.  in.:  at  end 
of  up- journey  170  lbs.,  reserve  300  lbs.;  at  end  of  down-loumey  108  Ibe., 
reserve  170  lbs.  Consumption  of  air  during  up- journey  03  ibs.,  during  down- 
journey  81  lbs. 

The  working  eTperience  of  IBOl  showed  that  the  air  consumption  per 
motor  car  for  a  double  journey  was  from  108  to  154  lbs.,  mean  138  lbs.,  and 
per  car  mile  from  38  to  43  lbs.,  mean  85  lbs. 

The  principal  advantages  of  tho  oompresaed>alr  system  for  urban  and 
subinban  tnimway  traffic  as  worked  at  Berne  consist  in  the  smooth 
and  noiseless  motion;  in  the  alisence  of  smoke,  steam,  or  heat,  of  overhead 
or  underground  conductors,  of  the  more  or  lass  grinding  motion  of  most 
electric  cars,  and  of  the  jerky  motion  to  which  underground  cable  tractlo<i 
in  subject.  On  all  these  grounds  the  system  has  vindicated  its  claims  an 
being  preferable  to  any  other  f>o  far  known  system  of  mechanical  traction 
for  street  tramways.  ItR  disadvantages,  on  the  other  hand,  consist  tn  the 
extretnel>^  delicate  adjustment  of  the  diiT«rent  parts  of  thn  system,  tn  th« 
comparatively  small  supply  of  air  carried  bv  one  motor  car,  which  neceeni- 
tates  tbe  car  reluming  to  the  depot  for  refliling  after  a  run  of  only  four 
milfs  or  40  minutes,  although  on  the  Nogent  and  Paris  lines  the  cars, 
which  are,  moreover,  larger,  and  carry  outside  passengers  oa  the  top, 
run  f.even  miles,  and  the  loading  pressure  is  517  lbs.  per  nq,  in.  as  agalnnt 
only  440  ibs.  at  Berne. 

L(>nger  distances  in  the  same  dii^ection  would  Involve  either  more  power- 
ful lUDtors,  a  larger  number  of  storage-cylinders,  and  consequently  heavier 
cars,  or  locidinf; Si^ations  every  four  or  oeven  miles;  and  In  tnis  respect  the 
system  is  manifestly  inferior  to  electric  traction,  which  easily  admits  of  a 
line  of  10  to  15  miles  in  length  being  continuously  fed  from  oneoeniral 
station  without  the  io^s  of  time  and  expense  causen  by  reloading. 

Tlie  cost  of  wurking  the  ^erne  U^e  is  coui(»ared  in  the  aune^rad  table 


PANS  AND  BLOWERS.  511 

with  lonie  other  tmrnwAys  wortted  under  almflar  oondltlona  by  horse  i^d 
tnechanieal  traction  Tor  the  veur  IHOl. 

For  deecription  of  the  Ifektrski  system  as  used  at  Nitntes,  Franee,  see 
paper  bv  Prof.  D.  8.  Jaenbus,  Trans.  A.  I.  M.  E..  xfx.  553. 

Amarleaii  Kxpertmeiito  on  Compressed  Air  for  Btroel; 
IUidl«rays«*^Experiineitrs  hare  been  made  recently  in  Wa»hin|rtot),  U.  0., 
and  in  Naw  Yurk  City  on  the  use  of  compressed  air  for  streeUrailway  trac- 
tion. The  air  was  compreSMd  to  9000  lbs.  per  sq.  in.  and  passed  thi^ugh  4 
redocingfondTO  and  a  heater  before  betnir  admitted  to  the  engine.  For  an 
extended  discussion  of  the  relatire  merits  of  compressed  air  and  nlectrlo 
traction,  with  an  account  of  a  test  of  a  four^tafpe  compressor  glvlpg  it 
pressure  of  2300  lbs.  per  sq.  in.,  see  Eng*aN€tB9,  Oct.  T  snd  Not.  4, 1897.  A 
Bummariaed  statement  of  Uie  probable  efficiency  of  eompi'eB>eil>ali' tractlqn 
lA  iciven  as  follows!  Efficiency  of  compression  to  KOQO  lbs.  per  sq.  In.  Qfif . 
By  wire-drawinf^  to  100  lbs.  57.ft^  of  the  arailable  enorey  of  the  air  will  be 
lost,  leavinfc  A5  X  .4^25  »  eT.5^)(  as  the  net  efficiency  of  the  air.  This  may 
be  doubled  by  heaiinf?^  making  5ft  eSjt,  and  If  the  motor  has  an  efficiency  of 
90%  ihe  net  «raclency  of  traction  by  compressed  air  will  beOfli^iS  x  .80  =  44.«J^. 
For  a  desoriptioQ  of  the  Hardie  oompi«essed-aii*  locomotive,  designed  for 
street-railway  work,  see  Etig'g  Nmes,  June  fl4,  1807,  For  use  of  compressed 
air  in  mine  faaulags,  see  Sng*g  Nmost  Febw  10, 1806. 


Compressed  Air  for  l¥or]ciii8r  ITndercrovndL  ItamM  In 

nines*— fnyV  Record^  May  19,  1804,  describes  an  fnstailiktion  of  com- 

Pressors  for  woridng  a  number  of  pumps  in  the  Nottingham  Mo.  16  Mine, 
lyznouth.  Pa.,  which  is  claimed  to  be  the  largest  in  America.  The  com- 
preesors  develop  above  2;i00  H.P.,  and  the  piping,  horizontal  and  vertical,  is 
6000  feet  in  length.    About  25,000  gallons  of  water  per  hour  are  raised. 

FANS  ANP  BlLODTBRfiU 

Contrlftanl  F«ns.^Tbe  ordinary  oentrlfugal  fan  eonsista  of  a  ninn- 
ber  of  blades  nxed  to  arms,  revolving  on  a  shaft  ttt  high  speed.  The  width 
of  the  blade  is  parallel  to  the  axis  or  the  shaft.  Host  engineers^  reference 
books  quote  the  experiments  of  W.  Ruckle,  Proo.  Inst,  M.E.,  1647,  as  still 
standanl.  Mr.  Buckle's  conclusions  are  given  below,  together  with  data  of 
more  recent  experiments. 

Exi>erlment8  were  made  as  U>  the  proper  sire  ofUie  Inlet  openings  and  on 
the  proper  proportions  to  be  given  to  the  vane.  The  fniet  openings  in  the 
sides  of  the  fan-chest  were  contracted  from  17^  in.,  the  original  oiameter, 
to  18  and  0  in.  diam.,  when  the  following  results  were  obtained: 

First,  that  the  power  expended  with  the  opening  contracted  to  }9  in.  dIam. 
was  as  2U  to  1  compared  with  the  opening  of  ITyiln.  diam. ;  the  velocity  of 
the  fan  being  nearly  the  same,  as  also  the  quantity  and  density  of  air 
delivered. 

Second,  that  the  power  expended  with  the  opening  contracted  to  6  in. 
diam.  was  as  2^  to  1  compared  with  the  opening  of  17^  In.  diam.;  the 
velocity  of  the  fan  being  nearly  the  parae,  and  also  the  area  of  the  efflux 
pipe,  but  the  density  of  the  air  decreased  one  fourth. 

These  experiments  show  that  the  Inlet  openings  must  be  made  of  sufficient 
sise,  that  the  air  may  have  a  free  and  uninterrupted  action  in  its  passage  to 
the  blades  of  the  fan;  for  if  we  impede  this  action  we  do  so  at  the  expense 
ofpower. 

with  a  vane  14  in.  long,  the  tips  of  which  revolve  at  the  rate  of  ZS6.B  ft. 
per  second,  air  is  condensed  to  0.4  ounces  per  square  inch  above  the  pres- 
sure  of  the  atmosphere,  with  a  power  of  9.611.  P. ;  but  a  vane  8  inches  long, 
the  diameter  at  the  tips  being  the  same,  and  having,  therefore,  the  same 
velocity,  condenses  air  to  6  ounces  per  square  inch  only,  and  takes  12  H.  P, 

Thns  the  density  of  the  latter  is  little  better  than  six  tenths  of  the  former, 
while  the  power  absorbed  in  nearly  l.i!5  to  1.  Although  tlie  velocity'  of  the 
tips  of  the  vanes  is  the  same  in  each  case,  the  velocities  of  the  lieefs  of  the 
respective  blades  are  very  different,  for,  while  the  tips  of  the  blades  in  each 
esse  move  at  the  same  rate,  the  velocity  of  the  heel  of  the  14-lncb  is  in  the 
ratio  of  1  to  1.67  to  the  velocity  of  the  heel  of  the  8-inch  blade.  The 
longer  blades  approaching  nearer  the  centre,  strikes  the  a|r  with  less  velo- 
<iUy,  and  allows  it  to  enter  on  the  blade  with  greater  freedom,  and  with 
considerably  less  force  than  the  shorter  one.  The  inference  Is,  that  the 
Short  blade  must  take  more  power  at  the  same  time  that  It  accumulntes  a 
less  quantity  of  air.  These  experiments  lead  to  the  conclusion  that  the 
length  of  the  vane  demands  as  great  a  consideration  as  the  proper 
diameter  of  the  inlet  opening.    If  there  were  no  other  object  in  view,  it 


512 


AIB. 


would  be  useless  to  make  the  ▼anes  of  the  fbn  of  a  srreater  width  than  tha 
inlet  opening  can  freelv  supply.  On  the  proportion  of  the  length  and  width 
"  "  .  ••     .  -...,.  .^^  j.^^^  jjj^  three  most  iiii- 

.  and  expenditure  of  power. 

,   8.8  times  greater  than  the 

heel;  and,  by  the  laws  of  centrifugal  force,  the  air  will  have  a  density  2.6 
times  gi-eater  at  the  tip  of  the  blade  than  that  at  the  heel.  The  air  cannot 
enter  on  the  heel  with  a  density  higher  than  that  of  the  atmosphere;  but  in 
its  passage  along  the  vane  it  becomes  compressed  in  proportion  to  its 
centrifugal  force.  The  greater  the  length  of  the  vane,  the  greater  will  be 
the  difference  of  the  centrifugal  force  between  the  heel  and  the  tip  of  the 
blade;  conseouenily  the  greater  the  density  of  the  air. 

Reasoning  from  these  experiments,  Mr.  Buckle  recommends  for  easy  ref- 
erence the  loUowing proportions  for  the  construction  of  the  fan: 

1.  Let  the  width  of  the  vanes  be  one  fourth  of  the  diameter;  2.  Let  the 
diameter  of  the  inlet  openings  in  the  sides  of  the  fanchest  be  one  half  the 
diameter  of  the  fan;  8.  Let  the  length  of  the  vanes  be  one  fourth  of  the 
diameter  of  the  fan. 

In  adopting  this  mode  of  construction,  the  area  of  the  inlet  openings  in 
the  sides  of  the  fan-chest  will  be  the  same  as  the  circumference  of  the  heel 
of  the  blade,  multiplied  by  its  width;  or  the  same  area  as  the  space 
described  by  the  heel  of  the  blade. 

Best  Proportions  of  Fans.    (Buckle.) 

Pressurb  from  8  ounces  to  6  ocncbs  per  square  inch;  or  5J2  ikches 
TO  10.1  INCHES  OP  Water. 


Diameter 
of  Fan. 

Vanes. 

Diameter 
of  Inlet 
Open- 
ings. 

Diameter 
of  Fan. 

Vanes. 

Diameter 
of  Inlet 
Open- 
ings. 

Width. 

Length. 

ft.  ins. 
0     9 

o,OH 

Width. 

Length. 

ft.    Ins. 

3  0 
8      8 

4  0 

ft.  Ins. 

0    9 
0,0H 

ft.  ins. 

1      6 

1  9 

2  0 

ft.  ins. 

4  6 

5  0 

6  0 

ft.  ins. 
1      6 

ft.  ins. 
1     6 

ft.  fns. 

2      8 
2      8 
8r   0 

PRRSSURB  FROM  8  OUNCES  TO  9  OUNCES  PER  SQUARE  INCH,  AND  CPWAR06, 
OR  10.4  INCHES  TO  15.6  INCHES  OF  WatBR. 

8        0 

8     6 
4      0 

0     7        10 

1      0 
1      8 
1      8 

4      6 
6      0 
8      0 

1     2 

1  J^ 

1    10 

1  0 

2  0 
2      4 

The  dimensions  of  the  above  tables  are  not  laid  down  as  prescribed  limits, 
but  as  approximations  obtained  from  the  best  results  in  practice. 

Experiments  were  also  made  with  reference  to  the  adm^ission  of  air  into 
the  transit  or  outlet  pipe.  By  a  slide  the  width  of  the  ojieniug  into  tltts  pipe 
was  varied  from  12  to  4  inches.  The  object  of  this  was  to  proportion  the 
opening  to  the  quantitv  of  air  required,  and  thereby  to  lessen  the  power 
necesnary  to  drive  the  ran.  It  was  found  that  the  less  this  opening  is  made, 
provided  we  produce  sufficient  blast,  the  less  noise  will  proceed  from  the 
fan ;  and  by  making  the  tops  of  this  opening  level  with  the  tips  of  the  vane, 
the  column  of  air  has  little  or  no  reaction  on  the  vanes. 

The  number  of  blades  may  be  4  or  6.  The  case  is  made  of  the  form  of 
an  arithmetical  spirul,  widening  the  space  between  the  oa«e  and  the  revolv- 
ing blades,  circuniferentially,  from  the  origin  to  the  opening  for  discharge. 

The  following  rules  deduced  from  experiments  are  given  in  Spretson's 
treatise  on  Casting  and  Founding: 

The  fan-case  should  be  an  arithmetical  spiral  to  the  extent  of  the  depth 
of  the  blade  at  least. 

The  diameter  of  the  tips  of  the  blades  should  be  about  double  the  diameter 
of  the  hole  in  the  centre:  the  width  to  be  about  two  thirds  of  the  radius  of 
the  tips  of  the  blades.  The  velocity  of  the  tips  of  the  blades  should  he  rather 


FAKS  AND  BLOWERS.  513 

more  than  Che  velocity  due  to  the  air  at  the  pressure  required,  say  one 
eiflrhth  more  velocity. 

la  some  cases,  two  fans  mounted  on  one  shaft  would  be  more  useful  than 
one  wide  one,  as  in  such  au  arrangement  twice  the  area  of  inlet  opening?  is 
obtained  as  compared  with  a  sinf^le  wide  fan.  Such  an  arrangement  may 
be  adopted  where  occasionally  half  the  full  quantity  of  air  is  required,  as 
on«*  of  Lhem  may  be  put  out  of  firear,  thus  saving  power. 

Pv^flsnre  due  to  Velocity  of  tl&e  Fan-bladeii.— '*By  increas- 
ing the  number  of  revolutions  of  the  fan  the  head'or  pressure  is  increased, 
the  law  being  that  the  total  head  produced  is  equal  (in  centrifugal  fans)  to 
twice   the  height  due  to  the  velocity  of  the  extremities  of  the  blades,  or 

H  =  —  approximatelyin  practice"  (W.  P.  Trowbridge,  Trans.  A  S.  M.  E., 

vii.  586.)  This  law  is  analogous  to  that  of  the  pressure  of  a  jet  striking  a 
plane  surface.  T.  Hawksley,  Proc.  Inst.  M.  £.,  1882,  vol.  Izix..  says:  '*The 
pressure  of  a  fluid  striking  a  plane  surface  perpendicularly  and  then  escap- 
ing at  rijght  angles  to  its  original  path  is  that  due  to  twice  the  height  h  due 
the  velocity." 
(For  discussion  of  this  question,  showing  that  it  is  an  error  to  take  the 

•ressure  as  equal  to  a  column  of  air  of  the  height  h=sv^-*-2g^  see  Wolff  on 

-^indmllls,  p.  17.) 

Buckle  says:  '*  From  the  experiments  it  further  appears  that  the  velocity 
of  the  tips  of  the  fan  is  equal  to  nine  tenths  of  the  velocity  a  body  would 
acquire  m  falling  the  height  of  a  homogeneous  column  of  air  equivalent  to 
the  density."  D.  K.  Clark  (R.  T.  &  D..  p.  024),  paraphrasing  Buckle,  appar 
ently,  says:  "  It  further  appears  that  the  pressure  generated  at  the  circum 
ferenceis  one  nJnth  greater  than  that  which  is  due  to  the  actual  drcumfer- 
entjal  vekxsity  of  the  fan."     The  two  statements,  however,  are  not  in 

harmony,  for  if  «  =  0.9  V^,  H=  5^^^^  =  1.884^  andnotl|^. 

If  we  take  Uie  pressure  as  that  equal  to  a  head  or  column  of  a!r  of  twice 
the  height  due  the  velocity,  as  is  correctly  stated  by  Trowbridge,  the  para< 
doxtcaf  statements  of  Buckle  and  ClarV^whlch  would  indicate  that  the 
actual  pressure  is  greater  than  the  theoreticfd— are  explained,  and  the 

formula  becomes  H=  .617—  and  v  =  1.278  \^gH=  0.9  VSgfl,  in  which  H 

g 
is  the  head  of  a  column  producing  the  pressure,  which  is  equal  to  twice  the 

theoretical  head  due  the  velocity  of  a  falling  body  (or  h  s  ^  j,  multiplied 

by  the  coefficient  .617.  The  difference  between  1  and  this  coefficient  ex- 
presses the  loss  of  pressure  due  to  friction,  to  the  fiict  that  the  inner  por- 
tions  of  the  blade  have  a  smaller  velocity  than  the  outer  edge,  and  probably 
to  other  causes.  The  coefficient  1.278  means  that  the  tip  of  the  blade  must 
be  given  a  velocity  1.278  times  that  theoretically  required  to  produce  the 
beadH. 

To  convert  the  head  H  cxprooocd  In  feet  to  pressure  in  lbs.  per  sq.  in. 
multiply  It  by  the  weight  of  a  cubic  foot  of  air  at  the  pressure  ana  tempera- 
ture of  the  air  expelled  from  the  fan  (about  .08  lb.  usually)  and  divide  by 
141.  Multiply  this  by  16  to  obtain  pressure  in  ounces  per  sq.  In.  or  by  'i.im 
to  obtain  inches  of  mercury,  or  by  27.71  to  obtain  pressure  in  inches  of 
water  oohimn.    Taking  .06  as  the  weight  of  a  cubic  foot  of  air, 

p  lbs.  per  sq.  in.        s  .00001066v*;  v  =  810  f^near]y; 

Pi  ounces  per  sq.  in.  s  .OOOlTOOv';  v  =s   80  Vpj     ** 

p,  inches  of  mercury  =  .00002169V*;  i;  =  820  f'p,     •« 

p,  faicbes  of  water      =  .0002954v*;  v=   60  i^p,     •• 

tn  which  V  =  velocity  of  tips  of  blades  in  feet  per  second. 

Testbig  the  al>ove  formula  by  the  experiment  of  Buckle  with  the  vane 
14  inches  long,  qooted  above,  we  have  p  =  .0000l066v>  s  0.56  os.  The  ex- 
periment gave  9.4  08. 

Testing  it  by  the  experiment  of  H.  I.  Snell,  given  below,  in  which  the 
circumferential  speed  was  about  160  ft.  per  second,  we  obtain  8.86  ounces, 
while  Uie  experiment  gave  from  2.88  to  8.50  ounces,  according  to  the  amount 
of  opening  for  discharge.  The  numerical  coefficients  of  the  above  formuls 
are  all  based  on  Buckleys  statement  that  the  velocity  of  the  tips  of  the  fan 
is  eqoal  to  nine  tentlis  of  the  velocity  a  body  would  acquire  in  falling  the 


5U 


AtB. 


bsifflit  of  a  bomogepeoiu  column  of  air  equivalent  to  the  preomre.  Stiould 
ottier  experiments  show  a  different  law,  the  ooefflcients  can  be  corrected 
aoconlinKlT.  It  is  orobable  that  they  wOl  vary  to  some  extent  with  differ- 
ent propoxtlons  of  fans  an4  different  speeds. 

TalclBfC  the  formula  v  a  80  i^*  we  hare  for  different  pretsures  In  ounces 
per  squara  inch  the  following  velocities  of  the  tips  of  the  blades  in  feet  per 
second: 

p.  a  ounces  per  square  Inch....    2     8     4     6     6     7     8     10     13     14 
V   -  feet  per  second 113  189  160  179  196  212  226  X58    277    290 

A  rule  fn  App,  Cye.  liech^  article  **  Blowers,"  gives  the  foUowInf^  velodiies 
of  circumference  for  different  densities  of  blast  in  ounces:  8, 170;  4,  180;  9, 
195:  6,  905;  7,  215. 

The  same  article  gives  the  following  tables,  the  first  of  which  shows  tliat 
the  density  of  blastls  not  constant  for  a  given  velocity,  but  depends  on  the 
ratio  of  area  of  nossle  to  area  of  blades: 

Velocity  of  circumference,  feet  per  second.  ISO  150  150  170  200  200  220 
Areaofnoc9Ele-»>  area  of  blades.... 2     ^-    H   H    H  ^^  H 


Density  of  blast,  os.  per  square  inch . 


1     2 


QUAlfTXTT  OF  AlB  OF  A  QlVBN  DkHSHT  DeLIVBKBD  BT  A  FaR. 

Total  area  of  nozzles  in  square  feet  X  velocity  in  feet  per  minute  corre- 
sponding to  deneity  (^ee  table)  ac  air  delivered  in  cubic  feet  per  minute. 


^n^  Velocity,  feet 

r  5000 

2  7000 

8  8600 

4  10,000 


^^i2^'  Velocity  feet 
nA»  •"In, 


per  sq.  in. 

6 
7 

8 


permit 
11,000 
12,250 
18,800 
14,150 


^oiSSSL*  Velocity,  feet 

owu!9f  ^  minute. 

ersq.  in.  i'«^™"»"^'»» 

9      15,000 

10  15,800 

11  16,600 

12  17,800 


Bxpeiitnenta  'vrltli  Blo'vrer*.  (Henry  I.  Boell,  Trans.  A.  8.  M.  B. 
Ix,  51.}— The  following  tables  give  velocities  or  air  discharging  through  en 
aperture  of  any  size  under  the  given  pressures  into  the  atmosphere.  The 
volume  discharged  can  be  obtained  by  multiplying  the  area  of  dlscharire 
opening  bv  the  velocltv,  and  this  product  by  the  coe£9cient  of  contraction: 
M  for  a  thin  plate  and  .98  when  the  orifice  Is  a  conical  tube  with  a  convert 
gence  of  about  8.5  degrees,  as  determined  by  the  experiments  of  Webbach. 

The  tables  are  calculated  for  a  barometrical  pressure  of  14.80  Iba^a 
986  OS.),  and  for  a  temperature  of  50*  Fahr.«  from  the  formula  F  a  ^9gh, 

Allowances  have  been  made  for  the  effect  of  the  oompreaeion  of  the  air, 
but  none  for  the  heating  effect  due  to  the  compression. 

At  a  temperature  of  flO  degrees,  a  cubic  foot  of  air  weighs  ,078  Iba.(  and 
eelling  g  m  69.1609,  the  above  formula  may  be  reduced  to 


Ti  »  60  VaLSSW  X  (285-4- iO  X  P. 

where  Vi  ss  velocity  In  feet  per  minute. 

p  s  pressure  above  atmosphere,  or  the  pressure  shown  by  gauge,  In  oz. 
per  square  inch. 


Pressure 

per  sq.  in. 

in  Inches  of 

water. 

Corre- 
sponding 
Pressure  in 
OS.  per  sq. 

inch. 

Velocity 
due  the 
Pressure  fn 
feet  per 
minute. 

Pressure 

per  sq.  in. 

In  inches  of 

water. 

Corre- 

oz.persq. 
inch. 

Velocity  due 

the  Pressure 

In  feet  per 

minute. 

.01817 
.08684 
.07268 
.10002 
.14586 
.18170 
.21804 
.29079 

696.78 
967.66 
1698.75 
1707.00 
1971.80 
8204.16 
9414.70 
9786.74 

1 

.86640 
.48608 
.808?9 
.56140 
.7967 
.8791 
1.0174 
1.1«8 

8118.88 
8416.64 
8690.06 
8846.17 
4868.08 
4886.06 
8694.08 
6687.66 

FAKS  AKD  BLOWEBS. 


516 


Press- 

Velocity 

Pfea». 

Velocity 

Press- 

Velocity 

Velocity 

ure 

due  the 

ure 

due  the 

ure 

due  the 

Pressure 

due  the 

(n  OS. 

Pramurc 

loos. 

Pressure 

in  OS. 

In  ft.  pel 
minute. 

in  OS. 

Pressure 

inch. 

{n  ft.  pel 
minute. 

|)ers<|. 
Inch. 

In  ft.  pel 
minute. 

persq. 
inch. 

[)er8q.in. 

In  ft  per 
minute. 

.85 

S,582 

2.25 

7,787 

6.60 

12,250 

11.00 

17,684 

.50 

8,658 

2.50 

8,218 

6.00 

12.817 

12.00 

18,850 

.75 

4.482 

2.75 

8,618 

6.50 

13,354 

18.00 

19,188 

1.00 

3,178 

8.00 

9,006 

7.00 

18,878 

14.00 

19,901 

1.2S 

6.792 

8.50 

9,789 

7.50 

14,874 

15.00 

20.641 

1.60 

6,949 

4.00 

10,421 

8.00 

14,861 

16.00 

21,360 

l.n 

6.8C1 

4.50 

11,066 

9.00 

16,795 

too 

7,888 

6.00 

11,076 

10.00 

16,684 

Pressure  in  ounoes 
per  square  inch. 

Velocity  in  feet 
per  minute. 

Pressure  in  ounces 
per  square  inch. 

Velocity  in  feet  per 
minute. 

.01 
.08 

.m 

.04 
.06 

816.90 
782.64 
895.26 
1068.86 
1165.90 

.06 
.07 
.08 
.09 
.10 

1006  24 

1867.78 
1468.20 
1860.70 
1685.00 

Bzperli 


neiiU  on  m.  Fan  'srltli  Varying  lMsclaarKe«op«ntntf« 
Bevolntlons  nearly  constant. 


& 


1519 
1479 
14f» 
1471 
1485 
1485 

1408 
1900 

1426 


0 

0 
10 
00 
28 
86 
40 
44 
48 
89.6 


8.50 
8.S0 
8. BO 
8.60 
8.50 
8.40 
8.25 
8.00 
8.00 
2.88 


0 
406 
678 
1858 
1894 
8400 
2605 
2752 
8002 
8973 


.80 
1.18 
1.80 
1.95 
2.55 
8.10 
8.80 
8.55 
8.60 
4.80 


8^3 
520 
694 
742 
774 
790 
TTtJ 
790 
827 


1046 
1048 
1048 
1048 
1048 
1078 
1126 
1222 
1222 
1544 


.837 

.496 

.66 

.709 

.718 

.70 

.635 

.646 

.586 


The  fan  wheel  was  28  Inches  in  diameter,  6K  inches  wide  at  its  periphery, 
and  had  an  inlet  of  12^  inches  in  diameter  on  either  side,  which  was 

Krtialty  obstructed  by  the  pulleys,  which  were  5  9/16  inches  in  diameter.  It 
d  efg^nt  blades,  each  of  an  area  of  45.49  square  inches. 
The  dlschanre  of  air  wsa  through  a  conical  tin  tube  with  sides  tapered  at 
an  angle  of  9U  degrees.    The  actual  area  of  opening  was  7%  greater  than 
given  in  the  tables,  to  compensate  for  the  vena  contracta. 

In  the  last  experiment,  80.5  sq.  In.  represents  the  actual  area  of  the  mouth 
of  the  blower  less  a  deductioti  for  a  narrow  strip  of  wood  placed  across  it  for 
the  purpose  of  iKriding  the  pressure-gauge.  In  calculating  the  volume  of  air 
djscnarged  in  the  last  experiment  the  value  of  vena  contrttcta  is  taken  at  .80. 


516 


AIR. 


Expert  mentB  were  undertaken  for  the  purpose  of  showing  the  results  oh* 
tained  by  running  the  same  fan  at  different  speeds  with  the  discharge-open- 
ing  the  same  throughout  the  series. 

The  discharge-pipe  was  a  conical  tube  8^  inches  inside  diameter  at  the 
end,  having  an  area  of  56.74.  which  is  7%  larger  than  .'S8  sq.  inches  ;  therefore 
fA  square  inches,  equal  to  .868  square  feet,  to  called  the  area  of  discharge,  as 
that  is  the  practical  area  by  which  the  volume  of  air  is  computed. 

Expertments  on  a  Fan  mrlib  Constant  Dtseharso-open- 
tne  and  Varying  Speed.— The  first  four  columns  are  given  by  Mr. 
Snell,  the  others  are  calculated  by  the  author. 


£ 

i 

00 

> 

i 

0-4 

Ha 

% 

1^ 

Velocity  due  Press- 
ure from  Formu- 
la© =80  Vp. 

OoefDcient  of  For> 
mula  »  =  a?  Vp" 
from  Experiment. 

Hi 

P 

600 

.60 

1386 

.25 

60.2 

56.6 

86.1 

8,630 

.182 

73 

800 

.88 

1787 

.70 

80.3 

75.0 

86.6 

4,856 

.429 

61 

1000 

1.88 

2246 

1.85 

100.4 

04. 

86.4 

6,100 

.845 

63 

laoo 

2.00 

2712 

2.20 

120.4 

113. 

86.1 

7,870 

1.479 

67 

1400 

2.75 

8177 

3.45 

140.5 

138. 

84.8 

8.683 

2.283 

66 

1600 

3.80 

8670 

6.10 

160.6 

156. 

82.4 

9,97^ 

8.803 

74 

1800 

4.80 

4178 

8.00 

180.6 

175. 

82.4 

11,837 

6.462 

6K 

2000 

5  95 

4674 

11.40 

200.7 

195. 

85.6 

12,701 

7.586 

67 

Mr.  Snell  has  not  found  any  practical  difPerence  between  the  efllciencies 
of  blowers  with  curved  blades  and  those  with  straight  radial  ones. 

From  these  experiments,  says  Mr.  Snell,  it  appears  that  we  may  expect  to 
receive  back  eb%to7Bi%ot  the  power  expended,  and  no  more. 

The  great  amount  of  power  often  used  to  run  a  fan  is  not  due  to  the  fSn 
itself,  but  to  the  method  of  selecting,  erecting,  and  piping  it. 

(For  opinions  on  the  relative  merits  of  fans  and  positive  rotary  blowers, 
see  discussion  of  Mr.  Rnell's  paper,  Trana  A.  S.  M.  E.,  ix.  66.  etc.) 

ComparatlTe  Efflclency  of  Fans  and  Posttlve  Bloiv^em.— 
(H.  M.  Uowe,  Trans.  A.  I.  M.  £.,  x.  482.)— Experiments  with  fans  and  positive 
(Baker;  blowers  working  at  moderately  low  pressures,  under  20  ounces,  show 
that  they  work  more  efficiently  at  a  given  pressure  when  delivering  large 
volumes  {i.e..  when  working  nearly  up  to  their  maximum  capacity)  than 
when  delivering  comparatively  small  volumes.  Therefore,  when  great  vari- 
ations in  the  quantity  and  pressure  of  blast  required  are  liable  to  arise,  tbe 
highest  efficiency  would  be  obtained  by  having  a  number  of  blowers,  always 
driving  them  up  to  their  full  capacity,  and  regulating  the  amount  of  bla^a 
by  altering  the  number  of  blowers  at  work,  instead  of  having  one  or  two 
very  large  blowers  and  regulating  the  amount  of  blast  by  the  speed  of  the 
blowers. 

There  appears  to  be  little  difference  between  the  efficiency  of  fans  and  of 
Baker  blowers  when  each  works  under  favorable  conditions  as  regards 
quantity  of  work,  and  when  each  is  in  good  order. 

For  a  given  speed  of  fan,  any  diminution  in  the  size  of  the  blast-orifice  de- 
creases the  consumption  of  power  and  at  the  same  time  raises  the  precnure 
of  the  blast ;  but  it  increases  the  consumption  of  power  per  unit  of  orifice 
for  a  given  pressure  of  blast.  When  the  orifice  has  lieen  reduced  to  the 
normal  size  for  any  given  fan,  further  diminishing  it  causes  but 
slight  elevation  of  the  blast  pressure;  and.  when  the  orifice  becomes  com- 
paratively small,  further  diminishing  it  causes  no  sensible  elevation  of  the 
blast  pressure,  which  remains  practically  constant,  even  when  the  orifice  it 
entirely  closed. 

Many  of  the  failures  of  fans  have  been  due  to  too  low  speed,  to  too  small 
pulleys,  to  improper  fastening  of  beltn,  or  to  the  belts  being  too  nearly  ver- 
tical; in  brief,  to  bad  meehaniral  arrangement,  rather  than  to  Inherent  d*- 
fecis  in  the  principles  of  the  inacbine. 


FANS  AND   BLOWERS. 


517 


If  several  fans  are  used,  it  la  probably  easeniial  to  high  efflcieDcy  to  pro- 
vide a  separate  blast  pipe  forench  (at  least  if  the  fans  are  of  difPereot  sise 
or  fcpeed),  while  any  number  of  positive  blowers  may  deliver  into  the  same 
pipe  without  lowering  their  efficiency. 

Capacity  of  Fanii  and  Blonvers. 

The  following  tables  show  the  ^aranteed  air-supply  and  air-removal  of 
leading  forms  of  blowers  and  exhaust  fans.  The  figures  given  are  often 
exceeded  in  practice,  especially  when  the  blowers  and  fans  are  driven  at 
higher  speeds  than  stated.  The  ratings,  particularly  of  the  blowers,  are 
below  those  generally  given  in  catalogues,  but  it  was  the  desire  to  present 
only  conservative  and  assured  practice.    (A.  R.  Wolff  on  Ventilation.) 

QUANTITT  OF  AlR  SUPPLIED  TO  BUILOIITOB  BT   BLOWERS   OF  VARIOUS  SlZlS. 


Diam- 
eter of 
Wheel 
in  feet. 


Ordinary 
Number 
of  Revs, 
per  min. 


850 
885 
275 
830 
200 


Iforse- 


Capacity 

cu.  ft. 
per  min. 


Iper  sq.  in. 


6. 

0.4 
18.5 
18.4 
«4 


10,635 
17,000 
29.618 
42,700 
46,000 


Diam- 
eter of 
Wheel 
n  feet. 


9 
10 
12 
U 
15 


Ordinary 
Number 
of  Revs, 
per  min. 


175 
160 
130 
110 
100 


Horse- 
power 
to  Drive 
Blower. 


89 
85.6 
49.5 
66 


Capacity 

cu.  ft. 
per  min. 
against  a 
Pressure 
of  1  ounce 
per  sq.  in. 


56,800 
70,840 
102,000 
189,000 
160,000 


If  the  resistance  exceeds  the  pressui'e  of  one  ounce  per  square  inch,  of 
above  table,  the  capacity  of  the  blower  will  be  correspondingly  decreased, 
or  power  Increased,  and  allowance  for  this  must  be  made  when  the  distrib- 
uting ducts  are  small,  of  excessive  length,  and  contain  many  contractions 
and  bends. 

QUARTiry  OP  Air  moved  bt  an  Approved  Forh  of  Exhaust  Fan,  ths 

FAH  DISCHARGIMO  DIRECTLY  FROM  ROOM  INTO  TBS  ATMOSPHERE. 


Diam- 
eter of 
Wheel 
in  feet. 


Ordinary 
Number 
of  Revs, 
per  min. 


Horse- 
power 
to  Drive 
Fan, 


Capacity 
in  cu.  ft. 
per  min. 


Diam- 
eter of 
Wheel 
in  feet. 


Ordinary 
Number 
of  Revs, 
per  min. 


Horse- 
power 
to  Drive 
Fan. 


Capacity 
in  cu.  ft. 
per  min. 


2.0 
2.5 

ao 

&5 


600 
560 
600 
500 


OJSO 
0.75 
1.00 
2.50 


6,000 

8,000 

12,000 

20,000 


4.0 
5.0 
6.0 
7.0 


475 
860 
800 
260 


8.50 
4.50 
7.00 
9.00 


28,000 
35,000 
50,000 
80,000 


The  capacity  of  exhaust  fans  here  stated,  and  the  horse-power  to  drive 
them,  are  for  free  exhaust  from  room  into  acmospliere.  Tne  capacity  de- 
creases and  the  horse-power  increases  materially  as  the  resistance,  resulting 
from  lengths,  smallness  and  bends  of  ducts,  enters  as  a  factor.  The  differ- 
ence in  pressures  in  the  two  tables  is  the  main  cause  of  variation  in  the  re- 
spective  records.  The  fan  referred  to  in  the  second  table  could  not  be  used 
with  as  high  a  resistance  as  one  ounce  per  square  inch,  the  rated  resistance 
of  the  blowerSi 

Caatlon  In  Regar4  to  XJme  of  Fan  and  Bloiver  Tables.— 

Many  enKi"*'©''S  repcrt  that  mHniifacturers'  tables  overrate  ihe  CHpacity  of 
their  fans  and  underestimate  the  horse-power  required  to  drive  them.  In 
some  cases  the  complaints  may  be  due  to  restricted  air  outlets,  long  and 
crooked  pipes,  slipping  of  belts,  too  small  engines,  etc. 


518 


AtH. 


OBHTRlFrcSAL  FANS. 

Flour  of  Air  tbronsb  an  OrlAce* 

VKLOCITT,    VOLUME,    AND    HP.    RBQUIRSD   VHBN    AIR    UlfDBR  GITRK  1 

IN  OCNOEB  PER  sq.  IN.  IS  ALLOWED  TO  ESCAPE  I.NTO  THE  ATMOSPHERE. 

(B.  F.  Bttirtevant  Co.)  


i 

hi 

•?s 

i:5d 

> 

1,828 

k 

12.6» 

8,565 

ir.95 

lis 

91.98 

85.87 

4,0B4 

88.96 

4,473 

81.06 

4,W0 

88.54 

6jes 

85.86 

5,473 

88.01 

5.7b8 

B 

6,048 
•,315 

«,9fn 

45.68 

?:SS 

47.84 
49.00 

.00043 
.00189 


.00648 
.00488 
.00635 
.00600 
.00978 
.01166 
.01366 
.01675 
.01794 
.080-22 
.02260 
.02506 


.0840 
.0660 
.1082 
.1368 
.1708 
.2044 
.2385 
.2728 
.8068 
.8410 
.8760 
.4090 
.4431 
.4772 
.6112 


It 


If 


7,884 
7,507 
7.728 
7,982 
8,136 
8,884 
8,528 
8,718 
8,903 
9,084 
9.262 
9,185 
9,606 
9,773 
9,W8 
lOJOO 


"^ii 


^»  3(1:^2  0 
5d|2||fk 

S*^    sir*?-*! 


60.59 
58.18 
63.68 
56.08 
66..W 
57.88 
60.28 
60.54 
61.88 
63.06 
64.3S 
65  68 
66.71 
67.87 
60.01 
70  14 


.09759 
.08021 
.03991 
.08568 
.03859 
.04144 


.04747 
.Q60h8 
.06376 
.05701 
.06031 
.06;i68 
.00110 
.07058 
.07412 


Ill 


h 


.&4M 

.5;  95 
.6186 
.6476 
.6818 
.7160 
.7600 
.7841 
.8180 
.8522 


.9205 

.9546 

.9687 

1.0K7 

i.osm 


"Hie  headlrigA  of  the  2d  and  8d  cohiiiinH  fn  the  above  table  have  been 
abridged  from  the  original,  which  read  a.s  follows:  Velocity  of  dry  air,  50** 
F.«  escaping  into  the  atmosphere  through  any  shaped  orifice  in  any  pipe  or 
reservoir  in  which  the  given  preasui-e  is  nminiained.  Volume  of  air  in  cubic 
feet  which  may  be  discharged  in  one  miunte  through  an  orifice  having  an 
effective  area  of  discharge  of  one  square  inch.  The  5th  column,  not  in  the 
original,  has  been  calculated  by  the  author  The  figures  represent  the 
horse-power  tbeorettcallv  required  to  move  1000  cu.  ft.  of  air  of  the  given 
pressures  through  an  onflce,  wlthont  allowance  for  the  work  of  compression 
or  for  frictioa  or  other  losses  of  the  fan.  These  losses  may  amount  to  from 
eOiC  to  IQOtC  of  the  given  horse-power. 

The  change  in  aensity  which  results  from  a  change  in  presaiire  has  been 
taken  Into  account  in  the  calculations  of  the  table.  Tlie  volume  of  air  at  a 
given  velocity  diechnrged  through  an  orifice  depends  upon  its  shape,  and  is 
always  less  than  that  measured  by  its  full  area.  For  a  plven  e/fecltre  area 
the  v€>tuBfie  is  proportional  to  the  velocity.  The  power  i"equired  to  move  afr 
through  an  oritlce  is  measured  by  the  product  of  the  velocitv  and  the  total 
resisting  pressure.  This  power  for  a  given  orifice  varies  as  the  cube  of  the 
velocity.  For  a  ^iven  volume  it  varies  aa  the  aquare  of  the  vekxsity.  In  the 
movement  of  air  by  means  of  a  fan  there  are  unavoidable  reaistanoM 
which,  iu  proportion  to  their  amount,  increase  the  actual  power  oonslder- 
ably  above  the  amount  here  given. 

For  any  hIm  of  centrifugal  fan  there  exists  a  certain  niaadnium  area  over 
which  a  given  pressure  may  be  maintained,  dependent  upon  and  propor- 
tional to  the  speed  at  which  it  is  operated.  If  this  area,  known  as  its 
*^*aapaeltyai'ea,'»or  sqnare  inches  of  nlast,  be  increased,  the  pressure  is 
lowere<l  (the  volume  being  increased),  but  if  decreased  the  pressure  remains 
eonstsnt.  Tlie  revolutions  of  a  given  fan  necessary  to  mainratn  a  given 
pressure  under  these  conditions  are  given  In  the  table  on  p.  519.  which  is 
based  upon  the  abve  table.  The  pressure  produced  by  a  given  fan  and  its 
effective  capacity  area  being  known,  its  nominal  capacity  and  the  horse- 
power required,  without  allowance  for  frictional  losses,  may  be  determined 
from  the  table  above. 

In  practice  the  outlet  of  a  fan  greatly  exceeds  the  capacity  area;  hence 
the  volume  movcxl  and  the  horse-power  required  are  in  excess  of  the 
amounts  determined  as  above. 


CENTRIFUGAL  FANS. 


519 


Steel-plate  Fttll  ttotlftlliA:  Vans.    (BufTalo  Forge  Co.) 
Capacities  in  cubic  feet  of  air  per  minute.    (2dee  also  table  on  p.  583.) 


Bevolutiona  per  Minute. 

Size, 
in. 

100 

loO 

200 

250 

800 

850 

400 

4oO 

600 

ooO 

600 

50 

1650     2475 

8800 

4125 

4950 

6775 

6600 

7425 

8250 

9075 

9900 

GO 

2480 

3T20 

4960 

6200 

7440 

8680 

9920 

11160 

12400 

13^0 

14880 

TO 

4fi00 

6700 

9000 

11«0 

18500 

15760 

18000 

20250 

22500 

80 

7070 

10603 

14140 

17675 

21210 

24745 

S82H0 

81815 

90 

lOiOO 

16600 

iweoo 

S2600U 

81^00 

3ft400 

4J600 

100 

14*280 

2149U 

28560 

85700 

42S40 

40080 

57120 

110 

18060 

I3ai40 

87920 

47400 

56880 

66360 

1» 

84800 

87J00 

49600 

6«XX) 

74400 

lj» 

81000 

46800 

&ii(io 

78000 

109S00 

140 

38834 

57581 

7670fi 

95885 

IfiO 

40M0 

73800 

96530 

mi5o 

The  Sturtevatit  Steel  Premitire-Mower  Applied  to  Cupola 
Fnrnaeee  and  Foreee. 


Cupola  Furnaces. 

Forges. 

Diameter 

Blast* 

Bey.  per 

Rev.  per 

Kamber 

of 

Melting 

pressure 

min.  of 

Number 

min.Blower 

of 

Cupola 
inside  of 

Capacity 

required 
in  Wind- 

Blower  nec- 

of Forges 
supplied 

necessary 

Blower. 

of  Cupola 

essary  to 

to  produce 

Lining, 
In, 

per  bour 

box  in 

produce 

pressure 

in  lbs. 

ounces 

required 

Blower. 

for 

persq.in. 

pressure. 

forge  Are. 

4/0 

1 

5,548 

2/0 

2 

4,804 

0 

8 

8,645 

ss 

I»fi00 

5 

8,669 

4 

8,109 

90 

1,900 

6 

8,288 

6 

8,601 

80 

2.900 

7 

8,080 

8 

2,806 

9& 

4,200 

8 

2,818 

10 

9,000 

-    40 

6,ft00 

10 

2,090 

14 

1,782 

46 

8,900 

12 

2,670 

10 

1,667 

58 

12,500 

14 

2,316 

26 

1.264 

8 

60 

16,500 

14 

2,028 

36 

1,104 

9 

72 

24.000 

16 

1.854 

45 

950 

10 

84 

34.000 

IG 

1,627 

60 

834 

The  above  tabto  relates  to  comtnon  cupolas  under  ordinary  condftfons  and 
to  forges  of  medium  sise.  Tbe  diameter  of  cupola  given  opposite  each  size 
blower  Is  the  greatest  which  is  recommended;  in  cases  wbere  there  Ik  a  sur- 
plus of  power  one  sise  larger  blower  may  be  used  to  advantage.  1  ht*  melt- 
ing cupacfty  per  hour  Is  based  upon  an  average  of  tests  on  some  of  the  best 
cupolAs  found,  and  Is  rallable  in  cases  where  the  cupola  is  well  constructed 
and  cansfuily  operated.  The  blast-pressure  required  In  wind-bojt  is  the 
maximum  under  ordinary  conditionK  when  coal  is  used  as  fuel.  When  coke 
is  employed  the  pressure  may  be  lower. 

The  cupola  pressures  given  are  those  in  the  wind-box,  while  tbe  btois 
pressure  for  forges  is  4  ounces  In  the  tuyer?  pipe.  The  corresponding  rev- 
olutions of  fan  given  are  in  each  case  sufficient  to  maintain  these  pre9Snr»»« 
at  the  fan  outlet  when  the  temperature  Is  50*.  The  actual  speed  must  be 
higher  tliaii  this  by  an  amount  proportional  to  the  resistance  of  pipes  and 
the  increase  of  temperature,  and  can  only  be  determined  by  a  knowledge  of 
the  existing  conditions. 

^or  other  data  concerning  Cupolas  see  Foundry  Practice.) 


520 


AIR. 


niameters  of  Bla«i-plpe«  Required  for  Steel  PrcMsure- 

blowem.    (B.  F.  SSturtevaut  Co.) 
Based  on  the  loss  of  pressure  resulting  from  transmission  being  limited  to 
one-half  ounce  per  square  inch. 


sun--  i^t'] 


0 


-   [ 

to       ] 


III  fi« 


Nnmlwraf  Blower. 


101) 

41X1 

100 
t200 

4O0 

UK) 

leoo 

100 

\m 

400 


4/0  £/0    0      t 


I 

,11^ 


1 

ia?6 


"  I'he  above  tahie  has  been  constructed  on  the  followinf?  basis:  Allowinf?  a 
loss  of  pressure  of  ^  oz.  in  the  process  of  transmission  through  any  length 
of  pipe  of  any  size  as  a  standard,  tlie  increased  friction  due  to  lengtheinng 
tliH  pipe  has  been  compentiated  for  bv  an  enlargement  of  the  pipe  sufficient 
to  keep  the  loss  still  at  ^  oz.  Thus  if  air  under  a  ))ressure  of  8  oz.  is  lo  be 
delivered  by  a  No.  6  blower,  through  a  pipe  100  ft.  in  length,  with  a  lows  of 
Woz.  pressure,  the  diameter  of  the  pipe  must  be  119^  in.  If  its  length  i» 
increased  to  400  ft.  its  diameter  should  also  be  increased  to  15^  in.,  or  if 
the  pressure  be  increased  to  1'^  oz.  the  pipe,  if  100  ft.  long.  muf>t  be  li%  in. 
in  <liaineter,  providing  the  loss  of  ^  oz.  is  not  to  be  exceeded.  This  lo»8  of 
^  oz  is  to  be  addetl  to  the  pressure  to  be  maintained  at  the  fan  if  the 
tabiilatf  d  pressure  is  to  be  secured  at  the  other  end  of  the  pipe." 

ISfllcteiicjr  of  Fans.— Much  useful  information  on  the  theoi-y  and 
practice  of  fans  and  blowers,  with  results  of  tests  of  various  forms,  will  l>e 
found  in  Heating  and  Ventilation^  June  to  Dec.  1J>97,  in  papers  by  Prof. 
R.  C.  Carpenter  and  Mr.  W.  G.  Walker.  It  is  shown  by  theory  that  the 
vohime  of  air  deli vere<l  is  directly  proportional  to  the  speed  of  rotation, 
that  the  pressure  varies  as  the  square  of  the  speed,  ancl  that  the  horse- 
power varies  as  the  cube  of  the  speed.  For  a  given  volume  of  air  moved 
the  horse-power  varies  as  the  square  of  the  speed,  showing  the  irreat  ad- 
vantage of  large  fans  at  slow  speeds  over  small  fans  at  higli  speeds  deliver- 
ing the  same  volume.  The  theoretical  values  are  greatly  modified  by  varia- 
tions in  practical  conditions.  Prof.  Carpenter  found  th:.t  with  three  fans 
running  at  a  speed  ot  6:^  ft.  per  minute  at  the  tips  of  the  vanes,  and  an  air- 
pressure  of  '2]4  in-  of  water  column,  the  mechanical  efficiency,  or  the  horse- 
power of  the  air  delivered  divided  by  the  power  required  to  drive  the  fan. 
ranged  from  dr^  lo  47i,  under  different  conditions,  hut  with  slow  speeds  it 
Whs  much  less,  in  some  cases  being  under  20j(.  Mr.  Walker  In  experiments 
on  disk  fans  found  efficiencies  ranging  all  the  way  from  1.4%  to  4^%.  the  size 
of  the  fans  and  the  speed  being  constant,  but  the  shape  and  angle  of  the 
bliules  varying.  It  is  evident  that  there  is  a  wide  margin  for  Improvementa 
in  the  forms  of  fans  and  blowers,  and  a  wide  field  for  experiment  U>  deter- 
mine tlie  cooditlous  that  will  give  maximum  efficiency. 


V. 


CEin'RIPUGAL  FANS.  521 

Centrlfliml  Ventilators  for  ntnes.— Of  different  appliances  for 
TenUlatini?  mines  various  forms  of  centrifuRal  machines haTlnr  proved  their 
efficiency  have  now  hlmost  completely  replaced  all  others.  Most  if  not  all 
of  the  machines  in  use  in  this  country  are  of  this  class,  being  either  open- 
periphery  fans,  or  closed,  with  chimney  and  spiral  casing,  of  a  more  or  less 
modified  Ouibal  type.  Tlie  theory  of  such  machhies  has  been  demouBtrated 
bv  Mr.  Daniel  Murgue  in  *'  Theories  and  Practices  of  CentrifuKal  Ventilating 
Machines,'^  translated  by  A.  L.  Stevenson,  and  is  discussed  in  a  paper  by  R. 
Van  A.  Norris,  Trans.  A.  I.  H.  E.  zx.  687.  From  this  paper  the  following  for- 
molsB  are  taken: 

Let  a  =  area  in  sq.  ft.  of  an  orifice  in  a  thin  plate,  of  such  area  that  its  re- 
sistance to  tiie  passage  of  a  given  quanti^  of  air  equals  the 
resistance  of  the  mine; 
o  =  orifice  in  a  thin  plate  of  such  area  that  its  resistance  to  the  pas- 
sage of  a  given  quantity  of  air  equals  that  of  the  machine; 
)  =  quantity  of  air  passing  in  cubic  feet  per  minute; 
'^  =  velocity  of  air  passing  through  a  in  feet  per  second ; 
F«  =  velocily  of  ah:  passing  through  o  in  feet  per  second; 
h  =  head  in  feet  air -column  to  produce  velocity  V\ 
h«  =  head  in  feet  air-column  to  produce  velocity  V^, 

ga0.65or;    F=i/^;    ^  =  O.«6o  V^; 

a  =3 .        =3  equivalent  orifice  of  mine; 

0.66  f^ 

or,  reducing  to  water-gauge  in  inches  and  quantity  In  thousands  of  feet  per 
minute, 

.4080  , 

o  =4/0  «s^  2q  ~  «iul^alent  orifice  of  machina 

The  theoretical  depression  which  can  be  produced  by  any  centrifugal  ven- 
tilator is  double  that  due  to  Its  tangential  speed.    The  formula 

lig        Hg' 

in  which  3* is  the  tangential  speed.  V  the  velocity  of  exit  of  the  air  from  the 
space  between  the  blades,  and  H  the  depression  roeiisured  in  feet  of  f\ir- 
coiumn.  Is  an  expression  for  the  Dienretical  depression  which  can  be  pro- 
duced by  an  uncovered  ventilator;  this  reaches  a  maximum  when  the  air 
leaves  the  blades  witlioiit  si>eed,  that  is,  V  =  0.  and  H  =  T*  -+-  2gr. 

Hence  the  theoretical  depreHslon  which  can  be  produced  by  any  uncovered 
ventilator  is  equal  to  the  helt;hc  due  to  its  tangential  speed,  andonehalf- 
thMt  which  can  be  produced  by  a  covered  ventilator  with  expanding 
chjinney. 

So  long  as  the  condition  of  the  mine  remains  constant: 

The  volume  produced  by  any  ventilator  varies  directly  as  the  speed  of 
rotation. 

The  depression  produced  by  any  ventilator  varies  as  the  square  of  the 
speed  of  rotation. 

For  the  same  tangential  speed  with  decreased  resistance  the  quantity  of 
air  increases  and  the  depression  diminishes. 

The  following  table  shows  a  few  results,  selected  from  Mr.  Norrls's  paper, 
giving  the  ran^e  of  effleiency  which  may  be  expected  under  different  clr- 
cum«(tances.  Details  of  these  and  other  fans,  with  diagrams  of  the  results 
are  given  In  the  paper. 


522 


AIB. 


Bxperlmento  on  BUn 

le^entllAtliMr  Pabs, 

1 

1^ 

<  i 

u 

H 

l- 

1   * 

P 

til 

i 

1 

a 

£  s 

64 

6517 

«8('..^^l 

2818 

8040 

4290 

1.80 

67.18 

88.40  75.9 

]8 

A 

100 

0282 

8«:  -ii 

8869 

8040 

6808 

8.60 

188.70 

1B6.48  85.4 

111 

6078 

84V  ■L!.^ 

8180 

8040 

6008 

8.80 

175.17  S09.64  88.6 

-& 

1«8 

7737 

8»i  '^^) 

8204 

8040 

6100 

8.00 

828.56  295.81  75.7 

► 

B 

100 

6'J82 

18(-.  -»-i 

1889 

1520 

8007 

1.40 

41.67    97.90  42.5 

-< 

180 

8167 

«7'J.-T'J 

2114 

1530 

8866 

8.00 

86.63 

194.96'44.6 

28 

c  : 

69 

8709 

6i',--r 

1010 

1520 

1610 

1.80 

11.87 

16.76,67.83 

88 

5-208 

8:.  "1,9 

1000 

1520 

1508 

8.15 

87.86 

48.64j57.88 

^\ 

40 

8140 

4lM'.i; 

1240 

8096 

1580 

0.87 

6.80 

18.8249.2 

83 

70 

5495 

13'-,:;.  0 

1825 

8096 

2507 

2.55 

55.85 

67.44  82.07 

50 

2749 

14V, -Ji 

2944 

1522 

6856 

0.50 

11.60 

28.. 55  40.68 

E-l 

69 

8798 

2a^.^'ii 

2982 

1522 

5451 

1.00 

82.42 

45.98  70.50     83 

96 

5!J78 

291 1,1.^0 

3121 

1522 

6676 

2.15 

101.50  120.64  84.10; 

200 

7540 

lais.r.ii 

666 

746 

1767 

8.85 

70.801 102. 79  68.40     26.9 

f] 

200 

7540 

18('>hH 

904 

746 

2898 

805 

86.89,129.07  67.80'    88.8 

200 

7540 

2(yrr-.>} 

1046 

746 

8774 

8.80 

92.50  150.08  61.70 

46.3 

10 

785 

9^  -nj 

2890 

8028 

8680 

0.10 

0.45 

1.80 

85. 

80 

1570 

5.,r  i) 

2856 

8022 

8687 

0.20 

1.80 

8.70 

49. 

25 

1962 

6C.yf) 

2665 

8028 

8399 

0.29 

2.90 

6.10 

48. 

80 

2866 

73:..f-.) 

2486 

8028 

8106 

0.40 

4.60 

9  70 

47. 

G8 

G 

85 

2747 

9-;,!-) 

8688 

8028 

8425 

0.50 

7.40 

18.00 

48. 

40 

8140 

111.'-^) 

2800 

8022 

8567 

0.70 

12.80   24.90 

49. 

60 

8925 

IS"^  :iii) 

2654 

8022 

8881 

0.90 

18.80   88.80 

48. 

60 

4710 

17^i:iH> 

2898 

8028 

8686 

1.86 

86.90   66.40 

55. 

70 

5495 

20i:  --> 

2904 

80^2 

8718 

1.80 

57.70  107.10 

54. 

80 

6280 

221'.  ■■-■'> 

2779     8022  1 

8540 

2.85 

78.80 

152.60 

52. 

Type  of  Fan.  Diaro.  Width.    No.  Inlets.     Diam.  Inlets 

A.  Gulbal,  double 20  ft.         6ft.  4  8ft.  lOin. 

B.  Same,  only  left  hand  running.  20  6  4  8       10 

C.  Guibal 80  6  8  8       10 

D.  Gulbal 25  8  1  11         6 

E.  Gulbal,  double 17^  4  4  8 

F.  Capell 12  10  8  7 

O.  Gulbal 85  8  1  12 


An  examination  of  the  detailed  results  of  each  test  in  Mr.  Norris's  table 
shows  a  mass  of  contradictions  from  which  it  la  exceedingly  dlflQcult  to  draw 
any  satisfactory  conclusions.  The  following,  he  states,  appear  to  be  more 
or  less  warranted  by  some  of  the  figures : 

1.  Influence  of  the  Condition  of  the  Ainonya  on  the  jFVxn.— Mines  with 
yarying  equivalent  orifices  give  air  per  100  feet  periphery-motion  of  tan, 
within  limits  as  follows,  the  quantity  depending  on  the  resistance  of  the 
mine: 


Equivalent      Cu  Ft.  Air  per 
Orifice.       100  ft.  Periphery- 
speea. 


Under  90  sq.  ft. 
80  to  80 
80  to  40 
40  to  50 
50  to  60 


1100  to  1700 
1800  to  1800 
1500  to  2300 
SSOOto&'KX) 
2700  to  4800 


Aver- 
age. 

1300 
1600 
2100 
2700 
3500 


Eouivalent    Cu.  Ft.  Air  per   Aver- 
Oriflce.     100  ft.  Periphery-    age. 
speed. 
8800  to  5100       4000 
4000  to  4700       4400 
8000to5600       4800 


60to  70 
70to  80 
POto  90 
90  to  100 
100  to  114 


5200  to  6  JOO       6700 


The  Influence  of  the  mine  on  the  efDciency  of  the  fan  does  not  seem  to  be 
Tei7  clear.    Eight  fans,  with  equivalent  orifices  over. 50  square  feet«glve 


CENTRIFUGAL  FAX8.  623 

efflcienUes  oyer  TVK ;  four,  vitti  nnaller  equfralent  mlDi^-oriflces,  give  about 
the  same  figures ;  while,  on  tbe  contra  17,  six  fans,  with  equivalent  orifloes  of 
over  50  imiare  feet,  give  lower  efflciencies,  as  do  ten  fans,  all  drawing  from 
mines  witn  umall  equivalent  orifices. 

It  would  seem  that,  on  tbe  whole,  large  airways  tend  to  assist  somewhat 
in  attaining  large  effldency. 

t.  Influence  of  the  Diameter  of  the  Fan.— This  seems  to  be  practieaDr  n/2, 
tbe  OD&  advantage  of  large  fans  bebig  in  their  greater  width  and  tbe  lower 
speed  required  of  the  engiiaes. 

8.  Influence  of  the  Width  of  a  Fan.— Th\B  appears  to  be  small  as  regards 
tbe  efl^eienicy  01  the  machine  ;  but  the  wider  rans  are,  as  a  rule,  exhausting 
more  air. 

4.  Influence  of  Shape  of  Slades.—This  appears,  within  reasonable  limits, 
to  be  pracUoally  nil.  Thus,  six  fans  with  tips  of  blades  curved  forward, 
three  fans  with  flat  blades,  and  one  with  blades  curved  back  to  a  tangent 
wito  the  circumference,  all  give  very  high  efficiencies-  over  TOi. 

5.  Influence  of  the  Shape  of  the  Spiral  Casing.— This  appears  to  be  con- 
siderable. The  shapes  of  spiral  casing  in  use  fall  into  two  daases,  tbe  first 
presenting  a  large  spiral,  beginning  at  or  near  tbe  point  of  cut-off,  and  the 
second  a  circular  casing  reaching  around  three  quarters  of  the  circumference 
of  the  fan,  with  a  short  spiral  reaching  to  the  evoj^e  chimney. 

FSans  having  the  first  form  of  easing  appear  to  give  in  almost  every  case 
large  eflBciendes. 

Fans  that  have  a  spiral  belonging  to  the  first  class,  but  very  much  con- 
tracted, give  only  medium  efficiencies.  It  seems  probable  that  the  proper 
shape  of  spiral  easing  would  be  one  of  snob  form  that  the  air  between  each 
pair  of  blades  could  constantly  and  freely  discharge  into  the  space  between  . 
the  fan  and  casing,  tbe  whole  being  swept  along  to  the  evasee  chimney.  Tbls 
would  require  a  spiral  beginning  near  the  point  of  out-off,  enlarging  by 
gradually  increasing  mcrements  to  allow  for  the  slowing  of  tbe  air  caused  by 
its  friction  agatost  the  casing,  and  reaching  the  chimney  with  an  area  such 
that  tbe  air  could  make  Its  exit  with  its  then  existing  speed—somewhat  less 
than  the  periphery-speed  of  the  fan. 

ft.  Influence  of  the  Shutter. —'fyiiie  certainly  appears  to  be  an  advantage,  as 
hy  it  the  exit  area  can  be  regulated  to  suit  the  varying  quantity  of  air  given 
\xf  tbe  faa,  and  in  this  way  re-entries  can  be  prevented.  It  is  not  uncommon 
to  find  shutterless  fans  into  the  chimneys  of  which  bits  of  paper  may  be 
dropped,  which  are  drawn  into  the  fan,  make  the  circuit,  and  are  again 
thrown  out.  This  peculiarity  has  not  been  noticed  with  fans  provided  with 
sbuCteiB. 

7.  Influence  of  the  Speed  at  which  a  Fan  is  Run.— It  is  noticeable  that 
most  of  tbe  fans  giving  high  efficiency  were  running  at  a  rather  high 
periphery  velocity.  The  best  speed  seems  to  be  between  6000  and  0000  feet 
per  minute. 

Tbe  fans  appear  to  reach  a  maximum  effldency  at  somewhere  about  tbe 
speed  given,  and  to  decrease  rapidly  in  efficiency  when  this  maximum  point 
is  passed. 

in  discoaslon  of  Mr.  Norris*8  paper,  Mr.  A.  H.  Btorrs  says:  From  the  "cu- 
bic feet  per  revolutiOQ  "  and  **  cubical  contents  of  fan-blades,*'  as  given  In  tbe 
.  table,  we  find  that  the  enclosed  fans  empty  themselves  from  one  half  to 
twice  per  revolution,  while  the  open  fans  are  emptied  from  one  and  tbree- 
9aarter  to  nearly  three  times.  Ttiis  for  fans  of  both  types,  on  mines  cover- 
ing  the  same  range  of  equivalent  orifices.  One  open  fan,  on  a  very  lar^a 
onfice,  was  emptied  nearly  four  times.  wh<ie  a  closed  fan,  on  a  still  larger 
orifice,  only  shows  one  and  one-half  tlm^-e.  For  tbe  open  fans  tbe  **  cubic 
feet  per  100  ft.  motion  "  is  greater.  In  proportion  to  the  fan  width  and  equiv- 
alent orifice,  than  for  the  enclosed  type.  Notwithstanding  this  apparently 
free  discharge  of  the  open  fans,  they  snow  very  low  efflciencies. 

As  illustrating  the  very  large  capacity  of  centrifugal  fans  to  pass  air,  if 
the  eonditions  of  the  mine  are  made  favorable,  a  ift-ft.  diom.  fan,  4  ft.  6  In. 
wide,  at  UX)  revolutions,  passed  8fl0.000  cu.  ft.  per  mtn.,  and  another,  of  same 
diameter,  but  sllgbtlv  wider  and  with  larger  intake  circles,  passed  &00,000  cu. 
ft  .the  water-gauge  In  both  instances  being  about  ^  in. 

T.  D.  Jones  says :  The  efficiency  reported  in  some  cases  by  Mr.  Nonis  Is 
larger  than  I  have  ever  been  able  to  determine  by  experiment.  My  own  ex- 
periments, reoofded  in  the  Pennsylvania  Mine  Inspectors'  Reports  from  1875 
to  IflBJ*  did  not  show  more  than  (X>%  to  e6%. 


524 


AIK. 


DISK  FANS. 

Experiments   made  iwrltli  a  Blaclunan  Disk  Fan,  4  ft 

diam  ,  by  Geo.  A.  Suter,  to  determine  the  volumes  of  air  delivered  under 
various  coudltiong.  and  the  power  required ;  with  c^alculations  of  efficiency 
and  ratio  of  increase  of  power  to  increase  of  velocity,  by  G.  H.  Babcock. 
(Trans.  A.  S.  M.  E.,  vli.  647) : 


d 
E 

> 

& 

Cu.  ft.of  Air 
delivered 
per  min., 

r 

ti 

fy 
P 

of? 

pi 

il 

a  8 

5- 

Wo 

350 

25.797 
33,575 
41, {h» 
47,756 
For 

0.65 
2.29 
4.42 
7.41 
series 

0.76 
1.99 
8.86 
6.47 
series 

1.682 

440 
634 
61;! 

1.257 
1.186 
1.146 
1.749 

1.262 
1.287 
1.139 
1.851 

8.628 

1.843 

1.6T7 

11.140 

6.4 
S.4 
8.97 
4. 

.9553 

1.068 

.9358 

340 

20,372 
26,660 
81.610 
86,648 
For 

9.d83 
13,017 
17,018 
18,649 
For 

.7110 

453 
636 
627 

1.882 
1.188 
1.167 
1.761 

1.808 
1.187 
1.165 
1.794 

2.618 
1.940 
1.676 
8.618 

8.65 
8.88 
8.60 
8.63 

•'•••• 

.6068 
.5205 
.4802 

340 
480 

570 

1.12 
8.17 
6.07 
8.46 
series 

Tir 

3.27 
6.00 
series 

0.28 
0.47 
0.75 
0.87 

*i!266' 
1.242 
1.068 
1.676 

'I'.aoi* 

1.307 
1.096 
1.704 

1.916 
1.894 
7.654 

2.25 
8.68 
8.24 

1.74 
1.60 
1.81 

.8939 
.8046 
.3319 
.8027 

ajo 

437 
516 

8,899 

10,071 

11.157 

For 

0.26 
0.45 
0.76 

'■i;824' 
1.181 
1.568 

*"i'.199* 

1.108 
1.329 

"a!  142 

1.457 
4.580 

8.66 
6.85 

4.96 
8.72 

.2681 
.8188 
.2202 

Nature  of  the  7Srp??ini«»nfa.— First  Series:  Drawing  air  through  80ft.  of 
48-in.  diam.  pipe  on  inlet  side  of  the  fan. 

Second  Series:  Forcing  air  through  80  ft.  of  48-in.  diam.  pipe  on  outlet  side 
of  the  fan. 

Third  Series:  Drawing  air  through  80  ft.  of  48-in.  pipe  on  inlet  side  of  the 
fan— the  pipe  being  obstructed  by  a  diaphragm  of  cneese-dolli. 

Fourth  Series:  Forcing  air  through  80  ft.  ot  48-in.  pipe  on  outlet  side  of  fan 
—the  pii>e  being  obstnicted  by  a  diaphragm  of  cheesecloth. 

Mr.  Snbcock  says  concerning  these  experiments:  The  first  four  experi- 
ments are  evidently  the  subiecc  of  some  error,  because  the  efficiency  is  suoh 
as  to  prove  on  an  average  that  the  fan  was  a  source  of  power  suflHcient  to  ' 
overcome  all  losses  and  nelp  drive  the  engine  besides.  The  second  series  is 
less  questionable,  but  still  the  efficiency  in  the  first  two  experiments  is  larger 
than  miftht  be  expected.  In  the  third  and  fourth  series  the  resistance  of  the 
cheese-cloth  in  the  pipe  reduces  the  efficiency  largely,  as  would  be  expected. 
In  this  caf:e  the  value  has  lieen  calculated  from  the  height  equivalent  to  the 
water- pressure,  rather  than  the  actual  velocity  of  the  air. 

This  record  of  experiments  made  with  the  disk  fan  shows  tiiat  this  kind  <^ 
fan  is  not  adapted  for  use  where  there  is  any  material  resistance  to  the  flow 
of  the  air.  In  the  centrifugal  fan  the  power  used  is  nearly  proportioned  to 
the  amount  of  air  moved  under  a  given  bead,  while  in  this  fan  the  power  re- 
quired for  the  same  number  of  revolutions  of  the  fan  increases  verv  mate- 
rially wirh  tlie  resistance,  notwithstnndingthe  quantity  of  air  moved  is  at  the 
same  time  considerably  reduced  In  fact,  from  the  inspection  of  the  third 
and  fourth  scries  of  tet-ts,  it  would  appear  that  the  power  required  is  verv 
nearly  the  same  for  a  given  pressure,  whether  more  or  less  air  oe  in  motion. 
It  would  seem  chat  the  main  advantage,  if  any.  of  the  disk  fan  over  the  cen- 
trifugal fan  for  slight  resistances  consists  in  the  fact  that  the  delivery  Is  t^e 
full  area  of  the  disk,  while  with  centrifugal  fans  intended  to  move  the  same 
quantity  of  air  the  opening  is  much  smaller. 


DISK   FANS. 


525 


It  will  be  seen  by  columns  8  and  9  of  the  table  that  the  power  used  in- 
creased much  more  rapidly  than  the  cube  of  the  velocity,  as  in  centrifugal 
fans.    The  different  experiments  do  not  agree  with  each  other,  but  a  general 
avera^  may  be  assumed  as  about  the  cube  root  of  the  eleventh  power. 
Fall  aud  Three-quarter  Souslnfc  Fans.    (Buffalo  Forge  Co.) 
i.Ufcpacities  at  different  velocities  and  pressures.    (See  also  table  on  p.  519.) 


Velocities  In  cubic  feet  per  minute;  Pres- 
sures in  ounces  at  Fan  Outlets. 

1 

Pulleys. 

imitt 

.per 

44892  ft 

.per 

6175  ft.  per 

Size  of 
Outlet. 

s 

1 

1 

min,  H  <^z. 

min.,  9^  oz. 

min.,  1  oz. 

i 

Capac- 
ity. 

Revs, 
per 
miu. 

Capac- 
ity. 

Revs, 
per 
min. 

Capac- 
ity. 

RevB. 
per 
min. 

50 

18Vix18^ 

^ 

7 

8,140 

492 

9,900 

600 

11,4<0 

693 

60 

S-J^xiKVi 

8 

11,470 

462 

18,960 

562 

16,120 

650 

TO 

26     x26 

^H 

9 

16,280 

861 

19,800 

441 

22,880 

509 

80 

2894x29« 

10 

21,460 

803 

26,100 

369 

30,160 

426 

90 

43 

n 

27,750 

266 

83,750 

325 

89,000 

376 

100 

3Tkix87H 

459^ 

16 

12 

34,410 

242 

41,850 

294 

48,860 

340 

110 

41      x41 

5114 

18 

13 

41,540 

217 

60,400 

265 

58,240 

30? 

130 

44%  X  4494 

5498 

20 

14 

49.580 

195 

60,800 

243 

69.680 

280 

i:»     iSyixiS^i 

61 

22 

15 

58,460 

187 

71,100 

227 

82,160 

263 

140  !  5-'Vix5,'M 

64-K 
69^ 

24 

16 

67,710 

172 

82,350 

214 

95.160 

248 

iW 

56     x.yj 

26 

17 

77,700 

161 

94,500 

196 

109,200 

227 

160 

599^x599^ 
6:)Hx63^ 

74J4 

28 

18 

88,800 

149 

108,000 

181 

124.800 

209 

ITO 

79 

30 

19 

100,270 

140 

121,a'50 

171 

140,920 

197 

ISO 

112,480 

136 

136,800 

165 

158,080 

191 

For  14  oz.  pi-essure,  speed  2584  ft.  per  minute,  the  capacity  and  tiie  revolu- 
tions are  eaoi  one-half  of  those  for  1  oz.  pressure. 

Blllclency  of  Disk  Fans*— Prof .  A.  B.  W.  Kennedy  (Industries,  Jan. 
17. 1890)  made  a  series  of  tests  on  two  disk  fans,  2  and  3  ft.  diameter,  known 
S8  the  Verity  Silent  Air-propeller.  The  principal  results  and  coDcluslona 
are  condensed  below. 

In  each  case  the  efficiency  of  tlie  fan,  that  is.  the  quantity  of  air  delivered 
per  effective  horse^power,  increases  very  rapidly  as  the  speed  diminishes, 
so  that  lower  speeds  are  much  more  economical  than  higher  ones.  On  the 
other  hand,  as  the  quantity  of  air  delivered  per  revolution  is  very  nearly 
constant,  the  actual  useful  work  done  by  the  fan  increases  almost  directly 
with  its  sp^i.  Comparing  the  large  and  small  fans  with  about  the  same 
air  delivery,  the  former  (running  at  a  much  lower  speed,  of  course)  is  much 
ttie  more  economical.  Comparing  the  two  fans  running  at  the  same  speed, 
however,  the  smaller  fan  is  very  much  the  more  economical.  The  delivery 
of  air  per  revolution  of  fan  is  very  nearly  directly  proportional  to  the  area 
of  the  fan's  diameter. 

The  air  dehvered  per  minute  by  the  8-ft.  fan  is  nearly  12.5/J  cubic  feet 
(R  being  the  numl>er  of  revolutions  made  by  the  fan  per  minute).  For  the 
8-ft.  fan  the  quantity  is  5.72?  cubic  feet.  For  either  of  thase  or  any  other 
similar  fans  of  which  the  area  is  A  square  feet,  the  delivery  will  be  about 
1.8 AR  cubic  feet.  Of  course  any  change  in  the  pitch  of  the  blades  might 
entirely  changre  these  figures. 

The  net  H.P.  taken  up  is  not  far  from  proportional  to  the  square  of  the 
number  of  revolutions  above  100  per  minute.    Thus  for  the  3-ft.  fan  the  net 

HP-   •»    '■^^-'  '">"  ""■  "•«  '^f-  ""> »"«  ■«*  H.P.  IB  <f^^*. 

The  denominators  of  these  two  fractions  are  very  nearly  proportfonal  in- 
versely to  the  square  of  the  fan  areas  or  the  fourth  power  of  the  fan  diam- 
eters. The  net  H.P.  required  to  drive  a  fan  of  diameter  D  feet  or  ai*ea  A 
square  feet,  at  a  speed  of  R  revolutions  per  minute,  will  therefore  be  ap- 

.      ^,      D^B-100)a  ^«(R-100)a 

proximately    -y^^^    or    -, 0, 400,000^ ' 

The  2-ft  fan  was  noiseless  at  all  speeds.  The  8-ft.  fan  was  also  noiselesa 
op  to  over  450  revolutions  per  minute.  • 


526 


Anu 


Speed  of  fan.  reyolutions  per  minute, 
Net  H.P.  to  drive  fan  and  belt 

gaUc  feet  of  air  per  itilDute 
ean  velocity  of  air  in  a-f t.  flue«  feet 

per  minute 

Mean  velocity  of  air  In  flue,  same 

diameter  as  fan 

Cu.ft.of  air  per  min.per  effective  H.P. 
Motion  firiven  to  air  per  rev.  of  fan,  ft. 
r!ul)lo  feet  of  air  per  rev,  of  fan. ...... 


Propeller, 
9  ft.  diam. 


750 
0.42 
4,188 


1,880 
0.980 
1.77 
6.68 


676 


0.82  0.287 
8,880    8,410 


1,290 

11,970 

1.81 

6.66 


677 


643      482 


1,066 
16.000 

d'.OO 


Propeller, 
8  ft.  diam. 


676 
1.02 
7,400 

1,046 


ii!8 


459 
0.57.5 
6,800 


10,070 
1.79 
12.6 


873 
0..*«4 
4,470 

632 


18.800 
1.70 
18.0 


POSITIVE  ttOTABT  Bt^CVrKHS^    (P.  H.  &  F.  M  Boote.) 


Bile  number 

Cubic  feet  per  revolution. . . . 

Revolutions     per     minute, 
Smith  flres 


Fumishee 
flres... 


blast   for  Smith 


Revolutions  per  minute  for  J 
cupola,  melting  iron. . , 


Sise  of  cupola,   inches, 
sidelining 


^:): 


Will  melt  Iron  per  hour,  tons^ 
Horse-poWer  required. , 


H 

H 

1 

2 

8 

4 

6 

6         7 

n 

^S 

8 

6 

8 

13 

28 

87        68 

8W 

260 

225 

200 

175 

150 

125 

100       75 

to 

to 

to 

to 

to 

to 

to 

to       to 

350 

800 

275 

250 

225 

200 

175 

160     125 

2 

6 

10 

16 

24 

82 

47 

70       80 

to 

to 

to 

to 

to 

to 

to 

to       to 

4 

8 

14 

30 

30 

43 

67 

100     185 

275 

275 

200 

186 

170 

ISO      187 

to 

to 

to 

to 

to 

to        to 

..  • 

,  , 

875 

325 

800 

275 

S50 

80O     175 

..  • 

18 

24 

80 

86 

42 

60       7S1 

to 

to 

to 

to 

to 

to       or 

24 

SO 

36 

42 

60 

60  8-55^8 

. .. 

... 

m 

^ 

3 

4H 

6 

'1^"?l! 

to 

to 

to 

to 

to 

■*i 

"i 

9 

8^ 

8 

6« 

n 

7 

19 

'^•Hi 

The  amount  of  iron  melted  is  ba.spd  on  30,000  cubic  feet  of  air  per  ton  oi 
iron.  The  home-power  is  for  nutzimum  speed  and  a  pressure  of  ^  pound, 
ordinary  oupoU  pressure.    (See  also  Foundry  Practioe.) 

BI«OWING«KN«INn8. 

€orlli»«  HorlBontal  Ci*o*«-coiDpoHn4l  Oon4leii«liic 

—        "  "  hiar-  •      


Bloiyliig*fengine».    (Philadelphia  EriKitieering  Woiks.) 


Indicated 
Honte-power. 

Revs, 
per 
mln. 

Ou.  Ft. 

Free 
Air  per 

mln. 

Blast- 
pres- 
sure 
per 

Til."- 

1^ 

< 

,iy 

15Exp. 
]261bs. 
Steam. 

13Kxp. 
lOOlbs. 
Steam. 

< 

2.2H0 
\:i90 
2,060 

40 
60 
40 
60 

80,400 
45,«K) 
30,400 
45.0tf0 

},5 

44 

42 

78 
72 

Ci)  84 
(t.')  84 

00 
60 

605.000 
476,000 

605,000 
550,000 

1,050 
1,596 

40 

30,4<)0 

4:..6(!() 

\W 

32 

60 

(2)84 

60 

356.000 

488,000 

1,340 

1.9H0 
1.152 
1,702 

40 
60 
40 
60 

26.800 
39.600 
26.80() 
30.600 

[,5 

40 
38 

?2 
70 

(2)T8 

60 
60 

445,000 
426,000 

545.000 
491,000 

938 
1.386 

780 
1,175 

.548 

40 

m 

40 
CO 
40 
GO 

20,h00 
39.  COO 
L^CtO 
23.5()0 
15.080 

lis 

86 

84 

28 

66 
CO 

50 

(2)78 
(«)78 
(2)72 

60 

60 
60 

41.5,000 
340,000 
270.000 

480,000 
430,000 

300.000 

Verttcni  eiifci lies  are  buUt  of  the  same 
the  Ktroke  ia  48  in.  instead  of  00,  and  they 
rirolutions  to  g!ve  the  same  pistun-speed 


diineiisioiis  as  above,  exct* pt  that 
are  run  at  a  higher  numlM.r  of 
and  the  same  I.  H.  P. 


STBAK-JKC  BLOWER  AHD  EXHAU8TEB. 


627 


The  calculations  of  power,  capacity,  etc.,  of  blowing-engines  are  the  same 
as  those  for  air-compressors.  They  are  built  without  any  provision  for 
cooling  the  air  during  corapressiou.    About  400  feet  per  minute  is  the  usual 

Eistou-Bpeed  for  recent  forms  of  engiiies,  but  with  posttiVe  air-valyeSj  which 
ave  been  introduced  to  some  extent,  this  speed  may  be  increased.  The 
efDcieucy  of  the  engine,  that  is,  the  ratio  of  the  I.H.P.  of  the  air-cylinder  to 
that  of  the  steam-aylinder,  is  usually  taketi  at  00  per  cent,  the  losses  by 
frictloii,  leakage,  etc.,  being  taken  at  10  per  eent. 

9TBA1K-JBT  BIiOWBR  A!ID  BXHAUSTBB. 

A  blower  and  exhauster  is  made  by  L.  Schutte  ft  Co.,  Philadelphia,  oa 
the  principle  of  the  steam- jet  ejector.   The  following  is  a  table  of  capacities: 


fUae 
No. 

Quantity  of 
Air  per  hour 

cubic  feet. 

Diameter  of 
Pipes  in  Inches. 

Size 

No. 

Quantity  of 
Air  per  hour 

ctibio  feet. 

Diameter  of 
Pipes  in  inches. 

Steam. 

Air. 

Air. 

000 
00 
0 

1 

2 
8 

4 

1,000 
2,000 
4.000 
6,000 

mooo 

18^000 
84,000 

9 

1 

6 
6 

I 

9 

10 

S0,000 
36,000 
42,000 
48,000 
64,000 
60,000 

8 

The  admissible  vacuum  and  counter  pressure,  for  which  the  appamtus  is 
constructed,  is  up  to  a  rarefaction  of  8U  inches  of  mercury,  and  a  counter^ 
prnt^ure  up  to  one  sixth  of  the  steam -pressure. 

The  table  of  capacities  Is  based  on  a  steam- pressure  of  about  60  lbs.,  and 
a  counter-pressure  of  about  8  lbs.  With  an  increase  of  steam-pressure  or 
decrease  of  counter-pressure  the  capacity  will  largely  increase. 

Another  steam-Jet  blower  is  used  for  boller-flriug,  ventilation,  and  similar 
purposes  where  a  low  counter-pressure  or  rarefaction  meets  the  require- 
ments. 

The  volumes  as  given  in  the  following  table  of  capacities  are  under  the 
supposition  of  a  steam-pressure  of  45  lbs.  and  a  eounter^pressure  of,  say, 
2  inches  of  water : 


Sfase 
No. 

Cubic 
feet  of 

Air 
delivered 
per  hour. 

Diameter 

of 
Steam- 

Diameter  In 
inches  of— 

Siae 
No. 

Cubfc 
feet  of 
Air  de- 
livered 
per  hour 

Diam. 

of 
Steam - 
pipe  in 

Diameter  in 
inches  of — 

Inlet 

Disoh. 

Tnlet. 

DIsch. 

00 
0 

1 
2 
3 

6,000 

12,000 

90,000 

60,000 

125,000 

1* 

4 

6 

8 

n 

14 

8 
4 
6 
8 
\    10 

4 

6 

250,000 

600.000 

1,000,000 

2,000,000 

¥ 

17 
24 
82 
42 

14 
20 
27 
86 

Tli«  88«AIIHj«8  •«  <t  iSeaiia   for  iTenttlAtlon* -Between  181 0 

and  1860  the  steam  jet  was  employed  to  a  considerable  extent  for  ventilat- 
ing  Eofrlish  collieries,  and  in  18&J  a  comniitte««  of  the  House  of  Commons 
r<*portea  that  it  was  the  most  powerful  and  at  the  same  tiine  the  cheapest 
method  for  the  ventilation  of  mines  ;  but  experiments  made  shortly  after- 
wards  proved  that  this  opinion  was  erroneous,  and  that  furnace  ventilation 
was  le^  than  half  as  explosive,  and  in  consequence  the  jet  was  soon  aban« 
doned  as  a  pennanent  method  of  ventilation. 

For  an  account  of  these  experiments  see  Colliery  Engineer^  Feb.  1800. 
The  Jet,  however,  Is  sometimes  advantageously  used  as  a  substitute,  for 
instance,  in  the  case  of  a  fan  standing  for  repairs,  or  after  an  explosion, 
when  the  furnace  may  not  be  kept  going,  or  in  the  case  of  the  fan  having 
been  randend  ttseleMi 


628  HSAiiKQ  AiffD  VBirriLArioir. 


HEATIKQ  AKD  VENlXLAfrlOir. 

Ventilation.  (A.  R.  Wolff,  Stevens  Indicator,  April,  1890.)— The  pop- 
ular inipressiou  that  the  impure  air  falls  to  the  bottom  of  a  crowded  room 
is  erroneous.  There  is  a  coD»tant  mitiKlins  of  the  fresh  air  admitted  with 
the  impure  air  due  to  the  law  of  diffusion  of  ganes,  to  difference  of  temper- 
ature, etc.  The  process  of  ventilation  is  one  of  dilution  of  the  impure  rir 
by  the  fresh,  and  a  room  is  properly  ventilated  in  the  opinion  of  the  hyi^en- 
ists  when  the  dilution  is  such  that  the  carbonic  acid  In  the  air  does  not  ex- 
ceed from  6  to  8  parts  by  volume  in  10,000.  Pure  country  air  contains  about 
4  parts  COa  In  10,000,  and  badlv-ventilated  quarters  as  high  as  80  parts. 

An  ordinary  man  exhales  O.d  of  a  cubic  foot  of  CO9  per  hour.  New  York 
j?a8  {^ives  out  0.75  of  a  cubic  foot  of  CO*  for  each  cubic  foot  of  gas  burnt. 
An  ordinary  lamp  gives  out  1  cu.  ft.  of  CO)  per  hour.  An  ordinary  candle 
{irives  out  0.3  cu.  ft.  per  hour.  One  oixlinary  gaslight  equals  in  vitiating 
effect  about  5^  men,  an  ordinary  lamp  1%  men,  and  an  ordinary  candle  H 
man. 

To  determine  the  quantity  of  air  to  be  supplied  to  the  inmates  of  an  un- 
lighted  room,  to  dilute  the  air  to  a  desired  standard  of  purity,  we  can  estab- 
lish equations  as  follows: 

Let  V  =  cubic  feet  of  fresh  air  to  be  supplied  per  hour; 

r  s  cubic  feet  of  CO,  in  each  10,000  cu.  ft.  of  the  entering  air: 

B  =  cubic  feet  of  CO,  which  each  10,000  cu.  ft.  of  the  air  in  the  room 

may  contain  for  proper  health  conditions; 
n  s  number  of  persons  in  the  room ; 
.6  =  cubic  feet  of  00^  exhaled  by  one  man  per  hour, 
v  X  r 

Then  ■  ■  +  .6n  eqiuUs  cubic  feet  of  00^  communicated  to  the  room  dur- 
ing one  hour. 

This  value  divided  by  v  and  multiplied  by  10,000  gives  the  proportion  of 
CO,  Id  10,000  parts  of  the  air  in  the  room,  and  this  should  equal  B,  the  stan- 
dard of  purity  desiied.    Therefore 

^  j°H^^-«-].  ,,,,|^^. „, 

6000 

If  we  place  r  at  4  and  i?  at  6,  v  =  ^ — ~n  s  SOOOn (2) 

0  —  4 

or  the  quantity  of  air  to  be  supplied  per  person  Is  8000  cubic  feet  per  hour. 

If  the  original  air  in  the  room  In  of  the  purity  of  external  air,  and  the  cubic 
contents  of  the  room  is  equal  to  100  cu.  ft.  per  inmate,  onlv  3000  -  100  =  2900 
cu.  ft.  of  fresh  air  from  without  will  have  to  be  supplieo  the  flrst  hour  to 
keep  the  air  within  the  standard  purity  of  6  parts  of  CO,  In  10,000.  If  ilie 
cubic  contents  of  the  room  equals  200  cu.  ft.  per  inmate,  only  8000  -  SOO  =  :!KM) 
cu.  ft.  will  have  to  be  supplied  the  first  hour  to  keep  the  air  within  the 
standard  purity,  and  so  on. 

Again,  if  we  only  desire  to  maintain  a  standard  of  purity  of  8  iNurtff  of 
carbonic  acid  in  10,000,  equation  (1)  gives  as  the  required  air-supply  per  hour 

t;  =s  -g — -n  =  1500n,  or  1500  cu.  ft.  of  fresh  air  per  inmate  per  hour. 

Cubic  feet  of  air  containing  4  parts  of  carbonic  acid  in  10.000  necessary  per 
person  per  hour  to  keep  the  air  in  room  at  the  composition  of 

6  7  8  9  10        15        20   |  parte  ofjjarbonic  acid  in 

8000       2000       1500       1200       1000       545       875     cubic  feet. 

If  the  original  air  In  the  room  Is  of  purity  of  external  atmosphere  (4  parts 
of  carbonic  acid  in  10,000),  the  amount  of  air  to  be  supplied  Uie  first  hour, 
for  given  cubic  spaces  per  inmate,  to  have  given  standards  of  purity  not 
exceeded  at  the  end  of  the  hour  is  obtained  from  the  f oUowing  tafila : 


YSNTILATIOir. 


529 


Cubic  Feet 
of 

in  Room 
I>er 

Proportion  of  Carbonic  Add  In  10,000  Parts  of  the  Air,  not  to 
be  Exceeded  at  End  of  Hour. 

G 

7 

8 

0 

10 

15 

20 

Individual. 

Cubic  Feet  of  Air.  of  Composition  4  Parts  of  Carbonic  Acid  in 
10.000,  to  be  Supplied  the  First  Hour. 

100 
200 
800 
400 
600 
600 
700 

2900 
8800 
2700 
2600 
2:500 
2400 
2900 
2200 
2100 
2000 
1500 
1000 
600 

1000 
1800 
1700 
1000 
1600 
1400 
1300 
1200 
1100 
1000 
600 
None 

1400 
1800 
1200 
1100 
1000 
900 
800 
700 
flOO 
500 
None 

1100 
1000 
900 
800 
700 
600 
500 
400 

aoo 

200 
None 

900 
80O 
700 
600 
600 
400 
800 
200 
100 
None 

445 
845 
245 
145 
45 
None 

275 

175 

75 

None 

800 

900 

1000 

1500 

9000 

2S00 

It  is  exceptional  that  systematic  ventilation  supplies  the  8000  cubic  feet 
per  inmate  per  hour,  whicn  adequate  health  considerations  demand.  Lar^e 
auditoriums  In  whi(^  the  cubic  suace  per  individual  is  £ri*eat,  and  in  which 
the  atmosphere  is  thoroughly  fresh  before  the  rooms  are  occupied,  €uid  the 
occupancy  is  of  two  or  three  hours*  duration,  the  systematic  air-supply  may 
be  reduced,  and  2000  to  2500  cubic  feet  per  inmate  per  hour  is  a  satisfactory 
allowance. 

Honpitals  where,  on  account  of  unhealthy  excretions  of  various  kinds,  the 
air-dilution  must  be  lareesc,  an  air-supply  of  from  4000  to  6000  cubic  feet  per 
inmate  per  hour  slioiild  be  provided,  and  this  is  actually  secured  In  some 
hospitcUs.  A  report  dated  March  15, 1882,  by  a  commission  appointed  to 
examine  the  public  schools  of  the  District  of  Columbia,  says : 

**In  each  class-room  not  lees  than  15  square  feet  of  floor-space  should  be 
allotted  to  each  pupil.  In  each  class-room  the  window-space  should  not  be 
le««  than  one  fourth  the  floor-space,  ami  the  distance  of  desk  most  remote 
from  the  window  should  not  be  more  than  one  and  a  half  times  the  height  of 
the  top  of  the  window  from  the  floor.  The  height  of  the  class  room  should 
never  exceed  14  feet.  The  provisions  for  ventilation  should  be  such  as  to 
provide  for  each  person  in  a  class-room  not  less  than  80  cubic  feet  of  fresh 
air  per  minute  (1800  per  hour),  which  amount  must  be  introduced  and 
thoroughly  distribute  without  creating  unpleasant  draughts,  or  causing  any 
two  parts  c^  the  room  to  diflFer  In  temperature  more  than  2**  Faiir.,  or  the 
maximum  temperature  to  exceed  70°  Fahr." 

When  the  air  enters  at  or  near  the  floor,  it  is  desirable  that  the  velocity  of 
inlet  should  not  excecil  2  feet  per  second,  which  means  larger  sizes  of 
register  openings  and  flues  than  are  usually  obtainable,  and  much  higher 
velocities  of  inlet  than  two  feet  per  second  are  the  rule  in  practice.  The 
velocity  of  current  into  vent-flues  can  safely  be  as  high  as  6  or  even  10  feet 
per  sieoond.  without  being  disagreeably  perceptible. 

The  entrance  of  fresh  air  into  a  room  is  co-incident  with,  or  dependent  on, 
the  removal  of  an  equal  amount  of  air  from  the  room.  The  ordinary  means 
of  removal  is  the  vertical  vent-duct,  rising  to  the  top  of  the  bnildinir.  Some- 
times reliance  for  the  production  of  the  current  in  this  vent-duct  is  placed 
solely  on  the  difference  of  temperature  of  the  air  in  the  room  and  that  of 
the  external  atmosphere;  sometimes  a  steam  coil  is  placed  within  the  flue 
near  its  bottom  to  heat  the  air  within  the  duct;  sometimes  steam  pipes 
(risers  and  returns)  run  up  the  duct  performing  the  same  functions;  or  steam 
jets  within  the  flue,  or  exnnust  fans,  driven  l)y  steam  or  electric  power,  act 
directly  as  exhausters^  sometimes  the  heating  of  the  air  In  the  flue  is  ac- 
complished by  gas-Jeta. 

Tub  draft  of  such  a  duct  is  caused  by  the  difference  of  weight  of  ths 


680 


HEATIKG  AKD  VENTILATION. 


heated  air  In  the  duct,  and  a  column  of  equal  height  and  cross-sectional  i 
of  weight  of  the  external  air. 

Let  d  =  density,  or  weight  In  pounds,  of  a  cubic  foot  of  the  external  air. 

Let  di  s  deusliy,  or  weight  in  pounds,  of  a  cubic  foot  of  the  heated  air 
within  the  duct. 

Let  h  c=  vertical  height,  In  feet,  of  the  vent-duct. 

Hd  —  d,)  =  the  pressure,  In  pounds  i>er  square  foot,  with  which  the  air  is 
forced  into  and  out  of  the  vent-duct. 

This  pressure  can  be  expressed  lu  height  of  a  colnmn  of  the  air  of  density 
within  the  vent-duct,  and  evidently  the  height  of  such  column  of  equal 


presssure  would  he] 


,  hjd  -  rfO 


(8) 


Or,  if  <  =  absolute  temperature  of  external  air,  and  ti  m  absolute  tomper> 
ature  of  the  air  in  vent-duot  in  the  form,  then  the  pressure  equals 


Mf ,  *  o: 

t     • 


(4) 


The  theoretical  velocity,  in  feet  per  second,  with  which  the  air  would 
travels  through  the  vent-duct  under  this  pressure  is 


.y 


V*(^  -  0 


8.03 


/^ 


.(5) 


The  actual  velocity  will  be  considerably  less  than  this,  on  account  of  loss 
due  to  friction.  This  friction  will  vary  with  the  form  and  cross-sectional 
area  of  the  vent-duct  and  Its  connections,  and  with  the  degree  of  smooth- 
ness of  its  Interior  surface.  On  this  account,  as  well  as  to  prevent  leakage 
of  air  through  crevices  in  the  wall,  tin  lining  of  vent-flues  is  desirable. 

The  loss  by  f  dction  may  be  estimated  at  approximately  &0)f.  and  so  we  find 
for  the  actual  velocity  of  the  air  as  it  flows  through  the  vent-duct : 


^ " ly^^^^^  t  ^^* ®'"'  •pp«>»*™**«*y» » "  ^i/^^*^1^  •  • 


ifi) 


If  r a  velocity  of  air  in  vent-duct,  in  feet  per  minute,  and  the  external  air 
be  At  3*2°  Fahr.,  since  the  absolute  temperature  on  Fahrenheit  scale  equals 
thermometric  temperature  plus  469.4, 


r=840, 


/*^ 


-o 


401.4 


CO 


from  which  has  been  computed  the  following  table  t 

Qnantlty  of  Air*  In  €nble  Feet*  lHecliaiw«A  P«r  HKf  Biit« 
^^ ffh  «  VeAillatln«  JDnet,  of  whleb  the  £ro«»-e 


throaffh  m  VeAillatln«  JDnet,  or  ^rlilelt  tlie  Cro— "eee* 
ttonal  Area  Is  One  Square  Foot  (the  External  TempeFa* 
ture  or  Air  belns  82<>  Fahr.)* 


Excess  of  Temperature  of  Air  in  Vent<iuot  above  that  of 

Heifrht  of 

External  Air. 

Vfut-duot  in 

feet. 

6« 

10» 

15«» 

20O 

85* 

80O 

60» 

100* 

150« 

10 

77 

108 

188 

158 

171 

188 

843 

842 

419 

15 

94 

183 

m 

188 

210 

280 

997 

419 

514 

80 

lOS 

1£8 

1H8 

217 

242 

265 

m 

484 

608 

25 

121 

171 

210 

242 

971 

297 

868 

541 

668 

SO 

188 

188 

980 

266 

897 

825 

419 

598 

726 

85 

148 

fm 

248 

286 

820 

851 

458 

640 

784 

40 

168 

217 

865 

806 

842 

875 

484 

«6 

888 

46 

169 

280 

284 

825 

868 

896 

514 

499 

889 

60 

171 

^^ 

297 

842 

883 

419 

541 

278 

987 

Multiplying  the  flKuresln  above  table  by  60  glveb  the  cubic  feet  of  air  dis- 
charged per  nour  per  square  foot  of  cross-section  of  vent-duct    Knowing 


MIK£-VBKTILATtOK*  531 

the  crosft-sectional  area  of  vent-ducts  we  can  find  the  total  discharge;  or 
for  a  desired  air-removal,  we  can  proportion  the  cross-sectional  area  of 
▼eot-ducts  required. 

ArtlUclal  Coollns  of  Air  for  VentllaUon*  {Enaineei-ing 
News^  Julv  7,  ]89-^.)~A  pound  of  coal  used  to  malce  steam  for  a  fairly  effi- 
cient ref  i-iKerating-macnine  can  produce  an  .actual  euoUog  effect  equal  to 
that  produced  by  the  melting  of  16  to  46  lbs.  of  ice,  the  amount  varylnsr 
wiih  the  conditions  of  worlciiig.  Or,  865  heat-units  per  lb.  of  coal  conyerted 
into  woric  in  the  refrigerating  plant  (at  the  rate  of  8  lbs.  coal  per  horse- 
power hour)  will  abstract  2275  to  6645  heat-units  of  heat  from  the  refriger- 
ated body.  If  we  allow  2000  cu.  ft.  of  fresh  air  per  hour  per  person  as  sufll« 
ctent  for  fair  rentilation.  with  the  air  at  an  initial  temperature  of  60<>  P.,  its 
weight  per  cubic  foot  will  be  .0786  lb.;  hence  the  hourly  supply  per  person 
will  weigh  2000  X  .0786  lb.  =  147.2  lbs.  To  cool  this  10<>,  the  specfflc  heat  of 
air  being  0.288,  will  require  the  abstraction  of  147.2  X  0.288  X  10  =  360  heat- 
units  per  person  per  hour. 

Taking  the  figures  given  for  the  refrigerating  effect  per  pound  of  coal  as 
above  stated,  and  the  required  abstraction  of  850  heat-units  per  person  per 
hour  to  have  a  satisfactory  cooling  effect,  the  refrigeration  obtained  from  a 
pound  of  coal  will  produce  this  cooling  effect  for  2e79  -f-8S0  =  6)^  hours  with 
the  least  efficient  working,  or  6645  ■+■  SfiO  =  18.7  hours  with  the  most  efficient 
^rorking.  With  ice  at  $5  per  ton,  Mr.  Wolff  computes  the  cost  of  cooling  with 
ice  at  about  $5  per  hour  per  thousand  persons,  and  concludes  that  this  is  too 
expensive  for  any  general  use.  With  mechanical  refrigeration,  however,  if 
we  assume  10  hours*  cooling  per  person  per  pound  of  coal  as  a  fair  practical 
service  in  regular  work,  we  have  an  expense  of  only  IScts.  per  thousand 
persons  per  hour,  coal  being  estimated  at  |8  per  short  ton.  This  is  for  fuel 
aloDe,  and  the  various  items  of  oil.  attendance,  Interest,  and  depreciation  on 
the  plant,  etc.,  must  be  considered  in  making  up  the  actual  total  cost  of 
mecnanical  refrigeration. 

Mlae-wentllatloii— Friction  of  Air  In  Underf^onnd  Paa- 
Milpes*— In  ventilating  a  mine  or  other  underground  passage  the  resistance 
to  be  overcome  fa.  according  to  most  writers  on  the  subject,  proportional  to 
the  extent  of  the  frictlonal  surface  exposed ;  that  is,  to  the  product  lo  of  the 
length  Of  the  gangwav  by  its  perimeter,  to  the  density  of  the  air  In  circula- 
tion, to  the  sqiiare  of  its  average  speed,  v,  and  lastly  to  a  coefficient  k^  whose 
numerical  value  varies  according  to  the  nature  of  the  sides  of  the  gangway 
and  the  irregularities  of  its  course. 

The  formula  for  the  loss  of  head,  neglecting  the  variation  in  density  as 

unimportant,  is  p  » ,  in  which  p  a  loss  of  pressure  in  pounds  per  square 

foot,  8  =B  square  feet  of  rubbing-surface  exposed  to  the  air,  v  the  velocity  of 
tlie  air  In  feet  per  minutCLa  the  area  of  the  passage  in  square  feet,  and  k  the 
coefficient  of  friction.  W.  Fairley,  in  Colliery  Engineer,  Oct.  and  Nov. 
1898,  gives  the  following  formulae  for  all  the  quantities  involved,  using  the 
same  notation  as  tlie  above,  with  these  additions :  h  =  horse-power  of  ven- 
tilation; I  =  length  of  air-channel ;  o  =  perimeter  of  air-channel;  q  =  quan- 
tity of  air  circulating  in  cubic  feet  per  minute;  u  a  units  of  work,  in  foot- 
pctu%da,  applied  to  circulate  the  air:  to  ss  water-gauge  in  iucbes.    Then, 

1     '  _ tot>«_ ksv^q  _  ksv*      2*_  g 
~   p  tt     ""  pv  ==  pv"  v 


.         u  qp    _ Sg^tc 

88,000  "  83,000  *^  88,000 ' 


5.*-^  = 


5.2w 


tfifl     9v*      ev*-*-a      «*  -H  a 


'^       a        q  \y  ksj    a       q        av 


532 


HEATIKG  AND  VBNTlLATIOK. 


T.pas  jktv*: 


V 


po«  =  fc»3«. 


pa u 


lev* 


kv» 


=  lo. 


10.  tt: 

11.  VB 

12.  ««s 


gps 


pa 
pa  ^ 


=  5.Sgu7  :=  83,OO0Dk. 


a    y  jk»     y  &»     y  *r 


ks 


'  k8 


vpa 
to' 


To  find  the  quantity  of  air  with  a  given  horse-power  and  efflclencT'  (e)  of 
engine: 

^      h  X  88.000  X  e 
«  = ^ • 


to 


The  value  of  ft,  the  coeflQcient  of  friction,  as  stated,  varies  aooordin] 
the  nature  of  the  sides  of  the  gangway.  Widely  divergent  values  have  I 
given  by  different  authorities  (see  Colliery  Engineer^  Nov.  1808),  the  most 
generally  accepted  one  until  recently  being  probably  that  of  J.  J.  Atkinflon, 
.0000000:217,  which  is  the  pressure  per  square  foot  in  decimals  of  a  pound  for 
each  RQuare  foot  of  rubbing-surface  and  a  velocity  of  one  foot  per  minute. 
Mr.  Fairley,  in  his  **  Theory  and  Practice  of  Ventilating  0>al-minea,**  gives  a 
value  less  than  half  of  Atkinson's,  or  .00000001 ;  and  recent  experiments  by  D. 
Murgue  show  tliat  even  this  value  is  high  under  most  conditions.  Murgue's 
results  are  given  in  his  paper  on  Ezperiinental  Investigations  in  the  Loes  of 
Head  of  Air  currents  in  underground  Workings,  Trans.  A.  I.  M.  £.,  1803. 
vol.  zzUi.  68.  His  coefflclents  are  given  in  the  following  table,  as  determined 
in  twelve  experiments: 

Coefficient  of  Loes  of 
Head  by  Friction, 


Rock, 
gangways. 


French. 

Straight,  normal  section OOOfti 

Straight,  normal  section 00094 

Straight,  large  section 00104 

Straight,  normal  section 001^ 

'Straight,  normal  section 00080 

Straight,  normal  section .00086 

Contmuous  curve,  normal  section 00069 

Sinuous,  intermediate  section 00051 

t  Sinuous,  small  section 00055 

i  Straight,  normal  section 00168 
Straight,  normal  section 00144 
Slightly  sinuous,  small  section 00:288 


British. 
.000,000.00488 
.000,000,00197 
.000,000,00549 
.000,000,00615 

.000,000,00168 
.000,000.00190 
.000.000.00838 
.000,000,00969 
.000,000,00891 
.000.000,00688 
.000,000,00761 
.000,000,01257 


Brick-lined 

arched 
gangways. 

Timbered 
gangways. 

The  French  coefBcients  which  are  given  by  Murgue  represent  the  height 
of  water-gauge  in  milliinetreR  for  each  square  metre  of  ruobing-surface  and 
a  velocity  of  one  metre  per  second.  To  convert  them  to  the  British  measure 
of  pounds  per  square  root  rt>r  each  square  foot  of  rubbing-surface  and  a 
velocity  of  one  foot  per  minute  they  have  been  multiplied  by  the  factor  of 
conversion.  .000005^83.  For  a  velocity  of  1000  feet  per  minute,  since  the  loes 
of  head  varies  as  v*,  move  the  decimal  point  in  the  coefficients  six  places  to 
the  right 


FA2JS  AND  HEATED  CHIMNEYS  FOB  VENTILATION.  533 

EqvlTalent  Orlflce.— The  head  absorbed  by  the  workingr-chambers 
of  a  mine  cannot  be  computed  a  priori,  because  the  openings,  cross-pas- 
sac^es,  irrtfgular-shaped  gob-piles,  and  daily  changes  In  the  size  and  shape  of 
the  chambers  present  much  too  complicated  a  network  for  accurate 
aiialysia.    In  order  to  oyercome  this  difficulty  Murgue  proposed  in  ]87i  the 
method  of  equivalent  orifice.    This  method  consists  in  substituting  for  the 
mine  to  be  considered  the  eauivalent  thin-lipped  oriflce,  requiring  the  same 
height  of  head  for  the  discnarge  of  an  equal  volume  of  air.    The  area  of 
this  orifice  is  obtained  when  the  head  and  the  discharge  are  known,  by 
means  of  the  following  formulie,  as  given  by  Fairley: 
Lei  9  =  quantity  of  air  in  thousands  of  cubic  feet  per  minute; 
to  =  iDches  of  water-gauge; 
A  =  area  in  square  feet  of  equivaient  orifice. 
Then 

Vw         2.7Vw         ^  0.87     .    «^-"l»*»X  V^^y  . 

Motive  Colamn  or  tbe  Head  of  Atr  Dne  to  lUirereiices 
of  Tempeimtiire.  et€«    (Fairley.) 
LetJtf  =  motive  column  in  feet; 

T  =  temperature  of  upcast; 

/  s  weight  of  one  cubic  foot  of  the  flowing  air; 

t  =  temperature  of  downcast; 

D  s  depth  of  downcasts 

Then 

To  find  diameter  of  a  round  airway  to  pass  the  same  amount  of  air  as  a 
■qnare  airway  the  length  and  power  remainihg  the  same: 
Let  D  s  diameter  of  round  airway,  A  ~  ares  of  square  airway;  0=  peri- 

meter  of  square  airway.    TheiiD*=4/  ~ 

If  two  fans  are  employed  to  ventilate  a  mine,  each  of  which  when  worked 
separately  produces  a  certain  Quantity,  which  may  h&  indicated  by  A  and  B 
then  the  quantity  of  air  that  will  pass  when  the  two  fans  are  worked  together 

will  be  j^A^  +  B*.    (For  mine- ventilating  fans,  see  page  621.) 

Helattve  Eflieleiicy  of  Fans  and  Heated  Chimneys  for 
Ventilation.— W.  P.  Trowbridge,  Trans.  A.  8.  M.  E.  vli.  531,  gives  a  theo- 
retical solution  of  the  relative  amounts  of  heat  expended  to  remove  a  given 
volume  of  impure  air  by  a  fan  and  by  a  chimney.  Assuming  the  total  effl- 
cieDcy  of  a  fan  to  be  only  l/:25,  which  is  made  up  of  an  efUclency  of  \/\^  for 
the  engine.  5/10  for  tlie  fan  Itself,  and  8/10  for  efficiency  as  regards  friction, 
the  fan  reauires  an  expenditure  of  heat  to  drive  it  of  only  1/38  of  the  anioimt 
that  would  be  required  to  produce  the  same  ventiliitlon  by  a  chimney  100  ft. 
high.    For  a  chimney  500  ft.  high  the  fan  will  be  7.6  times  more  efficient 

In  all  cases  of  moderate  ventilation  of  rooms  or  buildings  where  ihe  air 
Ls  heated  b«*fore  it  enters  the  rooms,  and  spontaneous  ventilation  is  pro- 
duced by  the  passage  of  this  heated  air  upwards  through  vertical  flues, 
DO  special  heat  is  reqiiired  for  ventilation;  and  if  such  ventilation  be  suffl- 
cient.  the  process  Is  raultlesR  as  far  as  cost  is  concerned.  This  is  a  condition 
of  things  which  may  be  realized  In  most  dwelling  houses,  and  in  many  halls, 
schoolrooms,  and  public  buildings,  provided  inlet  and  outlet  flues  of  ample 
cross-section  be  provided,  and  the  heated  air  be  properly  distributed. 

If  a  more  active  ventilation  be  demanded,  but  such  as  requires  the  small- 
est amount  of  power,  the  cost  of  this  power  may  outweigh  the  advantages 
of  the  fan.  There  are  many  cases  in  which  steam-pipes  in  the  base  of  a 
chimney,  requiring  no  care  or  attention,  may  be  preferable  to  mechanical 
ventilation,  on  the  ground  of  cost,  and  trouble  of  attendance,  repairs,  etc. 

•  Hurgue  gives  A  =  -^-r^,  and  Norrls  A  =  -^ — -.    See  page  581,  ante. 


534  aXATIKG  AKD  VBNTILATIOK. 

The  followliiiir  flsures  are  i^Ten  by  Atkinson  (Coll.  JRijTr.,  1M),  tihoming 
the  miDimum  depth  at  which  a  furnace  would  be  equal  to  a  TentilaUniir- 
machine.  atwumiiiR  that  the  sources  of  loss  are  the  same  in  each  case,  Le., 
that  the  loss  of  fuel  in  a  furnace  from  the  ooolinic  in  the  upcast  is  equlTalent 
to  t])e  power  expended  in  overcoming  the  friction  in  the  machine,  and  also 
assuming  that  the  ventilatintp>maohine  utiliases  90%  of  the  engin^power.  The 
coal  consumption  of  the  engine  per  I.H.P.  is  taken  at  8  lbs.  per  hour: 

Average  tempeiuture  in  upcast 100*  P.         150*  F.        900*  P. 

Minimum  depth  for  equal  economy...  MO  yards.  lOfOyards.  USD  yards. 

Heatlni:  and  TenOlattng  of  I«arve  BvUdlnss.    (A.  It 

'Wolff,  Jour.  Frank.  Inst.,  1898.)— The  transmission  of  heat  from  the  interior 
to  the  exterior  of  a  room  or  building,  through  the  walla*  celUnga.  windows, 
etc.,  is  calculated  as  follows : 
S  =  amount  of  transmitting  surface  in  square  feet; 
t  =  temperature  F.  inside,  to  at  temperature  outside; 
IC  s=  a  coefflcient  representing,  for  various  materials  composing  buildings, 
the  loss  by  transmission  per  souare  foot  of  surface  in  British  ther- 
mal units  per  hour,  for  each  aegree  oC  difference  of  temperatore 
on  the  two  sides  of  the  material : 
Q  =  total  beat  transmission  ssSKit-  U). 

This  quantity  of  heat  is  also  the  amount  that  must  be  conveyed  to  the 
room  in  order  to  make  good  the  loss  by  transmission,  but  it  does  not  cover 
the  additional  heat  to  be  conveyed  on  aooount  of  the  change  of  air  for  pur- 
poses of  ventilation.  The  coefficients  iT  given  below  are  those  prescribed  by 
law  by  the  German  Government  in  the  aesign  of  the  heating  plants  of  its 

Eublic  buildings,  and  generally  used  in  Germany  for  all  buildings.    They 
ave  been  converted  into  American  units  by  Mr.  Wolff,  and  ha  finds  thai 
they  agree  well  with  good  American  practice: 

YAtus  Qf  K  FOR  BUoH  Bquabc  Foot  op  Brick  Wau«. 

""iSck^wau'f        *"     ^'    ^^"    ^^"    **"    ^"     ^"      *"     ^'      ^' 
K  a  0.68    0.40    0  83    0.20    0.88    O.SO   0.174     0.15     0.129     0.115 

1  sq.  ft.,  wooden-beam  construction, ) as  flooring,  K  =  0.08S 

planked  over  or  ceiled,  ) as  ceiling,   fs  0.104 

J   M.   ft.,   fireproof    construction ,  J as  flooring,  K=(km 

floored  over,  \ as  celling,  K  ^  0.14ft 

Isq.  ft.,  single  window K^  1.0tt) 

1  sq.  rt.,  single  skylight iCs  1.118 

1  sq.  ft,  double  window iTcs  0.518 

Isq.  ft,  double  sky  light K^QAn 

Isq.  ft.,  door J^bO.414 

These  eoefflcients  are  to  be  increased  respectively  ss  follows:  IdjC  when  the 
exposure  is  a  northerly  one,  and  winds  are  to  be  counted  on  as  Important 
factors;  10%  when  the  building  is  heated  during  the  daytime  onlv,  and  the 
location  of  the  building  is  not  an  exposed  one;  f!0%  when  the  building  is 
heated  during  the  daytime  only,  and  the  location  of  the  building  is  eacposed; 
6(ht  when  the  building  is  heated  during  the  winter  months  intermittently, 
with  long  intervals  (say  days  or  weeks)  of  non-heating. 

The  value  of  the  radiating*surface  is  about  as  follows:  Ordinary  bronzed 
cast-iron  radlating-surfaces,  in  American  radiators  (of  Bundy  or  similar 
type),  located  in  rooms,  give  out  about  860  heat-units  per  hour  for  each 
square  foot  of  surface,  with  ordinary  steam-pressure,  say  8  to  ft  lbs.  per  t»q. 
\n.,  and  about  0.6  this  amount  with  ordinary  hot-water  heating. 

Non-painted  radiating-surfaces,  of  the  ordinary  **  Indirect- **  type<Cllmnz 
or  pin  surfaces),  give  out  about  400  heat-units  per  hour  for  each  square  foot 
of  heatlng-eurface,  with  ordinary  stfsm -pressure,  say  8  to  6  lbs.  per  sq.  in.; 
and  about  0.6  this  amount  with  ordinarv  hot-water  heating. 

A  person  gives  out  about  400  heat-units  per  hour:  an  ordinary  gas-burner, 
about  4800  heat-units  per  hour;  an  incandescent  electric  (16  candle-power) 
light,  about  1600  heat-units  per  hour. 

The  following  example  is  given  by  Mr.  Wolff  to  show  the  application  of 
the  formula  and  coefficients: 

Lecture-room  40  x  60  ft.,  80  ft.  high,  48,000  cubic  feet,  to  be  heated  to 
69*  F.;  exposures  as  follows:  North  wall,  60  x  80  ft.,  with  four  windows. 
each  14  X  4  feet,  outside  twaperature  0*  F.    Room  beyond  west  wall  and 


HEATIKG  AND  YENTIIiATIirG  OF  LAROB  BUILDINGS.  636 


room  OfwhMd  hmlUd  to  CO*,  ezoept  a  double  akyliirht  in  oeUioff.  14  x  M  ft., 
exposed  to  the  outakle  temperaturo  of  0".    Store-room  beyona  east  wall  at 
ae^.    Door  6  X  12  ft.  in  wall.    (>>rridor  beyond  south  wall  heated  to  60*. 
Two  dooni,  6  X  12,  in  wall.    Cellar  below,  temperature  88*. 
The  following  table  ohows  the  oalculation  of  heat  transmiasfon: 


II 


flO* 

33 
88 

10 
10 
10 
10 
09 
•0 
18 


Kind  of  Tranemitting 
Sorfaoe. 


Outeidewall 

Four  windows  (sfnKle). . . 
Inside  wall  (store-room). . 

Door 

Inside  wall  (corridor).... 

Door 

Inside  wall  (corridor) .... 

Door 

Roof 

Double  skylight 

Floor. 


Calculation 

of  Area  of 

Transmitting 

Surface. 


08X3S-448 
4X   8X    14 

42X22-  Tt 
6X12 

45X22-   72 

17x22-  « 
6X12 
88  X  42  -  888 
14X24 
82X48 


988 

448 
852 

72 
018 

72 
802 

72 

1,008 

336 

8,004 


8«442 

82,256 

8,408 

1,868 

1,886 

360 

802 

860 

10.080 

14,448 

10,416 


Supplementary  allowance,  north  outside  wall,  ^0f 

•*  •*  north  outside  windows,  K^ . 


Exposed  location  and  intermittent  day  or  night  use,  20%.,. 
Total  thermal  units 


88,276 

844 

8.226 


87.346 
26.204 


11S.&'M) 


If  we  assume  that  the  lecture-room  must  be  heated  to  69  degrees  Fahr.  In 
cbe  daytime  when  unoccupied,  so  as  to  be  at  this  temperature  when  first 
persons  arrive,  there  will  be  required,  ventilation  not  being  considered,  and 
{•roused  direct  low-pressnre  steam- radiators  beinfr  the  beating  media,  about 
;  13,550  -t-  260  s  455  sq.  ft.  of  radiating-surface.  (This  gives  a  ratio  of  about 
V05  cu.  ft.  of  contents  of  room  for  each  sq.  ft.  of  heating-surfaoe.) 

If  we  assume  that  there  are  160  persons  in  the  lecture-room,  and  we  pro- 
vide SSOO  cubio  feet  of  fresh  air  per  person  per  hour,  we  will  supply  160  X 

jCOO  s  400,000  cubic  feet  of  air  per  hour  (i.e.,  ^'     «  over  eight  changes  of 

•x>ntents  of  room  per  hour). 

To  heat  this  air  from  0*  Fahr.  to  69«  Fahr.  will  require  400,000  X  0.0189  X 
69  =  9(21,640  thermal  unit^  per  hour  (0.0189  being  the  product  of  a  weight  of 
h  cubic  foot  by  the  specific  heat  of  air).  Accordingly  there  must  be  provided 
.*t21,64O-»-4O0  s=  1304  sq.  ft.  of  indirect  surface,  to  heat  the  air  required  for 
ventilation,  in  sero  weather.  If  the  room  were  to  be  warmed  entirely  indi- 
ivclly,  that  is,  by  the  air  supplied  to  room  (including  the  heat  to  be'conveyed 
to  cover  loss  by  transmission  through  walls,  etc.),  there  would  have  to  be 
convejed  to  the  fresh-air  supply  521,640  +  1 13,550  =x  635.190  beat-units.  This 
would  Imply  the  provision  of  an  amount  of  indirect  beating-surface  of  the 
'*  dimax^*  tvpe  of  685,190 -»- 400  s  1589  sq.  ft.,  and  the  fresh  air  entering  the 
room  would  haTO  to  be  at  a  temperature  of  about  84'  Fahr.,  viz.,  69*  s= 

_^^.or<»  +  .6=«.F.hr. 

The  above  calculations  do  not,  however,  take  into  account  that  160  per. 
sons  in  the  leeture-room  give  out  160  x  400  s  64,000  thermal  units  per  hour; 
and  that,  say,  50  electric  lighU  give  out  50  X  1600  s  80,000  thermal  unitsTer 
hour;  or,  say,  50  gaslights,  50  x  4800  ss  240,000  thermal  units  per  hour.  The 
presence  of  160  people  and  the  gas-lighting  would  diminish  considerably  the 
amount  of  beat  required.  Practically,  it  appears  that  the  heat  generated 
bv  the  presence  of  180  people,  64,0(»  beat-units,  and  by  50  electric  lights, 
80,000  heat-units,  a  total  of  144,000  heat-units,  more  than  covers  the  amount 
of  heat  transmitted  through  walls,  etc.  Moreover,  that  if  the  50  gaslights 
give  out  240,000  thermal  units  per  hour,  the  air  supplied  for  ventilation  must 
enter  considerably  below  69*  Fahr.,  or  the  room  will  be  heated  to  an 
unbearably  hi^b  temperature.    If  400,000  cubic  feet  of  fresh  air  per  hour 


536 


HEATIKG  AND  VEKTILATIOK. 


are  supplied,  and  240,000  thermal  units  per  hour  generated  by  the  gas  i 

be  abstracted,  it  means  that  the  air  must,  under  these  conditions,  enter 
210  nno 

400  WO  X  0189  ~  *^°"'  ^"^  ****  '^*"  ^*''  ^^  *'  ***®"^  ^^  ^'^^^'  ^"■■*'*^'^' 
more,  the  additional  vitiation  due  to  gaslighting  would  necessitate  a  much 
larger  supply  of  fresh  air  than  when  the  vitiation  of  the  atmosphere  by  the 
people  alone  is  considered,  one  gaslight  vitiating  the  air  as  much  as  five 
men. 

Various  Rules  for  Compntlns  Badlatlns-snrfkee.—The 
following?  rules  are  complied  from  various  sources.  They  are  more  in  the 
nature  of  "rule-of -thumb"  rules  than  those  given  by  Mr.  Wolir,  quoted 
above,  but  they  may  be  useful  for  comparison. 

Divide  the  cubic  feet  of  space  of  the  room  to  be  heated,  the  square  feet 
of  wall  surface,  and  the  squai-e  feet  of  the  glass  surface  by  the  figures 
given  under  these  headings  in  the  following  table,  and  add  the  quotients 
together;  the  result  will  be  the  square  feet  of  radiating-surface  required. 
(F.  Schumaim.) 

SpjLos,  Wau.  jLND  Glass  Surface  which  Onb  SquABs  Foot  or  Radutino- 

BURFACB  WIIiL  HkAT. 


n  09 

|| 

if 

1 
8 
5 

¥ 

GO 

190 
210 
225 

Exposure  of  Booms. 

^ 

All  Sides. 

Northwest. 

Southeast 

1- 

< 

Wall 

Surface, 

sq.  ft. 

Glass 

Surface, 

sq.  ft. 

Wall 

Surface, 
sq.ft 

Glass 

Surface, 

sq.ft. 

Wall 

Surface, 

sq.ft. 

Glass 

Surface. 

sq.  ft. 

Once 
per 
hour. 

18.8 
15.0 
16.5 

7 

7.7 

8.5 

16.87 
17.25 
18.97 

8.05 
9.77 

16.66 
18.00 
19.80 

8.4 
9.24 

w.ao 

Twice 
per 
hour. 

1 
3 
ft 

75 
82 
90 

11.1 
12.1 
18.0 

6.7 
6.2 
6.7 

12.76 
18.91 
14.52 

6.55 
7.18 
7.60 

18.22 
14.52 
15.60 

6.84 
7.44 
8.01 

Em ISSIOK  OF  HSAT-UNITS  PER  SQUARK  FOOT  PKR  HOUR  FROM  CAST-IROM  PlPBS 

OR  Radiators.    Temp,  of  Air  in  Room,  70<^  F.    (F.  Schumann.) 


Mean  Temperature  of 
Heated  Pipe.  Radia- 
tor, etc. 

By  Contact. 

By  Radi- 
ation. 

By  Radiation 
and  Ck>ntacl. 

Air  quiet. 

Air 
moving. 

Air  quiet. 

Air 
moving. 

Hot  water 

.140» 
.ISO* 
.1600 

..170» 
.180' 
.1900 
.2000 

..210° 
.220« 
.230* 
.240' 
.250« 
.280" 
.2700 
.280" 
.2900 

.sooo 

56.51 

65.45 

75.68 

86.18 

96.93 

107.90 

119.13 

130.49 

142.20 

158.95 

165.90 

178.00 

189.90 

202.70 

216.30 

228.66 

240.85 

92.52 
109.18 
126.18 
143  30 
161.55 
179.83 
198.56 
217.48 
2:^7.00 
250.58 
279.  a3 
296.63 
316.50 
837.88 
358.85 
880.91 
401.41 

69.68 
69.69 
80.19 
91.12 
102.16 
114.45 
127.00 
139.96 
155  27 
169.56 
184.58 
200.18 
214.36 
233.42 
251.21 
267.73 
279.12 

115.14 
185.14 
155  87 
177.80 
199.48 
222.35 
246.13 
270.49 
297.47 
S;!3.51 
850.48 
878.18 
404.26 
486.12 
466.61 
496.38 
819.97 

152  15 

"       ** 

u        «t      •••••••• 

178  87 
906.S2 
234.42 

**       ** 

t«       «« 

"     **    .'!*!!.!! 

*•       "or  steam 
Steam 

264.05 
294  28 
3i5.55 
av7.48 
892.27 
426  14 

.•■ 

464  41 

It 

496  81 

«       

680.88 

«* 

571  25 

•• 

610  on 

«• 

648  64 

M 

680  S8 

IKDIRECT  HEATING-SURFACE.  637 

RADIATl^O-BtTRfACB  RKQUIRXD  FOR  DlFFBRBNT  KiNDS  OP  BriLDIKOS. 

The  Nason  Mfg.  Co.'s  catalogue  gives  the  following:  One  square  foot  of 
surface  will  heat  from  40  to  lOO  cu  ft,  of  space  to  75«  In  -  10«  latitudes. 
This  range  is  intended  to  meet  conditions  of  exposed  or  comer  rooms  of 
buildings,  and  those  less  so,  as  intermediate  ones  of  a  block.  A.s  a  general 
rule,  1  sq.  ft.  of  surface  will  heat  70  cu.  ft.  of  air  In  outer  or  front  rooms  and 
100  cii.  ft  in  inner  rooms.  In  large  stores  in  citiCH,  with  buildings  on  each 
«de,  1  to  100  is  ample.  The  following  are  approximate  proportions: 
One  oquare  foot  ndiating-surface  wUl  heat: 

Indwellings,       In  hall,  stores.     In  churches,  large 
■choolroomfl,       lofts,  factortos,         auditoriums, 
offlees,  etc.  etc.  etc. 

Bj^dlreetnidtaftlaii...       60to80ft.  TStolOOft  ]B0to800ft. 

By  Indirect  FBdlttUon.       40to50**  60  to  70 '*  100  to  140  *' 

Isolated  buOdlngs  exposed  to  preTalling  north  or  west  winds  should  have 
a  generous  addition  made  to  the  heating-surface  on  their  exposed  sides. 

The  following  rule  is  given  in  the  catalogue  of  the  Babcock  &  Wilcox  Co., 
and  is  also  recommended  by  the  Nason  Mfg.  Co.: 

R&diating  serf  ace  raav  be  calculated  by  the  rule:  Add  together  the  square 
feet  of  glass  in  the  windows,  the  number  of  cubic  feet  of  air  required  to  be 
changed  per  minute,  and  one  twentieth  the  surface  of  external  wall  and 
roof;  muRlpI/  this  sum  bv  the  difference  between  the  required  temperature 
of  the  room  and  that  of  the  external  air  at  its  lowest  point,  and  divide  the 
product  bj  the  difference  in  temperature  between  the  steam  in  the  pipes 
■Dd  the  required  temperature  of  the  room.  The  quotient  Is  the  required 
radiating-surfaoe  in  square  feet. 

Prof.  R.  C.  Carpenter  (Heating  and  Ventilation^  Feb.  15,  1807),  gives  the 
following  handy  formula  for  the  amount  of  heat  required  for  heating  build- 
ings by  direct  radiation: 

h^^C+O  +  HW, 

in  which  Ws:  wall-surface,  G  =  glass-  or  window-surface,  both  In  sq.  ft., 
C  =  contents  of  building  in  cu.  ft.,  n  =  number  of  times  the  air  nmst  be 
dian(;ed  per  hour,  and  h  =  total  heat  units  required  per  degree  of  difference 
of  temperature  between  the  room  and  the  surroundnig  space.  To  heat  the 
building  lo  70*  F.  when  the  outside  temperature  is  0**,  lO  times  the  above 
qiianlity  of  heat  will  be  required.  Under  ordinary  conditions  of  pressure 
aud  temperature  1  sq.  ft.  of  steam-heating  surface  will  supply  *JaO  heat  units 
per  hour,  and  1  sq.  ft.  of  hot- water  heating  surface  175  heat  units  per  hour. 
The  square  feet  of  radiating-surface  required  under  these  conditions  will 
heR=  0.25/1  for  steam-heating,  and  R  —  O.l/i  for  hot-water  heating.  Prof. 
Carpenter  says  that  for  residences  it  is  safe  to  assume  that  the  air  of  the 
principal  living-rooms  will  chanf^e  twice  in  an  hour,  that  of  the  halls  thre*) 
timen  and  that  of  the  other  rooms  once  per  hour,  under  ordinary  condi- 
tions. 

Orerliead  Steam-pipes.  (A.  R.  Wolff,  SitvenM  Indicator,  1887.)— 
When  the  overhead  system  of  steam-heating  is  employed,  in  which  system 
direct  radiatiog-pipes.  usually  1)4  in.  in  dlam.,  are  placed  in  rows  overhead, 
suspended  upon  horizontal  racks,  the  pipes  running  horizontally,  and  side 
by  Fide,  around  the  whole  interior  of  the  building,  from  2  to  3  ft.  from  the 
walls,  and  from  8  to  4  ft.  from  the  celling,  the  amount  of  1^  in.  pipe  re- 
quired, accordhig  to  Mr.  C.  J.  H.  Woodbury,  for  heating  mills  (for  which 
use  this  system  is  deservedly  much  in  vogue),  is  about  1  ft.  in  length  for 
every  00  cu.  ft.  of  space.  Of  course  a  great  range  of  difference  exists,  due 
to  tlie  special  character  of  the  operating  machinery  in  the  mill,  both  in  re- 
spect to  the  amount  of  air  circulated  by  the  machinery,  and  also  the  aid  to 
warming  the  room  bv  the  friction  of  the  journals. 

Indirect  Heatlac-enrfaee.— J.  h.  Kinealy.  In  Heating  and  Ven- 
tilation^ May  15, 1894,  gives  the  following  formula,  deduced  from  results  of 
experiments  by  C.  B.  Richards,  W.  J.  Baldwin,  J.  A.  Mills,  and  others,  upon 
indirect  heaters  of  various  kinds,  supplied  with  varying  amounts  of  air  per 
Ikour  per  square  foot  of  surface: 

^-  r^^ — '  »••  -  <'•.  -  »•>>  («•«• + ^)+ '»• 


638  HBATtNG  AKD   V EKTlLATlOlsr. 

N  s  cubic  feet  of  atr,  reduced  to  70*  F.,  supplied  to  the  heater  per  sqaare 
foot  of  heating-surface  per  hour;  To  =  temperature  of  the  steam  or  water 
In  the  heater:  ITj  s  temperature  of  the  air  wlien  it  euters  the  heater; 
Tt  =  temperature  of  the  air  when  it  leaves  the  heater. 

As  the  formula  is  based  upon  an  averafi^  of  experiments  ma^le  upon  alt 
sorts  of  indirect  heaters,  the  results  obtained  by  the  use  of  the  equation 
may  In  some  cases  be  slightlv  too  small  and  in  others  slightly  too  large, 
although  the  error  will  in  no  case  be  great.  No  single  formula  ought  to  b€ 
expected  to  apply  equally  well  to  all  dispositions  of  heating-surface  in  in- 
direct heaters,  as  the  efiRciency  of  such  heater  can  be  Tari^  between  anch 
wide  limits  by  the  construction  and  arrangement  of  the  surface. 

In  indirect  heating,  the  efilcieucy  of  the  radiadng-surface  will  Increase, 
and  the  temperature  of  the  air  will  diminish,  when  the  quantity  of  the  air 
caused  to  pass  through  the  coil  increases.  Thus  1  sq.  ft.  radJatlng-earface, 
with  steam  at  S12«,  has  been  found  to  heat  100  ca.  ft.  of  air  per  hour  from 
sero  to  1&0<*,  or  300  cu.  ft.  from  sero  to  100*  in  the  same  time.  The  best  re- 
sults are  attained  by  using  Indirect  radiation  to  supply  the  necessary  rentl 
latlon,  and  direct  radiation  for  the  balance  of  the  heat.    iSleam.) 

In  indirecc  steam-heating  the  least  flue  area  should  be  1  to  l^^  sq.  In, 
to  every  square  foot  of  heating-surface,  provided  there  are  no  long  nonaon- 
tal  reaches  lu  the  duct,  with  little  rise.  The  register  should  liave  twice  the 
area  of  the  duct  to  allow  for  the  fretwork.  For  hot  water  heating  from  S9)K 
to  90%  more  heatiug-surface  and  flue  area  should  be  given  than  for  low- 
pressure  RtHam.    (Bngineering  Record,  May  'M,  1894.) 

Boiler  HeatliigHiiirfkee  RequlreA.  (A.  R.  Wolff,  Stevens  Indt- 
eotor,  18t)7.)— When  the  direct  system  b  used  to  heat  buildings  In  which  the 
•treat  floor  Is  a  store*  and  the  upper  floors  are  devoted  to  sales  and  stock- 
rooms and  to  light  manufacturing,  and  In  which  the  fronts  are  of  stone  or 
Iron,  and  the  sides  and  the  rear  of  building  of  brick->a  safe  rule  to  follow  is  to 
supply  1  sq.  ft.  of  boiler  heating-surface  for  eaoh  700 cu.  ft.,  and  1  sq.  ft.  of 
radiating-surface  for  each  100  cu.  ft.  of  oontents  of  building. 

For  heating  mills,  shops,  and  factories,  1  sq.  ft.  of  boiler  heating-surface 
should  be  supplied  for  each  475  cu.  IX.  of  contents  of  buildiug;  and  the  same 
allowance  should  aLso  be  made  for  heating  exposed  wooden  dwellings.  For 
heating  fouodries  and  wooden  Khops.  1  sq.  ft.  ox  boiler  heating-surface 
Simula  be  provided  for  each  400  cu.  ft.  of  contents;  and  for  structures  la 
which  glass  enters  very  largely  In  the  construction— such  as  conservatories, 
exhibition  buildings,  and  the  llke-1  sq.  ft.  of  boiler  heating-surface  should 
be  provided  for  each  ?75  cu.  ft  of  contents  of  building. 

When  the  indirect  system  is  employed,  the  radiator-surface  and  the  boQer 
capacity  to  be  provided  will  each  have  to  be,  on  an  average,  about  ^  more 
than  where  direct  radiation  is  U8ed.  This  percentage  also  marks  approxi- 
mately the  Increased  fuel  consumption  in  the  indirect  system. 

Steam  (Babcock  &  Wilcox  Co.)  has  the  following:  1  itq.  ft.  of  boiler-surface 
will  supply  from  7  to  10  sq.  ft.  of  radiating-surface,  depending  upon  the  sisa 
of  boHer  and  the  efficiency  of  its  surface,  as  well  as  that  of  the  mdlating- 
surface.  Small  boilers  for  house  use  should  be  much  larger  uroportlonately 
than  large  plants.  Each  horse-power  of  boiler  will  supply  from  S40  to  SA 
ft.  of  1-in.  steam-pipe,  or  80  to  ISO  sq.  ft.  of  radiating  surface.  Cubic  feet 
of  space  has  little  to  do  with  amount  of  steam  or  surface  required,  but  is  a 
convenient  factor  for  rough  calculations.  Under  ordinary  conditions  I 
horse-power  will  heat,  approximately,  in— 

Brick  dwellings,  in  blocks,  as  In  cities 15,000  to  1M),000  cu.  ft. 

♦'      stores        ••       '* 10,000   "  16.000     '• 

"      dwellings,  exposed  all  round 10,000   *'  15,000     *« 

"      mills,  shops,  factories,  etc 7,000   ••  10,000     " 

Wooden  dwellings,  exposed 7,000   "  10,000      '• 

Foundries  and  wooden  shops 6,000   '*  10,000     ** 

Exhibition  buildings,  largely  glass,  etc 4.000  *'  15,000     «« 

SCeam-conflamption  In  Car^beatlnc* 

C,  M.  A  St.  Paul  Railway  Ts.sts.    {Engineering,  June  27, 1800,  p.  764.) 

Water  of  Condensation 

Outside  Tem perature.        Inside  Temperature.  per  Car  per  Hour. 

40  70  *^      70Tb^ 

80  70  85 

10  fO  SOd 


BE0I8TERS  AKD  COLD-AIB  DUOIB. 


539 


•f  MeuM  Supplyniuiliis,  wltb  Total 
lies  of  waier-eoln 


BoadtoUuieo  equal  to  8  tneliee  of 'Water-eblumii.'* 

,  Pressure  10  lbs.  per  square  inch  above  atm.,  Temperature  S80*  F. 

0.5874|/'e?; 


Formula,  d> 


where  d  =  Internal  diameter  In  inches; 


1  =  1 

eofcth 

of  mai 

nslnl 

eet;A 

=  159 

.8  feet 

head€ 

>f  stea 

m  top 

roducc 

►  flow. 

H 

Interual  Diameters  in  inches  for  Lengths  of  Mains  from  1  ft.  to  600  ft. 

1ft. 

10  ft. 

80  ft. 

40  ft. 

60  ft. 

80  ft. 

100  ft. 

200  ft 

800  ft. 

400  ft. 

600  ft. 

sq.ft. 

inch. 

Inoh. 

inch. 

inch. 

inoh. 

inch. 

inch. 

Inch. 

inch. 

inch. 

inch. 

1 

0.075 

0.110 

0.186 

0.157 

0.170 

0.180 

0.189 

0.216 

0.234 

0.846 

0.270 

10 

0.19 

0.80 

0.34 

0.89 

0.48 

0.45 

0.47 

0.54 

0.59 

0.68 

0.68 

20 

0.S5 

0.89 

0.45 

0.58 

0.66 

0.60 

0.62 

0.72 

0.78 

0.82 

0.89 

40 

0.88 

O.SS 

0.60 

0.69 

0.74 

0.79 

0.82 

0.05 

1.08 

1.09 

1.18 

60 

0.80 

0.61 

0.71 

0.61 

0.87 

0.98 

0.97 

1.11 

1.21 

1.28 

1.39 

80 

0.43 

0.68 

0.79 

0.90 

0.96 

1.04 

1.09 

1.26 

1.85 

1.43 

1.85 

100 

0.47 

0.75 

0.86 

0.90 

1.07 

1.14 

1.19 

1.36 

1.48 

1.67 

1.70 

aoo 

068 

0.99 

1.14 

1.80 

1.41 

1.60 

1.57 

1.80 

1.96 

2.07 

2.24 

900 

0.78 

1.16 

1.34 

1.68 

1.66 

1.76 

1.84 

8.12 

2.80 

8.48 

2.64 

400 

0.88 

1.80 

1.60 

1.79 

1.86 

1.98 

9.07 

8.87 

2.57 

2.78 

2.96 

500 

0.90 

1.48 

1.64 

1.88 

8.04 

2.16 

2.26 

2.60 

2.81 

2.96 

8.28 

600 

0.97 

1.58 

1.76 

8.03 

2.20 

2.88 

2.48 

2.79 

8.08 

8.21 

8.48 

800 

1.00 

1.7S 

1.98 

8.27 

246 

8.61 

2.78 

8.18 

3.40 

8.60 

8.90 

1,000 

1.19 

1.88 

2.16 

2.48 

2.60 

8.85 

2.98 

8.43 

3.71 

8.94 

4.27 

1,900 

1.88 

2.04 

2.88 

2.67 

2.90 

8.07 

3.21 

3.68 

4.00 

4.28 

4.59 

1,400 

1.86 

8.15 

2.47 

2.84 

8.06 

8.26 

8.41 

8.92 

4.25 

4.60 

4.88 

1,600 

1.43 

2.27 

2.61 

8.00 

8.25 

8.44 

8.60 

4.18 

4.49 

4.76 

5.16 

1,800 

l.SO 

8.88 

2.74 

8.14 

8.41 

8.61 

8.78 

4.84 

4.70 

4.96 

5.40 

2,000 

1.67 

2.48 

8.85 

8.28 

8.55 

8,76 

3.98 

4.52 

4.90 

5.19 

6.68 

8,000 

1.84 

8.92 

8.36 

3.85 

4.18 

4.43 

4.68 

6.82 

6.77 

6.11 

6.63 

4,000 

2  07 

8.28 

8.76 

4.82 

4.69 

4.06 

6.19 

6.96 

6.47 

6.86 

7.44 

*  Tntm  Robert  Briggs^spaper  on  American  Practice  of  Warming  Buildings 
by  Steam  (Proc.  Inst.  C.  E.,  18B8,  vol.  Ixzl). 

For  other  resistances  and  pre«uree  above  atmosphere  multiply  by  the 
respective  factors  below : 

Water  col  .    Cin.     12ln.      24  In.  (Press,  ab.  atm.  0  lbs.  8  lbs.  80  Ibo.  60  lbs. 
Multiply  by  0.8Q87   a6968     0.6064  |  Mnltiply  by       1.088  1.016   0.978    0.948 

Becl^tere  and  Oold-alr  Duets  for  tadlreet  Steam  Heattns. 
--The  Locomotive  gtvee  the  following  table  of  openhigs  for  registers  and 
cold^air  ducts,  whlda  has  been  found  to  give  satisfactoiy  results.  The  cold- 
sir  boxes  should  have  l^  sq.  in.  area  for  each  square  foot  of  radiator  suface, 
snd  never  less  than  9i  rae  sectlonni  area  of  the  hot-air  ducts.  The  hot-air 
ducts  should  have  2  sq.  in.  of  sectional  area  to  each  square  foot  of  radiator 
surface  on  the  flret  floor,  and  from  1^  to  2  inches  on  the  second  floor. 


Heating  Snrfaoe 
in  macks. 

Oold-air  Sapplr.  First  Floor. 

Sise 
Register. 

Ooldair 
8d  Floor. 

laches 

inches 

inches 

30  square  feet 

46  square  inches  «  Oby  9 

9  by  12 

4  by  10 

40      - 

60       •*        •*       m  eUylO 

10  by  14 

4  by  14 

60      " 

75       «        •*       B   8byl0 

10  by  14 

5  by  15 

60      " 

90       ••        •*      -   9  by  10 

12  by  15 

6  by  15 

70      "          " 

108       "        ••      «=   9  by  12 

12  by  19 

6byl8 

80      -         " 

120       ••        "      » 10  by  18 

12  by  22 

8byl6 

90      " 

185       «•        •*      =  U  by  12 

14  by  24 

9  by  15 

100     *• 

150       •         ••       =12  by  12 

16  by  20 

12  by  12 

The  siaes  in  the  table  approximate  to  tlie  rules  given,  and  it  will  be  found 
that  they  will  allow  an  ea«y  iknrof  air  and  a  full  dOTstributlon  throughout  the 
room  to  be  heated. 


640 


HFJITIKO  AND  VENTILATION. 


Fhyalesl   Propertle*   of  Steam   and  CoadeiiMd  'Wmtmr^ 
ander  C^ndltton*  of  Ordiaaiy  Praetlce  tn  ITamUiic  l^y 

i3rigK8.) 


(  Steam-pressure  i  above  atm. . . 
1  per  square  inehi  total 

lbs. 

0 

8         10 

80         00 

1 

lbs. 

14.7 

17.7     34.7 

44.7 

74.7 

B 

Temperature  of  steam 

Fahr. 

218« 

^SU^     289« 

274* 

oor^ 

C 

Temperature  of  air 

Fahr. 

00* 

60 

60« 

60» 

60» 

D 

Differences  B-G 

C  Heat  given  out  per  minute  per 

Fahr. 
) 

168« 

ie8» 

1T9» 

814* 

a47» 

K 

<     100  sq.  ft.  of  radlating-sur- 
I     face  =  D  X  8 

>  units 

466 

486 

587 

642 

741 

F 

Latent  heat  of  steam 

Fahr. 

965» 

968»     946» 

921* 

898* 

G 

Volume  of  1  lb.  weight  of  steam 

cu.  ft. 

86.4 

22.1  1  16.8 

9.24 

6.70 

H 

Weight  of  1  cubic  foot  of  steam 
( Volume  Q  of  steam  per  minute 

lb. 

0.0880 

0.0452  0.0618 

0.1082 

0.1758 

1 

J 

<     to  give  out  E  units 
(              sBxGh-F. 

.cu,ft. 

12.48 

11.21    9.20 

6.44 

4.70 

( Weight  of  1  cubic  foot  of  con- 

1 

K 

<     densed  water  at  tempera- 
1     tureB, 

-  lbs. 

59.64 

69.51   60.05 

58.07 

57.09 

L 

return  to  boiler  per  minute 

•cu.ft. 

0.0079 

0.0065  0.0096 

> 

0.0120 

0.0144 

Head  of  steam  equivalent  to 

H 

12  inches  water-column 
=  K-i-H. 

-  feet 

1569 

1817 

955.5 

586.7 

825.5 

Stkam-supplt  Maims. 

Head  h  of  steam,  equivalent 

N 

to  assumed  2  inches  water- 
column  for  producing  steam 
I    flow  d  =  H  -4-  6, 
j  Internal  diameter  d  of  tube* 
1     for  flow  Q  when  I  a     1  foot, 

feet 

261.5 

219.5 

150.8 

89.45 

54.25 

P 

[  inch 

0.484 

0.481 

0.474 

0.461 

0.440 

B 

Do.       do.  when  2  =  100  feet, 

inch 

1.217 

1.207 

1.190 

I.ISH 

1.188 

8 

Ratios  of  values  of  d. 

ratio 

1.028 

1.015 

1.000 

0.078 

0.948 

Watbr-Rbturn  Maiks. 

Head  h  assumed  at   khlnch 
water-column  for  producing 

) 

T 

V  foot 

0.0417 

0.0417 

0.0417  0.04^0.0417 

full-bore  water-flow  Q, 
i  Internal  diameter  d  of  tube* 
1     for  flow  Q  when  2  =     I  foot. 

) 

1            1 

U 

[  inch 

1 

0.147 

0  151 

O.irsI  0.178   0.186 

T 

Do.       do.  when  I  =  100  feet. 

inch 

0.868 

0.879 

0.8fl8.  0.484   0.468 

W 

Ratios  of  values  of  d 

ratio 

0.»26 

0.9.\2 

1.000    1.002    1.1T6 

*  P,  R,  U,  T  are  each  determined  from  the  formula  d  s  0.6874 


v^ 


ss. 


Slse  of  Steam  Pipes  for  Steam  Heatlns*  (See  also  Flow  of 
Steam  in  Pipes.)— tfAre«  of  Vf.rtical  tuaiu  pipes.  Direct  radiation,  (J.  R. 
WiUett,  Heating  and  Ventilation,  Feb.,  18»4.) 

Diameter  of  pipe,  inches.   in4     1H22U8^4        6        6 
Sq.ft.  of  radiator  surface  40     io      110    220   860   560   610    1110   8000   8000 
A  horizontal  brandt,  pipe  for  a  given  extent  of  radiator  surface  should  be 
one  size  larger  than  a  vertical  pipe  for  the  same  surface. 

The  Nason  Mfg.  Co.  gives  the  rollowing: 

Diameter  of  pipe,  ill 1^4    1H     2      2U       8       9U 

Radiator  surface  ra  ft.  (max<mum>..    1*^    200    500    1000    1500   SnOO 

When  mains  and  surfaces  are  very  much  above  the  boiler  the  pipes  netn! 
no;  be  as  large  as  given  above:  under  very  favorable  circumstances  and 


HEATINO  A  QBEEKH0U6E  BY  STEAM. 


541 


eondltions  a  4-1  nch  pipe  may  supply  from  2000  to  2500  sq.  ft.  of  surface,  a  6- 
inch  pipe  for  5000  sq.  ft.,  and  a  lO-inch  pipe  for  15,000  to  20.000  aq.  ft.,  if  the 
distance  of  run  from  boiler  is  not  too  f^reat.  Lefts  than  1^-inch  pipe  should 
Dol  be  used  horizontally  in  a  main  unless'for  a  single  radiator  connection. 

Steam^  by  the  Babcoclc  &  Wilcox  Co.,  says:  Where  the  condensed  water  , 
in  rtsturued  lo  tlie  boiler,  or  where  low  pressure  of  steam  is  used,  the  diame- 
ter of  mains  leading  from  the  boiler  to  ttie  radiating-surface  should  be 
equal  in  inches  to  one  tenth  the  square  root  of  the  radiating-surface.  mains 
included,  in  square  feet.  Thus  a  1-inch  pipe  will  supply  lOO  square  feet  of 
surface,  itself  included.  Return-pipes  should  be  at  least  9^  inch  in  diame- 
u*r,  and  never  less  than  one  half  the  diameter  of  the  main— longer  reluriis 
requiring  larger  pipe.  A  thorough  drainage  of  steam-pipes  will  elTeotually 
prevent  all  cracking  and  pounding  noises  tlierein. 

A.  R.  Wolff 'm  Practice.— 'SS.r,  Wolff  gives  the  following  figures  showing  hta 
•^•^•sent  practice  (laOT)  in  proportioning  mains  and  retuma  They  are  based 
on  an  estimated  loss  of  pressure  of  2i  for  a  length  of  100  ft.  of  pipe,  not  in- 
cluding allowance  for  bends  and  valves  (see  p.  678).  For  longer  runs  divide 
the  thermal  units  given  hi  the  table  by  0.1  ^length  in  ft.  Besides  giving  the 
themml  tmits  the  table  also  indicates  the  amount  of  direct  radiating  surface 
which  tbe  steam-pipes  can  supply,  on  the  basis  of  an  emission  of  890  thermal 
units  per  hour  for  each  square  foot  of  direct  radiating  nurface. 
Slxe  or  Pipes  for  Steam  Heatliiff. 


n 


S  itHi.  l^resaure 


3 


Ati^.  Prt'ssurr  =^ 


9 

li 
m 

"TO 
3flO 


I^ 

30 
BO 
120 

am 

fiflAl 


120 


m 


^-^2U.^ 


It. 

4 
4 


i^n?«Huro  tUbs.  Frewnrft 


-^^^0 

p^S  ^ 

lie 

m 

i^H 

pa 

OTO 

3TW3 

|b5Q 

B'iOO 

I^JXl 

StKW 

2?i00 

IWM 

2SW 

wno 

iSTTiO 

I50ifl 

»300 

rmm 

54110 

'^1600 

44r4) 

l^Hlfl 

TIMTO 

3000Q 

mm 

2K!m 

B7^ 

SftOOO 

9ief.o 

37000 

1Sft(Mi 

fi«JUO 

lasjio 

,  ft*K10 

£300f} 

flUXJO 

l»klO 

1  T(h.WL> 

aa^w 

hwom 

In. 
1 

n 

s 

4 

^ . . 

He^tlOf  a  CIrecalinaHe  1>y  meam,— Wm.  J.  Baldwin  answers  a 

qM*^'iluni  HI  [Ijt"  A'fu\ic-ui  M-nhiu,-t  as  bebh^v  ■  With  f\-^o  pounJs  steam- 
prcnMtm«\  i*«w  uujkny  bquai'v.  L>^>^1  oi  jLiw-t,^  of  Leatitit'^ur  liiCc  ia  necessary  to 
beat  100  square  feet  of  glass  on  the  roof,  ends,  and  sides  of  a  greenhouse 
in  order  to  maintain  a  night  heat  of  55*  to  66*,  while  the  thermometer  out- 
side rmnges  at  from  15*  to  20*  below  zero ;  also,  what  boiler-surface  Is  neoes* 
aary  f    which  Is  the  best  for  the  purpose  to  use— 2"  pipe  or  1^''  pipe  t 

jlns.— Reliable  authorities  agree  that  1.26  to  1.60  cubic  feet  of  air  in  an 
encioaed  space  will  be  cooled  per  minute  per  sq.  ft.  of  glass  as  many  degrees 
as  the  internal  temperature  of  the  house  exceeds  that  of  the  air  outside. 
Between  -f  65*  and  -  80*  there  will  be  a  difference  of  85*,  or,  say,  one  cubic 
foot  of  air  cooled  127.5*  F.  for  each  sq  ft.  of  glass  for  the  most  extreme 
condition  mentioned.  Multiply  this  by  the  number  of  square  feet  of 
glass  and  by  60,  and  we  have  the  number  of  cubic  feet  of  air  cooled  1*  per 
hour  within  the  building  or  house.  Divide  the  number  thus  found  by  48,  and 
it  gives  the  units  of  heat  required,  approximately.  Divide  again  bv  95a, 
and  it  will  give  the  number  of  pounds  or  steam  tfiat  must  be  oondensea  from 
a  pressure  and  temperature  of  five  pounds  above  atmosphere  to  water  at 
the  same  temperature  in  an  hour  to  maintain  the  heat.  Bach  square  foot 
of  sorfaoe  of  pipe  will  condense  from  ^i  to  nearly  H  lb.  of  steam  per  hour, 
according  as  the  coils  are  exposed  or  well  or  poorly  arranged,  for  which 
sn  average  of  ^  lb.  may  be  taken.  According  to  this,  it  will  require  8  sq.  ft. 
cf  pipe  surface  per  lb.  of  steam  to  be  condensed.  Proportion  the  heaUng* 
eurface  of  the  boiler  to  have  about  one  fifth  the  actual  radiating-surface,  if 
you  wish  to  keep  steam  over  night,  and  proportion  the  grate  to  bum  not 
more  than  six  pounds  of  coal  per  sq.  ft.  of  grate  per  hour.  With  very  slow 
combustion,  such  as  takes  place  in  base-burning  boilers,  the  grate  might  be 
proportioned  for  four  to  five  pounds  of  coal  per  hour.  It  is  cheaper  to  make 
coils  of  1^"  pipe  than  of  9f\  and  there  Is  nothing  to  be  gained  oy  using  2^ 
P4^  unless  the  coQs  are  very  long.    The  pipes  in  a  greenhouse  shoula  b% 


542  HKAXXKO  AND  YSNTII<AXIOISr, 

A. 

under  or  in  front  of  the  benches,  with  every  chance  for  a  Rood  circulation 
of  air.  **  Header"  oolls  are  better  than  '*return-bend"  CQllgfor  this  purpose. 
Mr.  Baldwin^s  rule  may  be  (piven  the  following  form  :  Let  H  =  heftt-units 
transferred  per  hour,  T;^  temperature  Inside  the  rreenhouse,  I  s=.  Wm\tvn- 
ture  outside.  5  «  sq.  ft.  of  f^lass  surface:  then  H  =  hnS(T  -  ^  X  <X)  -•-  48 
>  8  1.8^5(7  -  0.    Mr.  Wolff *8  coefficient  Jc  for  single  skylights  would  give 

Heatlnc  a  Greenliou««  by  Hot  W«t«r«— W.  M.  Mackay,  of  the 
Richardson  dt  Boynton  Co.,  In  a  lecture  before  the  Master  Plumbers  As^o- 
olatlon,  N.  Y.,  18B9,  save :  I  find  that  while  greenhouses  were  formerly 
heated  by  4-Inch  and  S-fnch  cattt-iron  pipe,  oo  account  of  ths  large  body  of 
water  which  they  contained,  and  the  supposition  that  they  gave  better  satis- 
faction and  a  more  even  temperature,  florists  of  long  experience  who 
have  tried  4*inch  and  B-inch  cast-iron  pipe,  and  also  S-toch  wrought-lron 
pipe  for  a  number  of  years  In  heating  their  greenhouses  by  hot  water, 
and  who  have  also  tried  steam-heat,  tell  roe  that  they  get  better  satisfacrion, 
greater  economy,  and  are  able  to  maintain  a  more  even  temperature  with  2- 
Inch  wroughtriron  pipe  and  hot  water  than  by  any  other  system  they  have 
used.  They  attribute  this  result  principally  to  the  fact  tSat  this  stae  pipe 
eon  tains  leas  water  and  on  this  aooountthe  heat  oaa  be  raised  and  lowered 
quicker  than  by  any  other  arrangement  of  pipes,  and  a  mora  mBtform  tern* 
perature  maintained  than  by  steam  or  any  other  aystam. 

aonVWATBB  JBEATING, 

(Naaon  Mfg.  Oo.) 

There  are  two  dlsthict  forms  or  modifloations  of  hot-water  apparatus,  de- 
pending upon  the  temperature  of  the  water. 

In  the  first  or  open-tank  system  the  water  Is  never  above  S19*  tempera- 
ture, and  rarely  above  200*.  This  method  always  gives  satisfaction  where 
the  surface  is  sufficiently  liberal,  but  in  making  it  so  its  cost  Is  considerably 
greater  than  that  for  a  steam-hentrng  apparatus. 

In  tlie  second  method,  sometimes  oalied  (erroneously^  hlgh-presam«  hot- 
water  beating,  or  the  closed-system  apparatus,  the  tanic  Is  dosed.  If  It  is 
provided  with  a  safety-valve  set  at  10  lbs.  it  Is  practioally  as  safe  as  the  open- 
tank  svstem. 

Ijair  of  Velocity  of  Flo^r.— The  motive  power  of  the  circulation 
In  a  hot- water  apparatus  is  the  difference  between  the  speciflo  gravltiei^  of 
the  ascending  and  the  descending  pipes.  This  effective  pressure  Is  very 
•mall,  and  is  equal  to  about  one  grain  for  each  foot  in  height  for  each  de- 
gree differenoe  between  the  pipes;  thus,  with  a  height  of  12"  in  **  up ''  pipe, 
and  a  difference  between  the  temperatures  of  the  up  and  down  pipes  of  8*, 
the  difference  in  their  specific  gravities  Is  equal  to  8. 10  grains  on  each  square 
Inch  of  the  section  of  return-pipe,  and  the  velocity  of  the  circulatloD  Is  pro- 
portioned to  these  differences  in  temperature  and  height. 

To  Calculate  Velocity  of  Flow.^Thus,  with  a  height  of  ascend- 
ing pipe  equal  to  lO'  and  a  difference  in  lemperatures  of  the  flow  and  return 
pipes  of  8*>,  the  difference  in  their  speoiflo  gravities  will  equal  81.6  grains,  or 
^  7000  s  .01166  lbs.,  or  X  2.81  (feet  of  water  in  one  pound)  m  .Oaw  ft«,  and  by 
the  law  of  falling  bodies  the  velocity  will  beequsl  to  8  V-Om  b  i.$is  ft.  per 
second,  or  x  60  s:  78.7  ft.  per  minnte.  In  this  calculation  the  effect  of  fne- 
tion  is  entirely  omitted.  Considerable  deduction  muft  be  made  on  this 
account.  Even  In  apparatus  where  length  of  pipe  Is  not  great,  and  with 
pipes  of  larger  areas  and  with  few  bends  or  ansies,  a  large  deduction  for 
friction  must  he  made  from  the  theoretical  velocity,  while  in  large  and 
complex  apparatus  with  small  head,  the  velocity  is  so  much  reduced  by 
friction  tliat  sometimes  as  much  aa  from  60^  to  90)(  must  be  deducted  to  ob- 
tain the  true  rata  of  circulation. 

Main  flow'pipes  from  the  heater,  from  which  branches  may  be  taken,  are 
to  be  preferrea  to  the  praotioe  of  taking  off  nearly  as  many  pipes  from  the 
heater  as  there  are  radiators  to  supply. 

It  is  not  necessary  that  the  main  flow  and  return  pipes  should  equal  In 
ca{)acity  that  of  all  their  branches.  The  hottest  water  will  seek  the  highest 
level,  while  gravity  will  cauM  an  even  distribution  of  the  heated  water  If  the 
surface  is  properly  proportioned. 

It  Is  good  practice  to  reduce  the  sIks  of  the  vertical  mains  as  they  aacend, 
■ay  at  the  rate  of  one  size  for  each  floor. 

As  with  steam,  so  with  hot  water,  the  Tiin*o  «»gst  be  uuoonflned  to  allow 


SOTfWATBR  HBATIirfi. 


543 


Cl 

An  exp(|ft8lQn  t^  la^reaqiFed  to  Jcpep  the  appftrMiw  filled  n^lth  water. 
rhich  U^^fer  e^piMicfii  }/2i  at  iU  bulk  on  bein&r  faeatad  from  4o^  to  21^9^  and 
the  cistern  muse  hare  capacity  tq  hold  certainly  this  increased  bulk-    It  is 


^rnmiMiaiMi  of  4i9  pipes  oamaq^eot  en  faavlnff  theiv  terapemtnres  tn- 

pp2i%  1/24  6t  itsbulk  € 
t  hare  capacity  tq  hold 


recommended  that  the  supply  cistern  be  placed  on  level  with  or  above  the 
hifflieak  pIpm  oi  Uie  ftppenittus,  in  onlar  to  receive  the  air  which  colleots  in 
t««  ipaiiis  and  jra^faMirs.  and  eatable  of  holding  at  least  1/90  of  the  water 
in  the  entii«  i^pparatois. 

Approximate  ProporUone  of  Uw^lmtlng^uwl^fiep  t^ 
Cubic  Capacities  of  Space  to  be  Heated* 


One  Square  7oot  of  Ra- 
diaimtr-^Fface  will 
neat  with-? 


In  Dwellinf^, 
School-rooms, 


In  Halls,  S^ofes, 
J^ifts,  fA^U^r 

ri^s,  etc, 


In  Churches, 
Large  Audito- 
riums, eto. 


High  temperature  dir 
reet  bot-wa|er  nuli- 
ation , . ,    , 

Low  temperature  di- 
rect hot- water  n|di- 
ation 

High  temperature  In- 
direofi  hot-wa^r  ra- 
diation   

Low  temperature  in- ) 
dtfeot  hot-water  ra-  V 
diatiop ) 


00  to  70  CM.  ft. 
ap  to  50  "  " 
96to0O"  »♦ 
0eto4O**     •* 


66  to  90  ou.  ft. 
?5|Qfi5  **    •* 
M  to  T^  »*    " 
eS  to  60  ''    •♦ 


tSO  to  180  eu.  ft. 

70  to  lap  "  " 
TO  to  1.50  ••  •' 
MtolpO  •♦    " 


MametCF  of  Haln  and  Braneli  Pipes  and  souare  feet  of  coi| 
surface  they  will  supply,  in  a  low-preesui-e  hot-water  apparatus  (:)lil^)  for 
direct  or  Indirect  radiation,  when  (toils  ^.pe  at  different  altitudes  fordirecti 
radiation  or  in  the  lower  story  for  indirect  radiation: 


Im 

Pirpcri  Badla^oq.  height  of  QpU  ftbqve  Bottom  of  Boiler, 

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30958 

544  HEATIKG  AND  YENTILATIOK. 

The  best  forms  of  hot- water- he&tlng  boilers  are  proportioned  about  as 
follows: 

1  sq.  ft.  of  srrate-surface  to  about  40  sq.  ft.  of  boner-surface. 
1  *^  "       boUer-     "  **        5  •'    "       radlatlngsurface. 

1  ••    '•       grate-      "  "     200  "    " 

Rules  for  Hot-nrater  Bleating. -J.  L.  Saunders  (Heatlmr  and 
Ventilation,  Deo.  15, 1894)  gives  the  following :  Allow  1  sq.  ft  of  radiating 
surface  for  every  8  ft.  of  glass  surface,  ana  1  sq.  ft.  for  every  90  sq.  ft.  of 
wall  surface,  also  1  sq.  ft.  for  the  following  numbers  of  cubic  feet  oz  space 
in  tbe  seveiBl  cases  mentioned. 

Indwelling-houses:  Libraries  and  dining-rooms,  first  floor..  85  to  40  oa  ft. 

Reception  halls,  first  floor 40  to  GO  *'  *' 

Stairhalls,  "     **   40 to  6ft  -  *» 

Chambers  above,  *•     "    50to  66  **  '* 

Libraries,  sewing-rooms,  nurseries,  etc., 

above  first  floor. 45to  65  "  •* 

Bath-rooms 80to  40  "  '* 

Public-schoolrooms 60to  85  "  " 

OiBoes 80to  65  "  " 

Factories  and  stores 65to  90  *'  " 

Assembly  halls  and  churches 90tol50  '*  ** 

To  find  the  necessary  amount  of  indirect  radiation  required  to  heat  a  room: 
Find  the  required  amount  of  direct  radiation  according  to  the  foregoing 
method  and  add  50^.  This  if  wrought-iron  pipe  coil  surface  Is  used;  If  cast- 
iron  pin  indirect-stack  surface  is  used  it  is  advisable  to  add  from  703(  to  90%, 

SizeM  of  hot-air  fiues^  coUl-air  dncisy  and  rt-giatevB  for  indirect  voork.^ 
Hot-air  flues,  first  floor:  Make  the  net  intemal  area  of  the  flue  equal  to 
9^  sq.  in.  to  every  square  foot  of  radiating  surface  iu  the  indirect  stack.  Hot* 
air  flues,  second  floor:  Make  tlie  net  internal  area  of  tbe  flue  equal  to^mi.m. 
to  every  square  foot  of  radiating  surface  in  the  indirect  stack. 

Cold-air  ducts,  first  floor :  Make  the  net  intemal  area  of  tbe  dnot  equal 
to  9^  sq.  in.  to  every  square  foot  of  radiating  surface  in  the  indirect  stadk. 
Gold  air  ducts,  second  floor :  Make  the  net  incemal  area  of  the  duct  equal 
'    "       '  re  foot  of  radiating  surface  in  tbe  Indirect  stack. 

1  have  their  net  area  equal  in  full  to  tbe  area  of  tbe 
hot-air  flues.    Multiply  the  length  by  tbe  width  of  the  register  in  inches  ;  9i 


to  V4  sq.  in.  to  every  square  foot  of  radiating  surface  in  tbe  Indirect  stack 

Hot-air  registers  should  hi 

hot-air  flues.    Multiply  the  It  _„ „ 

of  the  product  is  the  net  area  of  register. 

Arraiuceiiieiit  of  Mains  for  Hot-Crater  Heatliiff.  (W.  M. 
Mackay,  Lecture  before  Master  Plumbers*  Assoa,  N.  Y.,  1889  )— There  are 
two  different  systems  of  mains  in  general  use,  either  of  whkdi.  if  properly 
placed,  will  give  good  satisfaction.  One  is  the  taking  of  a  single  large-flow 
main  from  the  heater  to  supply  all  the  radiators  on  the  several  floors,  wlih  a 
corresponding  return  main  of  the  same  size.  Tbe  other  is  the  taking  of  a 
number  of  S-inch  wrought-iron  mains  from  the  heater,  with  tbe  same  num- 
ber of  return  mains  of  the  same  sise.  branching  oflT  to  the  several  radiators 
or  coils  with  1^-inch  or  1-inch  pipe,  according  to  the  size  of  the  radiator  or 
coil.  A  2inch  main  will  supper  three  l^-incn  or  four  l-inch  branches,  and 
these  branches  should  be  taken  from  tbe  top  of  the  horizontal  main  with  a 
nipple  aod  elbow,  except  in  special  casen  where  it  is  found  necessary  to  retard 
the  flow  of  water  to  the  near  radiator,  for  the  purpose  of  assisting  the  circu- 
lation in  tbe  far  radiator ;  in  this  case  the  branch  is  taken  from  the  aide  of 
the  horizontal  main.  The  flow  and  return  mainsare  usually  run  side  by  side, 
suspended  from  the  basement  celling,  and  should  have  a  gradual  ascent  f^m 
the  heater  to  the  radiators  of  at  least  1  inch  in  10  feet.  It  is  customary,  and 
an  advantage  where  2-inch  mains  are  used,  to  reduce  the  size  of  the  main  at 
every  point  where  a  branch  is  taken  off. 

The  single  or  Urge  main  system  is  best  adapted  for  large  buOdings ;  but 
there  is  a  limit  as  to  size  of  main  which  it  is  not  wise  to  go  beyond -gener- 
ally 6- inch,  except  in  special  cases. 

The  proper  area  of  cold- air  pipe  necessary  for  100  square  feet  of  indirect 
radiation  in  hot-water  heating  is  7B  square  inches,  while  the  hot  air  pipe 
should  have  at  least  100  square  inches  of  area.  There  should  be  a  damper  in 
the  cold-air  pipe  for  the  purpose  of  controlling  the  amount  of  air  admitted  to 
tbe  radiator,  depending  on  the  severity  of  the  weat))er. 


BLOWER  SYSTEM  OF  HEATING  AND  VENTILATING.   545 

"THB  BLOWBR  STSTEIfE  OF  HEATING  AND 
TENTIJLATING* 

The  system  provides  for  the  use  of  a  fan  or  blower  which  takes  its  supply 
of  fraen  air  fi^m  tiie  outside  of  the  building  to  be  heated,  forces  it  over 
steam  coils,  located  either  centrally  or  di video  up  into  a  number  of  indepen- 
deot  groups,  and  then  into  the  several  ducts  or  flues  leading  to  the  various 
rooms.  Tne  movement  of  the  warmed  air  is  positive,  and  the  deliverv  of 
the  air  to  the  various  points  of  supply  is  certain  and  entirely  independent 
of  atmospheric  conditions.  For  engines,  fans,  and  steam-coils  used  with  the 
Uower  syKtem,  see  page  510« 

Bxperlments  ^rttli  Radiators  of  60  sq*  ft*  of  Sarlkee. 
iMech.  New*,  Dec.,  1893.)— After  having  determined  the  volume  and  tem- 
perature of  the  warm  air  passing  through  the  flues  and  radiators  from 
natural  causes,  a  fan  was  applied  to  each  flue,  forcing  in  air.  and  new  sets  of 
measurements  were  made.  The  results  showed  that  more  than  t\\  o  and  one- 
third  times  as  much  air  was  warmed  with  the  fans  in  use,  and  the  falling  off 
in  the  temperature  of  this  greativ  increased  air- volume  was  only  about  \^.%%. 
The  condensation  of  steam  in  the  radiators  with  the  forced-air  circulation 
also  was  only  66^  greater  than  with  natural-air  draught.  One  of  the 
several  sets  of  test  figures  obtained  is  as  follows : 

Natural     Forced- 
Draught        air 
in  Flue.  Circulation. 

Cubic  feet  of  air  per  minute 457.5       V&I 

Condensation  of  steam  per  minute  in  ounces 11.7  19.6 

Steam  pressure  In  radiator,  pounds .* 0  9 

TRmperaiure  of  air  after  leaving  radiator 14*i®  134** 

i«  t«    M  before  passing  through  radiator.    61<*  61*> 

Amount  of  radiating  surface  in  square  feet 60  60 

Siseof  flue  in  both  cases  12  x  ISinches. 

There  was  probably  an  error  in  the  determination  of  the  volume  of  air  In 
theste  testii.  as  appears  from  the  following  calculation.  (W.  K.)  Assume 
that  1  lb.  of  steam  in  condensing  from  9  lbs.  pressure  and  cooling  to  the  tem- 
perature at  which  the  water  may  have  been  discharged  from  the  radiator 
gave  up  1000  heat-units,  or  69.5  h.  u.  per  ounce;  that  the  air  weighed  .076  lb. 
per  cubic  foot,  and  that  its  speciflc  heat  is  .888.    We  have 

Natural     Forced 
Draught.  Draught. 

Heat  given  up  by  steam,  ounces  x  62.5 =3    731  1325  H.XJ. 

Heat  received  by  air,  cu.  ft.  X. 076  xdiff.  of  tern.  X. 288  s    678  1899    '* 

Or,  in  the  case  of  forced  draught  Che  air  received  14^  more  heat  than  the 
steam  gave  out,  which  is  impossible.  Taking  the  heat  given  up  by  the  steam 
as  the  correct  measure  of  the  work  done  by  the  radiator,  the  temperature 
of  Uie  steam  at  ^37**,  and  the  average  temperature  of  the  air  in  the  case  of 
natural  draught  at  i(^  and  in  the  other  case  at  OS**,  we  have  for  the  tem- 
perature difference  in  the  two  cases  135°  and  144°  resi)ectively;  dividing 
these  into  the  heat- units  we  flnd  that  each  square  foot  of  radiating  surface 
transmitted  5.4  heat-units  per  hour  per  degree  of  difference  of  temperature, 
in  the  case  of  natural  draught,  and  8.5  neat-units  in  the  case  of  forced 
draught  (=  8.5  X  144°  =  1224  heal-unlts  per  square  foot  of  surface). 

In  the  Women's  Homoeopathic  Hospital  in  Philadelphia,  2000  feet  of 
one-inch  pipe  heats  250.000  cubic  feet  of  space,  ventilating  as  well;  this 
equals  one  square  foot  of  pipe  surface  for  about  850  cubic  feet  of  space,  or 
Iras  than  8  square  feet  for  1000  cubic  feet.  The  fan  is  located  in  a  sepa- 
rate building  about  100  feet  from  the  hospital,  and  the  air,  after  being  heated 
to  about  185°,  is  convejred  through  an  underground  hrick  duct  with  a  loss  of 
only  five  or  «ix degrees  in  cold  weather.   (H.  I.  Snell,  Trans.  A.  S.  M.  E  .ix.  106. 

HeattDs  a  Bnlldlns  to  70°  F«  Inside  wben  tbe  Oatslde 
Temperature  is  Zero*— It  is  customary  in  some  contracts  for  heating 
to  guarantee  that  the  apparatus  will  heat  the  Interior  of  the  building  to  70° 
io  zero  weather.  As  it  may  not  be  practix^ble  to  obtain  zero  weather  for 
the  purpose  of  a  test,  it  may  be  difficult  to  prove  the  performance  of  tbe 
guarantee.  E.  E.  Macgovem,  In  Engineering  Record,  Feb.  3.  1894,  gives  a 
calculation  tending  to  show  that  a  test  may  be  made  in  weather  of  a liigher 
temperature  than  zero,  if  the  heat  of  the  interior  is  raised  above  70°.  The 
higher  the  temperature  of  the  rooms  the  lower  is  the  efficiency  of  the  radi- 
sting-surface,  since  the  efficiency  depends  upon  the  difference  between  the 


546  HBATIKO  AKD  VBKTILATIOK. 

temperftture  iniide  of  tbe  radiator  and  the  temperature  of  the  room.  He 
concludes  that  a  heating  apparatus  sufllcieDt  to  heat  a  given  building  to  70* 
in  zero  weatlier  with  a  given  pressure  of  steam  will  be  found  to  heat  the 
same  building,  steam-pressure  constant,  to  110*  at  00«,  99*  at  50*,  SH*  at  40*. 
and  74*  at  S'^i*,  outside  temperature.  The  accuracy  of  these  figures,  how«Ter 
has  not  beeo  tested  br  experiment. 

The  following  solution  of  the  question  It  proposed  by  the  author.  It  gives 
results  quite  different  from  those  of  Mr.  MaogoTem,  but,  like  them,  lacks  ex- 
perimental confirmation. 
Let  5  =  sq.  ft.  of  surface  of  the  steam  or  hot-water  radiator; 
W  s  sq.  ft.  of  surface  of  exposed  walls,  windows,  etc.; 
T«  =s  temp,  of  the  steam  or  not  water,  7*1  s  temp,  of  inside  of  buiUing 

or  room,  T«  =  temp,  of  outside  of  building  or  room: 
a  s  heaUunits  transmitted  per  sq.  ft.  of  surface  of  radiator  per  hour 

per  degree  of  difference  or  temperature; 
b  a  average  heat-units  transmitted  per  sq.  ft.  of  walls  per  hour,  per 
degree  of  difference  of  temperature,  including  allowance  for 
ventilation. 
It  is  assumed  that  within  the  range  of  temperatures  considered  Newton *8 
law  of  cooling  holds  good,  vis.,  that  it  Is  proportional  to  the  differenoe  of 
temperature  between  the  two  sides  of  the  radiating-surfaoe. 

hW 
Then  aS(T»  -  T,)  =  bWiT^  -  r«).    Let  -^  =  C;    then 

If  Tt  =  70,  and  T,  =  0,  C=  ^*^  ^^. 

Let  T»  =  140*.  818.6*,  ¥»\ 

ThenC«     1,  S.0^  8.4. 

From  these  we  derive  the  following: 

Temperature  of  Outside  Temperatures,  2V 

Steam  or  Hot  -  80*  - 10*            0*       10*          80*          80»          40* 

Water.  7«.  Inside  Temperatures,  2j. 

140*  60  65            70         7ft            80            85            90 

818.5  56.6  63.8         70         76.7         83.4         80.8         96.9 

806  54.6  68.8         70         77.7         85.6         98.8       100.9 

Heatlns  1^7  Eleetrlclty.—If  the  electric  currents  are  generated  ny 

a  dynamo  driven  by  a  steam-engine,  electric  heating  will  prove  very  expen- 
sive, since  the  steam-engine  wastes  in  the  exhaust-steam  and  by  nsdiation 
about  W%  of  the  heat- units  supplied  to  it.  In  dii*ect  steam -heating,  with  a 
good  boiler  and  properly  covered  supply-pipes,  we  can  utilise  about  609(  of 
tiie  total  beat  value  of  the  fuel.  One  pound  of  coal,  with  a  heating  value  of 
18,000  heat-units,  would  supply  to  the  radiators  about  18,000  x  .00  =  780O 
heat -units.  In  electric  heating,  suppose  we  have  a  first- clitse  condensing- 
engine  developing  1  H.P.  for  every  8  lbs.  of  coal  burned  per  hour. 
This  would  be  equivalent  to  1,980,000  ft. -lbs.  -•-  778  s=  »45  heat-units,  or  1«» 
heat -units  for  1  fb.  of  coaL  The  friction  of  the  engine  and  of  the  dynamo  and 
the  loss  by  electric  leakage*  and  by  heat  radiation  from  the  conducting 
wires,  might  reduce  the  heat-units  delivered  as  electric  current  to  the  dec- 
trie  ladiator,  and  these  converted  into  heat  to  ^0%  of  this,  or  only  696  heat- 
units,  or  lefMS  Than  one  twelfth  of  that  delivered  to  the  steam-radiarors  in 
direct  steam -heating.  Electric  heating,  therefore,  will  prove  uneconomical 
unless  the  electric  current  is  derived  from  water  or  wind  power,  which  would 
otherwise  be  wasted.    (See  Electrical  Kngineerlng.) 


WBIGHX  OJt   WAI1S& 


547 


WATEB. 


Bxpsjurton  of  ITater.— The  following  table  fflTes  the  relative  toI- 
uin«s  of  water  at  (Ufferent  temperatures,  compared  with  its  volume  at  4*  O. 
according  to  Kopp,  as  corrected  by  Porter. 


Cent. 

Fahr. 

Volume. 

Cent. 

Fahr. 

Volume. 

Cent. 

Falir. 

Volume. 

4* 

«0.1« 

1.00000 

85" 

95» 

1.00686 

70* 

158<» 

1.02241 

5 

41 

1.00001 

40 

104 

1.00767 

75 

167 

i.oais 

10 

60 

1.000S5 

45 

118 

1.00067 

80 

176 

1.0«J7i 

15 

M 

1.00068 

60 

m 

1.01186 

85 

185 

1.03-^I8 

SO 

68 

1.00171 

65 

181 

1.01428 

90 

194 

1.08570 

s» 

77 

1.00S86 

60 

140 

1.01678 

05 

HQii 

2.03943 

so 

66 

1.004^6 

65 

140 

1.0I95I 

100 

212 

1.04882 

Welfcht  of  1  cu.  ft.  at  80.1»  F.  =  68.4246  lb.  -h  1.04882  »  60.888,  weight  of  1  ou. 
fL  at  212»  F. 

ireiclftt  of  ITater  at  Dimrent  Teiiiperatnrea.~The  weight 
of  water  at  maximom  density,  89.1*,  is  generally  taken  at  the  figure  given 
by  Bankine,  68.425  lbs.  per  cubic  foot.  Some  authorities  give  as  low  as 
68.379.  The  figure  62.6  commonly  given  is  approximate.  The  highest 
authoritative  figure  is  68.425.  At  62«  F.  the  figures  range  from  62.291  to  6^.860. 
Tlie  figure  62.855  is  generally  accepted  as  the  most  accurate. 

At  &*  F.  figures  given  by  different  writers  range  from  62.879  to  62.418. 
dark  gives  the  latter  figure,  and  Hamilton  Smith,  Jr.,  (from  Bosetti,)  givec 
62.416. 

ITeiclftt  of  UTater  at  Temperature*  above  ftl9*  F«— Porter 
(Bichards'  **  Steam-engine  Indicator/'  p.  52)  says  that  nothing  is  known 
about  the  expansion  of  water  above  212^.  Applying  formuln  derived  from 
experiments  made  at  temperatures  below  2i2o,  however,  the  weight  and 
volume  above  212*  may  be  calculated,  but  in  the  absence  of  experimental 
data  we  are  not  certain  that  the  formuln  hold  good  at  hii^iier  temperatures. 

Tliurston.  in  his  "  Engine  and  Boiler  Trials,"  gives  a  table  from  which  we 
take  the  following  (neglecting  the  third  decimal  place  given  by  him) : 


pi 

ill 

III 

P 

fli 

^1 

1^ 

g3. 

212 

69.71 

280 

67.90 

850 

65.5S 

420 

62.86 

400 

60.08 

2^ 

50.64 

290 

57.59 

860 

66.16 

480 

62.47 

600 

49.61 

280 

59.87 

800 

67.26 

870 

64.79 

440 

68.07 

610 

49.20 

240 

69.10 

810 

66.98 

880 

54.41 

450 

61.66 

520 

48.78 

250 

58.81 

tkiO 

66.58 

890 

64.08 

460 

61.26 

580 

48  86 

260 

58  52 

880 

66.24 

400 

58.64 

470 

50.85 

540 

47.94 

'zro 

58.21 

840 

65.88 

410 

68.26 

480 

60.44 

550 

47.62 

Box  on  Heat  gives  the  following : 

860* 
68.86 


Temperature  F...., 
Lbs.  per  cubic  foot, 


212* 
60.82 


800* 
67.-12 


860* 
55.94 


400* 
54.84 


450* 
52.70 


600* 

51.02 


600* 
47.64 


At  213*  flgarea  given  by  different  writers  (see  Trans.  A.  8.  M.  £.,  xUi.  409) 
lange  from  58.50  to  G0.B4Q»  aveiaging  about  69.77. 


548 


WATBR. 


UTeif^t  of  ITftter  per  Ovble  Foot,  from  8S«  to  212*  F.,  and  be%^ 
units  per  pouud,  reckoned  above  82^  F.:  The  following  table,  mado  by  in- 
terpolating the  cable  given  by  Clark  as  calculated  from  Ranklne's  formula, 
with  corrections  for  apparent  errors,  was  published  by  the  author  In  1884, 
Trans.  A.  S.  M.  E.,  vi.  VO.    (For  heat  units  above  S12*>  see  Steam  TiOdes.) 


> 

-1 

1 

ffl 

^1 

1 

|li 

^1 

1 

1 

»i 

d8.42 

0. 

78 

62.85 

46.08 

188 

61.68 

91.16 

168 

00.81  180.44 

83 

6SJ« 

1. 

79 

02.24 

47.08 

184 

61.67 

02.17 

100 

00.79187.45 

84 

6S.42 

8. 

80 

68.23 

48.04 

185 

01.65 

98.17 

170 

00.77;138.45 

85 

68.42 

8. 

81 

62.22 

49.04 

186 

61. G8 

04.17 

m 

00.751180.40 

86 

02.42 

4. 

82 

62.21 

50.04 

187 

61.61 

96.18 

178 

00.78 

140.47 

87 

62.42 

5. 

88 

62.20 

51.04 

188 

01.00 

00.18 

178 

00.70 

141.48 

88 

62.42 

6. 

84 

62.19 

58.04 

129 

01.58 

07.10 

174 

00.08 

148.49 

89 

02.42 

7. 

85 

62.18 

53.05 

180 

01.56 

96.10 

175 

00.00 

148.50 

40 

62.42 

8. 

86 

68.17 

64.05 

181 

61.54 

09.20 

170 

60.04 

144i51 

41 

62.42 

0. 

87 

62.16 

55.05 

188 

61 .52 

100.20 

177 

00.02 

145.68 

42 

62.42 

10. 

88 

68.15 

56.05 

188 

61.51 

101.81 

178 

00.50 

140.38 

48 

62.42 

11. 

80 

62.14 

57.05 

184 

61.49 

102.21 

170 

00.57 

147.5S 

44 

02.42 

18. 

00 

08.18 

68.06 

185 

61.47 

103.82 

180 

00.55 

148  54 

45 

68.48 

18. 

01 

62.12 

59.06 

186 

61.45 

104.82 

181 

00.53140.55 

48 

62.48 

14. 

02 

62.11 

60.06 

187 

61.48 

105.28 

188 

00.50;i.'W.''iO 

47 

62.48 

15. 

98 

62.10 

61.06 

188 

61.41 

106.28 

188 

60.48.151.57 

48 

02.41 

16. 

04 

62.09 

68.06 

189 

61.89 

107.84 

184 

60.461158.58 

40 

68.41 

17. 

05 

02.08 

68.07 

140 

61.87 

106.85 

186 

00.44  153.50 

fiO 

68.41 

18. 

06 

68.07 

64.07 

141 

61.86 

109.86 

180 

00.4MM.60 

61 

68.41 

10. 

07 

62.06 

65.07 

148 

61.84 

110.26 

187 

00.80  155.61 

6S 

62.40 

80. 

98 

62.05 

66.07 

143 

61  88 

111.86 

188 

60,87  156.68 

58 

62.40 

81.01 

00 

68.08 

67.08 

144 

01.80 

118.87 

180 

60.84  157.63 

54 

68.40 

22.01 

100 

62.02 

68.08 

145 

01.28 

118.28 

190 

60.88  158.64 

56 

62.80 

28.01 

101 

68.01 

69.08 

146 

01.86 

114.88 

101 

00.80.150.65 

50 

62.89 

84.01 

108 

68.00 

70.09 

147 

01 .24 

116.80 

108 

60.27il00  67 

67 

68.89 

26.01 

103 

61.99 

71.09 

148 

01.88 

116.80 

103 

00.25  101 .08 

58 

68.88 

26.01 

104 

61.97 

78.09 

149 

01.20 

117.80 

104 

00.28  102  09 

59 

68.88 

27.01 

105 

61.96 

73.10 

150 

01.18 

118.81 

106 

00.80  108.70 

80 

08.87 

88.01 

106 

61.95 

74.10 

151 

01.16 

110.81 

100 

00.17  104.71 

61 

68.87 

89.01 

107 

61.98 

75.10 

158 

01.14 

180.82 

197 

60.15,105.72 

03 

68.96 

80.01 

108 

61.98 

76.10 

158 

01.12 

181.88 

196 

60  18,166  73 

68 

68.86 

81.01 

100 

61.91 

77.11 

154 

61.10 

122.88 

199 

60.10,167.74 

64 

03.85 

82.01 

110 

61.89 

78.11 

165 

61.08 

128.84 

800 

60.07 

108.75 

65 

68.84 

83.01 

111 

61.88 

79.11 

166 

61.06 

124.85 

201 

00.05 

109.77 

66 

68.84 

84.02 

118 

61.86 

80.12 

167 

01.04 

125.85 

808 

00.02 

170.78 

67 

62.88 

85.02 

113 

61.85 

81.18 

158 

61.02 

126.86 

208 

00.00 

171 .19 

68 

68. as 

86.08 

114 

61.83 

82.18 

169 

61.00:187.87 

804 

50.97 

178.80 

60 

68.82 

87.02 

115 

61.82 

88.18 

160 

00.98  188.87 

905 

50.95 

178.81 

70 

62.81 

88.02 

116 

61.80 

84.13 

161 

00.96  129.38 

200 

50.88 

174. M 

71 

62.-S1 

80.08 

117 

61.78 

85.14 

162 

60.94  180.39 

2or 

60.89 

175.81 

72 

63.80 

40.02 

118 

61.77 

86.14 

163 

60.92  131.40 

208 

60.87 

176.85 

78 

68.89 

41.02 

110 

61.75 

87.15 

164 

60.90 

182.41 

200 

60.84 

17;  86 

74 

68.28 

42.03 

120 

61.74 

88.15 

165 

60.87 

138.41 

210 

50.68 

1M.87 

75 

68.88 

43.08 

181 

61.  ?2 

89.15 

166 

60.85 

134.4*4; 

211 

60.79:170.89 

76 

62.27 

44.08 

188 

61.70 

90.16 

167 

60.83 

135.43 

818 

59.70|]80.00 

62.26 

45.03 

I 

Comparisoii  of  Heads  of  ITater  In  Feet  'vrltli  Pressure*  In 
Vartoaa  Units. 

One  foot  of  water  at  89**.  1  Fahr.  =-  62.425  lbs.  on  the  square  foot: 
**  *'  **  =    0.4SS5  lbs.  on  the  Hiuare  inehi 

'*  "  =    0.0206  atmosphere; 

••  ••  ••  =    0.8826  inch  of  mercuiy  at  83*; 

M  «  M  ^77«.jfM}tof  airat83*>and 

'=^'")       atmospherleprtMttiv; 


PRESSURE  OF  WATER. 


549 


One  lb.  OB  the  square  foot,  at  88<».l  Fahr «  O.OJ009  foot  of  water; 

One  lb.  on  the  square  inch  *'        s   2.807      feet  of  water; 

One  atmosphere  of  29.922  inches  of  mercury....  ^  83.9  *'    "     " 

One  inch  of  mercury  at  82«.l =    1.188        **    "     " 

Onefootof  air  at  &Sdeg.,  and  one  atmosphere.,  s   0.001298    **    **     ** 

One  foot  of  average  sea-water =  1.026  foot  of  pure  water; 

One  foot  of  water  at  82"  F =  62.856  lbs.  per  sq.  foot; 

*'      ' »62«F ..=    0.43302  lbs.  per  sq.  inch; 

One  inch  of  water  at  tt2«  F =   0.036085"      "    *»      " 

One  pound  of  water  on  the  square  inch  at  6&*  F.  s=   2.8094  feet  of  water. 

Pressure  In  Ponnds  per  Square  Incli  for  IHlTerent  Heads 
of  Water. 


At  e3»  F.  1  foot  head  = 
per  cubic  foot. 


0.483  lb.  per  square  inch,  .433  X  144  =:  62.852  lbs. 


Head,  feet. 

0 

1 

2 

8 

4 

5 

6 

7 

8 

9 

0 

0.438 

0.866 

1.299 

1.782 

2.165 

2.598 

8.031 

8.464 

8.8»7 

10 

4.380 

4.768 

5.196 

5.629 

6.06« 

6.495 

6.928 

7.861 

7.794 

8.227 

20 

8.660 

9.098 

9.526 

9.959 

10  892 

10.825 

11.258 

11.691 

12.124 

12.557 

80 

12.000 

18.428 

18.856 

14.289 

14.722 

15.165 

15.688 

16.021 

16.454 

16.887 

40 

17.320 

17.763 

18.186 

18.619 

19.052 

19.4&'S 

19.918 

20.861 

20.784 

21 .217 

60 

21.6S0 

22.083 

22.516 

22.949 

28.882 

28.815 

24.248 

24.681 

25.114 

25.547 

60 

25.980 

26.413 

26.846 

27.ST9 

27.712 

28.145 

28.578 

29.011 

29.444 

29.877 

70 

30.810 

30.743 

31.176 

81.609 

32.042 

82.475 

82.906 

38.341 

88.774 

84.207 

80 

34.640 

16.078 

35.506 

35.969 

86.372 

86.805 

87.238 

87.671 

88.104 

38.537 

90 

88.970 

39.408  89.836 

40.269 

40,702 

41.135 

41.566 

42.001 

42.486 

42.807 

Head  in  Feet  of 


»f  "Water,  Correspondlne  to 
Pounds  per  Square  Incn. 


Pressures  In 


1  lb.  per  square  inch  =  2.80947  feet  head,  1  atmosphere  =  14.7  lbs.  per  so. 
loch  =  33.94  ft.  head.  ^ 


PreKSure. 


0 
10 
SO 
80 
40 
50 
60 
70 
80 
90 


23.0947 
46.1891 
09.2841 
92.8788 
115.4T36 
188.5682 
161 .6629 
184.7576 
207  8528 


2.809  4.610 
25.404  27.714 
'48.49950.808, 
71.594  78.903 
94.688  96.998 
117.78  120.091 
140.88  143.19! 
163.97166.28! 
187.07,189.38, 
210.16  212.47 
I     I 


6.928  9.238 
80.023  82.383 
58.118  65.427 
:6.218  "^.522 
99.807  101.62 
122.40  124.71 
145.50  147.81 
168.69  170.90 
191.69  IM  00 
214.78  217.09 
I 


11.547 
:M.642 
57.787 
80.881 
103.93 
128.02 
150.12 
178  21 
196.31 
219.40 


13.85' 
36.95'i 
60.046 
88.141 
106.24 
129.33 
152.42 
175.52 
198.61 
221.71 


16.166 
39.261 
62.3.56 


18.476  20  7a5 
41.670  43.880 

- 64.665  66.975 

86.450  87.760  00.06!) 
108.56  110.85118.16 
131.64  183.9.');  1.36.26 
154.78  157.04  159.35 
177.83  180.14  182.45 
200.92  e03. 23,205  54 
224.02  226.33,228.64  > 


Pressure  of  W^ater  due  to  Its  Welgl&t.— The  pressure  of  still 
waifP  iu  p4*un<iK  per  square  inch  ai^aiUvSt  the  sines  of  any  pipe,  channel,  or 
▼ejcsel  <»f  any  shape  whatever  is  due  solely  to  the  "  heatl,"  or  heiirht  of  the 
level  Kurface  of  the  water  above  the  point  at  which  the  pressure  is  con- 
sidered, and  is  equal  to  .48802  lb.  per  square  inch  for  every  foot  of  head, 
or  62.355  lbs.  per  square  foot  for  every  foot  of  head  (at  62^  F.). 

The  pressure  per  square  inch  is  equal  in  all  directions,  downwards,  up- 
wards, or  sideways,  and  is  independent  of  the  shape  or  size  of  the  containing 
vensel. 

The  pressure  a^lnst  a  vertical  surface,  as  a  retainlng-wall,  at  any  point 
la  in  direct  ratio  to  the  head  above  that  point,  increasing  from  0  at  the  level 
surface  to  a  masdmum  at  the  bottom.  The  total  pressure  against  a  vertical 
Strip  of  a  unit's  breadth  increases  as  the  area  of  a  right-angled  triangle 


556  WATEEL 

whobe  ]Mrp»naieut*^  hepreseuts  thfe  h4iithi  ot  tb6  strip  and  whoaS  baM 
reprfewiits  the  preesiire  on  a  unit  of  BUi-face  at  the  bottom ;  tb»l  to.  It  iti- 
creases  ai;  the  square  nf  the  depth.  The  Bum  Of  all  the  horiaoiital  pi-ensures 
is  represented  by  the  Area  of  the  triangle,  and  the  tTSUItant  of  thia  aum  is 
equal  to  this  sum  everted  at  apotnt  one  third  of  the  height  from  the  bottom. 
(The  centre  bf  gravity  of  the  area  oC  a  triangle  is  one  third  of  It^  height.) 

The  horisontal  pressure  is  the  same  If  the  surface  is  inclined  iostaad  of 
▼ertlcal. 

(For  an  elabomtlon  of  these  principles  see  TrautWioe*B  Pocket-Book,  or 
the  chapter  on  Hjrdt-ostatlcs  In  any  work  on  Physics.  For  dam^  retaining- 
walls,  etc.,  see  Trautwlne.) 

The  amount  of  pressure  on  the  interior  walls  of  a  pipe  has  no  appreciable 
eliect  upon  the  amount  of  flow. 

BuoTaney.— Wtien  a  body  Is  Imihefsed  in  a  liquid,  whether  it  float  or 
sihk.  it  Is  buofed  Up  by  itfbree  equal  to  the  weight  of  the  btllk  of  ttie  liquid 
displaced  by  the  body.  The  weight  of  a  floating  body  is  equal  to  tlie  weight 
of  the  bylk  of  the  liquid  that  it  displaces.  Ths  upward  pressure  or  buoy- 
ancy of  tne  liquid  may  be  regarded  m  exerted  at  the  centre  of  gravity,  of 
the  displaced  Water,  which  is  callbd  the  Deotrd  of  pressure  or  of  buoyancy. 
A  vertical  line  drawn  through  it  is  called  the  axis  of  bumancy  or  of  flota- 
tion. In  a  floatthg  body  at  rest  a  Une  Joining  the  eenti;e  or  gravity  and  the 
centre  of  buoyancy  Is  vertical,  and  is  called  the  axis  bc  ^uilibHum.  When 
an  external  force  causes  the  axis  of  equilibrium  to  lean,  if  a  vertical  line  be 
drawn  upward  from  the  centi^  of  buoys  noy  to  thia  axis,  the.  point  where  ie 
cuts  the  axi3  la  ealled  the  tnetcustixtire.  If  the  metaoehtre  is  above  the  centre 
of  gravity  thti  distance  between  them  is  called  the  metacentric  heigiit,  and 
the  body  Is  then  said  to  be  in  stable  equilibrium,  tending  to  hetum  to  Its 
orUinal  position  when  the  external  force  is  removed. 

Boillnc^point*— water  boils  at  «1S«  F.  (lOO*  C.)  at  mean  atmdopheric 

pressure  at  the  sea-level,  14.096  Ibe.  per  square  Inch.    The  tehiperature  at 

which  water  boils  at  any  given  pressure  is  the  same  as  the  temperature  of 

.  saturated  steam  at  the  same  pressure.    For  boiling-point  of  water  at  othei 

gi-ORSure  than  14.696  lbs.  per  square  inch,  see  table  of  the  Properties  ol 
aturated  Btealil. 

The  BoUlnir-peliit  of  W«ter  ma/  be  BUlaed.— When  water 
Is  entirely  freed  of  air,  which  may  be  acconipltslied  by  f nsesiiig  or  boiling, 
the  cohesloh  of  its  atoms  Is  greatly  increteed,  sd  that  Its  temperature  may 
be  raised  over  ftO*  above  the  ordinary  boiling-point  before  ebullition  lakes 
place.  It  was  found  by  Faraday  that  when  such  air-freed  water  did  boil, 
the  rupture  of  the  liquid  was  like  an  expioslou.  When  water  ts  surrounded 
by  a  nlm  of  oil,  its  boiling  temperature  may  be  ralKcd  considerably  above 
itH  normal  standard.  This  has  been  api^lied  as  a  theoretical  ezpliinatlon  In 
the  instance  of  boiler-explosions. 

The  freezing-point  also  may  be  lowered)  If  the  water  Is  perfectly  quiet,  to 
-  lO**  C,  or  18°  Fahrenheit  below  the  normal  fret'ziug-pqiuL  (Hamilton 
Smith,  Jr.,  on  Hydraulics,  p.  18.)  The  density  of  water  at  14*^  F.  is  .99Bi4,  its 
density  at  Sd<*.  1  being  1,  and  at  9^,  .09987. 

Freesins^^olnC— Water  freezes  at  8S«  F.  at  the  ordlnarv  atmospheric- 
pressure,  and  ice  melt«  at  the  same  temperature.  In  the  melting  of  1  pound 
of  ice  into  water  at  di^  F.  alK>ut  142  heat-unils  are  absorbed^  or  become 
latent:  and  in  fi^ezing  1  lb.  of  water  into  ice  a  like  quantity  of  neat  is  given 
out  to  the  Hurroundlng  inedlum. 

Sea*ilratefe-  freezes  at  27«  F.    The  Ice  is  fresh.    (Traulwrne.) 
^e  ttlid  snow.    (Froili  CIark.)>l  cubic  foot  ot  Ice  at  tS?  F.  Weighs 
57.(yu  lbs. ;  1  pound  of  ice  at  88°  F.  has  a  vduine  of  .0174  cu  ft.  s  80.067  eu.  in. 

Relative  volume  of  ice  to  water  at  82°  F.,  1.0636i,  the  expansion  in  paraing 
into  the  solid  state  behig  6.650^  Bpbdflo  gravity  of  lo6  «  O.M3|  water  at 
6-^°  F.  being  1. 

At  high  Pressures  the  meltingjboint  of  leb  is  lower  than  88*  F.,  being  at 
the  rate  of  .01 88°  F.  for  each  additional  atmosphere  of  pKsaure 

The  speciflc  heat  of  Ice  is  -.604,  that  of  water  being  I. 

1  cubic  foot  of  fresh  snow^  according  to  humidity  of  atmosphere 1 6  Ibe.  to 
18  lbs.  1  cubic  foot  of  snow  moistened  kntt  compacted  by  ralni  16  Iba  to 
.60  lbs.    (Trautwin^). 

Speciflc  Heat  of  t¥ater.  (From  Olark*s  Steam-engine.)— Calou* 
hLted  by  means  of  Hegnault^s  formula,  e:=  1  H- 0.00004< -f  a.«80mo»(S  In 
which  c  Is  the  speciflc  heat  Of  water  at  any  temperitutb  i  In  eeaMcrade  d«- 
greesi  the  speciflc  heat  at  the  freezing-point  beihg  1. 


THE  IMPCRITIES  09  WATEB. 


551 


1>emi 

tuc 

pera* 

■es. 

Fahr. 

1  British  Tlter- 
1    mal  Units 
per  pound, 
above  82*  F. 

ifi 

111! 
IIU 

Tempera- 
tures. 

British  Ther- 
mal Units 
per  pound, 
above  3S«F, 

Speclflo  Heat 
1  at  the  given 
Temperatara, 

111! 

Cent. 

Cent. 

Fahr. 

0» 

38- 

0.000 

1.0000 

120* 

248» 

517.449 

i.om 

1.00617 

10 

M 

18.004,  l.WW 

l.OOOt 

180 

M6 

-m.m]  1.0204 

1.0076 

ao 

68 

36.018,  1.0012 

1.0005 

140 

284 

264.1871  1.0232 

1.0087 

30 

86 

54.047'  1.0080 

1.0009 

150 

802 

Srr2.688   1.0262 

1.00»7 

40 

lot 

7-^.090 

1.0090 

1.0018 

100 

820 

391.131  1.0294 

1.0101 

50 

1«3 

90.157 

1.0042 

1.0017 

170 

8S8 

S09.600    1.0328 

1.0121 

60 

140 

108.5M7 

1.0096 

1.00S8 

180 

896 

828.8!^ 

1.0864 

1.0188 

70 

158 

186.378 

1.0072 

1.0030 

190 

874 

847.004 

1.0401 

1.0146 

W 

176 

144.508 

1.0089 

l.OOSS 

900 

892 

866.760 

1.0440 

1.0160 

90 

194 

162.686 

1.0109 

1.0042 

210 

410 

884.688 

1.0481 

1.0174 

100 

aft 

160  .MO 

l.«I30 

l.OOSO 

220 

428 

408.48.'^ 

1.0694 

I.OI89 

110 

230 

199.152 

K0154  1  1.0058  1 

330 

446 

4^2. 47h 

1.0568 

1.0204 

C^aa^resaibUtiar  •f  Wmter.— Water  is  very  sliKhtly  compressible. 
Its  cooipreseibUlty  Is  from  .000040  to  .000051  for  one  atmospliere,  di>creas»t«)fr 
with  increase  ot  temperature.  For  each  foot  of  pressure  distUled  water  will 
be  dtminished  in  volume  .0900015  to  .0000013.  water  is  so  incompressible 
that  «TeB  at  a  depth  of  a  mile  a  cubic  foot  of  water  will  weigli  only  about' 
half  a  pouBd  more  than  at  the  surface. 

VHJB  imFiJRrriEs  ^f  watbb. 

(A.  E.  Hunt  and  G.  H.  Clapp,  Trans.  A.  I.  M.  E.  xvii.  838.) 

ComnMroial  analyses  are  made  to  determine  concerning  a  given  water: 
(1)  ite  at>plioablllty  for  maliiiig  Oteam;  (2)  its  hardness,  or  the  facility  with 
which  it  will  **P»nn  a  lather"  necessary  for  washing;  or  (8)  its  adaptation 
to  other  manufacturing  purpoees. 

At  tbe  Buffalo  meeting  of  the  Chemieal  Section  of  the  A.  A.  A.  S.  it  was  de- 
cMeA  to  report  all  vater  analyses  to  parts  per  thousand,  hundred-thousand, 
andinl1lto«» 

To  convert  grains  per  imperial  (BritMh)  gallons  into  parts  per  100,000,  di- 
vide by  0.7.    To  convert  parts  per  100,000  into  grains  per  U.  S.  gallon,  mul- 


„^Y7/«. 


i  wsoflt  oomnion  ccimmercial  analysis  of  water  <s  made  to  determine  flt« 

fttaesB  for  ttiakfag  siwam.  Water  containing  more  than  ft  parts  per  100,000 
of  free  sulphuric  or  nitric  acid  is  liable  to  canee  serious  oorroeton,  not  only 
of  the  metal  of  the  boiler  itself,  but  of  the  pipes,  cylinders,  pistons,  and 
valves  with  whieh  the  steam  centee  in  <3antact. 

The  total  residue  in  water  used  for  making  steam  causes  the  interior  lin- 
ings ol  boilers  to  become  coated,  and  often  produces  a  dangerous  hard 
scale,  which  prevents  the  cooling  action  of  the  water  from  protecting  the 
ntetal  against  buratnc. 

Ltaae  and  magnesia  bicarbofiates  in  water  lose  their  excess  of  carbonic 
acid  on  boiling,  and  often,  especially  when  the  water  contains  sulphuric 
acid,  produce,  with  the  other  solid  residues  constantly  bein^  formed  by  the 
evaporation,  a  veiybard  and  Insoluble  scale.  A  larger  amount  than  100 
parts  per  100,000  of  total  nolid  residue  "wlti  ordinarily  cause  tronblesetne 
ueale,  and  should  condemn  Uie  water  for  use  in  steam-boilers,  «nless  a 
better  supply  cannot  be  obtaioed. 

The  following  Is  a  tabulated  form  of  the  causes  of  trouble  with  water  for 
steam  pui*poses,  and  the  proposed  remedies,  given  by  Prof.  L.  M.  Norton. 

Causks  09  iKcnoflVAnon. 

1.  Deposition  ef  suspended  mailer. 
€.  Pftpeeition  of  depooed  salts  from  oo>noe»ti«tiofi. 

8.  Deposition  of  carbonates  of  lime  and  magnesia  by  boiling  off  carbonlo 
t/^  which  holds  them  in  solution. 


552 


WATER. 


4.  Deposition  of  sulphates  of  lime,  because  sulphate  of  lime  is  but  slightly 
soluble  in  cold  water,  less  soluble  in  hot  water,  insoluble  above  270"  F. 

5.  Deposition  of  magnesia,  because  magnesium  salts  decompose  at  hif^ 
temperature. 

6.  Deposition  of  lime  soap,  iron  soap,  etc.,  formed  by  saponification  of 


ISXASB  FOB  PRBTBltTIMa  INCRUSTATION. 

1.  Filtration. 
9.  Blowing  off. 

8.  Use  of  internal  collecting  apparatus  or  devices  for  directing  the  cir« 
culaUon. 

4.  Heating  feed-water. 

5.  Chemical  or  other  treatment  of  water  In  boiler. 

6.  Introduction  of  zinc  into  boiler. 

7.  Chenllcal  ti-eatment  of  water  outside  of  boiler.' 


TABrLAB  View. 


Troublesome  Substance. 
Sediment,  nmd,  clay,  etc. 
Readily  soluble  salts. 

Bicarbonates  of  lime,  magnesia, ) 
iron.  f 

Sulphate  of  lime. 

Chloride  and  sulphate  of  magne- 1 

sium.  f 

Carbonate     of    soda    in    large) 

amounts.  ) 

Acid  (in  mine  waters). 

Dissolved    carbonic    acid     mid  ) 
oxygen.  f 


Trouble. 
Incrustation. 


Qrease  (from  condens«l  water). 
Organic  matter  (sewage). 


Corrosion. 

Priming. 
Corrosion. 

Corrosion. 

}  Corrosion  or 
f  incrustation. 
(      Priming, 
•\CorroBion,  or 
(  incrustation. 


Remedy  or  PBlUaticm. 
Filtration;  blowing  off. 
Blowing  off. 

Heating  feed.    Addition  of 
caustic  soda,  lime,   or 
magnesia,  etc. 
Addition    of    carb.   soda, 

bfirium  hjdmte,  etc. 
Addition  of  carbonate  of 
soda,  etc. 
t  Addition  of  barium  chlo- 
1      ride,  etc. 
Alkali. 

Feed  milk  of  lime  to  the 
boiler,  to  form  a  thin  in- 
ternal coating. 

Different  cases  require  dif- 
ferent remedies.  Consult 
a  specialist  on  the  subject. 


'  The  mineral  matters  causing  the  most  troublesome  boiler-scales  are  bicar- 
bonates and  sulphates  of  lime  and  mairnesia,  oxides  of  Iron  and  alumina, 
and  silica.  The  analyses  of  some  of  the  most  common  and  troublesome 
boiler-scales  are  given  in  the  following  table : 


Analyses 

of  Boller-seale.    (Chandler.) 

Sul- 
phate 

of 
Lime. 

Mag. 
nesla. 

Silica. 

Per- 
oxide 

of 
Iron. 

Water. 

Car- 
bonate 

of 
Ume. 

N.Y.C&B 

M              M 

[.R.Ry.,No.    1 

No.    2 

No.   8 

•'           No.   4 

••           No.    5 

No.    6 

No.   7 

"           No.   8 

"           No.   9 

No.  10 

74.07 

71.37 

62.86 

53.05 

46.88 

80.80 

4.85 

0.88 

4.81 

80.07 

9.19 

"is.w 

*8i!i7 
2.01 
8.84 

0.66 
1.76 
2.60 
4.79 
5.82 
7.76 
2.07 
0.66 
8.92 
8.94 

U.06 

1.14 

14.78 

«l               U 
•  1               (t 

0.98 

1.88 

19.08 

it              •* 

•«              «• 
•  «              •» 
t«              •* 

•«              M 

1.08 
1.08 
0.86 

8.44 
0.68 
0.16 

86.98 
86.85 
93.19 

THE  IMPUBin£8  OF  WATEB. 


553 


Analyses  Is  Psrcs   per  100,000  of    DTater  sItIiic 
Besulte  tn  Steasfbotlere.    (A.  E.  Hunt.) 


CkMd-mfne  water 

Salt-weU 

Sprinfc 

Monongahela  Blver. 


AUegheny  R,  near  Oil-work» 


I? 


119 
1.90 
96 
161 
94 
61 
41 


89 
48 
180 
88 
81 
1.04 


800 
990 
81 
88 
910 
1.90 
48 


780 
88 
76 
70 
90 
88 
88 


18.10 
86 


Many  mibstancee  have  been  added  with  the  Idea  of  causlog  chemical 
action  which  will  prevent  boiler-ecale.  As  a  general  rule,  these  do  more 
bann  than  good,  for  a  boiler  is  one  of  the  worst  possible  places  in  which  to 
carry  on  chemical  reaction,  where  it  nearly  always  causes  more  or  less 
corroaion  of  the  metal,  and  is  liable  to  cause  dangerous  explosions. 

In  cases  where  water  containing  large  amounts  of  total  solid  residue  la 
necessarily  used,  a  heavy  petroleum  oil,  free  from  tar  or  wax.  which  is  not 
acted  upon  by  acids  or  alkalies,  not  having  sufficient  wax  in  it  to  cause 
saponification,  and  which  has  a  vaporizing- point  at  nearly  600^  F.,  will  give 
the  beat  results  in  preventing  boiler-scale.  Its  action  is  to  form  a  thin 
greasy  film  over  the  boilf^r  linings,  protecting  them  largely  from  the  action 
of  acids  in  the  water  and  greasing  the  sediment  which  Is  formed,  thus  pre- 
venting the  formation  of  scale  and  keeping  the  solid  residue  from  the 
evaporation  of  the  water  in  such  a  plasilc  suspended  condition  that  It  can 
be  easily  ejected  from  the  boiler  by  the  process  of  *'  blowing  off.'*  If  the 
water  is  not  blown  off  sufficiently  often,  this  sediment  forms  into  a  ^*  putty*' 
that  will  necessitate  cleaning  the  boilers.  Any  boiler  using  bad  water  should 
be  blown  off  every  twelve  hours. 

Hardneee  of  UTater.— The  hardness  of  water,  or  its  opposite  quality, 
indicated  by  the  ease  with  which  it  will  form  a  lather  with  soap,  depends 
almost  altogether  upon  the  presence  of  compounds  of  lime  and  magnesia. 
Almost  all  soaps  consist,  chemically,  of  oleate,  stearate,  and  palmitate,  of 
an  allcaline  base,  usually  soda  and  potash.  The  more  lime  and  magnesia  in  a 
sample  of  water,  the  more  soap  a  given  volume  of  the  water  will  decompose, 
8o  as  to  give  insoluble  oleate,  palmitate,  and  stearate  of  lime  and  magnesia, 
and  consequently  the  more  soap  must  be  added  to  a  gallon  of  water  in  order 
that  the  necessary  quantity  of  soap  may  remain  in  solution  to  form  the  lather. 
The  relative  hardness  of  samples  of  water  is  generally  expressed  in  terms 
of  the  number  of  standard  soap-measures  consumed  by  a  gallon  of  water  in 
7ieldlng  a  permanent  lather. 

The  standard  soap-measure  is  the  quantity  required  to  precipitate  one 
grain  of  carbonate  of  lime. 

It  is  commonly  reckoned  that  one  gallon  of  pure  distilled  water  takes  one 
■oap-measure  to  produce  a  lather.  Therefore  one  is  deducted  from  the 
total  number  of  soap-measures  found  to  be  necessary  to  use  to  produce  a 
lather  In  a  gallon  of  water,  in  reporting  the  number  of  soap-measures,  or 
"  dMj^rees  **  of  hardness  of  the  water  sample.  In  actually  making  tests  for 
hardness,  the  *'  miniature  gallon,**  or  seventy  cubic  centimetres,  is  used 
rather  than  the  Inconvenient  larger  amount.  The  standard  measure  Is  made 
by  completely  dissolving  ten  grammes  of  pure  castile  soap  (containing  6qper 
cent  ollve-oll)  in  a  litre  of  weak  alcohol  (of  about  85  per  cent  alcohol).  This 
yields  a  solution  containing  exactly  sufficient  soap  in  one  cubic  centimeter 
of  the  solution  to  precipitate  one  milligramme  of  carbonate  of  lime,  or,  in 
other  words,  the  standard  soap  solution  is  reduced  to  terms  of  the  **  minia- 
ture gallon  **  of  water  t-aken. 

If  a  water  charged  with  a  bicarbonate  of  lime,  magnesia,  or  Iron  is  boiled. 


654 


WATEB. 


It  win,  on  tbe  excess  of  the  oorbonlo  add  beincr  ezpdled,  de|K»it  a  oonaid^ 
erable  quantity  of  the  lime,  marDesia,  or  iron,  avi  conBequently  the  water 
will  be  softer.  The  hardness  of  the  water  after  this  deposit  of  Umei,  afta 
long  boiling,  is  called  the  permanent  hardness  and  the  difference  between  fk 
and  the  total  hardness  is  called  temporary  h<»ninec», 

lime  salts  in  water  react  immediately  on  Boap-solutions,  precipitating  the 
oleate,  palmitate.  or  stearate  of  lime  at  once.  Magnesia  salts,  on  the  con- 
trary, require  some  considerable  time  for  reaction.  They  are.  however, 
more  powerful  hardeners  ;  one  equivalent  of  magnesia  salts  consuming  as 
much  soap  as  one  and  one-half  eouivalents  of  lime. 

The  presence  of  soda  and  potasn  salts  softens  rather  than  hardens  water. 
Each  grain  of  carbonate  of  lime  per  gallon  of  wat«r  causes  an  increased 
expenditure  for  soap  of  about  2  ounces  per  100  gallons  of  water.  iEng^g. 
J^erw.  Jan.  81. 1886.3 

Pniifyinfl;  Feed-^vrater  for  Steanfbollers*  (See  also  Incrus- 
tation and  Oori-oslon,  p.  710.>— Wheu  tlie  water  used  fur  steam-boilers  con- 
tains a  large  amount  of  scale-forming  material  it  is  usually  advisable  to 
purify  it  before  allowing  it  to  enter  the  boiler  rather  than  to  attempt  the 

Ererention  of  scale  by  the  introduction  of  chemicals  into  the  boiler.  Gar- 
onates  of  lime  and  ma^esia  may  be  removed  to  a  considerable  extent  bv 
simple  heating  of  the  water  in  an  exhaust-steam  feed-\7ater  heater  or,  still 
better,  by  a  live-eteam  heater.  (See  ci)*cular  of  the  Hoppes  Mfg.  Ck>.,  Bpring- 
fleld,  O.)  When  the  water  is  very  bad  it  is  best  treated  with  cfaemicala— 
lime,  soda-ash.  caustic  soda,  etc.— In  tanks,  the  precipitates  being  separated 
by  settling  or  filtering.    For  a  description  or  several  systems  of  water 

Suriflcation  see  a  series  of  articles  on  the  subject  by  Albert  A.  Cary  in  Bng^g 
fag.,  1897. 

Mr.  W.  B.  Ooggswell,  of  the  Sblvay  Process  Oo.'8  Soda  Works  In  Syracuse. 
K.  T.,  thus  describes  the  system  of  puriflcatlon  of  boiler  feed-water  in  use 
at  these  works  (Trans.  A.  S.  M.  E.,  xiii.  256): 

For  purifying,  we  use  a  weak  soda  liquor,  containing  about  18  to  16  grams 
Na^Coa  per  litre.  Say  lU  to  2  M*  (or  m  to  580  gals.)  of  this  liquor  Is  run 
into  the  precipitating  tanx.  Hot  water  about  60^  C.  is  then  turned  tn,  and 
the  reaction  of  the  precipitation  goes  on  while  the  tank  is  filling,  which  re- 

auires  about  16  minutes.   When  the  tank  is  full  the  water  is  filtered  through 
le  Hyatt  (4),  6  feet  diameter,  and  the  Jewell  (1),  10  feet  diameter.  Hi  ten  in 
80  minutes.    Forty  tanks  treated  per  24  hours. 

Ciharge  of  water  purified  at  once 85  M*.  9.275  gallons. 

Soda  in  purifying  reagent 15  kgs.  KatCOa. 

Soda  used  per  1,000  gallons &5lDs. 

A  sample  Is  taken  from  each  boiler  every  other  dav  and  tested  for  deg. 
Baum6,  soda  and  salt.    If  the  deg.  B.  is  more  than  2,  that  boiler  is  blown  to 
reduce  it  below  2  deg.  B. 
The  following  are  some  analyses  given  by  Mr.  Ooggswell ; 


Lake 

Water, 

grams  per 

litre. 

Mud  from 
Hyatt 
Filter. 

Scale  from 
Bollei^ 
tube. 

Soale 
found 

in 
Pump. 

CSalcium  sulphate. 

.261 
.186 
.091 
.016 
.087 
.68 

8.70 

61.84 

10  9 

Calcium  chloride. 

Cnlcium  c(irt)onate.  .  ...... 

68.87 
1.11 

19.76 
85.81 

87 

Magnesium  carbonate 

Magnesium  chloride 

Salt.NaCl 

.14 
8.80 
1.10 

Silica 

16.17 
8.75 

g 

Iron  and  aluminum  oxide. .  . 

1  8 

Total 

1.870 

87.10 

99.74 

90.0 

Softening;  Hard  "Water  for  liOcomotlTe  Use.— A  water-soft- 
ening f)iant  in  operation  i<t  Fossil,  in  Western  Wvoming,  on  the  Union  Pa- 
clflc  Railway,  is  described  in  Eng'g  NewSy  June  9, 1898.    it  is  the  Invention 


FLOW   OF   WATER.  555 

of  Arthur  Pennell,  of  Kansas  City*.  The  general  plan  adopted  is  to  first  dis- 
boIto  the  chemicals  in  a  closed  tank,  and  then  connect  this  to  the  supply  main 
so  that  its  contents  will  be  forced  into  the  main  tank,  the  supply-pipe  being 
so  arrani^  that  thorough  mixture  of  the  solution  with  the  water  is  ob- 
tained. A  waste-pipe  from  the  bottom  of  the  tank  is  opened  from  time  to 
time  to  draw  off  the  precipitate.  The  pipe  leading  to  the  tender  is  arranged 
to  draw  the  water  from  near  the  surface. 

A  water-tank  24  feet  in  diameter  and  16  feet  high  will  contain  about  46,600 
gallons  of  water.  About  three  hours  should  be  allowed  for  this  amount  of 
water  to  pass  through  the  tank  to  insure  thorough  precipitation,  giving  a 
permissible  consumption  of  about  15,000  gallons  per  hour.  Should  more 
than  this  be  required,  auxiliary  settling- tanks  should  be  provided. 

The  chemicals  added  to  precipitate  the  scale»formlng  impurities  are  so- 
dium  carbonate  and  quicklime,  varying  in  proportions  according  to  the  rela- 
tive propoilions  of  sulphates  ana  carbonates  in  the  water  to  be  treated. 
Suffleient  sodium  carbonate  is  added  to  produce  just  enough  sodium  sulphate 
to  combine  with  the  remaining  lime  and  magnesia  sulphate  and  produce 
glauberite  or  its'  corresponding  magnesia  salt,  thereby  to  get  rid  of  the 
sodium  sulphate,  which  produces  foaming,  if  allowed  to  accumulate. 

F6r  a  description  of  a  purifying  plant  established  by  the  Southern  Pacific 
R.  B.  Co.  at  Port  Los  Angeles,  Cal..  see  a  paper  by  Howard  Stlllmann  in 
Trans.  A.  8.  M.  £.,  vol.  zix,  Dec.  1897. 


HYDBACJLICS— FLOW  OP  WATKB. 

FormalsB  for  IHBcl&arse  ofHrmter  ttaoncli  Orlflees  and 

'Wetm.^For  rectangular  or  circular  orifices,  with  the  head  measured  from 
centre  of  the  orifice  to  the  surface  of  the  still  water  in  the  feeding  reservoir. 

g=aCV5HXa (l) 

For  weirs  with  no  allowance  for  increased  head  due  to  velocity  of  approach: 

Q^CH  V^OHX  LH. (8) 

For  rectangular  and  circular  or  other  shaped  vertical  or  inclined  orifices: 
formula  based  on  the  proposition  that  each  successive  horizontal  li»^er  ot 
water  passing  through  the  orifice  has  a  velocity  due  to  its  respective  head: 

Q=zeIHV2gXiVHb*-Vsi*) (8) 

For  rectangular  vertical  weirs: 

Q^eHV^gHxLh, (4) 

Q  =3  quantity  of  wat^r  discharged  in  cubic  feet  per  second;  C  s  approxi- 
mate coefficient  for  formulas  (1)  and  ('Z);  c  =  correct  coefficient  for  (8) 
and  (4). 

Values  of  thecoefflcients  c  and  Care  given  below. 

g  =3  82.16;  V^  =:  8.02;  H  ^  head  in  feet  measured  from  centre  of  orifice 
to  level  of  still  water;  Hb  =  head  measured  fix>m  bottom  of  orifice;  Ht  = 
head  measured  from  top  of  orifice;  hss  H^  corrected  for  velocity  of  ap- 

4  Va* 
proach,  Va,  =  £f -f  3  -- — ;  a  =  area  In  square  feet;  L  =  length  in  feet. 

Flow  of  Water  flrom  Ortflces*— The  theoretical  velocity  of  water 
fiowlng  from  an  orifice  is  the  same  as  tlie  velocity  of  a  falling  body  which 
has  fallen  from  a  height  equal  to  the  head  of  water,  =3  V^dgH,  The  actual 
velocity  at  the  smaller  section  of  the  vena  contraeta  is  substantially  the 
same  as  the  theoretical,  but  the  velocity  at  the  plane  of  the  orifice  Is 
C  V^^t  ^n  which  the  coefficient  C*has  the  nearly  constant  value  of  .69.  The 
smalfest  diameter  of  the  ve^ia  conttxtcta  is  therefore  about  .79  of  that  of  the 
oriilce.   If  C  be  the  approximate  coefficient  s  .68,  itDd  c  the  correct  ooeffi- 


656 


HYDRAULICS. 


etont,  the  ratio  -  Taries  with  different  ratios  of  the  head  to  the  dlamster 
c 

of  the  ▼ertfcal  orifice,  or  to  ~.    Hamilton  Smith,  Jr.,  givee  the  foUowfnff: 


For  5  =   .5 


.875 


1.5 


^  a. 9004   .9649  .9918   .9965   .9980 


2.5 
.9967 


.9907 


1. 


For  vertica]  rectangular  orifices  of  ratio  of  head  to  width  W\ 
For^s:    .6         .6        .8         1         1.5        8.        &        4.        &       a 

^  r=  .9488    .9657    .9688    .9690    .9968    .9974    .9968    .9998    .9998    .9096 

c 
For  IT-i-  D  or  JJ-»-  TTover  8,  O  =  c,  practically. 

Welsbach  ipives  the  following  yalues  of  c  for  circular  orificee  in  a  thin  wall. 
H  =  measured  head  from  centre  of  orifice. 


Dft 

Hft 

.066 

.88 

.88 

8.0 

8.0 

45. 

840. 

.(XlS 
.066 
.10 
.18 

.711 

.665 

.687 
.689 
.688 
.614 

.688 
.681 
.614 
.607 

.641 

.688 

.000 

For  an  orifice  of  D  s= 
effective  head  in  feet, 


.088  ft.  and  a  weU-rounded  mouthpiece,  H  being  the 


H=.066 

1.84 

11.5 

56 

888 

CS.0B9 

.907 

.975 

.994 

.904 

Hamilton  Smith,  Jr.,  found  that  for  great  heads,  818  ft.  to  886  ft.,  with  con. 
vencing  mouthpieces,  c  has  a  value  of  about  one,  and  for  smsJl  circular 
orifices  in  thin  plates,  with  full  contraction,  c  =  about  .60.  Some  of  llr. 
Smithes  experimental  values  of  c  for  orifices  in  thin  plates  discharging  into 
air  are  as  follows.    All  dimensions  in  feet 


Circular,  In  steel,  D  =  .080,  |  ^  = 
Circular,  in  brass,  D  =  .060,  |  ^  = 
Circular,  in  bra8s,D  =  .100,  |  ^  = 
Circular,  In  iron,  D  =>  .100,  \ 
Square,  in  brass,  .05  X  .05, 
Square,  in  brass,  .10  X  .10, 

For  the  rectangular  orifice,  L,  the  length,  is  horizontal. 

Mr.  Smith,  as  the  result  of  the  collation  of  much  experimental  data  of 
othera  as  well  as  his  own,  gives  tables  of  the  value  of  e  for  vertical  orifices, 
with  full  contraction,  with  a  free  dlBcharge  into  the  air,  with  the  inner  face 
of  the  plate,  in  which  the  orifice  is  pierced,  plane,  and  with  sharp  inner 
comers,  so  that  the  escaping  vein  onlv  touches  these  Inner  edges.  These 
tables  are  abridged  below.  The  coefficient  c  is  to  be  used  In  the  formulse  (8) 
and  (4)  above.    For  formuloB  (1)  and  (8)  use  the  coefficient  C7  found  from  the 

values  of  the  ratios  —  above. 
o 


Kectauj 


ular.  in  brass, 
DO.  W^=.050... 


:  .789 
:  .6495 
:   .186 
:   .6585 
:  .189 
;   .6337 
1.80 
.6061 
.818 
.6410 
:  .181 
.6898 
.861 
.6470 


8.43 
.6896 
.686 
.0865 
.457 
.6155 

1.81 
.6041 
.877 
.6888 
.930 
.6189 
.917 


8.19 

.6864 
1.74 

.6118 

.900 

.6006 
8.81 

.6088 
1.79 

.6157 
1.71 

.6084 
1.88 


8.T8 

.60n) 
1.T8 

.6048 
4.68 

.6026 
8.81 

.6187 
8.75 

.0078 
8.88 

.6180 


8.57  4.68 
.0060    .0051 

8.06  8.18 
.0088    .6095 


8.70  4.68 
.6118    .6097 

8.74  4.60 
.6060    .6065 

8.95  4.70 
.6176    .6168 


HYDBAULIO  FORMULAE. 


557 


Talnes  of  CoefleieBt  e  for  Vertle«l  OHflees  wltli  Sharp 
Bdces,  Full  Contraction,  and  Free  iHMliiarse  Into 
Air.     cHamilcon  Smith,  Jr.) 


Square  Orifloea.    Length  of  the  Side  of  the  Square,  In  feet 

.08 

.08 

.04 
.648 

.05 

.637 

.07 
.688 

.10 

.18 

.616 

.15 
.611 

.90 

.40 

.60 

.80 

1.0 

A 

.621 

.6 

.660 

.645 

.686 

.680 

.628 

.617 

.618 

.6IG 

.605 

.601 

.598 

.600 

1.0 

.648 

.686 

.628 

.628 

.618 

.613 

.610 

.em 

.606 

.608 

.601 

.600 

.509 

S.0 

.638 

.688 

.616 

.612 

.609 

.807 

.606 

.m 

.605 

.605 

:S8I 

.603 

fiOB 

6.0 

.628 

.616 

.612 

.609 

.607 

.605 

.605 

.6<R 

.601 

.604 

.60:^ 

.602 

10. 

.616 

.611 

608 

.606 

.605 

.604 

.604 

.603 

.608 

.603 

.608 

.602 

.601 

90. 

.606 

.606 

.004 

.603 

.608 

.602 

.602 

.608 

.602 

.601 

.601 

.601 

.600 

100.(T) 

.509 

.508 

.598 

.598 

.598 

.598 

.r.98 

.596 

.598 

608 

.598 

.698 

.598 

H. 

Circular  Orifices.    Diameters,  in  feet 

.OS 

.08 

.04 

.05  1  .07 

.10 

.12 
~^8 

.16 
.606 

.20 

.40 

.60 

.80 

I.O 

A 

.637i  .628 

.618 

.6 

.665 

.640 

.680 

.624!  .618 

.618 

.609 

.605 

.601 

.596 

.598 

.590 

1.0 

.644 

.681 

.088 

.617,  .612 

.608 

.605 

.608 

.600 

.598 

.596 

.599 

.591 

S. 

.663 

.681 

.614 

.610l  .607 

.604 

.601 

.600 

.599 

.599 

.597 

.596 

.596 

4. 

.688 

.614 

.609 

.605 

.608 

.60S 

.600 

..'S09 

.609 

.698 

.597 

.597 

.696 

6. 

.618 

.611 

.607 

.604 

.608 

.600 

.599 

.609 

.508 

.698 

.507 

.506 

.606 

10. 

.611 

.606 

.603 

.601 

.599 

.696 

.598 

.597 

.597 

.597 

.596 

.596 

.606 

«0. 

.601 

.600 

.509 

.598 

.597 

.59fl 

.596 

.596 

.596 

.596 

.596 

.695 

Mi 

«).(?) 

.5(Ki 

.506 

.596 

.605 

.594 

.594 

.594 

.504 

.594 

.604 

.694 

.503 

.598 

no.(f) 

.50a<  .608 

.602 

.688'  .592*    5921  .598'  .692>  .592>  .608'  .591^ 

.508 

.690 

KTnSATIilC  FOA!n[I7IiuE:.-FIiOW  OF  UTATBII  IN 
OPBN  AND  OliOSBB  OKANNBI^S. 

Flo-w  of  "Water  in  Pipes*— The  quantity  of  water  discharged 
through  a  pipe  depends  on  the  "head;"  that  is,  the  vertical  distance  be- 
tween the  level  surface  of  still  water  in  the  chamber  at  the  entrance  end  of 
the  pipe  and  the  level  of  the  centre  of  the  dischari^e  end  of  the  pipe ; 
also  upon  the  length  of  the  pipe,  upon  the  character  of  Its  interior  surface 
as  to  smoothness,  and  upon  the  number  and  sharpness  of  the  bends:  but 
It  is  independent  of  the  position  of  the  pipe,  as  hori2ontal,  or  inclined 
upwards  or  downwards. 

The  head,  instead  of  being  an  actual  distance  between  levels,  may  be 
caused  by  pressure,  as  by  a  pump,  in  which  case  the  head  is  calculated  ks  a 
rertical  distance  corresponding  to  the  pressure  1  lb.  per  sq.  in.  =  2.809  ft. 
head,  or  1  ft  head  =  .488  lb.  per  sq.  in. 

The  total  head  operating  to  cause  flow  is  divided  Into  three  parts:  1.  The 
v^ocUy-head^  which  is  the  height  through  which  a  body  must  fall  in  vacuo 
to  acquire  the  velocity  with  which  the  water  flows  into  the  pipe  =  t^  h-  2(7,  in 
which  V  is  the  velocity  in  ft.  per  sec.  and  9g  =  64.88;  2.  the  entry-head,  that 
required  to  overcome  the  resistance  to  entrance  to  the  pipe.  With  sharp- 
edged  entrance  the  entry-head  =  about  ^  the  velocity-head;  with  smooth 
rounded  entrance  the  entry-head  is  inappreciable;  8.  %h» /riction-head^  due 
to  the  frictional  resistance  to  flow  within  the  pipe. 

In  ordinary  cases  of  pipes  of  considerable  length  the  sum  of  the  entr>*and 
velocity  heads  required  scarcely  exceeds  1  foot.  In  the  case  of  long  pipes 
with  low  heads  the  sum  of  the  velocity  and  entry  heads  is  generally  so  small 
that  it  mi^  be  neglected. 

deneral  Formula  Ibr  Flo^vr  of  Water  In  Ptpee  or^^ondiilts* 
Mean  velocity  in  ft.  per  sec.  =  c  j/mean  hydraulic  radfus  x  slope 

Do.  for  pipes  running  full  =  ci/^l^I^^^X  slope, 
Id  which  6  Is  a  ooefllolent  determined  by  experiment.    (See  pages  560-604.) 


55« 


tttDllAtTLlOS. 


wet  perittietef* 

Iti  ptpm  ninnftiv  fnll,  or  exactly  h&lf  full,  and  In  Beraldreular  open  cha» 
Dels  running  full  it  is  equal  to  ^  diameter. 

The  MOpd  >fe  Ih6  iieftd  (oi*  pusMure  6it|>rM»sd  all  A  )ie«id,  Ifi  Met) 

-4-  lensrth  of  pipe  measured  in  a  straight  line  from  end  to  end. 

In  open  channels  the  slope  is  the  actual  slope  of  the  surface,  or  its  taW  per 
unit  of  length,  or  th«  sine  of  the  angle  of  the  slope  ^ith  the  hofison. 

R  r  =  mean  hydraulic  mdius^  a  =  slope  =  head  -«-  length^v  s±  velocity  In 
feet  per  sipcond  'all  dimensions  in  feetX  v  c  c  f^  f^  a  c  j/r$. 

<|tuitiitti|r  bf  Tt^Ater  Di*c]&ar8«d»  -If  Q  *=  dtsohaic*  in  cubic  feet 
per  fte^ond  ahd  a  »  Af^  of  ehattkiel,  ^  a  at;  s  otf  V*^ 


a  Vr 


ts  appl-ozimatelir  proportional  to  the  < 
4i*eBbondin^  to  i9/4D  of  the  diameter> 


discharge.   It  ts  a  nMutimum  a; 


306**,  correB|x>iidin^  to  i9/4D  of  the  diameter>  and  the  flow  of  a  conduit  1 V^ 
full  is  4boui  b  pel"  ceni  greater  than  that  oC  otte  completely  filled. 

Tftble  slTliis  PiiU  in  F«et  per  Bllle,  the  lM«t»nve  on  Slope 
correepotidllifl:  to  H  li^kIl  Of  1  IPt.,  aikd  alBO_the  Values 
or  •  and  V«  ^or  Vme  in.  the  Vormala  e  =  e  Vr«« 

» :^  H^  L  =  «ine  of  angle  of  slope  «b  fttU  of  waler-eurfaoe  <£0i  to  Miy  dis- 
tance (L),  divided  by  that  dtetanoe. 


Palllki 

fto 

Sine  Of 

VS. 

Fall  IB 

(Mope, 

Slue  of 

Feet^ 

Slope, 

Feet 

1  pSot 

Slope. 

VJ. 

per  HI. 

fta 

s. 

per  Ml. 

Hi 

a. 

«.« 

siian 

.0M0478 

.006681 

17 

810.6 

.0088197 

.056742 

.80 

ITCrthl 

.O0OOt^ 

.007588 

18 

fl93.8 

.0091091 

.058S»{ 

AO 

l?i.h»l 

.0000758 

.00^704 

19 

277.^ 

.0085965 

.068988 

:S 

lO'H^J 

iSSoiFsl 

.009731 

99 

£64 

.0087870 

.091646 

kyn) 

.010660 

4» 

240 

.0041667 

.064549 

::r^(i 

.oooViSSd 

.011532 

^ 

-xso 

.0046455 
.^049241 

.067419 

.w^ 

jL.'niVl 

!(X)015^^4 

.012847 

» 

m.\ 

*9d4 

^'-■v^ 

.0001^12 

.013085 

28 

188.« 

.0068690 

i! 

:'^sn 

:d002»7 

.013762 

80 

176 

.0056818 

.97^878 

I.t5 

4-Jf 

.01SW6 

«?i.8e 

ifiO 

.0006067 

.081660 

li 

:i'.;t.) 

.<)002841 

.016851 

40 

192 

,0076798 

.087099 

r{..M7 

.0008314 

.«1S205 

44 

120 

.0083888 

.091287 

« 

!■*;  ^h 

.ood.3r«B 

.0l^N68 

48 

110 

.0090909 

.099840 

2.25 

■-.':;  sr 

.00^261 

.020641 

62.8 

100 

.010 

.1 

2.5 

'J  1 : .' 

.O004V35 

.t)2l760 

05 

88 

.0113686 

.1089 

2.75 

lu,.^ 

.0005208 

.052822 

06 

80 

.W26 

.111809 

8. 

1^ 

.000M82 

.0288S7 

^.4 

76 

.0183888 

.116470 

8.26 

1625 

>0006154 

.024807 

90 

08 

.0161516 

108091 

8.5 

\^ 

.0006631 

.«25751 

^ 

60 

.0109087 

.I»l 

8.75 

.O0(W108 

.026650 

96 

66 

.0181818 

1948S9 

4 

1830 

.0007576 

.027524 

)05.« 

60 

.62 

141421 

I 

1056 

.0009470 

.0*)778 

120 

44 

.0227278 

.1S0«»9 

880 
7M.8 

.0011364 
.0013257 

.0887! 
.036416 

182 
160 

S 

.085 

.168114 
.174077 

.0808(00 

M 

.16015154 

.088925 

220 

24 

.0(10667 

.1W419I 

9 

586.6 

.0017014 

.041286 

264 

^ 

.06 

.298607 

W 

528 

.6018939 

.048519 

880 

16 

.0026 

.26 

11 

448.6 

.0020883 

.045648 

440 

K 

.0888888 

.2B06'<6 

It 

440 

.<M?678 

628 

W 

.1 

910^8 

1? 

406.1 

.0084621 

.04962 

660     ^ 

8 

.m 

.863668 

14 

ft^.l 

.tJ0265l5 

.051493 

880     ' 

« 

■T08O061 

.468988 

16 

85t 

.0028409 

.0588 

1066 

6 

.2 

447214 

16 

380 

.0080808 

.065048 

1820 

4 

.26 

.6 

HYDBAULtC  tOnUVLJR.  W9 

r  =  mean  hydraulic  depth  =  ^ZjTinjaf^.  =  H  diam.  tot  circular  pipes  run- 
nVng  full  t^t  ekadtl/  ttftlC  fUlL 


Dlam., 
a.  fe. 

ill  Feet. 

1 

Diam., 
ft.  In. 

id  Feet. 

Diam.t 
ft.  ib. 

in  Feet. 

D4amv, 
ft.  iit. 

in  F^t. 

H 

;O0B 

9 

.ro7 

4      6 

1.081 

9 

1.800 

'  V 

;108 

2      1 

.7122 

4     T 

1.070 

9      8 

1.821 

1  n 

.1S6 

2     li 

.7:16 

4      6 

I1O8O 

9     « 

l.Ml 

1 

.144 

9     * 

.TBD 

4     9 

1.089 

9      9 

1.981 

i 

.161 

i  t 

.TC4 

4    10 

1.099 

10 

1.981 

.m 

.777 

t" 

1.109 

10     8 

1.601 

■191 

B     6 

.TW 

1.118 

10     8 

1.620 

2 

.904 

8    r 

.601 

B      1 

I.W 

10     9 

1.689 

2^ 

.988 

I  1 

2  10 

.817 

0     S 

1.187 

H      ^ 

1.658 

B 

4 

:% 

.829 

.M2 

S  J 

1.146 

1:1S 

li     1 

i 

■^ 

2    11 

.854 

n 

\l     I 

!tl4 

a 

.866 

i.m 

.782 

7 

.us 

8     1 

.R'TB 

1.181 

12    h 

.m 

8 

9 

10 

:S 

11 

.918 

1 1 

n? 

m 

12      6 
12     9 

IB 

l.TtW 

i.Tte 

1.088 

11 

479 

.924 

1.916 

18     8 

a 

1 

1500 

i  f 

.935 

6 

1.225 

18     6 

1    1 

.946 

6     8 

1.260 

H 

|.«ti 

1    2 

•^1 

s  s 

.9.'57 

6     6 

1.275 

14      8 

1    8 

.968 

6     9 

1.299 

15 

9^ 

1    4 

if 

8    10 

.979 
.990 

h 

1:^ 

IS  • 

^.968 

.ol8 

1. 

.369 

18     8 

i'Ml 

,Q>M 

4      1 

1.010 

If 

1? 

2.061 

1    8 

.64$ 

il 

l.OM 

8 

17     6 

.2.091 

1^ 

•v9l 

1.081 

11 

J? 

$.151 

.1577 

1.041 
1.051 

i  4b8 

19 

S.180 

.m 

4     6 

1.479 

90 

2.238 

TattMk  4»f  tlk«  €6^a«i«li8  t^  tOhlefls*  condensed  ttom  P,  J.  Flyton 
on  Flow  of  Watei-.)— Ahnwit  ail  ihv  old  hydraitlfo  ft>rti«»lfle  ft>r  flndlHfr  the 
mean  veMiHty  inob<9n  Hhd  Closed  channels  have  constant  coefficietacsH  4nd  ara 
therefore  correct  for  only  h  sinail  ratie^  nf  chaartels.  Thej^  have  often  been 
found  to  gf v«  Itacofrect  reautto  with  dlsastrotis  effects.  Qtuiif uillet  and  Kut* 
ter  thorouf^hly  InvestiKated  the  Aniei-fcan,  Frent^h^  and  nthef  ekpeiiinenta, 
and  they  tt^y^  ^  the  reMUt  cf  tlieir  labors  the  formula  now  geneitiUy  known 
as  Kntt^r"!  fermilta.  There  Are  so  many  i^ryingt  Coliditicne  aifectlnff  the 
flow  of  watisf,  that  all  hydirauHc  f ottnuidB  afe  only  eppmziknattoAB  to  Iho 
correct  result. 

mieii  the  eb¥fftc«-Mc^  tn<Nisttr«meMt  H  tfood,  Ktttteir*s  ferniula  will  give 
n^sulis  seldom  exceeding  7^  error,  provided  the  rugosity  coefficient  of  the 
forrnuM  H  lrtk<^Wn  fbr  the  site.  For  small  o|»en  channeto  D' Ally's  and 
Bazin's  formulil^,  ahd  fOf  Catot-lVOh  pit)ee  D*Arcy*B  fM^mliM^  aro  jrenenOiy 
siVfophftd  aa  b^iH^  ap|»roltlhiateiy  CoTheistk 

K  oner's  Fonaillli  for  meaatires  te  fctet  la 


«;«' 


.         n     '  ^      » 

*  ,  /a,  »  .   .00281\        J!l.   1 


■  X  4^ 


in  wMeh  « «fe  im^lll  ^daty  &  fcet  1^  «Mohd ;  ^  ^  -  «  hyiinuitfo  mean 


560  HYDRAULICS. 

depth  in  feet  s  area  of  cross-section  in  square  feet  divided  by  wetted  perim- 
eter in  lineal  feet ;  »  =  fall  of  water-surface  (/i)  in  any  distance  (2)  divided 

by  that  distance,  =  r«  =  sine  of  slope ;  n  =  the  ooef&cient  of  rugosity,  de- 

peodiDg  on  the  nature  of  the  liuinf?  or  surface  of  the  channel.  If  we  let  the 
first  term  of  the  right-hand  side  of  the  equation  equal  e,  we  have  Cbezy's 
formula,  t»  =  c  Vr»  ^cX  \^'  X  V** 

Valaen  ofn  in  K  otter's  Formiala*— The  accuracy  of  Kutter^s  for- 
mula depends,  in  a  great  measure,  on  the  proper  selection  of  the  coefBcieut 
of  roughness  n.  Experience  is  required  in  order  to  give  the  right  value  to 
this  coefficient,  and  to  this  end  great  assistance  can  be  obtained,  in  making 
this  selection,  by  consulting  and  comparing  the  results  obtained  from  ex- 
periments on  the  flow  of  water  already  made  in  different  channels. 

In  some  cases  it  would  be  well  to  provide  for  the  contingency  of  future 
deterioration  of  channel,  by  selecting  a  high  value  of  n,  aa.  for  Instance, 
where  a  dense  growth  of  weeds  is  likely  to  occur  in  small  channels,  and  alito 
where  channels  are  likely  not  to  be  kept  in  a  state  of  good  repair. 

The  following  table,  giving  the  value  of  n  for  different  materials,  is  com- 
piled from  Kuiter,  Jackson,  and  Bering,  and  this  value  of  n  applies  also  in 
each  instance,  to  tiie  surfaces  of  other  materials  equally  rough. 

Value  of  n  im  Kittter^s  Formula  fob  Different  Chaicvklb. 

n  =  .009,  well-planed  timber,  in  perfect  order  and  alignment ;  otherwise, 
perhaps  .01  would  be  suitable. 

It  =  .010,  plaster  in  pure  cement :  planed  timber  :  glazed,  coated,  or  en- 
amelled stoneware  and  iron  pipes ;  glazed  surfaces  of  every  sort  in  perfect 
order. 

n  =  .011,  plaster  in  cement  with  one  third  sand,  in  good  condition  ;  also  for 
iron,  oemeni,  and  terra  cotta  pipes,  well  joined,  and  in  best  order. 

n  =  .012,  unplaoed  timber,  when  perfectly  continuous  on  the  inside ; 
flumes. 

n  =  .018,  ashlar  and  well-laid  brickwork  ;  ordinary  metal ;  earthen  and 
stoneware  pipe  in  good  condjtion,  but  not  new  ;  cement  and  terra-ootta  pipe 
not  well  Jomted  nor  in  perfect  order  ,  plaster  and  planed  wood  in  ini  perfect 
or  Inferior  condition  ;  and,  generally,  the  materials  mentioned  with  n  =  .010, 
when  in  imperfect  or  inferior  condition.  , 

n  =  .015,  second  class  or  rough-faced  brickwork  ;  well-dressed  stonework  ; 
foul  and  slightly  tuberculated  iron  :  cement  and  terra-ootta  pipes,  with  im- 
perfect Joints  and  in  bad  order  ;  and  canvas  lining  on  wooden  frames. 

u  =  .017,  brickwork,  ashlar,  and  stoneware  in  an  inferior  conditaon  ;  tu- 
berculated iron  pipes  ;  rubble  in  cement  or  plaster  In  good  order  ;  fine  gmveU 
well  rammed,  Mt  to  ^  inch  diameter ;  and,  generally,  the  materials  men- 
tioned with  11  =  .018  when  in  bad  order  and  condition. 

n  =:  .030,  rubble  in  cement  in  an  inferior  condition  ;  coarse  rubble,  rough 
set  in  a  normal  condition ;  coarse  rubble  set  dry  ;  ruined  brickwork  and 
masonry ;  coarse  gravel  well  rammed,  from  1  to  1 U  inch  diameter  ;  conals 
with  beds  and  banks  of  very  firm,  regular  gravel,  carefully  trimmed  and 
rammed  in  defective  places  ;  rough  rubble  with  bed  partially  covered  with 
silt  and  mud  ;  rectangular  wooden  troughs,  with  twtteos  on  the  inside  two 
inches  apart ;  trimmed  earth  in  perfect  order. 

n  =  .OSBiti,  canals  in  earth  above  the  average  in  order  and  regimen. 

n  =  .0*<i5.  canals  and  rivers  in  earth  of  tolerably  uniform  cross-section  ; 
slope  and  direction,  in  moaerately  good  order  ana  regimen,  and  tree  from 
stones  and  weeds. 

n  =  .0J75,  canals  and  rivers  in  earth  below  the  average  in  order  and  regi- 
men. 

n  =  .000,  canals  and  rivers  in  earth  in  rather  bad  order  and  regimen,  hav- 
ing stones  and  weeds  occasionally,  and  obstructed  by  detritus. 

n  =  .086,  suitable  for  rivers  and  canals  with  earthen  beds  in  bad  order  and 
regimen,  and  having  stones*  and  weeds  in  great  qu&mi  Jee. 

n  =  .06,  torrents  encumbered  with  detritus. 

Kutier's  formula  has  the  advantage  of  being  easily  adapted  to  a  change 
in  the  surface  of  the  pipe  exposed  to  the  flow  of  water,  by  a  change  in  the 
value  of  n.  For  cast-iron  pipes  it  is  usual  to  use  n  =  .018  to  provide  tor  the 
future  deterioration  of  the  surface.  _ 

Reducing  Kutter's  formula  to  the  form  v  ==  c  X  Vr  X  V«,  and  taking  n,  the 
coefficient  of  roughness  in  the  formula  =  .011,  .012,  and  .018,  and  s  =■  .001,  wt^* 
have  the  following  values  of  the  coefficient  c  for  different  diameters  of 
conduit. 


HYDRAULIC  FORMULAE. 


561 


Values  of  r  in  Formula  «  =  e  x  Vr  x  Vstor  Metal  Pipes  and 
Moderately  Smooth  Condnfta  Generally. 

By  KuTTER*8  FoRHUUL    (<  =  .001  or  greater.) 


Diameter. 

71  =.011 

n  =  .012 

n  =  .oia 

Diameter. 

n  =  .011 

n  =  .012 

n  =  .013 

ft.    in. 

c  = 

c  = 

c  = 

ft. 

c  = 

e  = 

<;  = 

0       1 

47.1 
61.6 
77.4 
87.4 

7 
8 
9 
10 

152.7 
165.4 
157.7 
159.7 

189.2 
141.9 
144.1 
146 

127.9 

8 

180.4 

4 

182.7 

6 

77.5 

69.5 

134.6 

105.7 

94.6 

85.8 

11 

161.6 

147.8 

186.8 

1        6 

116.1 

104.8 

94.4 

12 

168 

149.8 

137.7 

128.6 

111.8 

101.1 

14 

165.8 

152 

140.4 

188.6 

120.8 

110.1 

16 

168 

151.2 

142.1 

140.4 

127.4 

116.5 

18 

169.9 

156.1 

144.4 

145.4 

m.8 

121.1 

SO 

171.6 

167.7 

146 

149.4 

186.1 

124.8 

For  circular  pipes  the  hydraulic  mean  depth  r  equals  ^  of  the  diameter. 

According  to  Kutter's  formula  the  value  of  c,  the  coefflcient  of  dischaifre, 
is  the  Bame  for  all  slopes  greater  than  1  in  1000;  that  is,  within  these  limits 
c  is  constant.  We  further  And  that  up  to  a  slope  of  1  in  2640  the  value  of  c 
is,  for  all  practical  purposes,  constant,  and  even  up  to  a  slope  of  1  in  6000 
the  difference  in  the  value  of  c  is  very  little.  This  is  exemplified  in  the 
following : 

Talne  of  e  for  IHflrerent  Talaes  of  Vr'and  «  in  Hatter's 
Formnla,  witb  n  =  .01 3. 


V  = 

ei^xV*. 

Slopes. 

Vr 

1  in  1000 

1  in  2500 

1  in  3838.3 

1  in  6000 

1  in  10.000 

.6 

1 
2 

93.6 
116.6 
142.6 

91.6 
115.2 

14'i.8 

90.4 
114.4 
148.0 

88.4 
118.2 
148.1 

88.8 
109.7 
143.8 

The  reliability  of  the  values  of  the  coefflcient  of  Kutter's  formula  for 
pipes  of  less  than  6  in.  diameter  is  considered  doubtfuL  (See  note  under 
lable  on  page  564.) 

ITalnes  of  e  for  Earthen  Cliannelsy  by  Kntter^s  Formula, 
for  Use  in  Formnia  v  =  c  |/rg. 


Coefficient  of  Roughness, 

Coefficient  of  Roughness, 

n  =  .0225. 

n  =  .036. 

Vr  Id  teet. 

4'r  in  feet. 

0.4 

1.0 

1.8 

2.5 

4.0 

0.4 

1.0 

1.8 

2.6 

4.0 

Slope,  1  in 

c 

c 

c 

c 

c 

c 

c 

c 

c 

c 

1000 

85.7 

62.5 

80.8 

89.2 

99.9 

19.7 

37.6 

61.6 

69.8 

69.2 

1250 

a%  5 

62.8 

80.8 

89.3 

100.2 

19.6 

87.6 

61.6 

59  4 

694 

1667 

85.2 

62.1 

80.3 

89.5 

100  6 

19.4 

87.4 

51.6 

69.6 

69.8 

2600 

84.6 

61.7 

80.8 

89.8 

101.4 

19.1 

87.1 

61.6 

69.7 

^0.4 

8833 

84. 

61.2 

80.3 

90.1 

102.2 

18.8 

86.9 

61.6 

50.9 

71.0 

6000 

83. 

60.6 

80.8 

90.7 

108.7 

18.8 

86.4 

61.6 

60.4 

72.2 

7S00 

81.6 

59.4 

80.3 

91.5 

106.0 

17.6 

35.8 

61.6 

60.9 

78.9 

10000 

80.6 

58.6 

80.8 

92.3 

107.9 

17.1 

85.3 

61.6 

60.6 

75.4 

15640 

•28.5 

56.7 

80.2 

93  9 

112.2 

16.2 

84.8 

61.6 

62.5 

78.6 

20000 

27.4 

66.7 

80.2 

H.S 

116.0 

15.6 

33.8 

51.5     63.1 

80.6 

562 


HYDRAULICS. 


M^  Molesworth,  In  the  asd  edition  of  hie  *' Pocket-book  of  EnglneenuiK 
FormulBB,"  gives  a  modlflcatlon  of  Kutter'8  formula  as  follows:  For  flow  in 
cast-iron  pipes,  vac  Vrs,  Id  which 


In  which  d  s  diameter  of  the  pipe  in  feet 
(This  formula  was  given  incorrectly  in  Blolesworth's  «lst  edition.) 
moleanrorth's  FomBalm.~v  s  Vlers^  in  which  the  values  of  I;  are 

as  follows : 


Nature  of  Channel. 

Values  of  k  for  Velocities. 

Less  than 
4  ft.  per  sec. 

More  than 
4  ft.  per  sec 

Brickwork 

8800 

WOO 
6400 
5800 

8600 

]^rth                  .......   r  «.  *  ..  T  ,  T  t  .  - 

6800 

Shingle 

6000 

Rougli,  with  bowlders 

4700 

In  very  large  channels,  rivers,  etc.,  the  description  of  the  channel  affecta 
the  result  so  slightly  that  it  may  be  practically  neglected,  and  k  assumed  ss 
from  8600  to  9000. 

Flynn'B  Formalm.— Mr.  Flyun  obtains  the  following  expression  ot 
the  value  of  Kutter's  coefficient  for  a  slope  of  .001  and  a  vaiae  of  n  s  .OlS : 


c  =  . 


188.72 


1  + 


(.018v 


The  following  table  shows  the  close  agreement  of  the  values  of  c  obtained 
from  Kutter's,  Holeswortb's,  and  Fiyun's  forroulsB  : 


Diameter. 
6  inches 
6  Inches 
4  feet 
4  feet 
8  feet 
8  feet 


Slope, 
lln  40 
1  in  1000 
lln  400 
1  in  1000 
lln  TOO 
lln  2600 


Kutter. 
71.60 
09.60 

117. 

116.6 

180.5 

1S0.8 


Moleswortb. 

71.48 

60.79 
117. 
116.65 
180.68 
129.08 


Vlyrm, 
09.5 
00.5 
116.6 
116.6 
180.5 
180.6 


Mr.  Flynn  gives  another  simplified  form  of  Kutter^s  formula  for  use  with 
different  values  of  n  as  follows : 


'  =  (,  +  («/x-^))^ 


t^ 


In  tbe  tollowtngteble  tbe  value  of  f  Is  glTen  for  tbe  several  values  of  » ; 


n 

K 

n 

K 

n 

K 

n 

K 

n 

K 

.009 
.010 
.011 

245.68 
225.51 
209  06 

.012 
.018 
.014 

106.88 
188.72 
187.77 

.015 
.016 
.017 

165.14 
157.6 
150.94 

.018 
.019 
.020 

145.08 
189.78 
1^.96 

.081 
.022 
.0226 

180.65 
196.79 
124.9 

If  in  the  application  of  Mr.  Flynn*B  formula  given  above  within  the  limit* 
of  n  as  given  iu  the  table,  we  substitute  for  n,  Kt  and  Vr  their  TalUM.  WO 
have  a  simplified  form  of  Kutter's  formula. 


HYDHAtTLIO  PORHUL^.  563 

For  instance,  when  n  s  .011,  and  cf  =  8  feet,  we  have 

„ 209.05  V   ,/- 


1  + 


HxiJ)' 


Baali&^s  FormialflBt 

For  Tery  ev<3Q  surfaces,  liae  plastered  sides  and  bed,  planed  planks,  etc.. 


=  i/l  -I-  .0000045(10.16  +  J.)  X  V>7. 


For  even  surfaces  such  as  cut-stone,  brickwork,  unplaned  planUnfc,  mortar, 
etc. : 


V  =  i/l  H-  .000018(4.864  +  J)  X  Vrs. 
For  sUfifhtly  uneveo  surfaces,  such  as  mbUe  masonry : 


V  =  1/1 -♦■.00006(1.819  +  ;)  X  Vrs. 
For  uneren  surfaces,  such  as  earth : 


f  =  i/l  -I-  .00086(o.8488  +  i)  X  Vrs. 


V  : 

A  modification  of  Basin's  formula,  known  as  D'Arcy^s  Basin's : 


-i/i 


10008 


.085S4r  +  0.85 

For  small  channels  of  less  than  20  feet  bed  Basfn's  formula  for  earthen 
channels  in  rood  order  gives  very  fair  results,  but  Kutter^s  formula  is  Bupei-<- 
sedinK  it  in  almost  all  countries  where  Its  accuracy  has  been  investigated. 

ThH  last  table  on  p.  561  RhowH  the  value  of  c,  in  Kutter*s  formula,  for  a  wide 
range  of  channels  in  earth,  that  will  cover  anything  likely  to  occur  in  the 
ordinary  practice  of  an  engineer. 

D* Arey's  FormnlA  for  clean  iron  pipes  under  pressure  is 


Flynn's  modification  of  D*Arcy's  formula  is 
„_/l66256d[\^y  w~ 


in  which  d  =:  diameter  In  feet. 

D'Arcy's  formula,  as  given  by  J.  B.  Francis,  C.E.,  for  old  cast-iron  pipe, 
lined  with  deposit  and  under  pressure,  is 

\.0082<12d  +  1  /     * 
ltynn*B  modification  of  D*Arcy^s  formula  for  old  cast-iron  pipe  is 


564 


HYDRAULICS. 


For  Pipes  I<e«i  jIMan  6  Inelies  In  mameter,  coefflcients  (c) 
In  the  formula  v  =  e  Vrs,  from  the  formula  of  D'Arcy,  Kutter,  and  Fannini?. 


Diam. 

in 
inches. 

D'Arcy. 

for  Clean 

Pipes. 

Kutter, 

for 
n  =  .011 
*=.O01 

Fanning, 

for  Clean 

Iron 

Pipes 

Diam. 

in 
inches 

D*APcy, 

for  Clean 

Pipes. 

Kutter, 

for 
n  =  .011 
«  =  .001 

Fannini?, 

for  Clean 

Iron 

Pipes. 

k 

50.4 
66.7 
74.5 
8Q.4 

84.8 
88.1 

33. 

ao.i 

42.6 
47.4 
51.9 
65.4 

80.4 
88. 

4 

5 

90.7 
92.9 
96.1 
98.5 
101.7 
103.8 

58.8 

61.5 

66. 

70.1 

77.4 

88.9 

925 

M.8 

96.6 
108.4 

Mr.  Flynn,  in  giving  the  above  table,  says  that  the  facts  show  that  the  co- 
efflcifnts  diminish  from  a  diameter  of  5  inches  to  smaller  diameters,  and  it 
is  a  safer  plan  to  adopt  coefficients  varying  with  the  diameter  than  a  con- 
stant coefficient.  No  opinion  is  advanced  as  to  what  coefflcients  should  be 
used  with  Kutter's  formula  for  small  diameters.  The  facts  are  simply 
stated,  givini;  the  results  of  well-known  authors. 

Older  FormnlaD.— The  following  are  a  few  of  the  many  fomiulse  for 
flow  of  water  in  pipes  given  by  earlier  writers.  As  they  have  constant  coef- 
ficients, they  are  not  considered  as  reliable  as  the  newer  formulae. 


Prony,  »  =  97  Vw  -  .08; 


Eytelwein,    v  =  60 


l  +  bOdC 


or    V  =  106^^-0.18; 


Hawksley, 


"-^/iS 


64d' 


NeviUe, «  =  140  Vri  -  11  Vri. 


In  these  formulas  d  =  diameter  in  feet;  7t  =  head  of  water  In  feet;  I  = 
leuftth  of  pipe  In  feet;  a  =  sine  of  slope  =  -y-;  r  =  mean  hydraulic  depth, 

=  area  •+■  wet  perimeter  =  —  for  circular  pipe. 

Mr.  Santo  Crimp  (Eiig'g,  August  4, 1898)  states  that  observations  on  flow 
in  brick  sewers  show  that  the  actual  discharge  la  88%  greater  than  tliat  csl- 
culated  by  Eytelwein's  formula.  •He  thinks  Kutter's  formula  not  supeHor 
to  D'Arcy's  for  brick  sewers,  the  usual  coefficient  of  roughness  m  the 
former,  viz.,  .018,  being  too  low  for  large  sewers  and  far  too  small  in  the  case 
of  small  sewers. 

D'Arcy's  formula  for  brickwork  la 


m  \    *  r  ^ 


0087285;    .B  =  .229668. 


.VBLOCITY  OF  WATBR  IN  OPBN  CHANNBI.S. 

Irrlipailoii  Canals.— The  minimum  mean  velocity  required  to  prevent 
the  (Ifpo.sit  o(  fiilt  or  the  erowth  of  aquatic  plants  is  in  Northern  India 
taken  at  1\4  feet  per  second.  It  is  stated  that  in  America  a  higher  velocity 
is  required  for  this  purpose,  and  it  varies  from  8  to  8^  feet  per  second.  Tht* 
niaxunum  allowable  velocity  will  vary  with  the  nature  of  the  soil  of  tlie 
bed.  A  sandy  bed  will  be  disturbed  if  the  velocity  exceeds  8  feet  per 
second.  Oood  loam  with  not  too  much  sand  will  bear  a  velocity  of  4  feet 
per  second.  The  Cavour  Canal  in  Italy,  over  a  gravel  bed,  has  a  velocity  of 
about  5  per  second.    (Flvnn's  "  Irrifratron  Canals.''*) 

Mean  Surfkce  and  Bottom  Veloeltles.— According  to  the  for- 
mula of  Baziu, 

V  =  vmu  -  85.4  i'ra;   v  =  vb  +  10.87  Vre, 


VELOCITY  OF   WATER  IN  OPEN  CHANKEL8.        565 


.'.  vb  =  V  -  10.87  i^,  in  which  v  =  mean  velocity  in  feet  per  second, 
v«ax  ^  niaziiuum  surface  velocity  In  feet  per  second,  vb  =  bottom  velocity 
in  feet  per  second,  r  =  hydraulic  mean  depth  in  feet  =  area  of  cross-sectlou 
in  square  feet  divided  by  wetted  perimeter  in  feet,  8  =  sine  of  slope. 

The  least  velocity,  or  that  of  the  particles  in  contact  with  the  bed,  is 
almost  as  much  less  than  the  mean  velocity  as  the  greatest  velocity  Is 
greater  than  the  mean. 

Rankine  states  that  in  ordinary  cases  the  velocities  may  be  taken  as  bear- 
ing to  each  other  nearly  the  proportions  of  S,  4,  and  6.  In  very  slow  cur- 
rents  they  are  nearly  aa  2,  8,  and  4. 

Sttfe  jBottom  and  Mean  Velocities*— Ganguillet  &  Kutter  give 
the  following  table  of  safe  bottom  and  mean  velocity  in  channels,  calcuUted 
from  the  formula  v  s=vb  +  10.87  Vr«: 


Material  of  Channel. 


Soft  brown  earth , 

Soft  loam 

Sand 

Gravel 

Pebbles 

Broken  stone,  flint    

Conglomerate,  soft  slate. 

Stratified  rock 

Hard  rock 


Safe  Bottom  Veloc 

Mean  Velocity  v. 

ity  vb.  In  feet 

in  feet  oer 
second. 

per  second. 

0.240 

0.9m 

0.400 

0.656 

1.000 

1.318 

1.096 

8.685 

2.000 

8.088 

4.008 

6.670 

4.088 

6.664 

6.006 

8.804 

10.000 

18.127 

Ganguillet  &  Kutter  state  that  they  are  unable  for  want  of  observations 
to  judge  how  far  these  figures  are  trustworthy.  They  consider  them  to  be 
rather  disproportionately  small  than  too  large,  and  therefore  recommend 
them  more  confidently. 

Water  flowing  at  a  nigh  velocity  and  carrying  large  quantles  of  silt  is  very 
destructive  to  channels,  even  when  constructed  of  the  best  masonry. 

Restotanee  of  8oll«  to  Brosion  by  UTater.— W.  A.  Burr,  Bng^g 
Neuss^  Feb.  8, 1804,  gives  a  diagram  showing  the  resistance  of  various  soils  to 
erosion  by  flowing  water. 

Experiments  show  that  a  velocity  graater  than  1.1  feet  per  second  will 
erode  sand,  while  pure  clay  will  stand  a  velocity  of  7.85  feet  per  second. 
The  greater  the  proportion  of  clay  cairied  by  any  soil,  the  higher  the  per- 
raisslble  velocity.  Mr.  Burr  states  that  experiments  have  shown  that  the  line 
describing  the  power  of  soils  to  resist  erosion  is  parabolic.  From  his  dia- 
gram the  following  figures  are  selected  representing  dlflferent  classes  of 
soils: 

Pure  sand  resists  erosion  by  flow  of 1.1  feet  per  second. 

Sandy  soil,  15j6  clay 1.2 

Sandy  loam,  403(  clay 1.8       "  " 

Loamy  soil,  65)(  clay  8.0       **  " 

Clay  loam,  85j(  clay 4.8       " 

Agricultural  clay,  05ji  clay 6.2       "  " 

clay 7.86     " 

Abradinfl:  and  Tranaportlns  Ponrer  of  UTater.— Prof.  J. 
LeConte,  in  his  **  Elements  of  Geology, "^  states : 

The  erosive  power  of  water,  or  its  power  of  overcoming  cohesion,  varies  as 
the  square  of  the  velocity  of  the  current. 

The  transporting  power  of  a  current  vaiies  as  the  sixth  power  of  the  ve- 
locity. *  *  *  If  the  velocity  therefore  be  increased  ten  times,  the  transport- 
ing power  is  Increased  1,000,000  times.  A  current  running  three  feet  per 
second,  or  about  two  miles  per  hour,  will  bear  fragments  of  stone  of  the 
size  of  a  ben's  egg«  or  about  three  ounces  weight.  A  current  of  ten  miles  an 
hoar  will  bear  fragments  of  one  and  a  lialf  tons,  and  a  torrent  of  twenty 
miles  an  hour  will  carry  fragments  of  100  tons. 

The  transporting  power  of  water  must  not  be  confounded  with  its  erosive 
power,  'llie  resistance  to  be  overcome  in  the  one  case  is  weight,  in  the 
other,  cohesion  ;  the  latter  varies  as  the  square :  the  former  as  the  sixth 
power  of  the  velociigr. 

In  many  cases  of  removal  of  slightly  cohering  material,  the  resistance  fs  a 


Saa  HYDRAULICS. 

mlztqiv  of  tl)e«e  two  miatapoes.  And  the  power  of  faii|«viiig  nurferya  wfU 
THJT  §(  flome  rate  betweep  «*  ana  «•, 

SalcfwlQ  teiham  l^aa  fQm»4  t»?Pt  in  order  to  prevent  deposits  of  sewage  silt 
In  small  sewers  or  drains,  suep  as  t pose  from  6  ipcbes  to  9  inpYies  dfan^eter. 
a  mean  veloqitiy  of  pot  Jess  than  8  feet,  per  second  shoi;ld  )>e  produoen . 
Bewers  fron^  ]$  to  '<M  inpbes  difimeter  sboulq  nave  a  velocity  pf  not  lees  than 


The  spec|£  CT^vIt*  ofthe  m^tertajs  hpaa  marked  fffpc*  uppn  t!»p  i 
▼elocities  necessary  xo  move  tbem.    T.  E.  Blackwell  fpupd  t^^  coa}  of  a 


2^  feet  per  second,  and  in  sewers  of  larger  dimensions  fn  no  cf|se  sbpiikl  tbe 

T.  E.  Blacvtweir fpupd  tl^^  cc_. 

TO  gr.  of  i.86  wA«  moved,  by  H  "SHF'*^  ^f  ^^^  J-^  ^  l¥/t  9^U^^^' 
wnlle  stones  of  ^  u.  ^f.  of  d  It?  to  8.00  required  a  yeloqii^  of  %.tk  Uf^.l^  fi-  per 
second. 

ChaiUy  gives  the  following  formula  for  finding  tbe  veleoi^  required  to 
move  rounded  stones  or  shingle : 

In  which  V  =  velocity  of  water  in  feet  per  second,  a  =  ftyerflg^  4|A!neter  in 
feet  of  tbe  body  to  Be  moved,  g  =  its  specific  gravity. 

Geo.  Y.  Wfsner,  Evg^g  News,  Jan  10,  1805,  doubts  the  general  aeeurnpy  of 
statements  made  by  many  authorities  concerning  the  rate  ot  flow  of  a  eor- 
rent  and  tlie  size  of  particles  which  different  velooities  will  move.    He  says: 

The  scouring  action  of  any  river,  for  finy  given  rate  of  current,  must  be  an 
inverse  function  of  the  depth.  The  fact  that  some  engineer  has  founa  that 
a  given  velocity  of  current  on  some  stream  of  uaknpwn  depth  will  move 
sand  OP  eravef  has  no  bearing  whatever  on  what  mi^  be  esrpeeted  of  our> 
rents  of  the  same  velocity  in  streams  of  greater  depths.  In  onanqels  9  to  5 
ft.  deep  a  mean  velocity  of  8  to  6  ft.  per  second  may  produce  rapid  scouring, 
while  fn  depths  of  18  ft.  and  upwards  ouiTpnt  velocities  of  6  to  9  ^t.  f^r 
second  of  fen  have  no  effect  wiiatever  on  the  channel  bed* 
'  Gnide  of  |Sewerp,-pe  following  empirical  /ormuja  is  giypp  fa  B^u- 
meister^s  *'  Cleaning  and  Sewerage  of  Cities,"  for  tbe  minlmWR  grade  for  a, 
pewer  of  pleftr  diftm^t^r  equa^  tp  d  lucbes,  iind  either  pirpiuar  or  q?^|  in 
section; 

MlBlmum  gvMo,  in  per  cent,  =  -J  ,  ^, 
4b  the  lowest  liipit  of  grades  wkilch  csq  be  flushed,  01  to  Q«9  per  oeiit  may 


he  assumea  for  sewers  whiet)  are  sometimes  dry,  while  0.8  per  cent  Is  allow- 
able for  the  trunk  sewers  ip  large  olUes.    The  seweps  should  nin  i^ry  as 
rarely  as  possible. 
p«lAU«ii  pr  m#tinot«r  ^r  pipe  to  anaiitltF  IMteliipmsdi.-- 

In  niAiiy  ca^es  whfoh  arise  iu  practice  the  inforpiaMon  sought  is  the  diame- 
ter necessary  to  supply  a  given  quantity  of  water  under  a  given  head.  Tbn 
diameter  if  coiomonly  taken  to  vary  s£  the  two-flfth  PPWer  of  the  dis- 
charge.   This  is  almost  certainly  too  large.    Hagep  f|  formulfti  with  Prof. 

Unwin*scoef&cieqts,givec2sc| -^¥^1        ,  where  e  s  ,98f|  when  d  fmd  Q 

are  in  feet  and  cubic  feet  per  second. 

Mr.  Thioipp  has  proposed  a  formula  which  makes  d  vary  as  the  .888  power 
of  the  discharge,  and  the  formula  of  Itf.  Vallot,  a  Franoh  engineor,  pMfckes  d 
vary  as  the  .875  power  of  the  discharge.    l^Engmeertng.) 

FliOW  OF  WATBB-BXPVI^IIIIBBITIS  4.VO  VABIiPi. 

Tlie  ripw  Pf^  Wj^ter  tliroii«1i  fipw  CMf^Iron  Flp«  was 

recenijy  nio^ured  by  8,  pept  Kussejl,  of  the  St.  l^quis.  Mo.,  water-works. 
The  pipe  was  12  inches  in  diameter,  1031  feet  loqg,  and  laid  on  #  unifitrm 
grade  from  end  to  e»d.  Under  an  average  total  head  of  8.98  feet  the  flow 
was  48,dO0  cubic  feet  In  seven  hours;  under  an  average  head  of  8«87  feet  the 
flow  was  the  same:  under  an  average  total  head  of  8.41  feet  tl^e  flbw  was 
46,7tX)  cubic  feet  in  8  hours  and  %  minutes.  Making  allowance  for  Ioms 
of  head  due  to  entrance  and  to  curves,  it  was  found  tliat  the  value  of  c  m 
the  formula  vi=  0  i^ra  wp3  from  88  to  98.    (Idno^fi  Bfcord.  April  14. 1091. 

Flour  of  UTater  In  a  20-liich  Pipe  T 5,000  Wttft  VQmm*—K 
QPinpi^riiion  Qf  evperiipHntal  data  with  ualculatioim  by  diffewot  fopoiule  is 


FLOW  OF  WATEB-^^HXPERIM^NTS  AKD  TABLES.   567 


kIt«ii  bj  OhM.  B.  Bowh,  Tiwa.  A,  8.  C.  9L,  ]8B8,    TU  pipa  wrperimMitail 
wtth  WM  tbat  "uppijrlqg  tl)«  «i(y  o(  Hoboken,  N*  J- 

Rmuuts  Qbtainu)  bt  the  HAOKuiaAOK  Watsb  CoifPAiiT,  inQK  laGft-iaSTi 
ur  PuMPiMo  Through  ▲  dO-iN.  Cabt-iron  Main  75,000  Fbst  L(nio. 

Preisure  in  lbs.  per  sq.  In.  at  pumping-sUttioD: 

05         100  105  *^     HO  115  W  Its  180 

Total  eff^etive  head  In  feet : 

55  66  77  80  )00  119  ISO  )86 

lAKbmree  In  U.  8,  gallona  In  84  hours,  1 » 1000 : 

S^      11,165      a,au      9,506      9,ao4 
Actual  Telocitj  to  main  In  f^t  per  ieQOQ<) ; 

<.00       9^        9,36        9.&S        9.68 
Cost  of  Qoal  oonsumed  la  dellTerlpg  each  psiUion  gali.  fit  g(iven  velooitie^ 

19.40      18.15      18.00      18,10      18.90      18.00      $0,00      $0.00 
Theoretical  dlacbanre  by  D^Afcy's  f<>rpiula : 

9.748      81004       a.944       9.488       9.400      9,910      <100      4.807 

S?  ?.?••!  J"^?**''*^??!  ^?LJ!&ft^'»w  Qrmiemor^i 
Foot  to  8  Feet  par  miAi  wHo  Correaitop^Pi:  Valiiia« 
QteiwtVz^p  Vtb.   (P,  M.  Qr^ne,  io  9^' a  Iff^.  Feb.  84. 1804.) 


9.904       iUO      i980 
9.7B        9,l»        8,00 


t-( 

IP 

Bydraulto  Orada;  Feet  per  Mile  ^  h. 

21 

hx=0.6 

1.0 

1.5 

9.0 

8.0^ 

4.0 

D. 

r. 

J  a  0.0000947 

0.0001894 

0.0009841 

o.oQoonn 

0,00058ft 

0.0007578 

0.95] 

Vm     0.4549 

0.66T8 

08956 

0,9608 

1.9977 

1.4409 

ee    00.7 

97.0 

90.1 

100.7 

109.0 

1(M.7 

0.5  ] 

F=     0.7859 

1.0799 

1.3516 

1,5956 

1.0857 

9.8J94 

6=106.6 

110.9 

118.4 

115.2 

117.9 

110.7 

0.75] 

r=     0.07B8 

1.4998 

1.T906 

9,1017 

9.6806 

9.0660 

«=  110.5 

119.0 

199.6 

184.4 

197.5 

120.5 

1.0 

F=      1.1888 

1.7458 

9.1861 

9,5645 

8.9119 

8.767V 

0»  199.1 

196.8 

199.7 

181,8 

194.7 

186.0 

1.25 

r=    1.88:9 

9.0879 

9.5591 

9.0099 

8.7498 

4,8968 

0  =.-  197.5 

189.4 

185.5 

187.6 

140.7 

149.9 

1.5 

V:=      1.5743 

0.9198 

9.8961 

8.80T5 

4.9548 

4.0018 

c=  189.1 

1S7.8 

140.8 

142,6 

145.8 

148.1 

1.75| 

F=     1.7518 

0.B789 

8.2980 

8.7800 

4.7980 

5.5546 

e  =  195.0 

141.4 

146.0 

146.8 

150.9 

152.5 

8. 

9.0  \ 

F=     1.9918 

9.6«84 

6.6968 

4,1479 

6.1945 

60986 

e  B  190.7 

145  1 

148.4 

150.7 

154.1 

156.5 

«  ». 

r=     9.0654 

8.0688 

8.8868 

4.5010 

5.6868 

6.6195 

•.    ».w^ 

e  =  149.0 

146.4 

151.7 

154.2 

157.6 

160.1 

The  velocItlM  In  this  table  have  been  calculated  by  Ur.  Greene's  mP<lif|- 
cation  of  the  Chezy  formula,  which  tno(liflcatloo  is  found  to  giye  results 
which  differ  by  from  1,99  to  -  9.65  per  cent  (average  0.9  per  cenR  from  very 
carefully  meaaured  flows  in  pipes  from  16  to  48  inches  in  aiameter,  on  grades 
from  1.68  feet  to  10906  feet  per  mile,  and  in  which  the  velocities  ranged 
from  1.577  to  6.105  feetjwr  second.  The  only  assumptiop  made  is  that  the 
modlOad  formula  for  r  gives  correct  results  in  conduits  from  4  feet  to  ^ 
feet  In  diameter,  as  it  Is  Icnowii  to  do  in  conduits  less  than  4  feet  ip  diameter, 

Other  articles  on  Flow  of  Water  in  lonif  tubes  are  to  be  found  in  Eng*g 
Aeies  as  follows :  O.  B.  Pearsons,  Sept.  ^,  IB;  6;  E.  ShermanOouId,  Feb.  10, 
28,tfarch  9, 16,  and  98, 1889;  J.  U  Fiixgerald,  Sept.  6  and  13, 1800;  Jas.  Buaqe. 
32n.  9. 1808:  J.  T.  Fanning.  July  14. 1899;  A.  If  .Talbot.  Aug.  U,  1899. 


568 


HTDRATTLIOS. 


Flour  of  Water  In  €lrciilar  Pipes,  Senrer*,  ete.,  FloivUiK 
Full.    Bmsed  on  Hatter's  Formula,  nrltli  n  =  .01 3* 

Discharge  in  cubic  feet  per  second. 


Slope,  or  Head  Divided  by  Length  of  Pipe. 

Diam- 

eter. 

tin  40 

llnTO 

1  In  100 

lin200 

1  in  300 

1  in  400 

1  in  600 

linOOO 

Sin. 

.4M 

.844 

^ 

.204 

.166 

.144 

7l87 

.118 

6  " 

.762 

.576 

.482 

.841 

.278 

.241 

.880 

.197 

7" 

1.17 

.889 

.744 

.626 

.480 

.872 

.855 

.804 

8" 

1.70 

1.29 

1.08 

.766 

.024 

.64 

.516 

.441 

9" 

2.87 

1.79 

1.50 

1.06 

.868 

.75 

.717 

.618 

Slope.... 

liner 

TTnlo 

1  in  100 

1  in  200 

1  in  800 

1  in  400 

1  in  600 

linOOO 

lOinT 

S.M 

2.24 

2.01 

1.42 

1.16 

1.00 

.90 

.6S 

11  *' 

8.81 

2.94 

2.68 

1.86 

1  68 

1.81 

1.17 

1.07 

12  »• 

4.82 

8.74 

8.85 

2.87 

1.98 

1.67 

1.5 

1.87 

18" 

5.98 

4.66 

4.16 

2.95 

8.40 

2.08 

1.86 

1.70 

14  *• 

0.60 

5.72 

6.16 

8.62 

8.96 

2.67 

2.29 

8.09 

Slope.... 

1  in  100 

1  in  900 

linSOO 

1  in  400 

1  in  600 

1  in  600 

tin  TOO 

1  in  800 

15  in. 

6.18 

487 

8.67 

8.09 

2.77 

2.52 

2.84 

8.19 

18" 

7.88 

5.22 

4.26 

8.69 

8.80 

8.01 

8.70 

8.61 

18" 

10.21 

7.22 

5.89 

6.10 

4.56 

4.17 

8.86 

8.61 

90  " 

18.66 

9.65 

7.88 

6.88 

6.10 

6.57 

6.16 

4.88 

22  ** 

17.71 

12.52 

10.28 

8.86 

7.92 

7.88 

6.60 

6.86 

^T- 

1  in  200 

flnloO 

1  in  600 

1  in  800 

1  In  1000 

1  in  1260 

1  in  1600 

1  in  1800 

15.88 

11.28 

9.17 

7.94 

7.10 

6.85 

680 

5.89 

2fr.2iD. 

19.73 

13.96 

11.89 

9.8r 

8.82 

7.89 

7.20 

e.C8 

2  •'  4  •* 

24.15 

17.07 

13  94 

12.07 

10.80 

966 

8.83 

8.06 

2  "  6  " 

29.08 

20.56 

16.79 

14.54 

18.00 

11.68 

lO.tt 

9.09 

2  -  8  •' 

84.71 

24.54 

20.04 

11.85 

15.52 

18.88 

W.W 

11.57 

Slope... 

1  In  600 

1  in  750 

1  In  1000 

1  in  1260 

1  in  1500 

1  in  1760 

1  In  2000 

llnS5O0 

2  ft.  10  in. 

25.84 

21.10 

18.27 

16.84 

14.92 

18.81 

18.98 

11.55 

a  " 

80.14 

24.61 

21.81 

19.06 

17.40 

16.11 

15.07 

18.48 

8  "2  In. 

84.90 

28.50 

24.68 

22.07 

80.15 

18.66 

17.45 

15.61 

3  4.  4  *» 

40.06 

82  7-2 

28.84 

25.85 

83.14 

81.48 

20.04 

17.98 

3  "  6  " 

45.66 

87.28 
1  in  750 

82.28 

28.87 

86.86 

24.40 

82.88 

80.41 

Slope.... 

1  in  500 

1  in  1000 

1  in  1250 

1  in  1500 

1  in  1750 

1  in  2000 

1  in  8500 

SftrSin. 

51.74 

42.52 

86.59 

82.78 

29.87 

27.66 

85.87 

88.14 

8  "  10  " 

68.86 

.   47.65 

41.27 

86  91 

83.69 

81.20 

29.18 

86.10 

4  " 

65.47 

63.46 

46.80 

41.41 

87.80 

84.50 

82.74 

89.28 

4  "   6  in. 

89.75 

73.28 

68.47 

56.76 

61.82 

47.97 

44.88 

40.14 

5  " 

118.9 

97.09 

84.06 

75.21 

68.65 

63.56 

59.46 

58.18 

Slope  .. 

1  in  750 

1  in  1000 

tin  1600 

lin2000 

lin2800 

1  in  3000 

lln8500 

1  In  4000 

5fr.6in. 

125.2 

106.4 

88.54 

76.67 

68.58 

68.60 

57.96 

54.21 

6  '* 

167.8 

186.7 

111.6 

96.66 

86.45 

78.98 

78.07 

68  85 

6  "  8  *• 

195.0 

168.8 

187.9 

119.4 

106.8 

97.49 

90.86 

81.48 

7  •» 

237.7 

206.9 

168.1 

145.6 

180.2 

118.8 

110.00 

202.9 

7  •'  6  " 

285.8 

247.1 

201.7 

174.7 

156.8 

142.6 

182.1 

128.5 

%T- 

1  in  1500 

1  in  2000 

lin2500 

linSOOO 

1  in  8600 

1  in  4000 

1  In  4500 

lin5O0O 

289.4 

207.3 

195.4 

169.8 

156.7 

146.6 

188.2 

181.1 

8  "  6  In. 

281.1 

243.5 

217.8 

198.8 

184.0 

172.2 

168.8 

184.9 

gu 

8-27  0 

288.1 

258.8 

281.2 

214.0 

200.2 

186.7 

179.1 

»  "  8  " 

376.9 

326.4 

291.9 

266.5 

246.7 

280.8 

817.6 

900.4 

10" 

4.S1.4 

878.6 

884  1 

305.0 

282.4 

264.2 

819.1 

8S6.S 

For  U.  S.  gallonB  multiply  the  figures  in  the  table  by  7.4806. 
For  a  given  diameter  tlie  quantity  of  flow  varies  as  the  square  root  of  the 
«ine  of  the  slope.   From  this  principle  the  flow  for  other  slopes  than  those 


FLOW  OF  WATER  IIT  CIRCULAR  PIPES,    ETC.      569 


Siven  in  tbe  table  may  be  found.  Tbus,  wbat  is  the  flow  for  a  pipe  8  feet 
lameter,  alope  1  in  185  r  From  tbe  Uble  take  Q  =  907.8  for  slope  1  in  9000. 
Tbe  g^ven  dope  1  in  199  is  to  1  in  8000  as  16  to  1,  and  the  square  root  of  this 
ratio  is  4  to  1.    Therefore  tbe  flow  required  is  907.8  X  4  a  899.S  cu.  ft. 

Clrenlmr  Plp«s,  Conduits,  etc.,  Floirliiff  Full. 

Yahies  of  tbe  factor  ac  Vr  in  tbe  formula  Q  =  ae  Vr  X  VI  correspond- 
infc  to  different  values  of  tbe  coefficient  of  roughness,  n.  (Based  on  Kutter'a 
formula.) 


1 

Value  of 

acVr, 

ft.  taL 

ns  .ma 

n  s  .011. 

n«  .019. 

na.OlO. 

n  s  .015. 

n  s  .017. 

6.006 

6.0627 

5.8800 

4.8916 

8.0604 

8880 

91.95 

18.749 

16.706 

15.099 

12.481 

10.50 

46.98 

41.487 

87.140 

88.497 

87.808 

23  60 

86.05 

76.847 

68.44 

61.867 

51.600 

43.98 

141.9 

19S.G0 

119.70 

109.14 

85.496 

78.09 

914.1 

100.79 

171.66 

166.68 

180.58 

111.8 

807.6 

874.90 

947.88 

894.68 

188.77 

164 

491.9 

877.07 

840.10 

809.23 

960.47 

888.9 

660.6 

500.78 

459.07 

411.27 

847.28 

299.8 

789.4 

647.18 

584.90 

.  588.76 

451.88 

888.8 

911.8 

817.50 

789.50 

•  674.00 

570.90 

493.3 

1198.0 

1018.1 

917.41 

836.69 

700.56 

613.9 

1874.7 

1984.4 

1118.6 

1091.1 

866.91 

750.8 

16SS.1 

1484.8 

1845.0 

1880.7 

1045 

006 

1969.8 

1764.8 

1600.0 

1468.9 

1945.8 

1080.7 

9082.1 

9418.8 

8198 

9007 

1711.4 

1487.8 

8543 

8191.8 

9908.6 

9660 

2878.7 

1077 

4557.8 

4111.9 

8748.7 

8489 

2934.8 

9557.3 

5781.5 

5176.8 

4718.9 

4888 

3708.8 

8838.5 

7075.8 

6804.9 

5885.9 

5889 

4588.8 

4010 

8605.1 

7774.8 

7067 

6510 

5501.6 

48B8 

10896 

Bn8.8 

8601.6 

7814 

6717 

5884.3 

19196 

11044 

1006S 

0973 

7078.3 

6905.8 

14896 

19954 

11889 

10680 

98T7.0 

8986.8 

16604 

15049 

18751 

18663 

10917 

0680.7 

10118 

17888 

15847 

14597 

12504 

11061 

81858 

19884 

18184 

16700 

14426 

18678 

94S28 

2sn84 

90618 

18006 

16413 

144^4 

98090 

85444 

88885 

81464 

isue 

16883 

814B9 

98598 

96170 

84189 

90879 

18^ 

86156 

81987 

80854 

86081 

28352 

SO^ 

80104 

85680 

89668 

80041 

96012 

88938 

43807 

89858 

86077 

88801 

28850 

85451 

47751 

43419 

80809 

86758 

81860 

28117 

69491 

47780 

43778 

40438 

85078 

80065 

14  8 

67406 

88806 

47060 

44888 

88454 

83975 

15 

68748 

67106 

58888 

48418 

49040 

87147 

16 

74101 

67857 

fiSOOS 

57848 

40888 

44073 

17 

86700 

70000 

78594 

67140 

58387 

51660 

16 

100617 

91711 

84947 

77988 

67889 

60067 

19 

115769 

105570 

96091 

80750 

78901 

69801 

90 

189188 

190570 

110005 

10S550 

80488 

70260 

Floir  of  Water  In  Circular  Pipes,  Conduits,  etc.,  Flonrlns 
under  Pressure* 

Based  on  D^Arcy^s  f ormnlie  for  the  flow  of  water  through  oast-iron  pipes. 
With  comparison  of  results  obtained  by  Kutter^s  formula,  with  n  =  .018. 
(Condensed  from  Flynn  on  Water  Power.) 

Values  of  a,  and  also  the  values  of_  the  factors  c  f^  and  ae  V9  for  use  in 
the  formate  Qmav;   vmcVrX  Vs,  and   Q  s  ac  i^f  X  Vs* 


570 


HTDRAULtCSi 


Q  m  dtsobarge  In  cubic  feet  per  second,  a  a  area  In  square  f^et,  v  m  veloc- 
ity in  feet  per  second,  r  m  mean  hydraulic  depth,  ^  diam.  for  pipes  running 
full,  •  3  sine  of  slope, 

(For  values  of  Va  see  page  668.) 


Size  of  Pipe. 

Clean  Cast-iron 
Pipes. 

Value  of 

ac  Vr  by 

Old  Gtot-iron  Pipes 
Lined  with  Deposit. 

dss  diam. 

ass  area 
in 

For 

Pot  Dis- 

Kutter'8 
Formula, 

when 
n  s  .018. 

For 

For 

in 
ft    in. 

Velocity, 

charge, 

Velocity, 
cf7. 

Discharge, 
acVr, 

H 

.ooon 

6.261 

.00408 

8.688 

.00272 

I 

.00186 

6.7U2 

.00914 

4.507 

.00613 

H 

.00807 

9.809 

.02856 

6.361 

.01922 

1 

.00646 

11.61 

.06884 

* 

7.811 

.04257 

iH 

.00862 

18.68 

.11669 

9.260 

.07885 

^3 

.01287 

16.58 

.19116 

» 

10.48 

.18856 

W 

.01070 

17.83 

.28986 

11.66 

.19409 

% 

.02188 

18.96 

.41867 

^ 

18.76 

.87824 

^ 

.0841 

81.94 

.74786 

14.76 

.50821 

T^ 

.0491 

24.68 

1.2089 

16.66 

.81838 

4 

.0878 

29.87 

8.5680 

19.75 

1.7846 

6 

.186 

88.64 

4.5610 

82.56 

8.0681 

« 

.196 

37.28 

7.8068 

4.S22 

85.07 

4.9147 

7 

.867 

40.05 

10  802 

87.84 

7.8995 

8 

.849 

48.75 

16.270 

29.48 

10.871 

9 

.448 

46.78 

80.663 

16.08 

81.43 

18.891 

10 

.645 

49.46 

85.968 

88.26 

18.129 

11 

.660 

62.16 

84.428 

85.09 

88.168 

.786 

64  66 

42.918 

88.60 

86.76 

28.867 

1     8 

1.000 

69.34 

68.485 

89  91 

48.608 

1      4 

1.896 

68.67 

orJ.wJ6 

42.88 

69.78P 

1      6 

1.767 

67.75 

119.72 

102.14 

45.57 

80.581 

1     8 

8.182 

71.71 

156.46 

48.34 

106.85 

1    10 

8.640 

75.88 

198.88 

50.658 

188.74 

8.148 

78.80 

247.57 

824.63 

52.961 

166.41 

8     S 

8.687 

82.15 

802.90 

55.258 

808.74 

8     4 

4.276 

85.89 

865.14 

67.486 

845.00 

2     6 

4.909 

88.39 

483.92 

411.37 

69.456 

891.87 

S     8 

6.686 

91.51 

511.10 

61.56 

848.8 

8    10 

6.306 

94.40 

595.17 

63.49 

400.8 

7.068 

97.17 

886.76 

674.09 

65.85 

461.0 

8     8 

7.875 

99.98 

786.94 

67.21 

689.8 

S     4 

8.7% 

102.6 

895.7 

69 

608 

8     6 

9.681 

105.1 

1011.2 

1021.1 

70.70 

680.8 

8     8 

10.599 

107.6 

1186.6 

72.40 

764.6 

8    10 

11.641 

110.2 

1*71.4 

74.10 

856.9 

12.566 

112.6 

1414.7 

1463.9 

75.78 

951.6 

4      8 

14.186 

116.1 

1647.6 

78.12 

1108.8 

4      6 

16.904 

119.6 

1001.0 

8007 

80.43 

1879.8 

4     9 

17.781 

K'2.8 

2176.1 

88.20 

1456.8 

19.686 

126.1 

2476.4 

2659 

84.88 

1666,7 

6     8 

21.648 

129.8 

2799.7 

86.99 

1888.8 

5     8 

38.768 

132.4 

3146.8 

8129 

89.or 

8116.8 

6     9 

25.967 

186.4 

8516 

91.06 

8866 

88.274 

188.4 

8912.8 

4822 

98.08 

88B1.7 

6     8 

88.188 

144.1 

4782.1 

5839 

96.98 

8916.4 

38.486 

149.6 

6757.5 

6510 

100.61 

8878.6 

7     6 

44.179 

154  9 

6841.6 

7814 

104.11 

4601.9 

60.266 

160 

8048 

0272 

107.61 

5409.9 

8     6 

66.745 

165 

9364.7 

10889 

111 

6399.1 

68.617 

169.8 

10804 

13668 

114.9 

7887.8 

9     0 

70.888 

174.6 

12370 

14597 

117.4 

10 

78.540 

179.1 

14066 

16709 

180.4 

mM 

FLOW  OP  WATER  IN  CIRCULAR  PIPES,   ETC.       571 


Size  of  Pipe. 

Clean  Cast-iron 
Pipes. 

Value  of 
ac  Vr  by 

Old  Cast-iron  Pipeb 
Lined  with  Deposit. 

f/= 

diom. 

a  =  area 
in 

For 

For  Dis- 

Kutier'ft 
Formula, 

For 

For 

n 

Velocity, 

cliarge, 

when 

Velocity, 

Dischance, 

ft. 

in. 

oVr. 

ocv;. 

n  « .018 

cVr> 

acVr. 

10 

86.900 

188.6 

15898 

18996 

128.4 

10600 

11 

95  088 

187.9 

17856 

21464 

126.8 

12010 

11 

103.80& 

192.2 

19966 

24189 

129.3 

13429 

12 

iis.oge 

106.8 

22204 

26961 

182 

14935 

18 

m7i9 

300.4 

24508 

30041 

134.8 

16545 

IS 

18«.7a8 

204.4 

27184 

38801 

187.5 

18252 

13 

148.189 

206.8 

29618 

86752 

140.1 

20056 

14 

158.088 

M3.2 

82664 

40482 

142.7 

21971 

14 

166.130 

216.0 

35660 

44822 

145.2 

23986 

15 

176.715 

219.6 

38807 

48418 

147.7 

26108 

16 

im.m 

228.8 

421S5 

52758 

150.1 

28.385 

16 

aw.oea 

226.9 

45621 

67848 

152.6 

30686 

16 

«18.835 

2904 

49278 

62182 

155 

83144 

17 

SM.981 

238.9 

.^3082 

67140 

157.8 

85704 

17 

240.6*20 

287.8 

57074 

72409 

159.6 

88389 

18 

-i54.470 

240.7 

61219 

77982 

161.9 

41199 

19 

883.5;i9 

2*7.4 

70154 

89759 

166.4 

47186 

20 

814.159 

258.8 

79786 

102559 

170.7 

58638 

Floiv  ofWater  In  Clrenlar  Pipes  flrom  %  Ineli  to  12  Inches 
Diameter. 


Based  on  D*Arcy*s  formula  for  clean  cast-iron  pipes.    Q  = 

acVrVl' 

Value  of 

Dia. 

Slope,  or  Head  Divided  by  Length  of  Pipe. 

aeVr- 

1  In  10. 

1 1n  20.  1  in  40. 

1in60. 

lln80. 

lln 
100. 

lin 
150. 

lin 

200. 

Qnan'tityin 

cubic 

feet  p 

er  sec 

end. 

.60403 

% 

.00127 

.00090 

.00064 

.00052 

.00046 

.00040 

.00088 

.00028 

.00914 

^ 

.00289 

.O0«h4 

.00145 

.00118 

.00102 

.00091 

.00075 

.00065 

.02855 

% 

.00903 

.00(}38 

.00^51 

.00369 

.00819 

.00286 

.00288 

.00202 

.06834 

r 

.02003 

.01410 

.01001 

.00818 

.00708 

.00638 

.00517 

.00448 

.11659 

1^        08687 

.02607 

.0184.^ 

.01505 

.01803 

.01166 

.00952 

.00824 

.19116 

IV 1 

.06044 

.04274 

.03023 

.02468 

.02187 

.01912 

.01561 

.01352 

.28936 

1? 

.09140 

.06470 

.01575 

.03736 

.08235 

.02894 

.02363 

.02046 

.41857 

2^ 

.18077 

.09247 

.06539 

.053.^ 

.04624 

.04136 

.03377 

.02927 

.74786 

2Vi 

.28647 

.1672-i 

.11824 

.09656 

.08361 

.07479 

.06106 

.05288 

1.2060 

8^ 

.88225 

.27031 

.19113 

.15607 

.13515 

.12089 

.098n 

.06518 

2.5680 

4 

.81042 

.57309 

.40521 

.83068 

.28654 

.25630 

.20927 

.18123 

4.5610 

6 

1.4422 

1.0198 

.79109 

.58882 

.5099S 

.4.')610 

.87241 

.3-2251 

7.8068 

6 

2.8104 

l.6:a8 

1.1552 

.94331 

.8169G 

.73068 

.59(iC0 

.51666 

10.852 

7 

8.4814 

2.4265 

1.7157 

1.4110 

1.2132 

1.0852 

.88607 

.76734 

16.270 

8 

4.8284 

3.4143 

2.4141 

1.9713 

1.7072 

1.5270 

1.2468 

1.0797 

20  6S2 

9 

6.5802 

4.6178 

3.2651 

2.6662 

2.3089 

2.0652 

1.6862 

1.4606 

26.962 

10 

8.5222 

6.0265 

4.2Cn 

3.4795 

8.0132 

2.6952 

2.2006 

1.9058 

M.428 

11 

10.886 

7.6981 

5.4431 

4.4447 

3.8491 

3.4428 

2.8110 

2  4344 

42.918 

12 

18.571 

9.5965 

6.7853 

5.5407 

4.7982 

4.2918 

8.5043 

8.0347 

Value  of  f 

^  = 

.8162 

.2286 

.1581  1  .1291 

.1118 

.1 

.06166 

.07071 

672 


HTDRAULICS. 


Value  of 

DU. 
in. 

Slope,  or  Head  Divided  by  Length  of  Pipe. 

ocVt' 

liD250. 

lin 

lin 

lin 

lin 

lin 

lin 

lin 

800. 

850. 

400. 

450. 

600. 

550. 

600. 

.00408 

Vi 

.00025 

.00033 

.00022 

.00020 

.00019 

.00018 

.00017 

.00016 

.00914 

^ 

.0005« 

.00058 

.00049 

.0001(1 

.00043 

.00041 

.00089 

.00087 

.00655 

l 

.00181 

.00165 

.00153 

.00118 

.00184 

.0012$ 

.00122 

.00117 

.06384 

1 

.0040(1 

.00866 

.oas89 

.00817 

.00-^96 

.00288 

.00270 

.00259 

.11659 

IL 

.00787 

.00678 

.00628 

.00583 

.00519 

.0(^21 

.00497 

.00476 

.19116 

li2 

.01200 

.01104 

.01022 

.00956 

.00901 

.00665 

.00815 

.00780 

.28986 

1& 

.01»)0 

.01671 

.01547 

.01447 

.01888 

.01294 

.01234 

.01181 

.41357 

2 

.02615 

.02888 

.02211 

.02068 

.01948 

.0184S 

.01768 

.01688 

.74786 

s^ 

.04780 

.04818 

.03997 

.087SS 

.08528 

.08344 

.03189 

.03053 

1.2069 

8 

.07645 

.06980 

.06462 

.06045 

.05695 

.05406 

.06155 

.04935 

2.5680 

4 

.16206 

.1479S 

.18699 

.12815 

.12074 

.11461 

.10929 

.10468 

4.5610 

5 

.28848 

.26885 

.24879 

.22806 

.21487 

.20897 

.19448 

.19620 

7.3068 

6 

.46206 

.42189 

.39055 

.86584 

.84422 

82676 

.81156 

.29880 

10.852 

7 

.68628 

.62660 

.58005 

.64260 

.51124 

.48680 

.46273 

.44303 

15.270 

8 

.96567 

.88158 

.81617 

.76350 

.71986 

.68286 

.66111 

.62340 

20.652 

9 

1.8060 

1.1924 

1.1088 

1.0326 

.97292 

92854 

.88060 

.84310 

26.052 

10 

1.7044 

1.5562 

1.4405 

1.8476 

1.2697 

12058 

1.1499 

1.1008 

84.428 

11 

2.1772 

1.9878 

1.8402 

1.7214 

1.6219 

1.5396 

1.4680 

1.4065 

42.918 

12 

2.7141 

2.4781 

2.2910 

2.1459 

•^0219 

1.9198 

1.8800 

1.7521 

Value  of  V 

»  = 

.06324 

.05774 

.05;)45 

.05 

.04711 

.04472 

.04264 

.040fS 

For  U.  S.  gals,  per  sec.,  multiply  the  figures  In  the  table  by.. 
"     "       "     ^  min.,       »»  ^  •»      " 

"     "      "     "   houi,       •*  "  ••       « 

"     "       "     "    24  hi  J.,    •*  ..Ma 


7.4806 
448.88 
86929.8 
646815. 


For  any  other  slope  the  flow  is  proportional  to  the  square  root  of  the 
slope  ;  thus,  flow  in  slope  of  1  in  100  is  double  that  in  slope  of  1  in  400. 

Flow   of  UTater   In   Pipes    tronk  %   IneK   to   12   Incite* 
Diameter  for  a  Uniform  Telocity  of  100  Ft.  per  min. 


Diameter 

Area 

Flow  in  Cubic 

Flow  in  U.  8 

Flow  in  U.  8. 

in 

in 

Feet  per 

Gallons  per 

Gallons  per 

Inches. 

Square  Feet. 

Minute. 

Minute. 

Hour. 

H 

.00077 

0.077 

.67 

84 

1 

.00186 

0.186 

l.OS 

61 

•1 

.00807 

0.807 

2.30 

188 

1 

.00545 

0.545 

4.06 

845 

1^ 

.00852 

0.852 

6.38 

888 

^H 

.01227 

1.227 

9.18 

551 

l^ 

.01670 

1.670 

12.50 

750 

Sf 

.02182 

2.182 

16.32 

9'79 

^ 

.0841 

8.41 

25.50 

1,580 

8 

-^0491 

4.91 

a6.ra 

8808 

4 

.0878 

8.73 

66.28 

8,917 

6 

.136 

18.6 

102.00 

6,190 

6 

.196 

19.6 

146.88 

8,818 

r 

.267 

26.7 

199.92 

11,995 

8 

.849 

84.9 

261.12 

15,667 

9 

.442 

44.2 

880.48 

19,ai9 

10 

.546 

54.5 

408.00 

24,480 

11 

.660 

66.0 

498.68 

89.621 

12 

.785 

78.5 

687.62 

86.851 

Given  the  diameter  of  a  pipe,  to  flnd  the  quantity  in  eallons  ft  will  deliver 
the  velocity  of  flow  being  100  ft.  per  mlnuta  Square  the  diameter  in  Inchea 
and  multiply  by  4.0& 


LOSS  OF  HEAD.  573 

ItQ^  ss  quanttty  In  gallons  per  minute  and  d  s  diameter  In  inches,  then 
^^  d.X. 7854  XJOOX  7.4805^^^ 

For  any  other  Telocity.  V,  In  feet  per  minute,  Q'  =  *.08d«j^  a  .04S»d»V\ 

Qiyen  diameter  of  pipe  in  inches  and  velocity  in  feet  per  second,  to  find 
discharge  in  cubic  feet  and  in  gallons  per  minute. 

Qf  -  ^  ^  '^J^  ^  ^  ^  «  0.3872M««  cubic  feet  per  minute. 
=  .82725  X  7.4805  or  2.448dSv  U.  S.  gallons  per  minute. 

To  find  the  capacitv  of  a  pipe  or  cylinder  in  gallons,  multiply  the  sauare 
of  the  diameter  in  inches  by  the  length  in  inches  and  by  .0084.  Or  multiply 
the  square  of  the  diameter  in  inches  by  the  length  in  feet  and  by  .0408. 

^~  '~^1     "  •00e4<i*Z (exact)  .0064  X  13  a  .0406. 

liOSS  OF  HEAD. 

The  lose  of  head  due  to  friction  when  water,  steam,  air,  or  gas  of  any  Und 
ilows  through  a  straight  tube  Is  repreeented  by  the  formula 

/.*'«•.        _u ^  .  /64.4  hd 

^  d  8g' 


'^^/^o^;        whence  v=|/?l^*^ 


In  wliich  I  =  the  length  and  d  s  the  diameter  of  the  tube,  both  in  feet;  v  a 
velocity  in  feet  per  Hecond.  and  /  is  a  coefficient  to  be  determined  by  experi- 
ment.   According  to  Weisbacli,  /  a  .00644,  in  which  case 

which  Is  one  of  the  older  formulse  for  flow  of  water  (Downing*s).  Prof.  Un- 
win  says  that  the  value  of  /  is  possibly  too  small  for  tubes  of  small  bore, 
and  he  would  put/  =  .006  to  .01  for  4-inch  tubes,  and/  s  .0064  to  .012  for  8- 
inch  tubes.    Another  formula  by  Weisbach  is 

.0171 


.0144  +  - 


Banklne  gives 


[6\^  «• 
\)d  ftg 


/-.005(l+^) 


From  the  general  equation  for  velocity  of  flow  of  water  v  a  e  fr  V<,  s& 

for  round  pipes  ci/^  ^^  we  have  *•  =  c>^  ^  and^A  a  £^,  in  which 

c  is  the  coefllcient  c  of  D*  Arcy^s.  Bazin^s,  Kutter's,  or  other  formula,  as  found 
by  experiment.  Since  this  coefficient  varies  with  the  condition  of  the  inner 
surface  of  the  tube,  as  well  as  with  the  velocity.  It  is  to  be  expected  that 
values  of  the  loss  of  head  given  by  differen  *;  writers  will  vary  as  much  as  those 
of  oiiantity  of  flow.  Two*table9  for  loss  of  head  per  100  ft.  in  length  in  pipes 
of  different  diameters  with  dlffei-ent  velocitleH  are  given  below.  The  first 
is  given  by  Clark,  based  on  Ellix*  and  Rowland's  experiments;  the  second  is 
from  the  Pelton  Water-wheel  Co.'s  catalogue,  authority  not  stated.  The 
kws  of  head  as  given  in  these  two  tables  for  any  given  diameter  and  velocity 
differs  considerably.  Either  table  should  be  used  with  caution  and  the  re- 
sults compared  with  the  quantity  of  flow  for  the  given  diameter  and  head 
as  given  in  the  tables  of  flow  based  on  Kutter*8  and  D*Arcy*s  formql^. 


574 


HYDRAULICS. 


BelatlTO  liOMi  ot  Head  by  Frletlon  for  eaek 
liOnstli  or  Clean  Caat-tron  Pipe. 


100  Feet 


(Baaed  on 

Ellis  and  Howland*8  experiments.) 

Velocity 

Diameter  of  Pipes  In  Inches. 

In  Feet 

per 
Second. 

8          4 

» 

6 

7 

8 

9     1    10 

«| 

14 

Loss  of  Head  in  Feet,  per  100  Feet  Long. 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

of 

of 

of 

of 

of 

of 

of 

of 

of 

of 

Head 

Head 

Head 

Head 

Head 

Head 

Head 

Head 

Head 

Head 

3 

.vr 

.55 

.41 

.38 

.27 

.28 

.19 

.18 

.15 

.12 

2.5 

1.49 

.93 

.64 

.50 

.48 

.86 

.80 

.87 

.83 

.19 

8 

1.9 

1.2 

.82 

.72 

.61 

.51 

.44 

.89 

.83 

.27 

8.5 

8.6 

1.6 

1.2 

1.0 

.T 

.71 

.61 

.52 

.45 

.87 

4 

8.8 

2.2 

1.7 

1.8 

.9 

.92 

.79 

.60 

.59 

.49 

4.6 

1.6 

1.2 

1.2 

1.01 
1.8 

.87 
1.1 

.75 
.90 

.61 

6 

.76 

6.5 

.92 

6 

16 

18 

21 

24 

27 

80 

88 

86 

42 

48 

.11 

.095 

.076 

.065 

055 

.052 

.049 

.047 

.086 

.080 

2.6 

.17 

.147 

.117 

.109 

.068 

.065 

.078 

.067 

.066 

.046 

.25 

.21 

.17 

.15 

.13 

.12 

.106 

.10 

.061 

.087 

8.5 

.84 

.20 

.28 

.20 

.18 

.16 

.15 

.H 

.111 

.092 

.44 

.86 

.81 

.27 

.23 

.2-2 

.20 

.17 

.14 

.116 

4.5 

.60 

.46 

.89 

.81 

.80 

.28 

.25 

.22 

.18 

.15 

.70 

.58 

.48 

.41 

.87 

.84 

.80 

.87 

.88 

.18 

5.5 

.U 

.70 

.59 

.50 

.44 

.89 

.86 

.82 

.27 

.22 

.59 

.53 

.49 

43 

.4 

.82 

.27 

I«oee  of  Head  In  Pipe  by  Friction.— Loss  of  head  by  friction  in 
each  lUO  feet  in  length  of  differeut  diameters  of  pipe  when  discnarging  the 
following  quantities  of  water  per  minute  (Peltoa  water-wheel  Co.) : 


§ 

'                                      IiiaMe  I'Lirii'^pM- Jif  ri]>+']ri  Inclir'^. 

4> 

1 

2 

8 

4 

6         1          6 

^ 

^ 

& 

l1 

1    ^ 

Pi 

1 

1. 

•a 

i  II 

t 

^ 

tl 

Co 

■21 

1^^ 

It    - 

S5 

=£1 

o  1 

II 

li 

l| 

a 

^Ci.. 

%;>  a 

o  = 

^ 

u  z 

Esi 

t)  c 

u  B 

^ 

t  o 

i^ 

^ 

I-" 

3^ 

la 

¥ 

|. 

ff 

1^ 

1.^ 

¥ 

1  = 

|S 

V 

h 

^ 

h 

y 

h 

Q 

A 

^ 

J^ 

Q 

A 

1? 

go 

*2.3T 

.6,^ 

lias 

2fi2 

.701 

fi.m 

.5K1 

10  4 

.474 

16  « 

,395 

OT.5 

-1.0 

4.SD 

.im 

'^Ai 

:m*s 

1 .6! 

^M 

l.1i2 

16.7 

.m 

i!4  5 

■  HIN 

8ft  8 

i.^i 

WSO 

i.m 

A  1)» 

ri  .123 

2.T3 

n.m 

SOfi 

S0.9 

t.M 

8^.7 

1.37 

4:j 

!\,tJ 

VI  ^  1  >;s 

P.T7 

r.5i 

^.11 

U.7Q 

a.oe 

ye.ij  1 

a.  46 

40.»,«.06 

fiA  9 

tt.fJ 

IT  'S<\   1   'AH 

EJ-A 

7.85 

nu 

\7  70 

4.31 

at  .4 

3  45 

49.l!a.S7 

ro.7 

7.0 

'.^.^i  'j.i^T   n.4S  1  &.1U 

7.152 

ao.6 

fl.T^J     3e  6 

■3,57 

Sr.Sf3,»i 

^4 

Flour  of  Water  In  RlTeted  Steel  Plpeii.— The  laps  and  rivets 
teiKi  to  ilecrease  the  carryiii)?  cepaeity  of  the  pipe.  See  paper  on  "New 
Foi'inulaa  for  Calculating  the  Flow  of  Water  in  Pipes  and  Channels.'* 
by  W.  E.  Foss,  Jour.  Assoc.  Ehq.  S'^r  .  \iii.  S9.'i.  Also  Clemens  Hei^'hePs 
book  on  "  115  EzpeiimeiilN  on  the  Carrying  Capacity  of  Large  Riveted  Metal 
Conduits,"  Johu  Wiley  &  Sous,  1897. 


LOdS  01  HBAS. 


573 


'     i 

8    1 

•    1 

10   1 

" 

18 

F 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

2  0 

.388 

82.0 

.296 

41.9 

.264 

53 

.887 

66.4 

.216 

79.8 

.198 

94.8 

80 

.m 

48.1 

.611 

62.8 

.544 

79.6 

.488 

96.2 

.444 

119 

.407141 

4.0 

1.175 

64.1 

1.05J7 

88.7 

.913 

106 

.828 

181 

.747 

168 

.685 

188 

5.0 

1.T6 

80.2 

1.54 

105 

1.87 

182 

1.28 

168 

1.182 

198 

urn 

236 

ftO 

8.46 

96.2 

2.15 

125 

1.92 

159 

1.71 

196 

1.56 

287 

1.43 

283 

70 

3.26 

112.0 

2.85 

146 

2.52 

185 

2.28 

229 

2  07 

877 

1.91 

S30 

iDiiide  Diameter  of  Pipe  in  Inches. 

18 

14 

15 

16 

18 

20 

V 

h 

Q 

h 

Q 

K 

Q 

h 

Q 

h 

Q 

h 

Q 

2.0 

.188 

no 

.169 

128 

.158 

147 

.147 

167 

.182 

812 

.119 

862 

80 

.875 

166 

.849 

192 

.825 

221 

.806 

251 

.871 

818 

.845 

398 

4.0 

.632 

221 

.587 

256 

.548 

294 

.518 

885 

.456 

424 

.410 

528 

5.0 

.M8 

2T6 

.681 

821 

.822 

868 

.770 

419 

.686 

580 

.617 

664 

6.0 

1.825 

832 

1.229 

885 

1.148 

448 

1.076 

608 

.957 

686 

.861 

785 

7.0 

1.75 

887 

1.68 

449 

1.63 

516 

1.48 

M6 

1.27 

742 

1.148 

016 

22 

84 

26 

88 

80 

86 

V 

ik 

Q 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

2.0 

.106 

316 

.098 

377 

.091 

442 

.084 

613 

.079 

589 

.066 

848 

8C 

.242 

475 

.204 

565 

.188 

663 

.174 

770 

.168 

883 

.185 

1878 

4.C 

.873 

638 

.842 

754 

.315 

885 

.298 

1026 

.278 

1178 

.228 

1697 

5.C 

.561 

798 

.518 

942 

.474 

1106 

.440 

1283 

.411 

U7% 

.848 

2181 

6-0   .783 

950 

.717 

1131 

.662 

1327 

.615 

1539 

.574 

1767 

.479 

8545 

7.0i  1.040 

1109 

.953 

1319 

.879 

1548 

.817 

1796 

.762 

2061 

.686 

2868 

ExAMpLB.— Given  200  ft.  head  and  600  ft.  of  11 -inch  pipe,  carrving  119  cubic 
\eet  of  water  per  minute.  To  And  eifective  bead  :  In  right-uand  eolunin, 
under  11-Inch  pipe,  find  119  cubic  ft.;  opposite  this  will  be  found  the  loss  by 
rriction  in  100  ft.  of  leneth  for  this  amount  of  water,  which  is  .444.  Multiply 
this  by  the  number  of  hundred  feet  of  pipe,  which  is  6,  and  we  have 
S.66  ft.,  which  is  Uie  loss  of  head.  Therefore  the  effective  head  is  800  -  2.66 
t=  197.84. 

EzPLAHATiov.—The  loss  of  head  by  friction  in  pipe  depends  not  only  upon 
diameter  and  length,  but  upon  the  quantity  of  water  passed  through  it.  Th-^ 
head  or  pressure  is  what  would  be  indicated  by  a  pressure-gauge  attached 
to  the  pipe  near  the  wheel.  Beadings  of  gauge  should  be  taken  while  the 
water  £s  flowing  from  the  nozzle. 

To  reduce  heads  in  feet  to  pressure  in  pounds  multiply  by  .488.  To  reduce 
pounds  pressure  to  feet  multiply  by  2.300. 

Cox's  Formula*— Weisbach's  formula  for  loss  of  head  caused  by  the 
friction  of  water  in  pipes  is  as  follows  : 

Friction-head  =  /o.0144  +  ?:^^\  ^lZL*. 
\  VV  /  5.867d 

where  L  s  length  of  pipe  in  feet; 

V  B  velocity  of  the  water  in  feet  per  second; 
d  a  diameter  of  pipe  in  inches. 
William  C6z  (Amer,  Mach.^  Dec.  28, 1893)  gives  a  simpler  formula  which 
gives  almost  identical  results ; 

fl  ■  friction-head  in  feet  = -; -Tr^rrr (1) 

a  12U0 

Hd        4F«4-5F-g  ^ 

L    '^  1200         •   •    •   •    • W 


676 


HYDBAULI08. 


He  glvefl  a  table  by  means  of  which  the  yalue  of 
obtained  when  V  is  known,  and  vice  verta. 

1900 


laoo 


Is  at  onoe 


VALUKaOF  • 


V 

0.0 

0.1 

0.2 

0.8 

0.4 

0.6 

0.6 

0.7 

0.8 

0.9 

1 

.00588 

.00696 

.00618 

.00938 

.01070 

.01208 

.01858  .01506 

.01663 

.01628 

2 

.02000 

.02178 

.02868 

.02565 

.02758 

.02958 

.08170,  .08388 

.08618 

.00645 

8 

.04088 

.Q4SS& 

.04580 

.04888 

.05108 

.06375 

.06668  .05088 

.06280 

.06628 

4 

.06838 

.07146 

.07468 

.07788 

.06120 

.08458 

.06808;  .09156 

.09518 

.09678 

5 

.10200 

.10628 

.11018 

.11405 

.11808 

.12208 

.12620!  .18088 

.18468 

.186% 

6 

.14383 

.14778 

15280 

.16688 

.161.58 

.16625 

.17108:  .17688 

.18060 

.18678 

7 

.19083 

.19595 

.20118 

.20688 

.21170 

.21706 

.22253!  .22805 

-.22368 

.28928 

8 

.24500 

.26078 

.25668 

.26255 

.26658 

.27468 

.28070:  .28688 

.29818 

.S9945 

0 

.80588 

.31228 

.31880 

.32588 

.88208 

.88875 

.84568 

.85288 

.36980 

.86Q» 

10 

.87838 

.88045 

.88768 

.89488 

.40220 

.40958 

.41708 

.42456 

.48218 

.489^78 

11 

.44760 

.45528 

.46818 

.47105 

.47908 

.48706 

.49520 

.60888 

.61168 

.61995 

IS 

.52888 

.58678 

.64580 

.66888 

.66253 

.67125 

.68008 

.68868 

.59760 

.60678 

18 

.61683 

.62495 

.68418 

.64888 

.65270 

.66206 

.67168 

.68105 

.69068 

.70(«28 

14 

.71000 

.71978 

.72968 

.78965 

.74968 

.75958 

.76970 

.77966 

.7W)18 

.60M5 

16 

.81083 

.82138 

.88180 

.84288 

.85808 

.86.^75 

.87458 

.88588 

.69680 

.907-J8 

16 

.91883 

.92945 

.94068 

.95188 

.96320 

.97458 

.98608 

.99756 

1.00918;  1.02078 

17 

1.08Ja0'l  .04428 

1.0661C 

1.06805 

^0800:^ 

1.09208 

l.]0120'l. 11688 

l.r.;868  1.14095 

18 

1.15883 

1.16578 

1.17830 

1.19088 

1.2ffiV>3 

1.21625 

1.229081 1.24188 

1.254H0 

1.2677« 

19 

1.28083 

1.29395 

1.30718 

1.32088 

1.388T0 

1.84708 

1.36053  1.37405 

1.88768 

1.40128 

ao 

1. 41500 

1.42878 

1.4426.S 

1.45655 

1.47053 

1.48458 

1.49870,1.51288 

1. 58718 

1.54145 

21 

1.55688 

1.67028 

1.68480 

1.59988 

1.61403 

1.02875 

1.61853  1.65838 

1.678.30 

1.68826 

The  use  of  the  formula  and  table  is  illustrated  as  follows: 
Given  a  pipe  5  inches  diameter  and  1000  feet  long,  with  49  feet  head,  what 
will  the  discDargre  be! 

If  the  velocity  V  is  known  in  feet  per  second,  the  dischanse  Is  0.82725d>F 
cubic  foot  per  minute. 
By  equation  2  we  have 

4ri  +  6F-2  ^  fla_  ^.  49X1  „  0  245  ; 
1200  L  1000  '^' 

whence,  by  table,  V  =  real  velocity  s=  8  feet  per  second. 

The  discnarge  in  cubic  feet  per  minute,  if  V  is  velocity  in  feet  per  second 
and  d  diameter  in  inches,  is  0.32726d^r,  whence,  discharge 

=  0.82725  X  26  X  8  =  65.46  cubic  feet  per  minute. 

The  velocity  due  the  head,  if  there  were  no  friction,  is  8.025  \^  =  56.175 
feet  per  second,  and  the  discharge  at  that  velocity  would  be 
0.82725  X  25  X  r)6.175  =  460  cubic  feet  per  minute. 

Suppose  It  is  required  to  deliver  this  amount,  460  cubic  feet,  at  a  velocity 
of  2  feet  per  second,  what  diameter  of  pipe  will  be  required  and  what  will  be 
the  loss  of  head  by  friction? 


d  =  diameter  \ 


■V 


e 


V  X  0.32726 


y  2  X  0.; 


460 

82725 


V708  =  26.5  inches. 


Having  now  the  diameter,  the  velocity,  and  the  discharge,  the  frlcUon-head 
Is  calculated  by  equation  1  and  uoe  of  the  table;  thus, 


L  4r«-f  5r-2 

d  1200 


thus  leaving  49  —  0.76  =  say  48  feet  effective  head  applicable  to  power-pro- 
ducing purposes. 

Problems  of  the  lose  of  head  may  be  solved  rapidly  by  means  of  Cox's 
Pipe  Computer,  a  mechanical  device  on  the  principle  of  the  slide-rule,  for 
sale  by  Keuffel  &  Esser,  New  York. 


LOSS  09  HEAD. 


677 


Frlrilona]  Heads  at  GlTen  Hates  of  IMseliarge  In  Clean 
€ast-lron  Pipes  for  Baeli  1000  Feet  of  Ijenfftli. 

(Condenaed  from  EIHb  and  Howland's  Hydraulic  Tables.) 


4iDch 

6-Inch 

8-inch 

lO-inch 

12-Inch 

Hhich 

I*lpe. 

Pipe. 

Pipe. 

Pipe. 

Pipe. 

Pipe. 

|1 

11 

|l 

II 

11 

|d 

|1 

IS, 

|l 

85 

.64 

1.8S 

.50 
2.01 

.28 
.57 

.11 
.82 

.16 
.88 

.04 
.10 

.10 
.80 

.02 
.04 

.07 
.14 

.01 
.02 

SO 

.10 

.01 

100 

2.55 

16.06 

1.18 

1.08 

.64 

.88 

.41 

.11 

.88 

.05 

.21 

.03 

ISO 

8.83 

1.70 

2.28 

.98 

.60 

.61 

.82 

.48 

.10 

.31 

.05 

900 

5.11 

28.00 

2.27 

8.92 

1.88 

1.01 

.88 

.86 

.57 

.16 

.42 

.08 

8S0 

0.57 

48.47 

8.84 

6.00 

1.6fl 

1.68 

1.08 

.54 

.71 

.24 

.52 

.12 

aoo 

7.06 

62.20 

3.40 

8.62 

1.91 

2.18 

1.28 

.75 

.85 

.82 

.611 

.16 

8S0 

8.94 

84.8« 

8.97 

11.48 

2.29 

8.85 

1.48 

.99 

.99 

.43 

.73 

.21 

400 

10.21 

100.61J 

4.54 

14.89 

2.55 

8.6fi 

1.68 

1.27 

1.18 

.54 

.83 

.87 

600 

12.77 

170.53 

5.67 

88.01 

8.19 

5.64 

2.04 

1.93 

1.42 

.81 

1.04 

.40 

000 

15.82 

244.78 

6.81 

82.89 

8.88 

8.0S 

2.45 

2.72 

1.70 

1.14 

1.25 

.55 

700 

17.87 

832.88 

7.94 

44.54 

4.47 

10.8S 

2.86 

8.66 

1.98 

1.52 

1.4fl 

.78 

800 

9.06 

57.95 

5.09 

14.08 

8.27 

4.78  8.27 

1.96 

1.67 

.94 

000 

10.21 
11  85 
13.61 
15.88 
18.15 
20.42 
28.69 

78.18 
90.05 
180.20 
175.38 
288.62 
888.90 
856.22 

5.74 
6.38 
7.66 
8.94 
10.21 
11.47 
12.77 

17.68 
21.74 
81.10 
42.18 
M.84 
69.22 
85.87 

8.68 
4.08 
4.90 

5.93  2.55 
7.28  2  84 
10.S8S.40 

8.45 

8.00 
4.26 
5.74 
7.44 
9.86 
11.60 

1.88 
2.06 
2.50 
2.91 
3.83 
8.75 
4.17 

1.17 

1000 

1  48 

1*200 

8.08 

1400 

6.72  14.08  3.97 
6.53  18.22  4.54 
7.35  22.96,5.11 
8.17  88.25  5.67 

8.72 

1600 

8.51 

1800 

4  41 

aooo 

6.41 

ssoo 

15.96 

138.70 

10.21  48.87,7.09 
12.85:62.98  8.51 

17.82 
85.51 

5.21 
6.85 
8.34 

8  85 

11.96 

4000 

21.00 

16-lnch 

18-inch 

aO-Inch 

84.inch 

80^ 

Inch 

86-Inch 

Pipe. 

Pipe. 

Pipe. 

Pipe. 

Pi 

pe. 

Pipe. 

it 

1^ 

18. 

it 

A 

it 

Is 

li 

if 

|l 

ROO 

.80 

.22 

.68 

.18 

.51 

.06 

.85 

.04 

.28 

.01 

.16 

.01 

1000 

1.00 

.76 

1.26 

.44 

1.02 

.27 

.71 

.12 

.45 

.04 

.88 

.w 

1500 

2.89 

1.68 

1.89 

.98 

1.58 

.56 

i.oe 

.24 

M 

.W 

.47 

.04 

awo 

8  1fl 

2.82 

8.52 

1.60 

2.04 

.96 

1.42 

.41 

!  .91 

.15 

.68 

.06 

ssoo 

8.99 

4.84 

8.15 

245 

2.55 

1.47 

1.77 

.68 

i.ia 

.82 

.7« 

.09 

aooo 

4.7D 

6.19 

8.78 

8.48 

3.06 

8.09 

2.1S 

.87 

1.38 

.80 

.95 

.13 

8600 

5.59 

8.87 

4.41 

4.70 

8.57 

2.8! 

2.4S 

1.18 

1.59 

.40 

1.1C 

.17 

4000 

6.88 

10-87 

5.04 

6.09 

4.0« 

8.64 

2.84 

1.60 

1.88 

.52 

1.28 

.22 

4500 

7.18 

18.70 

5.67 

7.67 

4.50 

4.5« 

8.19 

1.88 

8.04 

.64 

1.42 

.27 

sooo 

7.96 

16.86 

6.80 

9.43 

6.11 

5.68 

8.55 

8.31 12. 27 

.78 

1.5fi 

.38 

6000 

7.57 

18.49 

6.18 
7.15 

8.03 
10.86 

4.86 
4.96 
5.67 
6.88 

8.28:2.72 

1.11 

1    <NI 

46 

7000 

4.43 
5.75 
725 

3.18 
3.63 
4.08 
4.54 
5.44 
6.36 

1.49;2.21 
1.93,2.58 
2.4»'2.84 
2.98*3  lis 

.68 

80OO 

80 

9000 

1.00 

JOOOO 

1.23 

liOOO 

4.25 
6.75 

3.78 
4.41 
5.05 

1.74 

14000 

Z  35 

I600O 



...... 

3.04 

180OO 

5.68 
6.80 

8  83 

ttOOO 

.... 

4.71 

678 


HYDRAULICS. 


KflTect  of  JBends  and   CorTes  In  Pipes.— Weisbach^s  rule  for 

bends :  Loss  of  head  In  feet  =  f.iai  +  1.847  (5)*]  X  J!*^  X  j2j,  in  which  r 

B  Internal  radius  of  pipe  in  feet,  R  =  radius  of  curvature  of  axis  of  pipe,  v 
=s  velocity  in  feet  per  second,  and  a  =  the  central  angle,  or  angle  subtended 
by  the  bend. 

Hamilton  Smith,  Jr..  in  bis  work  on  Hydraulics,  says:  The  experimental 
data  at  band  are  entirely  insufficient  to  permit  a  satisfactory  analysis  of 
this  quite  complicated  subject;  in  fact,  about  the  only  experiments  of  value 
are  those  made  bv  Bossut  and  Dubuat  with  small  pipes. 

€arTes«— If  the  pipe  has  easy  curves,  say  with  radius  not  less  than  5 
diameters  of  the  pipe,  the  flow  will  not  be  materially  diminished,  provided 
the  tops  of  all  curves  are  kept  below  the  hydraulic  grade-line  and  provision 
be  made  for  escape  of  air  from  the  tops  of  all  curves.    (Trautwine. ) 

Hydranlle  CSrade-llne*— In  a  straight  tube  of  uniform  diameter 
throughout,  running  full  and  discharging  freely  into  the  air,  the  hydraulic 
grade-line  is  a  straight  line  drawn  from  the  discharge  end  to  a  point  imme- 
aiately  over  the  entry  end  of  the  pipe  and  at  a  depth  below  the  surface 
equal  to  the  entry  and  velocity  heads.    (Trautwine.) 

In  a  pipe  leading  from  a  reservoir,  no  part  of  its  length  should  be  above 
the  hydraulic  grade-line. 

Flour  of  Water  In  Honae-serrlce  Pipes. 

Mr.  E.  Kuicbling,  C.E.,  furnished  the  following  table  to  the  Thomson 
Meter  Ck).: 


1 

Discharge,  or  Quantity  capable  of  being  delivered,  in 
Cubic  Feet  per  Minute,  from  the  Pipe, 

Condition 

cii 

under  the  conditions  specified  in  the  first  column. 

of 

Discharge. 

ill 

Nominal  Diameters  of  Iron  or  Lead  Service-pipe  in 

Inches. 

fSiS' 

fi 

H 

% 

H 

I 

1^ 

2 

8     I 

4 

6 

Through  86 
feet  of 
service- 

so 

MO 

1.98 

8.01 

6.18 

16.58 

88.84 

88.16178.85 

444.63 

id 

1-27 

2.22 

8.48 

7.08 

19.14 

88.50 

101.80  200.75 

513.42 

&0 

1.42 

2.48 

8.89 

7.92 

21.40 

48.(M 

118.82  284.44 

574.02 

eo 

1.56 

2.71 

4.26 

8.67 

23.44 

47.15 

124.68  245.87 

628.81 

75 

1.T4 

3.08 

4.77 

9.70 

26.21 

52.71 

189.89  274.89 

703.08 

100 

«.0l 

8.50 

5.50 

11.20 

80.27 

60.87 

160.96  317.41 

811.79 

pressure. 

ISO 

2.i"9 

8.99 

6.28 

12.77 

84.51 

69.40 

198.52  861.91 

925.58 

Through 
100  feet  of 
service- 

80 

0.66 

1.16 

1.84 

8.78 

10.40 

21.80 

58.19118.13 

317.28 

40 

0,77 

1.84 

2.12 

4.86 

12.01 

24.59 

67.19186.41 

366.80 

50 

0.86 

1.60 

2.87 

4.88 

18.43 

27.60 

75.18'l52.61 

409.64 

m 

OM 

1.65 

2.60 

5.84 

14.71 

80.12 

82.80  107.06'448.63 

75 

1.05 

1.84 

2.91 

5.97 

16.45 

83.68 

92.01|186.78'501.58 

:oo 

1/12 

2.18 

8.86 

6.90 

18.99 

88.89 

106.24  815.68lW9.18 

pressure. 

m 

139 

d.42 

8.83 

7.86 

21.66 

44.84 

121.141245.91 

660.86 
260.56 

Through 

80 

0.55 

0.96 

1,52 

8.11 

8.57 

17.66 

47.90   97.17 

100  feet  of 

40 

0.66 

1.15 

1.81 

3  72 

10.24 

20.95 

67.20, 116.01  311. 09 

service- 

so 

0.75 

1.81 

2.06 

4.24 

11.67 

28.87 

65.18|182.rK)'S54.49 

&*?"• 

60 

0.88 

1.45 

2.29 

4.70 

12.94 

26.48 

72.28146. 61  893.13 

75 

0.94 

1.64 

2.59 

5.82 

14.64 

29.96 

81.79  165.90,444.85 

vertical 

100 

1.10 

1.92 

8.02 

6.21 

17.10 

85.00 

95.55 

198.82:519.72 

rise. 

J80 

1.26 

2.20 

8.48 

7.14 

19.66 

40.83 

109.82 

222.76  597.81 

Through 

SO 

0.44 

0.77 

1.22 

2.50 

6.80 

14.11 

88.68 

78.64:211.64 

100  feet  of 

40 

0.55 

0.97 

1.63 

3.15 

8.68 

17.79 

48.68 

98.98  266.59 

service- 

50 

0.65 

1.14 

1.79 

8.69 

10.16 

20.82 

56.96 

115.87  812.08 

^r^r" 

60 

0.73 

1.28 

2.02 

4.15 

11.45 

28.47 

64.28 

180.69  851.78 

75 

0.84 

1.47 

2.32 

4.77 

18.15 

26.95 

78.76 

149.99  408.93 

vertical 

100 

1.00 

1.T4 

2.7.') 

5.65 

16.58 

81.93 

87.88 

177.67  4^.56 

rise. 

180 

1.15 

2.02 

8.19 

6.55 

18.07 

87.09 

101.88 

906.04  664.96 

PIBE-STBSAHB. 


679 


fn  tbte  table  It  taasRumed  that  the  pipe  is  stralirht  and  smooth  inside;  that 
the  friction  of  the  raain  and  meter  are  disregarded;  that  the  iolet  from  the 
main  is  of  ordinary  character,  sharpi  not  flaring  or  rounded,  and  that  the 
outlet  is  the  full  diametor  of  pipe.  The  deliveries  given  will  be  hioreased  if, 
first,  the  pipe  between  the  meter  and  the  main  is  of  larger  diameter  than  the 
ontlec;  second,  if  the  main  is  tapped,  sav  for  l-|nch  pipe,  but  is  enlarged 
from  the  tap  to  IH  or  lU  inch;  or,  third,  if  pipe  on  the  outlet  is  laiiger  than 
that  on  the  mlet  side  of  tne  meter.  The  exact  details  of  the  conditions  given 
are  rarely  met  in  practice;  consequently  the  quantities  of  the  table  may  be 
expected  to  be  decreased,  because  the  pipe  is  liable  to  be  throttled  at  the 
joints,  additional  bends  may  interpose,  or  stop-cocks  may  be  used*  or  the 
oack-pressure  may  be  Increased. 

Afip-lioan<l  Pipes*— A  pipe  is  said  to  be  air-bound  when,  in  conse- 
quence of  air  being  entrapped  at  the  hign  points  of  vertical  curves  in  the 
One,  water  will  not  flow  out  of  the  pipe,  although  the  supply  is  higher  than 
the  outlet.  The  remedy  is  to  provide  cocks  or  valves  at  the  high  points, 
throuKh  which  the  air  may  be  discharged.  The  valve  may  be  made  auto- 
matic oy  means  of  a  float. 

Terneal  Jets.  (Molesworth.)^H  s  head  of  water,  h  =  height  of  jet, 
d  =  diameter  of  Jet,  K  =  coefficient,  varying  with  ratio  of  diameter  of  jet 
to  bead;  then  h  s  KH, 

IfH=dX800       600         1000        1600        1800        2800       8600       4600, 
K=  .96         .0  .85  .8  .7  .6  A  .85 

ITitter  nellTered  ihrongli  Bletere*  (Thomson  Meter  Go.).— The 
best  modem  practice  limits  the  velocity  In  water-pipes  to  10  lineal  feet  per 
second.  Assume  this  as  a  basis  of  delivery,  and  we  find,  for  the  several  sizes 
of  pipes  usually  metered,  the  following  approximate  results: 
Nominal  diameter  of  pipe  in  inches: 

H  H         H  ^  1}4        »  8  4  6 

Quantity  delivered,  in  cubic  feet  per  minute,  due  to  said  velocity: 

0.46        1.88       1.85       8.98       7.86       18.1       89.5       68.4       117.9 

Prices  €lLarco<t  tor  Water  In  mflnDrent  Clttes  (National 
Meter  Ck>.): 

Average  minimum  price  for  1000  gallons  in  168  places 9.4  oentSi 

maximum    •*      "     "         "       "    »'       "     28      *• 

Extremes, accents  to 100      ** 

FIBE-STBEABI8. 

IHseliarKe  flrom  Nozzles  at  nunsrent  Pressnres. 

(J.  T.  Fanning,  Am.  Water-works  Ass'n,  189!^.  Eng'g  JVevw,  July  14, 1898.) 


KoKzle 

diam., 

in. 

streamt 
ft. 

Pressure 
at  Play- 

Horizon- 
tal Pro- 
jectlon  of 
Streams, 
ft. 

Gallons 

per 
minute. 

(tellons 
per  24 
hours. 

FricUon 

per  100 

ft.  Hose, 

lbs. 

Friction 
per  100 
ft.  Hose, 

Net 
Head,  ft. 

\    1 

70 

46.5 

89.6 

90S 

898.896 

10.76 

84.77 

80 

69.0 

67.0 

230 

881,800 

18.00 

81.10 

90 

79.0 

76.6 

867 

884,600 

17.70 

40.78 

100 

180.0 

88.0 

811 

447,900 

88.60 

64.14 

^H 

1 

70 

44.6 

61.8 

849 

868,680 

15.60 

85.71 

^h 

1 

80 

65.5 

69.6 

881 

404,700 

19.40 

44.70 

iM 

I 

90 

7«.0 

78.6 

824 

466,600 

86.40 

68.68 

^^ 

100 

106.0 

89.0 

876 

641,600 

88.80 

77.88 

iS 

70 

48.0 

66.0 

806 

440,618 

88.75 

68.48 

^h 

80 

68.6 

72.4 

848 

498.900 

88.40 

66.48 

ii 

90 

68.6 

81.0 

888 

658,800 

85.90 

88.71 

th 

100 

98.0 

98.0 

460 

062,500 

67.75 

86.98 

^l 

j 

70 

41.5 

77.0 

868 

580,149 

88.60 

74.88 

1? 

80 

61.6 

74.4 

410 

690,600 

40.00 

98.16 

if 

90 

66.5 

82.6 

468 

674,000 

61.40 

118.48 

iH 

L 

100 

88.0 

98.0 

640 

777,700 

78.00 

165.89 

580 


HYDRAULIOS. 


Friction  IjO«ms  in  Hose*— In  the  above  table  the  Totnmes  of 

water  discharged  per  Jet  were  for  stated  pressures  at  the  plav-plpe. 

Id  providini?  for  this  pressure  due  allowauoe  is  to  be  made  for  frictioo 
losses  in  each  hose,  according  to  the  streams  of  greatest  discharge  which  are 
to  be  used. 

The  loss  of  pressure  or  its  equivalent  looB  of  head  (h)  in  the  hose  may  be 

found  by  the  formula  h  =  t;*(4m)r— ^. 

In  this  formula,  as  ordinarily  used,  for  friction  per  100  ft  of  l^tn.  hose 
there  are  the  following  constants :  2H  in.  diameter  of  hose  d  =  .8088S  ft.; 
length  of  hose  2  =  100  ft.,  and  2g  =  64.4.  The  variables  are :  «  s  velocity  in 
feet  per  second;  h  =  loss  of  head  in  feet  per  100  ft.  of  hose;  m  =  a  uoefR- 
cient  found  by  experiment ;  the  velocity  v  is  found  fh)m  the  given  dis- 
charges of  the  jets  through  the  given  diameter  of  hose. 

Head  and   PreMure    liOimes   by  Friction   In    10O*ft« 
liCngtlis  of  Bnbber-lined  Smooth  aVj-ln*  Hoee, 


Discharge 

Velocity 

Ck>eflicieDt, 

Head  Lost, 

Pressure 

Gallons  per 

per  minute. 

per  second. 

m. 

ft. 

Lost.  lbs. 

84  hours. 

gallons. 

ft. 

per  sq.  in. 

200 

18.078 

.00450 

88.89 

9.98 

888,000 

850 

16.888 

.00446 

85.65 

15.48 

800,000 

aoo 

18.868 

.00448 

46.80 

80.81 

488,000 

847 

81.677 

.00489 

61.58 

26.70 

489,680 

860 

88.873 

.00489 

68.48 

29.78 

604,000 

400 

80.144 

.00186 

88.83 

88.55 

676,000 

450 

89.408 

.00434 

111.80 

48.58 

648.000 

600 

88.675 

.00488 

187.50 

59.67 

780,000 

580 

88.968 

.00481 

148.40 

64  40 

748,800 

These  frictions  are  for  given  volumes  of  flow  in  the  hose  and  the  veioci- 
ties  respectively  due  to  those  volumes,  and  are  independent  of  size  of 
nozzle.  The  changes  in  nozzle  do  not  affect  the  friction  In  the  hose  if  there 
is  no  change  in  velocity  of  flow,  but  a  larger  nozzle  with  equal  pressure  at 
the  nozzle  augments  the  discharge  and  velocity  of  flow,  ana  thus  materially 
increases  the  friction  loss  in  the  hose. 

liOsa  of  Pressure  (p)  and  Head  {h)  In  Hnbber-llned 
Smootli  3H"ln«  Hose  may  be  found  approximately  by  the  formuiee 

^  ~  4is0d5  *"^  ^  ~  laoid*'  ^^  ''^Wch  p  =s  pressure  lost   by  friction,   in 

Sounds  per  square  inch;  I  =s  length  of  hose  in  feet;  q  =  gallons  of  water 
ischarged  per  minute:  a  =  diam.  of  the  hose  in  inches,  ^  in.;  A  =  friction- 
head  in  feet.    The  coefllcient  of  d*  would  be  decreased  for  rougher  hose. 

The  loss  of  pressure  and  head  for  a  1^-in.  stream  with  power  to  reach  a 
height  of  80  ft.  is>,  in  each  100  ft.  of  ^in.  hose,  approximatelv  80  lbs.,  or  45 
ft.  net.  or,  say,  including  friction  in  the  hydrant,  \i  ft.  loss  of  nead  for  each 
foot  of  hose. 

If  we  change  the  nozzles  to  1^  or  14^  In.  diameter,  then  for  the  same  80  ft. 
height  of  stream  we  increase  the  friction  losses  on  the  hose  to  approxi> 
mately  %  ft.  and  1  ft.  head,  respectively,  for  each  foot-length  of  hose. 

These  computations  show  tne  great  difficulty  of  meuntaining  a  high 
stream  through  large  nozzles  unless  the  hose  is  very  short,  especially  for  a 
gravity  or  direct- pressure  syMem. 

This  single  ly^-in.  stream  requires  approximately  56  lbs  pressure,  equiva- 
lent to  189  ft.  head,  at  the  play-pipe,  and  45  to  60  ft.  head  for  each  100  ft. 
length  of  smooth  2U-in.  hose,  so  that  for  100,  800,  and  300  ft.  of  hose  we 
must  have  available  heads  at  the  hvdrant  or  fire-engine  of  106,  156,  and  206 
ft.,  respectively.  If  we  substitute  l^-in.  nozzles  for  same  height  of  stream 
we  must  liave  available  heads  at  the  liydrants  or  engine  of  185,  855  and  :fei5 
ft.,  respectively,  or  we  must  increase  the  diameter  of  a  portion  at  least  of 
the  long  hose  and  save  friction-loss  of  head. 

Bated  Capacities  of  Steam  FIre-enelnes,  which  is  perhaps 
one  third  greater  than  their  ordinary  rate  of  woilc  at  fires,  are  subatantially 
as  follows : 

8d  size,    550  gals,  per  mln.,  or    798,000  gals,  per  84  houn, 
ad    "        700    "  "  1,008.000 

1st  •*        900    "  "  1,296.000         ••  •• 

lext.,   1,100    *•  '•  1,6W,000         "  •• 


THE  SIPHOK. 


581 


PressoreM  required  at  Nozale  and  at  Pamp.wltli  <|aantlty 
and  Pressure  of  IVater  Neeessary  to  throw  IVater 
Various  Distances  tbrongrli  DllTerent-slzed  Nozzles-* 
using:  2>i-lnch  Rubber  Rose  and  Smootb  Nozzles* 

(From  EzpcrimftDts  of  Ellis  &  Leshure,  Fannliig's  "  Water  Supply.") 


Size  of  Nozzles. 

1  Inch. 

IH  Inch. 

Pressure  at  Dozzle,  lbs.  per  sq.  in 

•  Pressure  at  pump  or  hyclrant  with 
100  ft.  2^-incn  rubber  hose 

40 

48 
155 
109 

TO 

60 

78 
169 
142 
108 

80 

97 
219 
168 
181 

100 

121 
245 
186 
14S 

40 

54 
196 
113 

8t 

60 

81 
240 
148 
112 

80 

108 
277 
175 
187 

100 
185 

Gallons  per  minute .  

810 

Horizontal  distance  thrown,  feet 

VerUcal  distance  thrown,  feet 

103 
157 

Size  of  Nozzles. 

IH  loch. 

IH  Inch. 

Pressure  at  nozzle,  lbs.  per  sq.  in 

*  Pressure  at  pump   or  hydrant  with 
100  feet  SH-inch  rubber  hose 

40 

61 
242 
118 

Si 

60 

92 

297 
156 
115 

80 

128 
842 
186 
142 

100 

154 
883 
207 
164 

40 

71 
298 
124 

85 

60 

107 
358 
166 
118 

80 

144 
413 
200 
146 

100 

180 

Gallons  per  minute 

Horizontal  distance  thrown,  feet 

Vertical  distance  thrown,  feet. 

463 
224 
169 

*  For  greater  length  of  2V^-inch  hose  the  increased  friction  can  be  ob- 
tained by  noting  the  differences  between  the  above  given  '*  pressure  at 
nozzle'**  and  ** pressure  at  pump  or  hydrant  with  100  feet  of  hose.*'  For 
instance,  if  it  requires  at  hydrant  or  pump  eight  pounds  more  pressure 
than  it  does  at  nozzle  to  overcome  the  friction  when  pumping  through  100 
feet  of  8^-inch  hose  (using  1-inch  nozzle,  with  40-pound  pressure  at  said 
nozzle)  then  it  requires  16-pouiids  pressure  to  overcome  the  friction  in 
forcing  through  200  feet  of  same  size  hose. 

Decrease  of  Flonr  due  to  Increase  of  lienygtb  of  Hose. 
^J.  R  Freeman's  Experiments,  Trans.  A.  8.  O.  E.  1889.)— Ifthe  static  pres- 
sure is  80  lbs.  and  the  hydrant-pipes  of  such  size  that  the  pressure  at  the  hy- 
drant is  70  lbs.,  the  hose  2^  In.  nominal  dlam.,  and  the  nozzle  1^  in.  diam., 
the  height  of  effective  flre-stream  obtainable  and  the  quantity  in  gallons  pet 
minute  will  be: 


Best  Rubber- 

Linen  Hose. 

lined  Hose. 

Height,       Gals. 

Height,       Gals. 

feet.      per  mln. 

feet,     per  mln. 

78              261 

81              282 

42              184 

61              229 

27              146 

46              1^2 

With    50ft.  of  2^ln.  hose, 

»'     250  " 

.«     5Q0  «    .»       «f 

With  500  ft.  of  smoothest  and  best  rubber-lined  hose,  if  diameter  be 
exactly  2^  In.,  effective  height  of  stream  will  be  89  ft.  (177  gals.);  if  diameter 
be  ^  In.  itfger,  effective  height  of  stream  will  be  46  ft.  (192  gal^.) 

THB  SIPHON. 

The  Siphon  is  a  bent  tube  of  unequal  brat]che8,''open  at  both  ends,  and 
is  used  to  convey  a  liquid  from  a  higher  to  a  lower  level,  over  an  intermedi- 
ate point  hieher  than  either.  Ito  parallel  branches  being  in  a  verticalplane 
and  plungea  into  two  bodies  of  liquid  whose  upper  surfaces  are  at  different 
levels,  the  fluid  will  stand  at  the  same  level  both  within  and  without  each 
branch  of  the  tube  when  a  vent  or  small  opening  is  made  at  the  bend.  If 
the  air  be  withdrawn  from  the  Hiphon  through  this  vent,  the  water  will  rise 
in  the  branches  bv  the  atmospheric  pressure  without,  and  when  the  two 
columns  unite  and  the  vent  is  closed,  the  liquid  will  flow  from  the  upper 
reservoir  as  long  as  the  end  of  the  shorter  branch  of  the  siphon  is  below  the 
surface  of  the  hquid  in  the  reservoir. 

If  the  water  was  free  from  air  the  height  of  the  bend  above  the  supply 
level  might  be  as  great  as  83  feet. 


582  HTDBA0LICS. 

It  At*  area  of  croflB-aeetloii  of  th«  tube  In  raiiare  feet,  ffa  the  dIffereiMa 
In  level  between  the  two  reeerrolra  in  feet,  D  the  density  of  the  llqnid  in 
pounds  per  cubic  foot,  then  ADH  measures  the  Intensity  of  the  force  which 
causes  the  morement  of  the  fluid,  and  Ts  i^igH  =  8.02  i^H  fs  the  theoretical 
Telocity,  in  feet  per  second,  which  is  reduced  by  the  loss  of  head  for  entry 
and  friction,  as  in  other  cases  of  flow  of  liquids  through  pipes.  In  the  case 
of  the  difference  of  level  being  greater  than  88  feet,  however,  the  velocity  of 
the  water  in  the  shorter  leg  is  limited  to  that  ilue  to  a  height  of  88  feet,  or 
that  due  to  the  difference  between  the  atmospheric  pressure  at  the  entrance 
and  the  vacuum  at  the  bend. 

Leicester  Allen  {Am,  Mach.,  Nov.  2, 1893)  says:  The  supply  of  liquid  to  a 
siphon  must  be  greater  than  the  flow  which  would  take  plaoe  from  the  dia- 


charve  end  of  the  pipe,  provided  the  pipe  were  fllled  with  the  liquid,  tbe 
supply  end  stopped,  and  the  discharge  end  c  "     *       *"    "'"  "*"  "■ 

Is  idt  free,  unregulated,  and  unsubmerged. 


zrom  sncn  a  sizea  pipe  wicn  tne  specmea  nea 
4^  Slpl&on  on  the  irater-anpplr  of 

HSnfo  Neio8,  May  4, 1808.)— A  18-lnch  siphon, 
lift  of  89.19  feet  and  a  46<>  change  in  alignmen 


i^  illustrate  this  principle,  let  us  suppose  the  extreme  case  of  a  sipbon 
having  a  calibre  of  i  foot,  in  which  the  difference  of  level,  or  between  the 
point  of  supply  and  discharge,  is  4  inches.  Let  us  further  suppoee  this 
siphon  to  be  at  the  sea-level,  and  its  highest  point  above  the  level  of  the 
supply  to  be  27  feet.  Also  suppose  the  discluirge  end  of  this  siphon  to  be  un- 
regulated, unsubmerged.  It  would  be  inoperative  because  the  water  in  the 
longer  leg  would  not  be  held  solid  by  the  pressure  of  the  atmosphere  asainst 
it,  and  it  would  therefore  break  up  and  run  out  faster  than  it  could  oe  re- 
placed at  the  inflow  end  under  an  effective  head  of  only  4  Inches. 

liOnff  81plioiis*~Prof.  Joseph  Torrey,  in  the  Amer.  MachiniMt^ 
describes  a  Ions:  siphon  which  was  a  partial  failure. 

The  length  of  the  pipe  was  1792  feet.  Tlie  pipe  was  8  Inches  diameter,  and 
rose  at  one  point  9  feet  above  the  initial  level.  Tlie  flnal  level  was  90  feet 
below  the  initial  level.  No  automatic  air  valve  was  provided.  The  highest 
point  in  the  siphon  was  about  one  third  tbe  total  distance  from  the  pond  and 
nearest  the  i>ond.  At  this  point  a  pump  was  placed,  whose  mission  was  to 
All  the  pipe  when  necessary.  This  siphon  would  flow  for  about  two  hours 
and  then  cease,  owing  to  accumulation  of  air  in  the  pipe.  When  in  full 
operation  It  discharged  43^  gallons  per  minute.  The  theoretical  discbarge 
from  such  a  sized  pipe  with  the  specified  head  in  f>5>^  gallons  per  mitnite. 

*    '  'of  moant  Ternoo,  N.  TT. 

ion,  926  feet  long,  with  a  maximum 
nment,  was  put  In  use  in  1809  by  the 
New  York  City  Suburban  Water  Co.,  which  supplies  Mount  Vernon,  K.  Y. 

At  iu  summit  tbe  siphon  crosses  a  supply  main,  which  Is  tapped  to  charge 
the  siphon. 

The  air-chamber  at  the  siphon  Is  12  inches  by  16  feet  lone.  A  lj(-Incfa  tap 
and  cock  at  the  top  of  the  chamber  provide  an  outlet  for  the  collected  air. 

It  was  found  that  the  siphon  with  air-chamber  as  desc.Ibed  would  run 
until  126  cubic  feet  of  air  had  gathered,  and  that  this  took  place  only  half  as 
soon  with  a  14-foot  lift  as  with  the  full  lift  of  22.19  feet.  The  siphon  wiU 
operate  about  12  hours  without  being  recharged,  but  more  water  can  be 
gotten  over  by  charging  every  six  hours.  It  can  be  kept  running  28  hours 
out  of  24  with  only  one  man  in  attendance.  With  the  siphon  as  described 
above  it  is  necessary  to  close  the  valves  at  each  end  of  the  siphon  to 
recharge  it. 

It  has  been  found  by  weir  measurements  that  the  discharge  of  the  siphon 
before  atr  accumulates  at  the  summit  is  practically  the  same  as  through  a 
straight  pipe. 

nEASUBBHIBNT  OF  FI^OWING  WATKB. 

Pleaoniet«r.— If  a  vertical  or  oblique  tube  be  inserted  Into  a  pipe  con- 
taining water  under  pressure,  the  water  will  rise  in  the  former,  and  the  ver- 
tical height  to  which  it  rises  will  be  the  head  producing  the  pressure  at  the 
point  where  the  tube  is  attached.  Buch  a  tube  is  called  a  piezometer  or 
pressure  measure.  If  the  water  In  the  piezometer  falls  below  its  proper 
level  it  shows  that  the  pressure  in  the  main  pipe  has  been  reducedTby  an 
obstruction  between  the  piezometer  and  the  reservoir.  If  the  water  rises 
above  Its  proper  level,  it  indicates  that  the  pressure  there  has  been  In- 
creased by  an  obstruction  bevond  the  piezometer. 

If  we  imagine  a  pipe  full  of  waUtr  to  be  provided  with  a  number  of  pie- 
someters,  then  a  line  Joining  the  tops  of  the  columns  of  water  in  them  is 
the  hydraulic  grade-line. 


MEASUREMENT  OP  FLOWINO  WATER,  583 

Pltot  Tube  Ganee*— The  Pitot  ivihe>  Is  used  for  nieasurfni?  the  veloo- 
Itj  of  fluids  ill  motion.  It  has  been  used  wlih  preat  success  in  measurinr 
the  flow  of  natural  gas.  (S.  W.  Robinson,  Report  Ohio  Geol.  Survey,  iSflO.) 
(See  also  VanNostrand^sMag.,  vol.  xxxv.)  It  is  simplv  a  tube  so  bent  that 
a  short  Wj^  extends  into  the  current  of  fluid  flowing  from  a  tube,  with  tiie 
plane  of  ihe  entering  orifice  opposed  at  right  angles  to  the  direction  of  the 
current.  The  pressure  caused  by  the  impact  of  the  current  is  transmitted 
through  the  tube  to  a  pressure-gauge  of  any  Iciod,  such  as  a  column  of 
water  or  of  mercury,  or  a  Bourdon  spring-gauge.  From  the  pi'essure  thus 
indicated  and  the  known  density  and  temperature  of  the  flowing  gas  is  ob- 
tained the  head  corresponding  to  the  pressure,  and  from  this  the  velocity. 
In  a  modification  of  the  Pitot  tube  described  by  Prof.  Robinson,  there  are 
two  tui>e8  inserted  into  the  pipe  conveying  the  gas,  one  of  which  has  the 
plane  of  the  orifice  at  right  angles  to  the  current,  to  receive  the  static  pres- 
soro  phis  the  pressure  due  to  impact;  the  other  has  tlie  plane  of  its  orifice 
parallel  to  the  current,  so  as  to  receive  the  static  pressure  only.  These 
tubes  are  connected  to  the  legs  of  a  C7  tube  partly  filled  with  mercuiy,  which 
then  r^^isters  the  difference  in  pressure  in  the  two  tubes,  from  which  the 
velocity  may  be  calculated.  Ck>mparative  tests  of  Pitot  tubes  with  gas- 
meters,  for  measurement  of  the  flow  of  natural  gas,  have  shown  an  agree- 
ment within  9%. 

Vbe  Tentnrl  iVIeter.  invented  by  Cflemens  Heracbel,  and  described  in 
a  pamphlet  issued  by  the  Builders*  Iron  Foundry  of  Providenc  %  R  I.,  is 
ziamed  from  Venturi,  who  first  called  attention,  in  1796,  to  the  i-elarion  be- 
tween the  velocities  and  pressures  of  fiidds  when  flowing  through  converging 
and  diverging  tubes. 

It  consists  of  two  parts— the  tube,  through  which  the  water  flows,  and  the 
recorder,  which  registers  the  quantity  of  water  that  passes  through  the 
tuba. 

The  tube  takes  the  shape  of  two  truncated  cones  joined  in  their  smillest 
diameters  by  a  short  throat-pieoe.  At  the  up-stream  end  and  at  tlie  throat 
there  are  preasure-chamben*.  at  which  points  the  pressures  are  taken. 

The  action  of  the  tube  is  based  on  that  property  which  causes  the  small 
section  o€  a  gently  expanding  frustum  of  a  oone  to  receive,  without  material 
resultant  loss  of  head,  as  much  water  at  the  smallest  diameter  as  is  dis- 
charged at  the  large  end,  and  on  that  further  property  which  causes  tiie 
pressure  of  the  water  flowing  through  the  throat  to  be  less,  by  virtue  of  its 
greater  velocity,  than  the  pressure  at  the  up-stream  end  of  the  tube,  each 
pressure  being  at  the  same  time  a  function  of  the  velocity  at  that  point  and 
of  the^ydrostatic  pressure  which  would  obtain  were  the  water  motionless 
wichin*the  pipe. 

The  recorder  is  connected  with  the  tube  by  pressure-pipes  which  lea'l  to 
It  from  the  chambers  surrounding  the  up-stream  end  and  the  throat  of  the 
tube.  It  may  be  placed  in  any  convenient  position  within  1000  feet  of  the 
tube.    It  is  operated  by  a  weight  and  clockwork. 

The  difference  of  pressure  or  head  at  the  en  trance  and  at  the  throat  of  the 
meter  is  balanced  in  the  recoixler  by  the  difference  of  level  iu  two  columns 
of  oiercary  In  cylindrical  receivenc  one  within  the  other.  The  inner  carries 
afloat,  the  position  of  which  is  indicative  of  the  quantity  of  water  flowing 
through  the  tube.  By  its  rise  and  fall  the  float  varies  the  time  of  contact 
between  an  integrating  drum  and  the  couutere  by  which  the  successive 
readings  are  registered. 

There  is  no  limit  to  the  sixes  of  the  meters  nor  the  miantity  of  water  that 
may  be  measured.  Meters  with  81-incb,  86-inch,  48- inch,  aud  even  20-foot 
tubes  can  be  readily  mnde. 

JSeaaoremeni  bT  Tentnrl  Tubes.  (Trans  A.  9.  C.  B.,  Nov..  1H87, 
and  Jan.,  18B8.)— Mr.  llerschel  recommends  the  use  of  a  Venturi  iu»>e.  in- 
serted in  the  force-main  of  the  pumping  engine,  for  determining  the  quantity 
of  water  dlseharged.  Such  a  tube  applied  to  a  84-inch  main  Iiam  a  total 
length  of  about  SO  feet.  At  a  distance  of  4  feet  from  the  end  nearest  the 
engine  the  Inside  diameter  of  the  tube  is  contracted  to  a  throat  having  a 
diameter  of  about  8  inches.  A  pressure-gatige  is  attached  to  each  of  two 
chambers,  the  one  surrounding  and  communicating  with  the  entrance  or 
main  pipe,  the  other  with  the  throat.  According  to  experiments  made  upon 
two  tubes  of  this  kind,  one  4  in.  In  diameter  at  the  throat  and  18  in.  at  the  en- 
trance, and  the  other  about  86  in.  in  diameter  at  the  throat  and  9  feet  at  its 
entrance,  the  quantity  of  water  which  passes  through  the  tube  is  very  nearly 
the  theoretical  discharge  thrmigh  an  opening  having  an  area  equal  to  that 
of  the  throat,  and  a  velocity  which  is  that  due  to  the  Hifferenoe  in  Head  ftixown 


584 


HYDBAULICa 


by  the  tfroRauKes.  Mr.  Herachel  states  that  the  coefficient  for  these  tw« 
widely-varying  sizes  of  tubes  and  for  a  wide  ranee  of  yelocit v  through  the 
pipe,  was  found  to  be  within  two  per  cent,  either  way,  of  W.  In  other 
words,  the  quantity  of  water  flowing  through  the  tube  per  second  is  ex- 
pressed within  two  per  cent  by  the  formula  Tr=  0.96  X  ^  X  l/^i.  In  which 
A  is  the  area  of  the  throat  of  the  tube,  h  the  head,  in  feet,  correspond- 
ing to  the  difference  in  the  pi'essure  of  tlie  water  entering  the  tube  and  that 
found  at  the  throat,  and  ^  =  8^.16. 

nteftsarem^nt  of  Dlaebai'K^  of  PuiiftpliiC">eiigtiies  by 
means  of  Noazles*  (Trans.  A.  S.  M.  E.,  xiii,  557).— Tlie  nieasurt^meut 
of  water  by  computation  from  its  discharge  through  orifices,  or  through  the 
nozzles  of  flre-hose,  furnishpR  a  means  of  determining  the  quantity  of  water 
delivered  by  a  pumping-engine  which  can  be  applied  without  much  difficulty. 
John  R.  Freeman,  Trans.  A.  S.  C.  E.,  Nov.,  1889,  describes  a  series  of  expt>rl- 
mentA  covering  a  wide  range  of  pressures  and  sizes,  and  the  results  showed 
that  the  coefficient  of  discharge  for  a  smooth  nozzle  of  ordinary  good  form 
was  within  one  half  of  one  per  cent,  either  way,  of  0.977 :  the  diameter  of 
the  nozzle  being  accurately  calipered.  and  the  pressures  being  det«*rmined 
by  means  of  an  accurate  gauge  attached  to  a  suitable  piezometer  at  the  base 
of  the  play-pipe. 

In  order  to  use  this  method  for  determining  the  quantity  of  water  dis- 
charged by  a  pumping-engine,  it  would  be  necessary  to  provide  a  pressure- 
box,  to  which  the  water  would  be  conducted,  and  attach  to  the  box  as  many 
nozzles  as  would  k>e  required  to  carry  off  the  water.  According  to  Mr. 
Freeman's  estimate,  four  1^-inch  nozzles,  thus  connected,  with  a  pressure 
of  80  lbs.  per  square  inch,  would  discharge  the  full  capacity  of  a  two-and  a> 
half-million  engine.  He  also  suggests  the  use  of  a  portable  apparatus  with 
a  single  opening  for  discharge,  consisting  essentially  of  a  Siamese  nossle, 
■o-caTied,  the  water  being  carried  to  It  by  three  or  more  lines  of  fire-hose. 

To  insure  reliability  for  these  measurements,  it  is  necessarv  that  the  shut- 
off  valve  in  the  force-main,  or  the  several  shut-off  valves,  should  be  tight, 
so  that  all  the  water  discharged  by  the  engine  may  pass  through  the  noczlfs. 

Flow  tltrongli  Rectanffnlar  Orlflces*  (Approximate.  See  p.  566.) 

Cubic  Fbbt  op  Watkr  Discharokd  per  Minute  throuob  an  Oripicb  Okb 
iirch  square,  under  any  hsad  of  water  prom  8  to  78  inches^ 
For  any  other  orifice  multiply  by  Its  area  in  square  inches. 
Formula,  C*  =  -624  Vh"X  a.    ^  =  cu.  ft  per  mln. ;  a  =  area  in  sq.  In. 


805 
4.00 
406 
4.09 
4.U 
4.18 
4.21 
4.27 
4.80 
4.84 


measurement  of  an  Open  Stream  by  Teloelty  and  f^roaa- 
section* — Measure  the  depth  of  the  water  at  from  0  to  12  points  acniss 
tlie  81  ream  at  equal  distances  between.  Add  all  the  depths  in  feet  together 
and  divide  by  the  number  of  measurements  made;  this  will  be  the  avf rage 
depth  of  the  stream,  which  multiplied  by  its  width  will  give  its  ares  or  cro««i> 
section.  Multiply  this  by  the  velocitv  of  the  stream  in  feet  per  minute,  and 
the  result  will  be  the  discharge  in  cubic  feet  per  minute  of  the  stream. 

The  velocity  of  the  stream  can  be  found  by  laying  off  100  feet  of  the  bank 
and  throwing  afloat  into  the  middle,  noting  the  time  taken  in  passing  over 
the  100  ft.    Do  this  a  number  of  times  and  take  the  average ;  then,  dividing 


MEASUREMEKT  OF  FLOWINa  WATEB. 


585 


this  distance  bv  the  time  gives  the  velocity  at  the  surface.  As  the  top  of  the 
stream  flows  raster  than  the  bottom  or  sides— the  average  velocity  being 
about  8Sjt  of  the  surface  velocity  at  the  middle— it  is  convenient  to  measure 
a  distance  of  180  feet  for  the  float  and  reckon  it  as  100. 


Fio.  180. 
ISlners'  Ineb  IHeftsnreiiieiits* 


(Pelton  Water  Wheel  Co.) 


The  cut.  Fig.  180,  shows  the  form  of  measuring-box  ordinarily  used,  and  tho 
following  table  gives  the  disohaitfe  in  cubic  feet  per  minute  of  a  miner^s  inch 
of  water,  as  measured  under  the  various  heaos  and  different  lengths  and 
heights  of  apertures  used  in  California. 


Length 

Openings  2  Inches  High. 

Openings  4  Inches  High. 

Opening 

Head  to 

Head  to 

Head  to 

Head  to 

Head  to 

Head  to 

Hn 

Centre, 

Ceni  re. 

Centre, 

Centre, 

Centre, 

Centre, 

inches. 

5  inches. 

6  inches. 

7  inches. 

6  inches. 

6  inches. 

7  inches. 

Cu.ft. 

Cu.  ft. 

Cu.  ft. 

Cu.  ft. 

Cu.  ft. 

Cu.  ft. 

4 

1 .318 

1.473 

1.589 

l.SiO 

1.450 

1.570 

6 

1.355 

1.480 

1  .r,96 

1.3:« 

1.470 

1.695 

8 

1.359 

1.4S4 

1  600 

1.344 

1.481 

1.608 

10 

1.361 

1.4a5 

l.WW 

1.349 

1.487 

1.615     - 

1« 

1.368 

1.4J»7 

a. 604 

1  av2 

1.491 

1.620 

14 

1.864 

1.438 

1.604 

1.354 

1.494 

1.628 

16 

1.865 

1.489 

1  605 

1.856 

1.496 

1.626 

18 

1.365 

1-489 

1.606 

1.357 

1.498 

1.628 

80 

1.365 

1  490 

1.(K)6 

1.359 

1.490 

1.630 

22 

1.366 

1.I9U 

1  007 

1.359 

1.500 

1.631 

84 

1.866 

1.490 

1.607 

1.360 

1.501 

1.632 

2R 

1.366 

1.490 

1.607 

1.361 

1.602 

1.638 

28 

1.367 

1  491 

1.607 

1.861 

1.503 

1.634 

80 

1.8G7 

1.491 

1.606 

1.362 

1.508 

1.635 

40 

1.867 

1.492 

1.606 

1.368 

1.506 

1.637 

60 

1.868 

1.493 

1.609 

1.364 

1  507 

1.639 

60 

1.368 

1.493 

1.609 

1.365 

1.508 

1.640 

TO 

1.868 

1.493 

1.609 

1.365 

1.508 

1.641 

80 

1.868 

1.493 

1.609 

1.366 

1.509 

1.641 

90 

1.869 

1.493 

1.610 

1.366 

1.509 

1.641 

100 

1.360 

1.494 

1  610 

l..%6 

1.509 

1.642 

MoTK.—The  apertures  from  which  the  above  measurements  were  obtained 


586 


HTDRAULICS. 


were  through  material  1  finches  thick*  and  the  lower  edge  2  inches  above 
the  bottom  of  the  measunng-box,  thus  giving  full  contraction. 
/T>^^^^r^/  ^?*®."^^7®jr.  Wetai.    W«lr  Dam  ]llCe««nrement. 

(Pelton  Water  Wheel  Co.>>Place  a  boai*d  or  plank  in  the  stream,  as  shown 


Fio.  181. 

in  the  sketch,  at  some  point  where  a  pond  will  form  abore.  The  length  of 
the  notch  in  the  dam  should  be  from  two  to  four  times  its  depth  for  small 
quanUties  and  longer  for  large  quantities.  The  edges  of  the  notch  should 
be  bevelled  toward  the  intake  side,  as  shown.  The  overfall  below  the  notch 
sliould  not  be  less  than  twice  its  depth.  [Francis  says  a  fall  below  the  crest 
equal  to  one-half  the  head  is  sufficient,  but  there  must  be  a  free  access  of 
air  under  the  sheet! 

In  the  pond,  about  6  ft.  above  the  dam,  drive  a  stake,  and  then  obstruct  the 
water  until  it  rises  precisely  to  the  bottom  of  the  notch  and  mark  the  stake 
at  this  level.  Then  complete  the  dam  so  as  to  cause  all  the  water  to  flow 
through  the  notcli,  and,  after  time  for  the  water  to  settle,  mark  the  stake 
again  for  this  new  level.  If  preferred  the  stake  can  be  driven  with  its  top 
precisely  level  with  the  bottom  of  the  notch  and  the  depth  of  the  water  be 
measured  with  a  rule  after  the  water  is  flowing  free,  but  the  marks  are  pre- 
ferable in  most  cases.  The  stake  can  then  be  withdrawn;  and  the  distance 
between  the  marks  is  the  theoretical  depth  of  flow  corresponding  to  the 
quantities  in  the  table  on  the  following  page. 

Francis's  FormalsD  for  IVelm* 

As  given  by  As  modified  by 

Francis.  Smith. 

^su^pTeSed''!!'.^".^  '^°^''~'.^.'^°'  }     Q  =  3.83^/,*  8.29(/+  ^)h^ 

^suppJ^".*'.  I".""*  .':'^".\''.'^.".'^'! . .  }      Q  =  3.33(«  -  .Ihyh^        3.29«At 

Weirs  with  full  contraction Q  =  3.33(1  -  .2fi)h^       8.m(/  -  -)^' 

The  greatest  variation  of  the  Francis  formulaa  from  the  values  of  c  given  by 
Smith  amounts  to  ^\^.  The  modified  Francis  formulas,  says  Smith,  will  give 
results  sufficiently  exact,  when  great  accuracy  is  not  required,  within  the 
limits  of  hf  from  .5  ft.  to  2  ft.,  I  being  not  less  than  8  k* 


MEASUREMEirr  OF  FLOWING   WATER. 


587 


Q  =  (liflchance  in  cubic  feet  per  second,  I  =  length  of  weir  in  feet,  h  =effec- 
tlve  head  iu  feet,  ineasui-ed  from  the  level  of  the  crest  to  the  level  of  still 
water  above  the  weir. 

It  Q'  =  discharge  in  cubic  feet  per  minute,  and  V  and  h'  are  taken  in 

inches,  the  first  of  the  above  formulce  reduces  to  ^  =  0.4Vh'^.  From  this 
formula  the  f ollowing  table  is  calculated.  The  Talues  are  sufllcientiy  accu- 
rate for  ordinary  computations  of  water-power  for  weirs  without  end  con- 
traction, that  is,  for  a  weir  the  full  width  of  the  channel  of  approach,  and 
are  approximate  also  for  weirs  with  end  contraction  when  i  =  at  least  IWi, 
but  about  0%  In  excess  of  the  truth  when  I  =  4A. 

UTelr  Table* 

Gtvino  Cubic  Fkxt  of  Water  per  Minute  that  will  Flow  over  a  Weir 
one  inch  wide  amd  from  ^  to  so^  inches  deep. 

For  other  widths  multiply  by  the  width  in  inches. 


^in. 

^in. 

96  in. 

Hin. 

Win. 

^in. 

%in. 

in. 

cu.ft. 

cu.ft. 

cu.  ft. 

cu.  ft. 

cu.  ft. 

cu.  ft. 

cu.  ft. 

cu.  ft. 

0  • 

.00 

.01 

.06 

.09 

.14 

.19 

.26 

.32 

1  > 

.40 

.47 

.55 

.61 

.73 

.82 

.92 

1.02 

8 

1.18 

1.28 

1.85 

1.46 

1.58 

1.71) 

1.82 

1.95 

8 

2.07 

2.21 

2.84 

2.48 

2.61 

2.76 

2.90 

8.05 

4 

s.ao 

8.85 

8.50 

3.66 

8.81 

8.97 

4.14 

4.80 

5 

4.47 

4.64 

4.81 

4.98 

5.15 

5.33 

5.51 

5.69 

6 

B.87 

6.06 

6.25 

6.44 

6.6i 

6.82 

7.01 

7.21 

7 

7.40 

7.60 

7.80 

8.01 

8.21 

8.42 

8.63 

8.88 

8 

9.06 

9.26 

9.47 

9.69 

9.91 

10.13 

10.85 

10.67 

9 

10.80 

11.02 

11.25 

11.48 

11.71 

11.94 

12.17 

12.41 

10 

12.64 

12.83 

18.  IQ 

18.86 

13.60 

18.85 

14.09 

14.84 

11 

14.&9 

14.84 

15.09 

15  34 

15.69 

15.85 

16.11 

16.86 

12 

16.62 

16.88 

17.15 

17.41 

17.67 

17.94 

18.21 

18.47 

18 

18.74 

19.01 

19.29 

19.56 

19.84 

20.11 

20  89 

90.67 

14 

20.95 

21.23 

21.51 

21.80 

22.08 

22.:i7 

22.65 

22.04 

15 

23.28 

28.52 

28.82 

24.11 

24.40 

24.70 

25.00 

25.80 

16 

25.60 

25.90 

26.20 

26.60 

26.80 

27.11 

27.42 

27.73 

17 

28.08 

28.84 

28.65 

28.97 

29.28 

29.50 

29.91 

80.22 

18 

80.54 

80.86 

81.18 

31.50 

31  82 

8-M5 

82.47 

82.80 

19 

33.12 

83.45 

8:J.T8 

34  11 

34  44 

84.77 

35.10 

35.44 

90 

8.0.77 

86.11 

36.45 

86.78 

87.12 

87.46 

37.80 

38.15 

For  more  accurate  computations,  the  coefficients  of  flow  of  Hamilton 
Smith,  Jr.,  or  of  Bazin  should  be  used.  In  Smith's  hydniulics  will  be  found 
a  collection  of  results  of  experiments  on  orifices  and  weii-s  of  various  shapes 
made  by  manv  different  authorities,  tofrether  with  a  discussion  of  their 
several  formulaB.    (Set«  also  Trautwine's  Pocket  Book.) 

Baaiili'S  Experiments*— M.  Bazin  (Annaleg  des  Ponta  et  Chatiaa^ea, 
Oct.,  1888,  translated  by  Marichai  nnd  Trauiwine,  Proc.  Enj^rs.  Club  of  Phila.. 
Jan  ,  1890),  made  an  extensive  series  of  ex|>erinient8  with  a  sharpKsreMted 
weir  without  lateral  contraction,  the  air  bein^  admitted  freely  behind  the 
falling  sheet,  and  found  values  of  m  varying  from  0.42  to  0.50,  with  varia- 
tions of  the  length  of  the  weir  from  19%(  to  789^  in.,  of  the  height  of  the  cr«st 
above  the  bottom  of  the  channel  from  0.79  to  2.46  ft.,  and  of  the  ht^ad  from 
1,97  to  23.62  in.  From  these  experiments  he  deduces  the  following  formula : 

^=[o.425  +  0.2l(p^y]£.tf  |/^. 

in  which  Pis  the  height  in  feet  of  the  crest  of  the  weir  above  the  bottom  of 
the  channel  of  approach,  L  the  length  of  the  weir,  H  the  head,  both  in  feet, 
and  Q  the  discharge  in  cu.  ft.  per  sec.  This  formula,  says  M.  Basin.  Is  en- 
tirely practical  where  errors  of  2%  to  8jJ  are  admissible.  The  following 
table  is  condensed  from  M.  Basin's  paper : 


588 


WATER-POWBB. 


Valuks  of  the  Cokffioibnt  m  in  THE  FoBinTi«A  Q  »  mLH  VigH^  fob  a 
Sharp-crksted  Wbtr  wtthoot  I^teral  CONraAonoN;  thjc  *Aik  bkhaq 
Admitted  Freely  Behind  the  Fxlloiq  Shbet. 


Height  of  Crest  of  Weir  Above  Bed  of  ChanneL 

Head, 

mt" 

Feel... 0.66 

0.98 

1.81 

1.64 

l.wl  8.68 

S.SsI  4.92 

666 

o» 

Inches  7.87 

11.81 

16.75 

19.69 

23.62 

81.80 

89.88  60.07 
m       m 

78.76 
m 

OB 

Ft. 

In. 

m 

m 

m 

ni 

m 

m 

IH 

.164 

1.97 

0  458 

0.458 

0.451 

0.450 

0.449 

0.449 

0.449  0.448 

0.448 

0.4481 

.280 

2.76 

0.455 

0.448 

0.445 

0.448 

0.442 

0.441 

0.440  0.440 

0.489 

0.48Q1 

.895 

8.64 

0.457 

0.447 

0.442 

0.440 

0.488 

0.486 

0.436  0.435 

0.484 

O.4840 

.894 

4.72 

0.462 

0.448 

0.442 

0.438 

0.486 

0.488 

0.482i  0.480  0.430 

0.4291 

.5ao 

6.80 

0.471 

0.458 

0.444 

0.488 

0.485 

0.481 

0.4S0I 0.427 

0.426 

0.4:M6 

.656 

7.87 

0.480 

0.459 

0.447 

0.440 

0.486 

0.481 

0.428i0.425 

0.428 

0.4215 

.787 

9.45 

0.488 

0.465 

0.48S 

0.444 

0.488 

0.482 

0.428  0.424 

0.422 

0.4194 

.919 

11.02 

0.496 

0.472 

0.467 

0.448 

0.441 

0.488 

0.429  0.424 

0.4S 

0.4181 

1.050 

12.60 

0.478 

0.462 

0.452 

0.444 

0.486 

0.480  0.424 

0.42ri  0.4108 

1.181 

14.17 

0.488 

0.467 

0.456 

0.448 

0.48810.48210.424 

0.421 

a4156 

1.812 

15.75 

0.489 

0.472 

0.459 

0.461 

0.440 

0.4880.424 

0.421 

0.4144 

1.444 

17.82 

0.404 

0.476 

0.463 

0.454 

0.442 

0.485,0.485 

0.451 

0.4134 

1.575 

18.90 

•  *• .  ■ 

0.480 

0.467 

0.467 

0.444 

0.486' 0.42S 

0.421 

0.4122 

1.706 

20.47 

0.483 

0.470 

0.460 

0.446 

0.438  0.426 

0.4«1 

0.4112 
0.410? 

1.887 

22.05 

0.487 

0.478 

0.463 

0.448 

0.480;0.427 

0.421 

1.969 

23.02 

0.490 

0.476 

0.466 

0.451 

0.4410.427 

0.421 

0  409f 

* 

A  coDipaHRon  of  the  results  of  this  formula  with  those  of  ezperlinents, 
says  M.  iiazin,  justifies  us  in  belieyiiii?  that,  except  in  the  unusual  case  of  a 
very  low  weir  (which  nhould  always  be  avoided),  the  preceding  table  wiU 
Kive  the  coefficient  m  in  all  cases  within  1%;  provided,  however,  that  the  ar^ 
ranf^ments  of  the  standard  weir  are  exactly  reproduced.  It  is  especially 
important  that  the  admission  of  the  air  behind  the  falling  sheet  be  perfectur 
assured.  If  this  condition  is  not  complied  with,  m  may  vary  within  muda 
wider  limits.  The  type  adopted  gives  the  least  possible  variaUon  to  tha 
coefficient. 


WATEB-POWKEU 

I 

Poiver  or  a  Fall  of  lirateiwKfllcleiicj.— The  grocs  power  of 

a  fall  of  water  is  the  product  of  the  weight  of  water  discharged  in  a  unit  of 
time  into  the  total  bead,  i.e.,  the  difference  of*  vertical  elevation  of  the 
upper  surface  of  the  water  at  the  points  where  the  fall  In  question  befrfns 
an«i  ends.  The  term  **  head  **  used  in  connection  with  water-wheels  Is  the 
difference  In  heifrht  from  the  surface  of  the  water  in  the  wheel-pit  to  tlie 
surface  in  the  pen-stock  when  the  wheel  is  running. 

If  Q  =a  cubic  feet  of  water  discharged  per  second,  D  s  weight  of  a  cobh 
foot  of  water  s  62.86  lbs.  at  60o  F.,  jS  =  total  head  in  feet;  then 

DQH  s  gross  power  in  foot-pounds  per  second, 
and  DQH  -•-  550  ss.n^QH  s  gross  horse-power. 

If  Q' IB  taken  in  cubic  feet  per  minute,  H.  P. »  ^^^-  «  OOISOQ'A 

A  water-wheel  or  motor  of  anv  kind  cannot  utilise  the  whole  of  the  liead 
H,  since  tliere  are  losses  of  head  at  both  the  entrance  to  and  the  exit  from 
the  wheel.  There  are  also  losses  of  energy  due  to  friction  of  the  water  In 
its  passage  through  the  whe«>l.  I'he  ratio  of  the  power  developed  by  the 
wheel  to  the  gross  power  of  the  fall  is  tlie  efficiency  of  the  wheel.    F^  TSflt 

efficiency,  net  horse-power  s  .00142Q'H  s~^. 


WLL-POWBB,  689 

A  head  of  water  oan  be  made  use  of  In  one  or  other  of  the  following^  ways 
vis.: 

Ist.  By  ita  weight,  as  in  the  water-balance  and  oTershot-wheel. 

''Id.  By  its  pressure,  as  in  turbines  and  in  the  hydraulic  engine,  hydraulic 
presR,  crane,  etc 

3d.  By  its  Impulse,  as  in  the  undershot- wheel,  and  in  the  Pelton  wheeL 

4th.  By  a  combination  of  the  above. 

Hors«*poir6r  of  a  Bnniiliis  Stream*— The  gross  horse-power 
is.  H.  P.  s  \h  X  eHM  -4-  fiOO  B  .1184^,  in  «  hicb  O  is  the  discharge  in  cubio 
feet  per  second  actually  impinging  on  the  float  or  bucket,  and  JB  s  theoret- 
ical head  due  to  the  velocity  of  the  stream  *  —  at  ---- ,  in  which  v  Is  the 

xg      C4.4 

Telocity  in  feet  per  second*  If  ^  be  taken  In  cubic  feet  per  minute, 
fl.  P.  ^  .00189O'.fi. 

Thus,  if  the'fioats  of  an  undershot-wheel  driven  by  a  current  alone  be  6 
feet  X  1  foot,  and  the  velocity  of  stream  s  210  ft.  per  minute,  or  ^  ft.  per 
see.,  of  which  the  theoretical  head  Im  .10  ft..  Q  s  5  sq.  ft.  x  810  s=  1060  cu.  ft. 
per  minute  ;  H  a  .19ft. ;  H.  P.  «  1050  x  .19  X.00189  s  .8T7  H.  P. 

The  wheels  would  realise  only  about  .4  of  thLs  power,  ou  account  of  friction 
and  slip,  or  .161  H.P.,  or  about  .08  H.P.  per  square  foot  of  float,  which  is 
equivalent  to  88  sq.  ft.  of  float  per  H.  P. 

Ovrrent  Hoiom*— A  cu.Tent  motor  could  only  utilise  the  whole  power 
of  a  running  stream  If  it  could  take  all  tne  velocity  out  of  the  water,  so  that 
it  wovM  leave  the  floats  or  backets  with  no  velocity  at  all;  or  in  other  words, 
it  would  require  the  backing  up  of  the  whole  volume  of  the  sti-eam  until  the 
actual  bead  was  equivalent  to  the  theoretical  head  due  to  the  velocity  of  the 
stream.  As  but  a  small  fraction  of  the  velocity  of  the  stream  can  be  taken 
up  by  a  currant  motor,  its  elBcieiicy  is  very  small.  Current  motors  may  be 
used  to  obtain  small  amounts  of  power  from  large  streams,  but  for  large 
powers  they  are  not  practicable. 

Horse-poirer  of  Water  Flovrlns  in  a  Tube.— The  head  due  to 

the  veioeity  is  |- ;  the  head  due  to  the  pressure  is  J;  the  head  due  to  actual 

XQ  W 

heiglitabove  the  datum  plane  is  h  feet.  The  total  head  Is  the  sum  of  these  s 
=-  4-  Jk  4"^«  hi  fbo^  In  which  v  b  velocity  in  feet  per  second,/  as  pressure 
in  lbs.  per  sq.  ft.,  w  weight  of  1  cu.  ft.  of  water  b  62.86  lbs.  If  p  s  pres- 
sure In  Iba.  per  sq.  in.,  ~  v  2.S09p.     In  hydraulic  transmission  the  velocity 

and  the  height  above  datum  are  usually  small  compared  with  the  pressure- 
bead.  The  work  or  energy  of  a  given  quantity  of  water  under  pressure  a 
its  volume  In  cubic  feet  x  its  pressure  m  lbs.  per  sq.  ft.;  or  if  Q  ■>  quantity 
in  cubic  feet  per  second,  and  p  s  pressure  in  lbs.  per  square  inch,  IK  a 

144pQ,  and  the  H.  P.  s  i^  »  .2618p^. 

fllazlm«ii&  Bllleleney  of  a  liOnc  Condnlt«~A.  L.  Adams  and 
B.CGemmelL  (Eng'y  News,  Hay  4, 1898),  show  by  maihematical  analysis  that 
tlie  condltiotts  for  securing  the  maximum  amount  of  power  through  a  long 
eonduit  of  fixed  diameter,  without  regard  to  the  economy  of  water,  is  that 
the  draught  from  ttie  pipe  should  be  such  that  the  frictional  loss  in  the  pipe 
will  he  equal  to  one  thii  d  of  the  entire  static  head. 

BIlll«Poiirer«— A  *' mill-power  "  is  a  uuit  used  to  rate  a  water-power  for 
the  purpose  of  renting  1L  The  value  of  the  unit  is  different  in  different 
localities.    The  following  are  exam  pies  ( from  Emerson) : 

Holyoke.  J#aM.— Each  mill-power  at  the  respective  falls  is  declared  to  be 
the  right  during  18  hours  in  a  day  to  draw  88  cu.  ft.  of  water  per  second  at 
the  upper  fall  when  the  head  thc-e  is  i20  feet,  or  a  quantity  proportionate  to 
the  height  at  the  falls.    This  Is  equal  to  86.2  horse-power  as  a  maximum. 

Lowell,  Mtus.^-The  right  to  draw  during  15  hours  in  the  day  ro  much  water 
as  shall  give  a  power  equal  to  25  cu.  ft.  a  second  at  tlie  great  fall,  when  the 
fall  there  is  80  feet.    Equal  to  85  H.  P.  maximum. 

/,fiirf*ence,  ifoss.— The  right  to  draw  during  16  hours  In  a  day  so  much 
water  as  shall  give  a  power  equal  to  30  cu.  ft.  per  second  when  the  head  Is 
25  feet.    Equal  to  85  H.P.  maxim  urn. 

Mfinneapolia,  Minn.—dO  cu.  ft,  of  water  per  second  with  head  of  Hi  feet. 
Equal  to  74.8  H.P. 

Manchester,  N.  H.— Divide  7-25  by  the  number  of  feet  of  fall  minus  1,  and 


690  WATER-POWEB. 

Ihe  otiotient  will  be  the  number  of  cubic  feet  per  moond  In  fhat  fall.  Foi  20 
feet  fall  this  eauals  88.1  ru.  ft-.,  equal  to  86.4  H.  P.  maximum. 

Cohoes^  2V.  Y.— "  Mill' power  "  equivalent  to  the  power  given  hj  6  cu.  ft^ 
per  seooad,  when  the  fall  is  tO  feet.    Equal  to  18.6  H.  P.,  maximum. 

PoMaic.  N.  J.— Mill-power:  The  right  to  draw  8>^  cu.  ft.  of  water  per  aec., 
fall  of  fU  feet,  equal  to  fi\.*4  horae^power.  Maximum  rental  $700  per  year  for 
each  mill-power  s  $83.00  per  H.  P. 

The  horte-power  maximum  above  Riven  is  that  due  theoretically  to  the 
weight  of  water  and  the  height  of  the  fall,  flu«umiug  the  water-wheel  to 
have  perfect  efficiency.  It  should  be  multiplied  by  the  efficiency  of  the 
wheel,  say  75](  for  grood  turbines,  to  obtain  the  H.  P.  delivered  by  the  wheel. 

Value  of  a  ITafeivpower*— In  estimating  the  value  of  a  water- 
power,  especially  where  such  value  is  used  as  testimony  for  a  i  lainiiff  whose 
water-power  has  been  diminished  or  confiscated,  it  i»  n  common  custom  for 
the  person  making  such  estimate  to  say  that  the  value  is  represented  by  a 
sum  of  money  which,  when  put  at  interest,  would  maintain  a  steam-plaiit 
of  the  same  power  in  the  same  place. 

Mr.  Charles  T.  Main  (Trans.  A.  8.  M.  E.  xlii.  140)  points  out  that  thfe  ay*- 
tern  of  estimating  is  erroneous:  that  the  value  of  a  power  depends  upon  a 
great  number  of  conditions,  such  as  location,  quantity  of  water,  fall  or  iMad, 
uniformity  of  flow,  conditions  which  fix  tbe  expense  of  dams,  canals,  founda- 
tions of  buildings,  freight  charges  for  fuel,  raw  materials  and  finished  prod- 
uct,  etc.  He  gives  an  estimate  of  relative  cost  of  steam  and  water-power 
for  a  500  H.  P.  plant  from  which  the  following  is  condensed: 

The  amount  of  beat  required  per  H.  P.  varies  with  different  kinds  of  busi- 
ness, but  in  an  average  plain  cotton-mill,  the  steam  required  for  heatincand 
slashing  is  eqiiivalent  to  about  f&%  of  steam  exhausted  from  the  mgh- 
pressure  cylinaer  of  a  compound  engine  of  the  power  required  to  run  thai 
mill,  the  steam  to  be  taken  from  the  receiver. 

The  coal  consumption  per  II.  P.  per  hour  for  a  compound  engine  is  taken 
at  19i  lbs.  per  hour,  when  no  steam  is  taken  from  the  receiver  for  heating 
purposes.  The  gross  consumption  when  25^  is  taken  from  the  receiver  ia 
about  S.061b6. 

?9)l  of  the  iteam  la  used  as  in  a  compound  engine  at  1.76  lbs.  b  1.81  Iba 
W     •'  **        a  •»     high-pressure   ^'  8.00  lbs.  =   .76*' 

SLoi  •• 
The  running  expenses  per  H.  P.  per  year  are  as  follows  : 
S.06  lbs.  ooal  per  hour  as  ;t].116  Iba  for  10^  hours  or  one  day  a  6608.49 

lbs.  for  808  days,  which,  at  $3.00  per  long  ton  s  $8  71 

Attendance  of  boilers,  one  man  ^  f  8.00,  and  one  man  ^  $1 .86  =*  8  00 

»♦         •♦  engine,    ••     •*     ^$3.60.  8  16 

Oil,  waste,  and  supplies.  80 

The  oost  of  such  a  steam-plant  In  New  England  and  vicinity  of  500 
H.  P.  is  about  $65  per  H.  P.  Taking  the  fixed  expenses  as  4%  on 
engine,  S/%  on  boilers,  and  2%  on  other  portiouB,  repairs  at  2%,  in- 
terest at  5^,  taxes  Blimton9i  oost,  an  Insurance  at  ^ on  exposed 
portion,  the  total  average  per  cent  is  about  18>i)K,  or  $65  X  -18^  »      8  18 

Gross  cost  cf  power  and  low-pressure  steam  per  H.  P.  $81  80 

Comparing  this  with  water-power,  Mr.  Main  twys :  "  At-  Lawrence  the  cost 
of  dam  and  canals  was  about  $650,000,  or  $65  per  H.  P.  T^e  cost  per  H.  P. 
of  wheel-plant  from  canal  to  river  is  about  $45  per  H.  P.  of  plant,  or  about 
$65  per  H.  P.  used,  the  additional  $20  being  caused  by  making  the  plant 
large  enough  to  compensate  for  fluctuation  of  power  due  to  rise  and  fSall  »f 
river.  The  total  oost  per  H.  P.  of  developed  plant  Is  then  about  $1 W  i>er  H.  P. 
Placing  the  depreciation  on  the  whole  plant  at  ej(,  repairs  at  1^  lOMNeet  §i 
^  taxes  and  insurance  at  1%,  or  a  total  of  9j(,  gives:  . 

Fixed  expenses  per  H.  P.  $180  X  .00  ■>  $11  70 
Running    **        **       '*     (Estimated)      8  00 

$13  70i 

**  To  this  has  to  be  added  the  amount  of  steam  required  for  heating  pur* 
poses,  said  to  be  about  259(  of  the  total  amount  used,  but  In  winter  months 
the  consumption  is  at  least  87^j(.  It  is  therefore  necessary  to  have  a  boiler 
plant  of  about  87^  of  the  size  of  the  one  considered  with  the  sieam-plantt 


TUBBIKB  WHEELS.  691 

cotOng  About  $80  X  .875  «  $7.90  per  H.  P.  of  total  power  used.  The  ex- 
pense of  ninntng  this  boiler-pUnt  is,  per  H.  P.  of  ihe  the  total  plant  per  jear: 

Fixed  expenses  18^  on  $7.60, $0.94 

Coal .•••••.•.••.•....      8.80 

Labor 1.88 

Total $5748 

Hakinfp  a  total  cost  per  year  for  trater-powerlwlth  the  auxiliaiy  boiler  plant 
$13.704'$6.48b  $19.18  which  deducted  from  $81.80  make  a  difference  in 
favor  of  water-power  of  $8.67,  or  for  10,000  H.  P.  a  saving  of  $86,700  per 
year. 

"  It  is  fair  to  say/*  says  Mr.  Main,**  that  the  value  of  this  constant  power  is 
a  sum  of  money  which  when  put  at  interest  will  produce  the  saving ;  or  if  6jt 
is  a  fair  interest  to  receiTO  on  money  thus  invested  the  value  would  be 
$86,700  ^  .06  =  $446,000." 

Mr.  Main  makes  the  following  general  statements  as  to  the  value  of  a 
water-power :  '*Tbe  value  of  an  undeveloped  variable  power  is  usually  noth- 
ing if  Its  variation  is  great,  unless  it  is  to  oe  supplemented  by  a  steam-plant. 
It  is  of  value  then  only  when  the  cost  per  horse-power  for  the  double-plant 
is  less  than  the  cost  of  steam-power  under  the  same  conditions  as  mentioned 
for  a  permanent  power,  and  its  value  can  be  represented  In  the  same  man- 
ner as  the  value  of  a  permanent  power  has  been  represented. 

'*  The  value  of  a  developed  power  is  as  follows:  If  the  power  can  be  run 
cheaper  than  steam,  the  value  Is  that  of  the  power,  plus  the  cost  of  plant, 
less  depreciation.  If  it  cannot  be  run  as  cheaply  as  steam,  considering  its 
cost,  etc.,  the  value  of  the  power  itself  is  nothing,  but  the  value  of  the  piant 
is  such  as  could  be  paid  for  it  new,  which  would  bring  the  total  cost  of  run- 
ning down  to  the  cost  of  steam-i>ower,  less  depreciation." 

Mr.  Samuel  Webber,  Jrtm  Age,  Feb.  and  March,  1808,  writes  a  series  of 
articles  showing  the  development  of  American  turbine  wheels,  and  inci- 
dentally criticises  the  statements  of  Mr.  Main  and  others  who  have  made 
comparisons  of  costs  of  steam  and  of  water-power  unfavorable  to  the  latter. 
Hesays :  **  They  have  based  their  calculations  on  the  cost  of  steam,  on  large 
compound  engines  of  1000  or  more  H.  P.  ond  120  pounds  pressure  of  steam 
in  their  boilers,  and  by  careful  10-hour  trials  succeeded  in  figuring  down 
steam  to  a  cost  of  about  %20  per  H.  P.,  ignoring  the  well-known  fact  that  its 
average  cost  in  practical  use,  except  near  the  coal  mines,  is  from  $40  to  $50. 
In  many  instances  dams,  canals,  and  modern  turbines  can  be  all  completed 
for  a  cost  of  $100  per  H.  P. ;  and  the  interest  on  that,  and  the  cost  of  attend- 
ance and  oil,  wUl  bring  water-power  up  to  but  about  $10  or  $18 per  annum; 
and  with  a  man  competent  to  attend  the  dynamo  in  attendance,  it  can 
probably  be  safely  estimated  at  not  over  $15  per  H.  P." 

TVeBINE  WHEBIiS* 

Proportions  of  Tiirbln«s*~Prof.  De  Volson  Wood  discusses  at 
length  the  theory  of  turbines  in  his  paper  on  Hydraulic  Reaction  Motors, 
Trans.  A.  8.  M.  E.  xiv.  866.    His  principal  deductions  which  have  an  imme- 
diate bearing  upon  practice  ara  condensed  in  the  following : 
Notation, 

Q  =  volume  of  water  passing  through  the  wheel  per  second, 

hi  s  head  in  the  supply  chamber  above  the  entrance  to  the  buckets, 

h%^  head  in  the  tail-race  above  the  exit  from  the  buckets, 

z«  3s  fall  in  passing  through  the  buckets. 

if  =  Ai  4-  «i  —  ^t;  the  effeciive  head. 

|A,  s  coefficient  or  resistance  along  the  guides, 

i&g  =  coefficient  of  resistance  along  the  buckets, 

Tx  ^  radius  of  the  initial  rim, 

Tm  =  radius  of  the  terminal  rim, 
V  =  velocity  of  the  water  issuing  from  supply  chamber, 

«i  =  initial  velocity  of  the  water  in  the  bucket  in  reference  to  the  bucket, 

«t  =  terminal  velocity  in  the  bucket, 

M  s=  angular  velocitv  of  the  wheel, 

«  =s  terminal  angle  between  the  guide  and  Initial  rim  =  CAB,  Fig.  188, 

Yi  »  sngle  between  the  initial  element  of  bucket  and  initial  rim  sr  EAJ>. 
s  QFI^  the  angle  between  the  terminal  rim  and  terminal  element  of 

a  a  e^  Fig.  US  V  the  arc  subtending  one  gate  opening, 


ebucke 


592 


WATBB-POWEH. 


a  I  a  the  arc  subtending  one  bucket  at  entrance.   (In  practice  at  Is  larger 
than  a,) 

a*  =  gK  the  arc  subtending  one  bucket  at  exit, 

K  =  b/«  normal  section  of  passage,  it  being  assumed  that  the  passage! 
and  buckets  are  very  narrow. 

kx  =  bd,  initial  normal  section  of  bucket* 
fc,  =  gi.  terminal  normal  section, 
mr^  =s  velocity  of  initial  rim, 
Mf.  =  velocity  of  terminal  rim, 
6  =  HFI,  angle  between  the  terminal  rim  and  actual  directioo  of  the 
water  at  exit, 

Y  s  depth  of  K.  y,  of  a„  and  ^t  of  ^a,  then 

IC  s  Fasiu  «;  iTa  a  yt  tti  sin  y^;  K^  s  y,a,  sin  y,. 


^^' 


Fio.  189. 


FiQ.  183. 


Three  simple  systems  are  recofnaized,  r,  <  rj/caUed  outward  flow;  r.  >  r^ 
called  inward  flow;  r,  ss  r.,  called  parallel  flow.  The  first  and  second  may 
be  combined  with  tbe  third,  making  a  mixed  system. 

ValtLS  of  y^  (tfie  quitting  angle).~-The  efficiency  is  Increased  as  >•  de- 
creases, and  IS  firreateKt  for  y^  s  0.  Hence,  theoretically,  the  terminal  ele- 
ment of  the  bucket  should  he  tangent  to  the  Quitting  rim  for  best  eificiencv 
riiis.  however,  for  the  discharge  of  a  finite  quantity  of  water,  would 
require  an  infinite  depth  of  bucket.  In  practice,  therefore,  this  angle  must 
have  a  Unite  value.  The  larger  the  diameter  of  the  terminal  rim  tbe  smalKrr 
may  be  this  angle  for  a  given  depth  of  wheel  and  given  quantity  of  wau^r 
dJRcharged.    In  practice  y.  Is  from  10*  to  ao*. 

In  a  wheel  in  which  all  the  elements  except  y.  are  fixed,  the  velocity  of 
the  wheel  for  best  effect  must  increase  as  the  quitting  angle  of  the  bucket 
decreases. 

Values  o/  a  -f  y,  must  be  less  than  180<*,  but  the  beet  relation  cannot  be 
determined  by  analydis.  However,  since  the  water  should  be  deflected  from 
Its  course  as  much  as  possible  from  its  entering  to  its  leaving  the  wheel,  the 
angle  a  for  this  reason  should  be  as  small  as  practicable. 

In  practice,  a  cannot  be  zero,  and  Is  made  from  20*  to  80*. 

Tbe  value  r,  =  1.4r,  makes  the  width  of  the  crown  for  internal  flow  about 
the  same  as  for  rj  =rt  \^  for  outward  flow,  being  approximately  0.8  of  tbe 
external  radius. 

Values  of  fix  and  m«.— The  frictional  resistances  depend  upon  the  ronstntc- 
tion  of  the  wheel  as  to  smoothness  of  the  surfaces,  sharpness  of  the  angles, 


TURBINE  WHBEL8.  593 

mnilarlty  of  the  curved  i>aits,  and  also  npon  the  speed  It  is  nm.  These 
yalues  cannot  be  deflnitelv  assigned  beforehand,  but  Wei8ba<^  gives  for 
good  conditions  ^a,  =3  ^a,  =  0.06  to  0.10. 

They  are  not  uecessaril j  equal,  and  /ii  may  be  from  0.06  to  0.075,  and  m« 
from  0.00  to  0.10  or  even  larger. 

VahieM  of  y^  must  be  less  than  180*  —  «. 

TO  be  on  the  safe  side,  yx  n^y  be  SO  or  80  degrees  less  than  180"-2a,  giving 

Yx->180*>Sa~85    (say)    «166-Sa. 

Then  If  «  m  80^,  y^  a  05*.  Borne  designers  make  Yt  00*;  others  more,  and 
still  others  less,  than  that  amount.  Welsbach  suggests  that  it  be  less,  so 
that  the  bucket  will  be  shorter  and  friction  less.  This  reasoning  appears  to 
be  oorreei  for  the  inflow  wheel,  but  not  for  the  outflow  wheel.  In  the  Tre- 
raont  turbines,  described  in  the  Lowell  Hydraulic  Experiments,  this  angle 
Is  00*,  the  angle  a  80*,  and  y^  10*,  which  proportions  insured  a  posittve 
pressnre  in  the  wheel.  Fourneyron  made  y^  »  90*,  and  a  from  80*  to  34*, 
whbdi  values  made  the  initial  pressure  in  the  wheel  near  sero. 

Firm  of  Bucket  —The  form  of  the  bucket  cannot  be  determined  analytic- 
ally. From  the  initial  and  terminal  directions  and  the  volume  of  the  water 
flowing  through  the  wheel,  the  area  of  the  normal  sections  may  be  found. 

Tlie  normal  section  of  the  buckets  will  l>e : 

The  depths  of  those  sections  will  be : 

asina*    *»     a^sinyi'    '•      «i8lnY,', 

The  changes  of  curvature  and  section  must  be  gradual,  and  the  general 
form  regular,  so  thai  eddies  and  whirls  shall  not  be  formed.  For  the  same 
reason  the  wheel  must  be  run  with  the  correct  velocity  to  secure  the  best 
effect.  In  practice  the  buckets  are  made  of  two  or  three  arcs  of  circles, 
mutually  tangential 

The  Value  of  m.— So  far  as  analysis  indicates,  the  wheel  may  nm  at  any 
speed;  but  in  order  that  the  stream  shall  flow  smoothly  from  the  supply 
cnamber  Into  the  bucket,  the  velocity  F*  should  be  properly  regulated. 

If  Ml  "  Ms  B  0.10,  rt  -*-  rt  e  1.40,  a  s  25*,  y.  s  90*,  yt » 18*,  l£e  velocity  of 
Che  initial  rim  for  outwara  flow  will  be  for  maximum  efllciency  0.014  of  the 
velod^  due  to  the  head,  or  mTj  «  0.614  V9gH, 

The  velocity  due  to  the  head  would  be  V2yH  a  1.414  i^gSL 

For  an  Inflow  wheel  for  the  case  In  which  r|*  ss  £rg*,  and  the  other  dlmen 
sions  as  given  above,  Mr}  a  0.689  V^B, 

The  highest  efllciency  of  the  Tremont  turbine,  found  experimentally,  was 
0.79375,  and  the  corresponding  velocity,  0.68645  of  that  due  to  the  head,  and 
for  all  velocities  above  and  below  this  value  the  efficiency  was  less. 

In  the  Tremont  wheel  a  a  80*  instead  of  S5*,  and  y.  a  10*  instead  of  18*. 
These  would  make  the  theoretical  efficiency  and  velocity  of  the  wheel  some- 
what greater.  Experiment  showed  that  the  velocity  might  be  considerably 
larger  or  smaller  than  this  amoimt  without  much  diminution  of  the  efficiency. 

It  was  found  that  If  the  velocity  of  the  hiltlal  (or  interior)  rim  was  not  less 
than  ii%  nor  more  than  7b%  of  that  due  to  the  fall,  the  efficiency  was  7Sii  or 
more.  This  wheel  was  allowed  to  run  freely  without  any  brake  except  its 
own  friction,  and  the  velocity  of  the  initial  rim  was  observed  to  be 
1.385  V80£r,half  of  which  is  0.6676  VflgH.  which  is  not  far  from  the  velocity 
giving  maximum  effect;  that  is  tosay,wnen  the  gate  is  fully  raised  the  coeffl- 
dent  of  effect  is  a  maximum  when  the  wheel  is  moving  with  about  half  Its 
maximum  velocity. 

Number  0/ Burfc«rf«.— Successful  wheels  have  been  made  in  which  the  dis- 
tance between  the  buckets  was  as  small  as  0.75  of  an  Inch,  and  others  as 
much  as  8.75  Inches.  Turbines  at  the  Centennial  Exposition  had  buckets 
from  4^  Inches  to  9  Inches  from  centre  to  centre.  If  too  large  they  will  not 
work  properly.  Neither  should  they  be  too  deep.  Horizontal  partitions 
are  somedmes  introduced.  These  secure  more  efficient  working  in  case  the 
gates  are  only  partly  opened.  The  form  and  number  of  buckets  for  com* 
mercial  purposes  are  cniefly  the  result  of  experience. 


594  WATEB-POWEB. 

Ratio  of  i?ad«.— Theory  does  not  limit  the  dImeiiBloiis  of  the  wheel.  In 
practioe, 

for  outward  flow,  r^  ■*-  r^  Ik  from  1.S5  to  1.60; 
for  Inward  flow,  r, h-Ix  is  from 0.66  to 0.80. 

It  appears  that  the  inflow-wheel  has  a  higher  eflQciency  than  the  outward- 
flow  wheel.  The  Inflow- wheel  also  runs  romewhat  slower  for  best  effect. 
The  centrifugal  force  in  the  outward-flow  wheel  tends  to  force  the  water 
outward  faster  than  It  would  otherwise  flow  ;  while  in  the  Inward-flow  wheel 
it  has  the  contrary  effect,  acting  as  it  does  in  opposition  to  the  velocity  in 
the  buckets. 

It  also  appears  that  the  efiiclency  of  the  outward-flow  wlieel  Increases 
Bhehtly  as  tne  width  of  the  crown  Is  less  and  the  velocity  for  maximum 
efficiency  Is  slower  ;  while  for  the  inflow- wheel  the  efficiency  slightly  in- 
creases for  increased  width  of  crown,  and  the  velocity  of  the  outer  rim  at  the 
same  time  also  increases. 

Sjfficieney.— The  exact  value  of  the  efficiency  for  a  particular  wheel  must 
be  found  by  experiment. 

It  seems  hardly  possible  for  the  effective  efficiency  to  equal,  much  less 
exceed,  S0%,  and  all  claims  of  90  or  more  per  cent  for  these  motors  should  be 
discarded  as  improbable.  A  turbine  yielding  from  76%  to  BOi  ia  extremely 
good.    Experiments  with  higher  efficiencies  tiave  been  reported. 

The  celebrated  Tremont  turbine  gave  79>dj(  without  the  "  diffuser,**  which 
might  have  added  some  2^.  A  Jonval  turbine  (parallel  flow)  was  repotted 
as  yielding  0.75  to  0.90,  but  Morin  suggested  corrections  reducing  It  to  0.63  to 
0.71.  Weisbaeh  gives  the  results  of  many  experiments,  In  which  the  <^fh- 
dency  ranged  from  SOjt  to  84^.  Numerous  experiments  give  E  =  0.60  to  0.62S. 
Tlie  efficiency,  considering  only  the  energy  Imparted  to  the  wheel,  will  ex- 
ceed by  several  per  cent  the  efficiency  of  the  wheel,  for  the  latter  will  in- 
clude the  friction  of  the  support  and  leakage  at  the  Joint  between  the  sluice 
and  wheel,  which  are  not  included  in  the  former ;  also  as  a  plant  the  resistr 
anoee  and  losses  in  the  supply-chamber  are  to  be  still  further  deducted. 

The  Crowns.— The  crowns  may  be  plane  annular  disks,  or  conical,  or 
curved.  If  the  partitions  forming  the  buckets  be  so  thin  that  they  may  be 
discarded,  the  law  of  radial  flow  will  be  determined  bv  the  form  of  the 
crowns.  If  the  crowns  be  plane,  the  I'odial  flow  (or  radial  component)  will 
diminish,  for  the  outward  flow-wheel,  as  the  distance  from  the  axis  increases 
-»the  buckets  being  full— for  the  angular  space  will  be  greater. 

Prof.  Wood  deduces  from  the  formules  in  his  paper  the  tables  on  page  695. 

It  appears  from'these  tables:  1.  That  the  teraiinal  angle,  a,  has  frequently 
been  made  too  large  in  practice  for  the  best  efficiency. 

2.  That  the  terminal  angle,  a,  of  the  guide  should  be  for  the  inflow  less 
than  10*  for  the  wheels  here  considered,  but  when  the  Initial  angle  of  the 
bucket  Is  90^,  and  the  terminal  angle  of  the  guide  Is  5*  28\  ttie  gain  of  effi- 
ciency is  not  2%  greater  than  when  the  latter  is  85*. 

8.  Ttiat  the  initial  angle  of  the  bucket  should  exceed  90*  for  best  effect  for 
outflow-wheels. 

4.  That  with  the  initial  angle  between  60*  and  180*  for  best  effect  on  Inflow 
wheels  the  efficiency  varies  scarcely  1^. 

5.  In  the  outflow-wheel,  column  (0)  shows  that  for  the  outflow  for  best 
effect  the  direction  of  the  quitting  water  in  reference  to  the  earth  should  be 
nearly  radial  (from  76*  to  AT*),  but  for  the  Inflow  wheel  the  water  is  thrown 
forwai-d  in  quitting.  This  shows  that  the  velooity  of  the  rim  should  some- 
what exceed  the  relative  final  velocity  backward  in  the  bucket,  as  shown  In 
columns  (4)  and  (6). 

6.  In  these  tables  the  velocities  given  are  in  terms  of  f^F,  and  tho  co- 
efficients of  this  expression  will  be  tne  part  of  the  head  which  would  produce 
that  velocity  If  the  water  issued  freely.  There  Is  only  one  case,  column  (5), 
where  the  coefficient  exceeds  unity,  and  the  excess  is  so  small  it  may  be  dis- 
carded; and  It  may  be  said  that  in  a  properly  proportioned  turbine  with  the 
conditions  here  given  none  of  the  velocities  will  equal  that  due  to  the  head 
in  the  supplv-chamber  when  running  at  best  effect. 

7.  The  inflow  turbine  presents  the  best  conditions  for  construction  for 
producing  a  given  effect,  the  only  apparent  disadvantage  being  an  increased 
first  cost  due  to  an  Increased  depth,  or  an  increased  diameter  for  producing 
a  given  amount  of  work.  The  larger  efficiency  should,  however,  more  than 
neutralise  the  increased  fii-st  cost. 


TUBBINE  WHEELS. 


5dS 


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d  d  o  d 

11 

8. 

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iiig 

r-.  d  d  d 

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o 

li 

n 

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s|. 

e* 

d  d  d  d 

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llll 

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4. 
II 


1 

•4? 

1.48 
1.60 
1.55 
1.65 

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Kq  tq  tq  tq 

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o  o  d  G 

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III! 

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nil 

G  e»  o  <s 

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lies 

d  o  6  <£ 

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till 

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ei  <>  <»  d 

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§l|| 

596 


WATEU-POWER. 


Tests  of  Turbines.— Emerson  says  that  in  testing  turbines  it  Is  a  rnre 
thing  to  find  iwo  of  the  Kame  size  which  can  be  made  to  do  then*  best  at  the 
same  speed.  The  best  speed  of  one  of  the  leading  wheels  is  Invariably  wide 
from  tlie  tabled  rate.  Ic  was  found  that  a  54-in.  Leffel  wheel  under  12  ft. 
head  gave  much  better  results  at  78  revolutions  per  minute  than  at  ^0. 

Overshot  wheels  have  betm  known  to  give  7!^  efficiency,  but  th'^  average 
performance  is  not  over  60^. 

A  fair  a  verage  for  a  good  turbine  wheel  may  be  taken  at  75j(.  In  tests  of  18 
wheels  made  a*-  the  Philadelphia  Water-works  in  1859  and  1860,  one  wheel 
gave  less  Uian  60%  eflflcieucy,  two  between  ^0%  and  60^,  six  between  6  .■*>  and 
70%,  seve      etween  7i%  and  7Tji,  two  S2%,  and  one  87.77jf.    (Emerson.) 

Tests  of  Turbine  'Wbeels  at  the  Centennial  BxliIMtlon. 
1876.  (From  a  paper  by  R.  H.  Thurston  on  The  Systematic  Testing  of 
Turbine  Wheels  In  the  United  States,  Trans.  A.  S.  M.  E.,  viii.  359.)— In  187C 
the  Judges  at  the  International  Exhibition  conducted  a  series  of  trials  of 
turbines.  Many  of  the  wheels  offered  for  tests  were  found  to  be  more  or 
less  defective  In  fitting  and  workmanship.  The  following  is  a  statement  of 
the  results  of  all  turbines  entered  which  gave  an  efficiency  of  over  7^ 
Seven  other  wheels  were  tested,  giving  results  betweeu  0^  and  7b%. 


Maker*8  Name,  or  Name  the 
Wheel  is  Known  By. 

^  O 

"a 

1=^ 

u 

H 
1^ 

i 

Risdon 

87.68 
88.79 
83.80 
82.18 
81.21 
78.70 
79.59 
77.67 
77.43 
7694 
76.16 
76.70 
75.15 

86.20 

82.41 
70.79 

76.35 

National    

Geyelin  (single) 

Thos.  Tait 

71.66' 

Vi.bV 
■81V24' 

70.40 
65.90 
68.60 
79.92 

66.85 

51.(« 
67.23 

66.00 

Gk>ldie  &  MoCullough 

Rodney  Hunt  Mach.  CJo. 

Tyler  Wheel 

Gevelin  (duolex) 

69.50 

Knowlton  &  Dolan 

74.25 
73.83* 
74.89 

62.76 

70.'87 
62.06 

71.74 

E.  T.  Cope  &  Sons 

69.92 

York  Manufacturing  Ck> 

W.  F.  Moa«er&Oo... 

67.08 
71.90 

67.67 
70.52 

06.04 

The  limits  of  error  of  the  tests,  says  Prof.  Thurston,  were  very  uncertain; 
they  are  undoubtedly  considerable  as  compared  with  the  later  work  done  in 
the  permanent  flume  at  Holyoke— possibly  as  much  as  4%  or  5%. 

Experiments  with  "draught-tubes,"  or  "suction-tubes,"  which  were 
aeiually  "  diffusei-s  "  in  their  effect,  so  far  as  Prof.  Thurston  has  analysed 
them,  indicate  the  loss  by  friction  which  should  be  antlcinated  in  such 
cases,  this  loss  decreasing  as  the  tube  increased  in  size,  ana  increasing  as 
its  diameter  approached  that  of  the  wheel— the  minimum  diameter  tried. 
It  was  sometimes  found  very  difficult  to  free  the  tube  from  air  eompletelv, 
and  next  to  impossible,  during  the  interval,  to  control  the  speed  with  the 
brake.  Several  trials  were  often  necessary  before  the  power  due  to  the  full 
head  could  be  obtained.  The  loss  of  power  by  gearing  and  by  belting  was 
variable  with  the  proportions  and  arrangement  of  the  gears  and  pull**yt«, 
length  of  belt,  etc.,  but  averaged  not  far  from  90%  for  a  singlepair  of  bev-l- 
gears,  uncut  and  dry.  but  smooth  for  such  gearing,  and  but  ]Q%  for  the  same 
gears,  well  lubricated,  after  they  had  been  a  short  time  In  operation.  The 
amount  of  power  transmitted  was,  however,  small,  and  these  figures  are 
probably  much  higher  rhan  those  representing  ordinary  practice.  Intro- 
ducing a  second  pair— spur-gears— the  best  figures  were  but  little  changed, 
although  the  difference  between  .  le  case  in  which  the  lartrer  gear  was  the 
driver,  and  the  case  <n  w'  h  he  small  whee'  was  the  driver,  was  perceiv- 
able, and  was  in  favor  of  thr  Tormer  arr.- ngement.  A  single  straight  belt 
gave  a  loss  of  but  2jt  or  3i(,   .  crossed  belt  {i%  to  S;:^  when  transmitting  14 


TURBINE  WHEELS.  597 

hone-power  with  maximum  tlsrtatneas  and  transmtitfnff  power.  A  "  quarter 
turn  ^'  wasted  about  1(K  as  a  maximum,  and  a  **ouarter  twist  **  about  6%, 

DlmeBslons  of  Torblnea.— For  dimensions,  power,  etc.,  of  stand- 
ard makes  of  turbines  coiisiilt  the  catal<»ue8  of  different  manufacturers. 
The  wheels  of  different  makers  vary  greatly  in  their  proportions  for  any 
li^iven  capacity. 

Tlio  Pelton  "Wat^ri^^vbeol.— Mr.  Ross  E.  Browne  iEng^g  Newt,  Feb. 
90.  I89S)  thus  outlines  the  principles  upon  which  this  water-wheel  is 
constructed : 

The  function  of  a  water-wheel,  ope/ated  by  a  Jet  of  water  escaping  from 
a  nozzle.  Is  to  convert  the  energy  of  the  Jet,  due  to  its  velocity,  iuto  useful 
work  In  order  to  utilize  this  energy  fully  the  wheel-bucket,  after  catching 
the  Jet,  must  bring  it  to  rest  before  discharging  it,  without  inducing  turbu- 
lence or  agitation  of  the  particles. 

This  cannot  be  full/  effected,  and  unavoidable  dlfflcultles  necessitate  the 
loss  of  a  portion  of  the  energy.  The  principal  lo&ses  occur  as  follows: 
Fltst.  in  sharp  or  angular  diversion  of  the  Jet  in  entering,  or  in  its  course 
through  the  bucket,  causing  impact,  or  the  conversion  of  a  portion  of  the 
energy  into  heat  instead  of  useful  work.  Second,  in  the  so-called  frictional 
resistance  offered  to  the  motion  of  the  water  bv  the  wetted  surfaces  of  the 
buckets,  causing  also  the  conversion  of  a  portion  of  the  energy  into  heat 
instead  of  useful  work.  Third,  in  the  velocity  of  the  water,  as  it  leaves  the 
bucket,  representing  energy  which  has  not  been  converted  into  work. 

Hence,  in  seeking  a  high  efHciency :  1.  The  bucket-surface  at  the  entrance 
should  be  approximately  ;*Hrallel  to  the  relative  course  of  the  Jet,  and 
the  backet  should  be  curved  in  such 
a  manner  as  to  avoid  sharp  angular  de- 
fiection  of  the  stream.  If,  for  exam;  le. 
a  Jet  strikes  •*  surface  at  on  angle  and 
is  sharply  deflected,  a  portion  of  the 
water  is  M^ked,  the  smoothness  of  the 
stream  is  disturbed.  c«nd  h  re  results 
considerable  loss  by  impact  and  other- 
wise. The  entrance  and  deflection  in 
the  Pelton  bucket  are  such  as  to  avoid        Fio.  184.  Fia.  185. 

these  losses  in  the  main.    (Zee  Fig.  136.) 

2.  The  number  of  buckets  should  be  small,  and  the  path  of  the  Jet  in  the 
bucket  short;  in  other  words,  the  total  wetted  surface  should  be  small,  as 
the  loss  by  frictiou  will  be  proportional  to  ibis. 

8.  The  discharge  end  of  the  bucket  should  be  as  nearly  tangential  to  the 
wheel  periphery  as  compatible  with  the  clearance  of  the  bucket  which 
follows:  and  great  differences  of  velocity  in  the  parts  of  the  escaping  water 
should  be  avoided.  In  order  to  bring  the  water  to  rest  at  the  discharge  end 
of  the  bucket,  it  is  shown,  mathematically,  that  the  velocity  of  the  bucket 
should  be  one  half  the  velocity  of  the  Jet. 

A  bucket,  such  as  shown  in  fig.  185,  will  cause  the  heaping  of  more  or  less 
dead  or  turbulent  water  at  the  point  indicated  by  dark 
shaaing.  This  dead  water  is  subsequently  thrown  from 
the  wheel  with  considerable  velocity,  anti  reprfsents  a 
large  Iops  of  energy.  The  introduction  of  the  wedpe  in 
the  Pelton  bucket  (see  Fig.  134)  is  an  efHcient  means  ot 
avoiding  this  loss. 

A  wheel  of  the  form  of  the  Pelton  conforms  closely  in 
construction  to  each  of  these  requirements. 
In  a  te  *>  made  by  the  pronrietors  of  the  fdalio  mine, 
vm  iM  near  Grass  Yallev,  Cal.,  the  aiuiensions  and  results  were 

'^'  *"^  as  folk  «vs :  Main  supply-piptN  5S  in.  diameter,  fiOOO  ft. 

long,  with  %  head  of  ZSSU  feet  above  centre  of  nozzle.  The  los«  by  friccion 
io  the  pipe  was  1.8  ft,  reducing  the  effective  head  to  884.7  ft.  The  Pelton 
wheel  used  in  the  t:8twa:^  6  ft.  in  diameter  and  the  nozzle  was  l.KU  in. 
diameter.  The  work  done  was  measured  by  a  Prony  brake,  and  the  mean 
of  13  tests  showed  a  useful  effect  of  87.8^. 

Tlie  Pelton  wheel  is  also  used  as  a  motor  for  small  powei-s.  A  test  by 
M.  E.  Cooley  of  a  12-lnch  wheel.with  a  9^-inch  nozzle,  under  100  Iba.  pressure, 
gave  1.9  horse-power.  The  theomilcal  discharge  was  .0985  cubic  feet  per 
eecond,  and  the  theoretical  horse-power  2.45;  the  efllclency  being  80  per 
cent.  Tw-  other  styles  of  water-motor  tested  at  the  same  time  each  gave 
effldeodps  of  65  per  eot 


698 


WATER-POWBB. 


Pelton 'Water-wbeel  Tables.   (Abridged.) 
The  smaller  fliarures  under  those  denotlnj?  the  various  heads  give  the 
spouting  velocity  of  the  water  in  feet  per  minute.    The  cublc-f eel?  measure- 
ment is  also  based  on  the  flow  per  minute. 


Head 

ill  ft. 

Siaeof 
Wheels. 

6 
No.'l 

12 

18 

18 
in. 

Ko.« 

84 

in. 
No.  6 

8 

ft 

4 

ft. 

6 
ft. 

6 
ft. 

20 

2151.97 

Horra-power. 
Cubic  feet... 
Revolutions.. 

.05 
1.67 
684 

.12 

8.91 

342 

.20 
6.62 
228 

.87 

11.78 

228 

.66 

20.83 

171 

1  50 

46.93 

114 

8.64 

88.82 

65 

4.18 

180.86 

70 

6.00 

187  W 

57 

SO 

S685.e? 

Hoi-se-power. 
Cubic  feet.... 
Revolutions.. 

.10 

2.05 

887 

.88 

4.79 

418 

.88 

8.11 
279 

.69 

14.86 

279 

1.88 

85.51 

809 

8.76 

57.44 

189 

4.88 

108.04 

104 

7.60 

150.66 

83 

11.04 

830.76 

69 

40 

804P.89 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

.15 
2.87 
969 

5.58 

484 

.59 
9.37 
823 

1.06 

16.50 

823 

1.89 

89.46 

242 

4.84 

66.36 

161 

7.68 

107.84 

121 

11.85 

184.86 

96 

16.96 

285.44 

80 

50 

8408.61 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

.21 
2.64 
1088 

.49 
6.18 
641 

.84 

10.47 

361 

1.49 

18.54 

861 

8.65 

82.93 

270 

5.96 

74.17 

180 

10.60 

181.72 

135 

16.68 

806.13 

10» 

83  93 

206.70 

90 

60 

8727.8? 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

.28 
2.90 
1185 

3.13 

1281 

.66 

6.77 

592 

1.10 

11.47 

895 

1.96 

20.31 

895 

8.48 

36.08 

296 

7.84 

81.85 

197 

18.94 

144.82 

148 

21.77 

225.80 
118 

81.38 

885.00 

96 

70 

4036.00 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

.82 
7.31 
640 

1.89 

12.89 

427 

8.47 

21.94 
427 

4.39 

38.97 

820 

9.88 

87.76 

818 

17.58 

166.88 

160 

87.51 

848.89 

180 

89.3S 
851.04 

106 

80 

4303.90 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

.48 
8.35 
1868 

1.00 
7.82 
684 

1.70 

18  25 

456 

8.01 

28.46 

456 

5.36 

41.66 

842 

18.04 

98  84 

828 

21.44 

166.61 

171 

8.3.54 

860.78 

187 

48.16 

875.88 

114 

90 

4565.01 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

.61 
8.55 
1452 

1.20 
8.29 
726 

2.08 

14.06 

484 

3.60 

24.88 

481 

6.89 

44.19 

863 

14.40 

99.52 

242 

25.60 

176.76 

181 

40.04 

876.55 

145 

67.60 

898.08 

121 

100 

4812.00 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

.60 
3.74 
1580 

1.40 

8.74 

765 

8.82 

14.81 
510 

4.21 

26.22 

510 

7.49 

46.58 

882 

16.84 

104.88 

855 

29.98 

186.82 

191 

46.85 

801.51 

•  152 

07.86 

419.S2 

127 

ISO 

5271.80 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

.79 
4.10 
1677 

1  84 
9.57 

83« 

3.12 

16.21 

559 

6.54 

28.72 

559 

9.85 

61.02 

419 

22.18 

114.91 

279 

89.41 

204.10 

200 

61.66 

819.33 

167 

88.73 
450.61 
.     180 

140 

5603.65 

Horse-power. 
Cubic  feet.  .. 
Ete  volutions.. 

.09 
4.43 
1812 

2.33 

10.31 

906 

8.94 

17.153 

604 

6.99 

81.03 

601 

12.41 

55.11 

453 

27.96 

124.12 

802 

49.64 

220.44 

226 

rr.7i 

844.92 
181 

111.85 

406.48 

151 

160 

60S674 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

1.22 

4.78 
1968 

3.84 

11.05 

969 

4.8J 

18.74 

646 

8.54 

83.17 

646 

15  17 

68.92 

484 

84.16 

132.68 

823 

60.68 

285.68 

242 

91.94 

866.73 

198 

136.65 

680.73 

161 

ISO 

6155.97 

Horse  power. 
Cubic  feet..  . 
Revolutions.. 

1.45 
5.02 
2019 

3.39 
11.72 
1024 

5.75 

19.87 

683 

10.19 

85.18 

663 

18.10 

62.49 

513 

40.77 

140.74 

842 

r.'.4i 

249.97 
856 

113.80 

891.10 

806 

168.08 

568.96 

171 

200 

6805.17 

Horse-power. 
Cubic  feet. .  . 
Revolutions.. 

1.70 
5.29 
2160 

3.97 

12.86 
I98O 

6.74 

20.94 

720 

11.93 

87.08 

720 

21.20 

65.87 

640 

47.76 

148.85 

860 

84.81 

868.40 

270 

132.70 

418  35 

216 

101.00 

698.40 

180 

2oO 

7808.44 

Horse -power. 
Cubic  feet.... 
Revolutions.. 

2.88 
5.92 
2418 

5.56 
13.82 
1209 

9.42 
23.42 

806 

16.G8 

41.46 

806 

29.63 

73.64 

605 

66,74 

165.86 

403^ 

118.54 

291.69 

802 

186.47 

460.01 

841 

286.96 
663.45 

808 

POWER  OF  OCEAN  WAVES, 


599 


Pelton  'Waier-'wlteel  Tables.— Conftnueci 


Head 

in  it. 

Siseof 
Wheels. 

6 

in. 
No.l 

12 
ill. 
No.S 

18 
in. 
No.  8 

18 
in. 
No.  4 

24 
in. 
No.  5 

8 

ft. 

4 
ft. 

5 
ft. 

6 
ft. 

soo 

8334.62 

Hoi-Be-pow'r 
Cubic  feet.. . 
RevoIutioDB 

3.18 
6.48 

7.81 

16.13 

1326 

12.88 

25.66 

884 

21.93 

45.42 

884 

38.95   87.78 

80.67  181.69 

663       442 

156.83 

322.71 

881 

243.82 

504.91 

266 

350.04 

726.76 

221 

9008.48 

Horse-pow'r 
Cubic  feet... 
Revolutions 

3.94 
7.00 
2865 

9.21 

16.36 

1482 

15.61 

27.71 

055 

27.64 

49.06 

965 

49.09  110.50 

87.141196.26 

716       477 

196.88 

846.57 

858 

807.25 

546.80 

885 

448.27 

786  00 

888 

400 

9(04.00 

Horse-pow'r 
Cubic /eet... 
RevoIuUoiis 

4.8;: 
7.4fl 
8063 

11.25 
17.48 
1531 

19.0 

29  63 

1021 

88.77 
52.45 

1021 

59.98  135.06 
98.16  209.80 

765|      610 

239.94 

372.64 

382 

875.40 

688.02 

806 

540.85 

889.90 

856 

460 

10307.TB 

Honie-pow'p 
Cubic  feet... 
RevolutioDS 

5.75 
7.94 
8219 

13.48 
18.64 
1624 

23.76 

31.42 

:083 

40.29 

55.68 

1088 

71.57 

98.81 

812 

161.19 

222.5-^ 

541 

286.81 

395.24 

406 

385.84 

416.62 

428 

447.05 

618.88 

824 

64 1.78 

890.11 

270 

500 

10730.96 

Horae-pow*r 
Cubic  feet... 
Revolutions 

6.74 
8.87 
8436 

15.78 
19..M 
1718 

26.66 

83.18 

1142 

47.20 

68.64 

1142 

88.83 

104.15 

856 

188.80 

234.56 

571 

524.66 

651.88 

842 

755. JO 

938.25 

285 

000 

Home-powV 
Cubic  feet... 

62.04 

64.24 

1251 

110.19 

fiift.ift 

440.77 

456.88 

469 

689.03 

714.05 

875 

992.65 

114.09'25A.fift 

1027.80 

11786.94 

Revolutions 

ji'.: 

038 

625 

315? 

0«0 

Horse-pow'r 
Cubic  feet.. 

69.95 

66.86 

1302 

124.25 

118.75 
976 

279.82 

267.44 

661 

497.01 
476.02 

488 

777.62 

743.21 

890 

1119.29 

1069.77 

122eB.S4 

Revolutions 

8*5 

700 

Horse-pow'r 
Cubic  feet... 
Revolutions 

78.18 

69.38 

1851 

188.86 

128.28 

1013 

312.78 

277.54 

676 

555.46 

492.95 

606 

869.06 

771.86 

405 

1250.92 

ieraj.84 

.... 

.   ... 

1110.16 
887 

760 

18178.19 

Horse-pow'r 

Cubic  feet... 
Revolutions 

••; 

86.70 

71.82 

1899 

154.00 

127.66 
1049 

846.88 

287.28 

699 

616.03 

510.25 

524 

968.82 

798.33 

419 

1887.84 

1149  18 

819 

800 

13610  40 

Horse-pow'r 
Cubic  feet... 
Revolutions 

... 

.... 

95.52 

74.17 

1444 

160.66 

131 .74 

1063 

382.09 

296.70 

722 

678.66 

526.99 

642 

1061.81 

824.51 

438 

1528.80 

1186.81 

861 

•00 

Horse-pow'r 
Cubic  feet.. . 

.... 

118.98 

78.67 

1532 

202.45 

189.74 

1149 

455.94 

314.70 

766 

809.82 

558.96 

574 

1267.02 

874.68 

459 

1883.76 
1258.81 

14180.00 

Revolutions 

.... 

888 

1000 

Horse-pow'r 
Cubic  feet... 

133.50 

82.08 

1615 

2.37.13 
147.80 

I2in 

534.01 
331.72 

807 

948.48 

589.10 

60.'S 

1483.97 

921.83 

484 

2136.04 
1326.91 

15216  80 

Revolutions 

403 

THS  POWKH  OF  OCEAN  WATE8. 

Albert  W.  Stahl,  U.  8.  N.  (Trans.  A.  8.  M.  E.,  xiii.  438),  elves  the  following; 
fomiulsB  and  table,  based  upon  a  theoretical  discussion  or  wave  motion: 

The  total  energy  of  one  whole  wave-length  of  a  wave  7/  feet  high,  L  feet 
long,  nnd  one  foot  in  breadth,  the  length  being  the  distance  between  succes- 
sive crests,  and  the  height  the  vertical  distance  between  the  crest  and  the 

trough,  is  J?  a  BLH*  (l  -  4.985  ^)  foot-pounds.  J 

The  time  required  for  each  wave  to  travel  through  a  distance  equal  w  its 

own  length  Is  P  a  4/^-7^  ■«<^iids,  and  the  number  of  waves  )'«8slnfc  anv 


600 


WATER-POWBB. 


given  point  In  one  minute  Is  iV «  --  =  60 i/'-^.    Hence  the  total  ener^ 

of  an  Indefinite  series  of  such  waves»  expressed  In  horse-power  per  foot  of 
breadth,  is 

^  ^  ^  -  .03-»^l(i  -  4.935^). 


83000 


By  substituting  various  values  for  H-^L,  within  the  limits  of  such  values 
actually  occurring  in  nature,  we  obtain  the  following  table  of 

Total  Enbbot  or  Dbbp-sri.  Waves  in  Tbrms  of  Horss-povkr  pkk  Foot 
OF  Brjcadth. 


Ratio  of 
Length  of 
Waves  to 

Length  of  Waves  in  Feet. 

HelK'la  of 
Waves. 

85 

50 

75 

100 

150 

200 

(800 

400 

60 

.04 

.88 

.64 

1.81 

8.68 

7.43 

20.46 

48.01 

40 

.06 

.86 

1.00 

2.05 

5.65 

11.59 

81.95 

65.58 

ao 

.12 

.64 

1.77 

8.64 

10.08 

80.57 

56.70 

116.38 

90 

.85 

1.44 

8.96 

8.18 

21  79 

45.96 

ia.70 

860.  (« 

15 

.48 

2.88 

6.97 

14i81 

38.48 

80.94 

883.06 

4h:  88 

10 

.08 

5.53 

15.84 

81.29 

86.88 

irr.oo 

487.75 

1001.25 

6 

8.80 

18.68 

M  48 

1(15.68 

291.20 

597.78 

1647.:i 

3881.  ft) 

The  figures  are  correct  for  trochoidal  deep-sea  waves  only,  but  they  give 
a  close  approximation  for  any  nearly  regular  series  of  waves  in  deep  water 
and  a  fair  approximation  for  waves  In  shallow  water. 

The  question  of  the  practical  utilisation  of  the  energy  which  exists  in 
ocean  waves  divides  it^self  into  several  parts : 

I   1.  The  various  motions  of  the  water  which  may  be  utilized  for  power 
purposes. 

2.  The  wave  motor  proper.  That  Is,  the  portion  of  the  apparatus  In  direct 
contact  with  the  wat.r,  and  receiving  and  transmitting  the  energy  thereof  ; 
*^ogether  with  the  mechanism  for  transmitting  this  energy  to  the  machinery 
for  utilizing  the  same. 

.  Regulating  devices,  for  obtainlnj^  a  uniform  motion  from  the  irregular 
and  more  or  lees  spasmodic  action  ofthe  waves,  as  well  as  for  adjusting  the 
appnratuR  to  the  state  of  the  Mde  and  condition  of  the  sea. 

4.  Storage  arrangements  for  insuring  a  continuous  and  uniform  output  of 
power  during  a  calm,  or  when  the  waves  are  comparatively  small. 

The  motions  that  mav  be  utilized  for  power  purposes  are  the  foUowinir: 
1.  Vertical  rise  and  fall  of  particles  at  and  near  the  Hurface.  8.  Horizontal 
tonnd-fro  motion  of  particles  at  and  near  the  surface.  8.  Varying  slope  of 
Kurface  of  wave.  4.  Im^^etus  of  waves  rolUng  up  the  beach  in  the  form  of 
breakers.  5.  Motion  of  distorted  verticals.  All  of  these  motions,  except  the 
liiKt  one  mentioned,  have  at  various  times  been  proposed  to  be  utilized  for 

Eower  pnrposes;  and  the  last  is  proposed  to  be  used  in  appaiutus  described 
y  Mr.  Stahl. 

The  motion  of  distorted  verticals  Is  thn?  defined:  A  set  of  particles,  origi- 
nally in  the  same  vertical  straight  line  when  the  water  is  at  rest,  d<ies  not 
remain  in  a  vertical  line  during  the  passage  of  the  wave;  so  that  the  line 
coiinectliie  a  set  of  such  particles,  while  vertical  and  Ktralght  In  HtlU  water, 
becomes  ilistorted,  as  well  as  dis|)laced,  duriuK  the  passaKe  of  the  wave,  its 
upper  portiou  moving:  farther  and  more  rapidly  than  Its  lower  portion. 

Mr.  StahVs  paper  con lains  illiistraiioiis  of  several  wave-motors  designed 
tipon  various  principlen.  His  conolusious  as  to  their  practicability  Is  as  foU 
lows:  "  Possibly  none  of  the  methods  described  in  this  paper  may  ever  pn»ve 
couimerelally  successful;  Indeed  the  problem  may  not  be  susceptible  of  a 
flnanclaliy  successful  solution.  My  own  investigations,  however,  so  far  as  I 
have  yet  been  able  to  carry  them,  incline  me  to  the  belief  that  wave-power 
can  and  will  be  utllfa^d  on  a  paying  iMwis," 

Continuous  tTtlllzatlon  of  Tidal  Po'wer*  (P.  Decoeur,  Proa 
Inst.  C.  E.  1890.)— In  connection  with  the  training-walls  to  be  constructed  Ul 


PUMPS   AND   PUMPING   ENGINES,  CO 

the  estuarr  of  the  Seine,  it  Is  proposed  to  construct  lan;e  basins,  bv  means 
of  which  the  power  available  from  the  rise  and  fall  of  the  tide  could  be  util- 
ised. The  method  proposed  Is  to  have  two  basins  separated  by  a  banlc  rising 
above  high  water,  within  which  turbines  would  be  placed.  The  upper  basin 
^  ould  be  in  communication  with  the  sea  during  the  higher  one  third  of  the 
tidal  range,  rising,  and  the  lower  basin  during  the  lower  one  third  of  the 
tidal  range,  falling.  If  JT  be  the  range  in  feet,  the  level  in  the  upper 
basin  would  never  fall  below  %H  measured  from  low  water,  and  the 
level  in  ihe  lower  basin  would  never  rise  above  HH.  The  available  head 
varies  between  O.S^H  and  O.SOH,  the  mean  vulue  being  %H.  If  S  square  feet 
le  the  area  of  the  lower  basin,  and  the  above  conditions  are  fulflUed.  a 
quantity  1/SSHcu.  ft.  of  water  is  delivered  through  the  turbines  in  the  space 
of  9J4  hours.  The  mean  flow  is,  therefore,  SH  -*-  99,900  cu.  ft.  per  sec  ,  and, 
the  mean  fall  being  %H^  the  available  gross  horse-power  is  about  1/308'//*, 
where  S'  is  measured  in  acres.  This  might  be  increased  by  about  one  third 
j!  ■  riation  of  level  in  the  basins  amounting  to  Uff  were  permitted.  But 
to  reach  this  end  the  number  of  turbines  would  have  tn  he  doubled,  the 
mean  head  being  reduced  to  ^H,  and  It  would  be  more  difficult  to  transmit 
a  constant  power  from  the  turbines.  The  turbine  proposed  is  of  an  improved 
model  designed  to  utilize  a  large  flow  with  a  moderate  diameter.  One  has 
been  designed  to  produce  300  horse-power,  with  a  minimum  head  of  6  ft.  3 
in.  at  a  8|^ed  of  15  revolutions  i>er  minute,  the  vanes  having  13  ft.  internal 
diameter.    The  speed  would  be  maintained  constant  by  regulating  sluices. 


PUMPS  AXTD  PUMPING  ENGINES. 

Theoretical  Capacity  of  a  Pnmp.— Let  Q*  =  cu.  ft.  per  min.; 
G'  =■  Amer.  gals,  per  min.  =  7.4^')^';  d  =  diam.  of  pump  in  inches;  I  = 
stroke  in  inches;  N  =  number  of  single  strokes  per  min. 

Capacity  in  cu.  ft.  per  min.  =  Q'  =  ^  .  -^  .  (^=  .(miMbNdH: 

4      144      V-i 

Capacityingal8.permin.G'=  J  .  ^~ =  .WXMNdU; 

Capacity  in  gals,  per  hour    =.*2MNd*l. 

It  v*s  piston  speed  In  feet  per  min.,  d  =s  13.54 i/  ^    =  4.95 j/ . 

If  the  piston  speed  is  100  feet  per  min.: 

m  B  1200,  and  d  «  1.864  V^  s  .4i»  VG' ;    G'  =  4.06d«  per  min. 

The  actual  capacity  will  be  from  60jC  to  dSjCof  the  theoretical,  according  to 
ttie  tightness  of  the  piston,  valves,  suction-pipe,  etc. 

Tlieoretlcal  Horse-poiver  reqnlred  to  raise  Water  to  a 
ClTen  BLelsbt.— Horse-power  = 

Volume  in  cu.  ft.  per  min.  X  pressure  per  sq.  ft.  _  Weight  x  hplglit  of  lift 
38,000  "*  33,000 

O*  =  cu.  ft.  per  min.;  &  =  gals,  per  min.;  W  =  wt.  in  lbs. ;  P  =  pressure 
In  lbs.  per  rq.  ft.;  p  =  pressure  In  lbs.  per  sq.  in.;  H  ~  iielght  of  lift  in  ft.; 
IK=  0^360',  P=  U4p,p  »  .433//,  H  =  2.309p,  G'  =  7.m5Q'. 


J. 


HPs 

Q'P  „ 
83,000 - 

(^H  X  144  X 
88,000 

438 

Q'H 

5:.'9.2 

G'H 
3958.7* 

HP  = 

38,000  "" 

ex62  86x2.809p 

33,000 

i«9.;j 

G'p 
1714.5' 

For  the  actual  horse-power  required  an  allowance  must  be  made  for  the 
friction,  slips,  etc,  of  engine,  piunp,  valves,  and  passages. 


603 


WATER-POWEB. 


Deptb  of  Snetlon*— Theoretically  a  perfect  pump  wfll  draw  water 
from  a  height  of  nearly  84  feet,  or  the  heiipht  correspondinfif  to  a  perfect 
vacuum  (14.7  lbs.  X  2.309  s  88.96  feet);  but  since  a  perfect  vacuum  caunot  be 
obtained,  on  account  of  valve-leakage,  air  contained  in  the  water,  and  the 
vapor  of  the  water  itself,  the  actual  height  is  generally  less  than  80  feet. 
Wnen  the  water  is  warm  the  height  to  which  it  can  be  lifted  by  suction  de- 
creases, on  account  of  the  increased  pressure  of  the  vapor.  In  pumping  hot 
water,  therefore,  the  water  must  flow  into  the  pump  oy  gravitj-.  The  fol- 
lowing table  shows  the  theoretical  maximum  depth  of  suction  for  different 
temperatures,  leakage  not  considered: 


Temp. 
F. 

Absolute 
Pressure 
OfVapor, 
lbs.  per 
sq.in. 

Vacuum 

in 
Inches  of 
Mercury. 

Max. 

Depth 

of 

Suction, 

feet. 

Temp. 
F. 

Absolute 

Pressure 

oi  Vapor, 

lbs.  per 

sq.in. 

Vacuum 

in 
Inches  of 
Mercury. 

Max. 

Depth 

of 

Suction, 

feet. 

101.4 
186.9 
144.7 
158.8 
162.5 
170.8 
177.0 

27.88 
25.85 
28.81 
21.77 
19.74 
17.70 
15.6« 

81.6 
29.8 
27.0 
24.7 
23.4 
20.1 
17.8 

183.0 
188.4 
193.2 
197.6 
201.9 
205.8 
209.6 

8 
9 
10 
11 
12 
18 
14 

13.68 
11.59 
9.66 
7.61 
5.48 
8.44 
1.40 

15.5 
18.2 
10.9 
8.5 
8.2 
8.9 
1.6 

Amount  of  "Water  raised  by  a  Slnele-actliifl:  Lift-pamp. 

—It  is  cuinnton  to  estimate  that  tne  quantity  of  wnier  ruised  by  a 
single-acting  bucket-valve  pump  per  minute  Is  equal  to  the  number  of 
strokes  in  one  direction  per  minute,  multiplied  bv  the  volume  traversed  bv 
the  piston  in  a  single  stroke,  on  the  theory  that  the  water  rises  in  the  pump 
only  when  the  piston  or  bucket  ascends;  but  the  fact  is  that  the  column  of 
water  does  not  cease  flowing  when  the  bucket  descends,  but  flows  on  con- 
tinuously  through  the  valve  in  the  bucket,  so  that  the  discharge  of  the 
ptimp,  if  it  is  operated  at  a  high  speed,  may  amoimt  to  nearly  double  that 
calculated  from  the  displacement  multiplied  by  the  number  of  single  strokes 
ill  one  diret?tton. 

Proportioning  tbe  Steam-ey Under  of  a  Dlreet-aetlns 
Pn  in  p. —Let 

A  =r.  area  of  steam-cylinder;  a  =  area  of  pump-cyltnder: 

D  =  diameter  of  steam-cylinder;     d  =  diameter  of  pump-cylinder; 
p  =  steain-presKure,  lbs.  persq.  in.  ;p  =  resistance  per  sq.  in.  on  pumps; 
H=head  ^2.809p;  p  =  .483ff ;  ft-, 

c*       Mi  ^»  *u  work  done  in  pump-cylinder 

E=  efficiency  of  the  pump  = r— , . —-.  ^   »■        — i,—r-» 

*'      ''      work  done  by  the  steam-cylinder 


EAP 


,  />  =  y^^,  .=  p/f;P=^:p  =  f^^. 


A         p 
a°EP" 


H=2.d09EP- 


If  JP=75J<.//  =  1.:82P— . 

a 


.483g 
EP  ' 

E  Is  commonly  taken  at  0.7  to  0.8  for  ordinary  direct-acting  pumps.  For 
the  highest  class  of  pumping-engines  it  may  amount  to  0.9.  The  steiini- 
pressure  P  is  the  mean  effective  pressure,  according  to  the  Indicator-dia- 
gram; the  water- pressure  p  is  the  mean  total  prevssure  acting  on  the  pump 
plunger  or  piston,  including  the  suction,  as  could  be  shown  by  an  Indicator- 
diagram  of  the  water-cylinder.  The  pressure  on  the  pump-piston  Is  fn> 
auently  much  greater  than  that  due  to  the  height  of  the  lift,  on  account  of 
le  friction  of  the  valves  and  passages,  wliich  increases  rapidly  with  veliHrit  v 
of  flow. 

Speed  of  Water  tbronisrliL  PIpeM  and   Pnmp-pasMiffea. 
The  speed  of  the  water  is  commonly  from  100  to  200  feet  per  minute,    if  AW 
feet  per  minute  is  exceeded,  the  loss  from  friction  may  be  considerable. 

The  dlwneter  of  pipe  required  Is  4.«iA/-r^-^ri'"'°'"T  .  ■ 
•^  *^      ^  y  velocity  in  feet  per  minute 

For  a  Telocity  of  200  feet  per  minute,  diameter  «.35  x  Vgallons  permin. 


PtTMPfl. 


603 


Staes  of  lMreet«ACtliiff  Pamp**— The  tables  on  this  and  the  next 
[•AKK  ail;  nel^ctetl  frum  cataiO)?ue8  or  raanufacturerg,  as  repreMotiOK  the 
two  ooiiimofi  types  of  (iirect-actinur  pump,  viz.,  ihe  sinKle-cyModer  and  the 
dunl»*x.    Both  tvpe^  f^re  n«>w  made  by  moet  of  the  leadiofr  maniifacturere. 

The  DemD«  Single  Boiler-feed  or  Premnre  Pump.— Suitable 
for  putnping  clear  HquiUs  at  a  presAui'e  not  exceeding  150  Ibe. 


SIsea. 


■  I  t 


:W 


8 

4 
4 

5 


]0 
12 
14 


OqD 


6 
5 
5 
6 
6 
7 
7 
8 
10 
10 
IS 
19 
18 
U 


.07 

.09 

.10 

.11 

.15 

.85 

.88 

.49 

.09 

.85 

1.03 

1.47 

8.00 

8.61 


Capacity 

permln. 

at  Given 

Speed. 


ISO 
150 
150 
150 
150 
126 
185 
180 
100 
100 
100 
100 
100 
100 


10 
13 
15 
16 
88 
31 
48 
58 
69 
85 
102 
147 
900 
961 


7 

I 

12 
18 
18 
14 
19 
19 
81 


Sizes  of  Pipes. 


H 


9 
8 
o 

4 

5 


Tbe  Deane  Sluffle  Tank  or  Ijl^ht-aervlce  Pump.— These 

piiinps  will  all  stand  a  constant  working  pressure  of  75  lbs.  on  tlie  water- 
rylinders. 


Sizes. 

i 

Capacity 
per  min. 

^ 

Sizes  of  Pipes, 

1 

I 

• 

at  aiven 

•g 

1 

Speed. 

.5 

g 

it 

1 

1 

c 

.a 

a 

5 

1 

J 

1 

1 

4 

4 

5 

.87 

130 

35 

33 

9^ 

H 

^ 

11^ 

5 

4 

7 

.88 

185 

48 

46^ 

15 

i|a 

8  i« 

?t? 

?li 

7 

.78 

185 

90 

15 

j^ 

9 'S 

10 

1.91 

110 

810 

68 

17 

1 

^i 

8 

6 

18 

1.46 

100 

146 

67 

80^ 

1 

yi 

6 

7 

18 

8.00 

100 

200 

66 

17 

H 

8 

7 

18 

900 

100 

900 

67 

20^ 

1 

^H 

8 

8 

18 

9.61 

100 

261 

68 

80 

1 

1^ 

10 

8 

'  18 

8.61 

100 

261 

68K 

SO 

m 

2 

8 

10 

18 

4.08 

100 

408 

68 

90^; 

1 

IK 

8 

10 

10 

18 

4.08 

100 

408 

68^ 

80 

IH 

a 

8 

18 

10 

18 

4.08 

100 

408 

64 

84 

8 

'M 

8 

10 

18 

19 

5.87 

100 

587 

68H 

SO 

1H 

a 

8 

1:3 

18 

13 

5.87 

lOfl 

587 

64 

88V« 

8 

'•^H 

8 

10 

18 

18 

8.79 

70 

616 

95 

25 

m 

8 

8 

12 

18 

18 

8.79 

70 

616 

95 

88^1 

8 

2^!^ 

8 

li 

14 

13 

12.00 

70 

840 

95 

8 

2  Z 

8 

14 

16 

18 

15.66 

70 

1096 

95 

84 

8 

8  <6 

10 

18 

16 

18 

15.66 

70 

1096 

95 

34 

2 

2  Z 

10 

1«^ 

16 

18 

15.66 

70 

1096 

97 

34 

3 

•SV4 

10 

16 

18 

84 

26.48 

60 

1321 

115 

40 

8 

8^ 

18 

18 

18 

34 

86.48 

.^ 

1381 

m 

40 

3 

3H 

12 

G04 


WATBB-POWER. 


Efllelency  of  Small  IMrect-actiiMr  Pumps.— Chas.  E.  Enieiy, 
in  Keporu  of  JuUkos  of  Philadelpbia  Exhibition,  l87tf,  Oroup  xz..  says:  **£x« 
periinenis  made  with  steam-punips  at  the  American  Ingtftute  Exhibition  of 
1867  showed  that  averaKe-gized  steam-pumps  do  not,  on  the  average,  utiJise 
more  than  60  per  cent  of  the  indicated  power  in  the  steam-cylinders,  the  re- 
maiiider  being  absorbed  in  the  friction  of  the  engine,  but  more  particularly 
in  ilie  passage  of  the  water  through  the  pump.  It  may  be  safely  stated 
that  ordinary  steam-pumps  rarelv  require  less  than  1^  pounds  of  stenm 
per  hour  for  each  hor8e-i>ower  utiiizeil  in  raising  water,j^uivalenttoaduty 
of  only  15,000,000  foot-pounds  per  100  pounds  of  coal.  With  larger  steam- 
pumps,  particularly  wlien  they  are  proportioned  for  the  work  to  be  done, 
the  duty  will  be  materialiy  increased." 

The  'Wortfiinstoii  ]>nplex  Pomp* 

Standard  Sizbs  for  Ordinary  Servicb. 


►1^ 

a  0   . 

Sizes  of  Pipes  for 

g- 

s 

fc* 

Hi 

III 

Short  Lengths. 

1 

h 

3 

in 
=^i 

1=1 

length  increases. 

1 

0. 

t 

5§ 

ace's 
go3 

i 

i 

1 

i 

i 

1 

Hb"" 

2 

8 

.04 

100  to  250 

8to     20 

2U 

^ 

1 

iH 

1 

tn 

^ 

4 

.10 

100  to  200 

20  to     40     4 

H 

2 

1^ 

5 

.80 

100  to  200 

40to     8U     6 

H 

^ 

i>2 

6 

4 

6 

.88 

100  to  150 

70  to    100     5f^ 
&5to    125     ^ 

1 

8 

2 

^ 

4)4 

6 

.42 

100  to  1!50 

'K 

2 

4 

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zR 

5 

6 

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lOOtoLV) 

100  to    150 

7 

1^ 

2 

4 

tS 

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10 

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75  to  125 

100  to    170 

69^ 

1^ 

2 

4 

3 

9 

10 

.93 

76  to  125 

185  to   280 

^ 

2 

4 

3 

10 

6 

10 

1.22 

75  to  126 

ISO  to   800 

m 

2 

5 

4 

10 

7 

10 

1.66 

75  to  125 

345  to   410 

^ 

2 

6 

5 

12 

7 

10 

1.66 

76  to  125 

245  to   410 

^ 

^Vi 

3 

6 

5 

14 

7 

10 

1.66 

75  to  125 

215  to   410 

^ 

9^ 

3 

6 

5 

12 

8Vi 

10 

2.45 

75  to  125 

865  to   610 

12^ 

*^Vv 

8 

6 

5 

14 

8V6 

10 

2.45 

75  to  125 

865  to   610 

12 

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3 

6 

5 

10 

8w 

10 

2.45 

75  to  125 

8«5to   610 

12 

•>^ 

8 

6 

5 

18Vi 

8^ 

10 

2.45 

T6to  J26 

865  to   610 

12 

3 

^yi 

6 

5 

ao 

8^ 

10 

2.45 

75  to  125 

865  to   610 

12 

4 

5 

6 

5 

12 

10^ 

10 

8.57 

75  to  125 

680  to   890 

\n 

'i^ 

8 

8 

7 

14 

lOVd 

10 

8.67 

75  to  125 

580to   890 

'•JVa 

8 

8 

7 

16 

lOW 

10 

3.57 

75  to  1-25 

530  to   890;   14«.i 

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3 

8 

7 

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IOJ4 

10 

8.57 

75  to  126 

680  to    890'  Ht4 
530  to    890'  14^ 

3 

m 

.  8 

7 

20 

lOJd 

10 

8.57 

76  to  125 

i 

5 

8 

7 

14 

12 

10 

4.89 

76  to  125 

7^toie20;  17 

n 

8 

10 

8 

16 

12 

10 

4.89 

75  to  125 

730  to  1220.  17 

8 

10 

8 

18^ 

12 

10 

4.89 

75  to  125 

730  to  Vim 

17 

3 

m 

10 

8 

20 

12 

10 

4.89 

75  to  125 

7:10  to  12-»0 

17 

4 

6 

10 

8 

18^ 

14 

10 

6.66 

75  to  l-.»5 

990  to  1660 

\^. 

8 

»H 

12 

10 

20 

14 

10 

6.66 

75  to  1« 

990  to  1660 

4 

5 

12 

20 

17 

10 

15 

6.10 

60  to  100 

510  to  1020 

14 

3 

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8 

7 

20 

12 

16 

7.34 

50  to  100 

7«)  to  1460,  17 

4 

5" 

18 

10 

20 

15 
15 

15 
15 

11.47 
11.47 

50  to  100 
50  to  100 

1145  to  2.290    21 

25 

1145  to  2290 

., 

PUMPS. 


605 


Speed  of  Piston.— A  piscon  speed  of  100  feet  per  mlnnte  is  commonly 
assumed  as  correct  in  practice,  but  for  short-stroke  pumps  this  erfves  too 
bigh  a  speed  of  rotation,  requiring  too  frequent  a  reversal  of  the  ▼alves. 
For  lonir  stroke  pumps,  S  feet  and  upward,  this  speed  may  be  considerably 
exceeded,  if  valves  and  passages  are  of  ample  area. 

IVmnber  of  Strokes  reqnlred  to  Attain  a  Piston  Speed 

trom  50  to  125  Feet  per  Minute  for  Pnmps  l&aTlni^ 

Strokes  Arom  8  to  18  Inehes  In  lienstli. 


0*2 


as 

"50" 
S5 

60 

65 

70 

75 

80 

85 

90 

95 
100 
105 
110 
115 
120 

la 


Length  of  Stroke  In  Inches. 


8 


10 


12    I    15    I    18 


Number  of  Strokes  per  Minute. 


900 
890 
940 


900 
890 
840 
860 
880 
400 
490 
440 
460 
480 

soo 


150 

190 

100 

86 

75 

60 

50 

40 

165 

139 

110 

94 

89.5 

66 

55 

44 

180 

144 

120 

108 

90 

79 

60 

48 

195 

156 

180 

111 

97.5 

78 

65 

59 

910 

168 

140 

190 

105 

84 

70 

66 

995 

180 

150 

198 

119.5 

90 

75 

60 

940 

199 

160 

187 

120 

96 

80 

64 

955 

904 

170 

146 

127.5 

lOS 

85 

68 

970 

916 

180 

154 

185 

108 

90 

78 

S86 

998 

190 

168 

149.5 

114 

96 

76 

800 

940 

200 

171 

150 

190 

100 

80 

815 

259 

910 

180 

157.5 

196 

i05 

84 

880 

964 

990 

188 

165 

139 

110 

88 

845 

976 

980 

197 

179.5 

138 

115 

99 

860 

988 

940 

906 

180 

144 

190 

90 

875 

800 

950 

914 

187.6 

160 

195 

100 

88 
87 
40 
43 
47 
50 
58 
57 
60 
68 
67 
70 
78 
77 
80 
83 


PIstton  Speed  of  Pomplns«entclnes«  (John  Birkinbine,  Trans. 
A.  I.  M.  E.,  V.  450.)— In  dealing  with  such  a  ponderous  and  unyielding  sub- 
stance as  water  there  are  many  diflflcultles  to  overcome  in  making  a  pump 
work  with  a  high  piston  speed.  The  attainment  of  moderately  high  speed 
is,  however,  easily  accomplished.  Well-proportioned  pum ping-engines  of 
large  capacity,  provided  with  ample  water-ways  and  properly  constructed 
Tal ves.  are  operated  successfully  against  heavy  pressures  at  a  speed  of  950  ft 
per  minute,  without  "  thug,"  concussion,  or  injurv  to  the  apparatus,  and 
there  is  no  doubt  that  the  speed  can  be  still  further  Increased. 

fipeed  of  Water  tkrouffk  Talves.— If  areas  through  valves  and 
water  passages  are  sulBcieut  u>  give  a  velocity  of  950  ft.  per  min.  or  less, 
they  are  ample.  The  water  should  be  carefully  guided  and  not  too  abruptly 
deflected.    (F.  W.  Dean.  3S!ng.  Netea,  Aug.  10,  181)6.) 

BoUer*feed  Pnmps*— Practice  has  shown  that  100  ft.  of  piston  speed 
per  minute  is  the  limit,  if  excessive  wear  and  tear  is  to  be  avoided. 

The  velocity  of  water  through  the  suction-pipe  must  not  exceed  900  ft. 
per  minute,  else  the  resistance  of  the  suction  is  too  great. 

The  approximate  size  of  suction-pipe,  where  the  length  does  not  exceed 
25  ft.  and  there  are  not  more  than  two  elbows,  may  be  found  as  follows : 

7/10  of  the  diameter  of  the  cylinder  multiplied  by  1/100  of  the  piston  speed 
in  feet.  For  duplex  pumps  of  small  size,  a  pipe  one  size  larger  is  umially 
employed.  The  velocity  of  flow  in  the  discharge-pipe  should  not  exceed 
500  ft.  per  minute.  The  volume  of  discharge  and  length  of  pipe  vary  so 
greatly  in  different  installations  that  where  the  water  is  to  be  forced  more 
than  50  ft.  the  size  of  discharge-pipe  should  be  calculated  for  the  particular 
conditions,  allowing  no  greater  velocity  than  500  ft.  per  minute.  The  size  of 
discharge-pipe  is  calculated  in  single-cylinder  pumps  from  960  to  400  ft.  per 
minute.    Greater  velocity  is  permitted  in  the  larger  pipes. 

In  determining  the  proper  size  of  pump  for  a  steam-boiler,  allowances 
must  be  made  for  a  supply  of  water  sufficient  to  cover  all  the  demands  of 
engines,  fiteam*heating,  etc.,  up  to  the  capacity  of  generator,  and  should  not 
be  calculated  simply  according  to  the  requirements  of  the  engine.  In  prac- 
tice engines  use  all  the  way  from  19  up  to  50,  or  more,  pounds  of  steam  per 
H.P.  per  hour  when  being  worked  up  to  capacity.  When  an  engine  is  over- 
loaded or  underloaded  more  water  per  H.P.  will  be  required  than  when 
operating  at  its  rated  capacity.    The  average  run  of  horizontal  tubular 


606 


WATBBfFOWSB. 


boOwv  will  «fapor»te  from  9  to  S  Ilia,  of  water  per  aq.  ft  of  hOKklBf •mrfaoa 
por  hour,  bnlmajr  be  driven  up  to  6  lbs.  If  tbe  grate  raifaoo  is  too  Uuige  or 
Ibo  draught  too  isroac  for  aooDomioal  worUng:. 

jPWDap* Valves. ^A.  F.  Naelo  (TruDS.  A.  8.  M .  B.,  x.  B»l)  fflTM  a  number 
of  designs  with  dimensions  of  double-beat  or  Oomlah  valves  used  In  lam 
pumplng«nglne8,  with  a  discussion  of  the  theory  of  their  proportions.  The 
lollowlng  Is  a  summaiy  of  the  proportions  of  tbe  Talyes  deacrlbed* 

BUIOURT  09  VALTB  PnOPOaTIOMS. 


liOcaUon  of  Bngliie. 


Providence  hlgh.«er- 
vice  engine  .-.. 


ProTidenoe  Qornish- 

engine 

St.  I#oui8  Water  Wks. 

Milwaukee   ^      ' 

Chicago        •• 


wood  seats. ,, 

Chicago  Water  Wks. 


1  lb. 
reduced  to 
.66  lb, 

1.28 
I.8Q 


.40 

1.41 
1.81 

1.18 

.06 


W 


677  lbs. 


680 

900 

160 

161 
140 

188 
161 


I 


Good 


Good 

Some  noise 
(Some  noise  at 


Mr.  Nsgle  aaya :  There  is  one  feature  in  which  the  Oorafsh  valves  are 
ueoeesai'ily  defective,  namely^the  lift  must  always  be  quite  largtt  unleaa  grrai 
power  is  saorifloed  to  reduce  it.  It  Is  undeniable  that  a  smsli  ttft  is  prefer- 
able to  a  great  one.  and  hence  it  naturally  leads  to  the  substitution  of 
numerous  small  valves  for  one  or  several  large  ones.  To  what  extreme  rp> 
duotion  of  sise  this  view  might  safely  lasd  must  be  left  to  the  judi^ment  of 
the  engineer  for  the  pai*tiauiar  ease  in  hand,  but  certainly,  theoretically,  «v 
must  adopt  small  valves.  Mr.  Oorlias  at  one  time  carried  the  theory  m 
far  as  to  make  them  only  1%  ioches  In  diameter,  but  from  8  to  4  Inches  i$ 


the  more  oommoo  prsotloe  now.    A  small  valve  presents  proportionate! v  a 

„ .  ^  . "  ^'.charge  with  the  same  lift  than  a  larger  valve,  so  that 

whatever  the  total  area  oc  valva>8eat  opening,  its  full  contents  can  be  di»> 


larger  surfece  of  discb 


charged  with  less  lift  through  numerous  sniall  valves  than  with  one  larK« 
one. 

Henry  B.  Worthington  was  the  first  to  use  numerous  small  rubber  valve« 
in  preference  to  the  larger  metal  valves.  These  valves  work  well  under  all 
the  conditions  of  a  city  pumplng-eogine.  A  volute  spring  is  generally  usf4 
to  limit  the  rise  of  the  valve. 

In  theLeavitt  high-duty  sewerage-engine  at  Boston  (Am.  MackimiMt,  Bar 
81,  1884),  the  valves  are  of  rubbor,  |i(*inoh  thick,  the  opening  tn  valve-seat 
being  13^  X  4M  inches.  The  valves  have  Iron  face  and  back-plates,  sad 
fonu  their  own  mnges, 

OBNTRIFVOAIi  PUMPS. 

Belatton  of  Het^ltt  of  IiUU  to  Toloelt/.-The  height  of  hfl 

depends  only  on  the  tangential  velocity  of  tbe  oircumference,  every  tangM- 
tial  velocity  giving  a  constant  height  of  lift— eometimee  termed  *^  head  "- 
whether  the  pump  is  small  or  large.  The  quantity  of  water  discharged  te  ia 
proportion  to  the  area  of  the  discharging  oriAces  at  the  oircumference.  or  in 

Eroportion  to  the  square  of  the  diameter,  when  the  breadth  is  kept  tlie  same. 
;.  H.  Buel  (App.  Cm  Mech.,  il,  606)  gives  tbe  following: 
Let  Q  represent  t-he  quantity  of  water,  in  cubic  feet,  to  be  pumped  pr 
minute,  h  the  helsrbt  of  suction  in  feet,  h'  the  height  of  disoharge  in  feet,  aoi 
d  the  diameter  of  suction-pipe,  equal  to  the  diameter  Of  dlsoharge-plpe,  is 


CENTBIPUGAL  PUMPS. 


flOT 


fe^l)  tben,  Aopordtnvtqlink,  d  »  a86 


J       9 


9  being  llM  Mpeli 


eimtion  due  to  gravity. 

If  the  suction  takes  place  on  one  side  of  the  wheel,  the  inside  diameter  of 
the  wheel  is  equal  to  1  .ski,  and  the  outside  to  9.4d.  If  the  suqtioiq  takc^  place 
at  both  sides  of  the  wheel,  the  inside  diameter  of  the  wheel  is  equal  to  O.SSd, 
and  the  outside  to  l.fd.  Then  the  suction-pipe  will  have  two  branches,  the 
area  of  each  equal  to  \kalt  tlie  area  qf  d.  The  suction-pipe  should  he  as  short 
as  possible,  to  prevent  air  from  entering  tlie  ppmp.  The  tangential  velocity 
of  |he  ou|er  edge  of  wheel  for  the  deliverj  Q  is.  eqi^l  to  1.25  i^ig  {h  -f-  ^'> 
feet  per  second. 

]i"^  ur  ■■-■  iiro  piif  In  tiiitnbef*  conafrueted  ss  follows t  Divide  the  i.*ti]|ri|| 

^  [  ^N^imL  part--<  by  ^Iri^^^  iu;je  tijt^  TAdH,  [uiil  dj^^idf)  th«  bre^dtli  <»f  Ul^  yihf^ 
j  ..1-  imrtie  nifttinf  r  by  drtvmrt^  ti^iiiH'OttVri^  ch^clp^,  TI10  liitiirKi'cEiuiis  at  (he 
I    vb^rni  raiJil  wtlh  thi*  corraspotnllne  t;irciǤ  plve  points  of  Uia  ftmi. 

In  fX^^frinvMUls  ^vilh  Appold'^  iiuriip,  a  vt^kK'jpty  of  cireiiuif^n^nce  of  WO 
-■    |Mfr  liLiri   raJs*:*i  i\u-  iAat«r  1  ft-  hinh.  iwii  mnintftlued  it  at  thai  kn'«| 

ittioiiL  dittcijar^Mig  uhvi  and  iliuihlt^  thf  vehit^jty  ml^vd  the  wAtjnr  h*  faur 
Noiiifa  ihe  hei^hf,  »4  il<f*  c^iitririi^til  rurt^f^  wiu<  pr^iporUuiiaie  lo  t^  i^iuije 
^f  t|ie  v*?lorj1iy^  tohstqiit^ntly. 

too  (%.  per  iiilti.  TAib^  the  w^Uur   1  ft*  uithout  dlwlmrg^. 
1600      *^        ••         •*        ~         t»        i  «•  •*  '*      '^ 

sdoo    ••        ••        ••      M       ♦•     16  *•        ••  *• 

^Qfjf}       H  (•  u         «*  **       64  **  **  ** 

The  greatest  height  to  which  the  water  had  been  raised  without  discharge, 
in  the  experiments  with  the  1-ft.  pump,  was  67.7  ft.,  with  a  velocity  of  4154 
ft.  per  mln.,  being  rather  less  tlian  the  calculated  height,  owing  probably  to 
leakage  with  the  greater  pressure.  A  velociiy  of  1138  ft.  per  min.  raised  the 
water  5^  ft.  without  any  dischi^rge,  aqd  the  maximum  effect  from  the 
power  employed  In  raising  to  the  same  he'ieh'i  5^  f i.  was  obtained  at  the 
velocity  of  1678  ft.  per  min.,  giving  a  ditichf^rge  of  I406gal8.  per  min.  from 
the  1-lt.  pump.  The  addfiionai  velocity  required  to  effect  a  dischar|:e  of 
1400  gals,  per  min.,  through  a  1-ft.  pump  ^orkipg  fit  a  dead  level  without  any 
height  of  lift,  is  ttO  ft.  per  min.  Consequently,  adding  this  number  in  each 
case  tq  %\ie  velocity  given  above,  at  which  nq  dischance  talces  place,  the  fol- 
lowing velopities  are  obtained  for  the  maximum  effect  to  be  produced  in 
each  pufift  * 

10M  ft.  per  min.,  velooitgr  lor   1  ft.  height  of  lift. 
1660      **         **  •♦  t»     4  ♦»        ••         »• 

2550      •*  *•  ••  ♦♦    J6  "        ♦•         M 

4560      ♦•         **  •*  •♦    64  "       •*         " 

Qn,  in  general  term»«  the  velocity  In  feet  per  minute  for  the  circumference 
of  the  pump  to  be  driven,  to  raise  the  water  to  a  certain  height,  is  equal  to 
550  +  600  VheiRht  Of  lift  in  feet. 


I^HWi^pco  Ceiitr|fli|i;a|  PamjMu  C|i|iia  I|— Fqr  Iillltp  lyom 


.|,=I4=IM 

1 

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1280 

86 

86 

86 

8.3000   11.  To 

2200(.i» 

8 

R   '   SOOO  <  1  10 

2460 

I       1 

♦  Without  base. 

The  economical  capacity  corresponds  to  a  flow  not  exceeding?  10  ft.  per 
secpftU  iif  the  de)iTery-pipti<  ^ail  pipes  and  higU  rate  of  llow  cauise  a  great 
loss  of  power. 


608 


WATER-POWER. 


8lz«  of  PulleyM.  Wldtb  of  BelCs^  and  RevoluClons  per 
Mlnale  NaecMarj  to  Raise  the  Bated  <|uaiitUir  of  Water 
to  DlflTerent  Helicbte  ivltlE  PampH  ofClasii  B. 


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Billoleneles  of  OentrlAiflral  and  Beelprocatliic  Pnnipa*— 

W.  O.  Webber  (Trana.  A.  S.  M.  K.,  vH.  008>  gWes  diagrams  ehowinir  the 
relatlre  effloiencies  of  centrifugal  and  reciprocating  puriipe,  from  which  the 
following  figures  are  taken  for  the  different  lifts  stated : 
Lift,  feet: 

2     ftl0    15    8025S08540606080    100    1S0    180    200«40880 
Efficiency  reciprocating  pump: 

..     .     .80  .15  .55  .01  .66  .68  .71  .75  ,n  .82    .85    .87    .90    .89    .88    .85 
Efficiency  centrifugal  pump: 

.50  .60  .64  .68  .GO  .&  .66  .62  .58  .60  .40 

The  term  efficiency  here  used  indicates  the  value  of  W.  H.  P.  -♦-I.  H.  P., 
or  horse-power  of  the  water  raised  divided  by  the  indicated  horse-power  of 
the  st**am-cugiiie,and  does  not  therefore  show  the  full  efficiency  of  the  puuip, 
but  that  of  the  combined  pump  and  entrine.  It  is.  however,  a  very  simpTo 
way  of  showing  the  relative  values  of  different  kinds  of  pumplng-enginea 
having  their  motive  power  forming  a  part  of  the  plant. 

The  nighest  value  of  this  term,  given  by  Mr.  Webber,  is  .0164  for  a  lift  of 
ItOft..  and  3615  gals,  per  min.  This  was  obtained  in  a  test  of  the  Leavitt 
pumpintc  engine  at  Lawrence,  Mass..  July  24.  1879. 

With  reciprocating  pumps,  for  higher  lifts  than  170  ft.,  the  curve  of  efH 
ciencies  fall-*,  and  from  200  to  SQO  ft.  life  the  average  value  seem?  about 
.84.  Below  170  ft.  the  curve  also  falls  reversely  and  slowly,  until  at  about  90 
ft.  its  descent  becomes  more  mpid,  and  at  85  ft.  .787  appears  the  best 
recorded  performance.  There  are  not  any  very  satisfactory  records  below 
this  lift,  out  some  figures  are  given  for  the  yearly  coal  consumption  and 
total  number  of  gallons  pumped  hy  engines  in  Holland  under  a  16ft.  lift, 
from  which  an  efficiency  of  .44  has  been  deduced. 

With  centrifugal  pumps,  the  lift  at  which  the  maximum  efficiency  is  ob- 
tained is  approximately  17  ft.  At  lifts  from  12  to  18  ft.  some  malcers  of 
larxe  experience  claim  now  to  obtain  from  M%  to  lOjt  of  useful  effect,  but 
.613  appears  to  be  the  best  done  at  a  public  test  under  14.7  ft.  head. 

The  drainage-pumps  constructed  some  years  ago  for  the  Haarlem  Lake 
were  designed  tn  lift  70  tons  per  min.  15  ft.,  and  they  weighed  aiiout  150 
tons.  Centriftigal  pumps  for  the  same  work  weigh  only  5  tons.  The  weight 
of  a' centrifugal  pump  and  engine  to  lift  10,000  gals,  per  min.  85  ft.  high  Is 
6  tons. 

The  pnmps  placed  by  Gwynne  at  the  Ferrara  Marshes,  Northern  Italy,  in 
1865,  are,  ii  is  believed,  capable  of  handling  more  water  than  other  set  of 
pumpine-englnea  in  existence.  The  work  performed  by  these  pumps  is  the 
lifting  of  2000  tons  per  niln  —over  600.000,000  gals,  per  24  hours— on  a  mean 
lift  of  about  10  ft.  (maximum  of  1*2.5  ft).    (See  Engineering,  1876.) 

The  efficiency  of  centrifugal  pumps  seems  to  increase  as  tiM  siae  oC  pump 


DUTY  TBIALS  OP  PXJMPING-ENGIKB8. 


609 


fncraases,  approxImatelT  as  follows:  ▲  8"  patnp  (this  desfgnation  meaolnfl^ 
always  the  slae  of  dischai*Ke-outle(  in  iDches  of  diameter),  kI^dS  <m  ^ffl- 
clency  of  88^,  a  8"  pump  fy^  and  a  4"  pump  02%,  a  6"  pump  6O9K,  and  a  6" 
ptimp  64^  efficiency. 

Testa  of  C^ntiiAiiral  Pnmpa. 

W.  O.  Webber,  Trans.  A.  a  M.  E.,  Ix.  887. 


Maker. 

An. 
drewB. 

An. 
drews. 

An. 
drews. 

Heald 

A 
Sisca 

Sisco. 

Heald 

A 
Sisco. 

Berlin. 

Schwartx- 

Icopff. 

8l«e 

**•     suction... 

•*    disk 

Ber.  per  minute. 
Galls,  per  minute 
Height  in  feet.... 

Water  H.P 

pynam^eter  H.P. 
Efflcienpy 

No.  9. 

5" 

191.9 
1618.18 
12.26 
4.69 
10.09 
46.62 

No.  9. 

¥' 

195.6 
2028.82 
12.62 
6.47 
18.2 
58.0 

No.  9. 

J' 

200.6 

2499.88 

18.08 

8.28 

14.88 

67.67 

No.  10. 

10" 

18" 

80.6" 

188.8 
1678.87 

12.88 
6.28 
8.11 

64.6 

No.  10. 

10" 

18" 

80.y' 
802.7 
2044.9 

12.68 
6.61 

1074 

60.74 

No.  10. 

10" 

12" 

80.6" 
818.7 
2871.67 

18.0 
7.81 

14.08 

66.78 

No.  9. 

lol" 

20.6" 
600 
1944.8 
16.46 

"li 

78.1 

▼anes  or  Centrliiical  PiiiiiM,.>For  forms  of  pump  vanes,  see 
paper  by  W.  O.  Webber,  Trans.  A.  8.  U.  E.,  Iz.  226,  and  discussion  thereon 
by  Profs.  Thurston,  Wood,  and  others. 

The  Centrliual  Pump  need  «•  a  Sneilon  Dredge*— The 
Andrews  centrifufcal  pump  was  used  by  Gen.  Gillmore,  U.  8.  A.,  in  1871.  in 
deepening  the  channel  over  the  bar  at  the  mouth  of  the  8t.  John*s  Biver, 
Florida.  Thepump  wasaNo.  9.  with  suction  and  disciiarge  pipes  each  9 
inches  diara.  It  was  driven  at  800  revolutions  per  minute  by  belt  from  an 
eii^ne  developing  88  useful  horse-power. 

Although  200  revolutions  of  the  pump  disk  per  minute  will  easily  raise 
9000  fcallons  of  clear  water  18  ft  hlfch,  through  a  straight  vertical  9-inch 
pipe,  80O  revolutions  were  required  to  raise  »00  gallons  of  sand  and  water 
11  ft.  high,  through  two  inclined  suction-pipes  having  two  turns  each,  dis- 
charged through  a  pipe  having  one  turn. 

The  proportion  of  sand  that  can  be  pumped  depends  greatly  upon  Its 
specific  gravity  and  fineness.  The  calcareous  and  argillaceous  sands  flow 
more  freely  than  the  silicious^  and  fine  sands  are  less  liable  to  choke  the 
pipe  than  those  that  are  coarse.  When  working  at  high  speed,  BOf  to  66^  of 
sand  can  be  raised  through  a  straight  vertical  pipe,  giving  for  every  10  cubic 
yards  of  material  discharged  6  to  6H  cubic  yards  of  compact  sand.  With 
the  appliances  used  on  the  St.  John*s  bar,  the  proportion  of  sand  seldom 
exceeded  45%^  generally  ranging  from  SQ^  to  85j(  when  working  under  the 
most  favorable  conditions. 

In  pumping  2500  gallons,  or  18.6  cubic  yards  of  sand  and  water  per  minute, 
there  would  therefore  be  obtained  from  8.7  to  4.3  cubic  yards  of  sand.  Dun 
Ing  the  early  stages  of  the  work,  before  the  teeth  under  the  drag  had  been 
properly  arranged  to  aid  the  flow  of  sand  into  the  pipes,  the  yield  was  con- 
siderably below  this  average.  (From  catalogue  of  Jos.  Edwards  A  Co., 
Mfrs.  of  the  Andrews  Pump,  New  York.) 

DUTY  TRIAI<8  OF  PUIUPING-ENGINES. 

A  committee  of  the  A.  8.  M.  E.  (Trans.,  zll.  680)  reported  In  1891  on  a 
standard  method  of  conducting  duty  trials.  Instead  of  the  old  unit  of 
duty  of  foot-pounds  of  work  per  100  lbs.  of  coal  used,  the  committee  recom- 
mend a  new  unit,  foot-pounds  of  work  per  million  heat-units  furnished  by 
the  boiler.  The  variations  in  quality  of  coal  make  the  old  standard  unfit  as 
a  basis  of  duty  ratings.  The  new  unit  is  the  precise  equivalent  of  100  lbs.  of 
coal  In  cases  where  each  pound  of  coal  imparts  10,000  heat- units  to  the 
water  in  the  boiler,  or  where  the  evaporation  is  10,000  -♦-  965.7  »  10.866  lbs.  of 
water  from  and  at  212*  per  pound  of  fuel.  This  evaporative  result  is  readily 
obtained  from  all  grades  of  C^iinberland  bituminous  coal,  used  in  horizontal 
return  tubular  boilers,  and,  in  many  cases,  from  the  best  grades  of  authra- 
dteooaL 


610  WATEB-POWBB. 

The  oommiUee  also  r«cotniiMnd  that  th«  trork  done  be  deftermioed  hf 
plunger  diepUoemeot,  after  making  a  teet  for  leakagfi|  ttisteed  of  by  iiiea»« 
iiroment  of  flow  by  win  or  other  apparatun,  but  advliie  (he  uite  nt  eoch 
apparatus  when  practicable  for  obtaining  additional  data.  The  following 
extracts  are  taken  from  the  report.  When  important  tests  are  to  be  made 
the  complete  report  should  be  oonsulted. 

The  necessary  data  having  been  obtained,  the  duty  of  an  engine,  and  other 

JLuantities  relating  to  Its  performance,  may  be  computed  by  the  use  of  the 
oUowing  formules: 

1   T>  f  V  -  Foot-pounds  of  work  done  v  i  ooo  a» 

I.  i^uiy  ^  ^^^  number  of  heat-units  consumed  ^  ^»**"»*™^ 

^  AiP±p+^)yLxN  ^  j^^^^  (foot-pounds). 

C  V  144 
«.  Percentage  of  leakage  *  ^JcTxif^  100 (per eent). 

8.  Capacity  =  number  of  gallons  of  water  discharged  In  94  honrs 

* Dxui " 5 (g^onMi. 

«      4.  Percentage  of  total  f  liotlons, 

Ft  ff  P       AiP±P'^$)yLxirn 
^\l^_^^Z.^^    Jx.00 

or,  in  the  usual  case,  where  the  length  of  the  stroke  and  number  of  strokes 
of  the  plunger  ai*e  the  same  as  that  of  the  steam-piston,  this  last  formula 
becomes: 

Percentage  of  total  frictions  «  fl  -  ^^£^^1 X  ^^  ^P**"  <*"**>• 

In  these  formulas  the  letters  refer  to  the  following  quantities: 
A  =  Area,  in  square  inches,  of  pump  plunger  or  piston,  corrected  for  area 

of  piston  rod  or  rods; 
P  =  Pressure,  In  pounds  per  square  inch.  Indicated  by  the  gauge  on  the 

force  main; 
p  s  Pressure,  in  pounds  per  square  Inch,  corresponding  to  indication  of  the 

Tacuum-gauge  on  suction -main  (or  pressure-gauge,  if  tlie  suction- 

f^ipe  is  under  a  head).    Tlie  indication  of  the  vacuum-gauge,  in 
Itches  of  mercury,  may  be  converted  into  pounds  by  dividing  It  by 
8.035; 
•  ^  Pressure,  In  pounds  per  square  inch,  corresponding  to  distance  be- 
tween the  centres  of  the  two  gauges.    The  computation  for  this 
pressure  is  made  by  multiplying  the  distance,  expressed  in  feet,  by 
the  weight  of  one  cubic  foot  of  water  at  the  temperature  of  the 
pump-well,  and  dividing  the  product  by  144; 
L  =  Average  length  of  stroke  of  pump-plunger,  in  feet: 
N  =  Total  number  of  single  strokes  of  pump-plungt^rmadeduring  the  trial; 
Ab  =  Area  of  steam-cvllnoer,  in  square  inches,  corrected  for  area  of  piston- 
rod.    The  quantity  At  X  M.E.P.^  in  an  engine  having  more  than  one 
cylinder,  is  the  sum  of  the  various  quantities  relating  to  the  reapeo- 
live  cylinders; 
L»  =  Average  length  of  stroke  of  steam-piston,  In  feet; 
iV«  3  Total  number  of  single  strokes  of  steam-plston  during  trial; 
M.E.P.  =  Average  mean   effective  pressure,  in  pounds  per  square  Inch, 
measured  from  the  indicator-diagrams  taken  from  the  steam-cylin- 
der; 
I.H.P.  =  Indicated  horse-power  developed  by  the  steam-cvlinder; 
C  =  Total  number  of  cubic  feet  of  water  which  leaked  by  the  pump-plunger 

during  the  trial,  estimated  from  the  results  of  the  leakage  tesij 
D  =  Duration  of  trial  In  houra: 


DUTY  TRTAM  OF  PUMPING-BNGINE8.  611 

H  =  Total  number  of  heat-units  (B.  T.  U.)  consumed  by  engine  =  weight  of 
water  supplied  to  boiler  bv  main  feed-pump  X  total  beat  of  ateam 
of  boiler  pressure  reckoned  from  temperature  of  main  feed-water  -f 
welgkit  or  water  supplied  by  jacket-pump  x  total  heat  of  steam  of 
boiler-pressure  reckoned  from  temperature  of  Jacket- water  -{-  weight 
of  any  other  water  supplied  X  total  heat  of  steam  reckoned  from  Its 
temperature  of  supply.    The  total  beat  of  the  steam  is  corrected  for 
the  moisture  or  superheat  which  the  steam  uey  contain.    No  allow- 
ance  is  nuide  for  water  added  to  the  feed  water,  which  is  derived 
from  any  source,  except  the  engine  or  some  accessory  of  the  engine. 
Beat  added  to  tha  water  by  the  use  of  a  ilue -beater  at  the  boiier  is 
not  to  be  deducted.    Should  heat  be  abstracted  from  the  flue  by 
means  of  a  steam  reheater  connected  with  the  intermediate  re- 
ceiver of  the  engine,  this  heat  must  be  included  in  the  total  quantity 
supplied  by  the  boiler. 
Leakage  Test  of  PiiBip*~Th«  laaksge  of  an  inside  plunger  (the 
only  type  which  requires  testing)  is  most  satisfactorily  determined  by  mak- 
ing the  test  with  the  cylinder-head  removed.    A  wide  board  or  plana  may 
be  temporarily  bolted  to  the  lower  part  of  the  end  of  the  cylinder,  so  ns  to 
hold  hack  the  water  in  the  manner  of  a  dam,  and  an  opening  made  In  the 
temporary  head  thus  provided  for  the  reception  of  an  overflow-pipe.    The 
plunger  is  blocked  at  some  intermediate  point  in  the  stroke  (or,  if  this  posi- 
tion is  not  practicable,  at  tlie  end  of  the  stroke),  and  the  water  from  the 
force  main  is  admitted  at  full  pressure  behind  it.    The  leakage  escapes 
through  the  overflow-pipe,  and  It  is  collected  in  barrels  and  measured.   The 
test  should  be  made,  if  possible,  with  the  plunger  in  various  positions. 

Id  the  case  of  a  pump  so  planned  that  it  is  difficult  to  remove  the  cylinder- 
bead,  it  may  be  detdrable  to  take  the  leakage  from  one  of  the  openings 
which  are  provided  for  the  iaspeotion  of  the  suotion-valves,  the  head  being 
allowed  to  remain  in  place. 

It  is  assumed  that  there  is  a  practical  absence  of  valve  leakage.  Exami- 
nation for  such  leakage  should  oe  made,  and  if  it  occurs,  and  it  is  found  to 
be  due  to  disordered  valves,  it  should  be  remedied  before  making  the  plunger 
rest.  Leakage  of  the  discharge  valves  will  be  shown  by  water  passing  down 
into  the  empty  cylinder  at  either  end  when  they  are  under  pressure.  Leak- 
rtge  oC  the  suction- valves  will  be  shown  by  the  disappearance  of  water  which 
covers  them. 

If  valve  leakage  is  found  which  cannot  be  remedied  the  quantity  of  water 
thus  lost  should  also  be  tested.  One  method  is  to  measure  the  amount  of 
water  required  to  maintain  a  certain  pressure  in  the  pump  cylinder  when 
this  is  introduced  through  a  pipe  temporarilv  erected,  no  water  being  al- 
lowed to  enter  through  the  discbarge  valves  of  the  pump. 

Table  of  Data  and  Reaalta.— In  order  that  uniformity  may  be  se* 
cured,  it  is  suggeMed  thai  the  data  and  results,  worked  out  in  accordance 
with  the  standard  method,  be  tabulated  in  the  manjter  Indicated  in  the  fol- 
lowing scheme : 

DUTY  TRIAL  OF  ENGINE. 


1.  Number  of  steam-cylinders 

2.  Diameter  of  sceam-oyllnders... Ins. 

8.  Diameter  of  piston-rods  of  steam -cylinders ...  ins. 

4.  Nominal  stroKe  of  steam-pistons ft. 

5.  Number  of  water.plungei'S 

6.  Diameter  of  plungers ins. 

7.  Diameter  of  niston-rods  of  water-cylinders ins. 

8.  Nominal  stroKe  of  plungers ft. 

0.  Net  area  of  steam-pistons .  .  sq.  ins. 

10.  Net  area  of  plungers sq.  ins. 

11.  Average  length  of  stroke  of  steam-pistons  durini'  trial ft. 

It.  Average  length  of  stroke  of  plungers  during  trial    ft, 

(Give  also  complete  description  of  plant.) 

TBMPXRATURBS. 

18.  Temperature  of  water  in  pump-well degs. 

14.  Temperature  of  water  supplied  to  boiler  by  main  feed-pump.,  degs. 
)5.  Temperature  of  water  supplied  to  boiler  from  various  other 

degs. 


613  WATER-POWER. 

rSBD-'WATER. 

16.  Weight  of  water  supplied  to  boiler  by  main  feed-pump Rml 

17.  Weiffht  of  water  supplied  to  boiler  from  various  other  sources,  lbs. 

18.  Total  weight  of  feed- water  supplied  from  all  sources lbs. 

PRBS8URB8. 

10.  Boiler  pressure  indicated  by  gauge lbs. 

W.  Pressure  indicated  by  gauge  on  force  main lbs. 

21.  Vacuum  indicated  by  gauge  on  suction  main ins. 

22.  Pressure  corresponding  to  vacuum  given  In  preceding  line lbs. 

88.  Vertical  distance  between  the  centres  of  the  two  gauges ins. 

:M.  Pressure  equivalent  to  distance  between  the  two  gauges lbs. 

MISCKLLAKKOUS  DATA. 

25.  Duration  of  trial hrs. 

Stt.  Total  number  of  single  strokes  during  trial 

37.  Percentage  of  moisture  in  steam  supplied  to  engine,  or  number 

of  degrees  of  superheating %or  deg 

88.  Total  iealcage  of  pump  during  trial,  determined  from  resulu  of 

leakage  test lbs. 

89.  Mean  elective  pressure,  measured  from  diagrams  taken  from 

steam-cylinders H.E.P. 

PRIMCIPAI.  RSSULT8. 

80.  Duty ft.  lbs. 

81.  Percentage  of  leakage % 

82.  Capacity gals. 

83.  Percentage  of  total  friction % 

ADDITIONAL  RBSULTS. 

84.  Number  of  double  strokes  of  steam-piston  per  minute    

85.  Indicated  horse-power  developed  by  the  various  steam-cylinders  I.H.P. 

86.  Feed- water  consumed  by  the  plant  per  hour lbs. 

87.  Feed-water  consumed  by  the  plant  per  indicated  horse-power 

per  hour,  corrected  for  moisture  in  steam lbs. 

88.  Number  of  heat  units  consumed  per  indicated  horse>power 

per  hour B.T.U. 

89.  Number  of  heat  units  consumed  per  indicated  horse-power 

per  minute B.T.U. 

40.  Steam  accounted  for  by  indicator  at  cut-off  and  release  in  the 

various  steam-cylinders lbs. 

41.  Proportion  which  steam  accounted  for  by  indicator  bears  to 

the  feed-water  consumption 

42.  Number  of  double  strokes  of  pump  per  minute 

43.  Mean  effective  pressure,  measured  from  pump  diagrams  .....  M.E.P. 

44.  Indicated  horse-power  exerted  in  pump-cylinders I.H.P. 

45.  Work  done  (or  duty)  per  100  lbs.  of  coal  ft.  lbs. 

SAMPLE  DIAGRAM  TAKBIV  PROM  flrTBAM-OTUNDRRS. 

(Also,  if  possible,  full  meanurement  of  the  diagrams,  embracing  pressures 
at  the  initial  point,  cu^off,  release,  and  compression ;  also  back  pressure, 
and  the  proportions  of  the  stroke  completed  at  the  various  points  noted.) 

8AMPLB  DIAGRAM  TAKBN  FROM  PUMP-CnTLINDBRS. 

These  are  not  necessary  to  the  main  object,  but  it  is  desirable  to  give 
them. 

DATA  AND  RB8ULT8  OF  BOILCR  TB8T. 

(In  accordance  with  the  scheme  recommended  by  the  Boiler-test  Oom- 
mittee  of  the  Society.) 

TACVlJlfl  pumps— AIR-I^IFT  PfJlHP. 

Tlie  Pnlsomeier*— In  the  pulsometer  the  water  is  raised  by  suction 
into  the  pump-chamber  by  the  condensation  of  steam  within  it,  and  is  then 
forced  into  the  delivery-pipe  by  the  pressure  of  a  new  quantitv  of  steam  on 
the  surface  of  the  water.  Two  chambers  are  used  which  work  alternately, 
one  raising  while  the  other  is  discharging. 

Tett  of  a  Puliometer.^A.  U^t  of  a  pulsometer  is  described  by  De  Volson 
Wood  in  Trans.  A.  S.  M.  B.  xiii.  It  hnd  a  8H-lnch  suction-pipe,  stood  40  in. 
high,  and  weighed  695  lbs. 

The  steam-pipe  was  1  Inch  in  diameter.   A  throttle  was  placed  about  2  feef* 


VAOUtJM  PTTMP8 — ^AIR-LIFT  PUMP. 


613 


from  the  putnp.  and  pressure  gaufces  placed  on  both  sides  of  the  throttle, 
and  a  mercuiy  well  and  thermometer  placed  beyond  the  throttle.  The  wire 
drawbif?  due  to  throttling  caused  superheatinfr. 

Th«  pounds  of  steam  used  were  computed  from  the  Increase  of  the  tem 
peratuiti  of  the  water  in  passing  through  the  pump. 
Pounds  of  steam  X  loss  of  heat  =:  lbs.  of  water  sucked  In  X  increase  of  temp. 

The  loss  of  heat  in  a  pound  of  steam  is  the  total  heat  in  a  pound  of  satu- 
rated steam  as  found  from  '*  steam  tables  ^*  for  the  given  pressure,  plus  the 
heat  of  superheating^  minus  the  temperature  of  the  discharged  water  ;  or 

_       ass.             1*>B-  "water  x  increase  of  temp. 
Pounds  of  steam  =  u  -  0.i6t  -  T. 

The  results  for  the  foUr  tests  are  given  in  the  following  table  : 


Data  and  Results. 

Number  of  Test. 

1 

2 

8 

4 

Strokes  per  minute 

71 

114 

10 

270.4 

8.1 

1617 
404.786 

75.15 
4.47 

20.90 

12.26 

42.16 

82.8 
0.777 
0.012 
Of  008 
0.(066 
10,511,40U 

60 
110 
80 
277 
8.4 
081 

186.862 
90.6 
5.5 
54.06 
1226 
66.81 
67.80 
0  877 
0.0155 
0.0136 
0.0005 
18.801,000 

57 

127 

48.8 
800.0 

17.4 

1518 
228,425 

76.8 
7.40 

54.05 

10.67 

73.72 

66.6 
0.011 
0.0126 
0.0115 
0.0080 
11.059,000 

64 

Steam  press. in  pipe  befoi-e  throttl'g 
Steam  press,  in  pipe  after  throttrg 
Steam  temp,  after  throttling,deg.F. 
Steam  am'nt  of  superheat'g.deg.F. 
Steam  used  as  det*d  from  temp.,Ihe. 
Water  pumped*  lbs. 

104.8 

26.1 

270.1 

1.4 

1019.0 

248,063 

Water  temp.before  entering  pump. 

Water  temp.,  rise  of 

Water  head  by  gauge  on  lift,  ft  . . . 
Water  heod  by  gauge  on  suction. . . 
Water  head  by  gauge,  total  (H).... 
Water  head  by  measure,  total  {h\ 
Coeff.  of  friction  of  plant  (h)  -*-  (H) 

lilfflciency  of  pulsometer . . : 

Efflc.  of  plant  exclusive  of  boiler. .. 
Efflc.  of  plant  if  that  of  boiler  be  0.7 
Duty,if  I  Ib.evaporates  10  lbs.  water 

70.25 
4.55 
20.00 
10.67 
40.57 
41.60 
0.880 
0.0138 
0  0116 
0.0061 
12.086.800 

Of  the  two  teste  having  the  highest  lift  (54.05  ft.),  that  was  more  efficient 
•which  had  the  smaller  suction  (12.26  ft.),  and  this  was  also  the  most  efficient 
of  the  four  teste.  But,  on  the  other  hand,  the  other  two  tests  having  the 
same  lift  (.20.0  ft.),  that  was  thH  more  efficient  which  had  the  greater  suction 
(19.67),  so  that  no  law  in  this  regard  was  established.  Tlie  pressures  used, 
19,  30,  43.8,  26.1,  follow  the  order  of  magnitude  of  the  total  heads,  but  ai-e 
not  proportional  thereto.  No  attempt  was  made  to  determine  what  press- 
ure would  give  the  best  efficiency  for  any  particular  head.  The  pressure  uned 
was  lntrust«*d  to  a  practical  runner,  and  he  judged  that  when  the  pump  was 
running  regularly  and  well,  the  pressure  then  existing  was  the  proper  oiie 
It  is  peculiar  that,  in  the  first  test,  a  pressure  of  19  lbs.  of  steam  should  pro- 
duce a  greater  number  of  strokes  and  pump  over  bOi  more  water  than  26.1 
lb«..  the  lift  being  the  same,  as  in  the  fourth  experiment. 

Chas.  E  Emery  in  discussion  of  Prof.  Wood's  paper  says,  referring  to 
teste  made  by  himself  and  others  at  the  Centennial  Exhibition  in  1876  (see 


B'^nort  of  the  Judges,  Qroup  xx.).  tiiat  a  vacuum-pump  tested  by  him  in 
1871  gave  a  dutv  of  4.7  millions;  one  tested  by  J.  F.  Flagg,  at  the  Ciiicinnati 
Expo«ition  in  1875,  gave  a  maximum  duty  of  8.25  millions.    Several  vacuum 


and  small  steam-pumps,  compared  later  on  the  sanf^  basi!<,  were  reported 
to  have  given  duties  of  10  to  11  millions,  the  steam-pumps  doing  no  better 
than  the  vacuum-pumps.  Injectors,  when  used  for  lil'ting  water  not  re- 
quired to  be  heated,  have  an  efficiency  of  2  to  5  millions;  vacuiini-pnmps 
▼ary  generally  between  3  and  10;  small  steam-pumps  between  8  and  15  : 
lartrnr  steam -pumps,  between  15  and  80,  and  pumping-engiues  between  80 
and  140  millions. 

A  very  high  record  of  test  of  a  pulsometer  is  given  In  Eiig*g.  Nov.  24, 1803, 
p.  6.^,  vis. :  Height  of  suction  11.27  ft. ;  total  height  of  lift,  102.6  ft.  ;  hori- 
zontal length  of  delivery-pipe,  118  ft.  ;  quantity  delivered  per  hour,  26,188 
Britisli  gallons.    Weight  of  steam  used  per  H.  P.  per  hour,  02.76  lbs. ;  work 


614  WATBR-POWEE. 

done  tier  bo\ini^  6f  sMaih  91,345  foot^unds^  «qual  fo  ft  duty  Of  ^l,94^(lftl 
foot-pdtiiidB  pe  •  100  lbs.  of  coal^  if  10  lbs  of  stdam  imrfi  generated  per 
pound  of  coal. 

Tke  Jein»<inftp«— This  hmehlne  works  by  mcAim  of  thb  tMidency  of  a 
stream  or  let  of  fluid  to  dri^e  or  carry  c^ontlcuous  parttelM  of  fluid  Aluti|^ 
with  It.  Toe  water-Jei  pump,  iu  its  presQiit  .form,  was  invented  bj  Prof. 
Jaiiie's  Thomsoh,  and  nrst  described  in  1H52.  In  some  experiments  on  a 
staAlI  66till»  &8  lo  th^  efHbiertcy  of  the  let-punib,  the  R^^test  effibiency  Wi 
fouhd  to  lake  plAce  wheh  the  depth  frdm  which  th6  ^Aler  WAs  tlk-awtt  by  tl 
stlciidHplipe  iHras  Hbout  hine  tetiths  of  the  Ht^lRht  from  which  the  ^atef  n 
to  form  the  Jet ;  the  flow  up  the  suotion-pipe  being  in  that  case  about  one 
fifth  of  thai  i»f  the.Jer,  and  the  efficiency,  oonse(|tt^kitly^  t^  X  1/6  =  0.18. 
This  is  but  a  low  efhciehcy ;  but  !t  is  probable  that  it  may  be  increased  bj 
iinproyements  in  proportions  of  the  machine.    (Ranklnoi  Sk  fij 

Tl^e  Injeeld^  when  used  as  a  piihip  has  a  very  low  emctenc]r.  (Bee 
Injector!,  under  Steam-boilers.) 

Aljr*lift  Plllii|»ft— ThA  air-lift  pun^p  consists  of  a  vertical  water-pipe 
with  its.iower  end  subroeri^  in  a  well,  and  a  smIUIw  \pipe  d^fvering  air 
Into  it  at  the  bottom.  The  rising  colunln  in  the  pipe  consists  of  air  mingled 
with  water,  the  air  bein)^  in  bubble  of  Various  sizes,  and  is  therefore  lighter 
than  a  column  of  wati'rof  the  KUlie  helt^ht^  (Mhs^U^htly  the  water  ffi  the 
pide  is  raised  above  the  level  of  the  surrounding  water.  This  method  of 
raising  water  was  proposed  As  early  a^  179r\  by  Loi>teher,  of  FrsibHi|\  ahd 
was  mentioned  by  CoUoh  iu  lectures  in  Pllrls  in  167B,  but  Its  fhvt  t>rak»tloal 
application  probably  witt  by  Werner  Siemens  In  Berlin  In  1885-..  IM  J.  d. 
Pohle  experimented  on  the  principle  in  GktUfomla  in  iWOi  ahd  V.  Bi  patt^ittti 
on  apparatils  Involving  it  weh^  ftranted  to  Pohle  and  Hill  in  thb  aame  yekr. 
A  paper  describing  tests  of  the  alMfft  pump  made  hy  Bahdhll.  BrowiM  and 
Behr  was  read  before  the  Technical  Society  of  the  FttHflc  Coast  in  F^lk.  l^M 

The  dIAmeter  of  the  puinp-column  whs  8  in.,  of  the  ftlr-plpe  O.f  IH.^  and 
of  the  air-discharge  noesie  %  in.  The  air-pipe  had  fbur  sharp  bends  and  a 
length  of  ai  ft.  plus  the  depth  of  submersion. 

The  water  was  pumped  from  a  closed  pipe- well  (86  ft^  dsep  and  10  In.  lit 
diameter).  The  eflflciency  of  the  punlp  wAs  based  on  the  leask  woi-k  theo* 
retioally  required  to  Compre.H8  the  air  and  deliver  It  td  the  receiver.  If  itA 
efflciency  of  the  cohipresHor  be  taken  at  70%,  the  effleiennjr  of  the  pump  and 
compressor  together  would  be  TW  of  the  efficleuoy  found  fbr  the  pamli 
alone. 

For  a  given  mibmereloh  (h)  and  lift  (10*  the  ratio  of  the  twn  belrtg  keftt 
within  reasonable  limits,  (H)  being  not  much  greater  than  (h\  the  efficiency 
was  greatest  when  the  pressure  in  the  re<celver  did  not  greatly  exused  the 
head  due  to  the  submersioii.  The  smaller  the  ratio  H-t-h^  the  higher  war 
the  efficiency. 

The  pump,  as  erected,  showed  th6  f oUowhig  efflclenoles ; 

tor  H-^-h^       0.6  1.0  1.6  2.0 

Efficiency    =       S0j(  4/0%  90%  1»fl 

The  fact  tliat  there  are  absolutely  no  moving  parts  UMkes  tha  pitill|f 
especinlly  fitted  for  hAndling  dirty  or  gritty  Water^  sewage^  mine  water, 
and  add  or  alkali  solutlobs  lb  Chemical  or  metallurgical  wom. 

In  Ne  warkv  N.  J.,  pumps  of  this  type  are  at  work  having  a  total  vapaolt^r 
of  1.000^000  gallons  dailr,  lifting  water  fkora  three  8-in.  artesian  wells;  The 
Newark  Chemical  Worlcs  uee  an  air-lift  pump  to  raise  snlphurld  aoM  of  1.78* 
gravity.  The  Colorado  Central  ConsoUdatea  lllning  Co.,  in  one  or  its  minus 
at  Geofgetowot  Colo.,  lifts  water  in  one  ease  880  ft.^  using  a  series  of  Hfti. 

For  a  full  account  of  the  theory  of  the  pump,  and  details  of  tira  tesfk 
above  referred  to,  see  Eng^§  iVerra,  June  8«  l&H. 

fllfe  HTDBAVLtO  teAlH. 

£Acl<^ilLoy*—t'h» hydraulic  ram  Is  used  where  a  oonslderabte  iiow  of 
water  with  a  moderate  fall  is  available,  to  raise  a  small  portion  of  that  flow 
to  a  height  exceeding  that  of  the  fall.  The  following  are  rules  given  hy 
Eytehveln  as  the  results  of  his  exi>enment8  (from  Rankine): 

Let  Q  be  the  whole  nupply  of  water  in  cubic  feet  per  second,  of  which  q  fa 
lifted  to  the  height  h  abovtd  the  pond,  and  9  —  o  runs  to  waste  at  the  depth 
B^ below  the  pond;  L.  the  leti(rth  of  the  supply-plpe,  frdm  the  pond  lotba 
waste-clack  ;  X>,  its  diameter  in  feet;  then 

D==  VOW^.    L=iH  +  ^4-^^*reet; 
Volnmift  of  air  vessAl  =  if<A\iiai6  of  tieied  pipe; 


THE  HTORA.DLIO  RAH. 


616 


«««•-«'.  (-g^ 


:  l.ld  -  0.3 


•Q  when  ^  does  not  flxoeed  9fk 


D'AubulflBon  give 


>]y,  when  ^doM  not exoeed  tt. 


Clark,  usin^  dve  Klxths  of  the  vaIum  i^tven  by  D'Auhulsson^s  fornm]a«Kl  ves: 
BatlooClifttoffAU.  ...    4     6     8    10    M    14   16    18   90   S3    M   M 
Bfflclfllieypwovnt....     7B61S844878td6    10l4    0     4     0 

ProT.  R.  C.  QtkTpenter  (JIAm*^  MMiania,  18H)  reports  the  reeulti  of  four 
tests  of  A  HtDd  ooto«ti*ucted  by  Rmnsey  &  Co.,  8eii«ca  Palls.  The  ram  was 
fitted  tor  pipe  oottneetloti  for  1^-tnch  supply  and  U-ioch  dischaive.  The 
suppiy^p^  used  ^ms  lyi  inches  In  diameter,  about  60  te^  long,  withselbowfi, 
so  thabU  wMeqiifvalfiil  to  about 'C5  fMt  of  straight  pipe,  so  far  as  resist- 
ance Is  eoncemed.  Each  fun  was  made  with  a  different  stroke  for  the  waste 
or  dnck-valves  the  nupply  Md  delivery  heed  being  constant;  the  otilect  ot 
the  experiment  was  to  find  that  stroke  of  claek^Talve  which  would  e^ive  the 
highest  emctency. 


liongth  of  stroke,  per  cent. « . . , 
Numtter  of  Ktrokes  ner  minute 

Snpply  hesd.  fieel  of  wat«r 

Delivery  head,  feet  of  water., , 
Total  water  pumped,  pounds.., 
Tot^l  water  supplied,  pounds.. 
'^Sloieaoy^  percent , 


100 

80 

66 

62 

66 

61 

5.67 

8.77 

6.58 

19.75 

10.76 

10.75 

207 

006 

801 

1615 

1567  ' 

1518 

64.0 

66 

n.f 

4b 

66 
6.66 
10.75 
S07.5 
1455.5 
90 


The  efidency,  74.0,  the  highest  realized,  was  obtained  when  the -clack-valve 
trav«Ilei«  dteiaace Ritual  to 60)(  of  Ms  fd  strokei,  the  full  travei  being  15/16 


of  one  loch. 


iiwuuAgr  of  Water  Bellv«re<L  hj  4»km  Hydranlto 

(Chadwick  Lead  Worka.)— From  80  to  100  feet  conveyance,  one  seventh  of 
supply  from  spring  can  be  discharged  at  an  elevation  Ave  times  as  high  as 
die  fhil  ro  stipfAy  me  ratn;  or,  one  fourteenth  can  be  raided  and  discharged 
s^^ten  times  as  higki  as  the  fall  appHed. 

water  can  be  conveyed  V  a  ram  8000  feet,  and  elevated  000  feet.  The 
drive-pine  is  from  2^  to  50  feet  long. 

Hie  following  table  gives  the  caMckyof  several  sloes  of  nuns;  the  dimen- 
slon*  of  t^o  pipes  to  be  used,  and  the  size  of  the  spring  or  brook  to  which 
Cbey  are  adaptad: 


Qiflwitlty  of  Water 

Flimtabedper 

Mhi.  hy  the  Spring 

or  Brook  to  which 

the  Bam  is 

Adapted. 


No.t 

-u    « 

"  4 
"  6 
"  6 
•*  ft 
•*I0 


Qals.  per  min. 


8 
6 
18 
00 
06 


7 
••»  14 

•*75 


Caliber  of 
Pipes. 


Drive-pipe 

for  head 

or  fall  not 

over  10  ft. 


We%ht  of  P%)e  (Lead),  if  Wrought 
Iron,  then  of  Ot-dlnary  Weight. 


Discharge- 
pipe  for  not 
over  60  ft, 


per  foot. 
Sibs. 
8  '* 
6  *• 
8  " 
18  •• 
18  *• 


Dischange- 
plpe  for 

over  SO   ft. 

and  not  ex- 
ceeding 
ilOOft.  in 
height. 


per  foot. 
10  o«. 
IS    •* 
18    •• 

llb.4    •• 

8  ••» 
7  ^* 


per  foot, 
lib. 

1  «*  4on, 
1  *«  4oia 
H  " 
8  •* 
4  * 
8  •• 


616  WATBR-POWBB, 

HTBBAVIiIC-PBBSSUBB  TBAlf SBISSIOlf. 

Water  under  high  profwure  (700  to  9000  lbs.  per  square  mch  and  upw«rda| 
affords  a  very  satisfactory  method  of  transmlttinff  power  to  a  dLIstaDce, 
especially  for  the  movement  of  heary  loads  at  smalfvelocities,  as  l^  cranes 
and  elevators.  The  system  cousists  usually  of  one  or  more  pumps  capable 
of  deyeloping  the  required  pressure;  accumulators,  which  are  vertical  cyUn- 
ders  with  heaviiv-weigh ted  plunders  passing  through  stuffing-boxes  in  the 
upper  end.  by  which  a  Quantity  of  water  may  be  accumulated  at  the  pres- 
sure to  which  the  plunger  Is  weighted ;  thedistributiog-pipeB;  and  the  preves, 
cranes,  or  other  machinery  to  oe  operated. 

The  earliest  important  use  of  hydraulic  pressure  probably  was  in  the 
Bramah  hydraulic  press^  patented  In  1706.  Sir  W.  O.  Armstrong  in  1846  was 
one  of  the  pIoneerH  in  the  adaptation  of  the  hydraulic  svstem  to  cranes.  The 
use  of  the  accumulator  hv  Armstrong  led  to  the  extended  use  of  hydraulic 
machinery.  Recent  developments  and  applications  of  the  ^stem  are  largely 
due  to  Ralph  Tweddell.  of  London,  and  Sir  Joiseph  Whitworth.  Sir  Henry 
Bessemer,  in  his  patent  of  May  18, 1866,  No.  1292,  first  suggested  the  use  of 
hydraulic  pressure  for  compressing  steel  Ingots  while  in  the  fluid  state. 

Tbe  GroM  Amomii  or  IBnergy  of  the  water  under  pressure  stored 
in  the  accumulator,  measured  in  foot-pounds,  is  its  volume  in  cubic  feet  X 
Ita  pressure  in  pounds  per  square  foot.    The  horse-power  of  a  given  quantity 

steadily  fiowhig  Is  H.P.  s  ^^^  =  .a6l8pQ,  in  which  Q  is  the  quantiQr  flowing 

in  cubic  feet  per  second  and  p  tbe  pressui-e  in  pounds  per  square  inch. 

The  loss  of  energy  due  to  velocity  of  flow  in  the  pipe  is  calculated  as  fol- 
lows (R.  O.  Blaine,  ISng'g,  May  2:2  and  June  5, 1801): 

According  to  D'Arcy,  every  pound  of  water  loses  ~g-  times  its  kinetic 

energy,  or  energy  due  to  its  velocity,  in  passing  along  a  straight  pipe  L  feet 
in  length  and  D  feet  diameter,  where  A  is  a  variable  coefficient.    For  clean 

cast-iron  pipes  it  may  be  taken  as  A  s  .005  \l+  f^  )i  or  for  diameter  in 
inches  =  d. 

d=    H       I       2         Z  456  7  8  »10       12 

\  =  .016    .01  .0075  .00667  .00635  .006  .00583  .00571    .00668  .00556  .0065  .00649 

The  loss  of  energy  per  minute  is  60  x  68.86^  X  -q-  |-,  and  the  horse- 
power wasted  in  the  pipe  is  Tr=  -.g^gi^H'P')*^  j,j  ^^^^^^  ^  ^^^^  ^^j,  ^^ 

diameter  as  above,    n  =  pressure  at  entrance  in  pounds  per  square  inch. 
Values  of  .6868A  for  different  diameters  of  pipe  In  inches  are: 
d=Mi        12  3  4  5  6  7  8  9  10        18 

.00964  .00686  .00477  .00424  .00898  .00382  .00071  .00868  .00858  .00858  .00850  .00845 
EAelency  of  Hydranllo  Apparatns.— The  useful  effect  of  a 
diixiCt  hydraulic  plunger  or  ram  is  usually  taken  at  WifL.    The  following  is 
given  as  the  efflciencjr  of  a  ram  with  chain-and -pulley  multiplying  gear 


K>roperly  proportioned  and  well  lubricated: 
lultiplyli  ~' -^ 


iltiplylng....  2tol  4  to  1  6tol  8tol  lOtol  12tol  14tol  16tol 
Efficiency  jf...     80         76  72  67  63  59  64  60 

With  large  sheaves,  small  steel  pins,  and  wire  rope  for  multiplying  gear 
the  efficiency  has  been  found  as  high  as  Wfi  for  a  multiplication  of  80  to  1. 

Henry  Adams  gives  the  following  formula  for  effective  pressure  in  oraoes 
and  hoists: 

P  =  accumulator  pressure  in  pounds  per  squaro  Inch; 

m  =  ratio  of  multiplying  power: 

E  =  effective  pressure  in  pounds  per  square  Inch,  including  all  allowances 
for  friction; 

^=P(.84-.08m), 

J.  E.  Tuit  (E%ig%  June  15, 1888)  describes  some  experiments  on  the  fric- 
tion of  hydraulic  jacks  from  8^  to  18%-inch  diameter,  fitted  with  cupped 
leather  packings.  The  friction  loss  varied  from  5.6)(  to  18.8)(  according  to 
the  condition  of  the  leather,  the  distribution  of  the  load  on  the  ram,  etc. 
The  friction  increased  considerably  with  eccentric  loads.  With  hemp  pack- 
ing a  plunger,  14-inch  diameter,  showed  a  friction  loss  of  from  \\A%  to  ZA%. 
the  load  being  central,  and  from  15.0^  to  7.6)1  with  eccentric  load,  the  per- 
centage of  loss  decreasing  in  both  cases  with  increase  of  load. 


HTDRAULIC-PBESeUBB  TRANSMIS8I0K.  617 

Xlileknewi  of  Hjrdranlle  Cyllndem*— From  a  table  used  bj  Sir 
W.  U.  Armstroiie  we  take  the  followingr*  for  cast-iron  cyllodera,  for  aii  in- 
terior pressure  of  1000  lbs.  per  square  indi: 

Dlam.  of  cylinder,  inches..     9        4        0        8       10       IS      16     80     84 
Thickness,  inches 0.888  1.146  1.568  1.875  8.888  8.678  8.10  8.00  4.11 

For  any  other  pressure  multiply  by  the  ratio  of  that  pressure  to  1000. 
These  figures  correspond  nearly  to  the  formula  t  m  0.17Ba  -(-  0.48,  in  which 
t  =  thickness  and  d  =  diameter  in  inches,  up  to  16  Inches  diameter,  but  for 
20  inches  diameter  the  addition  0.48  is  reduced  to  0.19  and  at  84  Inches  it 
disappears.    For  formula  for  thick  cylinders  see  page  887,  ante. 

Cast  iron  should  not  be  used  for  pressures  exceeding  8000  lbs.  per  square 
Inch.  For  higher  pressures  steel  castings  or  foiiged  steel  should  be  used. 
For  working  pressures  of  7S0  lbs.  per  square  inch  ilie  test  preraure  should 
be  8600  lbs.  per  square  inch,  and  for  1500  lbs.  the  test  pressure  should  not  be 
less  than  Vm  lbs. 

Speed  of  Boistlnv  hj  Hydraulic  ProMnre.— The  maximum 
allowable  speed  for  warehouse  cranes  is  6  feet  per  second;  for  platform 
cranes  4  feet  per  second;  for  passenger  and  wagon  hoists,  heavy  toads,  8 
feet  per  second.  The  noaximum  speed  under  any  circumstances  should 
never  exceed  10  feet  per  second. 

The  Speed  of  t¥ater  Thronffli  TalTes  should  never  be  greater 
than  100  feet  per  second. 

Speed  of  ITater  Tbroaiph  PlpeB.-4fizp6riments  on  water  at  1600 
lbs.  pressure  per  squsre  inch  flowing  into  a  ilanging-machine  nun,  90-ineh 
diameter,  through  a  ^-inch  pipe  contracted  at  one  point  to  )4-lnch,  gave  a 
velocity  of  114  feet  6&:  secona  in  the  pipe,  and  466  feet  at  the  reduced  sec- 
tion. Through  a  ^-mch  pipe  reduced  to  9i^inch  at  one  point  the  velocity 
was  818  feet  per  second  In  the  pipe  and  881  feet  at  the  reduced  section  In  a 
K-inch  pipe  without  contraction  the  velocity  was  886  feet  per  second. 

For  many  of  the  above  notes  the  author  is  indebted  to  Mr.  John  Flatt, 
consulting  engineer,  of  New  York. 

Sltflf^presfliire  Bydntolle  Preaeee  In  IroD«irorke  are  de- 
scribed by  R.  M.  Daelen,  of  Germany,  in  Trans.  A.  L  M.  E.  1808.  The  fol- 
lowing distinct  arrangements  used  in  different  aystems  of  high-pressure 
hydraulic  work  are  discussed  and  illustrated: 

1.  8ceam-pump,  with  fly-wheel  and  accumulator. 

8.  Bteam-pump,  without  fly-wheel  and  with  accumulator. 

8.  Steam-pump,  without  fly-wheel  and  without  accumulator. 

In  these  three  systems  the  valve-motion  of  the  working  press  is  operated 
m  the  high-pressure  column.    This  is  avoided  in  the  following: 

4.  Single- seating  steom-intensifler  without  accumulator. 

6.  Steam-pump  with  fly-wheel,  without  accumulator  and  with  pipe-circuit. 

6.  Steam-pump  with  fly-wheel,  without  accumulator  and  without  pipe- 
circiiit. 

The  disadvantages  of  accumulators  are  thus  stated:  The  weighted  plungers 
which  formerly  served  in  most  cases  as  accumulators,  cause  violent  shocks 


metallic  valves  are  cut  by  the  water  (at  high  speed),  and  in  such  cases  only 
the  most  careful  maintenance  can  prevent  great  losses  of  power. 

Bydranlle  Poiver  In  I«ondon«— The  general  principle  involved 
is  pumping  water  into  nuiins  laid  in  the  streets,  from  wliich  service-pipes 
are  carried  into  the  houses  to  work  lifts  or  three-cylinder  motors  when 
rotatory  power  is  required.  In  some  cases  a  small  Pelton  wheel  has  been 
tried,  working  under  a  pressure  of  over  700  lbs.  on  the  square  inch.  Over  65 
miles  of  hydraulic  mafais  are  at  present  laid  (1898). 

The  reservoir  of  power  consists  of  capacious  accumulators,  loaded  to  a 
pressure  of  800  lbs.  per  square  inch,  thus  producing  the  same  effect  as  if 
large  supply-tanks  were  placed  at  1700  feet  above  the  street-level.  The 
water  is  taken  from  the  Thames  or  from  wells,  and  all  sediment  Is  removed 
therefrom  by  flltration  before  it  reaches  the  main  engine-pumps. 

Tliere  are  over  1760  machines  at  work,  and  the  supply  is  about  6,600,000 
gallons  per  week. 

It  is  essential  that  the  water  used  should  be  clean.  The  storage-tank  ex- 
tends over  the  whole  boiler-house  and  coal-store.  The  tank  is  divided,  and 
a  certain  amount  of  mud  is  deposited  here.  It  then  passes  through  the  sur- 
face condenser  of  the  engines,  and  it  is  turned  into  a  set  of  Alters,  eight  in 
number.   The  body  of  the  filter  is  a  cast-iron  cylinder,  containing  a  layer  of 


618  WATBR-POWBB. 

granular  fllserlng  material  resting  upon  a  false  bottom;  under  this  is  the  die> 
tributing  arrangement,  affording  pasmage  for  the  air,  and  under  this  the  real 
bottom  of  the  tank.  The  dirty  water  is  supplied  to  the  filters  from  an  over* 
head  tanlc.  After  passing  through  tiie  filters  the  clean  eflluent  is  pumped 
into  the  dean-water  tank,  from  which  the  pum ping-engines  derive  their 
supply.  The  cleaning  of  the  filters,  which  is  done  at  intervals  of  ii  hours,  is 
eflrected  so  thoroughly  tn  aitu  that  the  filtering  material  oeTdr  requires  to  be 
removed. 

The  engine-house  contains  six  sets  of  triple-expansion  engines.  The 
cylinders  are  15-tnch,  22-inch,  86-inch  X  S4-lnoh.  Each  cylinder  drives  a 
single  plunger*pump  with  a  6-inoh  ram,  secured  directly  to  the  croes-head, 
the  connecting-rod  being  double  to  clear  the  pump.  The  boiler-pressure  is 
ICO  lbs.  on  the  square  inch.  Bach  pump  will  deliver  800  gallons  of  water  per 
minute  under  a  pressure  of  800  lbs.  to  the  square  inch,  the  engines  making 
about  61  revolutions  per  minute.  This  is  a  high  velocity,  considering  the 
heavy  pressuro;  but  the  valves  work  silently  and  without  perceptible  shock. 

The  consumption  of  steam  is  14.1  pounds  per  horse  per  hour. 

The  water  delivered  from  the  main  pumps  passes  into  the  aceamulators. 
The  rams  are  20  inches  in  diameter,  and  have  a  stroke  of  23  teeL  Ther  are 
each  loaded  with  110  tons  of  slag,  contained  in  a  wroughc-iron  cylindrical 
box  suspended  from  a  cross-heaa  oo  the  top  of  the  ram. 

One  of  the  accumulators  is  loaded  a  little  more  heavily  than  the  other,  so 
that  they  rise  and  fall  successively;  the  more  heavily  loaded  actuates  a  stop- 
valve  on  the  main  steam-pipe.  If  the  engines  supply  more  water  than  la 
wanted,  the  lighter  of  the  two  rams  first  rises  as  far  as  it  can  go;  the  other 
then  ascends,  and  when  it  has  nearly  reached  the  top,  shuts  off  steam  and 
checks  the  supply  of  water  automatically. 

The  mains  in  the  public  streets  are  so  constructed  aad  laid  as  to  be  par^ 
f ectly  trustworthy  and  free  from  leakage. 

Every  pipe  and  valve  used  throughout  the  ^^etem  is  tested  to  2600  Iba.  per 
square  inch  before  being  placed  on  the  ground  and  again  tested  to  a  reduced 
pressure  in  the  trenches  to  insure  the  perfect  tightness  of  the  JointSb  Tbe 
Jointing  material  used  is  gutta-percha. 

The  average  rate  obtained  by  the  compaov  is  about  8  shillings  per  thoo- 
sand  gallons.  The  principal  use  of  the  power  is  for  intermittent  work  In  cases 
where  direct  pressure  can  be  employed,  as,  for  Inatanoe,  passenger  elevators, 
cranes,  presses,  warehouse  hoists,  etc 

An  important  use  of  the  hydraulic  power  is  its  application  to  the  extin- 
8;uishing  of  firo  by  means  of^Qreathond^i  injector  hydrant.    By  the  use  of 

riveting  was  Intro- 

. 1  were  first  used  about 

1866.    Portable  riveting-machines  were  introduced  In  1879. 

The  riveting  of  the  large  steel  plates  in  the  Forth  Bridge  was  done  by  small 
portable  macmiues  workTog  with  a  pressure  of  1000  lbs.  per  square  inch.  In 
exceptional  cases  8  tons  per  inch  was  used.    (Proc.  Inst.  IL  £r.^May,  1800.) 

An  application  of  hydraulic  pressure  invented  by  Andrew  Higginsoo,  of 
Liverpool,  dispenses  with  the  necessity  of  accumulators.  It  oonsiats  of  a 
three-throw  pump  driven  by  shafting  or  worked  by  steam,  and  dependa 
partially  upon  the  work  accumulated  in  a  heavy  fly-wheeL  The  water  in  its 
passage  from  the  pumps  and  back  to  them  is  in  constant  circulation  at  a 
very  leeble  pressure,  ixiquiring  a  minimum  of  power  to  preserve  the  tube  of 
water  ready  for  action  at  the  desired  moment,  when  by  the  use  ot  a  tap  the 
current  is  stopped  from  going  back  to  the  purapa,  and  is  thrown  upon  the 
piston  of  the  tool  to  be  set  in  motion.  The  water  is  now  oonflned.  and  tha 
driving-belt  or  steam-engine,  supplemented  by  the  momentom  of  the  heavy 
fiy-wheel,  is  employed  in  dosing  up  the  rivet,  or  bending  or  foigfng  the  ol>> 
Ject  Hubjected  to  Its  operation. 

Hrdranlle  Forsinc^—In  the  produetion  of  heavy  forglngs  from 
oast  ingots  of  mild  steel  it  is  essential  that  the  mass  of  netal  should  be 
operated  on  as  equally  as  possible  throughout  its  entire  thickness.  When 
employing  a  steam-hammer  for  this  purpose  it  hss  been  found  that  tha  ex- 
ternal snrCaoe  of  the  ingot  absorbs  a  large  proportion  of  the  sudden  Impact 
of  the  blow,  and  that  a  comparatively  small  effect  only  is  produced  on  the 


ceatrsi  portions  of  the  ingot,  owing  to  the  resistance  oifered  by  the  Inertia 
of  the  mass  to  the  rapid  motion  of  the  falling  hammer— a  disadvantage  that 
is  entirely  overcome  by  the  slow,  though  powerftai,  compression  of  the 
hydraulic  forging-prees,  which  appears  desdned  to  supersede  the  steaa^ 
haoMner  Cor  toe  productioa  ol  maaslre  steel  CoigingL 


HYDRAULIC-PRESSUBB  TRANSHISSICN.  G19 

In  the  Allen  ron^ng-press  the  force-pump  and  the  large  or  main  cylinder 
of  the  press  are  in  direct  and  constant  communication.  There  are  no  inter  - 
mediate  yalves  of  nny  kind,  nor  hoa  the  pump  any  clack-valvefi,  but  i* 
simply  forces  its  cylinder  full  of  water  direct  Into  the  cylinder  of  the  press, 
and  receives  the  same  water,  as  it  were,  back  again  on  the  return  stroke. 
Thus,  wlien  both  cylinders  and  the  pipe  connectinf;:  them  are  full,  the  laive 
ram  of  the  press  rises  and  falls  simultaneously  with  each  stroke  of  th<< 
pump,  keeping  up  a  continuous  oscillating  motion,  the  ram,  of  course, 
travellUig  the  shorter  distance,  owing  to  the  larger  capacity  of  the  presf 
cylinder.  (Journal  Iron  and  Steel  Insfitute,  1801.  see  also  illustrated  articit^ 
In  '*  Modem  Mechanism,"  page  666.) 

For  a  very  complete  illustrated  account  of  the  derelopment  of  the  hy« 
toullc  forging-press,  see  a  paper  by  H.  H.  Tweddell  in  Proo.  Inst.  0.  E.,  vol. 

Hjr^ntulle  Forffliis*pr«Mi»— A  SOOO-ton  forsiDg-press  erected  at 
the  Couillet  forges  in  Belgium  is  described  In  Eng.  andM.  Jour..  Nov.  %,  1896. 

The  press  Is  composed  eBsentiallj  of  two  parts— the  press  Itself  and  the 
compressor.  The  compressor  is  formed  of  a  vertical  steam-cylinder  and  a 
hydraulic  cylinder.  The  piston-rod  of  the  former  forms  the  piston  of  the 
latter.  The  hydraulic  piston  discharges  the  water  into  the  press  proper. 
The  distribution  is  mane  by  a  cylindrical  balanced  valve;  as  soon  an  the 
pressure  is  released  the  steam-piston  falls  automatically  under  the  action  of 
gravity.  Durine  its  descent  the  steam  passes  Co  the  other  face  of  the  piston 
to  reheat  ihe  cylinder,  and  finally  escapes  from  the  upper  end. 

When  steam  enters  under  the  piston  of  the  compressor-cylinder  the  pis- 
ton ilses,  and  its  rod  forces  the  water  into  the  press  proper.  The  pressure 
thus  exerted  on  the  piston  of  the  latter  is  transmlttea  through  a  cross  head 
to  the  forging  which  Is  upon  the  anvil.  To  raise  the  cixMs-nead  two  small 
sfngte-acting  steam-cylinders  are  used,  their  piston-rods  being  connected  to 
the  cross-head;  steam  acts  only  on  the  pistons  of  theee  cylinders  from  below. 
The  admission  of  steam  to  the  cylinders,  which  stand  on  top  of  the  press 
frame,  is  regulated  by  the  same  lever  which  directs  the  motions  of  the  com- 
pressor. The  movement  given  to  the  dies  is  sufficient  for  all  the  ordlnaiy 
purposes  of  forging. 

A  speed  of  80  blows  per  minute  has  been  attained.  A  double  press  on  the 
same  system,  having  two  compressors  and  giving  a  maximum  pressure  of 
WOO  tons,  has  been  erected  in  the  Krupp  works,  at  Essen. 

Vlte  Aiken  lateBsifler.  {Iron  Apt,  Aug.  ]890.>-The  object  of  tba 
machine  is  to  increase  the  pressure  obtained  by  the  ordinary  accumulator 
which  is  necessary  to  operate  powerful  hydraulic  machines  requiring  very 
high  pressures,  without  increasing  the  pressure  carried  in  the  accumulator 
and  the  general  hydraulic  system. 

The  Aiken  Intenslfier  consists  of  one  outer  stationary  cylinder  and  one 
inner  cylinder  which  moves  in  theouter  cylinder  and  on  a  fixed  or  stationary 
hollow  plunger.  When  operated  in  connection  with  the  hydraulic  bloom- 
ahear  the  method  of  working  is  as  follows:  The  inner  oyliodar  having  been 
filled  with  water  and  eonnected  through  the  hollow  plunger  with  the  hydrau- 
lic cylinder  of  the  shear,  water  at  the  ordinary  aocumulator*pret8ure  is  ad- 
mitted into  the  outer  cylinder,  which  being  four  times  the  sectional  area  of 
the  plunder  gives  a  pressure  In  the  inner  cylinder  and  shear  cylinder  con- 
nected therewith  of  four  times  the  aocumulator-pressure— that  Is,  if  the  so- 
cumulator-pressnre  is  500  lbs.  per  square  inch  the  pressure  in  the  intenslfier 
win  be  tOOO  lbs.  per  square  inca. 

Hydmalle    BBJiUie  ArlTliifl;  an   Alr-eompreeeor  and  ^ 


Fonirinc*liamnier«  {Iron  ^oe.  May  12,  18M.)— The  great  iiamnier  in 
Temi,  near  Rome,  is  one  of  the  largest  in  existence.  Its  falling  weight 
amounts  to  100  tens,  and  the  foundation  belonging  to  it  consists  of  a  block 
of  cast  iron  of  1000  tons.  The  stroke  is  16  feet4Hinchefi;  the  diameter  oC 
the  cylinder  6  feet  8U  Inches;  diameter  of  piston-rod  im  inches;  toUl  heiirht 
of  the  hammer,  08  feet  4  inches.  The  power  to  work  the  hammer,  as  well  at 
the  two  cranes  of  100  and  160  tons  respectively,  and  other  anxllfary  appU* 
ances  belonging  to  it,  Is  furnished  by  four  air-compressors  coupled  togetlier 
sad  driven  direetly  1^^  water -pressure  engines,  by  means  of  which  the  air  it 
compressed  to  73.5  pounds  per  square  inch.    Tne  cylinders  of  the  water- 


pressure  englDes,  which  are  provided  with  a  bronse  lining,  have  a  ISf^-inch 
bore.  The  stroke  is  17^  Incbes,  with  a  pressure  of  water  on  the  piston 
amounting  to  S64.6  pounds  per  square  Inch.  The  compreseon  are  bored  out 
to  81^  Inehee  diameter,  and  have  479^-inch  stroke.  Each  of  the  four  cylln* 
iers  requires  a  power  equal  to  t80  horse-power.    The  ooniprsefd  air  it  de» 


620  FUEL. 

Ifvered  Into  huge  reservoliti,  where  a  uniform  pressure  Is  kept  up  by  means 
of  fi  Kuitaiile  ««Hier-coIiiiiiii. 

The  Hydraulic  Forglnff  Plant  at  Bethlelieiii,  Pa««  is  de- 
scribed iu  a  paper  by  R.  W.  Davenpori,  read  before  the  Society  of  Naval 
En(2rineer8  and  Marine  Architects,  18U3.  It  includes  two  hvdraulic  forging- 
presses  complete,  with  engines  and  pumps,  one  of  1500  and  one  of  4500  tons 
capacity,  together  with  two  Whitworth  hydraulic  travelling  forging-eranes 
and  other  necessary  appliances  for  each  press;  and  a  complete  fluld-compreM* 
sloii  plant,  including  a  press  of  7000  tons  capacity  and  a  1%  ton  hydraulic 
traveUing  crane  for  serving  it  (the  upper  and  lower  beads  of  this  pre^s 
weighing  resoectlvely  about  135  and  190  tons). 

A  new  forgiug-preas  has  been  designed  by  Mr.  John  Frits,  for  the  Bethle* 
hem  Works,  of  14,000  tons  capacity,  to  be  run  by  engines  and  pumps  of  15,009 
horsepower.  The  plant  is  served  by  four  open-hearth  steel  furnaces  of  a 
united  capacity  of  120  tons  (if  sieel  per  lieat. 

Some  Reference*  on  Hydraulic  Transmission.— Reuleauz's 
'*  Uonstructor  ; "  "Hydraulic  Motors,  Turbines,  and  Pretwure-englnes,"  G. 
B'Mlfiier.  London,  1889  ;  R(^bin»ou's  *'  Hydraulic  Power  and  Hydraulic  Ma- 
chinery," London.  188H  ;  Colyer's  "  Hydraulic  Steam,  and  Hand-power  Lift- 
ing and  Pressing  Machinery,''  I/ondon,  1881.  See  also  ^rtgineet'tn^  (London), 
Aug.  1,  1884,  p.  99,  March  13,  1885,  p.  262;  May  22  and  June  6,  1891,  pp.  612. 
665 ;  Feb.  19,  189;!,  p.  25 ;  Feb.  10,  1898,  p.  170. 

FUEL. 

Tbeoiy  of  Combustion  of  Solid  Fuel.  (From  Rankine,  some- 
what altered.)— The  ingredients  of  every  kind  of  fuel  commonly  used  duv7 
be  thus  classed:  (1)  Fixed  or  free  carbon,  which  is  left  in  the  form  of  char- 
coal or  ooke  after  the  volatile  ingredients  of  the  fuel  have  been  distilled 
away.  These  Ingredients  burn  either  wholly  in  the  solid  state  (C  to  00|),  or 
part  In  the  solid  state  and  part  in  the  gaseous  state  (CO  +  O  =3  CO*),  the  lat- 
ter  part  being  flrst  dissolved  by  previously  formed  carbonic  acid  by  the  r». 
action  COt  +  C  =s  2CO.  Carbonic  oxide,  (X>,  is  produced  when  the  supply 
of  air  to  the  flre  is  insufficient. 

(2)  Hydrocarbons,  such  as  oleflant  gas,  pitch,  tar,  naphtha,  etc.,  all  ot 
which  must  pass  into  the  ^^aseous  state  before  being  burned. 

If  mixed  on  their  first  issuing  from  amongst  the  burning  carbon  with  a 
large  quantity  of  hot  air,  these  indammable  gases  are  completely  burned  with 
a  transparent  blue  flame,  producing  carbonic  acid  and  steam.  When  mixed 
with  oold  air  they  are  apt  to  be  chilled  and  pass  off  unbumed.  When 
raised  to  a  red  heat,  or  thereabouts,  before  beting  mixed  with  a  sufficient 

auantity  of  air  for  perfect  combustion,  Ihey  disengage  carbon  In  fine  pow- 
er, and  pass  to  the  condition  partly  of  marsh  gas,  and  partly  of  free  hydro* 
gen;  and  the  higher  the  temperature,  the  greater  is  the  proportion  of  carbon 
thus  disengaged. 

If  the  disengaged  carbon  is  cooled  below  the  temperature  of  ignition  be- 
fore coming  in  conuct  with  oxygen,  it  constitutes,  while  floating  In  the  gas, 
smotce.  and  when  deposited  on  solid  bodies,  soot. 

But  if  the  disengaged  carbon  is  maintained  at  the  temperature  of  ignition, 
and  supplied  with  oxygen  sufficient  for  its  combustion,  it  bums  while  float- 
ing in  the  inflammable  gas.  and  forms  red,  yellow,  or  white  flame.  The  flame 
fj'oni  fuel  is  the  larger  the  more  slowly  its  combustion  is  effected.  The 
flame  itself  is  apt  to  be  chilled  by  radiation,  as  into  the  heating  surface  of  a 
steam-boiler,  so  that  the  combustion  is  not  completed,  and  ptat  of  the  gas 
and  smoke  pass  off  unbumed. 

(8)  Oxygen  or  hydrogen  either  actually  forming  water,  or  existing  in 
combination  with  the  other  constituents  in  the  proportions  which  form  water. 
Such  quanti  ties  of  oxygen  and  hydrogen  are  to  left  be  out  of  aocx>unt  in  deter- 
mining the  heat  generated  by  the  combustion.  If  the  quantity  of  water 
actually  or  virtually  present  in  each  pound  of  fuel  is  so  great  as  to  make  its 
latent  heat  of  evaporation  worth  considering,  that  heat  is  to  be  deducted 
from  the  total  heat  of  combustion  of  the  fuel. 

(4)  Nitrogen,  either  free  or  in  combination  with  other  constituents.  This 
substance  is  simply  inert. 

(5)  Sulphnret  of  Iron,  w^hich  exists  in  coal  and  Is  detrimental,  as  tending 
to  cause  spontaneous  combustion. 

(6)  Other  mineral  compounds  of  various  kinds,  which  are  also  inerty  and 
form  the  ash  left  after  complete  combustion  of  the  fuel,  and  also  the  clinker 
or  glassy  material  produced  by  fusion  of  the  ash,  which  tends  to  choke  the 
grate. 


FtTBU 


621 


V^tel  tfeat  orcombastlon  or  Ptaelv,  (Ranklii«.)->Tbe  follow- 
IbfT  table  shows  the  total  heat  of  combusiion  witbA>xygeu  of  one  pound  of 
each  of  the  substances  named  in  it.  In  British  thermal  units,  and  also  in 
lbs.  of  water  evaporated  from  SIS^.  It  also  Bhow8*the  weight  of  oxygen  re- 
tipfred  to  combine  with  eacti  pound  of  the  combustible  and  the  weight  of 
air  necessary  in  order  to  supply  that  oxygen.  The  quantities  of  heat  are 
giTen  on  the  authority  of  MM.  Farre  and  Hilbermann. 


Combustible. 


Hydrogen  gas..... 

Carbon  imperfectly  burned  so  as 

to  make  carbonic  oxide. 

Carbon  perfectly  burned  so  as  to 

make  carbonic  acid. 

Oieflantgaa,  1  lb 

Various  liquid  hydrocarbons,  1  lb 

Carbonic  oxide,  as  much  as  is  mad«> 
by  the  imperfect  combustion  of 
1  lb.  of  carbon,  vis..  2^  lbs . . . 


Lbs.  Oxy- 
gen per 
lb.  Com- 
bustible. 


Lb.  Air 
(about). 


^iH 


86 
6 

IS 

16  8/7 


Total  Brit- 
ish Heat- 
units. 


63,082 

4,400 

14,600 

21,844 

from  SI  ,700 

to    19,000 

20,000 


Evapora- 

five  Power 

fromSlS* 

F.,  lbs. 


64.8 

4.66 

16.0 

SS.l 

fromS^ 

to   SO 

10.46 


The  imperfect  combustion  of  carbon,  making  carbonic  'oxide,  produces 
less  Uian  one  third  of  the  heat  which  is  yielded  by  the  complete  combustion. 

The  total  heat  of  combustion  of  any  compound  of  hydrogen  and  carbon 
is  nearly  the  sum  of  the  quantities  of  heat  which  the  constituents  would  pro- 
duce separately  by  their  combustion.    (Marsh-gas  is  an  exception.) 

In  computing  the  total  heat  of  combustion  of  compounds  containing  oxy- 
gen as  weU  as  hydrogen  and  carbon,  the  following  principle  is  to  be 
obsenred:  When  hydrogen  and  oxygen  exist  in  a  compound  in  the  proper 
proportion  to  form  water  (that  Is,  by  weight  one  part  of  hydrogen  to  eight 
of  oxygen),  these  constituents  have  no  effect  on  the  total  heat  of  combus- 
tion. If  hydrogen  exists  in  a  greater  proportion,  only  the  surplus  of  hydro- 
gen above  that  which  is  required  by  tne  oxygen  is  to  be  taken  into  account. 

The  following  is  a  general  formula  (Dulong^s)  for  the  total  heat  of  combus- 
tion of  any  compouna  of  carbon,  hydrogen,  and  oxygen: 

Let  C,  Hy  and  O  i>e  the  fractions  of  one  pound  of  the  compound,  wliich 
consists  respectively  of  carbon,  hydrogen,  and  oxygen,  the  remainder  being 
nitrogen,  asn,  and  other  impuritieR.  Jjet  h  be  the  total  heat  of  combustion 
of  one  pound  of  the  compound  in  British  thermal  units.    Then 


h  -  14.800|  a+4.«8(j5r-  -|)  }• 


Tlie  following  table  shows  the  composition  of  those  compounds  which  are 
of  importance,  either  as  furnishing  oxygen  for  combustion,  as  entering  into 
the  composition,  or  as  being  produced  by  the  combustion  of  fuel : 


Names. 

i 

III 

Air 

N77  +  02S 

100 
18 
17 
28 
44 
14 
10 
64 
84 
76 

N79-f021 

Water 

H.O 

CO 

COa 

CHa 

SOa 

H2  H 
H8  - 
C12- 
CIS- 
C12-1 
CIS- 

sa8H 

S32- 
804- 

[-016 

-N14 

-oie 

-032 
-HS 
-H4 
-082 
-H2 
-C12 

HS  -f  O 
H3     -N 

Arnmonia .*««* .* t--^ 

Carbonic  oxide ..........tt. 

C4-0 

Carbonic  ackl 

C  --OS 

Oleflant  gas 

C--H8 

Marsh-gas  or  flre-damp 

ffolphurous  acid 

8u1d*'  uretted  hvdroeen 

C-J-H4 

Sulphuret  of  carbon 

622 


FCEL. 


,  Since  e«ch  lb.  of  C.miulr«9  8W  l^-  of  O  to  burn  it  ttj  C0« » «nd  nff  ooaiatna 
S3\<>f  O.  l>y  weff?b^  ^  ■*■  <>-^  Of  il.6.1bH.  of  air  are  requicea  to  burn  1  lb.  of  G. 
Analyses  of  Gases  of  C»tiibBstloii»— The  foliowine  are  8el«*ct«d 
troin  a  largie  number  of  analyst^  of  suses  frotn  locomotive  boilere^  to  sliow 
ilie  rat\|ip:e,  of  corapoBition  under  different  circumstanoeB  (1\  H.  Diidlej, 
Trans.  A.  I.  M.  E  ,  iv.  260): 


Test 


11.5 
8.5 
S8 
5. 
8.4 

12 
34j 
6 


CO 


*.t 


6 

8 

17.1 
14. t 
8.4 
4.4 
1U.8 
13.6 


No  smoke  visible. 

Old  fli-e,  escaping;  gas  white,  engine  working  bard. 
Fre.sh  Are,  mucii  black  gas,         '*  *'  ** 

Old  iii-e,  damper  closed,  engine  standing  stiH. 
*'     **     smoke  white,  engine  work it\|iftMIUrd. 
New  are.  engine  nttt  vctnitlng  IMtrd. 
Smoke  black,  ebgine  not  >^-oH(ing  htard. 

dark,  blower  oii>  etntlne  ^tandlnf^  ttOL 
'^      whit«-,  eligine  working  hard. 


In  aiMl>'«^  on  the  Clevelahd  and  Pittsburgh  road,  in  every  instatire 
when  the  smoke  wafe  t^ie  blackest,  there  was  found  the  greatest  percentage 
of  unconsilkmed  oxygen  in  the  product,  sho^lhg  tttat  sontHhtng  besides  life 
mi/re  presAnc6  foV-oxy^n  is  required  to  effect  the  ootobusjtiote Of  the  volatile 
carbon  of  fuels. 

J.  X3.  ItoiiLliey  fTrans.  A.  B.  M.  E.,  vi.  74d)  found  as  the  mean  of  a  great 
numner  of  tetoaiyifes  of  fhie  ga^es  from  a  t>oIlsr  ustog  anthracite  coal : 
C?Oa,  18.10?    OO.O.^i    0,n.^;    N,  74  86. 

Tlie  loss  ot  heat  c^ue  to  bumfng  0  to  CO  instead  of  to  CO*  was  e.l8)t.  ^Tlie 
surplus  oxygen  averaged  li:i.3jf  of  the  O  required  for  the  C  of  the  fuel,  tlie 
average  for  different  weeks  ranging  from  88.6](  to  187^. 

Annlysea  made  to  detf^rmine  the  CO  produced  by  excewively  rapid  f1n'n«; 
gave  results  from  2  bi%  to  i.M%  CO  and  5.12  tr>  ft.OljJ  CO, ',  the  ratto  of  C  In 
the  CO  to  total  cartxxi  burned  Dfing  from  43.80;(  to  48.5fi](,  and  the  numbered 
pounas  of  air  supplied  to  the  furnace  per  pound  of  coal  being  from  88.2  to 
19.8  Wm.  Tiie  loss  dtie  to  burning  0  to  00  vtf^  from  27.84j(  to  80.86  of  ttie 
full  power  of  the  coal. 

.  Temperatare  of  th«  lPlre«  (kanklne^  S.  fe  ,  p.  288.>— By  tempc«r. 
ature  of  the  rire  is  mnant  ilie  leniperatm-e  of  the  products  6t  comhtist'ion  at 
the  instant  tli^it  the  coitibnst^on  is  complet**.  The  elevation  of  that  temper- 
atni-e  above  the  temperature  at  which  the  fliir  and  the  fuel  are  supplied  to 
the  furnace  may  be  computed  oy  diviaing  the  total  heat  of  com  bust  ion  oi 
one  lb.  of  fuel  by  the  weHd^t  an^  by  the  m»'aii  specific  beat  of  the  who)« 
products  of  coml)U8tion,  and  of  tne  air  employed  for  their  dilution  undef 
constant  pressure.  The  specific  heat  auder  constant  pressure  of  these  prod 
ucis  is  about  as  follows : 

Carbonic-acid  gas,  0.217 ;  steam,  0  475;  nitrogen  (pix>bably>w  twM&;air, 
0.^i8*^:  Hsnes.  probably  about  0.000.  Using  these  data,  the  following  results 
are  obtained  for  pure  carbon  and  for  olefiant  gas. burned,  respectively,  first, 
in  Just  sufficient  air,  theoretically,  for  their  combustion,  and,  second,  when 
an  vquftl  amount  of  air  is  supplied  In  addllton  for  dllutton. 


Fuel 

Products  undiluted. 

Products  diluted. 

Carbon. 

Oleflant 
Qas. 

Carbon. 

Oleflant 
Qas. 

<roial  hent  of  combrtstldn,  per  lb. . . 
Wl<  of  pT^durts  of  coinbuBcion,  lbs. 

Tlfeir  in^aA  t*pecillc  heat 

Sivciflc  heat  X  weiglit ^. 

ElvVatldn  or  temperature,  F. 

U.ftoe 

18 
0.887 
8.08 

4580O 

81.^00 

16.43 

0«*7 

4.22 

60S6O 

14,866 

05 

0288 

«44«» 

2I.8(W 
tl.fle 
0.«48 

7.9 

2no» 

[The  aboVe  calculations  are  made  on  the  assumption  tihat  the  specific 
heats  of  the  ga^s  are  constant,  but  they  probably  increase  with  t-ee  In- 
crease of  tempemture  (see  Specific  Heat),  in  which  case  the  temperafwne 
would  be  less  than  those  above  given.    The  temperature  would  be  f    ^ 


CLASSlFICATIOBr  OF  FUEL. 


C23 


fedaoed  hf  tfa»  heal  rettitered  latent  by  tlm  xsDnVenfiW  Into  stNun  6t  tMf 

water  present  in  the  fuel.]  .        »       -x  .^  ^ 

Uarch  12  and  Auiii  2,  lb86.)— -It  is  found  that  the  temneratures  obtahied 
by  eXvi^rMAi  tkii  Ahort  of  Uiose  obtained  by  calculalron.  Three  theo* 
nes  have  beeh  Wven  t4  lk6couul  foV  this :  1.  The  coolhig  effect  or  the 
sides  of  the  cdhtainiug  vetael;  2.  Tb^  V^tardati6n  of  the  evomtion  of  heat 
caused  by  dis^ckilation;  1  the  incr^Ase  of  the  ppeclflc  h^at  of  the  eases  at 
Tety  high  f  en]|)«miureB.  The  calculated  teniperatures  are  obtainable  only 
on  th^  conditio!)  Ihat  the  iarases  shAll  conibine  instanlaneously  and  simulta- 
neously throug:nolic  iheir  whole  n^ss.  ITiis  condition  is  practically  impos> 
sii)h»  In  expt^riihehts.  The  ^^ses  lormed  &t  the  begltahing  or  an  explosion 
dilute  the  remainiutf  combustiMe  Igaaee  and  tend  to  retard  or  check  the 
coiubustldh  m  thte  reniahi'deh 

CI^A^SiFIcA'TION    OF   l$OI<ID   FIJfel<S. 

Gnm^r  claAiB^  P>M  MeU  Aa  foltdwA  {Kiig^d  and  Myg  JVitcr.-,  July,  1874) : 

«  -jL^A-ir.^  Ratio—     PropttriionofColrt^bk' 

NaiA^df  Fuel.  H        ChftrtS7al  yieWed  bV 

or  O  +  N*.         the  Dry  Pure  Fuel. 

Pure  cellulose 8  0.28A0A 

WoOdT^B0mtelfefcHd«fa«aalii^Ht4lt6^X...  V  MK   1 

Peat  and  f33f(il  fuel ... .  6t^5  'SqS    .40 

Litrftice^tor  bkT»«'AcoaL.. .....  o 

Bl  turn  iDous  coals..... 4  et\ 

Anthracite..... .  l^X).^  .00  ( 

The  bituminous  coals  he  divides  into  Ave  claMM  as  beloW: 


Nune  of  Type. 


1.  Long:  Aiming  dry! 

coal.  f 

2.  Long  flam  in*  fati 

or  colcing  cttals,  > 
or  gas  cttais,         ) 


2.  Caking  fat  coals, 
or  blackstnithft 
coals. 


1 


4.  Short  {laming  fat  1 
or  ckiking  coals,  > 
teoking  coals,        ) 

V    LMib       Of      MXhttir  ) 

citic  tdtJBt  ) 


Et^ientary 
Ck>m|)i6sition. 

Ratio  ^ 

C. 

It. 

0. 

nse^ 

(fr..'H»4.Q 

\9.}S^\B 

4t^8 

dO^B^ 

5.8^5 

u.2eio 

«^S 

8i(^BC 

'5  (^4.i$ 

ii  (^5.5 

2^1 

88^91 

6.^4.: 

6.5(^5.6 

1 

•0^6^4.0^4     6.5^8 

1 

Propor- 
thiht)f 

vh^ldea 
byl>»- 
Ela- 
tion. 


KatUi« 

and 

AppeaS 

ahce  of 

Ookei 


0.60^.00 
.60^.68 

.6^.74 
.821^.90 


Pttlvem* 

.  lent. 

Malted, 
.      bat 

n-iable. 

Melted; 
some- 
what 
com- 

vei-y 
co^n» 

I     leht. 


*The  nitrognh  mr*?ly  «»xvt^e<1s  1  \P^r  \^^)\t  6t  th*  W*?ight  of  the  fVlel. 
+  Not  including  liiluiniiious  lignites,  which  respinble  petrol  'uius. 

Rankiiie  gives  the  fuHowing :  The  exirftin^  tiiffertjuces  in  the  chemical 
composition  and  properties  oif  <lifferenr  kln<1s  of  coal  Jire  very  prcnc.  Tiie 
pmjK)rtion  of  free  cnrbon  r«ng»'s  fi-om  80  lo  08  per  itent  ;  thai  Of  hs'drocav- 
Ijons  of  various  kinds  from  6  to  vtii  per  cent ;  that  of  wat^r.  or  oxygei;  and 
lij<lr<>jfen  in  the  proportions  wljich  form  water,  frt)hi  an  inappreciably 
small  quantity  to  2*  p^r  cent ;  that  of  ash,  from  \\^U>2(i  per  cent. 

The  numerous  varieties  of  coal  may  be  divided  into  principal  classes  as 
foH«)ws:  1,  anthracite  coal ;  :?,  semi- bituminous  coal  ;  8,  bituminous  tsoal; 
4,  long  flamiag  or  caunel  coal ;  6^  lignite  or  browa  coal. 


624  PCTBU 

BlmlnatlOA  of  H  and  O  In  Series  flrom  Wood  to  A  ntbjfaelte 

(QroveB  and  Thorp's  ChemlcAl  Technology,  toI.  i.,  Fuels,  p.  66.) 

Bubstanoe.  Carbon.    Hydrogen.    Oxygen. 

Woodyflbra.  SUM  5.S6  42.10 

Peat  nt>m  Vnlcalfe 09.67  5.W  M.47 

Lignite  from  Cologne 00.04  6.27  9B.0B 

Earth/ brown  coal 7S.18  6.88  21.14 

Coal  from  BeIeetat,8econdaty 76.00  6.84  19.10 

Coal  from  Rive  de  Oier 89.89  606  6.00 

Anthracite,  Mayenne,  transition  formation  91.68  8.90  4.46 

Prog;reesiTe  CItaDffe  firom  Wood  to  Grapblte* 

(J.  S.  Newberry  in  Johnson's  Cyclopedia.) 

WoOd.  Loss.   „j»     U)S8.n^,„gj5ojj  1.088.      ^jj^        UM8.         ^^ 

Carbon 49.1      18.06  80.46  12.88       18.10      8.67     14.58       1.42      18.11 

Hydrogen...    6.8       8.26     8.06     1.86         l.)20      0.98       0.27       0.14       0.13 
Oxygen 44.6     24.40  20.90  1&  18        2.07      1.82       0.05       0.00       0.00 

ioOO     4780   6i!70   2fi!n       21L87       TS     iTS       I2I       iTsi 

Olaaelilcatloii  of  Ooale,  as  Antbraelte.  Bttninliaoiia.  etc.— 

Prof.  Persifer  Fraser  (Trans.  A.  I.  M.  E.,  vi.  480)  propose  a  clasttiflca- 
tlon  of  coals  according  to  their  "  fuel  ratio/'  that  is,  the  ratio  the  fixed  car- 
bon bears  to  the  volatile  hydrocarbon. 

In  arranging  coals  under  this  classification,  the  accidental  impurities,  such 
as  sulphur,  earthy  matter,  and  moisture,  are  disregarded,  and  the  fuel  con- 
stituents alone  are  considered. 

Carbon  Fixed  Volatile 

Ratia  Carbon.  Hydrocarbon. 

I.  Hard  dry  anthracite.    100  to  12  100.     to  m,Zl%         0.     to   7  00]( 

U.  Semi-anthracite 12to8  92.81  to88.80  7.09to  11.11 

m.  8eml-bituminou8.  ...       8to  6  88.89to8S.83  11.11  to  10.07 

IV.  Bituminous 6to  0  SS.SSto  0.  10.07  to  100 

It  appears  to  the  author  that  the  above  classification  does  not  draw  the 
line  at  the  proper  point  between  the  semi -bituminous  and  the  bituininoiw 
coals,  vis.,  at  a  ratio  of  C  -h  V.H.C.  =  6,  or  fixed  carbon  83.83]K,  volatile  hv- 
drocarbon  I0.67)(,  since  it  would  throw  many  of  the  8team  coals  of  Clearfield 
and  Somerset  counties,  Fenn.,  and  the  Cumberland,  Md.,  and  Pocalionta*. 
Va.,  coals,  which  are  practically  of  one  class,  and  properly  rated  as 
semi-bituminous  coals,  into  the  bituminous  class.  The  dividftig  line  be- 
tween  the  semi -anthracite  and  semi-bituminous  coals.  C  •«-  V.H.C.  =  ^, 
would  place  several  coals  known  as  semi-anthracite  in  t^esemi-bitunilnous 
class.    The  following  is  proposed  by  the  author  as  a  better  classification  : 

Carbon  Ratia  Fixed  Carbon.  Vol.  H.C. 

L  Hard  dry  anthracite..    100  to  12  100      to92.81)(  0      to     7.90% 

II.  Semi-anthracite 12to  7  92.81to87.6  7.09to   12.6 

III.  Semi-bituminoos 7  to  8  87.6  to  75  12.6   to  9S 

IV.  Bituminous 8to0  75      toO  26      to  100 

Bliode  Island  Grapliltie  Antlmtelte.-A  peeulUr  graphite  is 
found  at  Cranston,  near  Providence,  R.  I.  It  resembles  l>oth  graphite  and 
anthracite  coal,  and  has  about  the  following  composition  (A.  E.  Hunt.  Trans. 
A.  I.  M.  E.,  xvii.,  078):  OraphiUc  carbon,  W%;  volatile  matter,  2.0(^;  sUIca, 
15.00j(;  phosphorus,  .045)(.    It  burns  with  extreme  difilculty. 

▲NAIiYSES  OF  COALS. 

Compoattlon  of  PennaTlTanla  Anthmcltee.  (Trans.  A.  I. 
M.  E.,  xTv.,  TOO.)- Samples  weighmg  100  ui  ;i:00  lbs.  were  collected  from  Ioia 
of  100  to  200  tons  as  shjpped  to  market,  and  reduced  by  proper  metliods  l<> 
laboratory  samples.  Tnirty-three  samples  were  analyzed  by  McCreath,  giv- 
ing results  as  follows.  They  show  the  mean  character  of  the  coal  of  the  more 
important  coal-beds  in  the  Northern  field  in  the  vicinity  of  Wilkesbarre,  ic 
the  Eastern  Middle  (Lehigh)  field  in  the  vicini^  of  Haxleton,  in  the  Westera 


AKALTSE8  OF  COALS. 


Middle  field  In  the  ▼fcfnfty  of  Shenandoah,  and  in  the  Southern  field  between 
ftlaiich  Chunk  and  Tamaqua. 


1^ 

1^ 

1 

u 

11 

< 

4 

a 
an 

Vol.  Matter. 
Per  cent  of 
total  com- 
bustible. 

Wharton... 

E.  Middle 

8.7J 

8.06 

86.40 

6.22 

.68 

..44 

28.07 

E.  Middle 

4.12 

8.06 

86.88 

6.92 

.49 

345 

27.99 

Primrose .. 

W.  Middle 

8.54 

8.72 

61.50 

10.65 

.50 

4.86 

21.93 

Mammoth . 

W.  Middle 

8.16 

8.72 

61.14 

11.06 

.90 

4.86 

21.88 

Primrose  F 

Southern 

8.01 

4.18 

67.98 

4.88 

.50 

4.46 

21.82 

BuckMtn.. 

W.  Middle 

8.04 

8.05 

62.66 

9.88 

.46 

4.56 

20.98 

Seven  Foot 

W.  Middle 

8.41 

8.96 

60.87 

11.28 

.51 

4.69 

20.82 

Mammoth . 

Southern 

8.09 

4.28 

68.61 

6.16 

.64 

4.66 

19.62 

Mammoth . 

Northern 

8.42 

4.86 

63.27 

6.20 

.78 

5.00 

19.00 

B.  Goal  Bed 

LoyalHOck 

1.80 

6.10 

68.84 

6.28 

1.03 

6.86 

10.29 

The  above  analyses  were  made  of  coals  of  all  sizes  (mixed).    When  coal  is 
screened  into  sizes  for  shipment  the  purity  of  the  different  sizes  as  rei^ards 
ash  vaiies  f^reatly.    Samples  from  one  mine  grave  results  as  follows: 
Screened  Analyses. 

Name  of      Through  Over  Fixed 

Coal.  inches.  inches.  Carbon.  Ash. 

ISgg 2.6  1.75  88.49  5.66 

Stove ...        1.76  1.25  88.67  10.17 

Chestnut. 1.25  .75  80.72  12.67 

Pea 75  .50  79  06  14.66 

Buckwheat...         .50  .25  76.92  16.62 

Bemlee  Basin,  Pa*,  Coals* 

Water.   Vol.  H.C.    Fixed  C.    Ash.    Sulphur, 
^.rnlee  Burin.   PulUvu.  Mdl'^f         »f         "^f         '^         »i« 

This  coal  is  on  the  dividing-line  between  the  anthracites  and  semi-anthra- 
cites, and  Is  similar  to  the  coal  of  the  Lykens  Valley  district. 

More  recent  analyses  (Trans.  A.  I.  M.  £.,  xiv.  721)  give : 

Water.     Vol.  H.C.    Fixed  Carb.       Ash.         Sulphur. 

Working  seam 0  65  9.40  88.69  6.84  0.91 

(0  ft.  below  seam ....  8.67  16.42  71.84  8.97  0.59 

The  first  is  a  semi-anthracite,  the  second  a  semi-bituminoua 

Space  Ocenpled  bT  Antbradte  Coal.    (J.  C.  I.  W.,  vol.  iii.)— The 
cuDiC  contents  of  2*^40  lbs.  of  hard  Lehigh  coal  is  a  little  over  86  feet ;  an 
average  Schuylkill  W.  A,  87  to  88  feet ;  Sbamokln,  38  to  39  feet;  Lorberry, 
nearly  41. 

According  to  measurements  made  with  Wllkesbarre  anthracite  coal  from 
the  Wyoming  Valley,  It  requires  82.2  cu.  ft.  of  lump,  83.9  cu.  ft.  broken, 
84.5  cu.  ft.  egg,  84.8  cu.  ft.  of  stove,  85.7  cu.  ft.  of  chestnut,  and  36.7  cu.  ft. 
of  pea,  to  make  one  ton  of  coal  of  2240  lbs. ;  while  it  requires  28.6  cu.  ft.  of 
lump,  80.8  cu.  ft.  of  broken,  80.8  cu.  ft.  of  egg,  31.1  cu.  ft.  of  stove,  81.9  cu. 
ft.  of  chestnut,  and  82.8  cu.  ft.  of  pea,  to  make  one  ton  of  2000  IbH. 

Composltloii  of  Antltradte  and  Seml-bUamlnons  Coals* 
(Trans.  A.  L  M.  E.,  vi.  48o.y— Hard  dry  anthracites,  16  analyses  by  Rogers, 
show  a  range  from  94.10  to  82.47  flz^  carbon,  1.40  to  9.58  volatile  matter, 
and  4.50  to  8.00  ash,  water,  and  impurities.  Of  the  fuel  constituents  alone, 
the  fixed  carbon  ranges  from  98.58  to  S9.68,  and  the  volatile  matter  from  1.47 
to  10.87,  the  corresponding  carbon  ratios,  or  C  •*-  Vol.  H.C.  being  from  67.02 
to  8.64. 

Semi'anthraciteB.—'i2  analyses  by  Rogers  show  a  range  of  from  90.28  to 
74.55  fixed  carbon,  7.07  to  13.75  volatile  matter,  and  2.20  to  12.10  water,  ash, 
and  impurities.  Excluding  the  ash.  etc.,  the  range  of  fixed  carbon  is  92.75 
to  64.42,  and  the  volatile  combustible  7.2i  to  15.68,  the  corresponding  carbon 
ratio  being  from  12.75  to  5.41. 


626 


FUBIi. 


Bemi'hitumifumM  OoaU.^iO  analysei  of  Panna.  and  ilarjland  ooala  fdva 
fixed  carbon  68.41  to  84.80,  volatile  matter  11.2  to  17.^8,  aiiaaab.  water.  ai.d 
impurities  4  to  13.i)9.  The  percentage  of  the  fuel  constituents  is  fixed  carbon 
79.84  to  88.80,  volatile  oombustible  11.90  to  20.16,  and  the  carbon  ratio  11.41  to 
8.96. 

▲merlcaii  Seml-bltamlnoas  and  Bltumlnoiis  Coals. 

(Selected  chiefly  from  various  papei*B  in  Trans.  A.  I.  M.  E.) 


Moist- 
ure. 

Vol. 
Hydro- 
arboD. 

Fixed 
Carbon 

Ash. 

Sul- 
phur. 

Penna.  SemibituminouB : 
Broad  Top,  extramee  of  5 

Somerset  Co.,  extremes  of  5 

Blair  Co..  averosre  of  S 

i   .79 
}    .78 

ji.«r 

il.89 
1.07 

0.74 
1.14 

o.'oo 

0.70 

0.81 
10.41 

(1.94 

l.ft 
1.97 
1.16 
1.26 
.49 

18.64 
17.88 
14.8.1 
18.M 
86.78 

21.21 

17.18 
15.51 
28  60 

23.94 

21.10 

20.09 

to 
25.19 

88.68 
SS.60 
42.55 
90.10 
0.01 
86.49 
39.09 

78.46 
76.14 
Tr.77 
65.90 
60.77 

68.94 

73.48 

78.60 
68.71 

60.28 

74.08 

66.69 

to 
74.08 

60  99 
54.15 
49.69 
59.61 
87.46 
59.06 
57.83 

6.00 
4  81 
6.68 
10.68 
9.45 

7.51 

6.58 

5.84 
5.40 

4,62 

3.86 

965 

to 

7.66 

3.76 
4.10 
4.58 
8.28 
11.88 
8.61 
8.80 

.91 

.88 

0.66 

8.08 

8.80 

Cambria  Co.,  average  of  7.  l 

lower  bed,  B.              ' ' " 
Cambria  Co.,  1,           ) 

1.98 
1.41 

upperbed.O.  f 

Cambria  Co..  South  Fork,  1 

Centre  Co..  1 

2.69 

Clearfield  Co.,  average  of  9,  t 

upper  bed,  C.              j "  " 

dearfleld  Co.,  average  of  8,  [ 

lower  bed,  D.              f""* 

Clearfield  Co.,  range  of  17  anal. . 

Bitnminoua : 
Jefferson  Co.,  average  of  36. . . . 

Clarion  Co.,  average  of  7 

Armstrong  Co.,  1 . . 

Oonneilsviile  Coal 

1.48 

0.48 

0.43 
to 
1.79 

1.00 

1.19 

8.00 

78 

Youghiog^heny  C'^al.  .,.,....-,, 

.68 

81 

Pitteburen.  Ocean  Mine 

... 

The  percentage  of  volatile  matter  in  the  Kittaninff  lower  bed  B  and  thi* 
Freeport  lower  bed  D  increases  with  great  uniformity  from  east  to  west;  thoe* 

Volatile  Matter.  Fixed  Car^n. 

Clearfield  Co,  bed  D 80.09  to  .».10  66.73  to74.76 

" B 98.56to86.18  64.87to80.88 

ClarionCo.,       "  B 85.70to42.66  47.61  to66.44 

''  D  87.15to40.80  51J»to68Jl8 

ConneUvrUle  €oal  and  Coke.  (Trans.  A.  I.  M.  E..  xiif.  838.)- 
Tbe  Connellsvllle  coal-field,  in  the  southwestern  part  of  Peniisjlvanla,  fa  a 
strip  about  3  miles  wide  and  60  miles  In  length.  The  mine  workings  are 
confined  to  the  Pittsburgh  seam,  which  here  has  Its  best  development  as  to 
size,  and  its  qualiry  best  adapted  to  coke-raakiug.  It  generally  lUtords 
from  7  to  8  feel  of  coal. 

The  following  analyses  by  T.  T.  Morrell  show  about  Its  range  of  compoel- 
tfon : 

Moisture.  Vol.  Mat.    Fixed  C.      Ash.     Sulphur.  Pbo«pb>. 
Herold  Mine  ....  1.26  88.83  60.79  8.44  .67  .013 

KIntzMine 0.79  81.91  56.46  9.52  1.38  .08 

In  oomparing  the  composition  of  coals  across  the  Appalachian  field.  In  the 
western  section  of  Pennsylvania,  it  will  be  noted  that  the  Conne^vflU 
variety  occupies  a  peculiar  position  between  the  rather  dry  semi-bituminous 
ooals  eastward  of  it  and  the  fat  bituminous  coals  flanking  it  on  the  west. 

Beneath  the  Connellsvllle  or  Pittsburgh  coal-bed  occurs  an  InterTaJ  of 
from  400  to  800  feet  of  **  barren  measures,**  separating  It  from  the  lower 
productive  coal  measures  of  Western  Penns.vlvaola.    The  following  tabJee 


AXALTSXS  Ot  COALS. 


627 


show  the  jrreat  siiiiilfrii/  In  compofiitlon  In  th«  Coali  of  iheae  upper  and 
lower  ooal-mearares  In  tne  same  geogrraphlcal  belt  or  boslb. 

Xnmljmmm  Crom  the  Upper  Coal-measures  (Peniia«)  In  a 
Weetivard  Order* 

Localities.       MoisCare.    Vol.  Mat.  Fbced  Carb.     Afib.        Sulpbuf. 

Anthracite 1.85  8.45  89.06  6.81  0.30 

Cumberlabd,  Md 0.8»  16.52  74.88  V.89  0.71 

Saliabury,  Fa l.M  »«85  88.77  5.96  1.24 

ConoellsvilJe,  Pa. 81.88  60.80  7.84  1.09 

(IreensbtirK,  Pa 1.0«  88.50  61.84  E.88  0.86 

Irwlo^Pa 1.41  97.66  54.44  5.86  0.64 

Analyses  fyom  the  IiO-wer  Coal-measnres  in  a  ITestiward 
Order. 

Looalitlefl.       Moisture.    Vol.  Mat.  Fixed  Carb.  A«b.  Sulphur. 

Anthracite 1.85              8.45  89.06  6.81  0  80 

BroadTop 0.77             18.18  78.84  6.89  1.03 

Bennington 1.40              97.23  61.84  6.98  2.60 

Johnstown 1.18              16.54  74.46  6.96  1.86 

BlalrsvUle 0.08             »l.d6  62.22  7.09  4.9i 

ArmstrongCo 0.90             88.20  52.08  6.14  8.60 

PenttsylTanla  iind  Ohio  Bftumlnons  Goals*   Tarlatlon 
m  €1iar«cier  4»r  €oAls  of  tbe  same  Beds  In  dlflRdrent  IMs- 

trlets*— f'rom  50  analyses  hi  the  reports  of  the  Pennsylvania  Qeological 
Survey,  tbe  following  are  selected.  They  are  divided  into  different  groups, 
and  the  extreme  analysis  in  each  group  is  given,  ash  and  other  impurities 
being  neglected,  and  the  percentage  in  lOO  of  combustible  matter  being 
alone  considered. 


97ayne8burg  coal'bed,  upper  b«'nch. . .  . 

Jelferflon  township,  Qi'eeiie  Co 

Hopewell  township.  Wasblngion  Oo. . 
Warnesburg  coal'bed,  lower  bench 

Morgan  township,  Greene  Co 

Pleasant  Vall^,  Washington  Co. .... . 

Sewlck  ley  coal'bed 

Wbltely  Creek,  Greene  Co. 

6ray*8  Bank  Creek,  Gi'eene  Co 

Fittaburgh  coal-bed: 

Upper  bench,  Washington  Co 

Lower  bench,         *•  "    

Main  bench,  Greene  Cc. 

Frick  &  Co..  Washington  Co.,  average 

Lower  bench,  Greene  Co 

Somerset  Co.,  semi-bituminous  (showing 

demase  of  toI.  mat.  to  the  eastward). 
Beaver  Co.,  Pa 

Diehl's  Bank,  Georgetown , . . 

Bryan's  Bank,  Georgetown 

Ohio. 
Pittsburgb  eoal-bcd  in  Ohio: 
Jefferson  Co.,  Ohio 

Belmont  Co.,  Ohio 

HarriBOD  Co., Ohio ■. 

Pomeroy  Co.,  Ohio 


No.  of    Fixed      Vol.    Carbon 
Analyses  Carbon    fi.  C.     Ratio. 


\  ! 


59.72 
68.92 

60.69 
54.81 

64.89 

60.85 

J  60.87 
159.11 
63.54 
50.97 
61.80 
54.88 
66.44 
67.83 
79.78 
175.47 

40.68 
02.07 


61.45 
68.46 
)66  14 
63.40 
64.93 
60.92 
62.83 


40.2R 
46.78 

89.81 
46.69 

85.61 
89.60 

89.18 
40.89 
86.46 
49.03 
38.20 
45.67 
83.56 
4-M7 
20.27 
24.53 

69.82 
87.48 


88.55 
86.54 
83.86 
86.54 
35.07 
39.08 
87.67 


1.48 
1.18 


1.54 
1.19 


1.65 

i.eo 

1.74 
1.04 
1.61 
1.19 
1.98 
1.87 
8  98 
3.(77 

0.68 
1.66 


1.09 
1.78 
1.96 
1.78 
1.86 
1.55 
1.60 


628 


FUEL* 


Analyweii  of  gonthern  and  Western  €oalfl. 

Moisture 


Ohio. 
Hocking  Valley 

Martlahd. 

Cu  mberland 


Virginia. 
South  of  James  River,  28  anal- 
yiies^range 

Averafce  of  28 

North  of  James  River,  eastern 
outcrop, 

Carbonite  or  Natural  Coke .... 

Western  outcrop,  11  analyses, 
range 

Averafreof  11 

Pocahontas  Flat-top* 
(Castner  &  Currants  Circular) 
WEST  ViRoiNiA  (New  River.) 

Quiunimont,t  8  analyses 

Nuttalburght 

ViRoiviA  and  Kbktuckt. 
Big  Stone  Gap  Field, ^  0  anal- 
yses, range 

Kentucky. 
Pulaski  Co.,  3  analyses,  range 

MuhlenbeiK  Oo^  4  analyseB, 
range 

Pike  Co.,  Eastern  Ky^  87  an- 
alyses, range 

Kentucky  Cannel  Coals,f  6  an> 
alyses,  range 


Vol.  Mat.  Fixed  C. 


TBNNK88BB. 

Scott  Co.,  Range  of  several.^. 

Roane  Co.,  Rockwood 

HamUton  Co.,  Melville 

Marion  Co.,  Etna  

Sewanee  Co.,  Tracy  City 

Kelly  Co.,  Whiteside 

OiooRaiA. 
Dade  Co 


Warren  Field: 

Je/Terson  Co.,  Birmingham.. 
"  "     Black  Creek.. 

Tuscaloosa  Co 

Cahaba  Field,    I  Helena  Vein 

Bibb  Co    ....  f  Coke  Vein.... 


5.00 
7.40 

1.23 

from  0.67 
to  2.46 
1.48 
0.40 
1.7D 
1.5^ 
1.66 

j  from 

\    to      .. 

1  0.62 

if rom  0.T6 
to    0.94 
0.31 
1.85 

j  from  0.80 
1     to    2.01 

j  from  1 .26 
1  to  1.82 
j  from  8.60 
1    to    7.06 

I  from  1.80 
to    1.60 
from., 
to  ,. 


to 


70 
1.88 
1.75 
8.74 

04 
1.60 
1.80 

1.20 


8.01 
.12 
1.59 
2.00 
1.78 


32.80 
29.90 

19.18 
15.47 

27.28 
88.60 
82.24 
18.60 
28.96 
0.64 
14.26 
21.88 
80.60 
96.06 
28.90 
18.48 

17.67 
18.19 
29.50 
25.85 

81.44 
86.27 

85.15 
89.44 
80.60 
88.90 
26.80 
41.00 
40.*iOI 
66.3()| 

88.88 

41.29 
26.62 
26.50 
23.72 
29.80 
21.80 

28.05 


42.76 
26.11 
88.83 
32.90 
80.60 


58.15 
60.45 

78.51 

46.70 
67.88 
58.89 
71.00 
59.98 
79.98 
81.61 
54.97 
70.80 
63.75 
74.-<i0 
75.22 

75.80 
79.40 
60.00 
70.67 

54.80 
63.50 

60.86 
52.48 
58.80 
58.70 
67.U0 
.•50.37 
50.80  coke 
88.70  coke 

46.61 
61.66 
60.11 
67.06 
68.04 
61.00 
74.20 

60.50 


48.80 
71.64 
54.64 
5.^.06 
66.58 


Ash. 


0.05 
2.06 

6.40 
0.00 

9.00 

15.76 

7.72 

10.00 

14.28 

8.86 

2.24 

8.86 

22.60 

10.06 

1.88 

5.68 

1.11 
4.02 
1.07 
2.10 

1.73 
8.25 

1.23 
5.52 
3.40 
6.60 
3.80 
7.80 
8.81 
4.80 

16.94 
1.11 

11.62 
8.68 

11.40 
7.80 
2.70 

15.16 


8.21 
2.08 
5.45 
11.34 
1.00 


*  Analyses  of  Pocahontas  Coal  by  John  Paititison,  F.C.S.,  18»0: 

C.         H.  O.        N.        S.       Ash.    Water.   Coke.    ^^^ 

Lumps  ..   86.51       4.44        4.06     0.66     0.61       1.64       1.80       78.8      21. £ 
Small...    88.18      4.20        5.88     0.66     0.56       4.68       1.40       70.8      90.2 
t  These  coals  are  coked  in  beehive  ovens,  andvield  from  9Sj(  to  64^  of  coke. 

J:Thi8  field  covers  about  VJO  square  miles  in  Virginia,  and  about  80  square 
les  in  Kentucky. 

•  The  principal  use  of  the  cannel  coals  is  for  enriching  illuminatlng-gaa. 
I  Volatile  matter  including  moisture. 

Y  Single  analyses  from  Morgan,  Rhea,  Anderson,  and  Roane  counties  fall 
within  this  range. 


ANALYSES   OF   COALS. 


629 


Moisture.  I  Vol    Mat 


Trsas. 

Eai^le  Mine 

Sabinas  Field,  Vein    I . . . . 

II.... 

III.... 

'•  IV.... 

Indiana. 

Caking  CoaU. 

Parke  Co 

SulliTan  Co.  coal  H 

CUy  Co 

Spencer  Co.  coal  L 

Block  CoaU* 

Clay  Co 

Martin  Co 

Daviess  Co 

lLUNOI8.t 

Bureau  Co.:  Ladd 

Seatonville. . 

Christian  Co. :  Fana 

Clliitoo  Co. :  Trenton 

Fulton  Co.:  Cuba 

Grundy  Co.:  Morris 

Jackson  Co.:  Big  Muddy. 
La  Salle  Co.:  Streator.... 

Logan  Co. :  Lincoln 

Macon  Co.:  Niantic 

Macoupin  Co.:  Qillespie.. 

Mt.  Olive. 

Staunton. 
Madison  Co.:  ColUnsville. 
Marion  Co. :  Centralia  . . . 
McLean  Co. :  Pottstown . . 

Perry  Co.:  Du  Quoin 

Sanfiramon  Co.:  Barclay.. 
St.  Clair  Co.:  St.  Bernard, 
Vermilion  Co.:  Danville. . 
Will  Co.:  Wilmington. ... 


8.54 
1.91 
1.37 
0.81 
0.45 


4.50 
3.39 
7.00 
S.50 

8.50 
S.60 
5.50 


12.0 
10.0 
7.8 
18.8 
4.2 
7.1 
6.4 
12.0 
8.4 
7.9 
12.6 
10.4 
6.8 
9.8 
8.3 
4.6 
11.8 
10.8 
14.4 
11.0 
16.5 


80  84 
20.04 
16.42 
29.85 
21.6 


45.50 
45.25 
89.70 
45.00 

81.00 
44.75 
86.00 


82.8 
38.8 
86.4 
80.4 
86.4 
82.1 
80.6 
85.8 
85.0 
36.3 
30.6 
36.7 
57.1 
29.9 
34.0 
35.5 
80.3 
27.8 
80.9 
82.6 
32.8 


Fixed  C. 


50.69 
68.71 
68.18 
50.18 
46.75 


45.50 
51.60 
47.80 
46.00 

67.60 
51.25 
58.50 


42.5 
40.9 
46.9 
52.0 
48.6 
49.7 
54.6 
4S.8 
44.5 
47.4 
45.8 
46.1 
26.8 
40.8 
45.5 
45.5 
49.9 
44.8 
4S.4 
58.0 
89.9 


Ash. 


Sul- 
iphur. 


14.98 
15.85 
18.02 
19.68 
29.1 


4.50 
O.W) 
6.00 
2.50 

8.00 
1.60 
5.00 


18.2 
15.8 

9.5 

4.8 
10.8 
11.1 

8.8 

8.9 
12.1 

8.5 
11.5 

6.8 
10.3 
16.1 

8.0 
14.4 

8.5 
17.1 

6.4 

8.6 
11.8 


8.15 


0.9 


1.5 
2.4 


1.5 
3.5 


8.9 


0.9 
i."4' 


•  Indiana  Block  Coal  (J.  S.  Alexander,  Trans.  A.  I.  M.  E.,  iv.  100).— The 
typical  block  coal  of  the  Brazil  (Indiana)  district  differs  in  chemical  com- 
position but  little  from  the  coking  coals  of  Western  Pennsylvania.  The 
physical  diflFerence,  however,  is  quite  marked;  the  latter  has  a  cuboid  struc- 
ture  nuide  up  of  bituminous  particles  lying  against  each  other,  so  that  under 
the  action  of  heat  fusion  throughout  the  m&<w  readily  takes  place,  while 
block  coal  is  formed  of  alternate  layers  of  rich  bituminous  matter  and  a 
charcoal-like  substance,  which  is  not  only  very  slow  of  combustion,  but  so 
retards  the  transmission  of  heat  that  agglutination  is  prevented,  and  the 
coal  bums  away  layer  by  laver,  retaining  Its  form  until  consumed. 

An  ultimate  analysis  of  block  coal  from  Sand  Creek  by  E.  T.  Cox  gave: 
C,  72.94;  H,  4.50;  O,  11.77;  N,  1.79;  ash,  4.50;  moisture,  4.50. 

t  The  Illinois  coals  are  generally  high  in  moisture,  volatile  matter,  sul- 
phur and  ash.  and  ai*e  consequently  low  in  heating  value.  The  range  of 
quality  is  a  wide  one.  The  Big  Muddy  coal  of  Jackson  Co.,  which  has  a 
nigh  reputation  as  a  steam  coal,  has.  according  to  the  analysis  given  above, 
about  86^  of  volatile  matter  in  the  total  combustible,  corresponding  to  the 
coals  of  Western  Pennsylvania  and  Ohio,  while  the  Staunton  coal  has  68jf, 
ranking  it  among  the  poorer  varinties  of  lignite.  A  boiler-test  with  this  coal 
(see  p.  686,  also  Trans.  A.  S.  M.  E.,  v.  266)  gave  only  6.19  lbs.  water  evapo- 
rated  from  and  at  212^  per  lb.  combustible.  The  Staunton  coal  is  remarkanle 
for  the  high  percentage  of  volatile  matter,  but  it  is  excelled  in  this  resiiect  by 


630 


PUEL. 


Hitemau.. 
Keb 

Chiibolm. 


Iowa.* 


Brookfleld. 
Mendota. . 
Hamilton . 


MisaouRi.* 


Hastini^ 
Cambria 


VEWAfKA* 


WyoifiKO.t 


Goose  Creek. , 


Deelf  Creek 

Sheridau  "•  ■% •••.< 

COLQIUDO.I 

Sunahtn^,  Colo,  a?erage. . 
Kewo«3Ue,  '*  "  ,. 
ElMoro,  "  "  ., 
Crested  Outteo,      " 

Utah  (Southern). 

Qaatledale 

Cedar  City , 

Ohwon. 
OooB  3ay , 


TaquinaBav  ,. 
John  Da^Hiver. 


VANdODyBR  ISLANP, 

Oomo»0oal-.,  • , 


Moisture, 


4.99 
9.81 
9.84 
9.18 

4.84 
9.03 
6.06 
r.83 


0.21 

4.8 
«.5 
f-7 
1892 
12.8 
Q.04 

9.8 
^.7 
1.32 

MO 

«.4S 
8.50 

ia,46 
ir.27 

lios 

4.65 
e.54 

i,r 


Vol.  Mat. 


86.27 
87.49 
40.16 
40.49 

40.27 
87.48 
84  24 
88.29 

27.88 


41.66 
44.  lit 
46.20 
40.00 
84.46 

27.17 


Fixed  C. 


2^.97 
44.75 
87.69 
^.69 


» 


47.S 
^7.24 


^.88 

41.6 
87.9 
46.8 
42.08 

Mr 

87,1 
48,6 

6&.aa 

7a.6Q 

4r.8n 
4a.nt 

94,96 
89,40 
«$,60 

68.87 


Ash. 


Sul. 
phur. 


44.87 

7.96 
12.31 
10.82 

4.79 
7.26 
1^,01 
7.14 

11,09 

13.7 

1:1 

7.2? 
3.6 

28.8 

U.i 
«.60 
8.)« 


9.n 

5,9ft 

8.06 
6.18 


2.58 
1.37 

•:S 

,06 


the  Bochead  coal  of  Llnllihgowdhine,  Scotland,  an  analysli  of  whio)i  by  Dr. 
■n  *_»,  T,       .  ._i       '^.84;  vol. 67.95:  f'~"'  -^  -*"■' 

^_     .  _._._  ._.96:wr  •  ■ 

hi^b  percentagre  of  H. 
*Tne  analyeee  of  Iowa,  Missouri,  Nebn 


Peony  18  as  follows:  Pro]|imaie— moisture  a84;  vol,  67.95;  f}zed  Q,  ^bCavh. 
21.4;  t71tiiiiate-^,68.94;  H,  &86;  O,  4.70;  N,  a96;  which  is  remarkable  tor  the 


•The  analyses  of  Iowa,  Mlssourt,  Nebraska,  i^Qd  Wyomlu 

selected  from  a  paper  on  The  Heating  Value  of  Western  Oqu_„  ^, ^ 

Forsyth,  Meoh.  Eni?r.  of  the  C,  B.  A  Q.  B.  R.,  mg'g  ^ettmJivm'.^f,  ife 

t  Ineludes  sulphur,  which  is  very  hi^h.  Coke  from  Cedar  Qfty  an^lyzecl : 
Water  and  volatile  matter,  1.42}  flxed  carbon,  76.70;  ASh,  lo.6U  ^Ulpnur,  &•«'• 

t  Colorado  Caa/«.^The  Colorado  ooals  are  of  e^tromely  ▼ariahle  coin- 
poaitiou,  rapsinfr  all  the  ym  'I'OW  lignite  to  aqthra<?ite.  Q.  C,  Hewitt 
(Trans.  A.  X.  M.  E..  yvll.  877)  si^ys  :  The  qoul  seapis.  where  uoehansfMl 
by  heat  and  flexure,  carry  a  lignite  oontainiuR  from  69  to  2QK  of  wafcep.  In 
the  south<«astern  comer  of  the  field  the  same  nave  beei)  ni^taraoFpheeed 


the  soutn<«astern  comer  ox  the  neiq  uie  same  have  oeei)  ni^taraoFphesed  to 
that  in  four  miles  the  same  seams  Are  an  ^nthpacite,  oqkinf?,  luid  4ry  cpal. 


areiy  agglutinate  in  a  heehive  oyen.    lu  aoo 

mile  the  same  seam  is  dry.  In  this  transition  area,  fk  small  pross-faiilt 
makes  the  coal  fat  for  twenty  or  more  feet  on  either  side.  The  <lry  seams 
also  present  wide  chemicol  and  physical  change^  in  short  distances.  A  soft 
and  loosely  bedded  eoal  has  in  a  hundred  feet  become  compaot  snd  hard 
without  the  intervention  of  a  fftult,  A  couple  0$  hundred  feet  haM  reduced 
the  water  of  combipation  from  12%  to  5^. 

Trans.  A.  I.  M.  K.  1890.)— The  Cho<!law  coal-lleld  is  a  direct  westwanlexten- 


ANALTSBS  O?  COALS. 


631 


gion  of  tbe  Arkansas  ooal-fleld.  but  its  ooals  are  not  like  Arkansas  eckali.  ax- 
cept  la  the  country  immediately  adloining  tbe  Arkansas  lina^ 

The  westeru  Arkansas  coals  are  dry  semi-bituminous  or  semi^antbracitto 
coaU,  iiiosiiy  uoii-cokiuic,  or  wiUi  quite  feeble  ooking  proix^rliea.  ranniiur 
from  U%  to  lGj(  in  volatile  matter,  the  bigbest  percentage  yet  founq.  accorfT 
ing:  to  Ur.  Winslow's  Arkansas  report,  being  17.65&. 

In  the  Mitchdi  basin,  about  10  miles  west  from  tbe  Arkansas  line,  ooal 
recently  opene*!  shows  ^9%  volatile  matter;  tbe  Mayberry  coal,  about  8  miles 
farther  west,  contains  2&%  volatile  matter;  and  the  Bryan  Mine  coal,  aboul 
the  same  distaooe  west,  shows  20%  volatile  matter.  About  80  milea  farther 
west,  the  coal  shows  from  9B%  to  41U)(  volatile  matter,  wbiob  is  alio  aboul 
the  percentage  in  coals  of  the  MoAleater  and  l«high  diatriota. 
l¥e«teni  lilcnltea,    (R.  W.  Raymond,  Trana  A.  1.  M.  E.,  toI.  ii.  18T«.) 


C, 

»v 

H. 

O. 

8. 

Moi*- 
tiire. 

4 

< 

Catortflc 

Power, 

ealorltfs. 

WrintP  DiabolO... 

T^Vbrr  t'ftiifjin  Tjfah  , * . . 

F>hoean<m,  Uuh- 

LaJ-bou  Jitatioi>,  Wyo , ,  .  * . . , 

rv>os  Bar.  Ore*on. . , , , , 

e4,ai 

00.64 

m.u 

S.06 

n.m 

3.7C 

i.m 

S5» 

1.01 

1-lM 

1.74 
1.85 
0  41! 
0  61 

15.«»3  ]^ 

15. 20. 1. or 

O.B4  1.0;i 

1ft. or  0  m 
liiaio.fls 

UASl\2.D» 

S41 
Q  K 
UM 
Sim 
13  i» 
MiM 

aw 

3  !R 

14.  e« 

BM 

I  m 
^M 

4  05 
4  18 

5.77 

».so 

5767 

CMOO 
6738 
6578 
i5«0 

Alaska..     , 

Canon  CitytOoJo!;]!'*^!!!!' 
BaJcpr  Oo..  Ore.  *.*, 

tJ7.S«7.« 

4610 
7880 

The  calorific  power  is  calculated  by  Dulong's  formula, 

8080C  +  844««(h  -  j). 

deducting  the  heat  required  to  yaporize  tbe  moisture  and  combined  water, 
that  is,  537  calories  for  each  unit  of  water.  1  calorie  s=  1.8  British  thermal 
nnit«. 

Analjaes  of  Porolffn  Ooals.    (Selected  from  D.  L.  Barneses  paper 
on  American  Locomotive  Practice,  A.  8.  O.  B.,  1808,) 


Volatile 
Matter. 


Fixed 
Carbon. 


Ash. 


Great  Britain : 

South  Wales. . 


Lancashire,  Eng., 
Derbyshire,  "  . 
Durham,  "  . 
Scotland 


Staffordshire,  Eng. 
South  America: 
Chill,  Conception  Bay 
*♦      Chiroqui 


Patagonia. 
3razU... 


Bi 

Canada 

Nova  Scotia 

Cape  Breton 

Australia 

Australian  lignite 

Sydney,  South  Wales.. 

Borneo 

Van  Diemen*s  Land 


8.6 

17.2 

17.7 

15  06 

17.1 

17.6 

90.4 

SI. OS 
24.11 
S4.S6 
40.5 

S8.8 
90.0 

16.8 
14.08 
96.6 
6.16 


88.8 
08.8 
80.1 
79.9 
86.8 
68.1 
80.1 
78.6 

70.56 
88.96 
62  tS 
67.9 

60.7 
67.6 

64.1 
89.89 
70.8 
0S.4 


8.8 

1.5 
3.7 
8.4 
1.1 
19.8 
«.4 
1.0 

7.68 
86.91 
18.4 

1.6 

19.6 
6.6 

10.0 
2.04 
14.9 
80.46 


Semi-bit  ooklngcoal. 
Boghead  oannel  gas  coaL 
Semi-bit.  steam-ooal. 


An  analysis  of  Pictou.  N.  S.,  ooal,  In  Trans.  A.  I.  M.  E.,  xiv.  560,  is:  Vol., 
SO 68;  carbon.  56.96;  ash,  1339;  and  one  of  Sydney,  C«pe  Breton,  coal  isi 
▼ol.,  34.07;  carbon,  61.43;  ash,  4.50. 


FUEIi. 

Nixon's  NaTlffatlon  Welsb  Coal  Is  remarkably  pure,  and  oon. 
tains  not  more  than  8  to  4  per  cent  of  asheM,  trying  88  per  cent  of  hard  and 
lustrous  coke.  The  qiiantlty  of  fixed  carbon  it  contains  would  classify  it 
among  the  dry  coals,  out  on  aceoimt  of  its  coke  and  its  intensity  of  com- 
bustion it  belongs  to  the  class  of  fat,  or  long-flaraing  coals. 

Chemical  analysis  gave  the  following  results:  Carbon,  90.87;  hydrogen, 
4.88;  sulphur,  .69;  nitrogen,  .49;  oxygen  (difTerence),  4.16. 

The  analysis  showed  the  following  composition  of  the  volatile  parts:  Car- 
bon, 22,63;  hydrogen,  84.96  ;  O  +  M-f  S.  49.61. 

The  heat  or  combustion  was  found  to  be,  as  a  result  of  ssTeral  experi- 
ments,  8864  calories  for  the  unit  of  weight.  Calculated  according  to  its 
composition,  the  heat  of  combustion  would  be  8805  calories  =  16,849  British 
thermal  units  per  pound. 

This  coal  is  generally  used  in  trial-trips  of  steam-vessels  In  Great  Britain. 

fluiplinff  Coal  ror  ▲nalyds.-J.  P.  Kimball,  Trans.  A.  I.  M.  E., 
zii.  317,  says :  The  unsuitable  sampling  of  a  coal-seam,  or  the  improper 
preparation  of  the  sample  in  the  lab<$ratory.  often  gives  rise  to  errors  in  de- 
terminations of  the  ash  so  wide  in  range  as  to  vitiate  the  analysis  for  all 
practical  purposes ;  every  other  single  determination,  excepting  moisture, 
showing  us  relative  part  of  the  error.  The  determination  of  sulphur  and 
ash  are  especially  liable  to  error,  as  they  are  intimately  associated  faf  the 


Wm.  Forsyth  J[n  his  paper  on  The  Heating  Value  of  Western  Coals  (Eno^if 
Netott  Jan.  17, 1806),  says  :  This  trouble  in  getting  a  fairly  average  sample  of 
anthracite  ooal  has  compelled  the  Reading  R.  R.  Co. ,  in  getting  their  samples, 
to  take  as  much  as  300  Ids.  for  one  sample,  drawn  direct  from  the  chateis,  as 
It  stands  resdy  for  shipment. 

The  dii'ectioiis  for  collecting  samples  of  coal  for  analysis  at  the  C.,  B.&  Q. 
laboratory  are  as  follows : 

Two  samples  should  be  taken,  one  marked  **  average,"  the  other  **  select.** 
Each  sample  should  contain  about  10  lbs.,  made  up  of  lumps  about  the  sixe 
of  an  oransre  taken  from  different  parts  of  the  dump  or  car,  and  so  selected 
that  they  shall  represent  as  nearly  as  possible,  first,  the  average  lot;  aeoond, 
the  bt^t  coal. 

An  example  of  the  difference  between  an  *'  average  '*  and  a  "  select  ** 
sample,  taken  from  Mr.  Forsyth's  paper,  is  the  following  of  an  Illinois  ooal: 
Moisture.    Vol.  Mat.    Fixed  Carbon.    Ash. 

Average 1.86  87.69  86.41  86.54 

Select 1.90  84.70  48.88  16.17 

The  theoretical  evaporative  power  of  the  former  was  9.18  lbs.  of  water 
from  and  at  212<>  per  lb.  of  coal,  and  that  of  the  latter  11.44  lbs. 

Belatlve  Value  of  Fine  Sizes  of  Antbraelte.— For  buniinif 
on  a  grate  coal-dust  is  commercially  valueless,  the  finest  commercial  ao- 
thraoites  being  sold  at  the  following  rates  per  ton  at  the  mines,  aooondlnff 
to  a  recent  address  by  Mr.  Eckley  B.  Coxe  (1808): 

Size.  Bamre  of  Size.  Price  at  Mines. 

Chestnut l^to^    inch  $2.75 

Pea %toP/16  1.25 


Buckwheat 9/16to9^  0.75 

Rice %toS/l6  0.26 

Bariey 8/16to2yS2  0.10 


L 


But  when  coal  is  reduced  to  an  impalpable  dust,  a  method  of  burning  it 
becomes  possible  to  which  even  {the  finest  of  these  sizes  is  wholly  una- 
dapted;  the  coal  may  be  blown  in  as  duKt.  mixed  with  its  proper  proportion 
of  air.  and  no  irrate  at  nil  is  then  required. 

Pressed  Fuel.  (E.  F.  Loiseau.  Trans.  A.  I.  M.  E.,  viii.  314.)— Pressed 
fuel  has  been  iiiaile  from  anthracite  dust  by  niixiiig  the  dust  with  ten  per 
cent  of  its  bulk  of  dry  pitch,  which  is  prepai*ed  by  separnting  from  tar  at  a 
temperature  of  5?2**  F.  the  volatile  matter  it  contains.  The  mixture  is  kept 
heated  by  steam  to  212°,  at  which  temperature  the  pitch  acquires  iu  ce- 
menting properties,  and  is  passed  between  two  rollem.  on  the  periphery  of 
which  are  milled  out  a  series  of  semi-oval  cavities.  The  lumps  of  the  mix- 
ture, about  the  nize  of  an  egg,  drop  out  under  the  rollers  on  an  endless  belt 
which  carries  them  to  a  screen  in  ei^ht  minutes  which  time  is  sufficient  to 
cool  the  lumps,  and  they  are  then  ready  for  delivery. 

The  enterprise  of  making  the  pressed  fuel  above  described  was  not  com- 
mercially successful,  on  account  of  the  low  price  of  other  coal.  In  France, 
however,  *'  bru/nettea "  are  itsguiarly  made  of  ooal-dust  ((>ituminous  and 
semi-bituwiuoutf)* 


RELATIVE  VALUE  OF  8TEAH  COALS.  833 

BBIiATITB  TAI^ITB  OP  8TBA1H  COAI.8. 

The  heating  value  of  a  coal  may  be  determined,  with  more  or  len  approx- 
imation to  accuracy,  by  three  different  methoda. 

Ist,  by  chemical  analysis  :  2d.  by  combustion  in  a  coal  calorimeter  ;  8d, 
by  actual  trial  in  a  steam-boiler.  The  first  two  methods  give  what  may  be 
called  the  theoretical  heating  value,  the  third  gives  the  practical  value. 

The  accuracy  of  the  first  two  methods  depends  on  the  precision  of  the 
method  of  analysis  or  calorim«*try  adopted,  and  upon  the  care  and  skill  of 
the  operator.  The  results  of  the  third  method  are  subject  to  numerous 
sources  of  variation  and  error,  and  may  be  taken  as  approximately  true 
oulv  for  the  particular  conditions  under  which  the  test  is  made.  Analysis 
ana  calorlmetry  giro  with  considerable  accuracy  the  heating  value  which 
may  be  obtained  under  the  conditions  of  perfect  combustion  and  complete 
abftorptlon  of  the  heat  produced.  A  boiler  test  gives  the  actual  result  under 
conditions  of  more  or  fees  imperfect  combustion,  and  of  numerous  and  va- 
riable wastes.  It  mar  give  the  highest  practical  heating  value,  if  the  condi- 
tions of  grate-bars,  draft,  extent  of  heating  surface,  method  of  firing,  etc.. 
are  tbe  best  possible  for  the  particular  coal  tested,  and  it  may  give  results 
far  beneftth  tbe  highest  if  these  conditions  are  adverse  or  uusuitable  to  the 
coal. 

The  resnlts  of  bofler  testa  being  so  extremely  variable,  their  use  for  the 
purpose  of  determining  the  relative  steaming  values  of  different  coals  has 
frequently  led  to  false  conclusions.  A  notable  instance  is  found  in  the 
record  of  Prof.  Johnson's  tests,  made  in  1844,  the  only  extensive  series  of 
tests  of  American  coals  ever  made.  He  reported  the  steaminar  value  of  the 
Lehigh  Goal  &  Navigation  Co.*s  coal  to  be  far  the  lowest  of  ail  the  anthra- 
cites, a  result  which  is  easily  explained  by  an  examination  of  the  conditions 
under  which  he  made  the  test,  which  were  entirely  unsuited  to  that  ooaL 
He  also  reported  a  result  for  Pittsburgh  coal  which  is  tar  beneath  that  now 
obfAiiiable  in  every-day  practice,  his  low  result  being  chiefly  due  to  the  use 
of  an  improper  furnace. 

Tn  a  paper  entitled  Proposed  Apparatus  for  Determining  the  Heating 
Power  of  Different  Coals  (Trans.  A.  I.  M.  E.,  xiv.  787)  the  author  described 
and  illustrated  an  apparatus  designed  to  test  fuel  on  a  large  scale,  avoiding 
the  errors  of  a  steam-boiler  test.  It  consists  of  a  fire-brick  furnace  enciosed 
in  a  water  casing,  and  two  cylindrical  shells  containing  a  great  number  of 
tubes,  which  are  surrounded  by  cooling  water  and  through  which  the  gases 
•f  combustion  pass  while  being  cooled.  No  steam  is  generated  in  the  ap- 
paratus, but  water  is  passed  through  it  and  allowed  to  escape  at  a  tempera- 
lure  below  200*  F.  The  product  of  the  weight  of  the  water  passed  through 
the  apparatus  bv  its  increase  in  temperature  is  the  measure  of  the  heating 
▼alue  of  tlie  fuel. 

There  has  been  much  difference  of  opinion  concerning  the  value  of  cheml- 
ieal  analysis  as  a  means  of  approximating  the  heating  power  of  coal.  It 
was  found  by  Scheurer-Kestner  and  Meunler-Dollfus,  in  their  extensive  series 
of  tests,  made  in  Europe  in  1868,  that  the  heating  power  as  determined  bv 
calorimetric  tests  was  greater  than  that  given  to  chemical  analysis  aocord- 
lug  to  Dillon g*s  law. 

Recent  tests  made  in  Paris  bv  M.  Hahler,  however,  show  a  much  closer 
agreement  of  analysis  and  calorimetric  tests.  A  brief  description  of  these 
tests,  translated  from  the  French,  may  be  found  in  an  article  by  the  authoi 
In  The  MineraX  Industry,  vol.  i.  page  97. 

Dttlong's  law  may  be  expressed  by  the  formula, 

Heating  Power  in  British  Thermal  UniU  s  14,600C  +  62,500  (h  -  !g-),* 

in  which  C,  H,  and  O  are  respectively  the  percentage  of  carbon,  hydrogen, 
and  oxygen,  each  divided  by  100.  A  study  of  M.  Mahler*s  calorimetric  tests 
shows  that  the  maximum  difference  between  the  results  of  these  tests  and 
the  calculated  heating  power  by  Dulong*s  law  in  any  single  case  is  only  a 
little  over  Zifi,  and  the  results  of  81  tests  show  that  Dulong's  formula  gives  an 
average  of  only  47  thermal  units  less  than  the  calorimetric  tests,  the 
average  total  heating  value  being  over  14,000  thermal  units,  a  difference  of 
less  than  4/10  of  IX. 

*  Kahler  gives  Dulong^s  formula  with*Berthelot*s  figure  for  the  heating 
value  of  carbon,  in  British  thermal  units, 

Heating  Power  »  14,650C  +  68,025  (h  -  ^"^j^^  ^  ^). 


634 


9UBL. 


Mahler*8  ctlortnMtrlc  &pparutU8  eonslflttf  of  A  mtrong  ttMl  Teesd  or 
"  bomb**  fmmensed  in  water,  proper  precaution  being  taken  to  prevent  radi- 
ation. One  (^ram  of  the  ooal  to  be  tened  is  placed  in  a  platinum  boat  wtrhin 
this  bomb,  oxygen  gas  is  introduced  under  a  pressure  of  :iO  to  85  atmospheres, 
and  the  coal  ignited  explosively  by  an  electric  spark.  Combustion  Is  com- 
plete and  instantaneous,  the  beat  is  radiated  into  the  surrounding  water, 
weighing  2900  grams«  ana  Its  quantity  Is  determined  by  the  rise  in  tempera- 
tttre  of  tills  water,  due  corrections  being  made  for  the  heat  capacity  or  the 
apparatus  itself.  The  accuracy  of  the  apparatus  is  remarkable,  duplicate 
teste  giving  results  varying  only  about  2  parts  In  1000. 

The  close  agrc ^  -*--^-  ^— .._  -^  .-i._.„^.^,_ 

coDdttoted,  and  < 


The  cloee  agreement  or  the  results  of  calorimetric  tests  when  properly 
iODdttoted,  and  of  the  heating  power  calculated  from  chemical  aDaiysis,  in- 
dicates that  either  the  oliemical  or  the  calorimetric  method  may  be  ac- 


cepted as  correct  enough  for  all  practical  purposes  for  determining  the  total 
heating  power  of  coal.  The  results  obtained  by  either  method  may  be 
taken  as  a  standard  by  which  the  results  of  a  boiler  test  ai-e  to  be  com- 
pared, and  the  difference  between  the  total  heating  power,  and  the  result  of 
the  boiler  test  Is  a  measure  of  the  inefficiency  of  tne  boiler  under  the  con- 
ditions of  any  particular  test. 

In  practice  with  good  anthracite  coal,  in  a  steam-boiler  property  propor- 
tloned.  and  with  all  conditions  favorable.  It  is  possible  to  obtain  in  the 
steam  W  of  the  total  beat  of  combustion  or  the  coal.  This  result  was  nearly 
obtained  in  the  teste  at  the  Oentennlal  Exhibition  In  1876.  In  five  different 
boilers.  An  efficiency  of  70j(  to  70j(  may  easily  be  obtained  in  regular  prac- 
tice. With  bituminous  coals  It  Is  difficult  to  obtain  as  close  an  approach  to 
the  theoretical  maximum  of  economy,  for  the  reason  that  some  of  the  vola' 
tile  combustible  portion  of  the  coal  escapes  unbumed,  the  difficulty  Increas- 
ing rapidly  as  the  content  of  volatile  matter  increases  beyond  20f.  With 
most  coals  of  the  Western  States  It  is  with  difficulty  that  as  much  as  90%  or 
W  of  the  theoretical  efficiency  can  be  obtained  without  the  use  of  gas-pro- 
ducers. 

The  chemical  analysis  heretofore  referred  to  Is  the  ultimate  analysis,  or 
the  percentage  of  carbon,  hydrogen,  and  oxygen  of  the  dry  coaL  It  Is  found, 
however,  from  a  study  or  nahler's  tests  that  the  proximate  analysis,  which 
gives  fixed  carbon,  volatile  matter,  moisture,  anti  asht  may  be  rellea  on  as 
giving  a  measure  of  the  heating  value  with  a  limit  of  error  of  only  about  ^ 
After  deducting  the  moisture  and  ash,  and  calculating  the  fixed  carbon  as  a 
percentage  of  the  coal  dry;and  free  from  ash,  the  author  has  constructed  the 
following  table : 

APPROXtltATB  HbATING  VALUB  OF  OOALB. 


Percentage 

Heating 

Equiv.  Watei 
Kvap.  from 

Percentage 

Heating 

Equlv.  Water 
Kvap.  from 

F.  0.  in 

Value 

F.  0.  In 

Value 

CJoalDiy 

B.T.U. 

and  at  Sia* 

Ooal  Dry 

B.T.U. 

and  at  8i8* 

and  Free 
from  Ash. 

per  lb. 
CombUe. 

per  lb. 
Oombustible. 

and  Free 
from  Ash. 

per  lb. 
ObmbMe. 

per  lb. 
Oombustlblei 

100 

14900 

15.00 

68 

15480 

16.08 

97 

i4reo 

16.88 

68 

16180 

15.66 

04 

15130 

16.65 

60 

14580 

16.00 

90 

15480 

16.03 

67 

14040 

14.68 

87 

15660 

16.81 

64 

18380 

18.70 

80 

15840 

16.40 

51 

12600 

13.04 

« 

10600 

16.81 

60 

18940 

18.67 

Below  503(  the  law  of  decrease  of  heating-power  shown  in  the  table  appar> 
eutly  does  not  hold,  aa  some  cannel  coals  and  lignites  show  much  higher 
heating-power  than  would  be  predicted  from  their  chemical  constitution. 

The  use  of  this  table  may  be  shown  as  follows: 

Given  a  coal  oontaiuing  moisture  8^.  ash  Bf,  fixed  carbon  6ljr,  and  volatile 
matter  99%.  what  Is  its  probable  heating  value  f  Deducting  moisture  and 
ash  we  And  the  flxed  earbon  is  61/90  or  eB%  of  the  total  of  fixed  carbon  and 
volatile  matter.  Oue  pound  of  the  coal  dry  and  free  from  ash  would,  by  the 
table,  have  a  heating  value  of  15,480  thermal  units,  but  as  the  ash  and  moist« 
ure.  having  no  heating  value,  are  10^  of  the  total  weight  of  the  coal,  the 
coal  would  have  90^  of  the  table  value,  or  18,938  thermal  units.  This  divided 
by  966.  tlu^  lnt«*nr  heat  of  steam  at  2X2^  gives  an  equivalent  evaporation  per 
lb.  of  coal  of  11.4'J  lbs. 


RELATIVE  VALUE  OF  STEAM  COALS.  635 

Th«  heating  value  that  can  be  ohtainWl  In  practice  from  thin  coal  would 
depend  upon  the  efflclency  of  the  boiler,  and  this  largely  upon  the  difflculty 
of  ihorouKhly  burning  its  volatile  combustible  matter  in  the  boiler  furnace. 
If  a  boiler  efnciency  of  65)(  could  be  obtained,  then  the  evaporation  per  lb.  of 
coal  from  and  at  81 2»  would  be  14.4d  X  .85  =  9.87  lbs. 

With  the  best  anthracite  coal,  in  which  the  combustible  portion  is,  say,  Vi% 
fixed  carbon  and  3)(  volatile  matter,  the  highest  result  that  can  be  expected 
in  a  boiler-test  with  all  conditions  favorable  is  V2M  lbs.  of  water  evaporated 
from  and  at  <12<*  per  lb.  of  combustible,  which  is  80^  of  15.28  lbs.  the  theo- 
retical heating -power.  With  the  best  seini-bltuminous  coals,  such  as  Cum- 
berland and  Pocahontas,  in  which  the  fixed  carbon  is  80^  of  the  total  com* 
hnstible,  U  5  lbs.,  or  76%  of  the  theoretical  16.4  lbs.,  may  be  obtained.  For 
Piitsburgh  coal,  with  a  fixed  carbon  ratio  of  €8%.  11  lbs.,  or  69%  of  the  theo- 
rftical  16.03  lbs.,  is  about  the  best  practically  obtainable  with  the  beat  boilers 
With  some  good  Ohio  coals,  with  a  fixed  carbon  ratio  of  60^,  10  lbs.,  or  W% 
of  the  theoretical  15.09  lbs.,  has  been  obtained,  under  favorable  conditions, 
with  a  fire-brick  arch  over  the  furnace.  With  coals  mined  west  of  Ohio, 
with  lower  carbon  ratios,  the  boiler  efficiency  is  not  apt  to  be  as  high  as  60%. 

From  these  figures  a  table  of  probable  maximum  boiler-test  results  from 
coals  of  different  fixed  carbon  ratios  may  be  constructed  as  follows: 

Fixed  carbon  ratio 97  80  68  60  54  50 

Evap.  from  and  at  212^  per  lb.  combustible,  maximum  in  boiler- tests: 

12.8       12.5        11  10  8.8         7.0 

Boiler  efficiency,  per  cent 80  76  69  66^       60  55 

Loss,  chimney,  radiation,  Imperfect  combustion,  etc  t 

20  24  81  84  40  45 

The  difference  between  the  loss  of  20jt  with  anthracite  and  the  greater 
]oss<>8  with  the  other  coals  is  chiefly  due  to  imperfect  combustion  of  the 
bituminous  coals,  the  more  highly  volatile  coals  sending  up  the  chimney  the 
greater  quantity  of  smoke  and  un burned  hydrocarbon  gases.  It  is  a  mea8in*e 
of  the  inefficiency  of  the  boiler  furnace  and  of  the  inefficiency  of  heating- 
surface  caused  by  the  deposition  of  soot,  the  latter  being  primarily  caused 
by  the  Imperfection  of  tlie  ordinary  furnace  and  its  unsuitability  to  the 
proper  burning  of  bituminous  coal.  If  In  a  boiler-test  with  an  ordinary  fur- 
nace lower  results  are  obtained  than  those  in  the  above  table,  it  is  an  indica- 
tion of  unfavorable  conditions,  such  as  bad  firing,  wrong  proportions  of 
boiler,  defective  draft,  and  the  like,  which  are  remediable.  Higher  results 
can  be  expected  only  with  gas-producers,  or  other  styles  of  furnace  espe- 
cially designed  for  smokeless  combustion. 

Kind  of  Fumaee  Adapted  for  IMflldreiit  Coals.  (Fi-om  the 
author's  paper  on  "The  Evaporative  Power  of  Bituminous  Coals,''  Trans. 
A.  &  M.  m..  iv,  257.)— Almost  any  kind  of  a  furnace  will  be  found  well 
adapted  to  burning  anthracite  coals  and  semi-bituminous  coals  containing 
less  than  ^20%  of  volatile  matter.  Probably  the  best  furnace  for  burning 
those  coals  which  contain  between  20%  and  40%  volatile  matter,  including  the 
&*otch,  English,  Welsh,  Nova  Scotia,  and  the  Pittsburgh  and  Monongahela 
river  coals,  is  a  plain  grate-bar  furnace  with  a  fire-brick  aixsh  thrown  over 
it,  for  the  purpose  of  keeping  the  combustion-chamber  thoroughly  hot.  The 
best  furnace  for  coals  contaming  over  40)(  volatile  matter  will  be  a  furnace - 
surrounded  by  fire-brick  with  a  Taree  combustion -chamber,  and  some  spe- 
cial appliance  for  introducing  very  not  air  to  the  giu^es  distilled  from  the 
coal.  or.  preferably,  a  separate  gas-producer  and  combustion-chamber,  with 
facilities  for  heating  both  air  and  gas  before  they  unite  in  the  combustion- 
clianiber.  The  character  of  furnace  to  be  especially  avoid  d  In  burning  all 
bituminous  coals  containing  over  20<  of  volatile  matter  is  the  ordinary  fur- 
nace, in  which  the  boiler  is  set  directly  above  the  grate  bars,  and  in  which  the 
hearing-surfaces  of  the  boiler  are  directly  exposed  to  radiation  from  the 
coal  on  the  grate.  The  question  of  admitting  air  above  the  grate  is  still  un- 
settled. The  London  Etiifineer  recently  said:  **  All  our  experience,  extending 
over  many  years,  goes  to  show  that  when  the  production  of  smoke  is  pre- 
vented by  special  devices  for  admitting  air,  either  there  Is  an  increase  in  the 
coni«umptlon  of  fuel  or  a  diminution  In  the  production  of  steam.  *  *  *  The 
best  smoke-preventer  yet  deviated  is  a  good  fireman.** 

]K>^iniPrard*d]*anght  Fnrnaeea*— Recent  experiments  show  that 
with  bituminous  coal  considerable  saving  may  be  made  by  causing  the 
draught  to  go  downwards  from  the  fretuhly-flred  coal  through  the  hot  coal 
on  the/rrate.  Similar  good  results  are  also  obtained  by  the  upward  draught 
hv  feeding  the  fresh  coal  under  the  bed  of  hot  coal  Instead  of  on  top.  (See 
B'lilera.) 


63G 


FUEL. 


Calorlmetrle  Tests  of  Amerlemn  Coals,— From  a  number  of 
tests  of  American  and  foreini  coals,  made  with  an  oxvgen  calorimeter,  by 
Qeo.  H.  Barms  (Trans.  A.  8.  M.  E.,  vol.  ziv.  816),  the  following  are  selected, 
showing  the  range  of  variation: 


Percentage 
of  Ash. 


Semubituminotu, 
George's  Or'k,  CumberlM,  Md.,10  tests 

Pocahontas,  Va.,  6  tests 

New  Riyer,  Va.,  6  tests. 

Elk  Garden,  Va^  1  test 

Wel8h,lteBt 

Bituminous. 

Youghiogheny,  Fa.,  lump 

**  **    slack 

FroDtenac,  Kansas 

Cape  Breton,  (Caledonia) 

Lancashire,  Ei^ 

Anthracite,  11  t^Bta 


Total  Heat 
of  Com- 
bustioD. 
B.  T.  U. 


6.1 
8.6 
8.2 
6.2 
3.S 
6.7 
7.8 
7.7 

6.0 
10.2 
17.7 

8.7 

6.8 
10.5 

9.1 


Total  Heat 
reduced  to 
Fuel  free 
from  Ash. 


14,217 

12,874 
14,606 
18,608 
18,922 
18,858 
18,180 
18,561 

12,941 
11,664 
10,506 
12,420 
12,122 
11,521 
18,189 


15,141 
14.065 
I5,0M 
14,507 
14,427 
14.606 
14,296 
14,714 

1S.7S2 
12,968 
12,765 
18.602 
18.006 
]2,9rS 
14.500 


BTapomilTe  Power  of  Bltamlnoiia  Coals, 

(Tests  with  Babcock  &  Wilcox  Boilers.  Trans.  A.  8.  M.  E.,  Ir.  267.) 


d 

i 

ST 

78 

14 

14 

is; 

11 

81 

i 

•pi 

1 

Name  of  Coal. 

Dura- 
tion  of 
Test. 

? 

U 

^ 

f 

s    - 

II 

S,ts 

n 

> 
S. 

& 

1 

I 

itf^hrs 

1 

O 
40 

1 

1679 

7.5 

11 

2»i 

1* 

1 

146 

1 

I.Welsh 

6.8 

2.07 

11.58 

12.46 

98 

2.  Anthracitescr'Bl/5 

1 

Powelton,  Pa., 

tlO^h 

GO 

8126 

8.8  17. « 

4.82 

11.82 

12.42 

272 

448 

Seml-bit,  4/5, 

1 

8.  Pittsbg'h  fine  slack 

4hr8 

88.7 

1679 

12.8  21.9 

4.47 

8.12 

9.29 

146 

250 

**    8d  Pool  lump 

10   '* 

48.5 

2760 

4.8,27.5 

4.76 

10.47 

ll.OO 

240 

410 

4.  (Castle  Shannon,  nr 

) 

Pittsb'gh,  %  nut, 

>42>4h 

69.1 

4784 

10.5.27.9 

4.18 

10.00 

11.17 

416 

570 

9^  lump, 
{i.  in,  *'  run  of  mine  " 

S 

6  days. 

1196 

.... 

1.41 

9.49 

104 

54 

**  Ind.  block,  "  very 
6.  Jackson,  O..  nut .. 

[Sd'ys 
8hr8. 

.... 

1196 

a... 

2.95 

9.47 

104 

111 

48 

8358 

9.6*32.1 

4.11 

8.08 

9.86 

202 

460 

'*  Staunton,  III,  nut.. 

8    " 

60 

8858 

17.7|26.1 

2.27 

6.09 

6.19 

202 

246 

7.  Ronton  screenings. 

5h60m 

21.2 

\W4 

IS.881.5 

2.95 

6.88 

7.98 

186 

151 

"  Wellington  scr*g8.. 
"  Black  Diani.  scrags 

6h80m 

21. '.i 

1561 

18  8  27 

2.98 

7.89 

0.66 

138 

150 

5h58m 

21.2 

1564 

19.836.4 

8.11 

6.20 

7.80 

186 

160 

**  Seattle  screenings. 

6  h  24  in 

21. -J 

1564 

18.4  31 .3 

2.91 

6.86 

7.92 

136 

150 

**  Wellington  lump.. 
**  Cardiflflump 

6h]9m 

21 .2 

1.564 

13.8  28.2 

3.52 

9.02 

10.46 

186 

171 

6  h  47  ni 

21.2 

1.564 

11.7  26.7 

8.69 

10.07 

11.40 

186 

189 

«k              14               »i     *^ 

7  h  28  ni 

21.2 

1564 

19.1,25.6 

3.35 

9.62 

11.88 

186 

174 

•*  South  Paine  lump. 

6  h  35  in 

21.2 

15(i4 

13.928.9 

3.53 

8.06 

10.41 

136 

182 

**  Seattle  lump  . . 

6h    5in 

'421.2115641  9.5  84.1 

3.57 

7.68 

8.41^ 

186 

184 

COEB. 


637 


Place  of  Test:  1.  London,  England ;  2.  Peacedale,  R  I.;  8.  Cfncfniiati,  O.; 

4.  PittsburKb,  Pa.;  5.  Chicago,  111.;  6.  Springfield,  O.;  7.  San  Francisco, 

Cat. 

In  ail  the  above  teste  the  furnace  was  supplied  with  a  fire-brick  arch  for 
preveiitiiifif  the  radiation  of  heat  from  the  coal  directly  to  the  boiler. 

Hreatherlns  of  Coal.  (I.  P.  Kimball,  Trans.  A.  I.  M.  E.,  viii.  904.)- 
Tht*  praciieal  effect  of  the  weathering  of  coal,  while  sometimes  increasing 
its  absolute  weight,  is  to  diminisli  the  quantity  of  carbon  and  dinposable 
hydrogen  and  to  increase  the  quantity  of  oxygen  and  of  indisposaoie  hy- 
drogen.    Hence  a  reduction  in  the  calorific  value. 

An  excess  of  pyrites  in  coal  tends  to  produce  rapid  oxidation  and  mechan- 
ical diaint<*gration  of  the  mass,  with  development  of  heat,  loss  of  coking 
power,  and  spontaneous  ignition. 

The  only  appreciable  rejults  of  the  weathering  of  anthracite  within  the 
ordinary  limits  of  exposure  of  stocked  coal  are  conHned  to  the  oxidation  of 
its  accest«oi7  pyrites.  In  coking  coals,  however,  weathering  reduces  and 
finally  destroys  the  coking  power,  while  the  pyrites  are  converted  from  the 
state  of  bisulphide  into  comparatively  innocuous  sulphates. 

RIchters  found  that  at  a  temperature  of  158^  to  180«  Fahr.,  three  coals  lost 
in  fourteen  days  an  average  of  ^,6ji  of  calorific  power.  (See  also  paper  by 
B.  P.  Rothwelt  Trans.  A.  1.  M.  E.,  iv.  66.) 

COKB. 

Coke  is  the  solid  material  left  after  evaporating  the  volatile  ingredients  of 
coal,  either  by  means  of  partial  combustion  in  nirnaces  called  coke  ovt- ns, 
or  by  distillation  in  the  retorts  of  gas-works. 

Coke  made  in  ovens  is  preferred  to  gas  coke  as  fuel.  It  is  of  a  dark-gray 
color,  with  slightly  metallic  lustre,  porous,  brittle,  and  hard. 

llie  proportion  of  coke  yielded  by  a  given  weight  of  coal  is  very  different 
for  different  kinds  of  coal,  ranging  from  0.9  to  0.^. 

Being  of  a  porous  texture,  it  readily  attracts  and  retains  water  from  the 
atmosphere,  and  sometimes,  if  it  is  kept  without  proper  shelter,  from  0.15  to 
V.20  or  its  gross  weight  consists  of  moisture. 

Analyses  of  Coke. 

(From  report  of  John  R.  Procter.  Kentucky  Geological  Survey.) 


Where  Made. 

Fixed 
Carbon 

Ash. 

Sul- 
phur. 

Connellsville,  Pa.      (Average  of  8  samples) 

Chattanooga,  Tenn.         "        **  4        *•       

Birmingham,  Ala.             »*        "4        "       

Pocahontas,  Va.               "        "8        "       

New  River,  W.  Va.           "        "8        "         

Bijf  Stone  Gap,  Ky.          "        "7        **        

88.96 
80.61 
87.89 
92.98 
92.88 
93.28 

9.74 
16.34 
10.54 
6.74 
7.21 
6.69 

0.810 
1.595 
1.195 
0.597 
0.562 
0.749 

Experiments  In  Coklnfir.    Conkkllsville  Region. 
(John  Fulton,  Anier.  Mfr.,  Feb.  10,  1898.) 


1 

u 

4 

1 

If 

ft 

Per  cent  of  Yield. 

4^ 

6 

55 

1 

II 

|l 

3| 
4" 

1 
2 
8 

4 

h.  m. 

67  00 

68  00 
45    00 
45    00 

lb. 
12,420 
11,090 
9,120 
9,020 

lb. 
99 
90 

77 
74 

lb. 
385 
359 
272 
849 

lb. 
7,518 
6,580 
6,418 
6,834 

lb. 
7,908 
6,039 
5.690 
5,683 

00.80 
00.81 
00.84 
00.82 

8  10 
3.24 
2.98 
3  87 

60.53 
59.33 
59.41 
59.18 

68.63 
62.57 
62.39 
68.00 

86.57 
36.62 
86  77 
36.18 

41, e.^) 

840 

1365 

24,860 

26,215 

00.82 

8.28 

59.66 

62.94 

86.24 

These  results  show,  in  a  general  average,  that  Connellsville  coal  carefully 
coked  in  a  modern  beehive  oven  will  yield  Gfi.17%  of  marketable  coke,  2,3(^ 
of  small  coke  or  braize,  and  0.82je  of  ash. 


638  FUEL. 

The  total  average  loss  in  volatile  matter  expelled  from  the  coal  in  coking 
amountB  to  SO.Tlji.  ,     »*..-.        *  j^#«.  ui-.u  -* 

The  modern  beehive  coke  oven  is  18  feet  In  diameter  and  7  feet  high  at 
crown  of  dome.    It  is  used  In  making  48  and  72  hour  coke.  .  ,  *     .. 

In  making  these  testa  ihe  coal  was  weighed  as  it  was  charged  into  the 
oven;  the  lesultant  marketable  coke,  small  coke  or  braise  and  asUes 
weighed  dry  a*  they  w?re  drawn  from  the  oven.  ^ .  ^  .        ,        , 

Coal  Waaliliiar.— In  making  coke  from  coals  that  are  high  In  ash  and 
BulDhur,  it  U  advisable  to  crush  and  wash  the  coal  before  coking  it.  A  eoai- 
washiiig  plant  at  Brookwood,  Ala,,  has  a  capacity  of  60  tons  ffer  hour.  The 
average  percentage  of  ash  in  the  coal  during  ten  days'  run  varied  from  14^  ip 
21%,  in  the  washed  coal  from  4  W  to  SA%.  and  in  the  coke  from  fl.l^o  10.5^ 
During  three  months  the  average  reduction  of  ash  was  60.9%.  {JSng,  ana 
MiniuQ  Jour.,  March  i"5.  1893.)  _       ^    ^  ,     ^ 

Recovery  of  By-prodaet«  ta  Coke  IWannlketnr©.— In  Ger- 
many considerable  progress  has  been  made  in  the  recovery  of  by  products. 
The  Koflfman-Otto  oven  has  been  most  largely  used.  Its  principal  feature 
being  that  it  is  connected  with  regenerators.  In  1884  40  ovcts  on  this 
S5'8tem  were  running,  and  In  1892  the  number  had  Increased  to  1S09. 

A  Hoffman-Otto  oven  in  Westphalia  takes  a  charge  of  6^  tons  of  dry  coal 
and  converts  it  into  coke  in  48  hom-s.  The  product  of  an  oven  annually  is 
1025  tons  in  the  Ruhr  district,  1170  tons  in  Silesia,  and  960  tons  in  the  baar  dis- 
trict The  yield  from  dry  coal  Is  76j<  to  77j<  of  coke.  'Z.h%  to  SjC  of  tar,  and  1 . \% 
to  1  i»  of  sulphate  of  ammonia  in  the.Ruhr  district;  65jt  to  70%  of  coke.  4%  to 
4  5<'of  tar,  and  \%  to  1.2.J%of  sulphate  of  ammonia  In  the  Upper  Silesia  region 
and  68<  to  TH  of  coke.  A%  to  4.3%  of  tar  and  1.8%  10  1 .9%  of  sulpliale  of  ammonia 
in  the  Saar  district.    A  group  of  60  Hoffman  oveus,  therefore,  yields  annually 

''''''"'"*"^^  Coke  Tar  Sulphate 

District.  ^5S:  toS.       ^XTs"'*' 

Ruhr     61>«»  I860  780 

UooerSilesIa    48,000  8000  840 

^persuesia............ ..........  ^^.^  ^^  ^^ 

An  oven'  which  "has  been  introduced  lately  Into  Germany  in  connection 
with  the  recovery  of  by-products  is  the  Semet-Solvay,  which  works  hotter 
than  the  Hoffman-Otto,  and  for  this  reason  7a%  to  77%  of  gas  coal  can  be 
mixed  with  28%  to  «7j(  of  coal  low  in  volatile  matter,  and  yet  yield  a  good 
coke.  Mixtures  of  this  kind  yield  a  larger  percentage  "' coif «»  ^uf ,  on  the 
otiier  hand,  the  amount  of  gas  is  lessened,  and  therefore  the  yield  of  tar  and 
ammonia  is  not  so  great. 

The  yield  of  coke  by  the  beehive  and  the  retort  ovens  respectively  Is 
given  as  follows  in  a  pamphlet  of  the  Solvay  Process  Co.:  ConnellsvlUe 
coal  !  beehive,  66%.  retort.  73%:  Pocahontas:  beehive.  62%.  retort,  83%  ;  Ala- 
bama :  beehive,  60%,  retort,  74%.  (See  article  in  Mineral  IndusUy,  vol.  vili., 
1900.) 

References:  F.  W.  Luerman,  Verein  Deutscher  Eisenhuettenleute  1891, 
Iron  Age,  March  31, 1892  ;  Amer.  Mfr.,  April  88,  1898.  An  excellent  series 
of  artiiiles  on  the  manufacture  of  coke,  by  John  Fulion,  of  Johnstown,  Pa., 
is  published  in  fhe  (Collier tt  Engineer,  beginning  In  January,  1S93. 

Mafclns:  Hard  Coke.— J.  J.  Fronheiser  and  C.  S  Price,  of  the  Cam- 
bria Iron  Co.,  .lohnsiown.  Pa.,  have  made  an  improvement  in  coke  manu- 
facture by  vvhicli  coke  of  any  degree  of  hardness  may  be  turned  out.  It  is 
accomplished  by  flint  grinding  the  coal  to  a  Cf>arse  powder  and  mixing  It 
with  a  hj'drate  of  lime  (air  or  water  slacked  caustic  lime)  before  it  Is 
charged  into  the  coke-ovens.  The  caustic  lime  or  other  fluxing  material 
used  is  mechanically  combined  with  the  coke,  flUIng  up  its  cell  walls.  It  has 
been  found  that  about  5%  by  weight  of  caustic  lime  mixed  with  the  fine  coal 
gives  the  best  results.  However,  a  larger  quantity  of  lime  can  be  added  lo 
comIs  C'tniaiiilnsf  mom  than  5,t  to  7%  of  ash.    (Amer.  Mfr.) 

Generation  of  Steam  f^on&  tlte  l¥aste  Seat  and  Gases  ot 
Coke-ovens.  (Krskme  Kanisey,  Amer.  M/r.,  Feb.  Itt,  1894  >— 1  he  ga^es 
from  a  numl>er  of  adjoining  ovens  of  the  beehive  type  are  led  into  a  long 
horizontal  flue,  and  thence  to  a  combustion  chamber  under  a  battery  of 
boilers.  Two  plants  are  in  satisfactory  operation  at  Tracy  City,  Tenn.,  and 
two  at  Pratt  Mines.  Ala, 

▲  Busbel  of  Coal.— The  weight  of  a  bushel  of  coal  In  Indiana  is  70  lbs,, 
in  Pennu.  70  lbs.:  in  Ala.,  Colo.,Ga.,  III..  Ohio,  Tenn..  and  W.  Va.  it  is  80  lbs, 

A  Busbel  of  Coke  Is  almost  uniformly  40  lbs.,  but  in  exceptional 


WOOD  AS  FUEL.  639 

cases,  when  the  coke  Is  very  light,  88.  M.  and  S8  Ibe.  are  regarded  as  a  bushel. 
In  others,  from  48  to  90  Ihs  are  given  as  tite  weight  of  a  bushel ;  in  this  case 
the  colce  would  be  uuite  heavy. 

ProdaeU  oftJbe  JHattllatlon  of  €oal.-~S.  P.  Sadler's  Handbook 
of  lodustriiil  Organic  Cheinisiry  gives  a  diagmm  showing  over  60  chemical 
products  that  are  derived  from  distillation  of  coal.  The  first  derivatives  are 
coal-gas,  gas-liquor,  coal-tar,  and  coke.  From  the  gas-liquor  are  derived 
ammonia  and  sulphate,  chloride  and  carbonate  of  ammonia.  The  coal-tar 
is  split  up  into  oils  li|f  nter  than  water  or  crude  naphtha,  oils  heavier  than 
water~otherwise  dead  oil  or  tar,  commonlv  called  creosote,— and  pitch. 
From  the  two  former  are  derived  a  variety  of  chemical  products. 

From  the  coal-tar  there  comes  an  almost  endless  chain  of  known  combina- 
tions. The  greatest  industry  based  upon  their  use  Is  the  manufacture  of 
dyes,  and  the  enormous  extent  to  wbica  this  has  zrown  can  be  judged  from 
the  fact  that  there  are  over  GOO  different  coal-tar  colors  in  use,  and  many  more 
which  as  yet  are  too  expensive  for  this  purpose.  Many  medicinal  prepara- 
tions come  from  the  series,  pitch  for  paving  purposes,  and  chemicals  for 
the  photo;:rapher,  the  rubber  manufacturers  and  tanners,  as  well  as  for 
preserving  timber  and  cloths. 

The  composition  of  the  hydrocarbons  In  a  soft  coal  Is  uncertain  and  quite 
complex ;  but  the  ultimate  analysis  of  the  average  coal  shows  that  it  ap- 

E roaches  quite  nearly  to  the  composition  of  CH4  (marah-gas).    (W,  a. 
lauvelt.  Trans.  A.  I.  M.  E.,  xz.  085.) 

mrOOD  AS  F17BI<. 

Wood,  when  newly  felled,  contains  a  proportion  of  moisture  which  varies 
very  much  In  different  kinds  and  in  different  specimens,  ranging  between 
W%  and  50j(,  and  being  on  an  average  about  40ji.  After  8  or  12  months*  ordi- 
nary drying  in  the  air  the  proportion  of  moisture  is  from  20  to  2&%.  This 
det^ree  of  dryness,  or  almost  perfect  dryness  if  required,  can  be  produced 
by  a  few  days*  drying  in  an  oven  supplied  with  air  at  about  240*>  F.  When 
coal  or  coke  is  used  as  the  fuel  for  that  oven.  1  lb.  of  fuel  suflSces  to  expel 
about  8  lbs.  of  moisture  from  the  wood.  This  is  the  result  of  experiments 
on  a  large  scale  by  Mr.  J.  R.  Napier.  If  air  dried  wood  were  used  as 
fuel  for  the  oven,  from  9  to  9^  lbs.  of  wood  would  probably  be  required  to 
produce  the  same  effect. 

The  specific  gravity  of  different  kinds  of  wood  ranges  from  0.8  to  1.3. 

Perfectly  dry  wood  contains  about  BOjt  of  carbon,  the  remainder  consisting 
almost  entirely  of  oxyeen  snd  hydrogen  In  the  proportions  which  form 
water.  The  coniferous  family  contain  a  small  quantity  of  turpentine,  which 
Is  a  hydrocarbon.  The  proportion  of  ash  in  wood  is  from  1^  to  Oi,  The 
total  heat  of  combustion  of  all  kinds  of  wood,  when  dry,  is  almost  ex* 
HCtly  the  same,  and  is  that  due  to  the  50j(  of  carbon. 

The  above  Is  from  Bankine;  but  according  to  the  table  by  S.  P.  Bharpless 
in  Jour.  C.  I.  W.,  iv.  36,  the  ash  varies  from  O.OSjt  to  1.20jC  in  American  woods. . 
and  the  fuel  value,  instead  of  being  the  same  for  all  woods,  ranges  from  ' 
8667  rfor  white  oak)  to  &516  calories  (for  long-leaf  pine)  =  6600  to  0888  British 
thermal  units  for  dry  wood,  the  fuel  value  of  0.60  lbs.  carbon  being  7878 
B.  T.  U. 

Heatlne  Value  of  HFood.— The  following  table  Is  given  In  several 
books  of  reference,  authoi-ity  and  quality  of  coal  referred  to  not  stated. 

The  weight  of  one  cord  of  different  woods  (thoroughly  air-dried)  is  about 
as  follows : 
Hickory  or  hard  nuiple. . . .  4.V)0  lbs.  equal  to  1800  lbs.  coal.  (Others  give  9000.) 

Wliiteoak 8850    "  "      1540    "      ••     (        "  1715.) 

Beech.redandbUckoak..  83»0    ''  '*      1800    '*      '*    (        "  1460.) 

Poplar,  chestnut,  and  elm..  2350    "  "       940    "     »*    (        '•  1050.) 

The  average  pine 2000    "  '•       800    »•      ♦•    (        *  085.) 

Referring  to  the  Ajrures  In  the  last  column,  it  is  said  : 

From  the  above  it  is  safe  to  assume  that  2^  lbs.  of  dry  wood  are  equal  to 
1  lb.  average  quality  of  soft  con  I  and  that  the  full  value  of  the  same  weight 
of  different  woods  is  very  nearly  the  same — that  is,  a  pound  of  hickory  is 
worth  no  more  for  fuel  than  a  pound  of  pine,  assuming  both  to  be  dry.  It 
is  Important  that  the  wood  be  dry,  an  each  10%  of  water  or  moisture  in  wood 
will  detract  about  IQ%  from  \t9  value  as  fuel. 

Taking  an  average  wood  of  the  analysis  061jf,  H  O.SjT,  O  42.0%,  ash  0.6%, 
perfectly  dry,  Its  fuel  value  per  pound,  according  to  Dulong*s  formula.  V  = 


640 


FUBLi 


[l4,500  C  +  03«OOO  (H  -^ )],  is  8170  British  thermal  unite.  If  the  wood,  as 

ordinaHlv  dried  in  air,  contains  2!i%  of  moisture,  then  the  Iieating  value  of  a 
pound  of  such  wood  is  three  quarters  of  8170  =6127  heat-units,  less  the 
neat  required  to  heat  and  evaporate  the  ^  lb.  of  water  from  the  atmospheric 
temperature,  and  to  heat  the  steam  made  from  this  water  to  the  tempera- 
ture of  the  chimney  gases,  sav  150  heat-units  per  pound  to  beat  the  water  to 
2I2<>,  906  units  to  evaporate  it  at  that  teniperature.  and  100  heat-units  to 
raise  the  temperature  of  the  steam  to  490"  F.,  or  1216  in  all  s  S(M  for  ^  lb., 
which  subtracted  from  the  6127,  leaves  6824  heat-units  as  the  net  fuel  value 
of  the  wood  per  pound,  or  about  0.4  that  of  a  pound  of  carbon. 

Composition  of  Wood* 

(Analysis  of  Woods,  by  M.  Eugene  Chevandler.> 


Woods. 

Composition. 

Carbon. 

Hydrogen. 

Oxygen. 

Nitrogen. 

Ash. 

Beech 

49.36j( 

49.64 

50.20 

49.87 

49.96 

6.01  jt 

5.92 

6.20 

6.21 

5.96 

42.69% 

41.16 

41.62 

41.60 

39.56 

0.91^ 

1.29 

1.15 

0.96 

0.96 

l.OCjC 

Oak  

1.97 

Birch 

Poplar 

Willow 

0.81 
1.86 
8.87 

Average 

40.70j( 

6.06^ 

41.8(9 

1.05^ 

1.80JJ 

The  following  table,  prepared  by  M.  VioIettCf  shows  the  proportion  of 
water  expelled  from  wood  at  gradually  Increasing  temperatures: 


Temperature. 

Water  Expeljed  from  100  Parte  of  Wood. 

Oak. 

Ash. 

Elm. 

Walnut. 

257*  Fahr 

15.26 
17.98 
82.13 
85.80 
44.81 

14.78 
16.19 
21.22 
27.51 
88.88 

15. 8i 

17.02 

86.94? 

33.38 

40.56 

15.56 

a02«Fahr 

847"  Fahr 

17.48 
SI. 00 

a9"i*»Fahr 

41.77? 

487"  Fahr 

86.56 

The  wood  operated  upon  had  been  kept  in  store  during  two  years.  When 
wood  which  has  been  strongly  dried  b}'  means  of  artificial  heat  Is  left  ex- 
posed to  the  atmosphere,  it  reabsorbs  about  as  much  water  as  it  contains 
in  iu  air-dHe<l  state. 

.    A  cord  of  loood  =  4  X  4  X  8  =  128  cu.  f  t.    About  56jr  solid  wood  and  14% 
interstitial  spaces.    (Marcus  Bull,  Phila.  1829.    J.  C.  I.  W..  vol.  i.  p.  298.) 

B.  E.  Fernow  gives  the  per  cent  of  solid  wood  in  a  cord  as  determined  offi- 
cially in  Prussia  (J.  C.  I.  W.,  vol.  Hi.  p.  20): 

Timber  cords,  74.07^  =  80  cu.  ft.  per  cord: 

Firewood  cords  (over  6"  diam.),  69.44jt  =  75  cu.  ft.  per  cord; 

*'  Billet "  cords  (over  8"  diam.).  65.55jt  =  60  cu.  ft.  per  cord; 

"  Brush  "  woods  less  than  8''  diam.,  18.5^;  Boote,  87.003t. 

CHARCOAI*. 

Charcoal  is  made  by  evaporating  the  volatile  constituente  of  wood  and 
peat,  either  by  a  partial  combustion  of  a  conical  heap  of  the  material  to  be 
charred,  covered  with  a  layer  of  earth,  or  by  the  combustion  of  a  separate 
portion  of  fuel  in  a  furnace,  in  which  are  placed  retorts  containing  the  ma- 
terial to  be  charged. 

Accordiug  to  Peclet,  100  parte  by  weight  of  wood  when  charred  In  a  heap 
yield  from  17  to  iSi  parts  by  weight  of  charcoal,  and  when  charred  In  a 
retort  from  28  to  80  parts. 

This  has  reference  to  the  ordinary  condition  of  the  wood  used  in  charcoal- 
making,  in  which  2.'>  pans  in  100  consist  of  moisture.  Of  the  remaining  75 
paru  the  carbon  amounts  to  one  half,  or  37i^  of  the  gross  weight  of  the 
wood.  Hence  it  appears  iliat  on  an  average  nearly  half  of  the  carbon  in  tiM 


CHARCOAL. 


641 


wood  is  lost  during  tlie  partial  combustion  in  a  heap,  and  about  one  quarter 
durinf^  the  distillation  In  a  retort. 

To  char  100  parts  by  weight  of  wood  In  a  retort,  12^  parts  of  wood  roust 
be  burned  in  tne  furnace.  HAOce  in  this  process  the  whole  expenditure  of 
wood  to  produce  from  88  to  80  parts  of  charcoal  is  11!^  parts;  so  that  if  the 
weight  of  charcoal  obtained  is  compared  with  the  whole  weight  of  wood 
exp«*nded,  its  amount  is  from  25/%  to  iSf%\  and  the  proportion  lost  is  on  an 
average  llVi  -«•  8TU  =  0.8,  nearly. 

According  to  Peclet,  good  wood  charcoal  contains  about  0.07  of  Its  weight 
of  asli.  The  proportion  of  ash  in  peat  charcoal  is  very  variable,  and  is  es- 
timated on  an  average  at  about  0.18.    (Rankine.) 

Much  information  concerning  charcoal  may  be  found  In  the  Journal  of  the 
Charcoal-Iron  Workers*  Assn.,  vols.  i.  to  vi.  From  this  source  the  following 
notes  have  been  taken: 

Yield  of  Cbarcoal  from  a  Cord  of  "Wood,— From  45  to  60 
bushels  to  the  cord  in  the  kiln,  and  from  80  to  85  iu  the  meiler.  Prof.  Egles- 
ton  in  Trans.  A.  L  M.  E.,  viii.  895,  says  the  yield  from  kilns  in  the  Lake 
Cbamplain  region  is  often  from  50  to  80  bushels  for  hard  wood  and  50  for 
soft  wood;  the  average  is  about  60  bushels. 

The  apparent  yield  per  cord  depends  largely  upon  whether  the  cord  is  a 
full  cord  of  188  cu.  ft.  or  not. 

In  a  four  months'  test  of  a  kiln  at  Goodrich,  Tenn.,  Dr.  H.  M.  Pierce  found 
results  as  follows:  Dimensions  of  kiln— inside  diameter  of  base.  S8  ft.  8  in. ; 
diam.  at  spring  of  arch,  86  ft.  8  in. ;  height  of  walls,  8  ft. ;  rise  of  arch,  5  ft ; 
capacity.  80  cords.  Highest  yield  of  charcoal  per  cord  of  wood  (measured) 
69.27  bushels,  lowest  50.14  busliels,  average  53.65  bushels. 

No.  of  charges  13,  length  of  each  turn  or  period  from  one  charging  to 
another  11  days.    (J.  C.  I.  W.,  vol.  vi.  p.  26.) 

Reaalta  from  IMfTerent  IHetlioda  of  dutrcoal-malLliis. 


Cooling  Methods. 


Character  of  Wood  need 


Ol^istjerna^s   eiperimeDts  Birch  dried  at  280  F, 

"Glided*  "*°'^'  ""^  *'  llAtrdry.av.  goo.!  yel- 1 

Swedish  oyelui.»v.  noulls  ■! '"'Zw.'??^' ""***'  "'" ' 
(  i     anil  pirio 

8vretii<;h     meilers     excep-  ' " 

tIrmAt - „,..... 

American  kilns,  av.  results  (  A  v.  good  yellow  pine 
meilers,  av.  re- ■(     weigh in^  abt.  2&  lbs. 


American 


^"*i  >     and  plrio  f 

H?p"  i  Fir  and  whJtt^  ploe  j 
...J  4  wcKhl,  mixed.  At,  JES- 
UIT**! }     lljs   t'f^rcM.  rt.  \ 

-f 


per  cii.  ft. 


Yield, 

u 

Is 

11 

fyi.i> 

ill 

1^5 

rr.Q 

■itf.B 

63.4 

05.8 

2i.fi 

54.2 

gj.o 

^^.7 

66.7 

70  0 

m  8 

es.o 

«,!? 

H  T 

59.5 

54.7 

1^^ 

22.0 

45.0 

42.9 

17.1 

35  0 

16.7 

15.7 

18.8 

18.8 
IS.S 

18.8 
17  5 

17.6 


Conaamptlon  of  Cbarcoal  In  Blaat-Aimacea  per  Ton  of 
Plf  Iron;  average  consumption  according  to  census  of  1880,  1.14  tons 
charcoal  per  ton  of  pig.  Tlie  consumption  at  the  best  furnaces  Is  much 
below  this  average.  As  low  as  0  853  ton.  is  recorded  of  the  Morgan  furnace; 
Bav  furnace,  0.858;  FJk  Rapids.  0.884.    (1892.) 

Absorption  of  Water  and  of  Gases  by  Cbarcoal^-Svedlius, 
in  his  hand>book  for  charcoal-burners,  prepared  for  the  Swedish  Govern- 
ment, says:  Fresh  charcoal,  also  reheated  charcoal,  contains  scarcely 
any  water  but  when  cooled  it  absorbs  it  very  rapidly,  so  that  after 
twenty-four  hours,  it  mav  contain  4%  to  S%  of  water.  After  the  lapse  of  a 
few  weeks  the  moisture  of  charcoal  may  not  increase  perceptibly,  and  may 
be  estimated  at  lOjC  to  15j(,  or  an  average  of  12%.  A  thoroughly  charred 
piece  of  charcoal  ought,  then,  to  contain  about  84  parts  carbon.  12  parts 
water,  8  parts  ash,  and  1  part  hydrofiren 


642 


FUEL. 


M.  S»u88ure.  openiting  with  blocks  of  fine  boxwood  oharcoal.  freshly 
burnt,  found  that  by  simply  placing  such  blocks  in  contact  with  certain 
gases  they  absorbed  them  in  ttie  following  proportion: 


Volumes. 

Ammonia 90.00 

Hydrochlorio-actd  gas 85.00 

Sulph'urous  acid 6S.O0 


Volumes. 

Carbonic  oxide. 9.42 

Oxygen 9.25 

Nitrogen 6.50 


Sulphuretted  hydrogen    ......  55.00      Carburetted  hydrogen. fi.OO 

'"    (laughing-g  -^      ""^       •*  " 


Nitrous  oxide  (laugfiing-gas). .  40.00 
Carbonic  acid.. 85.00 


Hydrogen. , 


1.75 


It  is  this  enormous  absorptive  power  that  renders  of  so  mu<:h  Talne  a 
comparatively  slight  sprinkling  of  charcoal  over  dead  animal  matter,  as  a 
preventive  of  the  escape  of  odors  arising  from  decomposition. 

In  a  box  or  case  containing  one  cubic  foot  of  charcoal  may  be  stored 
without  mechanical  compreeelon  a  little  over  nine  cubk:  feet  of  oxygen, 
representing  a  mechanical  pressure  of  one  hundred  and  twenty-stz  pounds 
to  the  square  inch.  From  the  store  thus  preserved  the  oxygen  ona  be 
drawn  by  a  small  hand*pump. 

componltlon  of  OliAreomI  Prodaced  at  Tarlons  Tempera* 
turen.    (By  M.  Violette.) 


Temperature  of  Car- 

Composition of  the  Solid  Product 

bonization. 

Carbon. 

Hydro- 
gen. 

Oxygen. 

Nitrogen 
and  Loss. 

Ash. 

Cent,       Fahr. 

Per  cent. 

Per  cent. 

Per  cent. 

Per  cent. 

Per  cent. 

1 

160»         808«» 

47.51 

6.12 

46.29 

0.06 

47.51 

2 

80O          892 

61.82 

8.99 

48.96 

0.28 

89.88 

8 

260          482 

65.59 

4.81 

28.97 

0.68 

82.))8 

4 

800          692 

73.24 

4.25 

21.96 

0.67 

24.61 

5 

890          662 

78.04 

4.14 

18.44 

0.61 

2d. 42 

6 

432           810 

81.64 

4.96 

16.24 

1.61 

16.40 

7 

1023          1873 

81.97 

2.30 

14.15 

1.60 

15.30 

The  wood  experimented  on  was  that  of  black  alder,  or  alder  buckthorn, 
which  furnishes  a  charcoal  suitable  for  gunpowder.  It  was  previously 
driedatl50deg.C.a802deg.  F.  r-  v 

HIS€fiI.LANBOirS  HOl^tB  FCBIiS. 

Bant  Fael-Daet  BiCplonlons.-Du8t  when  mixed  in  air  bums  witii 
such  extreme  rapidity  as  in  some  cases  to  cause  explosions.  Exploeions  of 
flour-mills  have  been  attributed  to  ignition  of  the  dust  in  confined  pas8age< 
Experiments  in  England  in  1876  on  the  effect  of  coal-dust  in  cariying  flame  in 
mines  showed  that  in  a  dusty  passage  the  flame  from  a  blown-out  shot  may 
travel  60  yards.  Prof.  F.  A.  Abel  (Trans.  A.  I.  H.  E  ,  xili.  280)  says  that  coaf- 
dust  in  mines  much  promotes  and  extends  explosions,  and  tnat  it  may  read« 
ily  be  brought  into  operation  as  a  fiercely  burning  agent  which  will  carry 
flame  rapidly  as  far  as  its  mixture  with  air  extends,  and  will  operate  a»  an 
explosive  agent  though  the  medium  of  a  very  small  proportion  of  fire-damp 
in  the  air  of  the  mine.  The  explosive  violence  of  the  combustion  of  dust  is 
largely  due  to  the  instantaneous  heating  and  consequent  expansion  of  the 
air.  (See  also  paper  on  "  Coal  Dust  as  an  Explosive  Agent/*  by  Dr.  R  W. 
Raymond.  Trans.  A..  I.  M.  E.  1894.}  Experiments  made  in  Germany  in  189.'). 
show  that  pulverized  fuel  may  be  burned  without  smoke,  and  with  high 
economy.  The  fuel,  instead  of  being  introduced  into  the  fire-box  in  the 
ordinary  manner,  is  first  reduced  to  a  powder  by  pulverizers  of  any  con- 
struction. In  the  place  of  the  ordinary  boiler  fire-box  there  is  a  combuKtIon 
chamber  in  the  form  of  a  closed  furnace  lined  with  fire-brick  and  provided 
with  an  air-injector  simihir  In  construction  to  those  used  in  oil-burning  fur« 
naces.  The  nozzle  throws  a  con.stant  stream  of  the  fuel  into  the  chamber. 
This  nozzle  is  so  located  that  it  scatters  the  powder  throughout  the  whole 


mSCELLAKEOUS  SOLID  FUEL8.  648 

fp«ce  of  the  fir(>>boz.  When  this  powder  Is  eoce  iRnlted,  and  It  fs  Teiy 
rpadilj  done  by  first  raiaitifir  the  lining^  to  a  high  temperature  by  an  open 
fire,  the  combustion  conthiuee  in  an  intense  and  reirular  manner  und<*r  the 
action  of  the  current  of  air  wliich  carries  it  in.    (MftB.  Record,  April,  ISOS.) 

Pondered  luei  wait  used  in  the  Crompton  rotary  puddling-rurnace  at 
Woolwich  ATBenal,  England,  in  18T8.    (Jour.  I.  &  8, 1.,  i.  1878,  p.  91.) 

Peat  or  Tnrf^  as  nsualiy  dried  in  the  air.  contains  from  25ji  to  80^  of 
water,  which  musi  be  allowed  for  in  estimating  Its  heat  of  combustion.  This 
water  liaring  been  evaporated,  the  analysis  of  M.  Regnault  gives,  in  100 
parts  of  perfectly  dry  peat  of  the  beat  quality:  C  W,  H  6^,  O  31](,  Ash  5%, 

In  same  examples  of  peat  the  quantity  of  ash  is  greater,  amounting  to  7% 
and  sometimes  to  U%. 

The  speciflc  gravity  of  peat  in  its  ordinary  state  is  about  0.4  or  O.B.  It  can 
be  compressed  by  machinery  to  a  much  greater  density.    (Ranklne.) 

Clnrlc  (Steam-engine,  i.  61)  gives  aa  tha  average  oompoaitioii  of  dned  Irish 
peat:  C  W.  B  e%,0  90%,  N  i.25i.  Ash  4%. 

Applying  DuIong'H  formula  to  this  analysis,  we  obtain  for  the  heating  value 
of  perfectly  dry  peat  10,S(iO  heat-units  per  pound,  and  for  air-dried  peat  oou' 
taining  25%  of  moisture,  after  making  allowance  for  evaporating  tne  water, 
7:)!)1  heat-units  per  pound. 

8«ivda0t  as  Pael««-The  heating  power  of  aawdust  is  naturally  the 
same  per  pound  as  that  of  the  wood  from  which  it  is  derived,  but  if  allowed 
to  get  wet  it  is  more  like  spent  tan  (which  see  below).  The  conditions  neces- 
sary for  burning  sawdust  are  that  plenty  of  room  should  be  given  it  In  the 
furnace,  and  sufficient  air  supplied  on  the  surface  of  the  mass.  The  same 
applies  to  shavings,  refuse  lumber,  etc.  Sawdust  is  frequently  bumed  in 
saw-mill^.  etc.,  by  being  blown  into  the  furnace  by  a  fan-blast. 

Horse-manure  has  been  successfully  used  as  fuel  by  the  Cable  Bail* 
way  Co.  of  Chicago.  It  was  mixed  with  soft  coal  and  burned  In  an  ordinary 
umace  provided  witli  «  flre-brick  arch. 

Vfet  Tan  Bark  aa  Fuel.— Tan,  or  oak  bark,  after  having  been  u^ed 
In  the  processes  of  tanning,  is  burned  as  fuel.  The  spent  tan  consists  of  the 
fibrous  portion  of  the  bark.  Axxjording  to  M.  Pedet,  five  parts  of  oak  bark 
produce  four  parts  of  drv  tan;  and  the  beating  power  of  perfectly  dn*  tan, 
«70Dtaining  10^  of  ash,  is  6100  English  units;  whilst  that  of  tan  in  an  ordinary 
mate  of  dryness,  containing  SOjt  of  water,  is  only  4284  English  units.  Tha 
.veight  of  water  evaporated  from  and  at  21S*  by  one  pound  of  tan,  equiva- 
lent to  these  heating  powers,  is,  for  perfectlv  dry  tan,  fi.46  lbs.,  for  tan  with 
80^  moisture.  8.84  lbs.  Experiments  by  Prof.  R.  H.  Thurston  (Jour.  Frank, 
Inst..  1874)  gave  with  the  Crockett  furnace,  the  wet  tan  containing  69%  of 
water,  an  evaporation  from  and  at  21 2«  F.  of  4.34  Iba.  of  water  per  pound 
of  the  wet  tan,  and  with  the  Thompson  furnace  an  evaporation  of  8.19  lbs. 
per  pound  of  wet  tan  containing  &&%  of  water.  The  Thompson  furnace  con- 
sisted of  six  flre-brick  ovens,  each  9  feet  X  4  feet  4  Inches,  containing  284 
auare  feet  ot  grate  in  all,  for  three  boilers  with  a  total  heating  surface  of 
M)  square  feet,  a  ratio  of  heating  to  grate  surface  of  9  to  1.  The  tan  waa 
fed  through  holes  In  the  top.  The  Crockett  furnace  was  an  ordinary  Are* 
brick  furnace,  6x4  feet,  built  in  front  of  the  boiler,  instead  of  under  it,  the 
ratio  of  besting  surface  to  grate  being  14.6  to  1.  According  to  Prof.  Thure- 
tou  the  conditions  of  success  in  burning  wet  fuel  are  the  surrounding  of  the 
rasas  an  completely  with  heated  surfaces  and  with  burning  fuel  that  it  may 
be  rapidly  dried,  and  then  so  arranging  the  apparatus  that  thorough  com- 
bustion may  be  secured,  and  that  the  rapidity  of  combustion  be  precisely 
eauat  to  and  never  exceed  the  rapidity  of  desiccation.  Where  this  rapidity 
of  combustion  is  exceeded  the  dry  portion  is  consumed  completely,  leaving 
an  uncovered  mass  of  fuel  which  refuses  to  take  fire. 

SIraiw  as  Fnel*  (Eng^g  Mechanics,  Feb.,  1898,  p.  U.>— Experiments  in 
Russia  showed  that  winter-wheat  straw,  dried  at  280"  F.,  had  the  following 
coropoKltion;  0,  46.1;  H.  5.6;  N,  0.42;  O,  48.7;  Ash.  4.1.  Heating  value  in 
British  thermal  units:  dry  straw,  6290;  with  H  water,  5770;  with  iO%  water. 
5448.  With  straws  of  other  grains  rhe  heating  value  of  dry  straw  ranged 
from  5590  for  buckwheat  to  6750  for  flax. 

Clark  (S.  E.,  vol.  1,  p.  62)  gives  the  mean  composition  of  wheat  and  barley 
straw  as  C,  86;  H.  5;  O.  88;  O,  0.50;  Ash,  4.75;  water.  15.75,  the  two  straws 
varying  less  than  \%.  The  heating  value  of  straw  of  this  composition,  accord- 
ing to  Dulong^s  formula,  and  deducting  the  heat  lost  in  evaporating  the 
war4»r,  is  5155  heat  units.    Clark  erroneously  giveR  it  as  8144  heat  units. 

Banaae  aa  Fuel  In  Sugar  nannfaetnre.- -Bagasse  is  the  name 
given  To  refuse  sugar-cane,  after  the  luice  has  been  extracted.    Prof.  L.  A. 


641  FUBL. 

Beenel,  In  apaper  read  before  the  LouislaDa  Sugar  Chemlsto*  Asaociation.  In 
1898,  savs:  *^  with  tropical  cane  containtng  \'i.b%  wood/  fibre,  a  juice  coniain- 
tag  16.l9i  solids,  and  88.37^  water,  bagasse  of,  say,  m  and  7^  mill  eactrao- 
Uon  would  have  the  following  percentage  composition: 

Woody  Combustible  w**«r 

Fibre.         Salts.  water. 

OejCbagasse 87  10  68 

7S%bagasse 45  ,9  48 

"Assuming  that  the  woody  fibre  contains  61%  carbon,  the  sugar  and  othf*r 
combustible  matters  an  average  of  42.1%,  and  that  13,906  units  of  heat  are 
generated  for  everv  ponnd  of  carbon  consumed,  the  66^  baciasse  is  capable 
of  generating  ]897,»4  beat  units  as  against  845,200.  or  a  difference  of  47,866 
units  in  favor  of  the  79%  bagasse. 

**  Assuming  the  temperature  of  the  waste  gases  to  be  450^  F.,  that  of  the 
surrounding  atmosphere  and  water  in  the  tiagasse  at  86°  F.,  and  the  quan- 
tity of  air  necessary  for  the  combustion  of  one  poimd  of  carbon  at  24  lbs., 
the  lost  heat  will  be  as  follows:  In  the  waste  gases,  heating  air  from  86*  to 
4fiO*  F.,  and  in  vaporizing  the  moisture,  etc.,  the  W%  bagasse  will  require 
118,546  heat  uniU,  and  116,150  for  the  70%  bagasse. 

*'  Subtracting  these  quantities  from  the  above,  we  find  that  the86)f  bagasse 
will  produce  185,888  available  heat  units,  or  nearly  9S%  less  than  the  7^ 
bagasse,  which  gives  809,050  units.  Accordingly,  one  ton  of  cane  of  8000  lbs. 
at  66j(  mill  extraction  will  produce  680  lbs.  bagasse,  equal  to  185,995,840  avail- 
able heat  units,  while  the  samf*  cane  at  7it%  extraction  will  produce  560  lbs. 


bagasse,  equal  to  167.468,000  units. 
"^A  similar  calculation  for  the  c 


^        Bcaseof  Louisiana  cane  containing  10)(  woody 

fibre,  and  W  total  solids  in  the  Juice,  assuming  76%  mill  extraction,  shows 
that  bagasse  from  one  ton  of  cane  contains  157,896,640  heat  unite,  from 
which  56,146,500  have  to  be  deducted.. 

**  This  would  make  such  bagasse  worth  on  an  average  nearly  08  lbs.  coal 
per  ton  of  cane  ground.  Under  fairly  good  conditions,  1  lb.  coal  will  evsp' 
orate  7H  lbs.  water,  while  the  best  boiler  plants  evaporate  10  lbs.  Therefore, 
the  bogsuiae  from  1  ton  of  cane  at  75^  mill  extraction  should  evaporate  from 
680  Ibfl.  to  919  lbs.  of  water.  The  Juice  extracted  from  such  cane  would  uu' 
der  these  conditions  contain  1860  lbs.  of  water.  If  we  assume  that  the 
water  added  during  the  process  of  manufacture  Is  lOjC  (by  weight)  of  the 
Juice  made,  the  total  water  handled  is  1410  lbs.  From  the  Juice  represented 
In  this  case,  the  commercial  massecuite  would  be  about  15^  of  the  weight  of 
the  original  mill  Juice,  or  say  8tf  lbs.  Said  mill  Juice  1500  lbs.,  plus  lOjC, 
equals  1650 lbs.  liquor  handled;  and  1650  lbs.,  minus  8:25  lbs.,  equals  1485  lbs., 
the  qiiantlty  of  water  to  be  evaporated  during  the  procetm  of  manufacture. 
To  effect  a  7U-lb.  evaporation  requires  100  lbs.  of  coal,  and  148^  lbs.  for  a  1C« 
lb.  evaporation. 

*'  To  reduce  1660  lbs.  of  Juice  to  syrup  of,  say,  87"  Baum6.  requires  the  evap 
oration  of  1770  lbs.  of  water,  leaving  480  lbs.  of  syrup.  If  this  work  be  ac- 
complished in  the  open  air,  it  will  require  about  166  lbs.  of  coal  at  7H  Ihe. 
boiler  evaporation,  and  117  at  10  lbs.  evaporation. 

"  With  a  double  effect  the  fuel  required  would  be  from  50  to  78  lbs.,  and 
with  a  triple  effect,  from  86  to  58  lbs. 

"  To  reduce  tiie  above  480  lbs.  of  syrup  to  the  consistency  of  commercial 
masseculte  means  the  further  evaporation  of  855  lbs.  of  water,  requiring 
the  expenditure  of  84  lbs.  coal  at  7^  lbs.  boiler  evaporation,  and  85^  Iba. 
with  a  10-lb.  evaporation.  Hence,  to  manufacture  one  ton  of  cane  into  sugar 
and  molasses,  it  will  take  from  145  to  100  lbs.  additional  coal  to  do  the  work 
by  the  open  evaporator  process;  from  85  to  118  lbs.  with  a  double  effect,  and 
only  TVilbs.  evaporation  in  the  boilers,  while  with  10  lbs.  boiler  evaporation 
the  bagasse  alone  is  capable  of  furnishing  9%  more  heat  than  is  actually  re- 
quired to  do  the  work.  With  triple-effect  Avaporation  depending  on  the  ex- 
cellence  of  the  boiler  plant,  the  1485  lbs.  of  water  to  be  evaporated  from  the 
luice  will  require  between  68  and  86  lbs.  of  coal.  These  values  show  that 
from  6  to  80  lbs.  of  coal  can  be  spared  from  the  value  of  the  bagasse  to  run 
engines,  grind  cane,  etc. 

'^It  accordingly  appears,"  says  Prof.  Becuel,  "  that  with  the  best  boiler 
plants,  those  taking  up  all  the  available  heat,  generated,  by  using  this  heat 
economically  the  bagasse  can  be  made  to  supply  all  the  fuel  reqtiired  by  out 
sugar- housea.** 


PETROLEUM. 


646 


PBTBOIiBUlH* 
Pvo4aeto  of  the  Distfllatlon  of  0m4e  Petrolenm. 


Crude  American  petroleum  of  sp.  gr.  0.800  may  be 
distillation  as  follows  (Robinson's  Gas  and  Petroleum 

split  up  by  fractional 
Engines): 

Teuijp.  of  ' 

Distillatiou 

Fahr. 

DIstillafe. 

Percent- 
ages. 

Speciao 
Gravity. 

Point. 
Deg.  F. 

llff» 

traces. 

1.6 
10. 
2.5 
8. 

.890to.69S 

.686  to  .667 
.660  to  .700 
.714  to  .718 
.786  to  .787 

113  to  l4d» 
]40tol58« 

Chymogene.  f   

Gasolene  (petroleum  spirit)... 

158toM8« 

a48« 

to 

14 

847* 

1  Polishing  oils.  .* 

838«aDd  1 
upwards,  f 

Kerosene  (lamp-oil) 

60. 

16. 
8. 
16. 

.802to.a«) 
.860  to  .916 

100  to  122 

Lubricating  oU 

Parafflne  wax 

Residue  and  Loss. 

880 



lilma  Petrol  ennii  produced  at  Lima,  Ohio,  is  of  a  dark  green  color, 
Terr  fluid,  and  niarlcs  46^  Bauni6  at  15*  C.  (sp.  gr.,  0.702). 

The  distillation  in  fifty  parts,  each  part  representing  SjC  by  volume,  gave 
the  following  results : 


Per 

8p. 

Per 

i?: 

Per 

Sp. 

Per 

Sp. 

Per 

8p. 

Per 

Sp. 

cent.     Gr. 

cent. 

cent. 

Gr. 

oeot. 

Gr. 

cent. 

Gr. 

cent. 

Gr. 

2       0.680 

18 

O.TUd 

84 

0.764 

50 

0.808 

68 

0.620 

88 

0.815 

4 

688 

80 

.728 

86 

.768 

58 

70 

.825 

90 

.815 

6 

686 

82 

.780 

88 

.778 

to> 

.806 

78 

.830 

S 

8 

690 

24 

.785 

40 

.778 

58 

78 

.880 

92 

10 

694 

86 

.740 

42 

.782 

60 

.800 

76 

.810 

toV 

9 

18 

696 

28 

.748 

44 

.788 

68 

.804 

78 

.820 

100 

1 

14 

700 

SO 

.746 

46 

.798 

64 

.806 

88 

.818 

M 

706 

ae 

.760 

48 

.800 

66 

.818 

86 

.816 

BBTURNS. 

lOper  cent  naphtha,  70*  Baum6.  6  per  cent  parafllne  oiL 

66       "        burning  oil.  10       **        residuum. 

The  distillation  started  at  28*  C,  this  being  due  to  the  large  amount  of 
naphtha  present,  and  when  eOi  was  reached,  at  a  tempeiuture  of  SlO"  C, 
the  hydrocarbons  remaining  in  the  retort  were  dissociated,  then  gaaes 
escaped,  lighter  distillates  were  obtained,  and,  as  usual  in  such  cases,  the 
temperature  decreased  from  810*  C.  down  gradually  to  200*  C,  until  7b%  of 
oil  was  obtained,  and  from  this  point  the  temperature  remained  constant 
until  the  end  of  the  distillation.  Therefore  these  hydrocarbons  in  statu 
moriendi  alMtorhed  much  heat.    (Jovr.  Am.  Chem.  Soc.) 

Value  of  Petroleam  ae  FneK— Thos.  Urquhart,  of  Russia  (Proc. 
Inst.  M.  E.,  Jan.  1880),  gives  the  following  table  of  tne  theoretical  evapora- 
tive power  of  petroleum  in  comparison  with  that  of  coal,  as  determined  by 
Messrs.  Favre  &  Silbermann: 


Fuel. 

Specific 
Gravity 

at 
82*  F., 
Water 
=  1.000. 

Chem.  Comp. 

Heating- 
power, 
British 

Thermal 
Units. 

Theoret. 
Evap.,  lbs. 
Water  per 

C. 

H. 

0. 

0.1 
1.1 
1.2 

8.0 

lb.  Fuel, 
from  and 
at  212«  F. 

Penna.  heavy  crude  oil ... . 

Caucasian  light  crude  oil.. 

heavy    "      ".. 

Petroleum  refuse 

S.  G. 
0.886 
0.884 
0.0:38 
0.928 

1.880 

86.3 
86.6 
87.1 

80.0 

?8."r 

13  6 
12.8 
11.7 

5.0 

Units. 
20.736 
22,027 
20,188 
19,882 

14,112 

lbs. 

21.48 

22.79 

20.85 

£0.58 

Good  English  Ck>al,  Mean 
of  96  Samples 

14.61 

646  F0fiti» 

In  experiments  on  Russtait  rftilways  with  Mtroleum  as  fuel  Mr.  TTrquhart 
obtained  an  actual  efficiency  equal  to  92%  of  the  theoretical  heatiofr- value. 
The  petroleum  is  fed  to  the  nirnace  by  means  of  a  spi-ay-injwstor  driven  by 
steam.  An  induoed  current  of  air  is  can  led  in  around  the  injeetornioale, 
and  additional  air  is  supplied  at  the  bottom  of  the  furnace. 

Oil  ▼■•  €oal  as  Fnel.  (Iron  Age,  Nov.  2, 1898.)— Test  by  the  Twin 
City  Rapid  Transit  Company  of  Minneapolis  and  St.  Paul.  This  test  showed 
that  with  the  ordinary  Lima  oil  weighing  dC  6/10  pounds  per  Kallon.  and 
costing  2^  cents  per  guloni  and  coal  that  gave  an  c vaporatfon  of  7U  lbs.  of 
water  per  pound  of  coal,  the  two  fuels  were  equally  economical  when  the 
price  of  coal  was  $8.85  per  ton  of  2000  lbs.  With  the  same  coal  at  fe.00  per 
ton,  the  coal  was  87)(  more  economical,  and  with  tlia  coal  at  $4.85  per  ton, 
the  coal  was  SQjC  more  expensive  than  the  oil.  These  results  include  the 
difference  in  the  cost  of  handling  the  coal,  ashes,  and  oil. 

In  1882  there  were  reported  to  the  Engineers'  Ciub  of  Philadelphia  some 
comparative  figures,  from  teste  undertaken  to  ascertain  the  relative  value 
of  coal,  petroleum,  and  gas. 

Lbs.  Water,  from 
and  at  812*  F. 

1  lb.  anthracite  coal  evapoiBted 0.70 

lib.  bituminous  coal 10.14 

1  lb.  f  uel  oil,  8e»  gmvity 16.48 

1  cubic  foot  gas,  20  C.  P. 1.28 

The  gas  used  was  that  obtained  in  the  distillation  of  petroleum,  having 
about  the  &ame  fuel-value  as  natural  or  coal-gas  of  equal  candle-power. 

Taking  the  efficiency  of  bituminous  coal  as  a  basis,  the  calorific  energy  of 
petroleum  is  more  than  60%  greater  than  that  of  coal;  whereas,  theoretically, 
petroleum  exceeds  coal  only  about  45)C— the  one  containing  14,500  heat-unltp, 
and  the  other  21 .000. 

Crude  Petroleum  ts*  Indiana  Block  Coal  for  SCeaaa* 
ratring  at  the  Soatlt  Chf catfo  Steel  Worka*  (E.  C.  Potter, 
Trans.  A.  I.  M.  B.,  xvii,  807.)-With  coal.  14  tubular  boilers  16  ft.  X  6  ft.  re- 
quired 25  men  to  operate  them :  with  fuel  oil,  6  men  were  required,  a  savinjl 
of  19  men  at  $2  per  day,  or  $38  per  day. 

For  one  weelc's  worlc  2781  barrels  of  oil  were  used,  against  848  tons  of  coal 
required  for  the  same  work,  sliowing  8.?3  barrels  of  oil  to  be  equivalent  to  f 
ton  of  coal.  With  oil  at  60  cents  per  barrel  and  coal  at  $2.19  per  ton,  the  rel 
ative  cost  of  oil  to  coal  Is  as  $1.98  to  $«.15.  No  evaporation  tests  wer^ 
made. 

Petroleuttt  as  a  HEetallnrslcal  Fnel*~C.  E.  Felton  (Trana  A.  I. 
M.  £..  xvli.  809)  reports  a  Heries  of  trials  with  oil  as  fuel  in  steel-heating  anc 
open-hearth  steel-f umaees,  and  In  raising  steam  with  results  as  follows:  1. 
In  a  run  of  six  weeks  the  consumption  of  oil,  partly  refined  (the  parafflne 
and  some  of  the  naphtha  being  removed),  in  heating  14-iiicb  ingots  in  Siemes  i 
furnaces  was  about  6H  gallons  per  ton  of  blooms.  8.  In  melting  in  a  aO-ton 
open  hearth  furnace  48  gallons  of  oil  were  used  per  ton  of  ingots.  8.  In  a 
SIX  weeks*  trial  with  Lima  oil  from  47  to  54  gallons  of  oil  were  required  i>*r 
ton  of  ingoU.  4.  In  a  six  months'  trial  with  Siemens  heating-furnaces  the 
consumption  of  Lima  oil  was  6  gallons  per  ton  of  ingots.  Under  the  most 
favorable  circumstances,  charging  hot  ingote  and  running  fliU  capacity,  4U 
to  5  gallons  per  ton  were  required.  5.  In  raising  steam  in  two  100-H.P. 
tubular  trailers,  the  feed- water  being  supplied  at  160^  Fm  the  average  evai>- 
oration  was  about  13  pounds  of  water  per  pound  of  oil*  the  beat  12  hours* 
work  being  16  pounds. 

In  all  of  the  trials  the  oil  was  vaporized  in  the  Archer  producer,  an  apparat- 
us for  mixing  the  oil  and  superheated  steam,  and  heating  the  mixture  to  a 
high  temperature.  From  0.5  lb.  to  0.75  lb.  of  pea-coal  was  used  per  gallon 
of  oil  in  the  producer  itself. 

PrBL  OA8. 

The  followlne  notes  are  extracted  from  a  paper  by  W.  J.  Taylor  on  "  Tlie 
Energy  of  Fuel "  (Trans.  A.  I.  M.  E.,  xvili.  205): 

Carbon  Oaa*— In  the  old  SiBmeus  producer,  practically,  all  the  hest  of 

{)rimary  combustion— that  is,  the  burning  of  solid  carbon  to  carbon  monux* 
de,  or  about  80^  of  the  total  car  (ion  enfli*gy— was  lOHt,  as  little  or  no  steam 
was  ut>ed  In  the  producer,  and  nearly  all  the  sensible  heat  of  the  gas  was 
dissipated  In  its  passage  from  the  producer  to  the  furnace,  which  was  usu- 
ally placed  at  a  censtdTerable  diHlHitoe. 
Modem  practice  has  improved  on  this  plan,  by  introducing  steam  with  the 


FUEL.  GAS.  647 

ulr  blown  into  the  producert  and  by  utilizing  the  sensible  heat  of  the  f^as  in 
I  he  combuBtion-f  uriiaee.  It  ouji^ht  to  be  possible  to  oxidize  one  out  of  every 
four  Hm.  of  carbon  with  oxygen  deriveo  from  water-vapor.  The  thermic 
reactions  in  this  operation  are  as  follows: 

Heat-units. 
4  lb«.  0  burned  to  CO  (8  lbs.  gasified  with  air  and  1  lb.  with  water) 

develop 17,600 

1.5  lbs.  of  water  (which  fuminh  1.88  lbs-  of  oxygen  to  combine  with  1 

lb.  of  carbon)  absorb  by  dissociation 10,333 

The  ^as.  consisting  uf  0.333  lbs.  OO.  0.107  lb.  H,  and  13.30  lbs.  N,  heated 

600«,ab«orb8 8,748 

Leaving  for  radiation  and  loss 8,610 

?7,600 
The  steam  which  is  blown  into  a  producer  with  the  air  Is  almost  all  con- 
densed into  finely-divided  water  before  entering  the  fuel,  and  consequently 
is  considered  as  water  in  these  calculations. 

Tlie  1.5  lbs.  of  water  liberates  .1671b.  of  hvdrogen«  which  is  delivered  to 
the  iBras.  and  yields  in  combustion  the  same  heat  that  it  absorbs  in  the  pro- 
ducer by  dissociation.  According  to  this  calculation,  therefore.  W%  of  the 
keac  of  primary  crmjbustion  Is  tbeoreticallv  recovered  by  the  dissociation  of 
steam,  and.  even  if  all  the  sensible  heat  of  the  gas  be  counted,  with  radia- 
tion and  other  minor  items,  as  loss,  yet  the  gas  must  carry  4  x  14.500  ~ 
(8748  -f  8519)  =  50.7*3  heatunlts,  or  BTjT  of  the  calorific  energy  of  the  carbon. 
This  estimate  shows  a  loss  in  conversion  of  13^,  without  crediting  the  gas 
with  its  sensible  heat,  or  charging  it  with  the  heat  required  for  generating 
the  necessary  steami  or  taking  into  account  the  loss  due  to  oxidizing  some 
of  the  carbon  to  COf.  In  good  producer- practice  tiie  proportion  of  00^  in 
the  gas  represents  from  4%  to  7%  of  the  C  burned  to  CO^.  but  the  extra  heat 
of  this  combustion  should  be  largely  recovered  in  the  dissociation  of  more 
water-vapor,  and  therefore  does  not  represent  as  much  loss  a.s  it  would  indi- 
cate. As  a  conveyer  of  energy,  this  gas  has  the  udvantage  of  cariying  4.46 
lbs.  less  nitrogen  than  would  be  present  if  the  fourth  pound  of  conl  had 
been  gasified  with  air:  and  in  practical  working  the  use  of  steam  reduces 
tlie  amount  of  clinkering  in  the  producer. 

Antlurmelte  Gas«~In  anthracite  coal  there  is  a  volatile  combustible 
varying  in  quantity  from  \.b%  to  over  7^.  The  amount  of  energy  derived 
from  the  coal  is  shown  in  the  following  theoretical  gasification  made  with 
coal  of  assumed  composition:  Carbon,  H5^;  vol.  HC.  5i(;  ash.  10^:  HO  lbs.  car- 
bon assumed  to  be  burned  to  CO;  5  lbs.  carbon  burned  to  COg;  three  fourtlis 
oif  the  necessary  oxygen  derived  from  air,  and  one  fourth  from  water. 

/ Products, . 

Process,  Pounds.    Cubic  Feet,    Anal,  bv  Vol. 

80  lbs.  O  burned  to ...  CO    186.66  S529.94  ;^3.4 

5  lbs.  C  burned  to CO,      18..3.i  157.64  20 

5  lbs.  vol.  HC  (distilled) 5.00  118.60  1.6 

120  \hs.  oxygen  are  requii'ed,  of  which 

80  lbs.  from  HoO  liberate H       8.75  712.50  9.4 

90  lbs.  from  air  are  associatied  with  N    801 .05  4064 .  17  58.6 

614.79  7580  15  100.0 

Energy  in  the  above  gas  obtained  from  100  lbs.  anthracite: 

186.66  lbs.  CO 607,304  heat-units. 

6.00   "    CH4 117,500         " 

8.75    •*        H   282,500  " 

1,157,804  •• 

Total  energy  In  gas  per  lb 2,848         " 

••100  lbs.  of  coal.. 1,849,500 

efficiency  of  the  conversion W. 

The  sum  of  CO  and  H  exceeds  the  results  obtained  in  practice.  The  sen- 
sible heat  of  the  gas  will  probably  account  for  this  disci-epancy,  and.  there- 
fore, it  Is  safe  to  assume  the  possibility  of  delivering  at  least  82%  of  the 
enersy  of  the  anthracite. 

BUnmlnons  Gae«->A  theoretical  gasification  of  100  lbs.  of  coal,  con- 
taining SSi%  of  carbon  and  82^  of  volatile  combustible  (which  is  above  the 
average  of  Pittsburgh  coal),  is  made  in  the  following  table.  It  is  assumed 
that  60  lbs.  of  C  are  burned  to  CO  and  6  lbs.  to  COa;  one  fourth  of  the  O  iA 


648  FUEL. 

derived  from  steam  and  three  fourths  from  air;  the  heat  yalue  of  th« 
▼olatile  combustible  is  taken  at  80,000  Iieat-units  to  the  pound.  In  comput> 
Ing  volumetric  proportions  all  the  volatile  hydrocarbons,  fixed  as  well  as 
condensing,  are  classed  as  marsb-icas,  since  it  is  only  by  some  such  t«nia- 
tlve  assumption  that  even  an  approximate  idea  of  the  volumetric  composi- 
tion can  be  formed.    The  energy,  however,  is  calculated  from  weight: 


-Producta.- 


Process.  Pounds.  Cubic  Feet.   Anal,  by  Vol. 

50  lbs.  C  burned  to CO  116.66  1580.7  27.8 

5  lbs.  C  burned  to CO,  18.88  157.6  2.7 

88  lbs.  vol.  HC  (dlsUlIed) 82.00  746.8  18.8 

80  lbs.  O  are  required,  of  which  20  lbs., 

derived  from  H.O,  liberate H  2.5  475.0  8.3 

60  lbs.  O,  derived  from  air,  are  asso- 
ciated with N  «K).70  2709.4  47.8 


870.10  5668.0  89.8 

Energy  in  116.66  lbs.  CO 504,564  heat-units. 

*»       "    82.00 lbs.  vol. HO....    640,000         •• 
•*       "      2.60  lbs.  H 166,000 

1,299,554         " 

Energy  In  coal 1,487,500         " 

Per  cent  of  energy  delivered  in  gas 90.0 

Heat-units  in  1  lb.  of  gas 3,484 

Water^icaa*— Water- gas  Is  made  in  an  intermittent  process,  by  blowlni* 
up  the  fuel-bed  of  the  producer  to  a  high  state  of  incandescence  (and  in 
some  cases  utilizing  ihe  resulting  gas,  which  is  a  lean  producer-gas),  then 
shutting  off  the  air  and  forcing  steam  through  the  fuel,  which  dissociates 
the  water  into  its  elements  of  oxygen  and  hydrogen,  the  former  combining 
with  the  carbon  of  the  coal,  and  the  latter  being  liberated. 

This  gas  can  never  play  a  very  important  part  In  the  industrial  field,  owing 
to  the  large  loss  of  energy  entaileci  in  its  production,  yet  thera  are  places 
and  special  purposes  whei*e  it  is  desirable,  even  at  a  ereat  excess  in  coat  per 
unit  of  heat  over  producer-gas;  for  instance,  in  small  high-temperature  nir- 
naces,  where  mucn  regeneration  is  impracticable,  or  ^nere  the  "  blow-up  '* 
gas  can  be  used  for  other  purposes  Instead  of  being  wasted. 

The  reactions  and  energy  required  in  the  production  of  1000  feet  of  water- 
gas,  composed,  theoretically,  of  equal  volumes  of  CO  and  H,  are  as  follows: 

500  cubic  feet  of  H  weigh 2.6.S5  lbs. 

500  cubic  feet  of  CO  weigh 86.80     *• 

Total  weight  of  1000  cubic  feet S0.5251b8. 

Now,  as  CO  is  composed  of  12  parts  C  to  16  of  O,  the  weight  of  C  in  36.89 
lbs  is  15.81  lbs.  and  of  O  21.08  lbs.  When  this  oxrgen  Is  derived  from  water 
it  liberates,  as  above.  2.685  lbs.  of  hydrogen.  The  heat  developed  and  ab- 
sorbed in  these  reactions  (roughly,  as  we  will  not  take  into  account  the  en- 
ergy required  to  elevate  the  coal  from  the  temperature  of  the  atmosphere 
to  say  lw)0<*)  is  as  follows: 

Heatunita. 
2.685  lbs.  H  absorb  In  dissociation  from  water  2.685  X  02,000..  =  163,870 

15.81  lbs.  C  burned  to  CO  develops  15.81  X  4400. =   69,5<M 

Excess  of  heat- absorption  over  heat-development =   88,806 

If  this  excess  could  be  made  np  from  C  burnt  to  CC)o  without  loss  by  radi- 
ation, we  would  only  have  to  bum  an  additional  iM  lbs.  C  to  supply  this 
heat,  and  we  could  then  make  1000  feet  of  water-gas  from  20.64  lbs.  of  car- 
bon (equal  24  lbs.  of  BSt%  coal).  This  would  be  the  perfection  of  gas-making, 
as  the  gas  would  contain  really  the  same  energy  as  the  coal;  but  instead,  wt- 
require  in  practice  more  than  double  this  amount  of  coal,  and  do  not  deliver 
more  than  S0%  of  the  energy  of  the  fuel  in  the  gas,  because  the  supporting 
heat  is  obtained  in  an  indirect  way  and  with  imperfect  combustion.  Besides 
this,  it  is  not  often  that  the  sum  of  the  CO  and  H  exceed  90%^  the  balance  be- 
ing CO9  and  N.  But  water-gas  should  be  made  with  much  less  loss  of  en- 
ergy by  burning  the  "  blow-up  "  (producer)  gas  in  brick  regenerators,  the 
stored -up  heat  of  which  can  be  returned  to  the  producer  by  the  air  used  in 
blowing-up. 

The  following  table  shows  what  may  be  considered  average  volumetriG 


FUISL  GAS. 


649 


analyses,  and  the  weight  and  energy  of  1000  cubic  feet,  of  the  four  types  of 
gaties  used  for  heating  and  illuminating  purposes: 


Natural 
Gas. 

Coal- 
gas. 

Water- 
gas. 

Produoer>gas. 

CO 

0.50 
2.18 
32.6 
0.81 
0.26 
8.61 
0.34 

6.0 

46.0 

40.0 

4.0 

0.5 

1.6 

0.5 

1.5 

82.0 

735,000 

45.0 
45.0 
2.0 

**4.'6  ' 

2.0 

0.6 

1.6 

45.6 

323,000 

Anthra. 

27.0 

13.0 

1.2 

"*2.'6' 

67.0 

0.8 

Bltu. 
27.0 

H  

12.0 

CH4 

2.5 

C-H* 

0.4 

CO,  :.:;;;;; .;.. 

2.6 

N?;;;..;;.v;;. ;.;..;:: ..::.::::::: 

56.2 

0 

Vapor  

0.8 

Pounds  in  loioo  cubic  feet 

i'ii.e 

I.IOO^JOO 

65.6 
187,456 

65.9 

Heat  units  in  1000  cubic  feet 

156.917 

Natural  Gas  In  Ohio  and  Indiana, 

(Eng.  and  M.  J.,  April  21, 1894.) 


Ohio. 

Indiana. 

Description. 

Fos- 
toria. 

Findlay 

St 
Mary^s. 

Muncie. 

Ander- 
son. 

Koko- 
mo. 

Mar- 
ion. 

Hvdroeen 

1.89 
92.84 
.20 
.55 
.20 
.35 

8.83 
.15 

1.64 
98.86 
.86 
.41 
.25 
.89 
8.41 
.20 

1.94 
98.85 
.20 
.44 
.28 
.»i 
2.96 
.21 

2.85 
92.67 
.26 
.45 
.25 
.85 

8.53 
.15 

1.86 
98.07 
.47 
.73 
.86 
.42 
8.03 
.15 

1.48 
94.16 
.80 
.55 
.29 
.80 
2.80 
.18 

1.20 

Marsh-gas 

98.57 

Olefiantgas 

Carbon  monoxide.. 
Carbon  dioxide... 
Oxygen 

.16 
.60 
.80 
.56 

Nitrogen 

Hydrogen  sulphide 

8.42 
.30 

Approximately  80,000  cubic  feet  of  gas  have  the  heating  power  of  one 
ton  of  coal. 

Prodncer^an  nrom  One  Ton  of  Coal. 

(W.  H.  Blauvek,  Truns.  A.  1.  M.  £.,  xviii.  614.) 


Analysis  by  Vol. 

Per 
Cent. 

Cubic  Feet. 

Lbs. 

Equal  to— 

CO   

H    

CH4 

25.3 
9.2 
8.1 
0.8 
3.4 

58.2 

83, -213. 81 
12.077.  *:« 
4.069.68 
1,050.24 
4,4tW..W 
76,404.9f) 

24.51.30 
63  r.6 
174  66 
77.78 
.•519.02 
5659.63 

804JS.85 

1050.51  lbs.  C+  1400.7  lbs.  O. 
68.56    •*    H. 
174.66    "    CH«. 

C,H4 

CO,* 

^  (oy  difference. 

77.78   •'    r,H4. 
141.51    "    C-f  877.441b8.0. 
^50.17    "    Air. 

KIO.O 

1. •«,*«.  00 

Calculated  upon  this  basis,  the  131,280  ft.  of  sras  from  the  ton  of  coal  con- 
tained  30.811.162  B.T.U  .or  I.\5  H.T.U.  per  cubic  ft ,  or  2270  B.T.U.  per  lb. 

The  composition  of  the  coal  from  which  thisKHS  was  made  was  as  follows: 
Water.  1.26]t;  volatile  matter,  36.23^:  fixed  carbon,  V:.W,%\  sulphur,  0.703(; 
ash,  3.78)(  One  ton  contains  1159.6  lbs.  carbon  and  734.4  lbs.  volatile  com- 
bustible, the  energy  of  which  is  31,302,200  B.T.U.  Hence,  in  the  processes  of 
gasification  and  purification  there  was  a  loi»s  of  35.23t  of  the  ene^gy  of  the 
coal. 

The  composition  of  the  hydrocarbons  in  a  soft  coal  is  uncertain  and  quite 
complex;  but  the  ultimate  analysis  of  the  average  coal  shows  that  it  ap- 
proaches quite  nearly  to  the  composition  of  CH4  (marsh-gas). 

Mr.  Blauvelt  emphasizes  the  following  points  as  highly  important  In  soft- 
coal  producer-practice: 


650  FUEL. 

FffBt  That  a  large  peroentaf^  of  the  energr  of  the  ooal  te  lost  when  the 
f^as  is  made  in  the  ordinary  low  produ^jer  and  cooled  to  the  temperature  of 
the  air  before  beinfcused.  To  prevent  these  wurces  of  loss,  the  producer 
should  be  placed  so  as  to  Ioko  as  little  as  possible  of  the  sensible  hrnt  of  the 
g^as,  and  prevent  condensation  of  the  hyarocarlion  vapors.  A  hifi;h  fuel-bed 
should  be  carried,  keeping  the  producer  cool  on  top,  tnereby  preventing  the 
breaking-down  of  the  hydrocarbons  and  the  deposit  of  soot,  as  well  as  keep- 
ing the  carbonic  acid  low. 

Second.  That  a  producer  should  be  blown  with  as  much  steam  mixed  with 
the  air  as  will  maintain  incandescence.  This  reduces  the  fiercentage  of 
nitrogen  and  increases  the  hydrc^^en,  thereby  greatly  enriching  the  gas. 
The  temperature  of  the  producer  is  kept  uown,  diniinisiiihg  tiie  Joss  of  heat 
by  riiiliiitloM  thronsrh  tlu*  wnlln,  and  in  e  large  measure  preven ling  clinkers. 

The  Combustion  of  Prodacer-ffaa*  (H.  H  Campbell,  Trans. 
A.  I.  Ai.  E.,  xlx.  l./H.>— Theconilmstion  of  iJie  components  of  ordinary  pro- 
ducer-gas may  be  represented  by  the  following  formulee: 

C,H«  -f  CO  =  SOOa  -f  2HaO;        8H  -|-  O  =  H,0; 
CH<  -H  40  =    CO,  -f  tfHaO;        CO  -f  O  =  CO,. 
Atkrage  Composition  by  Voi.umb  of  Producbr-oas:  A,  madb  with  Oprn 
Orates,  no  Steam  in  Blast;  B,  Open  Grates,  8tbam-jbt  in  Blast.    10 
Samples  of  Each. 

CO,.  O.  CjH*.  CO.  H.  CH4.  N. 

Amin 3.8  0.4  O.i  20.0  6.8  8.0  58.7 

A  max 5.6  0.4  0.4  84.8  8.5  6.2  64.4 

A  average...    4.84         0.4  0.84  22A  6.8  8.74  61.78 

B  min 4.6  0.4  0.8  20  8  6.9  2.S  57.S! 

B  max 6.0  0.8  0.4  2M.0  9.8  8.4  6^0 

B  average...    6.3  0.64  0.36  28.74         8.37  8.56  60.13 

The  coal  u^ed  contained  carbon  88](,  hydrogen  4.7%. 

The  following  are  analyses  of  products  of  combustion : 

00,.  O.  CO.        CH4.  H.  N. 

Minimum 15.8  0.8        trace,      trace.      traoa.     80.1 

Maximum 17.8  1.6  9.0  0.6  8  0       83.6 

Average 16.3  0.8  0.4  0.1  0.2       88.8 

Use  of  Steam  In  Producers  and  In  Boller-fVi maces*  (R. 
W.  Itayinond.  Trans.  A.  I.  M.  E.,  xx.  6;ij.)— No  possible  use  of  stenm  can 
cause  a  gain  of  heat.  If  sleum  be  introduced  Into  a  bed  of  Incaude^ceot 
carbon  it  is  decomposed  into  hvdrogen  and  oxygen. 

The  heat  absorbed  liy  the  reduction  of  one  pound  of  steam  to  hvdrogen  Is 
much  greater  in  ninount  than  the  he<it  generated  by  the  union  of  the 
oxygen  tlius  set  free  with  carbon,  forming  either  carbonic  oxide  or  carbonic 
acicT  Consequently,  tlie  effect  of  steam  alone  upon  a  bed  of  incandesceDl 
fuel  is  to  chill  it.  In  every  water-gas  apparatus,  designed  to  produce  by 
means  of  the  decomposition  of  steam  a  fuel- gas  relatively  free  from  nitro- 
gen, the  loss  of  heat  in  the  producer  must  be  compensated  by  some  reheat- 
ing device. 

'ihis  loss  may  be  recovered  if  the  hydrogen  of  the  steam  is  subsequently 
burned,  to  form  steam  sgain.  Such  a  combustion  of  the  hydrogen  is  con- 
templated, in  the  case  of  fuel-gas,  as  secured  in  the  subsequent  use  of  that 
g»i8.  Asxuining  the  oxidation  of  H  to  be  complete,  the  use  of  steam  wiU 
cause  neither  gain  nor  loss  of  heat,  but  a  simple  trnnsference.  the  heat 
iihsorbed  by  steam  decon) position  being  restored  by  hydrogen  combustion. 
In  practice,  it  may  lie  doubted  whether  this  restoration  is  ever  complete. 
But  it  is  certain  that  an  excess  of  steam  would  defeat  the  reaction  alto- 
gether, and  that  there  must  l>e  a  certain  proportion  of  steam,  which  per- 
mits the  rcHlization  of  important  advantages,  without  too  great  a  net  loss  in 
lient. 

The  advantage  to  be  secured  (in  holler  furnaces  using  small  sizes  of 
anthracite)  consists  pi  incipally  in  the  transfer  of  heat  fn-m  the  lower  side 
of  the  Are,  where  It  is  not  wanted,  to  the  upper  side.  wh«re  it  is  wanted. 
The  decomposition  of  the  steam  below  cools  the  fuel  and  the  grate-bars, 
when^as  a  blast  of  air  alone  would  ur«»dufe,  at  that  point,  intense  combus- 
tion (rorniing  at  fl.st  COa),  to  the  injury  of  the  grate,  the  fusion  of  part  of 
the  fuel,  etc. 

The  proportion  of  steam  most  ftconomlcal  is  not  ensily  determined.  The 
temperatute  of  the  steam  itself,  the  nature  of  the  fuel  niixlure.  and  th**  u^e 
or  uuD-use  of  auxiliary  air- supply,  introduced  into  the  gaifeK  above  or 


ILLUMINATINQ-aAS. 


651 


beyond  the  fire-bed,  are  factors  affecting  the  problem.  (See  Trans. 
A.  L  M.  E.,  Tx.  «25.) 

Gas  AnmJjnem  by  Volvme  and  hj  Drelfflit.>-To  convert  an  an- 
alysis of  a  mixed  kbs  Oj  volume  into  analysis  by  weif^lil:  Multiply  the  per- 
centage of  each  const  ituen  t  Ras  by  the  densi ty  of  that  gas  (see  p.  1 86).  Divide 
each  product  by  the  sum  of  the  products  to  obtain  the  pei-centages  by  weight. 

Gas-ftael  Ibr  Small  FnmaAea.— £.  P.  Reichhelm  {Am.  Madi,, 
Jan.  10,  1806)  dittcusses  the  use  of  gaseous  fuel  for  forge  fires,  for  drop- 
forging,  in  annealing-ovens  and  furnaces  for  melting  brass  and  copper,  for 
case-bardening,  muffle-furnaces,  and  kilns.  Under  ordinary  coudiiions.  In 
such  furnaces  he  estimates  that  the  loss  bv  draught,  radiation,  and  the 
beating  of  space  not  occupied  by  work  is,  with  coal,  BOjt,  with  petroleum  TOjf, 
and  with  gas  above  the  grade  of  producer-gas  25)e.  He  gives  the  following 
table  of  comparative  cost  of  fuels,  as  used  in  these  furnaces : 


Kind  of  Gas. 


Natural  gas 

Coal-gas,  80  candle-power 

Carburetted  water-gas.  

Gasolene  gas,  20  candle-power 

Water-gas  from  coke 

Water-gas  from  bituminous  coal 

Water-gas  and  producer -gas  mixed.  . 

Producer-gas 

Naphtha-gas,  fuel  2^  gals."  per  1000  ft 

Coal.  $4  per  ton,  per  1,000.000  heat>unit«  utilized 

Crude  petroleum.  8  cU.  per  gal .  per  1.000,000  heat-units. 


I- Si 


S5 


1,000,000 
675,000 
646,000 
600,000 

318,00ii 
877,0OC 
18fi.0<M' 
150,01K' 
306.3a' 


<St 


750,000 

506.250* 

484,500 

517,500 

284,750 

282,750 

138,750 

112,500 

229,':  74 


$1.25 
1.00 
.90 
.40 
.45 
.20 
.15 
.15 


92.40 

8.06 

1.78 

1.70 

1.59 

1.44 

1.88 

.65 

.78 

.78 


Mr.  Reichhelm  gives  the  following  figures  from  practice  in  melting  brani 
with  coal  and  with  naphtha  converted  Into  gas:  1800  lbs.  of  metal  require 
1080  lbs.  of  coal,  at  $4.65  per  ton.  equal  to  $2.51.  or,  say,  15  cents  per  lOu  lbs. 
Mr.  T.*8  report :  2500  lbs.  of  metal  require  17  gals,  of  naphtha,  at  6  cents  per 
gal.,  equal  to  $8.88,  or,  say,  1 1^  cents  per  100  lbs. 


rLLTTMINATIN'Q-GAS, 


Coal«CB^s  is  made  by  distilling  bitumhious  coal  in  retorts.  The  retort 
is  usiually  a  long  horizontal  semi-cylindrical  or  q  shaped  chamber,  holding 
from  160  to  8w  lbs.  of  coal.  The  retorts  are  set  in  "benches**  of  from 
3  to  9,  heated  by  one  fire,  which  is  generally  of  coke.  The  vapors  distilled 
from  the  coal  are  converted  into  a  fixed  gas  by  passing  througn  the  retort, 
which  is  heated  almost  to  whitenesR. 

Tbe  gas  passes  out  of  the  retort  through  an  '*  ascension-pipe  **  Into  a  long 
horizontal  pipe  called  the  hydraulic  main,  where  it  deposits  a  portion  of 
the  tar  it  contains:  thence  it  goes  into  a  condenser,  a  series  of  Iron  tuites 
RurrouDded  by  cold  water,  where  it  is  freed  fi-om  condensable  vapors,  as 
ammonia-water,  then  Into  a  washer,  where  it  is  exposed  to  jets  of  water, 
and  into  a  scrubber,  a  large  chamber  partially  filled  with  trays  made  of 
wood  or  iron,  containing  coke,  fragments  of  brick  or  paving-Rtones.  whifh 
are  wet  with  a  spray  of  water.  By  the  washer  and  scrubber  the  eras  is  freed 
from  the  last  portion  of  tar  and  ammonia  and  from  some  of  the  sulphur 
compounds.  Tne  gas  Is  then  finally  purified  from  sulphur  compounds  by 
passing  it  througn  lime  or  oxide  of  iron.  The  gas  is  drawn  from  the  hy- 
draulic main  and  forced  through  the  washer,  scrubber,  etc.,  by  an  exhauster 
or  gas  pump. 

The  kind  of  coal  used  is  generally  caking  bituminous,  but  as  usually  this 
coal  is  deficient  in  gases  of  high  illuminating  power,  there  is  added  to  it  a 
portion  of  cannel  coal  or  other  enricher. 

The  following  table,  abridged  from  one  in  Johnson *s  Cyclopedia,  showi 
the  analysis,  candle  power,  etc.,  of  some  gas-coals  and  enrichers: 


652 


ILLUMINATING-GAS. 


Gaa-coals,  etc. 


3^a 


Ookeper 

ton  of  2340 

lbs. 


lbs.    bush. 


Pittsburgh, Pa  .... 
Westmoi-eland,  Pa 

SterUnjr,  O 

Despard,  W.  Va... 

Darlinjrton,  O 

Petonia,  W.  Va  .  . 
Graliamlte,  W.  Va. 


86.76 
36.00 
37.50 
40.00 
48.00 
46.00 
58.50 


51.98 
58.00 
56.90 
58.80 
40.00 
41.00 
44.50 


7.07 
6.00 
6.60 
6.70 
17.00 
18.00 
2.00 


10.642 
10.528 
10,765 
9,800 
18,200 
15.000 


16.6*^ 
18.81 
20.41 
84.98 
42.79 
28.70 


1544 
1480 
1540 
1820 
1880 
1056 


40 
88 
86 
82 
82 
44 


<M20 
8993 
S494 
SM)6 
4510 


The  products  of  the  distillation  of  100  lbs.  of  average  gas-^oal  are  about  as 
follows.  They  vary  according  to  the  quality  of  coal  and  the  temperature  of 
distillation. 

Coke,  64  to  65  lbs. ;  tar,  6.5  to  7.5  lbs.;  ammonia  liquor,  10  to  12  lbs.;  puri- 
fied gas,  15  to  12  lbs. ;  impurities  and  loss,  4.5^  to  8.5%. 

The  composition  of  the  gas  by  volume  ranges  about  as  follows:  Hydro- 

S9n,  dS%  to  48%;  carbonic  oxide,  2%  to  14%;  marshgas  (Methane,  CH^),  43%  to 
ii  heavy  hydrocarbons  (ChHm,  ethylene,  propylene,  benzole  vapor,  etc.), 
7.Sto  4.5%:  nitrogen,  1%  to  3J{. 

In  the  biimiiig  of  the^as  the  nitrogen  is  inert;  the  hydrogen  aod  carbonic 
oxide  give  heat  but  no  iight.  The  luminosity  of  the  flame  is  due  to  the  de- 
composition bv  heat  of  the  heavy  hydrocarbons  into  lighter  hydrocarbons 
and  carbon,  the  latter  being  separated  in  a  state  of  extreme  subdiviHion. 
By  the  heat  of  the  flame  this  separated  carbon  is  heated  to  intense  white- 
ness, and  the  illuminating  effect  of  the  flame  is  due  to  the  light  of  incaiides* 
cence  of  the  particles  of  cart>on. 

The  attainment  of  the  highest  degree  of  luminosity  of  the  flame  depends 
upon  the  proper  adjustment  of  the  proportion  of  the  heavy  hydrocarbons 
(with  due  regard  to  their  individual  character)  to  the  nature  of  the  diluent 
mixed  therewith. 

Investigations  of  Percy  F.  Frankland  show  that  mixtures  of  ethylene  an^l 
hydrogen  cease  to  have  anv  luminous  effect  when  the  proportion  of  eih«'- 
leiie  does  not  exceed  10%  of  the  whole.  Mixtures  of  ethylene  and  carbonic 
oxide  cease  to  have  any  luminous  effect  when  the  proportion  of  the  former 
does  not  exceed  'M%,  while  ail  mixtures  of  ethylene  and  marsh-gas  have  more 
or  less  luminous  effect.  The  luminosity  of  a  mixture  of  10%  ethvlene  and  90% 
marshgas  being  equal  to  about  18  candles,  and  that  of  one  of  20%  ethylene 
and  80%  marsh-gas  about  25  candles.  The  illuminating  effect  of  marsh -ga^ 
alone,  when  burned  in  an  argand  burner,  is  by  no  means  inconsiderable. 

For  further  description,  see  the  Treatises  on  Gas  by  King.  Richards,  and 
Hnehei:  also  Appietoii's  Cyc.  Mech.,  vol.  i.  p.  900. 

DFater-sas*— Water-gas  is  obtained  by  passing  steam  through  a  bed  of 
coal,  colce,  or  charcoal  hen  ted  to  redness  or  beyond.  The  steam  is  decom- 
posed, its  hydrogen  being  liberated  and  its  oxygen  burning  the  carbon  of 
the  fuel,  producing  carbonic-oxide  eas.  The  chemical  reaction  is,  C  +  H*0 
=  CO  -f  an.  or  2C  -f  2H,0  =  C  -f-  CO,  -h  4H,  followed  by  a  splitting  up  of 
the  CO.,  making  2CO  -(-  4H.  By  weight  the  normal  gas  CO  +  8H  is  com- 
posed  of  C  -f  O  +  H  =  -^  parts  CO  and  2  parts  H,  or  98.88%  CO  and  6.6:<  H ; 

12+  U  +  S 
by  volume  it  is  composed  of  equal  parts  of  carbonic  oxide  and  hydrogen. 
Water-gas  produced  as  above  described  has  great  heating- power,  but  no 
illuminating- power.  It  may,  however,  be  used  for  lighting  oy  causing  It  to 
heat  to  whitenebs  some  solid  substance,  as  Is  done  in  the  Welsbach  Incan- 
descent light. 

An  illiiniinating-gas  is  made  from  water-gas  by  adding  to  it  hydrocarbon 
gases  or  vapors,  which  are  usually  obtained  from  petroleum  or  some  of  its 
pro<lucts.    A  history  of  the  development  of  modern  illuminating  water-gas 

KroceKses,  together  with  a  description  of^the  most  recent  forms  of  apparatus, 
I  given  by  Alex.  C.  Humphreys,  in  a  paper  on  **  Water-gas  in  tiie  Unite-i 
States,"  rend  before  tiie  Mechanical  Section  of  the  British  Association  fcr 
Advancement  of  Science,  in  18^9.  After  describing  many  earlier  patents,  he 
states  that  success  in  the  manufacture  of  water-gas  maybe  said  to  date 


AKALTSE8  OP  WATEE-GAS  AND  COAL-GAS  COMPARED.  653 


from  1874«  when  the  process  of  T.  S.  C.  Lowe  was  introduced.  All  the  later 
modt  succesttful  processes  are  the  modifications  of  Lowers,  the  essential 
features  of  which  were  **  an  apparatus  consisting  of  a  generator  and  super- 
heater internally  fired;  the  superheater  being  heatM  by  the  secondary 
combustion  from  the  generator,  the  heat  so  stored  up  in  the  loose  brick  of 
the  superheater  being  used,  in  the  second  pari  of  the  process,  in  the  fixing 
or  rendering  permanent  of  the  hydrocarbon  gases;  the  second  part  of  the 
proce«8  consisting  in  the  passing  of  steam  through  the  generator  fire,  and 
tlie  admission  of  oil  or  hydrocarbon  at  some  point  between  the  fire  of  the 
generator  and  the  loose  filling  of  the  superheater.*^ 

The  water-gas  process  thus  has  two  periods:  first  the  "blow," during 
which  air  is  blown  through  the  bed  coal  in  the  generator,  and  the  partially 
burned  gaseous  products  are  completely  bumecTin  the  superheater,  giving 
up  a  great  portion  of  their  heat  to  the  fire-brick  work  ooutained  in  it.  and 
then  pass  out  to  a  chimney:  second,  the  '*  run  '*  during  which  the  air  blast 
is  stopped,  the  opening  to  the  chimney  closed,  and  steam  is  blown  through 
the  incandescent  bed  of  fuel.  The  resulting  water-gas  passing  into  the  car- 
buretting  chamber  in  the  base  of  the  superheater  is  there  charged  with  hy- 
drocarbon vapors,  or  spray  (such  as  naphtha  and  other  distillates  or  crude 
oil)  and  passes  through  the  superheater,  where  the  hydrocarbon  vapors  be- 
come converted  into  fixed  illuminating  gases.  From  the  superheater  the 
combined  gases  are  passed,  as  in  the  coal-gas  process,  through  washers, 
acrubliers,  etc.,  to  the  gas-holder.  In  this  case,  however,  there  is  no  am- 
monia to  be  removed. 

The  specific  gravity  of  water-gas  increases  with  the  increase  of  the  heavy 
hydrocarbons  which  give  itilluminating  power.  The  following  figures,  taken 
from  different  authorities,  are  given  by  F.  H.  Shelton  in  a  paper  on  Water- 
gas,  read  before  the  Ohio  Gas  Light  Association,  in  1894: 
<!andle-power  ...  19.6      20.    S2.6  24.       25.4   96.3    28.8    29.6    .80  to  81.9 

JBp.gr.  (Air  =  1)..  .671    .690    .589     .60  to  .67    .64    .602     .70      .65    .65  to    .71 

Analyses  of  "WBter^gmm  and  Goal*ga«  Compared* 

The  following  analyses  are  taken  from  a  report  of  Dr.  Gideon  E.  Moore 
on  the  Granger  Water-gas,  1885: 


Composition  by  Volume.     {  Composition  by  Weight. 

Water-gas. 

Coal-gas. 
Heidel. 
berg. 

Water.ga8. 

Coal- 

Wor- 
cester. 

Lake. 

Wor- 
cester. 

Lake. 

gas. 

Nitrogen 

2.64 
0.14 
0.06 
11.29 
0.00 
1.58 
28.26 
18.88 
37.20 

8.85 
0.80 
0.01 
12.80 
000 
2  68 
23.68 
20.95 
35.88 

2.15 
8.01 
0.65 
2.56 
1.21 
1.33 
8.88 
34.02 
48.20 

0.04402 
0.00:365 
0.00114 
0.18759 

0.06175 
0.00758 
0.00018 
0.20454 

0.04569 

(Carbonic  acid.... 
Oxygen 

0.09992 
0.01569 

Kthyiene 

0  06889 

Propylene 

lienzole  vapor.... 
(Jarbonic  oxide... 

3Iar8h.gas 

Hydrogen 

0.03884 

0.07077 
0.46934 
0.17928 
0.04421 

6.11700 
0.37664 
0.19133 
0.04108 

0.07825 
0.18758 
0.41087 
0.06987 

100.00 

100.00 

100.00 

1.00000 

1.00000 

1.00000 

Density :  Theory. 
Practice . 

0.5825 
0.5915 

0.6057 
0.6018 

0.4580 

B.  T.  U.  from  1  cu. 

650.1 
597.0 

688.7 
646.6 

642.0 
577.0 



*  *  ■ 

ft.:  Water  liquid. 
**     vapor. 



Flame-temp 

5311.2»F. 

5281. 1'F. 

5202. 9«F. 



A  V,  candle-power. 

22.06 

26.31 

Th»*  hentlug  values  (B.  T.  U.)  of  the  gases  are  calculnted  from  the  analysi.s 
by  weight,  by  using  the  multipliers  given  below  (computed  from  results  of 


654 


1LLUMINATIHG-GA8. 


J.  Thomsen),  and  multiplylnir  the  result  by  the  weight  of  1  cu.  ft.  of  the  gaa 
at  tt'J**  F.,  and  atmosphei-io  pressure. 

The  flame  temperatures  (theoretical^  are  oalculatod  on  the  aasumption  of 
complete  combustion  of  the  f^aaes  in  au>,  without  excess  of  air. 

The  candle-power  was  determined  by  photometric  tests,  using  a  preseure 
of  M-in.  water-column,  a  candle  consumption  of  190  grains  of  spermaceti 
per  hour,  and  a  meter  rate  of  5  cu.  ft.  per  hour,  the  result  being  corrected 
for  a  temperature  of  OH?  F.  and  a  barometric  pressure  of  30  in.  It  appears 
that  the  candle-puwei*  may  be  regulated  at  the  pleasure  of  the  person  in 
charge  of  the  apparatus,  the  range  of  candle-power  being  from  20  to  ii9 
caudles,  according  to  the  manipulation  employed. 

€«lortile  K^ttlirMeiftto  of  ConatlinenU  of  IllttminailiiB* 

cat, 

Heat-uuits  from  1  lb. 


Ethylene , 

Propylene , 

Benzole  vapor.. 


Water 

Water 

Liquid. 
81.524.4 

Vapor. 

20,134.8 

81,222.0 

19,834.2 

18,064.0 

17,847.0 

Heat-units  from  1  lb- 
Water      Water 
Liiuid.      Vapor. 
Carbonic  oxide..    4,^.0       4,JS5.6 

Marsh  gas 24.021.0     21,508.8 

Hydrogen 61,624.0     51,804.0 


Iclenejr  of  a  'Watar-sas  Plant*— The  practical  efflciency  of  a& 
Illuminating  water-gas  setting  is  discussed  in  a  paper  by  A.  Q.  Qlasgow 
(Proc.  Am.  Gaslight  Assn.,  1800).  from  which  the  following  is  abridged  : 


.  Q.  QU 

, ^ jridged  . 

The  results  rel?er  to  1000  cu.  ft.  of  unpurifled  carburetted  gas,  reduced  to 
eO"  F.  The  total  anthracite  charged  per  1000  cu.  ft.  of  gas  was  SS.4  Ibe.,  ash 
and  unconsumed  coal  removed  9^  lbs.,  leaving  total  combustible  consumed 
28.5  lbs.,  which  is  taken  to  have  a  fuel- value  of  14600  B.  T.  U.  per  pound,  or 
a  total  of  840,750  heat- units. 


CJomposI- 
tlon  by 
Volume. 

Weight 

per 
lOOcu.  ft. 

Composi- 
tion by 
Weight. 

«fiS.'?= 

I.    Carburetteti 

Water-gas. 

CO 

CH4 

H 

8.8 
14.0 
28.0 
17.0 
85.6 

1.0 

.465842 

1.189968 

2.1868 
.75854 
.1991464 
.078596 

.09647 
.28607 
.45285 
.15710 
.04124 
.01627 

.02066 

.otTf^ao 

.11226 
.09314 
.14041 

N 

.00397 

L 

fCO,  

100.0 

8.6 
48.4 
61.8 

1.3 

4.8288924 

1.00000 

.45786 

.420065 

8.889540 

.289821 

.102175 

.1019 
.8051 
.0668 
.0242 

.O2S05 

n.    Uncarburetted 

CO  

H 

.19956 

gas. 

N 

00691 

100.0 

4210601 

1.0000 

.4617« 

fCO, 

17.4 
8.2 
T9.4 

2.138066 
.2856096 
6.2405221 

.2464 
.0829 
.7207 

.05842 

ni.    Blast  products 

escaping  from  ■ 

superheater. 

0.  ...  .   .... 

00718 

N.::. :::..: 

.17865 

100.0 

8.6591960 

1.0000 

.28645 

fCO- 

9.7 
17.8 
72.6 

1.189123 
1.390180 
5.608210 

.1436 
.1680 
.0684 

.031075 

CO.:.:....:: 

041647 

IV.    Generator 

N 

.167970 

blast- gases. 

100.0 

8.277518 

1.0000 

.240692 

The  heat  energv  absorbed  by  the  apparatus  is  23.6  X  14,500  =  340,750  heat- 
units  =  A.    Its  disposition  is  as  follows : 

i?,  the  energy  of  the  CO  produced ; 

C,  the  energy  absorbed  in  the  decomposition  of  the  steam; 

X>,  the  difference  l)etween  the  sensible  heat  of  the  escaping  ilium inatinp* 
gases  and  that  of  the  entering  oil ; 

JJ,  the  heat  carried  off  by  the  escaping  blast  products; 

F,  the  heat  lost  by  radiation  from  the  shells; 


EFFICIENCY  OF  A  WATKR-GAS  PLANT.  655 

O,  the  heat  carried  away  from  the  sheila  bj  cooTeciion  (air*current8)i 
H,  the  heat  rendered  latent  in  the  g^asifiaation  of  the  oil; 
/,  the  eenaible  heat  in  the  ash  and  unoonsumed  coal  recovered  from  the 
generator. 
The  heat  equation  is  A  »  B  +  C  + D  +  S+ F-^-Q-^- H-^-Ii  A  htdug 

known.    A  comparison  of  the  CO  in  Tables  I  and  11  show  that-^,  or  ti.hjL 

of  the  volume  of  carbu retted  gais  is  pure  water-gas,  distributed  thus  :  CO* , 
2  3jC;  CO,  28.0JC:  H,  33.4jt;  N.  o!w;  =  64.5j<.  1  lb.  of  CO  at  C0«  F.  =  13.581  cu. 
ft  CO  per  1000  cu.  ft.  of  gas  =  280  -4- 13.581  =  20.694  lbs.  £nergy  of  the  CO 
=  20.091  X  4895.tf  s  91,048  heat-units,  =  B.  1  lb.  of  H  at  60*  FT  =  189.'^  cu. 
ft.  H  per  M  of  gas  s  884  -4-  180.8  a  1.7668  lbs.  Energy  of  the  H  per  lb. 
(according  to  Thomsen,  considering  the  steam  generated  by  its  combustion 
to  be  condensed  to  water  at  76*  F.)  a  61,5eM  B.  T.  U.  In  Mr.  Glasgow's  ex- 
periments the  steam  entered  the  generator  at  881"  F. ;  the  heat  required  to 
raise  the  product  of  combustion  of  1  lb.  of  H,  viz..  8.96  lbs.  H^O,  from  water 
At  76*  to  steatn  4t  881*  must  ther^fot^  be  deducted  from  Thomsen *b  flirure,  or 
61,944  -  (8.06  X  1140.9)  :^  61  ,»86  B.  T.  U.  per  lb.  of  H.  Energy  of  the  H,  then, 
is  I.76S8  X  61,286  s:  90,588  heat-units,  s:  C.  The  heat  lost  due  ro  the  senaihle 
heat  in  the  illuminating-gases,  their  temperature  being  1460*  F.,  and  that  of 
the  entering  oil  285*  F.,  is  48.29  (weight)  X  .45786  sp.  heat  X  1215  (rise  of  tem- 
perature) =  26,864  heat -units  =  D. 

(The  speciflo  heat  of  the  entering  oil  Is  Approximately  that  of  the  issuing 
gas*) 

The  beat  carried  off  in  1000  cu.  ft.  of  the  escaping  blast  products  Is  86.592 
(weight)  X  .23645  (sp.  heat)  x  1474*'  (rise  of  temp.)  =  a0,18()  heat-units:  the 
teinperacure  of  the  escaping  blast  gases  being  1560*  F.,  and  that  of  the 
entering  air  76*  F.  But  the  amount  of  the  blast  gases,  by  registra- 
tion of  an  anemometer,  cheeked  by  a  calculation  from  the  analyses  of  the 
blast  gases,  was  2457  cubic  feet  for  every  1000  cubic  feet  of  carbu  retted  gas 
made.  Hence  the  heat  carried  off  per  M.  of  carburetted  gas  fs  80,180  x 
2.457  =  74,152  heat-units  =  K 

Experiments  made  by  a  radiometer  covering  four  square  feet  of  the  shell 
of  the  apparatus  gave  figures  for  the  amount  of  heat  lost  by  radiation 
=  ie,454  neat-units  c  F^  and  by  convection  a  15,696  heat-units  ==  Q. 

The  heat  rendered  latent  by  the  gaseflcation  of  the  oil  was  found  by  taking 
the  difference  between  all  the  heat  fed  into  the  carburetter  and  super- 
heater and  the  total  heat  dissipated  therefrom  to  be  12.841  heat-units  =  H. 
The  sensible  heat  in  the  aah  and  unconsumed  coal  is  9.9  lbs.  X  1500*  x  .95 
(sp.  ht.)  =  3712  heat-unite  sz  I. 

The  sum  of  aU  the  items  B  4- C+D+ J? -fF-f  (P  +  H-f/^  327,205  heat- 
units,  which  substracted  from  the  heat  energy  of  the  combustible  consumed, 
810,750  heat-units,  leaves  13,456  hea^units,  or  4  percent,  unaccounted  for. 

Of  the  total  heat  energy  of  the  coal  consumed,  or  340,750  heat-units,  the 
energy  wasted  Is  the  sum  of  items  i>,  E,  F,  (7,  and  /,  amounting  to  132,878 
heat-units,  or  89  per  cent;  the  remainder,  or  207,672  heat-units,  or  61  per 
cent,  being  utilised.  The  efficiency  of  the  apparatus  as  a  heat  machine  is 
therefore  61  per  cent 

Five  gallons,  or  85  lbs.  of  crude  petroleum  were  fed  Into  the  carburetter 
per  1000  cu.  ft.  of  gas  made;  deducting  5  lbs.  of  tar  recovered,  leaves  SO  lbs. 
X  20,000  =  600,000  heat-units  as  the  net  heating  value  of  the  petroleum  used. 
Adding  this  to  the  heating  value  of  the  coal,  840,750  B.  T.  IT.,  gives  940.T50 
neat-units,  of  which  there  is  found  as  heat  energy  in  the  carburetted  gas.  as 
in  the  table  below,  764,050  heat  units,  or  81  per  cent,  which  is  the  commer- 
cial efficiency  of  the  appai-atus,  I.e.,  the  ratio  of  the  energy  contained  in 
*-he  finished  product  to  the  total  energy  of  the  coal  and  oil  consumed. 

x1ie  heating  power  per  M.  cu.  ft.  of  ]    The  heating  power  per  M.  of  the 
the  carbiu'etted  gas  la  uncarburetted  gas  Is 

CX),       38.0  CO,   86.0 

c,H,«  146.0  x  -iiraao  x  21222.0  =  sns^oo  co  434.0  x  .otsioo  x  4305.6  =  i4«99i 

CO  280.0  X. 0781 00  X    43tt5.6  =   oeR'O  T      

('H4  170.0  X  .0146*)  X  24021.0  =  182210  J 

H  356.0  X  0U6694  X  61524.0  =:  122520 
N  10.0 


1000.0  827268 

1000.0  764050 

*  The  heating  value  of  the  illuminanta  Ci»H,f»  is  assumed  to  equal  that 
of  CtH«. 


H      518.0  X  .005594  X  61524.0  =  178277 
N        18.0 


656  tLLUMlN  ATI  KG-GAS. 

The  candlp-power  of  the  gas  ie  81,  or  0.2  candle-power  per  gallon  of  oU 
used.    The  calculated  specific  gravity  is  .6355,  air  being  1. 

For  description  of  the  operation  of  a  modem  carburetted  water-gas 
plant,  see  paper  by  J.  Stelfuz,  Eng^g,  July  20,  1K94,  p.  89. 

Space  required  for  a  'Water-sae  Plant.— Mr.  Shelton,  taking 
15  modem  plants  of  the  form  requiring  the  most  floor-space,  figures  ilie 
average  floor-space  required  per  1000  cubla  feet  of  daily  capacity  as  follows: 

^ater-gas  Plants  of  Capacity  Require  an  Area  of  Floor-space  for 

in  24  hours  of  each  1000  cu.  ft.  of  about 

100,000  cubic  feet 4  square  feet. 

800,000    "         •'    8.5    •» 

400.000    "         "    2.75  *• 

600,000    **        "    8  to2.58q.ft. 

7  to  10  million  cubic  feet 1.25  to  1.5  sq.ft. 

These  figures  include  scrubbing  and  condensing  rooms,  but  not  boiler  and 
engine  rooms.  In  coal-gas  plants  of  the  most  modern  and  compact  forms  one 
Willi  16  benches  of  9  retorts  each,  with  a  capacity  of  1,500,000  cubic  feet  per 
24  tiours,  will  require  4.8  sq.  ft.  of  space  per  1000  cu.  ft.  of  gas,  and  one  of  6 
benches  of  6  retorts  each,  with  300,000  cu.  ft.  capacity  per  24  hours  will  re- 
quire 6  s(|.  ft.  of  space  per  1000  cu.  ft.  The  storage-room  required  for  the 
gas-making  materials  is:  for  coal-gas,  1  cubic  foot  of  room  for  every  232 
cubic  feet  of  gas  made;  for  water-gas  made  from  coke,  1  cubic  foot  of  room 
for  every  878  cu.  ft.  of  gas  made;  and  for  water>gas  made  from  anthracite, 
1  cu.  ft.  of  room  for  every  645  cu.  ft.  of  gas  nude. 

The  comparison  is  still  more  in  favor  of  water-gas  if  the  case  Is  considered 
of  a  water-gas  plant  added  as  an  auxiliary  to  an  existing  coal-gas  plant; 
for,  instead  of  requiring  further  space  for  storage  of  coke,  part  of  that 
alreadv  required  for  storage  of  coke  produced  and  not  at  once  sold  can  be 
cut  off.  by  reason  of  the  water-gas  pLant  creating  a  constant  demand  for 
more  or  less  of  the  coke  sopi-oduced. 

Mr.  Shelum  gives  a  calculation  showing  that  a  water-gas  of  .625  sp.  gr. 
would  require  gas-mains  eight  per  cent  gi'eater  in  diameter  than  the  same 
quantity  conl-gas  of  .425  sp.  gr.  If  the  same  pressure  is  maintained  at  the 
holder.  The  same  quantity  may  be  carried  in  pipes  of  the  same  diameter 
if  the  pressure  is  increased  in  proportion  to  the  specific  gravity.  With  the 
same  pressure  the  increase  of  candle-power  about  balances  the  decrease  of 
flow.  With  five  feet  of  coal-gas,  giving,  say,  eighteen  candle-power,  1  cubic 
foot  equals  8.6  candle-power;  with  water-gas  of  23  candle-power,  1  cubic 
foot  equals  4.0  candle-power,  and  4  cubic  feet  gives  18.4  candle-power,  or 
mora  than  is  given  by  5  cubic  feet  of  coal-sras.  Water-gas  may  be  made 
from  oven-coke  or  eas-house  coke  as  well  as  from  anthracite  coal.  A  water- 
gas  plant  may  be  conveniently  run  in  connection  with  a  coal-gas  plant,  the 
surplus  retort  coke  of  the  latter  being  used  as  tlie  fuel  of  the  former. 

In  coal-gas  making  It  is  impracticable  to  enrich  the  gas  to  over  twenty 
candle-power  without  causing  too  great  a  tendency  to  smoke,  but  water- ga«i 
of  as  high  as  thirty  candle-power  is  quite  common.  A  mixture  of  coal-gas 
ait<i  water-gas  of  a  hieher  C.P.  than  *«>0  can  be  advantageously  distributetl 

Fuel-value  of,  IllumlnaUne-saa.— E.  G.  Love  (School  of  Mines 
Qtly,  January,  1892)  describes  F.  W.  Hartley's  calorimeter  for  determining 
the  cHlorific  power  of  eases,  and  gives  results  obtained  in  tests  of  the  car- 
buretted water-gas  made  by  the  municipal  branch  of  the  Consolidated  Co. 
of  New  York.  The  tests  were  made  from  time  to  time  during  the  past  twi> 
years,  and  tbe  flgures  give  the  heat-units  per  cubic  foot  at  60*  F.  and  80 
inches  pressure:  715.  602. 725,  782,  691,  738,735,  708,  784,  730,  781,727.  Average, 
721  heat  imits.  Similar  tests  of  mixtures  of  coal-  and  water-gases  made  by 
other  branches  of  the  same  company  give  694,  715,  684,  692,  727,  665,  696,  anil 
686  heat-units  per  foot,  or  an  average  of  694.7.  The  average  of  all  ihesn 
tests  was  710.5  neat-units,  and  this  we  mav  fairly  take  as  representing  th^* 
calorific  power  of  the  illuminating  gas  of  New  York.  One  thousand  feet  of 
this  gas,  costing  $1.25.  would  then^fore  yield  710,500  heat-units,  which  would 
be  equivalent  to  568,400  heat-units  for  $1.00. 

The  common  coal  gas  of  London,  with  an  illuminating  power  of  16  to  17 
candles,  has  a  calorific  power  of  about  668  units  per  foot,  and  costs  from  60 
to  70  cents  per  thousand. 

The  product  obtained  by  decomposing  steam  by  incandescent  carbon,  as 
efTected  in  the  Motay  process,  consists  of  about  iOH  of  CO,  and  a  little  over 
SOjtofH. 


FLOW  OF  GAS  IN  PIPES.  657 

TUs  mixture  would  have  a  heatlng*power  of  about  SOO  units  per  cubic  foot, 
and  if  sold  at  SOcents  per  lOOO  cubic  feet  would  furnish  600.000  units  for  $1.00, 
as  compared  with  568,400  units  for  $1.00  from  illuminating  ga»  at  $l.:i5  per  1000 
cable  feet.  This  illuminating-gas  if  sold  at  $1. 15  per  thousand  would  there- 
fore  be  a  more  economical  heaiinj?  agent  than  the  fuel-gas  mentioned,  at  SO 
cents  per  thousand,  and  be  much  more  advantageous  than  the  latter,  in  that 
one  main,  service,  and  meter  could  be  used  to  furnish  gas  for  both  lighting 
and  beating. 

A  large  number  of  fuel-gases  tested  bjr  Mr.  Love  gave  from  184  to  470  heat- 
nnits  per  foot,  with  an  average  of  800  units. 

Taking  the  cost  of  heat  from  illuininating^gas  at  the  lowest  llgure  given 
by  Mr.  Love,  vis.,  $1.00  for  600,000  heat-units,  it  is  a  very  expensive  fuel,  equal 
to  coal  at  $40  per  ton  of  2000  lbs.,  the  coal  having  a  caioriflc  power  of  oaty 
12,000  heat-uniu  per  pound,  or  about  8S%  of  that  of  pure  carbon: 

000,000  :  (12,000  X  SOOO) ::  $1 :  $40. 


FliOW  OF  OAS  IN  PIPES. 

The  rate  of  flow  of  gases  of  different  densities,  the  diameter  of  pipes  re 
quired,  etc.,  are  given  in  King's  TreaUse  on  Coal  Qas,  voL  ii.  874,  as  follows: 


If  d  =s  diameter  of  pipe  In  inches, 
Q  s  quantity  of  gas  in  cu.  ft.  per 

hour, 
I  =  length  of  pipe  in  yards, 
h  S3  pressure  m  inches  of  water, 
s  =  specific  gravity  of  gaa,  air  be- 
ing 1, 


Molesworth  gives  Q  s  lOOOi/^ 


■V: 


(1850)«/1* 


(1850)«d»  ' 


g=1850d.|/^=1350y^. 


^.T.Om,  Am.  Ga9^gki  Jour.  1894, gives  Q s ]20!i/lj^^. 

This  formula  Is  said  to  be  based  on  experimental  data,  and  to  make  allow. 
ance  for  obstructions  by  tar,  water,  aud  other  bodies  tending  to  check  the 
flow  of  gas  through  the  pipe. 

A  set  of  tables  in  Appletoirs  Cyc.  Mech.  for  flow  of  gas  in  2.  6,  and  12  in. 
pipes  is  calculated  on  the  supposition  that  the  quantity  delivered  varies 
as  the  square  of  the  diameter  instead  of  as  d*  x  ^if,  or  ^d*. 

These  tables  give  a  flow  in  large  pipes  much  less  than  tliat  calculated  by 
the  formulas  above  given,  as  is  shown  by  the  following  example.  Length  of 
pipe  100  yds.,  specific  gravity  of  gas  0.42,  pressure  l-ln.  water-column 

8-in.  Pipe.     6-in.  Pipe.     18-ln.  Pipe. 
gsiacOj/^ 1178  18.868  108,019 

g«1000i/^ 878  18,606  78,078 

'    Q^mij^/^^^ 1118  16,827  98,845 

Table  in  App.  Cyc 1200  11,657  46,628 


An  experiment  made  by  Mr.  Clegg,  in  London,  with  a  4-in.  pipe,  6  miles 
long,  pressure  8  in.  of  W8t«>r,  specilic  gravity  of  gas  .896,  gave  a  discharge 
Into  the  atmosphere  of  852  cu.  ft.  per  hour,  after  a  correction  of  33  cu.  ft. 


was  made  for  leakage.  

Substituting  this  value,  862  cu.  ft.,  for  Q  in  the  formula  Q  =  C  ^d^h  -*-  si, 
are  And  C.  the  coefficient,  =  997,  which  corresponds  nearly  with  the  formula 
gfiven  by  Molesworth.  , 


658 


ILLUMINATING-GAS. 


Serrleea  for  I«aiiip«.  (Molesworth.) 
Ft.  fi-om      Require 

Main.       Pipe- bore. 
...    40  9^tn. 

...    40  \iln. 

...    50  H^Q- 

...  100  ^in. 

(In  cold  climates  no  serTice  less  than  9i  in-  should  be  used.) 


4., 

6., 
10. 


BKAXlmuiift 


of  Gas  tlironsli   Pipes  In  en*  fH. 


Hour,  Speclfie  GraTltjr  being  iaken  "at  .45,  calenlal 
Drom  the  Formula  Q  =  1000  Vd*h  ■^■•i.   (Molesworth.) 


s:^ 


Length 

OF  Pipe  =  10  Yam 

IflL 

Diameter 

Pressure  by  the  Water-gauge  In  Inches. 

of  Pipe  in 
Incbee. 

.1 

.8 

.8 

.4 

.5 

.6 

.7 

.8 

.0 

1.0 

H 

13 

18 

28 

26 

89 

81 

84 

86 

88 

41 

« 

86 

87 

40 

53 

60 

64 

TO 

74 

70 

83 

'  % 

78 

108 

186 

145 

162 

187 

108 

205 

218 

830 

1 

140 

211 

25S 

898 

888 

866 

894 

422 

447 

471 

Ik 

260 

368 

451 

621 

682 

688 

689 

787 

781 

883 

IH 

411 

681 

711 

821 

918 

1006 

1082 

1108 

1832 

1290 

8 

843 

1198 

1460 

1686 

1886 

2066 

2281 

8385 

8580 

8667 

Lknoth 

OF  Pipe  s=  100  Yards. 

Pi-BB*tire  br  the  WaLer-gauipi^  in  Inches. 

.1  f  .2  i   -3 

.4 

.a 

.715 

1,0 

1.5 

8 

8.S 

^ 

B.     \ti     U 

1? 

19 

iil 

an 

88 

36 

4< 

33,    m     *2 

46 

Bl 

ea 

n 

«l 

BO 

lOB 

1T6 

1 

47 1   6:    m 

04 

ifn 

1^ 

I4t» 

1*7 

183 

8tl 

J)6 

>H 

8a|  1]Q    143 

IGS 

1B4 

aes 

V«0 

set 

»]9 

ass 

41» 

1^4 

isu   mi  ;£M 

SHO 

t.'ftj 

rtfifi 

4n 

45W 

Rika 

»l 

«<0 

5 

m\  377  m 

63a 

5^ 

7m 

84^ 

1»43 

li»3 

1193 

\^3^ 

^^ 

M  ^9  fitrr 

^^ 

114'^ 

vsn 

14T1t 

ItSIT 

taiM 

iSlV^ 

'^£im 

3 

73;^'Kr'A*Vr,0 

1470 

icri 

•mi 

23:23 

a.'5l)1^ 

^^« 

aa^ 

^-*i 

m 

\<m\i^-^im\ 

SJIil 

:tim 

*sm 

^14^0 

aci^J 

41HJ 

4831 

r»4i>> 

4 

i5i.t«i*ji;«'ri(;iH 

1  30]? 

a37a 

41^1 

4770 

&»H4 

ft&ia 

6740 

vBiS 

Length  of  Pipe  =  1000  Yards. 


Pressure  by  the  Water-gauge  in  Inches. 

.6 

.76 

1.0 

1.5 

2.0 

2.5 

8.0 

1 

88 

41 

47 

68 

67 

76 

8S 

1^ 

08 

113 

180 

150 

184 

805 

886 

8 

180 

281 

267 

327 

877 

488 

468 

^ 

329 

403 

466 

571 

650 

787 

807 

8 

520 

686 

786 

900 

1039 

1168 

1878 

4 

1067 

1806 

1508 

1847 

2138 

2885 

S613 

6 

1863 

2282 

86:35 

3227 

8787 

4107 

4864 

.    •« 

8030 

8600 

4157 

5091 

5870 

6678 

7800 

BtUM. 


65d 


LmoTK  01*  Pm  ts  sooo  Yarm. 


Pressure  by  the  Water-gauge  in  lochai. 

of  Pipe 

Indies. 

1.0 

1.6 

2.0 

9.6 

8.0 

119 

140 

109 

189 

807 

889 

409 

405 

580 

509 

075 

890 

955 

1067 

1108 

1179 

1448 

1607 

1868 

2041 

1&59 

«77 

90S9 

9989 

3220 

2788 

8847 

8865 

4821 

4784 

8S10 

4074 

6897 

wa 

6010 

5128 

0974 

7»45 

8100 

8878 

6007 

8165 

9498 

10541 

11547 

10510 

18880 

14879 

10088 

18215 

Mr.  A.  O.  Humphreys  says  his  experience  goes  to  show  that  these  tables 
give  too  small  a  now,  but  It  is  difficult  to  accurately  check  the  tables,  on  ac- 
count of  the  extra  friction  introduced  by  rough  pipes,  bends,  etc.  For 
bends,  one  rule  is  to  allow  1/42  of  an  inch  pressure  for  each  right-angle  bend. 

Where  there  is  apt  to  be  trouble  from  frost  it  is  well  to  use  no  service  of 
less  diameter  than  f^  in.,  no  matter  how  short  it  may  be.  In  extremely  cold 
climates  this  is  now  often  increased  to  1  in.,  even  for  a  single  lamp.  The  besi 
practice  in  the  U.  S.  now  condemns  any  service  lees  than  f^  in. 

STSAJff. 


The  Ventpemtttlfe  of  Steam  in  contact  with  water  depends  upon 
the  pressure  under  which  it  ia  generated.    At  the  ordinary  atmospheric 

Kressure  (14.7  lbs.  per  sq.  in.)  its  temperature  Is  21 2«  F.    As  the  pressure  is 
icreased,  as  by  the  steam  being  generated  in  a  closed  vessel,  its  tempera* 
ture,  and  that  of  thn  water  in  its  presence,  increases. 
-  SatnrAted  Steam  is  steam  of  the  temperature  due  to  Its  pressure— 
not  superheated. 

Svperlieated  Steam  Is  steam  heated  to  a  temperature  above  that  due 
to  Its  pressure. 

nry  Steam  is  steam  which  contains  no  moisture.  It  may  be  either 
saturated  or  superheated. 

l¥et  Steam  is  steam  containing  intermingled  moisture,  mist,  or  spray. 
It  has  the  same  temperature  as  dry  saturated  steam  of  the  same  pressure. 

Water  introduced  into  the  presence  of  superheated  steam  will  flash  into 
Yapor  until  the  temperature  of  tlie  steam  is  reduced  to  that  due  its  pres- 
sure. Water  in  the  presence  of  saturated  steam  has  the  fiame  temperature 
as  the  steam.  Should  cold  water  be  Introduced,  lowering  the  temperature 
of  the  whole  mass,  some  of  the  Kteam  will  be  condensed,  reducing  toe  press- 
ure and  temperature  of  tlie  remainder,  until  an  equilibrium  is  established. 

Temperature  and  Preeanre  of  Saturated  Steam.— The  re- 
lation between  the  temperature  and  the  pressure  of  steam,  according  to 
Regnauirs  experiments.  Is  expressed  by  the  formula  cBuchauan's,  as  given 

by  Clark)  fax  g--^-^^-^-—r 871.85,  in  which  p  Is  the  pressure  in  pounds 

per  square  Inch  and  t  the  temperature  of  the  steam  In  Fahrenheit  degrees. 
It  applies  with  accuracy  between  120*>  F.  and  446*>  F.,  corresponding  to  pres- 
surefl  of  from  1.68  lbs.  to  445  lbs.  per  square  inch.  (For  other  formuUe  see 
Wood*fl  and  Peabody^s  Thermodynamics.) 

Total  Heat  of  Saturated  Steam  (above  92?  F.).— According  to 
Regnault's  experiments,  the  formula  fur  total  heat  of  steam  Is  1/  =  1091 .7 -f- 
.805(t  —  320).  in  which  t  is  temperature  Fahr.,  and  H  the  heat-units.  (Ran- 
kine  and  many  others;  Clark  gives  1091.16  instead  of  1091.7.) 

I<atent  Heat  of  Steam.— The  formula  for  latent  heat  of  steam,  as 
given  by  Rankine  Mid  othera.  Is  L  =  1091.7  -  .695(f  -  82«).  Clauslus's  for- 
mula, In  Fahrenheit  units,  as  given  by  Clark,  is  L  =  1092.0  -  SOS^t  -  82"). 


660  STEAM. 

The  total  heat  In  steam  (above  92?)  Includes  three  elements: 

Ist.  The  heat  required  to  raise  the  temperature  of  the  water  to  the  tem- 
perature of  the  steam. 

id.  The  heat  required  to  evaporate  the  water  at  that  temperature,  called 
internal  latent  heat. 

8d.  The  latent  heat  of  volume,  or  the  external  work  done  by  the  steam  in 
maklnfir  room  for  itself  against  the  pi^essure  of  the  superincumbent  atmos- 
phere (or  surrouodini?  steam  if  inclosed  in  a  vessel). 

The  sum  of  the  last  two  elements  is  called  the  latent  heat  of  steam.  In 
BueVs  tables  (Weisbach,  vol.  ii.,  Dubois's  translation)  the  two  elements  are 
given  8ei>arately. 

I«ateiit  Heat  of  Tolnnia  of  Saturated  Steam.  (External 
Work.)— The  followiuK  formulas  are  sufficiently  accurate  for  occasional  use 
within  the  given  ranges  of  pi^ssure  (Clark,  8.  £.): 

From  14.7  lbs.  to  60  lbs.  total  pressure  per  square  inch. . .  56.900  +  .OTTSf. 
From  60  lbs.  to  SOO  lbs.  total  pressure  per  square  inch.. . .  60.191  +  .06551. 

Heat  required  to  Generate  1  lb.  of  Steana  from  water  at  82*  F. 

Heat-units. 
Sensible  heat,  to  raise  the  water  from  82«  to  212»  = . . . .  180.9 

Latent  heat,  1,  of  the  formation  of  steam  at  212<^  s 891.0 

8,  of  expansion  against  the  atmospheric 
pressure,  21 16.4  lbs.  per  sq.  *t.  X26.86  cu.  ft. 
=  65,786  foot-pounds  H-rra= 71.7     965.7 

Total  heat  above  82»F 1146.6 

The  Heat  Unitj.  or  Brltlah  X^^^nnal  Unit*— The  definition  of 
the  heat-unit  used  in  tlils  work  is  that  of  Rankine,  accepted  by  most  modem 
writers,  viz.,  the  quantity  of  heat  required  to  raise  the  temperature  of  1  lb. 
of  water  1*  F.  at  or  near  its  temperature  of  maximum  density  (89.1*  F.). 
Peabody*s  definition,  the  heat  required  to  raise  a  pound  of  water  from  6si* 
to  6'^<>  F.  is  not  generally  accepted.  (See  Thurston,  Trans.  A.  S.  M.  E., 
xiii.  351.) 

Speelllc  Heat  of  Saturated  Steam*— The  specific  heat  of  satu- 
rated steam  is  .806,  that  of  water  being  1;  or  it  is  1.281,  if  that  of  air  be  1. 
Tlie  expression  .806  for  specific  heat  is  taken  in  a  compound  sense,  relating 
to  changes  both  of  volume  and  of  pressure  which  takes  place  in  the  eleva- 
tion of  temperature  of  saturated  steam.    (Clark,  S.  £.) 

This  Htatement  by  Clark  is  not  strictly  accurate.  When  the  temperature 
of  saturated  steam  is  elevated,  water  being  present  and  the  steam  remain- 
ing saturated,  water  is  evaporated.  To  raise  the  temperature  of  1  lb.  of 
water  1^  F.  requires  1  theruial  unit,  and  to  evaporate  it  at  P  F.  higher  would 
require  0.695  lens  thermal  unit,  the  latent  heat  of  saturated  steam  decreas- 
ing 0.695  B.T.U.  for  each  increase  of  temperature  of  1"  F.  Hence  0.905  is 
the  specific  heat  of  water  and  its  saturated  vapor  combined. 

Wlien  a  unit  weight  of  saturated  steam  is  increased  in  temperature  and  in 
pressure,  the  volume  decreasing  so  as  to  Just  keep  it  saturated,  the  specifl c 
neat  is  nej^aiive,  and  decreases  as  teuipeiature  increasea  (See  Wood, 
Therm.,  p.  147;  Peabody,  Therm.,  p.  98.) 

Denaltjr  and  Tolume  of  Saturated  Steam.— The  density  of 
steam  is  ezpreMsed  by  the  weight  of  a  ^iven  volume,  say  one  cubk;  foot;  and 
tlie  volume  is  expressed  by  the  number  of  cubic  feet  in  one  pound  of  steam. 

Mr.  Brownlee's  expression  for  the  density  of  saturated  steam  in  terms  of 
n-Ml 
the  pressure  is  Z>  =  ^k-^*  or  log  D  =  .941  Iogp-2.519,  in  which  i>  is  the  den- 
sity, and  p  the  pressure  in  pounds  per  square  inch.    In  this  expression,  p**«> 
is  the  equivalent  of  p  raisea  to  ttie  16/17  power,  as  employed  by  Bankine. 

The  volume  v  t>eing  the  reciprocal  of  tlie  density, 

V  =  ^;^7,  or  log  V  =  2.519  -  .941  log  p. 

Relative  Volnooie  of  Steam.— The  relative  volume  of  saturated 
steam  is  expressed  by  the  uumber  of  volumes  of  steam  produced  from  one 


STBAIC  661 

▼oliime  of  water,  the  volume  of  water  beinff  measared  at  the  temperature 
89*  F.  The  relative  volume  is  found  by  muitiplyinf?  the  volume  in  cu.  ft.  of 
one  lb.  of  steam  by  the  weisrht  of  a  cu.  ft.  of  water  at  89*  F.,  or  es.4?5  lbs. 

CMUMOtta  Steam.— ^hen  saturated  steam  is  superheated,  or  sur- 
chan^ed  with  lifat,  it  advances  from  the  ooodition  of  saturation  into  that  of 
fira.«eity.  The  gaseous  state  is  only  arrived  at  by  considerably  elevating  the 
temperature,  supposing:  tiie  pressure  remains  the  same.  Steam  thus  suffl- 
cieiitlv  superheated  is  known  as  gaseous  steam  or  steam  n^as. 

Xoital  Heat  of  Gaaeons  Steam.— Regnault  found  that  the  total 
heat  of  gaseous  steam  increased,  lilce  that  of  saturated  steam,  uniformly 
with  the  temperature,  and  at  the  rata  of  .475  thermal  unite  per  pound  for 
each  degree  of  temperature,  under  a  constant  pressure. 

The  general  formula  for  the  total  heat  of  gaseous  steam  produced  from 
1  pound  of  water  at  88*  F.  is  ff  =  1074.6  +  .475«.  [This  formula  i>»  for  vapor 
generated  at  82*.  It  is  not  true  if  generated  at  218*,  or  at  any  other  tempera- 
ture than  82*.    (Prof.  Wood.)! 

The  Speellle  Heat  of  Gaseous  Steam  is  .476,  under  constant 
pressure,  as  found  by  Regnanlt.  It  Is  identical  with  the  coefficient  of  in- 
cneane  of  total  heat  for  each  degree  of  temperature.  [This  is  at  atmospheric 
pressure  and  812*  F.  He  found  it  not  true  fur  any  otner  pressure.  Tlieory 
ludicates  that  it  would  be  greater  at  higher  temperature)*.    (Prof.  Wooci.)J 

The  Speellle  Henelty  of  Gaaeone  Steam  is  .628,  that  of  air  being 
1.  That  IS  to  say,  the  vi  eight  of  a  cubic  foot  of  gaseous  steam  is  about  five 
eighths  of  that  of  a  cubic  foot  of  air,  of  the  same  pressure  and  temperature. 

The  density  or  weight  of  a  cubic  foot  of  gaseous  8t«am  is  expressible  by 
the  same  formula  as  Uiat  of  air,  except  that  the  multiplier  or  coefficient  m 
leM  In  proportion  to  the  less  specific  density.    Thus, 


_  2.7074P  X  .622  __  1 


«-f461        ""  «+46r 

in  which  IX  Is  the  weight  of  a  cubic  foot  of  gamK>us  steam,  p  the  total  pres- 
sure per  square  inch,  and  /  the  temperature  Fahrenheit. 

Superheated  Steam.  —The  above  remarks  concerning  gaseous  steam 
are  taken  from  Clark's  Sienm-engine.  Wood  gives  for  the  total  heat  (above 
82*)  of  superheated  steam  fl  =  1091.7  -|-  0.48(f  -  8'J*). 

The  following  is  abridged  from  Peabo<1y  (Therm.,  p.  115,  etc.). 

When  far  removed  from  the  temperature  of  saturation,  superheated  steam 
follows  the  laws  of  perfect  gases  very  nearly,  but  near  the  temperature  of 
saturation  the  departure  from  those  laws  is  too  great  to  allow  of  calculations 
by  them  for  engineering  purposes. 

The  specific  beat  at  constant  pressure,  Cp^  from  the  mean  of  three  experi« 
ments  by  Regnault.  Is  0.4805. 

Values  of  the  ratio  of  Q>  to  specific  heat  at  constant  volume: 

Pressurep,  pounds  per  square  inch..       6        60       100      200       800 
RatioCi>-HCv  =  ifc=      1.8861.888    1.880    1.824    1.816 

Zeuner  takes  fe  as  a  constant  =  1 .  838. 

SPBcmo  HsAT  AT  Constant  Voluxb,  Supbrhkatbd  Stbam. 

Pressure,  pounds  per  square  inch 6      60       100      200      300 

Specific  heat  CV 0.851.348    .846     .844     .841 

It  Is  quite  as  reasonable  to  assume  that  Cv  is  a  constant  as  to  suppose  tliat 
Cp  is  constant,  as  has  been  assumed.  If  we  take  Op  to  be  oonstaut,  then  Ojp 
will  appear  as  a  variable. 

If  p  =  pressure  In  lbs.  per  sq.  ft.,  v  =  volume  in  cubic  feet,  and  T  a 
temperature  in  degrees  Fahrenheit  +  460.7,  then  pv  =  93.57*—  Kipi. 

Total  heat  of  superheated  steam,  H  =  0.4805(r  -  10.38pi)  4-  867.2. 

The  Battonallsatlon  of  Resnault's  Experiments  on 
Steam*  <J.  McParlane  Gray,  Proc.  Inst.  M.  E.,  July,  ihHU.)  -The  fnrmulsa 
constructed  by  R^msult  are  strictly  emplHcal,  and  were  based  entirely  on 
his  experiments.  They  are  therefore  not  valid  beyond  the  range  of  temper- 
atures and  pressures  observed. 

Mr.  Gray  has  made  a  most  elaborate  calculation,  based  not  on  experiments 
but  on  fundamental  principles  of  thermodynamics,  from  which  he  de<luce8 
formulee  for  the  pressure  and  total  heat  of  steam,  and  presents  tables  calcu- 


6G2 


STEAK. 


lMt«d  therefrom  which  show  subucantial  afirre«'inent  with  Regnault*s  flicnrea. 
Re  frivkis  the  following  examples  of  steam-preraures  calculated  for  tempera- 
ture«  beyoud  the  range  of  R<»g7iaiilt's  experiments. 


Temperature. 

Pounds  per 
BQ.  in. 

Temperature. 

Pounds  per 

C. 

Fahr. 

C. 

Fahr 

sq.  in: 

sao 

240 

eso 

900 
280 
800 
9i» 

446 
464 
482 
600 
536 
672 
606 

406.9 
488.9 
679.9 
Q91.6 
940.0 
12G1.8 
1661.9 

840 
860 
880 
400 
415 
427 

644 

080 
716 
752 
779 
800.6 

2156.2 
8744.5 
8448.1 
4800.9 
6017.1 
5609.0 

These  pressiires  are  hif^her  than  those  obtained  by  Regnault*8  formula, 
which  privfs  for  415®  O,  only  4067.1  lbs.  per  square  inch. 

Table  of  the  Properties  of  Satnrated  Steam*— In  the  table 
of  properties  of  saturated  steam  on  th«  following  pages  the  fljc nre«  for  tem- 
perature, total  heat,  and  latent  heat  are  taken,  up  to  210  lbs.  absolute  pres- 
sure, from  the  tables  in  Porter's  Steam-engine  Indicator,  which  tables  naTe 
been  widely  accepted  as  standard  by  Amerienn  engineers.  The  flgiires  for 
total  heat,  given  in  the  originnl  ns  from  0*  F.,  have  been  changed  to  heat 
above  8-2«  F.  The  figures  for  weight  per  cubic  foot  and  for  cubic  feet  per 
pound  have  been  talcen  from  Dwelshauvers-Derj'^s  table, Trans.  A.  8.  M.  E., 
vol.  xi ,  as  being  probably  more  accurate  than  those  of  Porter.  The  figures 
for  relative  volume  are  from  BuePs  table,  in  Dubois's  translation  of  Wels- 
bacb,  vol.  ii.  They  agi-ee  auite  closely  with  the  rdn tive  v>  Inmes  calculated 
from  weights  as  given  by  Uwelshauvers.  From  I'll  tn  219  lbs.  the  figures 
for  temperature,  toial  heftf,  and  lat«Mit  boat  are  from  Dwelshauvers'  uble  ; 
and  from  220  to  1000  lbs.  nil  th«  figures  are  from  Duels  table.  The  figures 
have  not  been  carried  out  to  as  many  decimal  places  as  they  are  In  uiost  of  the 
tables  given  by  tbo  difTerent  authorities  ;  but  any  figure  beyond  the  fourth 
significant  figure  is  nnneceKsnry  in  practice,  nnd  beyoud  the  limit  of  error  of 
the  observation*  and  of  ibo  foruuila)  from  which  the  figures  were  derived. 

ITelfflit  of  1  Cable  Foot  of  Steam  In  Doclmalfi  of  a  Pound* 
Comparison  of  BlflTerent  Anthorltlea. 


Weight  of  1  cubic  foot 
according  to— 

m 

Weight  of  1  oublo  foot 
according  to— 

Por- 
ter. 

Clark 

Buel. 

Dery. 

.00299 

!6.W7 
.0972 
.1423 
.1869 
.2290 

Pea- 
body. 

Por- 
ter. 

Clark 

Buel. 

Deiy. 

Pea 

body 

1 

14.7 
SO 
40 
60 
80 
100 

.oaw 

.08797 

.0511 

.0994 

.1457 

.19015 

.28302 

.008 

.0380 

.0507 

.0974 

.14','5 

.186^ 

.2307 

.00303 

.0379?! 

.0607 

.0972 

.14'J4 

.1K66 

.2803 

.00-299 
.0876 
.0502 
.0064 
.1409 
.1843 
.«71 

120 
140 
160 
180 
200 
820 
iMO 

.27428 
.31386 
.85200 
.88805 
.42496 

.2738 
.8162 
.8590 
.4009 
.4431 
.4843 
.6248 

.2785 
.8168 
.8589 
.4012 
.44.38 
.4859 
.5270 

.2724 
.8147 
.1VS7 
.8088 
.4400 

.2605 
.3113 
.8580 
8945 
.4859 
.4772 
.5186 

There  are  considerable  diflferences  between  the  figures  of  weight  and  vol- 
iitnt'  of  steam  as  given  by  different  authorities.  Porter's  figures  are  baaed 
on  the  experiments  of  Falrbairn  and  Tate.  The  figures  given  by  the  other 
authorities  are  derived  from  tlieoretical  formulae  which  are  believed  to  give 
more  reliable  results  than  the  escperlments.  The  figures  for  temperature, 
total  heat,  and  latent  hefit  as  given  by  different  authorities  show  a  practical 
agreetnent.  all  being  derived  from  Regnanlt's  experiments.  See  Peabody^s 
Tables  of  Saturated  Steam;  aleo  Jacobus,  Ti'ttos.  A-  &•  M.  fi«f  vol.  xU.,  598. 


SIBAX. 


663 


Propertlea  of  Saturated  ttoam. 

p 

Ill 

III 

II 

Total  Heat 
above  38»  F. 

111 

is: 

is 

5^ 

In  the 

In  the 

II 

P 

Water 

h 
Heat. 

Steam 

H 
Heat. 

1^1 

I- 

^ 

< 

units. 

units. 

^ 

99.74 

.089 

82 

_ 

1001.7 

1091.7 

806060 

8833.8 

.00060 

».67 

.m 

40 

8. 

1094.1 

1086.1 

154830 

8478.8 

.00040 

29.56 

.176 

50 

18. 

1007.8 

1079.8 

loroao 

1784.1 

.00058 

89.40 

.254 

60 

88.01 

1100.8 

1078.8 

76870 

1883.4 

.00068 

».19 

.359 

70 

88  02 

1103.3 

1065.3 

64660 

876.61 

.00115 

88.90 

.608 

80 

48.04 

1106.3 

1058.8 

39690 

685.80 

.00158 

a8.51 

.^92 

00 

68.06 

1109.4 

1051.3 

29890 

469.80 

.00813 

28.00 

.948 

100 

68.08 

1118.4 

1044.4 

81880 

849.70 

.00886 

27.88 

1 

loa.t 

70.09 

1118.1 

1043.0 

90688 

834.88 

.00899 

85.«5 

2 

188.8 

94.44 

1120.5 

1086.0 

10730 

173.83 

.00577 

23.83 

8 

141.6 

109.9 

1185.1 

1015.3 

7885 

117.98 

.00648 

21.78 

4 

158.1 

181.4 

1188.6 

1007.8 

5588 

89.80 

.01118 

19.74 

6 

168.8 

180.7 

1181.4 

1000.7 

4580 

78.50 

.01378 

17.70 

6 

170.1 

138.6 

1133.8 

905.8 

8816 

61.10 

.01681 

15.67 

7 

178.9 

145.4 

1135.9 

990.5 

8808 

63.00 

.01887 

13.63 

8 

188.9 

151.5 

1187.7 

986.8 

8918 

46.60 

.02140 

11.60 

9 

186.8 

156.9 

1189.4 

968.4 

8607 

41.88 

.08891 

9.66 

10 

193.8 

161  9 

1140.9 

979.0 

2861 

87.80 

.08641 

7.S2 

11 

197.8 

166.5 

1148.8 

975.8 

2150 

84.61 

.08889 

5.49 

18 

902.0 

170.7 

1148.6 

972.8 

1090 

31.90 

.08136 

3.45 

13 

905.9 

174.7 

1144.7 

970.0 

1846 

89.58 

.06881 

1.41 

14 

809.0 

178.4 

1145.9 

967.4 

1781 

27.69 

.08685 

Gauge 

Pressure 
lbs.  per 
aq.  in. 

14.7 

818 

180.9 

1146.6 

965.7 

1646 

26.86 

.08794 

0.804 

15 

218.0 

181.9 

1146.9 

965.0 

1614 

25.87 

.08868 

1.3 

16 

816.8 

185.8 

1147.9 

962.7 

1519 

24.88 

.04110 

8.8 

17 

819.4 

188.4 

1148.9 

960.5 

1484 

88.98 

.04858 

3.8 

18 

888.4 

191.4 

1140  8 

958.3 

1359 

21.78 

.04598 

4.8 

19 

885.8 

194.3 

1150.6 

966.8 

1298 

90.70 

.04831 

6.8 

90 

887.0 

197.0 

1151.6 

954.4 

1281 

19.78 

.06070 

6.3 

81 

280.5 

199.7 

1158.8 

962.6 

1176 

18.84 

.05308 

7.8 

98 

883.0 

908.8 

1153.0 

950.8 

1126 

18.03 

.05545 

8.8 

88 

285.4 

804.7 

.7 

949.1 

1080 

17.80 

.05788 

9.8 

84 

887.8 

207.0 

1154.5 

947.4 

1038 

16.62 

.06018 

10.8 

85 

840.0 

809.3 

1155.1 

945.8 

996.4 

16.99 

.06853 

11.3 

86 

848.8 

211.5 

.8 

944.3 

962.8 

15.48 

.06487 

1S.8 

87 

844.3 

813.7 

1156.4 

942.8 

988.8 

14.88 

.06721 

13.8 

88 

846.8 

215.7 

1157.1 

941.8 

897.6 

14.88 

.06955 

14.8 

89 

848.:i 

217.8 

.7 

980.9 

868.6 

18.91 

.07188 

15.8 

80 

860.2 

219.7 

1158.8 

988.9 

841.8 

18.48 

.07480 

16.3 

31 

852.1 

281.6 

.8 

937.2 

815  8 

13.07 

.07658 

17.3 

88 

8540 

888.5 

1169.4 

935.9 

701.8 

18.68 

.07884 

18.8 

83 

255.7 

8853 

.9 

984.6 

769.8 

18.32 

.06115 

19.8 

84 

257.5 

887.1 

1160.6 

963.4 

748.0 

11.98 

.06846 

90.8 

85 

859.2 

828.8 

1161.0 

938.2 

787.9 

11.66 

.08576 

81.3 

86 

260.8 

230.5 

1161.6 

931.0 

708.8 

11.86 

.08806 

83.8 

87 

868.6 

838.1 

1162.0 

989.8 

690.8 

11.07 

.00085 

664 


STEAM. 


Properties  of  Saturated  Steam. 

«  > 

^ 

Total  Heat 

«! 

u^ 

S  k  • 

above  32*  F. 

►4      . 

P  s    * 

3JS 

IS 
III 

1 

S  1  '3 

ll'i 

o— 

I 

In  the 

In  the 

Water 

h 
Heat- 

Steam 

H 
Heat- 

-» lis 

It 

% 

O 

5 

units. 

units. 

>- 

Jc_ 

33.3 

38 

264.0 

888.8 

1168.5 

928T 

673.7 

10.79 

.09964 

•^4.8 

89 

265.6 

885.4 

.9 

927.0 

667.5 

10.63 

.09498 

26.8 

40 

267.1 

886.9 

1163.4 

926.5 

642.0 

10.86 

.00721 

26.3 

41 

868.6 

238.6 

.9 

925.4 

627.8 

10.05 

.09949 

27.3 

42 

270.1 

840.0 

1164  8 

924.4 

fl3.8 

988 

.1018 

28.3 

48 

271.5 

241.4 

.7 

923.3 

699.9 

9.61 

.1010 

29.8 

44 

2?-J.9 

842.9 

1165.2 

922.8 

687.0 

9.41 

.1068 

30.8 

45 

274.3 

844.3 

.6 

921.8 

674.7 

9.21 

.1086 

81.3 

46 

276.7 

845.7 

1166.0 

920.4 

6680 

902 

.1108 

82.8 

47 

277.0 

247.0 

.4 

919.4 

661.7 

8.84 

.1181 

38.8 

48 

278.3 

248.4 

.8 

918.6 

640.9 

8.67 

.1163 

84.3 

49 

879.6 

249.7 

1167.2 

917.5 

580.5 

8.50 

.1176 

85.8 

50 

880.9 

251.0 

.6 

916.6 

690.6 

8.84 

.1196 

80.8 

51 

282.1 

252.2 

1168.0 

915.7 

610.9 

6.19 

.1821 

8T.S 

62 

283.3 

253.5 

.4 

914.9 

601.7 

8.04 

.1948 

88.8 

68 

284.5 

254.7 

.7 

914. 0 

492.8 

7.90 

.1866 

S9.8 

64 

885.7 

236.0 

1169.1 

918.1 

484.8 

7.76 

.1288 

40.8 

65 

286.9 

867.8 

.4 

912.8 

47Ti.9 

7.68 

.1811 

41.8 

56 

288.1 

268.8 

.8 

911.6 

467.9 

7.50 

.138:) 

42.8 

67 

289.1 

259.5 

1170.1 

910.6 

460.8 

7.88 

.1855 

43.8 

58 

290.3 

260.7 

.6 

909.8 

458.7 

7.86 

.1877 

44.8 

69 

291.4 

261.8 

.6 

909.0 

445.6 

7.14 

.1400 

45.3 

60 

292.5 

262.9 

1171.2 

906.8 

438.6 

7.08 

.1422 

46.3 

61 

298.6 

264.0 

.6 

907.6 

431.7 

6.92 

.1444 

47.3 

62 

294.7 

265.1 

.8 

906.7 

425.8 

6.88 

.1466 

48.3 

63 

295.7 

266.2 

1172.1 

906.9 

418.8 

6.7V 

.1486 

49.3 

64 

296.8 

267.2 

.4 

906.8 

412.6 

6.68 

.1511 

50.3 

65 

297.8 

868.8 

.8 

904.5 

406.6 

6.68 

.1633 

51.3 

6C 

298.8 

269.3 

1178.1 

9087 

400.8 

6.48 

.1555 

52.3 

67 

299.8 

270.4 

.4 

903.0 

896.8 

6.34 

.1577 

.533 

68 

300.8 

271.4 

.7 

908.8 

889.8 

6.25 

.1599 

64.8 

69 

801.8 

272.4 

1174.0 

901.6 

884.5 

617 

.1621 

56.3 

70 

802.7 

2734 

.3 

900.9 

879.8 

6.09 

.1643 

56.3 

71 

303.7 

274.4 

.6 

900.8 

874.8 

6.01 

.1665 

57.3 

72 

304.6 

275.8 

.8 

899.5 

8({9.4 

6.98 

.1687 

58.3 

73 

305.6 

276.8 

1176.1 

898.9 

864.6 

5.85 

.1709 

59.3 

74 

806.6 

277.2 

.4 

898.2 

8fU).0 

6.78 

.1781 

60.3 

75 

807.4 

278.2 

.7 

897.6 

866.5 

6.71 

.1753 

61.3 

76 

306.8 

279.1 

1178.0 

896.9 

851.1 

6.63 

.1776 

62.8 

77 

309.2 

280.0 

.9. 

896.2 

846.8 

6.57 

.1797 

63.3 

78 

810.1 

280.9 

.6 

895.6 

348.6 

6.50 

.1819 

64.3 

79 

810.9 

281.8 

.8 

895.0 

888.5 

5.43 

.1840 

66.3 

80 

311.8 

882.7 

1177.0 

8948 

884.5 

6.87 

.1882 

66.3 

81 

812  7 

283.6 

.8 

698.7 

880.6 

5.31 

.1884 

67.3 

82 

313.5 

284.5 

.6 

893.1 

826.8 

6.86 

.1906 

68.3 

88 

314.4 

285.3 

.8 

898.6 

828.1 

6.18 

.1928 

69.3 

84 

315.2 

286.2 

1178.1 

891.9 

819.6 

6.18 

.I960 

70.8 

85 

316.0 

287.0 

.8 

891.8 

816.9 

6.07 

.1971 

STKAIL 


665 


Properties  of  Satnmted  SteAiu. 

£5 

. 

Total  Heat 

s^ . 

^§ 

I^JB 

td 

above  82«  F. 

»4     . 

|2^- 

te 

1^ 

11 

III 

Latent  Heat 
Heat-units. 

In  the 
Water 

h 
Heat- 

In  the 
Steam 

H 
Heat- 

i 

O 

< 

gfe 

units. 

units. 

_£"- 

^ 

71.^ 

86 

816.6 

287.9 

1178.6 

890.7 

312.5 

5.02 

.1993 

«.« 

87 

817.7 

288.7 

.8 

890.1 

809.1 

4.96 

.2015 

78.3 

88 

818.5 

289.5 

1179.1 

889.5 

305.8 

4.91 

.2066 

74.8 

89 

819.8 

290.4 

.8 

888.9 

802.5 

4.86 

.2068 

75.8 

90 

820.0 

291.2 

.6 

688.4 

299.4 

4.81 

.2080 

76.8 

9t 

820.8 

292.0 

.8 

887.8 

296.8 

4.76 

.2102 

T7.8 

93 

321.6 

292.8 

1180.0 

887.2 

298.2 

4.71 

.2123 

ra.s 

98 

822.4 

293.6 

.3 

886.7 

890.2 

4.66 

.2145 

79.8 

94 

828.1 

294.4 

.6 

886.1 

287.8 

4.62 

.2166 

80.8 

95 

828.9 

895.1 

.7 

885.6 

284.5 

4.57 

.2188 

81.3 

96 

824.6 

295.9 

1181.0 

885.0 

281.7 

4.58 

.2210 

88.3 

97 

325.4 

296.7 

.2 

884.5 

279.0 

4.48 

.8281 

88.8 

98 

826.1 

297.4 

.4 

884.0 

276.8 

4.44 

.2258 

848 

99 

826.8 

296.2 

.6 

888.4 

278.7 

4.40 

.2274 

85.8 

100 

8i7.6 

298.9 

.8 

882.9 

271.1 

4.86 

.2296 

86.8 

101 

8^.8 

2997 

1182.1 

682.4 

268.5 

4.8J 

.2317 

87.8 

102 

8.29.0 

800.4 

.8 

881.9 

266.0 

4.28 

.8839 

88.8 

108 

829.7 

801.1 

.6 

881.4 

263.6 

4.24 

.2860 

89.8 

104 

880.4 

801.9 

.7 

880.8 

261.2 

4.20 

.2382 

90.8 

105 

831.1 

802.6 

.9 

8808 

258.9 

4.16 

.2408 

91.3 

106 

881.8 

808.8 

1188.1 

879.8 

256.6 

4.12 

.2425 

9S.8 

107 

882.6 

804.0 

.4 

879.8 

254.8 

4.09 

.2446 

93.3 

108 

883.2 

304.7 

.6 

878.8 

252.1 

4.05 

.2467 

94.8 

109 

888.9 

805.4 

.8 

878.8 

249.9 

4.02 

.2480 

95.8 

no 

834.5 

806.1 

1184.0 

877.9 

247.8 

8.98 

.2510 

96.3 

111 

885.2 

806.8 

.2 

877.4 

245.7 

8.95 

.2581 

97.8 

112 

335.9 

807.5 

.4 

876.9 

243  6 

8.92 

.2553 

96.8 

118 

836.5 

808.2 

.6 

876.4 

241.6 

8.88 

.2574 

99.8 

114 

887.2 

808.8 

.8 

875.9 

289.6 

8.85 

.2596 

100.8 

115 

837.8 

809.5 

1185.0 

875.6 

237.6 

8.82 

.2617 

101.8 

116 

888.5 

810.2 

.2 

875.0 

285.7 

8.79 

.2688 

108.8 

117 

339.1 

810.8 

.4 

874.5 

288.8 

8.76 

.2660 

103.3 

118 

889.7 

311.5 

.6 

874.1 

231.9 

8.73 

.2681 

104.3 

119 

840.4 

812.1 

.8 

873.6 

280.1 

8.70 

.2703 

106.8 

190 

841.0 

812.8 

.9 

8r8.2 

228.8 

8.67 

.2724 

106.8 

121 

841.6 

818.4 

1188.1 

872.7 

226.5 

8.64 

.2745 

107.3 

122 

842.2 

814.1 

.3 

87^.8 

224.7 

8.62 

.2766 

108.3 

128 

342.9 

814.7 

.6 

871.8 

223.0 

8.50 

.2788 

109.3 

ld4 

848.5 

815.3 

.7 

871.4 

221.8 

8.56 

.2809 

110.3 

125 

844.1 

816  0 

.9 

870.9 

219.6 

8.53 

.2880 

111.8 

126 

844.7 

816.6 

1187.1 

WO.  5 

218.0 

3.51 

.2851 

112.8 

127 

845.8 

817.2 

.8 

870.0 

216.4 

3.48 

.2872 

113.3 

128 

845.9 

817.8 

.4 

869.6 

214.8 

8.46 

.2894 

114.8 

129 

840.5 

818.4 

.6 

869.2 

213.2 

8.43 

.2915 

115.8 

ISO 

847.1 

819.1 

.8 

868.7 

211.6 

3.41 

.2936 

116.3 

131 

S47.6 

819.7 

1188.0 

868.3 

210.1 

8.38 

.2067 

117.8 

182 

348.2 

820.3 

.2 

867.9 

208.6 

3.:36 

.2978 

118.3 

133 

318.8 

8J0.8 

.8 

867.5 

207.1 

3.38 

.8000 

119.3 

184 

849.4 

821.5 

.5 

867.0 

205.7 

3.31 

.8021 

666 


StEAH. 


Properties  of  Satttratod  Steam* 


. 

Total  Heat 

s« 

«Jg 

gi 

111 

< 

abore  a2«  F. 

u 

fun 

1; 

^  2 

u 

In  the 
Water 

h 
Heat- 
units. 

In  the 
Steam 

H 
Heat- 
UDite. 

ll 

190.3 

135 

860.0 

882.1 

1188.7 

866.6 

204.2 

8.29 

.8042 

Isil.S 

136 

850.5 

822.6 

.9 

866.9 

802.8 

8.97 

.8063 

139.8 

137 

851.1 

898.8 

1189.0 

865.8 

901  4 

8.24 

.8084 

188.8 

188 

851.8 

823.8 

.2 

865.4 

200.0 

8.88 

.8105 

184.3 

189 

852.8 

824.4 

.4 

865.0 

196.7 

8.20 

.8126 

196.3 

140 

869.8 

835.0 

.6 

864.6 

197.8 

8.18 

.8147 

198.3 

141 

853.8 

825.6 

.7 

864.2 

196.0 

3.16 

.8169 

197.8 

149 

85:{.9 

826.1 

.9 

868.8 

194  7 

8.14 

.3190 

198.3 

143 

aM.4 

826.7 

1190.0 

863.4 

193.4 

8.11 

.3811 

129.3 

144 

855.0 

327.2 

.9 

863.0 

192.2 

8.09 

.afctt 

180.8 

146 

865.5 

827.8 

.4 

862.6 

190.9 

8.07 

.89.-8 

131.8 

146 

856.0 

328.4 

.6 

862.8 

189.7 

8.06 

.3274 

189.3 

147 

B!».6 

828.9 

.7 

861.8 

188.5 

8.04 

.8295 

18.^.8 

148 

357.1 

829.5 

.9 

661.4 

187.8 

8.08 

.8816 

134.8 

149 

357.6 

830.0 

1191.0 

861.0 

186.1 

8.00 

.33s; 

186.8 

1.50 

868.9 

880.6 

.8 

860.6 

184.9 

8.96 

.3358 

186.8 

151 

858.7 

881.1 

.8 

860.2 

la^.i 

8.96 

.8379 

187.3 

159 

869.8 

831.6 

.5 

859.9 

182.6 

8.94 

.3460 

188.8 

153 

859.7 

882.9 

.7 

859.6 

1H1.5 

8.92 

.34:21 

189.8 

154 

860.8 

832.7 

.8 

659.1 

180.4 

8.91 

.8442 

140.3 

155 

860.7 

:{83.8 

1199.0 

868.7 

179.2 

8.89 

.S4&1 

141.3 

156 

861.8 

883.B 

.1 

858.4 

178.1 

8.87 

.8483 

149.3 

157 

861.8 

881.8 

.8 

858.0 

177.0 

8.85 

.8501 

148.8 

158 

862.8 

834.8 

.4 

857.6 

176.0 

2.84 

.85:i5 

144.8 

159 

862.8 

835.8 

.6 

857.8 

174.9 

8.88 

.3546 

145.8 

160 

863.3 

3;)5.9 

.7 

866.9 

178.0 

880 

.3567 

146.8 

161 

863.8 

336.4 

.9 

856.6 

178.9 

8.79 

..%N8 

147.3 

162 

864.8 

386.9 

1193.0 

856.1 

171.9 

8.77 

.3600 

148.3 

163 

864.8 

837.4 

.8 

865.8 

171.0 

8.76 

.86:» 

149.3 

164 

366.3 

837.9 

.3 

855.4 

170.0 

8.74 

.3C50 

IfiO.S 

165 

866.7 

888.4 

.6 

865.1 

169.0 

8.T8 

.3firi 

151.3 

166 

866.9 

888.9 

.6 

854.7 

168.1 

8.71 

.ae-j 

152.3 

167 

866.7 

889.4 

.8 

854.4 

167.1 

8.69 

..^713 

158.3 

168 

867.2 

839.9 

.9 

854.0 

166.8 

8.68 

.ST34 

154.3 

160 

867.7 

840.4 

1194.1 

863.6 

165.3 

8.66 

.3754 

155.8 

170 

868.2 

840.9 

.8 

868.8 

164.8 

8.65 

.8775 

156.3 

171 

868.6 

841.4 

.4 

853.9 

163.4 

8.63 

.8796 

167.3 

172 

869.1 

841.9 

.6 

668.6 

162.5 

8.62 

.8817 

158.3 

173 

869.6 

842.4 

.7 

869.8 

161.6 

8.61 

.8838 

159.8 

174 

870.0 

342.9 

.8 

861.9 

160.7 

8.50 

.S858 

160  8 

178 

870.5 

843.4 

.9 

851.6 

159.8 

8.58 

.9679 

161.3 

176 

871.0 

843.9 

1195.1 

861.2 

158.9 

8.56 

.8900 

192.  S 

177 

871.4 

844.3 

.2 

860.9 

158.1 

8.59 

.8931 

163.3 

178 

371.9 

844.8 

.4 

850.5 

167.2 

8.54 

.8942 

164.3 

179 

872.4 

345.3 

.6 

850.2 

156.4 

2.59 

.8962 

166.8 

180 

872.8 

845.8 

.7 

849.9 

156.6 

8.51 

.8963 

166.8 

181 

878.3 

846.3 

.8 

849.5 

154.8 

350 

.4004 

*E« 

189 

873.7 

346.7 

.9 

849.2 

154.0 

8.48 

.40'.!5 

168.8 

188 

374.2 

847.2      1196.1 

848.9 

168.8 

8.47 

.4046 

STEAM. 


667 


Propertl««  of  Batarated  Steam. 


Us 

lis 

11 

Tot^l  Heat 
above  82»  F. 

fill 

|iin 

^1 

P 

!4 

I? 
5=2 

Id  the 
Water 

h 
Heat, 
units. 

In  the 
Bteam 

H 
He»t. 
units. 

ff 

160.3 

184 

874.6 

847.7 

1196.2 

848.5 

152.4 

8.46 

.4066 

170.3 
171.8 
172.8 
178.8 
174.8 

185 
186 
187 
188 
189 

375.1 
375.5 
375.9 
876.4 
876.9 

348.1 
848.6 
849.1 
849.5 
850.0 

.8 
.5 
.6 
.7 
.9 

848.2 
847.9 
847.6 
847.8 
846.9 

151.6 
160.8 
160.0 
140.2 
148.6 

2.45 
8.48 
2.42 
2.41 
2.40 

.4087 
.4108 
.4129 
.4150 
.4170 

175.3 
176.8 
177.8 
17«-8 
179.8 

190 
191 
193 
193 
194 

1??:? 

878.2 
378.6 
379.0 

860.4 
850.9 
361.8 
851.8 
352.2 

1197.0 
.1 
.8 
.4 
.6 

846.6 
846.8 
845.9 
845.6 
845.8 

147.8 
147.0 
146.8 
146.6 
144.0 

2.89 
8.87 
2.36 
8.85 
2.84 

.4191 
.4212 
.4288 
.4254 
.4275 

180.3 
181.8 
183.8 
183.8 
181.8 

195 
196 
197 
198 
199 

379.5 
380.0 
380.3 
380.7 
381.2 

862.7 
353.1 
358.6 
854.0 
854.4 

.7 
.8 
.9 
1196.1 
.2 

845.0 
814.7 
844.4 
844.1 
843.7 

144.2 
148.5 
142.8 
142.1 
141.4 

8.88 
8.82 
8.81 
2.29 
2.28 

.4296 
.4817 

.4837 
.4358 
.4379 

185.8 
186.8 
187.8 
188.3 
189.8 

900 
801 
208 
808 
204 

881.6 
383.0 
382.4 
882.8 
383.2 

864.9 
855.3 
856.8 
366.2 
856.6 

.8 
.4 
.6 
.7 
.8 

843.4 
843.1 
842.8 
842.6 
842.2 

140.8 
140.1 
189.5 
138.8 
138.1 

2.27 
2.26 
2.25 
2.24 
2.28 

.4400 
.4420 
.4441 
.4462 
.4482 

190.8 
191.8 
193.8 
198.8 
194.8 

205 
206 
807 
206 
909 

888.7 
384.1 
884.5 
884.9 
886.8 

857.1 
857.8 
867.9 
858.8 
858.8 

1199.0 
.1 
.2 
.3 
.6 

841.9 
841.6 
841.8 
841  0 
840.7 

187.6 
136.9 
186.8 
185.7 
185.1 

2.22 
2.21 
2.80 
2.19 
2.18 

.4506 
.4538 
.4544 

.4564 
.4585 

195.8 
396.8 
197.8 
198.8 
199.8 

210 
211 
212 
218 
214 

385.7 
388.1 
886.5 
886.9 
887.3 

359.2 
359.6 
800.0 
360.4 
860.9 

.6 
.7 
.8 
.9 
1200.1 

840.4 
840.1 
889.8 
839.6 
839.2 

184.6 
183.9 
188.3 
182.7 
182.1 

2.17 
2.16 
2.15 
2.14 
2.13 

.4606 
.4626 
.4646 
.4667 
.4687 

200.8 
201.8 
902.8 
808.8 
204.8 

215 
216 
217 
218 
219 

887.7 

888.J 
388.5 
388.9 
889.8 

861.8 
861.7 
862.1 
362.6 
362.9 

.2 
.3 
.4 
.6 
.7 

888.9 
638.6 
688.3 
888.1 
837.8 

181.5 
130.9 
180.8 
129.7 
129.2 

2.18 
2.12 
9.11 
2.10 
2.09 

.4707 
.4728 
.4748 
.4768 

.4788 

205.3 
215.3 
825.8 
235.3 

280 
230 
240 
250 

880.7 
893.6 
397.8 
400.9 

870.0 
878.8 

1200.8 
1202.0 
1203.1 
1204.2 

B38.6« 
835.8 
893.1 
630.5 

12S.7 
128.8 
118.5 
114.0 

2.06 
1.96 
1.90 
1.88 

.4852 

.5061 
.6270 
.6478 

245.3 
255.8 

265.8 
275.8 

260 
270 
280 
290 

404.4 
407.8 
411.0 
414.2 

377.4 
380.9 
884.3 
387.7 

1205.3 
1206.8 
1207.3 
1208.3 

827.9 
825.4 
823.0 
830.6 

109.8 
105.9 
102.8 
99.0 

l.TB 
1.70 
1.64 
1.565 

.6686 
.6894 
.6101 
.6308 

£85.3 
335.3 

800 
350 

417.4 
432.0 

890.9 
406.8 

1209.2 
1213.7 

818.3 
807.5 

95.8 
82.7 

1.585 
1.325 

.6515 
.7545 

*The  discrepancies  at  S05.3  lbs.  ^auge  are  due  to  the  change   from 
Dwelshauyers-Dery's  to  Buel's  figures. 


668 


STEAX. 


Properties  of  Saturated  Steam* 

s  ° 

1 

Total  Heat 
above  8sr  F. 

1? 

u 

h 

Id  the 
Water 

h 
Heat- 
units. 

419.8 
482.2 

In  the 
Steam 

H 
Heat- 
units. 

p 

88D.3 
485.8 

400 
460 

444.9 
456.6 

1217.7 
1221.8 

797.9 
789.1 

1 

72.8 
65.1 

1.167 
1.042 

.86n 

.96W 

48S.8 
685.8 
665.8 
685.8 

600 

560 
000 
650 

4ffrA 

477.5 
486.9 
496.7 

448.5 
464.1 
464.2 
478.6 

1224.5 
1227.6 
1280.5 
1288.2 

781.0 
7786 
786.8 
759.6 

66.8 
68.6 
49.8 
46.6 

.942 
.850 
.790 
.781 

1.062 
1.164 
1.266 
1.868 

685.8 
785.8 
785.8 
836.8 

700 
760 
800 
850 

604.1 
612.1 
619.6 
586.8 

482.4 
490.9 
498.9 
506.7 

1S85.7 
1238.0 
1240.8 
1242.5 

788.8 
747.2 
741.4 
785.8 

42.4 

89.6 
87.1 
84.9 

.680 
.686 
.697 
.668 

1.470 
1.572 
1.674 
1.776 

885.8 
985.8 
085.8 

900 
050 
1000 

688.7 
540.3 
546.8 

514.0 
521.8 
628.8 

1244.7 
1246.7 
1248.7 

780.6 
725.4 
720.3 

88.0 
81.4 
80.0 

.582 
.606 
.480 

1.87B 

i.om 

8.062 

FliOW  OF  STEAM. 

Flo^r  of  Steam  thronsh  a  Nozzle.    (From  Clark  on  the  Steam- 

enfrtne.)— Tiie  flow  uf  steam  ot  a^reater  preiisure  into  an  atmosphere  of  a 
lew  pressure  increases  as  the  difference  of  pressure  Is  Increased,  until  the 
external  prsssure  becomes  only  58j(  of  the  absolute  pressure  in  the  boiler. 
The  flow  of  steam  is  neither  increased  nor  diminished  by  the  fall  of  the  ex- 
ternal pressure  helow  58)t,  or  about  4/7ths  of  the  inside  pressure,  even  to  the 
extent  of  a  perfect  vacuum.  In  flowing  through  a  nozsle  of  the  best  form, 
the  steam  exoands  to  the  external  pi*essure,  and  to  the  volume  due  to  this 
pressure,  so  long  as  it  is  not  less  than  bS%  of  the  internal  pressure.  For  an 
external  pressure  of  58](,  and  for  lower  percentages,  the  ratio  of  expansion 
is  1  to  1.624.  The  following  table  is  selected  from  Mr.  BrownleeV  data  exem- 
plifying the  rates  of  discharge  under  a  constant  Internal  pressure,  into 
various  external  pressures: 

Outfloir  of  Steam  ;  nrom  a  Glren  Initial  Preaenre  Into 
Tarlone  Ijonrer  Preesaree. 

Absolute  Initial  pressure  in  boiler,  75  lbs.  per  sq.  in. 


Absolute 

External 

Ratio  of 

Velocity  of 

Actual 

Discharge 

Pressure  in 

Boiler  per 

square 

inch. 

Pressure 

Expansion 

in 

Nossle. 

Outflow 

at  Constant 

Density. 

Velocity  of 

Outflow 
Expanded. 

per  square 
inch  of 

Oriflce  per 
minute. 

lbs. 

lbs.. 

ratio. 

feet  per  sec. 
fe7.6 

f eetp.  sec. 

Iba. 

76 

74 

1.012 

16.68 

76 

n 

1.087 

886.7 

401 

88.35 

75 

70 

1.068 

490 

521 

86.08 

75 

66 

1.186 

660 

749 

48.88 

75 

61.63 

1.198 

786 

876 

68.97 

76 

60 

1.219 

765 

938 

66.13 

76 

60 

1.434 

878 

1252 

64 

75 

45 

1.575 

890 

1401 

65.94 

75 

48.46     t 
1  58  p.  cent  f 

1.621 

890.6 

1446.5 

65.8 

76 

1.624 

890.6 

1446.5 

65.8 

75 

0 

1.624 

890.6 

1446.5 

66.8 

FLOW   OF  STEAM. 


669 


When  steam  of  varying  Initial  pressures  Is  discharged  Into  the  atmos- 
phere— the  atmospheric  pressure  being  not  more  than  6S%  of  the  Initial 
Rressore— the  velocity  of  outflow  at  constant  density,  that  is,  supposing  the 
iltial  density  to  be  maintained,  is  given  by  the  formula  V  s  8.5053  ^h. 

V  =  the  velocity  of  outflow  in  feet  per  second,  as  for  steam  of  the  initial 
density; 

h  =  the  height  in  feet  of  a  column  of  steam  of  the  given  absolute  initial 
pressure  of  uniform  density,  the  weight  of  which  is  equal  to  the  pres- 
sure on  the  unit  of  base. 

The  lowest  Initial  pressure  to  which  the  formula  applies,  when  the  steam 
Is  dischaiged  into  the  atmosphere  at  14.7  lbs.  per  square  inch,  is  (14.7  X 
100/58  =)  25. S7  lbs.  per  square  inch.  Examples  of  tlie  application  of  the 
formula  are  given  in  the  table  below. 

From  the  contents  of  this  table  it  appears  that  the  velocity  of  outflow  Into 
the  atmosphere,  of  steam  above  25  lbs.  per  square  inch  absolute  pressure, 
or  10  lbs.  effective,  increases  very  slowly  with  the  pressure,  obviously  be- 
cause the  density,  and  the  weight  to  be  moved,  increase  with  the  pressure. 
An  average  of  900  feet  per  second  may,  for  approximate  calculacions,  be 
talcen  for  the  velocity  of  outflow  as  for  constant  density,  that  is,  taking  the 
volume  of  the  steam  at  the  initial  volume. 

Ontfloir  of  SCeam  Into  the  ACmospliere.— External  pressure 
per  square  inch  14.7  lbs.  absolute.    Ratio  of  expansion  in  nozzle,  l.ttM. 


*  =  * 
o  *  = 

m 

III 

m 
III 

iU 

%^6 

Pit 

m 

'3.-  . 

Ill 

is? 

Hi 

m 

fill 

^ 

> 

^ 

a 

EC 

< 

> 

< 

p 

K 

lbs. 

feet 
p. sec. 

fpet 
per  81^. 

lbs. 

If.P. 

Iba. 

feet 

feet 
per  setj. 

lbs. 

H.P. 

«5.3? 

•^Bisa 

1401 

22  Hi 

4^& 

W 

sm  1 

14U 

77.91 

IS5.9 

3fl 

m 

140S 

iSa.N 

53  7 

lOO 

im 

1459 

WS.34 

173.7 

40 

874 

J419 

35  J« 

TU  4 

115 

OOi 

1466 

9^.76 

197  5 

50 

«so ; 

14*J9 

41  Oti 

«8.1 

135 

906 

1172 

115.(31 

a31.» 

eo 

885 

UXT 

5'j  S9 

imt 

155 

010 

1478 

m^jii 

Mfi4.4 

70 

»«» 

1444 

61.07 

123.1 

\m 

oia 

1481 

1J0.46 

Sft^.O 

75 

891 

!447 

^hUO 

];M1  fi 

215 

9T9 

14»3 

181.58 

mnn 

Napier's  Approximate  Rule.  -Flow  hi  pounds  per  second  =  ab- 
solute  pressure  x  area  in  square  inches  •*-  70.  This  rule  gives  results  which 
closely  oorrespond  with  those  in  the  above  table,  as  shown  below. 

Abs.  press.,  lbs.  p.  sq.  In.  25.87    40      60       75  100  186        165        S15 
Discharge  per  min.,  by 

table.  lbs 22.8185.18  52.59  65.80  86.84  115.61  140.46 

By  Napier*s  rule 21.74  3429  51.43  64.29  85.71  115.71  141.48 


181.58 
184.29 

Prof.  Feabody,  In  Trans.  A.  B.  M.  E..  xl,  187,  reports  a  series  of  experi- 
ments on  flow  of  steam  through  tubes  }a  inch  In  diameter, and  M,  ^,  and  IH 
inch  long,  with  rounded  entrances,  in  wnicli  the  results  agreed  closely  with 
Napier's  formula,  the  greatest  difference  being  an  excess  of  the  experimental 
over  the  calculated  result  of  H2%,  An  equation  derived  from  the  theory  of 
thermodynamics  is  given  by  Prof.  Peabody,  but  It  does  not  agree  with  the 
experimental  results  as  well  as  Napier's  rule,  the  excess  of  the  actual  flow 
bems:  6.6jt. 

Floiw  of  Steam  In  Pipes.— A  formula  commonly  used  for  velocity 
of  flow  of  steam  in  pipes  is  the  same  as  Downing's  for  the  flow  of  water  In 

smooth  oast-Iron  pipes,  viz.,  V=  60i/---D,  in  which  V wm  velocity  In  feet 

per  second,  L  =  length  and  D  =  diameter  of  pipe  in  feet,  H  s=  height  in 
f^t  of  a  column  of  steam*  of  the  pressure  of  the  steam  at  the  entrance. 


670  8TBAM. 

which  would  produce  a  pressure  equal  to  the  difference  of  pressures  at  the 
two  ends  of  the  pipe.  (For  derivation  of  the  coefficient  SO,  see  Brings  ou 
"Warming  Buildings  bv  Steam/'  Proc.  Inst.  C.  E.  188;!.) 

It  Qss  quantity  in  cubic  feet  per  minute,  d  =  diameter  in  inches,  L  and  B 
being  in  feet,  the  formula  reduces  to 

(These  formulcB  are  applicable  to  air  and  other  gases  as  well  as  steam.) 

If  Pi  ss  pressure  in  pounds  per  square  Inch  of  the  steam  (or  gas)  at  the  en- 
trance to  the  pipe,  pt  =  the  pressure  at  the  exit,  then  ]44(p,  —  p,)  =  differ- 
ence in  pressure  per  square  foot.  Let  w  =  density  or  weight  per  cubic  foot 
of  steam  at  the  pressure  pi,  then  the  height  of  column  equivalent  to  the 
difference  in  pressures 


^jf^144(p,-p.)^ 


and   Q  =  flO  X  .7854  X  WD*  V^ME.L££i2?. 


If  IT  s  weight  of  steam  flowing  in  pounds  per  minute  s  Qw,  and  d  is 
taken  in  inches,  L  being  in  feet. 


d = 0.199//  ^^'^  ^  -  o,mys^. 

Velocity  in  feet  per  minute  «  F  »  9  -h  .WM^j  « 10392  4/ii^ 


-'P%\d 


10L      • 

For  a  velocity  of  6000  feet  per  minute,  d  as  -— !^ -;  p,  -  p,  «  ^. 

"IPi  —  Pi)  «» 

For  a  Telocity  of  0000  feet  per  minute,  a  steam-pressure  of  100  lbs.  gauge, 

or  to  =.264,  and  a  length  of  100  feet,  d  s=  — : ;  pi  —  pt  =  -j-.    That  is,  a 

Pi  "~  Pt  " 

pipe  1  inch  diameter,  100  feet  long,  carrying  steam  of  100  lbs.  gauge^ressune 
at  6000  feet  velocity  per  minute,  would  have  a  loss  of  pressure  of  8.0  lbs.  per 
square  inch,  while  steam  travelling  at  the  same  velocity  in  a  pipe  8.8  inches 
diameter  would  lose  only  1  lb.  pressure. 
G.  H.  Babcock,  in  **  Steam,"  gives  the  formula 


TTsSTj/" 


'^Pi-P%)d* 


In  earlier  editions  of  "  Steam  *'  the  coefficient  is  given  as  SOO.— «vldent1v  an 
error,— and  this  value  has  been  reprinted  in  CHark's  Pocket-Book  (189d'edi< 
lion).  It  is  apparently  derived  from  one  of  the  numerous  formulce  for  flow 
of  water  in  pipes,  the  multiplier  of  L  in  the  denominator  being  used  for  an 
expression  of  the  increased  resistance  of  small  pipes.    Putting  this  formula 

in  the  form  W  =  ca/  — ^' -£J^l^ — ,  in  which  c  will  vary  with  the  diameter 

of  the  pipe,  we  have, 

For  diameter,  inches....         1  8  8  4  6  9  19 

Valueofo 40.7       58.1        68.8        68        08.8      78.7        79.8 

instead  of  the  constant  value  56.63,  given  with  the  simpler  formula. 
One  of  the  most  widely  accepted  formulae  for  flow  of  water  is  D*Arcy*8, 

V  =  ca/  j—^  in  which  c  has  values  ranging  from  65  for  a  ^-inch  pipe  up  to 


FLOW  OP  BTEAM. 


671 


111.5  for  24-lncli.    Usini:  D*Arcy's  coefQcieBto,  and  modifjring  his  fomiula  to 
make  it  apply  to  steam,  to  the  form 


i  =  c/ 


toL        * 


or    W 


-v= 


uKPi  -  P'i^i^ 


we  obtain, 

For  diameter,  inches. 
Value  of  c 


For  diameter,  inches ....     9 
Value  of  c 61.2 


1 
45.8 


10 
61.8 


2 

62.7 

12 
62.1 


8 
56.1 

14 
62.8 


4 
67.8 

16 

62.6 


5 

58.4 

18 
62.7 


6 

59.5 

20 
62.9 


7 
60.1 


63.2 


8 

60.7 

24 
68.2 


In  the  absence  of  direct  experiments  these  coeiiicients  are  probably  as 
accurate  as  any  that  may  be  deriyed  from  formulae  for  flow  of  water. 


Loss  of  pressure  in  lbs.  per  sq.  in.  =  pj  —  pj  =     ^^^  « 


liosa  of  Presanre  dne  to  Radiation  as  irell  Us  Friction.— 

E.  A.  Rudiger  (Mechanics^  June  80, 1888)  {srives  the  foilowin^^  formula  and 
tables  for  flow  of  steam  in  pipes.  He  takes  into  consideration  the  losses  ia 
pressure  due  both  to  radiation  and  to  friction. 

Loss  Of  power,  expressed  in  heat-nnits  due  to  friction,  Hf  =   ^;;.,. 

Loss  due  to  radiation,  Hr  =  0.262iid. 

In  which  TTis  the  weight  in  lbs.  of  steam  delivered  per  hour,  /  the  coefii« 
cient  of  friction  of  the  pipe,  2  the  length  of  the  pipe  in  feet,  p  the  absolute 
terminal  pressure,  d  the  diameter  of  the  pipe  in  inches,  and  r  the  coefficient 
of  radiation.   /  is  taken  as  from  .0165  to  .01  <5.  and  r  varies  as  follows : 

TABLE  OF  VALUBS  FOR  f*. 


Pipe  Covering. 


Uncovered  pijie 

2-inch  cement  composition 

2    **     asbestos  

2    **    asbesitos  flock 

2    **     wooden  log 

2    **     mineral  wool 

2    "     hairfelt 


Absolute  Pressure. 


40  lbs. 

65  lbs. 

90  lbs. 

115  lbs. 

487 

555 

620 

681 

146 

178 

193 

209 

157 

192 

l.»02 

2^^ 

150 

185 

197 

210 

100 

122 

145 

151 

61 

76 

85 

98 

48 

58 

66 

78 

The  appended  table  shows  the  loss  due  to  friction  and  radiation  in  a  steam- 
pipe  where  the  quantity  of  steam  to  be  delivered  is  1000  lbs.  per  hour,  I  = 
1000  feet,  the  pipe  being  so  protected  that  loss  by  radiation  r  =  64,  and  the 
absolute  terminal  pressure  being  90  lbs.: 


Diameter 
of  Pipe, 
inches. 

Loss  by 

Friction, 

Hf, 

Loss  by 
Radia. 

tion, 

Hr, 

Total 

Diam. 
of  Pipe, 
inches. 

Loss  by 

Friction, 

Hf. 

Loss  by 
Radia- 
tion, 
Hr. 

68,688 
67,072 
88,840 
100,606 
117,876 
134,144 

Total 
Loss, 

1 
2 

197,581 
64,727 
88.012 
12,080 
6,178 

*-^ 

16,76S 
20,960 
25,152 
29,844 
83,536 
41,920 
50,.^ 

214,800 
85,687 
51,164 
41,879 
89,709 
43,943 
51.117 

8^ 

876 
193 
63 
25 
12 
6 

69,064 
67.265 
88,908 
li  0,623 
117,888 
134,150 

672 


8TEAM. 


If  the  pipes  are  carrying  steam  with  minimum  loss,  then  for  same  r,  r, 
and  p«  the  loss  of  pressure  L  for  pipes  of  different  diameters  Taries  in- 
versely as  the  diameters. 

The  general  equation  for  the  loss  of  pressure  for  the  minimal  loss  from 
friction  and  radiation  is 

,      0.0007088  drip 

i  = w • 

The  loss  of  pressure  for  pipes  of  1  Inch  diameter  for  different  absolute 
terminal  pressures  when  steam  is  flowing  ^ith  minimal  loss  is  expressed  by 

the  formula  L  s  C/y^  in  which  the  coefficient  C  has  the  following  values: 

For  66  lbs.  abs.  term,  pressure C=s  0.00060887 

•♦    75  "      "       ••  "        0.00003684 

"    90  ••      ••        "  ••         0.0000B67S 

••  100  ••      ••       «  ••         0.00108188 

M  115  a      MM  M         0.00106051 

In  order  to  find  the  loss  of  pressure  for  any  other  diameter,  divide  the  loss 
of  pressure  in  a  1-inch  pipe  for  the  given  terminal  pressure  by  the  given 
diameter,  and  the  quotient  will  be  the  loss  of  pressure  for  that  diameter. 

The  following  is  a  general  summary  of  the  results  of  Mr.  Rudiger's  inve»> 
tigation : 

The  flow  of  steam  in  a  pipe  is  determined  in  the  same  manner  as  the  flow 
of  water,  the  formula  for  the  flow  of  steam  being  modified  only  by  substi- 
tuting the  equivalent  loss  of  pressure,  divided  by  the  density  of  the  steam, 
for  the  loss  of  head. 

The  losses  In  the  flow  of  steam  are  two  In  number— the  loss  due  to  the 
friction  of  flow  and  that  due  to  radiation  from  the  sides  of  the  pipe.  The 
sum  of  these  is  a  minimum  when  the  equivalent  of  the  loss  due  to  fric- 
tion of  flow  is  equal  to  one  fifth  of  the  loss  of  heat  by  radiation.  For  m 
greater  or  less  loss  of  pressure— i.e.,  for  a  less  or  greater  diameter  of  pipe 
—the  total  loss  increases  very  rapidlv. 

For  delivering  a  given  quantity  of  steam  at  a  given  terminal  pressure* 
with  minimal  total  loss,  the  better  the  non-conducting  material  emploj-ed, 
the  larger  the  diameter  of  the  steam-pipe  to  be  used. 

The  most  economical  loss  of  pressure  for  a  pipe  of  given  diameter  Is  equal 
to  the  most  economical  loss  of  pressure  in  a  pipe  of  1  inch  diameter  for  same 
conditions,  divided  by  the  diameter  of  the  given  pipe  in  inches. 

The  following  table  gives  the  capacity  of  pipes  of  different  diameters,  to 
deliver  steam  at  different  terminal  pressures  through  a  pipe  one  half  mile 
long  for  loss  of  pressure  of  10  lbs.,  and  a  mean  value  of  /  ss  0.0175.  Let  If 
denote  the  number  of  pounds  of  steam  delivered  per  hour : 


Diameter 
of  Pipe, 

Abs.  Term.  Pressure. 

Diameter 
of  Pipe, 
inches. 

Abs.  Term.  Pressure. 

incli^: 

65  lbs. 

80  lbs. 

100  lbs. 

66  lbs. 

80  lbs. 

100  lbs. 

1  

W 

102 

170 

2S8 

415 

579 

1,011 

1,595 

2,346 

8,275 

W 
118 

198 

812 

459 

641 

1,121 

1,768 

2,599 

8.629 

W 

125 

219 

846 

608 

710 

IJMO 

1,956 

2,875 

4,042 

f^ :• 

W 
4.897 
6,721 
9.C24 
]S.i68 
18,526 
24,870 
82,864 
41.061 
51,049 

W 
4,878 
6.889 
10,000 
14,701 
20,528 
27,556 
85,860 
45,507 
66.564 

W 
5,890 

7,018 
11  063 

j?2 

6 

IV 

7 

16  265 

2  *..!!  *!.!!. 

8 

«8.7I1 
80,488 
80,675 
60,849 

J4U 

9 

3  :.;:.:.!.: 

10 

su 

11 

r  ::::::.:: 

12 

62.581 

BesUtance  to  Flour  by  Bends,  Values,  ete.  (From  Briggs  on 
Warming  Buildings  by  Steam.)— The  resistance  at  the  entrance  to  a  tube 
when  no  special  bell-mouth  Is  given  consists  of  two  parts.  The  head  %fl-^2g 

is  expended  in  giving  the  velocfty  of  flow;  and  the  head  0  606  ^  in  over 


FLOW  OF  8TBAM.  673 

comloir  the  reflfatenoe  of  the  mouth  of  the  tube.    Hence  the  whole  looi  of 

head  at  the  eutranoe  te  1.606  zr- .    This  resistauce  is  equal  to  the  resistance 

•9 
of  a  strafght  tube  of  a  length  equal  to  about  60  times  its  diameter. 

Tbo  loss  at  each  sharp  right-angled  elbow  is  the  same  as  in  flowing 
through  a  length  of  straight  tube  equal  to  about  40  times  its  diameter.  For 
a  globe  steam  stop-valve  the  resistance  is  taken  to  be  1>^  times  that  of  the 
rifrh (-angled  elbow. 

Sixes  of  Steam-pipes  for  SCatlonary  Enfflnea*— Authorities 
on  ine  sieani-eneiue  generally  ugi*t*e  that  steain -pipes  supplying  engines 
should  be  of  sucn  sise  that  the  mean  velocity  of  stf'am  in  them  does  not 
exceed  6000  feet  per  minute,  in  order  that  the  loss  of  pressure  due  to  friction 
may  not  be  excessive.  The  velocity  is  calculated  on  the  assumption  that  the 
cylinder  is  filled  at  each  stroke.  In  very  long  pipes,  100  feet  and  upward,  it 
irt  well  to  make  them  larger  than  this  rule  would  give,  and  to  place  a  large 
steam  receiver  on  the  pipe  near  the  engine,  especially  when  the  engine  cuts 
oif  early  in  the  stroke. 

An  article  in  Power^  May,  1808,  on  proper  area  of  supply -pipes  for  engines 
gives  a  table  showing  the  practice  of  leading  builders.  To  facilitate  com- 
piirliion.  all  the  engines  have  been  rated  in  horse-power  at  40  pounds  mean 
effective  pressure.  The  table  contains  all  the  varieties  of  simple  engines, 
from  the  slide-valve  to  the  Corliss,  and  it  appears  that  there  is  no  general 
difference  in  the  sizes  of  pipe  used  in  the  different  types. 

The  averages  selected  xroni  this  table  are  as  follows: 

Diam.  ofpipe,  in 82U8    8U4     4U6       6       7       8       9  10 

Av.H.P.of  engines...  26    89     66    77    100    126    156    Ss25    806    400    606  6s» 

Calculated.formula(l)28    86     51    70     Ot    116    148    :»6    278    866   468  671 

formula  h)  24  87.5    54    78     06    121    160    216    294    884    486  600 

Formula  (1)  is:  1  H  P.  requires  .1375  sq.  in.  of  steam-pipe  area. 

Formula  (2)  is:  Horse-power  ss  6d>.  d  =  diam.  of  pipe  in  inches. 

The  factor  .1375  in  formula  (1)  is  thus  derived:  Assume  that  the  linear 
velocity  of  steam  in  the  pipe  should  not  exceed  6000  feet  per  minute,  then 
pipe  area  =  cyl.  area  X  piston-speed  -*-  6000  (a).  Assume  that  the  av.  mean 
effective  pressure  is  40  lbs.  per  sq.  in.,  then  cyl.  area  X  piston-speed  X  40  -h 
8:^,000  =3  horse-power  (6).  Dividing  <a)  bv  (b)  and  cancelling,  we  have  pipe 
arean-  H.P.  a  .1875  sq.  in.  If  we  use  8000  ft.  per  min.  as  the  allowable 
velocity,  then  the  factor  .1875  becomes  .1081;  that  is,  pipe  area  -•-  H.P.  a 
.1081,  or  pipe  area  X  0.7  as  horse-power.  This,  however,  gives  areas  of  pipe 
smaller  than  are  used  in  the  most  recent  practice.  A  formula  which  gives 
results  closely  agreeing  with  practice,  as  shown  in  the  above  table  is 

Horse-power  »  6d*,  or   pipe  diameter  ei/  5^  s  .408  VH.P. 

DUMETBRS  OF  CTLINDBRS  CORRBSPONDING  TO  VARIOUS  8IZBS  OF  StBAM- 
PIPB8  BASan  ON  PI8TOK-SPRBD  OF  EKOIVB  OF  600  FT.  PBK  MiNUTX.  ANO 
AL.LOWABLB  MbAN  VxLOCITT  OF  STBAH  IN  PiPB  OF  4000,  6000,  ANU  8000 
FT.  PSR  MlK.      (STBAM  ARSUMBD  TO  BB   ADMITTED  DUKINO   Fui.L  STROKE.) 

Diam.  Of  pipe.  Inches SS^88H4       4H5        6 

Vel.4000 6.8      63»     7.7      oTo     10.8    11.6    12.9    l.-i.S 

"     6000 6.8       7.9      9.6    H.l      12.6    14.2    15.8    19. 

••     8000 7.3       9.1    10.9    12.8     14.6    16.4    18.3    21.9 

Horse-power,  approz 80        81      45       62        80      100     125       180 

Dinm.  of  pipe,  inches 7         8       9        10        11       12      18       14 

Vel.4000. 18.1     20.7    23.2    26.8     28.4    81.0    88.6    86.1 

"     60O0 22.1     25.8    28.5    81.6     84.8    87.9    41.1    44.8 

"     8000 25.6     29.2    82.9    86.6     40.2    48.8    47.6    61.1 

Horse-power,  approz 845     820     406     500      606     718     846     981 

Formula.    Area  of  pipe  =  ^"^  of  cylinder  X  piston-speed 
mean  velocity  of  steam  m  pipe 
For  piston-speed  of  600  ft.  per  min.  and  velocity  in  pipe  of  4000,  6000,  and 
80OO  ft.  per  min.  area  of  pipe  =  reKpectively  .15.  .10,  ana  .075  X  area  of  cyl- 
inder.   Diam.  of  pipe  =  respectively  .3878.  .8162,  and  .2739  X  diam.  of  cylin- 
der.   Reciprocals  of  these  figures  are  2.5SS,  8.162,  and  8.651. 

Tbeflnt  line  in  the  above  table  may  be  used  for  proportioning  exhaust 


674 


STEAK. 


Thf 


ipes.  In  which  a  yeloclty  not  exeeedinf?  4000  ft.  per  mlnnte  Is  advisable. 
Jhe  last  line,  approz.  H.P.  of  engine,  is  based  on  the  velocity  of  6000  ft.  per 
xnin.  in  the  pipe,  using  the  corresponding  diameter  of  piston,  and  taking 
H.P.  =  ^(dinni.  of  piston  in  inches)'* 

Sixes  of  Steam-pipes  for  Marine  Bn^fUiee.— In  marine-engine 
practice  the  steam -pipes  are  generally  not  as  large  as  in  stationary  practice 
for  the  same  sizes  of  cylinder.    Beaton  gives  the  following  rules: 

Main  Steam-pipea  should  be  of  such  size  that  the  mean  velocity  of  flow 
does  Dot  exceed  8000  ft.  per  min. 

In  large  engines,  1000  to  2000  H.P.,  cutting  off  at  less  than  half  stroke,  the 
steam-pipe  may  be  designed  for  a  mean  velocity  of  0000  ft.,  and  10,000  ft. 
for  still  larger  engines. 

In  small  engines  and  engines  cutting  later  than  half  stroke,  a  velocity  of 
less  than  8000  ft.  per  minute  is  desirable. 

Taking  8100  ft.  per  min.  as  the  mean  velocity,  8  speed  of  piston  in  feet  per 
min.,  and  D  the  diameter  of  the  cyl., 

Diam.  of  main  steam-pipe  b  j 


Stop  and  Thi-ottle  Valves  should  have  a  greater  area  of  passages  than  the 
area  of  the  main  steam-pipe,  on  account  of  the  friction  through  the  cir- 
cuitous passages.  The  shape  of  the  passages  should  be  designed  so  as  to 
avoid  abrupt  changes  of  direction  ana  of  velocity  of  flow  as  far  as  possible. 

Area  of  Steam  Porta  and  Fcuaages  =s 

Area  of  piston  x  speed  of  piston  in  ft.  per  min.       (PJam.)*  X  speed 
6000  ■  7«»  • 

Opening  of  Port  to  Steam.— To  avoid  wire-drawing  during  admission  the 
area  of  opening  to  steam  should  be  such  that  the  mean  velocity  of  flow  does 
not  exceed  10,000  ft.  per  min.  To  avoid  excessive  clearance*  the  width  of 
port  should  be  as  short  as  possible,  tlie  necessary  area  being  obtained  by 
length  (measured  at  right  angles  to  the  line  of  travel  of  the  valve).  In 
iructice  this  length  is  usually  0.6  to  0.8  of  tlie  diameter  of  the  cylinder,  but 

long-stroke  engines  it  mav  equal  or  even  exceed  the  diameter. 

Exhaust  Passages  and  Pipes.— The  area  should  be  such  that  the  mean 
velocity  of  the  steam  should  not  exceed  6000  ft.  per  min.,  and  the  araa 
should  be  greater  if  the  length  of  the  exhaust-pipe  is  comparatively  long. 
The  area  of  passages  from  cvlinders  to  receivers  should  be  such  that  tlie 
velocity  will  not  exceed  5000  ft.  per  min. 

The  following  table  Is  computed  on  the  basis  of  a  mean  velocity  of  flow 
of  8000  ft.  per  min.  for  the  main  steam- pipe,  10.000  for  opening  toi' 
and  6000  for  exhaust.    A  a  area  of  piston,  D  its  diameter. 

Steam  akd  Exhat78t  Ofsnings. 


S,' 


Piston- 

Diam.  of 

Area  of 

Diam.  of 

Area  of 

Opening 

speed, 

Steam-pipe 

Steam^ipe 

Exhaust 

Exhaust 

to  Steam 

ft.  per  min. 

•*-D. 

•*■  A. 

H-il. 

800 

0.194 

0.0375 

0.228 

0.0600 

0.08 

400 

0.824 

0.0500 

0.258 

0.0667 

004 

500 

0.250 

0.0635 

0.288 

0.0883 

0.06 

600 

0.274 

0.0760 

0.816 

0.1000 

0.06 

700 

0.296 

0.0875 

0.841 

0.1167 

0.07 

800 

0.816 

0.1000 

0.865 

0.1888 

0.08 

900 

0.835 

0.1125 

0.387 

0.1600 

o.oe 

1000 

0.858 

0.1250 

0.400 

0.1667 

0.10 

SnCAM  PIPES. 

Bnrstlnff-tests  of  Copper  Steam-pipes.    (From  Report  of  Chief 

Engineer  Melville,  U.  S.  N.,  fur  1892,)— Some  tests  were  made  at  the  New 
York  Navy  Yard  which  show  the  UTireliability  of  brazed  seams  in  cop- 
per pipes.  Each  pipe  was  8  in.  diameter  inside  and  8  ft.  19^  in .  long. 
Both  ends  were  closed  by  ribbed  heads  and  the  pipe  was  subjected  to  a  hot* 
water  pressure,  the  temperatare  being  maintainea  constant  at  tn*  F.  TbM 


STEAK-PIPES.  675 

of  the  pipes  were  made  of  No.  4  sheet  copper  ("  Stubbs  **  ghuge)  and  the 
foiiilh  was  made  of  No.  8  sheet. 
The  following  were  the  results,  in  lbs.  per  sq.  in.,  of  bursting-pressure: 

Pipenumber 1  8  8           4  4' 

Actual  bursting-strength fW5  7S5  (KM)  13*25  1)!75 

Calculated"             "        lase  1836  1569  16(»  158fi 

DifTerence 601  651  619        &18  293 

The  theoretical  bursting-pressure  of  the  pipes  was  calculated  by  using  the 
figures  obtained  in  the  tests  for  the  strength  of  copper  sheet  with  a  brazed 
jomt  at  850<^  F.    Pipes  1  and  2  are  considered  as  having  been  annealed. 


causes  It  to  lose  the  fibrous  nature  that  it  has  acquired  in  rolling,  and  a 
serious  reduction  in  its  tensile  strength  and  ductility  results. 

All  the  brazing  was  done  by  expert  workmen,  and  their  failure  to  make  a 
pipe-Joint  without  burning  the  metal  at  some  point  makes  it  probable  that, 
with  copper  of  this  or  greater  thickness,  it  Is  seldom  accomplished. 

That  it  Is  possible  to  make  a  Joint  without  thus  injuring  the  metal  was 
proven  in  tne  cases  of  many  of  the  specimens,  both  of  those  cut  from  the 
pipes  and  those  made  separatelr,  which  broke  witli  a  fibrous  fracture. 

Bule  for  Tl&tckiiess  of  Copper  Steam-pipes.  (U.  S.  Super- 
▼ii*ing  Inspectors  of  Steam  Vessels.)—- .Multiply  tlie  working  steam-pressure 
in  lbs.  per  sq.  In.  allowed  the  boiler  by  the  diameter  of  the  pipe  in  inches, 
then  divide  tne  product  by  the  constant  whole  number  8000,  and  add  .0025  to 
the  quotient;  the  sum  will  give  the  thickness  of  material  required. 

EzAMPLs.~Let  175  lbs.  =  working  steam- pressn re  persq.  in.  allowed  the 

boiler,  5  in.  «  diameter  of  the  pipe;  then  ^^~^  +  .0625  s  .1718  +  inch, 

tnickness  required. 

Reinforcing  Stoam-plpes.  (Eng»,  Aug.  11,  1893.)— In  the  Italian 
Navy  copper  pipes  nbove  H  in.  diam.  are  reinforced  by  wrapping  them  with 
a  elose  spiral  of  copper  or  Delta-metal  wire.  Two  or  three  independent 
spirals  are  used  for  safety  In  case  one  wire  breaks.  They  are  wound  at  a 
tension  of  about  1V4  tons  per  sq.  in. 

iriro-ivonnd  Steam-pipos.— The  system  instituted  by  the  British 
Admiralty  of  winding  all  steam -pipes  over  8  in.  in  diameter  with  3/16-in. 
copper  wire,  thereby  about  doubling  the  bnrsting-pressure,  has  within  re- 
cent years  been  adopted  on  many  merchant  steamers  using  high-pressure 
steam,  says  the  London  Engineer.  The  results  of  some  of  the  Aamiralty 
tests  showed  that  a  wire  pipe  stood  Just  about  the  pressure  it  ou^ht  to  have 
Btonil  when  un  wired,  had  the  copper  not  been  injured  in  tlie  brazing. 

RlTeted  Steel  Steam-pipe*  have  recently  l>cen  used  for  high 
pressures..  See  paper  on  A  Method  of  Manufacture  of  Large  Steam-pipes, 
by  Phns.  H.  Manning,  Trans.  A.  S.  M.  E.,  vol.  xv. 

Valves  In  Steam-pipes. -Should  a  globe-valve  on  a  steam-pipe  have 
tlie  steam 'pressure  on  top  or  underneath  the  valve  is  a  disputed  question. 
With  the  steam-pressure  on  top,  the  stulfing-box  around  the  valve-stem  can- 
not  be  repacked  without  shutting  off  steam  from  the  whole  line  of  pipe;  on 
the  other  hand,  If  the  steam -pressure  Is  on  the  bottom  of  the  valve  it  all  has 
to  be  sustainefi  by  the  screw-thread  on  the  valve-stem,  and  there  is  danger 
of  stripping  the  thread. 

A  correspondent  of  the  AmeiHcan  IfacAinisf,  1892,  savs  that  it  is  a  very 
uncommon  thing  in  the  ordinary  globe-valve  to  have  the  thread  give  out, 
but  i>y  water-hammer  and  merciless  screwing  the  seat  will  be  crushed  down 
quite  frequently.  Therefore  with  plants  where  only  one  boiler  is  used  he 
advises  placing  the  valve  with  the  boiler-pressure  underneath  it.  On  plants 
where  several  boilers  are  connected  to  one  main  steam-pipe  he  would  re- 
verse the  position  of  the  valve,  then  when  one  of  the  valves  needs  repacking 
the  valve  can  be  closed  and  the  pressure  in  the  boiler  whose  pive  it  controls 
can  be  reduced  to  atmospheric  by  lifting  the  safety-vtilve.  Tne  i-epacking 
can  then  be  done  without  interfeiing  with  the  operation  of  the  other  boilers 
of  the  plant. 

He  proposes  also  the  following  other  rules  for  locating  valves:  Place 
valves  with  the  stems  horizontal  to  avoid  the  formation  of  a  water-pocket. 
Neverput  the  Junction- valve  close  to  the  boiler  if  the  main  pipe  is  above 
the  boUer,  but  put  it  on  the  highest  point  of  the  Junction-pipe.    If  the  other 


676  BTEAM. 

plan  tfl  followed,  the  pipe  Alls  with  water  whenever  this  holler  fai  stopped 
and  the  others  are  runuiiif?,  and  breakajce  of  the  pipe  may  cause  serious  re- 
sults. Never  let  a  junction-pipe  run  into  the  bottom  of  the  main  pipe,  but 
into  the  side  or  top.  Always  use  an  aiii^le-valye  wliei*e  convenient,  as  there 
is  more  room  in  them.  Never  use  a  gate  valve  under  high  pressure  unless  a 
by -pass  is  used  with  it.  Never  open  a  blow-off  valve  on  a  boiler  a  little  and 
then  shut  it;  it  is  sure  to  catch  the  sediment  and  ruin  the  valve;  throw  it 
well  open  bt-fore  closing.  Never  use  a  globe-valve  on  an  indicator  pipe.  For 
water,  always  use  gate  or  angle  valves  or  stop-cocks  lu  obtain  a  clear  pas- 
sage. Buy  if  possible  valves  with  renewable  disks.  Lastly,  never  let  a  man 
go  inside  a  boiler  to  work,  especially  if  he  is  to  hammer  on  it,  unless  you 
break  the  joint  between  the  boiler  and  the  valve  and  put  a  plate  of  fiieel 
between  the  flanges. 

A  Failure  of  a  Brazed  Copper  Steam-pipe  on  the  British 
steamer  Prodano  was  investigated  by  Prof.  J.  O.  Arnold.  He  found  that 
the  brazing  was  originally  sound,  but  that  it  had  deteriorated  by  oxidatiitn 
of  the  zinc  in  the  brazing  alloy  by  electrolysis,  which  was  due  to  the  presence 
of  fatty  acids  produced  by  decomposition  of  the  oil  used  in  the  engines. 
A  full  account  of  the  investigation  is  given  in  The  Engineer^  April  15, 1898. 

Tiie  ** Steam  I<oop'9  is  a  system  of  piping  by  which  water  of  con- 
densation in  steam-pipes  is  automatically  returned  to  the  boiler.  In  ita 
simplest  form  it  consists  of  three  pipes,  which  are  called  the  riser,  the  hori- 
sontal,  and  the  drop-leg.  When  the  steam-loop  is  used  for  returning  to  the 
boiler  the  water  of  condensation  and  entrainment  from  the  steam-pipe 
through  which  the  steam  flows  to  the  cylinder  of  an  engine,  the  riser  i»  ^u- 
eraliy  attached  to  a  separator;  this  riser  empties  at  a  suitable  height  mto 
the  horizontal,  and  from  thence  the  water  of  condensation  is  led  into  the 
limplegi  which  is  connected  to  the  boiler,  into  which  the  water  of  condensa 
lion  is  fed  as  soon  as  the  hydrostatic  pressure  in  drop-leg  in  connection  with 
the  steam-pressure  in  the  pipes  is  sufficient  to  overcome  the  boiler-preasure. 
The  action  of  the  device  depends  on  the  following  principles:  Difference  of 

Sreesure  may  be  balanced  by  a  water-column:  vapors  or  liquids  tend  lo  flow 
>  the  point  of  lowest  pressure;  rat«  of  flow  depends  on  difference  of  pres- 
sure and  mass;  decrease  of  static  pressure  in  a  steam-pipe  or  chamber  is 
proportional  to  rate  of  condensation:  In  a  steam -current  water  will  be  car- 
ried or  swept  along  rapidly  by  friction.  (Illustrated  in  Modem  Mechanism, 
p.  807.) 

Lose  flrom  an  UneoTered  Steam-pipe*  (Bjorling  on  Pumping^ 
engines.)— The  amount  of  loss  by  condensation  In  a  steam-pipe  carried  down 
a  deep  mine-shaft  has  been  ascertained  by  actual  practice  at  the  Clay  Cross 
Collieryt  near  Cheeterfleld,  where  there  is  a  pipe  7^  in.  internal  dlam..  1100 
ft.  long.  The  loss  of  steam  by  condensation  was  ascertained  by  direct 
measurement  of  the  water  deposited  in  a  receiver,  and  was  found  to  be 
equivalent  to  about  1  lb.  of  coal  per  I.H.P.  per  hour  for  every  100  ft.  of 
steam-pipe;  but  there  is  no  doubt  that  if  the  pipes  had  been  in  the  upcast 
shaft,  and  well  covered  with  a  good  non-conducting  material,  the  lo«  would 
have  been  less.   (For  Steam-pipe  OoveringSi  see  p.  460,  ante.) 


'^THK  HORSE-POWER  OF  A  STEAM-BOILER.       ;677 


THE  STEAM-BOILEB. 

The  Home-po^ver  of  a  Steam-boiler.— The  term  horse  power 
has  two  meanings  in  enjcineorinia: :  Firtt^  an  absolute  unit  or  measure  of  the 
rate  oftcork^  that  is,  of  the  work  done  in  a  certain  definite  period  of  time, 
by  a  source  of  enerxy,  as  a  steam-boiler,  a  waterfall,  a  current  of  air  or 
water,  or  by  a  prime  mover,  as  a  steam-enirine,  a  water-wheel,  or  a  wind- 
mill. The  value  of  this  unit,  whenever  it  can  be  expressed  in  foot-pounds 
of  energ:y,  as  in  the  case  of  steam-engines,  water-wheels,  and  waterfalls,  is 
88,000  fcx>tp-pounds  per  minute.  In  the  case  of  boilers,  where  the  work  done, 
the  conversion  of  water  into  steam,  cannot  be  expressed  in  foot-pounds  of 
available  energy,  the  usual  vahie  given  to  the  term  horse-power  is  the  evafv 
oration  of  80  ?dm.  of  water  of  a  temperature  of  100*  F.  into  steam  at  70  lbs. 

Sressure  above  the  atmosphere.  Both  of  these  units  are  arbitrary ;  the  first. 
),000  foot-pounds  per  minute,  first  adopted  by  James  Watt,  being  considered 
equivalent  to  the  power  exerted  by  a  good  London  draught-horse,  and  the 
80  lbs.  of  water  evaporated  per  hour  being  considered  to  be  the  steam  re- 
quirement per  indicated  horse-power  of  an  average  engine. 

The  second  definition  of  the  term  horse-power  i»  an  approximate  measure 
of  the  size,  capacity,  vcUue,  or  **  rating  "  of  a  boiler,  engine,  water-wheel,  or 
other  source  or  conveyer  of  energy,  by  which  measure  It  may  be  described, 
bought  and  sold,  advertised,  etc.  No  definite  value  can  be  given  to  this 
measure,  which  varies  largely  with  local  custom  or  individual  opinion  of 
makers  and  users  of  machinery.  The  nearest  approach  to  uniformity  which 
can  be  arrived  at  in  the  term  '*  horse  power,"  used  in  this  sense,  is  to  say 
that  a  boiler,  engine,  water-wheel,  or  other  machine,  "  rated'*  at  a  certain 
horse-power,  should  be  capable  of  steadily  developing  that  horse-power  for 
a  long  period  of  time  under  ordinary  conditions  or  use  and  practice,  leaving 
to  local  custom,  to  the  Judgment  of  the  buyer  and  seller,  to  written  contracts 
of  purchase  and  sale,  or  to  legal  decisions  upon  such  contracts,  the  interpre- 
tation of  what  is  meant  by  the  term  **  ordinary  conditions  of  use  and 
practice."    (Trans.  A.  8.  M.  E.,  voL  vli.  p.  226.) 

The  committee  of  the  A.  S.  M.  E.  on  Trials  of  Steam-boilers  in  1884  (Trans., 
vol.  vi.  p.  :i66)  diHcuMsed  the  question  of  the  horse-power  of  boilers  as  follows: 

The  (Committee  of  Judges  of  the  Centennial  Exnibition,  to  whom  the  trials 
of  competing  boilers  at  that  exhibition  were  intrusted,  met  with  this  same 
problem,  and  finally  agreed  to  solve  it,  at  least  so  far  as  the  work  of  that 
committee  was  concerned,  bv  the  adoption  of  the  unit,  80  lbs.  of  water  evap- 
orated into  drv  steam  per  hour  from  feed- water  at  100*  F.,  and  under  a 
pressure  of  70  lbs.  per  square  inch  above  the  atmosphere,  these  conditions 
being  considered  by  them  to  represent  fairly  average  practice.  The  quan- 
tity of  heat  demanded  to  evaporate  a  pound  of  water  under  these  conditions 
is  1110.2  British  thermal  units,  or  1.1496  units  of  evaporation.  The  uzaH  of 
power  proposed  is  thus  equivalent  to  the  development  of  88,806  heat-units 
per  hour,  or  84.488  units  or  evaporation.  .  .  . 

Your  committee,  after  due  consideration,  has  determined  to  accept  the 
Centennial  Standard,  the  first  above  mentioned,  and  to  recommend  tiiat  in 
all  standard  trials  the  commercial  horse-power  be  taken  as  an  evaporation 
of  80  lbs.  of  water  per  hour  from  a  feed-water  temperature  of  100*  F.  into 
steam  at  70  lbs.  gauge  pressure,  which  shall  be  considered  to  be  equal  to  84^ 
units  of  evaporation,  toat  is,  to  34^  lbs.  of  water  evaporated  from  a  feed- 
water  temperature  of  218*  F.  into  steam  at  the  same  temperature.  This 
standard  is  equal  to  88.805  thermal  units  per  hour. 

It  is  the  opinion  of  this  committee  that  a  boiler  rated  at  any  stated  number 
of  horse-powers  should  be  capable  of  developing  that  power  with  easy  firing, 
moderate  draught,  and  ordinarv  fuel,  while  exhibiting  good  economy  ;  and 
further,  that  the  boiler  should  be  capable  of  developing  at  least  one  third 
more  than  its  rated  power  to  meet  emergencies  at  times  when  maximum 
economy  is  not  the  most  important  object  to  be  attained. 

Unit  of  Eraporatlon.— It  is  the  custom  to  reduce  results  of  boiler- 
tests  to  the  cotumon  standard  of  weight  of  water  evaporated  by  the  unit 
weight  of  the  combustible  portion  of  the  fuel,  the  evaporation  being  consid- 
ered to  have  taken  place  at  mean  atmospheric  pressure,  and  at  the  temper- 
atiir«>  due  that  pre«.Mure,  the  feed-water  being  also  assumed  to  have  been 
snprlied  at  that  temperature.  This  Is,  In  teohnicnl  language,  paid  to  be  the 
equivalent  evnporation  from  and  at  the  boiling  point  at  atmospheric  pres- 
sure, or  "from  and  at  21;!**  F."    This  unit  of  evaporation,  or  one  pound  of 


678  THE  STEAH-BOILEB. 

water  evaporated  from  and  at  2]2<>,  is  equivalent  to  965.7  British  thermal 
units. 

REeasures  for  Comparing  ibe  Duty  of  BoUers.— The  meas- 
ure of  the  efflcieucy  of  a  builer  is  ihe  number  of  pounds  of  water  evaporated 
per  pound  of  combustible,  tlie  evaporation  being  reduced  to  the  standard  of 
**  from  and  at  212«  ;'*  that  is,  the  equivalent  evaporation  from  feed-water  at  a 
temperature  of  212*  F.  into  steam  at  the  same  temperature. 

The  measure  of  the  capacity  of  a  boiler  Is  the  amount  of  "boiler  horse- 
power "  developed,  a  horse-power  being  defined  as  the  evaporation  of  tO  lbs. 
of  water  per  hour  from  lOO**  F.  into  steam  at  70  lbs.  pressure,  or  34^  lbs.  per 
hour  from  and  at  212*. 

The  measure  of  relative  rapidity  of  steaming  of  boilers  is  the  number  of 
pounds  of  water  evaporated  per  hour  per  square  foot  of  wat«r-heating  sur- 
face. 

The  measure  of  relative  rapidity  of  combustion  of  fuel  in  boiler-fitmaces 
is  the  number  of  pounds  of  coal  burned  per  hour  per  square  foot  of  grate- 
aurface. 

STEAin-BOILBR  PBOPOBTIONS. 

Proportions  of  Grate  and  Heating  Snrfhce  repaired  for 
a  ItlTeu  Borae-ponrer.'The  term  horse-power  here  means  capiiciiy 
to  «vaporaie  80  lbs.  of  water  from  100*  F.,  temperature  of  feed-water,  lo 
steam  uf  70  lbs.,  gauge-pressure  =  34.6  lbs.  from  and  at  212*  F. 

Average  proportions  for  maximum  economy  for  land  boilers  fired  with 
good  anthracite  coal: 

Heating  surface  per  horse-power U.Saq.fk 

Grate  1/8^* 

Ratio  of  heating  to  grate  surface ..  84.6    ** 

Water  evap'd  from  and  at  212*  per  sq.  ft.  H.S.  per  hour   8     Iba. 

Combustible  burned  per  H. P.  per  hour... 8     •* 

Coal  with  1/6  refuse,  lbs.  per  a.  P.  per  hour S.6  *• 

Combustible  burned  per  sq.  ft.  grate  per  hour H     ** 

Coal  with  1/6  refuse,  lbs.  per  sq.  ft.  grate  pe**  hour. . . .  10.8  ** 

Water  evap'd  from  and  at  212*  per  lb.  combustible. . .  11.6  ** 

"      * '   "  coal  (1/6  refuse)  9.6  " 

The  rate  of  evaporation  Is  most  conveniently  expressed  in  pounds  evapo- 
rated from  and  at  21'J*  per  sq.  ft.  of  water-heating  surface  per  hour,  and  the 
rate  of  combustion  in  pounds  of  coal  per  sq.  ft.  of  grate-surface  per  hour. 

Heatlns-aorface.— For  maximum  economy  with  any  kind  of  fuel  a 
boiJer  should  be  proportioned  so  that  at  least  one  square  foot  of  heating- 
aurface  should  be  given  for  every  8  lbs.  of  water  to  be  evaporated  from  and 
at  212*  F.  per  hour.  Still  more  liberal  proportions  are  required  if  a  portion 
of  the  heating-surface  has  its  efficiency  reduced  by:  1.  Tendency  of  tlie 
heated  gases  to  short-circuit,  that  is,  to  select  passages  of  least  resistance 
and  flow  through  them  with  high  veloci^,  to  the  neglect  of  other  passages. 
8.  Deposition  of  soot  from  smoky  fuel.  8.  Incrustation.  If  the  heating-sur- 
faces are  clean,  and  the  heated  gases  pass  over  it  uniformly,  little  if  any 
increase  in  economy  can  be  obtained  by  increasing  the  heating-surface  be- 
yond the  proportion  of  1  sq.  ft.  to  every  8  lbs.  of  water  to  be  evaporated,  and 
with  all  conditions  favorable  but  little  decrease  of  economy  will  take  place 
if  the  proportion  is  1  sq.  ft.  to  every  4  lbs.  evaporated;  but  in  order  to  pro- 
vide for  driving  of  the  boiler  bej'ond  its  rated  capacity,  and  for  possible 
decrease  of  efficiency  due  to  tlie  causes  above  named,  it  Is  better  to  adopt  1 
sq.  ft.  to  8  11  s.  evaporation  per  hour  as  the  minimum  standard  proportion. 

Where  economy  may  be  sacriflced  to  capacity,  as  where  fuel  is  verv  clieap, 
it  is  customary  to  proportion  the  heating-surface  much  less  llberaily.  The 
following  table  shows  approximately  the  relative  results  that  may  be  ex- 
pected with  different  rates  of  evaporation,  with  anthracite  coal. 

Lbs.  water  evapor'd  from  and  at  212*  per  sq.  ft.  heating- surface  per  hoiin 
9  2.6         8  8.5        4  6  6  7  8  9  10 

Sq.  ft.  heating-surface  required  per  horse-power: 
17.8      13.8       11.5        9.8        8.6         6.8         5.8         4.9         4.8         8.8  &5 

Ratio  of  heating  to  grate  surface  if  1/8  sq.  ft.  of  G.  S.  is  required  per  H.P.: 
62        41.4       84.5       i».4       25.6       20.4       17.4       18.7       12.8       11.4        10.6 

Probable  relative  economy: 
100     100        100         95  90  85  80  76  70  66  60 

Probable  temperature  of  chimney  gases,  degrees  F.: 
450     450        450       518        586        662        790        787        866        028        900 


STEAK'BOILBB  PHOPOBTIOKa  679 

The  r6latlv«  economy  will  vary  not  only  with  the  amount  of  heatinff-BOr- 
face  WT  horse-power,  but  with  the  efficiency  of  that  heating- surface  as 
regards  its  capacity  for  transfer  of  heat  from  the  heated  gases  to  the  water^ 
which  will  depend  on  its  freedom  from  soot  and  incrustation,  and  upon  tha 
circulntion  or  the  water  and  the  heated  gases. 

With  bituminous  coal  the  efRciency  win  largely^epend  upon  the  thorough- 
ness with  which  the  combustion  Ir  eifected  la  the  furnace. 

The  efficiency  with  any  kind  of  fuel  will  greatly  depend  upon  the  amount 
of  air  supplied  to  the  furnace  In  excess  of  (hat  required  to  support  com> 
bustion.  With  strong  draught  and  thin  Area'  this  excess  may  be  very  greats 
causing  a  serious  los.s  of  economy. 

llEe««iiremeiit  of  Beating^siirlkee*— Authorities  are  not  agreed 
as  to  the  methods  of  measuring  the  heating-surface  of  steam-boilers.  Th» 
usual  rule  Is  to  consider  as  heating-surface  all  the  surfaces  that  are  sur- 
rounded by  water  on  one  side  and  by  flame  or  heated  gases  on  the  other,  but 
there  is  a  difference  of  opinion  as  to  whether  tubular  heating-surface  should 
be  figured  from  the  inside  or  from  the  outside  diameter.  Some  writers  nay, 
measure  the  heating-surface  always  on  the  smaller  side— the  fire  side  of  the 
tube  In  a  horizontal  return  tubular  boiler  and  the  water  side  in  a  water- tube 
boiler.  Others  would  deduct  from  the  heating-surface  thus  measured  an 
allowance  for  portions  supposed  to  be  ineffective  on  account  of  being  cov- 
ered by  dust,  or  being  out  of  the  direct  current  of  the  gases. 

It  has  hitherto  been  the  common  practice  of  boiler-makers  to  consider  all 
surfaces  as  heating-surfaces  which  transmit  heat  from  the  flame  or  gases 
to  the  wafer,  making  no  allowance  for  different  degrees  of  effectiveness; 
nlso,  to  use  the  e:i^£emal  instead  of  the  internal  diameter  of  tubes,  for 
greater  convenience  in  calculation,  the  external  diameter  of  boiler-tubes 
uMially  being  made  in  even  inches  or  half  inches.  This  method,  however, 
is  inaccurate,  for  the  true  heating-nurfape  of  a  tube  is  the  side  exposed  to 
the  hot  gases,  the  inner  surface  in  a  flre-tube  boiler  and  the  outer  surface 
III  a  water-tube  boiler.  The  resistance  to  the  passage  of  heat  from  the  hot 
gases  on  one  side  of  a  tube  or  plate  to  the  water  on  the  other  consists  almost 
entirely  of  the  resistance  to  the  passage  of  the  heat  from  the  gases  Into  th^ 
metal,  the  resistance  of  the  metal  itself  and  that  of  the  wetted  surface  being: 
practically  nothing.    See  paper  by  C.  W.  Baker,  Trans.  A.  S.  M.  E.,  vol.  xix. 

RiTLE  for  finding  the  heating-surface  of  vertical  tubular  boilers :  Multiply 
the  circumference  of  the  fire-box  (in  inches)  by  Its  height  above  the  grate  r 
multiply  the  combined  circumference  of  all  the  tubes  by  their  length,  and 
to  these  two  products  add  the  area  of  the  lower  tube-sheet ;  fronTthis  sum 
subtract  the  area  of  all  the  tubes,  and  divide  by  144 :  the  quotiebfe  is  th# 
number  of  square  feet  of  heating-surface. 

RuLB  for  finding  the  heatlng-surface  of  horizontal  tubular  boilers:  Tak^ 
the  dimensions  in  inches.  Multiply  two  thirds  of  the  circumference  of  th9 
shell  by  its  length;  multiply  the  sum  of  the  circumferences  of  all  the  tubes 
by  their  common  length;  to  the  sum  of  these  products  add  two  thirds  of  the 
area  of  both  tube-sheets;  from  this  sum  subtract  twice  the  combined  area  oC 
all  the  tubes;  divide  the  remainder  by  144  to  obtain  the  result  in  square  feeU 

RuUB  for  finding  the  square  feet  of  beating -surface  in  tubes :  Multiply  the 
number  of  tubes  by  the  diameter  of  a  tube  in  inches,  by  its  length  In  feet^ 
and  by  .9618. 

Horsevponrer,  Bander's  Bating.  Heatlnc^arfliee  per 
Borse'poirer.— It  is  a  general  practice  among  builders  to  furnish 'about 
12  square  feet  of  heating-surface  per  horse-power,  but  as  the  practice  is  not 
uniform,  bids  and  contracts  should  always  specify  the  amount  of  heating- 
surface  to  be  furnished.  Not  less  than  one  third  square  foot  of  grate-surf ac» 
should  be  furnished  per  horse-power. 

EngiTieeriiig  News,  July  6, 181^1,  gives  the  following  rough-and-ready  rul» 
for  finding  approximately  the  commercial  horse-power  of  tubular  or  water- 
tube  boilers:  Number  of  tubes  X  their  length  in  feet  X  their  nominaf 
diameter  in  inches  -i-  60  =  nLd  •*•  SO.  The  number  of  square  feet  of  surfaca 

in  the  tubes  is  --^  a=  ■— — ,  and  the  horse-power  at  12  square  feet  of  surface 

of  tabes  per  horse-power,  not  counting  the  shell,  =  nLd  -*-  45.8.  If  16  square 
feet  of  surface  of  tubes  be  taken,  it  Is  nLd  -4-  57.8.  Making  allowance  for 
the  heating-surface  In  the  shell  will  reduce  the  divisor  to  about  50. 

Horse-po'wer  of  Marine  and  I^ocomotlTe  Boilers.— The 
term  horse-power  Is  not  generally  used  in  connection  with  boilers  In  marine 
practice,  or  with  locomotives.  The  boilers  are  designed  to  suit  the  engines. 
•ml  are  rated  bjf 


r  extent  of  grate  and  heating-surface  onjy. 


680 


THE  StEAM- BOILER. 


Ormte-fiiirliACe*— Tlie  amount  of  grate-surface  required  per  hone 
power,  and  the  proper  ratio  of  heating-surface  to  flrrate-surface  are  ez- 
u^mely  Tariable.  dependinfr  chiefly  upon  the  character  of  the  coal  and  upon 
the  rate  of  draught  With  good  coal,  low  in  ash.  approximately  equal  resulu 
may  be  obtaineo  with  large  grate-surface  and  light  draught  and  with  small 
gmie-surface  and  strong  draught,  the  total  amount  of  coal  burned  per  hoar 
being  the  same  in  both  cases.  With  good  bituminous  coal,  like  Pittsburgh, 
low  in  ash,  the  best  results  apparently  are  obtained  with  strong  draught 
And  high  rates  of  combustion,  provided  the  grate-surfaces  are  cut  down  so 
that  the  total  coal  burned  per  hour  is  not  too  great  for  the  capacity  of  the 
heating-surface  to  absorb  the  heat  produced. 

With  coals  high  in  ash,  especially  if  the  ash  is  easily  fusible,  tending  to 
choke  the  grates,  large  grate-surface  and  a  slow  rate  of  combustion  are 
required,  unless  means,  such  as  shaking  grates,  are  provided  to  get  rid  of 
the  ash  as  fast  as  it  is  made. 

The  amount  of  grate-surface  required  j>er  horse-power  under  ▼arious  con- 
ditions may  be  estimated  from  the  following  table : 


*  c  "'  *-  5 


Good  i^ntkl 
atid  boiler. 

Fair  co^l   or 
boiler, 

Foor  coal  or 
boiler, 

Lignite  {incJj 
poor  boiler. 


1    10 

I? 


3.45 


gPu  P 


^  *-  *' 


3^5 

4. 

4.11 

AMU 

a. 

30. 


Founds  Of  Coal  burped  per  squmrtt  foot 
of  Grale  piur  hour. 


8  I  10  I  13  I  Ifi  I  10  I  i&  I  30  I  3S  I  4& 


Bq,  Ft-  Grate  per  H.  P. 


.80 


m 

.£4 

/i^ 

.17 

J4 

Ji 

JOt 

M 

.^ 

.^Jh 

Ji> 

Ji 

.IS 

.11 

Ai> 

,aa 

.>M 

AH) 

.IB 

.13 
,14 

.w 

.43 

.m 

s» 

.22 

,17 

.13 

.a 

.41 

33 

.ti 

,120 

.IT 

.14 

M 

.4;; 

.*i 

/^ 

.W 

J7 

.15 

j^ 

AH 

.38 

,29 

,aa 

.10 

n 

.fl9 

m 

At 

.85 

.as 

.-iS 

JK 

1.00 

M 

.6? 

.50 

.40 

.S9 

M 

M 

JO 

.11 

.13 

.n 

,14 
.17 


In  designing  a  boiler  for  a  given  set  of  conditions,  the  grate-eurf ape  should 
be  made  as  liberal  as  iK>ssibIe,  say  suflflcient  for  a  rate  of  combustion  of  10 
lbs.  per  square  foot  of  grate  for  anthracite,  and  15  Iba  per  square  foot  for 
bituminous  coal,  and  in  practice  a  portion  of  the  grate-surface  may  be 
bricked  over  if  it  is  found  that  the  draught,  fuel,  or  other  conditions  render 
it  advisable. 

Proportions  of  Areas  of  Flues  and  otlier  Oaa-passaces* 
''Rules  are  usually  given  making  the  area  of  gas-passages  bear  a  certain 
ratio  to  the  area  of  the  grate-surface;  thus  a  common  rule  for  horisontal 
tubular  boilers  is  to  make  thn  area  over  the  bridge  wall  1/7  of  the  grate- 
surface,  the  flue  area  1/8,  and  the  chimney  area  1/9. 

For  average  conditions  with  anthracite  coal  and  moderate  draught,  say  a 
Yate  of  combustion  of  13  lbs.  coal  per  square  fdot  of  grate  per  hour,  and  a  ratio 
of  heating  to  grate  surface  of  30  to  1,  this  rule  is  as  good  as  any,  but  it  is  evi- 
dent that  if  the  draught  were  increased  so  as  to  cause  a  rate  of  combustion 
of  24  lbs.,  requiring  the  grate-surface  to  be  cut  down  to  a  ratio  of  00  to  1,  the 
areas  of  gas-passages  should  not  be  reduced  in  proportion.  The  amount 
of  coal  burned  pf  r  hour  being  the  Siime  under  the  clianfed  conditions,  nnd 
there  being  no  reason  why  the  gases  should  travel  at  a  higher  velocity,  the 
actual  areas  of  the  pnssages  should  remain  as  before,  but  the  ratio  of  the 
area  to  the  grate-surface  would  in  that  case  be  doubled. 

Mr.  Barms  states  that  the  highest  efBoiency  with  anthracite  coal  is 
obtained  when  the  tube  area  is  1/9  to  1/lU  of  the  grate-surface,  and  with 
bituminous  coal  when  it  is  1/6  to  1/7,  for  the  conditions  of  medium  rates  of 
oombustion,  such  as  10  to  12  U)s.  per  square  foot  of  grate  per  hour,  and  19 
square  feet  of  heating-surface  allowed  to  the  horse-power. 

The  tube  areasliould  be  made  large  enough  not  to  choke  the  draught,  and 
BO  lessen  the  capacity  of  the  boiler;  if  made  too  large  the  gases  are  apt  to 
select  the  passages  of  least  resistance  and  escape  from  them  at  a  high 
▼elocity  and  high  temperature. 
'    This  condition  is  very  commonly  found  in  horizontal  tubular  boilers  where 


PBBFORICANCB  OF  BOILBB&  681 

the  nses  eo  chiefly  thronrh  the  upper  rows  of  tubes;  sometimes  also  In 
▼ertical  tubular  boUers,  where  the  gases  are  apt  to  pass  most  rapidly 
*hrouf?h  the  tubes  nearest  to  the  centre. 

Atr-paaMiffes  tbroaffli  Grate-bars.— The  usual  practice  is,  air- 
opening  =5  aOj(  to  50)(  of  area  of  the  grate ;  the  larger  the  better,  to  avoid 
stoppage  of  the  air-supply  by  clinicer;  but  with  coal  free  from  clinker  miich 
smaUer  air-space  may  be  used  without  detriment.  See  paper  by  F.  A. 
Scheffler,  Trans.  A.  8.  M.  S.,  vol.  xv.  p.  608. 

PBRFORMANCB    OF    BOII<BB8. 

The  performance  of  a  steam-boiler  comprises  lM>th  its  capacity  for  genera 
atiiig  sieam  and  its  economy  of  fuel.  Capacity  depends  upon  size,  both  of 
grate-surlace  and  of  heating-surface,  upon  the  icind  of  coal  burned,  upon 
the  draft,  and  ai^o  upon  the  economy.  Economy  of  fuel  depends  upon  tlie 
coniuleiene}«s  with  which  the  coal  is  burned  in  the  furnace,  on  the  proper 
regulation  of  the  air-supply  to  the  amount  of  coal  burned,  and  upon  the 
thoroughness  with  which  the  boiler  absorbs  the  heat  generated  in  the 
furnace.  The  absorption  of  heat  depends  on  the  extent  of  heating-sur- 
face in  relation  to  the  amount  of  coal  burned  or  of  water  evaporated,  upon 
the  arrangement  of  the  gas-passages,  and  upon  the  cleanness  of  the  sur- 
faces. The  capacity  of  a  boiler  may  increase  with  increase  of  economy 
when  this  is  due  to  more  thorough  combustion  of  theooal  or  to  better  regu- 
lation of  the  air-supply,  or  it  may  increase  at  the  expense  of  economy 
when  the  increased  capacity  is  due  to  overdriving,  causing  an  increased 
l(tss  I'f  heat  in  the  chimney  gases.  The  relation  of  capacity  to  economy 
is  therefore  a  complex  one,  depending  on  many  variable  conditions. 

Many  attempts  have  been  made  to  construct  a  fommla  expressing  the  rela- 
tion between  capacity,  rate  of  driving,  or  evaporation  per  square  foot  of 
heating-surface,  to  the  economy,  or  evaporation  per  pound  of  combustible, 
but  none  of  them  can  be  considered  satisfactory,  since  they  make  the 
economy  depend  only  on  the  rate  of  driving  (a  few  so-called  *^  constants,** 
however,  being  introduced  in  some  of  tliem  for  different  classes  of  boilers, 
kinds  of  fuel,  or  kind  of  draft),  and  fail  to  take  into  consideration  the  nu* 
merous  other  conditions  upon  which  economy  depends.  Buch  formulae  are 
Rankliie*s,  Clark^s,  Emenr^s.  Isherwood^s.  Carpenter^s,  and  Hale's.  A  dis- 
cussion of  them  ail  may  be  found  in  Mr.  R.  S.  Hale*8  paper  on  "  BfUciency 
of  Boiler  Heating  Surface,"  in  Trans.  A.  S.  M.  E.,  vol.  xvili.  p.  828.  Mr. 
Hale's  formula  takes  into  account  the  effect  of  radiation,  which  reduces  the 
economy  considerably  when  the  rate  of  driving  is  lees  than  8  lbs.  per  square 
foot  of  heating-surface  per  hour. 

Selecting  the  highest  results  obtained  at  different  rates  of  driving  obtained 
with  anthracite  coal  In  the  Centennial  tests  (see  p.  685),  and  the  highest 
results  with  anthracite  reported  by  Mr.  Barrus  in  his  book  on  Boiler  Tests, 
ithor  has  plotted  two  curves  showing  the  maximum  results  which 
may  be  expected  with  anthracite  coal,  the  first  under  exceptional  conditions 


the  author  has  plotted  two  curves  showing  1 

nay  be  expected  with  anthracite  coal,  the  first  under  exceptional  conditions 
such  as  obtained  in  the  Centennial  tests,  and  the  second  under  the  best 


conditions  of  ordinary  practice.  (Trans.  A.  S.  M.  E.,  xvili.  854).    From  these 
curves  the  following  figures  are  obtained. 
Lbs.  water  evaporated  from  and  at  212*  per  sq.  ft.  heating'surface  per  hour: 
1.6     1.7     2        2}i      8       8.5       4        4.5      5        6        7      8 

Lbs.  water  evaporated  from  and  at  212*  per  lb.  combustible : 

Gtotennial.  11.8    11.9    12.0    12.1    12.06    12      11.86    11.7    11.5    10  85    9.8  8.5 

Barrus 11.4    11.5    11.65  11.6    11.6    11.5    11.2      10.9    10.6     9.9     9.2  8.6 

Avg.  Cent'l 12.0    11.6    11.2    10.8    10.4     10.0     9.6     8.8     8.0  7.3 

Hie  figures  in  the  last  line  are  taken  from  a  straight  line  drawn  as  nearly 
as  possible  through  the  average  of  the  plotting  of  all  the  Centennial  tests. 
The  poorest  results  are  far  below  these  figures.  It  is  evident  that  no  formula 
can  oe  constructed  that  will  express  the  relation  of  economy  to  rate  of 
driving  as  well  as  do  the  three  lines  of  figures  given  above. 

For  pemi-bltuminous  and  bituminous  coals  the  relation  of  economy  to  the 
rate  of  driving  no  doubt  follows  the  same  general  law  that  it  does  with 
anthracite,  i.e.,  that  beyond  a  rate  of  evaporation  of  8  or  4  lbs.  per  sq.  ft.  of 
heatiug-surface  per  hour  there  is  a  decrease  of  economy,  but  tlie  figures 
obtained  in  different  tests  will  show  a  wider  range  between  maximum  and 
average  results  on  account  of  the  fact  that  it  is  more  difficult  with  bituminous 
than  with  anthracite  coal  to  secure  complete  combustion  in  the  furnace. 


682  THE  STEAM-BOILBB. 

The  amount  of  the  decrease  in  ecoDomy  due  to  drhrftig  at  mtei  esc«edlo|p 
4  lbs.  of  water  evaporated  per  square  foot  of  heatiUK-surface  per  hear 
differe  arreatly  with  different  boilers,  and  with  the  «ame  boiler  It  may  differ 
with  different  settlnRs  and  with  different  coal.  The  arrangement  afid  die 
of  the  frtis-passa^eR  seem  to  have  an  important  effect  upon  the  relation  of 
economy  to  rate  of  drivihR.  There  is  a  larpre  field  for  future  research  to 
determine  the  causes  which  influence  this  relation. 

General  Conditions  ^vhlcli  secure  Bconomy  of  Steam* 
lK>llers.— In  general,  the  hifheet  re»ult«  are  produced  whei«  the  tempera* 
ture  of  the  escaping  gases  is  the  least.  An  examination  of  this  queetion  la 
made  by  Mr.  G.  H.  Barms  in  his  book  on  *'  Boiler  Tests/^  by  seiectins  those 
tests  made  by  him,  six  in  number,  in  which  the  temperature  exceeds  the 
average,  that  is,  876*  F.,  and  comparing  with  five  tests  in  which  toe  tempei^ 
ature  is  less  than  875?  The  boilers  are  aU  of  the  common  horixontal  type, 
and  all  use  anthracite  coal  of  either  egg  or  broken  size.  The  average  nue 
temperatures  in  the  two  series  was  444*  and  848"  respectively,  and  the  dif- 
ference was  101".  The  average  evaporations  are  10.40  lbs.  and  11.09  lbs.  re- 
spectively,  and  the  lowest  result  corresponds  to  the  case  of  the  highest  flue 
temperature.  In  these  tests  it  appears,  therefore,  that  a  reduction  of  101* 
In  the  temperature  of  the  waste  gases  secured  an  increase  in  the  evaporatios 
of  6%.  This  result  corresponds  quite  closely  to  the  effect  of  lowering  the 
temperature  of  the  gases  by  means  of  a  flue*4ieater  where  a  reduction  of 
107*  was  attended  bv  an  increase  of  7%  in  the  evaporation  per  pound  of  coaL 

A  similar  comparison  was  made  on  horizontal  tubular  boilera  using  Cum- 
berland coal.  The  average  flue  temperature  in  four  tests  is  450*  and  the 
average  evaporation  is  11.84  lbs.  Six  boilers  have  temperatures  below  415*, 
the  average  of  which  is  888*,  and  these  give  an  average  evaporation  of  11.75 
lbs.  With  67*  leas  temperature  of  the  escaping  gases  the  evaporation  is 
higher  by  about  i%» 

The  wasteful  effect  of  a  high  flue  temperature  is  exhibited  by  other  boilers 
than  those  of  the  horisontal  tubular  class.  This  source  of  waste  was  shown 
to  be  the  main  cause  of  the  low  economy  produced  in  those  Tertical  boilers 
which  are  deficient  in  heating-surface. 

Belaiion  betwemi  the  Heaiing'Wrf(toe  and  Orate-auf/ace  to  obtain  th« 
SigfiMtt  KMciency.^A.  comparison  of  three  tests  of  horisontal  tubular 
boilers  with  anthracite  coal,  the  ratio  of  heating- surface  to  gtvte-surfaoe 
being  86.4  to  1,  with  three  other  tests  of  similar  boilers,  in  which  the  ratio 
was  48  to  1,  showed  practically  no  difference  in  the  results.  The  evidence 
shows  that  a  ratio  of  86  to  1  provides  a  sufficient  quantity  of  heating^surface 
to  secure  the  full  elTlciency  of  anthracite  coal  where  the  rate  of  combustion 
Is  not  more  than  12  lbs.  per  sq.  ft.  of  grate  per  hoiur. 

In  tests  with  bituminous  coal  an  increase  in  the  ratio  from  86.8  to  45L8  se- 
cured a  small  improvement  in  the  evaporation  per  pound  of  coal,  and  a  high 
temperature  of  the  escaping  gases  indicated  that  a  still  further  increase 
would  be  beneficial.  Among  the  high  results  prodticed  on  common  horison- 
tal tubular  boilers  using  bituminous  coal,  the  highest  occurs  where  the  ratio 
is  58.1  to  1.  This  boiler  gave  an  evaporation  of  12.47  lbs.  A  double-deck 
boiler  furnishes  another  example  of  high  performance,  an  evaporation  of 
13.42  lbs.  having  been  obtained  with  bituminous  coal,  and  in  this  case  the 
ratio  is  65  to  1.  These  exanoples  indicate  that  a  much  larger  amount  of 
beating-surface  is  required  for  obtaining  the  full  efficiency  of  bituminous 
coal  than  for  boilers  using  anthracite  coal.  The  temperature  of  the  eecap* 
ing  gases  in  the  same  boiler  is  invariably  higher  when  bituminotis  coal  a 
used  than  when  anthracite  coal  is  used.  The  deposit  of  soot  on  the  surfaces 
when  bituminous  coal  is  used  interferes  with  the  full  efficiency  Of  the  sux^ 
face,  and  an  increased  area  is  demanded  as  an  offset  to  the  loss  which  this 
deposit  occasions.  It  would  seem,  then,  thlit  If  a  ratio  of  86  to  1  is  suificient 
for  anthracite  coal,  from  45  to  60  should  be  provided  when  bitumlnons  coal 
is  burned,  especially  In  cases  whero  the  rate  of  combustion  is  above  10  or  IS 
lbs.  per  sq.  ft.  of  grate  per  hour. 

The  number  of  tubes  controls  the  ratio  between  the  area  of  grate-surface 
and  area  of  tube  opening.  A  certain  minimum  amount  of  tube-opening  is 
required  for  efficient  work. 

The  best  rasults  obtained  with  anthracite  coal  fn  the  ooiilmoii  horisontal 
boiler  are  in  cases  where  the  ratio  of  area  of  grate-Burface  to  area  of  tube- 
opening  is  larger  than  9  to  1.  The  conclusion  Is  drawn  that  the  highest  effi- 
ciency with  anthracite  coal  is  obtained  when  the  tube-opening  is  from  1/9  to 
J/iO  of  the  grate-snrtsAe. 


PEBFOBMANCB  OF  BOILEBS.  683 

When  bituminous  coal  is  burned  the  requirements  app«ar  to  be  different. 
The  effect  of  a  large  tube  opening  does  not  seem  to  make  the  extra  tubes 
inefficient  when  bituminous  coal  is  used.  The  highest  result  on  any  boiler  of 
tlie  horizontal  tubular  class,  fired  with  bituminous  coal,  was  obtained  where 
the  tube-opening  was  the  largest.  This  gave  an  evaporation  of  13.47  lbs.,  the 
ratio  of  grate>surface  to  tube-openiug  being  6.4  to  1.  The  next  highest  re* 
suit  was  12.42  lbs.,  the  ratio  being  6.2  to  1.  Three  high  results,  averaging 
12.01  lbs.,  were  obtained  when  the  average  ratio  was  7*1  to  1.  Without  going 
to  extremes,  the  ratio  to  be  desired  when  bituminous  coal  is  used  is  that 
which  gives  a  tube-opening  having  an  area  of  from  1/6  to  1/7  of  the  grate- 
surface.  This  applies  to  medium  rates  of  combustion  of,  say,  10  to  18  lbs.  per 
sq.  ft.  of  grate  per  hour,  12  sq.  ft.  of  water-heating  surface  being  allowed  per 
horse-power. 

A  comparison  of  results  obtained  from  different  types  of  boilers  leads  to 
the  general  conclusion  that  the  economy  with  which  different  types  cf 
boilers  operate  depends  much  more  upon  their  proportions  and  the  condi- 
tions under  which  they  work,  than  upon  their  type ;  and,  moreover,  that 
when  these  proportions  are  suitably  carried  out,  and  when  the  conditions 
are  favorable,  the  various  types  of  boilers  give  substantially  the  same  eco- 
nomic result. 

BflieteneT  of  a  8Ceam*boller«— The  efficiency  of  a  boiler  is  the 
percentage  of  the  total  heat  generated  by  the  combustion  of  the  fuel 
which  is  utilized  in  heating  the  water  and  in  raising  steam.  With  anthracite 
ooal  the  heating-value  of  the  combustible  portion  is  veiy  nearly  14,500 
B.  T.  U.  per  lb.,  equal  to  an  evapoi-atlon  from  and  at  212*  of  14,600  -4-  906 
B  15  lbs.  of  water.  A  boiler  whicn  when  tested  with  anthracite  coal  shows 
an  evaporation  of  12  lbs.  of  water  per  lb.  of  combustible,  has  an  efficiency  of 
12  •*- 16  ai  80%,  a  figure  which  is  approximated,  but  scarcely  ever  quite 
reached,  in  the  best  practice.  With  bituminous  coal  it  is  necessary  to  have 
a  determination  of  its  heating-power  made  by  a  coal  calorimeter  before  the 
efficiency  of  the  boiler  using  it  can  be  determined,  but  a  close  estimate  may 
be  made  from  the  chemicalanalysls  of  the  coal.    (See  Coal.} 

The  difference  between  the  efficiency  obtained  by  test  and  lOOjt  is  the  sum 
of  the  numerous  wastes  of  heat,  the  chief  of  which  is  the  necessary  loss  due 
to  the  temperature  of  the  chimn«>y-gase8.  If  we  have  an  analysis  and  a 
calorimetric  determination  of  the  heating-power  of  the  coal  (properly  sam- 
pled), and  an  average  analysis  of  the  chimney-gases,  the  amounts  of  the 
several  losses  may  be  determined  with  approximate  accuracy  by  the  method 
described  below. 

Data  given : 

1.  Amaltsis  of  thb  Coau  8.   Akaltsis  of  thb  Dry  Cbimmey- 

Comberland  Semi-bituminous.  oases,  by  WBiodT. 

Carbon 80.66  C.        O.         N. 

Hydrogen 4.60       CO.  =    18.6   a    8.71      9.80      

Oxygen 8.70       CO     =       .2=     .09        .11       

Kitrogen 1.08       O       =    11.8   »    ....     11.20      

Moisture 2.92       N       a    75.0   «     75.00 

Ash 8.25  

100.0    8.80  21.20   75.00 

100.00 

Heatlng-Talae  of  the  coal  by  Dulong's  formula,  14,848  heat-nnitsi 
The  gases  being  collected  over  water,  the  molstut^  in  them  is  not  deter- 
mined. 

3.  Ash  and  refuse  as  determined  by  boiler-test,  10.25,  or  9%  more  than  that 
found  by  analysis,  the  difference  representing  carbon  in  the  ashes  obtained 
in  the  boiler-test. 

4.  Temperature  of  external  atmosphere,  60"  F. 

6.  Relative  humidity  of  air,  60)(,  corresponding  (see  air  tables)  to  .007  lb.  of 
▼apor  in  each  lb.  of  air. 

0.  Temperature  of  chimney-gases,  660"  F. 

Calculated  results : 

The  carbon  in  the  chimney-gases  being  S.Bi  of  their  weight,  the  total 
weight  of  dry  gases  per  lb.  of  carbon  burned  is  100  -t-  8.8  =  26.82  lbs.  Since 
the  carbon  burned  is  80.65  -  2  =  7S.56%  of  the  weight  of  the  coal,  the  weight 
of  the  dry  gases  per  lb.  of  coat  is  26.82  X  78.56  ■*•  100  =  20.67  lbs. 

Each  pound  of  coal  furnishes  to  the  dry  chimney-gases  .7865  lb.  C,  .0106N, 

and  (^870-  ^^-i-lOOs  .02l41b.Oi  atotalof  .8177,8ajr.ftilb.  Thiaiub* 


684  THB  STEAH-fiOILEB. 

tracted  from  90.07  Hm.  leaves  10.85  lbs.  as  the  quantl^  of  dry  air  (taot  Inelad- 
Inff  moiiture)  wbich  enters  the  furnace  per  pound  of  coal,  not  oountinic  Um 
air  required  to  bum  the  available  hydrogen,  that  Is,  the  hydrogen  minus  one 
eighth  of  the  ozvgen  chemically  combined  in  the  coal.  Each  lb.  of  coal 
burned  oontained  .045  lb.  H,  wblch  requires  .045  X  8  &.  .86  lb.  O  for  ICa  com- 
bustion, or  this,  .027  lb.  is  furnished  l»y  the  coal  itself,  leaving  .889  lb.  to 
come  from  the  air.  The  quantity  of  air  needed  to  supply  this  oxygen  (air 
containing  2^  by  weight  of  oxygen)  is  .888  •«-  .28  v  1.45  lb.,  which  added  to 
the  10.85  lbs.  already  found  gives  81.80  lbs.  as  the  quantity  of  diy  air  sup- 
plied to  the  furnace  per  lb.  of  coal  burned. 

The  air  carried  in  as  vapor  is  .0071  lb.  for  each  lb.  of  dry  air,  or  21.8  X  .0071 
sr  0.15  lb.  for  each  lb.  of  coal.  Each  lb.  of  ooai  contained  .029  lb.  of  mois- 
ture, which  was  evaporated  and  carried  into  tlie  chimney-gases.  The  .045  lb. 
of  H  per  lb.  of  coal  when  burnt-d  formed  .046  x  0  »  .4U5  lb.  of  H*0. 

From  the  analysis  of  the  chimney-gas  it  appears  that  .00  -«-  8.80  a  2.8;iK  of 
the  carbon  in  the  coal  was  burned  to  CO  instead  of  to  COf. 

We  now  have  the  data  for  calculating  the  various  losses  of  heat,  as  follows, 
for  each  i>ound  of  coal  burned: 


20.87  lbs.  dry  gas  X  (M0»  -  60»)  X  sp.  heat  024  = 

.15  lb.  vapor  in  air  X  (560»  ~  60°)  x  sp.  heat  .48       *r 
.ftiO  lb.  moisture  In  coal  heated  from  60*  to  212*       -m 
*'       evaporated  from  and  at  213«;  .020  X  066        s 
*      steam  (heated  from  218«  to  560«)  x  846  x  .48  a 
.406  lb.  HjO  from  H  In  coal  X  (152  4-  966  +  818  x  19^  = 
.0387  lb.  G  burned  to  CO;  1or.s  by  incomplete  com- 
bustion. .0237  X  (14544  -  4451)  = 
.02  lb.  coal  lost  in  ashes;  .03  X  14544  = 
Radiation  and  unaccounted  for,  by  difference  = 

Utilized  In  making  steam,  equivalent  evaporation 
10.87  lbs.  from  and  at  212«  per  lb.  of  coal  a 

14,248.0         100.00 

The  heat  lost  by  radiation  from  the  boiler  and  furnace  is  not  easily  deter, 
mined  directly,  especially  if  the  boiler  is  enclosed  in  brickwork,  or  is  pro- 
tected by  non-conducting  covering.  It  is  customary  to  estimate  the  neat 
lost  by  radiation  by  difference,  that  is.  to  charge  radiiation  with  all  the  heat 
lost  wlilch  is  not  otherwise  accounted  for. 

One  method  of  determining  the  loss  by  radiation  Is  to  block  off  a  portion 
of  the  grate-surface  and  build  a  small  Are  on  the  remainder,  and  drive  this 
fire  with  just  enough  draught  to  keep  up  the  steam-pressure  and  supply  the 
heat  lost  by  radiation  without  allowing  any  steam  to  be  discharged,  weigh- 
ing the  coal  consumed  for  this  purpose  duriug  a  test  of  several  hours*  dura- 
tion. 

Estimates  of  radiation  by  difference  are  apt  to  be  greatly  in  error,  as  in 
this  difference  are  accumulated  all  the  errors  of  the  analyses  of  tlie  coal 
and  of  the  gases.  An  average  value  of  the  heat  lost  by  radiation  from  a 
boiler  set  in  bi-ickwork  is  about  4  per  cent.  When  several  boilers  are  in  a 
batterv  and  enclosed  in  a  boiler-house  the  loss  by  radiation  may  be  very 
much  less,  since  much  of  the  heat  radiated  from  the  boiler  is  returned  to  it 
in  the  air  supplied  to  the  furnace,  which  is  taken  from  the  boiler-room. 

An  important  source  of  error  in  making  a  *'  heat  balance  **  such  as  the 
one  above  given,  especially  when  highly  bituminous  coal  is  used,  may  be 
due  to  the  non -combustion  of  part  of  the  hydrocarbon  gases  distilled  from 
the  coal  immediately  after  firing,  when  the  temperature  of  the  furnace  may 
be  reduced  below  the  point  of  ignition  of  the  gases.    Each  pound  of  hydro- 

Ein  which  escapes  burning  is  equivalent  to  a  loss  of  heat  in  the  furnace  of 
,500  heat-units. 

In  analyzing  the  chimney  gases  by  the  usual  method  the  peroentagea  of 
the  constituent  gases  are  obtained  by  volume  instead  of  ov  weight.  To 
reduce  percentages  by  volume  to  percentages  by  weight,  roulttply  the  per- 
centage by  volume  of  each  gas  by  iU  specinc  gravity  as  oomparea  with  alr« 
And  divide  each  product  by  the  sum  of  the  producta. 


Heat- 
unita. 

Per  cent  of 
Heat-value 
oftheCoaL 

2480.4 
86.0 
4.4 

88.0 

4.8 

620.4 

17.41 
0.25 
0.08 
0.20 
COS 
8.66 

289.2 
i?9n.9 
624.0 

1.68 
2.04 
4.81 

4228.1 

"SjS 

0,014.9 

70.S9 

TESTS  OF  STEAM-UOILEnS. 


685 


If  0»  CO.  COfl .  auti  N  represent  the  per  cents  by  volume  of  oxygen,  car- 
bonic oxide,  carbonic  acid,  and  nitrogen,  respectively,  in  the  gases  of  com- 
bustiou: 

Lbs.  of  air  required  to  bum    )   _    _S.08^^ 
one  pound  of  carbon        \   "  cOj  -{-  ('O' 

Ratio  of  total  air  to  the  theoretical  requirement  =  ^^^ — . 

,  ^  ^  N-a.78;iO 

Lb«.  of  air  per  pound  \_{  Lbs.  of  air  per  pound  }  ^  j  Per  cent  of  carb»m 
of  coal  )      ]     of  carbon  Si     in  coal. 


Lbs.  dry  gas  produced  per  pound  of  carbon  = 


nCQ,4-80-f  7(CO-f-N) 


3HCO,  +  CO) 
TBST8  OF  8TEA]n[-BOI]:.EB8. 

BoUer-^tosts  at  tbe  Centennial  Bxbibition,  Pltlladel- 
plila.  18 76. —(See  Reports  and  Awards  Group  XX.  intemutionai  Exhibi- 
tion, Fhila.,  1876;  also,  Claris  on  tlje  Steam-engine,  vol.  i,  page  858.) 

Competitive  tests  were  made  of  fourteen  boilers,  using  good  anthracite 
coal,  one  boiler,  the  Galloway,  being  tested  with  both  anthracite  and  seml- 
bituminoos  coal.  Two  tests  were  made  with  each  boiler :  one  called  the 
capacity  trial,  to  determine  the  ecoDomy  and  capacity  at  a  rapid  rate  of 
driving;  and  the  other  called  the  economy  trial,  to  determine  the  economy 
when  driven  at  a  rate  supposed  to  be  near  that  of  maximum  economy  and 
rated  capacity.  The  following  table  gives  the  principal  resultH  obtained  in 
the  economy  trial,  together  with  the  capacity  and  economy  figures  of  the 
capacity  trial  for  comparison. 


Economy  Tents. 

Capacity 

Hame 
.   of 
feoUer. 

II 

1 

3- 

1 

1 

s 

_c 

f 

o 

1 

1 

^ 

ss 

t  - 

3  V 

U 

ti. 

£rl 

£ 

£ 

1 

a 

£» 

£?J 

U 

1 

1 

1 

10 

^_ 

ih^. 

^ 

££E5 

d^ 

^ 

E    1 

1 

^ 

p.ct 

IbH. 

lliw. 

% 

d*tg 

H.F 

Iba. 

Hoot 

U.B 

9  1 

10.4 

j.a> 

H,OW 

8a§ 

41 A 

119.S 

I+^.fi 

10J41 

Flnnpnich . . , 

V2  0 

10.4  1.6*^ 
11,3  1.87 

4ir, 

Si!  (J 
9.4 

57. H 

fii^.4 
(JS.S 

0.064 

I/3we  ...*.*»....... 

ii.ica 

ftmith. 

l.VB 

in.  I 

n.l^Ai 

11  goti 

411 

i'a 

wo.s 

125  0 

n.oijs 

Bahcock  &  WUoox 

37.7 

10.0 

IKtJa  4M 

n.^ii 

:i»*1 

g.T 

l^^i,U 

1i*fl.(J 

10. 3,^ 

Oalloway...*.  ..^, 

^S\.7 

iij; 

11.1  ^lea 

11  T^ 

30!1 

'i!4 

103.  rj 

vi-m 

11  3ii 

Dq^    nemlblt.  coal 

as. 7 

7  1* 

a. 83.20 

12.145 

.^ 

oia 

90,9 

li^.l 

iKfiOO 

Andrews,..*  *...*. 

t:^A 

8a^ 

10. :i  ^M 

1 1  jm 

4i0 

Tl> 

«.(! 

Gfl  r 

?,74S 

BAtTison.. *.....  .» 

?7,a 

i.;.4 

H.5a.7:- 

I0fl30 

517 

O.ft 

8y.4 

lfi«.4 

9«^ 

Wle^earid-,.  .»,... 

W.7 

iii.y 

»,5  3,ai 

lo.icw 

524 

-  > . . 

soia 

H7.:i 

162,8 

9.14A 

Aaderaoa..     *.... 

17.S. 

3,7 

0.3^,04 

uLei8 

417 

1&,7 

Ott.O 

133.8 

05€8 

Rally ._„ 

20,0 

I0> 

9J)3,8^ 

lo.sia 

'VB 

suo 

i»9.tt 

a  se? 

Exeter , 

JJ3.5 

0  a 

n.4i.,H.N 

\iim\ 

i^ 

4.5, 

7^J  1 

108.0 

Bfl74 

'Pierce  . .  ♦ .  +  ^ .  .,,**, 

n.(* 

nj 

rK0  4.4i 

10  Oil 

374 

5.2 

. .  I  - 

61,7 

G7.fl 

u.im 

Bogem^  Black... 

19. a 

^j, 

o.ws.ta 

fl,m3 

r^Ti 

a,] 

J5.7 

67  .ii 

3  4^ 

2.77 

iKi^ 

«5,0 

llO.ft 

10.^1 

Th'*  *"?  >Tr!  fi :%  rt 'Tn  n  ''^f  t?ir  r'f-ri- :■-■'.■   -m  t  .-■ 11-1  -^'v  1---  '  ■  .v,  .-.■- -  if  - 

liiCreuse  ua  caLiauii^-  u*  .t-i  jju:  c_^_  .•. , .  v>  ^  ^^v.-*. — ^  iii  cd-iiiuiiiy 

of  8  per  cent,  but  the  relation  of  economy  to  rate  of  driving  varied  ereatly 
fn  the  different  boilers.  In  the  Kelly  boiler  an  increase  in  capacity  of  29  per 
cent  was  attended  by  a  decrease  in  economy  of  over  18  per  cent,  while  the 
Smith  boOer  with  an  increase  of  iib  per  cent  in  capacity  showed  a  slighl 
increase  in  economy,         ... 


686 


THE  STEAM-BOILEB. 


One  of  the  most  lini>ortant  lessoDS  Mined  from  the  above  tests  Is  that 
tliere  is  no  neoessaiy  relation  between  the  type  of  a  boiler  and  economy.  Ol 
the  five  boilers  that  gave  the  best  results,  the  total  range  of  variation  lie- 
tween  the  highest  and  lowest  of  the  five  being  only  2,Z%,  three  were  water- 
tube  boilera,  one  was  a  horizontal  tubular  boiler,  and  the  fifth  was  a  com- 
bination of  the  two  types.  The  next  boiler  on  the  list,  the  Galloway,  was  an 
intemallv  fired  boiler,  all  of  the  others  being  externally  fired.  The  following 
is  a  brief  description  of  the  principal  constructive  features  of  the  fourteen 
boOers: 
B,^(.  J  4-in .  water-tubes,  inclined  20*  to  horisontal ;  reversed 

^^^ 1     draught. 

Firmenlch 8-in.  water-tubes,  nearly  vertical;  reversed  draught. 

Lowe Cylindrical  shell,  multitubular  flue. 

Cylindrical  shell,  multitubular  flue— water-tubes  in 
side  flues. 

2^in.  water-tubes,  inclined  16*  to  horiaontal;  re- 
versed draught. 

Cylindrical  shell,  furnace- tubes  and  water- tubes. 

Andrews Square  fire-box  and  double  return  multitubular  flues. 

n«rr<ann  J  ^  slabs  of  cast-lrou  spheres,  8  in.  in  diameter;  i^ 

llarrtson <     versed  draught. 

Wiegand \  *"*"*  "w*t«r-tube8,  vertical,  with  internal  circulating 

Anderson 8-in .  flue-tubes,  nearly  horizontal ;  return  circulation. 

v.|i^  j  8-in.  water-tubes,  slightly  inclined;  each  divided  by 

^ I     internal  diaphragm  to  promote  circulation. 

Exeter 27  hollow  rectangular  cast-iron  slabs. 

Pitirce Kotating  horizontal  cylinder,  with  flue-tubes. 

Rogers  &  Black Verticalcylindrical  boiler,  with  external  water-tubes. 

Tests  of  Tabaloas  Boilers.— The  following  tables  are  given  by  8. 
H.  Leonard,  Asst.  ^ngr.  U.  IS.  N.,  In  Jour.  Am.  Soc.  Ifaval  Enars.  1890.  The 
tests  were  made  at  different  times  by  boards  of  U.  S.  Naval  Engineers,  ex- 
cept tjietest^fjbejlocon^^ 


Sfulth. 

Babcock  &  Wilcox 
Galloway 


T^pe. 


Belleville.. 
Herreshoft 
Towne 


Ward 

Scotch..  .. 

LocomHive 
torpedo, 

Ward 

Thorny- 
croft.  (U. 
S.S.Cush- 


12.8 

0.8 
25.8 
4.3 
24.5 

7.9 
15.5 
63.5 
24.8 
88 
96.8 
120.8 

56.04 
45 


Evaporation 

from  and  at 

S12«»  F. 


10.42 

10.23 

8.68 
18.4 
67 

lo.rr 

10.01 
7.01 
9.9.S 
9.06 


8.44 


6.2 

8.1 

8 

8.7 

8.8 

1.7 

8.2 

10 
8.6 

12.8 

17.1 

20.06 

9.47 


6.4 

9.1 
28.8 
10 
80.4 

5.8 
11 

84.2 
11 

16.8 
80.6 
86.2 

82.1 


Weights,  lbs. 


HCQh 


11 


40,670 
452,770 
2.945 
8,050 
1,380 
1,640 


1,682 

1,930 

:  18,900 


E 
S 

E 

8  30,0001  80 

S  34,990 


47.7 


,88.3 

30.474  ^ 
20.1G0L«i 
24,W0i  *' 


58.2 
14.8 
21.8 

18.2 

41.2 
81.3 
12.8 
10.8 


8 

1 

6 

7 

07 

8 

7 

1 

8 

2 

1.8 


I* 


Natn. 

Jet. 

Jet. 
Natl. 
1.14 
Natn. 

Jet 

Jet. 
2.G8 
4.01 
8.18 
4.96 

8 


in 

190 
196 
148 

153? 

0 
) 
161 
77 
T8 
125 
124 

160 
M5 


♦Approximate. 
Per  cent  moistnre  in  steam:  Belleville,  6.31;  Herreshoff 
Scotch,  1st,  8.44;  2d.  4.29;  Ward,  11.6;  others  not  given. 


(first  test),  8.5 


TESTS  OF  BTEAM-BOILERS. 


687 


DlMBlfSXOKS  or  THB  BotLBRS. 


^    No. 

1 

2 

8 

4 

5 

6 

7 

8 

Length,  ft.  and  in.. 

8' 6" 

4/  9// 

0/   Qtf 

3'  2" 

V  0" 

16'  8 

10'  Z"* 

vy  0"t 

Widih, 

7  0 

3   8 

2   6 

1    7 

9  0 

6   4 

4   6  t 

8  Ot 

Height,"     "    ".. 

4  0 

8   8 

7   2 

7   6 

11    8 

Space,  cu.  ft 

69.6 

20  8 

42.7 

672.5 

680.8 

729.3 

560$ 

Grate- area,  sq.ft.. 

84.17 

0 

4.85 

8.68 

81.16 

28 

66.6 

38.8 

Heating-Burface, 

Ra3oHV8.*-f-b*;!! 

804 

805 

75 

146 

787 

1116 

2490 

8875 

83.6 

88 

17.6 

89.5 

28.8 

39.8 

37.4 

68 

*  Dlanaeter.    t  Diam.  of  dram,    t  Approximate. 

The  weight  per  I.H.P.  is  estimated  on  a  basis  of  20  lbs.  of  water  per  hour 
for  all  cases  expecting  the  Scotch  boiler,  where  25  lbs.  have  been  used,  as  this 
boiler  was  limited  to  80  lbs.  pressure  of  steam. 

The  following  approximation  is  made  from  the  large  table,  on  the  assump- 
tion that  the  evaporation  varies  directly  as  the  combustion,  and  35  lbs.  of 
coal  per  square  foot  of  grate  per  hour  used  as  the  unit. 


Type  of  Boiler. 


Belleville . . . 
Herreahoff. . 

Towne 

Scotch 

Locomotive 
Ward 


Com 

Evapora- 
tion per 

Weight 

Weight 
per  sq.  ft. 
Heating- 

bustion. 

cu.  ft.  of 

I.^JP. 

Space. 

surface. 

0.50 

0.50 

2.0s 

2.10 

1.00 

0.95 

0.72 

0.60 

1.00 

1.20 

1.18 

0.87 

1.00 

0.44 

2.40 

1.64 

8.90 

0.81 

8.70 

1.25 

8.20 

0.58 

1.27 

0.60 

Weight 
per  lb. 
Water 


Evapo- 
rated. 


8.50 
0.90 
1.30 
2.30 
8.S0 
1.58 


The  Belleville  boiler  has  no  practical  advantage  over  the  Scotch  either  in 
space  occupied  or  weight.  All  the  other  tnbulous  boilers  given  greatly 
exceed  the  Scotch  in  these  advantages  of  wei^^ht  and  space. 


ne  SUclt  Rates  of  BTaporatiqn*- 

Loco 


Eng'g,  May  9,  1884,  p.  415. 


comotive.       "  Torpedo-boat. 

Water  evap.  per  sq.  ft.  H.S.  per  hour 12.57       13.78  12.54       20.74 

*    lb.  fuel  from  and  at  212«.      8.22         8.94  8.37         7.04 

Thermal  units  transrd  per  sq.ft.  of  H.S.  12,142     13,263  18,113     20,084 

Efficiency 586         .687  .648       .468 

lE  is  doubtful  if  these  figures  were  corrected  for  priming. 

Econoiny  EfTeeted  by  Heating  tbe  Air  Supplied  to 
BoOer^fiiTnacee*  (Clark,  S.  E.)— Meuuier  and  Scheurer-Kestner  ob- 
tained about  7%  greater  evaporative  efficiency  in  summer  than  in  winter, 
from  the  same  boilers  under  like  conditions,— an  excess  which  had  been  ex- 
plained by  the  difference  of  lo9S  by  radiation  and  conduction.  But  Mr. 
Poupardin.  surmising  that  the  gain  might  be  due  in  some  degree  also  to  the 
greater  temperature  of  the  air  in  summer,  made  comparative  trials  with 
two  groups  of  three  boilers,  each  working  one  week  with  the  heated  air, 
and  the  next  week  with  cola  air.    The  following  were  the  several  efficien- 


cies: 


FiBST  Tbxaub:  Three  Boilkrs;  Ronchavp  Coal. 

Water  per  lb.  of    Water  per  lb.  of 
Coal.  Combustible. 

With  heated  air  (128»  F.) 7.77  lbs.  8.95  lbs. 

With  cold  air  (69«.8) 7.38  '*  8.63  " 

Difference  in  favor  of  heated  air  ....  0.44  *'  0.32  ** 

Second  Trials:  Sake  Coal;  Thrre  Other  Boilers. 

With  heated  air  (190«.4  F.) 8.70  lbs.  10.08  lb*. 

With  cold  air  (750.2) 8.09  "  9.34  " 

DilTerence  in  favor  of  heated  air 0.61  *'  0.64  ** 


688 


THE  STEAM-BOILER. 


These  results  show  economies  in  favor  of  heatlns  the  air  of  6)C  and  7H)t 
Mr.  Poupardfn  believes  that  the  f?ain  In  efficiency  is  due  chiefly  to  the 
better  combustion  of  the  ^aseB  with  heated  air.    It  was  observed  inat  with 
heated  air  the  flames  were  much  shorter  and  whiter,  and  that  there  was 
notably  less  smolce  from  the  chimney. 

An  extensive  series  of  experiments  was  made  by  J.  C.  Hoadlev  (Trans. 
A.  8.  M.  E.,  voL  vi.,  676)  on  a  "  Warm-bla8t  Apparatus,"  for  utiiizini?  the 
heat  of  the  waste  frases  iu  heating  the  air  supplied  to  the  furnace.  The  ap- 
paratus, as  applied  to  an  ordinary  horisontal  tu  ular  boiler  60  in.  diameter, 
21  feet  long. with  65  8^-inch  tubes,  consisted  of  240  2-inch  tubes,  18  feet  long, 
through  which  the  hot  gases  passed  while  the  air  circulated  around  them. 
The  net  saving  of  fuel  effected  by  the  warm  blast  was  from  10.7}(  to  i5.Si%  of 
the  fuel  used  with  cold  blast.  The  comparative  temperatures  averaged  as 
follows,  in  degrees  F. : 

Cold-blast    Warm-blast  nw^.^,wwv 
Boiler.         Boiler.       Difference. 

Inheatofflre 2498  9798  800 

Atbridgewall 1840  1600  960 

Insmokebox 878  875  9 

Air  admitted  to  furnace 89  889  80O 

Steam  and  wcter  in  boiler 800  800  0 

Gases  escaping  to  chimney 878  169  911 

Externalafr 89  89  0 

With  anthracite  coal  the  eva)x>ration  from  and  at  219<^  per  lb.  combiistlbU- 
vras,  for  the  cold-blast  boiler,  days  10.86  lbs.,  days  and  nights  10.61;  and  for 
the  warm-blast  boiler,  days  1 1.83,  days  and  nights  11.08. 

Results  of  Teste  of  Kelne  IFater^nbe  Boilers  -with. 
miTerent  Coals. 

(Communicated  by  E.  D.  Meier,  C.E.,  1894.) 


Number .......,..-- 1* 

1 

2 

8 

4 

6 

0 

7 

8 

KindofCoaL 

5* 

9d  Pool, 

Toughiogh- 

eny. 

r 

r 

r 

B 

If 
o 

1 

i 

Per  cent  ash 

5.1 
2900 

64 
58.7 
94.7 

5.08 

10.91 
11.50 

580« 
18,800 

77.0 

4.89 
2040 
44  8 
45.5 
28.5 

5.14 

9.94 
10.48 

1*2,936 
74.8 

2040 
44.8 
455 
22.7 

5.24 

10.61 

400 

12,{«6 
TH.h 

11.6 
2800 

50 

46 

85 

5.56 

7.81 
827 
567 
10,487 
67  2 

16.1 
1260 

21 

60 
88.7 

4.26 

7.59 
9.05 
671 
11,785 
62  5 

n.5 

8780 
73.8 
50.9 
26.2 

4.28 

8.88 
9.41 

ii,6io 

69.8 

PI  .8 
1168 
27.9 
41.9 
97.7 

4.86 

7.86 
9.41 
6G0 
9,789 
75JO 

12.8 

Heating-surface,  sg.  ft.. 
Grate-surface,  sq.  ft. — 

Ratio  H.8.  to  G.S 

Coal  per  sq.  ft.  Q.per  hr. 
Water  persq.  ft.  H.S.per 

hr.  from  and  at  212^. ... 
Water  evap.  from  and  at 

212®  per  lb.  coal 

Per  lb.  combustible.. .  . . 
Temp,  of  chimney  gases 
Calorific  value  of  fuel.  . . 
Efficiency  of  hoilpr  iierc. 

27:0 

50 
551 

86 

6.0s 

7.M 

8.96 

707 

10,a59 

Tests  Nos.  7  and  8  were  made  with  the  Hawley  Down-draught  Fun  ace. 
the  others  with  ordinary  furnaces. 

These  tests  confirm  the  8tatement  aln>ady  made  as  to  the  diffleultr  of 
obtaining,  with  ordinary  grate-furnaces,  a«  high  a  percenrage  of  the  calo- 
rific value  of  the  fuel  with  the  Western  as  with  the  Eastern  coali*. 

Test  No  8,  78.5j<  efficiency,  Is  remarkably  good  for  Pittsburgh  (Y(»ughiogh- 
eny)  coal.    If  the  Washington  cool  had  given  equal  efficiency,  the  saving  of 

fuel  would  be  '       ~  ,  ""*  =  20.2%.    The  results  of  tests  Nos.  7  and  8  indicate 

To. 5 

that  the  downward-draught  furnace  is  well  adapted  tor  burning  Illinois 
coals. 


BOILERS  USING  WASTE  GASES.  689 

KEaxlmmii  Boiler  Efllclency  ivlth  Cumberland  €oaI.— 

Aliout  r.'.5  lbs.  of  waier  per  lb.  combustible  from  and  at  'J]2^  in  about  the 
hij?hest  evaporation  that  can  be  obtained  from  the  best  steam  fuels  in  the 
United  States,  such  as  Cumberland,  Pocahontas,  and  Clearfield.  In  excep- 
tional cases  18  lbs.  has  been  reached,  and  one  teat  is  on  record  (F.  W.  Dean, 
Eng''o  NewSy  Feb.  1, 1894)  Rivine  13.23  lbs.  The  boiler  was  internally  fired, 
of  the  Belpaire  type,  68  inches  diameter,  81  feet  lonj?,  with  160  8-incn  tubes 
I'J^  feet  long.  Heating-surface,  1998  square  feet ;  firraie-8urface,45  square  feet, 
reduced  during  the  test  to  30^  square  feet.  Double  furnace,  with  fire-brick 
arches  and  a  long  combustion -chamber.  Feed-water  heater  in  smoke-lxix. 
The  following  are  the  principal  results : 

1st  Test.       9d  Test. 

Dry  coal  burned  per  sq.  ft.  of  ^rate  per  hour,  lbs 8.86  16.06 

Water  evap.  per  sq.  ft.  of  heatmg-surface  per  hour,  lbs    1.68  8.00 
Water  evap.  from  and  at  212<>  per  lb.  combustible,  in- 
cluding feed- water  heater 13.17  18.88 

Water  evaporated,  excluding  feed-water  heater 12.88  12.90 

Tern perature  of  gases  after  leaving  heater,  F 860*  46J* 

BOIIiEBS  17SING  WASTE  GASES. 

Proportioning  Boilers  for  Blast-Fiimaees.— (F.  W.  Gordon, 
^rans.  A.  I.  M.  E.,  vol.  xii.,  1888.) 

Mr.  Gordon *s  recommendation  for  proportioning  boilers  when  properly  set 
for  burning  blast-furnace  gas  is,  for  coke  practice,  80  sq.  ft.  of  heating-sur- 
face per  ton  of  iron  per  24  hours,  which  tne  furnace  is  expected  to  make, 
calculating  the  heatmg-surface  thus :  For  double-flued  boilers,  all  shell- 
surface  exposed  to  the  gases,  and  half  the  flue-surface;  for  the  French  type, 
all  the  exposed  surface  of  the  upper  boiler  and  half  the  lower  boiler- 
surface;  for  cylindrical  boilers,  not  more  than  GO  ft.  long,  all  the  heating- 
surface. 

To  the  above  must  be  added  a  batteiy  for  relav  in  case  of  cleaning,  repairs, 
etc..  and  more  than  one  battery  extra  in  large  plants,  when  the  water  carries 
much  lime. 

For  anthracite  practice  add  SQjf  to  above  calculations.  For  charcoal  prac- 
tice deduct  20jt. 

In  a  letter  to  the  author  in  Mav,  1894.  Mr.  Gtordon  says  that  the  blast- 
furnace practice  at  the  time  when  nis  article  (from  which  the  above  extract 
is  taken)  was  written  was  very  different  from  that  existing  at  the  present 
time;  besides,  more  economical  engines  are  being  introduced,  so  thai  less 
than  80  sq.  ft.  of  boiler-surface  per  ton  of  iron  made  in  24  hours  mav  now  be 
adopted.  He  says  further:  Blast-furnace  gases  are  seldom  used  for  other 
than  furnace  requirements,  which  of  course  Is  throwing  away  good  fuel.  In 
this  case  a  furnace  in  an  ordinary  good  condition,  ana  a  condition  where  it 
cau  take  its  maximum  of  blast,  which  is  in  the  neighborhood  of  200  to  225 
cubic  ft.,  atmOi<pheric  measurement,  per  sq.  ft.  of  sectional  area  of  hearth, 
will  generate  the  necessary  H.P.  with  very  small  heating-surface,  owing  to 
the  high  heat  of  the  escaping  gases  from  the  boilei-s,  which  frequently  is 
1000  degrees. 

A  furnace  making  200  tons  of  Iron  a  day  will  consume  about  900  H.P.  In 
blowing  the  engine.  About  a  pound  of  fuel  is  required  In  the  furnace  per 
pound  of  pig  metal. 

In  practice  it  requires  70  cu  ft.  of  air-piston  displacement  per  lb.  of  fuel 
consumed,  or  22,400  cu.  ft.  pel  minute  for  200  tons  of  metal  in  1400  working 


minutes  per  day,  at,  say,  10  lbs.  discharge -pressure.  This  is  equal  to  9^  lbs. 
M.E.P.  on  the  steam-piston  of  equal  area  to  the  blast-piston,  or  (100 1.H.P.  To 
this  add  ''^  for  hoisting,  pumping  and  other  purposes  for  which  steam  is  em- 


ployed around  blast-furnaces,  and  we  have  lldo  H.P.,  or  sav  5U  H.P.  per 
ton  of  iron  per  day.  Dividing  this  into  80  gives  approximately  h%  sq.  ft.  of 
heating-surface  of  boiler  per  H.P. 

^Tater^tubo  Boilers  nalnc  Blast- flurnace  Gaaes.— D.  S. 
Jacobus  (Trans.  A.  I.  M.  £.,  xvii.  50)  reports  a  test  of  a  water  tube  k)oiler  using 
blast-furnace  gas  as  fuel.  The  heating-surface  was  2535  sq.  ft.  It  developed 
328  H.P.  (Centennial  standard),  or  6.01  lbs.  of  water  from  and  at  21 2<*  per 
sq.  ft.  of  heating-surface  per  hour.  Some  of  the  principal  data  obtained 
were  as  follows:  Calorific  value  of  1  lb.  of  the  gas,  1418  B  T.U.,  including 
the  effect  of  its  Initial  temperature,  which  was  650**  F.  Amount  of  air  used 
to  bum  1  lb.  of  the  gas  s  0.9  lb.  Chimney  draui^ht,  \%  in.  of  water.  Area  of 
gas  inlet,  800  sq.  in.;  of  air  inlet,  100  sq.  in.    Temperature  of  the  chimney 


690 


THE  BTEAM-BOILE& 


gases,  775*  F.  Effloiency  of  the  boiler  calculated  from  the  temperatures 
and  aiialyseB  of  the  Kases  at  exit  and  enirance«  61%.  The  average  anaiyses 
were  as  follows,  hydrocarbons  being  included  in  the  niti-ogen : 


By  Weight 

By  Volume. 

At  Entrance. 

At  Exit. 

At  Entrance. 

At  Exit. 

co« 

10.60 
.11 
20.71 
62.48 
2.92 
11.45 
14.87 

fiG.87 
8.05 

68.80 

7.19 

.76 

7.95 

7.08 

.10 

97.80 

65.03 

18  64 

a:!:.:;:::;;:::::::::::: 

8.96 

CO 

Nitrosen    

1.96 
76  4i 

CinOO, 

Cin  CO. * 

Total  C 

Steam-boilers  Fired  ysirlth.  IFaste  Oases  lyom  Paddling 
and  Heating  Furnaces,— The  Iron  Age,  April  6, 1MI8,  contains  a  report 
of  a  number  ot  tests  of  steHUi-boilere  utilizing  the  waste  heat  from  pud 
dling  and  heating  furnaces  in  rolling-mills.  The  following  principal  data  are 
selected:  In  Nos.  1,  S,  and  4  the  boiler  is  a  Babcock  &  Wilcox  water-tutw 
boiler,  and  in  No.  S  it  is  a  plain  cvliuder  boiler,  42  in.  diani.  and  96  ft.  long, 
l^o.  4  boiler  was  connected  with  a  heating-furnace,  the  others  with  puddling 
furnaces. 

No.l.     No.  8.    No.  8.     No.  4. 

Heating-surface,  sq.  ft 1096         1196       143         1880 

Grate-surface,  sq.  ft 10.9         18  6       18.6       16.7 

Batio  H.8.  to  G.B. 69  87.9       10.6       8S.8 

M^ater  evap.  per  hour,  lbs 8858        S!ie9       1619       8056 

persq.  ft.  H.8.  perhr.,  lbs...         8.8  1.8       12.7         9.8 

'*       *'       per  lb.  coal  from  and  at  219«.         5.9  6.24       8.76       6.84 

M       ••         ♦»     "comb."      "     **    "  ....  7.80       4.81       8.84 

In  No.  9, 1 .88  lbs.  of  iron  were  puddled  per  lb.  of  coal. 
In  No.  8,  1 .  14  lbs.  of  iron  were  puddled  per  ib.  of  coal. 
No.  8  shows  that  an  insufficient  amount  of  heating-surface  was  proTided 
for  the  amount  of  waste  heat  available. 

R17IiE»  FOR  CONDUCTING  BOIIiBR-TBSTS. 

Code  of  1 899. 

(Reported  by  the  Committee  on  Boiler  Trials,  Am.  Boo.  M.  E.*) 

I.  Determine  at  the  outset  the  specific  object  of  the  proposed  trial, 
whether  it  be  to  ascertain  the  capacity  of  the  boiler,  its  efficiency  n«  a 
steam-generator,  its  efficiency  and  its  defects  under  usual  working  condi- 
tions, the  economy  of  some  particular  kind  of  fuel,  or  the  effect  of  changes 
of  design,  proportion,  or  operation;  and  prepare  for  the  trial  accordingly. 

IL  Examine  the  boiler^  boih  outside  and  inside;  ascertnin  the  dimensions 
of  grates,  heating  surfaces,  and  all  important  carts  ;  and  make  a  full  rec- 
ord, describing  the  same,  and  illustrating  Especial  features  by  sketches. 

in.  Notice  the  general  condition  of  the  boiler  and  its  equipment,  and 
record  such  facts  in  relation  thereto  as  bear  upon  the  objects  in  view. 

ir  the  obiect  of  the  trial  is  to  ascertain  the  maxihium  economy  or  capa- 
cit.vof  the  boiler  as  a  steam-generator,  the  boiler  and  all  its  appurtenances 
should  be  put  in  flrst-class  condition.  Clean  the  heating  surface  inside  and 
outside,  remove  clinkei-s  from  the  grates  and  fr^m  the  sides  of  the  furnace. 
Remove  all  dust,  soot,  and  ashes  from  the  chambers,  tsmoke-conDectioos, 
and  flues.  Close  nir-ieaks  in  the  masonry  and  |M)orly  fitted  cleaning-doorsu 
See  that  the  dani|)er  will  open  wide  and  close  tight.  Test  for  air-leaks  by 
firing  a  few  shovels  of  smoky  fuel  and  immediately  closing  the  damper,  ob- 
serving the  escape  of  smoke  through  the  crevices,  or  by  passing  the  flame 
of  a  candle  over  cracks  in  the  brickwork. 

•The  code  is  here  slightly  abridged.  The  complete  report  of  tlie  Com- 
mittee may  i>e  obtained  in  imniphlft  form  from  the  Secretary  of  the  Ameri- 
can Society  of  Meclmuicul  Kugiueers,  1^  West  Slat  St.,  New  York. 


RULES  FOR  COKDUCTING   B0ILEB-TE8TS.  691 

IV.  Determine  the  character  of  the  coal  to  be  used.  For  tests  of  the  effl- 
cieocy  or  capacity  of  the  boiler  for  comparison  with  other  boilera  the  coal 
should.  If  poRsible,  be  of  some  Icind  which  is  commercially  regarded  as  a 
standard.  For  New  England  and  that  portion  of  the  country  east  of  the 
Allegheny  Mountains,  good  anthracite  egg  coal,  containing  not  over  10  per 
cent,  of  ash,  and  semi-bituminous  Clearfield  (Pa.),  Cumberland  (Md.).  and 
Pocahontas  (Va.)  coals  are  thus  regarded.  West  of  the  Allegheny  Moun- 
tains, Pocahontas  (Va.)  and  New  River  (W.  Va.)  semi-bituminous,  and 
Youghiogheny  or  Plttal>urg  bituminous  coals  are  recognized  as  stiindaids.* 

For  tests  made  to  determine  the  performance  of  a  boiler  with  a  partic- 
ular kind  of  coal,  such  as  may  be  specified  in  a  contract  for  the  sale  of  a 
boiler,  the  coal  used  should  noi  be  hii^her  in  ash  and  in  moisture  than  that 
specified,  since  increase  in  ash  and  moisture  above  a  stated  amount  is  apt  to 
cause  a  falling  off  of  both  capacity  and  economy  In  greater  proportion  than 
the  proportion  of  such  increase. 

V.  Establish  the  correctness  of  all  apparatus  used  in  the  test  for  weighing 
and  measuring.    These  are  : 

1.  Scales  for  weighing  coal,  ashes,  and  water. 

8.  Tanks  or  water-meters  for  measuring  water.  Water-meters,  as  a  rule, 
should  only  be  used  as  a  check  on  other  measurements.  For  accurate  work 
the  water  should  be  weighed  or  measured  In  a  tank. 

3.  Thermometers  and  pyrometers  for  taking  temperatures  of  air,  steam, 
feed -water,  waste  gases,  etc. 

4.  Pressure-gauges,  draught -gauges,  etc. 

VI.  See  that  the  boiler  is  thoroughly  heated  before  the  trial  to  its  usual 
working  temperature.  If  the  boiler  is  new  and  of  a  form  provided  with  a 
brick  setting,  it  should  be  in  regular  use  at  least  a  week  before  the  trial,  so 
OS  to  dry  and  heat  the  walls.  If  it  hns  been  laid  off  and  become  cold,  it 
should  be  worked  before  the  trial  until  the  walls  are  well  heated. 

VIL  The  boiler  and  connections  should  be  proved  to  be  free  from  leaks 
b'^fore  beginning  a  test,  and  all  water  connections,  including  blow  and 
extra  feed-pipes,  should  be  disconnected,  stopped  with  blank  flanges,  or 
liied  throngn  special  openings  l>eyond  the  valves,  except  the  particular  pipe 
through  which  water  is  to  be  fed  to  the  boiler  during  the  trial.  During  thq 
test  the  blow-off  and  feed  pipes  should  remain  exposed  to  view. 

If  an  injector  Is  uned.U  should  receive  steam  directly  through  a  felted 
pipe  from  the  boiler  being  tested.t 

If  the  water  is  metered  after  it  passes  the  injector,  its  temperature  should 
be  taken  at  the  point  where  it  leaves  the  injector.  If  the  quantiiy  is  deter- 
mined before  It  goes  to  the  injector,  the  temperature  should  be  determined 
on  the  suction  side  of  the  inlector,  and  if  no  change  of  temperature  occurs 
other  than  that  due  to  the  Injector,  the  temperature  thus  determined  is 
properly  that  of  the  feed- water.  When  the  temperature  changes  between 
the  injector  and  the  boiler,  as  by  the  use  of  a  heater  or  by  radiation,  the 
temperature  at  which  the  water  enters  and  leaves  the  Injector  and  that  at 
which  it  enters  the  boiler  should  all  be  taken.  In  that  case  the  weight  to  be 
used  is  that  of  the  water  leaving  the  injector,  computed  from  the  heat  units 
if  not  directly  measured;  and  the  temperature,  that  of  the  water  entering 
the  boiler. 

Let  tr  =  weight  of  water  entering  the  injector; 

X  =       "        **  steam       *'  "        **       ; 

hi  =  heat-units  per  pound  of  water  entering  injector; 
A,  =     '*       **        **        **        '•  steam        '•  '*       ; 

hf  =     "       "       "       "       **  water  leaving         " 

*  These  coals  are  selected  because  they  are  about  the  only  coals  which 
possess  the  essentials  of  excellence  of  quality,  adaptability  to  various 
kinds  of  furnaces,  grates,  boilers,  and  methods  of  firing,  and  wide  distribu- 
tion and  general  accessibility  in  the  markets. 

tin  feeding  a  boiler  undergoing  test  with  an  injector  taking  steam  from 
another  boiler,  or  from  the  main  steam -pipe  from  several  boilers,  the  evap- 
orative results  may  be  modified  by  a  difference  in  the  quality  of  the  steam 
from  Buch  source  compared  with  that  supplied  by  the  ooiler  being  tested, 
and  in  some  cases  the  connection  to  the  uijector  may  act  as  a  drip  for  the 
main  steam-pipe.  If  it  is  known  that  the  steam  from  the  main  pipe  is  of 
the  same  pressuro  and  qualitv  as  that  furnished  by  the  boiler  undergoing 
the  test,  toe  steam  may  k>e  taken  from  such  main  pipe. 


692  THE  STEAM-BOILER. 

Then  to  +  x  =  weight  of  water  leaving  injector, 

/u  -  ht 

See  that  the  Ateam-main  Is  so  arranged  that  water  of  condensation  cannot 
run  back  into  the  boiler. 

VIII.  Duration  of  the  TeRt.—Yor  tests  made  to  ascertain  either  the  max- 
imum economy  or  the  maziuium  capacity  of  a  boiler,  irrespective  of  ilit* 
E articular  class  of  service  for  which  it  is  regularly  used,  the  duration  should 
e  at  least  ten  hours  of  continuous  running.  If  the  rate  of  combustion  ex- 
ceeds &5  pounds  of  coal  per  square  foot  of  grate-surface  per  hour,  it  may  lie 
8topp<?d  when  a  total  of  '^250  pounds  of  coal  has  been  burned  i>er  square  foot 
of  grate. 

IX  Starting  and  Stopping  a  Test.— The  conditions  of  the  boiler  and  fur- 
nace in  all  respects  sh(»uld  be,  as  nearly  as  possible,  the  same  at  the  end  an 
at  the  beginning  of  the  test.  The  steam -pressure  should  be  the  same  ;  the 
water-lHvel  the  same  ;  the  fire  upon  the  grates  should  be  the  same  in  quan- 
tity and  condition;  and  tiie  walls,  flues,  etc.,  should  be  of  tlie  same  tenmera- 
ture.  Two  methods  of  obtaining  the  desired  equality  of  conditions  of  ihe 
fire  may  be  used,  via.,  those  which  were  called  in  the  Code  of  1885  "  Uie 
standard  method  '*  and  **  the  alternate  method,"  the  latter  b<*iQg  employed 
where  it  is  inconvenient  to  make  use  of  the  standard  method.* 

X.  Sinndard  Method  of  Sttirting  and  Stopping  a  Te*/.— Steam  beine 
raised  to  the  working  pressure,  remove  rapidly  all  the  fire  fiom  the  grate, 
close  the  damper,  clean  the  ash-pit,  and  as  quickly  as  possible  start  a  new 
fire  with  weighed  wood  and  coal,  noting  the  time  and  the  water-level  t  while 
the  water  is  in  a  quiescent  state,  just  before  lighting  the  fire. 

At  the  end  of  the  test  remove  the  whole  fire,  which  has  been  burned  low, 
clean  the  grates  and  ash-pit,  and  note  the  water-level  when  the  water  is  in 
a  quiescent  state,  and  recoid  the  time  of  hauling  the  fire.  The  water-level 
should  be  as  nearly  as  possible  the  same  as  at  the  beginning  of  the  test.  If 
it  is  not  the  same,  a  correction  should  be  made  by  computation,  and  not  by 
operating  the  pump  after  tlie  test  is  completed. 

XI.  Attei-nate  Method  of  Starting  and  Stopping  a  Te^t.— The  boiler  being 
thoroughly  heated  by  a  preliminary  run,  the  fires  are  to  be  burned  low  and 
well  cleaned.  Note  the  amount  of  coal  left  on  the  grate  as  nearly  as  it  can 
be  estimated;  note  the  pressure  of  steam  and  the  water-level.  Note  the 
time,  and  record  it  as  the  starting-time.  Fresh  coal  which  has  been  weigheil 
should  now  be  fired.  The  ash-pits  should  be  thoroughly  cleaned  at  once 
after  starting.  Before  the  end  of  the  test  the  fires  should  be  burned  low. 
Just  as  before  the  start,  and  the  fires  cleaned  in  such  a  manner  as  to  leave  a 
bed  of  coal  on  the  grates  of  the  same  depth,  and  in  the  same  condition,  as 
at  the  start.  When  this  stage  is  reached,  note  the  time  and  record  it  as  ihe 
stopping-time.  The  water-level  and  steam -pressures  should  pi^eviously  be 
brought  as  nearly  as  possible  to  the  same  i>oint  as  at  the  start.  If  the  water- 
level  is  not  the  same  as  at  (he  start,  a  correction  should  be  made  by  com- 
putation, and  not  by  operating  the  pump  after  the  test  is  completed. 

XII.  Unifoi^iity  of  Condititms.— in  all  trials  made  to  ascertain  maximum 
economy  or  capacity  the  conditions  should  be  maintained  uniformly  con- 
stant. Arrangements  should  be  made  to  dispose  of  the  steam  so  that  the 
rate  of  evaporation  may  be  kept  the  same  from  beginning:  to  end. 

XIII.  Keeping  the  Records.— Take  note  of  every  event  connected  with  the 
progress  of  the  trial,  however  unimportant  it  may  appear.  Record  the 
time  of  every  occurrence  and  the  time  of  taking  every  weight  and  every 
observation. 

The  coal  should  be  weigiied  and  delivered  to  the  fireman  In  equal  propor- 
tions, each  sufficient  for  not  more  than  one  hour's  nm,  and  a  fresh  portion 

*The  Committee  concludes  that  il  is  best  to  retain  the  designations 
*'  standard  '*  and  "  alternate,''  since  they  have  become  widely  known  and 
established  in  the  minds  of  engineers  and  in  the  reprints  in  the  Code  of 
1885.  Many  enghieers  prefer  the  "  alternate  "  to  the  ^'standarti  ^^  method 
on  account  of  its  being  less  liable  to  error  due  to  cooling  of  the  boiler  at  the 
beginning  and  end  of  a  test. 

tThe  gauge-k'iass  should  not  be  blown  out  within  an  hour  before  the 
water-level  is  taken  at  the  beginning  and  end  of  a  test,  otlierwise  an  error 
in  the  reading  of  the  water-level  may  be  caused  by  a  change  in  the  tempera- 
ture and  density  to  the  water  in  the  pii^e  leading  from  the  bottom  oC  the 
glass  into  the  boiler. 


RULES  FOE  CONDUCTING  BOILER-TESTS.  693 

should  noc  bo  delivered  until  tho  previous  one  ban  all  been  fired.  Tlie  time 
required  to  consume  each  portion  sltould  be  noted,  the  time  lieln^  recorded 
at  the  instant  of  flrin?  tlie  last  of  each  portion.  It  is  desirable  tliat  at  the 
same  time  tlie  amount  of  water  fed  into  the  boiler  should  be  accurately 
noted  and  recorded,  includinf?  the  heig:bt  of  the  water  in  the  boiler,  and  the 
average  pressure  of  steam  and  temperature  of  feed  during  the  time.  By 
thus  recording  the  amount  of  water  evaporated  by  successive  portions  of 
coal,  the  test  may  be  divided  into  several  periods  if  desired,  and  the  degree 
of  uniformity  of  combustion,  evaporation,  and  economy  analyzed  for  each 
period.  In  addition  to  these  records  of  the  coal  and  the  feed-water,  half- 
nourly  observations  should  be  mode  of  the  temperature  of  the  feed>water, 
of  the  flue-gases,  of  the  external  air  in  the  boiler-room,  of  the  temperature 
of  the  furnace  when  a  f  uronce-pyrometer  is  used,  also  of  the  pressure  of 
steam,  and  of  the  readings  of  the  instruments  for  determining  the  moisture 
in  the  steam.  A  log  should  be  kept  on  properly  prepared  blanks  containing 
columns  for  record  of  the  various  observations. 

XIV.  Quality  of  Steam.— The  percentage  of  moisture  in  tlie  steam  should 
be  determined  by  the  use  of  eitner  a  throttling  or  a  separating  steam-calo- 
rimeter. The  sampling-nozzle  sliould  be  placed  in  the  vertical  steam-pipe 
rising  from  the  boiler.  It  should  be  made  of  i-inch  pipe,  and  should  extend 
across  the  diameter  of  the  hteam-pi()e  to  within  half  an  inch  of  the  opposite 
side,  being  closed  at  the  end  and  perforated  with  nut  less  than  twenty  i-inch 
holes  equally  distributed  along  and  around  its  cylindrical  surface,  but  none 
of  these  holes  should  be  nearer  than  }  inch  to  the  inner  side  of  tiie  steam- 
pipe.  The  calorimeter  nnd  the  pipe  leading  to  it  should  be  well  covei'ed 
with  felting.  Whenever  the  indiiratlons  of  ihe  throitling  or  separating 
calorimeter  show  that  the  percentiige  of  moisture  is  irregular,  or  occasion- 
ally in  excess  of  three  per  cent.,  the  results  should  be  checked  by  a  steam- 
separator  placed  in  the  steam- pipe  as  close  to  the  boiler  as  convenient,  with 
a  calorimeter  in  the  steam-pip<f  fust  beyond  the  outlet  from  the  separator. 
The  drip  from  the  separator  should  be  caught  and  weighed,  and  the  per- 
centage of  moisture  computed  therefrom  added  to  that  sliowii  by  the  calo- 
rimeter. 

Superheatine  should  be  determined  by  rneann  of  a  thermometer  placed  in 
a  mereury-weli  inserted  in  the  steam-pipe.  Tlie  degree  of  superheating 
should  be  taken  as  the  difference  between  the  reading  of  the  thermometer 
for  superheated  steam  and  the  readings  of  the  same  thermometer  for  satu- 
rated steam  at  the  same  pressure  as  determined  ^by  a  special  experiment, 
and  not  by  reference  to  ste^im-tables. 

XV.  Savipliny  the  Coal  aitd  Detei^tining  its  3/of«fMr«.— As  each  barrow- 
load  or  fresh  portion  of  coal  is  taken  from  tlie  cotiUpile,  a  represen- 
tative  shovelful  is  selected  from  it  and  placed  m  a  barrel  or  box  in  a  cool 

Elace  and  kept  until  the  end  of  the  trial.  The  samples  are  then  mixed  and 
roken  into  pieces  not  exceeding  one  inch  in  diameter,  and  reduced  by  the 
procent  of  repeated  quartering  and  crushing  until  a  flnal  sample  weighing 
about  Ave  pounds  is  obtained,  and  the  size  of  the  larger  pieces  is  such  that 
they  will  pass  tlirough  a  sieve  with  i-inch  meshes.  From  this  sample  two 
one-quart,  air-tight  glass  preserving- jars,  or  other  air-tip:ht  vessels  which 
will  prevent  the  escape  of  moisture  from  the  sample,  are  to  be  promptly 
fiUed.  and  these  samples  are  to  be  kept  for  subsequent  determinations  of 
moisture  and  of  heating  value  and  for  chemical  analyses.  During  the  pro- 
cess of  quartering,  when  the  sample  has  been  reduced  to  about  100  pounds, 
a  quarter  to  a  half  of  it  may  be  taken  for  an  approximate  determination  of 
moisture.  This  may  be  made  by  placing  it  in  a  shallow  iron  pan,  not  over 
three  inches  deep,  carefully  weighing  it,  and  setting  the  pan  in  the  hottest 
place  that  can  be  found  on  the  brickwork  of  the  boiler-setting  or  flues, 
keeping  it  there  for  at  least  IS  hours,  and  then  weighing  it.  The  determina- 
tion of  moisture  thus  made  is  believed  to  be  approximately  accurate  for 
anthracite  and  semi-bituminous  coals,  and  aUo  for  Pittsburg  or  Youghio- 
gheny  coal ;  but  it  cannot  be  relied  upon  for  coals  mined  west  of  Pittsburg, 
or  for  other  coals  containing  inherent  moisture.  For  these  latter  coals  it  is 
important  that  a  more  accurate  method  be  adopted.  The  method  recom- 
mended by  the  Committee  for  all  accurate  tests,  whatever  the  character  of 
the  coal,  is  described  Ar*  follows : 

Take  one  of  the  saniple.<t  contained  in  the  glass  jars,  and  subject  It  to  a 
thorough  air-drying,  by  spreading  it  Ir.  a  thin  layer  and  exposing  it  for 
severalhours  to  tlie  atmosphere  of  a  warm  room,  weighing  it  l>erore  and 
after*  thereby  determining  the  quantity  of  surface  moisture  it  contains. 


694  THE   STEAM-BOILER. 

Then  crush  the  whole  of  It  by  runninsr  it  throuf^h  An  ordinary  coffee-mill 
adjusted  so  as  to  produce  somewhat  coarse  {grains  (les8  than  ^  inch),  thor- 
oughly mix  the  crushed  sample,  select  from  it  a  portion  of  from  10  to  50 
grains,  weif;h  it  in  a  balance  which  will  easily  show  a  variation  as  small  as 
1  part  in  1000,  and  dry  it  in  an  air-  or  sand-bath  at  a  temperature  betireen 
240  and  280  degrees  Fahr.  for  one  hour.  Weigh  it  and  record  the  loss,  then 
heat  and  weigh  it  again  repeatedly,  at  intervals  of  an  hour  or  les^s,  until  the 
minimum  weight  has  been  reached  and  the  weight  begins  to  Increase  by 
oxidation  uf  a  portion  of  the  coal.  The  difference  between  the  original  and 
the  minimum  weight  is  taken  as  the  moisture  in  the  air-dried  coal.  This 
moisture  test  should  preferably  be  made  on  duplicate  samples,  and  the 
results  should  agree  within  0.3  to  0.4  of  one  per  cent.,  the  mean  of  the  two 
determinations  being  talcen  as  the  correct  result.  The  sum  of  the  percent- 
age of  moisture  thiisi  found  and  the  percentage  of  surface  moisture  previ- 
ously determined  is  the  total  moisture. 

Xvl.  Tieatment  of  AsJies  and  BeftLsc—The  ashes  and  refuse  are  to  be 
weighed  in  a  dry  state.  If  it  is  found  desirable  to  show  the  principal  char- 
acteristics of  the  ash,  a  sample  should  be  subjected  to  a  proximate  analysis 
and  the  actual  amount  of  incombustible  material  determined.  For  elabo- 
rate trials  a  complete  analysis  of  the  ash  and  refuse  should  be  made. 

XVII.  Calorific  Teats  and  Analytis  of  CoaL— The  quality  of  the  fuel 
should  be  determined  either  by  heat  test  or  by  analysis,  or  by  both. 

The  rational  method  of  determining  the  total  heat  of  combustion  is  to 
burn  the  sample  of  coal  in  an  atmosphere  of  oxygen  gas,  the  coal  to  be 
sampled  as  dii'ected  in  Article  XV  of  this  code. 

The  chemical  analysis  of  the  coal  should  be  made  only  by  an  expert 
chemist.  The  total  heat  of  combustion  computed  from  the  results  of  the 
ultimate  analvsis  may  be  obtained  by  the  use  of  DuIong*s  formula  (with 
consiauts  modified  by  recent  determinations),  viz., 


14.600  C  -f  62,000|h  -  -^- i  -f  4C00  8, 


in  which  C,  H,  O,  and  S  refer  to  the  proportions  of  carbon,  hydrogen,  oxy- 
gen, and  sulphur  respectively,  as  determined  by  the  ultimate  analvsis.* 

It  is  desirable  that  a  proximate  analysis  should  be  made,  thereby  deter- 
mining the  relative  proportions  of  volatile  matter  and  flxed  carl>on.  These 
proportions  furnish  an  indication  of  the  leading  characteristics  of  the  fuel, 
and  Kerve  to  fix  the  cla.sK  to  which  it  belongs. 

XVIII.  Analysis  of  Flue-tjases. — The  analysis  of  the  flue-gases  is  an 
especially  valuable  method  of  determining  the  relative  value  of  different 
methods  of  firing  or  of  different  kinds  of  furnaces.  In  making  these 
analyses  great  care  should  be  taken  to  procure  average  samples,  since  the 
composition  is  apt  to  vary  at  different  points  of  the  flue.  The  composition 
is  also  apt  to  vary  from  minute  to  minute,  and  for  this  reason  the  drawings 
of  gas  should  last  a  considerable  period  of  time.  Where  complete  deter- 
minations are  desired,  the  analyses  should  be  intrusted  to  an  expert 
chemist.  For  approximate  determinations  the  Orsat  or  the  Hem  pel  appa- 
ratus may  be  used  by  the  engineer. 

For  the  continuous  indication  of  the  amount  of  carbonic  acid  present  in 
the  flue-gases  an  instrument  may  be  employed  which  shows  the  weight  of 
COs  in  the  sample  of  gas  passing  through  it. 

XIX.  i>moke  Obsei-vations.— It  is  desirable  to  have  a  uniform  system  of 
determining  and  recording  the  quantity  of  smoke  produced  where  bitumin- 
ous coal  is  used.  The  system  commonlv  employoa  is  to  express  the  degree 
of  smokiness  by  means  of  percent-ages  dependent  upon  the  Judgment  of  the 
observer.  The  actual  measurement  of  a  sample  of  soot  and  smoke  by  some 
form  of  meter  is  to  bo  preferred. 

XX.  Miscellaneous.— In  tests  for  purposes  of  scientific  research,  in  which 
the  determination  of  all  tlie  variables  entering  into  the  test  is  desired, 
certain  observations  should  be  made  which  are  in  general  unnecessary  for 
ordinary  tests.  As  these  determinations  are  rarely  undertaken,  it  is  not 
deemed  advisable  to  give  directions  for  making  them. 

XXI.  Calciilal ions  of  Kmcifucy.— Two  methods  of  defining  and  calculat- 
ing the  efflcieney  of  a  boiler  are  recommended.    They  are: 

*  Favre  and  Silbermnnn  give  14,644  B.T.U.  per  pound  carbon:  Berthelot, 
14,647  B.T.U.  Favre  and  Silbermaun  give  6^,03:8  B.T.U.  per  pound  hydrogen; 
Tliomsen,  01,816  B.T.U.  -v     -» 


RULES  FOR  CONDUCrriKG  BOILER-TESTS. 


695 


1    irm^t^^^„  ^#  ♦i,^  K^ii^-       ^^*  absorbed  per  lb.  corabuBtible 

1,  Emciency  or  the  DOiler  =  -r^-i — rs i -»;  .>. r r.-.— . 

Calorific  value  of  1  lb.  combustible 
-   _,-,  ,  *  *,.    w  II  J        *  Heat  absorbed  per  lb.  coal 

2.  £:fficiencj  o£  the  boiler  and  grate  = 


Calorific  value  of  1  lb.  coal  * 
The  flrst  of  these  is  sometimes  called  ihe  efficiency  based  on  combustible, 
and  the  second  the  efflcieiicy  based  on  coal.  The  first  is  recommended  as  a 
standard  of  comparison  for  all  tests,  and  this  is  the  one  which  is  under- 
stood to  be  referred  to  when  the  word  '*  efficiency  ^'  alone  is  used  without 
qualification.  The  second,  however,  should  be  included  in  a  report  of  a 
tfst,  loffether  with  the  flrst,  whenever  the  obiect  of  the  test  is  to  determine 
the  efficiency  of  the  boiler  and  furnace  together  with  the  crate  (or  mechan- 
ical stoker),  or  to  compare  different  furnaces,  grates,  f u€^  or  methods  of 
firing. 

The  heat  absorbed  per  pound  of  combustible  (or  per  pound  coal)  Is  to  be 
calculated  by  multiplying  ihe  equivalent  evaporation  from  and  at  212  degrees 
per  pound  combustible  (or  coal)  by  966.7. 

XXIL  The  Heat  Baliince.— An  approximate  **heat  balance,"  may  be  in- 
cluded in  the  report  of  a  test  when  analyses  of  the  fuel  and  of  the  chimney- 
gases  have  been  made.  It  should  be  reported  in  the  following  form: 

HKA.T  BALANCB,  OB  DlSTBIBUTIOM  OF  THE  HXATINO  VaLCE  OF  THE  COM- 
BUSTIBLE. 

Total  Heat  Value  of  1  lb.  of  Combustible B.  T.  U. 

Per 
Cent. 

1 .  Heat  absorbed  by  the  boiler  ss  evaporation  from  and  at 

21*2  degrees  per  pound  of  combustible  x  965.7  

2.  Loss  due  to  moisture  in  coal  =  per  cent  of  moisture  re- 

ferred to  combustible  -h  100  x  [(«12  -  «)  4-  W«  + 
0.48(T--212)](frr  temperature  of  air  in  the  boiler- 
room,  T=  that  of  the  flue-gases) 

8.  Loss  due  to  moisture  formed  by  the  burning  of  hydro- 
gen =  per  cent  of  hydrogen  to  combustible  -i- 100  x  9 
X  [(218  -  0  4-  966  H  0.48(r—  212)] 

4.*  Loss  due  to  heat  carried  away  in  the  dry  chimney-gases 
:=.  weight  of  gas  per  pound  of  combustible  x  0.94  x 

(r-0 

5.t  Loss  due  to  incomplete  combustion  of  carbon 

__         CO  per  cent.  C  in  combustible      ^  ^„ 

•"CO^+CO^"  100  Xlu,l!SO.... 

6.  Loss  due  to  unconsumed  hydrogen  and  hydrocarbons, 
to  heating  the  moisture  in  the  air,  to  radiation,  aild 
unaccounted  for.  (Some  of  these  losses  may  be  sep- 
arately itemized  If  data  are  obtained  from  which 
they  may  be  calculated) 

Totals 

*  The  weight  of  gas  per  pound  of  carbon  burned  may  be  calculated  from 
the  gas  analyses  as  follows: 

Dry  gas  per  pound  carbon  =  il^A  +  f^  +  '  (^O+J?} ,  ,n  which  CO,.  CO, 

O,  and  N  are  the  percentages  by  volume  or  the  several  gases.  As  the  jsamp- 
ling  and  analyses  of  the  gases  in  the  present  state  of  the  art  are  liable  to 
considerable  errora,  the  result  of  this  calculation  is  usually  only  an  approxi- 
mate one.  The  heat  balance  itself  is  also  only  approximate  for  this  reason, 
as  well  as  for  the  fact  that  it  is  not  possible  to  determine  accurately  the  per- 
centage of  unburned  hydrogen  or  hydrocarbons  in  the  flue-gases. 

The  weight  of  dry  gas  per  pound  of  combustible  is  found  by  multiplying 
the  dry  gas  per  pound  of  carbon  by  the  percentage  of  carbon  in  the  combus- 
tible«  and  dividing  by  100. 

t  (jo,  and  CO  are  respectively  the  percentage  by  volume  of  oarbohic  acid 
and  carbonic  oxide  in  the  flue-gases.  The  quantity  10,150  =  number  of  heat* 
units  generated  by  burning  to  carbonic  acid  one  pound  of  carbon  contained 
iu  carbonic  oxide. 


695a 


THE  STEAH-BOILEB. 


ZX111.  Report  of  the  Trial.  -The  data  and  reaults  should  be  reported  in 
tbe  maoiier  eiven  in  either  one  of  the  two  following?  tables  [only  the  *'  Short 
Form  '*  of  table  is  criven  iiere],  omitting  lineK  where  the  testa  have  not  been 
made  as  elaborately  as  pro%  ided  fur  in  sucli  tables.  Additional  lines  may  be 
added  for  data  relating  to  the  spfciflc  object  of  the  test.  The  Short  Form  of 
Report,  Table  No.  2.  is  recomuieuded  for  comineruial  tests  and  as  aconven- 
ieiit  form  of  abridKing  the  longer  form  for  publication  when  saving  of  space 
^  desirable.  For  elaborate  trials  it  is  recommended  that  the  full  log  or  the 
trial  be  shown  graphically,  by  means  of  a  chart 

TABLE  NO.  2. 

Data  akd  Results  of  Eyapobatiyic  Test, 

Arranged  in  accordance  with  the  Short  Form  advised  by  the  Boiler  Test 

Committee  of  ihe  American  Society  of  Mechanical  Engineers. 

Code  of  1890. 

Made  by on boiler,  at to 

determine 

Kiiul  of  fuel 

Kind  of  furnace 


Method  of  starting  and  stopping  the  test  C'  stand 

ard  "  or  "  alternate/*  Arts.  X  and  XI,  Code) 

Grate  surface 

Water-healing  surface 

Superheating  surface 


TOTAL  qUAMTITIKS. 

1.  Date  of  trial 

2.  Duration  of  trial , 

8.  Weight  of  coal  as  fired  * 

4.  Percentage  of  moisture  in  coal  t 

5.  Total  weight  of  dry  coal  consumed 

6.  Total  ash  and  refuse 

7.  Percentage  of  ash  and  refuse  in  dry  coal. .... 

8.  Total  weight  of  water  fed  to  the  boiler  t 

9.  Water  actually  evaporated,  corrected  for  moist- 

ure or  superheat  in  steam 

9a.  Factor  of  evaporation  f 

10.  Equivalent  water  evaporated   into  dry  steam 

from  and  at  212  degrees.l  (Item  9  X  Item  9a.) 

HOURLY  <2UANTrnBS. 

11.  Dry  coal  consumed  per  hour 

1*.J.  Dry  coal  per  square  foot  of  grate  surface  per 

hour 

13.  Water  evaporated  per  hour  corrected  for  qual- 

ity of  steam  

14.  Equivalent  evaporation  per  hour  from  and  at 

212  degrees  |  

15.  Equivalent  evaporati(m  per  hour  from  and  at  212 

degrees  per  square  foot  of  water-heating  sur- 
face S • 


sq.ft. 


hours 

lbs. 

per  cent. 

lbs. 

per  cent, 
lbs. 


♦  Including  equivalent  of  wood  u-sed  in  lighting  the  fire,  not  including  un- 
hurnt  coal  withdrawn  from  furnace  at  times  of  cleaning  and  at  end  of  test. 
One  pound  of  wood  in  taken  to  be  equal  to  0.4  pound  of  coal,  or.  in  caj« 
greater  accuracy  is  desired,  as  having  a  heat  value  equivalent  to  the  eva|>- 
oratinn  of  6  pounds  of  water  from  and  at  212  degrees  per  poimd. 
(6  X  985.7  ss  5794  B.  T.U.)  The  term  "as  fired  "  means  in  its  actual  con- 
dition, including  moisture.  .^     ^     .      .        .-  .  .. 

t  This  is  the  total  moisture  in  the  coal  as  found  by  drying  it  artificially,  as 
described  in  Art.  XV  of  Code. 

t  Corrected  for  inequality  of  water-level  and  of  steam-pressure  at  be- 
ginning and  end  of  test. 

f  Factor  of  evaporation  =  -s;r«  » ^^  which  H  and  h  are  respectively  the 

total  heat  in  steam  of  the  average  observed  pressure,  and  in  water  of  the 
average  observed  temperature  of  the  feed. 
I  Tbe  symbol  '^U.  K,"  meaning  "'units  of  evaporation,"  may  be  coq* 


BULES  FOR  CONDUCTING   BOILER-TESTS. 


6956 


AYBBAGB  PRBSSURJBS,  l-KMPKRATVRBS,  BTC. 

16.  St««iin  pressure  b J  RHUge 

17.  Temperature  of  feed-water  entering  boiler.. 


Ib8.  per  sq.  in. 

18.  Temperature  of  escapine  gases  from  i>oiler 

19.  Force  of  draft  between  damper  aud  boiler |   ins.  of  water 

90.  Percentage  of  moisture  in  steam,  or  number  of  { 

degi*ee8  of  superheating per  cent.ordeg. 


HORSE-POWEB. 

il.  Horse- power  developed.    (Item  14  -i-  M^.)%„ 

a.  Builders*  rated  horse-power 

23.  Percentage  of  builders'  rated  horse-power  de 
veloped 


BCONOXIC  RESULTS. 

24.  Water  apparently  evaporated  under  actual  con- 

ditions per  pound  of  coal  as  fired.     (Item 
8  -»-  Item  8.) 

25.  Equivalent  evaporation  from  and  at  SIS  degret'S 

per  pound  of  coal  as  fired. |  (Item  9  -f-  Item  8.) 
S8.  Equivalent  evaporation  from  and  at  212  degrees 

per  pound  of  dry  coal. I    (Item  9  -+-  Item  5.). . 
27.  Equivalent  evaporation  from  and  at  212  degrees 

per  pound  of  combustible.    [Item  9  -i-  (Item 

5-  Item  6).] 

(If  Items  26,  26,  and  S7  are  not  corrected  for 

quality  of  steam,  the  fact  should  be  stated.) 

ETFIOIENCY. 

2fi.  Caloriflo  value  of  the  dry  coal  per  pound 

89   Calorific  value  of  the  combustible  per  pound.. . 
80.  Kfflciency  of  boiler  (based  on  combustible)**. , 
31.  Efficiency  of  boiler,  including  grate  (based  on 
dry  coal) 


COST  OF  BVJkPORATION. 

32.  Cost  of  coal  per  ton  of  lbs,  delivered  in 

boiler-room 

Si.  Cost  of  coal  required  for  evaporating  1000  pounds 
of  water  from  and  at  212  degrees , 


H.P. 
per  cent. 

lbs. 


B.  T.  U. 
per  cent. 


▼eniently  substituted  for  the  expression  *' Equivalent  water  evaporated  into 
dry  steam  from  and  at  212  degrees,"  its  definition  being  given  in  a  foot-noie. 

1  Held  to  be  the  equivalent  of  30  lbs.  of  water  evaporated  from  100  degrees 
Fabr.  into  dry  steam  at  70  lbs.  gauge-pressure. 

**  In  all  cases  where  the  word  *'  combustible  '*  is  used,  it  means  the  coal 
without  moisture  and  ash,  but  including  all  other  constituents.  It  Is  the 
sauie  as  what  is  called  in  Europe  '*  coal-diy  and  free  from  ash.** 

Factors  of  Bvaporation,— The  table  on  the  following  pages  was 
originally  published  by  the  author  in  Trans.  A.  S.  M.  E.,  vol.  vi.,  1884,  under 
the  title,  Tables  for  Facilitating  CSalculations  of  Boiler-tests.  The  table 
gives  the  factors  for  every  S^  of  temperature  of  feed-water  from  82*'  to  212*- 
F.,  and  for  every  two  pounds  pressure  of  steam  within  the  limits  of  ordinary 
working  steam-pressures. 

The  difference  in  the  factor  corresponding  to  a  difference  of  3"  tempera- 
ture of  feed  is  always  either  .0031  or  .0082.  For  Interpolation  to  find  a  factor 
for  a  feed-water  temperature  between  8i^  and  21 2«,  not  given  in  the  table, 
take  the  factor  for  the  nearest  temperature  and  add  or  siiotract,  as  the  case 
may  be,  .0010  If  the  difference  is  .0081,  and  .0011  if  the  difference  is  .0032.  As 
in  nearly  all  cases  a  factor  of  evaporation  to  three  decimal  places  is  accu- 
rate enough,  any  error  which  may  be  made  in  the  fotu-th  decimal  place  by 
interpolation  is  of  no  practical  importance. 

The  tables  used  In  calculating  these  factors  of  evaporation  are  those  given 
in  Charles  T.  Porter*s  Treatise  on  the  Ricluurds*  Steam-engine  Indicator. 

The  formula  is  Factor  s      ~^\  in  which  H  is  the  total  heat  of  steam  at  the 

observed  pressure,  and  h  tlie  total  heat  of  feed- water  of  the  observed 
temperature. 


69« 


THE    STEAM-BOILER. 


i.b«. 

Gaag«-preMiirM..,.0  + 
Abaolnto  praMurm    15 

Temptratoraw  I 


W+  I 
86        I 


Factors  or  Evapobatiok. 


5«  +  I 

«7        1 


S6  + 

n 


I^SOF. 

1.0008  1.01W8 

1.0149,1.0197 

1.0287  1.0254,1.0271  1.0277.1.0288,1.0290 

909 

85  1.0120 

80  1.0228 

68         86,1.0302  1.0809  1.0316  1.0321 

906 

66 

51 

1.0212 

60 

99,1.0317         34,        40         46         52 

908 

96 

88 

43 

91 

1.0831         49,        65         72         78         M 

900 

1.01291.0214 

76 

1.0323 

62         80,        97,1.0408  1.0409,1.0415 

197 

60 

40 

1.0806 

64 

94  1.0412,1.0428;        84l        41 

47 

194 

92 

77 

88 

65 

1.0425 

43         601        66         72 

76 

191 

1.0223 

1.0808 

69 

1.0417 

67 

74         91         97;  1.0603 

1.0510 

188 

55 

40 

1.0400 

48 

88 

1.0506  1.05221.0528,        Ss!        41 

185 

86 

71 

32 

80 

1.0519 

87 

54 1        60         66,        72 

182 

1.0817 

1.0408 

68 

1.0611 

61 

68 

851        91         98' 1.0604 

179 

49 

84 

95 

42 

82 

1.0600 

1.0616  1.06231.06291        85 

176 

80 

65 

1.0526 

74 

1.0613 

31 

48         64 

60         66 

178 

1.0411 

97 

67 

1.0605 

45 

68 

79         85 

92!        96 

170 

48 

1.0526 

89 

86 

76 

94 

1.07101.0717 

].07V8,1.0?» 

167 

74 

59 

1.0620 

68 

1.0707 

1.0725 

42|        48 

64 

60 

164 

1.0505 

91 

51 

99 

39 

56 

73         80 

86 

^ 

161 

87 

1.0622 

82 

1.0780 

70 

88 

1.0804  1.0611 

1.0817 

t.OfW^ 

158 

68 

58 

1.0714 

62 

1.0601 

1.0819 

86         42 

48 

54 

155 

09 

84 

45 

93 

33 

50 

67         73 

80 

M 

152 

1.0631 

1.0716 

76 

1.0624 

64 

82 

981.0905 

1.0911 

1.001: 

149 

62 

47 

1.0808 

65 

95 

1.0913 

1.0980        36 

42 

4S 

146 

93 

78 

89 

8? 

1.0926 

44 

61         67 

73 

79 

148 

1.0724 

1.0610 

70 

1.0918 

68 

75 

92         96 

1.1005 

1.1011 

140 

56 

41 

1.0901 

49 

80 

1.1007 

1.1028  1.1080 

36 

42 

187 

87 

72 

88 

60 

1.1020 

88 

65 

61 

67 

7^ 

184 

1.0618 

1.0908 

64 

1.1018 

61 

69 

66 

92 

98 

l.llOt 

181 

49 

84 

95 

43 

83 

1.1100 

1.1117 

1.1123 

1.1130 

36 

128 

81 

66 

1.1026 

74 

1.1114 

82 

48'        65 

61 

67 

125 

1.0912 

97 

57 

1.1105 

45 

63 

79.        86 

02 

98 

122 

43 

1.1028 

89 

86 

76 

94 

1.1211 

1.1217 

1.1228 

1.1229 

119 

74 

59 

1.1120 

68 

1.1207 

1.1226 

42 

48 

54 

60 

116 

1.1005 

90 

61 

99 

89 

66 

78 

79 

86 

92 

118 

86 

1.1122 

82 

1.1230 

70 

68 

1.1804*1.1810 

1.1817 

1.132S 

no 

68 

53 

1.1218 

61 

1.1301 

1.1819 

85         42 

48 

54 

107 

99 

84 

45 

92 

82 

60 

66         78 

79 

a> 

104 

1  1180 

1.1215 

76 

1.1828 

68 

81 

98  1.1401,1.1410 

1.1416 

101 

61 

46 

1.1307 

55 

94 

1.1412 

1.14-.'9         85 

41 

47 

96 

92 

77 

88 

86 

1.1426 

43 

60         66 

73 

79 

05 

1.1223 

1.1809 

69 

1.1417 

67 

75 

91         97 

1.1501 

1.1510 

93 

55 

40 

1.1400 

48 

88 

1.1806 

1.15221.1529 

35 

41 

89 

86 

71 

31 

79 

1.1519 

87 

58         60 

66 

72 

86 

1.1317 

1.1402 

63 

1.1510 

60 

68 

84         91 

97 

I.ICOS 

88 

48 

88 

94 

41 

81 

99 

1.1616  1.1682 

1.1626 

84 

80 

79 

64 

1.1625 

73 

1.1612 

1.1630 

47 

63 

69 

65 

77 

1.1410 

95 

66 

1.1604 

44 

61 

78 

84 

90 

96 

74 

41 

1.1526 

87 

85 

75 

92 

1.1709 

1.1715 

1.1722 

1.1728 

71 

72 

58 

1.1618 

66 

1.1706 

1.1728 

40 

46 

63 

59 

68 

1.1504 

89 

49 

97 

87 

65 

71 

78 

84 

90 

65 

35 

1.1620 

80 

1.1728 

68 

86 

1.1802 

1.1809 

1.1815 

l.l&il 

62 

66 

51 

1.1711 

69 

99 

1.1817 

88 

40 

46 

62 

60 

97 

»2 

43 

90 

1.1830 

48 

64 

71 

77 

63 

56 

1.1628 

1.1713 

74 

1.1821 

61 

79 

961.1902 

1.1906 

1  1014 

58 

59 

44 

1.180^ 

52 

92 

1.1910 

1.1927         83 

89 

45 

50 

90 

75 

86 

8] 

1.1923 

41 

58         64 

7t) 

76 

47 

1.1721 

1.1806 

67 

1.1915 

54 

72 

89         95 

1.2001 

1.8007 

44 

52 

87 

98 

46 

86 

1.2008 

1.2(R0  1.9026 

82 

89 

41 

88 

68 

1.19-29 

77 

1.9017 

84 

51 1        57 

64 

70 

38 

1.1814 

1.190() 

60 

1.200S 

48 

en 

82         88 

96 

1.2101 

85 

45 

81 

91 

89 

79 

96 

1.2113  1.91191.2196 

82 

^ 

70 

6'jll.2028'        70 

1.2110 

1.2128 

441     51      sr 

€8 

FACTORS  OF  EVAPOBATIOK. 


697 


a+is- 


AbwtntoPra»iiT>«..1».i  7ft    '   |    77        |   T8       |    gl       |    88       t   M       | 


78  + 
87 


Feci  water 
Temp. 

Factoks  of  Evaporation. 

212*F. 

1.0895 

1.0801 

1.080? 

1.0812 

1.0818 

1.0823  1.0329 

1.0384 

1.0389 

1.0844 

S09 

1.0887 

88 

88 

44 

49 

f>b 

60 

65 

70 

76 

906 

56 

64 

70 

75 

81 

86 

91 

97 

1.0402 

1.0407 

803 

90 

96 

1.0401 

1.0407 

1.0412 

i.wis 

1.0428 

1.0428 

as 

86 

«» 

1.0491 

1.0427 

8S 

88 

44 

49 

64 

59 

65 

60 

197 

53 

58 

64 

70 

75 

80 

86 

91 

06 

1.0501 

194 

84 

90 

96 

1.0601 

1.0507 

1.0512 

1.0617 

1.0622 

1.0527 

88 

191 

1.0515 

1.0521 

1.0627 

83 

88 

43 

49 

!A 

59 

64 

188 

47 

53 

68 

64 

60 

75 

80 

85 

90 

95 

185 

78 

84 

90 

95 

1.0601 

1.0606 

1.0611 

1.0616 

1.0622 

1.0626 

I8S 

1.0610 

1.0615 

1.0621 

1.0627 

32 

87 

48 

48 

53 

68 

179 

41 

47 

58 

58 

68 

69 

74 

79 

64 

89 

176 

72 

78 

84 

80 

95 

1.0700 

1.0705 

1.0711 

1.0716 

1.0721 

173 

1.0704 

1.0709 

1.0715 

1.0721 

1.0726 

82 

87 

42 

47 

52 

170 

85 

41 

46 

68 

57 

68 

68 

73 

78 

88 

167 

66 

72         78;       88 

89 

04 

09 

1.0805  1.0810' 1.0616 

164 

98 

1.08O3ll.0e09!l.08I5 

1.0820 

1.0825 

1.0831 

86         411        4« 

101 

1.0629 

35 

40,        46^ 

61 

57 

62 

67         72        77 

158 

00 

66 

72 

77 

88 

88 

OS 

961  0904.1.0908 

155 

02 

07 

1.0908 

1.0909 

1.0914 

1.0019 

1.0925 

1.0930,        35        40 

ISd 

1.0028 

1.0089 

84 

40 

45 

51 

66 

61 :        66'        71 

149 

64 

60 

66 

71 

77 

82 

87 

92,        07  1.1002 

146 

85 

91 

97 

1,1002 

1.1008 

1.1013 

1.1018 

1.10241.1029]        84 

143 

1.1017 

M02S 

1.1028 

84 

39 

44 

60 

55         60         65 

140 

48 

54 

69 

65 

70 

76 

81 

86,        91|        96 

187 

79 

85'        91 

96 

1.1102 

1.1107 

1.1112 

1.1117  1.1122  1.1127 

184 

I.IUO 

1.1116  1.1122 

1.1127 

83 

38 

48 

49         54         59 

181 

42 

47         63 

69 

64 

69 

75 

80         85         90 

1,J8 

78 

79         84 

90 

95 

1.1201 

1.1206 

1.1211  1.1216  1.1221 

1« 

1.1204 

1.1810  1.1215 

1.1221 

1.1286 

32 

87 

42         471        62 

12^ 

85 

41         47 

62 

68 

68 

68 

73'        78 

68 

119 

66 

72         78 

83 

80 

94 

99 

1.1305  1.1310 

1.1815 

116 

98 

1.1803  1.1809 

1.1815 

1.1820 

1.1825 

1.1831 

36         41 

46 

113 

1.1820 

84         40 

46 

61 

57 

62 

67         72 

TT 

110 

60 

66         71 

77 

82 

88 

98 

98,1.1403 

1.1406 

107 

91 

97 

1.1403 

1.1406 

1.1414 

1.1419 

1.1424 

1.1429         34 

30 

101 

1.1482 

1.1428 

84 

39 

45 

50 

55 

60         65 

70 

101 

63 

59 

65 

70 

76 

81 

86 

92,        97  1.1902 

98 

85 

90 

96 

1.1502 

1.1607 

1.1512 

1.1618 

1.1523  1.1528         33 

9fi 

1.1516 

1.152111.1527 

83 

38 

43 

49 

54 

59         64 

92 

47 

53 

58 

64 

69 

75 

80 

85 

90'        95 

89 

78 

84 

89 

96 

1.1600 

1.1606 

1.1611 

1.1616 

1.1621  1.1626 

86 

1  1609 

1.1615 

1.1621 

1.1626 

82 

37 

42 

47 

52         f»7 

8:1 

40 

46 

52 

67 

68 

68 

78 

78 

83         hS 

80 

71 

77 

83 

88 

94 

99 

1.1704 

1.1710  1.1715;  1.1720 

77 

1.1702 

1  1708 

1.1714  1.1719 

1.1725 

1.1730 

35 

41         46         51 

74 

84 

89 

45 

61 

56 

61 

67 

72         77         82 

71 

65 

70 

76 

8--.' 

87 

9.2 

98 

1.1603  1.1808,1.1813 

68 

96 

1  180-.' 

1.1807 

1.1813 

1.1818 

1.1824 

1.1829 

84'        39:        44 

66 

1.1827 

88 

88 

44 

49 

55 

60 

65         70         75 

62 

58 

04 

69 

75 

80 

86 

91 

96' l.]90r  1.1906 

69 

89 

95:1.1901 

1.1906 

1.1912 

1.1917 

1.1922 

1.1927|        82 

87 

56 

1.1920 

1.1026 

82 

37 

48 

48 

58 

58         63 

68 

63 

61 

57 

63 

68 

74 

79 

64 

89'        94 

09 

60 

82 

88 

94 

99 

1.2005 

1.8010 

1.8015 

1.8021  1.2026 

1.2031 

47 

1.2018 

1.2019 

1.2025 

1.2030 

86 

41 

40 

52 

57 

62 

44 

44 

60 

66 

61 

67 

72 

78 

83 

88 

98 

41 

76 

81 

87 

93 

98 

1.2103 

1.2409 

1.2114 

1.21191.2124 

8S 

1.2107 

1.2112  1.2118 

1.2124 

1.2129 

34 

40 

45 

50         55 

85 

88 

48         49 

55 

60 

65 

71 

76 

81         66 

82 

69 

76         80 

86 

91 

97 

1.2202 

1.2307 

1.28121.8217 

698 


THE  STEAX-BOILEB. 


6; 


AtoolBl« 

PreMum,  93 


«0  + 
96 


88  + 
97 


•4+       86+      88  + 
99         101         108 


90  + 
106 


98+      94  + 
107         109 


»  + 

m 


111 


'^Ternp.'*'!                                                      FACTORS  OF  EVAPORATIOir. 

212 

1.0849 

1.0868 

1.0868 

1.0868 

1.03671  0872 

1.0876 

1.0381  1.0385 

1.0889 

1.0803 

809 

80 

85 

90 

94 

99 

1.0408 

1.0408 

1.0412 

1.0416 

1.0421 

1.0425 

206 

1.0411 

1.0416 

1.0421 

1.0426 

1.0430 

35 

39 

43 

48 

68 

56 

808 

43 

48 

52 

57 

68 

66 

71 

75 

79 

83 

88 

800 

74 

79 

84 

89 

93 

08 

1.0502 

1.0506 

1.0511 

1.0515 

1.0519 

197 

1.0506 

1.0611 

1.0515 

1.0520 

1.0585 

1.052J* 

88 

38 

42 

46 

50 

194 

37 

48 

47 

61 

66 

60 

66 

09 

78 

78 

82 

191 

69 

73 

78 

88 

87 

92 

06 

1.0601 

1.0605 

1  0609 

1  0613 

188 

1.0600 

1.0605 

1.0610 

1.0614 

1.0619 

1.0688 

1.0628 

82 

36 

40 

45 

185 

81 

36 

41 

46 

60 

55 

59 

68 

68 

72 

76 

182 

63 

68 

72 

77 

81 

86 

90 

95 

99 

1  0703 

1.0707 

179 

04 

99 

1 .0704 

1.0708 

1.0718 

1.0717 

1.0782 

1.0726 

1.0730 

85 

39 

176 

1.0725 

1.0780 

86 

40 

44 

49 

&3 

57 

62 

66 

70 

178 

57 

62 

66 

71 

76 

80 

84 

89 

93 

97 

1.0801 

i:o 

88 

98 

98 

l.Cd02 

1.0607 

1.0611 

1.0616 

1.082U 

1.0824 

l.OftW 

33 

167 

1.0819 

1.0684 

1.0829 

34 

88 

43 

47 

61 

56 

60 

64 

164 

51 

56 

60 

65 

69 

74 

78 

S8 

87 

0! 

95 

161 

82 

8; 

92 

96 

1.0001 

1.0905 

1.0910 

1.0914 

1.0918 

1.0983 

1.0027 

156 

1.0913 

1.0918 

1.0923 

1.09i7 

38 

.37 

41 

45 

60 

64 

68 

155 

45 

49 

54 

59 

68 

68 

78 

77 

81 

85 

88 

152 

76 

81 

85 

90 

95 

99 

1.1004 

1.1006 

1.1012 

1.1016 

1.10S1 

149 

1.1007 

1.1012 

1.1017 

1.1021 

1.1026 

l.ia30 

85 

39 

48 

48 

52 

146 

:iS 

48 

48 

53 

57 

62 

66 

70 

76 

79 

83 

143 

"JO 

74 

79 

84 

88 

93 

97 

1.1102 

1.1106 

1,1110 

1.1114 

140 

1.1101 

1.1106 

1.1110 

1.1115 

1.119U 

1.1124 

1.1129 

83 

87 

41 

46 

137 

88 

87 

42 

46 

61 

55 

60 

64 

68 

73 

77 

134 

63 

68 

78 

78 

82 

87 

91 

95 

1.1200 

1.1804 

1.12C8 

131 

95 

99 

1.1204 

1.1209 

1.1218 

1.1818 

1.1222 

1.1227 

81 

35 

39 

138 

1.1226 

1.1231 

85 

40 

45 

49 

53 

68 

62 

66 

71 

185 

57 

62 

07 

71 

76 

80 

85 

89 

93 

98 

1.1302 

122 

88 

93 

98 

1.1802 

1.1807 

1.1811 

1.1316 

1.1820 

:.1885 

1.1320 

38 

119 

1.1320 

1.1824 

1.1829 

34 

88 

43 

47 

51 

56 

60 

61 

116 

51 

56 

60 

65 

69 

74 

78 

88 

87 

91 

•.k5 

113 

82 

87 

91 

96 

1.1401 

1.1405  1.1409 

1.1414 

1.1418 

1.1422  1.1426 

110 

1.1418  1.1418 

1.1422 

1.1427 

82 

86         41 

45 

49 

53 

68 

107 

44         49 

54 

68 

68 

67 

72 

76 

80 

85 

89 

104 

75         60 

S!i 

89 

94 

99 

1.1508 

1.1507 

1.1618 

1.1516 

1.1520 

101 

1.1506  1.1511 

1.1516 

1.1521 

1.1525 

1.1530 

84 

38 

43 

47 

M 

98 

881        4« 

47 

52 

56 

61 

65 

70 

74 

78 

82 

95 

09 

74 

78 

88 

87 

92 

96 

1.1601 

1.1605 

1.1609  1.1613 

9-J 

1.1600 

1.1605 

1.1609 

1.1614 

1.1619 

1.1623 

1.1628 

32 

86 

40 

45 

69 

81 

86 

41 

45 

60         54 

59 

63 

67 

72 

76 

86 

(W;          67 

7'* 

76 

81      a5 

00 

94 

98 

1.1708 

1.1707 

83 

981        98 
1  1724! 1.1729 

1.1703  1.1707 

1.1712  1.1717 

1.1721 

1.17251.1730 

34 

3S 

80 

84 

89 

48         48 

52 

56         61 

65 

69 

77 

56,        60 

65 

70 

74         79 

88 

88i        92 

96'l.iefW 

74 

87(        91 

96 

1.1801 

1.1806  1.1810  1.1814 

1.1819,1.1883 

1.18271        31 

71 

1.1818  1.1823 

1.1827 

32 

86;        41         46 

50         54 

58'        62 

68 

49,        54 

58 

68 

68         78         77 

81         85 

89;        94 

65 

80!        85 

89 

94 

99,1.1903  1.1908 

1.1912  1.1916 

1  lOaO  1  1025 

62 

1.1911  1.1916  l.lP'l 

1.1925 

1.1930 

34         89 

43         47 

52         56 

69 

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56 

61 

65         70 

74         78 

83         87 

50 

73      18      as 

87 

92 

96  1.8001 

1.2006  1.2010 

1.8014  1.9018 

63 

1  200411  f.'OOg, 1.2014 

1.2018 

1  8023 

1.2088,        32 

86 

41 

45 

4-1 

60 

85!        40 

45 

50 

64 

59 

63 

67 

72 

76 

80 

47 

66'        71 

7(; 

81 

85 

90 

94 

98 

1.2103 

1.2107 

1.8111 

44 

P8  1.210-J 

1.2107 

1.2112 

1.8116 

1.8121 

1.8125 

1.8180 

84 

.38 

42 

41 

1.21291        83 

HH 

43 

47 

52 

56 

61 

65 

69 

T>J 

88 

60'        64 

09 

74 

78 

8;^ 

87 

92 

06 

1.2200 

1.221M 

85 

91         96 

1.2200 

1.2205 

1.2209 

1.2214 

1.8218 

1.8823 

1.2887 

81 

85 

38 

1.822211.2227 

31 

86 

41 

46 

49 

64 

M 

68 

67 

FACTORS  OF  EVAPORATION, 


699 


Ibt.  too  f 

AbsoluM  Prea*. 

Ibt.  115. 


105  +    110  + 
190         185 


115  -f    UO  + 
laO         13& 


125  +     190  +     136  + 
140       I  145 


140  + 
156 


145  +     ISO  + 
NO  166 


Feed  water! 
T«Mp.      1 

Factors  of  Evaporatiok. 

212*» 

1.0397 

1.04071.0417 

1.0427 

1.0486  1.0445 

1.0458 

1.0462 

1.0470 

1.0478  1.0486 

209 

1.0429 

89 

49 

68 

67 

76 

85 

98 

1.0501 

1.0509 

1.0517 

S06 

60 

70 

80 

89 

99 

1.0508 

1.0616 

1.0625 

83 

41 

48 

tari 

92 

1.0502 

1.0511 

1.0521 

1.0580 

89 

48 

56 

64 

72 

80 

200 

1.0528 

83 

43 

52 

62 

70 

79 

87 

961.0604 

1.0611 

197 

55 

65 

74 

84 

98 

1.0602 

1.0610 

1.0619 

1.0627 

35 

43 

194 

86 

96 

1.0606 

1.0615 

1.0624 

83 

42 

60 

58 

66 

74 

191 

1.0617 

1.0627 

87 

47 

66 

65 

78 

82 

90 

98 

i.oro6 

188 

49 

59 

69 

78 

87 

96 

1.0705 

1.0713 

1.0721 

1.0729 

37 

185 

80 

90 

1.0700 

1.0709 

1.0719 

1.0727 

36 

44 

63 

61 

68 

182 

1.0712 

1.0722 

81 

41 

60 

69 

67 

76 

84 

92 

1.0900 

179 

43 

68 

68 

73 

81 

90 

99 

1.0607 

1.0815 

1.0828 

81 

176 

74 

84 

94 

1.0808 

1.0818 

1.0821 

1.0880 

89 

47 

55 

62 

178 

1.0806 

1.0816 

1.0825 

35 

44 

68 

61 

70 

78 

86 

94 

170 

37 

47 

67 

66 

75 

84 

98 

1.0901 

1.0909 

1.0917 

1.0925 

167 

68 

78 

88 

97 

1.0907 

1.0915 

1.0024 

82 

41 

49 

66 

164 

1.0900 

1.0910 

1.0919 

1.0929 

88 

47 

55 

64 

72 

80 

88 

161 

81 

41 

61 

60 

69 

78 

87 

95 

1.1008 

1  1011 

1.1019 

158 

62 

72 

82 

91 

1.1000 

1.1009 

1.1018 

1.1026 

35 

43 

50 

155 

98 

1.1008 

1.1013 

1.1023 

82 

41 

49 

58 

66 

74 

82 

152 

1.1025 

85 

44 

54 

63 

72 

81 

89 

97 

1.1105 

1.1118 

149 

56 

66 

76 

85 

94 

1.1103 

1.1112 

1.1120 

1.1128 

86 

44 

146 

87 

97 

1.1107 

1.11161.1126 

34 

43 

61 

60 

68 

75 

143 

1.1118 

1.1129 

88 

48 

67 

66 

74 

88 

91 

99 

1.1207 

140 

50 

60 

70 

79 

88 

97 

1.1206 

1.1214 

1.1222 

1.1280 

:J8 

137 

81 

91 

1.1201 

1.1210 

1.1219 

1.1228 

87 

45 

63 

61 

69 

134 

1.1212 

1.1282 

82 

41 

61 

59 

68 

76 

85 

93 

1.130O 

131 

43 

63 

63 

TO 

82 

91 

99 

1.1808 

1.1816 

1.1824 

82 

128 

75 

86 

94 

1.1804 

1.1813 

1.1322 

1.1331 

89 

47 

55 

63 

125 

1.1806 

1.1316 

1.1326 

86 

44 

53 

62 

70 

78 

86 

94 

122 

37 

47 

67 

66 

75 

84 

98 

1.1401 

1.1409 

1.1417 

1.1425 

119 

68 

78 

88 

97 

1.1407 

1.1415 

1.1424 

82 

41 

49 

56 

116 

99 

1.1409 

1.1419 

1.1429 

38 

47 

65 

64 

72 

80 

88 

113 

1.1431 

41 

60 

60 

69 

78 

86 

a5 

1.1503 

1.1511 

1.1519 

110 

62 

72 

82 

91 

1.1600 

1.1509 

1.1518 

1.1526 

34 

42 

60 

107 

93 

1.15031.1518 

1.1522 

81 

40 

49 

67 

ea 

73 

81 

104 

1.1524 

84 

44 

58 

62 

71 

80 

86 

97 

1.1606 

1.1612 

101 

65 

65 

75 

84 

94 

1.1602 

1.1611 

1.1620 

1.1628 

86 

43 

98 

86 

96 

1.1C06 

1.1616 

1.1625 

34 

42 

61 

69 

67 

75 

95 

1.1618 

1.1628 

37 

47 

66 

65 

78 

82 

90 

98 

1.1706 

92 

49 

59 

68 

78 

87 

96 

1.1705 

1.1713 

1.1721 

1.1729 

87 

89 

80 

90 

1.1700 

1.1709 

1.1718  1.1727 

86 

44 

S2 

60 

68 

86 

1.1711 

1.1721 

31 

40 

49 

68 

67 

75 

83 

91 

99 

83 

42 

52 

62 

71 

80 

89 

98 

1.1806  1.1815 

1.1823 

1.1880 

80 

73 

88 

98 

1.1802 

1.1812 

1.1820 

1.1829 

87 

46 

54 

6i 

77 

1.1804 

1.1814 

1.1824 

34 

43 

62 

60 

69 

77 

85 

9.S 

74 

85 

45 

56 

65 

74 

88 

91 

1.1900 

1.1908 

1.1916 

1.19-.»4 

71 

67 

77 

86 

96 

1.1905 

1.1914 

1.1922 

81 

39 

47 

.% 

68 

98 

1.1908 

1.1917 

1.1927 

36 

45 

54 

62 

70 

78 

86 

65 

1.1929 

89 

49 

68 

67 

76 

85 

93 

1.2001 

1.2009 

1  2017 

G2 

60 

70 

80 

89 

98,1.2007 

1.2016 

1.2024 

82 

40 

48 

50 

91 

1.2001 

1.2011 

1.2020 

1.2029 

38 

47 

55 

68 

71 

79 

56 

1.2022 

82 

42 

61 

60 

69 

78 

86 

94 

1.2102 

1.81)0 

53 

53 

63 

78 

82 

91 

1.2100 

1.2109 

1.211711. 2126 

34 

41 

60 

84 

94 

1.2104 

1.2113 

1.21.J3 

31 

40 

48 

67 

65 

72 

47 

1.2115 

1.2125 

85 

44 

54 

63 

71 

80 

88 

96 

i.22as 

44 

46 

56 

66 

76 

85 

94 

1.2202 

1.2211 

1.2219 

1.8227 

8.^ 

41 

77 

87 

97 

1.2207 

1.2216 

1.8225 

88 

42 

60 

68 

06 

as 

1.2208 

1.2819 

1.2228 

88 

47 

56 

64 

73 

81 

89 

97 

35 

40 

60 

59 

60 

78 

87 

95 

1.2304|1.2312 

1.2820 

1.2888 

92 

71 

81 

90 

1.23001.2309  1.2818 

1.2326 

35l        48 

61 

59 

700  THB  STEAM-BOILEB. 

STBEHOTH  OF  STKAllI-BOIIiEBS.    TABIOVS  BVI^Kfl 
FOB  €ON8TBlJ€!riONtf 

There  ia  a  great  lack  of  uniformitt  in  the  rules  prescribed  by  dllTer- 
ent  writers  and  by  legislation  firovernlnf^  the  oonstructton  of  st4»ain-boiler8 
In  the  United  States,  boilers  for  merchant  vessels  must  be  constructed  ac- 
cordlng  to  the  rules  and  rejrulatlons  prescribed  by  the  Board  of  Supervinng 
Inspectors  of  Steam  Vessels;  in  the  U.  8.  Kavy,  according  to  niies  of  the 
Navy  Department,  and  in  some  canes  according  to  special  acts  of  Ck>nKref«. 
On  land,  in  some  places,  as  in  Philadelphia,  the  construction  of  boilers  is 
governed  by  local  laws;  but  generally  tliere  are  nn  laws  iipon  the  subject, 
and  boilers  are  constructed  according  to  the  idea  of  Individual  engineers  and 
boiler- makers.  In  Europe  the  constmcflon  is  generally  regulat^  by  strin- 
gent inspection  laws.  The  rules  of  the  U.  8.  Supervising  Inspectors  of 
Steam- vessels*  the  Bl-itlsh  Lloyd*8  and  Board  Of  Trade,  the  French  Boreau 
Veritas,  and  the  Qernian  Lloyd's  are  ably  reviewed  in  a  paper  by  Nelson 
Foley,  M.  Inst.  Naval  Architects,  etc^  fead  at  the  Chicago  Engineeiing  Con- 
gress, Division  of  Marine  and  Naval  Engineering.  From  this  paper  tbe  fol- 
low injc  notes  are  taken,  chiefly  with  refetence  to  the  V.  S.  and  Britinh  rules: 

{Ahhreviation3,—T.  S.,  for  tensile  strength;  £h,  elongation;  Contr.,  0on- 
tractlon  of  area.) 

H[y4fmull«  TeMUt^-^Botird  of  Trade^  Lloyd\  and  BitreaU  VeritoM,^ 
Twice  the  working  pressure. 

United  States  8tatutes.^0ne  and  a  half  times  the  working  preseure. 

Mr.  Foley  propodes  that  the  proof  pressure  should  be  l)<i  times  the  work- 
ins:  pressure  -f  one  atmosphere. 

BetAblleli^d  Nominal  Factor*  of  ^mi^ty* -Board  of  Trade.— 
4.5  for  a  boiler  of  moderate  length  and  of  the  best  construction  and  work- 
manship* 

Ltoya^s.—Jfoi  very  apparent,  but  appears  to  He  between  4  and  5. 

Vnited  States  Staiutea.-^Indvfimte,  because  the  strength  of  the  Joint  is 
not  considered,  except  by  the  broad  distinction  between  single  and  doubl# 
riveting. 

Bureau  Veritas:  4.4, 

Oerman  LIoi/d*at  5  to  4.08.  according  to  the  thickness  of  the  plates. 

Ktateiial  iot  WtiTeUwm(t— Board  of  7>ade.— Tensile  strength  of 
rivet  bars  between  S6  and  80  toUs,  el.  in  1(K'  hot  less  than  HSH,  and  contr.  of 
area  not  less  than  W. 

lAovd^s.-^T.  8..  S6  to  80  tons;  el.  not  less  tfasn  SM  in  $".  The  matertsl 
must  stand  bending  to  a  curve,  the  Inner  radius  of  which  is  not  greater  than 
IH  times  the  thickness  of  the  plate,  after  having  beeh  unlfornliy  heated  t« 
a  low  cherry- red.  and  quenched  In  water  at  89^  F. 

United  States  StatuteH.^T^o  special  provision. 

Bules  Connected  irltli  BlTetlnff,— Bo<ird  of  7VfKie.<^The  shear- 
ing resistance  of  the  rivet  steel  to  be  taken  at  23  tons  per  square  inch.  5 1<> 
be  used  for  the  factor  of  safety  independently  of  any  addition  to  this  factor 
for  the  plating.  Rivets  in  double  shear  to  have  only  1.76  times  the  sinrl^ 
section  taken  in  the  calculation  Instead  of  2.  The  diameter  must  not  be  le^i 
than  tlie  thicknesH  of  the  plate  and  the  pitch  never  areater  than  8W'.  Tb<> 
thicknes.s  of  double  butt-straps  (each)  not  to  be  less  than  j^  the  thlcknees  t^f 
the  plate;  single  butt-straps  not  less  than  0/8. 

Dintance  from  centre  of  rivet  to  edge  of  hole  b  diameter  of  rivet  X  t)4 

Distance  between  rows  of  rivets 

S3  2  X  diam.  of  rivet  or  s  [(diam.  X  4)  *f  1]  -h  S,  if  chain,  4nd 
_.  yt(pltch  X  11)  4-  (diam.  X  4)]  X  (pitob-f  dUm.  X.^)  ^  )t{^jmg 

Diagonal  pitch  =  (pitch  X  6  -f  diam.  X  4)  -•- 10. 

Uoyd' 8. —Rivets  in  double  shear  to  have  only  1.75  times  the  single  sectkw 
taken  in  the  calculation  instead  of  2.  The  shearing  strength  of  rivet  steel  to 
be  taken  at  8!^%  of  the  T.  S.  of  the  material  of  shell  plates.  In  tuar  C8!»? 
where  the  strength  of  the  lonsrltndlnal  Joint  Is  satisfactorily  shown  bj  ex- 
priinent  to  be  greater  thaa  given  by  the  formula,  the  actual  strength  niAj 
be  taken  In  the  calculation* 

Vnited  States  Statutes.^tJo  rules. 

material  for  Cylndrleal  8liell«  Stibjeot  io  Internal  Pree- 
unre,— Hoard  of  Trade.— T.  S  l.e«  ween  27  and  82  tons*  In  the  normal  ooo- 
dUlon,  el.  hot  loss  than  18)t  in  10'',  but  should  be  about  ^  \  \t  antiealed.  n^t 


STRENGTH  OF  6TSAH-BOILER8.  701 

leM  than  HOf.    Strtps  3"'  wide  thookl  ttend  beodJBfr  miti)  the  sides  an 
piinillel  at  a  distance  from  each  other  of  not  more  than  three  tfauee  tha 

plato'8  thicknen. 

IJoyd'a.—T.  S.  between  the  Mnilte  of  95  and  80  tons  per  square  toob.  Kl. 
not  l«iw  til  ail  SOjt  in  H'\  Test  strips  heated  to  a  low  cherry-red  and  plunged 
into  water  at  8:2*  F.  must  stand  bendinf^  to  a  curve,  the  inner  radtas  of 
which  in  not  gieater  than  IV^  times  the  plate's  thloknesSb 

U.  S.  Statutes.— PI At^a  otyi'*  thick  and  under  shall  show  a  contr.  of  not 
toes  than  5QK:  when  over  ^"  and  np  to  9^",  not  less  than  4Bii ;  when  over 
9i'%  not  lefts  than  «)9(. 

Mr.  Foley's  comments  :  The  Board  of  Trade  rules  seem  to  Indicate  a  steel 
of  too  high  T.  S.  when  a  lower  and  more  ductile  one  can  be  got :  the  lower 
tensile  limit  should  be  reduced,  and  the  bending  test  might  with  advantage 
be  made  after  tempering,  and  made  to  a  smaller  radina  Lloyd's  rule  for 
quality  seems  more  sawfaotory,  bnt  the  temper  test  Is  not  severe.  The 
United  States  Statutes  are  not  sufflclently  strlngeot  to  insure  an  entirely 
satisfactory  mateslal. 

Mr.  Foley  suggests  a  material  which  would  meet  the  following :  25  tons 
lower  limit  In  tension  ;  \a%  in  8^'  minimum  elongation  ;  radius  for  bending 
test  after  tempering  =  the  plate's  thickness. 

SlieIl-plateFoniiaI«D.-Boa}*do/7Vade.*  P=  ^^^^J,^^. 

D  =  diameter  of  boiler  in  inches ; 
F  •=  working-pressure  in  lbs«  per  s(]uare  inch  ; 
t  =  thickness  in  inches  ; 

B  =  percentage  of  strength  of  joint  compared  to  solid  plate ; 
T  =  tensile  strength  allowed  for  the  material  in  lbs.  per  square  inch  ; 
^  =  a  factor  of  safety,  being  45,  with  certain  adoitlona  depending  on 
method  of  construction. 

t  =  thickness  of  plate  in  sixteenths  ;  B  and  D  as  before ;  C  =  a  constant 
depending  on  the  kind  of  Joint. 

When  longitudinal  seams  have  double  butt^raps,  C  =  20.  When  longi- 
tudinal seams  have  double  butt-straps  of  unequal  width,  only  covering  on 
on«*  side  the  reduced  section  of  plate  at  the  outer  line  of  rivets,  C  =  10.&. 

When  the  longitudinal  seams  are  lap-Jointed,  C  =  18.5. 

U.  S.  Statutes.— Vaing  same  notation  as  for  Board  of  Trade, 

p  _  ixaxi'for  single-riveting ;  add  20fi  for  double-riveting ) 
I?  X  o 

where  T  is  the  lowest  T.  S.  stamped  on  any  plate. 

Mr.  Foley  criticises  the  rule  of  the  United  States  Statutes  as  follows  :  The 
rule  ignores  the  riveting,  except  that  it  distinguishes  between  single  and 
double,  giving  the  latter  00%  ail  vantage  ;  the  circumferential  riveting  or 
class  of  seam  is  altogether  ignored.  The  rule  takes  no  account  of  workman- 
ship or  method  adopted  of  constructing  the  joints.  The  factor,  one  sixth, 
simply  covers  the  actual  nominal  factor  of  safety  as  well  as  the  lossot 
strength  at  the  joint,  no  matter  what  Its  percentage  ;  we  may  thereforo 
dismiss  it  as  unsatisfactory. 

Bales  for  Flat  Platea^^Boord  of  Trade ;  P e=    ^^^-  . 

P  =  working- pressure  hi  lbs.  per  square  Inch} 
5  =3  surface  supported  in  square  inches; 
t  3  thickness  in  sixteenths  of  an  inch; 
C  =  a  constant  as  per  following  table: 
C7  =  125  for  plates  not  exposed  to  heat  or  flame,  the  stays  fitted  with  nuts 
and  washers,  the  latter  at  least  three  times  the  diameter  of  the  stay 
and  %  the  thickness  of  the  plate: 
C  =  187.5  for  the  same  condition,  but  the  washers  %  the  pitch  of  stays  in 

diameter,  and  thickness  not  less  than  plate; 
C  =  200  for  the  same  condition,  but  doubling  plates  In  place  of  washers,  the 

width  of  which  Is  ^  the  pitch  and  thickness  the  same  as  the  plate; 
C  =  112.5  for  the  same  condition,  but  the  stays  with  nuts  only; 
C  =  75  when  exposed  to  impact  of  heat  or  flame  and  steam  In  contact  with 
the  plates,  and  the  stays  fltted  with  nuts  and  washers  three  times  the 
diameter  of  the  stay  and  %  the  plate's  thickness; 


702  THB  8TEAM-B0ILBB. 

C  s  87.6  for  the  same  ooDditton,  but  stays  fitted  with  nuts  only; 

C  =  100  when  exposed  to  beat  or  flame,  and  water  in  contact  with  the  plates, 

and  stays  screwed  into  the  plates  and  fitted  with  nuts; 
C  =  66  for  the  same  condition,  but  stays  with  riveted  heads. 

Cx  f* 
U.  S.  Statutes.— V^ng  same  notation  as  for  Board  of  Trade.    P  =  , 

where  p  =  greatest  pitch  in  Inches,  P  and  t  as  above; 

C  ss  118  for  plates  7/16"  thick  and  under,  fitted  with  screw  stay-bolts 
riveted  over,  screw  stav-bolts  and  nuts,  or  plain  bolt  fitted 
witli  single  nut  and  socket,  or  riveted  head  and  socket; 
C  s  180  for  plates  above  7/lf\  under  the  same  conditions; 
C  8  140  for  flat  surfaces  where  the  stays  are  fitted  with  outs  inside 

and  outside; 
C  s  800  for  flat  surfaces  under  the  same  condition,  but  with  the  addi- 
tion  of  a  washer  riveted  to  the  plate  at  least  ^  pUite^s  thick- 
ness, and  of  a  diameter  equal  :to^of  the  pitch  or  the  stay-bolts. 

N.B.— Plates  fitted  with  double  angle-irons  and  riveted  to  plate,  with  leaf 
at  least  %  the  thickness  of  plate  and  depth  at  least  )4  of  pitch,  would  be 
allowed  the  same  pressure  as  determined  by  formula  for  plate  with  washer 
riveted  on. 

N.B.— No  brace  or  stay-bolt  used  in  marine  boilers  to  have  a  greater  pitch 
than  lOHi''  on  fire-boxes  and  back  connections. 

Certain  experiments  were  carried  out  by  the  Board  of  Trade  which  showed 
that  the  resTstance  to  bulging  does  not  vary  as  the  square  of  the  plate's 
thickness.  There  seems  also  good  reason  to  believe  that  it  is  not  invenwiy 
as  the  square  of  the  greatest  pitch.  Bearing  in  mind,  says  Mr.  Foley,  that 
mathematicians  have  signally  failed  to  give  us  true  theoretical  foundations 
for  calculating  the  resistance  of  bodies  subject  to  the  simplest  forms  of 
stresses,  we  therefore  cannot  expect  much  from  their  assistance  in  the 
matter  of  fiat  plates. 

The  Board  of  Trade  rules  for  flat  surfaces,  being  based  on  actual  experi- 
ment, are  especially  worthy  of  respect;  sound  judgment  appears  also  to 
liave  been  used  in  framing  them. 

Furnace  FormulSB.— Board  or  TDADt.-^Long  Pumaees.— 

■P=  /  r  ^  ^  ^*  n*  ^"t  °<>'  where  L  is  shorter  than  (11. 5f  -  1),  at  which  length 

{■L  +  1)  X  Jy 
the  rule  for  short  furnaces  comes  into  play. 

P  =  working-pressure  in  pounds  per  square  inch;  t  =  thickness  in  inches; 
D  =  outside  diameter  in  inches:  L  —  length  of  furnace  In  feet  up  to  10  ft.; 
C  =  a  constant,  as  per  following  table,  for  drilled  holes : 

C  =  99,000  for  welded   or   butt* join  ted  with  single  straps,  double- 
riveted; 
C  =  88,000  for  butts  with  single  straps,  single-riveted: 
C  =  99,000  for  butts  with  double  straps,  single-riveted. 

Provided  always  that  the  pressure  so  found  does  not  exceed  that  given  by 
the  following  formulae,  which  apply  also  to  short  furnaces : 

C  "x  t 
P  3  — ^~-  for  all  the  patent  furnaces  named; 

^~  fx^Q^  "  6tI^<)  ^^^^  ^^^  Adamson  rings. 

C  =    8.800  for  plain  furnaces; 

C  s  14,000  for  Fox;  minimum  thickness  6/16",  greatest  %";  plain  part 

not  to  exceed  6"  in  length ; 
C  =3  13,500  for  Morison;  minimum  thickness  5/16",  greatest  %'';  plain 

part  not  to  exceed  6"  in  length: 
C  B  14,000  for  Purves-Brown;  limits  of  thickness  7/16"  and  H";  plain 

part  9"  in  length ; 
C  a   6,800  for  Adamson  rings;  radius  of  flange  next  fire  1)^". 

U.  S.  Statctks.— JLoii^  Furnaces,— Sa,ine  notation. 
P  =  ^ — ^^,  but  L  not  to  exceed  8  ft. 

Lt  "X.  Lf 

N.B.— If  rings  of  wrought  iron  are  fitted  and  riveted  on  properly  around 
•nd  to  the  flue  in  such  a  manner  that  the  tensile  stress  on  the  rivets  shall 


STRENGTH  OF  STEAM-BOILERS.  703 

not  exceed  6000  lbs.  per  sq.  In.,  the  distance  between  the  rings  shall  be  taken 
as  the  length  of  the  flue  in  the  formulae. 
Short  PuiTMcet,   Flain  and  Fatent.^P^  as  before,  when  not  8  tL 
89.6no  X  t* 
^^'^^     LXD    ' 
P  =  ^-^when 

C  =  14,000  for  Fox  corrueatfons  where  D  =  mean  diameter; 
C  =  14.000  for  Furvet}- Brown   where  D  =  diameter  of  flue; 
C  =  5077  for  plain  flues  over  16"  diameter  and  less  than  40",  when 
not  oyer  8  ft.  lengths. 

Mr.  Foley  comments  on  the  rules  for  long  furnaces  as  follows:  The  Board 
of  Trade  general  formula,  where  the  length  is  a  factor,  has  a  very  limited 
range  indeed,  viz.,  10  ft.  as  the  extreme  length,  and  185  thicknesses  —  12*\ 

as  the  short  limit.    The  original  formula,  P  =  ttt^*  ^  ^^^  o'  Sir  W. 

Fairbaim,  and  was,  I  believe,  never  intended  by  him  to  apply  to  short  fur* 
naces.  On  the  very  face  of  it,  it  is  apparent,  on  the  other  hand,  that  if  it  is 
true  for  moderately  long  furnaces.  It  cannot  be  so  for  very  long  ones.  Wo 
are  therefore  driven  to  the  conclusion  that  any  formula  which  includes 
simple  Z.  as  a  factor  must  be  founded  on  a  wrong  basis. 

with  Mr.  Traiirs  form  of  the  formula,  namely,  substituting  (L  +  1)  for  L, 
the  results  appear  sufficiently  satisfactorr  for  practical  purposes,  and  in- 
deed. a«  far  as  can  be  judged,  tally  wiin  the  results  obtained  from  experi- 
ment as  nearly  as  could  be  expected.  The  experiments  to  which  I  refer 
were  six  in  number,  and  of  great  variety  of  length  to  diameter;  the  actual 
factors  of  safety  ranged  from  4.4  to  6.2,  the  mean  being  4.78,  or  practically 
5.  It  seems  to  me,  therefore,  that,  within  the  limits  prescribed,  the  Board  of 
Trade  formula  may  be  accepted  as  suitable  for  our  requirements. 

The  United  States  Statutes  give  Fairbaim*s  rule  pure  and  simple,  except 
that  the  extreme  limit  of  length  to  which  It  applies  Is  Axed  at  8  feet.  As 
far  as  can  be  seen,  no  limit  for  the  shortest  length  is  prescribed,  but  the 
rules  to  me  are  by  no  means  clear,  flues  and  furnaces  being  mixed  or  not 
well  distinguished. 

Hmteiial  for  Stmys*— The  qualities  of  material  prescribed  are  as 
follows: 

Board  of  Trade.— The  tensile  strength  to  lie  between  the  limits  of  27  and 
9i  tons  per  square  inch,  and  to  have  an  elongation  of  not  less  than  90%  in 
10".  Steel  stays  which  have  been  welded  or  worked  in  the  Are  should  not 
be  used. 

UowTt.—^n  to  80  ton  steel,  with  elongation  not  less  than  20jt  In  6". 

U.  8.  Statutes.— The  only  condition  is  that  the  reduction  of  area  must  not 
be  less  than  40%  if  the  test  bar  is  over  1^"  diameter. 

I«oads  alloired  on  Stmym*— Board  of  Trade.— 9000  lbs.  per  square 
inch  is  allowed  on  the  net  section,  provided  the  tensile  strength  ranges  from 
27  to  82  tons.    Steel  stays  are  not  to  be  welded  or  worked  in  the  Are. 

X/oycTt.— For  screwed  and  other  stays,  not  exceeding  iW*  diameter  effec- 
tive, 8000  lbs.  jier  square  Inch  Is  allowed;  for  stays  above  iyi'\  9000  lbs.  ^o 
stays  are  to  be  welded. 

u.  S.  Statutea.—BTAces  and  stays  shall  not  be  subjected  to  a  greater  stress 
than  GOUO  lbs.  per  square  inch. 

[Rankine,  S.  E.,  p.  460,  says:  "The  Iron  of  the  stays  ought  not  to  be  ex- 
pc»ed  to  a  greater  working  tension  than  8000  lbs.  on  the  souare  inch,  in 
order  to  provide  against  their  being  weakened  by  corrosion.  This  amounts 
to  making  the  factor  of  safety  for  the  working  pressure  about  20.'*  It  is 
evident,  however,  that  an  allowance  in  the  factor  of  safety  for  corrosion  may 
reasonably  be  decreased  with  increase  of  diameter.    W.  K.] 

I  «lrd««.-Board  of  Trade.    P=  ,S^^t^J  t-     P=  working  pres- 

{rr   -—  V)l/  X  A» 

sure  in  lbs.  per  sq.  in.;  W  =  width  of  flame-box  in  inches:  L  =  length  of 
girder  in  Incnes;  p  =  pitch  of  bolts  in  inches;  D  =  distance  between  girders 
from  centre  to  centre  in  inches;  d  =  depth  of  girder  in  inches;  t  =  thick- 
ness of  sum  of  same  In  inches;  C  =  a  constant  =  6G00  for  1  bolt,  9900  for  2 
or  8  bolts,  and  11,220  for  4  bolts. 

lioydV— The  some  formula  and  constants,  except  that  C  =  11,000  for  4  or 
5  bolts,  11,550  for  6  or  7,  and  11,880  for  8  or  more. 

U»  &  Statutes.— The  matter  appears  to  be  left  to  the  designers. 


704  THE  STEAM-BOILER. 

Tnbe-nate«,-^oanf  of  Trade,  P  =  ^^^  '^wx'^^'  ^  ^  ***** 
horiBontal  dtatance  between  centres  of  tubes  In  inohe«i;  d  =  inside  diameter 
of  ordinary  tubes;  t  =  thickness  of  tube-plate  In  inches;  W=  extreme 
width  of  Gombustion-boz  In  inches  from  front  tube-plate  to  back  of  fire- 
box, or  distance  between  combustiou-box  tube-plates  when  the  boiler  is 
double-ended  and  the  box  common  to  both  ends. 

The  crushlDff  sti-ess  on  tube-plates  caused  by  the  pressure  on  the  flame- 
box  top  Is  to  be  limited  to  10,000  lbs.  per  square  Inch. 

naierial  for  Tubes.— Mr.  Foley  proposes  the  followini;:  If  iron,  the 
quality  to  be  such  as  to  give  at  least  22  tons  per  square  inch  as  the  minimum 
tensile  stren^i^h,  with  an  elongation  of  not  less  than  15^  in  6".  If  steel,  the 
elongation  to  be  not  leas  than  96)K  in  8"  for  the  material  before  being  rolled 
Into  strips;  and  after  tempering,  the  test  bar  to  stand  completely  dosing 
together.  Provided  the  steel  welds  well,  there  does  not  seem  to  be  any  ob- 
ject in  proyiding  tensile  limits. 

The  ends  should  be  annealed  after  manufacture,  and  stay-tube  ends  should 
be  annealed  before  scrawlng. 

Holdlnc-ppwer  of  BolIer«tnbe»«— Experiments  made  in  Wash- 
ington NavyVard  show  that  with  2^  In.  brass  tubes  in  no  case  was  the  holding- 
power  less,  roughly  speaking,  than  6000  lbs.,  while  the  average  was  upwards 
of  a0,000  lbs.  It  was  further  shown  that  with  these  tubes  nuts  were  siipt- r- 
fluous,  quite  as  good  results  being  obtained  with  tubes  simply  expanded  mto 
the  tube-plate  and  fitted  with  a  ferrule.  When  nuts  were  fitted  it  waa  shown 
that  they  drew  off  without  injuring  the  threads. 

In  Messrs.  Yarrow's  experiments  on  Iron  and  steel  tubes  of  2"  to  Sti" 
diameter  the  first  5  tubes  gave  way  on  an  average  of  38,740  lbs.,  which  would 
appear  to  be  about  %  the  ultimate  streni^th  of  the  tubes  themselves.  In  all 
thef    -.^-  ..-.    .. .  .. ...     . —    .^     -     ^ 


I  the  hole  through  the  tube- plate  was  parallel  with  a  sharp  edge 

to  it,  and  a  ferrule  was  driven  Into  the  tube. 

Tests  of  the  next  6  tubes  were  made  under  the  same  conditions  as  the  first 
5,  with  the  exception  tliat  In  this  case  the  ferrule  was  omitted,  the  tubes  be- 
ing simply  expanded  Into  the  plates.  The  mean  pull  required  wa8lS,270Ibs., 
or  considerably  less  than  half  the  ultimate  strength  of  tiie  tubes. 

j^ecf  of  beading  the  tubes,  the  holes  through  the  plate  being  parallel  and 
ferrules  omitted.  The  mean  of  the  first  3,  which  are  tubes  of  the  same 
kind,  gives  '<i6,876  lbs.  as  their  holding-power,  under  these  conditions,  as  com- 
pared with  23,740  lbs.  for  the  tubes  fitted  with  ferrules  only.  This  high 
figure  Is,  however,  mainly  due  to  an  exceptional  case  where  the  holding- 
power  is  greater  than  the  average  strength  of  the  tubes  themselves. 

It  Is  disadvantageous  to  cone  the  hole  through  the  tube-plate  unlesp  its 
sharp  edge  is  removed,  as  the  results  are  much  worse  than  those  obtaiited 
with  parallel  holes,  the  mean  pull  belug  but  10,031  lbs.,  the  experiments  be- 
ing made  with  tubes  expanded  and  fer ruled  but  not  beJaded  over. 

In  experiments  on  tuoes  expanded  Into  tapered  holes,  beaded  over  and 
fitted  with  ferrules,  the  net  result  is  that  the  holding-power  Is,  for  the  size 
experimented  on,  about  9i  of  the  tensile  strength  of  the  tube,  the  mean  pull 
being  88,797  lbs. 

With  tubes  expanded  Into  tapered  boles  and  simply  beaded  over,  better 
results  were  obtained  than  with  ferrules:  in  these  cases,  however,  the  sharp 
edge  of  the  hole  was  rounded  off,  which  appears  in  general  to  have  a  good 
effect. 

In  one  particular  the  experiments  are  Incomplete,  as  it  Is  impossible  to 
reproduce  on  a  machine  the  racking  the  tubes  get  by  the  expansion  of  a 
boiler  as  it  Is  heated  up  and  coolea  down  again,  and  it  Is  quite  possible, 
therefore,  that  the  fastening  giving  the  best  results  on  the  tesdng-machine 
may  not  prove  so  etficient  in  practice. 

N.6.— It  should  be  noted  that  the  experiments  were  all  made  under  the 
cold  condition,  no  that  reference  should  oe  made  with  caution,  the  circum- 
stances in  practice  being  very  different,  especially  when  there  is  scale  on 
the  tube-plates,  or  when  the  tube -plates  are  thick  and  subject  to  Intense 
heat. 

Iron  Tenus  Steel  Boll«r-tiib«s.  (Foley.)  ~  Mr.  Blechynden 
prefer:!  iron  tui>eN  to  those  of  steel,  but  how  far  he  would  go  in  attributing 
the  leaky-tube  defect  to  the  use  of  steel  tubes  we  are  not  aware.  It  appearm 
however,  that  the  results  of  his  experiments  would  warrant  him  In  going  a 
eonslderable  dintance  In  this  direction.  The  test  consisted  of  besting  ard 
cooling  two  tubes,  one  of  wrought  iron  and  the  other  of  steel.  Both  tubt^s 
were  294  in.  in  diameter  and  .16  In.  thickness  of  metal.    The  tubes  were 


©■ 


STRENGTH   OF  STEAM-BOILERS.  705 

Kut  In  tb0  same  furnace,  made  red-)i<H,  and  then  dipped  in  water.   The 
»Dcth  was  gauged  at  a  temperature  of  46^  F. 
l^iB  operation  was  twice  repeated,  with  reealts  as  follows : 

Steel.  Iron. 

Originallength 56.4fl6in.  B6.495in. 

Heated  to  1M«F.;  Increase 058**  .048" 

Coefficlen  t  of  expansion  per  degree  F .0000067  .0000009 

Heated  red-hot  and  dipped  In  water;  decrease       .007  in.  .003  in. 

Second  heating  and  cooling,  decrease 081  In.  .004  in. 

Third  heating  and  cooling,  decrease 017  in.  .000  in. 

Total  contraction „       .OftSin.  .OlSin. 

itr.  A.  O.  Kirk  writes :  That  OTorheatlng  of  tube  ends  is  the  cause  of  the 
leakage  of  the  tubes  in  boilers  is  provea  by  the  fact  that  the  ferrules  at 
present  used  by  the  Admiralty  prevent  it.  These  act  by  shielding  the  tube 
ends  from  the  action  of  the  flame,  and  consequently  reducing  evaporaUon, 
and  so  allowing  free  access  of  the  water  to  keep  them  cool. 

AHhotigh  many  causes  contribute,  there  seems  no  doubt  that  thick  tube- 
plates  must  bear  a  share  of  causing  the  misohlet. 

Bales  for  Conatr action  of  Boilers  In  IHerclftant  Teasels 
in  tlie  17ulted  0Uites« 

(Extracts  from  General  Rules  and  Regulations  of  the  Board  of  Supervising 
Inspectors  at  bteam-vessels  (as  amended  Itittb).) 
Xenslle  Strengtli  of  Plate*   (Section  8.>-*To  ascertain  the  tensile 
strength  and  other  qualities  of  ii-on  plate  there  shall  be  token  from  each 

sheet  to  be  used  In  shell  or  other 
parts  of  boiler  which  are  subject  to 
tensile  strain  a  test  piece  prepared 
in  form  according  to  the  following 
diagram,  viz.:  10  inches  in  length.  2 
inches  In  width,  cut  Out  in  the 
centre  in  the  manner  indicated. 
To  ascertain  the  tensile  strength 
and  other  qualities  of  itteelptai^*  there  shall  be  taken  from  each  sheet  to  be 
used  in  shell  or  other  parts  of  boiler  which  are  subject  to  tensile  strain  a  test- 
piece  prepared  in  form  according  to  the  following  diagram: 

The  straight  part  in  centre  shall        

be  9  inches  In  length  and  1  inch  in      'tJ  V  , .  .     ..         /~ 

width,  marked  with  light  prick-    |»^  ^<^iJaska«aL^ 

punch  marks  at  diutances  1  inch  i£ 
apart,  as  shown,  spaced  so  as  to  -^ 
give  8  inches  in  length.  tHi. 

The  sample  must  show  when 
tested  an  elongation  of  at  least  2&^  in  a  length  of  2  in.  for  thickness  up  to 
li  in.,  inclusive;  in  a  length  of  4  in.  for  over  14  to  7/16,  inclusive;  in  a 
length  of  0  in.,  for  all  plates  over  7/10  in.  and  under  l^l  in.  thickness. 

The  reduction  of  area  shall  be  the  same  as  called  for  by  f  be  rules  of  the 
Board.  No  plate  shall  contain  more  than  M%  of  phosphorus  and  .04^  of 
sulphur. 

The  samples  shall  also  be  capable  of  being  bent  to  a  curve,  of  which  the 
Inner  radius  is  not  greater  than  i]4  times  the  thickness  at  the  plates  after 
having  been  heated  uniformly  to  a  low  cherry-red  and  quenched  In  water 

[Prior  to  18M  the  shape  of  test-piece  for  steel  was  the  same  as  that  for  firoii» 
viz.,  the  grooved  stiape.  This  shape  has  been  condemned  by  authorities  on 
strength  of  materials  for  over  twenty  years.  It  always  gives  results  which 
are  too  high,  the  error  sometimes  amounting  to  25  per  cent.  See  pages  *i4ti, 
848.  ante;  also.  Strength  of  Mateiials,  W.  Kent,  Van  IT.  Science  Series  No.  41, 
and  Beardslee  on  Wrought-lron  and  Chain  Cables.] 

Bnetlllty*  (Section  6.)— To  ascertain  the  ductility  and  other  lawful 
qualities,  iron  of  45.000  lbs.  tensile  strength  shall  show  a  contraction  of  area 
or  15  per  cent,  and  each  additional  1000  lbs.  tensile  strength  shall  show  1 
per  cent  additional  contraction  of  area,  up  to  and  Including  55.000  tensile 
strength.  Iron  of  55,000  tensile  strength  and  upwards,  showing  85  per  cent 
reduction  of  area,  shall  be  deemed  to  have  the  lawful  ductllitv.  All  steel 
plate  of  ^^Inch  thickness  and  under  shall  show  a  contraction  of  area  of  not 
less  than  50  per  cent.    Steel  plate  over  H  inch  in  thickness,  up  to  ^  inch  in 


706 


THE  STEAH-BOILEB. 


thickness,  shall  show  a  rednctfon  of  not  less  than  45  per  cent.  All  steel  plate 
over  9s(  Inch  thickness  shall  show  a  reduction  of  not  less  than  40  per  c<*nt. 

Bumped  Heads  of  Boilers.  (Section  17  as  amended  18M.) — 
Pressure  Allowed  on  Bumped  ifearfj.— Multiply  the  thickness  of  the  plate 
by  one  sixth  of  the  tensile  strenfir^h,  and  divide  by  six  tenths  of  the  radius  to 
which  head  is  bumped,  which  will  give  the  pressure  i)er  square  inch  of 
steam  allowed. 

Pleasure  Allowable  for  Concaved  fleod«o/Po»7en.— Multiply  the  pressure* 
per  square  inch  allowable  for  bumped  hendB  attached  to  boilers  or  drums 
convexly,  by  the  constant  .6,  and  the  product  will  give  the  pressure  per 
square  I'nch  allowable  in  concaved  heads. 

The  pressure  on  unstayed  flat-lieads  on  steam-drums  or  ahells 
of  boilers,  when  flanged  and  made  of  wrought  iron  or  steel  or  of  cast  steel, 
shall  be  determined  by  the  following  rule: 

The  thickness  of  plate  in  inches  multiplied  by  one  sixth  of  its  tensile 
strength  in  pounds,  which  product  divided  by  the  area  of  the  head  in  square 
inches  multiplied  by  .09  will  give  pressure  per  square  inch  allowed.  The 
material  used  in  the  construction  of  flat-heads  when  tensile  strength  has 
not  been  officially  determined  shall  be  deemed  lo  have  a  tensile  strength  of 
45,000  lbs. 

Table  of  Pressures  allonrable  on  Steam-boilers  made  of 
Blveted  Iron  or  Steel  Plates* 

(Abstract  from  a  table  published  In  Rules  and  Regulations  of  the  U.  S. 
Board  of  Supervising  Inspectors  of  Steam- vessels.) 
Plates  M  inch  thick.    For  other  thicknesses,  multiply  by  the  raUo  of  the 
thickness  to  ^  Inch. 


60,000  Tensile 

66.000  Tensile 

60,000  Tensile 

65.000  Tensile 

70,000  Tensile 

jl 

Strength. 

Strength. 

Strength. 

Strength. 

Strength. 

1 

il 

j 

3I 

1 

J 

8 

^1 

1 

.  c 

'1 

1 

8' 

S^ 

§- 

1 

S=3 

1 

S' 

"S" 

115.74 

188.88 

127.31 

158.77 

188.88 

166.65 

150.46 

180.55 

108.08 

191  43 

38 

109.64 

131.66 

120.61 

144.73 

131.57 

167.88 

142.54 

171.04 

158.5 

184.a) 

40 

104.16 

1S4.99 

114.58 

137.49 

125 

160 

185.41 

162.49 

146.88 

174  99 

42 

99.2 

119.04 

109.12 

190.94 

119.04 

142  81 

128.96 

164.TO 

1S8.88 

166  6^ 

44 

94.69 

113.63 

104.16 

134.99 

118.68 

186.35 

128.1 

147.78 

182.56 

159.07 

46 

90.67 

108.68 

99.63 

119.56 

106.09 

130.42 

117.75 

141.3 

186.8 

152. 16 

48 

86.8 

104.16 

96.48 

114.57 

104.16 

124.99 

112.84 

135.4 

121.52 

145  82 

64 

77.16 

92.60 

84.87 

101.84 

92.69 

111.10 

100.3 

120.36 

108.02 

129  ft! 

60 

69.44 

83.32 

76.38 

91.65 

83.88 

99.99 

90.27 

106.82 

97.28 

116M 

66 

68.13 

75.76 

69.44 

83.82 

75.75 

90.90 

82.07 

98.48 

88.87 

106.04 

72 

67.87 

69.44 

68.65 

76.88 

69.44 

88.82 

75.22 

90.26 

81.01 

97.21 

78 

53.41 

64.09 

66.76 

70.5 

64.4 

76.92 

69.44 

88.82 

74.78 

89.73 

84 

49.6 

59.52 

64.56 

65.47 

69.52 

71.42 

64.48 

77,87 

60.44 

6S.S2 

90 

46.39 

65.44 

60.92 

61.1 

65.56 

66.66 

60.18 

72.21 

64  81 

77.  T7 

90 

48.4 

62.08 

47.74 

67.28 

52.08 

62.49 

66  42 

67.67 

60.76 

72.91 

The  figures  under  the  columns  headed  "  pressure  **  are  for  slngle-rivett^l 
boilers.  Those  under  the  oolumus  beaded  "  20ji  Additional^*  are  for  double- 
riveted. 

U.  8.  RuLB  FOR  Allowable  PiiBssriuEs. 

The  pressure  of  any  dimension  of  boilers  not  found  in  the  table  annexed 
to  these  rules  must  be  ascertained  by  the  following  rule: 

Multiply  one  sixth  of  the  lowest  tensile  strength  found  stamped  on  any 
plate  in  the  cylindrical  shell  by  the  thickness  (expressed  in  inches  or  rMirta 
of  an  inch)  of  the  thinnest  plate  In  the  same  cylindrical  slielUaitd  divide  l»y 
the  radius  or  half  diameter  (also  expressed  in  inches),  the  quotient  will  lie 
the  pressure  allowable  per  square  inch  of  surface  for  single- riveting,  10 
which  add  twenty  per  centum  for  double-riveting  when  all  tlie  rivet -holes 
in  I  lie  shell  uf  such  boiler  have  been  "  fairly  drilled  **  and  no  part  of  surh 
hole  hiiH  btHiu  punched. 

The  author  aesires  to  express  hi«  conrlemnation  of  the  above  rule,  and  (»f 
the  tables  derived  from  it,  ah  Kivaig  uk>  low  a  factor  of  safety.  (See  h\ho 
criticism  by  Mr.  Foley,  page  701,  ante.) 


STBENOTH  OF  6TEAU-B0ILEBS. 


707 


If  rb  =  burating-pressure,  i  =  thickness,  T  =  tensile  strehgtb,  e  :=  coef* 
fleient  of  sti'ength  of  riyeted  joint,  that  is,  ratio  of  strength  of  the  joint  to 

that  of  the  solid  plate,  d  =  diameter,  Pb  =  -^,  or  if  c  be  taken  for  double* 

lAtT 
riTetlng;  at  0.7,  then  Pb  =     .  ■» 
a 

i/6tT  OUT 

By  the  U.  S.  rule  the  allowable  pressure  Pa  »  -^tj  X  1.20  =  -^  ;  whence 

Pb  =  Z.5Pa;  that  is,  the  factor  of  safety  is  only  3.5,  provided  the  "  tensile 
strength  found  stamped  In  the  plate  ^*  Is  the  real  tensile  streutcth  of  the 
material.  But  in  the  case  of  iron  plates,  since  tbe  stamped  T.S.  is  obtained 
from  a  grooved  specimen,  it  may  be  greatly  in  excess  of  the  real  T.S.,  which 
would  make  the  factor  of  safety  still  lower.  According  to  the  table,  a  boiler 
40  in.  dlam.,^  In.  thick,  made  of  iron  stamped  60,000  T.8.,  would  be  licensed 
to  carry  150  lbs.  pressure  If  double-riveted.  If  the  real  T.8.  is  only  60,000  lbs. 
the  calculated  bursting-strength  would  be 


P= 


2tTc      g  X  50,000  X  .28  X  .70 
d     "  40 


=  437.6  lbs., 


and  the  factor  of  safety  only  487.5  -i- 150  =  3.01 1 
The  authoi'''a  fwm%Ua  for  safe  working-pressure  of  eztemally -fired  boilers 

MOOOt    ^       Pd 


with  longitudinal  seams  double-riveted,  ia  Ps 


-'*=  14000'^='^'^ 


pressure  in  lbs.  per  sq.  in.;  t  =s  thickness  and  d  =  diam.  in  inches. 

*2tTc 
This  Is  derived  from  the  formula  P  s  -— ,  taking  e  at  0.7  and  f^bUxt 

ateel  of  50,000  lbs.  T.S.,  or  6  for  60.000  lbs.  T.S.;  the  factor  of  safety  being 
increased  in  the  ratio  of  the  T.S.,  since  with  the  higher  T.8.  there  Is  greater 
danger  of  cracking  at  tbe  rivet-holes  from  the  effect  of  punching  and  rivet- 
ing and  of  expansion  and  contraction  caused  bv  variations  of  temperatiu^. 
For  external  shells  of  Intemally-flred  boilers,  these  shells  not  being  exposed 
to  the  fire,  with  rivet-holes  drilled  or  reamed  after  punching,  a  lower  factor 
of  safety  and  steel  of  a  higher  T.S.  may  be  allowable. 

If  the  T.S.  is  60,000,  a  working  pressure  P  =  —g —  would  give  a  factor  of 

safety  of  5.25. 

The  following  table  gives  safe  working  pressures  for  different  diameters 
of  shell  and  thicknesses  of  plate  calculated  from  the  author^s  formula. 

Safe  ITorklne  Pressures  In  Cylindrical  Shells  of  BoUen^ 
Tanks,  Pipes,  etc*,  In  Pounds  per  Square  Inclu 

Longitudinal  seams  double-riveted. 
(Calculated  from  formula  Ps  14,000  x  thickness •«- diameter.) 


0^ 

Diameter  in  Inches. 

lis 

iis 

24 

80 

86 

88 

40 

42 

44 

46 

48 

60 

62 

1 

86.5 

29.2 

24.8 

28.0 

21.9 

20.8 

19.9 

19.0 

18.2 

17.5 

16.8 

2 

72.9 

58.8 

48.6 

46.1 

43.8 

41.7 

89.8 

88.0 

86.5 

S5.0 

88.7 

8 

109.4 

87.5 

72.9 

60.1 

65.6 

62.5 

59.7 

67.1 

64.7 

62.5 

50.5 

4 

145.8 

116.7 

97.2 

92.1 

87.5 

88.8 

79.5 

76.1 

72.9 

70.0 

67.8 

5 

182.8 

145.8 

121.5 

115.1 

109.4 

104.2 

99.4 

95.1 

91.1 

87.5 

84.1 

6 

218.7 

175.0 

145.8 

138.2 

181.3 

125.0 

119.3 

114.1 

109.4 

105.0 

101.0 

7 

255.2 

201. 1 

170.1 

161.2 

158.1 

145.9 

139.2 

133.2 

127.6 

122.5 

117.8 

8 

291.7 

283.8 

194.4 

184.2 

175.0 

166.7 

159.1 

152.2 

145.8 

140.0 

184.6 

9 

828.1 

262.5 

218.8 

207.2 

196.9 

187.5 

179.0 

171.2 

164.1 

157.5 

151.4 

10 

864.6 

201.7 

243.1 

aao.a 

218.8 

SJ08.8 

198.9 

190.3 

182.8 

175.0 

168.8 

It 

401.0 

320.8 

267.4 

253.3 

240.6 

229.2 

218.7 

209.2 

200.6 

192.5 

185.1 

12 

487.5 

850.0 

291.7 

276.3 

262.5 

250.0 

238.8 

228.3 

218.7 

210.0 

201.9 

18 

478.9 

879.2 

316.0 

299.3 

284.4 

270.9 

258.6 

247.3 

8:37.0 

227.5 

218.8 

14 

410.4 

408.8 

340.3 

322.4 

306.8 

291.7 

278.4 

266.8 

255.2 

245.0 

286.6 

15 

546.9 

487.5 

864.6 

345.4 

828.1 

312.5 

Si98  3 

285.3 

278.4 

266.5 

262.4 

16 

588.3 

466.7 

888.9 

368.4 

360.0 

333.8 

318.2 

304.4 

291.7 

280.0 

269.2 

708 


CHJt  STEAM-BOItKB. 


11% 

l>i*rneter  In  Inches 

G4 

CO 

Cfl 

7'2 

78 

84 

PO 

00 

104 

m 

114 

ISO 

1 

Ifi.S 

H.fl 

13.3 

ja.s 

UM 

104 

fl.? 

fl.l 

e.6 

B.I 

7  r 

7,« 

« 

^.-1 

2&.i 

afl.3 

1^  S 

^.4 

20. i 

li.4 

I8.S 

17.SI 

3(1.* 

16  4 

H« 

s 

43. e 

43,7 

a^j 

m.t, 

m.7 

m.n 

29. i; 

ST  S 

S5  7 

i?j.3 

sa  0 

in  9 

4 

64, e 

f«.a 

58.0 

4Be 

44,0 

41  7 

38. » 

aa  &  34.3 

W.4 

ao.7 

393 

B 

m.o 

T«,9 

m.a 

M,S 

W  1 

JWJ.l 

4«.0 

«.6 

is.v 

40.5 

3^.4 

^5 

0 

97,%^ 

87.5 

TS.S 

758. » 

or.  3 

IU»5 

£«  B 

54.7 

61, S 

48.S 

41.1 

41  ]4 

7 

llJl.-J 

IffJ.l 

9^*.8 

SM 

71S.5 

7^.» 

«e  1 

08,«» 

«0.0 

58.7 

5i|.7 

51.0 

H 

l«S>.fl 

116.7 

lOH  t 

V7.H 

S0  7 

^.a 

77.8 

;^.9 

es.« 

«I,S 

fil.4 

5M  S 

tt 

I45.S 

lai.t: 

119. S 

1OT.4 

101  01  0S,8 

^,5 

f^.a 

77.3 

71.« 

<D.| 

A5  6 

10 

IflS.O 

1:M,6 

Itl.G 

lli/^Im.-J 

97.3 

Bl.l 

85. S 

»U0 

TU.ft 

TV  9 

]1 

J  78.  J 

ltk>.4, 

14ri.8 

13S.T 

1*8,^ 

114.6 

!06.»uoo.a 

ft4.4 

l«.l 

EU  4 

mii 

IS 

194.4 

175.  (J 

IM  1 

14&.H 

134  e 

l;S.O 

lie  7 

]0Q.« 

10-2. fl 

67,2 

95S  1 

w^  s 

13 

210,7 

1KU.6 

173  4 

,a8,t 

145.K 

136,1 

TsJfl  1 

tiH.r- 

111,5 

106.3 

90  8 

M.H 

U 

'^ii\.9 

m-i  5 

170.1 

1!>7.1 

U5.8 

136  1 

IS?7.6 

liJO.l 

ns,4 

107  5J0t^  1 

in 

54a.  1 

;il8.7 

lye.w 

isa.3 

lUS.^ilJMJ.a 

H5.ft:i:i6.T 

15I8.T 

1^1 .5 

llfi-lJlW  4 

i& 

iav  a 

:saij, 

£];!.l 

1»4.4 

ITB.shOflT 

lto«[H5.8 

187.5 

12&,« 

1«3.9ll|«.T 

B«l«i  K^TanUns  Isspectton  «r  Ii4»tl«rs  la  PliOaAelFblflu 

In  estimating  the  strenfcth  of  the  longfttidfniLl  s«a«i«  In  tli«  ejiliKlHeal 
ilMlls  of  boilfln  tlie  inspector  ebaO  applf  two  formulae,  A  aad  B : 

1  Pitch  ef  rivertB  —  dfcuneter  of  holeg  punched  to  receitie  the  rireU  _ 
^'  i  pSteiroTrivete 

peroeniage  of  atiength  of  the  sheet  at  the  sefm. 

i  Area  of  hole  filled  hy  rivet  X  Vo.  of  rowsof  rlv«(sfn  seam  X  ehear- 

j_    •< lug  strength  of  riret __.   - 

*   '     pitch  of  rivets  xtUckness  of  sheet  X  tensile  strength  of  ^eet      ~ 
percentage  of  strength  of  43ie  riyete  in  ttie  seaa. 

Take  the  lowest  of  the  percentages  as  found  by  formulaa  A  and  B  am4 
apply  tJuit  pereentage  as  the  *' strength  of  the  seam**  in  the  fofloiriDg 
formula  C,  which  determines  the  strength  of  the  longftodinal  aeams: 

i  IbkskaeBs  of  akeet  te  parte  of  tocb  X  straswrih  at  seam  as  obtained 

Q    <    »y<oraimlaAorBx«K*taaJt<eatreBgthaf  ironstaMpedoaplatog     ^ 

'   »         internal  radius  o<  boiler  in  inches  X  5  as  a  factor  of  safety  *^ 

safe  working  pressure. 

Table  of  Profortioks  and  Safe  Workiiig  Pressures  wrrn  Formula  A 
awD  C,  9  Oi,000  !«.,  T.S. 


Diameter  of  riv«t 

Diameter  of  rivet-hole. . 

Pitch  of  rivets 

Strength  of  seam,  5(..  «. 
ThJckneas  of  piate.    . . . 


a/" 

n/lB" 

«^ 

.608 


W16 


8  V>« 
.00 

y/16 


Diameter  of  tx>fler,  Iil.  . 


ilfisC^  Workiag  PresBU4«  with  liongitudioal  Seams 
«  Bii>gle-ri  voted. 


M 

!«r 

]«6 

19a 

sto 

942 

3P 

108 

183 

184 

176 

191 

» 

103 

194 

144 

105 

i6i 

U 

98 

117 

186 

185 

m 

» 

9] 

110 

189 

147 

m 

m 

88 

104 

188 

189 

156 

«i 

8S 

90 

116 

183 

145 

u 

74 

tl 

105 

180 

188 

48 

08 

68 

86 

no 

181 

M 

00 

78 

66 

86 

107 

00 

66 

88 

77 

86 

97 

StRENQTB  09  STBAH-BOtLeBS. 


roo 


Diameter  of  rivet.'. . . . . 
Diameter  of  rlvet-hoie. 

Pitch  of  rivets 

Strength  of  seam,  %- .  • 
ThickneBB  of  pl»te. .  . . 

Diameter  of  boiler,  in. 


n/16" 

.77 


5/16 


.75 


% 
15/16 


Safe  'forking  Preasurp  with  Longitudinal  Seams* 
Double- riveted. 


34 
80 
89 
84 
86 

as 

40 

fl 

64 
60 


160 

127 

119 

11? 

106 

101 

§6 

87 

19 

70 

64 


106 

385 

(MO 

158 

188 

215 

148 

176 

m 

140 

166 

190 

182 

156 

179 

m 

14S 

170 

119 

141 

161 

108 

128 

147 

99 

11B 

185 

88 

104 

1» 

79 

94 

108 

805 


215 
208 
19a 
183 
166 
152 
185 
188 


Pine*  and  Tabes  for  Steam-boilers.— (From  Rules  of  U.  8- 
Snperviving  InapectorB.  Steam -pressures  per  square  inch  allowable  on 
riveted  ^nd  lap^weld^d  flues  made  in  sections,  i;^ tract  from  table  in  Rules 
of  U.  S.  BupervlsJMg  Inspectors.) 

T  =.  least  thickness  of  material  allowable,  D  r=  greatest  diameter  in  inches, 
P  =  allowabU  pmssura.  For  thickness  greater  than  T  with  same  diameter 
P  is  isereased  fa  the  ratio  of  the  thickness. 

tl   18   19  20  21   SS{    38 
.87  .08  .89  80  .81  .82  M 


D  =  ln.  7  8  9  10  U  19  19  H     15  16 

r=iu,  .18  ,|»  .21  .21  .28  .28  .JS  .24  .26  .26  .. 

P  =  U)S.  189  184179174  178  IW  m   147  H3  130  186 184 131  1^  126  )t>5  m 

D  =  in.  84  25  26  27  28  29  80  81  82  83  84  85  86  87  88  89  40 

T  =  In.  .84  .85  .86  .87  .88  .80  .40  .41  .48  .48  .44  .46  .46  .47  .48  .40  .60 

Ps  ItM,  121  120  110  117  116  115  119  114  112  112  110  110  109  109  108  106  107 

For  diameters  net  orer  10  inches  the  greatest  length  of  section  allowable 
Is  5  feet;  for  diameters  10  to  28  inches,  8  feet;  for  diameters  23  to  40  inches,  80 
Inches.  If  lengths  of  sections  are  greater  than  these  lengths,  the  allowable 
pressvre  Is  reduced  proportienJ^elr. 

The  U*.  S,  ru)e  for  corrugated  flues,  as  an)eoded  in  1894,  is  as  follows:  Eule 
II,  Beetion  14.  The  strength  of  all  corrugated  flues,  when  used  for  furnscas 
or  steam  chimneys  (porrugation  not  less  than  1^  incbvs  deep  and  noteYcetad- 
Ing  8  inches  from  centres  of  eorrugatioii),  and  provided  that  the  plain  parts 
at  the  ends  do  not  eKoeed  6  inches  in  length,  and  the  plates  are  not  less  than 
5/lS  In^h  thi^k*  w}wii  new,  corrugated,  and  yr«cUcw  true  eM'pJeSi  l9  be 
calcnl^ted  fron»  the  following  formula: 


14,000 


X  r  ==  pressure. 


T  SK  thickness,  ja  Inohes;  D  s  mean  diameter  in  Inohes. 

Ribbed  J^u««.~Tbe  same  formula  is  given  for  ribbed  flues,  with  rib 
projections  not  less  than  IH  inches  deep  an4  not  more  than  9  inches 
spart. 

Fiat  Stared  Siurl3aee«  In  fteaiii*bo|lent*-Rule  n.,  Section  6,  of 
the  rules  of  the  u.  &.  Supervising  Inspectors  provides  as  follows: 

No  braces  or  stays  liersafter  employed  in  the  construction  of  hoilerf 
■hall  be  allowed  a  greater  strain  tlian  6000  lbs.  per  square  in«h  of 
section. 

Clark,  1b  hJs  treatise  on  thA  Steam-engine,  also  in  his  Pocket-book,  gives 
the  foUowiug  formula:  p  =s  407<a  -*-  d,  in  which  p  is  the  internal  pressure  lo 
pounds  per  square  inch  that  will  strain  the  plates  to  their  elastic  limit,  t  is 
the  thickness  of  the  plate  in  inches,  d  is  the  difttanoe  between  two  rows  of 
stsy-bolts  in  the  elear,  and  a  is  the  tensile  stress  in  the  plate  in  tons  of 
2240  U».  per  square  inch,  at  the  elastic  limit.  Substituting  values  of  s 
for  iron,  stesl,  and  copper,  12,  14,  and  8  tons  respectively,  ve  have  the 
XoUowing : 


710 


THE  8TEAM-B0ILBE. 


FORMUUB  FOR  UlTIM ATB  ELASTIC  STRXNGTH  OF  FX<AT  STAYCD  SURFACES. 


Iron. 

steel. 

Copper. 

PresBure 

p  =  500(4 
*  _PXd 
.       bOOOt 

p 

p  =  6700 - 

pxd 

5700 
^^5700* 

P 

p=8300i 

*         WW) 
^^83004 

Thickness  of  plate 

Pitch  of  bolts 

P 

l/^. 


For  Blameter  of  tUe  Stay-bolta,  Clark  gives  d'  =  .0024, 

in  which  d*  =  diameter  of  8Gre\ved  bolt  at  bottom  of  thread,  P  =  lonfriiudi- 
nal  and  i*  transverse  pitch  of  stay-bolts  between  centres,  p  =  internal 
pressure  in  lbs.  per  sq.  in.  that  will  strain  the  plate  to  its  elastic  limit,  a  = 
elastic  strenf^th  of  the  stay-bolts  in  lbs.  per  sq.  in.  Taking  «  =  1:2, 14,  and  8 
ions,  respectively  for  iron,  steel,  and  copper,  we  have 

For  iron,       d'  =  .000©9  VPF^,{or  if  P  =  P',  d'  =  .00p69P  i^; 

For  steel,      d'  =  .00064  VPP'p,     "        **        d'  =  .00064P  Vp; 

For  copper,  d'  =  .00084  ^'PFp,     "        "        d'  =  .00084P  Vp. 
In  using  these  formulsa  a  large  factor  of  safe^r  should  be  taken  to  allow 
for  reduction  of  size  by  corrosion.    Thurston's  Manual  of  Steam-boUers,  p. 
144,  recommends  that  the  factor  be  as  large  as  15  or  20.    The  Hartfonl 
Steam  Boiler  Insp.  &  Ins.  Co.  recommends  not  less  than  10. 

Birenetli  or  Stays.— A.  F.  Yarrow  (Engr.^  March  SO,  1691)  gives  the 
following  results  of  experiments  to  ascertain  the  strength  of  water-space 
stays: 


Description. 


Hollow  stavB  screwed  into  j 
plates  and  hole  expanded  ( 

Solid  stays  screwed  into} 
plates  and  riveted  over.    1 


Length 
between 
Platea 


4.75  in. 
4.64  in. 
4.80  in. 
4.80  in. 


Diameter  of  Stay  over 
Threads. 


lin.fhole  7/16  in.  and  5/16  In. 
1  in.(hole  9/16  In.  and 7/16  in. 


IIL 


Ulti- 
mate 
Stress. 


lbs. 
85,4.'i7 
20,99-^ 
«,008 
Sa,070 


The  above  are  taken  as  a  fair  average  of  numerous  tests. 

Stay-bolts  In  Carved  Snrteces,  as  In  ITater-Iesii  of  Verti- 
cal Boilers*— The  rules  of  the  U.  S.  Supei'vising  Inspectors  provide  as 
follows;  All  vertical  boiler' furnaces  constructed  of  wrought  iron  or  steel 
plates,  and  having  a  diameter  of  over  4*2  in.  or  a  height  of  over  40  in.  shall  be 
stayed  with  bolts  as  provided  by  f  6  of  Rule  II,  for  flat  surfaces;  and  the 
thickness  of  material  required  for  the  shells  of  such  furnaces  shall  be  de- 
termined by  the  distance  between  the  centres  of  the  stay-bolts  in  the  fur- 
nace and  not  in  the  shell  of  the  boiler;  and  the  steam-pressure  allowable 
shall  be  determined  by  the  distance  from  centre  of  stav-bolts  in  the  furnace 
and  the  diameter  of  such  stay-bolts  at  the  bottom  of  the  thread. 

The  Hartford  Steam-boiler  Insp.  &  Ins.  Co.  approves  the  above  rule  (27*e 
Locomotive,  March,  1892)  as  far  as  it  states  that  curved  surfaces  are  to  be 
computed  the  same  as  flat  ones,  but  prefers  CIark*8  foinnulas  for  ilat 
stayed  surfaces  to  the  rules  of  the  U.  8.  Supervising  Inspectors, 

Faslble-plass«^Fusible-phigs  Hhould  be  put  in  that  portion  of  the 
heating-surface  wTilch  first  becomes  exposed  from  lack  of  waier.  The  rules 
of  the  17.  8.  Supervising  Inspectors  specify  Banca  tin  for  the  purpose.  Its 
melting-point  is  about  A4h**  F.  The  rule  says:  All  steamers  shall  have 
inserted  in  their  boilers  plugs  of  Banca  tin,  at  least  ^  in.  in  diameter  at  the 
smallest  end  of  the  internal  opening,  in  the  following  manner,  to  wit: 
Cylinder- boilers  with  flues  shall  nave  one  plug  inserted  in  one  flue  of  each 
boiler;  and  also  one  plug  inserted  in  the  shell  of  euch  boiler  from  the  inside, 
Immediately  before  the  fire  line  and  not  less  than  4  ft.  from  the  forward 
end  of  the  boiler.  All  fire-box  boilers  shall  have  one  plug  inserted  in  the 
crown  of  the  back  connection,  or  in  the  highest  fire-surface  of  the  boiler. 


IMPROVED   METHODS  OP  FEEDING   COAL.  711 

All  upright  tubular  boilers  uged  for  m&rine  purposes  shall  have  a  fusible 
pluf;  Inserted  in  one  of  the  tubes  at  a  point  at  least  2  In.  below  the  lower 
f?auge-cnck,  and  said  plue  mav  be  placed  in  the  upper  head  sheet  when 
deemed  advisable  by  tnellocal  inspectors. 

Steam-domes.— Steam  domes  or  drums  were  formerly  almost  univer- 
sally nned  on  horizontal  boilers,  but  their  use  is  now  generally  discontinued* 
as  they  are  considered  a  useless  appendage  to  a  steam-boiler,  and  unless 


properly  designed  and  constructed  are  an  element  of  weakness, 

Htelfflit  of  Fumaee.— Recent  practice  in  the  United  States  makes 
the  height  of  furnace  much  greater  than  it  was  formerly.  With  large  sizes 
of  anthracite  there  is  no  serious  objection  to  having  the  furnace  as  low  as  12 
to  18  In.,  measured  from  the  surface  of  the  grate  to  the  nearest  portion  of 
the  heating  surface  of  the  boiler,  but  with  coal  containing  much  volatile 
matter  and  moisture  a  much  greater  distance  Is  desirable,  with  very  vola- 
tile coals  the  distance  may  be  as  great  as  4  or  5  ft.  Rankine  (S.  E.,  p.  457) 
says:  The  clear  height  of  the  *'  crown  "  or  roof  of  the  furnace  above  ihe  grate> 
bars  is  seldom  less  than  about  18  in.,  and  often  considerably  more.  In  the 
fire-boxes  of  locomotives  it  is  on  an  average  about  4  ft.  The  height  of  18  in. 
is  suitable  where  the  crown  of  the  furnace  is  a  biickarch.  Where  the  crown 
of  the  furnace,  on  the  other  hand,  forms  part  of  the  heating-surface  of  the 
laoiler,  a  greater  height  Is  desirable  in  every  case  in  which  it  can  be 
obtained :  for  the  temperature  of  the  boiler-plateK,  being  much  lower  than 
that  of  the  flame,  tends  to  check  the  combustion  of  the  inflammable  gases 
which  riM€  from  the  fuel.  Asa  general  principle  a  high  furnace  is  favorable 
to  complete  combustion. 

IHPBOTBB  mBTHOIM  OF  FBBBING  COAIi, 

nEeebantcal  Stokers,  (William  R.  Roney,  Trans.  A.  S.  M.  E.,  vol. 
xti.)— Mechanical  stokers  have  been  used  in  England  to  a  limited  extent 
since  1785.  In  that  year  one  was  patented  by  James  Watt.  It  was  a  simple 
device  to  push  the  coal,  after  it  was  coked  at  the  front  end  of  the  grate, 
back  towards  the  bridge.  It  was  worked  intermittently  by  levers,  and  was 
de«*igned  primarily  to  prevent  smoke  from  bituminous  coal.  (See  D.  K. 
Clark's  Treatise  on  the  Steam-engine.) 

After  the  year  1840  many  styles  of  mechanical  stokers  were  patented  in 
England,  but  nearlv  all  were  variations  and  modiflcatlons  of  the  two  forms 
of  stokers  patented  by  John  Jukes  in  1841,  and  by  E.  Henderson  in  1848. 

The  Jukes  stoker  consisted  of  longitudinal  flra-bart*,  connected  by  links, 
so  as  to  form  an  endless  chain,  similar  to  the  familiar  treadfiilll  horse-power. 
The  small  coal  was  delivered  from  a  hopper  on  the  frunt  of  the  boiler,  on  to 
the  grate,  which  slowly  moving  from  front  to  rear,  gradually  advanced  the 
fuel  into  the  furnace  and  discharged  the  ash  and  clinker  at  the  back. 

Tlie  Henderson  sioker  consists  primarily  of  two  horizontal  fans  revolving 
on  vertical  spindles,  which  scatter  the  coal  over  the  fire. 

Numerous  faults  in  mechanical  construction  nnd  in  operation  have  limited 
the  use  of  these  and  other  mechanical  stokers.  The  first  American  stoker 
was  the  Murphy  stoker,  brought  out  in  1878.  It  consists  of  two  coal  maga- 
zines placed  in  the  side  walls  of  the  boiler  furnace,  and  extending  back  from 
the  boiler  front  6  or  7  feet  In  the  bottom  of  these  magazines  are  rectangu- 
lar iron  boxes,  which  are  moved  from  side  to  side  by  means  of  a  rack  and 
pinion,  and  serve  to  push  the  coal  upon  the  grates,  which  incline  at  an  angle 
of  about  35»  from  the  inner  edge  of  the  coal  magazines,  forming  a  V-shaped 
receptacle  for  th»*  burning  coal.  Tlie  grates  are  composed  of  narrow  parallel 
bars,  so  arranged  that  each  alternate  l«ar  lifts  about  an  inch  at  the  lower 
end.  while  at  ttie  bottom  of  the  V,  and  filling  the  space  between  the  ends  of 
the  L'rate-dars,  \a  placed  a  cast-iron  toothed  bar,  arranged  to  be  turned  by  a 
crank.  The  purpose  of  this  bar  is  to  grind  the  clinker  coming  in  contact 
with  it.    Over  this  V-shaped  receptacle  is  sprung  a  fire-brick  arch. 

In  the  Roney  mechanical  Htokerthc  fuel  to  be  burned  Is  dumped  into  a 
hopper  on  the  boiler  front.  Set  in  the  lower  part  of  the  hopper  is  a"  pusher" 
to  which  is  attached  the  *' feed -plate  ^*  forming  the  bottom  of  the  hopper. 
The  ••  pusher,"  by  a  vibratory  motion,  carrying  with  it  the  "  feed-plate," 
gradually  forces  the  fuel  over  the  *'  dead-plate  "  and  on  the  grate.  The 
grate-liars.  In  their  normal  condition  form  a  series  of  steps,  to  the  top  step 
of  which  coal  is  fed  from  the  **  dead-plate."  Each  bar  rests  in  a  concave 
seat  in  the  bearer,  and  is  capable  of  a  rocking  motion  through  an  adjustable 
angle.  All  the  grate-bars  are  coupled  together  by  a  ^'rocker- bar."  A  vari- 
able back-and-forth  motion  being  given  to  the  *'  rocker-bar,"  through  a  con- 


712  THE   STEAM-BOILER. 

neoting-rod,  the  iprate^bars  rock  in  uniton,  now  terming  a  flerlea  of  Btepi, 
«nd  DOW  approximating:  to  an  inclined  plane,  with  the  grateg  partly  over- 
lapping,  like  sliingleg  on  a  roof.  When  the  erate-bars  rock  forward  the  fire 
will  tend  to  work  down  in  a  body.  But  before  the  coal  can  move  too  far 
the  bars  rock  back  to  the  stepped  position,  checking  the  downward  motion, 
breaking  up  the  cake  over  the  whole  surface,  and  admitting  a  free  volume 
of  air  through  the  fire.  The  rockiug  motion  is  slow,  being  from  7  to  10 
strokes  per  minute,  according  to  the  kind  of  coal.  This  alternate  starting 
and  checking  motion  is  continuous,  and  finally  lauds  the  cinder  and  ash  on 
ilie  dumping-grate  below. 

Mr.  Roney  gives  the  following  record  of  six  tests  to  determine  the  com- 
parative economy  of  the  Honey  mechanical  stoker  and  hand-firiiiK  on  return 
tubular  boilere.  60  inches  x  80  feet,  burning  Cumberland  coal  with  natural 
draught.    Rating  of  boiler  at  1S.5  square  feet,  105  U.  P. 

Three  tests,  hand-firing.    Three  tests.  Stoker. 

^;oS?f?onfaKd«t^2^5ib,^''yf     10.86    10.44    11.00  11.89    1«.85    1«.M 

H.r.  developed  above  rating,^       5.8      13.5        68  54.0     66.7     84.8 

Results  of  cninpsrative  tests  like  the  above  Fhould  be  WHi  with  caution 
In  drawing  frfncrultxations.  It  by  no  means  follows  from  the>««*  retniltn  that 
a  stoker  will  always  Hh«>w  such  comparative  excellence,  for  in  tl.is  cas**  the 
resultK  of  hand-firing  are  much  below  what  may  be  obtaincl  unler  favor- 
ab)**  fiivum  stances  from  hand-firing  with  good  Cumberland  coal. 

The  Haiirley  I>oiv^n»draiislit  Famaee*— A  fiiot  or  more  above 
the  oriiiiiury  prate  there  in  carried  a  second  grate  composed  of  a  series  of 
water  tubes,  opening  at  both  ends  into  steel  drums  or  headers,  throush  which 
water  Is  circulated.  The  coal  is  fed  on  this  upper  grate,  and  as  it  Is  par- 
tially consumed  falls  through  it  upon  the  lower  s^ate.  where  the  onmbustion 
Is  completed  in  the  ordinarr  manner.  The  draught  through  the  coal  oit  the 
upper  grate  is  downward  through  the  coal  and  the  grate.  The  volatile  gases 
are  therefore  carried  down  through  the  bed  ot  coal,  where  they  are  thor- 
oughly heated,  and  are  burned  in  the  space  beneath,  where  they  meet  the 
excess  of  hot  air  drawn  through  the  fire  on  the  lower  grate.  In  tests  in 
Chicago,  from  80  to  45  lbs.  of  coal  were  burned  per  square  foot  of  irrate  upon 
this  system,  with  good  economical  results.  (See  catalogue  of  the  Hawley 
l>own  Draut-'ht.  Furnace  Co.,  Chicago.) 

Vnder-reed  Stokers.— Results  similar  to  those  that  may  be  obtained 
witii  downward  draught  are  obtained  by  feeding  the  coal  a».  the  boftom  of 
the  bed,  pushing  upward  the  coal  already  on  the  bed  which  has  hod  its 
Tolaiile  niflt'erdifttilled  from  it.  Thev4»latlle  matter  of  the  freshly  flre<l 
ooal  then  hns  to  oaks  through  a  body  of  ignited  coke,  where  it  meets  a  nip- 
ply  of  hot  air.    (See  circular  of  The  American  Stoker  0>.,  New  York,  1806.) 

SMOKE  PRBTENTIOlf. 

A  committee  of  experts  was  appointed  in  St.  Louis  in  10)1  to  report  on  the 
smoke  problem.  A  sunimarv  of  its  report  is  given  in  the  Iron  Age  of  April 
7,  1898.  It  descril)e8  the  different  means  that  have  been  tried  to  prevent 
smoke,  such  as  gas-fuel,  steatu-jets,  fire-brick  arches  and  checker- w(»rk, 
ho]I'>w  walls  for  preheating  air,  coking  arches  or  chambers,  double  combus- 
tion furnaces,  and  automatic  stokers.  All  of  these  means  have  been  more  or 
less  effective  in  diminishing  smoke,  their  effectiveness  depending  largely 
upon  the  skill  with  which  ihey  are  operated  ;  but  none  Is  entirely  satisfac- 
tory. Fuel-gaR  is  objectionable  chiefly  on  accouut  of  its  expeut^e.  The 
average  quality  of  fuel  gas  mode  from  a  trial  run  of  several  cai'-loads  of 
Illin- lis  coal,  in  a  well-designed  fuel-gas  plant,  showed  a  calorific  value  of 
24Z,^U\  heai-units  per  1000  cubic  feet.  This  is  equivalent  to  5052.8  heat  units 
per  lb.  of  coal.  >vhereAS  by  direct  calorimeter  test  an  average  sample  of  the 
coal  gave  ll.IT-2  heal-uniis.  One  lb.  of  the  coal  showed  a  theoretlciil  evap- 
oration of  II  r>C  lbs.  water,  while  the  gas  from  1  lb.  showed  a  theorrtictil 
evaporation  of  5.^3  lb».  48  17  lbs.  of  cool  were  required  to  furnit-h  1000 cubic 
feet  of  the  gas.  In  SO  tests  the  smoke-preventing  furitacee  showed  only  7i% 
of  the  caparity  of  the  oanmon  furnaces,  rwluoed  the  work  of  the  b«iil»r» 
283{.  and  required  about  L'jC  more  fuel  to  do  the  same  work.  In  one  case  with 
steam-Jets  the  fuel  consiiinption  was  increawid  \2%  for  the  same  work. 

Prof.  O.  H.  I^iidnMh,  in  a  report  to  the  State  Boani  of  Health  of  Tennei*- 
see  {Em/ineering  AVtr<,  Juno  ti,  lSd3),  writes  as  follows  on  the  subject  of 
smoke  prevention: 


SMOKE   PREVENTION.  713 

As  pertofns  to  Bteam-boilera,  the  object  must  be  attained  by  one  or  more 
of  the  following;  agencies : 

1.  Proper  desigrn  and  setting  of  the  boiler-plant.  This  implies  proper  grate 
area,  sufBoient  draught,  the  necessary  air-space  between  grate-bars  and 
through  fu]-nace,  and  ample  combustion-room  under  boilers. 

2.  That  system  of  flring  that  is  best  adapted  to  each  particular  furnace  to 
secure  the  perfect  combustion  of  bituminous  coal.  Tbis  may  be  either:  (a) 
"'coke-firing/*  or  charging  all  coal  into  the  front  of  the  furnace  until  par- 
tially coked,  then  pushing  back  and  spreading;  or  (b)  '* alternate  side- fir- 
ing^; or  (c)  **  spreading/'  by  which  the  coal  is  spread  over  the  whole  grate 
area  in  thin,  uniform  layers  at  each  charging. 

3.  The  admission  of  air  through  the  furnace-door,  bridge-wall,  or  side  walls. 

4.  Steam- Jets  and  other  artincial  means  for  thoroughly  mixingfthe  air  and 
combustible  gases. 

5.  Preventing  the  cooling  of  the  furnace  and  boilers  by  the  Inrush  of  cold 
air  when  the  furnace-doors  are  opened  for  charging  ooal  and  handling  the 
Are. 

6.  Establishing  a  gradation  of  the  seTeral  steps  of  combustion  so  that  the 
coal  may  be  charged,  dried,  and  warmed  at  the  coolest  part  of  the  furnace, 
and  then  moved  by  successive  steps  to  the  hottest  place,  where  the  fliml 
combustion  of  the  coked  coal  is  completed,  and  compelling  the  distilled 
combustible  gases  to  pass  through  this  hottest  part  of  tne  fire. 

7.  Preventing  the  cooling  by  radiation  of  the  unburned  combustible  gases 
until  perfect  mixing  and  combustion  have  been  accomplished. 

8.  varying  the  supply  of  air  to  suit  the  periodic  variation  in  demand. 

9.  The  substitution  of  a  continuous  uniform  feeding  of  coal  instead  of 
Intenitiitent  charging. 

10.  Down-draught  burning  or  causing  the  air  to  enter  above  the  grate  and 
pasK  down  through  the  coal,  carrying  the  distilled  products  down  to  the  high 
trmperatui-e  plane  at  the  bottom  of  the  Are. 

The  number  of  smoke-prevention  devices  which  have  been  invented  is 
legion.    A  brief  classification  is  : 

(a)  Mechanical  stokers.  They  effect  a  material  saving  in  the  labor  of 
flring,  and  are  efficient  smoke-preventers  when  not  pushed  aiaove  their 
capaciiy,  and  when  the  coal  does  not  cake  badly.  They  ara  rarely  susct^pti- 
ble  to  the  sudden  changes  in  the  rate  of  flring  frequently  demanded  in 
service. 

(b)  Air-flues  in  side  walls,  bridge-wall,  and  grate-bars,  through  which  air 
when  passing  is  heated.  The  results  are  always  beneficial,  but  the  flues  are 
difficult  to  keep  clean  and  in  order. 

(c)  Coking  arches,  or  spaces  in  front  of  the  furnace  arched  over,  in  which 
the  fresh  coal  is  coked,  both  to  prevent  cooling  of  the  distilled  gases,  and  to 
force  them  to  pass  through  the  hottest  part  of  the  furnace  Just  beyond  the 
arch.  The  results  are  good  for  normal  conditions,  but  ineffective  when  the 
flres  are  forced.  The  arches  also  are  easily  burned  out  and  injured  by 
Working  the  fire. 

(d)  Dead-plates,  or  a  portion  of  the  grate  next  the  furnace-doors,  reserred 
for  warming  and  coking  the  coal  t)efore  it  is  spread  over  the  grate.  These 
give  good  results  when  the  furnace  is  not  forced  above  ite  normal  capacity. 
This  embodies  the  method  of  '*coke-flring"  mentioned  before. 

(a)  Down-draught  furnaces,  or  furnaces  in  which  the  air  is  supplied  to  the 
coal  above  the  grate,  and  the  products  of  combustion  are  taken  away  from 
beneath  the  Krate,  thus  caiu»ing  a  downward  draught  through  the  coal,  carry- 
ing the  distilled  gases  down  to  the  highly  heated  incandescent  coal  at  the 
bottom  of  the  layer  of  coal  on  the  grate.  This  is  the  most  perfect  manner 
of  producing  combustion,  and  Is  absolutely  smokeless. 

(f)  Steam  Jets  to  draw  air  in  or  iniect  air  into  the  furnace  above  the  grate, 
and  also  to  mix  the  air  and  the  combustible  gases  together.  A  very  efRcient 
smoke-preventer,  but  one  liable  to  be  wasteful  of  fuel  by  inducing  too  rapid 
a  draught. 

ig)  Baffle-plates  placed  in  the  furnace  above  the  fire  to  aid  in  mixing  the 
combustible  gases  with  the  air. 

{h)  Double  furnaces,  of  which  there  are  two  diflPerent  styles;  the  first  of 
which  places  the  second  grate  below  the  first  grate;  the  coal  is  coked  on  the 
first  grate,  during  which  process  the  distilled  gases  are  made  to  pass  over 
the  second  grate,  where  they  are  ignited  and  burned;  the  coke  from  the  first 
grate  is  dropped  onto  the  second  grate:  a  very  efficient  and  economical 
smoke-preventer,  but  rather  complicated  to  construct  and  maintain.  In  tba 
second  form  the  products  of  combustion  from  the  first  furnace  paw  through 


714  THE  STEAM-BOILER. 

the  firrate  and  fire  of  the  second,  each  furnace  belnj?  chamd  with  fresh  totA 
when  needed,  the  latter  generally  with  a  smokeless  coal  or  coke :  an  irra. 
tional  and  unpromisiu{c  method. 

Mr.  C.  F.  White,  Consul  tine  Enfirineer  to  the  Chicago  Society  for  the  Pre- 
vention of  Smoke,  writes  under  dat«  of  May  4, 1898  : 

The  experience  had  in  Ohica^^o  has  shown  plainly  that  It  is  perfectly  ea^y 
to  equip  steam-boilers  with  furnaces  which  shall  burn  ordinary  soft  coal  to 
such  a  manner  that  the  making  of  smoke  dense  enough  to  obstruct  the  visioii 
shall  be  confined  to  one  or  two  intervals  of  perhaps  a  couple  of  minutes* 
duration  in  the  ordinary  day  of  10  hours. 

Gas-llred  Steam-boilers*— Converting  coal  into  gas  In  a  separate 
producer,  before  burning  it  under  the  steam-boiler,  is  an  ideal  method  of 
smoke-prevention,  but  its  expense  has  hitherto  prevented  its  general  intro- 
duction. A  series  of  articles  on  the  subject,  illustrating  a  great  number  of 
devices,  by  F.  J.  Rowan,  is  published  in  the  Colliery  Engineer,  188^90.  See 
also  Clark  on  the  Steam-engine. 

FORCED  COJflBUSTION  IN  STBAH-BOIIjERS. 

For  the  purpose  of  increasing  the  amount  of  steam  that  can  be  generated 
by  a  boiler  of  a  given  size,  forced  draught  is  of  great  importance.  It  is 
universally  used  in  the  locomotive,  the  draught  being  obtained  by  a  steam- 
let  in  the  smoke-stack.  It  is  now  largely  used  In  ocean  steamers,  especially 
In  ships  of  war,  and  to  a  small  extent  m  stationary  boilers.  Economy  of  fuel 
is  generallv  not  attained  by  Its  use,  its  advantages  beine  confined  to  the 
securing  of  increased  capacity  from  a'boller  of  a  given  bulk,  weight,  or  cost. 
The  subject  of  forced  draught  is  well  treated  In  a  paper  by  James  Howden, 
entitled,  ^'Forced  Combustion  In  Steam-boilers'*  (Section  G,  Engineering 
Congress  at  Chicago,  in  1893),  from  which  we  abstract  tlie  following: 

Edwin  A.  Stevens  at  Bordentown,  N.  J.,  in  1837,  in  the  steamer  "North 
America,**  fitted  the  boilers  with  closed  ash-pits.  Into  which  the  air  of  com- 
bustion was  forced  t)y  a  fan.  In  1828  Ericsson  fitted  In  a  similar  manner  tha 
steamer  **  Victory,'*  commanded  by  Sir  John  Ross. 

Messrs.  E.  A.  and  R.  L.  Stevens  continued  the  use  of  forced  draught  for 
a  considerable  period,  during  which  they  tried  three  different  modes  of  using 
the  fan  for  promoting  combustion:  1,  blowing  direct  into  a  closed  ash-pit; 
8,  exhausting  the  base  of  the  funnel  by  the  suction  of  the  fan;  8,  forcing  air 
into  an  air-tight  boiler-room  or  stoke-hold.  Each  of  these  three  methods 
was  attended  with  serious  difficulties. 

In  the  use  of  the  dosed  ash-pit  the  blast-pressure  would  frequently  force 
the  gases  of  combuKtion,  in  the  shape  of  a  serrated  flame,  from  the  joint 
around  the  furnace  doors  in  so  great  a  quantity  as  to  affect  both  tJie  effi- 
ciency and  health  of  the  firemen. 

The  chief  defect  of  the  second  plan  was  the  great  size  of  the  fan  required 
to  produce  the  necessary  exhaustion.  The  size  of  fan  required  grows  in  a 
rapidly  increasing  ratio  as  the  combustion  increases,  both  on  account  of  the 
greater  air- supply  and  the  higher  exit  temperature  enlai^ing  the  volume  of 
the  waste  gases. 

The  third  method,  that  of  forcing  cold  air  by  the  fan  Into  an  air-tight 
boiler-room— the  present  closed  stoke-hold  system— though  it  overcame  the 
difficulties  in  working  belonging  to  the  two  forms  first  tried,  has  serious 
defects  of  its  own,  as  it  cannot  be  worked,  even  with  modern  hitrh-class 
boiler-const  met  ion,  much,  if  at  all,  above  the  power  of  a  good  cninaney 
draught,  in  most  boilers,  without  damaging  them. 

In  1875  John  I.  Thornyeroft  &  Co..  of  Ix>n(lon,  began  the  construction  of 
torpedo-boats  with  boilers  of  the  locomotive  type,  iii  which  a  high  rate  of 
combustion  was  attained  by  means  of  the  air-tight  boiler-room.  Into  which 
air  was  forced  by  means  of  a  fan. 

In  1882  H.B.M.  ships  *' Satellite*'  and  "Conqueror"  were  fitted  with  this 
system,  the  former  being  a  small  ship  of  1500 1.H.P.,  and  the  latter  an  Iron- 
clad of  4500  I.  H.P.  On  the  trials  with  forced  draught,  which  lasted  from  two 
to  three  hours  each,  the  highest  rates  of  combustion  gave  16.9  I.H.P.  per 
square  foot  of  fire-grate  in  the  "  Satellite,"  and  13.41  I.H.P.  in  the  "  Con- 
queror.'* 

None  of  the  short  trials  at  these  rates  of  combustion  were  made  without 
injury  to  the  seams  and  tubes  of  the  boilers,  but  the  system  was  adopted, 
and  it  has  been  continued  in  the  British  Navy  to  this  day  (1898). 

In  Mr.  Howden's  opinion  no  advantage  arising  from  increased  combustion 
over  natural-draught  rates  is  derived  from  using  forced  draught  in  a  closed 
ash-pit  sufficient  to  compensate  the  disadvantages  arising  from  difficulties 


FUEL  ECONOMIZERS.  715 

In  woilcftif;,  there  befng:  either  excessive  emoke  from  bituminous  coal  or 
reduced  eyaporative  economy. 

In  1880  Mr.  Howden  desif^iied  an  arrani^ement  intended  to  overcome  the 
defects  of  both  the  closed  ash-pit  and  closed  stoke-hold  systems. 

An  alr-tifirht  reservoir  or  chamber  is  placed  on  the  front  end  of  the  boiler 
and  surround Inj?  the  furnaces.  This  reservoir,  whicli  projects  from  8  to  10 
Inches  from  the  end  of  the  boiler,  receives  the  air  under  pressure,  which  Is 
passed  by  tlie  valves  into  the  ash-pits  and  over  the  fires  in  proportions 
suited  to  the  kind  of  fuel  used  and  the  rate  of  combustion  required.  The 
air  nsed  above  the-flres  is  admitted  to  a  space  between  the  outer  and  Inner 
furnace-doors,  the  innei*  havinf?  perforations  and  an  air-distributing  box 
throuf^h  which  the  air  passes  under  pressure. 

By  means  of  the  balance  of  air-pressure  above  and  below  the  fires  all 
tendency  for  the  fire  to  blow  out  at  the  furnace-door  is  removed. 

By  regulating  the  admissioji  of  the  air  by  the  valves  above  and  below  the 
flres,  the  highest  rate  of  combustion  possible  by  the  air-pressure  used  can 
be  effected,  and  in  same  manner  the  rate  of  combustion  can  be  reduced  to 
far  below  that  of  natural  draught,  while  complete  and  economical  combus- 
tion at  all  rates  is  secured. 

A  feature  of  the  system  is  the  combination  of  the  heating  of  the  air  of 
combustion  by  the  waste  gases  with  the  controlled  and  regulated  admission 
of  air  to  the  furnaces.  This  arrangement  is  effected  most  conveniently  by 
passing  the  hot  fire-gases  after  they  leave  the  boiler  through  stacks  of 
vertical  tubes  enclosed  in  the  uptake,  their  lower  ends  being  immediately 
above  the  smoke-box  doors. 

Installations  on  Howden's  system  have  hitherto  been  arranged  for  a  rate 
of  combustion  to  give  at  full  sea-power  an  average  of  from  18  to  22  LH.P. 
per  square  foot  of  fire-grate  with  fire-bars  from  5'  0"  to  6'  6"  in  length. 

It  is  believed  that  with  suitable  arrangement  of  proportions  even  80 
LH.P.  per  square  foot  can  be  obtained. 

For  an  account  of  recent  uses  of  exhaust-fans  for  increasing  draught,  see 
paper  by  W.  R  Roney,  Trans.  A.  8.  M.  E.,  vol.  xv. 

FUEIi  ECONOIHIZERS. 

Green'*  Fuel  Economizer.— Clark  gives  the  following  average  re- 
sults of  comparative  trials  of  three  boilers  at  Wigan  used  with  and  without 
economuEers : 

Without  With 

Economizers.    Economizers. 

Goal  per  square  foot  of  grate  per  hour. 21.6  21.4 

Water  at  1W>  evaporated  per  hour 73.55  70.32 

Water  at  212°  per  pound  of  coal 9.60  10.56 

Showing  that  in  burning  equal  quantities  of  coal  per  hour  the  rapidity  of 
evaporation  is  increased  9.3j6  and  the  elHciency  of  evaporation  lOjC  by  the 
addition  of  the  economizer. 

Tlie  average  temperatures  of  the  gases  and  of  the  feed -water  before  and 
after  passing  the  economizer  were  as  follows: 

With  6-ft.  grate.         With  4-ft,  grate. 
Before.   After.  Before.  After. 

Average  temperature  of  gases 649  840  501         8l2 

Average  temperature  of  reed- water.       47  157  41         137 

Taking  averages  of  the  two  grates,  to  raise  the  temperature  of  the  feed- 
water  100°  the  gases  were  cool^  down  250**. 
Performance  of  a  Green  Economizer  irltln  a  Smoky  Coal. 

— ^The  action  of  Green's  Economizer  was  tested  by  M.  W.  Grossetej^te  for  a 
period  of  three  weeks.  The  apparatus  consists  of  four  ranges  of  vertical 
pipes,  6^  feet  high,  3^  inches  Iii  diameter  outside,  nine  pipes  in  each  range, 
connected  at  top  and  bottom  by  horizontal  pipes.  The  water  enters  all  the 
tubes  from  below,  and  leaves  them  from  above.  The  system  of  pipes  is  en- 
veloped in  a  brick  casing,  into  which  the  gaseous  product.s  of  combustion 
are  introduced  from  above,  and  which  they  leave  from  below.  The  pipes 
are  cleared  of  soot  externally  by  automatic  scrapers.  The  capacity  for 
water  is  24  cubic  feet,  and  the  total  external  heating-surface  is  290  square 
feet.  Tlie  apparatus  is  placed  in  connection  with  a  boiler  having  355  square 
feet  of  surface. 

This  apparatus  had  been  at  work  for  seven  weeks  continuously  without 
liaving  been  cleaned,  and  had  accumulated  a  y^-inch  coating  of  soot  and 


716 


TUB  STBSAH^BOILICai 


Mtli,  whMn  itst  perConnaooe,  In  ihm  name  condldov,  wm  ehmrrmi  for  oB0 
week.  Durinfi:  the  second  week  it  was  cleaned  (wice  «v«ry  day;  bul  duriar 
the  third  week,  after  havinir  hevo  cimuied  on  Monday  mominK,  it  aas 
worked  contlnuouidy  without  further  cleaniax.  4- sinoka^makiof?  coal  was 
u«od.    The  eoosumpiioa  was  maintained  sanaibly  oonstant  from  day  to  day. 

Qtmmi'm  EooMoMrzaa.— Rbsultb  or  EKPnaiMCNn  on  vvb  Bfticiehct  as 

ATPaoTKO  ay  tbr  Btatb  op  tbf  Hvbwacz.    (W,  Grosaetesto.) 


Temperature  of  Feed- 
water, 

Temperature  of  Gas- 
eous Produpts. 

(February  and  Marcli). 

Enter- 
ing 
Feed- 
heater. 

Leay- 
ingr 
Feed- 
heater. 

Differ- 
ence. 

Enter- 
heater. 

f125- 
heater. 

Differ- 
ence. 

tot  Week 

M  Week 

Fahr. 
T8.6» 
77.0 
78.4 
78.4 
70.0 
80.6 
80.« 
79.0 

Fahr. 
161.  i« 

aaoo 

196.0 

181.4 
178.0 
170.6 
160  0 
17«.4 

Fahr. 
M.0» 
Itt.O 
1«2.6 
108.0 
09.0 
90.0 
68.4 
98.4 

Fahr. 
849» 

$m 

SB1 

071 

ST 

889 
901 

Fahr. 
i»l» 
WT 

tt4 

800 

829 
868 
»1 

Fahr. 
686* 
MB 

Tuesday 

WedoMday 

Thursday 

Friday 

ftat4irday 

ft47 
608 

•tt 
66t 

660 

1st  Week.  «d  Week.  8d  Week. 

Coal  consumed  per  hour 914  ibs.     916  the.      BIS  lbs. 

Water  evafx>rated  from  «•  F.  per  liour.  .1194  1686  14<8 

Water  per  pound  of  coal 6.66  7.06  6,70 

It  is  apparent  that  theiv  is  a  gnsiX  adrantaise  in  aleaninf^  the  pipes  daiW 
—the  elevation  of  temperature  haviufp  been  increased  by  it  from  88<>  to  15S*. 
In  the  third  week,  without  cleaning,  the  eievatien  of  temperatura  rslapevd 
la  three  days  to  the  level  of  the  flret  weekt  even  on  the  iirst  day  U  was 
quickly  reduced  by  as  nuich  as  half  the  extent  of  relapse.  By  eleanlM  Uie 
pipes  daily  an  increased  elevation  of  temperature  of  65<*  F.,  was  obtained, 
arbllat  a  gala  of  H  was  effected  in  the  evaporative  efficiency. 

INCRUSTATION  ANH  COBBOMON. 

l9&criiat»$|on  »iid  Sc»le*-'-Incrustation  (a^  distinKuisbed  from 
mere  sediments  due  to  dirty  water,  which  ^re  easily  blown  out,  or  jgatfaered 
up,  by  means  of  sediment-collectors)  is  due  to  the  presence  of  salta  in  the 
feed-water  (carbonates  and  sulphates  of  Jime  and  mafnesla  for  the  roA>6t 
part),  which  are  precipitated  when  tlie  water  Is  heated^and  form  hard  de- 
posits upon  the  boiler-plates.    (See  Impurities  in  Water,  p.  661,  ante.) 

Where  the  quantity  of  these  salts  is  not  very  larf^e  (12  {grains  per  gallon, 
say)  scale  pre ven lives  may  be  found  effective.  The  chemical  preventives 
either  form  with  the  salts  otlier  salts  soluble  in  hot  water;  or  preefpttate 
them  in  tlie  form  of  soft  mud,  which  does  not  adhere  to  the  plates,  and  can 
be  washed  out  from  time  to  time.  The  selection  of  the  chemical  mutt  de- 
pend upon  the  composition  of  the  water,  and  it  should  be  Introduced  rc^u- 
Uiri^  with  the  feed. 

EiAMPLBS.— Suiphate-of-lirae  scale  prevented  by  carbonate  of  soda:  The 
sulphate  of  soila  produced  is  sohit)ie  in  water*  and  the  carbonate  of  lime 
falls  down  in  grains,  does  not  adhere  to  the  plates,  and  may  therefore  be 
blown  out  or  gathered  into  sediment-collectors.    The  chemical  reaction  iff: 

Sulphate  of  lirae+Oarbonate  of  eoda  ^  Sulphate  of  soda-4-Carbon<it.^  of  lin>e 
CaS04  Na,CO,  Na,R04  C'aCO, 

Imodium  phosphate  will  decompose  the  sulphatas  of  Ijme  and  niugmwin: 

iSulphat^  of  lime  -f  tZodinm  ptipsphatA}  ^  Calcium  plios.  -f-linlphale  of  eada. 

CaS<)4  Ne,HP(>4  CaHP04  Mrt,?04 

Sul.of  ma(rnesia+ Sodium  phosphate  =  phospliateof  magnesia 4-Su1  of  soda. 
MgS04  NaaHPOi  Mgin»04  Na,l904 


INCRUSTATION  AKP  COBBOSION.  717 

Wbere  tba  quantity  of  galto  <«  IWRe,  code  prerMitiref  are  not  of  miiieh 
ii«e.  Some  otlier  source  of  supply  must  be  80tt«lu,  or  tbe  bad  water  purified 
before  it  is  allowed  to  enter  tbe  boilers.  The  damaj(e  done  to  boilers  by  un- 
suitable water  is  enormous. 

Pure  water  may  be  obtained  by  ooliectinff  rain,  or  oondeniter  steam  by 
means  of  surfooe  condensers.  The  water  thus  obtained  ahoitia  be  mixed 
with  a  little  bad  water,  or  treat/ed  witb  a  little  alkali,  as  undiluted,  pure 
water  corrodes  Iron ;  or,  after  eaeh  periodic  cleaning,  the  bad  may  be  used 
for  a  day  or  two  to  put  a  skin  upon  tbe  piates. 

Carbonate  of  lime  and  maf?oe«a  may  be  precipitated  eitber  by  heatiat;  the 
water  or  by  mbcing  milk  of  liine  (Porter  Clark  proeeas)  with  it,  the  water 
beiuir  then  filtered. 

Corroaioa  may  be  produced  by  the  use  of  pure  water,  or  by  the  presence 
of  acids  in  the  water,  caused  perhaps  io  tbe  eiiRfneK^ylinder  by  the  action  of 
hiirh-presBune  steam  upon  tbe  gresae.  reaultiag  in  tbe  production  of  fatty 
adds.    Acid  water  may  be  neutralised  by  the  addition  of  ihne. 

Awaouat  of  8edlaMB<  which  may  collect  in  a  lOa-H.P.  steam-boiler, 
eraporatins  2000  lbs.  of  water  per  hour,  tbe  water  cootaiaing  dilTerent 
amouDta  of  impurity  ia  solution,  provided  that  no  water  is  blown  off: 

GraiBS  of  soHd  impurities  per  U.  8.  galico: 

6      10      2090      40      t»       eo7oa9«ioo 


£q«iTaletit  parts  per  UiO^WO: 
HM    17.14    84.98   hiA* 


€SM    85.71    10S.85      ISO    197.1    1M,8    171.4 
Sediment  deposited  in  1  hour,  pounds: 

.«7      .m    l.Osae    I.MS     2.056    2.571      8.065    8.8       4«11     4.88     5.14 
In  one  day  of  10  hours,  pounds: 

2jat     &,li    10.28    15.42     20.68    85.71      80.85    86.0     41.1     46.8     61.4 
In  oao  week  of  8  days,  pounds: 
16.tt   80.65    81.7     «2.55    128.4    164.8      185.1    «18.0    M8.8    277.8    808.5 

If  a  100-H.P.  boiler  has  ItKX)  sq.  ft,  heatiog-surface.  one  week's  ruuuing 
witlK»ut  blowing  off.  with  water  eootainiaK  100  grains  of  solid  matter  per 
gallon  la  solwtioD,  would  make  a  scale  nearly  M  f tu  thick,  if  eveoly  depos^ 
ued  all  over  the  beating- surface,  aseusLung  the  eeale  to  have  a  sp.  fpr,  of 


2.5  =s  106  lbs.  par  OU.  ft.;  ^  X  i;^  X  158  X  i/Vi  ^  812 
Assn.  io  1885  reported  as  follows: 


Hoilgr  mtWJm  C4»iBPORMa«^The  BsMrariaa  Steam-boiler  InspeetioQ 


Generally  tbe  unusual  sub&tafioes  in  wator  can  be  retained  la  aoIuUe  form 
or  precipitated  as  mud  by  adding  cauiiitic  soda  or  lime.  This  is  especially 
desli-able  when  the  boilers  have  smalt  interior  apaces. 

It  iM  neceenary  to  have  aclbemical  aBal3'tils  of  the  water  in  order  to  fully 
determine  the  kind  SAd  quantity  of  the  preparaition  to  be  used  for  the 
above  purpose. 

All  secret  compounds  for  removing  boiler-scale  should  be  avoided.  (A  list 
of  27  such  eompeuAds  manufactured  and  aoid  by  <ilermao  firms  is  then  given 
which  have  beea  analysed  by  the  associatiou.) 

Such  secret  preparatiocis  are  either  nonsenEical  or  fraudulent,  or  contain 
either  one  of  tne  two  aubstanoes  reconuneuded  by  the  associatioa  for  re- 
moving scale,  generallv  soda,  wttich  is  cosLored  to  conceal  ita  iireeence,  and 
somettines  adulterated  with  useless  or  even  injurious  matter. 

Theee  additions  as  weU  as  giving  the  cout pound  some  scraage,  faadf  ul 
name,  are  meant  simply  to  deceive  the  boiler  owner  and  conceal  from  kii« 
the  faot  that  he  is  buying  colored  soda  or  similar  aubscanoes,  for  which  he  la 
payingan  exorbitant  price. 

The  CAiicago,  UilwaAikee  &  St.  P.  B.  B.  uses  for  the  prevention  «f  soale  la 
looomotive-boilers  an  alkaline  compound  consisting  of  8750  gals,  of  water. 
2800  Ibe.  of  70)(  caustic  soda,  and  1600  lbs.  of  58jC  soda-asb.  Between  W^wm^ 
kee  and  Maditwin  the  water-supply  contains  from  1  to  4)^  lbs.  of  iiicruatusg 
solids  per  1000  gals.,  prlucipaliy  calcium  carbonate  and  sulphate  and  mag- 
nesiujzi  sulphate.  The  amount  of  compowKl  necesssry  to  preveoi  tlie  in- 
crustation M  IH  to  7  pints  per  1000  gals,  of  water.  This  is  reaUy  only  ioae 
fourth  of  the  quantity  needed  for  chemical  oomhijaatioa,  but  tbe  actioo  of 
the  compound  is  regenerative.  The  soda-ash  (sodium  carbonate)  extracts 
carbonic  acid  from  the  cai^oaaies  of  lime  aa>d  magnesia  and  pi^eeipltates 
them  In  a  granular  form.  Tbe  bicarbonate  of  soda  thus  formed,  however, 
loses  Its  carbonic  acid  by  tbe  heat,  and  is  again  changed  to  the  active  oar- 
honate  torm.    Theoretically  this  action  migut  ooutmue  AttdeOoitely ;  hut  4MI 


718  THE  SfBAM-BOlLEft. 

account  of  the  loss  by  blowfngf  off  and  the  preaence  of  other  Imparities  In 
the  water,  it  is  found  that  the  noda-ash  will  precipltaie  only  about  four 
times  the  theoretical  quantity.  Scaling^  in  entirely  prevented.  One  eneine 
made  122,000  miles,  and  inspection  uf  the  boiler  showed  that  it  was  as  clean 
as  when  new.  This  compound  pi'ecipliates  the  impurities  in  a  srcmular 
form,  and  careful  attention  must  be  paid  to  washing  out  the  precipitate. 
The  practice  is  to  chancre  the  water  every  600  miles  and  wash  out  the  boilf  r 
every  1:200  miles,  usiiifir  the  blow-off  cocks  also  whenever  there  is  any  indica- 
tion of  foaming,  wliich  seems  to  be  caused  by  the  precipitate  in  the  water, 
but  not  by  tlie  alkali  itself.    (ISng'o  News,  Dec.  6,  1891.) 

Kerosene  and  other  Petroleom  Oils  I  Foamlns*— Kerosene 
has  recently  been  highly  recommended  as  a  scale  preventive.  See  paper 
by  L.  F.  Lyne  (Trans.  A.  S.  M.  E.,  ix.  JM7).  The  Am.  Mach.,  Mav  82,  jfeo, 
■ays:  Kerosene  used  In  modeiate  quantities  will  not  make  the  boUer  foam; 
it  is  recommended  and  used  for  loosenine  the  scale  and  for  preventing  the 
formation  of  scale.  Neither  will  a  small  quantity  of  common  oil  always 
cause  foaming;  It  is  sometimes  injected  into  small  vertical  boilers  to  pre- 
vent priming,  and  is  supposed  to  have  the  same  effect  on  the  disturbed  sur- 
face of  the  water  that  oil  has  when  poured  on  tbe  rough  sea.  Yet  oil  in  boilers 
will  not  have  the  same  effect,  and  give  the  desired  results  in  all  cases.  The 
pi-esence  of  oil  in  combination  with  other  impurities  increases  the  tendency 
of  many  boilers  to  foam,a8  the  oil  with  the  impurities  Impedes  the  free  escape 
of  steam  from  the  water  surface.  The  use  of  common  oil  not  only  tends  to 
cause  foaming,  but  is  dangerous  otherwise.  The  grease  appears  to  combine 
with  the  impurities  of  the  water,  and  when  the  boiler  is  at  rest  this  com- 
pound sinks  to  the  plates  and  clings  to  them  in  a  loose,  spongy  mass,  pre- 
venting the  water  from  coming  in  contact  with  the  plates,  and  thereby  pro- 
ducing overhe<iting,  which  may  lead  to  an  explosion.  Foaming  may  also 
be  caused  by  forcing  the  flre.  or  by  taking  the  steam  from  a  point  over  the 
furnace  or  where  the  ebullition  is  violent;  the  greasy  and  dirty  state  of  new 
boilers  is  another  good  cause  for  foaming.  Kerosene  should  k>e  used  at  first 
in  small  quantities,  the  effect  carefully  noted,  and  the  quantity  increased  if 
necessary  for  obtaining  the  desired  results. 

R.  C:.  Carpenter  (Trans.  A.  S.  M.  E..  vol.  zi.)  says:  The  boilers  of  the  State 
Agricultural  College  at  Lansing.  Mich.,  were  badly  Incnisted  with  a  hard 
scale.  It  was  fully  three  eighths  of  an  inch  thick  in  many  places.  The  first 
application  of  the  oil  was  made  while  the  boilers  were  being  but  little  used, 
by  inserting  a  gallon  of  oil,  filling  with  water,  heating  to  the  boiling-poiot 
and  allowing  the  water  to  stand  in  the  boiler  two  or  three  weeks  before 
removal.  By  this  method  fully  one  half  the  scale  was  removed  during  Uie 
warm  season  and  before  the  boilers  were  needed  for  heavy  firing.  The  oil 
was  then  added  in  small  quantities  when  the  boiler  was  in  actual  use.  For 
boilers  4  ft.  in  diam.  and  13  ft.  long  the  best  results  were  obtained  by  the 
use  of  2  qts.  for  each  boiler  per  week,  and  for  each  boiler  S  ft.  In  diam.  3  qts. 
per  week.  The  water  used  in  the  boilers  has  the  following  analysis: 

CaCOi  (carbonate  calcium) 206  parts  In  1,000,000. 

MgCO,  (carbonate  magnesium) 78      "      "         " 

FaCO,  (carbonate  iron) 22      "      "         »• 

Traces  of  sulphates  and  chlorides  of  potash  and  soda. 
Total  solid  parts,  825  to  1,000,000. 

Tannate  of  Soda  Compound.— T.  T.  Parker  writes  to  Am.  Mach.: 

Should  you  flud  kerosene  not  doing  any  good,  try  this  recipe:  50  lbs.  sal-soda, 
85  lbs.  Japonica;  put  the  ingredients  in  a  50-gal.  barrel,  fill  half  full  of  water, 
and  run  a  steam' hose  into  it  until  it  dissolves  and  bolls.  Remove  the  hose, 
fill  up  with  water,  and  allow  to  settle.  Use  one  quart  per  day  of  ten  hours 
for  a40-H.P.  boiler,  and,  if  possible,  introduce  it  as  you  do  cvHnder  oil  to 
your  engine.  Barr  recommends  tannate  of  soda  as  a  remedy  /or  scale  com- 
posed of  sulphate  and  carl>onate  of  lime.  As  the  japonira  yields  the  tannic 
acid,  I  think  the  roKultant  equivalent  to  the  tannate  of  soda. 

Petroleum  Oils  heavier  than  kerosene  have  been  used  with  gootl  re- 
sults. C'rude  oil  should  never  b<^  used.  The  more  volatile  oils  It  contains 
make  explosive  gases,  and  its  tarry  constituents  are  apt  to  form  a  spongy 
incrustation. 

RemoTal  of  Hard  Scale.— When  boilers  are  coated  with  a  hard 
scale  difficult  to  remove  the  addition  of  ^  lb.  caustic  soda  per  horse-power, 
and  steaming  for  some  hours,  according  to  the  thickness  of  the  scale,  just 
before  cleaning,  will  greatly  facilitate  that  operation,  rendering  the  scale 


INCRUSTATION  AND  CORROSION.  TIO 

■oft  and  loone.  This  should  be  done,  if  possible,  when  the  boflers  are  not 
otherwJKe  in  use.    {Steam.) 

Oorroston  In  Marine  Boilers.  (Proc.  Inst.  M.  E.,  Aug.  1884).— The 
inveiitiKationa  of  the  Committ«e  on  Boilers  served  to  show  that  the  internal 
corrosion  of  boilers  is  greatly  due  to  the  combined  action  of  air  and  sea- 
water  when  under  steam,  and  when  not  under  steam  to  the  combined  action 
of  air  and  moisture  upon  tlie  unprotected  surfaces  of  the  metal.  There  are 
other  deleterious  influences  at  work,  such  as  the  corrosive  action  of  fatty 
acids,  the  galvanic  action  of  copper  and  brass,  and  the  Inequalities  of  tem- 
perature; these  latter,  however,  are  considered  lo  l>e  of  minor  importance. 

Of  the  several  methods  recommended  for  protecting  the  internal  surfaces 
of  boilers,  the  three  found  most  effectual  are:  First,  the  formation  of  a 
thin  layer  of  hard  scale,  deposited  by  working  the  boiler  with  sesrwater; 
secopd,  the  coating  of  the  surfaces  with  a  thin  wash  of  Portland  cement, 
particularly  wherever  there  are  signs  of  decay;  third,  the  use  of  zinc  slabs 
suspended  m  tne  water  ana  steam  spaces. 

As  to  general  treatment  for  the  preservation  of  boilers  in  store  or  when 
laid  up  in  the  reserve,  either  of  the  two  following  methods  is  adopted,  as 
may  be  found  most  suitable  in  particular  cases.  First,  the  boilers  are 
dried  as  much  as  possible  by  airing-stoves,  after  which  2  to  3  cwt.  of  quick- 
lime, according  to  the  size  of  the  boiler,  is  placed  on  suitable  trays  at  the 
bottom  of  the  holler  and  on  the  tubes.  The  boiler  is  then  closed  and  made 
as  air-tight  as  possible.  Periodical  inspection  is  made  every  six  months, 
when  if  the  lime  be  found  slacked  it  is  renewed.  Second,  the  other 
method  Is  to  fill  the  boilers  up  with  sea  or  fresh  water,  having  added  soda 
to  it  in  the  proportion  of  1  lb.  of  soda  to  every  100  or  130  lbs.  of  water.  The 
suMciency  of  the  saturation  can  be  tested  by  introducing  a  piece  of  clean 
new  iron  and  leaving  it  In  the  boiler  for  ten  or  twelve  hours;  if  It  shows 
signs  of  rusting,  more  soda  should  be  added.  It  is  essential  that  the  boilers 
be  entirely  filled,  to  the  complete  exclusion  of  air. 

Great  care  is  taken  to  prevent  sudden  changes  of  temperature  in  boilers. 
Directions  are  given  that  steam  shall  not  be  raised  rapidly,  and  that  care 
shall  be  taken  to  prevent  a  rush  of  cold  air  through  the  tubes  by  too  sud- 
denly opening  the  smoke-box  doors.  The  practice  of  emptying  boilers  by 
blowing  out  IS  also  prohibited,  except  in  cases  of  extreme  urgency.  As  a 
rule  th*""  water  is  allowed  to  remain  until  it  becomes  cool  before  the  boilers 
are  emptied. 

Mineral  oil  has  for  many  years  been  exclusively  used  for  internal  lubrica- 
tion of  engines,  with  the  view  of  avoiding  the  effects  of  fatty  acid,  as  this  oil 
does  not  readily  decompose  and  possesses  no  acid  properties. 

Of  all  the  preservative  methods  adopted  in  the  Britisli  service,  the  use  of 
zinc  properly  distributed  and  fixed  has  been  found  the  most  effectual  in 
saving  the  Iron  and  steel  surfaces  from  corrosion,  and  also  in  neutralizing 
by  its  own  deterioration  the  hurtful  influences  met  with  in  water  as  ordina- 
rily supplied  to  boilers.  The  zinc  slabs  now  used  fn  the  navy  boilers  are  Vi 
in.  long,  6  In.  wide,  and  %  inch  thick;  this  size  being  found  convenient  for 
general  application.  The  amount  of  zinc  used  in  new  boilers  at  pres»*nt  is 
one  slab  of  the  above  size  for  every  80  I.H.P.,  or  about  one  square  foot  of 
zinc  surface  to  two  square  feet  of  grate  surface.  Rolled  zinc  is  found  the 
most  suitable  for  the  purpose.    To  make  the  zinc  properly  efflcient  as  a 

Erotector  especial  care  must  be  taken  to  insure  perfect  metallic  contact 
etween  the  slabs  and  the  stays  or  plates  to  which  they  are  attached.  The 
slabs  should  be  placed  in  such  positions  that  all  the  surfaces  in  the  boiler 
shall  be  protectea.  Each  slab  should  be  periodically  examined  to  see  that 
its  connection  remains  perfect,  and  to  renew  any  that  may  have  decayed ; 
this  examination  is  usually  made  at  intervals  not  exceeding  three  months. 
Under  ordinary  circumstances  of  working  these  zinc  slabs  may  be  expected 
to  last  fn  fit  condition  from  sixty  to  ninety  days,  immersed  in  hot  sea- water; 
but  in  new  boilers  they  at  first  decay  more  rapidly.  The  slabs  are  generally 
secured  by  means  of  iron  straps  2  in.  wide  and  %  inch  thick,  and  long 
enough  to  reach  the  nearest  stay,  to  which  the  strap  is  flrnily  attached  by 
screw-bolts. 

To  promote  the  proper  care  of  boilers  when  not  In  use  the  following  order 
has  been  issued  to  the  French  Navy  by  the  Government:  On  board  all  ships 
in  the  reserve,  aa  well  as  those  which  are  laid  up,  the  boilers  will  be  com- 
pletely filled  with  fresh  water.  In  the  case  of  large  boilers  with  large  tubes 
there  will  be  added  to  the  water  a  ceriain  amounts  of  milk  of  lime,  or  a 
solution  of  soda  may  be  used  instead.  In  the  vane  of  tubulous  boilers  with 
small  tubes  milk  of  lime  or  soda  may  be  added,  but  the  solution  will  not  be 


720 


THE  STEAM-BOILER. 


80  fltronff  as  in  the  case  of  the  larger  tube,  so  as  to  avoid  any  danger  of 
contractiDg  the  effective  area  by  deposit  from  the  solution :  but  the  streofcth 
of  the  solution  wili  be  just  sufnclent  to  neutralize  any  acidity  of  the  'nrater. 
{Iron  Age,  Not.  S,  1893.) 

Use  of  Zinc*— Ziiio  is  often  used  In  lK>ilera  to  prevent  the  corrosive 
action  of  water  on  the  metal.  Tlie  action  appears  to  be  an  electrical  one, 
the  iron  being  one  pole  of  the  battei-y  and  the  zinc  being  the  other.  The 
hydrogen  goes  to  tne  iron  shell  and  escapes  as  a  gas  into  the  steam.  The 
oxygen  goes  to  the  zinc. 

On  account  of  this  action  it  is  generally  believed  that  zinc  will  always 
prevent  corrosion,  and  that  It  cannot  be  harmful  to  the  boiler  or  tank. 
Some  expei'iences  go  to  disprove  this  belief,  and  In  numerous  cases  zinc  has 
not  only  h««n  of  no  use,  but  has  even  been  harmful.  In  one  case  a  tubular 
boiler  had  been  troubled  with  a  deposit  of  scale  consisting  chiefly  of  or- 
ganic matter  and  lime,  and  zinc  was  tried  as  a  preventive.  The  beneficial 
action  of  the  zinc  was  so  obvious  that  its  continued  use  was  advised,  with 
frequent  opening  of  the  boiler  and  cleaning  out  of  detached  scale  until  all 
the  old  scale  should  be  removed  and  the  boiler  become  clean.  Eight  or  ten 
months  later  the  water-supply  was  changed,  it  being  now  obtained  from 
another  stream  supposed  to  he  free  from  lime  and  to  contain  only  organic 
matter.  Two  or  three  months  after  its  introduction  the  tubes  and  shell 
were  found  to  be  coated  with  an  obstinate  adhesive  scale,  and  composed  of 
zinc  oxide  and  the  organic  matter  or  sediment  of  the  water  used.  The 
deposit  had  become  so  heavy  in  places  as  to  cause  overheating  and  bulging 
of  the  plates  over  the  Are.    (7V/e  Locomotive.) 

EflTect  of  neposit  on  Fines.  (Rtmkine.)— An  external  crust  of  a 
carbonaceous  kind  is  often  deposited  from  the  flame  and  smoke  of  the  fur- 
naces in  the  flues  and  tubes,  and  if  allowed  to  accumulate  seriouslv  impairs 
the  economy  of  fuel.  It  Is  removed  from  time  to  time  by  means  of  scrapera 
and  wire  brushes.  The  accumulation  of  this  crust  is  the  probable  cause  of 
the  fact  that  in  some  steamships  the  consumption  of  coal  per  indicated 
horse-power  per  hour  goes  on  gradually  increasing  until  it  reaches  one  and 
a  half  times  its  original  amount,  and  sometimes  more. 

nanserouM  Steam-boilers  discovered  hjr  Inspection*— 
The  Hartford  Steam-boiler  Inspection  and  Insurance  Co.  reports  that  its 
inspectors  during  1898  examined  163,^29  boilers,  inspected  66,698  boilers, 
botn  internally  and  externally,  subjected  7861  to  hydrostatic  pressure,  and 
found  597  unsafe  for  further  use.  The  whole  number  of  defects  reported 
was  12*J,893,  of  which  13,390  were  considered  dangerous.  A.  summary  is 
given  below.    {The  Locomotive^  Feb.  1894.) 


SUMILART,  BY  DKTKCTS,  FOR  THE  YkAR  1898. 


Nature  of  Defects. 


Whole    Dan 
No.    gerons. 


Deposit  of  sediment 9,774  MS 

Inci-ustation  and  scale ...  1 8,369  865 

Internal  grooving 1,«49  148 

Int4^rnal  corrosion 6,252  897 

External  corrosion 8,000  536 

DefHive  braces  and  stays  1,966  466 

Settings  defective 8,094  862 

Furnaces  out  of  shape. . .  4,575  254 

Fractured  plates 8,5.32  640 

Burned  plates 2,762  825 

Blist«>red  plates 8,381  164 

Defective  rivets 17,415 

Defective  heads 1,357  S50 


Nature  of  Defects. 


Whole     Dan- 
No.    gerous. 
Leakage  around  tubes. . .  81 .91 1      2,909 

Leakage  at  seams 5,424 

Water-gauges  defective.  8,670 

Blow-outa  defective l,ASO 

Deficiency  of  water  ....  904 
Safety- valves  overloaded  723 
Safety-valves  defective..  942 
Pressure-gauges  def'tive  6,958 
Boilers  without  pressure- 
gauges 115 

Unclassified  defects 75?. 


4^ 

660 
425 
107 
SC3 

aoo 

662 


115 

4 


Total 128,898    19,390 


The  above-named  company  publishes  annually  a  classified  list  of  boiler- 
explosions,  compiled  clileflv  from  newspaper  reports,  showing  that  fix^m 
200  to  300  explosions  lake  place  In  the  United  States  every  year,  killing  fn>m 
200  to  300  persons,  and  injuring  from  300  to  450.  The  lisu  are  not  pretended 
to  be  complete,  and  may  include  only  a  fraction  of  the  actual  number  of 
explosions. 

Steam-boilers  as  Magazines  of  Bxploslve  EnersT.— Prof. 
R.  H.  Thurston  (Trans.  A.  S.  M.  E.,  vol.  vi.).  in  a  paper  with  the  above 
title,  presents  calculations  showing  the  stored  energy  in  the  hot  water  and 
steam  of  various  boilers.  Concerning  the  plain  tubular  boiler  of  the 
form  and  dimensions  adopted  as  a  staudai-d  by  thQ  Hartford  Steam-boiler 


Instirance  Co.,  he  says:  It  Is  60  itiches  in  diameter,  containing  66  8-incb 
tubes,  and  is)  15  feet  long.  It  has  850  feet  of  heatine  and  SO  feet  of  grate 
surface;  is  rated  at  60  horse-power,  but  isoftener  driven  up  to  75;  veiglm 
9500  pounds,  and  contains  nearly  its  own  weight  of  water,  but  only  21 
pounds  of  steam  when  under  a  pressure  of  75  pounds  per  square  inch, 
which  is  below  its  safe  allowance.  It  stores  52,000,000  foot-  pounds  of  en- 
ergy, of  which  but  4  per  cent  is  in  the  steam,  and  tliia  is  enough  to  drive 
the  boiler  Just  about  one  mile  into  the  air,  with  an  Initial  velocity  of  nearly 
600  feet  per  second. 

SAFBTY-TAI«TBS. 

Oaleulatloii  of  freight,  etc.,  for  liOTor  Safety-TalTes* 

Let  W  =  weight  of  hall  at  end  of  lever,  in  pounda; 
w  =  weight  of  lever  itself,  in  pounds; 
V  =  weight  of  valve  and  spindle,  in  pounds; 
Z  =  distance  l>etween  fulcrum  and  centre  of  ball,  in  inches; 
i  =       "  **  **  "        *'       "  valve,  in  inches; 

p  =       "  "  «'  '*        "       "  gravity  of  lever,  in  in.; 

A  —  area  of  valve;  in  square  Ipches; 
J*  s=  pressure  of  steam,  in  lbs.  per  sq.  in.,  at  which  valve  will  open. 

Then    PAXl=  W  X  L  +  wXO  +  Vxli 
whence   P= ai      — • 


IT: 


PAl  ^  tog -VI 
L 


-       PAl^  teg  -  VI 
X.=  ^ . 

BzAMPLs.— Diameter  of  valve,  i";  distance  from  fulcrum  to  centre  of  ball. 
86";  to  centre  of  valve,  4";  to  centre  of  gravity  of  lever,  16^"s  weight  of 
valve  and  spindle,  8  lbs.;  weight  of  lever,  7  lbs.:  required  the  weight  of  ball 
to  make  the  bio  wing-off  pressure  80  lbs.  per  sq.  in.;  area  of  4''  valve  ss  IHBM 
sq.  in.    Then 

_,      PAl-tog^  n       80  X  12.566  X  4  ->  7  X  15^^  -  8  X  4  _,^  ^  ,^„ 
ir= j^ =  ~ 108.4  lbs. 

The  following  rules  governing  the  proportions  of  lever- valves  are  given  by 
the  U.  S.  Supervisors.  The  distance  from  the  fulcrunl  to  the  valve-stem 
must  in  no  case  be  less  than  the  diameter  of  the  valve-opening;  the  length 
of  the  lever  must  not  be  more  than  ten  times  the  distance  from  the  fulcrum 
to  the  valve-stem;  the  width  of  the  bearings  of  the  fulcrum  nmst  not  be 
less  than  three  quarters  of  an  inch;  the  length  of  the  fulcrum-link  must  not 
be  less  tban  four  Inches;  the  lever  and  fulcrum-link  must  be  made  of 
wrought  iron  or  steel,  and  the  knife-edged  fulcrum  points  and  the  bearings 
for  these  points  must  be  made  of  steel  and  hardened;  the  valve  must  be 
guided  by  its  spindle,  both  above  and  below  the  gi'ound  seat  and  above  the 
lever,  through  supports  either  made  of  composition  (gun-metal)  or  bushed 
with  it;  and  the  spindle  must  fit  loosely  in  the  bearings  or  supports. 

Rules  for  Area  of  Safety-TalveB. 

(Rule  of  U.  S.  Supervishig  Inspectors  of  Steam -vessels  (as  amended  1891).) 

Lever  safety-valves  to  be  attached  to  marine  boilers  shall  have  an  area  of 

not  lees  than  1  sq.  in.  to  2  sq.  ft.  of  the  grate  surface  in  the  boiler,  and  the 

seats  of  all  such  safety-valves  sliall  have  an  angle  of  inclination  of  45"  to  the 

centre  line  of  their  axes. 

Spring- loaded  safety-valves  shall  be  required  to  have  an  area  of  not  less 
than  1  sq.  in.  to  3  sq.  ft.  of  grate  surface  of  the  boiler,  except  as  hereinafter 
otherwise  provided  for  water-tube  or  coil  and  sectional  boilers,  and  each 
spring- loaded  valve  shall  be  supplied  with  a  lever  that  will  raise  the  valve 
from  its  seat  a  distance  of  not  less  than  that  equal  to  one  eighth  the  diam* 
eter  of  the  valve-opening,  and  the  seats  of  all  such  safety-valves  shall  have 
an  angle  of  inclination  to  the  centre  line  of  their  axes  of  46».  All  spring- 
loadea  safety-valves  for  water-tube  or  coil  and  sectional  boilers  required  to 


I^i  TItfi  StfiAM-BOlLBB. 

carrj  a  steam -pressure  exceeding  ITS  lbs.  per  square  inch  shall  be  required 
to  have  an  area  of  not  less  than  1  sq.  in.  to  6  sq.  ft.  of  the  grate  surface  of 
the  boiler.  Nothing  herein  shall  be  construed  so  as  to  prohibit  ihe  use  of 
two  safety -valves  on  one  water- tube  or  coil  and  sectional  boiler,  provided 
the  combined  area  of  such  valves  is  equal  to  that  required  by  rule  for  one 
such  valve. 

Rnle  In  Phlladclplila  Ordinances  i  Bnreao  of  Steam* 
engine  and  Boiler  inspection.— Every  boiler  when  fired  sepa- 
rately, and  every  set  or  series  of  boilers  when  placed  over  one  fire,  shall 
have  attached  thereto,  without  the  interposition  of  any  other  valve,  two  or 
more  safety-valves,  the  aggregate  area  of  which  shall  have  such  relations  to 
the  area  of  the  grate  and  the  pressure  within  the  boUer  as  is  ezpreased  in 
schedule  A. 

ScHBDULB  A.— Least  aggregate  area  of  safety-valve  (being  the  least  sec- 
tional area  for  the  discharge  of  steam)  to  be  placed  upon  all  stationary  boil- 
ers with  natural  or  chimney  draught  [see  note  a]. 

28.5g 

in  which  A  is  area  of  combined  safety-valves  in  inches;  O  Is  area  of  grate  in 
square  feet;  P  is  pressure  of  steam  in  pounds  per  square  inch  to  be  carried 
iu  the  boiler  above  the  atmosphere. 

The  following  table  gives  the  results  of  the  formula  for  one  square  foot  of 
grate,  as  applied  to  boilers  used  at  different  pressures: 

Pressui-es  per  square  inch: 

10       20       80       40       60       60       70       80       90       100       110       120 

Area  corresponding  to  one  square  foot  of  grate: 
1.21    0.79    0.58    0.40    0.38    0.83    0.29    0.25    0.28     0.21     0.19     0.17 

[Note  a.]  Where  boilers  have  a  forced  or  artificial  draught,  the  inspector 
roust  estimate  the  area  of  grate  at  the  rate  of  one  square  foot  of  grate-sur- 
face for  each  16  lbs.  of  fuel  burned  on  the  average  per  hour. 

Comparison  of  Tarlons  Rales  for  Area  of  I^ever  Saitoty- 
Talves.  (From  an  article  by  ilie  author  in  American  Machinist,  Hay  *^4, 
1894,  with  some  alterations  and  additions.)— Assume  the  case  of  a  boiler 
rated  at  100  hoi-se-power;  40  sq.  ft.  grate;  ViOO  nq.  ft.  heating-surface;  using 
400  lbs.  of  coal  per  hour,  or  10  n)s.  per  sq.  ft.  of  grate  per  hour,  and  evapora- 
ting 3600  lbs.  of  water,  or  8  lbs.  per  sq.  ft.  of  heating-surface  per  hour; 
steam-pressure  by  gauge,  100  lbs.  What  size  of  safety-valve,  of  the  lever 
type,  should  be  requii-ed  ? 

A  compilation  of  various  rules  for  finding  the  area  of  the  safety-valve  disk, 
from  Hie  Locomotive  of  July,  189a,  Is  given  in  abridged  form  below,  to- 
gether with  the  area  calculated  by  each  rule  for  the  above  example. 

Disk  Area  in  aq.  iiL 

U.  S.  Supervisors,  heating-surface  in  sq.  ft.  •+■  25* 48 

English  Board  of  Trade,  grate-surface  in  sq.  f t.  h-  2 20 

Moiesworth,  four  fifths  of  grate-surface  in  sq.  ft 82 

Thurston,  4  times  coal  burned  per  hour  x  (gauge  pressure  -J- 10) 14.5 

Thuraton.  >  (»  X  heating-gurface) 

2  firauge  pressure  +10 

Rankine,  .006  x  water  evaporated  per  hour 21.6 

Committee  of  U.  S.  Supervisors,  .005  x  water  evaporated  per  hour 18 

Suppose  that,  other  data  remaining  the  same,  the  draught  were  Increased 
so  as  to  burn  \Z%  lbs.  coal  per  square  foot  of  grate  per  hour,  and  the  grate- 
surface  cut  down  to  80  sq.  ft.  to  correspond,  making  the  coal  burned  per 
hour  400  lbs.,  and  the  water  evaporated  8600  lbs.,  the  same  as  before;  then 
the  EngliKh  Board  of  Trade  rule  and  Moiesworth *s  rule  would  give  an  area 
of  disk  of  only  15  and  24  sq.  in.,  respectively,  showing  the  absurdity  of  mak- 
ing the  area  of  grate  the  basis  of  the  calculation  of  disk  area. 

Another  rule  by  Prof.  Thurston  is  given  in  American  Machinist.  Dec  ISTT, 
viz.: 

Disk  area  =  ^  '"*^-  ^'  °-  !^^^£L£1»P:  P^r  hour 
gauge  pressure  -f  10 
Tliis  gives  for  the  example  considered  16.4  sq.  In. 

♦  The  edition  of  1»)3  of  the  Uules  of  the  Supervisors  does  not  contain  \hm 
rule,  bub  gives  the  rule  grate-surface  ■*-  2. 


SAPETT-TALrBS,  723 

One  rule  by  Rankitie  Ib  1/1 80  to  1/180  of  the  nnmber  of  pounds  of  water 
RTaporated  per  hour,  equalH  for  the  above  case  27  to  aO  sq.  m.  A  coinmuni- 
taon  in  Powtrr^  July,  1890.  Kives  two  other  rules: 

Ist.  1  8q.  ni.  disk  area  for  8  sq.  ft.  gvAie,  which  would  glre  18.3  sq.  in. 

2d.  H  w]-  in*  disk  area  for  1  8q.  ft.  grate,  which  would  give  80  sq.  in.;  but 
if  the  grate-surface  were  reduced  to  80  sq.  ft.  on  account  of  Increased 
draught,  these  rules  would  make  the  disk  area  only  10  and  22.5  sq.  in., 
respectively. 

The  Philadelphia  rule  for  100  lbs.  gauge  pressure  gives  a  disk  area  of  0.21 
sq.  in.  for  each  «q.  ft.  of  grate  area,  which  would  give  an  area  of  8.4  sq.  in. 
fur  40  sq.  ft.  grate,  and  only  6.3  sq.  in.  if  the  grate  is  reduced  to  30  sq.  ft 

Accoraing  to  the  rule  this  aggregate  area  would  have  to  be  divided  between 
two  valves.  But  if  the  boiler  was  driven  by  foi-ced  draught,  then  the  in- 
spector **  must  estimate  the  area  of  grate  at  1  sq.  ft.  for  each  16  lbs.  of  fuel 
burned  per  hour." 

Under  this  condition  the  actual  grate-surface  might  be  cut  down  to  400  -i- 
16  =  25  sq.  ft.,  and  by  the  rule  the  combined  area  of  the  two  safety-valves 
would  be  only  25  X  0.21  =  5.25  sq.  In. 

Nystrom's Pocket-book,  edition  of  1691.  gives  9^  sq.  in.  for  1  sq.  ft.  grate; 
also  quoting  from  Weisbach,  vol.  ii,  1^3000  of  the  heating-surface.  This  in 
the  case  considered  is  1200/3000  =  .4  sq.  ft.  or  57.6  sq.  in. 

We  thus  have  rules  which  give  for  the  ar»*a  of  safety-valve  of  the  same  100- 
horse-power  boiler  results  ranging  ail  the  way  from  5  25  to  67.6  sq.  in. 

All  of  the  rules  above  quoted  give  the  area  of  the  disk  of  the  valve  as  the 
thing  to  be  ascertained,  and  it  is  this  area  which  is  supposed  to  bear  some 
direct  ratio  to  the  gi-ate-surface,  to  the  heating-surface,  to  the  water  evap< 
orated,  etc.  It  is  dtfRcult  to  see  why  this  area  lias  been  considered  even 
approximately  proportional  to  these  quantities,  for  with  small  lifts  the  area 
of  actual  opening  Dears  a  direct  ratio,  not  to  me  area  of  disk,  but  to  the 
circumference. 

Thus  for  various  diameters  of  valve : 

Diameter 1         2  8  4  '>  6  7 

Area 785      8.14      7.07      12.67       ia.64       2a27     88.48 

Circumference 8.14       6.28     9.42     12.57       15.71        18.85     21.99 

Circum.  X  lift  of  0.1  in 81  .68        .94        1.2&         1.57         1.89       2.20 

liatiotoarea 4  .2         .18         .1  .08  .067       .057 

The  apertures,  therefore,  are  therefore  directly  proportional  to  the  diam- 
eter or  to  the  circumference,  but  their  relation  to  the  area  is  a  varying  one. 

If  the  lift  =  )4  diameter,  then  the  opening  would  be  equal  to  the  area  of 
the  disk,  for  circumference  X  14  diameter  =  area,  but  such  a  lift  is  fai* 
beyond  the  actual  lift  of  an  ordinary  safety-valve. 

A  correct  rule  for  size  of  safety-valves  should  make  the  product  of  the 
diameter  and  the  lift  proportional  to  the  weight  of  steam  to  be  discharged. 

A  ** logical"  method  for  calculating  the  size  of  safety-valve  is  given  in 
The  Locomotive,  July,  1892,  ba>«d  on  the  assumption  that  the  actual  opening 
should  be  sufficient  to  discharge  all  the  steam  generated  by  the  boiler. 
Napier*s  rule  for  flow  of  steam  is  taken,  viz.,  flow  through  aperture  of  one 
8C|  in.  in  lbs.  per  second  =  absolute  pressure  -+-  70,  or  in  lbs.  per  hour  =  51.-i3 
X  absolute  pressure. 

If  the  angle  of  the  seat  is  45*,  as  specified  in  the  rules  of  the  U.  S.  Buper- 
visors,  the  area  of  opening  in  sq.  in.  =  circumference  of  the  disk  X  the  lift 
X  .71,  .71  being  tiie  cosine  of  45o;  or  diameter  of  disk  X  lift  X  2.23. 

A.  O.  Brown  in  his  book  on  The  Indicator  and  Its  Practical  Working 
(Lundon,  1894)  gives  the  following  as  the  lift  of  the  ordinary  lever  safety- 
valve  for  100  lbs.  gauge-pressure: 

Diam.  of  valve..      2       2^^       8       8^       4       4^       6         6     inches. 
Rise  of  valve 0588  .0523  .0507  .0492  .0478  .04(>2  .0416  .0430  inch. 

The  lift-  decreases  with  increase  of  steam -pressure;  thus  for  a  4-inch  valve: 
Abs.  pressure,  lbs.  45  65  85  105  115  135  156  175  195  215 
Gauge-press.,  Ibfl..  SO  50  70  90  100  120  140  160  180  200 
Rise,  inch 1034  .0775  .0620  .0617   .0478  .0413  .0385  .0827  .0296  .0270 

The  effective  area  of  opening  Mr.  Brown  takes  at  70^  of  the  rise  multiolied 
by  the  circimiference. 

An  approximate  formula  corresponding  to  Mr.  Brown's  figures  for  diam- 
eters between  2^  and  6  in.  and  gauge-pressures  between  70  and  200  lbs.  Is 

Lift  =  (.0808  -  OOSld)  X  -j — ^- .  in  which  d  =  dUm.  of  vajve  in  ift. 

at)s.  pressure 


724 


THB  STEAM-BOILER. 


If  we  combine  this  formula  with  the  formiitn 

Flow  in  lbs.  per  hour  =>  area  of  opeuini?  io  sq.  Id.  X  51.43 x  abs.  preamire,  and 

Area  =  diameter  of  valve  X  lift  X  :2.^.  we  obtain  the  foHowioir,  which  tiM 
author  suffgetits  ai  probably  a  more  correct  formula  for  the  diacharsring 
c&pacity  of  tlie  ordinary  lever  safety -valre  than  either  of  those  above  f^iven. 

Flow  iD  lbs.  per  hour  b  d(.0008  ^  .OOSld)  X  115  X  &.3A  X  5L4S  s  d(795  —  4]d). 

From  which  we  obtain  : 
Diameter,  inches....     11^2       3Ud«,4(4        5         6         7 
Flow,  lbs.  per  hour..  7S4    1100    1430    1?S    9016    »S    2SS4    2950    8994    8S5< 

Hone-power 85      87       47       68       9r       7t)       84       98      110      119 

the  hone-power  being  taken  as  an  evaporation  of  30  lbs.  of  water  per  hour. 

If  we  solve  the  example,  above  eiven,  of  the  boiler  evaporattog  8600  lbs.  of 
water  per  hour  by  this  table,  we  find  It  requires  one  7-inch  valve,  or  a  2^ 
and  a  8-Inch  valve  combined.  Tlie  7-inch  valve  has  an  area  of  .%.5  sq.  in., 
and  the  two  smaller  valves  taken  toeether  have  an  area  of  only  IS  sq.  In.; 
another  evidence  of  the  absurdity  of  considering  the  area  of  diak  as  the 
factor  which  determined  the  capacity  of  the  valve. 

It  is  customary  in  practice  not  to  use  safety-valves  of  greater  dJamster 
than  4  in.  If  a  greater  diameter  Is  called  for  by  the  rule  that  is  adopted, 
then  two  or  more  valves  are  used  Instead  of  one. 

Mprinff-loaded  Safe ty-valves.— Instead  of  weights,  springs  are 
somtftimes  employed  to  hold  down  safety-valves.  Ihe  calculations  am 
similar  to  those  for  lever  safety-valves,  the  tension  of  the  spring  oorreeoond- 
inr  to  a  given  rise  being  fint  found  by  experiment  (see  Springs,  page  947). 

The  rules  of  the  tJ.  S.  Supervisors  allow  an  area  of  1  sq.  in.  of  the  valve 
to  8  sq.  ft.  of  grate,  in  the  case  of  spring-loaded  valves,  except  in  water*tube, 
coll,  or  sectional  boilers,  in  which  1  sq.  In.  to  6  sq.  ft  of  gi*ate  is  allowed. 

Spring-loaded  safety-valves  ai*e  usually  of  the  reactionary  or  "  pop  "  type. 
In  which  the  escape  of  the  steam  is  opposed  by  a  lip  above  the  vaiTe-aeat. 
agaiust  which  the  escaping  steam  reacts,  causing  the  valve  to  lift  higher 
than  the  ordinary  valv«. 

A.  Q.  Brown  gives  the  following  for  the  rise,  effective  area,  and  quantity 
of  steam  discharged  per  hoar  by  valves  of  the  "  pop  "  or  Richardson  type. 
The  effective  is  taken  at  only  50%  of  the  actual  area  due  to  the  rise,  on  account 
of  the  obstruction  which  the  Up  of  the  valve  offere  to  the  escape  of  steam. 


Dia.  value,  in 
Lift,  Inches. 
Area,  sq.  In. 

1 
.125 
.196 

.854 

2 

.173 
.550 

,785 

3 
.225 
1.061 

1.875 

4 

.275 
1.728 

.1^ 

2.121 

6 
.325 
8.658 

6 
.875 
3.635 

Qauge-pres., 

Steam  dis 

L'harged  per  houi",  lbs. 

flOlbs. 

60 

70 

90 
100 
180 
140 
160 
ISO 
200 

474 
660 
861 
1050 
1144 
1332 
1516 
1696 
1883 
2062 

856 
1800 
15A6 
1897 
«065 
2405 
2738 
3C64 
8400 
3724 

1380 
1878 
2417 
2947 
3206 
3786 
42&4 
4760 
5288 
6786 

1897 
2680 
8450 
4207 
4580 
6882 
6070 
6794 
7W0 
8258 

2668 
8620 
4660 
6680 
6185 
7202 

9175 
10180 
11150 

8825 
4695 
6144 
7870 
8828 
9342 
10635 
11900 
18260 
14465 

4178 
5901 
7596 
9260 
10080 
11785 
13365 
14956 
16596 
18175 

5188 
7842 
9384 
11866 
1S875 
14410 
16405 

im& 

20870 
82810 

6178 
8718 
11820 
18665 
14805 
17340 
19745 
88096 
245«) 
86855 

8678 
12070 
16685 

18046 
80625 
M0I5 
87810 
8KV95 
88K0 
37185 

If  we  take  30  lbs.  of  steam  per  hour,  at  100  lbs.  gauge-pressure  =  1  H.P., 
we  have  from  the  above  table: 

Diameter,  inches...    1    1^     2     2U     8     3U     4     4U     5       6 

Horse-power 88    69    107    158    206    277    886    418    496    687 

A  safety-valve  should  be  capable  of  discharging  a  much  greater  quantitv 
of  steam  than  that  corresponding  to  the  rated  horse- power  of  a  boiler,  since 
a  boiler  having  ample  grate  surface  and  strong  draught  may  generate  more 
than  double  the  quantity  of  steam  its  rating  calls  for. 

The  Consolidated  Safetv- valve  Oo.'s  circular  gives  the  following  rated 
capacity  of  its  nickel-seat  ^*  pop  "  safety-valves: 

Size,  In     ....     1      IH    ^H      2      S^      8       SU       4       4U       5       SU 

Boiler  i  from     8      10     20     85     60      76      100     186     160     176     200 

n.P.  ]       to    10      16     80     60     75      100      186      160      176      800     27^ 

The  figures  in  the  lower  line  from  2  inch  to  6  Inch^inoluaive,  oorrespood  to 

the  formula  H.P.  =  90(dlameter  -  I  inch). 


THB  INJECTOR. 


725 


THB   INJBGTOR. 

Equation  of  the  Injeetor* 

Let  5  be  the  trnmbei*  of  pounds  of  steam  used ; 

W  Che  number  of  pouods  of  water  lifted  and  forced  Into  the  boiler; 
h  the  height  In  feet  of  a  column  of  water,  equivalent  to  the  absolute 

pressure  in  the  boiler; 
Ag  the  helfifht  in  feet  the  water  Is  lifted  to  the  injector; 
ii  the  temperature  of  the  water  before  it  enters  the  injector; 
f,  the  temperature  of  the  water  after  leaving  the  injector; 
B  the  total  heat  above  Z2^  F.  In  one  pound  of  steam  in  the  boiler,  in 

heat-tmits: 
L  the  lost  work  in  friction  and  the  equivalent  lost  M-ork  due  to  radia- 
tion and  lost  heat; 
778  the  mechanical  equivalent  of  heat. 
Then 

aiH  -  (,. .  «.,) .  mf,  - 1.)  +  <^+^'>  +  ^t  +  ^. 

All  equivalent  formula,  neglecting  Wh^  -f  X,  as  small,  Is 


[wih- 


fO  + 


w+s 


p 


1441 


1 


(t,  -  a**/ 


^  -  1/  -Uj  -  sa^yd  -  .I85ip* 


In  which  d  =  weight  of  1  cu.  ft.  of  water  at  temperature  U\  p  =  absolute 
pressure  of  steam,  lbs.  per  sq.  in. 

The  rule  for  finding  the  proper  sectional  area  for  the  narrowest  part  of 
the  noszles  is  given  as  follows  by  Rankine,  8.  E.  p.  477: 

Are*  to  «qu»re  Iddhes  =  «'""°  f^  PgL"""^  g-^  teedwgtgr. 
800  Vp>'es8ure  in  atmospheres 

An  important  condition  which  mtist  be  fulfilled  in  order  that  the  Injector 
will  work  is  that  the  supply  of  water  must  be  sufficient  to  condense  the 
steam.  As  the  temperature  of  the  supply  or  feed -water  is  higher,  the 
amount  of  water  re<]uired  for  condensing  purposes  will  l>e  greater. 

Tlie  table  below  nves  the  calculated  value  of  the  mazimuin  ratio  of  water 
to  the  steam,  and  the  values  obtained  on  actual  trial,  also  the  highest  adniis- 
sitile  temperature  of  the  feed-water  as  shown  by  theory'  and  the  highetit 
actually  found  by  trial  with  several  injectors.  


Oaoge- 
pres- 
sure. 

ponnae 

8q.  in. 


]0 
20 
80 
40 
&0 
80 
TO 
00 
90 
100 


Maximuic  BATto  Water 
TO  Stsam. 


Calculated 

from 

Theory. 


Actual  Expe* 
riment. 


36.5 

25.6 

80.0 

17.87 

16.2 

14.7 

18.7 

12.9 

12.1 

11.5 


H.     P.      M. 


80.9 
22.5  19.0 
lQ.Oir.2 
15.8  15.0 
13.3  14.0 

11.2  11.2 

12.3  11.7 

11.4  11.2 


21.5 

19.0 

15.86 

13.3 

12.6 

12.9 


Gauge 
pre»- 
8ure« 

pounds 

per 
sq.  In. 


Maximum  Tempsraturb  of 
Fi£ED- Water. 


Theoretical. 

Experi'tal  Rei 

4- 

If 

H. 

P. 

H. 

u^' 

"iT8« 

135* 

i-io* 

iao* 

182 

162 

126 

156 

140 

lis 

19» 

120 

150 

.... 

, ,  , 

114 

143 

115 

128 

109 

139 

141* 

128 

105 

134 

141* 

118 

122 

99 

129 

• .  • 

. . .  > 

95 

125 

.... 

87 

117 

. .  • .  • 

77 

107 

.... 

.... 

13>« 

134 

134 

132 

181 

ISO 

130 

131 

182* 

132* 

134* 

121* 


♦  temperature  of  delivery  above  212'>.    Waste-valve  closed. 
H,  Hancock  inspirator;  P,  Park  injector;  M,  Metrooolitan  injector;  S,  8el» 
lers  1876  injector. 


726  THE  STEAM-BOILEE, 

EffleleneT  of  tlie  Injector.— Experiments  at  Cornell  UnfTersity, 
described  by  Prof.  R.  C.  (.Iarp«nter,  in  CtinHier^s  MaQOZine^  Feb.  18W,  show 
that  the  injector,  when  considered  merely  as  a  pump,  has  an  exceedini^ly 
low  efficiency,  the  duty  ranjfin^  from  161,000  to  ;i,752.000  under  differeDt  cir- 
cumstances  of  steam  and  delivery  pressure.  Small  dlrect-Acting  pumps, 
such  as  are  used  for  feedin^^  IxiilerR,  show  a  duty  of  from  4  to  8 
million  11m  ,  and  the  best  puinping-enKines  from  100  to  140  million.  When 
used  for  feeding  water  into  a  ooller,  however,  the  injector  has  a  thermal 
efficiency  of  10^,  less  the  trlflini?  loss  due  to  radiation,  since  all  the  heat  re- 
jected passes  inU)  the  water  wiiich  is  carried  into  the  boiler. 

The  loss  of  work  in  the  injector  due  to  friction  reappeai-g  as  heat  which  is 
carried  into  the  boiler,  and  the  lieat  which  is  converted  into  useful  work  in 
the  injector  appears  in  the  boiler  as  stored-upenergy. 

Although  the  injector  thus  has  a  perfect  efficiency  as  a  boiler-feeder.  It  is 
nevertheless  not  the  most  economical  means  for  feeding  a  boiler,  since  ii 
can  draw  only  cold  or  moderately  warm  water,  while  a  pump  can  feed 
water  which  has  been  heated  by  exhaust  steam  which  would  otherwise  be 
wasted. 

Performance  of  InJectors.~In  Am,  Mach.^  April  13,  1808,  are  a 
number  of  letters  from  diffei-ent  manufacturers  of  injectors  in  reply  to  the 
question:  "  What  is  the  best  performance  of  the  injector  in  raising  or  lifting 
water  to  any  height  ?''    Some  of  the  replies  are  tabulated  below. 

W.  Sellers  &  Co.— 25.51  lbs.  water  delivered  to  boiler  per  lb.  of  steam;  tem- 
perature of  water.  64" ;  steam  pressure,  66  lbs. 

Schaeffer  &  Budenberg— 1  gal.  water  delivered  to  bolle-  for  0.4  to  0.8  lb. 
steam. 

Injector  will  lift  by  suction  water  of 

140*  F.         188*  to  188«     !««•  to  118»      11S»  to  107* 
If  boiler  pressure  is .  80  to  60  ll)s.    60  to  00  lbs.    90  to  190  lbs.    VJQ  to  150  lbs. 

If  the  water  is  not  over  80**  F.,  the  injector  will  fore?  against  a  pressure  75 
lbs.  higher  than  that  of  the  steam. 
Hancock  Inspirator  Co. : 

Liftlnfeet 22 

Boiler  pressure,  absolute,  lbs 75.8 

Temperature  of  suction 84. 9» 

Temperature  of  delivery 134® 

Water  fed  per  lb.  of  steam,  lbs. . .    1 1 .02 

The  theory  of  the  Injector  is  discussed  in  Woml's,  Peabody*s,  and  Ront- 
gen's  treatises  on  Thermodynamics.  See  also  "  Theory  and  Practice  of  the 
InWt<jr,"  by  Strickland  L.  Kneass,  New  York,  1895. 

Boller-feedlns  Pumps.— Since  the  direct-acting  pump,  commonly 
used  for  feeding  lK)ilei-s,  has  a  very  low  efficiency,  or  less  than  one  tenth 
that  of  a  good  engine,  it  is  generally  better  to  use  a  pump  driven  by  belt 
from  the  main  engine  or  driving  sliaft.  Ths  mechanical  work  needed  to  feed 
a  boiler  may  be  estimated  as  follows:  If  the  combination  of  boiler  and  en- 
gine is  such  that  iialf  a  cubic  foot,  say  32  lbs.  of  water,  is  needed  per  home- 
power,  and  the  boiler-pressure  is  100  lbs.  per  sq.  in.,  then  the  work  of  feed- 
ing the  quantity  of  water  is  100  lbs.  X  144  sq.  in.  X  ^  ft. -lbs.  per  hour  =  120 
ft.-lbs.  per  min.  =  120/33,000  =  .0036  H.P.,  or  less  than  4/10  of  \%  of  the 
power  exerted  by  the  engine.  If  a  direct-acting  pump,  which  dischanres  lis 
exhaust  steam  into  the  atmosphere,  is  used  for  feeding,  and  it  has  only  1/10 
the  efficiency  of  the  main  engine,  then  the  steam  used  by  the  pump  will  be 
equal  to  nearly  4%  of  that  generated  by  the  boiler. 

The  following  table  by  Prof.  1).  S.  Jacobus  gives  the  relative  efficiency  of 
steam  and  power  pumps  and  injector,  with  and  without  heater,  as  used 
upon  a  boiler  with  80  lbs.  gauge-pressure,  the  pump  having  a  duty  of 
1(3,000,000  ft.-lbs.  per  100  lbs.  of  coal  when  no  heater  is  used ;  the  injector 
heating  the  water  from  60*  to  150"  F. 

Direct-acting  pump  feeding  water  at  60<>,  without  a  heater 1 .000 

Injector  ft»eding  water  at  150*.  without  a  heater 065 

Injector  feeding  water  through  a  heater  lu  which  It  is  heated  from 

150°to200«» 988 

Direct-acting  pump  feeding  water  through  a  heater,  in  which  It  is 

lieated  from  60*  to  200* 879 

Geai'ed  pump,  run  from  the  enf^ine,  feeding  water  through  a  heater, 

in  wiiich  it  is  heated  from  60°  to  200« 888 


28 

22 

11 

64.1 

95.6 

75.4 

85.4» 

47.8« 

5S.2- 

117. 4» 

178.7» 

131.1 

13.67 

8.18 

18.8 

FEED-WATER  HEATEBS. 


FBBD-Hr ATBR  HBATBRS. 

Percentage  of  Savlna:  for  Bacli  Beeree  of  Inereaiie  tn  Tem- 
perature of  Feed-water  Heated  bjr  lATaete  Steam, 


Tnitial 

Temp. 

of 

Pressure  of  Steam  In  Boiler,  lbs.  per  sq.  In.  above 

Atmosphere. 

Initial 
Temp. 

1    '         ' 

Feed. 

0 

20 

40 

60 

80 

100 

120 

140 

IGO 

180 

200 

3y» 

.0872 

.0861 

.0855 

.0851 

.0647 

.0844 

.0841 

.0830 

.0837 

.0835 

.0833 

82 

40 

.0678 

.0867 

.0661 

.oaw 

.0853 

.0860 

.0847 

.0845 

.0843 

.0641 

.0839 

40 

60 

.0886 

.0875 

.0868 

.0864 

.0660 

.0867.0854 

.oav2 

.0850 

.0648 

.0846 

60 

60 

.0894 

.0888 

.0876 

.0872 

.0667 

.0664  .0862 

.0859 

.0856 

.0655 

.0653 

60 

70 

.0902 

.0890 

.0884 

.0679 

.0875 

.0872. 0869 

.0867 

.0864 

.0802 

.0860 

70 

80 

.0910 

.0898 

.0891 

.0887 

.0883 

.0879  .0877 

.0874 

.0872 

.0670 

.0868 

80 

90 

.0919 

.0907 

.0900 

.0695 

.0888 

.08871.0884 

.0683 

.0879 

.0877 

.0875 

90 

100 

.0927 

.0915 

.0906 

.0903 

.0899 

.0895  .0892 

.0890 

.0887 

.0685 

.0883 

100 

110 

.09:J6 

.0923 

.0916 

.0911 

.0907 

.0903  .0900 

.0698 

.0695 

.0893 

.0891 

110 

130 

.0945 

.0932 

.0025 

.0919 

.0915 

.0911  ,.0908 

.0906 

.0903 

.0901 

.0899 

120 

130 

.0954 

.0941 

.0934 

.09t28 

.0924 

.09201 .0917 

.0914 

.0912 

.0909 

.0907 

130 

140 

.0963 

.0950 

.0943 

.0937 

.0932 

.0929 

.0925 

.0923 

.0920 

.0918 

.0916 

140 

150 

.0973 

.0959 

.0951 

.0946 

.0941 

.09.37 

.0934 

.0981 

.0929 

.0926 

.0924 

150 

1«0 

.0982 

.0968 

.0961 

.0955 

.0950 

.0946 

.0043 

.0940 

.0987 

.0935 

.0933 

160 

170 

.0992 

.0978 

.0970 

.0964 

.0959 

.0955 

.0962 

.0949 

.0946 

.09*4 

.0941 

170 

180 

.1002 

.0988 

.0961 

.0978 

.0969 

.0906 

.0961 

.0968 

.0955 

.0953 

.0951 

180 

100 

.1012 

.0096 

.0089 

.0963 

.0978 

.0974 

.0971 

.0968 

.0964 

.0962 

0960 

190 

900 

.1022 

.1008 

.0999 

.0998 

.0988 

.0984 

.0980 

.0977 

.0974 

.0972 

.0969 

200 

210 

.1033 

.1018 

.1009 

.1003 

.0998 

.0994 

.0990 

.0967 

.0984 

.0981 

.0979 

210 

220 

.1029 

.1019 

.1018 

.1008 

.1004 

.1000 

.0997 

.0994 

.0991 

.0989 

280 

230 

.1039 

.1081 

.10-^4 

.1018 

.1012 

.1010 

.1007 

.1003 

.1001 

.0999 

280 

240 

.1050 

.1041 

.1034 

.1029 

.102-1 

.1020 

.1017 

.1014 

.1011 

.1009 

240 

250 

.106,1 

.10512 

.1045 

.1040 

.1035 

.1031 

.1027 

.1025 

.1022 

.1019 

250 

An  approximate  rule  for  the  conditions  of  ordinary  practice  is  a  saving 
of  1%  is  made  by  each  lncrea.se  of  11*  in  the  temi)erature  of  the  feed-water. 
This  corresponds  to  .0909%  per  dejfree. 

The  calcularion  of  saving  is  made  as  follows:  Boiler-pressure,  100  lbs. 
gauge;  total  heat  in  8teani  above  32*»  =  1185  B.T.U.  Feed- water,  original 
temperature  eo**,  final  temperature  209®  F.  Increase  in  heauunits.  150. 
Heat-units  above  32**  in  feed -water  of  original  t#?mperature  =  28.  Heat- 
units  in  steam  above  that  in  cold  fee<l-water,  1 185  -  28  =  1137.  Saving  by  the 
feed-water  heater  =  150/1157  =  12.96)(.  The  same  result  is  obtained  t^  the 
use  of  the  table.  Increase  in  temperature  150®  x  tabular  figure  .0864  = 
VZ.96%.  Let  total  heat  of  1  lb.  of  steam  at  the  boiler-pressure  =  H;  total 
heat  of  1  lb.  of  feed-water  before  entering  the  heater  =  ^i,  and  after  pass- 
ing through  the  heater  =  h^;  then  the  saving  made  by  the  heater  is    '^    '. 

Strains  Caused  by  Cold  Feed-urater.— A  calculation  is  made 
in  The  Locomotive  of  March,  1893.  of  the  possible  strains  caused  in  the  sec- 
tion of  the  shell  of  a  boiler  by  cooling  it  by  the  injection  of  cold  feed- water. 
Assuming  the  plate  to  be  cooled  200"*  F.,  and  the  coefficient  of  expansion  of 
steel  to  be  .0000067  per  degree,  a  strip  10  in.  long  would  contract  .013  iu.,  if  it 
were  free  to  contract.  To  resist  this  contraction,  assuming  that  the  strip  is 
firmly  held  at  the  ends  and  that  the  modulus  of  elasticity  is  29,000,000,  would 
require  a  force  of  37,700  lbs.  per  sq.  in.  Of  course  this  amount  of  strain  can- 
not actually  take  place,  since  the  strip  is  not  firmly  held  at  the  ends,  but  is 
allowed  to  contract  to  some  extent  by  the  elasticity  of  the  .surrounding 
metal.  But,  says  The  Locomotive^  we  may  feel  pretty  confident  that  in  the 
case  considered  a  longitudinal  strain  of  somewhere  in  the  neighboriiood  of 
8000  or  10,000  lbs.  per  sq.  In.  may  be  produced  by  the  feed-water  striking 
directly  upon  the  plates;  and  this,  in  addition  to  the  normal  strain  pro- 
duced by  the  steam-pressure,  is  quite  enough  to  tax  the  girth-seams  beyond 
their  elastic  limit,  if  the  feed-pipe  discliarges  anywhere  near  them.  Hence 
it  is  not  surprising  that  the  girth-seams  develop  leaks  and  cracks  in  99 
cases  out  of  every  100  in  which  the  feed  discharges  directly  upon  the  flre- 
Bheeta. 


728 


tHE  dTEAH-BOlLER 


flTEABI    0BPARATORS. 

If  moist  steam  flowliiff  at  a  high  velocity  In  a  pipe  has  its  dlreotloD  sud- 
denly changed,  the  particlee  of  water  are  by  their  momentum  projected  m 
their  ori{^tnal  direction  a^ainnt  the  bend  in  the  pipe  or  wall  of  the  chamber 
in  which  the  change  of  direction  lakes  place.  By  making  proper  provision 
for  drawing  off  the  water  thu.**  separated  the  gteam  may  be  dried  to  a 
greater  or  less  extent. 

For  long  steam-pipes  a  large  drum  should  be  provided  near  the  engine 
for  trapping  the  water  condensed  in  the  pipe.  A  drum  8  feet  diameter.  15 
feet  high,  has  given  goo<l  results  in  separating  the  water  of  condensation  of 
a  steam-pipe  10  inches  diameier  and  800  feet  long. 

BfBclenicjr  of  SCeam  Separatom.—Prof.  R.  C.  Carpenter,  in  1891. 
made  a  series  of  testai  of  six  steam  separators,  furnishing  them  with  Kteam 
containing  different  percentages  of  moisture,  and  testing  the  quality  of 
steam  before  entering  and  after  passing  the  separator.  A  condeosed  table 
of  the  principal  results  is  given  below. 


o| 

Test  with  Steam  of  about  10%  of 
Moisture. 

Tests  with  Varying  Moisture. 

Quality  of 
Steam 
before. 

Quality  of 
Bteam 
after. 

Efflciency 
per  cent. 

Quality  of 
Steam 
before. 

Quality  of 
Steam 
after. 

ciency. 

B 

A 
D 
0 
E 
F 

87.0^ 

90.1 

80.6 

90.6 

88.4 

88.9 

98.8]t 

08.0 

95.8 

98.7 

90.9 

99.1 

90.8 
80.0 
59.fl 
88.0 
15.5 
28.8 

66.1  to  97.6% 
61.9  •♦  98 
78.9  "  96.1 
67.1  "  96.8 
68.6  "  98.1 
70.4  ♦♦  97.7 

97.8to90)( 
97.9  "  99.1 
95.5  '*  98.9 
98.7  "  96.4 
79.^  »•  06.5 
84.1  ♦*  97.9 

87.6 
70.4 
71.7 
63.4 
86.9 
98.4 

Conclusions  from  the  tests  were:  1.  That  no  relation  existed  between  the 
volume  of  the  several  separators  and  their  efficiency. 

9.  No  marked  decrease  in  pressure  was  shown  by  any  of  the  separi^tors, 
^he  most  being  1.7  lbs.  in  E. 

8.  Although  changed  direction,  reduced  velocity,  and  perhaps  centrifugal 
force  are  necessary  for  good  separation,  still  some  means  must  be  provided 
to  lead  tho  water  out  of  the  current  of  the  steam. 

The  high  efficiency  obtained  from  B  and  A  was  largely  due  to  this  feature. 
In  B  the  Interior  surfaces  are  corrugated  and  thus  catch  the  water  thrown 
out  of  the  steam  and  readily  lead  it  to  the  bottom. 

In  A,  as  soon  as  the  watt^r  falls  or  is  precipitated  from  the  steam,  it  comes 
in  contact  with  the  perforated  diaphragm  through  which  it  runs  iuto  the 
space  below,  where  it  is  not  subjected  to  the  action  of  the  steam. 

Experiments  made  by  Prof.  Carpenter  on  a  "  Straitoa  "  separator  in  1894 
showed  that  the  moisture  in  the  steam  leaving  tUe  separator  was  less  than 
1%  when  that  in  the  steam  supplied  ranged  from  6%  to  il%. 

BBTEBSflNATION  OF  THE  SKOISTUBB  IN  8TEAHK- 
STEARE  CAIiOBiniETERS. 

In  all  boiler- tests  it  is  important  to  ascertain  the  quality  of  the  steam, 
i.e..  1st,  whether  the  steam  is  ** saturated"  or  contains  the  quantify 
of  heat  due  to  the  pressure  according  to  standard  experiments:  0d,  whether 
the  quantitv  of  heat  is  deficient,  so  that  the  steam  is  wet;  and  8d.  whether 
the  heat  is  in  excess  and  the  steam  superheated.  The  best  method  of  ascer- 
taining the  quality  of  the  steam  is  undoubtedly  that  employtnl  br  a  com- 
mittee which  tested  the  boilers  at  the  American  Institute  Exhibition  of 
1871-2,  of  which  Prof.  Thurston  was  chairman,  i.e.,  condensing  ail  the  water 
evaporated  by  the  boiler  by  means  of  a  surface  condenser,  weighing  the 
contlensiiig  water,  a'  d  talking  its  temperature  as  it  enters  and  as  it  leaves 
the  condenser;  but  this  plan  cannot  always  be  adopted. 

A  substitute  for  this  method  is  the  barrel  calorimeter,  which  with  careful 
operation  and  fairly  accurate  instruments  may  generally  be  relied  on  to 
give  results  w\ihin  two  per  cent  of  accuracy  (that  is,  a  sample  of  steam 
which  gives  the  appareni  result  or  2%  of  moisture  may  contain  anywhere  be 
tween  0  and  4jO.  This  calorimeter  is  described  as  follows:  A  sample  of  the 
steam  Is  taken  by  inserthig  a  perforated  ^-Inch  pipe  into  and  through  the 
main  pipe  near  the  boiler,  and  led  by  a  hose,  thoroughly  felted,  to  a  barrel, 
holding  preferably  400  ]bs.  of  water,  which  is  set  upon  a  platform  scale  aad 


©ETERMINATIOK  OF  THE  MOISTURE  IN  STEAM.  729 

|yroTlded  with  a  cock  or  valve  for  allowlDg  the  water  to  flow  to  waste,  and 
with  a  small  propeller  for  stirring  the  water. 

To  operate  the  calorimeter  the  barrel  is  flUed  with  water,  the  weight  and 
temperature  ascertained,  steam  blown  through  the  hose  outside  the  barrel 
until  the  pipe  is  thoroughly  warmed,  when  the  hose  is  suddenly  thrust  into 
the  water,  and  the  propeller  operated  until  the  temperature  of  the  water  is 
increased  to  the  desired  point,  say  about  110"  usually.  The  hose  is  then 
withdrawn  quickly,  the  temperature  noted,  and  the  weight  again  taken. 

An  error  of  1/10  of  a  pound  In  weighing  the  condensed  steam,  or  an  error 
of  U  degree  in  the  temperature,  will  cause  an  error  of  over  1^  in  the  <»lcu- 
lated  percentage  of  moisture.    See  Trans.  A.  S.  M.  E.,  vi.  2SS. 

Tbe  calcnlation  of  the  percentage  of  moisture  is  made  aui  below: 


«=fH[>-*'-^''-*4 


Q  =  quality  of  the  steam,  dry  saturated  steam  being  unity. 

H  =  total  beat  of  1  lb.  of  steam  at  the  observed  pressure. 

r  =     *'       "    "     **     **  water  at  the  temperature  of  steam  of  the  ob- 
served pressure. 

^_.     M       (4    «i     «     M  condensing  water,  originaL 
h.^ '     "     "  "  "     flnai. 

W  =  weight  of  condensing  water,  corrected  for  water-equivalent  of  the 
apparatus. 

tr  »  weight  of  the  steam  condensed. 

Percentage  of  moisture  =  1  —  Q. 

If  Q  Is  greater  than  unity,  the  steam  is  superheated,  and  the  degrees  of 
■upefheoting  =  8.0888  (H  -  T)  (Q  -  1>. 

IMflieiiltT  of  Obtaining  a  Correct  Sample.—Becent  experimen  ts 
by  Prof.  D.  S.  Jacobus,  Trans.  A.  S.  M.  E.,  zvi.  1017,  show  that  it  is  practi- 
cally impossible  to  obtain  a  true  average  sample  of  the  steam  flowing  in  a 
Eipe.  For  accurate  determinations  all  the  steam  noade  bv  the  boiler  should 
e  passed  through  a  separator,  the  water  separated  should  be  weighed,  and 
a  calorimeter  test  made  of  the  steam  just  after  it  has  passed  the  separator. 
Coll  Calorimeters.— Instead  of  the  open  barrel  in  which  the  steam 
is  condensed,  a  coll  acting  as  a  surface-condenser  may  be  used,  which  is 
placed  in  the  barrel,  tlie  water  in  coil  and  barrel  being  weighed  separately. 
For  description  of  an  apparatus  of  this  kind  designed  by  the  author,  which 
be  has  found  to  give  results  with  a  probable  error  not  exceeding  y^  per  cent 
of  moisture,  see  Trans.  A.  S.  M.  E.,  vi.  2M.  This  calorimeter  may  oe  used 
contlnuouiAy,  if  desired,  instead  of  intermittently.  In  this  case  a  continu- 
ous flow  of  condensing  water  into  and  out  of  the  barrel  must  be  established, 
and  the  temperature  of  inflow  and  outflow  and  of  the  condensed  steam 
read  at  short  Intervals  of  time. 

TlurottUng  Calorimeter*— For  percentages  of  moisture  not  ex- 
ceeding 8  per  cent  the  throttling  calorimeter  is  most  useful  and  convenient 
and  remarkably  accurate.  In  this  instrument  the  steam  which  reaches  it 
in  a  V4-lnch  pipe  is  throttled  by  an  orifice  i/ld  Inch  diameter,  opening  into  a 
chamber  which  has  an  outlet  to  the  atmosphere.  The  steam  in  this  cham- 
ber has  its  pressure  reduced  nearly  or  quite  to  the  pressure  of  the  atmos- 
phere, but  the  total  heat  in  the  steam  before  throttling  causes  the  steam  in 
lite  chamber  to  be  superheated  more  or  less  aocoraing  to  whether  the 
steam  before  throttling  was  dry  or  contained  moisture.  The  only  observa- 
tions required  are  those  of  the  temperature  and  pressure  of  the  steam  on 
each  side  of  the  orifice. 

Tbe  author's  formula  for  reducing  the  observations  of  the  throttling 
calorimeter  is  as  follows   (Ebcperiments  on  Throttliug  Calorimeters,  Am. 

Ifach.,  Aug.  4, 1892) :  w  =  100  X  ^  "  ^  ""j[^^^^  "  ^^  *°  wh/ch  w  =  percent- 
age of  moisture  in  the  steam ;  H  =  total  heat,  and  L  =  latent  heat  of  steam 
In  the  main  pipe;  h  =  total  heat  due  the  pressure  In  the  discharge  side  of 
the  calorimeter,  =  1146.6  at  atmospheric  pressure;  K=  speciflc  heat  of  su- 
perheated steam;  T=  temperature  of  the  throttled  and  superheated  steam 
in  the  calorimeter;  f  =  temperature  due  the  pressure  In  the  calorimeter, 
s=  21S*  at  atmospheric  pressure. 

Taking  K  at  0.48  and  the  pressure  In  the  discharge  side  of  the  calorimster 
as  atmospheric  pressure,  the  formula  becomes 

ig-ioox^"'"^-^  -0  48(r-2iy)^ 

From  this  formula  the  following  table  is  calculated : 


730 


THE  STEAM-BOILER. 


HoitTURS  IV  Btbam^Dktbiuiikations  bt  Throttuko  CALoaniETKa. 


I 

liAug«- pressures. 

^ .  ** 

cnbef, 

^tt 

5 

10 

ao 

so 

40 

50 

eo 

70 

76 

80 

a 

w 

lil 

Q 

Per  Cent  of  Motstuns  Jn  6t«»m, 

0* 

0.51 

ooo 

l.M 

2,W 

2,50 

2.«» 

3.34 

S56 

3.71 

a.fi& 

3.99 

4.18 

lO- 

0,0J 

Q.S2 

1-0:; 

1-M 

1  97 

2.36 

2.71 

3,02 

3.17 

332 

345 

3.58 

SO" 

.51 
,00 

1.4.V 

i.**> 

2.17 
1  « 

a.4rt 
1.04 

s.tta 

£!.00 

«.77 
2  iS 

«.flO 
23& 

S.I33 

30» 

S.4B 

40° 

.30 

.77 

I.IO 

1.40 
.87 

1.55 
l.Ot 

1.60 
US 

1  80 
l.aj 

1.94 

&0» 

■  »*. 

r« 

60* 

.OS 

.33 

.47 

.60 

.T^i 

.85 

TCP 

,06 

.17 

.31 

* '   ' 

,  ■ .  ■ 

Dif.p.deif 

.ONB 

.(K(?7 

miri 

fWJ] 

or.2rt 

.OMl 

.(K.9*'! 

,fl63i> 

omt 

0M2 

.0544 

.OMfi 

Gaujce-prosHureft, 

:3  ten 

'«?p!s 

|K 

100 

110 

120 

IW      110 

160     1^ 

170 

leo 

m 

ax» 

^0 

Per  Cent  of  MQiHture  in  aieaui. 

<►• 

4.3ft   *  IW   4.«A 

5. OH 

5  ao 

6.4fl 

6.6** 

!S.«7   a. 05 

ft^J 

63» 

71« 

10- 

3  84    4  0!^    4.V0 

I.Sfi! 

i.TS 

4.M 

^  IS 

5.30   5.4S 

5  ea 

6.82 

ft.58 

«o- 

S  ;!9   3.5?J   3  74 

sail 

4.17 

4  37 

4.m 

4.74    4  Ot 

fioe 

6.36 

600 

ao^ 

S  74    *^m   a  18 

a,4j 

3.61 

3.S0J 

3.99 

4.171  4  34 

4.&1 

4.ffr 

6.41 

4CP 

3.10    2. -12   2.03 

a  H3 

3.0ft    3  24 

3.43    3. fill  3.7S 

3  !M 

4.10 

im 

M"    . 

l.m    l,B7i  s^.08 

a.yu 

S.4&  ii.e<^ 

a  87f  3. Oil  3.21 

,137 

«..'» 

4* 

eo" 

1  tr9  1  aa  15;; 

1  7J 

1.B3   t!  12 

2.30 

2  4fl    2.04 

'2m 

2,»II 

8.<r7 

TO* 

.5a 

.77 

.^7 

IJH 

1..^,  IM 

1.74 

l.tfl 

K.o; 

*.!» 

«.3(4 

309 

so* 

.00 

.n 

M 

.(53 

.m\  1.00 

1-18 

L8i 

1.50 

l.W 

1.S1 

a.si 

SO" 

/07 

.as 

.44 

,61 

.7H 

.M 

ro» 

1.^ 

1.8^ 

JOO- 

.05 

.21 

,»^ 

.B8 

,67 

1  M 

ntr 

,10 

,7* 

Dirp.dfjj 

fX%49 

mb} 

o:^ 

.n^frft 

.o(vni> 

.0*561 

Ami 

.066fl 

OTide 

.OftTO 

mr^ 

.tr^l 

Separating  Calorimeters.— For  percentaKtss  of  moisture  beyond 
the  range  of  the  throttling  calorimeter  the  geparatiog  calorimeter  is  used, 
which  is  simply  a  steam  separator  on  a  small  scale.  An  improved  form  of 
this  calorimeter  is  described  by  Prof.  Carpenter  in  Potper^  Feb.  1888. 

For  fuller  information  on  various  kinds  of  calorimeters,  see  papers  b^ 
Prof.  Peabody,  Prof.  Carpenter,  and  Mr.  Barrus  in  Trans.  A.  S.  »!.  E.,  voK 
z,  zi,  zii,  1880  to  1891 ;  Appendix  to  Report  of  Com.  on  Boiler  Te«t«« 
A.  8.  M.  E..  vol.  vl,  1884:  Circular  of  Schaeffer  &  Budenberg,  N.  Y..  "Calo- 
rimeters. Throttling  and  Separating.**  1894. 

Identlfleatloni  of  Dry  Steam  by  Appearance  of  a  Jet*  — 
Prof.  Denton  (Tranti.  A.  S.  M.  E.,  vol.  z.)  found  thai  jets  uf  steam  show  un- 
mistakable change  of  appearance  to  the  eye  when  steam  varies  less  than  1% 
from  the  condition  of  saturation  either  in  the  direction  of  wetness  or  super- 
heating. 

If  a  jet  of  steam  flow  from  a  boiler  into  the  atmosphere  under  circumstances 
such  that  very  little  loss  of  heat  occurs  through  radiation,  etc.,  and  the  jet 
be  transparent  close  to  the  oriflce,  or  be  even  a  grayish-white  color,  the 
steam  may  be  assumed  to  be  so  nearly  dry  that  no  portable  condensing 
calorimeter  will  be  capable  of  measuring  the  amount  of  water  in  the  steam. 
If  the  jet  be  strongly  white,  tiie  amount  of  water  may  be  roughly  judged  up 
to  about  8^,  but  beyond  this  a  calorimeter  only  can  determine  the  ezact 
amount  of  moisture. 


CHIUNETS. 


731 


A  oommon  brass  pet-cock  maj  be  used  as  an  orifice,  but  It  should,  If  possl* 
ble,  be  set  into  the  steam-drum  of  the  boiler  and  never  be  placed  further 
away  from  the  latter  than  4  feet,  and  then  only  when  the  intermediate  reser- 
voir or  pipe  is  well  covered. 

Usual  Amount  of  REoUitare  In  Steam  Escaping  Arom  a 
Boiler*— In  the  common  forms  of  horisontal  tubular  laiid  boilers  and 
water-tube  boilers  with  ample  horizontal  drums,  and  supplied  with  water 
free  from  substances  likely  to  cause  foaming,  the  moisture  in  the  steam 
does  not  generally  exceed  2%  unless  the  boiler  is  overdriven  or  the  water- 
level  is  carried  too  high. 

CHIMNEYS. 

Clalmney  Dransbt  Theory.^The  commonly  accepted  theory  of 
chimney  draufrht.  based  on  Feclet's  and  Rankine's  hypotheses  (see  Banklne, 
S.  E.).  is  discussed  by  Prof.  De  Volson  Wood  in  Trans.  A.  8.  M.  E.,  vol.  zi. 

Pedei  represented  the  law  of  draught  by  the  formula 


*  =  ^0  +  «'H-^). 


In  which  A  is  the  "  head,"  defined  as  such  a  height  of  hot  gases  as,  if  added 
to  the  column  of  gases  in  the  clnmney,  would  produce  the 
same  pressure  at  the  furnace  as  a  column  of  outside  air,  of  the 
same  area  of  base,  and  a  height  equal  to  that  of  the  chimney; 
u  is  the  required  velocity  of  gases  in  the  chimney; 

0  a  constant  to^  represent  the  resistance  to  the  passage  of  air 

through  the  coal; 

1  the  length  of  the  flues  and  chimney; 

m  the  mean  hydraulic  depth  or  the  area  of  a  cross-section  divi- 
ded by  the  perimeter; 

/  a  constant  depending  upon  the  nature  of  the  surfaces  over  which 
the  gases  pass,  whether  smooth,  or  sooty  and  rough. 

Rankine's  formula  (Steam  Engine,  p.  888),  derived  by  giving  certain  values 
to  the  constants  (so-called)  in  Peclet*s  formula,  is 

Ii(0.084)  ^       T,       /    • 

in  which  H  s=  the  height  of  the  chimney  in  feet; 

r,  =  403*  F.,  absolute  (temperatuie  of  melting  ice); 

T,  =  absolute  temperature  of  the  gases  in  the  chimn^; 

r,  =  absolute  temperature  of  the  external  air. 
Prof.  Wood  derives  from  this  a  still  more  complex  formula  which  gives 
the  height  of  chimney  required  for  burning  a  given  quantity  of  coal  per 
second,  and  from  it  he  calculates  the  following  table,  showing  the  height  of 
chimney  required  to  bum  respectlvelv  94,  90,  and  16  lbs.  of  coal  per  square 
foot  of  grate  per  hour,  for  the  several  temperatures  of  the  chimney  gases 
given. 


Chimney  Gas. 

Ooal  per  sq.  ft.  of  grate  per  hour,  lbs. 

Outside  Air. 

Absolute. 

Temp. 
Fahr. 

94 

20 

16 

Height  Jf.  feet. 

590" 
absolute  or 

700 
800 
1000 
1100 
1900 
1400 
1600 
9000 

239 
889 
689 
680 
789 
989 
1189 
1&89 

280.9 
179.4 
149.1 
148.8 
159.0 
169.9 
168.8 
206.5 

167.8 
115.8 
lOO.O 
98.9 
100.9 
105.7 
111.0 
182.9 

67.8 
65.7 
48.7 
48.9 
49.1 
61.9 
68.5 
63.0 

738 


CHIMNBT8. 


ProfT^oocl  says:  **  Thia  restili  Is  not 


,  Qr08e«F., 


BaakiiM*!  f onnuU  f^^es  a  maximum  draught  wben  r 

when  the  outside  temperature  Is  6CP.    Prof .  wood  saya 

a  fixed  value,  but  departures  from  theory  in  practloe  do  not  affect  tha  result 
largely.  There  is,  then,  in  a  properly  constructed  chimney,  properly  work- 
ing, a  temperature  giving  a  maximum  draught,*  aad  that  temparatore  is  not 
far  from  the  value  given  oy  Bankine,  although  in  special  cases  It  may  be  90* 
or  75®  more  or  less/* 

AJl  attempu  to  base  a  practical  formula  for  ohimneys  upon  tha  theoret- 
ical formula  of  Peclet  and  Bankine  have  failed  on  aooouat  of  Uie  impoa- 
Bibility  of  assigning  com^ct  values  to  the  so-called  **«QnstanUi*^  G  aad  /. 
(See  Trans.  A.  8.  M.  E..  xi.  W4.) 

Force  or  IntenaUy  of  Urauslit*— The  force  of  the  draught  Is  equal 
to  the  difference  between  the  welgbt  of  the  oolumn  of  hot  gases  inside  of  the 
chimney  and  the  weight  of  a  column  of  the  external  air  of  the  same  height. 
It  is  measured  by  a  draughtrgauge,  usually  a  U«tuba  partly  filled  with  vater, 
one  leg  connected  by  a  pipe  to  the  interior  of  the  flue,  aad  the  other  ofMo  to 
the  external  air. 

If  D  is  the  density  of  the  air  outside,  d  the  density  of  the  hot  gaa  Inside, 
In  lbs.  per  cubic  foot,  h  the  height  of  the  ohimney  in  feet,  and  .192  the  fax^tor 
for  converting  pressure  In  lbs.  per  sq.  ft,  into  inches  of  water  column,  then 
the  formula  for  the  force  of  draught  expressed  in  inches  of  water  is, 
jr».lWfc(D-d). 

The  density  varies  with  the  absolute  temperature  (see  Bankine). 

ds^  0.084;    i)=3a0807^, 
''I  ^ 

where  u  Is  the  absolute  temperature  at  82<>  F..  =s  49S.,  r^  the  absolute  tern- 
perature  of  the  chimney  gases  and  r*  that  of  the  external  air,  Subatituting 
these  values  the  formula  for  force  of  draught  becomes 
'89.79         41.41  \^/7JM 

To  find  the  maximum  Intensity  of  draught  for  any  given  chiraney,  the 
heated  column  being  600*  F.,  and  the  external  air  60*.  multiply  the  height 
above  grate  in  feet  by  .0078,  and  the  product  is  the  draught  in  litohca  of  water. 
Helgflit  of  Water  Colanm  Due  to  CnbalAnced  Pressure  In 
CMmniey  100  Peet  Higli*    (I'he  Locomotive,  l^^ 


,198ft(- 


7.9S\ 


is^ 

Temperature  of  the  External  Air— 

Barometer,  14.7  lbs.  per  sq.  In. 

|5S 

S  § 

0» 

lOo 

20* 

W 

40« 

60» 
.998 

60* 

?oo 

80* 

90« 

100* 

aoo 

.458 

.419 

-.884 

.868 

.821 

.208 

.9M 

.200 

.182 

.157 

290 

.488 

.453 

.419 

.888 

.855 

.826 

.298 

.209 

.244 

.217 

.199 

240 

.520 

.488 

.451 

.421 

.888 

,9fi9 

.880 

.801 

.276 

.260 

.825 

260 

.555 

.5J8 

.484 

.458 

.420 

.892 

.868 

.331 

.809 

.282 

.257 

880 

.684 

.649 

.615 

.482 

.451 

.422 

.894 

.365 

.840 

.818 

.588 

•800 

.611 

.676 

.541 

.611 

.478 

.449 

.400 

.892 

.367 

.840 

.815 

820 

.687 

.603 

.668 

.638 

.505 

.476 

.447 

.419 

.894 

.8ff7 

.343 

340 

.662 

.688 

.593 

.663 

.580 

.501 

.472 

.443 

.419 

.808 

.367 

360 

.687 

.653 

.618 

.688 

.555 

.526 

.497 

.468 

.444 

.417 

.892 

880 

.710 

.676 

.611 

.611 

.578 

.549 

.520 

.492 

.467 

.440 

.415 

400 

.782 

.697 

.662 

.682 

.59S 

.570 

.541 

.618 

.488 

.461 

.486 

4ao 

.753 

.718 

.684 

.653 

.620 

.691 

.668 

.684 

.509 

.482 

.457 

440 

.774 

.789 

.706 

.674 

.641 

.612 

.684 

.655 

.580 

.608 

.478 

460 

.798 

.768 

.7>I4 

.694 

.660 

.632 

.608 

.674 

.549 

.522 

.497 

480 

.810 

.776 

.741 

.710 

.678 

.649 

.620 

.691 

.566 

.540 

.515 

600 

.829 

.791 

.760 

.780 

.697 

.669 

.6.^9 

.610 

.586 

.559 

.534 

*  Mucn  confusion  to  students  of  the  rheoiT  of  chimneys  hsa  resulted  from 
their  understanding  the  words  maximum  draught  to  mean  majcimum  int^en- 
slty  or  pressure  of  draught,  as  measured  by  a  draught-gauge.  It  here  means 
maximum  quantity  or  weight  of  eases  passed  up  the  chimney.  The  maxi- 
mum intensity  is  found  onlv  with  maximum  temperature,  but  after  the 
temperature  reaches  about  622^  F.  the  density  of  the  gas  decreases  more 
rapidly  than  its  velocity  increases,  so  that  the  weight  is  a  maximum  about 
6220  F.,  as  shown  by  Ranlcine.-W.  K. 


CPXIiKBTSU 


733 


Fop  AQy  oiher  heiffbt  of  obtmn^y  tti^Q  100  ft.  the  heigbt  of  w<^ter- column 
U  found  by  siuiple  proportion,  tbe  height  of  wnter  coiuuin  b^ing  (iirectly 
proportioued  to  the  height  of  cniuiney. 

Tne  o^Ieulations  hiive  been  made  for  «  chimney  100  ft.  high,  with  varloun 
teniperatureH  out»i4e  aqd  Inside  of  the  Que,  (wd  on  the  Buppoaitioii  ^hat  tlie 
teinperatupe  of  the  chimney  ifl  uniform  from  top  to  bottom.  This  is  the 
iiiuUs  on  which  all  oaloulatlons  respecting  the  drauglit-powei'  of  cl|iu)nevg 
have  been  made  by  Ranlcine  and  other  writers,  but  it  is  very  far  fi>oiii  the 
truth  in  most  eases.  The  dUTsKUOe  will  be  shown  by  comparing  the  read- 
ing of  the  draughtHprauge  with  the  table  giyeq.  In  one  case  a  chimnt*y  1^  f  (, 
biirb  showed  a  temperature  at  the  bMe  of  9^,  and  at  the  top  of  if6Q^. 

3oa,  ill  his  '*  Treatise  on  Heat,^^  gives  tho  followlpg  table  ( 

DbADOHT  POWURS  of  CHIMNBYB,   1?TP.,  WITB  TH*  IlfTKBNAI.  Al^  AT  552**,  AND 
TH«  £;XTKRNAL  AlR  AT  02^,  AND  WITQ  THE  PaVPBR  NRAULY  ClQSED. 


-5 

Theoretical  Velocity 

^« 

«' 

Theoretical  Velocity 

£^-- 

^n,- 

in  feet  per  second. 

in 

If! 

in  feet  per  second. 

m 

Cold  Air 

Hot  Air 

Cold  Air 

Hot  Air 

«s 

Entering. 

at  Exit. 

Kg 

Bntering. 

at  Exit. 

10 

.073 

17.8 

:i:- .  '.r 

80 

.585 

60.6 

101.2 

90 

.146 

86.8 

.'■0  1} 

90 

.657 

68.7 

107.4 

90 

.219 

81.0 

*;■>  i> 

100 

.780 

56.5 

113.0 

40 

.202 

86.7 

:iJ 

120 

.876 

62.0 

124.0 

SO 

.865 

40.0 

N.3.0 

160 

1.096 

69.8 

188.6 

60 

.488 

43.8 

87.6 

175 

i.trr 

8o:o 

140  0 

70 

.611 

47.8 

MS 

aoo 

1.460 

1600 

Rate   of   Comliiiatloii   Due   %»   Hetslit   of   dilmiiey.-* 

Trowbridge's  *'Heat  and  Heat  fi;iigiues^'  gives  ilie  folluwing  table  showing 
the  heights  of  chimney  for  producing  pertain  rates  of  combustion  per  sq. 
ft.  of  saqilon  of  the  chimney.  It  may  be  approximately  true  for  anthracite 
in  moderate  and  large  sises,  but  greater  hoi«hts  than  are  given  in  the  table 
are  needed  to  secure  the  given  rates  of  combustion  with  small  siaes  of 
anthracite,  and  for  bituminous  coal  smaller  heights  will  suffice  if  the  ooal 
Is  reasonably  free  from  ash— M  or  less. 


Lbs.  of  Coal 

Lbs.  of  Coal 

Uw.  Of  Coal 

Burned  per 

Lbs.  of  Coal 

Burned  per 

Burned  per 

Sq.  Ft.of 

Burned  per 

Sq.  Ft.  of 

Heights 

Hour  per 

So.  Ft. 
of  Section 

Grata,  the 

Heigbta 
in 

Hour_per 

6q.  Ft 
of  Section 

Grate,  the 
Ratio  of 

feet. 

Grate  to  Sec- 

feet. 

Grate  to  Sec- 

of 

tion  of 

of 

tion  of 

Chimney. 

Chimney  be- 
ing 8  to  1. 

Chimney. 

Chimney  be- 
ing 8  to  1. 

SO 

SS 

li 

S 

186 

18 

15.8 
16  4 

70 

9.5 

00 

181. 

16.9 

3g 
45 

84 

10,6 

85 

180 

17.4 

18.1 

8 

144 
148 

18.0 
18.5 

50 

IQS 

ido 

158 

10.0 

55 

111 

18.8 

106 

166 

19.5 

60 

14.5 

110 

160 

200 

63 

m 

15.1 

Thurston's  rule  for  rate  of  pombustion  effect«»d  bv  a  given  Aeigbt  of  chim- 
ney (Trans.  A.  8.  M.  fi.,  xi.  991)  is:  Subtract  1  from  twice  the  square  root  of 
the  height,  and  the  result  is  t\\o  rate  of  combustion  in  pounds  per  square  foot 
of  grate  per  hour,  for  anthracite.  Or  rate  =  2  V/^  -  \,  in  which  h  is  the 
height  in  feet.    This  rule  gives  tlie  following: 

A=    50        60        70        80        9U     100    110       126       !50       175      900 
2  fT»- 1  =  13.14    14.49    16.78    16.89    17.97    19   19.97    SI .80    88.49    25.45   27.28 

The  results  agree  oloeel^  with  Trowbridge's  table  given  above.    In  prao* 


734 


CHIMNEYS. 


tfce  the  high  rates  of  combustion  for  high  chimneys  given  by  the  formula 
are  not  generally  obtained,  for  the  reason  that  with  high  chimneys  there  are 
usually  long  horizontal  flues,  serving  manv  boilers,  and  the  friction  and  the 
interference  of  currents  from  the  several  boilers  are  apt  to  cause  the  inu*u- 
sity  of  draught  in  the  branch  flues  leading  to  each  boiler  to  be  much  less 
than  that  at  the  base  of  the  chimney,  '^e  draught  of  each  boiler  is  also 
usually  restricted  by  a  damper  and  by  bends  in  the  gasoassages.  In  a  bat- 
tery of  several  boilers  connected  to  a  chimney  150  ft.  high,  the  author  found 
a  draught  of  9i-inch  water-column  at  the  boiler  nearest  the  chimney,  and 
only  ^-inch  at  the  boiler  farthest  away.  The  first  boiler  was  wasting  fuel 
from  too  high  temperature  of  the  chimney-gases,  IKK)*,  having  too  large  a 
grate-surface  for  the  draught,  and  the  last  boiler  was  working  below  its 
rated  capacity  and  with  poor  economv,  on  account  of  insufficient  draught. 

The  effect  of  changing  the  length  of  the  flue  leading  Into  a  chimnev  00  ft. 
high  and  2  ft.  9  in.  square  Is  given  In  the  following  table,  from  Box  on 
•*  Heat  '* : 


Length  of  Flue  In 
feet. 

Horse-power. 

Length  of  Flue  in 
feet. 

Horse-power. 

80 
100 
800 
400 
600 

107.6 
100.0 
85.S 
T0.8 
63.5 

800 
1.000 
1,500 
2,000 
3,000 

S6.1 
614 
48.8 
88.2 
817 

The  temperature  of  the  gases  in  this  chimney  was  assumed  to  be  558«  F., 
and  that  or  the  atmosphere  cy*. 

Hlffli  Clitinneys  not  NecesMirjr,— Chimneys  above  150  ft.  in  height 
are  very  costly,  and  their  increased  cost  is  rarely  Justifled  by  IncreasMl  ef. 
flciency.  In  recent  practice  It  has  become  somewhat  common  to  hulld  two  or 
more  smaller  chimneys  instead  of  one  large  one.  A  notable  example  is  the 
Spreckels  Sugar  Reflnery  in  Philadelphia,  where  three  separate  chimneys  are 
used  for  one  boiler-plant  of  7500  H.P.  The  three  chimneys  are  said  to  have 
cost  several  thousand  dollars  less  than  a  single  chimney  of  their  combined 
capacity  would  have  cost.  Very  tall  chimneys  have  been  characterised  by 
one  writer  as  **  monuments  to  the  folly  of  iheir  builders." 

Helfflits  of  Cblmnejr  required  for  IMITerent  Pnels,— The 
minimum  height  necessary  vaiies  with  the  fuel,  wood  requiring  the  least, 
then  good  bituminous  coal,  and  fine  sises  of  anthracite  the  greatefit.  It 
also  vaiies  with  the  character  of  the  boiler— the  smaller  and  more  circuitous 
the  gas-passages  the  higher  the  stack  i-equired;  also  with  the  number  of 
boilers,  a  single  boiler  requiring  less  height  than  several  that  discharge 
into  a  horizontal  flue.    No  general  rule  can  be  given. 

SIZE  OF  CHIUKNETS. 

The  formula  given  below,  and  the  table  calculated  therefrom  for  chimneys 
up  to  96  In.  diameter  and  200  ft.  high,  were  flret  published  by  the  author 
in  1884  (Trans.  A.  S.  M.  E.  vi.,  81).  They  have  met  with  much  approval 
since  that  date  by  engineers  who  have  used  them,  and  have  been  frequently 
published  in  boiler-makers*  catalogues  and  elsewhere.  The  table  is  now 
extended  to  cover  chimneys  up  to  12  ft.  diameter  and  800  ft.  high.  The  sises 
corresponding  to  the  given  commercial  horse-powers  are  believed  to  be 
ample  for  all  cases  in  which  the  draught  areas  through  the  boiler- flues  and 
connections  are  sufficient,  say  not  less  than  2(i%  greater  than  the  area  of  the 
chinmey,  and  in  which  the  draught  between  the  boilers  and  chimney  is  ntit 
cliocken  by  long  horizontal  passages  and  right-angle<l  bends. 

Note  that  the  figures  in  the  table  correspond  to  a  coal  consumption  of  5  lbs. 
of  coal  per  horse  pinoer  per  Iiour.  This  liberal  allowance  is  made  to  cover 
the  contingencies  of  poor  coal  being  used,  and  of  the  boilers  being  driven 
beyond  their  rated  capacity.  In  large  plants,  with  economical  boilers  and 
engines,  good  fuel  and  other  favorable  comiitions,  which  will  reduce  the 
maximum  rate  of  coal  consumption  at  any  one  time  to  less  than  5  lbs.  per 
H.  P.  per  hour,  the  figures  in  the  table  may  be  multiplied  by  the  ratio  of  5  ro 
the  maximum  expected  coal  consumption  per  H.P.  per  hour.  ThuM,  wUh 
conditiouH  which  make  the  maximum  coal  consumption  onh'  2.5  lbs.  per 
hour,  the  chimney  300  ft.  high  x  12  ft.  diameter  should  be  suflffclent  for  6155 
X  2  =  12,310  horse-poxYer.    The  formula  Is  based  pn  the  following  data : 


SIZE  OF  CHIMNKYS. 


735 


§1 

5 

sa 

Has  Sisas  is992 

82^{3   88SS 

s§SS 

o 

0 

§ 

d 
S 

d 
8 

d 
§ 

d 
g 

d 

s 

d 

3 
d 

o 

d 

8 

~d~ 

s 

d 

s 

d 

d 

s 

1 

1 

|iiiliig§ii 

III  liil  ilii 

m  1118  ig|§ 

iill  §iig 

ilii 

P  nu  mi  im 

1  i  sssi  Sill  liil  nil 

a  siis  mi  !Si§  n  n 

N  Is 

SS  SISS  Sill 

:  i  SSSS  8S2S  *Si 

«s  SSBi  S8S5 

S3S8    IgSS    gS  : 

7-- 

-:-- 

S5SS    ggSB    2  :  ; 

S82f:    S2 

S  : 

|| 

gi»33    2  : 

It 

6158S    S55JS    S538    SSSS    2308    SS5S 

-,0,0.      «^««       r,025       gggjjj      5jjigg      gggg 

ft 

{::::!$    SS&S    S:5S2    iS&S^SI    SS;S»8    S28S 

^0.««       ^-,^«       •2gC5      jjgjjg       5gjgg       ojOgg 

sa 

25^    S8 

«s  s 

!92S 

1    S 

Sg 

s  s 

«§§ 

a§S2 

736  CHIMNEYS. 

1.  The  draught  power  of  the  cblmDey  varies  as  the  square  root  of  the 
height. 

2.  The  retarding  of  the  ascending  gases  by  friction  may  be  considered  as 
equivalent  to  a  dmiinutioD  of  the  area  of  the  chimoey,  or  to  a  lining  of  the 
chimney  by  a  layer  of  gas  which  has  no  velocity.  The  thiclCDess  of  this 
lininc  is  assumed  to  be  2  inches  for  all  cliimneys,  or  the  diminution  of  area 
equal  to  the  perimeter  x  2  inches  (neglecting  the  overUpping  of  the  comers 
of  the  lining).  Let  D  a  diameter  in  ifeet,  A  s=  area,  ana  K  =  effective  area 
in  square  feet. 

For  square  chimneys,  E=  D^  — la^*^"!  ^'^' 

For  round  chimeys,     ^  =  ^  (l>*  -  ^)  =A-  0.B91  4/2. 

For  simplifying  calculation?*,  the  coefficient  of  Va  may  be  taken  a«  0.6 
for  both  square  and  round  chimneys,  and  the  formula  becomes 

E=A-OA^n. 

8.  The  power  varies  directly  as  this  effective  area  E, 

4.  A  chimney  should  be  proportioned  so  as  to  be  capable  of  giving  sufUclent 
draught  to  cause  the  boiler  to  develop  much  more  than  Its  rated  power,  in 
case  of  emergencies,  or  to  cause  the  combustion  of  6  lbs.  of  fuel  per  rated 
horse-power  of  boiler  per  hour. 

6.  The  power  of  the  chimney  varying  directly  as  the  effective  area,  B^  and 
as  the  square  root  of  the  height,  H,  the  formula  for  horse-power  of  boiler  for 
a  given  size  of  chimney  will  take  the  form  H.P.  =  CE  ^H^  in  which  C  is  a 
constant,  the  average  value  of  which,  obtained  by  plotting  the  results 
obtained  from  numerous  examples  in  practice,  the  author  finds  to  be  8.83. 

The  formula  for  horse- power  then  is 

H.P.  =  3.83S  VH^,    or    H.P.  =  8.88(^  -  .6  V2)  yS. 

ir» 
being  assumi 


If  the  horse-power  of  boiler  is  given,  to  find  the  sise  of  chimney,  the  height 
ed, 


For  round  chimneys,  diameter  of  chimney  =  dlam.  of  i7+  ^"• 
For  square  chimneys,  side  of  chimney  =  ^^  +  4". 

If  effective  area  E  is  taken  in  square  feet,  the  diameter  in  inches  is  d  = 
13.54  j/f-f  4",  and  the  side  of  a  square  chimney  in  inches  is  « =:=  12  VE'\-  4". 

/O  3  H  P  *• 
If  horse-power  is  given  and  area  assumed,  the  height  H  =  \j^-~v — ')  • 

In  proportioning  chimnevs  the  height  is  general Iv  first  assumed,  with  due 
consideration  to  the  heights  of  surrounding  bulidingH  or  hills  near  to  the 
proposed  chimney,  the  length  of  horizontal  flues,  the  character  of  coal  to  be 
used,  etc.,  and  then  the  diameter  required  for  the  assumed  height  and 
horse-power  is  calculated  by  the  formula  or  taken  from  the  table. 

Tlie  Protection  of  Tall  Chimney-shafta  ft*om  Ijitflitiiliic. 
— C.  Molyneux  and  J.  M.  Wood  (/mfiMf rte«,  March  28.  1890)  recommend  for 
tall  chimneys  the  use  of  a  coronal  or  heavy  band  at  the  top  of  the  chinmey, 
with  copper  points  1  ft.  in  height  at  intervals  of  2  ft.  throughout  the  circum- 
ference. The  points  should  be  gilded  to  prevent  oxidation.  The  most  ap- 
proved form  of  conductor  is  a  copper  tape  about  ^  in.  by  ^  in.  thicc, 
weighing  6  ozs.  per  ft.  If  iron  is  used  it  should  weigh  not  less  tnan  ^  lbs. 
per  It.  Tliere  must  l)e  no  insulation,  and  the  copper  tape  should  be  fastened 
to  the  chimney  with  holdfasts  of  the  same  material,  to  prevent  voltaic 
action.  An  allowance  for  expansion  and  contraction  should  be  made,  say  1 
in.  in  40  ft.  Slight  bends  in  the  tape,  not  too  abrupt,  answer  the  purpose. 
For  an  earth  terminal  a  plate  of  metal  at  least  8  ft.  sq.  and  1/10  in.  tliick 
should  be  buried  as  deep  as  possible  in  a  damp  spot.  The  plate  should  be  of 
the  same  metal  as  the  conductor,  to  which  it  should  be  soldered.  The  best 
earth  terminal  is  water,  and  when  a  deep  well  or  other  large  body  of  water 
is  at  hand,  the  conductor  should  be  carried  down  into  it.  Right-angled 
bends  in  the  conductor  should  be  avoided.  No  bend  in  it  should  be  over  SO*. 


SIZE  OF  CHIMliEYS. 


737 


Some  Tall  Briek  Gbljnney*. 


1.  HaUsbrtlckner  HAtte,  Sax. 

2.  Townseud'a,  Glasfpow..  .. 
8.  Tennant^s,  Glasgow 

4.  Dobson  &  Barlow,  Bolton, 

Eng 

5.  Fall  River  Iron  Co.,  Beaton 

6.  Clark  Thread  Co.,  Newark 

N.J 

7.  Merrimac  Mill8,Low*l,Mam 

8.  WashiDgton    Mills,    Law 


renoe,  Mass. 


0.  AmoBkea«r  Milla,  Mancbes- 
ter,N.H 

10.  Narrafranciett    E.   L.    Co., 

Providence,  R.  I 

11.  Lower  Pacific  Milte.  Law 

rence.  Mass 

12.  Passaic  Print  Works,  Pas- 

saic, N.  J  

18.  Edison  Bta,B*klyn,Twoe*ch 


460 
454 

485 

867H 
850 

835 


250 

250 


214 


200 

160 


16  7' 

18'*  6'/ 

18' 2" 
11 

11 
1-3 

10 

10 

14 


0 
50"  X  180" 


Outside 
Diameter. 


Capaci^  by  the 

Autnor^s 

Formula. 


83' 
82 
40 


88'10' 
80 


18' 


each 


H.  P. 


Pounds 

Coal 

per 

hour. 


13,221 

0,795 

8,245 
5,568 

6,485 
6,980 

3,830 

8,880 

7,515 

2,248 

2,771 
1,541 


66,105 

48,976 

41,226 
27,700 

27,175 
29,900 

19,195 

19,106 

37,575 

11,240 

18,855 
7,705 


KoTCS  ON  THS  Abotb  CHniKiCTs.— 1.  ThIs  chimney  Is  Rituated  near 
Freiberg,  on  the  right  bank  of  the  Mulde.  at  an  elevation  of  219  feet  above 
that  of  the  foundry  works,  so  that  its  total  height  above  the  sea  will  be  71194 
feet.  The  works  are  situated  on  the  bank  of  the  river,  and  the  furnace* 
gases  are  conveyed  across  the  river  to  the  chimney  on  a  bridge,  through  a 
pipe  8227  feet  in  length.  It  is  built  throughout  of  brick,  and  will  cost  about 
|40,000.~i#/r.  and  Bldr. 

2.  Owing  to  the  fact  that  it  was  struck  by  lightning,  and  somewhat 
damaged,  as  a  precautionary  measure  a  copper  extension  subsequently  was 
added  to  it,  making  its  entire  height  488  feet. 

1,  2,  8,  and  4  were  built  of  these  great  heights  to  remove  deleterious 
gase«  from  the  neighborhood,  as  well  as  for  draught  for  boilers. 

6.  The  structure  rests  on  a  solid  granite  foundation,  56  X  80  feet,  and 
16  feet  deep.  In  its  construction  there  were  used  1,700.000  bricks.  2000  tons 
of  Ktone,  2000  barrels  of  mortar,  1000  loads  of  sand,  1000  barrels  of  Portland 
cement,  and  the  estimated  cost  Is  $40,000.  It  is  arranged  for  two  flues,  9 
feet  6  inches  br  0  feet,  connecting  with  40  boilers,  which  are  to  be  nin  in 
connection  witn  four  triple^xpansion  engines  of  1350  horse-power  each. 

6.  It  has  a  uniform  hatter  of  2.85  inches  to  every  10  feet.  Designed 
for  21  boilers  of  200  H.  P.  each.  It  is  surmounted  by  a  cast-iron  cop- 
ing which  weighs  six  tons,  and  is  composed  of  thirty-two  sections, 
which  are  bolted  together  by  inside  flanges,  so  as  to  present  a  smooth 
exterior.  The  foundation  is  in  concrete,  composed  of  cnished  lime- 
stone 6  parts,  sand  8  parts,  and  Portland  cement  1  part.  It  is  40  feet 
squnre  and  6  feet  deep.  Two  qualities  of  briek  were  used;  the  outer 
portions  were  of  the  flrst  quality  North  River,  and  the  hacking  up  was  of 
good  quality  New  Jersey  brick.  Every  twenty  feet  in  vertical  measurement 
an  iron  ring,  4  inches  wide  and  %  to  %  inch  thick,  placed  edgewise,  was 
built  into  the  walls  about  8  Inches  from  the  outer  circle.  As  the  chimney 
starts  from  the  base  it  is  double.  The  outer  wall  is  5  feet  2  inches  In  thick- 
ness, and  Inside  of  this  is  a  second  wall  20  inches  thick  and  spaced  off  about 
20  inches  from  main  wall.  From  the  interior  surface  of  the  main  wall  eight 
buttresses  are  carried,  nearlv  touching  this  Inner  or  main  flue  wall  in 
order  to  keep  it  in  line  should  it  tend  to  sag.  The  interior  wall,  starting 
with  the  thickness  described,  is  gradually  reduced  until  a  height  of  about 
90  feet  Is  reached,  when  it  is  diminished  to  8  Inches.    At  165  feet  It  ceases. 


73b  CHIMNEYS. 

and  the  rest  of  the  chlmnej  is  wf  tliout  llDing.    The  total  weiftht  of  the  chlm* 
nej  and  foundation  is  SOOO  tons.    It  was  completed  In  September,  IflW. 

7.  Connected  to  12  boilers,  with  1200  square  feet  of  grate-surfaoe.  Draugbt- 
gaupe  1  9/16  Inches. 

8.  Connected  to  8  boilers,  V  8"  diameter  x  18  feet.  Grate-surface  448 
■quare  feet. 

9.  Connected  to  64  Manning  vertical  boilers,  total  grate  snrfiaoe  1810  aq.  ft. 
Designed  to  bum  18.000  lbs.  anthracite  per  hour. 

10.  Designed  for  12.000  H.F.  of  engines;  (compound  condensing). 

11.  Grate-surface  484  square  feet;  H.F.  of  boilers  (Galloway)  about  2500. 
18.  Eiffht  boilers  (water-tube)  each  450  H.P. ;  12  engines,  each  800  HP.  Plant 

designed  for  86,000  incandescent  lights.    For  the  first  60  feet  the  exterior 
wall  is  28  inches  thick,  then  24  inches  for  20  feet,  90  inches  for  80  feet.  16 
inches  for  20  feet,  and  12  inches  for  20  feet.    The  interior  wall  is  9  inches 
thick  of  flre-brick  for  60  feet,  and  then  8  Inches  thick  of  red  brick  for  the 
next  80  feet.    Illustrated  in  Iron  Age,  January  8, 1890. 
▲  number  of  the  aboye  chimneys  are  illustrated  in  Ptneer^  Dec.,  1800. 
Chimney  at  Knoxville,  Tenn.,  Illustrated  in  Eng^gNewa,  Not.  2, 1808. 
6  feet  diameter,  120  feet  high,  double  wall: 

Exterior  wall,  height     20  feet,  80  feet,  80  feet.  40  feet; 

*'    thickness  21^  in.,  17 in.,  18  in,,  8H  in.; 
Interior  wan,  height     86    ft..  85  ft.,    29  ft.,  21ft.; 
"      thianies8l8^in.,8Hln.,4in.,0. 

Exterior  diameter.  W  6"  at  bottom ;  batter.  7/16  Inch  in  12  Inches  from  bot- 
tom to  8  feet  from  top.  Interior  diameter  of  Inside  wall.  6  feet  uniforni  to 
top  of  interior  wall.  Space  between  walls,  16  Inches  at  bottom,  diminishing 
to  0  at  top  of  int«rior  wall.  The  interior  wall  is  of  red  brick  except  a  lining 
of  4  inches  of  fire-brick  for  20  fe«ft  from  bottom. 

8tabllUy  of  dilmneFa*— Chimneys  must  be  designed  to  resist  the 
maximum  force  of  the  wind  in  the  locally  in  which  they  are  built,  (see 
Weak  Chimneys,  below).  A  general  rule  for  diameter  of  base,  of  brirk 
chimneys,  approved  bv  many  years  of  practice  in  England  and  the  Unit^ 
States,  18  to  make  the  diameter  of  the  base  one  tenth  of  the  height.  If  th9 
chimney  is  square  or  rectangular,  make  the  diameter  of  the  iaitoribed  circle 
of  the  base  one  tenth  of  the  height.  The  **  batter  *^  or  taper  of  a  chimney 
should  be  from  1/16  to  U  inch  to  the  foot  on  each  side.  The  brickwork 
should  be  one  brick  (8  or  0  Inches)  thick  for  the  first  29  feet  from  the  top,  in- 
creasing U  brick  (4  or  4^  inches)  for  each  25  feet  from  the  top  downwards. 
If  the  inside  diameter  exceed  5  feet,  the  top  length  should  be  1^  bricks;  and 
if  under  8  feet,  it  may  be  U  brick  for  ten  feet. 

(From  The  Locomotive^  1884  and  1886.)  For  chimneys  of  four  feet  In  dian»- 
eter  and  one  hundred  feet  high,  and  upwards,  tlie  best  form  is  circular,wtili 
a  straight  batter  on  the  outside.  A  circular  chimney  of  this  sise,  in  addition 
to  being  cheaper  than  any  other  form,  is  lighter,  stronger,  and  looks  much 
better  and  more  shapely. 

Chimneys  of  any  considerable  height  are  not  built  up  of  unifomn  thickness 
from  top  to  bottom,  nor  with  a  uniformly  varying  thickness  of  wall,  but  the 
wall,  heaviest  of  course  at  the  base,  is  reduced  by  a  series  of  steps. 

Where  practicable  the  load  on  a  chimney  foundation  should  not  exceed  two 
tons  per  square  foot  in  compact  sand,  gravel,  or  loam.  Where  a  solid  rock- 
bottom  is  avaUable  for  foundation,  the  load  may  be  greatly  increased.  If 
the  rock  is  sloping,  all  unsound  portions  should  be  removed,  and  the  face 
dressed  to  a  series  of  horizontal  steps,  so  that  there  shall  be  no  tendency  to 
slide  after  the  structure  is  fiiiislied. 

All  boiler-chimneys  of  any  considerable  size  should  consist  of  an  outer 
stack  of  sufficient  strength  to  give  stability  to  the  structure,  and  an  inner 
stack  or  core  independent  of  the  outer  one.  This  core  is  by  many  engineers 
extended  up  to  a  height  of  but  60  or  60  feet  from  the  base  of  the  chimney, 
but  the  better  practice  is  to  run  it  up  tlie  whole  height  of  the  chimney;  it 
may  be  stopped  off,  say,  a  couple  feet  below  the  top,  and  the  outor  shell  con* 
tracted  to  the  area  of  the  core,  but  the  better  way  is  to  run  it  np  to  about  8 
or  12  inches  of  the  top  and  not  contract  the  outer  shell.  But  under  no  cir- 
cumstances should  the  core  at  Its  upper  end  lie  built  into  oi' connected  with 
the  outer  stack.  This  has  been  done  in  several  instances  bv  bricklayers,  and 
the  result  has  been  tlie  expansion  of  the  inner  core  which  lifted  the  top  of 
the  outer  stack  squarely  up  and  crroked  the  brickwork. 

For  a  height  of  luO  feet  we  would  make  the  outer  shell  in  three  steps,  the 
first  20  feetUgh,  16  inches  thick,  the  second  80  feet  high,  18  inobes  thick,  the 


SIZE  OF  CHTMNBTS.  T39 

thfi.'  W  feet  liljch  and  8  Inches  thick.  These  are  the  mfnlmnm  thicknessec 
&i1rrJ8Hible  for  chimneys  of  thin  lieight,  and  the  batter  should  be  not  less 
than  1  In  86  tn  fi^ive  stability.  The  core  should  also  be  built  in  three  steps 
each  of  which  may  be  about  one  third  the  height  of  the  chimney,  the  lowest 
12  inches,  the  middle  8  inches,  and  the  upper  step  4  inches  thick.  This  will 
insure  a  good  sound  cora.  The  top  of  a  chimney  may  be  protected  by  a 
cast-iron  cap;  or  perhaps  a  cheaper  and  equally  good  plan  is  to  lay  the 
omauiental  part  m  some  good  cement,  and  plaster  the  top  with  the  same 
niatpHal. 

Hreak  ClilinnejrB*— James  B.  Francis,  in  a  report  to  the  lAwrence 
Mfff.  Co.  in  I8i3  (Eng'g  Netea,  Aug.  US,  1880),  gives  some  calcuUtlons  con- 
cerning  the  probable  eiTectH  of  wind  on  that  company's  chimney  as  then 
constructed.  Its  outer  shell  is  octagonal.  The  inner  shell  is  cylindrical, 
with  an  air-space  between  it  and  the  outer  shell;  the  two  shells  not  being 
bonded  together,  except  at  the  openings  at  the  base,  but  with  projections  in 
the  brickwork,  at  intervals  of  about  SO  ft.  in  height,  to  afford  lateral  sup- 
port by  contact  of  the  two  shells.  The  principal  dimensions  of  the  chimney 
are  as  follows : 

Height  above  the  surface  of  the  ground SIX  ft. 

Diameter  of  the  inscribed  circle  of  the  octagon  near  the  ground.  15  ** 
Diameier  of  the  inscribed  circle  of  the  octagon  near  the  top ...    10  ft.  1^  In. 

Thickness  of  the  outer  shell  near  the  base,  6  bricks,  or 23U  in. 

Thickness  of  the  outer  shell  near  the  top,  S  bricks,  or 11)^  ** 

Thickness  of  the  inner  shell  near  the  base,  4  bricks,  or 1!>     ** 

Thickness  of  the  inner  shell  near  the  top,  1  brick,  or '^  ** 

One  tenth  of  the  height  for  the  diameter  of  the  base  is  the  rule  commonly 
adopted.  The  diameter  of  the  inscribed  circle  of  the  bane  of  the  Lawrence 
Manufacturing  Company's  chimney  being  15  ft.,  it  is  evidently  much  less 
than  is  usual  in  a  chimney  of  that  height. 

Soon  after  the  chimney  was  built,  and  before  the  mortar  had  hardened,  it 
iiras  found  that  the  top  had  swayed  over  about  29  in.  toward  the  east.  This 
was  evidently  due  to  a  strong  westerly  wind  which  occurred  at  that  time, 
it  was  soon  brought  back  to  the  perpendicular  by  sawing  into  son>e  of  the 
Joints,  and  other  means. 

The  stability  of  the  chimney  to  resist  the  force  of  the  wind  depends  mainly 
on  the  weight  of  its  outer  shell,  and  the  width  of  its  base.  The  cohesion  of 
the  moriar  may  add  considerably  to  its  strength;  but  it  is  too  uncertain  to 
be  relied  upon.  The  Inner  shell  will  add  a  little  to  the  stability,  but  it  may 
be  cracked  by  the  heat,  and  its  beneficial  effect,  if  any,  is  too  uncertain  to 
be  taken  Into  account. 

The  effect  of  the  joint  action  of  the  vertical  pressure  due  to  the  weight  of 
the  chimney,  and  the  horizontal  pressure  due  to  the  force  of  the  wind  is  to 
shift  the  centre  of  pressure  at  the  base  of  the  chimney,  from  the  axis  to- 
ward one  side,  the  extent  of  the  shifting  depending  on  the  relative  magni- 
tude of  the  two  forces.  If  the  centre  of  pressure  Ih  brought  too  near  the 
side  of  the  chimney,  it  will  crush  the  brickwork  on  that  side,  and  the  chini- 
Dey  will  fall.  A  Hue  drawn  through  the  centre  of  pressure,  perpendicular  to 
the  direction  of  the  wind,  must  leave  an  area  of  brickwork  between  it  and 
the  side  of  the  chimney,  sufficient  to  support  half  the  weight  of  tlie  chim- 
ney; the  other  half  of  the  weight  being  supported  by  the  brickwork  on  the 
windward  side  of  the  line. 

Different  experimenters  on  the  strengrh  of  brickwork  give  very  different 
results.  Kirkaldy  found  the  weights  which  caused  several  kinds  of  bricks, 
laid  in  hydraulic  lime  mortar  and  in  Roman  and  Portland  cements,  to  fail 
slightly,  to  vary  from  19  to  60  tons  (of  9000  lbs.}  per  sq.  ft.  If  we  take  in  this 
case  25  tons  per  sq.  ft.,  as  the  weight  that  would  cause  It  to  begin  to  fail,  we 
shall  not  err  greatly.  To  support  naif  the  weight  of  the  outer  shell  of  the 
chimney,  or  3*^*8  tons,  at  this  rate,  requires  an  area  of  12.88  sq.  ft.  of  brick- 
work. From  these  data  and  the  drawings  of  the  chinmev,  Mr.  Francis  cal- 
culates that  the  area  of  12.88  sq.  ft.  is  contained  In  a  portion  of  the  chimney 
extending '.2.428  ft.  from  one  of  its  octagonal  sides,  and  that  the  limit  to 
which  the  centre  of  pressure  may  be  shifted  Is  therefore  5.072  ft.  from  the 
axis.  If  shifted  beyond  this,  lie  save,  on  the  assumption  of  the  strength 
of  the  brickwork,  it  will  crush  and  the  chimney  will  fall. 

Calculating  that  the  wind-pressure  can  affect  only  the  upper  141  ft.  of  the 
chimney,  the  lower  70  ft.  being  protected  by  buildings,  he  calculates  that  a 
wind-pressure  of  44.02  lbs.  per  sq.  ft.  would  blow  the  chimnev  down. 

Baiudue,  in  a  paper  printed  in  the  transactions  of  the  Institution  of  Engi- 


'S'40 


OfitMKKYa. 


BMtHi,  Id  A<<otUMd,  for  lMr-6R,  Mir8:  "  tt  bad  prarlAtislj  been  ftneerUIned 
by  nbservation  of  the  eticceifl  bnd  failure  of  ootuftl  ohlmneys,  moA  ««pecially 
of  thone  which  mnp^ctivelr  stood  And  fell  durln^r  the  violent  utorms  of  18SA. 
that,  ill  order  that  a  round  ohimney  may  be  iufflcientljr  atable,  iu  weiipht 
should  be  such  that  a  pressure  of  vrind.  of  About  55  lbt>  per  wq.  fL  of  a  plAoe 
surface,  directly  ftiCinfC  the  wind,  or  sfT^  lbs.  per  sq.  ft.  of  the  plane  projec- 
tion of  a  cvlintlHcal  surface,  »  .  .  Shall  not  eauaa  the  resultant  pressure 
At  Any  bed -Joint  to  deviate  from  the  Axis  of  the  chimney  by  mora  toan  one 
quarter  of  the  outside  diameter  At  that  joint," 

According  t-o  RAtiklne*6  rule,  the  LAWrence  Wff.  Oo.*8  chlmnef  Is  adapted 
to  A  maximum  pressure  of  wind  on  a  plane  Acting  on  the  whole  height  of 
IB. BO  lbs.  per  sq.  ft.,  or  of  A  pressurs  of  SltTO  lbs.  per  sq.  ft.  Aotlner  on  the 
uppertnoet  141  ft.  of  the  chimney. 

mtel  Cmmnejm  ai^  largely  oominff  into  ttee,  especlAlly  for  tAll  cbim. 
neys  of  iron-works,  from  160  to  800  fbet  in  heiftht  The  AdvAntAces  olAimed 
Are:  fcfeftter  strenf^th  And  SAfety;  ftmA!ler  soaca  rsquired;  smAlTer  coet,  by 
80  to  60  per  cent,  as  compAred  with  bHck  colmneys;  AvoldAnce  of  inflltra^ 
tion  of  air  and  consequent  checking  of  the  draught,  common  in  brfok  chim- 
neys. They  are  usually  made  cylindrical  in  shape,  with  a  wide  curveil  flare 
for  10  to  35  feet  At  the  bottom.  A  heAvy  oAst-lron  base  plate  is  provided,  to 
which  the  chimney  is  riveted,  and  the  plate  ts  secured  to  a  masHive  founda- 
tion by  holding-down  bolts.  No  guys  Are  used.  F.  W.  Gordon,  of  the  Phila. 
Engineering  Works,  gives  tho  following  method  of  calculating  their  resist- 
ance to  wind  pressure  (Potcer.  Oct.  1893)  i 

In  tests  by  Sir  WilllAm  li'AlrbAlrn  we  find  four  experiments  to  determine 
the  strength  of  thin  hollow  tubes.  In  the  tAble  will  be  found  their  elements, 
with  their  broAking  strAin.  These  tubes  were  plAoed  upon  hollow  blocks. 
And  the  weigliu  ituspended  At  tbe  centra  from  a  block  fitiied  to  the  inside  of 
the  tube. 


OleAr 
BpAn, 
ft,  in. 


Thick- 

leeslron, 

in. 


Outside 
DlAm»> 
tar,  in. 


BmitionAl 

ArsAi 

in. 


BreAklng 

Weight, 

Ibe. 


BreAkln^Wt, 

Ibs^byClArlce'A 

FormttiB, 

Constant  1.9. 


i: 

IV. 


17 

33    5 
S3    6 


.11$ 
.0631 
.110 


IS 
12.4 
17.88 
18.18 


1.8001 
4.8009 
8.48T 
8.74 


2.7tM 
11,440 

8,400 
14,840 


«,«B7 
0,184 
7,80t 
18.010 


Edwin  Clarke  has  formulated  a  rule  from  experimental  conducted  by  him 
during  his  Investigations  Into  the  Use  Of  iron  and  steol  for  hollov  tube 
bridges,  which  is  as  follows  : 

Center  break-  j  -■^'^^  Q^  mAterial  in  sq.in.  x  MeAn  depth  in  in.  X  OonatAnt 
tng  loAd,in  tons. )  ^  CleAr  span  in  feet. 

When  the  constant  uesd  is  1.8,  the  cAloulAtion  tor  the  tubes  experimented 
upon  by  Mr.  FAlHiAini  Are  given  in  the  lAst  column  of  the  tAoIe.  D.  K. 
ClArk*s  *'  Kules,  TAbles.  Attd  IMtAj"  pa^e  818,  gives  a  rule  for  hollow  tube* 
AS  follows  <  Wm  ZAAD^TS  -»*  L,  Wm  breAking  weight  in  pounds  In  centre; 
i>  =  extreme  diAmeier  in  inches;   2*  s  thickness  in  inches;  £.«  length  he- 


tween  supports  in  inches;  S  at  ultimAte  tensile  strength  in  pounds  per  eq.  In. 
[ing  a^  the  strength  of  a  sauAre  inoh  oC  a  riveted  joint.  At  85,000  lbs. 


Taking 


per.  so.  in.,  thin  rtile  figures  as  follows  for  the  dilterent  exemplee  experi- 
mented upon  by  Mr.  FAirbalrn  :  I,  96?0;  11.  idlOO;  ill,  770O;  IV,  15.320. 

This  shows  A  close  epproximAtion  to  the  breAking  weight  obtained  by 
experiments  And  thAt  derived  from  ndwln  Clarke's  and  D.  K.  GlArk*s  nilea. 
We  therefore  assume  thAt  this  system  of  OAtoulAtlou  is  practicAlly  correct. 
And  thAt  it  is  eminently  eAfe  when  a  lArge  fACtor  of  safety  is  provided,  and 
from  tlie  fact  diet  a  chimney  mAJr  be  stAuding  for  OMtny  yoArs  witlntut 
receiving  anything  like  the  etrain  tsJcen  as  the  basis  of  the  calculation,  vis., 
fifty  pounds  per  square  foot.  Wind  pressure  at  fifty  pounds  per  square  foot 
may  be  asAumed  to  be  travelling  in  a  horisontal  direction,  and  be  of  the 
same  velocity  from  the  top  to  the  bottom  of  the  stack.  This  Is  the  extreme 
Assumption.  If,  howewr,  the  chimney  is  round,  its  effective  Area  would  be 
only  half  of  Its  diameter  plane.  We  assume  that  the  entire  force  may  be 
concentrated  in  the  oeiitrs  of  the  height  of  the  section  of  the  chlnuK^ 
ttttder  conatderAUon. 


BtZB  OF  CHUINETS. 


741 


Taking  as  an  example  a  ISS-foot  !ron  chimney  at  I^e:hkeepB!e,  N.  Y.,  the 
average  diameter  of  which  i»  90  inches,  the  effective  surface  m  square  feet 


iipon  which  the  foroe  of  the  wind  may  play  will  therefore  be  714  titiwB  185 
diTided  by  2,  which  mulilplied  br  50  gfTCS  a  total  wind  foroe  of  S9,487 
pouDds.^  The  ret^istance  of  the  chimney  to  breakiug  across  the  top  of  the 


ay  up,  we  have  a  beam  of  the  same  character.  It  is  a 
B  nail  way  up  the  chimney,  where  It  is  90  inches  in  diam- 
thick.    Taking  the  diametrical  section  above  this  line. 


foundation  would  be  S  14  X  1<K*  (that  is,  diameter  of  base)  X .%  X  8S,00D  -^ 
(7S0  X4) «  956,488.  or  10.6  times  the  entire  force  of  the  whid.  We  multiply 
the  half  height  above  the  Joint  In  inches,  750,  by  4,  because  the  chimney  m 
ixmsidered  a  fixed  beam  with  a  load  suspended  on  one  end.  In  calculating 
its  strength  half  way  up,  we  have  a  beam  of  the  same  character.    It  is  a 

fixed  beam  at  a  line  naif  1  *        -  .   — 

eter  and  .187  inch  thick. 

and  the  fonse  as  concentrated  in  the  centre  of  it.  or  half  vra^  up  from  tha 
point  under  consideration,  its  breaking  strength  Is:  8.14  X  90*  X  .187  X  35,000 
-f-  (881  X  4)  =  100,«0;  and  the  fbrce  of  the  wind  to  tear  it  apart  through  ita 
croos  section,  7H  x  ^'M  X  60-i-S«  11,888,  or  a  little  more  than  one  tenth  of 
the  sa^ngth  of  the  stack. 
The  Babcock  &  Wilcox  Co.*s  book  **  Steam**  HlustrateB  a  steel  chimney 
Lt  the  works  of  the  Maryland  Steel  Co,,  Sparrow's  Point,  Md.  It  is  985  ft. 
in  height  abotre  the  bai«et  with  internal  brick  lining  13'  9"  uniform  inside 


at  the  works  of  the  Maryland  Steel  Co.,  Sparrow's  Point,  Md.    It  is  985  f 
in  height  abotre  the  bai«et  with  internal  brick  lining  13'  9"  uniform  insic 
diameter.    The  shell  is  85  ft.  diam.  at  the  base,  tapering  in  a  curve  to  17  ft. 
85  ft.  above  the  base,  thence  tapering  almost  Imperceptibly  to  14'  8"  at  the 
top.    The  upper  40  feet  is  of  34-lnch  plates,  the  next  four  sections  of  40  ft. 


are  respectively  fl/88, 


'^- 


ll/»),  and  M  inch. 


Mseft  of  Foundatlona  fbr  Steel  Cltlaiiieja. 

(Selected  firom  circular  of  Phila.  Buglneering  Works.) 
Half-Linkd  CBimncTs. 

Diameter,  clear,  feet 8         4         6         8           7         0  11 

Height^feet  100       100       150       150         180       160  160 

Leeat diameter  foundation..  Ift'O'^    16'4''    90'4''   lil'lO"    8S7"    88'8"  SWW^ 

Least  depth  foundation. d'        6"         O'         S'           O'         10'  10* 

Height,  feet 1S5      800        800        S50       975  800 

Least  diameter  foundation. 18^6"   S8'8"      SS'        29^'   88'G"  80' 

Least  depth  foundation 7'        !(/        lO'        IS'        18'  14' 

UTelclit  of  Sbeet-tron  Smoke-etacka  per  Foot. 
(Porter  Mfg.  Ck>.) 


Diam., 
Inches. 


10 
18 
14 

16 

80 
88 
84 


Thick, 
nees 
W.Q. 


Ko.10 


Weight 

perft. 


7.80 
8.68 
0.68 
11.68 
18.75 
16.00 
16.35 


Diam., 
inches. 


96 
88 
80 
10 
18 
14 
16 


Thick- 
neas 
W.Q. 


No.  16 
•t 

«« 
No.  14 


Weight 
perft. 


17.60 

18.75 

90.00 

0.40 

11. n 

18.60 
16.00 


Diam. 
inches. 


90 
29 
94 
86 
88 
80 


Thick- 
ness 
W.Q. 


No.  14 


Weight 
perft 


18.88 
20.00 
91.66 
98.88 
85.00 
96.66 


Bkeet-lron  Clilinneja*    (Olumbus  Machine  Co.) 


Diameter 
Chimney, 
inches. 

Length 

Chimney, 

feetL 

Thick. 

ness 

Iron, 

B.  W.  G. 

WjOght, 

Diameter 

Chimney, 

inchea 

Length 

(}himney, 

feet. 

Thick. 

ness 

Iron, 

B.  W.  0 

W.Jg., 

10 

90 

No.  16 

160 

80 

40 

No.  15 

860 

16 

20 

»•        ]Q 

940 

89 

40 

M        1^ 

1.020 

80 

20 

**     16 

880 

84 

40 

u     14 

1,170 

22 

90 

**     16 

860 

86 

40 

M        1^ 

1.910 

24 

40 

"     16 

760 

88 

40 

M      18 

1.800 

20 

40 

«i     1^ 

8:26 

40 

40 

"     19 

1,680 

.     28 

40 

'*     15 

900 

742 


THE  8TEAM-EKGIK1S. 


THE  STEAM-ENGIKE. 

BzpaiiBloii  of  fltteftm.  Isothermal  and  Adlabatle*— Aoeord- 

ing  to  Mariotte*8  law,  the  volume  of  a  perfect  gas,  the  temperature  beiag 

kept  constant,  varies  inverse^  as  its  pressure,  or  p  oc  - ;  pv  =  a  constant. 

Tlie  curve  constructed  from  this  formula  is  called  the  Uothermal  curve,  or 
curve  of  equal  temperatures,  and  is  a  common  or  rectangular  hyperbola. 
The  relation  of  the  pressure  and  volume  of  saturated  steam,  as  deduced 
from  Regnault*s  experiments,  and  as  given  in  Steam  tables,  is  approxi- 
mately* according  to  Rankiue  (S.  E.,  p.  408),  for  pressures  not  exceeding  IM 


•U 


ii         i.o«» 


a  constant.     Zeuner  ^^^ 


ll)«.,  p  «  -r^,  orpoc  V 

found  that  the  exponent  1.0046  gives  a  closer  approximation. 
When  steam  expands  in  a  closed  cylinder,  as  in  an  engine,  according  to 

Kankine  (S.  E.,  p.  885),  the  approximate  law  of  the  expansion  Is  p  oc  — --,  or 

pec  v~V,  orpv^-*^  =  a  constant.  The  curve  constructed  from  thisfoi^ 
uiula  is  called  the  adiabatic  curve,  or  curve  of  no  transmission  of  heat. 

Peabodr  ;Therni.,  p.  112)  says :  **  It  is  probable  that  this  equation  was 
obtained  by  comparing  the  expansion  lines  on  a  large  number  of  indicator- 
diagrams.  .  .  .  There  does  not  appear  to  be  any  good  reason  for  using  an 
exponential  equation  in  this  connection, . . .  and  the  action  of  a  laggi^l  steam- 
engine  cylinder  is  far  from  being  adiabatic.  .  .  .  For  general  purposes  the 
hyperbola  Is  the  best  curve  for  comparison  with  the  expansion  curve  of  an 
indicator-card.  .  .  ."  Wolff  and  Denton,  Trans.  A.  S.  M.  E.,  fi.  175,  say ; 
**  From  a  number  of  cards  examined  from  a  variety  of  steam-engines  in  cur* 
rent  use,  we  find  that  the  actual  expansion  line  varies  between  the  lO/l 
adiabatic  curve  and  the  Mariotte  curve." 

Prof.  Thurston  (A.  8.  M.  E  ,  ii.  208),  says  he  doubts  if  the  exponent  eva* 
becomes  the  same  in  any  two  engines,  or  even  in  the  same  engines  at  dtf 
ferent  times  of  the  day  and  under  varyinjr  conditions  of  the  day. 

Bxpanalon  of  Steam  according  to  Marlotto's  Laiv  and 
to  the  Adiabatic  liaw.    (Trans.  A.  8.  M.  £.,  U.  ifiO.)— Marioite^s  law 

pv  =  piVi ;  values  calculated  from  formula  —  s=  -^{l  -I-  hyp  log  B),  In  whid 

Pa       ** 
12  =  Vt-^  v„  Pi  =  absolute  initial  pressure.  An  s  absolute  mean  pressureL 
Vi  s  initial  volume  of  steam  in  cylinder  at  pressure  pi,  Va=  final  volume  of 
steam  at  final  ^pressure.    Adiabatic  law:  pv^  >=  p|V|V;  values  calculated 
from  f ormula—  =  10«  -  *  -  95  -  V- 


Ratio  of  Mean 

Ratio  of  Mean 

Ratio  of  Mean 

tolnidal 

Ratio 

to  Initial 

RaUo 

to  Initial 

Ratio  of 

Pressure. 

of 

Pressure. 

of 

Pressure. 

Expan- 

Expan- 

Expan- 

sion 22. 

Mar. 

Adiab. 

sion  i?. 

Mar. 

Adiab. 

sion  £. 

Mar. 

Adiab. 

1.00 

1.000 

1.000 

8.7 

.624 

.600 

6. 

.465 

.438 

1.85 

.978 

.976 

8.8 

.614 

.690 

6.25 

.458 

.425 

1.60 

.987 

.981 

8.9 

.605 

.580 

6.5 

.448 

.418 

1.75 

.891 

.881 

4. 

.697 

.671 

6.75 

.481 

.408 

,847 

.884 

4.1 

.588 

.662 

7. 

421 

.808 

2,2 

.813 

.796 

4.8 

.680 

.664 

7.25 

.411 

.388 

.781 

.765 

4.8 

.572 

.646 

7.6 

.408 

.374 

.786 

.748 

4.4 

.564 

.588 

7.75 

.898 

.865 

.758 

.738 

4.6 

.^MJ 

.680 

8. 

.885 

.857 

2.8 

.726 

.704 

4.6 

.549 

.628 

8.85 

.877 

.349 

8. 

.700 

.678 

4.7 

.542 

.616 

8.5 

.869 

.318 

.688 

.666 

4.8 

.636 

.609 

8.75 

.862 

.885 

.676 

.654 

4.9 

.528 

.602 

9. 

.856 

.888 

sis 

.666 

.648 

6.06 

.522 

.496 

9.85 

.849 

.881 

.664 

.630 

68 

.506 

.479 

9.5 

.848 

.815 

.644 

.6fi20 

6.6 

.49-2 

.464 

9.75 

.886 

.800 

8.8 

.684 

.610 

5.75 

.478 

.450 

10. 

.880 

.808 

XBAK  AKD  TERMINAL  ABSOLUTS  PBBSSUBHS.     743 


BzMnd^A   Steam.— For  calculations  of 
Bed  tnat  steam  expaods  according  to  Marlotts*0 


lean  PreMnre  of   

jimss  it  is  Konerulij  assumed  t , „ 

law,  the  conre  of  the  expansion  line  being  a  hyperbola.  The  mean  praaiiir^ 
1  above  yaouum,  la  then  obtained  from  the  formuUt 

1  4-  hyp  log  R 


»Pi- 


or   Pm  =  Piil  +  hyp  log  12), 


in  which  Pm  is  the  absolute  mean  preisure,  pj  the  absolute  initial  pressure 
taken  as  uniform  up  to  the  point  or  cut-off,  Pt  the  terminal  pressure,  and  B 
the  ratio  of  expansion.   If  { s  length  of  strolce  to  the  cut-off,  L  =  total  stroke. 


p,l+l>ilh7pXDgj 


and  if  It »  y,    As  «  Pi' 


1+hyplogB 


nean  and  Terailiial   Absolute    PreMiiifea«^Hariotte»0 

Laiv*— The  yalnes  in  the  following  table  are  based  on  Marlotte's  law, 
except  those  in  the  last  column,  which  give  theonean  prennre  of  supertieated 
steam,  which,  according  to  Bankine,  expands  in  a  cylinder  according  to 
the  law  p  «  «  ~  il.   These  latter  ralues  are  calculated  f r(«m  the  formula 

Bg^lT-lMg-  B'^  may  be  found  by  extracting  the  square  root  of  4 
Pi  a  /» 

four  times.  From  the  mean  absolute  pressures  given  deduct  the  mean  bade 
pressure  (absolute)  to  obtain  the  mean  effectlTe  pressure. 


Bate 
of 
Expan- 
sion. 

Cut- 
off. 

Ratio  of 

Mean  to 

Initial 

Pressure. 

Ratio  of 

Mean  to 

Terminal 

Pressura. 

Ratio  cf 
Terminal 

to  Mean 
Pressure. 

Ratio  of 

Initial 

to  Mean 

Pressure. 

Ratio  of 

Mean  to 

Initial 

Dry  Steam. 

80 
88 

0.068 
0.066 
0.068 

o.oce 

0.045 
0.060 
0.066 
0.068 
0.066 

o.on 

0.075 
0.077 
0.068 
0.091 
0.100 
0.111 
0.185 
0.148 
0.150 
0.166 
0.175 
O.80O 
0.885 
0.890 
0.275 
0.800 
0.388 
0.850 
0.875 
0.400 
0.460 
O.fiOO 
0.660 
0600 
0.685 
0.660 
0.675 

0.1467 
0.1547 
0.1688 
0.1741 
0.1860 
0.1098 
0.8161 
0.8858 
0.8473 
0.8690 
0.2630 
0.8743 
8.8004 
0.3069 
0.8808 
0.8558 
0.8849 
0.4210 
0.4847 
04658 
0.4807 
0.5818 
0.6606 
0.5966 
0.6308 
0.6615 
0.6995 
0.7171 
0.7440 
0.7664 
0.8095 
0.8465 
0.8786 
0.9066 
0.9187 
0.9898 
0.9405 

4.40 
4.85 
4.» 
4.18 
4.09 
4.00 
8.89 
8.77 
8.71 
8.64 
8.59 
8.66 
8.48 
8.40 
8.80 
3.80 
8.08 
8.95 
8.90 
8.79 
8.74 
2.61 
8.60 
8.89 
889 
8.80 
2.10 
8.05 
1.96 
1.91 
1.80 
1.69 
1.60 
1.51 
1.47 
1.48 
1.39 

6.887 
0.281 
0.885 
0.889 
0.844 
0.860 
0.856 
0.865 
0.869 
0.875 
0.279 
0.880 
0.887 
0.894 
0.806 
0.818 
0.821 
0.889 
0.346 
0.860 
0.864 
0.888 
0.400 
0.419 
0.487 
0.454 
0.476 
0.488 
0.605 
0.6^ 
0.666 
0.591 
0.686 
0.668 
0.660 
0.699 
0.718 

6.88 
6.46 
6.11 
5.75 
5.88 
6.00 
4.68 
4.24 
4.06 
4.85 
8.72 
8.65 
8.44 
8.84 
8.08 
8.81 
2.60 
8.87 
2.30 
2.15 
2.08 
1.99 
1.78 
1.68 
1.68 
1.51 
1.48 
1.89 
1.84 
1.81 
1.84 
1.18 
1.14 
1.10 
1.09 
1.07 
1.06 

0.186 

S6 

S4 

22 

SO 
18 
16 

0.186 

15 

14 

13.88 
18 

0.854 

12 

11 
10 
0 

............ 

8 

6.M 
6.00 

0.870 
•••  d.*4i7  '" 

5.n 

6.00 
4M 

0.506 

4.00 
8.08 

0.688 

lis 

0.648 

2.86 
8.66 

0.707 

S.60 
2.88 
2.00 
1.88 
1.66 
1.60 

0.766 
0.800 
0.840 
8.874 
0.900 

1.54 
1.48 

0.980 

744 


TEB  BTEAM-ENGINB. 


Calevlation  of  Mean  EflTeetiTe  PreMnre,  <Aeaniii€e  and 
Compreflslon  OoiiBldered*->Iii  the  above  tables  no  aooount  ia  taken 

of  clearance,  which  In  actoal 
steam-engines  modlfles  the  ratio 
of  expanaon  and  the  mean  prea- 
sure;  nor  of  comnresBion  and 
back-pressure,  which  diminish 
the  mean  effeocire  pressure.  In 
the  following  calculatkm  these 
elements  are  considered. 

L  K  length  of  stroke,  I  =  length 
before  cut-off,  x  s  length  of  com* 
pression  part  of  stroke,  e  =  clear- 
anoe,  px  s  initial  pressure,  p^  = 
back  pressure^  pe  »  preasurs  of 
clearance  steam  at  coid  of  com- 
fi  pression.  All  pressures  are  abso- 
^^  lute,  that  is,  measured  from  a 
perfect  vacuum. 
Fio.  187. 

Area  of  ABCD  =  p»(l  +  c)(l  +  hyp  log  j;J|)  X 

C  -poc(l  +  hyp  log  ?^)  -l)5(»  +  c)(l  +  hyplog£±S); 

0  -  (Pa  -  Po)C  =  PiC  - PftC*  +C). 

Areaof  A  =  ABCD  -  (B  +  C  -f  D) 

«  Pxil  +  e)(l  +  hyp  log  :5l+£) 

-  [p6(i-«)  4-l>6(«  +  c)(l+hyplog2^)+p.o-  pj(«+c)J 

-Pid+oO+bypiog^) 

-PftCci-*)  +Or+c)hyplog^^]-IH«. 

Mean  effecttve  pressure  >■  "^^ — • 

BzAMPUi.— Let  £  »  1,  I  s  0.86,  «  ar  0.86,  e  s  0.1, pt  a  00 lbs.,  p^  e£Ibi. 
Area  A  «  00(.86+  4)(l  +hyp log -H.) 

-2  [u  -  .8^+  JB  hyp loK-^]  -  »X  a 

s  81(1  +  1.146) -8[.75  + 86X1.868]  -6 

Bs  46.045  —  8.377  —  6s  86.668  s  mean  effective  pressure. 

The  actual  indicator-diagram  generally  ahows  a  mean  pressure  consider, 
ably  less  than  that  due  to  the  initial  pressure  and  the  rate  of  expansion.  The 
causes  of  loss  of  pressure  are:  1.  Friction  in  the  stop- valves  and  steam- 
pipes.  2.  Friction  or  wire-drawing  of  the  steam  during  admission  and  cut- 
olx,  due  chiefly  to  defective  valve-gear  and  contracted  steam-passages. 
8.  Liduefaction  during  expansion.  4.  Exhausting  before  the  engine  has 
completed  its  stroke.  5.  Compression  due  to  early  closure  of  exhausU 
6.  Friction  in  the  exhaust-ports,  passages,  and  pipes. 

RA-evaporation  during  expansion  of  the  steam  condensed  during  admis- 
sion, and  valve-leakage  after  cut-off,  tend  to  elevate  the  expansion  line  of 
the  diagram  and  increase  the  mean  pressure. 

If  the  theoretical  mean  pressure  be  calculated  from  the  initial  pressure 
and  the  rate  of  expansion  on  the  supposition  that  the  ezpansion  curve  txtr 


liXFAl^SION  OF  8TKA1L  745 

lows  Hariotte^s  law,  pv  a  a  constant,  and  the  neoenary  corrections  are 
made  for  clearance  and  compression,  the  expected  mean  pressure  in  practice 
mav  be  found  by  multiplylDg  the  calculated  results  by  the  factor  in  the 
following  table,  according  to  Seaton. 

Particulars  of  Engln&  Factor. 

Eanaansi^e  engine,  special  Talye-gear,  or  with  ftieparate 
cut-off  valve,  cylinder  jacketed 0.M 

Expansive  engine  having  large  ports,  etc.,  and  good  or* 
dlnary  valves,  cylinders  jacketed 0.9  to  0.M 

Expanave  engines  with  the  ordinary  valves  and  gear  at 
in  genend  practice,  and  usjacketed  0.8toOL85 

Compound  engines,  with  expansion  valve  to  h.p.  cylin- 
der; cylinders  jaclieted,  and  with  large  ports,  etc 0.0  to  O.M 

Compound  engines,  with  ordinary  slide-valves,  cylinders 
jacketed,  and  good  ports,  etc 0.8  to  0.85 

Compound  engines  as  In  general  practice  In  the  merchant 
service,  with  early  cut-off  in  both  cylinders,  without 
jackets  and  expansion-valves 0l7  to  0.8 

Fast-running  engines  of  the  type  and  design  usually  fitted 
in  war-ships 0.6to0.8 

If  no  correction  be  made  for  clearance  and  compression,  and  the  engine 
Is  in  accordance  with  general  modem  practice,  the  theoretical  mean  pres- 
sure may  be  multiplied  by  0.96,  and  the  product  by  the  proper  factor  in  the 
tahle,  to  obtain  the  expected  mean  pressure. 

CMLren  tlie  Initial  Preaanre  and  the  Awerase  Preaanre.  to 
Find  the  Ratio  of  BxpanaloB  and  tbo  Period  of  Admla- 
•Ion. 

P  m  initial  absolute  pressure  fai  lbs.  per  sq.  In. ; 

p  B  average  total  pressure  during  stroke  In  lbs.  per  sq.  in.; 

X  ■■  length  of  stroke  in  inches; 

I  B  period  of  sdmlsslon  meosiured  from  beginning  of  stroke; 

c  s  clearance  in  inches; 

B a>  actual  ratio  of  expansion  ■  ■  T--  ••••••••••   (P 

TO  +  hyplogJg), 
'  B 

To  find  aTerage  pressure  p,  taking  account  of  dearsnoe^ 

^_at-l-c)  +  TO  +  e)hypbgB-n) ^ 

wheDOO  j>£-fi\!>i>(I  +  e)a  +  lqrp>ogS)t 

Oiven  p  and  P,  to  find  R  and  I  (by  trial  and  error)  .^There  being  two  un- 
known quantities  B  and  2,  assume  one  of  them,  viz.,  the  period  of  admission 
J,  subetltute  it  In  equation  (8)  and  solve  for  B,    Substitute  this  value  of  B  in 

the  formula  OX  or  2  s  ■   ^?  -  e,  obtained  from  formula  (1%  and  find  I    If 

the  result  is  greeted  than  the  sssumed  value  of  I,  then  the  assumed  value  of 
the  period  of  admission  is  too  long;  if  less,  the  assumed  value  Is  too  short. 
Assume  a  new  value  of  f,  substitute  It  In  formula  (8)  as  before,  and  continue 
by  this  method  of  trial  and  error  till  the  required  values  of  B  and  I  are 
ODtained. 
fiZA]iPLB.~PB70,  pai  48.78,  £-60",  caS'stoflndl.    Assume  I  a  81  in. 

hyp  log  It «  .653,   whence   B  s  1.9S, 


746  THE  STEAM-EKGIlirB. 


which  is  greater  than  the  assumed  value,  21  inchM. 
Now  assume  2  =  15  inches  : 
48.78^ 

hyp  log  R  = 


Therefore  R  ts  as,  and  I  s  15  Inches. 

Period  of  Adminion  Required  for  a  Given  Actual  Ratio  of  Expantion: 

I  =  ^^-Clnlnches (4) 

In  percentage  of  stroke,  I  =  ^OH-pct.  clearance  ^  ^  ^  dearance.    .   (5) 
Terminal  pre»eure^^}f-^^  =  5 («) 

Li  -f-C  JS 

Pi-eseure  at  any  oiherlPoint  of  the  JErpantion.— Let  Lx  b  length  of  stroke 
up  to  the  given  point. 

Pressure  at  the  given  point  s-:^^^ (7) 

Ltft  c 

UrOBK  OF  STEAIK  IN  A  SINOI^B  CYLINBEB. 

To  facilitate  calculations  of  steam  expanded  in  cylinders  the  table  on  the 
next  page  is  abridged  from  Clark  on  the  Steam-engine.  The  actual  ratios 
of  expansion,  column  1,  range  from  1.0  to  8.0,  for  which  the  hjperbolte 
logarithms  are  given  in  column  2.  The  8d  column  contains  the  periods  of 
admission  relative  to  the  actual  ratios  of  expansion,  as  percentages  of  the 
stroke,  calculated  by  formula  (5)  above.  The  4th  column  gives  the  values 
of  the  mean  pressures  relative  to  the  initial  pressures,  the  latter  being  taken 
as  1,  calculated  by  formula  (2).  In  the  calculation  of  columns  8  and  4,  clear- 
ance is  taken  into  account,  and  its  amount  is  assumed  at  7%  of  the  stroke. 
The  final  pressures,  in  the  5tb  column,  are  such  as  would  be  arrived  at  by 
tlie  continued  expansion  of  the  whole  of  the  steam  to  the  end  of  the  stroke, 
the  initial  pressure  being  eaual  to  1.  They  are  the  reciprocals  of  the  ratios 
of  expansion,  column  1.  Tne  6th  column  contains  the  relative  total  per- 
formances of  equal  weights  of  steam  worked  with  the  several  actual  ratios 
of  expauMon;  the  total  performance,  when  steam  is  admitted  for  the  whole 
of  the  stroke,  without  expansion,  being  equal  to  1.  They  are  obtained  by 
dividing  the  figures  in  column  4  by  those  In  column  5. 

The  pressures  have  been  calculated  on  the  supposition  that  the  preesnre  of 
steam,  during  Its  admission  into  the  cylinder,  is  uniform  up  to  the  point  of 
cutting  off,  and  that  the  expansion  is  continued  regularlv  to  the  ena  of  the 
stroke.  The  relative  performances  have  been  calculated  without  any  allow- 
ance for  the  effect  of  compressive  action . 

The  calcularions  have  been  made  for  periods  of  admission  ranginsr  from 
100j(,  or  the  whole  of  the  stroke,  to  6.4%,  or  1/16  of  the  stroke.  And  Uiough, 
nominally,  the  expansion  is  16  times  in  the  last  Instance,  it  is  actually  only 
8  times,  as  given  in  the  first  column.  The  great  difference  between  the 
nominal  and  the  actual  ratios  of  expansion  is  caused  by  the  dearance, 
which  Is  equal  to  7%  of  the  stroke,  and  causes  the  nominal  volume  of  ateam 
admitted,  namely,  6.4%,  to  be  augmented  to  6.4  +  7  =  18.43(  of  the  stroke,  or, 
say,  double,  for  expansion.  When  the  steam  is  cut  off  at  1/9,  the  actual 
expansion  is  only  6  times;  when  cut  off  at  1/5,  the  expansion  is  4  ttines; 
when  cut  off  at  ^,  the  expansion  is  ^  times;  and  to  effect  an  actual  expan- 
sion to  twice  the  initial  volume,  the  steam  is  cut  off  at  4IS^  of  the  Mtok^ 
not  at  half -stroke. 


WORK  OF  8TBAU  IK  A  8IKGLB  CYLUTDEB.        747 


BzpAiislTe  Worklmr  of  8team>-Actnml  Ratios  of  Bzpaii- 
■Ion,  with  the  KelatlTe  Periods  ol  Adaiiiielon,  Prese* 
urea,  and  Perfor 


Steam-pressure  100  lbs.  absolute, 
'if  the  stroke. 


Clearance  at|each  end  of  the  cylinder  7% 

(SlNGLB  CtLINDBR.) 


1 

8 

8 

4 

5 

• 

7 

8 

9 

1  Actual  Ratio  of  Ex- 
pansion, or  No,  of 
volumes  to  which 
the  Initial  Volume 
is  Expanded. 

flthmo?Aotu*ai 
sion. 

11 

5    •^ 

11 

Ratio  of  Total  Per- 
formance of  Equal 
WelRbts  of  Steam. 
(Col  4 -H  Col  5.) 

III 
Si 

Quantity  of  Steam 
Consumed  per 
H.P.     of     Actual 
Work  done  per  bow 

Net  Capacity  of  (bl- 
inder per  lb.  of  fOO 
lbs.     Steam    ad- 
mitted in  1  stroke. 
Cubic  feet. 

1 

.0000 

100 

1.000 

1.000 

1.000 

58,273 

84.0 

4.05 

1.1 

.0068 

90.8 

.996 

.909 

1.096 

63,850 

31.0 

4.45 

1.18 

.1696 

88.8 

.986 

.847 

1.164 

67,&W 

29.2 

4.78 

1.28 

.2070 

80 

.960 

.813 

1.906 

70,246 

28.8 

4.98 

1.8 

.2624 

75.8 

.969 

.769 

1.261 

78,513 

86.9 

5.26 

1.89 

.3296 

70 

.958 

.719 

1.325 

77,242 

25.6 

6.68 

1.45 

.8n6 

66.8 

.942 

.600 

1.365 

79,555 

24.9 

5.87 

1  M 

.4817 

fi2.5 

.925 

.649 

1.425 

88,055 

28.8 

6.28 

1.6 

.4700 

69.9 

.918 

.625 

1.461 

85,125 

23.8 

6.47 

1.75 

..5605 

54.1 

.888 

.571 

1.546 

90,115 

22.0 

7.08 

1.88 

.6314 

50 

.860 

.582 

1.616 

94,200 

81.0 

7.61 

2 

.6081 

46.5 

.886 

.5 

1.672 

97,432 

20.8 

8.09 

2.88 

.8241 

40 

.787 

.439 

1.798 

104,466 

19.0 

9.28 

2.4 

.8r65 

87.6 

.766 

.417 

1.887 

107,0P0 

18.5 

9.71 

S.65 

.9745 

88.8 

.726 

.877 

1.926 

112,2•^0 

17.7 

10.72 

2.0 

1.066 

29.9 

.692 

.345 

2.006 

116,8a^ 

16.9 

11.74 

8.3 

1.168 

26.4 

.658 

.318 

2.068 

121,886 

16.8 

12.95 

8.86 

1.209 

26 

.637 

.298 

2.129 

124,066 

16.0 

18.56 

8.0 

1.281 

22.7 

.608 

.278 

8.187 

127,450 

15.5 

14.57 

8.8 

1.885 

21.2 

.580 

.268 

8.940 

180,538 

15.2 

15.88 

4 

1.886 

19.7 

.569 

.260 

2.278 

132.770 

14.9 

16.19 

4.2 

1.485 

18.5 

.561 

.288 

2.315 

134.900 

14.7 

17.00 

4.5 

1.501 

16.8 

.526 

.222 

2.870 

188,180 

14.84 

18.21 

4.8 

1.560 

15.8 

.503 

.208 

2.418 

140,920 

14.05 

19.48 

6 

1.609 

14.4 

.488 

.200 

2.440 

142,180 

13.08 

20.28 

5.2 

1.649 

13.6 

.476 

.198 

2.466 

148,780 

13.78 

21.04 

6.5 

1.706 

12.5 

.457 

.182 

2.511 

146,825 

18.58 

28.25 

6.8 

1.758 

11.4 

.438 

.172 

2.547 

148,390 

18.34 

28.47 

6.9 

1.775 

11.1 

.482 

.169 

2.566 

148,940 

13.29 

83.87 

6.2 

1.825 

10.8 

.419 

.161 

2.586 

150,680 

13.14 

86.09 

6.8 

1.841 

10 

.418 

.159 

2.507 

151,870 

13.08 

85.49 

6.6 

1.887 

9.2 

.898 

.152 

2.619 

152,606 

12.98 

26.71 

7 

1.946 

8.8 

.881 

.148 

2.664 

156,200 

12.75 

28  88 

7.8 

^1.988 

7.7 

.869 

.187 

2.693 

186,960 

12.61 

89.54 

7.6 

2.088 

7.1 

.857 

.182 

2.711 

157,975 

18.53 

80.70 

7.8 

2.054 

6.7 

.348 

.128 

2.719 

158,414 

12.60 

81.57 

8 

2.079 

6.4 

.842 

.125 

2.736 

159,488 

11.88 

82.88 

AssvMPTioNB  OF  THK  TABLB.^Tbat  tlie  Initial  pressure  Is  uniform;  that 
the  expansion  Is  complete  to  the  end  of  the  stroke;  that  the  pressure  In  ex- 
pansion Taries  InTerselv  as  the  Tolume;  that  there  Is  no  back-pressure  of 
exhaust  or  of  compression,  and  that  clearance  Is  7%  of  the  stroke  at  each 
end  of  the  cylinder.  No  allowance  has  been  made  for  loss  of  steam  by  cyl* 
inder-condeusation  or  leakage. 

Volume  of  1  lb.  of  steam  of  100  lbs.  pressure  per  sq.  In.,  or  14,400 

lbs.  per  sq,  ft. 4.88cu.ft. 

Froduet  of  initial  pressure  and  volume 68,868  f(.-lbi. 


748 


THE  STEAH-EKOnSTB. 


Thou^  a  uniform  cloamnce  of  9j(  at  each  end  of  the  stroke  has  been 


the  clearance,  T%,  that  has  been  anumed,  the  table  gives  approzimate  re- 
sults sufficient  for  most  practical  purposes,  and  more  trustworthy  than  re- 
sults deduced  by  calculations  based  on  simple  tables  of  hyperbolic  loga- 
ritbais,  where  ofearance  is  iiegleoted. 

Weieht  of  steam  of  100  lbs.  total  initial  pressure  admitted  for  one  stroke, 
per  cubic  foot  of  net  capacity  of  the  cylinder,  in  decimals  of  a  pound  = 
reciprocal  of  fli^res  in  column  9. 

Total  actual  work  done  by  steam  of  100  lbs.  total  initial  pressure  in  one 
stroke  per  cubic  foot  of  net  capacity  of  cylinder,  in  foot-pounds  =  flgwes 
in  column  7  -*-  fleures  in  column  0. 

RULV 1:  To  find  the  net  cs^Micity  of  cylinder  for  a  given  weight  of  steam 
admitted  for  one  stroke,  and  a  given  actual  ratio  of  expanston.  (Column  9 
of  table.)-'Multiply  the  volume  of  1  lb.  of  steam  of  the  given  pressure  by  the 
given  weight  in  pounds,  and  by  the  actual  ratio  of  ezpasstoa.  Multiply  the 
product  by  100,  and  divide  by  100  plus  the  percentage  of  clearance.  The 
quotient  is  the  net  capacity  of  the  cylinder. 

Rule  S:  To  find  the  net  capacity  of  cylinder  fbr  the  performance  of  a 
given  amount  of  total  actual  work  in  one  stroke,  with  a  given  initial  press- 
ure and  actual  ratio  of  ezpansion.^Divide  the  given  work  bv  the  total 
actual  work  done  by  1  tb.  of  steam  of  the  same  pressure,  and  with  the  same 
actual  ratio  of  ezpflmslon;  the  quotient  is  the  weight  of  steam  necessary  to 
do  the  given  work,  for  which  the  net  capacity  Is  found  by  Rule  1  preceding. 

NorB.^1.  Conversely,  the  weight  of  steam  admitted  per  cubic  foot  of  net 
capacity  for  one  stroke  is  the  reciprocal  of  the  cylinder-capacity  per  pound 
of  steam,  as  obtained  by  Rale  1. 

t.  The  total  actual  work  done  per  cubic  foot  of  net  capaci^  for  one  stroke 
is  the  reciprocal  of  the  cylinder-capacity  per  foot>ponnd  of  work  done,  as 
obtained  by  Rule  2. 

8.  The  total  actual  work  done  per  square  inch  of  piston  per  foot  of  the 
stroke  is  l/144th  part  of  the  work  done  per  cubic  foot. 

4.  The  reslstaiice  of  back  pressure  of  exhaust  and  of  compressian  are  to 
be  added  to  the  net  work  required  to  be  done,  to  find  the  total  actual  work. 

ArPENDDC  TO  ABOTS  TABLK— MtTLTIPLrBRS  FOR  NkT  CTLDrDBS-CAPAOnT,  AXD 

Total  Actual  Work  donb. 


(For  steam  of  other  pressures  than  100  lbs.  per  square  iscfa.) 

Hultipliera. 

Total  Pres- 

MultipUers. 

Total  Free- 

For  Col.  7. 

For  Col.  0. 

Pk>r  Col.  7. 

ForOol.9. 

sures  per 
square  inch. 

Total  Work 

by  1  lb.  of 

Steam. 

Capacity 
of 

sures  per 
square  mch. 

Total  Work 

by  lib.  of 

Steam. 

Capacity 
of 

Cylinder. 

Cylinder. 

lbs. 

lbs. 

66 

.ore 

1.00 

100 

1.000 

1.O0 

70 

.081 

1.40 

110 

1.009 

.917 

re 

.086 

LSI 

190 

1.011 

.843 

80 

.088 

1.94 

ISO 

1.016 

.781 

86 

.001 

1.17 

140 

1.028 

.780 

00 

.006 

i.n 

150 

1.096 

J6S3 

95 

.098 

1.06 

160 

1.031 

.644 

The  figures  In  the  second  column  of  this  table  are  derived  by  multiplying 
the  total  pressure  per  squai-e  foot  of  anv  given  steam  by  the  volume  in 
cubic  feet  of  1  lb.  of  snch  eteam.  and  dividing  the  product  by  01869,  which 
is  the  product  in  foot-pounds  for  steam  of  100  lbs.  pressure.  The  quotient 
Is  the  multiplier  for  the  given  pressure. 

The  figures  in  the  third  column  are  the  quotients  of  the  figures  In  the 
seoond  column  divided  by  the  ratio  of  the  pressure  of  the  given  steam  to  100 
lbs. 

measurea  for  Comparing  Uie  Bnty  of  Bmstnesa-OHpaoity  Is 
measured  in  horse-powers,  expressed  by  the  initials,  uTP.:  1  H.P.  m  8S.00P 
ft.4bs.  per  minute,  a  550  fu-lbs.  per  seoond,  m  1,980^000  fk-Ihs.  per  hour. 


WORK  OF  STEAM  tK  A  8IKGL1S  CTLINDEB.        749 

1  ft*Ib.  a  a  prMKure  of  1  lb.  exerted  tbrouftlk  aspaee  of  1  ft  Economy  Is 
meaaureil.  1,  in  pounds  of  coal  f)«r  horie-i>ower  per  hour;  8,  in  pounds  of 
steam  per  horse-power  per  hour.  The  second  of  these  measures  is  the  more 
accurate  and  soientittc^  since  the  eni^lne  Iksee  steam  and  not  ooal,  and  It  is 
iudepndent  «>f  the  economy  of  the  boiler. 

Ill  gas-enirine  tests  the  common  measure  Is  the  number  of  coble  f^et 
of  gas  (measunHl  at  atmospheric  pressure)  per  horse^power,  but  as  all  pas 
Ih  not  of  the  same  quality,  it  is  neceemry  for  comparison  of  tests  to  give  the 
analysis  of  the  gas.  When  the  gas  for  one  enghie  is  made  in  one  gas-pro- 
fliicer,  then  ihe  number  of  poitnds  of  coal  used  in  the  producer  per  hour  per 
horse-power  of  the  engine  is  the  proper  measure  of  economy. 

Economy,  or  duty  of  an  engine*  is  also  measured  in  the  number  of  foot- 
pounds of  nork  done  per  pound  of  fuel*  As  1  horse-power  is  equal  to  1.980,- 

000  ft.-Iba.  of  work  in  an  hour,  a  duty  of  1  lb.  of  coal  per  H.P.  per  hour 
would  be  equal  to  1,060,000  ft-lbe.  per  lb.  of  fuel;  8  lbs.  per  H.P.  per  hour 
tNiiuUs  M0,000  ft.-lbs.  per  lb.  of  f nel«  eto. 

The  duty  of  puraping-engliies  is  commonly  expressed  by  the  number  ot 
foot-pouuds  of  work  done  per  100  lbs.  of  coal. 

Whrn  the  duty  of  a  pumping-englne  is  thus  giten,  the  eqnlvaleDt  number 
of  pounds  of  fuel  consumed  per  hone-power  per  hour  is  found  by  dividing 
106  by  the  number  of  millions  of  foot-pounds  of  duty.  Thus  a  pum ping- 
engine  giving  a  duty  of  99  millions  is  equivalent  to  196/90  b  2  lbs.  of  fuel  per 
hnnif^power  per  hour. 

Bflclency  MeaaivreA  tn  Thennal  Vnlts  per  Xllavte*-- 
8i»m«  writeits  expr%*88  the  efficleuoy  of  an  engine  in  lenns  of  the  uuhil>ei-  of 
thermal  units  used  by  the  engine  per  minute  for  each  Indicated  horse-power, 
instead  of  by  the  number  of  pounds  of  steam  used  per  hour. 

The  heat  chargeable  to  an  engine  per  pouod  of  steam  Is  ihe  difference  be- 
iween  the  total  heat  in  a  pound  of  steam  at  the  boiler-pressure  and  that  in 
a  pound  of  the  feed  water  entering  the  boiler.  In  the  case  of  condensing 
engines,  suppose  we  have  a  teniperature  in  the  hot-well  of  10!^  F.,  oorre- 
^ponding  toa  vacuum  of  28  In.  ol  mercury*  or  an  absolute  pressure  of  1  lb. 
per  sq.  in.  abova  a  perfect  vacuum  :  we  may  feed  the  water  Into  the  boiler 
M  thatrremperature.  In  the  case  of  anon-condenslng-engine,  by  using  a  por^ 
tion  of  the  exhaust  steam  In  a  good  feed-water  heater,  at  a  pressure  a  trifle 
above  the  atmosphere  (due  to  the  resistance  of  the  exhaust  pas^^ages 
111  rough  the  heater),  we  may  obtain  feed-water  at  212*.  One  pound  of  steam 
Bsed  by  the  etigine  then  would  be  equivalent  to  thermal  units  as  follows : 

1  Yessure  of  steam  by  gauge: 

SO  95  100  105  160  m  «00 

f  otal  heat  In  steam  above  89* : 

1179.8     1179.6     1185.0     1189.5      1193.6     1197.0     1S00.3 

Subtracting  69.1  and  180.9  heat-units,  respectively,  the  heat  above  S2*  in 
feed -water  or  101*  and  S12*  F.,  we  laave^ 

Heat  given  by  boiler: 

FtedatlOl* 1103.7     1110.6     1116.»      1120.4     }124.4     1187.9     1181.1 

S^eedat8l8* 891.9       990.7     1004.1      1006.6     1018.6     1016.1      1019  8 

Thermal  units  per  minute  used  by  an  engine  for  each  pound  of  steam  used 
per  Indicated  horse-power  per  hour: 

Feed  at  101* 18.40       18.51       18.00       16.67       15.74       16.80       18.86 

Feed  at  212* 16.58       16.66       16.74       16.81       16.88       16.04       16.99 

BxAKPLBS.-->A  trlpte-expsnsion  engine,  condensing,  with  steam  at  175  lbs., 
rauge  and  vacuum  28  in.,  uses  18  Ibe.  of  water  per  LH.P.  per  hour,  and  a 
high-speed  non-condensing  engine,  with  steam  at  100  lbs.  gauge,  uses  30 
lbs.    How  many  thermal  units  per  minute  doea  each  consume  t 

AM.'-iZ  X  18«80  =3  244.4,  and  80  X  16.74  •»  508.2  thermal  units  per  minute. 

A  perfect  engine  converting  ail  the  lieat-^nergy  of  the  steam  Info  woik 
wouM  require  83,000  ft.>lbs.  -^  778  :=  42.4164  thenmil  units  per  minute  per 
Indicated  horse*power.  This  figure,  42.4164,  therefore,  divided  by  the  num- 
ber of  tliermal  units  per  minute  per  I.H.P.  consumed  by  su  engine,  gives  its 
efficiency  as  compared  with  an  ideally  perfect  engine.  In  the  examples 
above,  42.4164  divided  by  844.4  and  by  S02.8  giv^S  17^6^  and  ^Abjl  efficiency, 
resnecttrelv. 

Total  ITorlc  Horn*  br  One  Pontid  of  Steam  fixpanded  fa 
a  Single  Cylinder*  (CoJunm  7  of  table  H- If  \  pound  of  watu*  he  con- 
verted Toto  steam  of  atmospheric  pressure  ss  21 16.8  lbs.  per  sq.  ft.,  it  occu- 
pies a  volume  equal  to  26.86  cu.  fu    The  work  done  is  equal  to  8116.8  Ibft 


750 


THE  STEAM-ENGINE* 


X  26.86  ft.  s  55J86  ft.  lbs.  The  heat  eqalvalent  of  thh  work  ts  (55.788  -*-  77B 
s=)71.7  units.  This  is  the  work  of  1  lb.  of  steam  of  one  atmosphere  acting 
on  a  piston  without  expansion. 

The  KrosB  work  thus  done  on  a  piston  by  1  lb.  of  steam  eeneittted  at  total 
pressures  varying  from  16  lbs.  to  100  lbs.  per  sq.  in.  varies  m  round  numbera 
from  66,000  to  6^,000  ft. -lbs.,  equivalent  to  from  78  to  80  uniU  of  heat. 

This  work  of  1  lb.  of  steam  without  expansion  is  reduced  by  clearance 
according  to  tbe  proportion  it  bears  to  the  net  capacity  of  the  cylinder.  If 
the  clearance  be  t%  of  the  stroke,  the  work  of  a  given  weight  of  steam  with- 
out expansion,  admitted  for  the  whole  of  the  stroke,  is  reduced  in  tiie  ratio 
of  107  to  100. 

Having  determined  by  this  ratio  the  quantity  of  work  of  1  lb.  of  steam  with- 
out expansion,  as  reduced  bv  clearance,  the  work  of  the  same  weight  of  steam 
for  various  ratios  of  expansion  may  be  found  by  multiplying  it  by  the  relative 
performance  of  equal  weights  of  steam,  given  in  the  oth  column  of  tlie  table. 

Quantity  of  Steam  Consained  per  Hone-poiv^er  or  Total 
UTork  per  Hour.  (Column  8  of  table.)— The  measure  of  a  horse-power 
Is  the  performance  of  88,000  ft. -lbs.  per  minute,  or  1,980,000  ft.-lbs.  per  hour. 
This  work,  divided  by  the  work  of  1  lb  of  steam,  gives  the  weight  of  Kteam 
required  per  horse-power  per  hour.  For  example,  the  total  actual  work 
done  in  the  cylinder  by  1  lb.  of  100  Ibs.^eam,  without  expansion  and  with 
7%  of  clearance,  is  58,*4!73  ft.-lbs. 


and  -JJw^  =  84  lbs.  of  steam,  is  the  weight 


of  steam  consumed  for  the  total  work  done  in  the  cylinder  per  horse-power 
per  liour.  For  any  sliorter  period  of  admission  with  expansion  the  weight 
of  steam  per  horse-power  is  less,  as  the  total  work  of  1  lb.  of  steam  Is  more, 
and  may  be  found  by  dividing  1.980,000  ft.-lbs.  by  the  respective  total  work 
done;  or  by  dividing  84  lbs.  by  the  ratio  of  performance,  column  6  In  the 
table. 

ACTUAL    BXPAN8ION8. 

With  miTereiit  Clearanoee  and  Ont*oflk» 

Computed  by  A.  F.  Nagle. 


Per  Cent  of  Clearance. 

Cut- 

off. 

0 

1 

8 

8 

4 

6 

6 

7 

8 

9 

10 

.01 

100.00 

50.6 

84.0    '25.75 

20.8 

17.6 

16.14 

13.88 

12.00 

10.9 

10 

.Osi 

50.00 

38.67 

45.50  120.60 

17.b8 

18.00 

13.26 

11.89 

10.80 

9.91 

8.J7 

M 

88.83 

25.25 

20.40  I17.I6 

14.86 

18.12 

11.78 

10.70 

9.82 

0.08 

8.46 

.04 

25.00 

20.20 

17.00    14.71 

13.00 

11.66 

10.60 

9.73 

9.00 

8.80 

7,J-6 

.06 

•JO.OO 

16.83 

14.57 

12.87 

11.55 

10.50 

9.64 

8.92 

8.31 

7.7« 

7.W 

.06 

16.67 

14.43 

12.75 

11.44 

10.40 

9.55 

8.88 

8.23 

7.71 

7.27 

6.88 

.07 

14.28 

I2.6,i 

11.88 

10.30 

9.46 

8.75 

8.15 

7.64 

7.20 

6.81 

C  47 

.08 

1'.».50 

11.2-4 

10.2 

9.36 

8.67 

8.06 

7.57 

7.18 

6.75 

6.41 

6  11 

.00 

11.11 

10.10 

9.27 

8.58 

8.00 

7.50 

7.07 

6.69 

6.85 

6.06 

5.79 

.10 

10.00 

9.18 

8.50 

7.92 

7.43 

7.00 

6.62 

6.80 

6.00 

6.74 

6.50 

.11 

9.00 

8.42 

7.84 

7.86 

6.93 

6.66 

6.24 

5.94 

6.68 

6.45 

5.24 

Ai 

8.83 

7.78 

7.29 

6.86 

6.50 

6.18 

6.80 

6.63 

6.40 

6.10 

5O0 

.14 

7.14 

6.78 

6.37 

6.06 

6.78 

6.53 

5.80 

6.10 

4.91 

4.74 

4.58 

.16 

6.25 

5.94 

5.67 

5.42 

6.20 

5.00 

4.82 

4.65 

4.50 

4.88 

4  28 

.ao 

6.00 

4.81 

4.64 

4.48 

4.88 

4.20 

4.08 

8.96 

8.86 

8.76 

8.67 

.25 

4.00 

8.88 

8.77 

3.68 

3.58 

3.50 

8.42 

8.84 

8.27 

8.81 

3.14 

.30 

8.33 

3.26 

8.19 

8.12 

8.06 

8.00 

2.94 

2.90 

2.84 

8.80 

8.75 

.40 

2.50 

2.46 

2.43 

2.40 

2.86 

2.38 

2.80 

8.88 

8.25 

2.82 

2.20 

.50 

2.00 

1.98 

1.96 

1.94 

1.92 

1.00 

1.80 

1.88 

1.66 

1.85 

l.«3 

.60 

1.67 

1.66 

1.65 

1.64 

1.63 

1.615 

1.606 

1.607 

1.588 

1.580 

1.571 

.70 

1.48 

1.42 

1.42 

1.41 

1.41 

1.400 

1.395 

1.890 

1.885 

1.880 

1.3W 

.80 

1.25 

1.25 

1.244 

1.241 

1.238 

1.285 

1.238 

1.880 

1.227 

1.8M 

1.822 

.00 

1.111 

1.11 

1.109 

1.108 

1.106 

1.105 

1.101 

1.106 

1.108 

1  101 

1.100 

1.00 

1.00 

1  00 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

l.OOrt 

WOBK  OF  8TBAM  IN  A  SINGLE  CYLINDBB.        751 

RelatlTe  BIBeleney  of  1  lb,  of  SCeam  nrlth  and  "nrttlioat 
Glearmnco;  back  pressure  and  compressioii  not  considered. 

Ue^  toUl  p^-ur,  -,-  P(I  +  c)  +  iXI  +  c)^hyp.log.B-ft 

UitP^l;  £,  =  100;  {>2e;  eat 7. 

a»+a»hmiog.H:-7     »^.»xi.w»-7     ^ 
»»- iflo ioo -••»'• 

If  the  clearance  be  added  to  the  stroke,  so  that  clearance  becomes  lero, 
the  same  quantity  of  steam  being  u^ed,  admission  I  being  then  a  { -f-es 
ftS,  and  stroke  i;+c  SB  107. 

»+a»hyp.iog.Jg--o      „^.a,xi.aoi»     ^ 

p.= jgj « j^ =  .707. 

That  is.  If  the  clearance  be  reduced  to  0.  the  amount  of  the  clearance  7 
being  added  to  both  the  admission  and  tne  stroke,  the  same  quantity  of 
steam  will  do  more  work  than  when  the  clearance  is  7  in  the  ratio  707 :  687, 
or  11^  more. 

Baek  Prosaare  Considered*— If  back  pressure  s  .10  of  P.  this 
amount  has  to  be  subtracted  from  p  and  p,  giving  p  =s  .587,  p*  s  .807,  the 
work  of  a  given  quantity  of  steam  used  without  clearance  being  greater 
than  when  clearance  is  7  p^r  cent  in  the  ratio  of  607 :  587,  or  ISjt  more. 

EITeci  of  Compression.— By  early  closure  of  the  exhaust,  so  that  a 
portion  of  the  exhauMt-steam  is  compressed  into  the  clearance-space,  much 
of  the  loss  due  to  clearance  may  be  avoided.  If  expansion  is  continued 
down  to  the  back  pressure,  if  the  back  pressure  is  uniform  throughout  the 
exhaust4troke,  and  If  compression  begins  at  such  point  that  the  exhaust- 
steam  remaining  in  the  cylinder  is  compressed  to  the  initial  pressure  at  the 
end  of  the  back  stroke,  then  the  work  of  compression  of  the  exhaust  steam 
equals  the  work  done  during  expansion  by  the  clearance-steam.  The  clear- 
ance-space being  filled  by  the  exnaust-steam  thus  compressed,  no  new  steam 
is  required  to  flU  the  clearance-space  for  the  next  forwMid  stroke,  and  the 
work  and  efficiency  of  the  steam  used  in  the  cylinder  are  just  the  same  as  if 
there  were  no  clearance  and  no  compression.  When,  however,  there  Is  a 
drop  in  pressure  from  the  final  pressure  of  the  expansion,  or  the  terminal 
pressure,  to  the  exhaust  or  back  pressure  (the  usual  case),  the  work  of  com- 
pression to  the  initial  pressure  is  greater  than  the  work  done  by  the  expan- 
sion of  the  clearance-steam,  so  that  a  loss  of  efficiency  results.  In  this 
case  a  greater  efficiency  can  be  attained  by  inclosing  for  compression  a  less 
quantity  of  steam  than  that  needed  to  fill  the  clearance-space  with  steam  of 
the  initial  pressure.  (See  Clark,  3.  E.,  p.  809,  et  »eq.;  also  F.  H.  Ball,  Trans. 
A.  8.  M.  E.,  xiv.  1067.)  It  is  shown  by  Clark  that  a  somewhat  greater  effi- 
ciency is  thus  attained  whether  or  not  the  pressure  of  the  steam  be  carried 
down  by  expansion  to  the  back  exhaust-pressure.  As  a  result  of  calcula- 
tions to  determine  the  most  efficient  periods  of  compression  for  various 
percentages  of  back  pressure,  and  for  various  periods  of  admission,  he  gives 
the  table  on  the  next  page : 

Clearance  In  Xow-  and  Hlffh-speed  Bnfflnes*  (Harris 
Tabor,  Am,  Mach.^  Sept.  17,  1S91.)— The  construction  of  the  high-speed 
engine  is  such,  with  its  relatively  short  stroke,  that  the  clearance  must  be 
much  larger  than  in  the  releasing-valve  type.  The  short-stroke  engine  is, 
of  necessity,  an  engine  with  large  clearance,  which  is  aggravated  when  a 
variable  compreraion  is  a  feature.  Conversely,  the  releasing- valve  gear  is, 
from  necessity,  an  engine  of  slow  rotative  speed,  where  great  power  is 
obtainable  from  long  stroke,  and  small  clearance  Is  a  feature  in  its  construc- 
tion. In  one  case  the  clearance  will  vary  from  8^  to  12%  of  the  piston-dis- 
placement, and  in  the  other  from  2^  to  9%.  In  the  case  of  an  englno  with  a 
clearance  equalling  lOjt  of  the  piston-displacement  the  waste  room  becomes 
enormous  when  considered  In  connection  with  an  early  cut-off.  The  system  of 
compounding  reduces  the  waste  due  to  clearance  in  proportion  as  the  steam 
Is  expanded  to  a  lower  pressure.  The  farther  expansion  is  carried  through 
a  train  of  cylinders  the  greater  will  be  the  reduction  of  waste  due  to  clear- 
acce.   This  la  shown  from  the  fact  that  the  high-speed  engine,  expanding 


753 


THE  STEAM-ENGINE. 


steam  much  len  than  the  Corliss,  will  show  a  greater  Rain  when  changed 
from  simple  to  compound  than  its  rival  under  similar  coadltJoits. 

COMPRKSSION  OF  StKAM  IN  THE  CYLIKDKR. 

Best  Periods  of  Compression ;  Clearance  7  per  cent. 


Total  Back  Pressure,  in  percentages  of  the  total  initial  pressure. 

Cut-off  in 

_ 

Percent- 

ages of 

s^ 

5 

10 

15 

20 

25 

30 

85 

the 

Stroke. 

Periods  of  Compression,  in  parts  of  the  stroke. 

10^ 

85^ 

57% 

44i 

S2< 

15 

68 

62 

40^ 

29 

29% 

20 

62 

47 

47 
42 

87 
84 

27 

26 

82 

81 

i7% 

25 

30 

42 

89 

82 

25 

20 

16 

u% 

12* 

35 

30 

85 

29 

28 

19 

15 

18 

11 

40 

86 

82 

27 

21 

18 

14 

18 

11 

45 

83 

80 

26 

20 

17 

14 

12 

10 

60 

80 

27 

28 

18 

16 

18 

12 

10 

65 

27 

24 

21 

17 

15 

18 

11 

9 

flO 

24 

22 

19 

16 

14 

12 

11 

9 

65 

22 

20 

17 

16 

14 

12 

10 

8 

70 

10 

17 

16 

14 

14 

12 

10 

8 

75 

17 

16 

14 

18 

12 

11 

9 

8 

Notes  to  Table.— 1.  For  periods  of  admission,  or  percentages  of  back 
pressure,  other  than  those  given,  the  periods  of  compression  may  be  readily 
round  by  interpolation. 

2.  For  any  other  clearance,  the  values  of  the  tabulated  periods  of  com- 
pression are  to  be  altered  in  the  ratio  of  7  to  the  given  percentage  of 
clearance. 

Cylinder-condensation  may  have  considerable  effect  upon  the  best  point 
of  compression,  but  it  has  not  yet  (1893)  been  determined  by  experiment. 
(Trans.  A.  S.  M.  E.,  xfv.  1078.) 

Cyllnder-condenBatlou.—Rankine,  8.  E.,  p.  421.  says :  Conduction 
of  heat  to  and  from  the  metal  of  the  cylinder,  or  to  and  from  liquid  water 
contained  in  the  cylinder,  has  the  effect  of  lowering  the  pressure  at  the  be- 
ginning and  raising  it  at  the  end  of  tho  stroke,  the  lowering  effect  being  on 
the  whole  greater  than  the  raising  effect.  In  some  experiments  the  quantity 
of  steam  wasted  through  alternate  liquefaction  and  evaporation  in  the 
cvlinder  has  been  found  to  be  greater  than  the  quantity  which  performed 
the  work. 

Percentac®  of  I*ofl«  hf  Cyllnder-condenMitloii,  tatlceo  at 
Cut-off*  (From  circular  of  the  Ashcroft  Mfg.  Co.  on  the  Tabor 
Indicator,  1889.) 


t 

Percent,  of  Feed -water  accounted 
for  by  the  Indicator  diagram. 

Percent,  of  Feed -water  Oonmimp- 
tion  due  to  Cyllnder-condensat'n. 

Simple 
Engines. 

Compound 
Enf^ines, 
h.p.  cyl. 

Triple-ex- 
jpaJiHion 
Engines, 
b.p.  cyl. 

Simple 
Engines. 

Compound 
Engines, 
h.p.  cyl. 

Triple-ex- 

Engines, 
h.p.  cyl. 

6 

58 
66 
71 
74 
78 
82 
86 

42 
84 
29 
26 
82 
18 
14 

10 

74 
76 

85 

88 

26 
84 
82 

18 
15 
18 

16 
20 
80 
40 
60 

7B 
80 
84 
87 
90 

88 

80 
16 
18 
10 

WORK  OF  STEAM  IK  A  SINGLE  CYLIKDEB.        753 


Theoretical  Compared  wltli  Actnal  Water-consiuttp* 
tlon,  Slusle-eyllnder  AntooiaUe  Cat-off  Engines.  (From 
the  catalogrue  of  the  Buckeye  Engine  Co.)— The  following  table  has  been 
prepared  on  the  basis  of  the  pressures  that  result  in  practice  with  a  con- 
stant  boiler- pressure  of  80  lbs.  and  different  points  of  cut-off,  with  Buckeye 
engines  and  others  with  similar  clearance.  Fractions  are  omitted,  except 
in  the  percentage  column,  as  the  degree  of  accuracy  their  use  would  seem 
to  imply  is  not  attained  or  aimed  at. 


Cut-off  Part 

Mean 
Effective 
Pressure. 

Total 
Pressure. 

Indicated 

lbs.  Water, 
perl.H.P. 
per  hour. 

Assumed. 

of  Stroke. 

Actn  Rate. 

Per  ct.  Loss. 

.10 
.16 
.80 
.26 

.ao 

.85 
.40 
.45 

.50 

18 
27 
85 
42 
48 
58 
67 
61 
64 

11 
15 
20 
25 
80 
85 
88 
43 
48 

20 
19 
19 
20 
90 
21 
22 
28 
5J4 

82 
27 
25 
25 
24 
25 
26 
27 
27 

68 

41 

81.6 

25 

21.8 

19 

16.7 

15 

13.6 

It  will  be  seen  that  while  the  best  indicated  economy  is  when  the  cut-off 
is  about  at  .15  or  .20  of  the  stroke,  giving  about  30  lbs.  M.E.P.,  and  a  termi- 
nal 8  or  4  lbs.  above  atmosphere,  when  we  come  to  add  the  percentages  due 
to  a  constant  amount  of  unindicated  loss,  as  i>er  sixth  column,  the  most  eco- 
nomical point  of  cut-off  is  found  to  be  about  .80  of  the  stroke,  giving  48  lbs. 
II.E.P.  and  80  Ibe.  terminal  pressure.  This  showing  agrees  substantially 
with  modem  experience  under  automatic  cut-off  regulation. 

Kn^rlmentB  on  Cyllnder-condeneatlon.— Experiments  bj 
llajor  Thos.  English  {Bhig'g,  Oct.  7, 1887,  p.  886)  wiih  an  engine  10  X  14  in., 
lacketed  in  the  sides  but  not  on  the  ends,  indicate  that  the  net  initial  con- 
densation (or  excess  of  condensation  over  re-evaporation)  by  the  clearance 
surface  varies  directly  as  the  Initial  density  of  the  steam,  and  inversely  as 
the  square  root  of  the  number  of  revolutions  per  unit  of  time.  The  mean 
results  gave  for  the  net  initial  condensation  by  clearance-space  per  sq.  ft.  of 
surface  at  one  rev.  per  second  6.06  thermal  units  in  the  engine  when  run 
non-condeusing  and  5.75  units  when  condensing. 

O.  R.  Bodmer  iEng*g,  March  4,  1892,  p.  299)  says :  Within  the  ordinary 
limits  of  expansion  desirable  in  one  cylinder  the  expansion  ratio  has  prac- 
tically no  influence  on  the  amount  of  condensation  per  stroke,  which  for 
simple  engines  can  be  expressed  by  the  following  formula  for  the  weight 
of  water  condensed  [per  minute,  probably;  the  original  does  not  state] : 

SjT-t) 
W  =  O"   8^^,  where  T  denotes  the  mean  admission  temperature,  t  the 

mean  exhaust  temperature,  8  clearance-surface  CsQuare  feet),  N  the  num- 
ber of  revolutions  per  second,  L  latent  heat  of  steam  at  the  mean  admission 
temperature,  and  C  a  constant  for  any  given  type  of  engine. 

Mr.  Bodmer  found  from  experimental  data  that  for  nigh-uressure  non- 
jacketed  engines  G  =  about  0.11,  for  condensing  non- jacketed  engines  0.065 
to  0.11,  for  condensing  jacketed  engines  0.QB5  to  0.053.  The  figures  for  jack- 
eted engines  apply  to  those  jacketed  in  the  usual  way,  and  not  at  the  ends. 

C  vanes  for  different  engines  of  the  same  class,  but  is  practically  con- 
stant for  anv  given  engine.  For  simple  high-pressure  non-jacketed  engines 
it  was  found  to  range  from  0.1  to  0.112. 

Applying  Mr.  Bodiner's  formula  to  the  case  of  a  Corliss  non-jacketed  non- 
condensing  engine,  4-ft.  stroke,  24  in.  dlam  ,  60  revs,  per  min.,  initial  pres- 
sure 90  lbs.  gauge,  exhaust  pressure  2  lbs.,  we  have  2*  -  f  =  112*,  iv=  1, 
Z.  =  880,  flf  =  7 sq.  ft.;  and,  taking  C  =  .112  and  W  =  lbs.  water  condensed 

112  X  112  X  7 
per  minute,  W  as  ' — /^      —  =  .09  lb.  per  minute,  or  5.4  Ibe.  per  hour.    If 

the  steam  used  per  I.H.P.  per  hour  according  to  the  diagram  is  20  lbs.,  the 
actual  water  consumption  is  25.4  lbs.,  corresponding  to  a  cylinder  condenaa- 
tion  of  SR%, 


764 


THB  STEAM-BNGIKB. 


INBICATOB-0IAGBA1II  OP  A   MIN6I<B-CTI<INDBB 
BNGINB. 

HeflnltlonB.— 2%«  Atmospheric  Ldne^  AB^  Is  a  line  drawn  by  ih»  ] 
of  the  indicator  when  the  connections  with  the  engine  are  c* 
■ides  of  the  piston  are  open  to  the  atmosphere. 


.  > 

K 

• 

D 
C 

■\ 

^-^ 

A 
O 

k 

'B 
X 

Fio.  138. 


The  Vacuum  Line,  OX,  is  a  reference  liue  usually  drawn  about  14  7/10 
pounds  by  scale  below  the  atmospheric  line. 

77ie  Clearance  JUne^  OY,  is  a  reference  line  drawn  at  a  distance  from  the 
end  uf  the  diagram  equal  to  the  same  percent  of  its  len^tli  as  the  clearance 
and  waste  room  is  of  the  piBlouHlisplacement. 

lite  Line  uf  Boiler-presaure,  JK,  is  drawn  parallel  to  I  he  atmospheric 
line,  and  at  a  distance  from  it  by  scale  equal  to  llie  boiler-pressure  shown 
by  the  gauge. 

The  Admission  Line,  CD,  shows  liie  rise  of  pressure  due  to  the  admission 
of  steam  to  the  cylinder  bv  opening  the  steam-valve. 

ITie  Steam  Line,  DE,  is  drawn  when  the  steam-valve  is  open  and  steam  is 
being  admitted  to  the  cylinder. 

The  Point  of  Cut-off,  E,  is  the  point  where  the  admission  of  8t«>am  is 
stopped  by  the  closing  of  the  valve.  It  is  often  difficult  to  determine  the 
exact  point  at  which  the  cut-off  takes  place.  It  is  usually  located  where  the 
outline  of  Uie  diagram  changes  its  curvature  from  convex  to  concave. 

Tli€  Expansion  Curve,  EF,  shows  the  fall  in  pressure  as  the  steam  in  the 
cylinder  expands  doing  work. 

The  Point  of  Release,  F,  shows  when  the  exhaust- valve  opens. 

The  Exhtiust  Line,  FG,  represents  the  change  in  pressure  that  takes 
place  when  the  exhaust-valve  opens. 

Tfie  Back-pressure  Line,  GH,  sliows  the  pressure  against  which  the  piston 
acts  during  its  return  stroke. 

The  Point  of  Exhaust  Closure,  H,  is  the  point  where  the  exiuiust -valve 
closes.  It  cannot  be  located  definitely,  as  tue  change  in  pressui-e  is  at  flrst 
due  to  the  gradual  closing  of  the  valve. 

The  Compression  Curve,  HC,  shows  the  rise  in  pressure  due  to  the  com- 
pression of  the  steam  remaining  in  the  cylinder  after  the  exhaust-valve  lias 
closed. 

The  Mean  Height  of  the  Diagram  equals  its  area  divided  by  its  length. 

The  Mean  Elective  Pressure  Is  the  mean  net  pressure  urging  the  piston 
forward  =  the  mean  height  x  the  scale  uf  the  indicator-spring. 

To  find  the  Mt^an  Effwlive  Pressure  from  the  7)»ayram.— Divide  the 
length,,  X./?,  into  a  number,  say  10,  equal  parts,  setting  oflT  half  a  part  sXL, 
half  a  part  at  ii.  and  nine  othfr  parts  between;  erect  ordinates  perpendicu- 
lar to  the  atinoHpherlc  line  at  the  points  of  divlftion  of  LB,  cutting  the  dia- 
gram; add  together  the  lengths  of  these  ordinate's  intercepted  between  tli»» 
upper  and  luwer  lines  of  the  diagram  and  divide  by  their  number.    This 


INDICATED  HORSE-rOWEU  OF  ENGINES,  755 

f?ive»  the  mean  lieiKht.  which  multiplied  by  the  Rcale  of  the  indfcator-Rpring 
jfives  the  M.E.P.  Or  flinl  ihe  aren  by  a  plunlmeter,  or  other  meanH  (nee 
Meimumtion.  p.  55),  niid  divide  by  the  leiijirth  LH  to  obtain  the  mean  heif^ht. 

The  Jnitinl  PifMure  is  the  pressure  aciing  on  the  piston  at  the  beginning 
of  the  stroke. 

Tlte  Trt-minal  Presmtre  is  the  pressure  above  the  line  of  perfect  vacuum 
that  would  exiMt  at  the  end  of  the  sttroke  if  the  steam  had  not  been  released 
earlier.  It  is  found  by  continuing  the  expansion-curve  to  the  end  of  the 
diagram. 

19IBICATBD  HOBSB-POWBB  OF  BN6INB8.  8IN6I.B- 
OYLINDER. 

Indicated  Horee-power  I.H.P.=  ^S» 
80,000 

in  which  Ps=  mean  effective  pressure  in  lbs.  per  sq.  in. ;  L=  length  of  stroke 
in  feet;  a  =  area  of  piston  in  square  Inches.  For  accuracy,  one  half  of  tlie 
secUonal  area  of  the  piston-rod  must  be  subtracted  frt)m  the  area  of  tlie 
piston  if  the  rod  passes  through  one  head,  or  the  whole  area  of  the  rod  If  it 
passes  through  both  heads;  n  =  No.  of  single  strokes  per  min.  =  8  X  No.  of 
revolutions. 

PaS 
I.H.P.  =  QgQQgt  In  which  S=  piston  speed  in  feet  per  minute. 

hi  which  d  s  diam.  of  cyl.  in  inches.  (The  flgares  288  are  exact,  since 
7854  -«-  88  =  23.8  exactly.)  If  product  of  piston-speed  X  mean  effective 
pressure  =  42,017,  then  the  horse-power  would  equal  the  square  of  the 
diameter  in  inches. 

Handf  Rule  for  Estliiiatliifl;  ilie  Horse-poorer  of  a 
Hncle-eylinder  Bni^lne. — Square  the  diameter  and  divide  by  2.  This  is 
correct  whenever  tlie  product  of  the  mean  effective  pressure  andt^e  piston* 
speed  =  U  of  42,017,  or.  say,  21,000,  viz.,  when  lOC.P.  =  80  and  8=  700; 
when  M.E.P.  =  39  and  8=  600;  when  M.E.P.  =  88.2  and  8  =  B60;  and  when 
M.E.P.  s=  42  and  8  =  500.  These  conditions  correspond  to  those  of  ordinary 
practice  with  both  Corliss  engines  and  shaft-irovernor  high-speed  engines. 

OtTen  Horse-poorer,  Mean  EffectlTe  PreMiure.  and 
Plaion-epeed,  to  And  Size  of  Cylinder.— 

^re^^mo^l^.      Dl«neter  =  !»5y^-.  (Exact.) 

Brake  Horee-power  Is  the  actual  horse-power  of  the  engine  as 
measured  at  the  fly-wheel  by  a  friction-brake  or  dvuamometer.  It  is  the 
indicated  horse-oower  minus  the  friction  of  the  engine. 

Table  for  Boofflilj  ApproxlmatlnK  the  Horee-power  of 
a  Compound  Bnclne  from  the  IHameter  of  Its  Low^* 
preeeare  Cylinder.— The  indicated  horse-power  of  an  engine  being 

Pali* 

,  in  which  P  s  mean  effective  pressure  per  sq.  in.,  «  =  piston-speed  in 

ft.*  per  min.,  and  d  =  diam.  of  cylinder  in  inches;  If  s  =  000  ft.  per  min., 
which  is  approximately  the  speed  of  modem  stationary  engines,  and  P  =  35 
Ibe.,  which  is  an  approximately  average  figure  for  the  M.E.P.  of  single- 
cylinder  engines,  and  of  compound  engines  referred  to  the  low-pressure 
cylinder,  then  I.H.P.  =  ^d*;  hence  the  rough-and-ready  rule  for  horse'power 
given  above:  Square  the  diameter  in  inches  and  divide  by  2.  This  applies  to 
triple  and  quadruple  expansion  engines  as  well  as  to  single  cylinder  and 
compound.  For  most  economical  loading,  the  M.E.P.  referred  to  the  low- 
pressure  cylinder  of  compound  engines  is  usually  not  greater  than  that  of 
simple  engines;  for  the  greater  economy  is  obtained  by  a  greater  number  of 
expan.Hlons  of  steam  of  higher  pressures,  and  the  greater  the  number  of 
expansions  for  a  given  initial  pressure  the  lower  the  mean  effective  pressure. 
The  following  table  gives  approximately  the  figures  of  mean  total  and  effeo- 


75Q 


THE  6TEAM-BNGISE. 


tive  preqsuros  for  the  different  types  of  enRines.  together  with  the  factor  I9 
whtcn  the  square  of  the  diameter  ^s  to  be  multiplied  to  obtain  the  norse- 
power  at  iQQst  eoonomical  loading,  for  a  piston-speed  of  tiOO  ft.  pur  minute. 


Tjrpe  of  Engine. 


114 


Non-condensing. 


Single  Cylinder. 

Compound 

Triple.... , 

Quadruple,...,. 


IQO 

6. 

20 

.5->8 

52.2 

15.5 

86.7 

600 

120 

7.5 

16 

.403 

48.2 

15.6 

82.7 

^ 

JO. 

16 

,330 

S:l 

1I&.& 

87.a 

«t 

IJ).5 

16 

.28»l 

15.5 

40.fi 

»• 

.5d4 
.467 
.6831 

.684 


Ck)ndeniins  Engines. 


Single  Cylinder. 

100 

10. 

10 

.830 

33.0 

2 

1  81.0 

600 

.443 

Compound 

Triple. 

130 

16. 

8 

.247 

29.6 

9 

jfr.6 

«t 

.3M 

160 

9Q. 

a 

.200 

82.0 

9 

ao.o 

f» 

.429 

Quadruple 

300 

25. 

8 

.169 

38.8 

8 

«1.8 

*• 

.454 

For  any  other  plstonrspeed  than  600  ft.  per  min.,  multiply  the  figures  in 
the  last  column  by  the  ratio  of  the  piston-speed  to  600  ft. 

WomtnM  V|or«e«i»owe9*-^Tha  term  '*  nominal  home-power**  origi- 
nated  in  the  time  oC  W«tt,  and  ^vas  used  to  e^pi^ss approximately  the  povrer 
of  an  engine  as  calculated  from  its  diameter,  estimating  the  mean  pn»Mure 
in  the  cylinder  at  7  lbs.  above  the  atmoKphere.  It  has  long  been  obsolete  in 
America,  and  ia  nearly  oNolete  in  |2ngland. 

n[or«««power  Constant  of  a  ytven  Qnctne  Iter  m  Fixed 
Sp«e4  =  product  of  ita  area  of  piston  iu  squai'e  inches,  length  of  stroke  in 

feet,  and  number  of  single  atrojceg  per  minute  divided  by  83,000,  op  ^^ 

se  O.  The  product  of  the  mean  effective  pressure  as  fqund  by  the  diagram 
and  this  constant  is  the  indicated  horne-power. 

Hor«e»poweF  Coiiatant  Qf  a  ifiven  Bniitne  for  Yarytntf 
Speeds  =  product  of  its  area  of  piston  and  length  of  strolce  divldea  by 
88,000.  This  multiplied  by  the  mean  effective  prps^ure  aiid  by  the  number 
of  single  Btrokes  per  minute  is  the  indicated  horse-power. 

Horse-povrep  Constant  of  any  Eniglne  of  a  glTen  IHam- 
eter  of  Cylinder,  whatever  the  length  of  stroke  =  area  of  piston  -1- 83,000 
=  square  of  the  diameter  of  piston  in  inches  X  .QP0Q238.  4  tahfe  of  (MU)#(aiit8 
derived  from  this  formula  (s  given  below. 

The  constant  multiplied  by  the  piston-speed  in  feet  per  minute  and  bv 
the  M.E.P.  gives  the  iVH.P.  -^      hj 

Errors  of  IndtpatQrs«— The  most  common  error  Is  that  of  the  apring, 
which  may  vary  from  its  uormal  rating;  the  error  may  he  determined  by 
proper  testing  apparatus  and  allowed  for.  But  after  making  this  correction, 
even  with  the  beat  work,  the  reaults  a}*e  liable  to  variable  errara  which  may 
amount  to  2  or  3  per  cent.  See  Barruq,  Trans.  A.  S.  M.  E.,  v.  810;  Denton. 
A.  B.  M.  E..  zi.  m\  David  Smith,  U.  B.  N.,  Proc.  Eng'ir  Congress.  1898 
Marine  Division.  .^  n         n        ,        , 

Indicator  **  Rigs,*'  or  Reduolng-motlons  ;  Interpretation  of  Diagrams  for 
Errors  of  Steam-diBtributlon,  etc.  For  these  see  circulars  of  manufacturers 
of  IndioatoPR;  also  works  on  the  Indicator. 

Table  of  Eugrtno  Constants  for  Use  In  F|rarln|r  Ho|*sfm 
noiver.— "  Horse-power  oonstant "  for  cylinders  from  1  inch  to  60  mches  in 
diameter,  advancing  by  8th8,  for  one  foot  of  piston-speed  per  minute  and  one 

EDund  of  M.E.P.  Find  the  diameter  of  the  cj'linder  in  the  coTumn  at  the 
de.  If  the  diameter  contains  no  fraction  the  constant  will  be  found  in  the 
column  headed  Even  Inches.  If  the  diameter  is  not  in  even  inches,  follow 
the  line  horisontall^*  to  the  column  corresponding  to  the  rebuired  frftctifon. 


UTDICATEO  H0B9S-PQWES  0|>  ENQIKES. 


767 


The  constants  muItlpHed  hj  the  piston-speed  and  by  the  M.E.P.  give  the 

horse-power. 


Diameter 

of 
Cylinder. 


OOOO^SS'. 
O0O0Q&d;. 


.0045019 
.0s»1149 
.0077153 
.(tt036S6 
i.0310S»t 
.(Ktt80'>7 
1.0345997 
|.03&md 
.088:3184 
[.040:25^1 
I  04^:!335 
|.0442«84 
'  .010:3.180 
1.0484031 
'.050(»ii9 
l.05eS5|< 
.065121-4 
1.0674357 
1.0697979 
i.0QiieO70 
,  .0046049 
.0071699 
.0097^1^ 
,.07a48^ifl 
1.0749704 
.0776057 
,.0804067 
;.088199sj 
l.08608T4i 


or 
.85. 


or 
.3TS. 


.000087S 
.0001905 
000«ai4 
.0004990 
0000600 
0O0IW97 
OOltfilO 
0016196 
OOeOMS 
OOtfOOt 


or 
»5, 


0080131 
0086714 
0041783 


0056S49 

ooft»4; 

0070819 
0079W8 
,0088198 
0097UMI 
,010747^4 
0117885 
,0188054 
,0189969 
,0151783 
0108997 
,0170780 
0189989 
OJ08&14 
,0;J17785 
0[»050e  .Q83»I8-J 
0947585 
,0;»8V^| 
08791891 
08957229 
081*47471 


.0000450 

.0001848 
.000^111 
.0004654! 
.0000876 
.0000078, 
.0019044 
.0016098, 
.0000916 
.0096618 
.0080794 
,0086447' 
.0048670, 
,0049181 
,0060861 
,0008817 
,0071850! 
,0080860, 
,00898481 
,0096808 
0108789 
,01101581 
.01800401 
0141406 
0168840 
.0105668 
.0178855 
,0191^4 


,0000585 

.0001487 
.0002915 
.0004819 
,0007199 
.0010055 
.0018387 
.0017195 
.0041479 


0848800. 
0S66654I 
0885575' 
O404078> 
.04848451 
.04451941 
0466010 
.04878*40, 
.050909:1 
.0531849. 
06540701 
.0577-484 
.0600905 
.00251-48 
.0019753 
.0074864 
.0700449 
.0720510 
.0753047 
.0780060 
.0807549 
.0885514 
.0H639.S5 


0810688! 
0884885 
034945T 
08651001 
0*4818811 
0897881 
0314008' 
0838460 
0:»0489i 
0:308993 
0«T973 
0407480; 
0487868 
0447771 
0468065 
,0490010 
0511868 
0634163 
0556953 
,0580818 
.06030691 
,06*48175! 
.06388671 
,06780861 
.07080811 
.07*49801 
.0750308 
.0783476, 
.0H11019 
.0K:Jtt048 
.0867548 


.0081475 
.0087187 
.0048875 
.0060089 
.006T179 
.0064795 
.0078887 
.0081452 
.0090499 
.0100019 
.0110015 
.0180487 
0J814a^ 
.0148869 
.0154759 
.0107185 
,0179988 
.0108816 
.P307119 
.0881899 
.0886155 
.0861887 
.0207096 
.0888879 
.0899989 
.0817075 
.0884687 
.0858775 
.0871389 
.0890379 
.0400895 
,0489687 
,0450365 
.O47HJ90 
,049-J7l9 
,0614615 
,0686988 
.0609835 
,0583150 
.0606959 
,0688*485 
.0655987 
.0681215 
,0705293 
.0783099 
07597r)5 
.0780887 
.08144v« 
084*4579 
.0871189 


or 
.086. 


.0000628 


0001040 
.0003187 
.0005091 
.0007530 
.0010445 
.0018887 
.0017705 
.O0b«O48 
.0086867 
.0Q8,M68 
.0087934 
.00^188 
.0060900 
.0068105 
.0005780 
,0073938 
.0082660 
.0001068 
.0101843 
.0111899 
.0101880 
.0182837 
.0144821 
.0160880 
.0163716 
.0181087 
.0195015 
.0208879 
.0883818 
.0888088 


.0809098 
.0885830 
.000*4050 
.0819851 
,0886828 
.0355070 
,0873004 
,0892798 
.0418368 
,0482480 
,045*4947 
.0473961 
.0495430 
.0617886 
,0589818 
0562785 
,0586109 
0009969 
0084804 
0659115 
0684408 
0710166, 
0786406 
0763180 
0790:318 
0817980 
0846183 
0674743 


+  H 
or 
.76. 


.0000789 
.OOQiaOO 
.0003<'U7 
.0005970 
.0007869 
.0010844 
.0014895 
,0018822 
.0022085 
,0087508 
.0082869 
.0038690 
.0M4997 
.0051780 
.0059089 
.0066774 
.0074! 
006367^4 
,0002835 
.0108474 
.0118589 
.0188179 
.013484^ 
.0145789 
.0157809 
,0170304 
.0188875 
.0196748 
.0810015 
,0ft26O44 
.0888019 
.0»6869 
.0871097 
.0887899 
.0804179 
.0H21484 
,0a39165 
.0867872 
.0876055 
.0895814 
.0414»19 
.0434959 
.0455547 
.0476609 
,0408149 
.0620164 
.064*M55 
.0565622 
.0688065 
.0618984 
.06:37879 
.066*4850, 
.0687597 
.0718419 
,0739719 
.0766494 
.0793745 
.082I474 
.0849675 
.06788.54 


or 

.876. 


0000887 
0001967 
0003574 
.0005656 
,0008815 
0Q11849 
0014750 
,0018740 
.0028*400 
,0&48]47 
.0088561 
0089458 
.0045819 
.0058061 
.0059^79 
0007774 
.0076044 
.0094791 
.0094013 
.0108718 
.0118880 
.0184&37 
.0185604 
0147860 
.0169845 
.0)71899 
.0184989 
.0198480 
.0818418 
.00^6877 
.0841818 
.0867888 
.0878109 
,0889471 


,0841415 
.0869681 
.0878424 
.0897648 
.04173.37 
.0487.507 
.04.'S8154 
0479876 
.0500875 
U688949 
.0545499 
,0568.528 
,0692089 
0616007 
0640468 
0605398 
0690799 
0716681 
,0748039 
,0709874 
0797185 
0884971 
0853234 
0881978 


758 


THE  STEAM-ENGINE. 


Horse-po'wer  i»er  Poand  Mean  EflTectlTe  Pressare* 

„           ,       Area  ill  sq.  in.  X  pisUm-spt'ed 
Formula, ^^-^ 


DJiim.of 
Cvlltuier, 

HfM'tKl  of  Piston  In  ft4<?t  p<;r  nsinuU?* 

iiiciit^. 

100 

1100 

3O0 

lOO 

500 

,1904 

600 

TOO 

fltMJ 

»0O 

4 

AU^ 

.-MA 

.S94i 

.9m 

4^ 

,OIK:i 

.0904'      .1410 

.l»3« 

.0410 

:^fm 

.3374 

,4388 

h"^ 

.mWi 

-119a,      .I7ft&j 

.«SHO 

.2975 

.3570 

.4I4S5 

^4T«I 

.63U 

m 

.07ai 

.1440     Mm 

.afigN} 

,3000 

.4330 

.ftoio 

.6760 

.fU80 

iT 

OHTiT 

.r,u\    .riTo 

.S4OT 

.4264 

.Bill 

.599S 

.6854 

.7711 

CH 

.lOOti 

*JOn'      .3017 

.40S* 

.msB 

,eoss 

.70»9 

.8044 

«)f^ 

7 

.lino 

.ffiilS,     .JMO0 

.4fie6 

.5831 

.0897 

.8108 

93:^i0 

1   04^4 

TH 

J3.19 

.Sfl7W'      .4010 

5355 

.0604 

.8033 

.^1 

!.07lLt 

1    3fM« 

B 

.15v*Ji 

.304(31     .4570 

,60fle 

.7®ie 

.9139 

1  41063 

1    21M> 

1 .  ;i7i:^ 

e^ 

J?J^> 

.3^139      .ftlfrf* 

,(^78 

.8598 

1.0317 

1,2037 

1.375© 

1.54T6 

9 

.IM^ 

.:^K%,     .57H1 

.7711 

.11039 

1  1B67 

I  3495 

K54-ie 

1   73^4} 

m 

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.4*^96      .6444 

.S.'3S«2 

1.0T40 

1.s;H88 

1   W^ 

1.711^4 

]    ii.)i 

1™ 

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.4700      -714^ 

.OBiJO 

1.1  MW 

lAim 

I  '.>' 

) 

11 

.aSfil) 

.57f*i,    .%ao 

1,1.M!>    1  4399 1   l.T'.i79 

3.0159 

i  .\, 

3 

la 

JJ4i7 

.(W,M    1  (hWS 

rsTt* 

1.7130  ati56a 

3-3999 

i.\i:- 

^5 

T3 

■iftrj 

.StUi    1.3<KJ7 

1.6089 

30111    2.4133 

B.B155 

s.ans 

SG^OO 

14 

.40^^') 

.0.^10    1  19fM 

T  86fi9 

t?.33S4   g.TlWfl 

a.«ft4 

a,731M 

4  IVlts 

15 

.5iV1 

1  ono,  ]Mn]R 

3  H'-'O 

a.rt77fl    3  3130 

3.T4B5 

4  mkt> 

4.81% 

16 

Gooa 

i.viRe  iJtiTM 

2.4^*71 

3.0464    3  flS57 

4.S8M 

4,S743 

5.ISS5 

17 

.887% 

l.i.T5G    lOO-V, 

3.0513 

3  i^9l!  4  02«B 

4.6147 

s.ioefi 

6.1904 

IB 

.7711 

I.54'.^J    2  3134 

3.|ift45 

3R%T.6i  4.6S!07 

5.8*78 

6  UM) 

fi,^ni 

IS 

.859^ 

1.71841  a  5775 

3  43fi7 

4.a9:i9|  6.i!^1 

6.0143 

e.K-: 

5 

90 

.06i>0 

1  0O4O   a  «ifln 

3  8liw(^ 

4.7fS0<l    5.7120 

fy.mm  7  (.: 

0 

ai 

1.0496 

Siiwaa'  3.i4N^ 

4.19K1 

5.3479    €.3975 

7.34711  S.^i'.iL 

:■    ...2 

m 

1.1M9 

S.go^JH,  3.455^ 

4,6*177 

5  75li6 

6.9115 

8.0614,  9.31.^ 

ii)..^6r 

m 

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a  51S0    3  7771 

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B.50e* 

lO.ora 

IK331 

SI 

1.3709 

B.r4l8.  4.1136 

6.4^35 

0.a'>44 

8  3353 

10.9B7 

13  338 

35 

1 .4i^7^ 

ajiVfjO    4.40^') 

5.&:jOt> 

7  4375 

8  fti'50 

10415 

11.900 

|8.S8« 

2<i 

1    Qi»<P 

51.317S    4.»30fl 

e.4355 

8  0444 

D  f.^34 

n  'Mi 

13.U71 

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2T 

1  73- tl 

3.470U.  5.2051 

6  9WI 

8. 0751 

10  410 

12.145 

13  8S0 

15.615 

i 

1  .imi» 

^T.m    ft.fiTiH 

7  4037 

y.ii39a 

n.i9e 

13.061 

14.987 

1«.7«3 

39 

e.ooif. 

imm,  (t.<NM7 

§00(13 

lO.tKXi 

13  009 

14  on 

16.013 

18.0H 

.^) 

e  14^»<» 

4.2Hin    0.4-360 

8.rjO.SO 

10710 

Ig  853 

14  994 

17.136 

la.im 

31 

ir.^WTJ 

4  :>744  o.yoi5 

9.1487 

11.430 

13,?iS 

16,010 

18«97 

aO,5«B 

S-i 

a.  4371 

4  «T4'-ii  7.31  H 

9.74tJ5 

13  M 

14.0M3 

17,060 

14.4»7 

31.934 

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5JS*;W    7  77r^'> 

30  3(57 

13  169 

15,fi5l 

18,143 

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^.396 

34 

i.^r^n 

B.^-iOeO    fl.'3!S3M 

11.005 

13  756 

J6.508 

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24.763 

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14.5^ 

17  493 

20,409 

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15.433 

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37 

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10.391 

19,549 

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3  43fl7 

6.&731  10  310 

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17.184 

20.630 

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80.90 

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14  4B0 

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31 .7i,'0 

25.340 

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40 

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7.aifii>n  434 

15  2^ 

19.0*9 

33  848 

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H.noiu  I'i.ooe 

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30  004 

34.006 

31*. 006 

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36  4W7 

43 

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16.783    SO.flM 

35,180 

29.378 

38.^77 

37.^5 

43 

4.401KS 

«  WI13  13,20-J 

17.002    23.003 

30.804 

3&.ea5 

3S606 

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4J5077 

9  -21:4  18.83^1 

IB  431    '33.088 

:£7.046 

8S.S54 

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41.469 

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19.3TB    24  098 

38  917 

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44 

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10  073    Ifi  108 

30,144 

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35.968 

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31  aio 

30  387 

dl.515 

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lt.i3QP 

47.817 

48 

a  4Ki^ 

10.907    16.4fi1 

31.931 

37  418 

33.110] 

3S.38& 

43  868 

49.363 

40 

5.7Ni 

IT  439    IT.  543 

33.858 

38  573 

34,3afi 

40  001 

45.715 

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50 

li.ftri(X) 

11.900    \7^^ 

SiH.eOO 

29.750 

85.TO0 

41,650 

47.600 

53.1150 

51 

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43.333 

49,623 

55,713 

m 

fi  4!iv> 

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3.V743 

33,17« 

38.613 

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51.464 

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13  .CI    30.050 

30  74^ 

31437 

40.113 

46.79fi 

53,488 

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13  K.H)    'JO  W-H) 

37.7BO 

34.700 

41.640 

48.581 

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64.461 

55 

T.ia-l.S 

]i.mt 

!>|  55W 

28.79a 

arenas 

43.197 

50.397 

57,596 

6(796 

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7.4(i;i7 

14  9'i7 

?i.3!3l 

^^.8.^^ 

37  31« 

44.78* 

&2.316 

59  7*» 

67.173 

57 

7,73-jr- 

15.4!'i5 

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30  090 

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54  128 

61.861 

69  594 

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1(1.013 

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40.032 

48  088 

56.014 

64  061 

73.067 

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K*>«49 

TO  570 

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'I3J39 

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49.709 

57  WB 

66. £73 

74.683 

GO 

«.5<x**ll|l7.130 

'i!j,70l 

34,373 

43  810 

51.408 

59.976 

6S.Bi4 

n.iit 

IKDICATBD  HORSE-POWER  OF  ENGINES. 


759 


To  draw  tbe  Cleaimnee-Une  on  tbo  Indlrator-dlainmm. 

the  actual  clearance  not  being  known.— The  clearauoe-Iine  uiajr  be  obtained 
approximately  by  drawing  a  straight  line,  cbcui^  acrofls  the  comprewion 
curve,  first  having  drawn  OX  parallel  to  the  atmospheric  line  and  14.7  lbs. 
below.  Measure  from  a  the  distanoe  ud,  equal  to  co,  and  draw  YO  perpen- 
dicular to  OX  through  d;  then  wiU  TB  divided  by  AT  be  the  percentage  oC 


FiQ.  189. 


clearance.  The  clearance  may  also  be  found  from  the  expansion- line  by 
constructing  a  rectangle  e/hg.  and  drawing  a  diagonal  gf  Ut  intersect  the 
line  XO.  'rhis  will  give  the  point  O,  and  by  erecting  a  perpendicular  to  XO 
we  obtain  a  clearance-line  OY. 

Both  these  methods  for  finding  the  clearance  require  that  the  expansion 
and  compression  curves  be  hyperbolas.  Prof.  Carpenter  {Potoer,  Sept., 
1808)  says  that  with  good  diagrams  the  methods  are  usually  very  accurate, 
and  give  results  which  check  substantially. 

The  Buckeye  Engine  Co.,  however,  say  that,  as  the  results  obtained  are 
seldom  correct,  being  sometimes  too  little,  but  more  frequently  too  much, 
and  as  the  indications  from  the  two  curves  seldom  agree,  the  operation  has 
little  practical  value,  though  when  a  clearly  defined  and  apparently  undis- 
iorted  compression  curve  exists  of  sufficient  extent  to  admit  of  the  applica- 
tion  of  the  process,  it  may  be  relied  on  to  give  much  more  correct  results 
than  the  expansion  curve. 

To  drmiv^  the  Hyi»erbollc  Cnrre  on  the  Indlcator»dIa» 
lA^-Select  any  point  /in  the  actual  curve,  and  from  this  point  draw  a 


line  perpendicular  to  the  line  JB,  meet- 
ing the  latter  in  the  point  J,  The  line 
JB  may  be  the  line  of  boiler-pressure, 
but  this  is  not  material ;  it  may  be  drawn 
at  any  convenient  height  near  the  top  of 
diagram  and  parallel  to  the  atmospheric 
line.  From  j  draw  a  diagonal  to  a,  the 
latter  point  being  the  intersection  of  ( 
the  vacuum  and  clearance  lines;  from  I  - 
draw  IL  parallel  with  the  atmospheric 
line.  Prom  L,  the  point  of  intersection  - 
of  the  diagonal  Jk  and  the  horizontal 
line  /A  draw  the  vertical  line  LM.  The 
point  M  is  the  theoretical  point  of  cut-off,  and  LM  the  cut-off  line.  Fix 
upon  any  number  of  points  I,  2, 8,  etc.,  on  the  line  JB,  and  from  thene  points 
draw  diagonals  to  K.  From  the  intersection  of  these  diaironals  witli  LM 
draw  horizontal  lines,  and  from  1,  ^  3,  etc.,  vertical  lines.  Where  these  lintrs 
meet  will  be  points  in  the  hyperbolic  curve. 

Pendalam  Indicator  WtUs.—Fmoer  (Feb.  1888)  gives  a  graphical 
repretentation  of  the  errors  in  Indicator-dlagraDas,  caused  by  the  use  of  tar 


Fio.  140. 


760  THE  8TEAM-EKGIKE. 

oorrect  form   of  the  pendulum  rlgRlng.    It  Is  shown  that  the  "  bnimbo  " 
pulley  on  the  pendulum,  to  which  the  cord  is  attached,  does  not  gener- 
ally give  aa  good  a  reduction  as  a  simple  pin 
^  ~  attachment    When  the  end  of  the  pendulum  a 

slotted,  working  in  a  pin  on  the  crosshead,  the 
error  is  ape  to  be  considerable  at  both  ends  of 
the  card.  With  a  yertical  slot  in  a  plate  fixed 
to  the  crosshead,  and  a  pin  on  the  pendulum 
working  in  this  slot,  the  reduction  Is  perfect, 
when  the  cord  Is  attached  to  a  pin  on  the  pen- 
dulum, a  slight  error  being  Introduced  if  the 
brumbo  pulley  is  used.  With  the  connection 
between  the  pendulum  and  the  crosshead  made 
by  means  of  a  horizontal  link,  the  reduction  is 
nearly  perfect,  If  the  construction  Is  such  that 
the  connecting  link  vibrates  equally  above  and 
Fio.  141.  below  the  horizontal,  and  the  cord  is  attached 

by  a  pin.  If  the  link  Is  horizontal  at  mid-stroke 
a  seriouK  error  is  introduced,  which  is  magnified  if  a  brumbo  pulley  also  is 
used.    The  adjoining  figures  show  the  two  forms  recommended. 

Tlfteoretlcal  Wat«r*conauiiBptloii  cmlcnlated  firom  the 
Indlc«toi>eard.— The  following  method  is  given  by  Prof.  Carpenter 
(Potrer,  Sept.  1898) :  p  =  mean  effective  pressure,  2  =  length  of  stroke  in 
feet,  a  =  area  of  piston  in  square  inches,  a  -h  144  =  area  in  square  feet,  c  = 
percentage  of  clearance  to  the  stroke,  b  =  percentage  of  stroke  at  point 
where  water  rate  is  to  be  computed,  n  =  number  of  strokes  per  minute, 
<X>fi  =  number  per  hour,  w  =  weight  of  a  cubic  foot  of  steam  having  a  pres- 
sure as  shown  by  the  diagram  corresponding  to  that  at  the  point  where 
water  rate  is  required,  to*  =  that  corresponding  to  pressure  at  end  of  com- 
pression. 

Number  of  cubic  feet  per  stroke  =  z(  loo^/l^* 

Corresponding  weight  of  steam  per  stroke  in  lbs.  =  i(  lOQ^/lIi''^ 

led 
Volume  of  clearance  s  ■     .„. 

14,400 

Weight  of  steam  in  clearance  =  ■"!?.. 

Total  weight  of »  _  ./b+c\wa  _  lean/  _     la    r  .    ,  _  ^-i 

steam  per  stroke  J  "  *V  lOO   / 144       14,400  "  14,40oL     "^  J' 

Total   weight  of  steam  {       60nfa  r ..    ,     .  ^      ^   .T 
from    diagram   per  hour  f  =  i4;ioo  L^   +<?>«»-  <^«^J- 

The  indicated  horse-power  Is  »  I  a  n  -1-  83,000.  Hence  the  steam-oonsumiv 
tion  per  indicated  horse-power  is 

= -jmni: = --^[(6  +  ow  -  cir'j. 

88,000 

Changing  the  formula  to  a  rule,  we  have:  To  find  the  water  rate  from  th« 
indicator  diagram  at  any  point  in  the  stroke. 

RULB.— To  the  percentage  of  the  entire  stroke  which  has  been  completed 
by  the  piston  at  the  point  under  consideration  add  the  percentage  of  clear- 
ance. Multiply  this  result  by  the  weight  of  a  cubic  foot  of  steam,  having  t. 
pressure  of  that  at  the  required  point.  Subtract  from  this  the  product  of 
percentage  of  clearance  multiplied  by  weight  of  a  cubic  foot  of  steam  hav- 
ing a  pressure  equal  to  that  at  the  end  of  the  compression.  MulUply  this 
result  by  187.80  divided  by  the  mean  elTectlve  pressure.* 

NoTB.—Thl8  method  only  applies  to  points  In  the  expansion  curve  or  be- 
tween cut-off  and  release. 

♦For  compound  or  triple-expansion  engines  read:  divided  by  the  equlra- 
l«nt  mean  effective  pressure^  on  the  supposition  that  all  work  is  done  in  one 


COMPOUND  EKG1NE8. 


761 


The  beneficial  effect  of  compression  in  redticing  the  water-coDRumptlon  of 
an  eni^ne  is  clearly  shown  by  the  formula.  If  the  conapression  Is  carried  to 
such  a  point  that  It  produces  a  pressure  equal  to  that  at  the  point  under 
consideration,  the  weight  of  steam  per  cubic  foot  is  equal,  and  to  =  10*.  In 
this  case  the  effect  of  clearance  entirely  disappears,  and  the  formula 
187.8,^  , 

P 
In  case  of  no  oompression,  w'  beoomes  aero,  and  the  water-rate  cs 


187  5, 


UP-^cywi 


Prof.  Denton  (Trans.  A.  8.  M.  IS.,  xir.  1863}  gives  the  following  table  of 
theoretical  wate^consumption  for  a  perfect  Marfotte  expansion  with  steam 
at  150  lbs.  abore  atmosphere,  and  3  lbs.  absolute  back  pressure : 


Ratio  of  Expansion,  r. 

M.E.P.,  lbs.  per  sq.  in. 

Lbs.  of  Water  per  hour 
per  horae-power,  W. 

10 
16 
80 
25 
80 
85 

53.4 
88.7 
80.3 
26.9 
23.8 
19.5 

9.68 
8.74 
8.90 
7.84 
7.68 
7.45 

The  difference  between  the  theoretical  water -consumption  found  by  the 
formula  and  the  actual  consumption  aa  found  by  test  represents  '*  water  not 
accounted  for  by  the  indicator,^*  doe  to  cylinder  condensation,  leakage 
throusrh  porta,  raniation,  elc. 

IjeatLafi^  of  Steam*— Leakage  of  steam,  except  in  rare  instances,  has 
«o  ill  tie  efftK^t  upon  the  lines  of  the  diagram  that  it  can  scarcely  be  detected. 
The  only  satisfactory  way  to  determine  the  tightness  of  an  engine  is  to  take 
it  when  not  in  motion,  apply  a  full  boiler > pressure  to  the  valve,  placed  in  a 
closed  pOHition,  and  to  the  piston  as  well.  «Oiich  is  blocked  for  the  purpose  at 
M>me  point  away  from  the  end  of  the  stroke,  and  see  by  the  eye  whether 
leakage  occurs.  The  indicator-cocks  provide  means  for  bringing  into  view 
steam  which  teaks  through  the  steam-valves,  and  In  most  cases  that  which 
leaks  by  the  piston,  and  an  opening  made  m  the  exhau8t*pipe  or  observa* 
tions  at  the  atmospheric  escape-pipe,  are  generally  sufficient  to  determine 
the  fact  with  regard  to  the  exhaust- vnlves. 

The  steam  accounted  for  by  the  indicator  should  be  computed  for  both 
the  cm -off  and  the  ralease  points  of  the  dfagram.  If  the  expansion-line  de- 
parts much  from  the  hyperooHc  curve  a  very  different  result  is  shown  at 
one  point  from  that  shown  at  the  other.  In  such  cases  the  extent  of  the 
loss  occasioned  by  cylinder  condensation  and  leakage  is  indicated  in  a  much 
more  truthful  manner  at  the  cut-off  than  at  the  release.  (Tabor  Indicator 
Circular.) 

OOnCPOITND  BNOINB8. 

Oomponnd,  Triple*  and  Qnadrnple^zpanslon  Bn^nes. 

—A  compound  engine  IS  one  having  two  or  moixs  cyHmlers,  and  in  which 
the  steam  after  doing  work  in  the  first  or  bigh-pressuie  cylinder  completes 
its  expansion  in  the  other  cylinder  or  cylindei's. 

The  term  "compound"  is  commonly  restricted,  however,  to  engines  in 
which  the  expansion  takes  place  In  two  stages  only^hlgh  and  low  pres.«ure, 
the  terms  triple-expansion  and  quadruple-expansion  engines  hein?  used  when 
the  expansion  takes  place  respectively  in  three  and  four  stages.  The  number 
of  cylinders  may  be  greater  than  the  number  of  stages  of  expansion,  for 
constructive  reasons;  thus  In  the  compound  or  two-stage  expansion  engine 
the  low-pressure  stage  may  be  effected  In  two  cylinders  so  as  10  obtain  the 
advantages  of  nearly  equal  sizes  of  cylinders  and  of  three  cranks  at  augleti  of 
!«)•.  In  triple- expansion  engines  there  are  frequently  two  low-pressure 
cylinders,  one  of  them  Ijelng  placed  tandem  with  the  high-pressure,  and  the 
other  with  the  Intermediate  cylinder,  &s  in  mill  engines  with  two  eranks  at 
90**.  In  the  triple-expansion  engines  of  the  steamers  Campania  and  Lucania^ 


768 


THE  8TEAH-EK0UCB. 


with  three  cranks  at  ISO*,  there  are  Ave  cylinders,  two  hlfrh,  one  Intermedl* 
ate.  and  two  low,  the  hifch-presstire  cylinders  being  tandem  with  the  loiw. 

Adwantasea  of  Compoiindliiir*— The  advantages  secured  by  divid- 
ing tlie  expaimion  into  two  or  more  stages  are  twofold:  1.  Reduction  of  waates 
of  steam  by  cTlinder-condensation,  clearance,  and  leakage;  SS.  Dividing  the 
pressures  on  tbe  cranks,  shafts,  etc.,  in  large  engines  so  as  to  avoid  excessive 
pressures  and  consequent  friction.  Tlio  diminished  loss  by  cylinder-conden- 
sation is  effected  by  decreasing  the  ruiige  of  temperature  of  the  metal  sur- 
faces of  tbe  cylinders,  or  the  difference  of  temperature  of  the  steam  at 
admission  and  exhaust.  Wlien  high-pressure  steam  is  admitted  into  a  single- 
cylinder  engine  a  large  portion  is  condensed  by  the  comparatively  cold 
metal  surfaces:  at  the  end  of  the  stroke  and  during  tlie  exhaust  the  water 
is  re-evaporated,  but  the  steam  so  formed  escapes  into  the  atmosphere  or 
into  the  condenser,  doing  no  work:  while  if  it  is  taken  into  a  second 
cylinder,  as  in  a  compound  engine,  it  does  work.  The  steam  lost  in  the  flrst 
cylinder  by  leakage  and  clearance  also  does  work  in  the  second  cnrlinder. 
Also,  if  there  is  a  second  cylinder,  the  temperature  of  the  steam  exiiausted 
from  the  first  cylinder  is  higher  than  if  there  is  only  one  cylinder,  and  the 
metal  surfaces  therefore  are  not  cooled  to  the  ame  degree.  The  difference 
In  temperatures  and  in  pressures  corresponding  to  the  woric  of  steam  of 
160  lbs.  gauge-pressure  expanded  90  times,  in  one,  two,  and  three  cylinders, 
is  shown  in  the  following  table,  by  W.  H.  Weightman,  .^m.  Mtich.,  July  28, 
19M: 


Diameter  of  cylinders,  in. . 

Area  ratios 

Expansions 

Initial  steam  •  pressures- 
absolute— pounds  .... 

Mean  pressures,  pounds. 

Mean  effective  pressures, 
pounds 

Steam  temperatures  into 
cylinders 

Steam  tem  perat  ures  out  of 
the  cylinders 

Difference  in  temperatures 

Horse-power  developed. . . 

Speed  of  piston 

Total  initial  pressures  on 
pistons,  pounds 


Single 
Cyl- 
inder. 


60 


80 

1<» 
83.06 

28.06 

866« 

184«.3 
161.8 
800 
&22 

4r)5.218 


Compound 
Cylinders. 


S3 
1 
5 

165 
86.11 

58  11 

866» 

259».0 
106.1 
399 
290 

112.000 


61 
8.416 
4 

88 
19.68 

15.68 


]84«.2 

408 
290 

84,7.52 


Triple-expansion 
Qylinders. 


ri4 


165 
121.44 

60.64 

866« 

298».5 
72.6 
269 


46 
2.70 
2.714 

60.8 
44.*^^ 

22.85 

898«.6 

284*.l 
59.4 
268 


64.162      68.817      58,TTS 


61 

4.741 
2.714 

S2.4 
16.49 

12.49 

234«.l 

184*.2 
49.9 
264 


'<  Woolf "  and  Receiver  Types  of  Gompound  Bncliiea*-' 

The  compound  Hieum-eugine,  consisting  of  two  cylinders*  is  reducible  to  two 
forms.  1,  in  which  the  steam  from  the  h.p.  cylinder  is  exhausted  direct  into 
the  1.  p.  cylinder,  as  in  the  Woolf  engine;  and  2,  in  which  the  steam  from  the 
h.  p.  cylinder  is  exhausted  into  an  intermediate  reservoir,  whence  the  steam 
is  supplied  to,  and  expanded  in,  the  1.  p.  cylinder,  as  in  the  **  receiver- 
engine." 

If  the  steam  be  cut  off  in  the  flrst  cylinder  before  the  end  of  the  stroke, 
the  total  ratio  of  expansion  is  the  product  of  the  ratio  of  expanalon  in  the 
first  cylinder,  into  the  ratio  of  the  volume  of  the  second  to  that  of  tlie  first 
cylinder:  that  is,  the  product  of  the  two  ratios  of  expansion. 

Thus,  let  the  areas  of  the  first  and  second  cylinders  be  as  1  to  8^,  the 
strokes  being  equal,  and  let  the  steam  beoutoff  in  the  first  at  ^stroke;  then 

Expansion  in  the  1st  cylinder 1  to2 

»*    "2d        "       lto8« 

Total  or  combined  expansion,  the  product  of  the  two  ratios...  1  to  7 

IToolf  Knotne,  without  Clearanee— Ideal    Blasimme.— 

The  diagrams  of  pres.snre  of  an  ideal  Woolf  engine  are  sliown  in  Fig.  14;^  as 
they  would  be  described  by  the  indicator,  according  to  the  arrows.  In  tliese 
diagrams  pq  is  the  atmospheric  line,  mn  tbe  vacuum  line,  cd  the  admiasior 


COMPOUND  ENGINES. 


763 


d    *^c 


in 


line,  dg  th«  hyperbolic  curre  of  expansion  in  the  flnit  cylinder,  and  gh  the  con- 

secuUve  expansion-line  of  back  pressure 

for  the  return -stroke  of  the  flret  piston, 

and  of  positive  pressnre  for  the  steam-  n  f-»\\m. 

stroke  of  the  second  piston.    At  the  point 

h.  at  the  end  of  the  stroke  of  the  second 

piston,  the  steam  is  exhausted  into  the 

condenser,  and  the  pressure  falls  to  tlie 

level  of  perfect  vacuum,  mn. 

The  dfafirram  of  the  second  cylinder, 
below  gh^  is  characterised  by  the  absence 
of  any  spedflc  period  of  adfmission ;  the 
whole  ox  the  steam-line  gh  being  expan- 
sional,  generated  by  the  expansion  of 
the  initial  body  of  steam  contained  in 
the  first  cylinder  into  the  second.  When 
the  return-stroke  Is  completed,  the 
whole  of  the  steam  transferred   from      _ 

the  first  is  shut  into  the  second  cylin-    «,,'  ^aa     w^^t.  WwnTvi    Tn»AT 
der.    The  final  pressure  and  volume  of   ^'«-  7„;7^2?J;' SSSTiT 
the  steam  in  the  second  cylinder  are  the  Indicator  diagrams. 

same  as  if  the  whole  of  the  Initial  steam  had  been  admitted  at  once  into  the 
second  cylinder,  and  then  expanded  to  the  end  of  the  stroke  in  the  manner 
of  a  single-cylinder  engine. 

The  net  work  of  the  steam  is  also  the  same,  according  to  both  distributlona. 

Reeelver^encliie,  irlilioai  Clearance -Ideal  IMacrams*— 
In  the  ideal  receiver-engine  the  pistons  of  the  two  cylinders  are  con- 
nected to  cranks  at  right  angles  to  each  other  on  the  same  shaft.  The 
receiver  takes  the  steam  exhausted  from  the  first  cylinder  and  supplies  It  to 
the  second,  in  which  the  steam  is  cut  off  and  then  expanded  to  the  end  of 
the  stroke.  On  the  assumption  that  the  initial  firessure  in  the  second  cylin- 
der is  equal  to  the  final  pressure  in  the  first  and  of  course  equal  to  the  pres- 
sure in  the  receiver,  the  volume  cut  off  in  the  feoond  cylinder  must  be 
equal  to  tlie  volume  of  the  first  cylinder,  for  the  second  cylinder  must  admit 
as  much  steam  at  each  stroke  as  is  discharged  from  the  flrst  cylinder. 

in  Fig.  143  cd  is  the  line  of  admission  and  kg  the  exhaust-line  for  the  flrst 


< 

i 

.y\ 

/ 

7, 

y 

I  '• — 

V 

1*; 

-^ 

>^ 

t 

Fio.  148.  -RscEiyEB-SNGiNB,  Ideal 
Indicator-diagrams. 


Fio.  144.~Ribcbivkr    Ekoinb,    Idkal 
Diagrams  reduced  and  combined. 


cylinder;  and  dg  is  the  expansion-curve  and  pq  the  atmospheric  line.  In 
the  region  below  the  exhaust-line  of  the  first  cylinder,  between  it  and  the 
line  of  perfect  vacuum,  ot,  the  diagram  of  the  second  cylinder  is  formed;  /it, 
the  fecoiid  line  of  aUmiesion.  coincides  with  the  exiiauHt-ltne  hg  of  the  flrst 
cylinder,  showing  in  the  ideal  diagram  no  intermediate  fall  of  pressure,  and 
ik  is  the  expansion-curve.  The  arrows  indicate  the  order  in  which  the  dia- 
grams are  formed. 

In  the  action  of  the  receiver-engine,  the  expansive  working  of  the  steam, 
though  clearly  divided  into  two  consecutive  stages,  is,  as  in  the  Woolf 
engine,  essentially  continuous  from  the  point  of  cut-off  in  the  flrst  cylinder 
to  the  end  of  the  stroke  of  the  second  cylinder,  where  it  is  delivered  to  the 
condenser;  and  the  flrst  and  second  diagrams  may  be  placed  toother  and 


764 


THB  BTEAM-EKOIirB. 


ooRibined  to  form  a  continuous  diagram.  For  this  purpose  ta^e  Che  aeoond 
diaf^ram  as  the  basis  of  the  combined  diafrram,  namely,  hiUo^  Piff.  144.  The 
period  of  admiRslon,  hi,  is  one  third  of  the  stroke*  and  as  the  ratios  of  the 
cylinders  are  as  1  to  8,  hi  is  also  the  proportional  leni^h  of  the  first  diagram 
as  applied  to  the  second.  Produce  oh  upwards,  and  set  oft  oe  equal  to  the 
total  heiffht  of  the  first  diaj^ram  above  the  vacuum^Hne;  and,  upon  the 
shortened  base  /it,  and  the  height  Ao,  oompleta  the  first  diagram  with  the 
steam-line  ccf,  and  the  expansion-line  at. 

It  is  shown  by  Clark  (S.  E.,  p.  432.  et  aeq.)  in  a  series  of  arithmetical  cal- 
culationSf  that  the  receiver-engine  is  an  elastio  system  of  compound  engiliie, 
in  which  considerable  latitude  is  afforded  for  adapting  the  pressure  in  the 
receiver  to  the  demands  of  the  second  cylinder,  without  oonstderably  dimin- 
ishing the  effective  work  of  the  engine.  In  the  Woolf  engine,  on  the 
contrf^ry,  it  is  of  much  Importance  that  the  Intermediate  volume  of  space 
between  the  fii-st  and  second  cylinders,  which  is  the  cause  of  an  interme> 
diate  fall  of  pressure,  should  be  reduced  to  the  lowest  practicable  amount. 

Supposing  that  there  is  no  loss  of  steam  in  passing  through  the  engine, 
by  cooling  and  condensation,  it  is  obvious  that  whatever  steam  passes 
through  the  flnt  cylinder  must  also  find  its  way  through  the  second  cylin- 
der. By  varying,  therefore,  in  the  receiver-engine,  the  period  of  admissioa 
in  the  second  cylinder,  and  thus  also  the  voltune  of  steam  admitted  for  each 
stroke,  the  steam  will  be  measured  into  it  at  a  higher  pressure  and  of  a  \ew» 
bulk,  or  at  a  lower  pressure  and  of  a  greater  bulk;  the  pressure  and  density 
naturally  adjusting  themselves  to  the  volume  that  the  steam  from  the  re- 
eeiver  is  permitted  to  occupy  In  the  second  cylinder.  With  a  sufiSciently 
restricted  admission,  the  pressure  in  the  raoeiver  may  be  maintained  at  the 
pressure  of  the  steam  as  exhausted  from  the  first  cylinder.  On  the  con* 
trary,  with  a  wider  admission,  the  pressure  in  the  receiver  may  fail  or 
**  drop  **  to  three  fourths  or  even  one  naif  of  the  pressure  of  the  exhaust' 
steam  from  the  first  cylinder. 

(For  a  more  complete  discussion  of  the  action  of  steam  in  the  Woolf  acd 
receiver  engines,  see  Olark  on  the  Steam-engine.) 

Oomblned  IMaffniniB  of  Componnd  Biislne»«->The  only  way 
of  making  a  correct  combined  disgram  from  the  indicator-diagrams  of  tlie 
peveral  cylinders  in  a  compound  engine  is  to  set  off  all  the  diagrams  on  the 
same  horixontal  soale  of  Tolumes,  adding  the  clearanoes  to  the  cylinder  ca- 


Fia.  145. 


pacities  proper.  When  this  Is  att^ended  to,  the  successive  diagrams  fall  ex- 
Actly  into  their  right  places  relatively  to  one  another,  and  would  compere 
pi-oi>4*rly  with  any  theoretical  expansion -curve.    (Prof.  A.,  B.  W.  Kennedy. 

hwj.  Inst.  M.  B.,  Oct.  leae.) 


OOUrOVlSD  Bir-HKBS. 


765 


This  method  of  comblnlnj^  diacrams  is  commonly  adopted,  but  there  are 
objections  to  its  accuracj,  since  the  whole  quantitj  of  steam  consumed  In 
the  first  cylinder  at  the  end  of  the  stroke  is  not  carried  forward  to  Mm 
second,  but  a  part  of  H  is  reuUoed  in  the  first  cylinder  for  compression.  For 
a  method  of  combiuinK  diagrams  in  which  compression  Is  taken  account  of, 
see  discussions  by  Thomas  Mudd  and  others,  in  Proc.  Inst.  M.  E.,  Feb., 
1887.  p.  48.  The  usual  method  of  eombinioc  diagrams  la  also  critfasiaed  by 
Frank  H.  Bail  as  inaccurate  and  misfeadDig  {Amu  Mack^  April  IS,  18M: 
Trana.  A.  8.  M.  B.,  xIt.  1406,  and  zv.  408). 

Figure  146  shows  a  combined  diagram  of  a  quadniple-expanaion  engina, 
drawn  according  to  the  usual  method,  that  ia,  the  diagrams  are  first  reduoed 
In  length  to  relative  aoalea  that  oorreepood  with  the  relative  piatoa-displace- 
ment  of  the  three  cylinders.  Then  the  diagrams  are  placed  at  suoh  distaacea 
from  the  elearance-liae  of  the  proDoeed  combined  diagraok  as  to  correctly 
represent  the  clearance  in  each  cylinder. 

CAleolated  Expanalona  and  ProMurea  In  Ti¥o«eyllnder 
Compound  £ncin«*«  (James  Tribe,  Ata,  Mcich.^  Sept.  &  Ocu  1891.) 


TWO-CTLIHPKE 

Compound  NoN-ooinnNsnfo. 

Back  preaaure  %  lb.  above  atmosphere. 

IniUal    gauge - 

pressure 

Initial     absolute 

100 

110 

120 

180 

140 

150 

160 

170 

175 

pressure 

115 

126 

135 

14S 

155 

165 

m 

186 

190 

ToUl  expansion. 

7.89 

7.84 

8.41 

9 

9.61 

10.24 

10.89 

11.50 

11.9 

Expansionsin 

each  cylinder.. 

2.7 

2.8 

2.9 

8 

3.10 

8.2 

8.8 

3.4 

3.46 

Hyp.  log.  plus  1. 

1.99S 

2.0^ 

'^.064 

2.0?8 

2.131 

2.168 

2.198 

2.228 

2.S88 

Forward      High. 

84.8 

90.5 

06 

101.4 

106.5 

111.5 

116.8 

120.9 

123.8 

pressures    Low., 
back     .       High. 

81.8 

32.8 

88.1 

38.7 

84.3 

S4.8 

85.2 

83.0 

86.7 

42.6 

44.6 

46.5 

48.3 

50 

51.5 

53 

51.4 

66 

pressures    Low.. 

15.6 

15.5 

16.5 

15.5 

15.5 

15.6 

15.6 

16.6 

15.0 

Mean       m.u 
effective]  »«»^ 
preasures  \  *^'^" 
Katlo^yllnder 

48.3 

46.0 

49.6 

68.1 

60.6 

60 

68.8 

66.0 

68.2 

15.8 

16.8 

17.6 

18.2 

18.8 

19.8 

19.7 

80.1 

80.8 

areas  

2.67 

2.78 

2.81 

2.91 

8 

3.11 

3.21 

3.31 

8.87 

CONDKNSINa. 


The  probable  percentage  of  loss,  line  3,  Is  thus  explained:  There  Is  always 
a  loss  of  heat  due  to  condensation,  and  which  increases  with  the  pressure  of 
steam.  The  exact  percentage  cannot  be  predetermined,  as  it  dependa 
largely  upon  the  quality  of  the  non-conducting  covering  used  on  the  cy]ln> 
der,  receiver,  and  pipes,  etc..  but  will  probably  be  about  as  shown. 

Propofllona  ofCyllndera  In  Componnd  Enclnea.— Authori- 
ties differ  as  to  the  proportions  by  volume  of  the  high  and  low  pressure 
cylinders  v  and  F.   Thus  Graahof  gives  Fh-  v  s  0.66  f^;  Hrabak,  0.90 .f^; 


766    .  THE  BTBAM-BNQINB. 

Weraer,  i^;  and  BAnklne^^/r*.  r  being  the  ratio  of  ezpanaioo.    Busley 
makes  the  ratio  dependent  on  the  boiler-pressure  thus: 

Lb8.persq.ln eo  90  105  1» 

V-*-v...7/. =   8  4  4.5  5 

(See  Searon*8  Manual,  p.  95,  etc.,  for  analytical  method;  Bennett  p.  4M. 
etc. ;  Clark Vi  Steam-engine, p.  445. etc;  Clark,  Rules,  Tables,  Data,  p.  849,  etc.) 

Mr.  J.  McFarlane  Gray  states  that  he  finds  the  mean  effective  pressure  in 
the  compound  engine  reduced  to  the  low-pressure  cylinder  to  be  approxi- 
mately tlie  square  root  of  6  times  the  boiler-pressure. 

Approximate  Horse-po'wer  of  a  modem  Compomid 
niarlne-enirlne.  (Seaton.v-The  following  rule  will  give  approziniatt* iv 
the  horse-power  developed  by  a  compound  engine  made  in  accordance  with 

modem  marine  practice.    Estimated  H.P.  = ~r . 

D  =  diameter  of  l.p.  cylinder;  p  =  boiler-pressure  by  gauge; 
B  =  revs,  per  min.;  S  =  stroke  of  piston  in  feet. 

Ratio  of  Cylinder  Capacity  In  Compound  Marino  "Bn- 
fflnea.  (Seaton.)— The  low-pressure  cylinder  is  the  measure  of  the  power 
of  a  compound  engine,  for  so  long  as  the  initial  steam-pressure  and  rat<>  of 
expansion  are  the  same,  it  signifies  very  little,  so  far  as  total  power  only  is 
concerned,  whether  the  ratio  between  the  low  and  high -pressure  cylinders 
is  S  or  4;  but  as  the  power  developed  should  be  nearly  equally  di vide<l  be* 
tween  the  two  cylinders,  in  order  to  get  a  ^ood  and  steady  working  engine, 
there  is  a  necessity  for  ezeix;ising  a  considerable  amount  of  discretion  in 
fixing  on  the  ratio. 

In  choosing  a  particular  ratio  the  objects  are  to  divide  the  power  evenly 
and  to  avoid  as  much  as  possible  *'  drop  **  and  high  initial  strain. 

If  Increased  economy  is  to  be  obtained  by  increased  boiler  pressures,  the 
rate  of  expansion  should  vary  with  the  initial  pressure,  so  that  the  prefsure 
at  which  the  steam  enters  the  condenser  should  remain  constant.  In  this 
case,  with  the  ratio  of  cylinders  constant,  the  cut-off  in  the  hlgh-pressure 
cylinder  will  vary  inversely  as  the  initial  pressure. 

Let  R  be  the  ratio  of  the  cylinders;  r,  the  rate  of  expansion;  p*  the  inltinl 
pressure:  then  cut-off  in  high-pressure  cylinder  =i  B-*-r\r  varies  with  p,, 
so  that  the  terminal  pressure  pn  Is  constant,  and  consequently  r  ^pi-*-  j>»; 
therefore,  cut-off  in  nigh-piessure  c.vlindi»r  =  i?  X  pn-^px. 

Ratio*  of  Cylinders  as  Found  In  Marine  Praetlce*— The 
rate  of  expansion  may  be  taken  at  one  tenth  of  the  boiler-pressure  (or  about 
one  twelfth  the  absolute  pressure),  to  work  economically  at  full  siwed. 
Therefore,  when  the  diameter  of  the  low-pressure  cylinder  does  not  exceed 
100  inches,  and  the  boiler-pressure  70  lbs.,  the  ratio  of  the  low-pressure  to 
the  high-pressure  cylinder  should  be  3.5;  for  a  boiler-pressure  of  dO  lbs.,  3.75; 
for  90  lbs.,  4.0;  for  100  lbs.,  4.5.  If  these  proportions  are  adhered  to,  there 
will  be  no  need  of  an  ezpansion-valve  to  either  cylinder.  If.  however,  to 
avoid  **  drop,'*  the  ratio  be  reduced,  an  expansion-valve  should  be  fitted  to 
the  high-pressure  cylinder. 

Where  economy  of  steam  Is  not  of  first  importance,  but  rather  a  large 
power,  the  ratio  of  cylinder  capacities  may  with  advantage  be  decreased, 
so  that  with  a  boiler-pressure  of  100  lbs.  it  may  be  8.75  to  4. 

In  tandem  engines  there  is  no  necessity  to  divide  the  work  equally.  Tlie 
ratio  is  generally  4,  but  when  the  steam-pi-essure  exceeds  90  lbs.  absolute  4.5 
is  better,  and  for  100  lbs.  5.0. 

When  the  power  requires  that  the  1.  p.  cylinder  shall  be  more  than  100  in. 
diameter,  it  should  be  divided  in  two  cylinders.  In  this  case  the  ratio  of  the 
combined  capacity  of  the  two  I.  p.  cylinders  to  that  of  the  h.  p.  may  be  8.0 
for  85  lbs.  absolute.  8.4  for  95  lbs..  3.7  for  105  Ihs..  and  4.0  for  115  lbs. 

Receiver  Space  In  Compound  Bn^ne*  should  be  from  1  to 
1.5  times  the  capacity  of  the  high-pressure  cylinder,  when  the  cranks  are  at 
an  angle  of  from  90®  to  12G«.  When  the  cranks  ore  at  180"  or  nearly  this, 
the  space  may  be  very  much  reduced.  In  the  case  of  triple-compound  en- 
gines, with  cranks  at  120*.  and  thn  intermediate  cylinder  leading  the  high- 
pressure,  a  very  small  receiver  will  do.  The  pressure  in  the  receiver  should 
never  exceed  half  the  lioiler- pressure.    (Seaton.) 


OOMFOirKD  EKOINBS.  767 

Wora^ulm  for  Caleulatine  tlie  Bzpanvloii  and  the  IVork 
of  Steam  In  Compound  Bn«lne«» 

(Oondensed  from  Ciark  on  the  **  Steam-engine.**) 

a  K  area  of  the  first  cylinder  hi  iiquare  inches; 

of  m  area  of  the  second  cylinder  in  square  Inches; 

r  BB  ratio  of  the  capacity  of  the  second  cylinder  to  that  of  the  first; 

L  a  leneth  of  stroke  in  feet,  supposed  to  be  the  same  for  both  cylinders; 

I  =  period  of  admission  to  the  first  cylinder  in  feet,  excluding  clearance; 

c  =3  clearance  at  each  end  of  the  cvlinders,  in  parts  of  the  stroke,  in  feet; 

J^'  3  length  of  the  stroke  plus  the  clearance,  bi  feet; 

r  8  period  of  admission  plus  the  clearance,  In  feet; 

9  a  length  of  a  given  part  of  the  stroke  of  the  second  cylinder,  in  feet; 

P  as  total  initial  pressure  in  the  first  cylinder,  in  lbs.  per  square  inch,  sup- 
posed to  be  uniform  during  admission; 

F'  as  total  pressure  at  the  end  of  the  given  part  of  the  stroke  «; 

p  ss  average  total  pressure  for  the  whole  stroke; 

k  ss  nominal  ratio  of  expansion  in  the  first  cylinder,  or  L  -t- 1; 

R'  s  actual  ratio  of  expansion  In  the  first  cylinder,  or  L'  •*-  V; 
S"  M  actual  combined  ratio  of  expansion,  iu  the  first  and  second  cylinders 
together; 

n  s>  ratio  of  the  final  pressure  in  the  first  cylinder  to  any  intermediate 
fall  of  pressure  between  the  first  and  second  cylinders: 

JV  M  ratio  of  the  Tolume  of  the  intermediate  space  in  the  Woolf  engine, 
reckoned  up  to,  and  including  the  clearance  of,  the  second  piston, 
to  the  capacity  of  the  first  cylinder  plus  its  clearance.  The  value 
ol  N  ia  correctly  expressed  by  the  actual  ratio  of  the  volumes  as 
stated,  on  the  assumption  that  the  intermediate  space  is  a  vacuum 
when  it  receives  the  exhaust-steam  from  the  first  cylinder.  In  point 
of  fact,  there  is  a  residuum  of  unexhausted  steam  in  the  interme- 
diate space,  at  low  pressure,  and  the  value  of  iV  is  thereby  prao- 

tically  reduced  below  the  ratio  here  stated.    If  m      ^  ■  —  L 

to  «  whole  net  work  in  one  stroke,  in  foot-pounds. 

Batto  of  expansion  in  the  second  cylinder: 

In  the  Woolf  engine,  ^   ^^         t 

In  the  receiver* engine,^ — ^^— *-• 

Tot^al  actual  ratio  of  expansion  k  product  of  the  ratios  of  the  thrde  eon* 
secutive  expansions,  in  the  first  cylinder,  in  the  intermediate  efiace»  and 
in  the  second  cylinder, 

In  the  Woolf  engine,  ^  (  rp  +  a); 
In  the  receiver-engine,  r^,  or  rJZ*. 

Combined  ratio  of  expansion  behind  the  pistons  m  ^^ — r2^  a  R". 

n 

Work  done  in  the  two  cylinders  for  one  stroke,  with  a  given  cut-off  and  & 
given  combined  actual  ratio  of  expansion: 

Woolf  engine,  w  •■  aP[r(l  -J-  hyp  log  fi")  -  r]. 


Beoeiver  engine,  w  -  op[«'(l  +  hyp  log  iJ")  -  «  (l  +  ^^)]» 

when  there  is  no  intermediate  fall  of  pressure. 

When  there  is  an  intermediate  fall,  when  the  pressure  falls  to  9^,  %,  \i  ot 
the  final  pressure  in  the  Ist  cylinder,  the  reduction  of  work  is  0.2;(,  l.i^,  4.6st 
of  that  when  there  is  no  fall. 


768  THfi  STBAM-BKGIKB. 

Total  work  In  tlie  two  ^]lnd«n  of  a  reoolYdr-60gftie»  for  one  stfoto  for 
any  iatermedlate  tail  of  prassnre^ 

EzAMPLc-Let  a  «  1  sq.  In.,  P«  68  Iba.,  V  m  ^4St tL,  n  m  i,  y*  m  5.068. 

W  «  1  X  68[».4«(6/4  hyp  lo^  6.669)  -  .48(l  4.^±>||~)]  ,  421.86  tL4b^ 

,  Calculation  of  IMaiiiet«m  of  Crllndera  of  a  compound  oon. 
deoBiog  engluo  of  HOOO  U.P.  at  a  speed  of  7UU  feei  por  minute,  with  100  lbs. 
boiler-preMure. 

100  IbB.  Rauge-presfture  a  116  absolute,  less  drop  of  6  lbs.  between  boiler 
and  cylinder  a  no  lbs.  initial  absolute  pressure.  Assuming  terminal  pres- 
sure  in  I.  p.  cylinder  a  6  lbs.,  the  total  expansion  of  steam  in  both  cyiioders 
=  1 10  -«.  6  =  18.33  lbs.  Hyp  log  18.33  =  d.U00.  Back  pressure  in  1.  p.  cylinder, 
3  lbs.  absolute. 

TUe  following  formula)  are  used  in  the  calculation  of  each  cylinder  : 

(1)  Area  of  cylinder  =  ^  ^  H.P^^jjOO 

''  M.K.P.  X  piston-speed 

(2)  Mean  effectiTe  pressure  =  mean  toUl  presitun?  —  back  prpwure. 
(H)  Mean  total  pressure  as  terminal  pressure  x  (1  -f-  hyp  Ior  /?). 

(4)  Absolute  initial  pressure  =  absolute  terminal  pressure  x  ratio  of  ex- 
pansion. 

Fii-st  oaloulate  the  area  of  the  low-pressure  cylinder  as  If  all  the  work 
were  done  in  that  cylinder. 

From  (3),  mean  toial  pressure  =  0  x  (I  4-  hyp  log  18.38)  =  83.454  lbs. 

From  (i),  mean  effeoiive  pressure  e=  S3.4M-  3  -  jsO.454  lbs. 

From  (1),  area  of  cylinder  =  ^^^  ^'^  =  4010  sq.  Ins.  =  70.0  inn.  diam. 

If  half  the  work,  or  1000  H.P.,  is  done  in  the  1.  p.  cylinder  the  ME.  P.  will 
be  half  that  found  above,  or  10.927  lbs.,  and  the  mean  total  pressure  10  ]fiS74- 
8  =  18.227  lbs.  ^ 

From  (8),  1  +  hyp  log  R  =  lS.wr  ^  G  «=  9.6045. 

Hyp  log  iJ  =  1.U045,  whence  i2  in  1.  p.  cyl.  =  3.a35. 

From  (4),  8.335  X  6  =  60.01  lbs.  initial  pressure  in  I.  p.  cyl.  and  teruUnal 
pressure  in  h.  p.  cyl.,  assuming  no  drop  between  cylinders. 

110-^22.01  =  18.33-^8.335=  6.497,  R  iu  h.  p.  cyl. 

From  (3),  mean  total  pre5».  In  h.  p.  cyl.  =  20.01  x  (I  4- hyp  log  5.49T)  =  64  11 

From  (2).  64.11  - 20.01  =  84.10,  M.E.P.  In  h.  p.  cyl.  ^    ''*'     ^  ^      *"•*'• 

From  (1).  area  of  h.  p.  cyl.  *=  1^^^=  1882  sq.  ins.  =  42  Ins.  diam. 

Ovlinder  ratio  ^  4010  -h  1866  ^  3.386. 

The  area  of  the  h.  p.  cylinder  may  be  found  more  dh'ectly  by  dividinxr  the 
area  of  the  1.  p.  cyl.  by  the  ratio  of  expansion  in  that  cylinder.  46 lo  -»- 
3.335  =  i;^  sq.  ms. 

In  the  above  calculation  no  account  is  taken  of  clearance,  of  compression 
of  drop  between  cylinders,  nor  of  area  of  piston-rods.  It  also  assumes  tliat 
the  diagram  in  each  cylinder  is  the  full  theoretical  diagram,  with  a  horisontul 
sieam-line  and  a  hyperbolic  oxpansion  line,  with  no  allowance  for  .^un<l- 
ing  of  the  corners.  To  make  allowance  for  these,  the  mean  effective  pres- 
sure in  each  cyliuder  must  be  multiplied  by  a  diagram  factor,  or  the  ratio 
of  the  area  of  an  actual  diagram  of  the  class  of  engine  considered,  with  tlio 
giveii  nitial  and  terminal  pressures,  to  the  area  of  the  theoretical  diagram 
Such  diagram  factors  will  range  from  0.6  to  0.64,  as  in  the  Uble  on  p.  T4a. 
-  "^•^,  ?^*V**  ^f,  CyUndera.-Th8  Question  what  is  the  beat  ratio  of 
areas  of  the  two  cylinders  of  a  compound  engine  IssUU  (lOOl),  a  dispuied 
one,  but  there  appears  to  be  an  increasing  tendency  In  faror  of  Uii-ge  ratios, 
even  as  great  as  7  or  8  to  1,  with  consicierable  terminal  drop. in  the  hieii- 
SfTnIl*;^"?i?S:-  f  discussion  of  the  subject,  together  wlih'^a  deseHption 
or  a  new  method  of  drawmg  theoretical  diagrams  of  multiple-expansion 
engines,  taking  into  consideration  drop,  clearance,  and  oompressioDTwili  ha 
found  in  a  paper  by  Bert  C.  Ball,  iu  Trans.  A.  S,  rf,  E.,  xxl  SSSt 


TBIPLE-BZPAKSIOK  EK9IKE&  769 

TBIPI.E«SXPAlfSION  BNGINBS. 

Proportion*  of  Cylinders.— H.  H.  Suplee,  Mechaniett  Not.  188T, 
drives  ifid  foUowiog  method  of  proporkioning  cyllodera  of  triple-expaQBioii 
engines: 

Ab  in  the  case  of  compound  engines  the  diameter  of  the  low-pressare 
cylinder  is  first  determined,  heing  made  large  enough  to  furnish  the  entire 
power  required  at  the  mean  pressure  due  to  the  initial  pressure  and  expan. 
sion  ratio  given;  and  then  thn  cylinder  is  only  given  pressure  enough  to  per- 
form one  third  of  the  work,  and  the  other  cylmders  are  proportions  so  as  to 
divide  the  other  two  thirds  between  them. 

Let  us  suppose  that  an  initial  pressure  of  IM  lbs.  is  used  and  that  900  H.P. 
Is  to  be  developed  at  a  piston-speed  of  800  ft  per  nin.,  and  that  an  expan- 
sion ratio  of  16  is  to  be  reached  with  an  absolute  back  pressure  of  H  lbs. 

The  theoretical  M.E.P.  with  an  absolute  initial  pressure  of  160  +  M.7  ss 
1«4.7  lbs.  initial  at  16  expansions  ie 

less  2  lbs.  back  pressure,  9  88.88  -8s  86.88. 

In  practice  only  about  0.7  of  this  pressure  Is  actually  attained,  so  that 
86.83  X  0.7  a  S5.781  lbs.  is  the  M.E.P.  upon  which  the  engine  is  to  be  pro- 
portioned. 

To  obtain  900  H.P.  we  must  have  88,000  X  900  s  90,700,000  foot-pounds,  and 
this  divided  by  the  mean  pressure  (95.78)  and  by  the  speed  in  feet  (800)  will 

800  X».78  ■"**'**•  "^ 

for  the  area  of  the  L  p.  cylinder,  which  is  about  equivalent  to  48  in,  dlam. 
Now  as  one  third  oC  the  work  la  to  be  done  ta  the  1.  p.  cyUndor,  thA  MJLF* 

in  it  will  be  85.78  -f  8  =  a59  lbs. 

The  cut-off  In  the  hlgh-pressare  cylinder  Is  yeneislly  arranged  to  cut  off 
at  0.6  of  the  stroke,  and  so  the  ratio  of  the  h.  p.  to  the  1.  p.  cylinder  is  equal 
to  16  X  0.6  =  9.0,  and  the  h.  p.  cylmder  will  be  1440  h- 9.6  =  150  eq.  In.  area,  or 
about  14  in.  diameter,  and  the  M.B.P.  in  the  h.  p.  cylinder  is  eqaal  to 
9.r.  v:  8.59  =  82.46  lbs. 

If  the  intermediate  eyiiatfer  h  made  a  mean  slan  between  Uie  ether  two^ 
its  size  would  be  determined  by  dividing  the  area  of  the  1.  p.  cylinder  by  the 
square  root  of  the  ratio  between  the  low  and  the  high;  but  \n  pnuitloe  wis  is 
found  to  give  a  result  too  large  to  equalize  the  stresses,  so  that  instead  the 
area  of  the  int.  cylinder  is  found  i>y  dividing  the  ai^ea  of  the  1,  p.  pistQn  by 
1.1  times  the  square  root  of  the  ratio  of  1.  p.  to  h.  p.  cylinder,  wnleli  in  this 
case  is  1440  -4-  (1.1  V9.6)  =.  42*^5  sq.  in.,  or  alittle  more  than 88 in.  diam. 

To  put  the  above  into  the  form  of  rules,  we  have 

.  J       Area  of  low-pressure  piston 

Area  n,  p,  cyi.  w  outH>ff  in  b.  p.  oyl.  X  rate  of  expandon. 

ATM  to.ermedtato  vt «      ^"^  °"°^P""°""'''^ 

1.1  X  i^ratio  of  I.  p.  to  h.  p.  cyl. 

The  choice  of  expansion  ratio  Is  governed  by  the  initial  presanm,  and  is 
generally  chosen  so  that  the  terminal  pressure  in  the  1.  p.  cylinder  shall  be 
about  10  lbs.  absolute. 

Annnlftr  Bins  method.— Jay  M.  Whitham,  Trans.  A.  a  M.  E.,  x. 
677,  gives  the  following  method  of  ascertaining  the  diameter  of  pistons  of 
triple  exiHinsion  engines: 

Lay  down  a  theoretical  indicator-diagram  of  a  simple  engine  for  the  par- 
ticular expansion  desired.  By  trial  find  (with  the  polar  planimeter  or  otner- 
wise)  the  position  of  horizontal  lines,  parallel  to  the  baok-preasura  Una,  such 
that  the  three  areas  into  which  they  divide  the  diagram,  representing  low, 
intermediate,  and  high  pressure  diagrams,  marked  respectively  A,  B,  and  C, 
are  equal 

Find  the  mean  ordinate  of  each  area:  that  of  **  C  **  will  be  the  mean  un- 
balanced pressure  on  the  small  pl»ton;  that  of  '*  B  "  will  be  the  mean  unbal- 
anced prcarore  on  the  area  remaining  after  subtracting  the  area  of  the  small 
ptatoB  from  that  of  the  intermediate ;  and  that  of  the  area  **A  **  will  denote 


770 


T&B  BTEAM-EKOIHIB, 


the  mean  unbalanced  pressure  on  a  square  Inch  of  the  annular  ring  of  the 
large  piston  obtained  by  subtracting  tiie  intermediate  from  the  large  piston 
We  thus  see  that  the  mean  ordinates  of  the  two  lower  cvda  act  on  annular 
rings. 
Let  H  =  area  of  small  piston  in  square  inches; 

is     **    **•  intermediate  piston  in  square  inches; 
Lss     **    **  large  piston  in  square  inches; 
Ph  =  mean  unbalanced  pressure  per  square  inch  from  card  **  C  **; 

p^  3         M  M  M  ••  M  M  «•  »»  **A*** 

S  SB  piston-speed  in  feet  per  minute; 
(I.H.r.)  s  indicated  horse-power  of  engine. 

Then  for  equal  work  in  each  cylinder  we  have: 
Area  of  small  piston  =  H  a 


: 83,000 X?~^-»-(jAXfi);    ....   a 


88.000  xi^H-(p,xS); 
:  H  +  83,000  X  ^~^*  *  (PI  X  fl); 


(^ 


Area  of  annular  ring  of  J 
intermediate  cylinder  | 

Area  of  interme- ) 
diate  piston     | 

I  H  P 
Area  of  annular  ring  of  large  piston  s  83,000  x  -^-o^*  "^  (P  X  ^* 

Areaof  large  piston  mi  a  I -f  88,000  x^~^*-^(PlX  S);     .    .    <») 

This  method  is  illustrated  by  the  following  example:  Given  I.H.P.  =  8000, 
piston-speed  fir  =  900  ft.  per  min.,  ratio  of  expansion  10,  initial  steam-rres- 
sure  at  cylinder  137  lbs.  absolute,  and  back -pressure  in  large  cylinder  4  lbs. 
absolute.    Find  cylinder  diameters  for  equal  work  in  each. 

The  mean  ordinate  of  "C  **  is  found  to  be  ph  s  87.414  lbs.  per  aq.  In. 
««        ti  M         **  **  n  *^  **      **        '*      m  -s  1B.7!R2  **     **      ** 


Then  by  (1),  (8),  and  (I 
8000 


)  we  have: 


H  e  83,000  X  ^ -I- 87.414  X  900  8 
8000 


JX  =  15.782  •* 
J>|B  11.780  •• 


9e08q.ltt.,dlam.8SK"; 


J  a  960+ 88,000  X^-«- 15.788  X  900  s  8806  sq.  In.,  diam.  W; 

LBi8808+88,000  X  ^  •«- 11 .780  X  VOO  «  6482  sq.  in.,  diam.  90^ 
8 

Mr.  Whitham  recommends  the  following  cylinder  ratios  when  the  pteton- 
•peed  is  from  7S0  to  1000  ft.  per  rain.,  the  terminal  pressure  in  the  large 
cylinder  being  abouc  10  lbs.  absolute. 

Ctlindbr  Ratios  RacomcENnKo  roa  Tbiplk-kxpansion  Bngivbs. 


Boiler-pressure 
(Gauge). 


Small 


Intermediate. 


Large. 


180  1  9.25  5.00 
140  1  8.40  5.85 
150  1  2.66  0.90 
leO  1  8.70  7.25 
170  and  upwards— quadruple-expansion  engine  to  be  used. 

He  gives  the  following  ratios  from  examination  of  a  number  of  actual 
engines : 

No.  of  Engines   Steam-boiler  Qyllnder  Ratios. 

Averaged.          Pressure.  h.p.                int.                    Lp. 


9 

180      : 

1         8.10 

4.6 

8 

136 

1         8.07 

6.00 

11 

140 

8.40 

6.84 

t 

146 

1         8.86 

5.88 

88 

160 

1         8.54 

6.90 

V 

100         1 

I        8.M 

T.M 

TRIPLB-EXPANSIOIS"  EISTQINES. 


771 


A  Common  Role  for  FroportlottlniT  ^«  C^llndeM  of  ilii/!- 
tiple-expansion  engi"*^  is:  for  two-oy Under  compound  en^irloes,  tbe  cylinder 
ratio  is  Uie  squara  root  of  the  number  of  expansions,  and  for  triple-expansion 
engines  the  ratios  of  the  high  to  the  intermediate  and  of  tbe  intermediate 
to  the  low  are  each  equal  to  tbe  cube  root  of  the  number  of  expansions,  the 
ratio  of  the  high  to  the  low  being  the  product  of  the  two  ratios,  that  is,  the 
square  of  the  cube  root  of  tbe  number  of  expansions.  Applying  this  rule  to 
tlie  pressures  above  given,  assuming  a  termnial  pressure  (araolute)  of  10  ibs. 
and  8  lbs.  respectively,  we  have,  for  triple-expansion  engines: 


Boiler. 

Terminal  Pressure,  10  lbs. 

pressure 

(Absolute). 

No.  of  Ex- 
pansions. 

Cylinder  Ratios, 
areas. 

No.  of  Ex- 
pansions. 

Cylinder  Ratios, 
areas. 

130 
140 
150 
160 

13 
14 
15 
16 

1  to  2.85  to  6.63 
1  to  2.41  to  5. 81 
1  to  2.47  to  6.06 
1  to  2.62  to  6.35 

20* 

1  to  2.63  to  6.42 
1  to  8.60  to  6.74 
1  to  2.66  to  7.06 
1  to  2.71  to  7.87 

The  ratio  of  the  diameters  Is  the  square  root  of  the  ratios  of  the  areas,  and 
the  ratio  of  the  diameters  of  the  first  and  third  cylinders  is  the  same  as  the 
ratio  of  the  areas  of  first  and  second. 

Seaton,  in  his  Marine  Engineering,  says:  When  the  pressure  of  steam  em- 
ployed exceeds  115  lbs.  absolute,  it  is  advisable  to  employ  three  cylinders, 
through  each  of  which  the  steam  expands  in  turn.  The  ratio  of  the  low- 
pressure  to  high- pressure  cylinder  in  this  system  should  be  6,  when  the 
steam-pressure  is  125  lbs.  absolute;  when  186  lbs.  absolute,  6.4;  when  146 
lbs.  absolute,  5.8;  when  155  lbs.  absolute,  6.2;  when  165  lbs.  absolute,  6.6. 
Tbe  ratio  of  low-pressure  to  intermediate  cylinder  sliould  be  about  one  half 
that  between  low-pressure  and  high- pressure,  as  given  above.  That  Is,  If 
the  ratio  of  I.  p.  to  h.  p.  is  6,  that  of  I.  p.  to  int.  should  be  about  3,  and  conse- 
quently that  of  int.  to  h.  p.  about  2.  In  practice  the  ratio  of  Int.  to  h.  p.  is 
nearly  S.25,  so  that  the  diameter  of  the  int.  cylinder  is  1.5  that  of  the  h.  p. 
The  introduction  of  the  triple-compound  engme  has  admitted  of  ships  being 
propelled  at  higber  rates  of  speed  than  formerly  obtained  without  exceeding 
the  consumption  of  fuel  of  similar  ships  fitted  with  ordinary  compound 
engines;  In  such  cases  the  higber  power  to  obtain  the  speed  has  been  devel- 
oped by  deci'easiug  the  rate  of  expansion,  the  low-pressure  cylinder  being 
only  0  times  the  capacity  of  the  high-pressure,  with  a  working  pressure  of 
170  lbs.  absolute.  It  is  now  a  very  general  practice  to  make  the  diameter  of 
the  low  pressure  cylinder  equal  to  the  sum  of  the  diameters  of  the  h.  p.  and 
int.  cylinders;  hence. 

Diameter  of  int.  cylinder  =  1.5  diameter  of  h.  p.  cylinder; 
Diameter  of  1.  p.  cylinder  =  2.5  diameter  of  h.  p.  cylinder. 

In  this  case  the  ratio  of  1.  p.  to  h.  p.  is  6.25;  the  ratio  of  int.  to  h.  p.  is  2.25; 
and  ratio  of  1.  p.  to  int.  is  2.78. 
Bati4Mi  of  Cylinders  for  DUV^rent  Classes  of  Enelnes. 

(Proc.  Inst.  M.  E.,  Feb.  1887,  p.  36.)— As  to  the  best  ratios  for  the  cylinders 
in  a  triple  engine  there  seems  to  be  great  difference  of  opinion.  Considera- 
ble latitude,  however,  is  due  to  the  requirements  of  the  case,  inasmuch  as 
it  would  not  be  expected  that  the  same  ratio  would  be  suitable  for  an  eco- 
nomical land  engine,  where  the  space  occupied  and  the  weight  were  of 
minor  importance,  as  in  a  war-ship,  wliere  the  conditions  were  reversed.  In 
the  land  engine,  for  example,  a  theoretical  terminal  pressure  of  about  7 
lbs.  above  absolute  vacuum  would  probably  be  aimed  at,  which  would  give 
a  ratio  of  capacity  of  high  pre<«sure  to  low  pressure  of  1  to  8^|  or  1  to 
9;  whilst  in  a  war-ship  a  terminal  pressure  would  be  required  of  12  to  13  lbs. 
which  would  need  a  ratio  of  capacity  of  1  to  5;  yet  in  both  these  instances 
the  cylinders  were  correctly  proportioned  and  suitable  to  ttie  requirements 
of  the  case.  It  is  obviously  unwise,  therefore,  to  introduce  any  hard-and- 
fast  rule. 

Types  of  Tliree-staiEe  Expansion  Enfi^lnes*— 1.  Three  cranks 
at  1*^  deg.  2.  Two  crantcs  with  1st  and  2d  cylmders  tandem.  8.  Two 
cranks  with  1st  and  3d  cylinders  tandem.  The  most  common  type  is  the 
first,  with  cylinders  arranged  in  the  sequence  high,  intermediate,  low. 


772 


TH«  9rEAH.£K0IKB. 


8e«»*ttt*  #f  rMUikfl.~lIr.  ITrtlle  (Proc.  iMi.  11.  £..  tflB?)  farors  the 
MQwaott  biglslow,  fntcrmediare,  wmW  Mr.  Mudd  favors  Mgrh,  intermediate, 
low.  The  former  Beqfaeaoe,  hi^h,  tow,  taktermediate,  gave  ao  approxlaiatery 
horiiontal  exhau8t>Iinar  and  tluM  niafmixeB  the  nmge  of  temVterature  and 
the  iaiifcy  lead;  the  latter  Mquenee,  high,  httermedrnte,  low,  increased  the 
mnffB  aad  also  Iha  kiad. 

Mr.  MorrtooD,  in  discuMiar  the  qweitloa  of  se<|ueiiee  of  enmks,  presented 
a  dtacram  •hawini^  that  with  the  creiika  arraiifted  in  the  seouenee  bf^h, 
low,  intermediate^  the  me—  coaiprewioa  into  the  recetver  was  19^  per  cent 
of  the  stroke;  with  the  sequence  ht^h,  intermediate,  low,  tt  was  ST  per  cent. 

In  the  former  case  the  comjpi-ession  was  Just  what  was  required  to  keep 
the  reeeftrer-presBure  practically  imiffDrm;  in  the  latter  case  thecompreasioti 
caused  a  variation  in  the  receiver-pressure  to  the  extent  sonMUOMa  of 
ZZUIhs. 

veleeitj  «t  Steam  tfaronclt  Paasaces  In  Compound 
EnKlnea.  (Froo.  Inst.  Iff.  E.,  Feb.  i%7.)— In  the  ^8.  Fara,  taking  the  area 
of  the  cjlmder  ninltipUed  by  the  piston-speed  in  feet  per  second  and 
(ttvidiag'  hy  the  aiea  of  the  port  the  yelodtj  of  the  initial  steam  through 
the  hlgh-preseure  cylinder  port  would  be  about  100  feet  per  second ;  the  ex- 
haust would  he  about  W.  In  the  intermediate  cylindar  the  initial  steam 
had  a  veloeity  of  about  1€0,  and  the  exhaust  of  180.  In  the  low-pressure 
cylhider  the  inittal  steam  entered  through  the  port  with  a  velocity  of  250, 
and  tai  the  exhaust-port  the  velocity  was  about  140  feet  per  second. 

<iUA]IR1JPI«I^KXJPABiUON  BI««IW1IS. 

H.  H.  SupTee  (Trans.  ▲.  8.  M.  E.,  x.  583)  states  that  a  study  of  U  dttteram 
q;uadrupIe-expanaion  engines,  nearly  all  intended  to  be  operated  at  a  prM* 
sure  of  180  lbs.  per  sq.  in.,  gave  average  oyliader  ratios  of  1  u>  8,  to  1^78,  Co 
7.70,  or  nearly  in  the  proportions  1,  8;  4^  8. 

If  we  take  the  ratio  of  areas  of  aaar  two  adJoiaiBg-cylinderB  as  the  foarth 
root  of  the  number  of  expansions,  tAa  ratio  of  the  let  to  the  4th  wttl  be  the 
cube  of  the  fourth  root.  On  this  basis  the  ratios  of  areas  for  different  pres- 
sures and  Eatea  of  expsasion  wiU  be  as  foUowa : 


Gao^B. 

Abaolnte 

Terminal 

Ratio  of 

KatfoB  of  Areas 

peSBBMSAt 

Pressures. 

Pressures. 

Expansion. 

of  Cylinders. 

1« 

14.6 

1:1.95:8.81:    7.43 

160 

178 

•  10 

1T.5 

1:2.05:4.18:    8.55 

9 

81.9 

1:2.16:  4.68:  10.12 

1« 

10.2 

1  :  2.01:  4.02:    8.07 

280 

105 

-^10 

10.5 

1:2.10:4.42:    9.28 

8 

84.4 

1 :  2.83  :  4.91 :  10.98 

12 

17.9 

1:2.06:4.28:    8.70 

200 

818 

.  10 

21.5 

1:2.15:4.64:    9.06 

8 

86.9 

1:8.98:5.19:11.81 

12 

19.6 

1:».10:4.48:    9.M 

SSO 

885 

•  19 

88.5 

1:2.89:4.85:10.67 

8 

29.4 

1:9.38:5.42:  19.68 

Saatoa  saors:  When  the  presmire  of  steam  employed  exceeds  190  lbs.  abso- 
ute,  four  eyllndera  should  be  efiiplored,  with  the  steam  expanding  through 
^ach  successively;  and  tlie  ratio  of  I.  p.  to  h.  p.  should  be  at  least  7.5,  and 
if  economy  of  fuel  is  of  prime  consideration  tt  should  be  8:  then  the  ratio 
of  first  intermediate  to  h.  p.  should  be  1.8,  that  of  second  intermediate  to 
first  hit.  8,  and  that  of  I.  p.  to  second  Int.  2.2. 

In  a  paper  read  before  the  North  East  Coast  Institution  of  Itegineers  and 
Shipbuiklers,  1890,  Williani  Russell  Cummins  advocates  the  use  of  a  foiir> 
eylinder  engine  with  four  cratike  as  being  more  suitable  for  high  speeds 
than  the  three^Iinder  three-cmnk  engine.  The  cylinder  ratios,  he  claims, 
should  be  designed  so  as  U>  obtain  equal  initial  loads  in  each  cylinder.  The 
ratios  determined  for  the  triple  engine  are  1,  2.04,  6.54,  and  for  thequadru- 
pie  1, 8.08,  4.46, 10.47.  He  advocat««  long  stroke,  high  piston-speed.  lOO  rev- 
cdutions  per  minute,  and  260  lbs.  boiler-pressure,  unjacketed  (^Unders,  and 
aapantta  steam  aad  exhausts  valves. 


QUADRUPLB-BXPANdlOl^   EKGINES. 


7:8 


Bit 


ieten  of  Cirlindera  i»r  Ri^e^tit  Trtple-expannlon 
TBakglnem^  Cnlelkf  marine* 

Compiled  from  several  sources,  189(V  1896. 


Diam.  Id  Inches: 

H  =  high  pressure 

,  /  =  intermediate. 

L  =  low  pressure. 

H 

/ 

L 

H 

I 

L 

H 

I 

L 

H 

I 

L 

3 

5 

8 

16 

25.6 

41 

22 

88 

i40 
140 

36 

68 

04 

4H 

7.5 

18 

16H 

23% 

88.£ 

38 

61.5 

100 

5 
6.5 

8 
10.5 

12 

16.5 

16.5 

W.6 

4  81 
131 

83 
23.5 

88 
38 

61 
60 

281 
28r 

56 

86 

7 

9 

12.  J 

17 

27 

44 

84 

87 

56 

39 

61 

97 

7.1 

11.8 

18.S 

17 

26.5 

42 

25 

40 

64 

40 

59 

88 

7.5 

12 

19 

17 

28 

45 

26 

42 

69 

40 

67 

106 

8 

11.5 

16 

18 

27 

40 

20 

42.5 

TO 

40 

66 

100 

9 

14.6 

22. f 

18 

29 

48 

28 

44 

n 

41 

06 

101 

9.8 

15.7 

25. ( 

18 

805. 

51 

^ 

44 

70 

41% 

67 

i(m 

30 

16 

25 

18.7 

29.5 

43.^ 

48 

78 

42 

59 

92 

11 

16 

84 

19^ 

23.6 

85.4 

30 

48 

rr 

43 

66 

92 

11 

18 

25 

29.6 

47S 

32 

46 

70 

43 

68 

110 

11 

18 

30 

20 

80 

45 

32 

51 

82 

43% 

67 

10(H4 

IJ.* 
11.5 

18 
175 

98.{ 

80.f 

90 

88.fi 

<86 
138 

82 
33 

54 

58 

82 
88 

45 

«.5I 
:i2.5  \ 

71 

68 

113 

)85.7 

12 

19.8 

.W.7 

20 

33 

52 

8:3.9 

55.1 

84. f 

<85.7 

13 
14 

22.4 

83.5 
80 

21 
21 

32 
36 

48 
51 

34 
34 

54 
50 

85 
90 

47 

75 

J  81.6 
181.6 

14.9 

24 

89 

21.7 

83.5 

49. S 

34.5 

51 

86 

37* 
37  f 

79 

t98 
198 

15 

21 

89 

21.9 
22 

34 

67 

34.6 

67 

92 

15 

24.6 

38 

84 

61 

Where  the  flfi^ires  are  bracketed  there  are  two  cylinders  of  a  kind.  Two 
28"  =  one  89.6",  two  81"  =  one  48.8",  two  32.5"  =  one  46.0",  two  38"  =  one 
60.9",  two  87"  =  one  52.8",  two  40"  =  one  66.6",  two  81.5"  =  one  115",  twe 
85.T"  =  one  121",  two  98"  =  one  140".  The  average  ratio  of  diameters  of 
cylinders  of  all  the  engines  In  the  above  table  is  nearly  1  to  1.60  to  2.56  and 
the  ratio  of  areas  nearly  1  to  2.56  to  6.55. 

TIfte  Proi^rean  lil  Steam*eiig:lnea  between  1876  and  1893  Is  shown 
in  the  following  comparison  of  the  Corliss  engine  at  the  Centennial  Exhibi- 
tion in  1876  and  the  Allis-CorlisB  quadruple-expansion  engine  at  the  Chicago 
Exhibition. 

1898.  1876. 

=■*«- {^X^^\      «""p" 

Cylinders,  nuihber 4  2 

diameter. 24,  40,  60,  70 In.  40ln. 

'*         stroke 72in.  120  In. 

Fly-wheel,  diameter 30ft.  80ft. 

width  of  faca 76  in.  24  in. 

weight 186,000  lbs.  125,440ib8. 

Revolutions  per  minute 60  36 

Capacity,  economical 2000  H.  P.  1400  HP. 

maximum 8O0O  H,P.  2500  H. P. 

TotAlwelght 650.000  lbs.  l,360,f  88  lbs. 

Ttie  crank-shaft  body  or  wheel-seat  of  the  Allis  engine  hUs  a  diameter  of 

21  inches,  journals  19  inches,  and  crank  beai-ings  18  Inches,  with  a  total 
lengtfa  of  18  feet  The  erank-dislcs  are  of  cast  iron  -nd  are  8  feet  in  diam- 
eter.   Tbe  crank-pins  are  9  inches  In  diameter  by  9  inches  long. 

A  Honble^tAniieiii  Trlpte-expaikiiien  finfflne,  built  by  Watts, 
Campbell  &  Co.,  Newark,  N.  J.,  is  desicnDed  in  .4m.  Mach.,  April  26,  1894. 
It  is  two  three-cylindet-  taiuleiii  enyine.*;  coupled  to  t>ne  shaft,  cranlts  iit  fiO«, 
cylinders  'il,  32  and  48  by  60  in.  8tn»ke.  6.'>  n'volutioiis  |>er  minute,  rated  H.P. 
200O;  fly-wlieel  28  feet  diameter,  12  ft.  face,  weight  174,000  lbs.;  main  Khaft 

22  in.  diameter  at  the  swell;  main  jouiimls  19  x  38  in.;  crank-pins  !i^  x  10 
in.;  distance  between  centre  lines  of  two  engines  24  ft.  7V6  !"•;  Corliss 
Talves,  with  separate  eccentrics  for  the  exhaust-yalves  of  the  l.p.  cylinder. 


THE  STEAM-ENGINE. 


-urn  *M\B 


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ECONOMIC  PERFORMAKCB  OF  STEAM-ENGINES.    775 


BcoNomc  pkbforhancb  of  stbam-bnginks. 

Eeonomy  of  ExpanslTe  ITorMlnff  under  Tartons  Condi- 
tlons,  Single  €|llnder. 

(Abridged  from  Clark  on  the  Steam  Engine.) 

1.  SiNOLB    CTLINDBRS    WITH    SUPKRHBATBD    StBAM,    NONCONDKN8INO.— In* 

side  cylinder  locomotive,  cylinders  and  steam-pipes  enveloped  by  the  hot 
f^ises  in  the  smoke-box.  Net  boiler  pressure  100 lbs.;  net  maximum  press- 
ure in  cylinders  80  lbs.  per  sq.  in. 

Cut-off,  per  cent 20258085       40       5060       70       80 

Actual  ratio  of  expansion  8.91  3.81  2.87  2.58  2.26  1.86  1.59  1.89  1.23 
Water  per  LH.P.  per  hour« 

lbs. 18.5    19.4     20     21.2    22.2    24.5     27       80       88 

2.  SnroLa  Ctlindkbs  with  Supbrhbatbd  Stbam,  Condknsino.— The  best 
results  obtained  by  Him,  with  a  cylinder  239^  x  67  in.  and  steam  super- 
heated 150*  F.,  expansion  ratio  2H  to  4^,  total  maximum  pressure  in  cylin- 
der 68  to  69  lbs.  were  16.63  and  16.60  lbs.  of  water  per  I.H.F.  per  hour. 

8.  SnfOLB  CTI.INDER8  OF  Small  Sizb,  8  ob  9  IN.  DiAM.,  Jackstbd,  Non- 
coNDENSiNO.— The  best  results  are  obtained  at  a  cut-off  of  20  per  cent,  with 
73  lbs.  maximum  pressure  in  the  cylinder;  about  25  lbs.  of  water  per  LH.P. 
per  hour. 

4.  Single  Ctlikdkbs,  not  Stkam-jacubisd,  CoNDENsma.— Best  results. 


Corliss  and  Wheelock . 

Hirn,  No.  6 

Mair,M 

Baehe 

Dexter 

Dallas 

Gallatin 


Cylinder, 

Diam. 

and 

Stroke. 


ins. 
18X48 

88«X67 
32X66 
25X24 
26X36 
36X30 

30.1  X  80 


Cut-off. 


per  cent. 
12.5 
16.8 
24.6 
15.6 
18.8 
18  8 
15.0 


Actual 
Expan- 
sion 
Ratio. 


ratio. 
6.96 

6.84 
8.84 
b.m 
4.46 
5.07 
4.94 


Total 
Maxi- 
mum 
Pressure 
In  Cylin- 
der per 
sq.  in. 


lbs. 
104.4 
61.5 
64.6 
87.7 
80.4 
46.9 
81.7 


Water  as 
Steam 

I.ff.P. 
per  hour. 


lbs. 

19.58 

19.98 

26.46 

26.25  ' 

23.86 

26.60 

21.80 


Same  Engines,  average  Results. 


Long  Stroke. 

Inches. 

Cut-off,  Per  cent 

T.b8. 

Lbs. 

Corliss  and  Wheelock. . . 
Him « 

Short  Stroke. 
Baohe 

18X48 
23«X67 

25X24 
26X36 

86X30 

80.1  X30 

12.5 
16.3 

16.6 
{  18.8  to  88.8  I 
}  average  25  f 
j  18.3  to  26.4 
<  average  19.8  ( 
i  12.8  to  18.5  * 
1  average  15.8  f 

104.4 
61.5 

87.7 
79.0 

46.8 

78.2 

19.58 
19.98 

26  25 

Dexter,  Nos.  20.  21,  22.  23 

Dallas,  Nos.  27,  28,  20  . . . 

Gallatin,  Nos,  24,  25,2^2.1. 
26 \ 

24.05 
96.86 
28.50 

Feod-wator  Oonaamptlon  ofOlflTeroBt  Type*  of  Engines, 

—The  following  tables  are  lakeii  froui  the  circular  of  the  Tabor  Indicator 
(Ashcroft  Mfg.  Co.,  1880).  In  the  first  of  the  two  columns  under  Feed- water 
required,  in  the  tables  for  simple  engines,  the  figures  are  obtained  by 
computation  from  nearly  perfect  indicator  diagrams,  with  allowance  for  cyl- 
inder condensation  according  to  the  table  on  page  752,  but  without  allow- 
ance for  leakage,  with  back-pressure  in  the  non-condensing  table  taken  at  16 
lbs.  atwve  zero,  and  iu  the  condunsing  table  at  3  lbs.  above  zero.  The  com- 
pression curve  is  supposed  to  be  hyperbolic,  and  commences  at  0.91  of  the 
return-stroke,  with  a  clearance  of  3%  of  the  piston-displacement. 
Table  No.  2  gives  the  feed-water  consumption  for  Jacketed  compound-con* 


776 


THE  8TEAH-ENGINB. 


densbif?  eiurinei  of  the  boat  dass.  The  water  coodeiiBed  In  the  jacket!  b 
included  In  the  auaiitiUes  Riven.  The  ratio  of  areas  of  the  two  cyhnders  are 
as  1  to  4  for  120  ids.  pressure;  the  clearance  of  each  cylinder  is  Sjt;  and  the 
cut  off  in  the  two  cylinders  occurs  at  the  same  point  of  stroke.    The  initial 

£ressure  in  the  I.  p.  cylinder  is  1  lb.  per  sq.  in.  below  the  back-pressure  of  the 
.  p.  cylinder.  Tne  average  back  pressure  of  the  whole  stroke  in  the  1.  p. 
oyhnder  is  4.5  lbs.  for  lOjC  cut-off;  4.76  lbs.  for  20%  cut-off;  and  6  Iba.  for  »% 
out>off.  The  steam  accounted  for  by  the  indicator  at  cut-off  in  the  h.  p. 
cylinder  (allowing  a  small  amount  for  leakage)  is  .74  at  10)(  cut-off,  .78  at 
20%,  and  .82  at  80$  cut-off.  The  loss  by  condensation  between  the  cylinders 
is  such  that  the  steam  accounted  for  at  cut-off  in  the  1.  p.  cylinder,  ex- 
pressed in  proportion  of  that  shown  at  release  in  the  h.  p.  cylinder,  is  .85  at 
IM  cut-off.  .87  at  20%  cut-off,  and  .89  at  90%  cutoff. 

The  data  upon  which  table  No.  8  is  calculated  are  not  given,  but  the  feed- 
water  consumption  is  somewhat  lower  than  has  yet  been  reached  (18M),  the 
lowest  steam  consumption  of  a  tiiple-exp.  engine  yet  recorded  being  11.7  lbs. 
TABLfEi  r^o.  1. 
Fbbd- WATER  Consumption,  Bimplb  Engimcs. 

NON-COKDBNSING  ENGINES.  CONDENSING  ENaiNBS. 


< 

1 

i 

5 

Feed-water  Re- 

1 

1 

1 

Feed-water  Re- 

quired per  I.  H. P. 
per  Hour. 

quired  per  l.H.P. 
per  Hour. 

I 

^1 

0^'>2M 

« 

o5|.S 

e 

5 

1 

a 

SI 

H 

IP 

a 

& 

1 

e 

ti 

1 

ssfz 

lil5 

■ 

60 

8.70 

87.26 

40.95 

f 

60 

14.42 

18.28 

20.00 

70 

12.89 

30.99 

83.68 

70 

16.96 

17.96 

19.69 

10 

80 

18.07 

27.61 

29.88 

6. 

80 

19.50 

17.76 

19.47 

90 

19.76 

25.43 

27.43 

90 

82.04 

17.57 

19.87 

. 

100 

23.45 

28.90 

25.73 

100 

24.58 

17.41 

19.07 

■ 

60 

21.12 

27.55 

29.43 

10 

60 

22.84 

17.68 

19.34 

70 

26.57 

25.44 

27.04 

70 

26.08 

17  47 

19.09 

20 

80 

82.02 

31.04 

85.68 

80 

29.72 

17.80 

18.89 

90 

87.47 

23.00 

24.57 

i 

90 

33.41 

17.15 

18.70 

100 

42.92 

22.25 

28.77 

100 

87.10 

17.02 

18.56 

60 

80.47 

27.24 

89.10 

60 

29.00 

17.98 

19.61 

70 

37.21 

25.76 

27.48 

70 

33.65 

17.75 

19.27 

80  ■ 

80 

48.97 

24.71 

26.29 

15" 

80 

38.28 

17.60 

19.06 

90 

60.73 

23.91 

25.38 

90 

42.92 

17.45 

18.91 

. 

100 

67.49 

28.27 

84.68 

^ 

100 

47.66 

17.8;J 

18  74 

60 

37.75 

27.98 

89.63 

' 

60 

34.73 

18.58 

20  09 

70 

45.50 

26.66 

28.18 

70 

40.18 

18.40 

19.85 

40V 

80 

63.iJ5 

25.76 

27.17 

20 

80 

45.6-1 

18.87 

10. CO 

90 

61.01 

26.03 

86.35 

90 

51.06 

18.14 

19.51 

100 

68. T6 

24.47 

25.73 

. 

100 

66.53 

18.02 

19.36 

1 

60 

4d.4..> 

88.94 

80  60 

f 

60 

44.06 

80.10 

81. t4 

TO 

51.94 

87.79 

29.31 

70 

50.81 

20.04 

81.41 

W 

80 

60.44 

26.99 

28.38 

so- 

80 

57.57 

19.91 

21.85 

90 

68.96 

26.3» 

27.6tf 

90 

64.32 

19.78 

81  .(16 

100 

77.48 

25.78 

86.99 

100 

60 
70 

71.08 

51.86 
69.10 

19.67 

21.63 
81.49 

9U.98 

28  W 
22.74 

lo 

80 
90 

66.85 
74.60 

21.30 
21.84 

2^.58 
8;J.4! 

■ 

100 

88.86 

81.18 

88.M 

CALCULATED  PERFORMANCES  OP  BTBAM-EKGINES.    777 


TABLE  No.  2. 

Fbbd-watbr  Conscmption  for  Compound  Condewbiko  Engiks 


Cut-off, 

Initial  Pressure  above 
Atmosphere. 

Mean  Effective  Press- 
Atmosphere. 

Peed-water 

Required 

perT.H.P.  per 

Hour,  Lbs. 

per  cent. 

HP.  Cyl.. 
lbs. 

L.P.  Cyl.. 
Ibt. 

H.P.  Cyl.. 
lbs. 

L.P.  Cyl, 
lbs. 

10       . 

-  t 

90        - 

80 
100 

lio 

80 
100 
1)20 

80 
100 
190 

4.0 
7.8 
11.0 

4.3 
8.1 
12.1 

4.6 
8.5 
11.7 

11.67 
16.88 
18.54 

26.73 
38.18 
89.'^ 

87.61 
46.41 
66.00 

2.66 
3.87 
6.23 

5.48 
7.56 
9.74 

7.48 
10.10 
W.«6 

16.92 
15.00 
18.86 

14.60 
13.67 
18.09 

14.90 
14.21 
18.«: 

TABLE  No.  8. 

FSBP-WATBR  CONBUXPTION  FOR  TRIPLK-KXPAItSION  CONDENSncO  ENGINES. 


Cut-off. 

luitial  Pressure  above 
Atmosphere. 

Mean  Effective  Pressure. 

Feed-water 

Required 

perLH.P. 

per  Hour, 

lbs. 

p«r 

cent. 

H.P.  Cyl.. 
lbs. 

I.  Cyl., 
Ibe. 

L.P.Cyi., 

H.P.  Cyl., 
lbs. 

L  Cyl., 
lbs. 

L.P.  Cyl., 
Ibe. 

40    • 
60    • 

120 

140 
160 

120 
140 
160 

120 
140 
160 

87.8 
43.8 
49.8 

88.8 
45.8 
51.3 

89.8 
46.8 
52.8 

1.8 

2.8 
8.8 

2.8 
3.9 
5.3 

8.7 

4.8 
6.8 

38.6 
465 
55.0 

51.6 
59.5 

ro.o 

60.5 
70.5 
82.6 

17.1 
18.6 
20.0 

22.8 
28.7 
25.5 

26.7 
28.0 
80.0 

6.5 
7.1 
8.0 

8.6 
9.1 
10.0 

10.1 
10.8 
11.8 

12.05 

11.4 
10.75 

11.65 
11.4 
10.85 

12.2 

11.6 
11.15 

Most   Eeonomleal   Point   of  Cat-oflT  In  Steaiii"«BclBea, 

(See  paper  by  Wolff  and  Denton,  Trans.  A.  8.  M.  E.,  vol.  ii.  p.  147-281 ;  also, 
Ratio  of  Expansion  at  Maximum  Efficiency,  R.  H.  Thurston,  vol.  ii.  p.  128.) 
—The  problem  of  the  best  ratio  of  expansion  is  not  one  of  economy  of  con- 
sumption of  fuel  and  economy  of  cost  of  boiler  alone.  The  question  of 
interest  on  cost  of  engine,  depreciation  of  value  of  eneine.  repairs  of  engine, 
etc..  enters  as  well;  for  as  we  increase  the  rate  of  expansion,  and  thus, 
williin  certain  limits  flzed  by  the  back-pressure  and  condensation  of  steam, 
decrease  the  amount  of  fuel  i-e<]uired  and  cost  of  boiler  per  unit  of  work, 
we  have  to  increase  the  dimensions  of  the  cylinder  and  the  size  of  the  en- 
inne.  to  attain  the  required  power.  Wo  thus  increase  the  cost  of  the  engine. 
etc..  as  we  increase  the  rate  of  expansion,  while  at  the  same  time  we  de- 
crease the  fuel  consumption,  the  cost  of  boiler,  etc.  Bo  that  there  Is  in 
every  enj^hie  some  point  of  cut-off,  determinable  by  calculation  and  fpraphi- 
cal  construction,  which  will  secure  the  f^reatest  efficiency  for  a  given  expen- 
diture of  money,  takiuK  into  consideration  the  cost  of  fuel,  wages  of  engineer 
and  firemen,  interest  on  cost,  depreciation  of  value,  repnirs  to  and  insurance 
of  boiler  and  engine,  and  oil,  waste,  etc.,  used  for  engine.  In  case  of  freight- 
carrying  vessels,  the  value  of  the  room  occupied  by  fuel  should  be  consid- 
ered in  estimating  the  coKt  of  fuel. 

81so»  sibd  Calculated  Performanees  of  Terlieal  SlKh- 
fipeed  Eufl^nes.— The  following  tables  are  taken  from  a  circular  of  the 
Field  Engineering  Co.,  New  York,  describing  the  engines  made  by  the  I^ke 
Erie  Englfneering  Works,  Buffalo,  N.  Y.  The  engines  are  fair  representatives 
of  the  type  now  coming  largely  into  use  for  driving  dynamos  directly  with- 
out belts.  The  tables  were  calculated  by  E.  F.  Williams,  designer  of  the 
engines.    They  u^e  here  somewhat  abridged  to  save  space: 


77S 


THE  STEAU-EKGINE. 


Stmpi 

e  Enfflnes 

-Tfon-condenslnir* 

Il 

1 

2 

11.1'.  when 
Cutting  off 

Dim  en 

KlUELl^  1  pf 

Wheela. 

4 

i 

^a 

i 

h 
> 

rtt  l/jtitruk^-. 

al  ^  atn>ke. 

at  ^i  stroke. 

H^ 

70 

80 

SO 

70 

BO 

DO 

toIbo 

«» 

Ft. 
4 

111. 

4 

1 

•25 

&^ 

lbs. 

lbi». 

tbg. 

lbs. 

lb». 

lbs. 
30 

lb8    'Jbfl. 

lbs. 

'JH 

it! 

10 

170 

a) 

e,-) 

3tJ 

3a 

a: 

:( 

18 

.^l*< 

27 

Ji.; 

3*) 

M 

41 

47 

41 

4» 

W 

i¥t 

6 

^ 

an 

14 

liTT 

41 

40 

tM; 

5a 

C3 

71 

03 

74 

85 

yu" 

1* 

in 

4 

1« 

16 

;;*(i 

53 

[}] 

t  i 

iS7 

81 

9-i 

m 

W 

lU 

fi'tt" 

41-, 

184 

18 

i^i 

e« 

KO 

% 

84 

100 

116 

UfJ 

lao 

m 

714 

n 

5 

10 

«) 

Ifil 

% 

115 

Li*^ 

liO 

14* 

l.fi 

I4G 

i?i 

196 

8'4^' 

IS 

4^ 

<; 

18 

'J4 

lD?i 

nu 

U-l 

173 

151 

181 

^m 

1?« 

ai& 

:U8 

10 

]» 

7 

\»J 

28 

lan 

17^ 

iitt; 

Its  I 

*i7 

s?Tsi 

;iia 

27ei  5i;i4 

473 

irs" 

3m 

^ 

24^ 

82 

1L1) 

521 

I'fiT 

3i^» 

38tJ  aae 

»Hfl 

340 

400 

400 

134" 

Si 

» 

27 

34 

irj 

was 

aws 

345i|  'lU'J 

J  70 

414 

4«7 

500 

li^il" 

41 

10 

Mean  eff .  pr 

sslb. 

itft 

;i5 

30,sU-"i 

4*2 

37 

43.i* 

m 

Note*  —  Th- 
DOmLual^power 

Ratio  of  ezp 

atis*n. 

5 

4 

Terminal  pr 

►sPurt? 

nitiiif^  of  the  eu- 

(about)  .. 
Cy].coiiaeii» 

Ihti. 

17. & 

130 

-^i  » 

aa.4 

^ 

iT.O 

^•9  8 

83.3' 

Hfl,S 

^be»  Ls  at  80  IhL 

ati^i 

2fi 

ii(^ 

;.►*; 

:!f 

iii 

^4 

2L 

*JI 

Saiige    pti*afflire. 

Steam  per 

1  fl  1', 

Hteam  cyUolf  at 

per  hour. 

ibti 

:i^i9 

30 

'J7.4 

31.2 

'29  0  27  9 

3-J 

31.4 

30 

^  ■irolEQ. 

Compound 


Eni^lnes  —  lYoB-eondeBSlns  —  Hlffli  ■ 
Cylinder  and  Receiver  Jacketed* 


pressure 


H.P.  when  cutting  H.P.whencutting 

H.P.whencuttiiiir 

A 

S 

oflf  at  ki  Sti-oke 
iu  h.p.  Cylinder. 

off  at  J^  Stroke 
in  h.p.  Cylinder . 

off  at  ^  Stroke 
in  h.p.  Cylinder. 

Diam. 

^ 

a 

C'l^liiult-r, 
iuchiiii. 

'i 

"2 

Cyl. 

Cyl. 

Cyl. 

Cyl. 

Cyl. 

Cyl. 

^ 

^  a 

Ratio, 

Ratio, 

Ratio, 

Ratio. 

Ratio, 

RAtio. 

1 

r 

3^:1. 

4Vi:l. 

3^:1. 

4m  1. 

3H:l. 

4H:l. 

cl; 

cU 

III 

80 

90 

180 

150 

80 

90 

180 

IfiO 

80 

90 

180 

150 

m 

m 

J 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

Ibe. 

Ibei. 

"i^llii 

33~ 

10 

870 

7 

~15 

^ 

~82 

~S 

"11 

85 

46 

~44 

~65 

C4 

79 

^ 

7^ 

13H 

I'J 

318 

0 

19 

24 

40 

29 

89 

45 

69 

66 

TO 

81 

101 

m 

0 

IfSUf 

14 

i»77 

14 

28 

86 

60 

48 

58 

67 

87 

88 

104 

121 

159 

u 

m^ 

l!l 

16 

246 

18 

37 

47 

78 

57 

76 

87 

114 

109 

186 

158 

196 

;^H 

ia 

-i(, 

18 

222 

26 

58 

68 

112 

81 

109 

185 

164 

156 

195 

286 

2S1 

n]4 

■il 

■-■o 

185 

32 

65 

84 

139 

100 

185 

154 

202 

182 

SMI    279 

846 

134 

*;^!    4 

158 

43 

88 

112 

186 

135 

181 

20C 

271 

868 

328    374 

464 

10 

m\^ 

•J8 

188 

57 

118 

151 

249    180 

242 

2'*7 

863 

846 

4331  502 

623 

18 

^tC 

38 

;^:» 

120 

74 

152 

194 

821 1  282 

812 

867 

468 

446 

558    647 

HXi 

ao 

■^jij 

r4 

a 

112 

94 

194 

249 

412,  297 

400 

457 

601 

572 

715|  829 

1090 

^i!4 

t^u 

5:! 

12 

93 

188 

2a') 

33o 

603    436 

587 

670 

880 

888 

10481 1215 

I5ir< 

l!SJ.^  H:t 

m 

\s 

80 

180 

374 

477 

789!  570 

767 
14.0 

877 
16 

1151 
21 

1096 
20 

13701589 

1973 

lileun  eflfec.  press 

..lbs 
n 

3.3 

6.8 

8.7 

14.4 

10.4 

« 

Ratio  of  ezpansio 

13^ 

18^ 

lOM 

13% 

6«      1       9H 

Cyl.  condensation 

14 

14 

16  1  16 

12 

12 

18 

18 

10 

10      11 

11 

Ter.  press,  (about 

lbs. 

7.8 

7.7 

7.9 

9     92 

10.4 

10.5 

12 

14 

16.5  14  6 

17  8 

IjOsh  from  expat 

iding 

1 

l>elow  atniospht 

•re.  % 

84 

16 

17 

8  1    5 

0 

0 

0 

0 

0       0 

0 

8t  perl  HP.  ph 

r.Ibs 

55 

42 

47 

29    88  3 

27.7 

28  7 

25.4 

30 

26.2    21 

20 

The  original  table  contains  flgures  of  horse-power,  etc., for  110  and  190  lb&, 
cylinder  i  atio  uf  4  to  1 ;  and  140  lbs.,  ratic  iy^  to  1. 


CALCULATED  PERFORMANCES  OF  STEAM-ENGINES.  779 


- 

Componnd-eng:!  nes- 

-Condensliiff— 

S  team-Jaeketed* 

Il.r.wUeiiciuOii« 

H  P  wben  cuttingiH.R whencuUinj? 

1 

riJT  at  VJ  Stroke 
In  h.p,  OjlitiUtT. 

off  HI  i^  Stioke 

off  at  J4  Stroke 

Cv  Under, 

id  h  p.  CjlindtM-. 

in  h.p.  CjlimJer. 

'^  li 

fnulifrs. 

j= 

CyL 

Cyl 

Qyl 

Cyl. 

CyL 

CyL 

^ 

t:  a 

RMtio, 

Ratio. 

Ratio, 

Raiio. 

RttLlo, 

Rittlo, 

•I 

1^ 

a^:^ 

4:  1. 

m^.h 

4:1. 

m-.i. 

4:1, 

P^ 

^ 

A^ 
J 

80 

110 

!15 

12& 

m 

no 

ii:^ 

125 

fiO 

no 

115 

125 

EC 

W 

n^, 

ll)«. 

Ib^. 

lbs. 

Ib^ 

ib». 

lbs. 

Ibii, 

IbB. 

lbs. 

lbs. 

Um. 

fi 

6H 

1'.' 

10 

STtt 

44 

^ 

5;j 

€2 

T^t 

70 

fiS 

75 

70 

^ 

ori 

'm 

«^ 

■  ^ 

lauj 

12 

ma 

56 

TtS 

(i? 

78 

TO 

00 

87 

B5 

m 

123 

1i;d 

1,34 

skI 

s 

i&^ 

u 

r.7 

83 

11^ 

HX} 

ins 

las 

Vi^i 

l:.*fl 

UJ 

133 

MSH 

i7y 

201) 

*j4 

unv 

10 

je 

'^^ 

Km 

nr 

irjt 

i:.a 

i.ic^ 

174 

n;'j 

lli-> 

174 

2f^?',l 

234 

m 

11 

13 

'^i^ 

IK 

aaa 

12Vti 

;.^10 

lr<7 

21  IS 

19:> 

*i^0 

24^ 

iJtia   2f4) 

aJ3 

.w. 

374 

u^^ 

'^ 

■ib 

-JO 

m 

]ya 

:^ 

*J31 

mi 

a4i 

Hi)S 

2*jii 

537]   308 

423 

414 

4»i2 

n 

s*(^ 

^4 

IM 

i^&8 

S4>1 

am 

sfii 

H.i;i 

413 

400 

439    41;! 

B68 

S.'jS 

ei» 

17 

H^iH 

^M 

13*^ 

^in 

407 

41ft 

4KJ 

4B:i 

.VH 

53fi 

5ys  r*54 

Ttil 

T44 

H3U 

ly 

^^ 

32 

1:!0 

4Jfi 

GiT-J 

5a  ri 

624 

55tt 

7n 

61^1 

758'   714 

B«l 

virs 

HJ70 

21 

"^W 

i-s 

!M 

11:; 

r>Tt! 

??,' 

<|H6 

bOl 

715 

yiTi 

W7 

aT2    S>I5 

12,58 

1230 

lS7a 

£<J 

^H 

&S! 

4^ 

sa 

H^IS 

Iiai 

lOW 

1174 

104^ 

i^t] 

I2iiy 

14'Jr^i:J4l 

l?!ll4 

!W1 

'jwj;; 

£tl 

aa 

60 

m 

BU 

l4Mtt 

t!7 

1316 

15:^4 

1370 

1757 

IT 

im;il7.'j7 

U  i  3a 

17, 

^i5(5 
4:i 

-^tw-^ 

>  I  eau  e  fftfC.  [irt-as . .  lbs. 

4B 

ItiLJo  Df  Expansion . , . 

]? 

!^ 

itsii 

10 

V2H     1       6^H 

81^ 

<^'L  cnnrli*i}«itMtn,:^. 

IK 

Itt 

UO     i^ 

irj  1  !5 

13  1  itf  1  1-^  \  ta 

14  1  14 

Ft.   p>'Tl 

Ti.r 

v.h 

rJhfc 

17.a;iii,6 

1CJ5  15.1! 

17  a']64 

lfl..3|l5,H!l7.r4l7,0 

I  El.  hJ  16.0 

The  orijcinal  table  coDtains  figures  for  95  lbs.,  cyliuder  ratio  3^  to  1;  and 
120  lbs  ,  ratio  4  to  1. 

Triple-expansion  Encines,  Non-oondeniilne:.— Receiver 
only  Jacketed. 


Horse-power 

Horse-power 

Horse-power 

Diameter 

$ 

s. 

when  Cutting 

when  Cutting 

when  Cutting 

CvUnders, 

off  at  42  per 

off  at  50  per 

off  at  67  per 

w 

a 

cent  of  Stroke 

cent  of  Stroke 

cent  of  Stroke 

}d 

3  3 

in  Fii-st  Cylin- 

in First  Cylin- 

in First  Cylin- 

V 

10 

der. 

der. 

der. 

H.  P. 

LP. 

L.  P. 

180  lb.s. 

200  lbs. 

180  lbs. 

2lX)lbs. 

180  lb.s. 

200  lbs. 

494 

**% 

12 

370 

55 

64 

70 

84 

95 

108 

5l2 

8V6 

12 

318 

70 

81 

90 

106 

120 

187 

6v2 

10V« 

lovl 

14 

2n 

104 

121 

133 

158 

179 

204 

^fz 

12 

19 

16 

246 

136 

168 

174 

207 

234 

267 

9 

14H 

^H 

18 

222 

195 

226 

250 

296 

835 

882 

10 

16 

25 

20 

185 

241 

279 

308 

366 

414 

471 

11^ 

18 

'^ 

24 

158 

82:J 

374 

413 

490 

565 

632 

18^ 

22 

28 

138 

433 

502 

554 

657 

744 

848 

15 

24H 

38 

32 

120 

558 

647 

714 

847 

959 

1093 

17 

27 

48  . 

34 

112 

715 

829 

915 

1089 

1230 

1401 

20 

38 

52 

42 

93 

1048 

1215 

1341 

1592 

1801 

2058 

23« 

88 

60 

48 

80 

13T0 

1589 

1754 

2082 

2356 

2685 

Mean  effective  press.,  lbs. 

25 

29 

32 

38 

43 

49 

No.  of  expansions 

16 

13 

10 

Per  cent  cyl.  condens .... 

14 

12 

10 

Steam  p.  LH.P.  p.hr.,  lbs. 

20.76 

19.36 

19.25 

17.00 

17.89 

17.20 

Lbs.  coal  atB  lb.  evap.  lbs. 

2.59 

2.39 

2.40 

2.12 

2.23 

2.15 

THE  STEAH-EXOINB. 


^rf|il«-exiwiiiloii  Bitt:llicPB-€aB4«>nfliM|r-8tMi«i- 


Horse- poller 

Horse-power 

Horse-power 

Horse-poiwer 

Diameter 

b 

when  Ctit- 

when  Cut- 

when  Cut. 

when  Cut- 

Cylinder?*, 

i 

I 

thig  off  at  yi 
Stfolc^  In 

tine  off  at  ^  thig  off  at  H 
KtrnlE,  ill         Strol.'Ui 

ting  off  at « 
f^U-\v  in 

a 

First  C>  it u- 

1  Li  lit  Cj  lIiJ 

Fii>L  t'y  tin- 

Vu-si Cylin- 

S2 
P 

der. 

dt*r. 

der. 

der: 

^ 

fU 

^ 

120   14^^    im 

Kv  im 

100 

tao 

140 

160 

ISO 

1^ 

MO 

X 

■i 

v5 

&_ 

lbs.  Hw    Ibfl. 

ll*S>j  Ibfl. 

IbH. 

lbs. 

lbs 

lbs. 

lbs. 

IbF. 

Ibf. 

m 

7U 

12 

10 

870 

35J    4^:     4H 

44;    13 

BU 

riT 

7e 

B4 

»1 

97 

110 

r^h 

wiv 

T!i^ 

12 

818 

45!     6:«-     OiJ 

5ti      67 

76 

73 

(K 

107 

104 

13^,  J#0 

^h 

lOtj, 

loVi, 

14 

sr.v 

67!    7  LI'    dJ 

Wjl   HH) 

112 

KW 

Ts: 

150 

tSt 

If«!  KW 

IH 

V£ 

IQ 

10 

246 

87;  m  n^ 

iw  m 

U7    U\ 

ISO 

^ 

lOIl 

2«i'  .JTi 

9 

im 

^^ 

18 

2Sh» 

125'  14  s    175.' 

m  187 

tril    L\13 

a57 

m 

aeo 

34^    W 

10 

:fi 

ta 

20 

185 

154   ISS    aHf 

IJ>^J    2.31 

♦2M    2f« 

317 

mi 

«&e 

423    481 

nv» 

i«» 

^J*^ 

24 

158 

206   a4>    -S4 

lTkhI  sio 

54M    S.i5 

436 

m 

477 

5f.?i    iM5 

IS 

^ 

:*:iS 

iAi 

188 

277    3211    3J^i 

3JG    415 

J 67    45C 

ft7l 

m$ 

640 

761,  «5 

]& 

^H 

:k 

^ 

ItfO 

8571  til    m 

i4tt  :m 

wi  im 

m 

SM 

«e5 

Will  115 

H 

m 

4^i 

m 

11-2 

458   54  i    e^-.i 

572  n*w 

7??   714 

^1 

loss 

lOfWH 

|-.*^^i  rJSO 

«) 

vt 

w 

42 

98 

670   TOi.    frJ*^ 

J^'ims 

nm  io«a 

iSHii 

ifm 

15ftJ 

ISI4I-.M96 

»8M 

m 

60 

\S 

80 

8771041  1300 

loofj  vm 

IJWTI^M 

i«m 

*jmf 

tjt):^^ 

^411  2740 
44rM 

Mdaa  efte?.  press., lbs. 

161     19l    £3 

m^    ji 

27     1* 

33 

S8.t 

"ii 

No.  of  expansions.... 

26.8 

mO  1              n.4 

8.P 

Percent  cyl.  condens. 
St.p.I.H.P.p.hr.Jb9. 

19 

19     \'} 

10  .  16 

i(i    ri 

1-4  \  U 

«       ^1    8 

14.7 

18.0  13. :3 

14^  llffi 

n.2  1-1  ;) 

t3. 6^3.0 

15.7,H,&1I.2 

Coal' fttsm.e  tap.,  lbs. 

1.8^ 

l.t^lM 

i.:s,i.7i 

l.fi,'il.7R 

i.TO^T.ea 

1.96  1,86  1.77 

Type  eC  EnslDe  to  be  Heed  nrhere  Exltaiiet-eieaiii  la 
needed  for  HeaCliiic-— IQ  '"^^i^  factories  itiore  or  tess  of  the  steam 
exhausted  from  the  engines  is  utilized  for  boiling,  drying,  heatings,  etc. 
Where  all  the  exhaust -steam  is  so  nsed  the  qnestioe  €»f  economicftl  use  of 
steam  in  tlie  engine  itself  is  eUinlnat^d,  and  the  hfgh-pretsure  simple  engine 
is  entirely  suitable.  Where  only  part  of  the  exhaust-steam  is  used,  and  the 
quantity  so  used  varies  at  different  times,  the  qiiestioti  of  adopting  a  sftnple. 
a  condensing,  or  a  compound  engine  becomes  more  complex.  Thui  problem 
is  treated  bv  C.  T.  Main  in  Trans.  A.  S.  M.  £.,  vol.  x.  p.  48.  He  shows  that 
the  ratios  of  the  volumes  of  the  cylinders  in  compound  engines  should  vary 
according  to  the  anionnt  of  exhaust-steam  that  can  be  used  for  heating.  A 
case  is  given  in  which  three  different  pressures  of  steam  are  required  or 
could  be  used,  as  in  a  worsted  dye-house:  the  high  or  boiler  pressure  for 
the  engine,  an  intermediate  pressure  for  crabbing,  amd  low.pressure  for 
boiling,  drying,  etc.  If  it  did  not  malce  too  much  complication  of  parts  in 
the  engine,  the  boiler-pressure  might  be  used  in  the  high-pressure  cylinder. 
exhausting  into  a  receiver  from  which  steam  could  be  taken  for  runnfng 
small  engines  and  crabbing,  the  steam  remaining  in  riie  receiver  pansfng 
into  the  intermediate  cylinder  and  expanded  there  to  from  5  to  10  lbs.  above 
the  atinosufaere  and  exhausted  into  a  second  receiver.  FiMm  this  recetrer 
is  drawn  the  low-pressure  steam  needed  for  drying,  boiling,  warming  mills, 
etc.,  the  steam  remaining  in  receiver  passing  into  the  condensing  Cylinder. 
ComparffNon  of  (be  Beonomy  of  CompoHiid  aad  Slnele- 
cylind^r  Corlla^  Condenetnj;  Hitslftee.  eaeb  ^stpandlnc 
about  Sixteen  Tlrnee.  (D.  S.  Jacobus,  Trans.  A.*S.  M.  £.,  xii.  Ma j 

The  engines  used  in  obtaining  comparative  results  are  located  at  Stations 
I.  and  II.  of  the  Pawtuoket  Water  Co. 

The  tests  show  that  the  compound  engine  is  about  30)f  more  eoonoinical 
than  the  single-cvlinder  engine.  The  dimensions  of  the  two  engines  are  aa 
follows:  Single  20"  X  48";  compound  15"  and  SO\i"  X  30^'.  The  steam 
used  per  horse-power  per  hour  was:  single  20.85  lbs.,  compound  13.78  lbs. 

Both  of  the  engines  are  steam -jacketed,  practically  on  the  barrels  only; 
with  steam  at  full  boiler-pressure,  viz.  single  106.8  lbs.,  compound  197.6  Iba. 


PEUFOilllANeES  OF  STGAM-SKGIKES. 


The  steam-pressure  in  the  case  of  the  compound  engine  fs  127  lbs.,  or  2t 
lbs.  hifcher  than  for  the  single  engme.  If  the  steam-presstTre  be  railsed  thhl 
amount  ra  the  case  of  the  single  engine,  and  the  indicator-cards  be  increased 
accordingly,  the  consirmption  for  the  dngle-cylinder  engine  would  be  19.97 
lbs.  per  hour  per  horse-power. 

Xiro-«j'lliMler  t«.  Tliree-eylliiiler  Compomtd  "BmgHn^^^ 
A  Wbeelock  triple-expansion  engine,  built  for  the  Merrick  Thread  Co., 
Iloljoke,  Blass.,  is  constructed  so  that  the  intermediate  cylinder  may  be  cut 
out  of  the  circuit  and  the  high-pressure  and  low-pressure  cylinders  run  as  a 
two-cylkider  compound*  using  the  same  oondi  lions  of  initial  steam -pressure 
and  load.  The  diameters  of  the  cylinders  are  IS,  IS,  and  34i|  inches,  the 
stroke  of  the  flrs^t  two  being  36  in.  aiid  that  of  the  k>w-ptessure  cylinder  48 
in.  The  results  of  a  test  reported  by  3.  M.  Green  and  G.  I.  Rockwood.  Trans. 
A.  S.  M.  E.,  vol.  xiii.  647,  are  as  follows:  In  lbs.  of  dry  steam  used  per  I.H.P. 
per  hour,  12  and  24^  in.  cylinders  only  used,  two  tests  13.00  and  12.76  lbs., 
averafce  t2.91.  All  three  cylinders  used,  two  tests  12.67  and  12.90  lbs.,  avera^ 
12.79.  The  difference  is  only  1%,  and  would  indicate  that  more  than  two  cylin' 
ders  are  unnecessary  in  a  compound  engine,  but  it  is  pointed  out  bv  rrof. 
Jacobus,  that  the  conditions  of  the  test  were  especially  faTorable  for  the 
two-cylinder  engine,  and  not  relatively  so  favorable  for  the  three  cylinders. 
The  steam -pressure  was  142  lbs.  and  the  number  of  expansions  about  25. 
(See  also  discussion  on  the  Rockwood  type  of  engine.  Trans.  A.  6.  M.  E.,  vol. 
xH.> 

BITeet  of  Vfmter  eotttatmd  In  Steam  on  tlte  Kfllelenejr  of 
file  Steam-ens^ne.  (From  a  lecture  by  Walter  C.  Kerr,  before  the 
Frankhn  Institute,  lt$9l.)  -Standard  writers  make  Kttle  mention  of  the  effect 
of  enti-ained  moisture  on  the  expansive  properties  of  steam,  but  by  common 
consent  rather  than  any  demonstration  tliey  seem  to  agree  that  moisture 
produces  an  ill  effect  simply  to  the  percentage  amount  of  its  presence. 
That  Is.  Si%  moisture  will  increase  the  water  rate  of  an  engine  M. 

Experiments  reported  in  1393  by  R.  C.  Carpenter  and  L.  S.  Marks.  Tranrf. 
A.  S.  M.  E.,  XV.,  in  which  water  in  varying  quantity  was  Introduced  Into  the 
steam-pine,  causing  the  quality  of  the  steam  to  ransre  from  99^  to  56^  dry, 
showed  tnat  throughout  the  range  of  qualities  used  the  consumption  of  dry 
steam  per  indicated  horse-power  per  hour  remains  practically  constant,  and 
indicated  that  the  water  was  an  Inert  quantity,  doing  neither  good  nor  harm. 

It  appears  that  the  extra  work  done  by  the  heat  of  the  entrained  water 
during  expansion  is  sensibly  equal  to  the  extra  negative  work  whicli  it  does 
during;  exnaust  and  compression,  that  the  heat  carried  in  by  the  entrained 
water  performs  no  useful  function,  and  that  a  fair  measure  of  the  economy 
of  an  engine  is  the  consumption  of  6ry  and  saturated  steam. 

Relattre  Commercial  Ceonomr  of  Beat  Modern  Types  of 
Compound  and  Trlple-expannon  Bnglnes.  (J.  E.  i}enton, 
American  Machinist,  Bee.  17,  1891.)— The  follow mg  table  and  deductions 
show  the  relative  commercial  economy  of  the  compound  atid  triple  type  for 
the  heat  stationary  pi*actice  in  steam  plants  of  500  indicated  horse-power. 
The  table  Is  based  on  the  tests  of  Prof.  SchrOter,  of  Munich,  of  engines  built 
at  Augsburg,  and  those  of  Geo.  H.  Barrus  on  the  best  plants  of  America,  and 
of  detailed  estimates  of  cost  obtained  from  several  first-class  builders. 


Lbs.  water  per  hour  per 

H.P. ,  by  measurement. 
Lbs.  coal  per  hour  per 

H.P.,  assuming  8.5  lbs. 
.    actual  evaporation.        ) 
Lbs.  water  per  hour  per  I  io  wt    io  an 

H.P.,  by  measurement.  V^'^    ^-^ 
Lbs.  coal  per  hour  per  ) 

H.P.,  assuming  8.5  lbs.  > 

actual  evaporation.        ) 


fl8.6     14.0 
1.60     1.6B 


1.46     1.90 


Trip  motion,  or  Corliss  engines  of 
the  twia-compound-receiver  con- 
densing type,  expanding  16  times. 
Boiler  pressure  120  lbs. 

Trip  motion,  or  Corliss  engines  of 
the  triple-expansion  four-cylin- 
der-reoeiver  condensing  type,  ex- 
panding S3  times.  Boiler  pressure, 
160  lbs. 

The  figures  In  the  first  column  represent  the  best  recoixied  performance 
(1691),  and  those  In  the  second  columu  the  probable  reliable  performance. 

Increased  cost  of  triple -expansion  plant  per  horse-power.  Including 
boilers,  chimney,  heaters,  foundations,  piping  aud  erection $4.50 

The  following  table  shows  the  total  annual  cost  of  operation,  with  coal  at 
$4.00  per  ton,  the  plant  running  300  days  iu  the  year,  for  10  hours  and  for 
2i  hours  per  di^y: 


78? 


TUE  STEAU-EHQIKl!. 


Hounf  ninping  per  <J«y 

10 

24 

Expense  for  coftl.    Compound  plant 

Per  H.P. 

$9.90 

9.00 

0.90 

Per  H.P. 
^.90 

Expense  for  coal.    Triple  plataf. . , 

Annual  saving  of  triple  plant  in  fuel 

25.02 
2.60 

Annual  interest  at  55K  on  $4.50 

$0.98 
0.88 

0.16 

0.06 

$0.23 

Annual  depreciation  at  6^  on  $4.50 

Annual  extra  cost  of  oil,  1  gallon  t>^r  84 -hour 

day,  at  $0.50,  or  15^  of  extra  f uel  608t 

Annual  extra  cost  of  repairs  at  9%  on  $4.50  per 

34  hours. 

0.2S 
0.36 
0.14 

$0.67 

$0.96 

Annual  saving  per  H.P 

$0.23 

$1.64 

The  saving  between  the  compound  and  triple  types  is  much  less  than  that 
involved  in  the  step  from  the  single-expansion  condensiiig  to  the  compound 
engine.  The  increased  cost  per  horse-power  of  the  triple  plant  over  the 
compound  is  due  almost  entirely  to  the  extra  cost  of  the  triple  engine  and 
its  foundations,  the  boilers  costing  the  same  or  slightly  more,  owing  to  their 
extra  strength.  In  the  case  of  the  single  ver»u»  the  compound,  nowever. 
about  one  third  of  the  increased  cost  of  the  compound  engine  is  offset  by  the 
less  cost  of  the  latter's  boilers. 

Taking  the  total  cost  of  the  plants  at  $88.50,  $86.60  and  $41  per  horse- 
power respectively,  the  figures  in  the  table  imply  that  the  total  annual  sav- 
ing is  as  follows  for  coal  at  $4  per  ton: 

1.  A  compound  500  horse-power  plant  costs  $18,260,  and  saves  about  $1690 
for  10  hours^  service,  and  $4885  for  S4  hours'  service,  per  year  over  a  single 
plant  costing  $16,760.  That  is,  the  compound  saves  its  extra  coat  in  10-hour 
service  in  about  one  year,  or  in  24-hour  service  in  four  months. 

2.  A  triple  500  horse-power  plant  costs  $20,500,  and  saves  about  $114  per 
year  in  10-hour  service,  or  $^  In  24-hour  service,  over  a  compound  plant, 
thereby  saving  it«  extra  cost  in  10-hour  service  in  about  li^  years,  or  in  24- 
hour  service  in  about  2^  years. 

Triple  -  expannlon  Pumpinic-eii&lne  at  RUlwankee- 
Hlvlient  Bconomy  on  Record,  1 893.  (See  paper  on  *'  Maximum 
Contemporary  Economy  of  tbe  Steam-engine,"  by  R.  H.  Thurston,  Trans. 
A.  8.  M.  E.,  XV.  818.)-Cylinders  38,  4S  and  74  in.  by  60  in.  stroke;  ratios  of 
volumes  1  to  8  to  7;  total  number  of  expansions  10.65;  clearances,  h.p. 
iA%;  int.  1.5%;  I.  p.  0.77)(;  volume  of  receivers:  Ist,  101.3  cu.  ft.;  ad,  181  eu. 
ft.;  steam-pressure  gauge  during  test,  average  121.5  lbs.;  vacuum  13.84  Ihs. 
absolute;  revolutions  20.S  per  minute;  indicated  horse-power,  h.p.  175.4,  ink 
169.6,  1.  p.  228.9;  total,  573  9;  total  friction,  horse  power  6e.9l  =  9.22jr;  drv 
steam  per  I.H.P,  per  hour  11.678;  B.T.U.  per  I.H.P.  per  min.  217.6;  duty  in 
foot-pounds  per  lOO  lbs.  of  coal,  148,806,000;  per  million  B.T.U.,  137,656,000. 

Steam  per  I.H.P.  per  hour,  from  diagram,  at  cut-off. . . .    9.85  9.12  8..tr 

"  release..  .  10.1  10.0  8.93 

Steam  accounted  for  by  indicator  at  cut-off,  per  cent. . .  87.1  86.0  7^/..* 

* *  •'  release,        "      ...  94.0  93.2  88.2 

Per  cent  of  total  steam  used  by  Jackets 9.25 


HiKlieiit    Economy    of 


the   Tiv^o  -  cjFllnder   Componnd 

tests  of  the  Fawtucket-Corliss  eoKine, 


Pu  inpinK-enelnes.— Repeated 

15  and  80i^  by  30  in.  stroke,  gave  a  water  consumption  of  13.69  to  14.16  lln. 
per  I.H.P.  per  hour.  Steam -pressure  123  lbs.;  revolutions  per  min.  48; 
expansions  about  16.  Cylinders  Jacketed.  The  lowest  water  rate  waa  with 
Jackets  in  use;  both  Jackets  supphed  with  steam  of  boiler  prwtaure.  The 
average  saving  due  to  jackets  was  only  al>out  2U  per  cent.  (Trana.  A.  S. 
M.  E.,  xi.  828  and  1038;  xiii.  176.) 

This  record  was  beaten  in  1894  by  a  Leavltt  pumplng-englne  at  Louisville. 
Ky.  (Trans.  A.  S.  M.  E.  xvi.)  Cylinders  27.21  and  54.13  in.  diam.  by  10  ft 
stroke;  revolutions  per  min.  18.57;  piston  speed  871.6  ft;  expansions  SO.4: 
steam* pressure,  gauge,  140  lbs.    Cylinders  and  receiver  Jacketed.    Steam 


PERFORMANCES  OF  STBAM-EKGIKES. 


783 


used  per  I.H.P.  per  hour,  12.288  lbs.  Duty  per  million  B.T.17.  »  188,196,000 
ft.lbB. 

Test  of  a  THple-expansion  Piunpliic^iilrtiie  jwtth.  and 
-vrttlioiit  JTaekeiS)  at  I^keton,  Ind.,  by  Prof.  j.  E.  Denton  (Trans.  A. 
8.  M.  E.,  sir.  1340).— Cylinders  84,  84  and  54  In.  by  86  in.  stroke;  28  revs,  per 
min. ;  H.P.  developed  aboutSSO;  boiler-pressure  loO  lbs.  Tests  made  on  eight 
different  days  with  different  sets  of  conditions  in  jackets.  At  150  lbs.  boiler- 
pressui-e,  and  about  20  expansions,  with  any  pressure  above  48  lbs.  in  all  of 
the  jackets  and  reheaters,  or  with  no  pressure  in  the  higrh  jacket,  the  per- 
formance was  as  follows:  With  3.59(  or  moisture  in  the  steam  entering  the 
engine,  the  jackets  used  16%  ot  the  total  feed-water.  About  20%  of  the  latter 
was  condensed  during  admission  to  the  high  cylinder,  and  about  13.86  lbs. 
of  feed-water  was  consumed  per  hour  per  indicated  horse-power.  With  no 
jackets  or  reheaters  in  action  the  feed-water  consumption  was  14.99  lbs.,  or 
8.99^  more  than  with  jackets  and  reheaters.  The  oonsuuiption  of  lubricating 
oil  was  two  thirds  of  a  gallon  of  machine  oil  and  one  and  three  quarter  gal- 
lons of  cylinder  oil  per  24  hours.  The  friction  of  the  engine  in  eight  tests  on 
different  days  varied  from  6.1%  to  B.'i%. 

If  vire  regard  the  measurements  of  indicated  horse-power  and  water  as 
liable  to  an  error  of  one  per  cent,  which  is  probably  a  minimum  allowance 
for  the  most  careful  determinations,  the  steam  economy  is  the  same  for  the 
following  conditions: 

(a)  Any  pressure  from  48  to  181  in  the  intermediate  and  low  jackets  and 
receivers. 

(6)  Any  pressure  from  0  to  151  in  the  iacket  of  high  cylinder. 

(c)  Any  cut-off  from  21j(  to  SSi%  in  higli  cylinder,  from  29%  to  4$^  in  inter- 
mediate cylinder,  from  40^  to  589(  in  low  cylinder. 


"Water  Conanmpttoit  of  Three  Type*  of  Snlser  Enfflnee* 

(B.  Donkin,  Jr.,  Eng'g^  Jan.  15, 1892,  p.  77.) 

Summary  and  Avsraocs  of  Twentt-one  Publisheo  Expehimbnts  or  the 

Sdlzbb  Type  of  Steam-engine.    All  Horizontal  Condensino 

AND  Steam- JACKETED.    From  1872  to  1891. 


1 

H 

S. 


Com. 
pound. 

Triple.. 


lbs. 
72  to 

95 
84  to 

104 
104  to 

156 


ft. 

per  min 

272  to 

488 
884  to 

689 
444  to 

607 


i 

II 
P 


157  to 
400 

183  to 
524 

198  to 
615 


Steam  Consump 
tion,  pounds  per 
I. H.P.  per  hour, 
indudingSteara- 
pipe  water  and 
Jacket  Water. 


lbs. 
18.7  to  19  8 
Mean  19.4 
13.85  to  16.0 
Mean  14.44 
11.85  to  12.86 
Mean  12.36 


Steam  Consump- 
tion, pounds  per 
I. H.P.  per  hour, 
exclud  V  Steam- 
pipe  water,  but 
includingjacket 
Water. 


lbs. 
17.9  to  19.2 
Mean  18.95 
18.4  to  15.5 
Mean  14.8 
11.7tol2.7 
Mean  12.18 


I 


5exp. 

18?^-78 

10  ezp. 

,   1888-91 

I  6exp. 

_  j  18S8-89 

Triple-expansion  Corliss  engine  at  Narragansett  E.  L.  Co.,  Providence,  R. 
I.,  built  by  E.  P.  Allis  Co.  Cylinder  14, 25  and  83  in.  by  48  In.  stroke  tested  at 
99  revs,  per  min.;  125  lbs.  steam-preRsure;  steam  per  I.H.P.  per  hour  12  91 
lbs. ;  H.P.  516.  A  full  account  of  this  engine,  with  recoids  of  tests  is  given  by 
J.  T.  Henthom,  in  Trans.  A.  B.  M.  E.,  xTi.  648. 

Buckeye-cross  compound  engine,  tested  at  Chicago  Exposition,  by  Geo. 
H.  Barms  (Sng'g  Record.  Feb.  17. 1894).  Cylinder  14  and  28  by  24  in.  stroke; 
tested  at  165  r.  p.  m. ;  120  lbs.  steam-pressure.    I.H.P.  in  four  tests  coiideiis- 

Ing  and  one  non-condensing 295       224       123       277       267 

Steam  per  horse-power  per  hour 16.07    15.71    17.22    16.07    23.24 

RelatlTe  Eeonomv  of  Compoand  Non-eondenelnff  En* 
a^nee  under  Variable  Loada.  -F.  M.  Riu*s,  in  a  paper  on  tiit*  Stemn 
Distribution  in  a  Form  of  Single-acting  Engine  (Trans.  A.  S.  M.  £.  xiii.  537), 
discusses  an  engine  designed  to  meet  the  following  problem  :   tiiven  an 


784  THE  STBAM-ENGIKB. 

oztreme  nsige  of  conditions  as  to  load  or  steain-pre«8ure,  eiihor  or  both,  to 
fluctuate  to&rether  or  apart,  violently  or  with  easy  g^radatlons.  to  construct 
an  engine  wnoee  econoinioal  performance  should  ba  aa  good  aa  though  the 
engine  were  specially  designed  for  a  momentary  condition -the  adjustmeot 
to  he  complete  and  uutomatlo.  In  the  ordinary  non-coDdeusins:  compound 
engine  witii  ligiit  loads  the  high -pressure  cylinder  is  frequently  forced  to 
supply  all  the  power  and  in  addition  drag  along  with  it  the  low-pressure 
piston,  whose  cylinder  indicates  negative  work.  Mr.  Ritea  shows  the 
peculiar  value  of  a  receiver  of  predetermined  volume  which  acts  as  a  clear- 
ance chamber  for  compression  in  the  Ii igh-pressure  cylinder.  The  Westing- 
house  compound  single-acting  engine  ia  designed  upon  this  principle.  Tlie 
following  results  of  tests  of  one  of  these  engines  rated  at  175  H.P.  for  most 
economical  load  ara  given  : 

Watkk  IUtbs  undkb  Vabtihq  Loads,  lbs.  pkr  H.P.  per  hods. 

Horsepower 210        170        140        115        100         60  50 

Non-condensing 22.8       21.9       22.2       22.2       22.4       M.6       28.8 

Condensing 18.4       18.1       18.2       18.2       18.8       18.8       20.4 

Eflleleiicy  of  BfoBMsondeiisliiir  Componiid  Bb^Iims.    (W. 

Lee  ChuiH!h.  Am.  Maeh.^  Nov.  19,  1891.)— The  compound  engine,  non-con^ 
denslng,  at  its  best  performance  will  exhaust  from  the  low-pressure  crlin. 
der  at  a  pressure  2  to  6  pounds  above  atmosphere.  Buch  an  engine  will  be 
limited  In  its  economy  to  a  very  short  range  of  power,  for  the  reason  that 
its  valve-motion  will  not  permit  of  any  great  increase  beyond  its  rated 
power,  and  any  material  de>crease  below  Its  rated  power  at  once  brings  the 
expansion  curve  in  the  low-pressure  cylinder  below  atmosphere.  In  other 
words,  decrease  of  load  tells  upon  the  compound  engine  somewhat  sooner, 
and  much  more  severely,  than  upon  the  non-compound  engine.  The  loss 
commences  the  moment  the  expansion  line  crosses  a  line  parallel  to  the 
atmospheric  line,  and  at  a  distance  above  it  representing  the  mean  efTective 
pressura  necessary  to  carry  the  frictioual  load  of  the  engine.  When  expan- 
sion falls  to  this  point  the  low-pressure  cylinder  becomes  an  air-pump  over 
more  or  less  of  its  stroke,  the  power  to  diive  which  must  come  from  the 
high  pressure  cylinder  alone.  Under  the  light  loads  common  in  many 
industries  the  low-pressure  cylinder  is  thus  a  poeitiye  resistanoe  fcv  the 

f:reater  portion  of  its  stroke.  A  careful  study  of  this  problem  revealed  the 
unctions  of  a  fixed  intermediate  clearance,  always  in  communicaiion  with 
the  high-pressure  cylinder,  and  having  a  volume  bearing  the  same  ratio  to 
that  of  the  high-pressure  cylinder  that  the  high^pressure  cylinder  beans  to 
the  low-pressure.  Diagrams  were  laid  out  on  this  principle  and  lustifled 
until  the  best  theoretical  results  were  obtained.  The  designs  were  then  laid 
down  on  these  lines,  and  Uie  subsequent  performance  of  tlie  engines,  of 
which  some  600  have  been  built,  have  fully  confirmed  the  Judgment  of  the 
designers. 

The  effect  of  this  constant  clearance  is  to  supply  sufficient  steam  to  the 
low-pressure  cylinder  under  light  loads  to  hold  its  expansion  om*ve  up  to 
atmosphere,  and  at  the  same  time  leave  a  sufficient  clearance  volume  in  tlie 
high -pressure  cvlinder  to  permit  of  governing  the  engine  on  its  compreasioa 
under  light  loads. 

Economy  of  Bngrlnes  under  Varying  Loads*  (From  Prof. 
W.  C.  Unwin  s  lecture  befoi-o  the  Society  of  Arts,  London,  1892.)— The  gen- 
eral result  of  numerous  triiUs  with  large  engines  was  that  with  a  constant 
load  an  indicaied  horse-powor  should  be  obtained  with  a  consumption  of 
1^  pounds  of  coal  per  indicated  horse-power  for  a  condensing  engine,  and 
1^4  pounds  for  a  non-oondfnsing  engine,  figures  which  corre9|K>nd  to  about 
i^4  pounds  to  '2\4  pounds  of  coal  per  effective  horse-power.  U  was  much  more 
diftlcult  to  aHcettain  the  consumption  of  coal  in  onltnary  every -day  work, 
but  such  facts  as  were  known  showed  it  was  more  than  on  trial. 

In  electric-lighting  stations  the  engines  work  under  a  very  fluctuating 
lo«d,  and  the  results  are  far  more  unfavorable.  An  excellent  Willafas  non. 
condensing  engine,  which  on  full-load  trials  worked  with  under  2  pounds 
per  effective  horse-power  hour,  in  the  ordinary  daily  working  of  the  station 
UBt*d  714  pounds  per  effective  horst^-power  hour  in  1886,  which  was  reduced 
to  4.3  pounds  in  IKIX)  and  3.8  pounds  in  1891.  Probably  in  very  few  cases 
were  the  engines  at  elei;tric- light  stations  working  under  a  oonsumption  of 
4^  pounds  per  effective  horse-power  hour.  In  the  case  of  small  isolated 
motors  working  with  a  fluctuating  load,  still  more  extravagant  results  ^ 
Obtained. 


PEBFORMANCBS  OF  STEAM^ENGIKES.  'i'85 

Enoincs  in  Eubctric  CtNTiui.  Stations. 

Year 1886.  1890.  1892. 

Coal  used  per  hour  per  effective  H.P 8.4      6.6     4.9 

••      •*       •*      *•    Indicated  **  6.6     4.85    8.8 

At  electric-ItKbtinpr  stations  the  load  factor,  viz..  the  ratio  of  the  average 
load  to  the  Diazimum,  lis  extremely  sraall,  and  the  entwines  worked  under 
very  unfavorable  condition*,  which  largely  accounted  for  the  excessive  fuel 
consumption  at  these  stations. 

In  steam-engines  the  fuel  consumption  has  generally  been  reckoned  on 
the  indicated  horse-po^ver.  At  full-power  trials  this  was  satisfactory 
enough,  as  the  Internal  friction  is  then  usually  a  small  fraction  of  the  total. 
Experiment  has,  however,  thowti  that  the  internal  friction  is  nearly  con- 
stant, and  hence,  when  the  engine  is  lightly  loaded,  its  mechanical  efficiency 
is  greatly  reduced.  At  full  load  small  engines  have  a  mechanical  efficiency 
of  0.8  to  0.85,  and  large  engines  might  reach  at  least  0.9,  but  if  the  internal 
friction  remained  constant  this  efflclenoy  would  be  much  reduced  at  low 
powers.  Thus,  if  an  engine  working  at  100  indicated  horse-power  had  an  efll- 
ciency  of  U.tt5,  then  when  the  indicated  horse-power  fell  to  50  the  effective 
horse-power  would  be  85  horse-power  and  the  efRciency  only  0.7.  mmilarly, 
at  ^  horse-power  the  effective  horse-power  would  be  10  and  the  efficiency 
0.4. 
Experiments  on  a  Corliss  engine  at  Creusot  gave  the  following  results  : 

Effective  power  at  AiU  load 1 .0         0.75       0.60       0.26       0.125 

Condenning,  mechanical  efficiency 0.82       0.70       0.74       0.63       0.48 

Non  condensing,  '*  **  0.86       0.88       0.78       0.67       0.53 

At  light  loads  the  economy  of  gas  and  liquid  fuel  engines  fell  off  even 
more  rapidly  than  in  steam-engines.  The  engine  friction  was  large  and 
nearly  constant,  and  in  some  cases  the  combustion  was  also  less  perfect  at 
light  loads.  At  the  Dresden  Central  Station  the  gas-engines  were  kept 
working  at  nearly  their  full  power  by  the  use  of  storage-batteries.  The 
results  of  some  ejroerlments  are  given  below  : 

Hrake- load, per      Uas-englne,  cu.  ft.     Petroleum  Eng.,       Petroleum  Eng., 
cent  of  full  of  Gas  per  Brake        Lbs.of  Oil  per  Lbs.  of  Oil  per 

Power.  H.P.  per  hour.  B.H.P.  per  hr.  B.H.P.  per  hr. 

100  22.2  0.06  O.SS 

76  28.8  1.11  O.Oe 

50  28.0  1.44  1.20 

20  40.8  S.88  1.8i2 

12H  66.8  4.25  8.07 

Steam  €onsninptlon  of  Biifi:tiies  of  Various  Sixes.— W.  C. 
TTnwin  (Cassier's  Magaxine,  1891)  gives  a  table  showing  results  of  49  tests  of 
engines  of  different  tvpes.  In  non-condensing  simple  engines,  the  steam 
consumption  ranged  from  66  lbs.  per  hour  in  a  5-horse-power  engine  to  23 
lbs.  in  a  184-H.P.  Harris-Corliss  engine.  In  non  condensing  compound  en- 
ginesL  the  only  type  tested  was  the  Willans,  which  ranged  from  27  lbs.  In  a 
10  H.F.  slow-speed  engine,  \^i  ft.  per  minute,  with  steam-pressure  of  81  lbs. 
to  19.3  lbs.  in  a  40-H.P.  engine,  401  ft.  per  minute,  with  steam-pressure  165 
lbs.    A  Willans  triple-ezi>tiusion  non-condensing  engine,  89  H.P.,  172  lbs. 

firessure,  and  400  ft.  piston  speed  per  minute,  gave  a  consumption  of  18.5  lbs. 
n  condensing  engines,  nine  tests  of  simple  engines  gave  results  ranging  only 
from  16.4  to  22  lbs.,  and,  leaving  out  a  beam  pumping-engine  running  at  slow 
speed  (240  ft.  per  minute)  and  low  steam -pressure  (45  lbs.),  the  range  is  only 
from  1&4  to  lv.8  lbs.  In  compound-condensing  engines  over  100  H.P.,  In  18 
tests  the  range  la  from  18.0  to  20  lbs.  In  three  triple- expansion  engines  the 
figures  are  11.7, 12.2,  and  12.45  lbs.,  the  lowest  being  a  Sulxer  engine  of  360 
IT.  P.  In  marine  compound  engines,  the  Fusiyania  and  Colchester,  tested 
by  Prof.  Kennedy,  gave  steam  consumption  of  21.2  and  21.7  lbs.;  aud  the 
Meteor  and  Tartar  triple-expanhion  engines  gave  15.0  and  19.8  lbs. 

Taking  the  most  favorable  results  which  can  be  regarded  as  not  excep- 
tional, it  appears  that  in  test  trials,  with  constant  aud  full  load,  the  expen- 
diture of  steam  and  coal  is  about  as  follows: 

Per  Indicated  Horse-     Per  Effective  Horse- 
power Hour.  power  Hour. 

Kind  of  Engine.  * * »  . * » 

Coal,         Bteam,  Coal,         Steam, 

lbs.  lbs.  lbs.  lbs. 

Non-condensing 1.80  16.5  2.00  18.0 

Condenaing 1.60  13.5  1.75  15.8 


W6 


THE  STEAM-EKOIKB. 


Tliese  may  be  regarded  as  minimum  values,  rarely  snrpasaed  by  the  most 
efficient  machinery,  and  only  reached  with  Tcry  good  machinery  in  tho 
favorable  cnnditions  of  a  test  trial. 


Small  Enfi:liiea  and  Enjelnea  wfltli  Flactnattns  I«oada  are 

usually  very  wasteful  of  fuel.    The  following  figures,  illustraUng  their  low 
economy,  are  given  by  Prof.  Unwin,  Cassler^s  Magazine^  IS5H. 

€k>AL  COKSUMPTION  PBR  IVDIOATKD  HOSSK-POWER  IN  SlULL  EltOIXKS. 

In  Workshops  in  Birmingham,  Bug. 

ProbableLH.P.  at  full  load...      12        45        60        46        75        00        60 

Average  I.H.P.  during  obser- 
vation     2.96     7.S7     8.2       8.6     28.64    19.08    20.0S 

Coal  per  I.H.P.  per  hour  dur- 
ing observation,  lbs 86.0     21.25    22.61    18.13    11.68      9.58      8.50 

It  is  largely  to  replace  such  engines  as  the  above  that  power  will  be  dis- 
tributed from  central  stations. 

Steam  ConsumpUon  In  Small  Enffines. 

Tests  at  Royal  Agricultural  Society^s  show  at  Plymouth,  Eng.    Engineer* 
ing,  June  27,  1890. 


Rated  H.P. 

Com- 
pound or 
Simple. 

Dlam.  of 
Cylinders. 

stroke, 
ins. 

Max. 
Steam - 
pressure. 

Per  Brake  H.P., 
per  hour. 

If^ 

h.p. 

i.p. 

Coal. 

Water. 

f^i- 

5 
3 
2 

simple 

compound 

simple 

7 
8 
4H 

"b"' 

10 
6 
7.^ 

75 
110 
75 

12.12 
4.82 
11.77 

78.1   lbs. 
42.03    " 
89.9      " 

6.1  lb 
8.72" 
7.64  " 

Steam-eoii«umptlon    of    Eniplnea    at    Various    Sp««ds. 

(Profs.  Denton  and  Jacobus,  Trans.  A.  S.  M.  £.,  x.  722)— 17  X  30  in.  engine, 
non-condensing,  fixed  cut-off,  Meyer  valve. 

Stbam-consumptiok,  lbs.  per  I.H.P.  PER  Hour. 
Figures  taken  from  plotted  diagram  of  results. 

Revs,  per  min 8     12    16     20       24       32       40       48       56  72  88 

H  cut  off,  lbs 89    3.5    82      30      29.3      29      28.7    28.5    28  8  2S  27.7 

H       **          •• 39    34    31    29.5      29      28.4      28      27.6    27.1  26.8  25.6 

H       *•         *' 39    36    34      S3       32      30.8    29.8    29.2    38.8  28.7  .... 

Stbam-oonsdmption  of  Saick  Engine;  FrsEo  Speed,  60  Rkts.  per  Min. 
Varying  cut-off  compared  with  throttling -engine  for  same  horse-power 
and  boiler-pressures: 
Cutoff,  fraction  of  stroke    0.1    0.15    0.2    0.25    0.3     0.4    0.5    0.6    0.7    0.8 

Boiler-pressure,  90  lbs...     29     27.5     27      27      27.2  27.8  28.5 

60  lbs..       39     34.2   32.2  31.5    81.4  31.6  82.2  84.186.5    39 

Throttling -ENoiNE,  %  Cut-off,  for  Corresponding  Horse •powkrs. 

Boiler-pressure,  90  lbs...     42      37     33.8  31.5    29.8    

eOlbs 50.1      49    46.8    44.6     41     

Some  of  the  principal  conclusions  from  this  series  of  tests  are  as  follows : 

1.  There  is  a  distinct  gain  in  economy  of  steam  as  the  speed  increases  for 
^.  ^,  and  ^  cut-off  at  90  lbs.  pressure.  The  loss  in  economy  for  about  14 
cut-off  is  ai  the  rate  of  1/12  lb.  of  water  per  H.P.  for  each  decrease  of  a 
revolution  per  minute  from  86  to  20  levolutious,  and  at  the  rac«  of  H  lb-  of 
water  below  26  revolutions.  AIko,  at  all  speeds  the  14  cut-off  is  more  eco- 
nomical than  eitljHi-  the  ^  or  ^  cut-off. 

2.  At  90  n)s.  boiler-pressure  aiul  above  ^  cutoff,  to  produce  a  given  H.P. 
requires  about  20^  less  Kteam  than  to  out  off  at  %  stroke  and  regulate  by  the 
throttle. 

3.  For  tlie  same  conditions  with  60  lbs.  boiler-pressure,  to  obtain,  by 
throttling,  the  same  mean  effective  pressure  at  ^cut-off  that  is  obtained  by 


PERFORMAl^CBS  OF  STEAM-ENGINES.  787 

cuttlni^  ofF  about  ^,  requires  about  W  more  steam  than  for  the  latter 
condition. 

HlfTli  Piston-speed  In  Enieines.  (Proc.  Inst.  M.  E.,  July,  1888,  p. 
8:21}.— The  torpedo  boat  is  an  exeeUent  example  of  the  advance  towards 
hif^h  speeds,  and  shows  what  can  be  accomplished  by  studying  lightness 
and  strength  In  combination.  In  running  at  22Vi  knots  an  hour,  an  engine 
with  cylinders  of  16  in.  stroke  will  make  480  revolutions  per  minute,  which 
gives  1380  ft.  per  minute  for  piston -speed;  and  it  is  remarked  that  engines 
running  at  that  high  rate  work  much  more  smoothly  than  at  lower  speeds, 
and  that  the  difficulty  of  lubrication  diminishes  an  the  speed  increases. 

A  Hli^li-speed  Corliss  Engine.— A  Corliss  engine,  SO  X  42  in.,  has 
been  running  a  wire- rod  mill  at  the  Trenton  Iron  Co.^s  works  since  1877,  at 
100  revolutions  or  1120  ft.  piston-speed  per  minute  (Trans.  A.  8.  M.  E.,  ii. 
7^).  A  piston-speed  of  1200  ft.  per  min.  has  been  realized  Id  locomotive 
practice. 

Xlie  lilmltatlon  of  Kn|ct>^«"*Po®  A*  (Chas.  T.  Porter,  in  a  paper 
on  the  Limitation  of  Engine-speed,  Trans.  A.  S.  M.  £.,  xlv.  806.)— -The 
practical  limitation  to  high  rotative  speed  in  stationary  reciprocating  steam  - 
engines  is  not  found  in  the  danger  of  heating  or  of  excessive  wear,  nor,  as 
is  generally  believed,  in  the  centrifugal  force  of  the  fly-wheel,  nor  in  the 
tendency  to  knock  in  the  centres,  nor  in  vibration.  He  gives  two  objections 
to  very  nigh  speeds:  First,  that  **  engines  ought  not  to  be  run  as  fast  as 
they  can  be ;"  second,  the  large  amount  of  waste  room  in  the  port,  which 
is  required  for  proper  steam  distribution.  In  the  important  respect  of 
economy  of  steam,  the  high-speed  engine  has  thus  far  proved  a  failure. 
Large  gain  was  looked  for  from  high  speed,  because  the  loss  by  condensa- 
tion on  a  given  surface  would  be  divided  into  a  greater  weight  of  steam,  but 
this  expectation  has  not  been  realised.  For  this  unsatisfactory  result  we 
have  to  lay  the  blame  chiefly  on  the  excessive  amount  of  waste  room.  The 
ordinary  method  of  expressmg  the  amount  of  waste  room  in  the  percentage 
added  by  it  to  the  total  piston  displacement,  is  a  misleading  one.  It  should 
be  expressed  as  the  percentage  which  it  adds  to  the  length  of  steam  admis- 
sion. For  example,  if  the  steam  is  cut  off  at  1/5  of  the  stroke,  S%  added  by 
the  waste  room  to  the  total  piston  displacement  means  409(  added  to  the 
volume  of  steam  admitted.  Engines  of  four,  Ave  and  six  feet  stroke  may 
properly  be  run  at  from  700  to  WO  ft.  of  piston  travel  per  minute,  but  for 
ordinary  sizes,  says  Mr.  Porter,  600  ft.  per  minute  should  be  the  limit. 

Inllnonee  of  tbe  Steaufjacket*— Tests  of  numerous  engines  with 
and  without  steam-jackets  show  an  exceeding  diversity  of  results,  ranging 
all  the  way  from  80)(  saving  down  to  zero,  or  even  in  some  cases  showing  an 
actual  loss.  The  opinions  of  engineers  at  this  date  (1804)  is  also  as  diverse  as 
the  results,  but  there  is  a  tendency  towards  a  general  belief  that  tbe  jacket  is 
not  as  valuable  an  appendage  to  an  engine  as  was  formerly  supposed.  An  ex* 
tensive  rimmi  of  facts  and  opinions  on  the  steam-jacket  is  given  by  Prof. 
Thurston,  in  Trans.  A.  S.  M.  E.,  xiv.  462.  See  also  Trans.  A.  S.  M.  £:.,  xiv. 
873  and  1310;  xUl.  176:  xil.  426  and  1340;  and  Jonr.  F.  I.,  April,  18B1,  p.  276. 
The  following  are  a  few  statements  selected  from  these  papers. 

The  results  of  tests  reported  by  the  research  committee  on  steam-jackets 
appointed  by  the  British  Institution  of  Mechanical  Engineers  in  1886,  indi- 
cate an  increased  efficiency  due  to  the  use  of  the  steam-jacket  of  from  Mi  to 
over  80j(,  according  to  varying  circumstances. 

Sennett  asserts  that  *Mt  has  been  abundantly  proved  that  steam- 
jackets  are  not  only  advisable  but  absolutely  necessary,  in  order  that  high 
rates  of  expansion  may  be  efficiently  carried  out  and  the  greatest  possible 
economy  of  heat  attained." 

Isherwood  finds  tbe  gain  by  its  use.  under  the  conditions  of  ordinary 

Eractloe,  as  a  general  average,  to  be  about  iO%  on  small  and  8%  or  9%  on 
Li^e  engines,  varying  through  intermediate  values  with  intermediate  sizes, 
it  being  understood  that  the  jacket  has  an  effective  circulation,  and  that 
both  heads  and  sides  are  jacketed. 

Professor  Unwin  considers  that "  in  all  cases  and  on  all  cylinders  the 
jacket  is  useful;  provided,  of  course,  ordinary,  not  superheated,  steam  is 
used;  but  the  advantages  may  diminish  to  an  amount  not  worth  the  interest 
on  extra  cost." 

Professor  Cotterfll  says:  Experience  shows  that  a  steam-jacket  is  advan- 
tageous, but  the  amount  to  be  gained  will  vary  according  to  circumstances. 
In  many  cases  it  may  be  that  the  advantage  is  small.  Great  caution  is 
necessary  in  drawing  conclusions  from  any  special  set  of  experiments  on 
the  influence  of  jacketiner. 


788  THE   STEAM-ENGINE. 

Mr.  E.  D.  Leavitt  has  ezprefijS4*d  the  opinion  that,  in  hiH  practfoe, 
jackets  produce  an  increase  of  efficiency  of  from  15%  toSOjC. 

lo  tl»e  Puwtu«ket  piunpiOK  eiiKuie.  15  aad  80^  x  30  in.,  50  rers.  per  mfo., 
eteam-pressure  125  lr>s.  gsMg4i,  cut-off  ^  in  h.p.  aiid^  in  l.p.  cylinder,  the 
Wrrels  only  jacketed,  tiit^  saviitflf  by  the  jackets  wad  rrom  1%  to  4%. 

Tha  superintendent  of  the  Holly  Mff?.  Co.  (compound  pumpin^-engiaee) 
says:  *Un  regard  to  the  beoefitg  derived  from  steam-jackets  on  our  ateaoi- 
cyliiidera,  I  am  somewliat  of  a  skeptic.  From  data  taken  on  our  own  en> 
glnes  and  tests  made  I  am  yet  to  be  convinced  that  there  is  any  practicai 
value  in  the  steaiu- jacket."  .  .  .  '*  You  might  praciicaily  say  that  there 
is  no  difference.'* 

Profesaor  Schr&ter  from  his  work  on  the  triple-expansion  engines  at  AnK»- 
burg,  and  from  the  results  of  his  tests  of  the  jacket  efBciency  oo  a  small 
engine  of  the  Sulzer  type  in  his  own  laboratory,  concludes:  U>  The  value 
of  the  jacket  may  vary  within  very  wide  limits,  or  even  become  nef^a- 
tive.  (2;  The  shorter  the  cut-off  the  greater  the  gain  by  the  use  of  a 
jacket.  (8)  The  use  of  higlier  pressure  in  tlie  jacket  than  in  the  cylinder 
produces  an  advantage.  The  gi-eater  this  differenoo  the  better.  i4)  The 
high -pressure  cylinder  may  be  left  un  jacketed  without  great  loss,  but  the 
others  should  always  be  jacketed. 

The  test  of  the  Laketon  triple-expansion  pumping-engine  showed  a  gain 
of  S.9ft  by  the  use  of  the  jackets,  but  Prof,  yenton  points  out  (Trans.  A.  .8 
M.  £.,  xiv.  1412)  that  all  but  1.0^  of  the  gain  was  ascrlbable  to  the  greater 
range  of  expansion  used  with  the  jackets. 

Teiit  of  a  Componiid  Cond«iwliic  Eaigliie  witit  mmA  ^rflth* 
out  MmeKetm  at  different  lioads,  (R.  C.  Oarpenter,  Trans.  A.  S. 
M.  E.,  xiv.  41^^.)— Cylinders  S aud  1(> in.xl4  hi. stroke;  11^ ibs.  boUer-preasure; 
rated  capacity  1(X)  H.P. ;  265  revs,  per  min.  Vacuum,  23  in.  From  tlie  re«uitt 
of  several  tests  curves  are  plotted,  from  which  the  following  principal  flgnrtfa 
are  taken. 

IndicatedH.P 80     40     60     60     70     60     90  100    110     120     1/5 

Steam  per  I. H.P,  per  hour: 

With  jackets,  lbs 22.6  21.4  20.3  19.6    19    18.7  18.6  18.9    19.5    20.4  21.0 

Without  jackets,  lbs 22.    20.6  19.6  19.2  19.1    10.8    SO.l   .... 

Saving  by  jacket,  p.  c 10.9   7.8   4.6    8.1  1.0-1.0  -1j6  .... 

This  table  gives  a  clue  to  the  great  variation  in  the  apparent  saving  due  to 
the  steam-jacket  as  reported  by  different  experimenters.  With  this  par- 
ticular engine  it  appears  that  when  running  at  its  most  economical  rate  u( 
100  H.P.,  without  jackets,  very  little  saving  is  made  by  use  of  the  jackets. 
When  running  light  the  jacket  makes  a  coMsiderable  saving,  but  when  over- 
loaded it  is  a  detriment. 

At  the  load  which  oon^esponds  to  the  most  economical  rate,  with  no  steam 
fn  jackets,  or  IQO  H.P.,  the  use  of  the  jacket  makes  a  saving  of  only  1%;  but 
at  a  k>ad  of  60  H.P.  the  saving  by  use  of  the  jacket  is  about  lis,  and  the 
shape  of  the  curve  indicates  that  the  relative  advantage  of  the  jacket  woukl 
be  still  greater  at  lighter  loads  than  60  H.P. 

Coanterbalanelns  Snistiftee*— Prof.  Unwin  gives  the  formula  for 
counterbalancing  verticiu  engines: 


0) 


in  which  TT,  denotes  the  weight  of  the  balance  weight  and  p  the  radius  to 
its  centre  of  gravity,  Wn  the  weight  of  the  crank-pin  and  half  the  weight  of 
the  oounecthig-rocf,  and  r  the  length  of  the  crank.    For  horicontal  engines: 

W^=%{W^-{-W,i^     to    «(Tr, -f  TT.)^, (9 

in  which  W*  denotes  the  weight  of  the  piston,  piston-rod,  cross-head,  and 
the  other  half  of  the  weight  of  the  connecting-rod. 

The  American  Machinist,  commenting  on  these  formulse,  says:  For  hori- 
zontal engines  formula  (3)  is  often  used;  formula  (1)  will  give  a  counter- 
balance too  light  for  vertical  engines.  We  should  use  formula  (2)  for 
computing  the  counterbalance  for  both  horizontal  and  vertical  engines, 
ejLcepting  locomotives,  in  which  the  counterbalance  should  be  heavier. 


PEBF0BUAN0E8  OP  STEAM-XKaiNES. 


789 


PreTentlni:  Vibrations  of  Rnsines.— Manj  saggestions  have 
been  made  for  remedying  the  vibration  and  noise  attendant  on  the  working 
of  the  big  engines  which  are  employed  to  run  dvnamog.  A  plan  which  has 
given  great  satisfaction  is  to  build  hair-felt  into  the  fonudatious  of  the 
4»ngine.  An  electric  company  has  had  a  SOhorse-power  engine  removed 
from  ita  foundations,  whicn  were  then  taken  up  to  the  depth  of  4  feet.  A 
layer  of  felt  5  inches  thick  was  then  placed  on  the  foundations  and  run  up  2  feet 
oil  all  sides,  and  on  th«  top  of  this  the  brickwork  was  built  up.— Safety  Valve, 

Meam-«iifflne  FonndaUons  Bml^ddcd  In  A|r.— In  the  sugar- 
retiiiery  of  Ulaus  ^preckeiy.  at  Philadelphia,  Pa.,  the  enginee  are  distributed 

Sracticaliy  all  over  the  buildings,  a  large  proportion  of  them  being  on  upper 
oors.  Some  are  bolted  to  iron  beams  or  girders,  and  are  consequently 
innocent  of  all  foundation.  Some  of  these  engines  ran  noiaaleaslv  and  satis- 
factorily, while  others  produced  more  or  less  vibration  and  rattle.  To  cor- 
rect the  latter  the  engineers  suspended  foundations  from  the  bottoms  of  the 
engines,  so  that,  in  looking  at  them  from  the  lower  floors,  they  were  literally 


banging  in  the  air.— /» on  Age,  Mar.  13.  1890. 
Cost  of  Coal  for  Steam-poiirer.- 

amouut  and  the  ou8t  of  coal  p«r  day  and  p« 


-The  following  table  shows  the 
amouut  and  the  ou8t  of  coal  p«r  day  and  per  vear  for  various  borse-poweis, 
from  t  to  1000,  based  on  the  assumption  of  4  lbs.  of  coal  being  used  per  hour 
per  horse-power.  It  is  useful,  among  other  things,  in  estimatiug  the  saving 
tliat  may  be  made  in  fuel  by  substituting  more  economical  boilers  and 
engines  for  those  already  in  use.  Thus  with  coal  at  $3.00  per  ton,  a  saving 
of  19000  per  year  in  fuel  may  be  made  by  replacing  a  steam  plant  of  1000 
H.P.,  requiring  4  lbs.  of  coal  per  hour  per  horse-power,  with  one  requiring 
only  2  lbs. 


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Mi.oui^4.ooq 

Storing  Steam  lIe«t«~There  is  no  satiHfactory  method  for  equalizing 
the  load  on  the  engines  and  boilers  in  eleotric-Iigh I  stations.  Storage-batteries 
have  been  used,  but  thej'  are  expensive  in  flrst  cost,  repairs,  and  attention. 
Mr.  Halpin,  of  London,  proposes  to  store  heat  during  the  day  in  specially 
constructed  reservoirs.  As  the  water  in  the  boilers  is  raised  to  260  lbs.  pres- 
sure, it  is  conducted  to  cylindrical  reservoirs  resembling  Eeglish  horizontal 
boilers,  and  stored  there  for  use  when  wanted.  In  this  wav  a  compaiativei v 
small  boiler-plant  can  be  used  for  heating  the  water  toS50  lbs.  pressure  all 
through  the  twenty-four  honrs  of  the  day,  and  the  stored  water  may  be 
4n^wii  on  At  any  time,  according  to  the  magnitude  of  the  demaud.    Tho 


790  THE  STEAM-ENGINE. 

steam-etifrtnes  are  to  be  worked  by  the  steam  generated  b^  the  release  of 
pressure  from  this  water,  and  the  valves  are  to  oe  arranged  in  such  a  way 
that  the  steam  shall  work  at  180  lbs.  pressure.  A  reservoir  8  ft.  in  diameter 
and  30  ft.  long,  containing  84,000  lbs.  of  heated  water  at  S50  lbs.  pressure, 
would  supply  5250  lbs.  of  steam  at  190  lbs.  pressure.  As  the  steam  consump- 
tion of  a  condensing  electric- light  engine  is  about  18  lbs.  per  honse-powrr 
hour,  such  a  reservoir  would  supply  *<i86  effective  horse-power  hours.  In 
1878,  in  France,  this  method  of  storing  steam  was  usea  on  a  tramway. 
M.  Francq,  the  engineer,  designed  a  smokeless  locomotive  to  work  by  st<«m- 
power  supplied  by  a  reservoir  containing  400  gallons  of  water  at  220  lbs. 
pressure.  The  reservoir  was  charged  with  steam  from  a  stationary  boiler 
at  one  end  of  the  tramway. 

Comt  of  Steam-povirer*  (Chas.  T.  Main,  A.  S.  M.  E.,  x.  48.)— Estimated 
costs  in  Mdw  England  in  1888,  per  horse-power,  based  on  engines  of  2000  H.F. 

Compound    Condens-    ^^l^i" 
Engine,      iog  Engine.  g^'^^K 

1.  Cost  engine  and  piping,  complete $25.00  $90.00  $17.50 

2.  Engine-house 8.00  7.50  7.50 

8.  Engine  foundations 7.00  6.60  4.60 

4.  Total  engine  plant 40.00  83.00  29.50 

6.  Depreciation,  4j(  on  total  cost 1.60  1.32  1.18 

6.  Repairs,  2je  "       "       "     0.80  0.66  O..** 

7.  Interest.  53t  **       "       "     2.00  1.65  1.4:5 

8.  Taxation,  1. .5^  on  9^  cost 0.45  0.371  0.333 

9.  Insurance  on  engine  and  house. 0.1G5  0.138  0  125 

10.  Total  of  lines  5,  6,  7,  8,  9 6.015  4J»  €m 

11.  Cost  boilers,  feed-pumps,  etc 9.38  18.38  16.00 

12.  Boiler-house 2.92  4.17  5.00 

13.  Chimney  and  flues 6.11  7.30  8.00 

14.  Total  boiler-plant 18.^  24.80  S9.00 

15.  Depreciation,  5$(  on  total  cost 0.918  1.240  1.4.V 

16.  Repaii-s,  ;i5(            •*      **       "    887  .496  .6«0 

17.  Interest,  5jt           "      "       *'    918  1.240  1.450 

18.  Taxation,  l.Sji  on  9i  cost 207  .279  .326 

19.  Insurance,  0.b%  on  total  cost 092  .124  .  145 

20.  Total  of  lines  15  to  19 2.502  8.879  8.951 

21.  Coal  used  per  I.H.P.  per  hour,  lbs 1.75  2.50  3.00 

22.  Cost  of  coal  per  I.H.P.  per  day  of  10)4      c's-  cts.  •  cts. 

hours  at  $5.00  per  ton  of  ^240  lbs 4.00  5.72  6.86 

23.  Attendance  of  engine  per  day 0.60  0.40  0.85 

24.  "  "  boilei-8  "      "    0.53  0.75  0.90 

25.  Oil,  waste,  and  supplies,  per  day 0.25  0.22  0.*J0 

26.  Total  daily  expense 5.38  7.09  8.81 

27.  Yearly  running   expense,  808  days,   per 

I.H.P :.. ..!   ....$16,570  $21,837         $25695 

28.  Total  yearly  expense,  lines  10,  20,  and  27..  24.087  29UU»  38.248 
21).  Total  yearly  expense  per  I.H.P.  for  power 

if  60^  of  exhaust-steam  is  used  for  heat- 
ing      12.597  14.907  16.063 

80.  Total  if  all  ex.-steam  is  used  for  heating. . .      8.624  7.916  7.700 

When  exhaust-steam  or  a  part  of  the  receiver-steam  is  used  for  heating,  or 
if  part  of  the  steam  in  a  condensing  engine  is  diverted  from  the  condenser, 
and  used  for  other  purposes  than  power,  the  value  Of  such  steam  sliould 

be  deducted  from  the  cost  of  the  total  amount  of  steam  generated  in  order 
t<)  arrive  at  the  cost  properly  chargeivble  to  power.    The  flgurea  in  llnfs  **9 


BOTABT  STEAM-ENGINES.  791 

Atod  80  are  baied  on  an  anumptlon  made  by  Mr.  Main  of  loaaea  of  heat 
AxnpuDtiog  to  SOX  between  the  boiler  and  the  eihau8t-pip«,  an  allowance 
which  is  probably  too  larffc. 


*5*i*«  *^o.P*R«a  ^7  Ohaa.  E.  Emery  on  ••  Coat  of  Steam  Power,"  Trana. 
1.  a  B.,  Tol.  S1I,  No¥.  2888,  and  Trana*  ▲.  I.  B.  E.,  toI.  x,  Mar.  1  to. 


▲.0. 


ROTARY  STEAn-BNGINES. 

Steana  Turbines. —The  steain  turbine  is  a  small  turbine  wheel  which 
runs  with  steam  a»  tht*  ordinary  turbine  does  with  wat«r.  (For  description 
of  the  Par80D8  and  the  Dow  Rteam  turbines  see  Modern  Mechanism,  p.  208, 
etc.)  The  Parsons  turbine  is  a  series  of  parallel-flow  turbines  mounted  side 
by  side  on  a  shaft;  the  Dow  turbine  is  a  series  of  radial  outward-flow  tur* 
bmes,  placed  lilce  a  series  of  concentric  rings  in  a  single  plane,  a  stationary 
fniide-iinfT  being  between  each  pair  of  movable  rings.  The  speeds  of  the 
steam  turbines  enormously  exceed  those  of  any  form  of  euKfne  with  recip- 
rocating piston,  oreven  of  tlie  so-called  rotary  engines.  The  three-  and  four- 
cylinder  engines  of  the  Brotherhood  type,  In  which  the  several  cylinders 
are  usually  grouped  radially  about  a  common  crank  and  shaft,  often  exceed 
1000  revolutions  per  minute,  and  have  been  driven,  experimentally,  above 
SOOO;  but  the  steam  turbine  of  Parsons  makes  10,000  and  even  20,000  revolu- 
tiona,  and  the  Dow  turbine  is  reputed  to  have  attained  25,000.  (See  Trans. 
A.  8.  M.  E.,  vol.  X.  p.  680,  and  zli.  p.  888;  Trans.  Assoc,  of  Eng'^  Societies, 
vol.  vill.  p.  583;  Eiig'g,  Jan.  13, 1888,  and  Jan.  8,  1892;  Eng'g  Netm,  Feb.  27, 
180-3.)  A  Dow  turbine,  exhibited  in  1889,  weighe<1  68  lbs.,  and  developed  10 
H.P.,  with  a  consumption  of  47  Ibe.  of  steam  per  H.P.  per  hour,  the  steam 

eresaure  beinjir  70  lbs.  The  Dow  turbine  is  used  to  spin  the  fly-wheel  of  the 
[owell  torpedo.  The  dimensions  of  the  wh^el  are  18.8  in.  diam.,  0.5  in. 
width,  radius  of  grratioa  5.57  in.  The  energy  stored  in  it  at  10,000  revs, 
per  min.  is  600.000  ft.-lbs. 

Tke  De  Laval  Steam  Turbine,  shown  at  the  Chicago  exhibition, 
1893,  is  a  reaction  wheel  somewhat  similar  to  the  Pelton  water-wheel.  The 
steam  Jet  Is  directed  by  a  nozzle  a$;ainst  the  plane  of  the  turbine  at  quite  a 
small  angle  and  tangenilally  against  the  circumference  of  the  medium 
periphery  of  the  blades.  The  angle  of  tlie  blades  is  the  same  at  the  dde  of 
admission  and  discharge.  The  width  of  the  blade  is  constant  along  the 
entire  thickness  of  the  turbine. 

The  steam  is  expanded  to  the  pressure  of  the  surroundings  before  arrlv- 
infc  at  the  blades.  This  expansion  takes  place  in  the  nozzle,  and  is  caused 
simply  by  making  its  sides  diverfj^ini?.  As  the  steam  passes  through  this 
channel  its  specinc  volume  Is  increased  in  a  greater  proportion  than  the 
cross  section  of  the  channel,  and  for  this  reason  its  velocity  is  increased, 
and  also  its  momentum,  till  the  end  of  the  expansion  at  the  last  sectional 
area  of  the  nozzle.  The  greater  the  expansion  in  the  nozzle  the  greater  Its 
Telocity  at  this  point  A  pressure  of  75  lbs.  and  expansion  to  an  absolute 
pressure  of  one  atmosphere  give  a  flnal  velocity  of  about  26:25  ft.  per  second. 

Expansion  is  carried  further  in  this  steam  turbine  than  in  ordinary  steam- 
engines.  This  is  on  account  of  the  steam  expanding  completely  during  its 
work  to  the  pressure  of  the  surroundings. 

For  obtaining  the  greatest  possible  effect  the  admis.slon  to  the  blades  must 
be  free  from  blows  and  the  velocity  of  discharf^e  as  low  as  possible.  These 
conditions  would  require  in  the  steam  turbine  an  enormous  velocity  of 
periphery — as  high  as  1'^  to  1650  ft.  per  second.  The  centrifugal  force, 
nevertheless,  puts  a  limit  to  the  use  of  very  high  velocities.    In  the  5  horse- 

Kwer  turbine  the  velocity  of  periphery  is  574  ft.  per  second,  and  the  num- 
r  of  revolutions  30,000  per  mmute. 

However  carefully  the  turbine  nvty  be  manufactured  it  is  impossible,  on 
account  of  unevenness  of  the  material,  to  pet  Its  centre  of  gravity  to  corre- 
spond exactly  to  Its  geometrical  axle  of  revolution;  and  however  small  this 
difference  may  be,  it  becomes  very  noticeable  at  snch  high  velocities.  De 
Lavai  has  succeeded  in  solving  the  problem  by  providing  the  turbine  with  a 
flexible  shaft.  This  yielding  shaft  allows  the  turbine  at  the  hiph  rate  of 
speed  to  adjust  itself  and  revolve  around  its  true  centre  of  gravity,  the 
centre  line  of  the  shaft  meanwhile  deHcribinp  a  surfar*e  of  revolution. 

In  the  gearing -box  the  speed  i.s  re<iuced  from  30.000  revolutions  to  8000 
by  means  of  a  driver  on  the  turbine  shafts,  which  sets  in  motion  a  cog-- 
wheel of  10  times  its  own  diameter.  Thes*'  pearines  are  provided  with  spiral 
cogs  placed  at  an  anple  of  about  4.')*'.  The  nhatt  of  the  larger  cof-wneel, 
running  at  a  speed  of  8000  revolutions,  is  provided  at  its  outer  ena  with  a 
pulley  lor  the  further  transmission  of  the  power. 


792  THE  8TEAH-:eN6tK£« 

Botarj  Steam-englnes^  other  than  steam  turbines,  have  been 
invented  bv  the  thousatidB,  bui  not  one  has  attained  a  commercial  success. 
The  poGsible  advantages,  such  as  saving  of  space,  to  be  gained  bjr  a  rotaiy 
engine  are  overbalanced  by  its  waste  of  steam. 

The  Tourer  Splierlcml  Enginei  one  of  the  most  recent  forms  of 
rotary-engine,  is  dcM^ribed  in  Proc.  Itist.  M.  E.,  188&,  also  in  Modem 
Mechanism,  p.  296. 

DiaiBNSIONS  OF  PARTS  OP  BKGINBS. 

The  treatment  of  this  subject  by  the  leading  authorities  on  the  steam -en« 
fflne  is  verv  unsatisfactory,  being  a  confused  mass  of  rules  and  formuln 
cwsed  partly  upon  theoi^  and  partly  upon  practice.  The  practice  of  builders 
shoe's  an  exceeding  diversity  of  opinion  as  to  correct  dimensions.  Tlie 
treatment  given  below  is  chiefly  the  result  of  a  study  of  the  works  of  Rankii<e, 
Seaton,  Unwin,  Tliurston.  Marki*,  and  Whitham,  and  is  largely  a  condemn* 
tion  of  a  series  of  articles  by  the  author  published  in  the  American  Ma- 
cfcinisf,  in  1894,  with  many  alterations  and  much  addiu'onal  matter.  lu  or> 
der  to  make  a  comparison  of  many  of  the  formulae  they  have  been  applied 
to  the  assumed  cases  of  tix  engines  of  different  sizes,  and  in  some  cases 
this  compnrison  has  led  to  the  construction  of  new  formulas. 

CjUnder*  (Whitham.)— Length  of  bore  =  stroke  4-  breadth  of  piston- 
riug  —  ^  to  ^  in;  length  between  heads  b  stroke  +  thickness  of  piston  4- 
suin  of  clearances  at  both  ends;  thickness  of  piston  c  breadth  of  ring-f 
thickness  of  flange  on  one  side  to  cai-ry  the  ring  -)-  thickness  of  follower^ 
pUte. 

Thickness  of  flange  or  follower. . . .    ^  to  U  tn.         9|  in.  1  fts. 

For  cylinder  of  diameter 8  to  10  in.  Mia.  60  to  100  tn. 

Clearanee  of  Plflton«  (Seaton.)— The  clearance  allowed  varies  with 
the  sise  of  ihe  engine  f  itim  ^  to  9^  in.  for  roughness  of  castings  and  1/16  io 
kiln,  for  each  working  joint.  Kaval  and  other  very  fast-running  engines 
nave  a  larger  allowance.  In  a  vertical  direct-acting  engine  the  parts  which 
wear  so  as  to  bring  the  piston  nearer  the  bottom  are  three.  Tit.,  the  shaft 
Joiimiils.  the  crank-pin  brasses,  and  piston-rod  gudgeon-bmnssw. 

']%lelcne*a  of  Cylinder.  (Thurston. )~For  engines  of  the  older 
types  and  under  moderate  steam-pressures,  some  builders  have  for  many 
years  restrioted  the  stress  to  about  S560  lbs.  per  sq.  in. 

f  «ap,D  +  6 (1) 

IS  a  common  proportion;  f,  D,  and  b  being  thickness,  diam..  and  a  constant 


anced  stCMm-pressure  per  sq.  in.  In  this  expression  6  is  made  larger  for 
horizontal  tiian  for  vertical  cylinders,  as,  for  example,  in  large  engines  0.& 
in  the  one  case  and  0.2  in  the  otlier,  the  one  requiring  re^boriiig  more  than 
the  other.  The  constant  a  is  from  0.0U04  to  O.OOOS:  the  first  value  for  verti- 
cal cylinders,  or  short  strokes;  the  second  for  horisontal  engines,  or  for 
long  strokes. 

Tlilcfcneae  or  Cylinder  and  tta  Conneetf  on*  fl^r  Blarlne 

Enielnes.    (Seaton  ).^Z>  =  the  diam.  of  the  cylinder  in  inches;  p  =  load  on 

the  safety-valves  in  lbs.  per  sq.  in.;  /,  a  constant  multiplier  as  thickness  of 

barrel  -f  .85  in. 

Thickness  of  metal  of  cylinder  barrel  or  liner,  not  to  be  less  thaap  X  D-*- 

8000  when  of  cast  iron.* (Q 

• 

Thickness  of  cylliider-barrel  «  ^^^  ■  +  0.€  la. CD 

••  ••  liners  1.1  X/ W 

Thickness  Of  Hncr  when  of  steel  p  X  D-t-  AOOO  -f  0.5 
"         metal  of  steam-ports         =0.6   x/. 
••  "       valve-box  sides    =r0.66X/. 

*  When  made  of  exceedingly  good  material,  at  least  twice  metted.  tlM 
thickness  may  be  0.8  of  t)>at  given  by  the  above  rules. 


DQtEKSIONS  07  PABTS  OF  BKaUSTES. 


79» 


Iblckne68  of  metal  of  valve-box  covers  «  0.7  X  /. 

"  **•  cylinder  bottom  =  1.1  x  /,  if  slofrle  tbiekneflB. 

"  "  ••             "     r=  0.65  X /,  If  double       •• 

••  "  "       covers  =  1.0  x/,  if  single        ** 

•*  "  "           "     =0.6  x/,  lfdoA>la      *• 

••  cylinder  flanjce  =1.4  x/. 

••  "  cover-flange     =1.8  x/. 

••  ••  valve-box^      =1.0  x/. 

••  •*  door*  flange       =0.9  X/. 

••  "  face  over  porta  =  1.2  x  /. 

•  "  "  '♦     =1.0  x/.wbenthoreteafalfle^aoe. 

•  **  false-face  =0.8  X  /  when  cast  iron. 

••  ••  •'                =0.6  x/.whenuteelorbronie. 

Wldtliam  giTes  the  following  from  different  authorities: 

VanBuren-i*-<^-«»^^+0.«V2>; (ft 

4  U  -  0.08  VDp 16) 

Tredgold:     «-^-^±^ (7^ 

Welabach:    <  «  0.8  +  0.0008aSpZ>. (8^ 

Seatoo:         f  e  0.5  +  0.0004pD. (9) 

Haswell-    i«- 0.0004pD4.Jii(verUcal); (10) 

nasweu.    <<  «o.OOOBpZ)+g(horiaontal).  .   .   .   .  (H> 

Whltbam  recommends  (6)  where  provision  is  made  for  the  reboring,  and 
where  ample  strength  and  rigidity  are  secured,  for  horisontal  or  vertical 
cylinders  of  large  or  small  diameter;  (9)  for  lanre  cylinders  using  steam 
under  100  lbs.  gauge  •pressure,  and 

_    ^           eai0.008I>4^forsmallcyllttden.  ..••••  (Ifl) 
Marks  gives  t«O.O0an|pll {m 

This  Is  a  smaller  value  than  is  given  by  the  other  formulas  quoted;  but 
3IarkB  says  that  it  Is  not  advisable  to  make  a  stoamH^lInder  lees  than  0.75 
In.  thick  under  any  circumstances. 

The  following  table  gives  the  calculated  thickness  of  cylinders  of  engines 
of  10,  80,  and  50  In.  diam.,  assuming  p  the  maximum  unbalanced  pressareon 
the  piston  s  100  lbs.  per  sq.  io.  As  the  same  engines  will  be  used  for  calcu- 
lation of  other  dimensions,  other  particulars  concerning  (hem  are  here 
given  for  ref erence. 


DlMXHSIONB,  STO.,  OF  EnGIKBB. 

Engine  Kd 

land  2. 

8«nd4. 

5  and  6. 

Indicated  horse 'power I.H.P. 

I>iam.  of  oyL,  in D 

Stroke,  feet7. L 

60 

10 

1     ....        2 

260    ...      125 
600 
78.54 
42 
7854 
100 

450 

80 

706.86 
828 
70,686 
100 

1260 
60 
4    ....      8 

Revs.permiBL r 

90    ....    45 

Piston  speed,  ft.  per  min 8 

TOO 

Areaof  piston,  sq.  In a 

Mean  effective  pressure  . .  .M.E.P. 

Max.  total  onbalanced  press P 

Max.  total  per  sq.  in p 

1963.5 
80 
196,850 
100 

'?94 


THE  STEAM-ENGINB. 


^ 


Thicknbss  of  Cylxndbr 

BY  FORMUIA. 

1)  .OOOipD  +  0.6,  short  stroke. 
1)  OO^p  +  0.5»  long  stroke . . 

<6)  .0001pD  +  .15i<D 

(6)  .08  V^ 

*^        1900     ^ 

(8)  .OOOWtoD  +  0.8 

'"    .0004pD4-0.6. 


(9).< 
(101  .( 
Cll)  .< 


(IS) 


.0004pl>  +  H  (vertical) . 
OOOSpD  +  ^  (horiKOotal) . 
.008D  4^  (small  engines).. 


Average  of  first  eleven . 


land  2. 


8  and  4. 


.78 


.90 

1.00 

.88 

.80 

1.70 

8.00 

.99 

1.40 

.57 

1.18 

.» 

1.64 

M 

1.71 

1.13 
.90 
.63 
.63 

1.78 
1.70 
1.88 
1.68 

.80(?) 
.28(?) 

".si, 

84if)% 


1.48 


5and8w 


2.60 
8.00 

1  er 
i.» 

1.68 
8.111 
2.78 

2.45 
S.50 
2.18 

2.63 

i'ibin 


2.28 


The  average  corresponds  nearly  to  the  formula  t  =  .00087Dp  +  0.4  in.  A 
convenient  approximation  iat  ss  .OOOWp  +  0.8  in.,  which  gives  for 

Diameters 10        20  80  40  60  60  In. 

Thicknesses 70       1.10       1.60       1.90       2.80       2.70  In. 

The  last  formula  corresponds  to  a  tensile  strength  of  cast  iron  of  12,500 
lbs.,  with  a  factor  of  safety  of  10  and  an  allowance  of  0.3  in.  for  reboring. 

Cyllndei>lieads«— Thurston  Hays :  Cylinder-heads  may  be  given  a 
thickneas,  at  theedgeit  and  in  the  flanges,  exceeding  somewhat  that  of  th« 
cylinder.  An  excess  of  not  less  than  26^  is  usual.  It  may  be  thinner  in  the 
middle.  Where  made,  as  is  usual  in  large  engines,  of  two  disks  with  inter- 
mediate radiating,  connecting  ribs  or  webs,  that  section  which  is  safe 
against  shearing  is  probably  ample.  An  examination  of  the  designs  of 
experienced  builders,  by  Professor  Thurston,  gave 


t  -  J^  A.  u  inch, 
8000^  r4"»^. 


(1) 


2)  being  the  diameter  of  that  circle  in  whjch  the  thickness  fa  taken. 

Thurston  also  gives  t  =  .005D  Vp  +  0.26 (2) 

Marks  gives  <  =  0.008D|p ,3) 

He  also  savs  a  good  practical  rule  for  pressures  under  100  lbs.  per  sq.  in.  is 
to  make  the  thickness  of  the  cylinder-heads  1^  times  that  of  the  walls;  and 
applying  this  factor  to  his  foi*mula  for  thickness  of  wall»\.  or  .OOO-JSpD,  we 
have 

t  ^  .00085p2> (4) 

Whitham  quotes  from  Seaton, 

t  =  ^^2000^*  ^****^**  *^  ^^^*^  ^  .OOOSpD  4-  .85  incn.    .    .    .    (5) 
Seaton*s  formula  for  cylinder  bottoms,  quoted  above,  is 

t  =  1 . 1/,  in  which  /  =  .000apZ>  -f  .85  inch,  or  t  =  .00088pD  +  .93.     .     (6) 
Applying  the  above  formuIfB  to  the  engines  of  10.  SO.  and  AO  inches  diame- 
ter, with  maximum  unbalanced  steam-pressure  of  100  lbs.  per  sq.  in.,  we 
have 

Cylinder  diameter,  Inches  =3     10  30  50 


0)«« 

.00033i)p-H 

.25 

s 

.53 

1.25 

1.82 

(2)  <  = 

.005D  i  p  -f 

.25 

= 

.75 

1.75 

2.75 

(8)<  = 

.003D  i^ 

=- 

.80 

.90 

1.50 

4)  <  = 

.000d5/)p 

= 

.85 

1.05 

1.75 

(5)  <  = 

.OOOSDp  -f  . 

.ooaw/5p  -f 

25 

= 

.75 

1.75 

2.75 

(6)*  = 

.93 

= 

1.15 

1.59 

2.08 

Aven 

iseof  6  .... 

.65 

1.38 

2.10 

DIMENSIONS  OF  PARTS  OF   ENGINES.  795 

The  ayeraee  Is  expressed  by  Che  formula  i  a  .OOO06Dp  4*  M  taek, 
Meyer's  '*  Modem  Locomotive  Ck>nstructfon/*  p.  M,  Rires  for  looomoilTtt 
eylinder-heads  for  pressures  up  to  120  lbs.: 

FordUmeCerB,!n 19toSS       16tol8       ]4to15       lltolS      9tol0 

Thickness,  In. IM  1  I  fi  H 

TaldnfT  the  pressure  at  190  lbs.  per  sq.  lo.,  the  thicknesses  1^  in.  and  H  in. 
for  cylinders  S8  and  10  in.  diam.,  respectively,  correspond  to  the  formula 
t  =  .000857)p  +  .88  inch. 

ITeb-atllDBifted  €jllnder-eoTem«— Seaton  objects  to  webs  for 
stilTeninsr  cast-iron  cylinder-coveni  as  a  source  of  dancer.  The  strain  on 
the  web  IB  one  of  tension,  and  if  there  should  be  a  nick  or  defect  in  the 
outer  edge  of  the  web  the  sudden  application  of  strain  is  apt  to  start  a 
crack.  He  recommends  that  high-pressure  cylinders  over  94  In.  and  low- 
pressure  cylinders  over  40  in.  diam.  should  have  their  covers  cast  hoUow. 
wiih  two  thickn^Bses  of  metal.  The  depth  of  the  cover  at  the  middle  should 
be  about  M  the  aiam.  of  the  piston  for  pressures  of  80  lbs.  and  upwards, 
and  that  of  the  low-pressure  cylinder-cover  of  a  compound  engine  equal  to 
that  of  the  high*pressare  cylinder.  Another  rule  Is  to  make  the  depth  at 
the  middle  not  less  than  1.8  times  the  diameter  of  the  piston-rod.  In  the 
British  Navy  the  cyiinder-covers  are  made  of  steel  oastlogs,  9^  to  IM  in. 
thick,  generally  cast  without  webs,  stiffness  b^lng  obtained  by  their  form, 
which  is  often  a  series  of  corrugations. 

Cyllnder-liesid  Holt*.— Diameter  of  bolt«ircIe  for  oylinder-head  m 
diameter  of  oylindur  +  ^  X  thickness  of  cylinder  4-2X  diameter  of  bolts. 
The  bolts  shoukl  not  be  more  than  6  inches  anart  (Whithara). 

Marks  gfres  for  number  of  bolta  b  s  '^IS^^  "  .OOQlSn^,  in  which  c  a 

ouuuc  e 

area  of  a  single  bolt,  p  s  boiler-pressure  in  lbs.  per  sq.  In.;  6000  lbs.  Is  taken 
m»  the  safe  strain  per  sq.  in.  on  the  nominal  area  of  the  bolt. 

Beaton  says:  Cylinder-cover  studs  and  bolts,  when  made  of  steel,  should 
be  of  such  a  sise  that  the  strain  in  them  does  not  exceed  6000  lbs.  per  sq.  in. 
When  of  less  than  %  inch  diameter  it  should  not  exceed  4600  lbs.  per  sq.  in. 
When  of  iron  the  strain  should  be  SOU  less. 

Thurston  says :  Cylinder  flanges  are  made  a  little  thicker  than  the  cylin- 
der, and  usually  of  equal  thickness  with  the  flanges  of  the  heads.  Cylinder- 
bolts  should  be  so  closely  spaced  as  not  to  allow  springing  of  the  flanges 
and  leakage,  say,  4  to  5  times  the  thickness  of  the  flanges.  Their  diameter 
should  be  proportioned  for  a  maximum  stress  of  not  over  4000  to  6000  Iba. 
p«r  square  inch. 

If  .D  9  diameter  of  cylinder,  o  b  maximum  steam-pressure,  b  m  number 
of  bolts,  s  m  sise  or  diameter  of  each  bolt,  and  6000  lbs.  be  allowed  per  sq. 
in.  of  nominal  area  of  the  bolt,  .7864I>^  -  8d376^;  whence  b$*  m  .OOQSb^; 

b  =  .0008^^;  9  =  .014141)^/-^.    For  the  three  engines  we  have: 

Diameter  of  cylinder,  inches 10  90  9 

Diameter  of  bolt^ircle,approz.....  18  86  67 J 

CRroamferenoe  of  circle,  approz....  40.8  110  180 

Minimum  No.  of  bolts,  circ.  -t- € f  18  80 

Diam.  of  bolts,  s  -  .01414Di/| 9^  in.      1.00     t  JO 

The  diameter  of  bolt  for  the  10-lnoh  cylinder  to  O.Ot-ln.  brtho  formula, 
but  9i  inch  Is  as  small  as  should  be  taken,  on  account  of  possible  overstrain 
by  the  wrench  in  screwing  up  the  nut. 

Tbe  Ptoton*  Details  of  ConstracUon  of  Ordloary  Pis* 
tons*  (Seaton.)— Let  D  be  the  diameter  of  the  piston  in  inches,  p  the  effec- 
tive preaaurs  per aqqare  Inch  on  it, «  a  constant  multiplier,  foiMid  as  followf: 


796  THB  SnSAX-SNGXirB. 

The  thldmeai of  Cnst «(  plfi<«n  near  tiM bou  s  :;.t  xm 

*  •*  **  ♦*  ilm  «o.irx«. 
••  back  •*  --0.1«x« 
**  boss  around  the  rod  s  0.8  xx» 
M  flange  ioside  packioff-risir  s  0.28  x «. 

•  •*  at  edge  =0.«6x». 
••  packing-ring  ss  O.IS  X «. 
**  Junk-ring  at  edge  1 0.83  X ». 

**       loaida  packii«-riiif  »  0.S1  X  «. 

**  metal  around  piston  edge  b=  0.$ft  x  x» 

TbB  breadth  ot  packiAg'riag  m^MXm, 

**   depth  of  piatoo  et  ceiit«ie  a*  1.4  X  & 

**   lap  of  junk-riog  on  the  piston  k  0.45  x  a?. 
**   apace  between  piston  bodjr  and  packhv-riiigOT  0.8  xor. 

•«   (Oametar  of  j*ink-rinf  boJta  >•  0.1   x  »  4-  ••«  1^ 

-*   pitch        ''         "         '*  » 10  diameters. 

**   number  of  weba  in  tho  piston  «6P+i0)-t-l& 

"   thickjoesa     ••«*'«  ■0.l8>?t 

Marks  gires  the  approximate  rule:  TbIokaesB  of  pistoo-haad»  03,  ia 
vbiob  / «  leDgtb  of  stroke,  and  d  «  diameter  of  cjUnder  in  inches.  Whit- 
ham  sajrs  in  a  borisontaJ  engine  the  rings  support  the  pistmi,  or  a(  iMwt  a 
part  of  it,  under  ordlnair  oooditiooa.  The  pressare  doe  to  the  weight  of 
Ihe  piston  upon  an  area  eqiml  to  0.7  Che  diameter  of  the  cylinder  Y. 
breadth  of  ring»faae  should  never  ezoeed  «0O  Ihs.  p#r  sq.  hi.  He  akK>  gives 
a  fonnula  mumi  used  in  this  oouotryt  Brsadth  of  rtng-fhos  m  0.15  x  duun- 
eter  of  cylinder* 

For  oiirepgineswahafis  diameter  Si  ....«•••• 10  M  50 

lUcknesB  of  piston-head. 

8 arlts,  VfZ^I  kmc  stroke 8.81  6.4B  7.00 

arks,     **  ;  short  stroke •.•••.  8.04  6.51  8.32 

Beaton,  depth  at  centre  a  1.4:9 ,  ..  4.80  9.80  ]5.<j0 

SeatoQ,  breadth  of  ring  «  .6&r .«• 1.80  4.41  6.93 

Whithsm,  breadtb  of  ring  »  .150 1.00  4.50  7.50 

IMnntefer  •f  Platon  P»Cfcliifl:«rtiiffa.  —  Thew  are  generally 
turned,  before  they  are  cut,  about  ^  incb  diaiiteter  larger  than  the  cylinder, 
for  cylinders  up  to  80  inches  diameter,  and  then  enough  Is  cut  out  of  tlie  ring 
to  spring  them  to  the  diameter  of  the  cylinder.  For  hui^er  cylinders  tlie 
rinfvs  are  tamed  proportionately  larger.  Beaton  raoommeDds  an  excess 
of  \%  of  the  dl»nieter  of  the  cylinder. 

CrcWNSeeWon  of  the  RtiiM.— The  thickness  Is  commonly  made 
1/SOth  of  the  diam.  of  cyl.  +  H  ^<ich.  and  the  width  m  thickness  +  M  inch. 
For  an  ecofntric  ring  the  mean  thickness  may  be  the  same  as  for  a  nng  of 
uniform  thickness,  and  the  minimum  thickness  ^  %  the  maximum. 

A  circular  issued  by  J.  H.  Dunbar,  manufacturer  of  packing^njrc 
Toungstoirn,  O.,  says:  Unless  otherwise  crder^ed,  the  thidcness  of  rings  vt  ill 
be  made  equal  to  .03  x  their  diameter  This  thickness  has  been  found 
to  be  satisfactory  in  pi«otice.  It  admits  of  the  ring  being  nnade  about  8/16" 
to  the  foot  larger  than  the  cylinder,  and  has.  when  new,  a  tension  of  about 
two  pounds  per  inch  of  circumference,  which  is  ample  to  prevent  leakage, 
if  the  surface  of  the  ring  and  cylinder  are  smooth. 

As  regards  the  width  of  rings,  authorities  **  scatter  "  from  very  narrow  to 
very  wide,  the  latter  being  fully  ten  times  the  former.  For  instance,  Unwin 
gives  Wsd  .014  -t.  .08.  Whit>iam'8  formula  Is  TTai  d  .16.  In  both  for- 
nulsslTls  the  width  of  the  ring  In  inches,  and  d  the  diameter  of  the  cylinder 
in  Inehes.  Unwind  formula  makes  the  width  of  a  90"  ring  WnsWx  .014 
-^  .06  a  .86'',  while  Whltham*s  Is  20  x  .16  «  V'  for  the  same  diameter  of 
Blag.  TNm  Is  ranch  less  dllf^renoe  in  the  practice  of  engine-builders  la  thi< 
respect,  but  there  to  still  room  for  a  standard  width  ot  ring.  It  to  believed 
that  foe  eorlindera  over  W'  diameter  H"  to  a  popular  and  praoHoal  width, 
and  W'  for  cvlinders  of  that  size  nnd  under. 

Fti  of  Piston-rod  Into  Piston*  (Beaton.)— The  most  eonvenlent 
and  reliable  practice  is  to  turn  the  piston-rod  end  with  a  shoulder  of  1/16 
Inch  for  small  englnee,  and  ^  hich  for  huge  onee,  make  the  teper  8  In.  to 


DIMENSIONS  OF  PABT5  07  SNQINS8.  797 

the  foot  antfl  the  aectloo  of  tbi  rod  to  thrse  fourtbi  of  that  of  tho  body»  then 
turn  tb«  nimaiiiiiHr  f-art  parallel;  the  rod  should  then  fit  into  the  piston  so 
as  to  leave  HI  loch  betiveec  it  and  the  shoulder  for  larse  plstoiis,  and  1/16  in* 
for  small.  The  shoulder  prevents  the  rod  from  split  tine  the  piston,  and 
allows  of  the  rod  beingr  turned  true  after  long  wear  without  encroaching  on 
the  Uper. 

The  piston  Is  secured  to  the  rod  by  a  nut,  and  the  stie  of  the  rod  should 
be  such  that  the  Strain  on  the  sectloA  at  the  bottom  of  the  thread  does  not 
exceed  6000  Ibe.  per  sq.  in.  for  iron,  7D0O  lbs.  for  steel  The  depth  of  this  nut 
iie<*d  not  exceed  the  diameter  which  would  be  found  by  allowiug  these 
strains.    The  nut  nhouid  be  locked  to  prevent  its  working  looee. 

Diameter  of  Plflton«ro<U«— Unwin  glveft 

d"mht>^, 0 

in  which  D  is  the  cylinder  diameter  In  Inehes,  p  to  ths  maxlmiim  tmbalanoed 
pressure  in  llw.  per  sq.  in.,  and  the  constant  b  e  0.0167  for  iron,  and  h  a 
U.0144  for  steel.  Thurston,  from  an  examination  of  a  consldeiable  number 
of  rods  in  ust,  glTes 

+  £,neaitr. (S) 


,^^ 


(L  in  feet.  D  and  d  in  Indies),  In  whleh  a  s  lO,000  and  upward  in  the  various 
types  of  engines,  the  marine  serew  engines  or  ordinary  fast  engines  on 
f>bore  given  the  lowest  values,  while  "Mow-speed  engines'*  being  less 
liable  to  accident  from  shook  give  a  s  15,000,  often. 

Connections  of  the  plston>roa  to  theptoton  and  to  theorosshead  should 
liave  a  factor  of  safety  of  at  least  8  or  lo.   Harks  gives 

d'^s  0.01701)^9,  for  iron;   for  steel  (t'^       «  0.01061)  Vp;  .    .    (8) 

and  d"  a  0.06001  /DU^,  for  iron;    for  steel  d*'  m  0.06S26  Vl^,     (4) 

in  whlOii  f  to  the  length  of  stroke,  all  dimensions  in  inches.  Deduce  the 
diameter  of  pteton-rod  by  (8),  und  If  this  diameter  to  less  than  1/I8t,  then  use 
W)« 

SeittongiTM:  Dtometer  of  pteton-rod  »  '>f>'ff'"»r^'  «=?»■"»«■■  ^ 

The  following  are  the  values  of  JBh 

Naval  enginesi  direct-acting FatW 

•*  **        return  connuectlng-rod,  2  rods ^"=90 

Mercantile  ordinary  stroke,  direct-acting i^'ssfio 

*•         long  "  ♦•  F=i9 

ylong    ••  "  F=46 

dium  stroke,  oscillating J*  a*  46 


veiTl 
mediii 


Note.— Long  and  very  long,  as  oompared  with  the  stroke  usual  for  the 
power  of  engine  or  siie  of  cylinder. 

In  oonsidering  an  expansive  engine  p.  the  eftectlve  pressure  should  be 
taken  as  ttie  absolute  working  pressure,  or  16  lbs.  above  that  to  which  the 
boiler  safety-valve  to  loaded;  for  a  oompound  engine  the  value  of  p  for  the 
high-pressui«  ptotoo  should  be  taken  aa  the  absolute  pressure,  less  15  Ilis., 
or  the  same  as  the  load  on  the  safety-valve;  for  the  medium-pressure  the 
load  may  be  taken  as  that  due  to  half  the  absolute  boiler-pressure;  and  for 
the  low-pressure  ey Under  the  pressure  to  which  the  escape- valve  Is  loaded 
-f  15  lbs.,  or  the  maximum  absolute  pressure,  which  can  be  got  In  the  re- 
ceiver, or  about  Hb  lbs.  It  Is  an  advantage  to  make  all  the  rods  of  a  com- 
pound engine  alike,  and  this  Is  now  the  rule. 

Applying  the  above  formulae  to  the  engines  of  10»  80,  eo4  60  in.  diameter, 
both  short  m^  lonnf  strolte,  we  hi^v^: 


798 


THE  STEaM-KKGINB. 


mameter-or  Piston-rods. 


Diameter  of  Cylinder,  Inches 

10 

80 

60 

Stroke,  incheB , 

12 
1.07 
1.44 

1.18 

1.79 

1.85 

(1.06) 

l.« 

1.67 

24 
l.CT 
1.44 

1.40 

1.91 
1.78 

2.22 

80 
5.01 
4.88 

8.13 

6.87 

8.70 

(8.15) 

8.84 

5.01 

00 
5.01 
4.82 

8.88 
5.87 
5.18 

4.72 
6.67 

48 
8.85 
7.90 

6.10 

8.05 

6.04 

(5.25) 

5.46 

8.85 

96 

Un  win.  Iron,  .0167D  V^ 

Unwin,  steel,  .01441)  Vp 

8.85 
7.90 

Thu™ton,^/^^  +  |    (itofeet). 

Thurston,  same  with  a  s  15,000 

Marks,  iron,  .0179D  VS 

Marks,  iron.  .08001  Vx>*i*0. 

6.85 
8.05 

Marks,  steel,  .0106i>  i^ 

8.64 

Marks,  steel,  .035:25  Vz>«2«p 

Seaton.  naval  engines,  t:;  i^ 

7.W 

Beaton,  land  engine, -^  vJJ 

11  11 

Aygrage  of  four  for  Iron  ..a. 

1.40 

i.as 

4.80 

5.26 

7.11 

8.74 

The  figrures  in  brackets  opposite  Marks*  third  formula  would  be  rejected 
since  they  are  less  than  >6  of  the  stroke,  and  the  figures  derived  by  his 
fourth  formula  would  be  taken  instead.  The  figure  1.79  opposite  bis  first 
formula  would  be  rejected  for  the  engine  of  24-inch  stroke. 

An  empirical  formula  which  gives  results  approximating  the  above  aver- 
agM  is  d"  s  .018  VD/p. 

The  calculated  results  from  this  formula,  for  the  six  engines,  are,  respec* 
tivelv,  1.42,  1.88,  8.90,  6.61,  6.87, 9.01. 

Piston-rod  Guides.— The  thrust  on  the  guide,  when  the  oonnectiDg- 
rod  is  at  its  maximum  angle  with  the  line  of  the  piston-rod.  Is  found  from 
the  formula:  Thrust  =  total  load  on  piston  x  tangent  of  msxinium  angle 
of  connecting-rod  =  p  tan  $.  This  angle,  9,  is  the  angle  whose  sine  =s  half 
stroke  of  piston  -i-  length  of  oonnectlng-rod. 

Ratio  of  length  of  connecting-rod  to  stroke ^  ^  8 

Maximum  angle  of  connecting-rod  with  line  of 

plston-rod 14<»20'  11»  38'  9»  9ff 

Tangent  of  the  angle 258              .204  .169 

Secant  of  the  angle  1.0827  1.0206  1.014 

Seaton  says:  The  area  of  the  guide-block  or  slipper  surface  on  which  the 
thrust  is  taken  should  in  no  case  be  less  than  willadmit  of  a  pressure  of  400 
lbs.  on  the  square  inch;  and  for  good  working  those  surfaces  which  take  the 
thrust  when  going  ahead  should  be  suffioientlv  large  to  prevent  the  maxi- 
mum pressure  exceeding  100  lbs.  per  sq.  in.  When  the  surfaces  are  kept 
well  luoricated  this  allowance  may  be  exceeded. 

Thurston  says:  The  rubbing  surfaces  of  guides  are  so  proportioned  that 
if  F  be  their  relative  velocity  in  feet  per  minute,  and  p  be  the  intensity  of 
pressut-e  on  the  guiile  in  lbs.  per  sq.  in.,  pF  <  60,000  and pF  >  40,000. 

The  lower  is  the  safer  limit;  but  for  marine  and  stationary  engines  It  is 
allowable  to  take  p  s  60,000  -»-  F.    Accoi-ding  to  Ranklne,  for  locomotives, 

44800 
p  =  ^.  where p  is  the  pressure  In  lbs.  per  sq.  in.  and  Fthe  velocity  of 

rubbing  in  feet  per  minute.  This  includes  the  sum  of  all  pressures  forcing 
the  two  rubbing  surfaces  together. 

Some  British  builders  of  portable  engines  restrict  the  pressuro  between 
the  guides  and  cross-heads  to  less  than  40,  sometimes  85  lbs.  per  square  inch. 

For  a  mean  velocity  of  000  feet  per  minute,  Prof.  Thurston^s  formulas 
give,  p  <  100,  p  >  06.7;  Rankine's  gives |^  =  72.2  lbs.  per  ac^.  in. 


DIHBKSIONS  OF  PARTS  OF  ENGINES.  799 

^Vhitham  gtrea, 

^sareaof  ■Udesin  square  inches  e ^         a    .'i94d^j_ 

p.  Vn«  -  1       p.  i^n«  -  1 

in  which  P  s  total  unbalanced  premore,  Pi  =  pressure  per  square  Inch 
on  piston,  d  =  diameter  of  cylinder,  pt  =  pressure  allowable  per  square  inch 
oo  slides,  and  n  =  length  of  connecting-rod  -*-  length  of  crank.  This  Is 
eqiifyalent  to  the  formula,  A^  P  tan  9  -•-  po.  For  n  =s  &,  P|  ss  100  and  po 
=  80,  ^  =  .2004ds.  For  the  three  engines  10,  ^  and  60  in.  diam.,  this  would 
give  for  area  of  slides,  A  =.  *iO,  ]80  and  500  sq.  in.,  respectively.  Whitham 
says:  The  normal  pressure  on  the  slide  may  be  as  high  as  600  lbs.  per  sq.  in., 
but  this  is  wht^n  there  is  good  lubrication  and  freedom  from  dust.  Station- 
ary and  marine  engines  are  usually  designed  to  carry  100  lbs.  per  sq.  in., 
and  the  area  in  this  case  is  reduced  from  60j(  to  609(  by  grooves.  In  locomo- 
tive engines  the  presMure  ranges  from  40  to  50  lbs.  per  sq.  in.  of  slide,  on  ac- 
count  of  the  inaccessibility  of  the  slide,  dirt,  cinder,  etc. 

There  is  perfect  agreement  among  the  authorities  as  to  the  formula  for 
area  of  the  slides,  A  =  P  tan  9  ■*•  p^\  but  the  value  given  to  po,  the  allow- 
able pressure  per  square  inch,  ranges  all  the  way  from  35  lbs.  to  600  lbs, 


The  Connectms-rod*  Ratio  of  length  of  connrcting-rod  to  length 
of  s/ro/lce.— Experience  has  led  generally  to  the  ratio  of  2  or  2^  to  I ,  the 
Iatt«r  giving  a  long  and  easy- working  rod,  the  former  a  rather  short,  but 
yet  a  manageable  one  (Thurston).  Whitham  gives  the  ratio  of  from  2  to  4!^ 
and  Marks  from  2  to  4. 

Dimension*  of  the  Connecting-rod.— The  calculation  of  the  diameter  of 
a  connecting-rod  on  a  theoretical  basis,  considering  it  as  a  strut  subject  to 
both  compressive  and  bending  stresses,  and  also  to  stress  due  to  its  inertia, 
in  high-speed  engines,  is  quite  complicated.  See  Whitham,  Steam-engine 
Design,  p.  217;  Thurston,  Manual  of  S.  E.,  p.  100.  Empirical  formulas  are  as 
follows:  For  circular  rods,  largest  at  the  middle,  D  =  diam.  of  cylinder,  /  = 
length  of  connecting-rod  in  inches,  p  =  maximum  steam-pressure  per  sq.  in. 


(1)  Whitham,  diam.  at  middle,  d"  =  0.0372  V  Dl  Vp. 

(2)  Whitham,  diam.  at  necks,  d"  =  1.0  to  1.1  x  diam.  of  piston-rod. 

(3)  Sennett,  diam.  at  middle,  d"  =^Vp, 

00 

(4)  Sennett,  diam.  at  necks,  df^  =^  Vp. 

(5)  Marks,  diam.,  d"  «  0.01792>  Vp.  if  diam.  is  greater  than  1/24  length. 

(6)  Marks,  diam.,  d"  »  0.02768  V  Dl  Vp  If  diam.  found  by  (6)  is  lees  thao 
1/84  length. 

(7>  Thurston,  diam.  at  middle,  d"  =  a  yDLVp  ■\- C,  D  \n  inches,  L  in 
feet,  a  =  0.15  and  C  s  H  inch  for  fast  engiues,  a  =■  0.06  and  C  =  %  inch  for 
moderate  speed. 

(8)  Seaton  says:  The  rod  may  be  considered  as  a  strut  free  at  both  ends, 
and,  calculating  Its  diameter  accordingly, 

diameter  at  middle  =  V^('+*«r«) 

4o.O 

where  R  s  the  total  load  on  piston  P  multiplied  by  the  secant  of  the  maxi- 
mum angle  of  obliquity  of  the  connecting-rod. 

For  wrought  iron  and  mild  steel  a  is  taken  at  1/9000.    The  following  are 
the  values  of  r  in  practice: 
Naval   engines—Direct^acting  r  =  0  to  11; 

"  "        Betum  connecting-rod      r  =  10  to  13,  old; 

••  ••  "  ••  r  =  8  to  9,  modem; 

"  •«        Trunk  r  =  11.5  to  18. 

Mercantile  "        Direct -acting,  ordinary     r  =  12. 
-  •'  -  long  stroke  r  =  13  to  1«. 

(9)  The  following  empirical  formula  is  given  by  Seaton  as  agreeing  closely 
with  gcKXl  modern  practice: 

Diameter  of  connecUng-rod  at^  middle  =j  \lK-i-  4,  l_=.  length  of  rod  Iq 
iDcheB,  and  K»  0.01>  VeiXective  load  on  piston  in  pounds. 


800 


THB  t^TBAM-BKOtKB. 


The  diam.  at  the  endn  mav  be  0.87S  of  the  diam.  at  the  middle. 

Se&ton*B  empirical  formula  when  translated  into  tei-ms  of  D  and  />  is  the 

same  as  the  second  one  by  Marks,  viz.,  d"  s  0.02758  V  Dl  VpT  Wbiihara*s 
(1)  is  also  pracilcallj'  the  same. 

(10)  Taking  Seaton*s  more  oomplex  formula,  with  length  of  connecting- 
rod  s  8.5  X  length  of  sti'oke^and  r  s  12  and  16,  respectiTd^r,  li  niduoM  u>: 
Diam.  at  middle  s  .08894  f'P  and  .08411  VP  for  short  and  long  stroke  eo- 
ginea,  respectiTely. 

Applying  the  above  formulas  to  the  engines  of  our  list,  we  have 

IHameter  of  Oonneetlnff-rods. 


Diameter  of  Cylinder,  inchee. . 


Stroke,  inches 

Length  of  connectiog-rod  I 

(8)d"  =  ^  i^  =  .0188DVp.,. 
(6)  <l"a.0I79D  Vp 


(6)  d"  =5  .02758  l/i)Z  Vp 

<7)  d"  «  0.15V'x>i;  Vp  +  H 

aiyd"  ^omVdlVp  +  H 

(9)d"«.08  4^. 

CO)  d'*  a  .08804  VP;  .08411  VP.  . 


Average . 


10 


1.88 
1.79 


8.87 


2.07 
8.0B 


2.14 


8.64 
8.67 
8.14 


5.46 
5.87 


7.00 


7.97 
6.09 


60 

150 


5.46 


5.85 


5.65 
7.97 
6.41 


2.84     8.86     6.38     6.87    10.68    I0.S6 


SO 


48 
180 


9.09 
8.95 


11.11 


18.29 
10.16 


06 
810 


9.09 


9.51 


FormuUe  6  and  6  (Marks),  and  also  formula  10  (Seaton),  give  the  larger 
diameters  for  the  long-stroke  engine;  formnle?  give  the  larger  diameters 
for  the  short-stroke  engines.  The  average  figures  show  but  little  difTereitce 
in  diameter  between  long-  and  short-stroke  engines;  this  is  what  might  be 
expected,  for  while  the  connecting-rod,  considered  simply  as  a  column, 
would  require  an  increase  of  diameter  for  an  Increase  of  length,  the  load 
remaining  the  same,  yet  in  an  engine  generally  the  shorter  the  connecting- 
rod  the  greater  the  number  of  revolutions,  and  consequently  the  greater  the 
strains  <iue  to  inertia.  The  influences  tending  to  increase  the  diameter 
therefore  tend  to  balance  each  other,  and  to  render  the  diameter  to  some 
extent  Independent  of  the  length.  The  average  figures  correspond  nearly 
to  the  simple  formula  d"  =  .021 D  Vp.  The  diameters  of  rod  for  the  three 
diameters  of  engine  by  this  formula  are,  respectively,  8.10,  6.80,  and  10.50  in. 
Since  the  total  pressure  on  the  piston  P  s  .7864I>^,  the  formula  is  equiva- 
lent tod'  =  .0387  vTi 

Connectlni^-rod  End*.— For  a  connecting-rod  end  of  the  marine 
type,  where  the  end  is  secured  wiih  two  bolts,  each  bolt  should  be  propor- 
tioned for  a  safe  tensile  strength  equal  to  two  thirds  the  maximum  puU  or 
thrust  in  the  connecting-rod. 

The  cap  is  to  be  proportioned  as  a  beam  loaded  with  the  maximum  pull 
of  the  connecting-rod,  and  supported  at  both  ends.  The  calculation  should 
be  made  for  rigidity  as  well  as  strength,  allowing  a  maximum  deflection  of 
1/100  inch.  For  a  strap-and-key  connecting-rod  end  the  strap  is  designed  for 
tensile  strength,  considering  that  two  thirds  of  the  pull  on  the  connecting- 
rod  may  come  on  one  arm.  At  the  point  where  the  metal  is  8k>tted  for  the 
key  and  gib,  the  straps  must  be  thickened  to  make  the  croes-seciion  equal 
to  that  of  the  remainder  of  the  strap.  Between  the  end  of  the  strap  and  the 
slot  the  strap  is  liable  to  fall  in  double  shear,  and  sufficient  metal  must  be 
provided  at  the  end  to  prevent  such  failure. 
•  The  breadth  of  the  key  Ih  generally  one  fourth  of  the  width  of  the  strap, 
and  the  length,  parallel  to  the  strap,  should  be  such  that  the  cros»«ection 
will  have  a  shearing  strength  equal  to  the  tensile  strength  of  the  section  of 
the  strap.    The  taper  of  the  key  is  generally  about  %  inch  to  the  foci. 


DDCSKSIOirS  OF  PABT8  OF  BKGIKES. 


801 


Tftper#d  OonneetiBC-ro^to.— In  modem  htehnnMed  MKrlnw  it  fti 
customary  to  make  the  oonnectlng-rodH  of  reotanguiar  instead  of  eireular 
section,  the  sideii  beius  parallel,  and  the  depth  iDCreoelnir  refnilarly  from 
the  croMhead  end  to  the  crank-pin  end.  Aooordlng  to  Oraahor«  the  bending 
action  oo  the  rod  due  to  its  inertia  is  f^reateet  at  6/10  the  ten^h  from  the 
croashead  and,  and,  according  to  this  theory,  that  is  the  point  at  which  the 
section  should  be  fip-eatest,  although  in  praotioe  the  section  is  made  greatest 
at  tlie  crank-pin  end. 

Professor  Tliurston  furnishes  the  author  with  the  following  rule  for  tapered 
connecting- rod  of  rectangular  section:  Take  the  section  as  computed  by  tho 

formuU  d"  =  O.l  VDL  Vp  +  8/4  for  a  circular  section,  and  for  a  rod  4/8  the 
actual  lengfth,  placing  the  computed  section  at  2/8  the  lengrth  from  the  small 
end,  and  carmng  the  taper  straight  through  this  fLsed  section  to  the  large 
end.  This  brings  the  computed  section  at  the  surge  point  and  makes  It 
heavier  than  tlie  rod  for  which  a  tapered  form  Is  not  required. 
Taking  the  above  formula,  multiplying  L  by  4/8,  and  changing  it  to  I  in 

Inches,  ft  becomes  d  =  1/80  ^Dl  Vp  +  8/4'^  Taking  a  recUngular  section 
of  the  same  area  as  the  round  section  whose  diameter  is  d,  and  making  the 
depth  of  the  section  h  =s  twice  the  thickress  f,  we  have  .7B54cl*  =  ht  =  2t*, 

whence  t  =  .e27d  =  .0209  f^DJ  Vp  +  .-*7",  which  is  the  formula  for  the  thick- 
ness or  distance  between  the  parallel  sides  of  the  rod.  Making  the  depth  at 
the  crosshead  end  s  1.5X,  and  at  2/3  the  length  s=  2t,  the  eqtdralent  depth  at 
the  crank  end  is  S.25t.  Applying  the  formula  to  the  ahorMiroke  engines  of 
our  examples,  we  have 


Diameter  of  cylinder,  inches. 

Stroke,  inches 

Length  of  oonnecting-rod  ■ 

Thickness,  i  »  .0809  VdI  Vp  +  .47  m, 

Depth  at  crosshead  end,  l,httz 

Depth  at  crank  end,  2^/...    


The  thicknesses  t,  found  by  the  formula  i  s  .0809  y^lVp  +  -47,  agree 
closely  with  the  more  simple  fornrala  t  s  .0]Z>  f^  +  .60'^  the  thicknesses 
'  Mtlated  by  this  formula  Doing  E 


6,£<l 


respectively  1.6,  8.6.  and  6.6  inches. 


Tl&e  Graiik"pln«- A  crank-pin  should  be  designed  (1)  to  avoid  heating, 
(2>  for  strength.  (8)  for  rigidity.  The  beating  of  a  crank-pin  depends  on  the 
prejisore  on  Its  rubbingsurface,  and  on  the  coeflQcient  of  friction,  which 
latter  varies  greatly  according  to  the  effecd  veneas  of  the  lubrication.  It  also 
depends  upon  the  facility  with  which  the  heat  produced  may  be  carried 
away:  thus  it  appears  that  locomotive  crank-pins  may  be  prevented  to  some 
degree  from  overheating  by  the  cooling  action  of  the  air  through  which  they 
peas  at  a  high  speed. 


Marks  glTes  I  a  .0000247/pJ^D*  «  1.08^ 


aH.P.) 


O) 


Whitham  gives  I  «  0.9075/  35J?^. (2) 

JLi 

In  which  I  ss  length  of  crank-pin  loumal  in  inches,  /  a  coefScfent  of  friction, 
which  may  be  taken  at  .06  to  .06  for  perfect  lubrtcatioo.  and  .08  to  .10  for  im . 
perfect;  p  s  mean  pressure  in  tbe  cylinder  in  pounds  per  square  inch;  D 
=  diameter  of  cylinder  In  inches;  H  a  number  of  single  strokes  per  minute; 
I.H.P.  =  indicated  horse-power;  L  =  length  of  stroke  in  feet.  These 
formulsd  are  independent  of  the  diameter  of  the  pin,  and  Marks  states  as  a 
general  law,  within  reasonable  limits  as  to  pressure  and  speed  of  rubbing, 
Uke  longer  a  bearing  is  mode,  for  a  s^ven  pressure  and  number  of  revolutions, 
the  cooler  it  will  work ;  and  its  diameter  Las  no  effect  upon  its  heating. 
Both  of  the  above  formula  are  deduced  empirically  from  dimensions  of 
crank-pins  of  existing  marine  engines.  Marks  savs  that  about  one-fourth 
the  length  required  for  crank -pins  of  propeller  engines  will  serve  for  the  pins 
of  skle-wheel  engines,  and  one  tenth  for  locomotive  enghies,  making  tho 


802  THB  BTEAM-BKGIinB. 

formula  for  looomotlTe  orank-plns  I  au  .00000847A»iVZ)*,  or  if  p  as  1B0«  / 
=  .06,  and  if  a  600, 1  s=  mSD». 

Whitham  recommends  for  preesnre  per  square  Inch  of  projected  area,  for 
naval  entwines  500  pounds,  for  mercbani  engmes  400  pounds,  for  paddle-wheel 
ensrines  800  to  QOO  pounds. 

Thurston  says  the  pressure  should,  in  the  steam-engine,  never  exceed  600 
or  600  pounds  ner  square  inch  for  wrought-iron  pins,  or  about  twice  that 
figure  for  steel.    He  gives  the  formula  for  length  of  a  steel  pin,  in  inches, 

l^PR-*-  600.000, (8) 

In  which  P  and  R  are  the  mean  total  load  on  the  pin  in  pounds,  and  the 
number  of  revolutions  per  minute.  For  locomotives,  the  divisor  may  be 
taken  as  500.000.  Where  iron  is  used  this  figure  should  be  reduced  to  800,000 
and  250,000  for  the  two  cases  taken.  Pins  so  proportioned,  if  well  made  and 
well  lubricated,  may  always  be  depended  upon  to  run  cool:  if  not  well 
formed,  perfectly  cylindrictd,  well  finished,  and  kept  well  oiled,  no  crank-pin 
can  be  relied  upon.  It  is  assumed  above  that  good  bronae  or  white-metal 
bearings  are  used. 

Thurston  also  says :  The  size  of  crank -pins  required  to  prevent  heating  of 
the  Journals  may  be  determined  with  a  fair  degree  of  precision  by  either  of 
the  formulas  given  below : 

'■^4^wF  <K«*ine,  18«9; C4) 

ita——crhmii*€n,isn)\ CO 

P7f 
I  ■  jjgOQQQ  (Van  Bupen,  1866) (B) 

The  first  two  formulsB  give  what  are  considered  by  their  authors  fair  work- 
ing proportions,  and  the  last  gives  minimum  length  for  iron  pins.  C^- 
velocity  of  rubbing-surface  in  feet  per  minute.) 

Formula  (1)  was  obtained  by  observing  locomotive  practice  in  which  great 
liabflity  exists  of  annoyance  by  dust,  and  great  risk  occurs  from  inaccHisi- 
bility  while  running,  and  (2)  by  observation  of  crank-pins  of  naval  screw, 
engines.    The  first  formula  is  therefore  not  well  suited  for  marine  practice. 

Steel  can  usually  be  worked  at  nearly  double  the  pressure  admissible  wiUi 
iron  runninff  at  similar  speed. 

Since  the  length  of  the  crank-pin  wOl  be  directly  as  the  power  expended 
upon  it  and  inversely  as  the  pressure,  we  may  take  it  aa 

'=-^4^- CO 

in  which  a  Is  a  constant,  and  L  the  stroke  of  piston,  in  feet.  The  vahiea  of 
the  constant,  as  obtained  by  Mr.  Skeel,  are  about  as  follows:  a  s=  0.04  where 
water  can  be  constantly  used;  a  =  0.016  where  water  is  not  generallv  used; 
a  =  0.05  where  water  is  seldom  used;  a  =  0.06  where  water  Is  never  needed. 
Unwin  gives 

,        LH.P.  ^ 

IssO (8 

r     » 

in  which  r  s  crank  radius  hi  inches,  a  s  0.8  to  a  s  0.4  for  iron  and  for  marine 
engines,  and  a  =  0.066  to  a  s  0.1  for  the  case  of  the  beet  steel  and  for  loco- 
motive work,  where  it  is  often  necessary  to  shorten  up  outside  pins  as  much 
as  possible. 

J.  B.  Stan  wood  (Bng^g,  June  12, 1891),  in  a  table  of  dlmensionaof  parts  of 
American  Corliss  engines  from  10  to  80  inches  diameter  of  cylindn',  gives 
sises  of  crank-pins  which  approximate  closely  to  the  formula 

Z  =  .275iy'  +  .5in.;    d  =  .f^D" (9) 

By  calculating  lengths  of  iron  crank-pins  for  the  engines  10. 80.  and  50  inches 
diameter,  long  and  Bnort  stroke,  by  the  several  formuhe  above  given,  it  ia 
found  that  there  is  a  great  difTerence  in  the  results,  so  that  one  formula  in 
certain  eases  gives  a  length  three  times  as  great  as  another.  Nos.  (4),  (5).  and 
^fi)  give  lenf^bs  much  greater  than  the  others.  Marks  (1),  Whitham  (*2), 
Thurston  (7),  /  =  .06 1.HJP.  -<-  £,  and  Unwin  (8),  I  =  0.4  IH.P.  -i-  r,  give  re- 
Wits  which  agree  more  closely. 


Tl 


1)IHBNSI0I^8  OF  PARTS  OF  EKGIKE8. 


803 


The  cakmlated  leiiKths  of  iroD  crank-pins  for  the  tev&nd  cases  by  formulsB 
U>«  (^),  (j)t  aiKl  C8)  areas  follows: 

I«enstli  of  Cimnk-pins. 


Diameter  of  cjlinder D 

Stroke L(ft.) 

Revolutions  per  minute R 

Horse-power l.H.P. 

Maximum  pressure it)s. 

Mean  pressure  oer  cent  of  max 

Mean  pressure.. P. 

Length  of  crank-pio 

<1)  Whitham,  I  =  .9075  x  .06  l.H.P. -»-  L. 
(2)  Marks,       I  =  l.aiS  X  .05 1.H.P.-f-  L. 

(7)  Thurston,  I  =  .06  l.H.P.  -*-L 

(8)Unwin,       1  =  .4  l.H.P. -f-r 

i8)       »*  l=.8LH.P. -f-r 

Avera<te 

(8)  Unwin,  best  steel,  I  =  .lULZ-  . . 

PR 
(S)  Thurston,  steel,     Z  =  g^^^.... 


10 

1 
350 

50 
7,854 

48 

8.18 
2.59 
8.00 
8.88 
8.50 


8.78 


10 
3 
185 
60 
7,ffi4 
4.! 
8,899 

1;09 
1.80 
1.50 
1.87 
1.86 


1.86 


80 

450 
70,686 
88.3 
88,888 

8.1 
9.34 
10.80 
18.0 
9.0 


9.86 


80 

5 

65 

450 

0.686 

88.8 

88,888 

4.06 

4.67 

5.40 

6.0 

4.5 


4.98 


60 
4 

90 

1,850 
1M,SM 

80 
58,005 

14.18 
16.88 
18.75 
£0.88 
15.68 


17.18 


50 

8 

45 

1.850 
1M,S60 

80 
58,905 

7.09 
8.11 
9.88 
10.48 

7.81 


856 


.83 
1.87 


8.0 
4.95 


1.5 
2.47 


5.81 
8.84 


2.61 
4.42 


The  calculated  lengths  for  the  long-stroke  engines  are  too  low  to  prevent 
excessivepressures.    See  **  Pressures  on  the  Crank-pina,"  below. 

The  Stren^li  of  the  Crank^pin  is  determined  substantially  as  is 
that  of  the  crank.  In  overhung  cranlcs  the  load  is  usually  assumed  as 
carried  at  its  extremity,  and,  equating  Its  moment  with  that  of  the  resist- 
ance of  the  pin, 

HPl  =  i/Satird;    and    d  : 


in  which  d  s=  diameter  of  pin  in  inches,  P  =  maximum  load  on  the  piston, 
i  =  the  maximum  allowable  stress  on  a  square  inch  of  the  metal.    For  iron 
it  may  be  taken  at  9000  lbs.    For  steel  the  diameters  found  by  this  formula 
mav  be  reduced  10^.    (Thurston.) 
Unwin  gives  the  same  formula  in  another  form,  vis.: 


=  f  ^f «  = 


^5* 


the  last  form  to  be  used  when  the  ratio  of  length  to  diameter  is  assumed. 
For  wrought  iron,  t  =  6000  to  9000  lbs.  per  sq.  in., 

//^  =  .0947  to  .0827;      i/S  =  .0291  to  .0238. 

For  steel,  t  =  9000  to  18,000  lbs.  per  sq.  In., 

//^  a  .0837  to  .0723;      j/^  =  .0388  to  .0194. 

Whitham  gives  d  =  0.0827  l^M  =  2.1058//'  ^  j:^'^'  for  strength,  and 

d  =  0.405  yPif  for  rigidity,  and  recomm^^nds  that  the  diameter  be  calculated 
by  both  formulas,  and  the  largest  result  taken.  The  first  is  the  same  as 
Unwin''s  formula,  with  t  taken  at  9000  lbs.  per  sq.  in.  The  second  is  based 
Upon  an  erroneous  assumption. 


804 


THK   BTBAM-BNGIHB. 


Marks,  calouUting  the  diameter  for  rigidity,  gives 


p  s=  mazimum  steam-pressure  In  pounds  ner  sQtiare  inoh,  D  ts  diamater  of 
cjlinder  In  Inohes,  Z^s  leQRth  of  stroke  in  feet,  N^  number  of  single  strokes 
per  minute.  He  says  there  Is  no  need  of  an  iiiyestigatioii  of  the  strength  of 
a  orank-pin,  as  the  condition  of  rigidity  gives  a  great  excess  of  strength. 

Marks**  formula  Is  based  upon  the  assumption  that  the  whole  load  may  be 
concentrated  at  the  outer  end,  and  cause  a  deflecttoB  of  .01  ineh  at  that 
point. 

It  is  serviceable,  he  says,  for  steel  and  for  wrought  iron  alike. 

Using  the  average  lengths  of  the  crank-plns  a&eady  found,  wa  have  the 
following  for  our  six  engines  : 

Ptametar  of  Crank-plns. 


Diameter  of  cylinder 

Strolce,  ft 

length  of  orank-pin. . , . . . 

UnwiUfda  aV — T- 

Marks,  d  ->  .066  VW^-- 


10 

1 

8.W 

10 

80 

«1l 

80 

8 

4.98 

50 

4 
17.13 

2.89 

1.82 

7.84 

5.98 

18.40 

1.88 

.85 

6.44 

8.T8 

19.41 

50 

8 

8.5i 

9.84 
7.80 


Preaanrea  on  tlie  Crank^plna.— If  we  take  the  mean  prassura  upon 
the  cranl(-plii  =  mean  pressure  on  pt«con,  neglecting  the  effect  of  the  vary* 
ing  angle  of  the  connecting-rod,  we  have  the  following,  using  the  average 
lengths  already  found,  and  the  diameters  according  to  unwin  and  Marka; 


Engine  No. . 


Diameter  of  cylinder,  inches 

Stroke,  feetw 

Mean  pressure  on  pin,  pounds. , . . 

Proj«(^ed  sji^M  of  pin,  Unwhi 

'     Marks 

Pressure  per  square  inch,  Unwin.. 
"     Marks.. 


1 

2 

a 

4 

5 

10 

10 

80 

80 

50 

1 

8.899 

..4. 

nj^ 

5 
88.888 

4 
58,905 

tt.l» 

286 

78.4 

28.7 

218.8 

8.78 

1.16 

63.5 

18.6 

218.5 

580 

1.806 

815 

796 

277 

878 

8,845 

860 

1.228 

277 

The  results  show  that  the  application  of  the  formulse  for  length  and  diam- 
eter of  cranlc-pins  give  quite  low  pressures  per  square  Inch  of  proJect«*d 
area  for  the  short-stroke  high-speed  engines  or  the  larger  sizes,  but  too  liigh 

Iiressures  for  all  the  other  engines.  It  is  therefore  evident  that  after  oaleu- 
ating  the  dimensions  of  a  crank-pin  according  to  the  f or niulsB  given  ihatthe 
resultR  Khould  be  modified,  If  necessary,  to  bring  the  pressure  per  square 
inch  down  to  a  reasonable  figure. 

In  order  to  bring  the  pressures  do^'U  to  500  pounds  per  square  Inch,  we 
divide  the  mean  pressures  by  500  to  obtain  the  projected  a'^a,  or  product 
of  length  by  diameter.  Making  /  =  I.5d  for  engines  Nos.  1,  2,  4  and  6,  the 
revised  table  for  the  six  engines  is  as  follows : 

Engine,  No 1        2 

Length  of  crank-pin,  inches 8.15    8.15 

Dianierer  of  cranK-pin 2.10    2.10 

Croaahead-pln  or  Wrlat-pln.— Whitham  says  the  bearing  surface 
for  ihe  wrisi-pin  is  found  by  tlie  funnula  for  orank-pin  design.  Beaton  says 
the  diameter  at  tlie  middle  must,  of  courne,  be  sufficient  to  withstand  the 
bt^ndinf?  ticlion,  and  generally  from  this  cause  ample  surfsoe  is  providttd  for 
go(Kl  working;  but  in  any  case  the  nrt^a,  calculated  by  multiplying  the  diam- 
eter of  thelournal  by  Us  length,  should  be  such  that  the  pressure  does  not 
exceed  I'JOO  lbs.  per  sq.  in.,  taking  the  maximum  load  on  the  piston  as  the 
total  pressure  on  It . 

Fur  small  engines  with  the  gudgeon  shrunk  Into  the  Jaws  of  the  connect- 


8        4         5 

8 

9.86    8.37    17.19 

18..30 

7.84    6.58    12.40 

8.87 

DIMENSIONS  OJT  PAXtS  OV  HUTGINBa.  806 

iBs^ro^  «d4  whtUm  fa  Wnmm  fttt«f  hil»  A  KMM  la  t 

secured  by  a  wrought-  Iron  cap  amA  tw»  bo&ta,  f 

IHameter  of  gudxeoo  m  1.25  x  dtem^  of  pbloB-rodL 
length  of  gudgeon  m  !,4  X  otasa.  of  piaton-fo^ 

If  tlM  proMUTO  on  the  seotfon,  as  oalmkiUd  hr  imMtphlng  leoBfb  bf 
dianaeCer,  eacceeda  1900  lbs.  per  so.  Ii>..  thto  )eit|tli  ebould  be  mcreageq. 

J.  B.  Staawood,  ta  Ms  ^^Ready  Beftsrenee^  book,  gif«e  fbr  feacth  of 
eroesbead-pla  0.89  to  •.<  dSam.  of  wislfMi,  and  diam.  s  9.18  feoO.t  dfim.  of 
platan.  8laea  ke  gi«*ea  tor  dlaai.  of  pfateo-pod  O.M  ta  0. IT  dians.  of  pfekm, 
bis  dimeoslons  for  diameter  and  length  of  erosBkeatf-piB  are  about  1.115  aad 
1 .8dlam.  of  jBieto»-rod  peapeoil vely.  Takfog  the  mtahanm  alknraUts  preea- 
ure  a*  IfOO  Ma  per  sq.  In.  and  maklng^  tlie  lenglh  of  the  ereaAead-pIn  s* 
4/S  of  its  diameter,  we  have  d  m  f'7^40,  t »  '/P  -*>  80,  in  whkh  J^ac  max* 
Imum  total  foad  on  piston  in  tbs.,  d  s  diam.  and  I  b  length  of  pin  In  fnchea. 
For  the  engines  of  our  example  we  haves 

Diameter  of  piston,  inches • «.,••  10  80  60 

Maximum  load  on  piBtoii,  lbs TB64  70,686  196,350 

DfanMter  of  csgsshead-pte,  inehes ASS  8.6i  11.68 

Length  of  crosshead-pin,  inches SLQS  8.86  14.17 

Stanwood'S  rule  givfs  diameter,  inches 1.8  to 2  iw4(o8  8.8  talO 

Skanwood's  TOlto  gives  length,  inctea. t.5to8  7.5ta8  l».6tol5 

fitanwood's  largsst  dineasions  glva  piMHiiw 

per8q.in.,lbs 1808  1860  1809 

Which  pressures  aro  graaler  than  the  naactannm  sJlowed  by  flantow. 

THe  Crank-artn.— The  crank -arm  is  to  be  treated  as  a  lever,  so  that 
if  a  is  the  thickness  in  direction  paraLel  to  the  shaft-axis  and  8  its  breadth 
at  a  section  or  tnehes  from  th»  crank-pin  centre,  then,,  bending  moment  Jf 
ai  that  sectioa  s  Pv,  F  being  the  thrust  of  the  eonneetiag-rod,  and  /  the 
safe  straini  per  square  fach. 

If  a  orank-arm  weraooDstruetad  ao  Ihat  hvaried  as  V^Ca*  gtven  hj  the 
above  rule)  it  would  be  of  such  a  curved  form  as  to  be  Inconvennnt  to  man* 
ufacture,  und  oonsequeotly  ib  ia  customarv  ia  practice  to  find  the  maxi* 
miroi  valus  of  h  and  draw  tangiBnt  lines  to  the  curve  at  the  points  ;  thaas 
lines  are  generally,  fbr  the  same  reason,  tangpsntial  ta  Ui*  boss  of  the  crank- 
arm  at  the  shaft. 

The  shearing  strain  Is  the  same  thronghont  the  cmak-annt  and,  conse- 
quently, ia  large  compared  with  the  bendiDg  strain  close  to  the  crank -ulu ;, 
and  so  it  ia  not  sufficient  to  provide  there  only  for  bending  strains.  ^nt« 
8ectk>a  at  this  polot  sbonld  be  sueb  that,  h»  addition  to  wfas(t  is  gfven  by  tnti 
calculation  from  the  bending  moment,  there  is  an  extra  sqaarw  inch  tfor 
every  8000  lbs.  of  thrust  on  the  connecting-rod  (3eaton>. 

The  length  of  the  boas  h.  into  which  the  shaft  is  fitted  is  from  8.7S  to  1.0 
of  the  diameter  of  the  shaft  A  and  its  thickness  e  must  be  calculated  from 
the  twisting  strain  Ph.  (L  s  length  of  crank.) 

For  AMfeftent  valnea  of  length  off  boss  Jt,  the  followter  ^^ahiet  of  thickness 
of  boss  e  are  gtven  by  Beaton: 

When  A  =  P,  then  e  b  O.SS  D;  If  steel,  0.8. 
/»  s  0.9  P,  thea  e  a  aa8  D,  if  steel,  OJBS. 
h  s  0.8  D,  then  e  s  0.40  D,  If  steel,  1^88. 
h  s  a?  JO.  then  e  s  0^41  i),  U  steel,  M4. 

The  crank-eye  or  boss  into  which  the  pin  t»  llttei  As«tt  hear  lb»  sama 
relation  to  the  pin  that  the  boss  does  to  the  shaft. 

The  diameter  of  the  shaft-end  onto  wfakh  the  crank  is  fitted  should  be 
1.1  X  diameter  of  shaft. 

Thurston  says;  The  emplrkal  proportions  adapted  by  huUdeva  wHt  aonv 
monly  be  found  to  fall  well  within  the  caleutated  safe  margin.  These  pro- 
portions are,  from  the  pmotlce  of  suocessf at  designefs,  about  aafbflows : 

For  the  wrought-lron  crank,  the  hub  is  1.79  to  1.8  times  the  least  diameter 
of  that  part  of  the  shaft  carrying  full  load ;  the  eya  ia  2.0  to  8.85  the  diame- 
ter of  the  inserted  portion  of  the  pin,  and  thair  depths  arc^  for  the  hub,  1.0 
to  Ui  tha  diameter  of  shaft,  and  for  the  eye,  lJS8to  1.8  the  diameter  of  pint 


804  THE   STEAM-BKOIMTK. 

Marks,  caloiiUting  the  JIametar  for  rigidity,  gives  / 


i 


d  m  O.0a6i^pPZ>«  r.  0.04"3 


Ids  per  aqnarf  '^if  £f    fl 
of  anliivwjf  f;  I?     ^ 


p  =  mazimuTQ  Btenm-pretmire  In  pounds 
cylinder  in  incties.  L  3  length  of  stroke  ' 
per  minute.    He  says  there  is  po  need  c 

a  crank-pin,  as  the  oondiUon  of  rigidity  „ 

Marks's  formula  Is  based  upon  the  assumptir^  ^^i  fjt  ftf     '■ 
concentrated  at  the  outer  end,  and  cause  aJTMl  ?P  H     ll 

It  is  serviceable,  he  says,  for  steel  and  taJK^^       It 

Using  the  average  lengths  of  the  cr"-^=^''L#;        'f 

following  for  our  Hiz  engines :  pJH  1    4 


c  engines : 
Ptamet«r  of. 


jreof 
jepth 
we. 
jotU 
owfor 
of  one 
iTesan 

jg  to  the 
Are  as  f  ol 


Diameter  of  cylinder </ 

Stroke,  ft ,  /^ 

length  of  crank-pin......    /    rfi- 


Unwin,  d 
Harks,  d 


.oe^Vpi'D*..,., 


Pre««iiro0  on  the 

the  cranlc-pin  =  mean    , 
Ing  angle  of  the  conr 
lengths  already  four 

Engine  No. .  /   ^uce 

-— '  ^•entre 

Diameter  of  cyl'  ,    

Stroke, feet.,   ^k-arm 

Mean  preasur'    

Projected  a*-,-^th,  

Pressure  r/'    1/  ^^ 
"       />*y  flOOOa 

i 


.88 

37,149 
2.05 

3.48 
16,493 


1.39 
6.23 
1.76 


80,661 
2.60 


4.55 


16,498 


1.06 


7.T0 

6.16 
808 
13,86 
6.87 

2.94 


788,149 
6.78 


0.64 


7.81 


4O.686 
5.68 


9.7t) 

7.76 
8.88 
17.46 
4.46 


1,848,489 
7.28 

18.0 

894,428 

6.01 


60 

48 

196,350 
12.40 


12.85 

10.04 
5.02 

22.59 
9.92 

4.46 


8,479,822 
9.41 

15.7 
2,434,740 

13.13 


60 
96 

196.850 
8.87 


15.82 

12.65 
6.82 

JB8.47 
7.10 

8.55 


7,87i,en 

11.87 

21.0 

1,741,685 

9.89 


'   ^  Shaft. -TTwIatlng  BertaUince.— From  the  general  forrnula 
^torsion,  we  have:  r=  ^  d*8  =  .19635d»S,  whence  d  :=  1/  — .  in  which 

fss  torsional  moment  in  inch-ixmnds,  d  =b  diameter  in  inches,  and  5  =  the 
gearing  resistance  of  the  material  in  pounds  per  square  inch 

If  a  constant  force  P  were  applied  to  the  crank-pin  taneentiaJlv  to  Its  path, 
tke  work  done  per  minute  would  be  <-  &  .7 


PXi  X  js  X  fi- 88,000XI.H.P.. 


in  which  L  m  length  of  crank  in  Inches,  and  i?  s  revs,  per  min,,  and 
mean  twisting  moment  T  m  i:^i  x  63,025.    Therefore 


tbe 


•/bAT  »/ 


821,42?I.H.P.   / 
B8 


DIMENSIONS  OF   PARTS   OF   ENGINES. 


807 


take  the  f  onn 


wf: 


XF^ordssa 


V^' 


^  factors  that  depend  on  the  strength  of  the  material 

'«fety.    Taking  S  at  46,000  pounds  per  square  inch  for 

^  000  for  steel,  we  have,  for  simple  twisting  by  a  uni- 


8 

B7.1 
42.8 


10 

71.4 
68.5 


6 
a- 8.8 
a  as  8.0 


6  8  10 
8.5  8.86  4.15 
8.18  8.6     8.77 


'  strength  of  wrought  iron  9000  lbs.,  steel 

'yes  a  s:  8.804  for  wrought  iron,  2.877  for 

on,  for  crank-azlee  of  wrought  iron, 

,  /,  the  safe  strain  per  square  inch,  should 

Lhe  shafts  are  more  tnan  lO  inches  diameter, 

irom  the  ingot  and  of  good  materials,  will  ad- 

for  small  shafts,  and  10,000  lbs.  for  those  abore 

ae  allowance  between  large  and  small  shafts  is  to  com- 
.lective  material  observable  in  the  heart  of  large  shafting, 
.anmering  failing  to  affect  it. 

*  /  I  H  P 
.aula  dm  at/  ■ '    '  *  assumes  the  tangential  force  to  be  nniform 

.  chat  It  is  the  only  acting  force.  For  engines  In  which  the  tangential 
.orce  varies  with  the  angle  between  the  crank  and  the  oonnectloc-rod,  and 
with  the  variation  in  steam-pressure  In  the  cylinder,  and  also  is  influenced 
by  the  inertia  of  the  reciprocating  parts,  and  In  which  also  the  shaft  may  be 
subjected  to  bending  as  well  as  torsion,  the  factor  a  must  be  increased,  to 
provide  for  the  maximum  tangenlial  force  and  for  bending. 

Seaton  gives  the  following  table  showing  the  relation  between  the  mazi* 
fflum  and  mean  twisting  moments  of  engines  working  under  various  condi- 
tions, the  momentum  of  the  moving  parts  being  neglected,  which  is  allow* 
able: 


Max. 

Steam  OatK>ff 

Twist 

Divided 

by 

HMO 

Twist, 

Onbe 
Root 

at 

of  the 

Moment 

Single^srank  expansive...  

0.8 

8.686 

1.88 

0.4 

8.126 

1.29 

M                             M 

0.6 

1.886 

1.28 

M                              •• 

0.8 
0.S 
0.8 

1.098 
1.616 
1.415 

1.20 

Two^Under  expiuulve^  mnls  ait  90*. . . . 

1.17 
1.18 

*                              M                                 ••                   ^^ 

0.4 

1.296 

1.09 

M                               M                                 M                   ^^^^ 

0.5 

1.856 

1.06 

•                                 MM 

0.6 

1.27D 

1.06 

M                             M                                M 

0.7 

1.829 

1.10 

M                             U                                U 

0.8 

1.867 

1.11 

Three^syUnder  oompound,  cranks  120*. . . . 

h.p.O.M.p.0.66 

1.40 

1.12 

I.  p.  cranks    1 
opposite  one  at- other,  and  h.p.  midway  i 

M                  M 

1.26 

1.06 

Seaton  also  gives  the  following  rules  for  ordinary  practice  for  ordinary 
two-cylinder  marine  engines: 


•  /T  H  p  • 

Diameter  of  the  tonnel-8baft8Bi^-^~-X.F;  or  04 


806 


tBK  STSAH-ElTGtinL 


The  web  fa  made  0.7  to  0.7S  the  width  of  adJoooDt  hub  or  ^ye,  AnA  Is  gireik  4 
depth  of  0.6  to  0.0  that  of  adjacent  hub  or  eye. 

For  the  cast-iron  crank  the  hub  and  eye  are  a  little  laraer,  rangini^  in 
diameter  respectlTely  fi^m  1 .8  to  2  and  from  2  to  2J3  times  tBe  diameters  of 
shaft  and  pin.  The  flanges  are  made  at  either  end  of  nearly  the  full  depth 
«C  hub  or  eye.    Cast-iron  has,  however,  fallen  very  generally  into  disuee. 

The  Orahk-shaft  is  usually  enlar^  at  the  seat  of  the  crank  to  about  1.1 
its  diameter  at  the  Journal.  The  size  should  be  nicely  adjusted  to  allow  for 
the  shrinkage  or  forcing  on  of  the  crank.  A  difference  of  diameter  of  one 
fifth  of  i%,  Will  usually  suffice :  and  a  common  rule  of  practice  giyem  an 
allowance  of  but  one  half  of  this,  or  .001. 

The  formulSB  given  by  diiiterent  writers  for  crank-arms  practically  agree, 
since  they  all  consider  the  crank  as  a  beam  loaded  at  one  end  and  fixed  at 
the  other.  The  relation  of  breadth  to  thickness  may  vary  according  to  the 
taste  of  the  designer.  Calculated  dimensions  for  our  six  engines  are  as  fol 
lows: 

IMmeiistons  of  €irank-anns. 


Diam.  of  cylinder,  ins. . . 

Stroked,  ins 

Max.  pressure  on  pin  P, 

(approx.)lbe 

Diam.  crank-pin  d 

I>iam.shaft,ai 

(a  B  4.09,  6.09  and  5.22).. 
Length  of  boss,  .8Z>. . .. 
Thickness  of  boss,  »4D. 
DIam.  of  boss,  l.SD..... 
Length  crank-pin  eye,  .8d 
Thickness  of  crank- pin 

eye,.4d 

Max.  mom.  Tat  distance 

^8  —  UD  from  centre 

of  pfn, Inch-lbs... 
Thickness  of  crank-arm 

a  as  .75D 

Greatest  breadth, 

/"or" 
**y  9000O 

tfin-mom.  T^  at  distance 
d  from  centre  of  pinspd 

Least  breadth,       

/  6^0 
*»"y   9000a 


7854 
2.10 


V8.74 

8.19 
1.10 
4.93 
1.76 


S7,149 
2.05 

8.48 

16,493 

8.82 


7854 
8.10 


8.46 

2.rr 

1.39 
6.23 
1.76 

.88 


80,661 
8.60 

4.65 

16.498 

2.06 


80 
80 

70,686 
7.84 


7.70 

6.16 
8.08 
18.86 
5.87 

8.94 


788,149 
6.78 

9.54 

628,886 

7.81 


80 
GO 


70,686 
6.68 


9.70 

7.76 
8.88 
17.46 
4.46 

2.88 


1,818,489 
7.28 

18.0 

894,428 
6.01 


60 

48 

196,350 
12.40 


12.66 

10.04 
5.02 

22.S0 
9.92 

4.46 


8,479,822 
9.41 

16.7 

2,484,740 

18.18 


50 
96 


196,860 
8.87 


15.88 

18.65 
6.82 

88.47 
7.10 

8.56 


7.871,671 
11.87 

21.0 

i,74i.ea5 

9.60 


The  SliaDt.— TurlstinM;  BeslsUmce.— From  the  general  formula 


for  torsion,  we  have:  T=  r^  d*8  =  .19636d*S,  whence  d 

10 


=  (/ 


6.1  r 
a 


in  which 


T  s  torsional  moment  In  inch-pounds,  d  s  diameter  in  inches,  and  S  =  the 
shearing  resistance  of  the  material  in  pounds  per  square  inch. 

If  a  constant  force  P  were  apidied  to  the  crank-pin  tangentially  to  Its  path, 
the  work  done  per  minute  would  be 

PXLX^  X  ««  88,000XLH.P.. 

in  which  L  m  length  of  crank  In  inches,  and  R  ss  revs,  per  mln.,  and  the 
mean  twisting  moment  T  m   '    '    '.  x  68,025.    Therefore 


.       t/bAT        ^»/821,427I.H.P.   / 


DIMENSIONS  OF   PARTS   OF   ENGINES. 


807 


This  m*7  take  the  f onn 


d 


•V 


™f^.„*..//Ep. 


In  which  ^and  a  are  factors  that  depend  on  the  strength  of  the  material 
and  on  the  factor  of  safejnr.  Taking  8  at  46,000  pounds  per  square  Inch  for 
wrought  iron,  and  at  00^000  for  steel,  we  have,  for  simple  twisting  by  a  uni- 
form tangential  force. 


Factor  of  safety   «  6        «        8       10 

6       8       8       10 

Iron -P=86.?    42.8    67.1    71.4 

a- 8.8   8.5   8.85   4.15 

Steel ^-iS6.8   ».l    4S.8   68.5 

as  8.0   8.18  8.6     8.77 

Unwln,  taking  for  safe  working  strength  of  wrought  iron  9000  lbs.,  steel 
18,500  lbs.,  and  cast  iron  4600  lbs.,  gives  a  s  8.804  for  wrought  iron,  2.877  for 
steel,  and  4.16  for  cast  iron.  Thurston,  for  crank-azlee  of  wrought  iron, 
gives  a  s  4.15  or  more. 

Beaton  savs:  For  wrought  Iron,/,  the  safe  strain  per  square  inch,  should 
not  exceed  9000  lbs.,  and  when  the  shafts  are  more  tnan  \0  inches  diameter, 
8000  lbs.  Steel,  when  made  from  the  ingot  and  of  good  mateiials,  will  ad- 
mit of  a  stress  of  12,000  lbs.  for  small  shafts,  and  10,000  lbs.  for  those  abore 
10  inches  diameter. 

The  diiTerence  in  the  allowance  between  large  and  small  shafts  is  to  com* 
pensate  for  the  defective  material  observable  In  the  heart  of  large  shafting, 
owing  to  the  hammering  failing  to  affect  it. 

'  /  I  H  P 
The  formula  dmai/    '    '  *  assumes  the  tangential  force  to  be  nnif orm 

and  that  it  Is  the  only  acting  force.  For  engines  in  which  the  tangentisl 
force  varies  with  the  angle  between  the  crank  and  the  oonnectine-rod,  and 
with  the  variation  in  steam-pressure  in  the  cvlinder,  and  also  is  influenced 
by  the  inertia  of  the  reciprocating  parts,  and  In  which  also  the  shaft  may  be 
subjected  to  bending  as  well  as  torsion,  the  factor  a  must  be  increased,  to 
provide  for  the  maximum  tangential  force  and  for  bending. 

Seaton  gives  the  following  table  showing  the  relation  between  the  maxi- 
mum and  mean  twisting  moments  of  engines  working  under  various  condi- 
tions, the  momentum  of  the  moving  parts  being  neglected,  which  is  allow* 
able: 


Max. 

Steam  Cutoff 

Twist 

Divided 

by 

Mean 
Twist. 

Onbe 
Boot 

ItanrlptloooCEnglna 

at 

of  the 
BatkK 

Moment 

BlngloKsrank  expansive.... 

0.8 

8.095 

1.88 

0.4 

9.126 

1.89 

M                 ••        ^^ ^ 

0.6 

1.886 

1.28 

M                               •• 

0.8 
0.8 
0.8 

1.098 
1.016 
1.416 

1.20 

1.17 
1.18 

•                               ••                                 •• 

0.4 

1.896 

1.09 

••                               »                                 " 

0.5 

1.SS6 

1.06 

•                               ••                                  •• 

0.6 

1.270 

1.06 

••                               "                                  « 

0.7 

1.889 

1.10 

U                            U                               tA 

0.8 

1.867 

1.11 

TlireeHsylinder  compound,  cranks  190*. . . . 

h.p.0Al.p.0>M 

1.40 

1.12 

*•                  "               1.  p.  cranks    \ 
opposite  one  another,  and  h.p.  midway  f 

M                  M 

1.26 

1.06 

Beaton  also  gives  the  following  rules  for  ordinary  practice  for  ordinary 
fewoHsylinder  marine  engines: 


IMameter  of  the  tunnel-shafts  Bii/^^~-X^.  or  a\ 


808  -..  THE  STBAM-ENGINB. 

Compound  en^^es,  cranks  at  right  angles: 
Boiler  pressure  70  lbs.,  rate  of  expansion  6  to  7,  Jr*  ss  70,  a  cs  4.18. 
Boiler  pressure  80  lbs.,  rate  of  expansion  7  to  8,  i^  s  7S,  a  s  4.1d. 
Boiler  pressure  00  lb&,  rate  of  expansion  8  to  0,  JT*  «=  75,  a  &:  4.S2. 

Triple  compound,  three  cranks  at  120  degrees: 
Boiler  pressure  150  Ibe.,  rate  of  expansion  10  to  19,  JF*  b  fiS,  a  a  S.9& 
Boiler  pressure  160  lbs.,  rate  of  expansion  11  to  18,  ir*  ss  tf4,  a  s=  4. 
Boiler  pressure  170  lbs.,  rate  of  expansion  12  to  15,  JF*  s  07,  a  s  4.06. 

ExpansiTe  engines,  cranks  at  rlfi^t  angles,  and  the  rate  of  expansion  S^ 
boiler-pressure  60  lbs.,  J*  a  90,  a  =3  4.48. 

Siiigle-erank  compound  engines,  pressure  80  lbs..  JF*s  96.  a  b  4.66. 

For  the  engines  we  are  considering  it  will  be  a  very  liberal  allowance  for 
tmtio  of  maxlmnm  to  mean  twisting  moment  if  we  take  it  as  equal  to  the 
ratio  of  the  maximum  to  the  mean  pressure  on  the  piston.  The  factor  a, 
then,  in  the  formula  for  diameter  of  the  shaft  vriH  be  multiplied  by  the  cube 

root  of  this  raUo.  ori/—  «1.84.  a/~^  » l-A  •"^^/^  "  *'*•  ^^  *^ 

10,  80,  and  60-in.  engines,  respectively.  Taking  a  =  8.5,  which  corresponds 
to  a  sheariue  strength  of  60,000  and  a  factor  of  safety  of  8  for  steel,  or  to 
45,000  and  a  factor  of  6  for  Iron,  we  faave  for  the  new  coefficient  dj  (n  the 

formula  rf^  =  a^i/  '    '   \  the  values  4.69, 5.08,  and  6.82,  from  whldi 

obtain  the  diameters  of  shafts  of  the  six  engines  as  follows: 

EngineNo 12  8  4  6  6 

Dlam.ofcyI 10        10        80        80  60  60 

Horse-power,  I.H.P 50        60       460       460  1860  1S50 

Rers.  per  mln.,  ie. 260       125       180        66  00  46 

Diam.ofsh&dBaii/t:^^...,  2.74     8.46     7.67     9.70     12.55     15.82 

These  diameters  are  calculated  for  twisting  only.  When  the  shaft  is  also 
fubjected  to  bending  strain  the  oaloulation  must  be  modified  as  below : 

Resistance  to  Bendlnff*— The  strength  of  a  circular-section  shaft 
to  resist  bending  is  one  half  of  that  to  resist  twisting.  If  £  is  the  bending 
moment  in  ixioh«lbs.,  and  d  the  diameter  of  the  shaft  in  inches, 


wo 


Bm^  X/;  end  d  =  y^^X  10.2; 


M 


/  is  the  mfb  strain  per  square  Inch  of  the  material  of  which  the  shaft  Is 
composed,  and  its  value  may  be  taken  as  given  above  for  twisting  (Seaton). 

EqnlTalent  Tuvlstlns  moment.— When  a  shaft  is  subject  to 
both  twisting  and  bending  simultaneously,  the  combined  strain  on  any  sec- 
tion of  it  may  be  measured  by  calculating  wliat  is  called  the  equivalent 
tvfMing  mcment;  that  is,  the  two  strains  are  so  combined  as  to  be  treated 
as  a  twisting  strain  only  of  the  same  magnitude  and  the  size  of  shaft  cal- 
culated aooordingly.  Rankine  gave  the  following  solution  of  the  combined 
actloa  of  the  two  strains. 

If  2*  s  the  twisting  moment,  and  B  ss  the  bending  moment  on  a  section  of 
a  fftiaft,  then  the  equivalent  twisting  moment  Ti  =  B+  VB*  4-  T*. 

Seaton  says;  Orank-shafts  are  subject  always  to  twisting,  bending,  and 
shearing  strains;  the  latter  are  so  small  compared  with  the  former  that 
they  are  usually  neglected  directly,  but  allowed  for  indii*ectly  by  means  of 
the  factor/. 

The  two  principal  strains  vary  throughout  the  revolution,  and  the  maxi- 
mum equivalent  twisting  moment  can  only  be  obtained  accurately  by  a 
series  or  calculations  of  bending  and  twisting  moments  taken  at  fixed  inter- 
vals, and  from  them  constructing  a  curve  of  strains. 

(Tonsfdeting  the  engines  of  our  examples  to  have  overfaimg  cranks,  the 
maximum  bending  moment  resulting  from  the  thrust  of  the  connecting-rod 
on  tlie  crank-pin  will  take  place  when  the  engine  is  passing  its  centres 
(neglecting  the  efiTect  of  the  inertia  of  the  reciprocating  parts),  and  It  will 
be  the  product  of  the  total  pressure  on  the  piston  by  the  distance  between 


DIMENSI0K8  OF  PABTS  07  ENGI17ES. 


809 


two  fMurallel  Udob  pftsaiDfr  through  the  centres  of  the  oraok-pin  and  of  the 
ihaft  beariDir,  at  right  angles  to  their  axes;  which  distance  is  equal  to 
^  length  of  crank-pin  bearing  +  length  of  hub+H  length  of  shaft-bearing  -f 
any  clearance  that  may  be  allowed  between  the  crank  and  the  two  bearings. 
For  our  six  engines  we  may  take  this  distance  as  equal  to  ^  length  of 
crank-pin  4- thickness  of  crank-arm  + 1.5  X  the  diameter  of  the  shaft  as 


already  found  by  the  calculation  for  twisting, 
is  then  as  below: 


The  oAlculatioQ  of  diameter 


Engine  No, 

1 

2 

3 

4 

5 

6 

Diam.  of  cyl.,  in.  . 

10 

10 

80 

80 

60 

50 

Horse-power 

60 

80 

400 

4S0 

1250 

1260 

Revs,  per  min..  .. 

SSO 

185 

180 

65 

90 

46 

Max.prees.  on  pi8,P 

'i^ 

7,854 

70,686 

70,660 

190,850 

196,860 

Iieverage,*JDin.... 
Bd.moJ*L^BiuAb 

7.94 

£3.S0 

86.00 

86.80 

42.25 

49.087 

«.8M 

1, 580,428 

1,887,888 

7,286,680 

8,295,786 

Twist,  mom.  T, 

47,124 

M,S48 

1,080,290 

8,180,580 

4,712,400 

9,424,800 

£quiv.Twi8t.  mom. 

r»=5-f  VB^+T^ 

(approx.) 

118,000 

175,000 

8,468.000    4.647.080 

15,840,000 

20,860,000 

*  Leverage  s  distance  between  centres  of  crank -pin  and  shaft  bearing  s 
^  +  8.2Sd. 

HaTlnff  already  fonnd  the  diameters,  on  the  assumption  that  the  shafts 
were  subjected  to  a  twisting  moment  7  only,  we  may  find  the  diameter  for 
resisting  combined  bending  and  twisting  bv  multiplying  the  diameters 
already  found  by  the  cube  roots  of  the  ratio  Tx  •«-  T,  or 


1.40       1.37 
Giving  corrected  diameters  d^  =. . .  8.84       4.89 


1.46       1.84       1.64       1.86 
11.85      12.99     80.58     81.68 


By  plotting  these  results,  using  the  diameters  of  the  cylinders  for  abscissas 
and  diameters  of  the  shafts  for  ordlnates,  we  find  that  for  the  long-stroke 
engines  the  results  lie  almost  in  a  straight  line  expi-essed  by  the  formula, 
diameter  of  shaft  s  .43  x  diamuter  of  cylinder;  for  the  short -stroke  engines 
the  line  is  slightly  curved,  but  does  not  diverge  far  from  a  straight  line 
whose  equation  is,  diameter  of  shaft  =  .4  diameter  of  cylinder.  Using  these 
two  formulas,  the  diameters  of  the  shafts  will  be  4.0, 4.8. 18.0, 12.9,  20.0, 21.6. 

J.  B.  Stanwood,  in  Engineering^  June  18,  1891.  gives  dimensions  of  shafts 
of  Corliss  engines  in  Ameiiean  practice  for  cvUnderi  10  to  80  in.  diameter. 
The  diameters  range  from  4  15/16  to  14 15/16,  following  precisely  the  equation, 
diameter  of  shaft  =  ^diameter  of  cylinder  -  1/16  inch. 

Fly*ir1keel  Sliaits.— Thus  far  we  have  considered  the  shaft  as  resist- 
ing the  force  of  torsion  and  tbe  bending  moment  produced  by  the  pressure 
on  the  crank-pin.  In  the  case  of  fly-wheel  engines  the  shaft  on  the  opposite 
side  of  the  bearing  from  the  crank  pin  has  to  be  designed  with  reference  to 
the  bending  moment  caused  by  the  weight  of  the  fly  wheel,  tbe  weight  of 
the  shaft  itself,  and  the  strain  of  the  belt.  For  engines  in  which  there  is  an 
outboard  bearing,  the  weight  of  fly-wheel  and  shaft  being  supported  by 
two  bearings,  the  point  of  the  shaft  at  which  the  bending  moment  is  a 
maximum  may  be  taken  as  the  i>oInt  midway  between  the  two  bearings  or 
at  the  middle  of  the  fly-wheel  nub,  and  the  amopntof  the  moment  is  the 
product  of  the  weight  supported  by  one  of  the  bearings  into  the  distance 
from  the  centre  of  that  bearing  to  the  middle  point  of  the  shaft.  The  shaft 
is  thus  to  be  treated  as  a  beam  supported  at  the  ends  and  loaded  In  the 
middle.  In  the  case  of  an  overhung  fly-wheel,  the  shaft  having  only  one 
bearing,  the  point  of  maximum  moment  should  be  taken  as  the  middle  of 
the  bearing,  and  its  amount  is  very  nearly  tbe  product  of  half  the  weight 
of  tbe  fly -wheel  and  tbe  shaft  into  tlie  distance  from  the  middle  of  its  hub 
from  the  middle  of  the  bearing.  The  bending  moment  should  be  calculated 
and  combined  with  the  twisting  moment  as  above  shown,  to  obtain  the 
equivalent  twisting  moment,  ana  the  diameter  neoessary  at  the  point  of 
maximum  moment  calculated  therefrom. 

In  the  case  of  our  six  engines  we  assume  that  the  weights  of  tbe  fly- 
wheels,  together  with  the  shaft,  are  double  the  weight  of  fly-wheel  rtm 

obtained  from  the  formula^ Tr=  783,400  -^^^  (gUen  under  Fly-wheels); 


810 


THE  STEAM-BNGIKE« 


that  the  shaft  Is  supported  by  an  outboard  beaiini;,  the  distance  between 
the  two  bearings  being  ^,  5,  and  10  feet  for  the  lO-ln.,  80-in.,  and  fiO-in. 
engines,  respectively.  The  diameters  of  the  fly-wheels  are  taken  such 
thai  their  rim  velocity  will  be  a  little  less  tlian  6000  feet  per  minute. 

EngineNo 1  <3  8  4  5  6 

Diam.  of  cyl.,  inches 20  10  80  80  50  60 

Diam.  of  fly-wheel,  ft 7.5  15  14.6  89  21  48 

RevH.p«rmin 850  185  180  05  90  45 

Half  wt.fly-wh*l  and  shaft,lb.  268  586  5,963  11,980  28.881  S8,7i» 

Lever  arm  for  max. mom., in.  15  15  80  80  00  00 

Max.  bending  moment,  in..lb.  4080  8040  179,040  858,060  1,583,070  3,106,140 

As  these  are  verr  much  less  than  the  bending  moments  calculated  from 
the  pressures  on  the  crank -pin,  the  diameters  already  found  are  sufficient 
for  the  diameter  of  the  shaft  at  the  fly -wheel  hub. 

In  the  case  of  engines  with  heavy  band  fly-wheels  and  with  long  fly-wheel 
shafts  it  is  of  the  utmost  importance  to  calculate  the  diameter  of  the  shaft 
with  reference  to  the  bending  moment  due  to  the  weight  of  the  fly-wheel 
and  the  shaft. 

B.  H.  Coffey  (Potcer,  October,  1892)  gives  the  formula  for  combtoed  bend- 
tag  and  twisting  resistance.  T,  =  .196d»S,  in  which  T,  =  B-h  VB*-^T»i  T 
being  the  maximum,  not  the  mean  twisting  moment;  and  finds  empirical 
working  values  for  .1965  as  below.  He  says:  Four  points  should  be  oonaid- 
ered  in  determining  this  value:  First,  the  nature  of  the  material;  second, 
the  manner  of  applying  the  loads,  with  shock  or  otherwise:  third,  the  ratio 
of  the  bending  moment  to  the  torsional  moment— the  bending  moment  in  a 
revolving  shaft  produces  reversed  strains  in  the  material,  which  tend  to  rup- 
ture it;  fourth,  the  siae  of  the  section.  Inch  for  inch,  large  sectkms  are 
weaker  than  small  ones.  He  puts  the  dividing  line  between  lame  and  small 
sections  at  10  in.  diameter,  and  gives  the  following  safe  values  at  Sx  .196  for 
steel,  wrought  iron,  and  cast  iron,  for  these  conditions. 

Valus  or  S  X  .196. 


BaUo. 

Heavy  Shafts 
with  Shock. 

light  shafts  with 

Shock.    Heavy 

Shafts  No  Shock. 

Light  Sh«fU    ' 
No  Shock. 

^toT. 

Steel. 

Wro^t 
Iron, 

Cast 
Iron. 

Steel. 

Wro't 
Iron. 

Cast 
Iron. 

Steel. 

Wro't 
Iron. 

Cast 
Iron. 

StolOorless 

8  to  5  or  less  

1  to  lor  less 

B  gi-eater  than  T. . 

1045 
941 
855 
784 

880 
785 
715 
655 

440 
393 
358 
328 

1566 
1410 
1281 
1176 

1820 
1179 
1074 
964 

660 
589 
687 
498 

2090 
1888 
1710 
1508 

17B0 
1570 
1480 
1810 

880 
785 
715 
656 

Mr.  Coffey  gives  as  an  example  of  improper  dimensions  the  fly-whe«l 
shaft  of  a  1500  H.P.  engine  at  Wllllmantic,  Conn.,  which  broke  while  the  en- 
gine was  running  at  485  H.P.  The  shaft  was  17  ft.  5  in.  long  between  centres 
of  bearing,  18  in.  diaro.  for  8  ft.  In  the  middle,  and  15  in.  diam.  for  the  re- 
mainder, including  the  bearings.  It  broke  at  toe  base  of  Uie  fillet  connect- 
ing the  two  large  diameters,  or  56^  in.  from  the  centre  of  the  bearing.  He 
calculates  the  mean  torsional  moment  to  be  446,664  Inch -pounds,  and  the 
maximum  at  twice  the  mean;  and  ilie  total  weight  on  one  oearini;  at  87,530 
lbs.,  which,  multiplied  by  56>^  in.,  gives  4.945,445  in. -lbs,  bending  monieni  at 
the  flilet.  Applying  the  formula  Ti  =  B  +  ^B*  +  T*,  gives  for  equivalent 
twisting  moment  9,971,046  iu.-lbs.  Substituting  this  value  in  the  formula 
7*1  =  .196,  Sd*  gives  for  8  the  shearing  strain  1^070  lbs.  per  sq.  in.,  or  if  the 
metal  had  a  shearing  strength  of  45,000  lbs.,  a  factor  of  safety  of  only  3. 
Mr.  Coffey  considers  that  6000  lbs.  is  all  that  should  t>e  allowed  for  5  under 
these  circumstances.  This  would  give  d  =  80.85  in.  If  we  take  from  Mr. 
Coffey *8  table  a  value  of  .1965  =  1 100,  we  obtain  d*  s  9000  nearly,  or  d  s  80.8 
ra..  iUKtend  of  1.5  in.,  the  actual  diameter. 

Itenfftli  of  Sliaft*beariiiKS.— There  is  as  great  a  difference  of 
opinion  among  writers,  and  as  great  a  variation  in  practice  conceminip  length 
of  Jourual*bearings,  as  there  is  concerning  crank-pins.    The  length  or  a 


DIHBNSIOKS  OF  PARTS  OF  BNGIKES.  811 

Journal  beiD^  determined  from  considerations  of  Its  he&tlnfp,  the  obsenr*- 
Uons  concerning  iieating  of  cranlc-pins  apply  also  to  shaft-bearings,  and  the 
formulee  for  lengih  of  crank-pins  to  aToia  heating  may  also  be  used,  using 
for  the  total  loa4i  upon  the  bearing  the  resultant  of  all  the  pressures  brought 
upon  it,  by  the  pressure  on  the  crank,  by  the  weight  of  the  fly-wheel,  anoby 
the  pull  of  the  belt.  After  determining  this  presaure,  howeTer,  we  must 
resort  to  empirical  values  for  the  so-called  constants  of  the  formulsp,  really 
vaiiables,  wnich  depend  on  the  power  of  the  bearing  to  carry  away  heat, 
and  upon  the  quantity  of  heat  generated,  which  latter  depends  on  the  pres- 
sure, on  the  number  of  square  feet  of  rubbing;  surface  passed  over  in  a 
minute,  and  upon  the  coefficient  of  fricUon.  This  coefficient  is  an  exceed- 
ingly variable  quantity,  ranging  from  .01  or  less  with  perfectly  polished 
journals,  having  end-play,  and  lubricated  by  a  pad  or  oil-bath,  to  .10  or  more 
with  ordinary  oil-cup  lubrication. 

For  shafts  resisting  torsion  only.  Marks  gives  for  length  of  bearing  I  = 
.0000247/pjyrz>*.  in  which /is  the  coefficient  of  friction,  p  the  mean  pressure 
in  pounds  per  square  inch  on  the  piston,  N  the  number  of  single  strokes  per 
minute,  and  D  uie  diameter  of  the  piston.  For  shafts  under  the  combined 
stress  due  to  pressure  on  the  crank -pin,  weight  of  fly-wheel,  etc.,  he  gives 
the  following:  Let  Q  =  reaction  at  bearing  due  to  weight,  8  =  stress  due 
steam  pressure  on  piston,  and  Ri=s  the  resultant  force;  for  horisontal  engines, 
R^  S3  V'O*  -f  S*.  for  vertical  engines  R^  =:  Q  ■{-  S,  when  the  pressure  on  the 
crank  Isln  the  same  direction  as  the  pressure  of  the  shaft  on  its  bearings, 
and  Ri  =  Q-  S  when  the  steam  pressure  tends  to  lift  the  shaft  from  its 
bearings.  Using  empirical  values  for  the  work  of  friction  per  square  inch 
of  projected  area,  taken  from  dimensions  of  crank -pins  in  marine  vessels, 
he  finds  the  formula  for  length  of  shaft-journals  I  =  .QOOOSS&fRxN,  and 
recommends  that  to  cover  the  defects  of  workmanship,  neglect  or  ofling, 
and  the  introduction  of  dust,  /  be  taken  at  .16  or  even  greater.  He  says 
that  500  lbs.  per  sq.  in.  of  projected  area  may  be  allowed  for  steel  or  wrought- 
iron  shafts  in  brass  bearings  with  good  results  if  a  less  pressure  isnotatUin- 
able  without  inconvenience.  Marks  says  that  the  use  of  empirical  rules  that 
do  not  take  accoimt  of  the  number  of  turns  per  minute  has  resulted  in  bear- 
ings much  too  long  for  slow- speed  engines  and  too  short  for  high-speed 
engines. 

Whitham  gives  the  same  formula,  with  the  coefficient  .00002575. 
I     Thurston  says  that  the  niazimum  allowable  mean  intensity  of  pressure 

may  be,  for  all  cases,  computed  by  his  formula  for  journals,  I  s  £nKnnd*  ^'' 

by  Rankine's,  I  s  ^J^-t  in  which  Pis  the  mean  total  pressure  In  pounds, 

Fthe  velocity  of  rubbing  surface  In  feet  per  minute,  and  d  the  diameter  of 
the  shaft  in  inches.  It  must  be  borne  In  mind,  he  says,  that  the  friction  work 
on  the  main  bearing  next  the  crank  is  the  sum  of  that  due  the  action  of  the 
piston  on  the  pin,  and  that  due  that  portion  of  the  weight  of  wheel  and 
shaft  and  of  pull  of  the  belt  which  is  carried  there.  The  outboard  bearing 
carries  practically  only  the  latter  two  parts  of  the  total.  The  crank-shaft 
journals  will  be  madn  longer  on  one  side,  and  perhaps  shorter  on  the  other, 
than  that  of  the  crank-pin.  In  proportion  to  the  work  falling  upon  each,  i.e., 
to  their  respective  products  of  mean  total  pressure,  speed  of  rubbing  sur- 
faces, and  coefficients  of  friction. 

Unwin  says:  Journals  running  at  IfiO  revolutions  per  minute  are  often 
only  one  diameter  long.  Fan  shafts  running  160  revolutions  per  minute  have 
Joumahi  six  or  eight  diameters  long.  The  ordinary  empirical  mode  of  pro- 
portioning the  length  of  journals  is  to  make  the  length  proportional  to  the 
diameter,  and  to  make  the  ratio  of  length  to  diameter  increase  with  the 
•peed.  For  wrought*iron  journals: 

Revs,  per  mln.  =s     50     100    150  900   250    500    1000       ^c:.004i?+l. 

Length  H- dlam.  =  1.3     1.4    1.6  1.8    2.0   S.O    5.0. 

Cast-iron  journals  may  have  I  •«-  d  s=  9/10,  and  steel  journals  1-%-d  m  1)4, 
of  the  above  values. 

Unwin  gives  the  following,  calculated  from  the  formula  I  =    '       '  \  in 

whfch  r  is  the  crank  radius  in  inches,  and  H.P.  the  horse-power  transmitted 
to  the  orank-pin. 


813 


THB  STBAX-SlfOIHB. 

TuouRicAi.  JocBiui.  Lbvotb  n  IvaaaoL 


Umdom 

RfliToluttoBS  of  Joornal  per  n 

rlimtaw 

Journal 

la 

pounds. 

w 

100 

200 

800 

fiOO 

lOOO 

1,900 

.« 

.4 

.8 

1.2 

2. 

4. 

8,000 

.4 

.8 

i.e 

2.4 

4. 

& 

4,060 

.8 

i.e 

8JI 

4.8 

8. 

1ft. 

5,0QD 

1.0 

2. 

4. 

§. 

10. 

80. 

10,000 

8. 

4. 

6. 

12. 

20. 

40. 

]^QQa 

a. 

0. 

12. 

18. 

80. 

ao^ooD 

4. 

8. 

16. 

24. 

40. 

ao,oo» 

6. 

12. 

M. 

80. 

.... 

40,000 

«. 

16. 

». 

.... 

.... 

6Q,00» 

10. 

90. 

40. 



Apptyhsg^  these  differeiit  fonnhne  to  our  six  ensteee,  we  liaTe: 


Enj^o  No........ •..«••....       1 


Dlwn.  «7L 

Horaa-power.. 

R»Ta.  per  mUi 

Keaa  prMsure  on  eraak-pin  s  S 

Hair  wt.  oi  flj-wbeel  and  abaft  =  Q,. 
Raanltaot  pvaw.  OA  beariat: 

IHam.  of  BlMtftioarnal. 

liMgtk  of  shaft  journal: 
Marfca,       I  =  .000a3i>5//?|iV(/=.10) 
ifMtbam,  t «  .00006r5/R,i?(/=  lO). 
PV 

'**«*«»• '-6b,ooSi 

■''**^'""44;8t)Oj- 

Umrin,      l>rC0M/241X 

v,n^    i.'JLSi _.... 


Average  ■ 


10 

60 
9B0 
&.290 


8,8!0 
8.8i 

5.88 
4.87 

2.61 

5.22 

7.68 
8.38 


10 

50 
125 
aj880 
536 

8,885 
4.82 

2.71 
2.15 

1.82 

2.78 
6.50 
1.60 


4.«     2.20 


80 
450 

lao 

a&»l85 
5,966 

28,924 
U.85 

20.87 
16.58 

14.00 


81.T0 
IT.«6 
12.00 


80 
450 

6» 


88.185  58,205 


11,926 


96,194  64,580 
12.00   80.58 


11.07 
8.77 


io.» 

16.86 
600 


50 

1^250 

90 


20,«7»t 


87.78 
20.95 

28.96 


25.10 
27.09 

20.63 


50 

l.afiO 

45 

58.90 
52.»«9 

79,800 
ai.S2 

23.17 
18.85 

lO.di 


22.47 

25.89 

ia.48 


17.05   10.00  29.54   19.22 


If  we  divide  the  mean  resnfttant  prrssore  on  the  beariiw  bj  tha  prorlecled 
area,  thai  ia,  hgr  tftia  product  of  the  diasoeter  and  length  of  the  journal,  indBC 
the  givaleafcand  smallest  leni^  out  of  the  seiea  mifrtha  fbr  each  Joiimal 
clvea  above,  we  obtain  the  pressura  per  squara  iaoh  upon  the  boariiiy,  as 
foUowa: 


FingiV^I  If  A  ., ......x.    ...    a.      4.. 

1 

2 

8 

4 

5 

6 

Pressui-e  per  sq.  In., 
Lonfcest  lournal . . .  ^ 

shortest 

Joaraat. 

250 
112 
ITS 

4.V 
115 
254 

178 

176 
97 
124 

886 
128 
289 
1B0 

1»1 

88 
106 

853 

145 

191 

Jourual  of  leofi^th  a 

diam . . 

175 

Many  of  the  formulad  give  for  the  lone-stroke  engines  a  length  of  journal 
ksa  than  tbe  dlasaetor.  but  such  short  joomals  are  rarsl^  used  ia  praeiiee. 
The  last  Una  in  the  above  table  has  been  calculated  on  the  ■ypneJiina  thai 


DIHEKSI0K8  OF  PARTS  09  BKOIKES.  813 

the  foiiniabof  tbe  loDg<«tiDSr»*  riagtoea  are  made  of  a  length  equal  to  the 
diameter. 

lu  tbe  dimenidona  of  CorHev  engines  given  by  J.  B.  Btanwood  (Eho.^  June 
13.  1801),  the  lengths  of  the  louraalii  for  enginee  of  dlam.  of  cyl.  10  to  SO  in. 
are  the  sanne  an  the  diam.  of  Uie  cylinder,  and  a  llUle  more  than  twice  ihe 
diam.  of  the  journal.  For  engines  above  *iO  in.  diam.  of  cyl.  the  ratio  of 
length  to  diam.  is  decreased  so  that  an  engine  of  ao  in.  diam.  has  a  journal 
26  in.  lonpr,  its  dlamerer  being  14||  in.  These  lengths  of  journai  are  greater 
than  thoiie  given  by  any  of  the  forroulsd  above  quoted. 

There  thus  appears  to  be  a  hopeless  confusion  in  the  various  forraulee  for 
length  of  siiafi  joumaU,  but  this  is  no  more  than  is  to  be  expected  from  the 
variation  In  the  coefficient  of  fiiciiou,  and  in  the  heat-conducting  power  of 
iournals  in  actual  use.  the  coefficient  varying  from  .10  (or  even  .To  as  given 
by  Uarlcs)  down  to  .01,  according  to  tlie  condition  of  the  bearing  su  traces 

pvr 
and  the  efficiency  of  lubrication.  Thurston''8  formula,  I  *«^^  ^^, ,  induces  to 

QU,WM)a 

the  form  I  m  .000004aG8Pii,  in  which  Pu:  mean  total  load  on  journal,  and 
R  =  revolutions  per  minute.  This  is  of  the  same  form  as  Marks*  and 
Whlthani*s  formulsa,  in  which,  if  /  the  ooeffioient  of  friction  be  taken  at  .10, 
the  coefficients  of  PR  are,  respectively,  40000005  and  .00000519.  Taking  the 
nieMU  of  these  three  forniulse,  we  have  I  =  .QOOOOSSPR^  if /=  .10  or  2  = 
.OOOOSSfPB  for  any  other  value  of/.  The  author  believes  this  to  lie  as  safe 
a  formula  as  anv  for  length  of  journals,  with  the  limitation  that  if  It  brings 
a  result  d  lenf^h  of  journal  less  than  the  diameter,  then  the  length  should 
be  made  equal  to  the  diameter.  Whenever  with  JTs  .10  it  gives  a  length 
which  is  inconvenient  or  Impossible  of  construction  on  account  of  limited 
space,  then  provisioo  should  os  made  to  reduce  the  value  of  the  coefficient 
of  friction  below  .10  by  means  of  foraed  lubrication,  end  piay«  etc..  and  to 
carry  away  the  heat,  as  by  water-cooled  journal-boxes.  The  value  of  P 
should  be  taken  as  the  resultant  of  i  lie  mean  pressure  on  the  crank,  and  the 
load  brought  on  the  bearing  by  the  weight  of  the  shaft,  fly-wiieel,  etc.,  as 
calculated  by  the  formula  already  ^ivrn,  viz.,  ff,  s  VO^  +  ^  foi"  horhiontal 
engines,  and i?i  c  Q  +  5for  vertical  eiiRtni's. 

For  our  six  enginee  the  formula  I  =s  .0000053Pi?  gives,  with  the  limitation 
for  the  louR-stroKe  engines  that  the  length  shall  not  be  less  than  the  diam* 
eter,  the  following:  " 

KnglneKo... 1 

Length  of  journal 4.89 

pressure  per  square  inch  on  journal. .     196 

Crmnk  -  Alittitii    •wltit   Centre-ermnk   and   Poiib1e*eimiilL 

Amis*— In  centre-crank  engines,  one  of  the  crank-arms,  and  its  adjoining 
journal,  called  the  after  journal,  usuallr  transmit  the  power  of  the  enjrine 
to  the  work  to  be  done,  and  the  journal  resists  both  twisting  and  bending 
moments,  while  the  other  journal  is  subjected  to  bending  moment  only. 
For  tbe  after  crank- journal  the  diameter  should  be  calculated  the  same  as 
for  an  overhung  crank,  using  the  formula  for  combined  bending  and  twist- 
ing moment,  T,  s=  B  +  VB^  -f  r>,  in  which  7,  is  the  equivalent  twisting 
moment,  B  the  bending  moment,  and  T  the  twisting  moment.   This  value 

of  Ti  Is  to  be  used  In  the  formula  diameter  s  a/  .lZ,  The  bending  mo- 
ment is  taken  as  the  maximum  load  on  piston  multiplied  by  one  fourth  of 
the  length  of  the  crank-shaft  between  middle  points  of  the  two  journal 
bearings.  If  the  centre  crank  Is  midway  between  the  bearings,  or  by  one 
lialf  the  distance  measured  parallel  to  the  shaft  from  the  middle  of  the 
ci*ank-pln  to  the  middle  of  the  after  bearing.  This  supposes  the  crank- 
stiaft  to  be  a  beam  loaded  at  its  middle  and  supported  at  the  emis,  hut 
Wbitham  would  make  the  bending  moment  only  one  half  of  this,  couhider- 
ing  tbe  shaft  to  be  a  beam  secured  or  fixed  at  the  eiids,  with  a  point  of  con* 
traflexure  one  fourth  of  the  length  from  the  end.  The  first  supposition  is 
the  safer,  but  since  the  bending  moment  will  in  any  case  be  much  less  than 
the  twisting  moment,  the  result  in«  diameter  will  be  but  little  greater  than 
if  Whltham^s supposition  Is  used.    For  the  foiward  journal,  which  is  sub- 

S/lQ  j>0 

)ected  to  bending  moment  only,  diameter  of  shaft  a  j^  ^J^,  in  which  B 


9        S 

4 

5           6 

4.80    16.48 

19.06 

80.fl0    t1.6t 

173     1» 

166 

loe     in 

813  THB  ST&AJf-SlfOIHB. 


LOMlOB 

RflTolutioBS  of  Joomal  per  mluataw 

Jounua 

Id 

pounds. 

w 

100 

900 

800 

fiOO 

laoo 

I.MO 

.9 

.4 

.8 

1.2 

9. 

4. 

8,000 

.4 

.8 

1.0 

9.4 

4. 

& 

4»oeo 

.8 

1.0 

8.9 

4.8 

8. 

18. 

5.0QD 

1.0 

2. 

4. 

8. 

10. 

SO. 

10,000 

8. 

4. 

8. 

19. 

80. 

40. 

16,000 

a. 

0. 

12. 

18. 

80. 

80,000 

4. 

8. 

16. 

94. 

40. 

ao.oo» 

e. 

12. 

M. 

88. 

.... 

40,000 

8. 

18. 

88. 

.... 

.... 

60,000 

10. 

90. 

40. 





.... 

Appljhsg'  these  dHferent  fonnhte  to  our  six  enghiee,  we  have: 


En^ltoe  No . 


DiWQ.  «7L 

Horae-power.. 

Eevt.  per  mUi , 

]Ce«»preesui«QBeraikk.pin  s  &.... 
H«ir  wt.  oC  flj-wheel  ami  abaft  =  Q. . 
RewilUmt  pvew.  «A  beanat: 

Diam.  of  BlMift^nMa. 

|g^«Tg^h  of  shaft  journal: 
Marks,       I  =  .000a3^/2?.iV(/=r.i0) 
n,  t  m  .00006T6/»,i?(/=  10). 

I      -^^ 

•"60,00(W 

/^r-f  90) 

44,800d    

I«»CflW«41)rf 


UmriDv 
Unwta* 


Average . , 


10 

60 
9B0 
8.990 
268 

8,8t0 
8.84 

5.88 
4.9T 

8.61 


5.99 
7.68 
8.38 


4.92 


10 
50 
125 

8«2eo 

536 

8,885 
4.80 

2.71 
2.15 

1.89 


9.78 
6.50 
1.60 


2.90 


80 
450 
130 
2&»185 
6,006 

29,024 
U. 

20.87 
16.68 

14.00 

8i.ro 
jr.96 

19.00 


17.05 


450 
66 

88.185 
11,906 

96,194 
12.00 

11.07 
8.77 


10.00 


60 

1«290 

90 
58,905 
26,470 


64,580 
80.68 

87.78 
90.96 


r.48  96.86, 


18.86 

18.86   27.00 
600 


50 

I.SSO 
45 

58.005 
5^940 

79,900 
».69 


18.85 
16.96 


86.16f  92.47 

26.89 

80.83|  10.48 


99.54'  19^ 


If  we  divide  the  mean  rssvltant  prvsaare  on  the  bearioff  bj  the  prorlecled 
area,  that  ia,  bgr  tftie  product  of  the  diameter  and  length  of  the  JourxMil,  tutec 
the  greatest  and  smallest  len|>ftb  out  of  the  seien  leagfhs  for  emdb  Joiinud 
-^m  above,  w«  obtain  the  preasnra  per  square  hioh  apon  the  beMrtB«;  as 


EngiaaKo 


Pressure  per  sq.  in.,  shortest  ^rnat. 

Longest  loumal 

Average  jmtmal 

Jourual  of  length  =  diam 


250 
112 
ITS 


455 
115 
954 
178 


176 
97 
194 


IH 

1*28  1  88 
868  1  106 
180 


6 

853 
145 
191 
178 


Many  of  the  formuin  give  for  the  long-stroke  engines  a  length  of  journal 
IsBathan  tte  dlasaeter,  but  such  short  >HirBals  are  na^lj  nsed  ia  praetiee;. 
The  last  Una  in  the  above  toble  has  been  calculated  on  tha  lypwtfinis  thaO 


DIMEKSIOKS  OF  PABtS  OP  BKGIKES.  813 

the  Jouniftbof  tbe  long^ilroSr^*  ringflnea  are  made  of  a  length  equal  to  the 
diameter. 

lu  the  dlmentiiona  of  Corlieii  engfnee  dven  by  J.  B.  Btanwood  (Eng.,  June 
12.  1801).  the  leogtbe  of  the  lournabi  for  engtuee  of  diam.  of  cyl.  10  to  80  in. 
are  the  lanie  aa  the  diam.  of  Uie  oylfoder,  and  a  little  more  than  twice  the 
diam.  of  the  Journal.  For  engines  above  20  in.  diam.  of  cyl.  the  ratio  of 
length  to  diam.  Is  decreased  so  that  an  engine  of  90  in.  diam.  has  a  Journal 
26  In.  lonflT,  its  diameter  being  14)|  in.  These  lengths  of  Journal  are  greater 
than  those  given  by  any  of  the  formulae  above  quoted. 

There  thus  appears  to  be  a  hopeless  confusion  in  the  ▼arious  formuls  for 
length  of  sliafi  JoumalH,  but  tliia  is  no  more  than  is  to  be  expected  from  the 
variation  in  the  coefficient  of  fi-iction,  and  in  the  heat-conducting  power  of 
iournals  in  actual  use.  the  coefficient  varying  from  .10  (or  even  .10  as  given 
by  Marks)  down  to  .01,  aooording  to  the  oonditioa  of  the  bearing  suiTacea 

and  the  efficiency  of  lubrication.  Thurston's  formula,  I  «„^  ^,^  r,  reduces  to 

QOfOUOa 
the  farm  I »  .000004aC8P/2.  in  which  Pv  mean  total  load  on  JouioaK  and 
R  =  revolutions  per  minute.  This  is  of  the  same  form  as  Marks*  and 
Wliit))ani*a  formule,  in  which,  if  /  the  ooeffioient  of  friction  be  taken  at  .10, 
the  coefficients  of  PR  are,  respectively,  .OOOOO0S  and  .00000619.  Taking  the 
njcrtn  of  these  three  forniulee.  we  have  /  =  .OWOOBSPR,  if /=  .10  or  f  = 
.00005S/PR  for  any  other  value  of/.  The  author  believes  this  to  Im*  as  safe 
a  formula  as  any  for  length  of  Jouraals.  with  the  limiUtion  that  if  it  brings 
a  result  of  leni?th  of  Journal  less  than  the  diameter,  then  ttie  length  should 
be  made  equal  to  the  diameter.  Whenever  with  /  ss  .10  it  gives  a  length 
which  is  inconvenient  or  impossible  of  construction  on  account  of  limited 
space,  then  provision  should  be  made  to  reduce  the  value  of  the  coefficient 
of  friction  below  .10  by  means  of  forced  lubrication,  end  play«  eto..  and  to 
carry  away  the  heat,  as  by  wnter- cooled  journal-boxes.  The  value  of  P 
should  be  taken  as  the  resultant  of  :tie  mean  pressure  on  the  crank,  and  %h» 
load  brought  on  the  bearing  by  the  weight  of  the  shaft,  fly-wheel,  etc.»  as 
calculated  by  the  formula  already  fnivvti,  viz.,  £,  =  ^Q'  -f  fi*  for  horizontal 
engines,  andi^i  ss  Q  +  5  for  vertlcul  enginf s. 

For  our  six  engines  the  formula  /  s  .0000058Pi?  gives,  with  the  limitation 
for  the  long-stroke  etigines  that  the  length  shall  not  be  less  than  the  diam* 
eter,  the  following;  ■ 

SnglneNo 19        8  4  5  6 

I^Migth  of  Journal 4.8»   4.2»    16.48    19.09   80.flO   S1.69 

Pi*e6Sttfe  per  square  inch  on  Journal..      196     173     128       155       lOe      171 

Cimak  ■  OlisftM    irltlt    Centre-crank   and   ]>onb1e*eraiik 

Arma*— In  centre-crank  engines,  one  of  the  crank-arms,  and  ita  adjoining 
Journal,  called  the  after  Journal,  usually  transmit  the  power  of  the  euRine 
to  the  work  to  be  done,  and  the  jonmaf  resists  both  twiHting  and  bending 
moments,  while  the  other  Journal  is  subjected  to  bending  moment  only. 
For  the  after  crank- journal  the  diameter  should  be  calculated  the  same  as 
for  an  overhung  crank,  using  the  formula  for  combined  bending  and  twist- 
ing moment,  Tj  =  B  -f-  YB*  -f  T^,  in  which  Tj  is  the  equivalent  twisting 
moment,  B  the  beuding  moment,  and  T  the  twisting  moment.   This  value 

of  7*1  Is  to  be  used  in  the  formula  diameter  =  a/-^  \  The  bending  mo- 
ment is  taken  as  the  maximum  load  on  piston  multiplied  by  one  fourth  of 
the  length  of  the  crauk-shaft  between  middle  points  of  the  two  Journal 
bearings,  if  the  centre  crank  is  midway  between  the  bearings,  or  by  one 
half  the  distance  measured  parallel  to  the  shaft  from  the  middle  of  tiie 
crank- pin  to  the  middle  of  the  after  bearing.  This  supposes  the  orank* 
shaft  to  be  a  beam  loaded  at  its  middle  and  supported  at  the  ends,  but 
H'hltham  would  make  the  bending  moment  only  one  half  of  this,  consider- 
ing the  shaft  to  be  a  beam  secured  or  fixed  at  the  ends,  with  a  point  of  con> 
traflexure  one  fourth  of  the  length  from  the  end.  Tlie  first  supposition  is 
the  safer,  but  slnoe  the  bendiutf  moment  will  in  any  case  be  much  less  than 
the  twlstmg  moment,  the  result  in«r  diameter  will  be  but  little  greater  than 
if  Whitham^s supposition  Is  used,    f'ur  the  foiward  Jouriml,  which  is  sub- 

S/lQ  *2R 

)ected  to  bending  moment  only,  diameter  of  shaft  a  aV  Z:zz^  In  wlUch  B 


814 


THB  STEAK-EKGIKB. 


Is  the  maxiroum  betidtnp  moment  and  8  the  safe  Bheating  strength  of  fh« 
metal  per  square  inch. 

For  our  six  enfrfnes,  aftsuminfi:  them  to  be  centre-crank  engflnes,  and  coo- 
Biderinfc  the  crank-shaft  lo  be  a  beam  supported  at  the  ends  and  loaded  in 
the  middle,  and  assuming  lengths  between  centres  of  shaft  bearings  as 
giTen  below,  we  have: 


Engine  No 

1 

9 

8 

4 

6 

0 

Length  of  Ahaf  t,  assumed, 

inches,  L 

Max.  press,  on  crank-pi n,P 

B  =  ^PL,  inch-lbs 

Twisting  moment,  T 

Equiv.   twisting  moment, 

b+Vb*  +  t* 

Diameter  of  after  journal. 

20 
7,854 

89,270 
47,194 

101,000 
8.98 

8.68 

24 
7,854 

49,687 
94,948 

156,000 
4.60 

8.90 

48            60            78 
70,686      70,686    196,850 

848,282  1.0604»0  3.729,750 
1,060,290  9,120,580  4,712,400 

2,906,000  8,480,000  9,740,000 
11.16       18.00       18.95 

10.98       11.16       16.89 

96 
196,350 

4,712,400 
9.494,800 

15,240,000 
SI  .20 

r     8000 
Diam.  of  forward  journal, 

u.^^/''''^ 

18.18 

"       V    8000  

The  lengths  of  the  journals  would  be  calculated  in  the  same  manner  as  in 
the  case  of  overhung  cranks,  by  the  formula  I  =  .O0006.yp/?,  in  which  P  i« 
the  resultant  of  the  mean  pressure  due  to  pressure  of  steam  on  the  piston, 
and  the  load  of  the  fly-wheel,  sliaft,  etc.,  on  each  of  the  two  bearlnes. 
Unless  the  pressures  are  ^ually  divided  between  the  two  bearings,  the 
calculated  lengths  of  the  two  will  be  different;  but  It  is  usually  ciistomarr 
to  malce  them  both  of  the  same  length,  and  in  no  case  to  make  the  length 
less  than  the  diameter.  The  diameters  also  are  usually  made  alike  for  the 
two  journals,  using  the  largest  diameter  found  by  calciilation. 

The  craok-pin  for  a  centre  crank  should  be  of  the  same  lenirth  as  for  an 
overhung  crank,  since  the  length  is  determined  from  considerations  of 
heating,  and  not  of  strength.  The  diameter  also  will  usually  be  the  same, 
since  it  is  made  great  enough  to  make  the  pressure  per  square  inch  on  the 

? projected  area  (product  of  length  by  diameter)  small  enough  to  allow  of 
ree  lubrication,  and  the  diameter  so  calculated  will  be  greater  than  ts  re- 
quired for  strengtli. 

Grank'Shaft  ivUh  Tiv^o  Cranks  coupled  at  90<'«  —  If  the 
whole  power  of  the  engine  is  transmitted  through  the  after  journal  of  the 
after  crank-shaft,  the  greatest  twisting  moment  is  equal  to  1.414  times  the 
maximum  twisting  moment  due  fo  the  pressure  on  one  of  the  crank-pins. 
If  T  =  the  maximum  twisting  moment  produced  by  the  steam-pressure  on 
one  of  the  nistons,  then  7,  the  maximum  twisting  moment  on  the  after  part 
of  the  crank-shaft,  and  on  the  line-shaft,  produced  when  each  crank  makes 
an  angle  of  45»  with  the  centre  line  of  the  engine,  is  1.4147".  Substituting 
this  value  in  the  formula  for  diameter  to  resist  simple  torsion,  vis.,  d : 
8/5.17'         .  .  8/5.1  Xl.4Hr     ^.    ^  _  ,  ««»  .'/r 


-iH,  we  have  d 
S 


'^^ 


8 


or   d=1.9 


1.,  In  which  T  is 


the  maximum  twisting  moment  produced  by  one  of  the  pistons,  d  &r  diam- 
eter In  Inches,  and  8  =  safe  working  sheaiing  strength  of  the  material. 
For  the  f orwai-d  journal  of  the  after  crank,  and  the  after  journal  of  the 
forward  crank,  the  torsional  moment  i.s  that  due  to  the  pressure  of  steam 
on  the  forward  piston  only,  and  for  the  forward  journal  of  the  forward 
crank,  if  none  of  the  power  of  the  engine  is  transmitted  through  it,  the 
torsional  moment  is  zero,  and  its  diameter  is  to  be  calculated  for  bending 
moment  only. 

For  Combined  Torsion  and  Flexnre.—Let  B|  s  bendto^  mo- 
ment on  either  journal  of  the  forward  crank  due  to  r**^*'""""  pressure  on 


DIMEKSI0K8  OF  FARTS  OF  XNGINES.  815 

r 

forwan!  piston,  fi,  =s  bendingr  moment  on  either  journal  of  the  after  crank 
du«  to  maximum  preesum  on  after  piston,  Tj  as  maximum  twisting  momen'^ 
on  after  Journal  of  forward  crank,  and  T^  =  maximum  twisting  moment  on 
after  Journal  of  after  crank  due  to  pressure  on  the  after  piston. 
Then  equivalent  twisting  moment  on  after  journal  of  forward  cnmk  m  B^ 

On  forward  Journal  of  after  crank  =  Pg  -j-  VB^'*  -f  Ti*, 

On  after  Journal  of  after  crank  s  B,  +  VB,» -f  (Ti  +  ^1)*. 

These  rallies  of  equivalent  twisting  moment  are  to  he  used  in  the  formula 

for  diameter  of  Journals  d  s  A/ii-^,   For  the  forward  journal  of  the 


,fi 


a 

i0.2Bt 


forward  crank-shaft  d  s   „, 

8 

It  Is  customary  to  make  the  two  Journals  of  the  forward  crank  of  ont. 
diameter,  viz.,  that  calculated  for  the  a^ter  Journal. 

For  a  Tbree-eylluder  Eng^lne  with  cranks  at  120*,  the  greatest 
twisting  moment  on  the  after  part  of  the  shaft.  If  the  maximum  pressures 
on  the  three  pistons  are  equal,  is  equal  to  twice  the  maximum  presiUre  on 
any  one  piston,  and  it  takes  place  when  two  of  the  cranks  make  ansles  of 
80»  with  the  centre  line,  the  tnird  crank  being  at  right  angles  to  it.  (For  de- 
monstration,  see  Whitham's  **  Steam-engine  Design,^'  p.  262.)  For  combined 
torsion  and  flexure  the  same  method  as  above  given  for  two  crank  engines 
is  adopted  for  the  flrst  two  cranks;  and  for  the  third,  or  after  crank.  If  all 
the  power  of  the  three  cylinders  Is  transmitted  through  It,  we  have  the 
equivalent  twisting  moment  on  the  forward  Journal  =  Bg  -f  VBj'-J-crtH-r,)*, 
and  on  the  after  Journal  a  Bt  +  i  i^s'  +  (7*1  +  T*  -f  3t)*«  ^t  ^d  7,  being 
respectively  the  bending  and  twisting  moments  due  to  the  pressure  on  the 
third  piston. 

Crank  ■•hafts  for  Triple-expansloii  IHarlBe  Bna^lnea, 
according  to  an  article  in  The  Engineer^  April  25,  1600,  should  be  made 
larger  than  the  formulfle  would  call  for.  in  order  to  provide  for  the  stresses 
due  to  the  racing  of  the  propeller  in  a  sea-way,  which  can  scarcely  be  cal- 
culated. A  kind  of  unwritten  law  has  sprung  up  for  fixing  the  size  of  a 
crank-shaft,  according  to  which  the  diameter  of  the  shaft  is  made  about 
0.45I>,  where  D  is  the  diameter  of  the  high-pressure  cylinder.  This  Is  for 
solid  shafts.  When  the  speeds  are  high,  as  in  war-ships,  and  the  stroke 
short,  the  formula  becomes  0  4D,  even  for  hollow  shafts. 

The  ValTS-stem  or  TalTe«rod«— The  valve-rod  should  be  designed 
to  move  the  valve  under  the  most  unfavorable  conditions,  which  are  when 
the  stem  acts  by  thrusting,  as  a  long  column,  when  the  valve  is  unbalanced 
(a  balanced  valve  may  become  unbalanced  by  the  Joint  leaking)  and  when  it 
Is  imperfectly  lubricated.  The  load  on  the  valve  Is  the  product  of  the  ar^a 
into  the  greatest  unbalanced  pressure  upon  it  per  square  inch,  and  the  co- 
etBcient  of  friction  may  be  as  high  as  20^.  The  product  of  this  coefflcient 
and  the  load  is  the  force  necessary  to  move  the  valve,  which  equals  the 
maximum  thrust  on  the  valve- rod.  From  this  force  the  diameter  of  the 
valve- rod  may  be  calculated  by  Hodgkinsou's  formula  for  columns.    An 

empirical  fonnnla  given  by  Seaton  is:  Diam.  of  rod  s  d  =4 /i^ ,  hi  which 


{  =  length  sod  b  ss  breadth  of  valve,  in  inches;  p  =  maximum  absolute 
pressure  on  the  valve  in  lbs.  per  so  in.,  and  Fa,  codDclent  whose  values  are, 
for  Iron:  long  rod  lO.OOO,  short  12,000;  for  steel:  long  rod  12.000,  short  14.500. 

Whitham  gives  the  short  empirical  rale:  Diam.  of  valve-rod  =  1/80  diam. 
of  cyl.  =  ^  diam  of  piston-rod. 

tnjie  or  not-Unk.   (Seaton.)-Let  D  be  the  diam.  of  the  valve  rod 


-/ 


Wp  . 
12,000' 


then  Diameter  of  block-pin  when  overhung  m  D, 

•*  "  **    secured  at  both  ends  =  0.76  x  />. 

**  eccentric- rod  pins  b  0.7   x  D. 

**  suspension-rod  pins  a  0.66  x  D, 

«•  ••  *'     pin  when  overhung  m  0.7S  X  D. 


816  THE  STEAM-EKOIKB. 

Breadttiof  link  s 0.8to0» x  O. 

LenRth  of  block  s  1.8  to  1.6  x  D, 

TbickDesB  of  ban  of  link  at  middle     *        s  0.7  x  D. 
If  a  single  stiBpeDSion  rod  of  round  flection^  its  diameter  s  0.7   x  D, 
If  two  saBpension  rods  of  round  section,  their  diameter  s  0.C6  x  />. 
Size  of  Double-bar  Liukii*— When  the  distance  between  oentm  of 
eccentric  pins  =  6  to  H  times  throw  of  eccentrics  (throw  =  eoceatricity  s 
half -travel  of  valve  at  full  gear)  Z>  as  before : 

Depth  of  bars  =  1.S6  x  D4-^  in. 

ThlcknesB  of  bars  =0.5   x  f>  +  ^  in. 

Length  of  slidiog-block  =  3.6  to  8  X  -D- 

Diameter  of  eccentric-rod  pins  =  0.8  x  D  4*  M  hi- 
*'      centre  of  sliding- block  =  1.8  x  D, 

When  the  distance  between  eccentric-rod  pins  s  6  to  6^  times  tiiiow  oC 
eccentrics: 

Depth  of  bars  s  1.26  x  D  +  W  in. 

Thickness  of  bars  a=  0.5   X  D  +  H  in. 

Length  of  sliding-block  =  S.6  to  8  X  D. 

Diameter  of  eccentric-rod  pins  =  0.75  x  D. 
Diaiaeter  of  eccentric  bolts  (top  end)  at  bottom  of  thread  s  0.48  X  D  whea 
of  Iron,  and  0.8S  x  D  when  of  steel. 

The  Eeeenirtc— Diam.  of  eccentric-sheave  s  8.4  X  throw  of  eccentric 
+  l.)i  X  diam.  of  shaft.    D  as  before 

Breadth  of  the  sheave  at  the  shaft as  1.15  X  D  + 0.85  inch 

Breadth  of  the  sheave  at  the  strap b  D-f  0.6  inch. 

Thickness  of  metal  around  the  shaft ss  0.7  x  D  +  0.5  Inch, 

Thiclcness  of  metal  at  circumference s=  0.6  x  D  -I-  0.4  inch. 

Breadth  of  kev «  0.7  x  I>  +  0.6lnch. 

Thickness  of  lEey e  0.86  X  D  +  0.5  inch. 

Diameter  of  bolts  connecting  parts  of  strap b  0.6  X  />  +  0.1  loch. 

THICK19E8B  OF  ECCXNTRIC-BTIUP. 

When  of  bronze  or  malleable  cast  iron: 

Thickness  of  eccentric-strap  at  the  middle m  0.4  X  D  +  0.6  inch. 

••      '»    "    sides ■  0.8  XD +  0.5  inch. 

When  of  wrought  iron  or  cast  steel: 

Thickness  of  eccentric-strap  at  the  middle a  0.4   X  D  4-  0.5  inch. 

"  "      "    *'    sides a  0.i27  X  D  +  0.4  inch 

Tito  Eeeeutrlc-rod.— The  diameter  of  the  eccentric-rod  in  the  bodj 
and  at  the  eccentric  end  mav  be  calculated  in  the  same  way  as  that  of  the 
coimectingrod,  tlie  length  being  taken  from  centre  of  strap  to  centre  of 
pin.    Diameter  at  the  link  end  =  0.8D  +  0.2  inch. 

This  is  for  wrought -iron;  no  reduction  in  size  should  be  made  for  steel. 

Eccentric-rods  are  often  made  of  rectangular  section. 

ReversinK^sear  should  be  so  designed  as  to  have  more  than  sufficient 
strength  to  withstand  the  strain  of  both  the  valves  and  their  gear  at  the 
same  time  under  the  most  unfavorable  circumstances;  it  will  then  have  the 
stiffness  requisite  for  good  worlting. 

Assuming  the  work  done  in  reversing  the  link-motion,  TT,  to  be  only  that 
due  to  overcoming  the  friction  of  the  valves  themselves  through  their  whole 
travel,  then,  if  T  be  the  travel  of  valves  in  inches;  for  a  compound  engine 

w-  r/^X6Xp>k    ,    r/i'X6'Xp'\. 

^"laV      5       /"^wv        5        /• 

{1.  b^  and  p^  being  length,  breadth  and  maximum  steam-pressure  on  valve 
of  the  second  cylinder;  and  for  an  expansive  engine 

^.,x|('-2i.|><i');    or    .|t.x6Xp,. 

To  provide  for  tlie  friction  of  link-motion,  eccentrics  and  other  gear,  and 
for  abnormal  conditiuns  of  the  same,  take  the  work  at  one  and  a  half  timea 
the  above  amount. 


PLY-WHBMA  817 

To  find  the  strain  at  anv  part  of  the  gear  haYinp  motion  when  reversing, 
divide  the  work  so  found  by  the  space  moved  through  by  that  part  in  feet; 
the  quotient  Is  the  strain  In  pound^  and  the  sdse  may  be  found  from  the 
ordinary  rules  of  construction  for  any  of  the  parts  of  the  srear.    (Seaton.) 

Enslne-ft'amea  or  Bed-plate«.— No  definite  rules  for  the  design 
of  eugme-f  rames  have  been  given  by  authors  of  worlds  on  the  steam-engine. 
The  proportions  are  left  to  the  designer  who  uses  "  rule  of  thumb,"  or 
copies  from  existing  engines.  F.  A.  Halsey  {Am.  Mach,,  Feb.  14,  1895)  has 
made  a  comparison  of  proportions  of  the  frames  of  horizontal  Corliss 
Imagines  of  several  builders.  The  method  of  comparison  is  to  compute  from 
the  measurements  the  number  of  square  incben  in  the  smallest  cross-seo- 
tion  of  the  frame,  that  is,  immediately  behind  the  pillow-block,  also  to 
compute  the  total  maximum  pressure  upon  the  piston,  and  to  divide  the 
latter  qnantity  by  tho  former.  The  result  gives  the  number  of  pounds 
pressure  upon  the  piston  allowed  for  each  square  inch  of  metal  in  the 
frame.  He  finds  that  the  number  of  pounds  per  square  inch  of  smallest 
section  of  frame  ranges  from  217  for  a  lOx  80-in.  engine  up  (o  575  for  a 
28  X  48-inch.  A  80  X  60-inch  enghie  shows  350  lbs.,  and  a  82-Inch  engine 
which  has  been  running  for  many  years  shows  067  lbs.  Generally  the 
strains  increaiie  with  the  size  of  the  engine,  and  more  cross-section  of  metal 
is  allowed  with  relatively  long  strokes  than  with  short  ones. 

From  the  above  Mr.  Halsey  formulates  the  general  rule  that  in  engines 
of  moderate  speed,  and  having  strokes  up  to  one  and  one-half  times  the 
diameter  of  the  cylinder,  the  load  per  square  Inch  of  smallest  section 
should  be  for  a  lOinch  engine  800  pounds,  which  figure  should  be  increased 
for  larger  bores  up  to  500  pounds  for  a  80- inch  cylinder  of  same  relative 
stroke.  For  high  speeds  or  for  longer  strokes  the  load  per  square  inch 
should  be  reduced. 

FLT-WHEBIiS. 

The  function  of  a  fly-wheel  Is  to  store  up  and  to  restore  the  periodJcal  fluc- 
tuations of  energy  given  to  or  taken  from  an  engine  or  machine,  and  thus 
to  keep  j^prozizDately  constant  the  velocitiy  of  rotation.   Ranklne  calls  the 

quantity  ^^r  the  coefQcient  of  fluctuation  of  speed  or  of  unsteadiness,  in 

which  £t  is  the  mean  actual  energy,  and  ^E  the  excess  of  energy  received  or 
of  work  performed,  above  the  mean,  during  a  given  Interval  The  ratio  of 
the  periodical  excess  or  deficiency  of  energy  £iE  to  the  whole  energy  exerted 
in  one  period  or  revolution  General  Monn  found  to  be  from  1/6  to  ^  for 
single-cyUnder  engines  using  expansion;  the  shorter  the  cut-off  the  higher 
the  value.  For  a  pair  of  engines  with  cranks  coupled  at  90°  the  value  of  the 
ratio  is  about  ^,  and  for  three  engines  with  cranks  at  iHXy,  1/12  of  its  value 
for  Bingle-cylinaer  engines.  For  tools  working  at  Intervals,  such  as  punch- 
ing, sk>ttlng  and  plate^utting  machines,  coinmg- presses,  eta,  AEis  nearly 
equal  to  the  whole  work  performed  at  each  opei'ation. 

AE 
A  fly-wheel  reduces  the  coefflcient  ^^^  to  a  certain  flzed  amount,  being 

about  1/8^  for  ordlnaiy  ntachinery,  and  1/50  or  1/60  for  machinery  for  fine 
purposes. 

If  m  be  the  reciprocal  of  the  intended  value  of  the  coefflcient  of  flaotua- 
tion  of  speed,  A£  the  fluctuation  or  energy,  /  the  moment  of  inertia  of  the 

fly-wheel  alone,  and  a^  its  mean  angular  velocity,  J  =  ^    -'.    As  the  rim  of 

do 
a  fly  wheel  is  usually  heavy  in  comparison  with  the  arms,  f  may  be  taken 
to  equal  PTr',  in  which  W  =  weight  of  rim  in  poimds,  and  r  the  radius  of  the 

wheel;  then  W  s=  '"^^^    =  "*^.^    ,  if  v  be  the  velocity  of  the  rim  In  feet  per 

second.    The  usual  mean  radius  of  the  fly-wheel  In  steam-engines  is  from 
three  to  five  times  the  length  of  the  crank.    The  ordinary  values  of  the  prod- 
uct mg,  the  unit  of  time  bemg  the  second,  lie  between  1000  and  2000  feet. 
(Abridged  from  Rankhie,  B  E.,  p.  62.) 
Thurston   gives   for  engines  with    automatic  valve-gear  W  s  S60.000 

j^^  %  in  which  A  s  area  of  piston  In  square  inches,  S  =  stroke  in  feet,  p  s 

mean  steam-pressnre  In  lbs.  per  f^q.  in.,  /2  s  revolutions  per  minute,  D  s  out* 
side  diameter  of  wheel  In  feet.   Thurston  also  gives  for  ordlnaiT  fomui  ot 


818  THE  BTEAM-EN0I17B. 

noncondensfDft  eofdne  with  a  ratio  of  expaoaloo  between  S  and  S,  ITs 

^~,  inwbfcbaraiiKea  from  10,000,000  to  15,000,000,  aTeraRinfi:  12,000,000. 

Forga»«DglDe8,  in  which  the  cfaai^geis  fired  with  every  revolution,  the  Amrr- 
icnn  Machinist  ^ves  this  latter  formula,  with  a  doubled,  or  ^^4,000.000. 
Presumably,  if  the  charge  is  fired  every  other  revolutioD,  a  abould  be  asain 
doubled. 

RanUne  C  Useful  Rules  and  Tables,**  p.  247)  idves  JV  «  476,000  j!f^  .  In 

which  F  is  the  variation  of  speed  per  cent,  of  the  mean  speed.  Thurston's 
first  rule  above  given  corresponds  with  this  if  we  take  Fat  1.9  per  cent. 

fiartnell  (Proc.  Inst.,  M.  E.  188:2.  427)  says:  The  value  of  V,  or  the 
variation  permissible  in  portable  engines,  should  not  exceed  8  per  cent,  with 
an  ordinary  load,  and  4  per  cent  when  beavilv  loaded.  In  fixed  engioea,  for 
ordinary  purposes.  F  =  2H  to  8  per  cent.  For  good  governing  or  special 
purposes,  such  as  cotton -spinning,  the  variation  should  not  exceed  lyi  to  2 
per  cent. 

F.  M.  Rites  (Trans.  A.  8.  M.  E.,  xiv.  100)  develops  a  new  formula  for  weight 
f  ^  y  I  Br  P  f^ 

of  rim,  viz.,  W  =  — iSi^i""^'  •"*<*  weight  of  rim  per  horse-power  =  -^j^,  in 

which  C  varies  from  10,000,000,000  to  20,000,000,000;  also  using  the  latter  value 

of  C,  he  obtains  for  the  energy  of  the  fly-wheel  ~  =  oH^^^W^  "^ 

CxH.P.(8.14)«D»/?t  _  850.000  HP.      ™_  _^_i  ^___  ner  H  P    -  ^^ 

The  limit  of  variation  of  speed  with  such  a  weight  of  wheel  from  ezceas  of 
power  per  fraction  of  revolution  is  less  than  .00:28. 

The  value  of  the  constant  C  given  by  Mr.  Rites  was  derived  from  practice 
of  the  Westingbouse  single-acting  engines  used  for  eiectric-lightinsr.  For 
double-acting  engines  in  ordinary  service  a  value  of  C  =  5.000,000,000  would 
probably  be  ample. 

From  these  f ormulsB  it  appears  that  the  weight  of  the  fly-wheel  for  a  given 
horse -power  should  vary  inversely  with  the  cube  of  the  revolutions  and  the 
square  of  the  diameter. 

J.  B.  Btanwood  (.Eng'g,  June  12,  1801)  says:  Whenever  480  feet  Is  the 
lowest  Dlston-speed  probable  for  an  engine  of  a  certain  siae,  the  fily-wlieel 
weight  for  that  speed  approximates  closely  to  the  formula 

IT  =  weight  In  pounds,  d  s  diameter  of  cylinder  in  inches,  »  s  alroke  io 
incheii.  D  =  diameter  of  wheel  in  feet,  R  —  revolutions  per  minute,  corre 
sponding  to  480  feet  piston-speed. 

In  a  Ready  Reference  Book  published  by  Mr.  Stanwood,  Cincinnati.  1893, 
he  irives  the'  same  formula,  with  coefficients  as  follows:  For  slide-valve  en- 
gine^ ordinary  duty,  850,000:  same,  electric-lighting,  700.0UO;  for  automatic 
high-6p<.>ed  engines,  1.000,000;  for  Corliss  engines,  ordinary  duty  700,000. 
electrilc-ligbdng  1,000,000. 

Thurston's  formula  above  given,  W=  j^^^  with  a  =  12,000,000,  when  re- 

d*a 
duoed  to  terms  of  d  and  s  In  inches,  becomes  W  s  ^,400 0=77. 

If  we  reduce  it  to  terms  of  horse-power,  we  have  I.H.P.  a      *V^. 

38,000 
in  which  P  =  mean  effective  pressure.     Taking  this  at  40  Ibe.,  we  obtain 

W  =  5,000,000,000^^.   If  mean  effective  pressure  ■  80  Iba.,  then  Wz 
0,666,000,0( 

Emit  TheisR  {Am.  MacJi.,  Sept.  7  and  14,  189S)  gives  the  following  values 
ot  d,  the  coefflcient  of  steadiness,  which  is  the  reciprocal  of  what  Bankiue 
calls  the  coefflcient  of  fluctuation : 


FLY-WHEELS, 


819 


For  enidnes  openitfnpr— 

Hammering  and  crushing  machinery dm  B 

Pumping  and  shearing  machinerv ds  20  to  80 

Weaving  and  paper-making  machineiy d  =  40 

Mflling  machinery » d  =  50 

Spinning  machinery ds50tol00 

Ordinary  driving-engines  (mounted  on  bed-plate), 

belt  tranamlasion d  a  86 

Gear-wheel  traosmiasion ds60 

lir.  TheiMi's  formula  for  weight  of  fly-wheel  in  pounds  is  TTss  i  x   i^,'    '  't 

where  d  is  the  coefUcient  of  steadiness,  V  the  mean  velocity  of  the  fly- 
wheel rim  in  feet  per  second,  n  the  number  of  revolutions  per  minute,  t  = 
a  coefficient  obtained  by  graphical  solution,  the  values  of  which  for  dif- 
ferent conditions  are  given  In  the  following  table.  In  the  lines  under  **  cut* 
off,"  p  means  **  compression  to  initial  pressure,**  and  O  **  no  compression  '*: 

Values  or  i.    Sirolb-ctlindbb  NoN-ooNDicNsniG  EnoiKBa. 


1% 

Cut-off,  lA 

Cutoff,  M. 

Cut-off,  J<. 

Cut-off,  J<. 

nl 

Comp. 
P 

o 

Comp. 
P 

o 

Comp. 
P 

0 

Comp. 
P 

0 

900 

400 
600 

273.600 
240.810 
194,670 
168,200 

218.580 
187,480 
145,400 
108,690 

242.010 
808,200 
168,590 
162.070 

809,170 
179.460 
186,460 
185,260 

820,760 
188,510 
165,210 

201,920 
170,040 
146,610 

198,840 
174,680 

182,840 
167,860 

•800 



SiMOLECTLINOCR  CONDKNSINO  EnOINBS. 

HI 

Cutoff.  H. 

Cut-off,  1/6. 

Cutoff,  H- 

Cut-off,  H. 

Cut-off,  J<. 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

0 

167:140 
138,060 

Comp. 
P 

189,600 
174,680 

0 

Comp. 
P 

0 

200 
400 

265.560 
194,550 
148.780 

176,360 
117.870 
140,090 

284,160 
174,880 

178,660 
118.860 

204,210 
164,720 

161,880 
151,680 

172.690 

156,990 

600 

Two-CYLimJICR  Engihbs,  Crakes  at  90*. 


if-l 

Cut-off,  1/6. 

Cut-off,  li. 

Cutoff,  H- 

Cut^iff,  J6. 

Hi 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

0 

200 
400 
600 
800 

71,flfi0 
70,160 
70,040 
70,040 

Mean 
60.140 

60.490 
57,000 
67,480 
60,140 

tMean 
1  M,840 

49.273 
49,150 
49,220 

I  Mean 
J- 50,000 

87,9-30 
85,500 

i  Mean 
f  86,950 

Thrbb-ctlindbr  Enotnes, 

Crakes 

AT120*, 

B<2  = 

|-a5 

Cut-off,  1/8. 

Cut-off,  H- 

Cut-off,  H- 

Cut-off.  ^. 

Comp. 
P 

88.810 
80,190 

O 

82,240 
81,670 

Comp. 
P 

O 

Comp. 
P 

O 

Comp. 
P 

0 

20O 
800 

88,810 
85,140 

85,600 
83,810 

34,540 
86,470 

88.450 
82,850 

85.260 
83,810 

82,870 
82,370 

i^s  a  mean  vnlne  of  i  for  these  engines  we  VfXt^j  ^se  88,8|0. 


820  THE  6TBAH-ENQIKE. 

CentiiAigal  Force  In  Fljr-nrlieels.— Let  W  a  weigbt  of  lim  in 
pounds;  R  a  mean  radius  of  rim  in  teei;  r  =:  reToluiions  per aninute,  g  = 
82.16;  V  =  ▼eloclty  of  liin  m  feet  per  necoiid  =  fiwi2r-»-  60. 

Centrifugal  force  of  whole  rim  =  .?r^.  ^  =  ^^  "^  .000841  H'«r». 

The  resultant,  acting  at  right  angles  to  a  diameter  of  half  of  this  force, 
tends  to  disrupt  one  half  of  the  wheel  f  i-om  the  other  half,  and  is  resist^  by 
the  section  of  the  rim  at  each  end  of  the  diameter.   The  resultant  of  half  the 

9 
radial  forces  taken  at  right  angles  to  the  diameter  is  1  >«-  Hv  =  >  of  the  nun 

of  these  forces:  hence  the  total  foroe  F  is  to  be  divided  by  8  x  8  X  1.5706 
ss  6.283d  to  obtain  the  tensile  strain  on  the  croKS-section  of  the  rim,  or,  total 
Bttaiu  on  tlie  cross-section  s  fif  s  .000054^7  WRr^,  The  weight  IF,  of  a 
rim  of  cast  iron  1  inch  square  in  section  is  2v/Z  X  8.185  s  19.(351?  pounds, 
whence  strain  per  square  moh  of  sectional  area  of  rim  »  ifi  ?  .001UCI6(>A>t* 
=  .0002664Z)«r«  =  .0000870 F«,  In  which  D  =  diameter  of  wheel  in  feet,  and  F 
is  velocity  of  rim  in  feet  per  minute.  Bi  b  .091^",  if  v  is  taken  In  feet  per 
second. 

For  wrought  iron ^i  a  .0011866/2«r>  =r  .00088421>*t«  s  .OOOOSeSF*. 

For  steel Sj  =*  .00115981?<r«  =  .OOOWOlDV*  =  .00O0894F*. 

For  wood Sx  =*  .0000888ir»»'»  =  .0000282Z;«i »  =  .00000»5r>. 

The  specific  gravity  of  the  wood  being  taken  at  0.5  =  37.5  lbs.  per  cv.  ft.^ 
or  1/12  the  weight  of  cast  iron. 

j^xamo/e.— Required  the  strain  per  square  Inch  in  the  rim  of  a  caat-iron 
wheel  30  ft.  diameter,  60  revolutions  per  minute. 

AMKioei\  16S  X  501  X  .0010656  s=  868.1  lbs. 

Required  the  strain  per  squ&i-e  incli  in  a  cast-iron  wheel^rim  ruuning  a 
mile  a  minute.    AMSwet.  .000027  X  5280«  =  752.7  lbs. 

In  cast-iron  fly-wheel  rims,  on  account  of  their  thickness,  there  Is  difficulty 
in  securing  soundnetiS,  and  a  tensile  strength  of  10,000  lbs.  per  sq.  in.  is  as 
much  as  can  be  assumed  with  safety.  Ut;ine  a  factor  of  safety  of  10  gives  a 
maximum  allowable  strain  in  the  rim  of  lOOO  lbs.  per  sq.  in.,  which  corre- 
spoiids  to  a  rim  velocity  of  6085  ft.  per  minute. 

For  any  given  material,  as  cast  iron,  the  strength  to  resist  centrifugal  force 
depends  only  on  tlie  velocity  of  the  rim,  and  not  upon  its  bulk  or  weigbt. 

Chas.  E.  Emery  KCas^.  Mag.,  1892)  says:  By  calculation  half  the  strength 
of  the  arms  is  available  to  strengthen  the  rim,  or  a  trifle  more  If  the  fly- 
wheel centres  are  relatively  large.  The  arms,  however,  are  subject  to  trans- 
verse strains,  from  belts  and  from  clumKes  of  speed,  and  there  Is,  moreover, 
no  certainty  that  the  arms  and  rim  will  be  adjusted  so  as  to  pull  exact  I  v 
together  in  resisting  disruption,  so  the  plan  ol  considering  the  rim  by  itself 
and  making  it  strong  enough  to  resist  disruption  by  centrifugal  force  within 
safe  limits,  as  is  assumed  in  the  calculations  above,  is  the  safer  way- 
It  does  not  appear  that  flv-wheels  of  customary  construction  should  be 
unsafe  at  the  comparatively  low  8pee<ls  no\r  in  common  use  if  proper 
materials  are  used  In  constniction.  The  cause  of  rupture  of  fly- wheels  tnat 
have  failed  is  usually  either  the  "  running  away  *'  of  tiie  engine,  such  aa  may 
be  caused  bv  the  breaking  or  slackness  of  a  governor-belt,  or  incorrect 
design  or  defective  materials  of  the  fly-wbeel. 

Chas,  T.  Porter  (Trnus.  A.  S.  M.  E.,  xi v.  808)  states  that  Horace  of  the 
bursting  of  a  fly-wheel  with  a  solid  rim  in  a  hlgh-sneed  engine  is  known,  lie 
attributes  the  bursting  of  wheels  built  in  segnienfn  to  insufficient  strength 
of  the  flanges  and  bolis  by  which  the  segments  are  held  to{?ether.  (See  also 
Thurston,  **  Manual  of  the  Steam-engme.'"'  Part  II,  page  413,  etc.) 

Arm*  of  Fly-w^lieela  and  Pulleys*  —  Professor  Torrey  (Am. 
Mack  ,  July  80,  1>^91)  gives  the  following  f(;rmulafor  arms  of  elliptical  crose- 
sectlon  of  cast-iron  wheels  : 

W  =  load  in  pounds  acting  on  one  arm:  S  sa  strain  on  belt  In  pounds  per 
inch  of  width,  taken  at  5C  for  single  and  112  for  double  belts;  v  ss  width  of 
belt  In  inches;  n  =  number  of  arms;  L  =  length  of  arm  in  feet;  6  k  breadth 

of  arm  at  hub;   d  s  depth  of  arm  at  hub,  both  In  inches :    W  s=  — ; 

WL  **  ' 

b  =  5^^ .    The  breadth  of  the  arm  is  its  least  dimension  =  minor  axis  of 

the  ellipse,  and  the  depth  the  major  axis.  This  formula  is  bas^d  on  a  factor 

of  safety  of  10. 


FLY-WfiBBL8.  821 

Ib  udnfir  the  fommla,  tMt  Mtmnd  •oni«  depth  tor  the  Mtn,  And  otietiiate 

the  required  breadth  to  go  with  It.  If  1i  t?!*^  %  too  round  an  arm,  assume 
the  breadth  a  little  s^reater,  and  repeat  the  calculation.  A  second  trial  will 
almost  always  give  a  good  section. 

The  size  of  the  arms  at  the  hub  having  been  calculated,  they  may  be 
somewhat  reduced  at  the  rim  end.  l%e  actual  amount  cannot  becalealated, 
as  there  are  too  many  unknown  quantities.  However,  the  defxth  and 
breadih  can  be  reduced  about  one  third  at  the  rim  without  danger,  and  tbls 
will  give  a  well-shaped  arm. 

Pulleys  are  often  cast  in  halves,  and  bolted  together.  When  this  is  done 
the  greatest  care  should  be  taken  to  provide  sufficient  metal  in  the  bolts. 
This  is  apt  to  be  the  very  weakest  point  in  such  pulleys.  The  combined  area 
of  the  bolts  at  each  Joint  should  be  about  28/100  the  crose-section  of  the  pul 
ley  at  that  point.    (Torrey.) 

9/BD 

Unvtn  gives  d  cs  0.68874/  ~^  for  single  belte  \ 

d  =  0.?«  y-^tor  doQblebelte} 

2>  being  the  diameter  of  the  pulley,  and  B  the  breadth  of  the  rim,  both  in 
inches.  These  formule  are  based  on  an  elliptical  seotlon  of  arm  in  which 
b  =  O.id  or  d  =  2M  on  a  width  of  belt  s  4/5  the  width  of  the  pulle/  rim, 
a  maximum  driving  force  transmitted  by  the  belt  of  56  lbs.  per  inch  of  width 
for  a  single  belt  and  112  lbs.  fbr  a  double  belt,  and  a  safe  working  stress  of 
cast  iron  of  2SS0  lbs.  per  square  inch. 
If  in  Torrey'B  formula  we  make  b  =  0.4d,  it  reduees  to 


*/WL  %/WL 


trample. —Given  a  pulley  10  feet  diameter;  8  arms,  each  4  fteet  long;  faae, 
86  inches  wide;  belt,  30  inches:  required  the  breath  and  depth  of  the  arm  at 
the  hub.    According  to  Unwin, 


%/bd  i/aexiw 

d  =  0.C3S7  J/  — -  =  0.683.^  — § —  =  5.16  for  single  belt,  b  a  106} 


d  =  0.788  //  -^  =  0.798//  — g —  s  6.50  for  double  belt,  5  s  aOO. 

According  to  Torrey,  if  we  take  tJto  formula  b  sa  — ^  and  aeeume  d  %  B 

and  6.5  inches,  i-espectively,  for  single  and  double  belts,  we  obtain  6  =  1.06 
and  1.88,  respectively,  or  practically  only  one  half  of  the  breadth  according 
to  Unwin.  and,  since  transverse  strength  is  proportional  to  breadth,  an  arm 
only  one  half  as  strong. 

ToiTey's  formula  is  said  to  be  based  on  a  factor  of  safety  of  10,  but  this 
factor  can  be  only  apparent  and  not  real,  since  the  assumption  that  the 
strain  on  each  arm  is  equal  to  the  strain  on  the  belt  divided  by  the  number 
of  arms,  is,  to  say  the  leant,  inaccurate.  It  would  be  more  nearly  correct  to 
say  that  the  strain  of  the  belt  is  divided  among  half  the  number  of  arms. 
Unwin  makes  the  same  assumption  in  developing  his  formuUi,  but  savs  it  is 
only  in  a  rough  sense  true,  and  that  a  large  factor  of  safety  must  be  allowed. 
He  therefore  takes  the  low  figure  of  8'^^  lbs.  per  square  inch  for  the  safe 
working  strength  of  cast  Iron.  Unwin  says  that  his  equations  agree  well 
-.vlth  practice. 

IHameiers  of  Fly-nrheela  for  Tarions  Speeds*— If  6000  feet 
pf  r  minute  be  the  maximum  velocity  of  rim  allowable,  then  6000  r=  vH2>,  in 
which  B  =  revolutions  per  minute,  and  D  s  diameter  of  wheel  in  feet» 

„      6000       1910 
whence  I>«—  =  -^. 


S22 


THE  8TEAH-EKGINE. 


HaXXMUIC  DiaMSTER  or  FlY-WHECL  ALIX>WABLB  POB  DlVnEBXMT  If UMBBBS 

OF  Bbvolutions. 


AssuminuT  Maximum  Speed  of 

AssumiDg  Maximum  Speed 
of  6000  feet  per  minute. 

ReTOlutlons 

5000  feet  per  minute. 

per  minute. 

Circum.  ft. 

Diam.  ft. 

Circum.  ft. 

Diam.  ft. 

40 

125 

80.8 

150. 

47.7 

60 

100 

81.8 

190. 

88.8 

60 

88.8 

26.5 

100. 

81.8 

TO 

71.4 

28.7 

86.W 

87.3 

80 

68.5 

19.9 

75.00 

83.9 

90 

65.5 

17.7 

66.66 

21.8 

100 

60. 

15.9 

60.00 

19.1 

120 

41.67 

18.8 

60.00 

16.9 

140 

85.71 

11.4 

42.86 

13.6 

160 

31.25 

9.9 

87.6 

11.9 

180 

87.77 

8.8 

88.88 

10.6 

dOO 

25.00 

8.0 

80.00 

9.6  . 

290 

22.73 

7.8 

27.27 

8.7 

240 

20.88 

6.6 

85.00 

8.0 

960 

19.28 

6,1 

88.08 

7.3 

280 

17.86 

6.7 

81.48 

6.8 

800 

16.66 

6.3 

80.00 

6.4 

850 

14.29 

4.5 

17.14 

6.5 

400 

12.6 

4.0 

15.00 

4.8 

400 

11.11 

8.5 

18.88 

4.8 

600 

10.00 

3.2 

12.00 

8.8 

Strains  In  the  Rln&B  of  Fly»band  'WlieelB  Prodneed  hy 
Oentrlfngal  Force.  (James  B.  Stan  wood.  Trans.  A.  8.  M.  £.,  xiv.  :i&i.) 
—Mr.  Sianwood  mentions  one  case  of  a  fly-band  wheel  where  the  periphery 
Telocity  on  a  17'  9"  wheel  is  over  7500  ft.  per  minute. 

In  band  saw-mills  the  blade  of  the  saw  is  operated  successfully  over 
wheels  8  and  9  ft.  in  diameter,  at  a  periphery  velocity  of  9000  to  10,000  ft.  per 
minute.  These  wheels  are  of  cast  iron  throughout,  of  heavy  thickness,  with 
a  larfre  number  of  arms. 

In  shingle-machines  and  chipping-macbines  where  cast-iron  disks  from  8  to 
6  ft.  in  diameter  are  employeci,  v^-ith  knives  inserted  radially,  the  speed  is 
freouentlv  10,000  to  11,000  ft.  per  minute  at  the  periphery. 

If  the  run  of  a  fly-wheel  alone  be  considered,  the  tensile  strain  in  pounds 

per  square  inch  of  the  rim  section  is  T  s  •—  nearly,  in  which  V  s=  velocity 

in  feet  per  second;  but  this  strain  is  modified  by  the  resistance  of  the  arms, 
which  prevent  the  uniform  circumferential  expansion  of  the  rim,  and  induce 
a  bending  as  well  as  a  tensile  strain.  Mr.  Stanwood  discusses  the  strains  in 
band -wheels  due  to  transverse  bending  of  a  section  of  the  rim  between  a 
pair  of  arms. 

When  the  arms  are  few  in  number,  and  of  large  cross-section,  the  ring 
will  be  strained  transversely  to  a  greater  degree  than  with  a  greater  number 
of  lighter  arms.  To  illustrate  the  necessary  rim  thiclcnesses  for  Tarioua 
rim  velocities,  pulley  diameters,  number  of  arms,  etc.,  the  following  table 
is  given,  based  upon  the  formula 

t« 7-B 


-"  \  F»        10/ 


in  which  t  =  thickness  of  rim  in  inches,  d  =  diameter  of  pulley  in  fnchf^ 
N  =  number  of  arms,  V  s=  velocity  of  rim  in  feet  per  second,  and  f*  =  the 
sreatest  strain  in  pounds  per  square  inch  to  which  any  $bre  is  subjected. 
T))e  vi^ue  of  ^  is  taken  at  6000  lbs.  oer  sq.  in. 


XXT-WEEEL8. 


823 


TbtekiiMft  of  Rtui*  In  8oU4  Wheels. 

Diameter  of 
Pulley  In 
inches. 

Velocity  of 
second. 

Velocity  of 

Rim  ill  feet  per 

minute. 

No.  of 
Arms. 

TblckneSB  in 
inches. 

24 
M 

48 
106 
106 

SO 

88 
88 
184 
184 

8,000 
6,280 
6,880 
11,040 
11,040 

6 
6 
6 
10 
86 

8/10 
16/82 

If  the  limit  of  rim  velocity  for  all  wheels  be  assumed  to  be  88  ft.  per  sec- 
ond, equal  to  1  mile  per  minute,  F  =  6000  lbs.,  the  formula  becomes 

.      .475d  ^  ^      d 
.67iV«  "■        JV«' 

When  wheels  are  made  in  halves  or  in  sections,  the  bendlne  strain  may 
be  such  as  to  make  t  greater  than  that  given  above.  Thus,  when  the  joint 
comes  half  way  between  the  arms,  the  bending  action  Is  similar  to  a  beam 
supported  simply  at  the  ends,  uniformly  loaded,  and  ilaW  greater.  Then 
the  f crmula  becomes 

.  .nsd 

*"  jn(JL  ^  1)' 

V  F*        lO^' 

or  for  a  flzed  maximum  rim  velocity  of  88  ft.  per  second  and  F  =  0000  lbs., 

t  =  — ^t—   ^  Begmental  wheels  it  is  preferable  to  have  the  Joints  opposite 

the  arms.  Wheels  In  halves,  if  very  thin  rims  are  to  be  employed,  should 
have  double  arms  along  the  Une  of  separation, 

Attendoo  should  be  given  to  the  proportions  of  large  receiving  and  tight- 
ening pulleys.  The  thiolniess  of  rim  for  a  48-tn.  wheel  (shown  hi  table)  with 
a  rim  velocity  of  88  ft  per  second,  Is  16/16  in.  Many  wrecks  have  been 
caused  bj  the  failure  of  receiving  or  tightening  pulleys  whose  rims  have  beet 
too  thin.  Fly>wbeels  calculated  for  a  given  coefficient  of  steadiness  are  fre- 
quently lighter  than  the  minimum  safe  weight.  This  is  true  espedally  of 
large  wheels.  A  rough  guide  to  the  minimum  weight  of  wheels  can  be  de- 
duced from  our  formulsB.  The  arms,  hub.  lugs,  etc.,  usually  form  from  one 
quarter  to  one  third  the  entire  weight  of  the  wheel.  If  6  represents  the  face 
of  a  wheel  in  inches,  the  weight  of  the  rim  (consMered  as  a  simple  annular 
ring)  win  be  to  =  .8sidtb  0)6.  If  the  limit  of  speed  is  88  ft.  per  seoond,  then 
for  solid  wheels  f  =  0.7d  -i-  iV*.  For  sectional  wheels  (Joint  between  arms) 
t  =  1.06d '*~N\  Weight  of  rim  for  soUd  wheete,  w  =  jsfd^b  -%-  N*  In  pounds. 
Weight  of  rim  in  secnonal  wheels  with  joints  between  arms,  10  3  .B6d>6  -»- 
iV  in  pounds.  Total  wdght  of  wheel:  for  aoUd  wheel,  W  ^^76dsb  -1-  j\r«  to 
J66cPb  -»-  iV*,  In  pounds.  For  segmental  wheels  with  Joint  between  arms, 
ir=1.06re«6-i-^*tol.8d*6-«-JV^,  Inpounds. 

(This  subject  Is  further  discussed  by  Mr.  Stanwood,  in  vol.  zv.,  and  by 
Prof.  Oaetano  Lansa,  in  voL  zvl..  Trans.  A.  S.  M.  E.) 

A  'Wooden  Rim  Fly-i¥lteei>  built  in  1891  for  a  pair  of  Corliss  en- 
gines  at  the  Amoskeag  Mfg.  Oo.'s  mill,  Manchester,  N.  H.,  Is  described  by 
C  H.  Manning  in  Trans.  A.  S.  M.  E.,  xiii.  618.  It  is  30  ft.  diam.  and  108  in.  face. 
The  rim  Is  VJ  inches  thick,  and  is  built  up  of  44  courses  of  ash  plank,  2,  3, 
and  4  inches  thick,  reduced  about  U  inch  in  dressing,  set  edgewise,  so  as  to 
break  Joints,  and  glued  and  bolted  together.  There  are  two  hubs  and  two 
sets  of  arms,  18  In  each,  all  of  cast  iron.   The  weights  are  as  follows: 

Weight  (calculated)  of  ash  rim 81.866   Iba. 

•*       of  84  arms  (foundry  45,080) 40,848     •* 

•*    8hubs(       »'       86,080)  81,89iic  * 

Oounter-weights  In  6  arms 664     ** 

Total,  excluding  bolts  and  screws 104,868±  " 

Ihe  wheel  was  tested  at  76  revs,  per  min.,  being  |i  surface  speed  of  nearly 
7800  feet  per  minute.  • 


822 


THE  8TEAH-EKGINE. 


HAxminc  Diambtbb  of  Flt-whxel  Alix>wablb  ror^r  Iran  *nd  of  wooden 
OF  Bbyolutionb.         Mlog  the  same  in  boin 

..-s-seetfon  would  be  direcily 

: : — ;; — : ^ —  .-•.<>  stand  the  strain  directly  os 

Assuminflr  Maximum  Speed  of  ^  tb^  tensile  strengths  divi.le<i 
5000  feet  per  minute.      ,^  different  materials.    Ca«l  iron 


Revolutions 
per  roioute. 


Clrcum.  ft. 


126 
100 
88.8 

n.4 

68.5 
55.5 
60. 
4 


^  a  tensile  streoRlh  of  1,440,000  lbs. 

Dtair      1.440,000 -+-460=  aSOO.  whilst  ash,  of 

jbs.  per  cubic  foot,  and  with  l,i5S.t«00 

*  ^ives  a  resnlt  1,152.000  h-  84  =  88>^ 

/tiod-rimmed  pulley  is  ten  times  safer 

jgs  are  good.    This  would  allow  the  wood- 

^teed  to  VlO.58  =8.85  times  that  of  a  sound 

y'/f  tlie  uriUlmantlc  Linen  Co.   (UUk- 

.v;i>.)— Rim  28  ft.  tiiam.,  110  In.  face.    7 lie  rim  is 

y^^nuMt  one  under  the  centre  of  each  belt,  with  li 


/ '  ^,  is  ordinary  whitewood,  ^  in.  in  thickness,  cut  into 
■^4  feet  in  length,  and  either  6  or  8  inches  in  width. 
',,^fby  building  a  complete  circle  18  inches  in  width,  flret 


40 
60 
60 
TO 
80 
90 
100 
120 
140 
160 
180 
200 
220 
240 

260  '^?>{f'^ja  positionr  The  nails  pass  through  three  and  mto  liie 

880  ^'''^V'li  At  the  end  of  each  arm  four  H-inch  bolts  secure  the 
800  y^i^SnS  covered  by  wooden  plugs  glued  and  driven  into  the  face 
850     iK^'^ 

4r     ^^^i^^aodFly-nrheelsfbr  Extreme  Speeds.    (Eng'gNeia, 

i      'fki^.)—'^^^  power  required  to  produce  the  Mannesmann  tubes  is 

'''ijjr^  'rarying  from  2000  to  10,000  H.P..  according  to  the  dimensions  of 

■"—       >'^5**5lflce  this  power  Is  only  needed  for  a  short  time  (it  takes  only  30 

^^;m^  to  convert  a  bar  10  to  12  ft.  long  and  4  In.  in  diameter  Into  a 

^/^then  some  time  elapees  before  the  next  bar  Is  ready,  an  engine  of 

#        ^,^F  provided  wlih  a  large  fly-wheel  for  storing  the  energy  will  supply 

' S^Jiough.  for  one  set  of  rolte.    These  fly-wheels  are  so  large  and  run  at 

>«^L««t  Mpeeda  that  the  ordinaty  method  of  constructing  them  cannot  b« 

iSffjSd.   A  wheel  at  the  Mannesmann  Works,  made  in  Komotjin,  Hungarf , 

ff^  usual  manner,  broke  at  a  tangential  velocity  of  125  ft.  per  second. 

/»f/|r- wheels  designed  to  hold  at  more  than  double  this  speed  consist  of  i 

^Sriron  hub  to  which  two  steel  disks,  20  ft.  in  diameter,  are  bolted ;  around 

^^oireumference  of  the  wheel  thus  formed  70  tons  of  No.  5  wire  are  woutd 

ijjer  a  tension  of  60  lbs.    In  the  Mannesmann  Works  at  Landers,  Wales, 

^jji^  a  wheel  makes  240  revolutions  a  minute,  corresponding  to  a  tangential 

JSocity  of  16,080  ft.  or  2.85  miles  per  minute. 

THJB  SLIBS-VAIiVB. 

Ileflnlilone*^ Travel  =  total  distance  moved  by  the  valve. 

Tfirow  of  the  Eccentric  =  eccentricity  of  the  eccentric  e  distance  fk-om  the 
centre  of  the  shaft  to  the  centre  of  the  eccentric  disk  s  U  the  travel  of  i\» 
valve.  (Some  writers  use  the  term  ^  throw  "  to  mean  tiie  whole  travel  ot 
the  valve.) 

Lap  of  the  tvi7ve.  also  called  outside  lap  or  steam-lap  s  distance  the  out»r 
or  steam  edge  of  toe  valve  extends  bevond  or  laps  over  the  steam  edge  of 
the  port  when  the  valve  is  in  its  central  position. 

Ingide  lap,  or  exhaust-Jap  •  distance  the  inner  or  exhaust  edge  of  tbe 
valve  extends  beyond  or  laps  over  the  exhaust  edge  of  the  port  when  tia 
valve  is  in  its  central  jposition.  The  inside  lap  is  sometimes  made  zero,  or 
even  negative,  in  which  latter  case  the  distance  between  the  edge  of  tlie 
valve  and  the  edge  of  the  port  la  sometimes  called  exhaust  clearance,  or 
inside  clearance. 

Lead  of  the  valve  c  tlie  distance  the  steam-port  is  opened  when  tbe  engine 
is  on  its  centre  and  the  piston  is  at  the  beginning  of  tne  stroke. 

Lead-angle  =  the  angle  between  the  position  of  the  crank  when  the  tsItc 
begins  to  be  opened  and  its  position  when  the  piston  is  at  the  beginning  of 
the  stroke. 

The  valve  is  said  to  have  lead  when  the  steam-port  opens  beforsthe  plfton 


THE  SLIDE-VALVE* 


825 


befflns  its  stroka  If  the  piston  begins  its  stroke  before  the  admlssfoii  of 
■team  begins  the  taItb  is  said  to  have  negative  lead,  and  its  amount  is  the 
lap  of  the  edge  of  the  Talve  over  the  edge  of  the  port  at  the  instant  when 
the  piston  stroke  begins. 

/xip-aiH|fe  m  the  angle  throi7gh  which  the  eooentrio  must  be  rotated  to 
eause  the  sleam  edge  to  travel  from  its  central  position  the  distance  of  the 
lap. 

Angmiar  advancB  of  the  eccentric  b  lap-angle  4-  lead  angle. 

Linear  advance  =s  lap  +  lea<  i. 

Bli^et  of  Wsmm^  MftA*  •t«..  upon  tlte  Steam  IMstrlbnCloB,-- 
Qiren  valve-travel  89^  in./lap  9i  in.,  lead  1/ltf  in.,  exhaust-lap  ^  in.,  re- 
quired crank  position  for  admission,  cut-off,  release  and  compreanon,  and 
greatest  port-opening.  (Halsey  on  Slide-valve  Gears.)  Draw  a  circle  of 
diameter  fh  9  travel  of  valve.  From  O  the  centre  set  off  Oa  =  lap  and  ab 
a  lead,  erect  perpendiculars  0»,  ac,  bd:  then  ee  is  the  lai>an»:le  and  cd  the 
lead-angle,  measured  as  arcs.  Set  oft  /pra  cd,  tlie  lead-angle,  then  Og  is 
the  position  of  the  crank  for  steam  admission.  Set  off  Sec -f  cd  from  A  to  <; 
then  Oi  is  the  crank-angle  for  out -off,  tJiAfk-^-fh  is  the  frsction  of  stroke 
completed  at  cut-off.  set  off  Of  ss  exhaust-lap  and  draw  /m;  em  is  the 
exhaust-lap  angle.  Set  off  ib»  b  «e  4-  cd  —  em,  and  On  is  the  position  of 
crank  at  rdease.  Setoffi)»a:ec  +  c<t-l*  Mt,  and  Q|sis  the  position  of  crank 
for  compression,  fo  •«-/% Is  the  fraction  of  stroke  completed  at  rel<wee,  and 
hq-*-hf  \b  the  fraction  of  the  return  stroke  completed  when  compression 
begins;  OA,  the  throw  of  the  eocentric,  minus  da  the  lap,  equals  ah  the 
maximum  port-opening. 

If  a  Tstve  has  neither  lap  nor  lead,  the  line  joining  the  centre  of  the  eooen- 


t  Cat-off 


ReleaM 


Fio.  146. 

trie  disk  and  the  centre  of  the  shaft  being  at  right  ansles  to  the  line  of  the 
ciaiik,  the  engine  would  follow  full  stroke,  admission  4if  steam  beginning  at 
the  iMJginniuK  of  the  stroke  and  ending  at  the  end  of  the  stroke. 

Adding  lap  to  the  valve  enables  us  to  cut  off  steam  before  the  end  of  the 
Ktroke;  the  eccentric  being  advanced  on  the  shaft  an  amoimt  equal  to  the 
lap-angle  enables  steam  to  be  admitted  at  the  beginning  of  the  stroke,  a« 


826 


THE  8TEAM-BKGIKE. 


before  lap  was  added,  and  advancing  It  a  further  amonnt  eonal  to  the  leftd 
anjrle  causes  steam  to  be  admitted  before  the  beRinnfoK  of  the  stroke. 

uavinip  given  lap  to  the  valve,  and  having  advanced  the  eccentric  on  the 
shaft  from  its  central  position  at  right  angles  to  the  crank,  through  the 
angular  advance  =  lap-angle  and  lead-angle,  the  four  events,  admission, 
cut-off,  release  or  exhaust-opening,  and  compression  or  exhaust'Closure, 
take  place  as  follows:  Admission,  when  the  crank  lacks  the  iead-angle  of 
having  reached  the  centre;  cut-off,  when  the  crank  lacks  two  lap-angles  and 
one  lead-angle  of  having  reached  the  centre.  During  the  admission  of 
steam  the  crank  turns  through  a  semicircle  less  twice  the  lap-angle.  The 
greatest  port-opening  is  equal  to  half  the  travel  of  the  valve  less  the  lap. 
Therefore  for  a  givon  port-opening  the  travel  of  the  valre  must  be  in- 
creased if  the  lap  is  increased.  Wiien  exhaust-lap  is  add«^  to  the  valve  it 
delays  the  opening  of  the  exhaust  and  hastens  its  dosing  by  an  angle  of 
rotation  equal  to  the  exhaust- lap  angle,  which  is  the  angle  llirough  which 
the  eccentric  rotates  from  its  middle  position  while  the  exhaust  edge  of  the 
valve  uncovers  its  lap.  Release  then  takes  place  when  the  crank  lacks  one 
lap-angle  aud  one  lead-angle  minus  one  exhaust-lap  angle  of  having  readied 
the  centre,  and  compression  when  the  crank  lacks  lap-angle -i- lead-angle  + 
exhaust-lap  angle  of  having  reached  the  centre. 

The  above  discussion*  of  the  relative  position  of  the  crank,  piston,  and 
valve  for  the  different  points  of  the  stroke  Is  accurate  only  with  a  connect- 
ing-rod of  infinite  length. 

For  actual  connecting-rods  the  angular  position  of  the  rod  causes  a 
distortion  of  the  position  of  the  valve,  causing  the  events  to  take  plaoe  too 
late  in  the  forward  stroke  and  too  enily  to  the  return.  The  correction  of 
this  distortion  may  be  accomplislied  to  some  extent  by  setting  the  valve  so 
as  to  give  equal  lead  on  both  forward  and  return  stroke,  and  by  altering 
the  exhaust-lap  on  one  end  so  as  lo  equalize  the  release  and  compression. 
F.  A.  Halsey,  in  his  Blide-valve  Gk*ani.  describes  a  method  of  equalizing  the 
cut-off  without  at  the  same  time  affeciins:  the  equality  of  tne  lead.  In 
designing  slide-valve$  the  effect  of  angularity  of  the  connecting-rod  should 
be  Rtiidied  on  the  drawing-board,  and  preferably  by  the  use  of  a  model. 

SiveeC'a  VmlvthdiugrwLUkt—To  find  outside  and  inside  lap  of  valve 
for  different  cut-oflls  and  compressions  (see  Fig.  U7):  Draw  a  cirde  whose 


A*  M 


FiQ.  147.— 8weet*s  Yalve-dlagram. 


diameter  equals  travH  of  Talve.  Draw  diameter  BA  and  continue  to  A^, 
so  that  the  length  AA^  beara  the  name  ratio  to  XA  rr  the  length  of  ron- 
necting-rcvd  do^K  to  length  of  engine-crank.  Draw  small  circle  E  with  a 
ladius  equal  to  lead,     l^ay  off  AC  so  tliat  ratio  of  AC  to  AB  ss  cut-off  in 

Sarts  of  the  stroke.  Erect  perpendicular  CD.  Draw  DL  tangent  to  M\ 
raw  XS  perpendicular  to  D£;  xS  is  then  outside  lap  of  valve. 

To  And  release  and  compression:  If  there  is  no  inside  lap,  draw  FS 
through  X  parallel  to  DL.  F  and  B  will  be  position  of  crank  for  release 
and  compression.  If  there  is  an  inside  lap,  draw  a  circle  about  X,  in  which 
radius  XF  equals  inside  lap.  Draw  HO  tangent  to  this  circle  and  parallel 
to  DL\  then  H  and  O  are  crank  position  for  release  and  compression. 
Draw  i/iHTand  MQy  then  AN  is  piston  position  at  release  and  ^If  piston 
position  at  compression,  AB  being  considered  stroke  of  engine. 

To  make  compression  alike  on  each  stroke  it  Is  necessary  to  increase  the 
Inside  lap  on  crank  end  of  valve,  and  to  decrease  by  the  same  amoiut  the 


THE  SLIDE-VALVE. 


827 


Inside  lap  on  back  end  of  valTe.  To  determine  tills  amount,  throusrb  Jf  witb 
a  radius  MiO  s  A  A*,  draw  arc  M  P,  from  P  draw  PT  perpendicular  to  AB, 
then  TM  is  the  amount  to  be  added  to  inside  lap  on  crank  end,  and  to  be 
der1uct(*d  from  inside  lap  on  back  end  of  valve,  inside  lap  belnf?  XT. 

For  the  Bilfjiam  Valve  Diaoiam,  w«  Halsey  on  Slide-valve  Gears. 

The  Zenner  TalFe-dlagrmm  is  given  in  most  of  the  works  on  the 
Bteam-eiiiflne,  and  in  treatises  on  valve-gears,  as  Zeuner*B,  Peabody*8,  and 


Fki.  148.— ZeuDer*s  Valve-diagram. 

8panfder*8.  Hie  following  is  condensed  from  Holmes  on  the  Steam-engine: 
Describe  a  circle,  with  radius  OA  equal  to  the  half  travel  of  the  valve. 
From  O  measure  off  OB  equal  to  the  outside  lap,  and  BC  eoual  to  the  lead. 
When  tbe  crank- pin  occupies  the  dead  centre  A,  the  valve  has  already 
moved  to  the  right  of  its  central  position  by  the  space  OB-^-BC.  From  C 
erect  the  perpendicular  CE  and  Join  OE.  Then  will  OE  be  the  position 
occupied  by  toe  line  joining  the  centre  of  tbe  eccentric  with  the  centre  of 
the  crank-shaft  at  the  commencement  of  the  stroke.  On  the  line  OE  at 
diameter  describe  the  circle  OCE ;  then  any  chords,  as  Oe,  OB^  Oe\  will 
represent  the  spaces  travelled  by  the  valve  from  its  central  position  when 
the  crank-pin  occupies  respectively  the  positions  opposite  to  Z>,  E,  and  F. 
Before  the  port  Is  opened  at  all  the  valve  must  have  moved  from  its  central 
pofdtioo  by  an  amount  equal  to  the  lap  OB.  Hence,  to  obtain  the  space  by 
which  the  port  is  opened,  subtract  from  each  of  the  arcs  Oe,  OE^  etc.,  a 
length  equal  to  OB.  This  is  represented  graphically  by  describing  from 
centre  O  a  circle  with  radius  equal  to  the  lap  OB  ;  then  the  spaces  /«,  gE^ 
etc.,  intercepted  between  the  circumferences  of  the  laiMsircle  Bfe'  and  the 
valTe-drcle  OCE,  will  give  the  extent  to  which  the  steam-port  Is  opened. 

At  the  point  k,  at  which  the  chor  1  Ok  is  common  to  both  valve  and  lap 
circles,  it  is  evident  that  the  valve  has  moved  to  the  right  by  the  amount  of 
the  lap,  and  is  consequently  lust  on  the  point  of  opening  the  steam-port. 
Hence  the  steam  is  admitted  before  the  commencement  of  the  stroke,  when 
Ibe  crank  occupies  the  position  O//,  and  wbile  the  portion  ffA  of  t^e  reyp- 


828  THB  BTEAH-ElTQIirB. 

lutloo  sUn  remains  to  be  aocompUahed.  When  the  oraok-pin  Feeflfaes  tlia 
position  A^  that  Is  to  say,  at  the  commenoement  of  the  stroke,  the  port  is 
already  opened  by  the  space  00-OB=s  BC^  called  the  lead.  From  Uik 
point  forward  till  the  crank  occupies  the  position  OiT  the  port  continues  to 
open,  but  when  the  crank  Is  at  Os  the  yalve  has  reached  the  furthest  limit 
of  its  travel  to  the  ri&bt,  and  then  commences  to  return,  till  wheii  in  Uie 
position  OJ^the  edge  of  the  valve  Just  covei-s  the  steam-port,  as  Is  shown 
by  the  chord  Oe\  being  again  common  to  both  lap  and  valve  circles.  Hence 
when  the  crank  occupies  the  position  OF  the  cut-ofT  takes  place  and  the 
steam  commences  to  expand,  and  continues  to  do  so  till  the  exhaust  opens. 
For  the  return  stroke  the  steam-port  opens  again  at  B*  and  doses  at  Jr. 

There  remains  the  exliauBt  to  be  considered.  When  the  line  jolnlnir  the 
centres  of  the  eccentric  and  crank-«haf t  occupies  the  position  opposite  to 
OG  at  right  angles  to  the  line  of  dead  centres,  the  crank  is  in  the  line  OP  at 
right  angles  to  OE ;  and  as  OP  does  not  fntereect  either  ▼alve-circle  she 
valve  occupies  its  central  position,  and  consequently  closes  the  port  by  the 
amount  of  the  inside  lap.  The  crank  must  tnei-efore  move  throosrh  such 
an  angular  distance  that  its  line  of  direction  OQ  must  intercept  a  onord  on 
the  valve-circle  OK  equal  in  length  to  the  inside  lap  before  the  port  can  be 
opened  to  the  exhaust.  This  point  is  ascertained  precisely  in  the  same 
manner  as  for  the  outside  lap,  namely,  by  drawing  a  circle  from  centre  O. 
with  a  radius  equal  to;  the  Inside  lap;  this  is  the  small  inner  drede  In  the 
figure.  Where  this  circle  intersects  toe  two  valve-circles  we  get  fonr  points 
which  show  the  positions  of  the  crank  when  the  exhaust  opens  and  closes 
during  each  revolution.  Thus  at  Q  the  valve  opens  the  exhaust  on  the  side 
of  the  piston  which  we  have  been  considering,  whll<*  at  R  the  exhaust  closes 
and  compression  commences  and  continues  till  the  fresh  steam  Is  read- 
mitted at  H. 

Thus  the  diagram  enables  us  to  ascertain  the  exact  position  of  the  crank 
when  each  critical  operation  of  the  valve  takes  place.  Making  a  riwLtni  of 
these  operations  of  one  side  of  the  piston,  we  have:  Steam  admitted  before 
the  commencement  of  the  stroke  at  H.  At  the  dead  centre  A  the  valve  is 
already  opened  by  the  amount  BC.  At  E  the  port  is  fully  opened,  and 
valve  has  reached  one  end  of  its  travel.  At  i^ steam  Is  cut  off,  consequently 
admission  lasted  from  H  to  F.  At  P  ralve  occupies  central  position,  and 
ports  are  closed  both  to  steam  and  exhaust.  At  Q  exhaust  opened,  conse- 
quently expansion  lasted  from  J^  to  Q.  At  K  exhaust  opened  to  maximum 
extent,  and  valve  reached  the  end  of  its  travel  to  the  left.  At  R  exhaust 
closed,  and  compression  begins  and  continues  till  the  fresh  steam  is  admitted 
eXH, 

Problbm.— The  simplest  problem  which  occurs  Is  the  following :  Given 
the  length  of  throw,  the  angle  of  advance  of  the  eccentric,  and  the  laps  of 
the  valve,  find  the  angles  of  the  crank  at  which  the  steam  is  admitted  and 
cut  off  and  the  exhaust  opened  and  closed.  Draw  the  line  0£,  representinir 
the  half -travel  of  the  valve  or  the  throw  of  the  eccentric  at  the  given  anfrle 
of  advance  with  the  perpendicular  00»  Produce  OK  to  K.  On  O^and  OK 
as  diameters  describe  the  two  valve-circles.  'With  centre  and  radii  equal  to 
the  given  laps  describe  the  outside  and  Inside  lap-cirdes.  Then  the  Inter- 
section of  these  circles  with  the  two  valve-drdes  give  points  through  whidi 
the  lines  OH,  OF,  00,  and  OR  can  be  drawn.  These  lines  give  the  required 
positions  of  the  crank. 

Numerous  other  problems  will  be  found  In  Holmes  on  the  Steam-engine, 
including  problems  in  valve-setting  and  the  application  of  the  24euner  dia- 
gram to  link  motion  and  to  the  Meyer  valve-eear. 

Port  Opening:*— 11ie  area  of  port  opening  should  be  such  that  the  ve- 
locity of  the  Bteamln  passin-  "*- "^  '"  -»-— .j  --^ ^  -.w«.*. 


^  ^     dng  through  it  should  not  exceed  6000  ft.  per  min. 

The  ratio  of  port  area  to  piston  area  will  then  vary  with  the  piston-speed  ss 
follows: 

^**7t^per**mlS*^°' [     100   800300400500600700800900    lOOO    WOO 

^'^^iroa'x^*'*'''"}   '^^^  -^    ^^  '^^  -^    '*    '^^  •***  '^'    •"'     •* 
For  a  velocity  of  6000  ft.  per  min.. 

Port  area  =s  ^  Q^  diam.  of  cyl.  X  piston  speed 

The  length  of  the  port  opening  may  be  equal  to  or  something  less  than  the 
diameter  of  the  cylinder,  and  the  width  =  aiea  of  port  opening  -«-  its  length. 

The  bridge  between  steam  and  exhaust  ports  should  oe  wide  enough  to 
prevent  a  isak  of  st^am  into  the  exhaust  due  to  o?ertrave|  o^  t|)e  valve. 


THE  SLIDB-YAtVB. 


829 


AuohhMliMB  irises:  Width  of  ezhaask  port  m  width  of  tttaam  port  -f 
H  travel  of  valve  -  width  of  bridge. 

LmUL  (From  Peabody*B  Valve-(teari.V-The  lead,  or  tha  amoant  that 
Ihe  valve  is  open  when  the  eofrine  ia  od  a  dead  point,  varlea,  with  the  type 
and  Blxe  of  the  anglne.  from  a  very  small  amount,  or  even  nothing,  up  to  M 
of  an  inch  or  more.  Statiooanr-enffines  running  at  slow  spaed  may  have 
from  1/M  to  1/16  inch  load.  The  effect  of  comprasaion  Is  to  All  the  waaie 
space  at  the  end  of  the  cylinder  with  steam;  consequently,  engines  having 
much  compression  need  less  lead.  Locomotive-«nRtnes  having  the  valves 
controlled  oy  the  ordinary  form  of  Stephenson  link-motion  may  have 
a  small  lead  when  mnning  Mlowly  and  with  along  cnt-off,  but  when  at  speed 
with  a  short  cut-off  the  lead  is  at  least  H  ^^^ch;  and  locomotives  that  have 
valve-gear  which  gives  constant  lead  commontv  have  ^  Inch  lead.  The 
lead-angle  is  the  angle  the  crank  makes  with  the  line  of  dead  points  at 
admlssloo.    It  may  vary  from  0»  to  d*. 

Inatd«  Ii^ad*— Wei«bach  (vol.  if.  p.  296)  says:  Eatperlment  diows  that 
the  earlier  openlug  of  the  exhaust  ports  is  especially  of  advantage,  and  in 
the  best  engines  the  lead  of  the  valve  upon  the  side  of  the  exhaust,  or  the 
Inside  lead;  is  1/85  to  1/15;  i.e.,  the  slide-valve  at  the  lowest  or  highest  posi- 
tion of  the  piston  has  made  an  opening  whose  height  is  1/25  to  1/15  of  the 
whole  throw  of  the  slide-valve.  The  outside  lead  of  the  slide-valrd  or  the 
lead  on  the  steam  side,  on  the  other  hand,  is  mueh  amaller,  and  Is  of  leu 
only  1/100  of  the  whole  uirow  of  the  valve. 


BAet 


of  dianfflnc  Ontalde  Itap.  Inatde  Iiap,  TrmY«l 
and  Ancalar  Adiranoe*    (Thurston.) 


Incr. 
O.L. 
Incr. 

I.L. 
Incr. 

T. 
Inor. 
A.A. 


Admission 


Is  later, 
ceases  sooner 

unchanged 

begins  sooner, 
conUnues  longer 
[ns  earlier, 
'  unaltered 


Expansion 


occurs  earlier, 

continues  longer 

begins  aa  before, 

continues  longer 

begins  later, 

ceases  sooner 

begins  sooner, 

per,  the  same 


is  unchanged 

occurs  later, 
ceases  earlier 
begins  later, 
1  later 


begins  earlier, 
per,  unchanged 


OompresskM 


begins  at 

same  point 

begins  sooner, 

oontinoes  longer 

begins  later, 

ends  sooner 

begins  earlier, 

pjr.  the  same 


Zeuner  gives  the  following  relations  (Weisbach-Dubois,  vol.  11.  p.  807): 
If  5  a  travel  of  valve,  p  s  maximum  port  opening; 
L  =s  steam-lap,  I  s  exhaust-lap; 

/2  3  ratio  of  steam-lap  to  half  travel  »  Tg*   L^^xS; 

'  I  r 

r  a  ratio  of  exhaust  lap  to  half  travel  bs  .^,   {  a  -  x  fi; 


Sis2p  +  2Ls»p-{-2B  +  8;   8t 


1-jr 


If  a  s  angle  BOF  between  positions  of  crank  at  admission  and  ac  cut-off. 
and  ^  s  angle  QOB  between  positions  of  crank  at  release  and  at 
^sln(l90«-a)  uiBll!?!Lril 


compression,  then  i?  =  ^- 


Batio  of  Lap  and  of  Port«op«nittc  to  TalYe^raTel.—The 

table  on  page  831.  givlne  the  ratio  of  lap  to  tra\*el  of  valve  sud  ratio  of  travel 
to  port  opening,  is  abridged  from  one  given  by  Buel  In  Weisbaoh-Dubois, 
vol.  11.  It  is  caknilated  from  the  above  formulss.  Intermediate  values  may 
be  found  by  the  formules,  or  with  sufficient  accuracy  by  interpolation  from 
the  figures  in  the  table.  By  the  table  ou  page  880  the  crank-aogle  may  be 
found,  that  is,  the  angle  between  its  position  when  the  engine  is  ou  the 
centre  and  its  position  at  cut-off,  relea«e.  or  compression,  wlien  these  are 
known  in  fractions  of  the  stroke.  To  iUusiraie  the  iiae  of  the  tables  the 
following  example  is  given  by  Buel:  width  of  port  s  2,ii  iu.;  width  of  port 
openinfc  =  width  of  pen  -f  0.8  in.;  overtmvel  =  3.6  in.;  lengili  of  connect- 
ing-rod =  i\^  times  tctroke  ;  cut-off  =  0.7R  of  stroke  ;  rul<;a»e  s  0.95  of 
Stroke  ;  lead-angle,  10°,    From  the  first  table  we  find  crank-angle  =>  im.q. 


830 


THE  STEAM-EKGIITB. 


add  lead-ani^le,  makingr  1S4.6.*  From  the  second  table,  for  angle  between 
admission  and  cut-off,  125",  we  have  racfo  of  travel  to  port-opening  =  8.72, 
or  for  ]24.6<»  =  &74,  which,  multiplied  by  port-opening  2.5.  gives  9.45  in 
travel.  The  ratio  of  lap  to  travel,  by  the  table,  is  .2324,  or  9.45  X  .2334  =  2.2 
in.  lap.  For  exhaust-lap  we  have,  for  release  at  .95,  crank-angle  =s  151.8; 
add  lead-angle  lO"  =  161.8",  From  the  second  table,  by  interpolation,  ratio 
of  lap  to  travel  s=  .0611,  and  .0611  X  9.45  =  0.77  in.,  the  exhaust-lap. 

Lap-angle  s=  U  (180"  —  lead- angle  —  crank- angle  at  cut-off); 

=  S  (180"  -  10  -  114.6)  =  27.7". 
Angular  advance   s=  lap-angle  -f  lead*angle  b=  27.7  -f  10  s  87.7". 
Exhaust  lap-angle  =  crank-angle  at  release  -f  lap-angle  -f  lead-angle  - 180"; 

=  151.8 -H^7 -MO  -  180"  =  9". 
Crank-angle  at  com-  i 
pression  measured  y  =  180"  -  lap-angle  >  lead-angle  —  ezhanat  lap-angle; 
on  return  stroke     1 

rr  180  -  27.7  -  10  -  9  8  188.8"  ;  corraepondlng,   bj 
table,  to  a  piston  position  of  .81  of  the  return  stroke;  or 
Crank-angle  at  compression  =  180"  ~  (angle  at  release  -  angle  at  cut-off) 

4-  lead-angle; 
=r  180  ~  (151.8-  114.6)-}- 10  s  183.8". 
The  positions  determined  above  for  cut-off  and  release  are  for  the  forwanl 
stroke  of  the  piston.  On  the  return  stroke  the  cut-off  will  take  place  at 
the  same  angle,  114.6",  correspouding  by  table  to  66.6j(  of  the  return 
stroke,  instead  of  76jf.  By  a  slight  adjustment  of  the  angular  advance 
and  the  length  of  the  eccentric  rod  the  cut-off  can  be  equalised.  The 
width  of  the  bridge  should  be  at  least  2.5  -f  0.25  -  2.2  =  0.55  in. 

Crank  Angles  for  Oonneetlns^rodA  of  DUnftrent  I«enstli. 

Forward  and  Return  Strokks. 


ill 

Ratio  of  Length  of  Connecting-rod  to  Length  of  Stroke. 

2 

% 

8 

^ 

4 

6 

Infi- 
nite. 

For. 

Ret. 

For. 

Ret. 

For. 

Ret. 

For. 

Ret. 

For. 

Ret. 

For. 

Bet. 

For. 
or 

ReL 

.01 

10.3 

182 

"l0.5 

12.8 

10.6 

12.0 

"iol 

12.4 

10.8 

18.8 

10.9 

18.1 

11.5 

.02 

14.6 

18.7 

14.9 

18.1 

15.1 

17.8 

16.2 

17.5 

16.8 

17.4 

16.5 

17.1 

16.8 

.03 

17.9 

22.9 

18.2 

22.2 

18.5 

21.8 

18.7 

21.5 

18.8 

21.3 

19.0 

81.0 

19.9 

.04 

20.7 

26.6 

21.1 

25.7 

21.4 

25.2 

21.6 

24.9 

81.8 

94.6 

28.0 

84.8 

28.1 

.05 

28..J 

29.6 

28.6 

28.7 

84.0 

28.2 

24.2 

27.8 

24.4 

87.5 

94.7 

27.8 

25.8 

.10 

88.1 

41.9 

33.8 

40.8 

84.8 

40.1 

846 

89.6 

84.9 

89.2 

86.8 

88.7 

869 

.15 

41 

51.5 

41.0 

60.2 

424 

49.3 

42.9 

48.7 

48.2 

48.8 

48.6 

47.7 

45.6 

.20 

48 

59.6 

48.9 

68.2 

49.0 

67.3 

60.1 

66.6 

60.4 

66.8 

60.9 

55.6 

53.1 

.25 

64.3 

66.9 

65.4 

65.4 

66.1 

64.4 

66.6 

68.7 

67.0 

68.8 

67.6 

88.6 

60.0 

.80 

60.3 

78.5 

61.5 

72,0 

62.2 

71.0 

62.8 

70.8 

63.8 

69.8 

68.9 

00. 1 

66.4 

.35 

66.1 

79  8 

67.8 

78.8 

68.1 

77.3 

68.8 

76.6 

099 

78.1 

69.9 

75.8 

78.5 

.40 

71.7 

85.8 

78.0 

64.8 

78.9 

83.8 

74.5 

82.6 

76.0 

88.0 

76.7 

81  3 

™.6 

.45 

77.2 

91  5 

78.6 

90.1 

79.6 

89.1 

80.2 

88.4 

80.7 

87.9 

81.4 

87.1 

84.8 

.SO 

82.8 

97.2 

84.8 

95.7 

85.2 

94.8 

85.9 

94.1 

86.4 

93.6 

87.1 

92.9 

90.0 

.55 

885 

102.8 

89.9 

101.4 

90.9 

100.4 

91.6 

99.8 

92.1 

99.3 

98.9 

08.C 

95.7 

.60 

94.2 

106.3 

86.7 

107.0 

96.7 

108.1 

97.4 

106.6 

98.0 

106.0 

98.7 

104.8 

101.6 

.65 

100. a 

118.9 

101.7 

112.7 

102.7 

111.9 

103.4 

111.2 

108.9 

110.8 

104.7 

110.1 

107.5 

.70 

106.5 

119.7 

108.0 

118.6 

100.0 

117.8 

109.7 

117.2 

110.8 

116.7 

110.9 

116.1 

113.6 

.75 

113.1 

125  7 

114.6 

124.6 

115.6 

123.9 

116.8 

188.4 

116.7 

128.0 

fl7.4 

182.4 

120.0 

.80 

120.4 

132 

121.8 

181.1 

122.7 

180.4 

123.4 

129.9 

123.8 

129.6 

184.5 

180.1 

126.9 

.85 

128.5 

139 

129.8 

138.1 

180.7 

137.6 

181.3 

187.1 

181.7 

188.8 

188.8 

186.4 

184.4 

.90 

138.1 

146  9 

189.2 

146.2 

189.9 

145.7 

140.4 

146.4 

140.8 

146.1 

141.8 

144.8 

148.1 

.96 

150.4 

156.8 

151.8 

156.4 

151.8 

156.0 

152.2 

155.8 

168.6 

166.6 

168.8 

156.8 

154.9 

.96 

153.5 

150.3 

154.8 

158.9 

154.8 

158.6 

155.1 

168.4 

156.4 

158.2 

166.7 

168.0 

156.9 

.97 

157.1 

162.1 

157.8 

161.8 

158.2 

161.5 

158.5 

161.8 

168.7 

161.2 

169.0 

161.0 

100.1 

.98 

161.3 

165.4 

161.9 

165.1 

163.2 

164.9 

162.5 

104.8 

162.6 

164.7 

168.9 

164.6 

168.7 

99 

166.8 

169.7 

167.2 

169.5 

167.4 

169.4 

167.6 

169.8 

167.7 

189.8 

187.9 

109.1 

168.5 

1.00 

180 

180 

180 

180 

180 

180 

180 

180 

180 

180 

180 

180 

180 

^ 

THE  SLIDB-VALVB. 


831 


B«l«ttTe  notions  of  Cr«ra8»heacl  and  €rank«— If  L  ^  length 
of  c<mnectii)^-rod,  R  =  length  of  crank,  B  =  angle  of  crank  with  centre  line 
of  engine,  D  =  displacement  of  cross-head  from  the  beginning  of  its  stroke, 

I««p  and  Travel  of  Talve. 


Ansrle  between   Positions 
of  Crank  at  Points  of 
Admission  and  Cut-off, 
or    Release    and  Com- 
pression. 

1 

1 

ii 

fcween  Positions 
nk  at  Points  of 
ion  and  Cut-off, 
ease   and    Com- 

1 

1 

►^1 
1 

Angle  between  Positions 
or  Crank  at  Points  of 
Admission  and  Cut-off, 
or   Release  and   Com- 
pression. 

1 

II 
ft 

P 

pt 

P 

t^ 

W 

.4880 

58.70 

85«» 

.8686 

7.61 

I860 

.1918 

8.24 

85 

.4709 

48  22 

90 

.8686 

6.88 

140 

.1710 

8.(M 

40 

.4609 

88.17 

95 

.8378 

6.17 

145 

.1504 

2.86 

45 

.4619 

86.27 

100 

.8814 

5.60 

150 

.1294 

8.70 

60 

.4568 

21.84 

105 

.8044 

5.11 

155 

.1062 

8.56 

65 

.4485 

17.70 

110 

.8868 

4.09 

160 

.0868 

8.42 

60 

.4880 

14.93 

115 

.2687 

4.82 

165 

.0659 

2.80 

66 

.4817 

18.77 

120 

.8600 

4.00 

170 

.0486 

8.19 

70 

.4096 

11.06 

125 

.8809 

8.72 

175 

.0218 

8.09 

75 

.8967 

9.68 

180 

.2113 

8.46 

180 

.OUXI 

8.00 

80 

.8880 

8.55 

PERIODS  OP  ADICIISSION,  OR  CnTT-OPP«POR  TARIOIJS 
I.AP8  ANB  TRAVBLS  OP  SIilOB-TAIiVBH. 

The  two  following  tables  are  from  Clark  on  the  Steam-engrine.  In  the  first 
table  are  given  the  periods  of  admission  corresponding  to  travels  of  valve 
of  from  18  in.  to  8  in.,  and  laps  of  from  2  in.  to  9^  in.,  with  ^  in.  and  ^  in.  of 
lead.  With  greater  leads  than  those  tabulated,  the  steam  would  be  cut  off 
earlier  than  as  shown  in  the  table. 

The  influence  of  a  lead  of  5/16  in.  for  travels  of  from  t%  in.  to  6  in.,  and 
laps  of  from  ^  in.  to  IH  in-«  &s  calculated  for  in  the  second  table,  is  exhibited 
by  comparison  of  the  periods  of  admission  In  the  table,  for  the  same  lap  and 
travel  The  greater  lead  shortens  the  period  of  admission,  and  increases  the 
range  for  expansive  working. 

Periods  of  AdiiilMaloih%  or  Points  of  Cnt-ofl*  fbr  CMlTeii 
TraTela  and  liaps  of  Sllde^walTes* 


•S       jA 

Periods  of  Admission,  or  Points  of  Cut-off, 

for  the  following 

go's 

1 

Laps  of  Valves  in  inches. 

S^ 

2 

1» 

iH 

1 

% 

r4 

« 

H 

H 

in. 
18 

in. 

k 

& 

& 

$r 

& 

& 

^ 

& 

10 

;4 

88 

87 

89 

92 

95 

96 

97 

96 

98 

99 

8 

'^ 

72 

78 

84 

88 

92 

94 

96 

96 

96 

98 

6 

14 

50 

62 

71 

79 

86 

89 

91 

94 

96 

97 

6^ 

« 

43 

56 

68 

77 

85 

88 

91 

94 

96 

97 

ii 

;« 

82 

47 

61 

78 

62 

86 

89 

92 

95 

97 

4H 

'§ 

14 

36 

51 

66 

78 

88 

87 

90 

04 

90 

4^ 

« 

17 

89 

57 

72 

78 

83 

88 

92 

95 

8^ 

'« 

80 

44 

63 

71 

79 

64 

90 

94 

8^ 

23 

60 
27 

61 
48 

71 
67 

79 

70 

86 
80 

91 

2^ 

88 

2^ 

jL. 



83 

62 

70 

81 

832 


THE  STEAM-EKGIKE. 


Perlodfl  of  AdmlMloo,  or  Points  of  Cttl-ofl*,  for  gUten 
Trmirels  and  I«ap»  of  SllAe^ralTes, 

Constant  lead,  6/18. 


Travel. 

Lap. 

Inches. 

M 

K 

H 

% 

1 

1M 

1^ 

1% 

m 

1  ^ 

IB 
89 
47 
65 

61 
06 
08 

l| 

" 

i3 

17 
84 
43 
60 
65 

J 

mu 

14 
80 
88 

^ 

il 

18 



•  • 

82 

71 
74 
70 
78 
80 
81 

60 
68 
67 
70 
78 
74 

46 

40 
56 
60 
63 
66 

27 

86 
48 
47 

60 
65 

13 
36 
83 
88 
44 

vn. 

Svr 

11 

33 
80 

8 

^ 

20 

8^1 

88 
84 

78 
78 

68 
71 

60 
6S 

48 
61 

84 
40 

S8 

30 

$ 

9 

!^ 

85 

80 

78 

64 

68 

45 

34 

80 

a] 

1 

86 

81 

75 

66 

67 

40 

88 

36 

0 

8^ 

87 

88 

76 

68 

60 

63 

43 

83 

10 

i\ 

1 

87 

88 

78 

70 

68 

65 

46 

86 

85 

4 

88 

84 

70 

78 

66 

68 

40 

40 

SO 

4^ 

80 

86 

81 

76 

TO 

68 

66 

47 

S7 

^ 

00 

OT 

83 

70 

78 

67 

61 

64 

45 

$ 

08 

80 

86 

81 

78 

70 

66 

58 

51 

5^ 

08 

00 

87 

63 

78 

78 

07 

68 

56 

^ 

04 

OS 

80 

86 

83 

78 

78 

68 

68 

e^ 

06 

08 

91 

88 

85 

83 

78 

74 

60 

Dlnsrnun  for  Port-opealnffy  CmP^S^  and  lAPr- The  diaiprain 
on  the  opposite  page  was  published  in  Potoer.  AuR.,  1808.  It  abowa  at  a 
glance  the  relations  existing  between  the  outside  lap,  steam  port-opening, 
and  cut-off  in  slide  valve  engines. 

In  order  to  use  the  diagram  to  find  the  lap,  having  given  the  cut-off  and 
maximum  port-opening,  follow  the  ordinate  repi-eaenting  the  latter,  taken 
on  the  horizontal  8cale|Until  it  meets  the  oblique  line  representing  the  given 
cut'Off.  Then  read  off  this  height  on  the  vertical  lap  scale.  Thus,  with  a 
port-opening  of  1^  inch  and  a  cut-off  of  .50,  the  intersection  of  ihe  two  lines 
occurs  on  the  horizontal  8.    The  required  lap  is  therefore  8  in. 

If  the  cut  off  and  lap  are  given,  follow  the  horizontal  representing  the 
latter  until  It  meets  the  oblique  line  representing  the  cut-off.  Then  vertically 
below  this  read  the  corresponding  port*opening  on  the  horizontal  scale. 

If  the  lap  and  port-opening  are  given,  the  resulting  cut-off  maj  be  ascer- 
tained by  finding  the  point  of  intersection  of  the  ordinate  representing  the 
port-opening  witli  the  hoiisontal  representing  the  lap.  The  oblique  line 
passing  through  the  point  of  intersection  will  give  the  cut-off. 

If  it  is  desired  to  taJce  lead  into  account,  multiplv  the  lead  hi  Inches  by  the 
numbers  In  the  following  table  corresponding  to  the  cut-off,  and  deduct  the 
result  from  the  lap  as  obtained  from  the  diagram: 


Cut-off. 

MulUplier. 

Cut-off. 

MultipUer. 

.SO 

4.717 

.60 

1.356 

.85 

8.781 

.635 

1.888 

.80 

8.048 

.65 

1.888 

.88 

8.717 

.70 

1.106 

.875 

8.881 

.75 

1.000 

.40 

8.171 

.80 

0.004 

.46 

1.030 

.85 

0.816 

.50 

1.706 

.875 

O.T?2 

.55 

1.615 

.00 

0.781 

THE  SUDE-TALYE. 


833 


Cut-Off 
J  )   ^     M  .m    .375 .40       .15          ,50             ^               ^ 

\  I  i  N     /  /  T^v 

llu'tl   /    /    7Y 

tttiiu  ^  ^  t  -/i  <- 

ttttit-^  1-  -t  7-4^/^ 

tttttt-t  1 1  V  zy 

f"   Ulh  L4  J^   tj-f 

-4  44714  t  t  J^^J 

Tjiitijj    7tj.     ^-^ 

Juitttri  1  jJ~T  _7_ 

itttul  tJ^JjT-     Z 

tt\utt-i4^  tjj-     / 

I       w    ^  >  >/    A^  ^- 

n       /  /  ///  y   J7" 

imttLij///y  ^y  I 

Uuwttijz/    Z     7     " 

Wl  I  1  ^  ^77  /-  V    ^* 

'  if  / /  >  ^/  ^    7     -^ 

l/Mr^rT^//  /   7      ^^  ^ 

iffniiy  ///  Z.7     ^^ 

ml   ' '  nw  /  7   y       ^^ 

urn'  //// y  y   y     ^^  ,^ 

mwlLy///  y  y     y  j^"'' 

mfhiu yy  y"^  y.^^^^^ 

mf/y/// y  /     ^'"^'^ ^^^ 

wh//(/y  y   yyy^'^  _..,. 

mlNm///\yC^^'^ 

Wyyy'y^^' 

H^^^' 

Pr 

I  ^  ^  \ 

jfnTtmnni  Steam  Port  opening  In  Inches. 
DIAGRAM  FOR  SLIDE  VALVES. 


Fia.  14a. 


834  THE  STEAM-Eli^OIKB. 

Plston^ralTe.— The  piston-valve  fs  a  modified  form  of  the  fiUde-valv^ 
The  lap,  lead,  etc.,  are  calculated  In  the  same  manner  as  for  the  oommoa 
slide-valve.  The  diameter  of  valve  and  amount  of  port-opening  are  calcu- 
lated on  the  basis  that  the  most  contracted  portion  of  the  steam-paMam 
between  the  valve  and  the  cvlinder  should  nave  an  area  such  that  the 
velocity  of  steam  through  it  will  not  exceed  6000  ft.  per  minute.  The  area 
of  the  opening  around  the  circumference  of  the  valve  should  be  about  double 
the  area  of  the  steam-passage,  since  that  portion  of  the  opening  that  is 
opposite  from  the  steam-passage  is  of  little  effect. 

Settlns  the  Valves  or  an  Enslne.— The  principles  dlscmsed 
above  are  applicable  not  only  to  the  designing  of  valves,  but  also  to  adjust- 
ment of  valves  that  have  been  improperly  set;  but  the  final  adjustment  of 
the  eccentric  and  of  the  length  of  the  rod  depend  upon  the  amount  of  lost 
motion,  temperature,  etc,  and  can  be  effected  only  after  trial.  After  the 
valve  has  been  set  as  accurately  as  possible  when  cold,  the  lead  and  lap  for 
the  forward  and  return  strokes  being  equalised,  indicator  diagrams  stiould 
be  taken  and  the  length  of  the  eocentric-rod  adjusted,  if  necessaxy,  to  coir 
rect  slight  irregularities. 

To  Pat  an  fin^lne  on  Its  Centre.— Place  the  engine  in  a  posi- 
tlon  where  the  piston  will  have  nearly  completed  its  outward  stroke,  and 
opposite  some  point  on  the  cross-head,  such  as  a  comer,  make  a  mark  upon 
the  guide.  Against  the  rim  of  the  pulley  or  crank-disk  place  a  pointer  and 
mark  a  line  with  it  on  the  pulley.  Then  turn  the  engine  over  the  centre  uniil 
the  cross-head  is  again  in  the  same  position  on  its  inward  stroke.  This  will 
bring  the  crank  as  much  below  the  centre  as  it  was  above  it  before.  With  the 
pointer  in  the  same  position  as  before  make  a  second  mark  on  the  puller- 
rim.  Divide  the  distance  between  the  marks  in  two  and  mark  the  middle 
point.  Turn  the  engine  until  the  polnt-er  is  opposite  this  middle  point,  and 
It  will  then  be  on  its  centre.  To  avoid  the  error  that  may  arise  from  the 
looseness  of  crank-pin  and  wrist-pin  bearings,  the  engine  should  be  turned 
a  little  above  the  centre  and  then  be  brought  up  to  it,  so  that  the  crank  pin 
will  press  against  the  same  brass  that  it  does  when  the  first  two  marks  are 
made. 

Ijlnk*motlon«— Link-motions,  of  which  the  Stephenson  link  Is  the 
moKC  commonly  used,  are  designed  for  two  purposes:  first,  for  reversing  the 
motion  of  the  engine,  and  second,  for  varying  the  point  of  cut-off  by  varying 
the  travel  of  the  valve.  The  Stephenson  link-motion  is  a  combination  <» 
two  eccentrics,  called  forward  and  bnck  eccentrics,  with  u  link  connecting 
the  extremities  of  the  eccentric-rods;  so  that  by  varying  the  positiou  of 
the  link  the  valve- rod  may  be  put  in  direct  connection  with  either  eccentric, 
or  may  be  given  a  movement  controlled  in  part  by  one  and  in  part  by  the 
other  eccentric.  When  the  link  is  moved  by  the  reversing  lever  into  a  posi- 
tion such  that  the  block  to  which  the  valve-rod  Is  attached  is  at  either  end 
of  the  link,  the  valve  receives  its  maximum  travel,  and  when  the  link  is  in 
mid-gear  the  travel  is  the  least  and  cut-off  takes  place  early  in  the  stroke. 

In  the  ordhiary  shifting-link  with  open  rods,  that  is,  not  crossed,  the  lead 
of  the  valve  increases  as  the  link  is  moved  from  full  to  mid-gear,  that  is,  as 
the  period  of  steam  admission  is  shortened.  The  variation  of  l«ul  is  equa- 
lized for  the  front  and  back  strokes  by  curving  the  link  to  the  radius  of  the 
eccentric-rods  concavely  to  the  axles.  With  crossed  eccentrio-rods  the  lead 
decreases  as  the  link  is  moved  from  full  to  mid-gear.  In  a  valve-motion 
with  stationary  link  the  lead  is  constant.  (For  illustration  see  Clark*s  Steam- 
engine,  vol.  ii.  p.  22.) 

The  linear  advance  of  each  eccentric  Is  equal  to  that  of  the  valve  In  full 
gear,  that  is,  to  lap + lead  of  the  valve,  when  the  eccentric- rods  are  attached 
to  the  link  in  such  position  as  to  cause  the  half- travel  of  the  valve  to  equal 
the  eccentricity  of  the  eccentric. 

The  angle  between  the  two  eccentric  radii,  that  is,  between  lines  drawn 
from  the  centre  of  the  eccentric  disks  to  the  centre  of  the  shaft  equals  !»• 
less  twice  the  angular  advance. 

Buel,  in  Appleton's  Cyclopedia  of  Mechanics,  vol.  H.  p.  816.  discusses  the 
Stephenson  fink  as  follows:  "  The  Stephenson  link  does  not  give  a  perfectly 
correct  distribution  of  steam;  the  lead  varies  for  different  points  of  cut-off 
The  period  of  admission  and  the  beginning  of  exhaust  are  not  alike  for  both 
ends  of  the  cylinder,  and  the  foi'ward  moUon  varies  from  the  backward. 

"  The  correctness  of  the  distribution  of  Bte4im  by  Stephenson's  link-motion 
depends  upon  conditions  which,  as  much  as  the  circumstances  will  permit, 
ought  to  be  fulfilled,  namely:  1.  The  link  should  be  curved  in  the  arc  of  a 
circle  whose  radius  is  equal  to  ihe  length  of  the  eccentric- rod,    &  The 


THK  SUDE-VALVB. 


835 


eccentric-rods  ought  to  belong;  the  longer  they  are  In  proportion  to  the 
eooentrlcity  the  more  symmetrioal  wUI  the  travel  of  the  valve  be  on  both 
sides  of  the  centre  of  motion.  8.  The  link  ought  to  be  short.  Each  of  its 
points  describes  a  curve  in  a  vertical  plane,  whose  ordinates  grow  larger  the 
farther  the  considered  point  is  from  the  centre  of  the  link;  and  as  the  horl- 
SMital  motion  only  is  transmitted  to  the  valve,  vertical  oscillation  will  cause 
irregularities.  4.  The  link-hanger  ought  to  be  long.  The  longer  it  is  the 
nearer  will  be  the  arc  in  which  the  link  flwings  to  a  straight  line,  and  thus 
the  leas  its  vertical  oscillation.  If  the  link  is  suspended  in  its  centre,  the 
curves  that  are  described  by  pointscquidistaii  t  on  both  sides  from  the  centre 
are  not  alike,  and  hence  results  the  variation  between  the  forward  and  back- 
ward gear.  If  the  link  is  suspended  at  its  lower  end,  its  lower  half  will  have 
leas  vertical  oscillation  and  the  upper  half  more.  6.  The  centre  from  which 
the  link-hanger  swings  changes  its  position  as  the  link  is  lowered  or  raised, 
and  also  causes  irregularities.  To  raduce  them  to  the  smallest  amount  the 
arm  of  the  lifting-shaft  should  be  made  as  long  as  the  eccentric- rod,  and  the 
centre  of  the  lifting-shaft  should  be  placed  at  the  height  corresponding  to 
the  central  position  of  the  centre  on  which  the  link-hanger  swings.*' 

All  these  conditions  can  never  be  fulfilled  in  practice,  and  the  variations 
in  the  lead  and  the  period  of  admission  can  be  somewhat  regulated  In  an 
artificial  waT,  but  for  one  sear  only.  This  is  accomplished  by  giving  differ- 
ent lead  to  the  two  eccentrics,  which  difference  will  be  smaller  t»e  longer  the 
eccentric-rods  are  and  the  shorter  the  link,  and  by  suspending  rhe  link  not 
exactly  on  Its  centre  line  but  at  a  certain  distance  from  it,  giving  what  ia 
called  '*  the  offset." 

For  application  of  the  Zenner  dtagrnm  to  link-motion,  see  Holmes  on  the 
Steam-engine,  p.  290.  See  also  Clark's  Railway  Machinerv  (18S&),  01ark*B 
Steam-engine,  Zeuner's  and  Anchindoss's  Treatises  on  Slide-valve  Gears, 
and  Halsey*s  Locomotive  Link  Motion.    (See  Appendix,  p.  10T7.) 

The  following  rules  are  given  by  the  American  Machinist  for  laying  out  a 
link  for  an  upright  slide-valve  engine.  By  the  term  radius  of  link  Is  paeant 
Che  radius  of  the  link-arc  o5,  Fig.  150,  drawn  through  the  centre  of  the  slot; 


Fio.  150. 

this  radiiis  Is  generally  made  equal  to  the  distance  from  the  centre  of  shaft 
U>  centre  of  the  link-block  pin  F  when  the  latter  stands  midw^  of  its  travel. 
Tbc  distance  between  the  centres  of  the  ecceu trie-rod  pins  «|  e.  should  not 
be  less  than  2U  times,  and,  when  space  will  permit,  three  times  the  throw  of 
the  eccentric.  By  the  throw  we  mean  twice  the  eccentricltvof  the  eccentric. 
The  slot  link  is  generally  suspended  from  the  end  next  to  the  forward  eccen- 
tric at  a  point  in  the  link-arc  prolonged.  This  will  give  comparatively  a 
small  amount  of  slip  to  the  link-block  when  the  link  is  in  forward  gear;  but 
this  slip  wiU  be  ioci^ased  when  the  link  is  in  backward  gear.    Thia  increase 


836  TUB  STBAil-KKdmB. 

«f  slip  is.  bowofer,  eontldMred  of  Utile  ImporUnce,  becAUM  m«rlM  MUln^^ 
faanile,  work  but  verj  Utile  In  tbe  backward  f|f>«r.  Wben  it  Is  neeMMiy 
tbai  tbo  motion  «haU  bo  m  ofBciont  in  backward  ffoar  aa  in  forward  c«ar, 
^taaa  tho  Uok  should  ba  auapeodad  from  a  point  midway  between  tbe  twe 
«coentrk:-rod  pJna;  in  marine  engine  praotloe  thfa  point  is  feneraUy  loaatc4 
«n  tbe  UnkHUX);  for  equal  cutoff^  it  is  better  to  move  tbe  point  ol  soapeB* 
<loD  a  small  amount  towards  the  eeeentrles. 

For  obtainln/c  tbe  dinienaions  of  the  Uvk  in  inches :  liSt  L  denote  tbe 
length  of  the  valve,  B  the  breadth,  p  the  absolute  steam-preeiMBre  per  sq. 
In., and  M a faotorof  oompntationused as  bdtow;  then  Ba  .01  f'Lxi^Xpw 

Breadth  of  tbe  link «  J?  X  1.6 

TbiokoewToftbebar »  Bx  A 

'     Rtbofalidinc-blook a  i?  X  ^ 

neter  of  ecoentrfc-rod  pins m(Rx   •7>+i4 

ir  of  suspension-rod  pin. «  (JS  X   .6)  4*12 

^    • '  »<«X.«»)  +  S 


eter  of  suspension- rod  pin  when  o^w^ung.. 

eter  of  block-pin  when  overhung • ••  ic-t-M 

]>buaeter of  Uock-pin wbeo secured  ntbotbcttds  m(Bx  ^)  +  34 


Tbe  length  of  the  link,  that  is,  the  distaaoe  from  e  to  h,  mesMrsd  on  a 
•traight  line  Joiniog  tbe  ends  of  the  Unk-aro  in  the  slbt,  should  be  such  a»  to 
saiow  the  oeotre  of  tbe  Uak-block  pin  JP  to  be  pUoed  ina  line  with  tbeeooea- 
trio-rod  pins,  leaving  sufficient  room  for  the  slip  of  the  block*  Another  type 
of  link  frequently  used  In  marine  engines  Is  the  double-bar  link,  and  tfiis 
type  is  again  divided  into  two  elassaa:  one  elasa  embraeea  those  links  which 
jiave  the  eocenu'kMod  ends  aa  well  as  the  valve^pindle  end  between  ibe 
IMMV,  as  shown  at  B  (with  these  links  tbe  travel  of  the  valve  la  less  than 
ttie  throw  of  the  eooentric);  the  other  class  embraces  tho«e  Kuka,  sbown  at 
€K  for  whicb  the  eocentric-roda  are  made  with  fork-ends,  so  aa  to  connect  to 
fMs  OB  tbe  outside  of  the  bars,  allowing  the  block  toriide  to  the  end  of  the 
fink,  io  that  tbe  centres  of  the  eccentrto-rod  ends  and  the  Uock-pla  are  in 
line  when  In  full  f^ear,  making  the  travel  of  tbe  valve  equal  to  tbe  throw  of 
tbe  eccentric  The  dimensions  of  these  links  when  the  distance  between 
the  eccentric-rod  piaa  la  ^H  to  894  ^<VM  the  throw  oC  eccentrics  can  bo 
found  as  follows: 

Depth  of  bars *=  (JT  X  l.«5) -f- W" 

Thickness  oJ haw.... a<»X     .6)4-8" 

Diameter  of  centre  of  sUding-block «  i2  X  1.8 

When  the  distance  between  the  eccentrlo-rod  pins  is  equal  to  8  or  4  timee 
the  throw  of  the  eccentrics,  then 

Depth  of  bars • =  (»  X  1.88)  +  «" 

Thickness  of  bars «, s  (ii  X     ^)+H" 

All  the  other  dimeosiODB  may  be  fbimd  by  the  Ibrst  table.  These  are  em- 
pirical rules,  and  the  results  may  have  to  be  sligbtly  changed  to  suit  given 


conditions.  In  marine  engines  tlie  eocentric-rod  ends  for  all  cUwses  of  links 
have  ad  JUKtable  brasses.  In  locoinotlveM  the  slot-liuk  is  usually  employed, 
and  in  tnese  the  pin-holes  have  case-hardened  bushes  dilven  into  the  pin- 
boles,  and  have  no  adjustable  brasses  in  the  ends  of  the  eccentric- rods.  Tbe 
link  in  B  is  generaHy  suspended  by  one  of  the  eecentric-rod  pins;  and  the 
link  in  C  is  suspended  by  one  of  the  pins  is  the  end  of  the  link,  or  by  one  of 
the  eccentrio-rod  ptn».  (See  note  on  Locomotive  Link  Motion  in  Appendix. 
p.  1077.) 

Otlier  Forms  of  Talwe-Gear.  as  the  Jbv,  Marshall,  Hackworth, 
Bremme.  Walachoert,  (^oril^,  e  c,  urt*  described  in  Cburk's  Steam-engine, 
Tol.  ii.  The  design  of  the  Reynolds- Corlira  valve-gear  is  discussed  by  A.  H. 
Eldridge  in  Potoer,  Sep.  1898.  See  also  Henthom  on  the  Corliss  engine. 
Bulesror  laying  down  the  centre  lines  of  the  Joy  valve-gear  are  given  la 
^MsWecm  mtcMnM,  Nov.  la,  I890i  For  ioy's  «'  l»uid-pNHUse  Iwiwiiing 
md^"*  see  mo'Pt  Vaj  M«  1804. 

OOTERIVOB8. 

I^advliua  eur  Fly-hall  Gowemor.^Tlie  hMdlnntlon  of  the  arma 
of  a  revolving  pendulum  to  a  verticaJ  axiH  is  such  that  the  height  of  the 
point  of  snapeDKion  h  above  the  horizontal  plane  in  which  the  centre  of 
gravity  of  the  balls  revolve  (assuming  the  weight  of  the  rods  to  be  r— ^ 


OOVEimoii.s.  B37 

eoropAred  with  the  wdlf^ht  of  the  hmUn)  bears  to  the  radius  r  of  tbe  circle 
deecrlbeU  bj  ibe  centres  of  the  balls  the  ratio 


h  welfffat 


r       centrifugal  foroe 


vt         gr 


which  ratio  Is  independent  of  the  weight  of  the  halls,  v  being  the  Teloolty 
of  the  eentres  of  the  balls  in  feet  j>er  second. 

If  7*  s  number  of  revohitlons  of  ttie  balls  in  1  seeondf  v  bb  9mrT  «  ar.  In 
whieh  a  b  the  snpilar  vekxsl^,  or  2vT,  and 

O^  9  ,       0.8146 «  _^      0.7IB,     . 

9  beisff  taken  at  3S.16w   If  JT  s  number  of  rers.  per  miBute»  h  m  -Lg- 

inches 

Foe  revolutions  per  minute 40        45        60        60        75 

The  height  In  indbee  will  be fil.OO    17.88    14.08   9.775   6.f66    ' 

Number  of  turns  per  minute  required  to  cause  the  arms  to  take  a  given 
anftfe  with  the  vertical  axis:  lioi  I  s  length  of  tta0  arm  in  inches  from  the 
et'Otrs  ol  auqiension  to  the  centre  of  gyrallou,  and  «  the  requked  angle; 
then 

Tlie  siiBple  guvMuor  is  not  isochronous:  that  is,  it  does  not  revolve  at  a 
mittorm  speed  in  all  positions,  the  speed  changing  as  the  angle  of  the  arms 
dianges.  To  remedv  this  defect  Madeil  governors,  such  as  Porter's,  are 
used.  From  the  bails  of  a  common  n>vemor  whose  collective  weight  is  A 
let  there  l>e  hung  by  a  pair  of  links  of  lengths  equal  to  the  pendulum  arms 
a  load  B  capable  of  siMtaigon  the  spindle,  having  its  centre  of  gravity  in 
the  axis  of  rotation.  Then  the  oeutrlf  ugnl  force  is  tliat  due  to  A  alone,  and 
the  effect  of  gravity  is  Hint  dne  to  ^  +  SB:  oonseqaently  the  altitude  for  a 
given  speed  is  increased  in  tlie  mtio  {A  -f  SB) :  A^  as  compared  with  that  of 
a  simple  revolving  pendohun,  and  a  given  absolute  variation  in  altltudie  pro- 
duces a  smaller  proportionate  variaooo  in  speed  than  In  the  common  gover- 
nor. (SsBUne.  &  B.,  p.  661.) 

For  the  weighted  governor  let  I  =  the  length  of  the  arm  from  the  point  of 
suspension  lo  the  eentnt  of  gravity  of  the  bail,  and  let  the  length  of  tbe  sus- 
pending-llnk,  I,  =  (he  length  of  the  portion  of  the  arm  from  the  point  of 
SMspension  oC  the  arm  to  tho  point  of  attachment  of  tbe  link;  O  s=  the  weight 
of  one  ball,  Q  s=  half  the  weight  of  the  sliding  weight,  A  a  the  lieiidit  of  the 
governor  Ikon  tho  point  of  snspension  to  the  plane  of  revohitlon  of  the 
balls,  a  s  the  angular  velocity  =  ;ivr,  T  being  the  number  of  revelations  per 

«oond;  tlHm  „  = -/H^ (i+«'|);  fc  .^«(>+ T^D   «««  '"'.  - 

fc=s  "|5i"0"^T*  a)  *°  Inches,  N  being  the  number  of  revolutions  per 
Bshrate. 

For  various  forms  oC  governor  SM  App.  Cyd.  Mech.,  vol.  IL  61,  and  Clark's 
Bteam-ensiDe,  vol.  IL  p.  6B. 

To  Chance  tlie  Speed  of  an  Baclne  Hairlns  a  Fly-lmll 
Gowernora— A  slight  difference  in  the  speed  of  a  governor  changes  the 
position  of  its  weights  from  that  required  for  fnll  load  to  that  required  for 
no  load.  It  Is  evident  therefore  that,  whatever  the  speed  of  the  engine,  the 
normal  speed  of  the  governor  must  be  that  for  which  the  governor  was  de- 
signed ;  i.e.,  the  speed  of  the  governor  must  be  kept  the  same.  Tochange  the 
speed  of  the  engina  the  problem  is  to  so  adjust  the  pulleys  which  drive  the 
governor  that  the  engine  at  its  new  speed  shall  drive  it  just  as  fast  as  it  was 
driven  at  its  original  speed.  In  order  to  increase  the  engine-speed  we  must 
decrease  the  pulley  upon  the  shaft  of  the  enKif^,  i.e.,  the  driver,  or  increase 
that  on  the  governor,  i.e.,  the  driven,  in  the  proporUon  that  the  gpood  of  the 
cngfno  if  to  ho  increased. 


838  THE  BTEAM-BKGIKB. 

Fl7-wbeel  or  Shalt  Govemon.— At  the  CenteDnlal  ICThiWtlw 
in  1876  there  were  shown  a  few  sieam-euginea  In  which  the  goveroora  wera 
coniaioed  in  the  fly-wheel  or  band-wheel,  the  fly-balls  or  weu^hta  revolrioc 
around  the  shaft  in  a  vertical  plane  with  the  wheel  and  shifting  the  eccen- 
tric HO  as  automatically  to  vary  the  travel  of  the  valve  and  the  point  of  cut- 
off. This  form  of  governor  has  since  come  into  extensive  use,  especially  for 
high-speed  engines.  In  its  utiual  form  two  weights  are  carried  on  am  is  the 
ends  of  which  are  pivoted  to  two  points  on  the  pulley  near  Its  circum- 
ference, 180"  apart.  Links  connect  these  arms  to  the  eccentric  The 
eccentric  is  not  rigidly  keyed  to  the  shaft  but  is  free  to  move  trans- 
versely across  it  for  a  certain  distance,  havin^^  an  oblong  hole  which  allows 
of  this  movement.  Centrifugal  force  causes  the  weights  to  fly  towards  the 
circumference  of  the  wheel  and  to  puU  the  eccentric  into  a  position  of  min- 
imum eccentricity.  This  force  is  resisted  by  a  raring  attached  to  each  arm 
which  tends  to  pull  the  weights  towards  the  shaft  and  shift  the  eooentric  to 
the  position  of  maximum  eccentricity.  The  travel  of  the  valve  is  thus 
varied,  so  that  it  tends  to  cut  off  earlier  in  the  stroke  as  the  engine  increases 
its  speed.  Many  modifications  of  this  general  form  are  in  use.  For  discus- 
sions of  this  form  of  governor  see  Hartnell,  Proc.  Inst.  If .  £.,  1882,  p.  408; 
Trans.  A.  8.  M.  E^  ix.  800;  xl.  2081 ;  xiv.  9i;  xv.  i»9 :  Modem  Mechanism, 
p.  889;  Whitham's  Ck>nstructive  Steam  Engineering;  J.  Begtnip,  Am.  Mack.^ 
Oct.  19  and  Dec.  14, 1888,  Jan.  18  and  March  1, 1894. 

CAleulatloii  of  8piiii|ni  for  8limfl«BOTenioni«  (Wllaon  Hart^ 
nell,  Proc.  Inst,  M<  E.,  Aug.  18H2.)— The  springs  for  shaft-governors  may  be 
conveniently  calculated  as  follows,  dimensions  being  In  Inclies: 

Let  W  s  weight  of  the  balls  or  weights.  In  pounds; 

Vi  and  r*  »  the  maximum  and  minimum  radial  distances  of  the  oentrs 

of  the  oalls  or  of  the  centre  of  gravity  of  the  weights; 
li  and  /«  ss  the  leverages,  i.e.,  the  perpendicular  distances  from  the  en 

tre  of  the  weight>pin  to  a  line  in  the  direction  of  the  centrifugal  force. 

drawn  through  the  centre  of  gravity  of  the  weights  or  balls  at  radi^ 

ri  and  r^; 
mi  and  m^  =  the  corresponding  leverages  of  the  springs; 
Ci  and  Cf  s  the  centrifugal  forces,  for  100  revolutions  per  minnte,  s» 

radii  Vi  and  r^; 
Pi  and  P^  =■  the  con^espondinic  pressures  on  the  spring; 
(It  is  convenient  to  calculate  these  and  note  them  down  for  reference^! 
Ct  and  C4  ss  maximum  and  minimum  centrifugal  forces; 
8  s  mean  speed  (revolutions  per  minnte); 
81  and  ;S|  =  the  maximum  and  minimum  number  of  revolutions  pec 

minute: 
Pi  and  P4  =  the  pressures  on  the  spring  at  the  limiting  number  of  reva< 

lutions  (a;  and8t); 
Pi  -  Pi  ss  i>  ss  the  difference  of  the  maximum  and  minimum  pressuref 

on  the  springs; 
F  ss  the  percentage  of  variation  from  the  mean  speed*  or  the  sensitive 

t  s  the  travel  of  the  spring; 
«  B  the  initial  pressure  on  the  spring; 
V  ss  the  stiffness  in  pounds  per  inch; 
w  SB  the  maximum  pressure  ss  u  -f  t. 

The  mean  speed  and  sensitiveness  desired  are  supposed  to  be  given.    Then 


«.  =  ^-M  = 

«,  =  5+°^; 

c,  =  o.a  X  I-,  X  W-; 

Ct  =  0.28  X  r,  X  W; 

^■  =  ^'><sr.= 

P,  =  C,  V  -*  ; 

1,., 

^•  =  -^'><(,oi)'= 

--^•.x(t^)'= 

V 

V 

It  is  usual  to  give  the  8prin^-niaker  the  values  of  p.  and  of  v  or  fr.    To 
ensure  proper  space  being  provided,  the  dimensions  of  the  spring  should  be 


OOKDENSEBS,   AIR-PUMPS,  ETC.  839 

calculated  by  the  formulsB  for  strength  and  extension  of  springs,  and  the 
least  length  of  the  spring  as  compressed  be  determined. 

The  governor-power  =s  -g— *  X  » 

With  a  straight  centripetal  Une,  the  governor-power 


eL+£.x 


(^)- 


For  a  preliminary  determination  of  the  governor-power  it  may  be  taken 
as  equal  to  this  in  all  cases,  although  it  is  evident  that  with  a  curved  cen- 
tripetal line  it  will  be  slightly  less.  The  diiference  D  must  be  constant  for 
the  same  spring,  however  great  or  little  its  initial  compression.  Let  the 
spring  be  screwed  up  until  Us  minimum  pressure  is  iV  Then  to  And  the 
specdP*  s  P»  +  2>, 

The  speed  aft  which  the  governor  would  be  Isochronous  would  be 
lOOi 


W^c 


Suppose  the  pressure  on  the  spring  with  a  speed  of  100  revolutions,  at  the 
maximum  and  minimum  radii,  was  200  lbs.  and  100  lbs.,  respectively,  then 
the  pressure  of  the  spring  to  suit  a  variation  from  9S  to  100  revolutions  will 

be  100  X  (]^)*  -  90.3  and  200  X  (j^)'»  ^^-^     That  Is,  the   Increase 

of  resistance  from  the  minimum  to  the  maximum  radius  must  be  820  -  00  as 
180  lbs. 

The  extreme  speeds  due  to  such  a  spring,  screwed  up  to  different  press- 
ures, are  shown  in  the  following  table: 


Bevolutlons  per  minute,  balls  shut. 

Pressure  on  springs,  balls  shut.... 

Increase  of  pressure  when  balls  open  fully. 

Pressure  on  springs,  balls  open  fully 

Revolutions  per  minute,  balls  open  fully.  . 
Variati  .n,  per  cent  of  mean  speed 


80 

90 

05 

100 

110 

180 

64 

81 

00 

100 

121 

144 

180 

ISO 

180 

1801 

180 

180 

IM 

211 

220 

280 

261 

274 

W 

102 

105 

lor 

112 

117 

10 

6 

6 

8 

1 

-1 

The  speed  at  which  the  governor  would  become  is'K'hronous  is  114. 

Any  spring  will  trlve  the  right  varlatioc  at  ttome  speed;  hence  in  experi- 
menting with  a  governor  the  correct  8pring  may  be  found  from  any  wrong 
one  by  a  very  simple  calculation.  Thus,  if  a  governor  with  a  spring  whose 
stiffness  is  50  lbs.  per  inch  acts  best  when  the  engine  runs  at  OR,  90  being  its 

proper  speed,  then  50  X  y^  =  45  lbs.  is  the  stiffness  of  spring  required. 

To  determine  the  speed  nt  which  the  governor  acts  best,  the  springs  may 
be  screwed  up  until  it  heirinK  to  "  hunt  **  and  then  slackened  until  the  gov- 
ernor is  as  sensitive  as  Is  compatible  with  steadintsss. 

COIfDBNSBBS,  AIR-PfJlHPS    OIBOUIiATINCI* 
PUnPS,  BTC* 

Tlie  Jet  Condenser*  (Chiefly  abridged  from  8eaton*s  Marine  BngI- 
neering.A-The  Jet  condeniiier  is  now  uncommon  in  marine  practice,  being 
generally  supplanted  by  the  Hurface  condenser.  It  is  commonly  used  where 
iresli  water  is  available  for  boiler  feed.  With  the  Jet  condenser  a  vacuum  of  24 
In.  was  considered  fairiy  good,  and  28  in.  as  much  as  was  possible  with  mosl 
oondenserR;  the  temperature corre(ipondlngro24  In.  vacuum,  orS lbs.  pressure 
abiiolute.  Is  140®.  In  practice  the  temperature  in  the  hot-well  varies  from  llO* 
to  120o,  and  occasionally  as  much  as  130^  Is  maintained.  To  find  the  quantity 
of  Injectton-water  per  pound  of  steam  to  be  condent»ed :  I^t  7\  =  tempera- 
ture of  Bteam  at  the  exhaust  pressure i  Tg  =  temperature  ox  the  cooling* 


840  THB   ST£AM-£NGIlfrB« 

water;  T^  =  temperature  of  the  water  after  ooDdenaatton,  or  of  the  hoi-well; 
Q  =  pounda  of  the  cooling.water  per  lb.  of  steam  condeneed;  theu 

Another  formula  is:    Q  « -^,  in  which  IT  to  the  welgbt  of  atMnn  eoB- 

denmd.  H  the  units  of  heat  Riven  up  by  1  lb.  of  steam  in  condeusing,  and 
S  the  nae  in  temperature  of  the  cooUnfr-water. 

This  is  applicable  both  to  Jet  and  to  surface  condensers.  The  allowance  made 
for  the  injection- water  of  engines  working  in  the  temperate  zone  hi  usually 
S7  to  ao  times  the  weight  of  steam,  and  for  the  tropics  80  to  8ft  times;  80 
times  is  sufficient  for  ships  which  are  occaalonaUy  in  the  tropics,  and  this  is 
what  i^as  usual  to  allow  for  general  traders. 

Area  of  injection  orilloe  =  weight  oi  injection- water  in  lbs.  per  min.  -•-  660 
to  780. 

A  rough  rule  sometimes  used  is:  Allow  one  fifteenth  of  a  square  inch  for 
every  cubic  foot  of  water  condensed  per  hour. 

Anothc^r  rule:  Area  of  injection  orifice  =  area  of  piston  •*■  880. 

The  Tclume  of  the  Jet  condenser  is  from  one  fourth  to  one  half  of  that  of 
the  cylinder.  It  need  not  be  more  than  one  third,  exo^t  for  very  quick* 
runnrbf?  eni^nes. 

l^ector  Condenaers,— For  ejector  or  Injector  condensers  (BuDrlet's. 
Bcbutte'n.  etc.)  the  calculations  for  quantity  of  condensing-water  is  the  same 
as  for  Jet  condensers. 

The  8iirAic«  €oncl«iiaer>€oolliis  SnrAiee.—Peclet  found  that 
with  cooling  water  of  an  initla]  temperature  of  68«  to  7:«.  on«t  sq.  ft.  of  oo|  per 
plate  condensed  21.6  lbs.  of  steam  per  hour,  while  Joule  states  that  100  Itw. 
per  hour  can  be  oondenaed.  In  practice,  with  the  compound  envioe,  bran 
condenser- tubes,  18  B.W.O  thicK,  18  lbs.  of  steam  per  sq.  ft.  per  hour,  with 
the  cooling- water  at  an  tnMal  temperature  of  eO^,  is  considered  very  fair 
work  when  the  temperature  of  the  feed- water  to  to  be  maintained  at  14)^. 
It  has  been  found  that  the  surface  in  the  condenser  may  be  half  the  beatteg 
surface  of  the  boiler,  and  under  some  circumstances  considerably  leas  than 
thto.  In  general  practice  the  following  holds  good  when  the  temperature  of 
aea- water  Is  about  G(y*: 

I'erminalpre8.,lb8.,abe....       80      80         15        l^U        10         8  6 

0q.ftperIH.P 8      S.SO      SS5       8.00      1.80       1.00        IM 

For  ships  whose  station  Is  in  the  tropics  the  allowance  shouM  be  Inereaaed 
hyWH.  andforahtps  which  occasionally  visit  the  tropics  10^  increaae  will 
fdve  satisfactory  results.  If  a  ship  to  oouatantly  employed  in  cold  climates 
10^  leFs  suffices 

Wbitbam  (Bteam-engine  Design,  p.  888,  also  Trans.  A.  8.  M.  E ,  fz  481) 

gives  the  foUowhig:  5  =s    ,„  _  .^  hi  which  S  =  condensing-surfiice  in  sq. 

ft.;  Ti  =  temperature  Fahr.  of  steam  of  the  pressure  indicated  by  the 
vacuum-gauge;  t  s=  mean  temperature  of  the  circulating  water,  or  tbe 
arithmetical  mean  of  the  initial  and  final  temperatures:  L  s  latent  bent  ol 
saturated  steam  at  temperature  Tx;  k  =  perfect  oonducbtvity  of  1  sq.  ft.  of 
the  metal  used  for  the  condensingBurface  for  a  range  rf  1*  F.  (or  567  B  T  U. 
per  hour  for  brass,  according  to  Isherwood^s  experiments):  c  =  fraction  de- 
noting tbe  efficiency  of  the  oondeuping  surfboe;  W  e  pounds  of  steam  con- 
densed per  hour.  .Jfrom  experiments  hy  Loring  and  Emeiy,  on  U-8.S  I>a]lHi 

c  to  found  to  be  0.828,  and  ck  =  180;  making  the  equation  S  =  iuQ.>£r  _77x. 

Whitham  rroommends  thto  formula  for  designing  engines  having  Indepn* 
dent  circulutinf?  pumps  When  the  pump  Is  worked  by  the  main  engine  the 
value  of  ^'  should  he  increased  about  10^. 

Talcing  Ti  at  1%«  F.,  and  L  s  lOSO,  corresponding  to  96  In.  vacuum,  cmd  t 

tar  summer  temperatures  at  75®.  we  have:   8  «  fgniaB  ->  tfi  *"  IS"' 

For  a  mathematical  discussion  of  the  efficiency  of  surface  condensers  see 

a  pnppr  hv  T.  v..  Stnnrofi  in  Pioc  loRt.  C.  E-,  exxxvi.  June  IW),  p.  :«1. 

C^ondenaor  Tubes  are  f^nerallv  math'  of  s  »lid  «!niwn  bmsK  iiibeK.  and 
teMf»*.l  iiDfli  by  hv«lrauljc  pres-uiv  ami  sJt'atti,  Thny  ar»»  usually  ina<l**<>f  a 
oompositioD  of  Gd%  of  best  bduciiMi  copper  uud  tf:,^  of  best  SiJ(s>ian  spi-lter. 


CONDENSERS,  AIE-PUMP8,  ETC. 


841 


Ihe  Admiralty,  however,  always  specify  the  tubes  to  be  made  of  70%  of  best 
selected  copper  and  to  have  \%  of  Un  in  the  composition,  and  test  the  tubes 
to  a  pressure  of  300  lbs.  per  sq.  in.    (Beaton.) 

The  diameter  of  the  condenser  tubes  varies  from  H  inch  In  small  conden« 
sers,  when  they  are  very  short,  to  I  inch  in  very  large  condensers  and  long 
tubes.  In  the  mercantile  marine  the  tubes  are,  as  a  rule,  H  inch  diameter 
externally,  and  18  B.W.G.  thick  (0.049  inch);  and  16  B.W.G.  (0.069),  under 
some  ezoeptional  oircumstaaces.  In  the  British  Navy  the  tubes  are  also, 
as  a  rule,  H  inch  diameter,  and  18  to  19  B.  W.O.  thick,  tinned  on  both  sides; 
when  the  condenser  is  made  of  brass  theJ^dmiralty  do  not  require  the  tubes 
to  be  tinned.  Borne  of  the  smaller  enc^es  have  tubes  %  inch  diameter,  nxid 
19  B.W.G.  thick.  The  smaller  the  tubes,  the  lai^ger  is  the  surface  wh^oh 
can  be  fcot  in  a  certain  space. 

In  the  merchant  service  the  almost  universal  practice  is  to  circulate  the 
water  through  the  tubes. 

Whithaiii  says  the  velocitv  of  flow  through  the  tubes  should  not  be  less 
than  400  nor  more  than  700  ft.  per  min. 

TiilM*platea  are  usually  made  of  brass.  Boiled-brass  tube -plates 
should  be  from  1.1  to  1.5  times  the  diameter  of  tubes  In  thickness,  depending 
on  the  method  of  packing.  When  the  packings  go  completely  through  the 
plates  the  latter,  but  when  only  partly  through  the  former,  is  sufficient. 


Hence,  for  94-inch  tubes  the  plates  are  usually  ^  to  1  inch  thick  with  glands 
and  tape-packings,  and  1  to  1^  inch  thick  with  wooden  ferrules. 
The  tube-plates  should  be  secured  to  their  seatings  by  bittsa  studs  and 


nuts,  or  brass  screw-bolts;  in  fact  there  must  be  no  wrought  iron  of  any 
kind  inside  a  condenser.  When  the  tube-plates  are  of  large  area  it  is  advis- 
able to  stay  them  by  brass-rods,  to  prevent  them  from  collapsing. 

SpacinflT  of  Tubes,  etc.— The  holes  for  feirules,  glands,  or  india- 
rubber  are  usually  ^  inch  larger  in  diameter  than  the  tubes;  but  when  ab- 
solutely necessary  the  wood  ferrules  may  be  only  8/3*2  inch  thick. 

The  Pitch  of  tubes  when  packed  with  wood  ferrules  is  usually  )4  inch 
more  than  the  diameter  of  the  ferrule-hole.  For  example,  the  tubes  are 
generally  arranged  zigzag,  and  the  number  which  may  be  fitted  into  a 
square  foot  of  plate  is  as  follows: 


Pitch  of 
Tubes. 

No.  in  a 
sq.ft. 

Fitch  of 
Tubes. 

No.  in  a 
sq.ft. 

Pitch  of 
Tubes. 

No.  in  a 
sq.fk 

1" 

1^- 

m 

ISO 
187 

16/83" 
1  8/16" 
1  7/22" 

128 
121 

116 

1^/82" 
15/16" 

110 
106 
99 

avantlty  of  Cooling  IVater.— The  quantity  depends  chiefly  upon 

itsTnliial  temperature,  whieh  in  Atlantic  praciice  may  vary  from  40**  in  the 
winter  oftemperate  zone  to  80^  In  subtropical  s^as.  To  raise  the  tempera- 
ture to  100<>  in  the  condenser  will  require  thi^e  times  as  nuuiy  thermal  units 
in  the  former  case  as  in  the  latter,  and  therefore  only  one  third  as  much 
cooUng-water  will  be  required  in  the  former  case  as  in  the  latter. 


3*1  =  temperature  of  steam  entering  the  condenser; 

Tm  s=  '*  **  circulating- water  entering  the  condenser; 

2^  «_  4«  «*  4*  ».         1  —  ._•=..  .  » 

3^  = 


leaving  the  condenser; 
**  water  condensed  from  the  steam; 


Q  =  quantity  of  circulating  water  In  lbs.  =  "'4-f-0.8(j^  -^3^^ ^ 

•»»  —  ■'0 

It  Is  usual  to  provide  pumping  power  sufilclent  to  supply  40  times  the 
weight  of  steam  for  general  traders,  and  as  much  as  50  times  for  ships  sta- 
tioned in  subtropical  seas,  when  the  engines  are  compound.  If  the  circulat- 
ing-pump is  douole-acting,  its  capacity  may  be  1/58  in  the  former  and  1/42 
in  the  latter  case  of  tlie  capacity  of  the  low-pressure  cylinder. 

▲lr-pamp«— The  air-pimip  in  all  condensers  abstracts  the  water  con- 
densed and  the  air  originally  contained  in  the  water  when  it  entered  the 
boiler.  In  the  case  of  iet- condensers  it  also  pumps  out  the  water  of  con- 
densation and  the  air  which  it  contained.  The  size  of  the  pump  Is  calculated 
from  these  ooodltions,  making  allowance  for  efficiency  of  the  pump^ 


842 


THE  STEAM-ENQIKE. 


OrdinaiT  sea-water  contains,  mecbanlcally  mixed  with  It,  1/80  of  Its  toI- 
ume  of  afr  when  under  the  atmospheric  pressure.  Suppose  the  pressure  in 
the  condenser  to  be  2  lbs.  and  the  atmospheric  pressure  15  lbs.,  n^lectinif 
the  effect  of  tensperature,  the  air  on  entering  the  condenser  will  be  expanded 
to  15/2  times  Its  original  volume;  so  that  a  cubic  foot  of  sea-water,  when  it 
has  entered  the  condenser^  is  represented  by  19/SO  of  a  cubic  foot  of  water 
and  15/40  of  a  cubic  foot  of  air. 

Let  q  be  the  volume  of  water  condensed  per  minute,  and  Q  the  volume  of 
sea- water  required  to  condense  it;  and  let  Tg  be  the  temperature  of  the 
condenser,  and  Ti  that  of  the  sea- water. 

Then  19/20  {q-\-  Q)  will  be  the  volume  of  water  to  be  pumped  from  the 
condenser  per  minute, 

and   jg(q+Q)X  rl^^jl  the  quantity  of  air. 

If  the  temperature  of  the  condenser  be  taken  at  190*,  and  that  of  aea- 
water  at  60»,  the  quantity  of  air  will  then  be  .418(g  +  QX  bo  that  the  total 
volume  to  be  abstracted  will  be 

.05(3  +  Q)  +  .4i8(«  +  Q)  =  t,fmq  +  Q). 

If  the  average  quantity  of  injection-water  be  taken  at  26  times  that  con- 
densed, 9  +  Q  wul  equal  97q.  Therefove,  volume  to  be  pumped  from  the 
condenser  per  minute  =  87q,  nearly. 

In  surface  condensation  allowance  must  be  made  for  the  water  occasion- 
ally admitted  to  the  boilers  to  make  up  for  waste,  and  the  air  contained  in 
it,  also  for  slight  leak  in  the  joints  and  glands,  so  that  the  air-pump  is  made 
about  half  as  large  as  for  let-condensation. 

The  efficiency  of  a  single-acting  air-pump  is  generally  taken  at  O.S,  and 
that  of  a  double-acting  pump  at  0.85.  when  the  temperatur  of  the  sea  is 
60^,  and  that  of  the  (Jet)  condenser  is  120*,  Q  being  the  volume  of  the  cooling 
water  and  q  the  volume  of  the  condensed  water  In  cubic  feet,  and  n  the 
number  of  strokes  per  minute. 

The  volume  of  the  single-acting  pump  a  g.74(^^)  • 


The  volume  of  the  double-acting  pump  =  4(  2 — 1 ) . 


The  following  table  gires  the  ratio  of  capacity  of  cylinder  or  cylinders  Uf 
that  of  the  air-pump;  m  the  case  of  the  compound  engine,  the  low-preflMire 
cylinder  capacity  only  is  taken. 


Description  of  Pump. 

Description  of  Engine. 

Ratto. 

Single-acting  vertical 

6to   8 

**                "     

Surface  " 

l^toS.... 

8  to  10 

t»                       u 

Jet 

8     to  5.... 

10  to  IS 

•t                    tt 

Surface  •• 

"          8     to6... 

12  to  15 

«•                 tk 

Surface  " 

15  to  18 

Double-acting  horizontal.. 

Jet         •* 

expansion  l>i;to2.... 

10  to  18 

•t                   kk 

Surface  " 

1^  to2.... 

18  to  16 

(•                   it 

Jet          - 

8     to5... 

16  to  19 

M                                         M 

Surface  *• 

••          8     to6... 

19  to  24 

"                                       "               .  . 

Surface  " 

compound    

«4toS8 

Tbe  Area  tbrongb  Valve-eeats  and  past  the  valves  should  not  be 
less  than  will  admit  the  full  quantity  of  water  for  condensation  at  a  velocity 
not  exceeding  400  ft.  per  minute.  In  practice  the  area  is  generally  u 
eioessof  this. 

Area  through  foot-valves     =  i>>  x  'S'-«- 1000  square  Inches. 
Area  through  head- valves    =  D^xS-*-  800  square  inches. 
Diamerer  of  discharge-pipe  =  D  X  Vs  -•-  35  Inches. 
D  s  diam,  of  air-pump  in  inches,  5  =  its  speed  in  ft.  per  mln. 

James  Tribe  {Anu  Afiic/i.,  Oct.  8,  1891)  gives  the  following  role  for  aliw 


COKDENSBBS,  AIK-PUMPS,  ETa  843 

pumps  used  with  Jet-condensers:  Volume  of  slngle-acUn?  afr-pump  driven 
by  main  engine  =  volume  of  low-pressure  cvlinder  in  cubic  feec,  multiplied 
by  3.5  anil  divided  by  the  number  of  cubic  feet  contained  in  one  pound  of 
exhaust-steam  of  tfie  given  density.  For  a  double-acting  air-pump  the 
same  rule  will  apply,  but  the  volume  of  steam  for  each  stroke  of  the  pump 
^ill  be  but  one  half.  Should  the  pump  be  driven  independently  of  the 
engine,  then  the  relative  speed  must  be  considered.  Volume  of  jet-con- 
denser =  volume  of  air-pump  x  4.  Area  of  injection  valve  s  vol.  of  air- 
pump  in  cubic  inches  -h  5^. 

€trealatIiiC"Panap*— Let  Q  be  the  quantity  of  cooling  water  in  cubic 
feet,  n  the  numbei-  of  strokes  per  minute,  and  S  the  length  of  stroke  in  feet. 

Capacity  of  circulatlng-pump  »  Q-t-n  cubic  f  eetu 
Diameter"        ••  "       =  I8.B54/— 2- inches. 

y    n  X  o 

The  following  table  gives  the  ratio  of  capacity  of  steam-cylinder  or  cyliiii 
ders  to  that  of  the  circulating- pump : 

Description  of  Pumpw  Description  of  Engine.  Ratio. 

Single-acting.  Expansive  lU  to  2  times.  18  to  10 

8     to5    -  90to86 

"  CJompound.  26  to  80 

Doable    **  Expansive  l^  to  2  timea  25  to  80 

••  **          8     to6    *•  86  to  46 

**          **  Compound.  46  to  56 

The  ctear  area  through  the  valve-seats  and  past  the  valves  should  be  such 
that  the  mean  velocity  of  flow  does  not  exceied  450  feet  per  minute.  The 
flow  throu^  the  pipes  should  not  exceed  500  ft.  per  min.  in  small  pipes  and 
600  in  large  pipes. 

For  Centrifugal  Cireulatina -pumps,  the  velocity  of  flow  in  the  inlet  and 
outlet  pipes  should  not  exceedi  400  ft.  per  min.  The  diameter  of  the  fan- wheel 
in  from  2^  to  8  times  the  diam.  of  ttie  pipe,  and  the  speed  at  its  periphery 
450  to  500  ft.  per  min.  If  W  =  quantity  of  water  per  minute,  in  American 
gallons,  d  =  diameter  of  pipes  in  inches,  R  =  revolutions  of  wheel  per  min., 

1700 
diam.  of  fan-wheel  s  not  less  than  -^-.    Breadth  of  blade  at 


y  M.44' 


tip  =  -^T.    Diam.  of  cylinder  for  driving  the  fan  s  about  2.8  Vdiam.  of  pipe, 

and  its  Rtroke  =  0.28  X  diatn.  of  fan. 

Feed-pnmpa  for  Marine  Bnslne««~With  surface-condensing 
engines  the  amount  of  water  to  be  fed  by  the  pump  is  the  amount  condensed 
from  the  main  engfaie  plus  what  may  be  needed  to  supply  auxiliary  engines 
and  to  supply  leakage  and  waste.  Since  an  accident  may  happen  to  the 
surface-condenser,  requiring  the  use  of  jet-condensation,  the  pumps  of 
engines  fitted  with  surface-condensers  must  be  sufficiently  lari?e  to  do  duty 
under  such  circumstances.  With  jet-condense:«  and  boilers  usins:  salt  water 
the  dense  salt  water  in  the  boiler  must  be  blown  off  at  intervals  to  keep  the 
density  so  low  that  deposits  of  salt  will  not  be  formed.  8ea-water  contains 
about  1/32  of  its  weight  of  solid  matter  in  solution.  The  boiler  of  a  surface- 
condensing  engine  may  be  worked  with  safety  when  the  quantity  of  salt  is 
four  timee  that  in  sea-water.  If  Q  =  net  quantity  of  feed-water  reouired  in 
a  given  time  to  make  up  for  what  is  used  as  steam,  n  a  number  of  tImeA  the 
saltnees  of  the  water  in  the  boiler  is  to  that  of  sea- water,  then  the  gixN«  feed- 
water  =     ^  ,Q.    In  order  to  be  capable  of  fllling  the  boiler  rapidly  each 

feed-pump  is  made  of  a  capacity  equal  to  twice  the  gross  feed-water.  Two 
feed-pumps  should  be  supplied,  so  that  one  may  be  kept  In  reserve  to  be 
used  while  the  other  is  out  of  repair.  If  Q  be  the  quantity  of  net  feed-  water 
ill  cubic  feet,  \  the  length  of  stroke  of  feed-pump  In  feet,  and  n  the  num- 
bt^r  of  strokes  per  minute. 


Diameter  of  each  feed-pump  plunger  In  incbea  ■■  i/< 


650  xg 
«Xl  ' 


844 


THB  STEAH-EKGtKS. 


If  fTbe  the  n^'' feed-water  in  pounds,  _ 

Diameter  of  each  feed-pnmp  plunger  in  incfaee  as  k/ — ^-p- 

Am  ETaperAtlTe  Svrlkce  Cendenaer  built  aft  the  Vinfoia  Agrt 
culUiral  OoUeice  ta  described  \xj  James  H.  FttcsiTraasL  A.  8.  H.  B.,  xi^.^oL 
It  coDsiats  of  two  rpctangnlar  end  ciiaznben  eonoected  by  a  series  of  hori- 
Eontal  rows  of  tubes,  each  row  of  tubes  immersed  in  a  pan  of  watefi 
Through  the  spaces  between  thesurfaoe  of  the  water  In  ««cfa  pan  and  the 
bottom  €f  tbe  pan  above  air  is  drawn  by  means  of  an  ezbaost-fsa.  At  tlia 
top  of  one  of  toe  end -<^am bens  is  an  inlet  for  steam,  and  a  horizontal  dia- 
phra«rm  aljoot  raMway  csuse«  the  steam  to  traverse  tbe  upper  half  of  the 
tubes  and  back  throoKta  the  lower.  An  outlet  at  the  bottom  leads  to  tbe  air- 
pump.  Tbe  condenser,  exclusive  of  connection  to  tbe  exhaust-fan,  occupies 
a  floor  space  of  6'  4U"  x  l'  i%",  and  4'  IH"  hirfi.  There  are  «7  rows  of 
tubes,  8  in  some  ana  7  in  othere:  210  tubes  in  sJj.  The  tubes  are  of  t»asB, 
Ko.  20  B.W  Q.,  94"  external  diameter  and  4'  9W'  in  length.  Tbe  oooUng  anr- 
face  (Internal)  is  176.5  sq.  ft.  There  are  87  ooolmg  pans,  each  4'  9^''  X  \'  M^", 
and  1  7/16''  deep.  These  pans  have  galvanisea  Iron  bottoms  which  slfde 
into  horioontal  grooves  M^'^irkls  and  H''  deep,  planed  Into  the  tnbe^heeta. 
Tbe  total  evaporating  surface  is  SM.8  sq.  ft.  w  ater  is  fed  to  every  third  pan 
through  small  cocks,  and  overflow-pipes  feed  the  rest  A  wood  casing  con- 
nects one  side  with  a  SO"  Buffalo  Forge  Ck>.*s  disk- wheel.  This  wheel  is 
belted  toa  8"  x  4"  vertical  engine  The  air-pump  is  5^4"  dianetsr  with  a 
6"  stroke.  Is  vertical  and  single-acting. 

The  action  of  this  condenser  Is  as  follows:  The  passsge  of  air  over  the 
water  surfaces  removes  the  vapor  as  It  rises  and  thus  hastens  evaporation. 
The  heat  necessaiy  to  produce  evaporation  is  obtained  from  tbe  steam  tn  the 
tubes,  causfng  the  steam  to  eondense.  It  was  designed  to  condense  800  lbs 
■team  per  hour  snd  give  a  vacuum  of  28  in.,  with  a  terminal  pressure  in  tha 
QyUnder  of  80  lbs.  absolute. 

Besults  of  tests  show  that  the  cooUng-water  required  is  practically  equal  in 
amount  to  the  steam  used  by  the  engine.  And  since  coosumptlon  of  ste£.ia 
li  reduced  by  the  sppUcatioa  of  a  condenser,  its  use  will  aciiiSUIy  reduoe  tbe 
total  quanti^  of  water  required.  EVom  a  curve  showing  the  rate  of  evapora- 
tion per  square  foot  of  surface  in  ptm  air.  and  also  one  show  ng  the  imie 
when  a  current  of  air  of  about  S800  ft.  per  min.  velocity  is  passed  over  its 
surface,  the  following  approximate  figures  are  taken : 


T^smp. 

Evaporation,  lbs.  per 
sq.  ft.  per  hoar. 

Temp. 

F. 

Evaporation,  Iba.  per 
sq.  fL  per  l.our. 

StiUAir. 

Current. 

SUUAir. 

Current. 

100» 

110 
ISO 
180 

0.8 

0.95 

0.4 

06 

1.1 

1.0 
8^ 
8.6 

140* 
160 
lOO 
170 

0.8 
1.1 
1.5 
8.0 

5.0 

6.7 

Vke  ContlBVoiui  Use  o^T  Oondienaiiic-sirater  Is  described  In  a 
se^es  ot  arUoles  in  Foioer,  Aug. -Dee.,  189«.  It  finds  its  apsHoatlon  In  situa- 
tions where  water  for  condea^ng  purposes  is  expensive  or  difllcuit  to  obtain. 

In  San  Francisoo  J.  a  H.  6tat  eoob  the  water  after  It  has  left  tbe  hot- 
well  by  means  of  a  mtem  of  pans  upon  the  roof.  These  pans  are  shallow 
txongnis  of  galvainiBea  iron  arrsnged  m  tiers,  on  a  slight  laoMne,  so  that  tie 
water  flows  back  and  forth  for  1500  o»  ttOO  ft,  oooling  by  evaporatk»  wmH 
radiation  as  it  flows.  Tbe  pans  are  about  6  ft.  in  width,  and  the  water  as  it 
flows  has  a  depth  of  about  iialf  an  inch,  tire  temperature  being  reduced  ftxjva 
about  HQo  to  90**.  The  water  from  the  hot-well  is  pumped  ap  to  the  hkchest 
point  of  the  cooUng  system  and  allowed  to  flow  as  above  described,  disehaxg- 
mg  Anally  Into  tbe  main  tank  or  reservoir,  whence  it  again  flows  to  the  oon- 
denser  as  required.  As  the  water  in  the  reservoir  lowers  from  evapocation.  an 
auxiliary  feed  from  the  dty  mains  to  the  condenser  Is  operated,  thereby 
keeping  the  amount  cf  water  in  circulation  practically  constant.  An  accu- 
mulatloa  of  oil  from  the  engines,  with  dust  from  the  surrounding  streets, 
makes  a  cleaning  necessary  about  once  in  six  weeks  or  two  moochs.  It  is 
found  by  comparative  trials,  running  condensing  and  non  condensing,  that 


CONDJSNSBUS,  AIR-PUMPS,  ETC.  845 

about  50^  l60B  vater  Ib  taken  from  tlie  cUj  mains  wbea  the  vbole  ajpiMuratai 
is  in  uge  than  vfa<«  the  engine  is  run  non-condenslng.  S9(o  SB  in.  of  vacuum 
•ra  maintained.  A  better  Tacuum  ia  obtained  on  a  wann  day  with  a  brisk 
breese  blowing  than  on  a  coid  day  with  but  a  ttUebt  movement  ot  the  air. 

In  another  ^ant  tbe  vater  from  the  hot-well  is  spn^ed  from  a  number  of 
fountains,  and  also  from  a  piv^e  extending  around  its  border,  into  a  lans* 
pood,  the  exposure  cooling  it  sufficiently  for  the  obtaining  of  a  good  Tacuum 
by  its  continuous  use. 

In  the  system  patented  by  Messrs.  Bee,  of  Lille,  France,  the  water  is  dt»* 
diarged  from  a  pipe  laid  in  the  form  of  a  rectangle  and  elevated  above  a 
pond  through  a  series  of  special  noades,  by  which  it  is  projected  into  a  fine 
oiray.  On  coming  Into  oootact  with  the  air  In  this  state  of  extreme  div^ 
sJon  the  water  ie  cooled  40°  to  60«,  with  a  loss  by  evaporation  of  only  one 
tenth  of  its  mass,  and  produces  an  excellent  yacuum.  A  JiOOO<H.P.  cooler 
upon  this  system  has  been  erected  at  lAnnoy,  one  of  WOO  U  J*,  at  Iftadrid.,  and 
one  of  1200  H.P.  at  liege,  as  well  as  others  at  Roubaixand  Tourooing.  Tbe 
system  could  be  used  upon  a  roof  if  ground  space  w«re  limited. 

In  the ''  self-ooohng*'  system  of  H.  R.  Worthington  the  injecttoorwatar  is 
taken  from  a  tank,  and  after  having  passed  through  ihe  condenser  is  dis- 
charged in  a  heated  condition  to  the  top  of  a  cooUog  tower,  where  it  is  f^cat- 
tered  by  means  of  distributing-pipes  and  tricklee  down  through  a  cellular 
structure  made  of  6-io.  terraKx>tta  pipea,  2  ft.  loc^,  stood  on  end.  Tlie 
water  Is  cooled  by  a  blast  of  air  furnished  by  a  disk  fan  at  the  bottom  of  tho 
tower  and  the  absorption  of  heat  caused  by  a  portion  of  the  water  being 
vaporlaad,  and  is  lea  to  the  tank  to  be  again  started  on  its  olronit.   {Swfg 

In  tbe  evaporative  condeaiser  of  T.  Ledward  &  C3o.  of  Brockleor,  Iiondom, 
the  water  trickles  over  tbe  pipes  of  Iho  large  condenser  or  radiator,  and  by 
evaporation  carries  away  the  neat  necescary  to  be  abstracted  to  condense 
tbe  steam  Inside.  Tbe  condensing  pipes  are  fitted  with  corrugationa 
mountod  with  circular  ribs,  wheriiby  the  radiatmg  or  cooling  nirlaoe  is 
largely  increased.  Tbe  pipes,  which  are  cast  in  sections  about  76  in.  long  by 
8>4  in.  bore,  have  a  cooling  surface  of  26  sq.  ft,  which  is  found  suflQmenc 
under  favorable  ooaditiona  to  permit  of  tbe  oondcnaation  of  SiO  to  90  lbs. 
of  steam  per  hour  when  producing  a  vacuum  of  13  Iha.  per  pq.  in.  In  a 
condenser  of  this  type  at  Rixdorf,  nesr  Berlin,  a  vacuum  ranging  from  )M 
to  26  In,  of  mercury  was  constantly  maintained  during  tbe  hottest  weather 
of  August.  Tbe  initial  temperature  of  the  cooling-water  used  in  tbe  appara- 
luB  mder  notfce  ranged  trom  G0<»  to  8S*  F.,  and  the  temperatitfe  in  the  sun, 
to  which  the  condenser  was  exposed,  varied  each  day  from  lOO"  to  115*^  F. 
During  the  experhnents  it  was  Ibund  that  it  was  possible  to  nm  one  engine 
under  a  load  of  100  horso-powcr  and  maintain  the  full  Taemnn  without  tbe 
use  of  any  co<rihijwater  ct  all  on  the  pfprs,  radiation  afforded  by  the  pipes 
ak>tte  sufflcing  to  condense  tbe  steam  for  this  power. 

In  Klein's  condensing  wnter-cooler,  the  hot  water  coming  from  the  eon- 
denser  enters  at  the  top  of  a  wooden  structure  about  twenty  feet  in  height, 
and  Is  conveyed  into  a  series  of  parallel  tiaiTow  metal  tanks.  The  water 
OTerflowing  from  these  tanks  Is  spread  as  a  thin  film  over  a  series  of  wooden 
partitions  suspended  vertically  about  8J4  inches  npare  within  the  tower. 
The  upper  set  of  partitions,  corresponding  to  the  number  of  metal  tanks, 
reaches  half-way  down  the  tower.  From  there  down  to  the  well  is  so*, 
pended  a  second  set  of  partitions  placed  at  ri^t  angles  to  the  tr«t  set.  This 
Impedes  the  rapidity  of  the  downfiow  of  the  water,  and  also  thoroughly 
mixes  the  water,  thus  alTording  a  better  cooling:  A  f  nn-blower  at  the  base  of 
the  tower  drives  a  strong  onrreat  of  air  with  a  velocity  of  about  twenty  feet 
per  second  against  the  tbfn  film  of  water  running  down  over  tlie  iMUtitions. 
It  to  estimated  that  for  an  effectual  cooling  two  thousand  times  more  air 
tl»an  water  must  be  forced  throuf^h  the  apparatus,  ^'ith  such  a  velocity 
the  air  absorbs  about  two  per  cent  of  aqueous  vapor.  The  notion  of  the 
strong  air -current  fs  twofold:  first,  it  absorbs  heat  from  the  hot  water  by 
being  Itself  warned  by  radiatioii ;  and,  R«»condlT.  It  increases  the  evapora- 
tion, which  procees  absorbs  a  great  amount  of  hf«t.  These  two  cooling 
effecM  ara  dlffersnt  during  tbe  different  seasons  of  the  year.  During  the 
winter  months  tha  direet  cooling  effect  of  the  oold  air  Is  greater,  while 
during  soauner  the  heat  absorption  by  evaporation  la  the  more  important 
factor.  Taking  aM  the  year  round,  the  effect  remains  very  mueh  the  same. 
The  evaporation  ie  never  so  great  that  the  deficiency  of  water  wouI<l  aot 
be  sopplied  by  the  additional  amount  of  water  resniting  from  the  condemmt 
ateanK  while  In  very  coM  winter  months  it  may  be  necessary  to  occarioualiy 
rid  the  cistern  of  suiphM  water.    It  was  found  that  the  vacunm  obtafend  bf 


846  Tfi£  8T£AM-£KGtK£. 

thiA  continual  use  of  the  same  condensing-water  varied  during^  the  rear 
between  :t7. 6  and  S8.7  inches.  The  great  saving  of  space  is  eyident  from 
the  fact  that  only  the  five-hundredth  part  of  the  floor-space  is  required  sa 
if  cooling  tanks  or  ponds  were  used.  For  a  lOO-horse-power  engine  the 
floor-space  I'equired  is  about  four  square  yards  by  a  height  of  twenty  feet. 
For  one  horse-power  3  6  square  yards  cooling-surface  is  necessaiy.  The 
vertical  suspension  of  the  partitions  is  very  essential.  With  a  venUlator  SO 
inches  in  diameter  and  a  tower  6  by  7  feet  and  SO  feet  high,  10,500  gallons  of 
water  per  hour  were  cooled  from  104®  F.  to  68*^  F.  The  following  record 
was  made  at  Mannheim,  Germany:  Vacuum  in  condenser,  28.1  inchesj^em- 
perature  of  coudensing-water  entering  at  top  of  tower,  104<*  to  108*  F.; 
temperature  of  water  leaving  tl:e  cooler.  60.2^  to  71.6"  F.  The  engiue  was 
of  toe  Sulzer  compound  type,  of  1^  horse-power.  The  amount  of  power 
necessary  for  the  arrangement  amounts  to  about  three  per  cent  of  the  total 
horse-power  of  the  ensnne  for  the  ventilator,  and  from  one  and  one  half  to 
three  per  cent  for  the  lifting  of  the  water  to  the  top  of  the  cooler,  the  total 
being  four  and  one  half  to  six  per  cent. 

A  novel  form  of  condenser  nas  been  used  with  considerable  success  in 
Germany  and  other  parts  of  the  Continent.  The  exhaust-steam  from  the 
engine  passes  through  a  series  of  brass  pipes  immersed  in  water,  to  which 
it  gives  up  its  heat.  Between  each  section  of  tubes  a  number  of  galvanized 
disks  are  caused  to  rotate.  These  disks  are  cooled  by  a  current  of  air 
supplied  by  a  fan  and  pass  down  into  the  water,  cooling  it  by  abatract- 
ing  the  heat  given  out  by  the  exhaust- steam  and  carrying  it  up  where  it  is 
driven  olT  by  the  air-current.  The  disks  serve  also  to  agitate  the  water  and 
thus  aid  it  in  abstracting  the  heat  from  the  steam.  With  85  per  cent 
vacuum  the  temperature  of  the  cooling  water  was  about  190<*  F.,  and  a 
consumption  of  water  for  condensing  is  guarantee<l  to  be  less  than  a  pound 
for  each  pound  of  steam  condensed.  For  an  engine  40  in.  X  SO  in.,  70  revo- 
lutions per  minute,  90  lbs.  pressure,  there  is  about  1160  sq.  ft.  of  condensing- 
surface.  Another  condenser,  1600  sq.  ft.  of  condensing-surface,  is  used  for 
three  engines,  89  in.  x  48  in.,  87  in.  X  40  in.,  and  30  in.  x  40  in.,  respectively. 
— T%e  Steamthip. 

Tlie  Increase  of  Poorer  that  may  be  obtained  by  adding  a  condenser 
giving  a  vacuum  of  !Sf6  inches  of  mercury  to  a  non-condensing  engine  maybe 
approximated  by  considering  it  to  be  equivalent  to  a  net  gain  of  1^  pounds 
mean  effective  pi^essure  per  square  inch  of  piston  area.  If  J  =  area  or  piston 

in  square  Inches,  8  s  piston-speed  in  ft.  per  minute,  then  .^    '  =  rrz-^  =  H.P. 

8o,WU       XiSU 

made  available  by  the  vacuum.  If  the  vacuum  =  13.2  lbs.  per  sq.  in.  =  S7.9 
in.  of  mercury,  then  H.P.  =  AS-t-2BO0. 

The  saving  of  steam  for  a  given  horse-power  will  be  represented  approxi- 
mately by  the  shortening  of  the  cut-off  when  the  engine  is  run  with  the 
condenser.  Clearance  should  be  included  in  the  calculation.  To  the  mean 
effective  pressure  non -condensing,  with  a  given  actual  cut-off,  clearance 
considered,  add  8  lbs.  to  obtain  the  approximate  mean  totai  pressure,  con- 
densing. From  tables  of  expauRion  ot  steam  find  what  actual  cut-off  will 
give  this  mean  total  pressure.  The  difference  between  this  and  the  original 
actual  cut-off,  divided  by  the  latter  and  by  100,  will  give  the  peroentaie  of 
saving. 

The  following  diagram  (from  catalogue  of  H.  R.  Worthington)  shows  the 
percentage  of  power  that  may  be  gained  by  attaching  a  condenser  to  a  non- 
condensing  engine,  assuming  that  the  vacuum  is  12  lbs.  per  sq.  in.  T/ie  dia- 
gram also  shows  the  mean  pressure  in  the  cylinder  for  a  given  initial  pre»- 
Bure  and  cut-off,  clearance  and  compression  not  considered. 

The  pressures  given  in  the  diagram  are  absolute  pressures  above  a  vacuum. 

To  find  the  mean  effective  pressure  produced  in  an  engine-cylinder  with  90 
lbs.  gauge  ( s  105  lbs.  absolute)  pressure,  cut-off  at  ^  stroke:  find  lCi(»  in  the 
left-hand  or  initial -pressure  column,  follow  the  horizontal  line  to  the  right 
until  it  intersects  the  oblique  line  that  corresponds  to  the  M  cut-off,  and  read 
the  mean  total  pressure  from  the  row  of  figures  directly  above  the  point  of 
intersection,  which  in  this  case  is  G3  lbs.  From  this  subtract  the  mean  abso- 
lute back  pressure  (say  3  lbs.  for  a  condensing  engine  and  15  lbs  for  a  uou- 
condeusing  engiue  exhanstinji^  into  the  atmosphere)  to  obtain  the  mean  ef- 
fective pressure,  which  in  this  case,  for  a  non-condensing  engine,  given  48 
lbs.  To  find  the  gain  of  power  by  the  use  of  a  condenser  with  thw  engine 
read  on  the  lower  scale  the  figures  ihac  correspond  in  position  to  48  Ibk.  in 
the  upper  row,  in  this  case  25j(.  As  the  diagram  does  not  take  into  oousid> 
eration  clearance  or  compi'essiuu.  ihe  results  are  only  approximate. 


Bis,  PBTBOLBUM,  AND  FOT-AIB  ENQIKES.       3i/ 


M    [    !    i    !    [    !    t    I 

40    \^   ^    lO    17     15    1^    IZ    II     K) 


t^Cjerrl  syf  PDwer  &ained  by  Vacuum. 


FlO.  151. 

Krapomtors  and  IMvtlllers  are  used  with  marine  eneines  for  Um 
purpose  of  providiu)?  f  resli  water  for  the  boilers  or  for  drinking  purfK^ws* 

Jveir^s  Evaporator  consists  of  a  small  horizontal  boiler,  contrived  so  as 
to  be  easily  talcen  to  pieces  and  cleaned.  The  water  in  it  is  evaporated  by 
the  steam  from  the  main  boilers  passing?  through  a  set  of  tubes  placed  in  its 
bottom.     The  steam   generated  in   this   boiler  is  admitted  to  the  low- 

Sressure  valve-box,  so  that  there  is  no  loss  of  energy,  and  the  water  con- 
ensed  in  it  is  returned  to  the  main  boilers. 

In  Weirds  Feed-heater  the  feed-water  before  entering  the  boiler  is  heated 
up  very  nearly  to  boiling-point  bv  means  of  the  waste  water  and  steam 
from  the  low-pressure  valve-box  of  a  compound  engine. 

GAS,  PETBOLEUM,  AND  HOT-AIB  ENGINES. 

dafl-englnes*— For  theory  of  the  gas-engine,  see  paper  by  Dugald 
Clerk,  Proc.  Inst.  C.  E.  1882,  vol.  Ixix.:  and  Van  Nostrand^s  Bcience  Series. 
No.  flfc  86«  ateo  Wood^B  Thermodynamica.  Three  standard  works  on  m..o- 
engiweB  are  A  Practical  Treatise  on  the  *  Otto '  Cycle  Oas-engine,**  by  Win. 
Norris;  *'  A  Text-book  on  Gas,  Air,  and  Oil  Engines,"  by  Bryan  Donkhi;  and 
''  The  Qasand  Oil  Engine,''  by  Dugald  Clerk  (6tb  edition,  1896). 

Id  the  ordinary  type  of  single-cylinder  gas-engine  (for  example  the  Otto) 
known  as  a  four-cycle  engine  one  ignition  of  gas  takes  place  in  one  end  of 
the  cylinder  every  two  revolutions  of  the  fly-wheel,  or  every  two  double 
strokea  The  following  sequence  of  operations  takes  place  during  four  con- 
secutive strokes:  (a)  inspiration  during  an  entire  stroke ;  (6>  compression 
during  the  second  (return)  stroke;  (c)  ignition  at  the  iead-potnt,  and  expan- 
sion during  the  third  stroke  t  id)  expulsion  of  the  burnt  gas  during  tiie  fourth 
(veturn)Mroiu».   -i^au  jm  iiocbae  £a  166S  iaia  dgwa  the  law  that  there  are 


848        QAS,   PETBOLBUM^   AKD  HOT-AIB  ESTGIXTES. 

four  oonditions  neoesgaiy  to  realize  the  best  results  from  the  elastic  force 
of  gas:  (I)  The  cylinders  sliould  have  the  p^reatest  capacity  with  the  smallest 
circumferential  surface:  (2)  the  speed  should  be  as  nigh  as  possible;  (3)  the 
cut-off  should  be  as  early  as  possible;  (4)  the  initial  pi^essure  should  be  as 
high  as  possible.    In  modem  engines  it  is  customary  for  ignition  to  take 

Elace,  not  at  the  dead  point,  as  proposed  by  Beau  de  Bochas,  but  somewhat 
Iter,  when  the  piHtou  nas  already  made  part  of  its  forward  strolce.  At  first 
sight  it  might  be  Kupposed  that  this  would  entail  a  loss  of  power,  but  experi- 
ence shows  that  tliough  the  area  of  the  diagram  is  diminished,  the  power 
registered  by  the  friction-brake  is  greater.  Starting  is  also  made  easier  by 
this  method  of  working.  (The  Simplex  Bngine,  Proc.  Inst.  M.  B.  1889.) 

In  the  Otto  engine  tne  mixture  of  gas  and  air  is  compressed  to  about  8 
atmospheres.  inHien  explosion  takes  place  the  temperature  suddenly  rises 
to  somewhere  about  2900*  F.    (Bobinson.) 

The  two  great  sources  of  waste  in  gas-engines  are:  1.  The  high  tempera- 
ture of  the  rejected  products  of  combustion;  2.  Loss  of  heat  throu^n  the 
cylinder  walls  to  the  water-lacket.  As  the  temperature  of  the  water-jacket 
is  increased  the  efficiency  of  the  engine  becomes  higher. 

With  ordinary  coal-gas  the  consumption  may  be  taken  at  SO  cu.  ft.  per 
hour  per  I.H.P.,  or  S4  cu.  ft.  per  brake  H.P.  The  consumption  will  vary  with 
the  quality  of  the  gas.  When  burning  Dowson  producer-gas  the  consump- 
tion of  anthracite  (Welsh)  coal  is  about  1.8  lbs.  per  I. H.P.  per  hour  for 
ordinary  working.  With  large  twin  engines,  100  H.P.,  the  consumption  is 
reduced  to  about  1.1  lb.  The  mechanical  einciency  or  B.H.P.  ••-  LH.P.  in 
ordinary  engines  Is  about  9b%;  the  friction  loss  is  less  in  larger  enginea. 

Elllelency  of  tlie  0«a-engine«  (Thurston  on  Heat  as  a  Form  of 
Energy.) 

Heat  transferred  Into  useful  work V!% 

•*  **  to  the  jacket-water tt 

"     lost  in  tlie  exhaust-gas 16 

"       '*    by  conduction  and  radiation 15 

-   W 

This  represents  fairly  the  distribution  of  heat  in  the  best  forms  of  gas- 
engine.  The  consumption  of  gas  in  the  best  engines  ranges  from  a  mini- 
mum of  18  to  20  cu.  ft.  per  I. H.P.  per  hour  to  a  maximum  exceeding  in  the 
smaller  engines  25  cu.  ft.  or  80  cu.  ft.  In  small  engines  the  consumption  per 
brake  horse-power  is  one  thirdgreater  than  these  figurea 

The  report  of  a  test  of  a  ITO-H.P.  Crossley  (Otto)  gas-engine  In  Eni^and, 
'189^,  using  producer-gas,  shows  a  consumption  of  but  .86  lb.  of  coal  per  H  JP. 
hour,  or  an  absolute  combined  efficiency  of  21.^  for  the  engine  and  pro- 
ducer.   The  efficiency  of  the  engine  alone  is  In  the  neighborhood  of  88^ 

The  Taylor  gas-producer  is  used  in  connection  with  the  Otto  gas-engine 
at  the  Otto  Qas-engine  Works  in  Philadelphia.  The  only  loss  is  due  to 
radiation  through  the  walls  of  the  producer  and  a  small  amount  of  beat 
carried  off  in  the  water  from  the  scrubber.  Experiments  on  a  100-H.P. 
engine  show  a  consumption  of  ^/lOO  lb.  of  carbon  per  l.H.P._per  hour.  This 
result  is  supeiior  to  any  ever  obtained  on  a  steam-engine.    (Iron  Age^  1888.) 

Testa  of  tike  Simplex  CMus-enslne*  (Proc.  Inst.  M.  B.  1880.)— 
Cylinder  7%  X  1594  in.,  speed  160  revs,  per  min.  Trials  were  made  with  town 
gas  of  a  heating  value  of  G07  heat-units  per  cubic  foot,  and  with  Dowsob 
gas,  rich  hi  CO,  of  about  160  haat- units  per  cubic  foot. 

Town  Gas.  Dowson  Gas. 


12  8               I                 S.              8. 

Effective  H.P 6>0     8.87  9.88  7.i«          8.81         5.96 

GasperH.P.  per  hour,  cu.  ft..  21.55    20.18  20.78  88.06       114.85       97.88 

Water  per  H.P.  per  hour,  lbs.  54.7     44.4  48.8  68.8 

Temp,  water  entering,  F 61<»       61»  61«  48* 

"      effluent 185<»      144*  178»  144» 

The  gas  volume  is  reduced  to  82<»  F.  and  80  in  barometer.  ▲  50-H.P.  engine 
working  85  to  40  effective  H.P.  with  Dowson  generator  consumed  51lbs. 
English  anthracite  per  hour,  equal  to  1 .48  to  1.8  lbs.  per  effective  H.P.  A  16- 
H.P.  engine  working  12  H.P.  used  19.4  en.  ft.  of  frasner  effective  H.P. 

A  820-K.P.  Ctes-enfflno.— The  Aour-milis  of  M.  Leblanc,  at  Pantin. 
France,  have  been  provided  with  a  S20-horse-power  fuel-gas  engine  of  the 
Simplex  type.  With  coal-gas  the  machine  gives  450  horse-power.  There  is 
ane  oyUnder,  84.8 in.  diam. ;  the  piston-sMroke  ia40  i|L;  and  the  speed  100  reva. 


6AS-EK0Iinss. 


849 


per  mio.  Special  arratipfements  have  been  devised  In  order  to  keep  the 
different  parts  of  the  machine  at  appropriate  temperatures.  The  coal  used 
is  0.B\'2  lb.  per  indicated  or  1 .08  lb.  per  brake  horse-power.  The  water  used 
is  8|i  {gallons  per  brake  horse-power  per  hour. 

Teat  of  an  Otto  Oas-enstne.  {Jour.  F,  /.,  Feb.  1890,  p.  115.)— En- 
gine 7  H.P.  nominal;  working  capacity  of  cylinder  .2094  cu.  ft.;  clearanoe 
sf>ace  .1796  cu.  ft. 

Heat- units.  Per  cent. 

Transferred  into  work 23.34 

Taken  by  jacket-water 40.94 

"      '^  exhaust 27.82 


•F. 

Tempemture  of  gas  supplied . .    62.2 

•*  *♦    "    exhaust...  774.3 

"  •*  enterittgwater   B0.4 

"  "  exit  water....    89.8 

Pressure  of  gas,  in.  of  water. .      8.06 

Revolution  per  rain.,  av^ge —  161 .6 

Explosions  missed  per  min., 

averaire 6.8 

Mean  effective  pressure,  lbs. 

persq.in. 69. 

Horse -power,  indicated 4.94 

Work    per    explosion,    foot- 
pounds  SS04. 

Explosions  per  minute 74 . 

Gas  ner  I.H  J*,  per  hour,  cu.  ft.    28.4 


Ck)mpo8itiott  of  the  gas: 

By  Volume.    By  Weight 
CO, 

&^.r.v.::: 

CO 

CH4 

H  

N 


0.50^ 

1.923^ 

4.38 

lO.fiSO 

1.00 

2.797 

5.88 

15.410 

27.18 

88.042 

61.67 

9.021 

9.06 

2J.278 

99.96 


99.995 


Temt  ot  the  Clerk  Gas-enffine.  (Proo.  Inst.  0.  E.  1882,  vol.  lxix.>- 
Cyiinder  6  x  W  in.,  150  rovg.  per  uiin.;  mean  available  pressure,  70.1  lbs.,  9 
I.H.P.;  maximum  pressure,  2ji0  lbs.  per  sq.  in.  above  atmosphere;  pressure 
before  ignition,  41  lbs.  above  atm.;  temperature  before  compression,  60*  F., 
after  compression,  813*  F.;  temperatiu-e  after  igaition  calculated  from  pres- 
sure, 2805'  F. ;  gas  required  per  I.H.P.  per  hour,  83  cu.  ft. 

JioreRecjfnt  Test*  of  gas-engines,  ISfe,  have  given  higher  economical  re- 
sults than  those  above  quoted.  The  gas-consumption  (city  gas)  has  been  as 
low  as  15  cu.  ft.  per  I.H.T.  per  hour,  and  the  efficiency  at  high  as  27j{  of  the 
heating  value  oithe  gas.  The  princii>al  improvement  in  praotioe  has  been 
Che  use  of  much  higher  compression  of  the  working  charge. 

Gombaetlon  of  tbe  Gaa  In  tl&eOtto  Biictne«-John  ImrayJn 
discussion  of  Mr.  Clerk's  paper  on  Theory  of  thetkui-eneine  m^-  T^^ 
change  which  Mr.  Otto  introduced,  and  which  rendered  the  engine  a  sucoesf 
"^i^S^  *°*???,**'  burning  in  the  cyUnder  on  explosive  mixture  of  gwand 
air.  he  burned  it  in  cpmpanv  with,  and  arranged  &  a  certain  way  in  Veepect 
of,  a  large  volume  of  mcombustible  gas  which  was  heated  by  it,  and  which 
diminished  the  speed  of  combustion.  W.  R.  Bousfleld,  in  the  same  disous" 
Bion,  says:  In  the  Otto  engine  the  chaive  varied  from  a  charge  which  Wag 
^  £?Pl''S'^S  «»**^"ro  ^\  the  point  of  ignition  to  a  charge  which  was  merely 
^r^J^t^^'i^.^SJh  ^iV^'^U  ^^V"  *K°*"<»»  ^^  place  there  was  n  expli 
sion  close  to  the  Doint  of  ignition  that  was  graduaUy  communicated  through- 
out the  mass  of  the  cylinder.  As  the  Ignition  g6t  fartheraway  from  the 
primary  pomt  of  Ignition  the  rate  of  transmission  became  slower,  and  if  the 
engine  were  not  worked  too  fast  the  ignition  should  gradually  catch  up  to 
n^1«^lhiSilJf4F  ^^  "*r^\?"  '?*  combustible  ga8T>eIng  ttfus  consumed. 
i?i5- tK  *7k**'  u  7  combustion  is,  however,  disputed  bjMr.Cierk,  who 
holds  that  the  whole  quantity  of  combustible  gas  is  ignited  in  an  Instant. 

(Clerk  on  Die  Ga«-eneine.)-Mixtures  of  air  and  cSdham  coal-gas.     tSdw* 


ature  before  explosion,  17"  C. 


Mixture. 


Gas. 

J  vdl. 
1  " 
1  •• 

a  •' 

1  " 

1  " 

1  '* 

1  *• 

1 


Air. 

14  vols. 

18  " 

12  '* 

11  " 

9  " 

7  " 

6  " 

6  *• 

4 


Max.  Press 
above  Atmos., 
lbs.  per  sq.  in. 

40. 

61.6 

60. 

61. 

78. 

87. 

90. 

91. 

80. 


Temp,  of  Explo- 
sion calculated 
from  observed 
Pressure. 

806»C. 
1088 
1203 
1220 
1557 
1788 
1792 
1812 
1505 


Use   of  Car1»nrette«l  Air  In  Oas-cngines 


■gas.     Temper- 
Theoretical 
Temp,  of  Explo- 
sion if  all  Heat 
were  evolved, 
1786<»a 
1012 


2670 
8834 
3808 


-Air  passed  ovei; 


650        GAS,  PETROLEUM,  A^t)  HOT-AtR  ENGIKES. 

^(asoliDe  or  volatile  petroleum  spirit  of  low  sp.  itt.,  0.65  to  0.70,  liberates 
tfome  of  the  gasoline,  and  the  air  thus  saturated  with  vapor  is  equal  in  heat- 
ing or  lighting  power  to  ordinary  coal-gas.  It  may  therefore  be  used  as  a 
fuel  for  gas-engines.  Since  the  vapor  is  given  off  at  ordinni-y  temperatures 
gasoline  is  Tery  explosive  and  dangerous,  and  should  be  kept  in  an  under- 
ground tank  out  or  doors.  A  defect  in  the  use  of  carburetted  air  for  gas- 
engines  is  that  the  more  volatileproducts  are  given  olT  first,  leaving  ao  oily 
residue  which  is  often  useless.  Some  of  the  substances  in  the  oil  that  are 
taken  up  by  the  air  are  apt  to  form  troublesome  deposits  and  incnistationa 
when  burned  in  the  engine  cylinder. 

Tlie  Otto  Gasollne-enstne.  (Eng'g  New,  May  4,  1888.)— It  is 
claimed  that  where  but  a  small  gasoline-engine  is  used  and  the  gasoline 
bought  at  retail  the  liquid  fuel  will  be  on  a  par  with  a  steam-engine  using  6 
lbs.  of  coal  per  horse -power  per  hour,  and  coal  at  $3.fiOper  ton,  and  will 
besides  save  all  the  handling  of  the  solid  fuel  and  ashes,  as  well  aa  the  at- 
tendance for  the  boilers.  As  very  few  small  steam-engines  conaame  leas 
than  6  lbs.  of  coal  per  hour,  this  is  an  exceptional  showing^ for  economy.  At 
8  cts.  per  gallon  for  gasoline  and  1/10  gal.  required  per  H.P,  per  hour,  the 
cost  per  H.P.  per  hour  will  be  0.8  cent. 

Gasoline-engines  are  coming  into  extensive  use  (1808).  In  these  eni^nes 
the  gasoline  is  pumped  from  an  underground  tank,  located  at  some  distance 
outside  the  engine-room,  and  led  through  carefully  soldered  pipes  to  the 
working  cylinder.  In  the  combustion  chamber  the  gasoline  is  sprayed  into 
a  current  of  air,  by  which  it  is  vaporized.  The  mixture  is  then  compressed 
and  ignited  by  an  electric  spark.  At  no  time  does  the  gasoline  come  In  con- 
tact with  the  air  outside  of  the  engine,  nor  is  there  any  flame  or  burning 
gases  outside  of  the  cylinder. 

^Napl&tlia-enKlnea  are  in  use  to  some  extent  in  small  yachts  and 
launches.  Tiie  naphtha  is  vaporised  in  a  boiler,  and  the  vapor  is  used  ex- 
pansively in  the  engine-cylinder,  as  steam  is  used;  it  is  then  condensed  and 
returned,  to  the  boiler.  A  portion  of  the  naphtha  vapor  is  used  for  fuel  un- 
der the  boiler.  According  to  the  circular  of  the  builders,  the  Gas  Engine 
and  Power  Oo.  of  New  York,  a  S-H.P.  engine  requires  from  8  to  4  quarts  of 
naphtha  per  hour,  and  a  4-H.P.  eng^lne  from  4  to  tf  quarts.  The  chief  ad  van- 
tam  of  tne  naphtha-engine  and  boiler  for  launches  are  the  saving  of  weight 
and  the  quickness  of  operation.  A  S-H.P.  engine  weighs  900  lbs.,  a  4-H.P.  800 
lbs.  It  takes  only  about  two  minutes  to  get  under  headway.  (Modem 
Mechanism,  p.  270.) 

Kot-air  (or  Caloric)  Bnglnea.— Hot-air  ensrines  are  nsed  to  some 
extent,  but  their  bulk  is  enormous  compared  with  their  effective  power.  For 
an  account  of  the  largest  hot-air  engine  ever  built  (a  total  failure)  see 
Church's  Life  of  Ericsson.  For  theoretical  luTestigaton,  see  Rankine's 
Steam-engine  and  Rontgen's  Thermodynamics.  For  description  of  con- 
structions, see  Appietonii  Cyc  of  Mechanics  and  Modem  Mechanism,  and 
Babcock  on  Substitutes  for  Steam,  Trans.  A.  S.  M.  E.,  vii.,  p.  608. 

Teat  of  a  Kot-alr  Bn^liie  (Robinson).~A  vertical  doubl»«ylinder 
(Caloric  Engine  Oo.'s)  13  nominal  U.P.  engine  gave  90.19 1.H.P.  in  the  work- 
ing cylinder  and  11.88 1.H.P.  in  the  pump,  leaving  6.81  net  I.E. P.;  while  the 
effective  brake  H.P.  was  6.9,  ffiviug  a  mechanical  efficiency  of  07}(.  Con- 
sumption of  coke,  8.7  lbs.  per  brake  H.P.  per  hour.  Mean  pressure  on 
pistons  15.87  lbs.  per  square  inch,  and  in  pumps  15.9  lbs.,  the  area  of  working 
cylinders  being  twice  that  of  the  pumps.  The  hot  air  supplied  was  about 
11(X)«  F.  and  that  rejected  at  end  of.stroke  about  BW  F.  .    ,         «. 

T&e  Priestman  Petroleam-eiiJgine.  (J^ntr.  Frank.  InMt,  Feb. 
1893  )— The  following  is  a  description  of  the  operation  of  the  engine:  Any 
ordinary  high -test  (usually  150»  test)  oil  is  forced  under  air-pressure  to  an 
atomizer,  where  the  oil  is  met  by  a  current  of  air  and  broken  up  into  atoms 
and  sprayed  into  a  mixer,  where  it  is  mixed  with  the  proper  proportion  of 
supplementary  air  and  sufficiently  heated  by  the  exhaust  from  the  cylinder 
passing  around  this  chamber.  The  mixture  is  tben  drawn  by  suction  into 
the  cylinder,  where  it  is  compressed  by  the  nlston  and  ignited  by  an  electric 
spark,  a  governor  controlling  the  supply  of  oil  and  air  propoitionately  to 
the  work  performed.  The  burnt  products  are  discharged  through  an  ex- 
baust-valve  which  is  actuated  by  a  cam.  Part  of  the  air  supports  the  com- 
bustion of  the  oil,  and  the  heat  generated  by  the  combustion  of  the  oil 
expands  the  air  that  remains  and  the  products  resulting  from  the  explosion, 
and  thus  develops  its  power  from  air  that  it  takes  in  while  running.  In 
Other  words,  the  engine  exerts  its  power  by  inhaling  air,  heating  that  air, 
and  expelling  the  products  of  combustion  when  done  with.  In  the  largest 
'-  -  only  the  1/250  part  of  a  pint  of  oil  is  used  at  any  one  Ume,  and  in 


BPFICIEirCT  OF  LOCOMOTTVES. 


851 


the  smallest  sixes  the  fuel  Is  prepared  in  correct  quantities  Taryiog  from 
lAOOOof  a  pint  upward,  accordliifc  to  whether  the  enfcine  is  runuins  on  lif^ht 
or  full  duty.  The  cycle  of  operations  is  the  same  as  that  of  the  Otto  gas- 
eneine. 

Trials  of  a  5-K.P.  Priestman  Petroleum-ensliie.  (Prof. 
W.  C.  Unwin,  Proc.  Inst.  C.  E.  IH'ja.)— Cvlinder,  8}^  X  12 in.,  making:  normally 
800  revs,  per  min.  Two  oils  were  used,  Russian  aud  American.  The  more 
important  results  were  ^ivenin  the  following  table: 


■\ 


on  used 

Brake  H.P  .... 

I.H.P 

Mechanical  efficiency. 

Oil  used  per  brake  H.P. 
hour,  lb 

Oil  used  per  Indicated 
H.P.hour,lb 

Lb.  of  air  per  lb.  of  oil . . 

Mean  explosion  pressure, 
lbs.  per  sq.  in 

Mean  compression  pres- 
sure, lbs.  per  sq.  in  . . 

9fean  terminal  pressure, 
IbH.  per  sq  In 


Trial  V. 

Full 
Power. 

Trial  I. 

Full 
Power. 

Trial  IV. 

Full 
Power. 

Trial  II. 

Half 
Power. 

7.722 
9.360 
0.824 

Ruaso- 
lene. 
6.7© 
7.408 
0.01 

Russo- 
lene. 
6.882 
8. 882 
0.876 

Russo- 
lene. 
8.62 
4.70 
0.760 

0.842 

0.046 

0.068 

1.881 

0.604 
33.4 

0.864 
31.7 

0.816 
48.2 

1.068 
21.7 

151.4 

181.8 

128.5 

48.6 

35.0 

spr.6 

S6.0 

14.8 

85.4 

23,7 

25.5 

15.6 

Trial  III. 
Light. 

Russo- 
lene. 


0.880 


6.TS4 
10.1 


9.6 
6.0 


To  compare  the  fuel  consumption  with  that  of  a  steam-engine,  1  lb.  of 
oil  might  be  taken  as  equivalent  to  l^  lbs.  of  coal.  Then  the  consumption 
in  the  oll-englne  was  equivalent,  in  Trials  I.,  IV.,  and  V.,  to  1.42  lbs.,  1.4d  lbs., 
and  LSGlbs.  of  coal  per  brake  horee-power  per  hour.  From  Trial  IV.  the 
following  values  of  tne  expenditure  of  heat  were  obtained: 

Percent. 

Useful  work  at  brake 18.81 

Engine  friction 2.81 

Heat  shown  on  indfc^tor-diagram 16.18 

Rejected  in  jacket- water  ...  47.64 

*•        in  exhaust-gas«*8 26,72 

Radiation  and  unaccounted  for 9.61 


Total. 


99.90 


LOCOMOTIVES. 


Bflietoner  of  IfOcomoUTes  and  Reslstaaee  of  Trains. 

(Oeorge  R  Henderson,  Proc.  Kngrs.  Club  of  Phiia.  1886.)— The  efflcieucv  of 
locomotives  can  be  divided  into  two  principal  parts :  the  flrst  depending 
upon  the  size  of  the  cylinders  and  wheels,  the  valve-gear,  boiler  and  steam- 
passages,  of  which  the  tractive  power  is  a  function;  and  the  second  upon 
the  speed,  grade,  curvature,  and  friction,  which  combine  to  produce  the 
resistance. 
The  tractive  power  may  be  determined  as  foltows : 

Let  P=  tractive  power;  ,,  ^ 

p  =  average  eflTective  pressure  in  cylinder; 
a  =  stroke  of  piston: 
d  =  diameter  of  cylinders; 
J)  zs  diameter  of  driving-wheels.    Then 


^--. 


iwd^pS  __  d*pS 


4iri> 


852 


LOCOMOTIYES. 


The  average  effective  pressure  can  be  obtained  from  an  indicator-dia- 
»aiii,  or  by  calculation,  when  the  Initial  pressure  and  ratio  of  ezpanfiion  an* 
known,  titKether  with  the  oiher  properties  of  the  valve-aiotion.  The  sub- 
joined table  from  •*  Auchincloss^*  gives  the  proportion  of  mean  effective 
pressure  to  boiier-pressure  above  atmosphere  for  various  proporiions  of 
cut-off. 


o-»-!  <S^,, 


Stroke, 
Cut  off  at— 


1 

.15 

125  =  Hi 

.a 

16 

.24 

173 

.28 

2 

.83 

25  =  M 

.4 

8 

.46 

.833  =  U 
.876  =  « 

!46 


(M.E.P. 

Boiler- 

pres.  =  I). 


:§.=  « 

.57 
.6d 
.67 
.78 


Stroke, 
Cut  off  at- 


:75=ji 
:8»  =  « 


M.E.P. 

(Bofler- 

pres.  =  1). 


.79 
.82 
.85 
.89 
.93 
.96 


These  values  were  deduced  from  experiments  with  an  English  locomotive 
by  Mr.  Gooch.  As  diagrams  vary  so  mucli  from  different  cauMes,  this  table 
will  only  falrlv  represent  practical  cases.  It  is  evident  that  the  cut-off  must 
be  such  that  the  boiler  will  be  capable  of  supplying  sufRcient  steam  at  the 
given  speed. 

In  the  following  calculations  it  Is  assumed  that  the  adhesion  of  the  engine 
is  at  least  equal  to  the  tractive  power,  which  Is  generally  the  case— if  the 
engine  be  well  designed— except  when  starting,  or  running  at  a  very  lev 
rate  of  speed,  with  a  small  expansive  ratio.  When  running  faster,  economy, 
and  also  the  sise  of  the  boiler,  necessitate  a  higher  ratio  of  expansion,  that 
reducing  tlie  tractive  power  below  the  adhesion.  If  the  adhesion  be  !««« 
than  the  tractive  power,  substitute  it  for  the  latter  in  the  following  for- 
mulas. 

The  resistances  can  be  computed  in  the  following  manner,  first  consider- 
ing the  train: 

There  Is  a  resistance  due  to  friction  of  the  Journals,  pressure  of  wind,  etc., 
which  increases  with  the  speed.  Most  of  the  experiments  made  with  a  vies 
of  determining  the  resistance  of  trainw  have  been  with  European  rollingstock 
and  on  European  railwayH.  The  few  trials  that  have  been  made  here  seem 
to  prove  that  with  Ameiican  systems  this  resistance  is  less. 

The  following  table  gives  the  resistance  at  different  speeds,  assumed  for 
American  practice : 

Speed  In  miles  per  hour : 
<=5         10         15        2025808540466056        60 

Resistance  in  pounds  per  ton  of  3240  lbs.: 
V=    8.1       8.4         4.        4.8      5  8      7.1       8.6     10.2     12.1    14.8     16.8    19.t; 

CoeflBcient  of  resistance  In  terms  of  load  : 

I  =  .0015    .0017    .OO-JO    .0024  .0029  .0035  .0043  .0051  .0060  .0071  .0064   .0096 


0+^) 


I  =  .0015 

The  resistance  due  to  curvature  is  about  .5  lb.  per  ton  per  degree  of  cur- 
vature, or  the  coefficient  =  .OOOSSc,  where  e  =  the  curvature  In  degrec« 

The  effect  of  grades  may  be  determined  by  the  theory  of  the  Inclined 
plane. 

Consider  a  load  L  on  a  grade  of  m  feet  per  mile.  The  component  of  the 
weight  L  acting  in  the  line  of  traction,  or  parallel  to  the  track,  ia 

^  »to  *  =  ^  =  .C0019Lm. 

To  combine  these  coefficients  In  one  equation  representing  the  reetstanc? 
of  the  train : 
Let  L  =  uei^ht  of  train,  exclusive  of  engine,  in  pounds; 

R  =  reHi stance  or  train,  in  pounds. 

s,  c,  and  m,  as  above.    Then 

/?=  "t.[.0015(l  4- J!.]|j)+  OOOaSc  ±  .00019m], 


INERTIA  AKD  RESISTAliCES  OF  RAILROAD  TRAINS.   85S 

Uie  ±  rijnk  mMnlog  that  this  coefBdent  is  positive  for  asoendlog  and  nega- 
tive for  descending  grades. 

To  find  a  grade  upon  which  a  train  would  desoeod  by  Itself,  take  the  last 
ooefflcieut  minus  and  make  B  =  Ot  whence 


»  =  r.»(i+^)  +  i.«c. 


TF  being  weight  of  engine  and  tender,  and  «  being  probably  about  .8. 
Tranaformlng,  we  have 


As  locomotires  usually  have  a  long  rigid  wheel-base,  the  coefficient  for 
curYature  had  better  be  doubled.  The  resistance  due  to  the  friction  of  the 
working  partA  will  be  considered  as  being  proportional  to  the  tractive  power, 
so  that  the  effective  tractive  power  will  be  represented  by  uP,  the  resistance 
being  (1  ->  u)P. 

Combiuing  all  tliese  values,  there  results  the  equation  between  the  trac- 
tive power  and  the  weight  of  the  train  and  engine: 

ttP~  W{.0(X»e  ±  .00019m)  =  I^  +  .0002Sc  ±  .00019m, 

i  and  tender,  and  u  being  prol 

ttP-  yrr.OOOSc  ±  .00019m) 
^^      1+  .OOOaSc  ±  .00019m     ' 
and 

Pa,  IXf  4-  .0002SC  ±  .00019m)  -f  Tn.0006c  ±  .00019m) 
u 
These  deductions,  says  Mr.  Henderaon,  agree  well  with  railroad  practice. 
The  figures  given  above  for  resistances  are  very  much  less  than  those 

given  by  the  old  formulae  (which  were  certainly  wrong\  but  even  Mr.  Hen- 
erBOn*s  figures  for  high  speed  are  too  high,  according  to  a  diagram  given  by 
D.  L.  Barnes  in  Eng^g  Mng.^  June,  1894,  from  whteh  the  following  figures  are 
derived: 

Speed,  miles  per  hour 50      60      70      80      90      100 

Resistance,  pounds  per  gross  ton..    12     12.4    18.5     15       17       20 

Sng^ff  2V€ira.  March  8, 1894,  gives  a  formula  which  for  high  speeds  gives 
figures  for  resistance  between  those  of  Mr.  Barnes  and  Mr.  Henderson.  See 
tests  reported  in  Erig^g  New»  of  June  9, 1892.  The  formula  is,  resistance  in 
pounds  per  ton  s  ^  velocity  in  miles  per  hour  +  2.    This  gives  for 

Speed  6      10     15    902B8D      854045     6080     70   8090  100 

Resistance..  S^   4.5    594    7    8^    0.5    1094  1«  13^  l^S  17    19.5  22  24.5  27 

For  tables  showing  that  the  resistance  varies  with  the  area  exposed  to  the 
resistance  and  friction  of  the  air  per  ton  of  load,  see  Dashiell,  Trans.  A.  S. 
M.  £..  VOL  ziii.  p.  371. 

Inertia  ana  Rcatataneea  of  Railroad  Trains  at  IncreaaInK 
8peoda*~A  series  of  tables  and  diagrams  la  given  in  R.  R.  G<iz.,  Oct.  8l, 
lew),  to  show  the  resistances  due  to  inertia  in  starting  trains  and  accelerat- 
ing their  speeds. 

The  mechanical  principles  and  formulas  from  which  these  data  were  cal- 
culated are  as  follows: 

tf  =  speed  in  miles  per  hour  to  be  acquired  at  the  end  of  a  mile. 

/7  -H  2  =  average  speed  in  miles  per  hour  during  the  first  mile  run. 

V  =  velocity  in  feet  per  second  at  the  end  of  a  mile;  then  F  -i-  2  =  aver- 
age velocity  In  feet  per  second  during  the  first  mile  run. 

&280  -•-  l/'Z  s  time  in  seconds  requtred  to  run  first  mile  =  10560  -t-  V. 

V-t-  (10560  -•-  D  =  r«  -»-  10660  =  .0000947F*  =  Constant  gain  in  velocity  or 
acceleration  in  feet  per  second  necessary  to  the  acquirement  of  a  velocity  V 
at  the  end  of  a  mile. 

<7  =  acceleration  due  to  the  force  of  gravity,  i.e.,  82.2  feet  per  second. 

The  forces  required  to  accelerate  a  given  mass  In  a  given  nme  to  dllferent 
velocities  are  in  proportion  to  those  velocities.  The  weight  of  a  body  Is  the 
measure  of  the  force  which  accelerates  it  in  the  case  of  gravity,  and  as  we 
are  considering  1  lb.,  or  the  unit  of  weight,  as  the  mass  to  be  accelerated, 
we  have  g:  (^  -i- 10660) ::  1  la  to  the  force  required  to  accelerate  1  lb.  to  the 
velocity  K  at  the  end  of  a  mile  run,  or,  what  is  the  same,  to  accelerate  it  at 
the  rate  of  F*  -i-  10560  feet  per  second. 

From  this  the  pull  on  the  drawbar— It  is  the  same  as  the  force  Just  men- 
tioned, and  is  properly  termed  the  inertia^  in  pounds  per  pouoa  of  train 
weight  is  F*  -+-  ii(m  X  82.2),  which  equals  .00000294 F'. 


854  LOCOMOTIVES. 

This  last  formula  also  gives  the  grade  in  per  ceot  which  will  give  a  i 
ance  equal  to  the  iuertia  due  to  acceleration. 

The  grade  in  feet  per  mile  is  .00000294  F»  X  5280  =  .01553T'». 

The  resistance  offered  in  pounds  per  ton  is  2000  times  as  much  as  per 
pound,  or  .00588 F«. 

When  the  adhesion  of  locomotive  drivers  is  600  lbs.  per  ton  of  weight 
thereon— this  is  about  the  maximum— then  the  tons  on  drivers  necessary  to 
overcome  the  inertia  of  each  ton  of  total  train  load  are  .00588F*  ■*■  600  = 
.0000098F*.  In  this  determination  of  resistances  no  account  has  been  taken 
of  the  rotative  energy  of  the  wheels. 

Bfllcleney  of  the  Meeliaiilfliii  of  a  I<oeoiiiotlTe.  —  Dniitt 
Halpiu  (Proc.  Inst.  M.  £.,  Jauuary,  18K9,)  writes  as  follows,  concerning  the 
tractive  efficiency  of  locomotives;  With  simple  two-cylinanr  engines,  hav- 
ing four  wheels  coupled,  experiments  have  been  made  by  the  late  locomo- 
tive superintendent  of  the  £astem  Railway  of  France,  M.  Begray,  with  the 
greatest  possible  care  and  with  the  best  apparatus,  and  the  result  arrived  at 
was  that  out  of  100 1.H.P  in  the  cylinders  48  H.P.  only  was  available  on  the 
draw-bar.  Moreover,  the  loss  of  57%  had  been  conflrraed  independently  on 
the  Pennsylvania  Railroad,  with  an  engine  having  18^  x  24-in.  cylinders 
and  6  ft.  (i  in.  wheels  four-coupled;  up  to  65  miles  an  hour,  the  power  on 
the  draw-bar  was  found  to  be  only  42^  of  that  in  the  cs'linders. 

Frank  C.  Wagner  (Proc.  A.  A.  A.  8.,  1900,  p.  140),  commenting  on  the  above 
tests,  says  it  does  not  seem  possible  that  they  fairly  represent  average  con- 
ditions. He  gives  an  account  of  some  dynamometer  tests  which  indicate 
that  in  ordinary  freight  service  the  power  used  to  drive  the  locomotive  and 
tender  and  to  overcome  the  friction  of  the  mechanism  is  from  IQjC  to  S&jt  of 
the  total  power  developed  in  the  steam-cylinder.  In  one  test  the  weight  of 
the  locomotive  and  tender  was  16)(  of  the  total  weight  of  the  train,  while  the 
power  consumed  in  the  locomotive  and  tender  was  from  SOjC  to  S3%  of  the  in- 
dicated horse  power. 

The  Slxe  of  IjOcomotlTe  Cylinders  is  usually  taken  to  be  such 
that  the  engine  will  just  overcome  the  adhesion  of  its  wheels  to  the  rails  un- 
der favorable  circumstances. 

The  adhesion  of  the  wheel  is  about  one  third  the  weight  when  the  rail  is 
clean  and  sanded,  but  Is  usually  assumed  at  0.25.  (Thurston.) 

A  committee  of  the  American  Association  of  Master  Mechanics,  after 
studying  the  performance  reports  of  the  best  engines,  proposes  the  follow- 
ing formula  for  weight  on  driving-wheels:  W  =  -^ — jr — -  in  which  the 
mean  pressure  in  the  cylinder  is  taken  at  0.85  of  the  boiler-pressure  at 
starting,  C  is  a  numerical  coefficient  of  adhesion,  d  the  diameter  of  cylinder 
in  inches,  D  that  of  the  drivers  In  inches,  P  the  pressure  in  tlie  boiler  in 
pounds  per  square  inch,  5  ibe  stroke  of  piston  in  inches.  Cis  taken  an  0.25 
for  passenger  engines,  0.24  for  freight,  and  0.22  for  ** switching'^  engines. 

The  common  builder's  rule  for  determining  the  size  of  cylinders  for  the 
locomotive  is  the  following,  in  which  we  accept  Mr.  Fomey*s  assumption 
that  the  steam-pressure  at  the  engine  may  be  taken  as  nine  tenths  that  in 

the  boiler:   The  tractive  force  is,  approximately,  F  =  ^,    ^       where 

C  is  the  circumference  of  tires  of  driving-wheels,  3  =  the  stroke  in  inches, 
Pi  =  the  initial  unbalanced  steatn -pressure  in  the  cylinder  in  pounds  per 
square  inch,  and  A  —  the  area  of  one  cylinder  in  square  inches.    If  l5^  = 

diameter  of  driving  wheel  and  d  =  diameter  of  cylinder,  F=  ») . 

Taking  the  adhesion  at  one  fourth  the  weight  IF, 

jr-0  25Tr-  0  gp«  X  ^  X  4^  _  0.9p,d«g. 
""  ~  C  ~        I)      • 

whence  the  area  of  each  piston  is 


0.25CTr  /0.2SZ>Tr 

^  "■  0.9  X  4  X  pi5'        ~y     0.9piS  • 

The  above  formules  give  the  maximum  tractive  force;  for  the  mean  tra<^ 
tive  force  substitute  for  p^  in  the  formulas  the  mean  effective  pressure. 


BOILERS,    GRATE-StJRPACE,   SMOKE-STACKS,    ETC.    855 

Von  Borries*8  rule  for  the  diameter  of  the  low-pressure  cylinder  of  a  com- 
pound locomotive  Is  d*  =  — x« 

where  d  =  diameter  of  l.p.  cylinder  in  inches; 
D  =  diameter  of  driving-wheel  in  inches; 
p  s  mean  elTective  pressure  per  sq.  in.,  after  deducti&     eternal 

machine  friction; 
h  =  stroice  of  piston  in  inches; 
£  =s  ti-active  force  required,  usually  0.14  to  0.16  of  the  adhesion. 

The  value  of  p  depends  on  the  relative  volume  of  the  two  cylinders,  and 
from  indicator  experiments  may  be  taken  as  follows: 
m.^Mi  ^#  -B<na4n<>     Ratio  of  Cylinder     p  in  percentage     p  for  Boiler-press 
Class  of  Engine.  Volumes.  of  Boiler-pressur©.      ureof  176Ibs, 

Large-tender  eng*s     1 : 2  or  1 ;  9.05  42  74 

Tank-engines l:8orl:8.2  40  71 

Tlie  Slxe  ot  I<oeoiiiotlTe  Boilers.  (Forney's  Catechism  of  the 
Locomotive.)— They  should  be  proportioned  to  the  amount  of  adhesive 
weight  and  to  the  speed  at  which  the  locomotive  is  intended  to  work.  Tlius 
a  locomotive  with  a  great  deal  of  weight  on  the  driving-wheels  could  pull  a 
heavier  load,  would  have  a  greater  cylinder  capacity  than  one  with  little  ad- 
hesive weight,  would  consume  more  steam,  and  therefore  should  have  a 
larger  bolter. 

The  weight  and  dimensions  of  locomotive  boilers  are  in  nearly  all  cases 
determine  by  the  limits  of  weight  and  space  to  which  they  are  necessarily 
confined.  It  may  be  stated  generally  that  within  these  limiU  a  locomotive 
boiler  cannot  be  made  too  large,  m  other  words,  boilers  for  locomotives 
should  always  be  mad**  as  large  as  is  possible  under  the  conditions  that  de  • 
termine  the  weight  and  dimensions  of  the  locomotives. 

Wootten'a  l40ConiotlTe«  (Clark's  Steam-engine ;  see  also  Jour. 
Frank.  lust.  1881,  and  Modern  Mechanism,  p.  485.V-J.  E.  Wootten  designed 
and  constructed  a  locomotive  boiler  for  the  combustion  of  anthracite  and 
lignite,  though  specially  for  the  utilization  as  fuel  of  the  waste  produced  in 
the  mining  and  preparation  of  anthracite.  The  special  feature  of  the  engine 
ii.  the  flre-boz,  which  is  made  of  great  length  and  breadth,  extending  clear 
over  the  wheels,  giving  a  grate-area  of  from  64  to  BR  sq.  ft.  The  draught 
diffused  over  these  large  areas  is  so  gentle  as  not  to  lift  the  fine  pp***^icles  of 
the  fuel.  A  number  of  express-engines  having  this  type  of  boiler  are  engai^ed 
on  the  fast  trains  between  Philadelphia  and  Jersey  City.  The  fire-box  shell 
In  8  ft.  8  in.  wide  and  10  ft.  5  in.  long  ;  the  fire-box  is  8x0^  ft.,  making  76  sq. 
ft.  of  grate-area.  The  grate  is  composed  of  bars  and  water-tubes  alternately. 
l*lie  regular  types  of  cast-iron  shaking  grates  are  also  used.  The  height  of 
the  fire-box  is  only  2  ft.  6  in.  above  the  grate.  The  grate  is  terminated  by 
a  bridge  of  fire-brick,  beyond  which  a  combustion-chamber,  27  in.  long, 
leads  to  the  flue-tubes,  about  184  in  number.  1^4  in.  diaro.  The  cylinders  are 
itl  in.  diam.,  with  a  stroke  of  22  inches.  The  driving-wheels,  four-coupled, 
are  5  ft.  8  in.  diam.  The  engine  weighs  44  tons,  of  which  29  tons  are  on  driv- 
ing wheals.  The  heating-surface  of  the  fire-box  is  135  sq.  ft.,  tluit  of  the 
flue-tubes  is  9S'i  sq.  ft.;  together,  1117  sq.  ft.,  or  14.7  times  the  grate-area. 
Hauling  15  passenger-cars,  weighing  with  passengers  360  tons,  at  an  average 
speed  of  42  milen  per  hour,  over  ruling  gradients  of  1  In  89,  the  engine  con- 
sumes 62  IbK.  of  fuel  per  mile,  or  34^^  lbs.  per  sq.  ft.  of  errate  per  hour. 

Qualities  Basentlal  for  a  Free-steamlnc  I^oeomotlTe* 
(From  a  paper  by  A.  E.  Mitchell,  read  before  the  N.  Y.  Railroad  Club; 
Eng'g  News,  Jan.  24,  1891.)— Square  feet  of  boiler-heating  surface  for  bitu- 
minous coal  should  not  be  less  than  4  times  the  square  of  the  diameter  in 
inches  of  a  cylinder  1  inch  larger  than  the  cylinder  to  be  used.  One  tenth 
of  this  should  be  in  the  fire-box.  On  anthracite  locomotives  more  heating- 
surface  is  required  in  the  fire-box,  on  account  of  the  larger  grate-area 
required,  but  the  heating-surface  of  the  flues  should  not  be  materially 
decreased. 

Grate-siirlkce,  Smoke-siackay  and,  Exliaaat-iiozzlea  for 
liOCOlliotlTes.  lAm.  Mach.,  Jan.  8,  1891.)— For  grate-surface  for  anthra- 
cite coal:  Multiply  the  displacement  in  cubic  feet  of  one  piston  during  a 
stroke  by  8.5:  the  product  will  be  the  area  of  the  grate  in  square  feet. 

For  bituminous  coal :  Multiply  the  displacement  in  feet  of  one  piston 
during  a  stroke  by  6Vi;  the  product  will  be  the  grate-area  in  square  feet  for 
engines  with  cylinders  12  in.  in  diameter  and  upwards.    For  engines  with 


856 


LOCOMOTIVES. 


smaller  cjllnders  the  ratio  of  flrate-areato  ptetondlBplacefneDtdiotild  be  7^ 
to  1,  or  even  more,  if  the  de^tgn  of  the  engme  will  admit  this  proportion. 

The  fi^rate-areas  io  the  following  table  have  been  found  by  the  foregoing 
rules,  and  agree  very  closely  with  the  average  practice  : 

Smokestacks.— The  internal  area  of  the  smallest  cross-section  of  the  stack 
should  be  l/\7  of  the  area  of  the  grate  in  soft-coal-bumiiig  engines. 

A.  E.  Mitchell,  Supt.  of  Motive  Power  of  the  N.  T.  L.  E.  ft  W.  R.  R.,  says 
that  recent  practice  varies  from  this  rule.  Some  roads  use  the  same  sixe  of 
stacic,  18^  in.  ciiani.  at  throat,  for  all  engines  up  to  90  In.  diam.  of  cylinder. 

The  area  of  the  orifices  in  the  ezhaust-nozales  depends  on  the  quantity  and 
quality  of  the  coal  burnt,  size  of  cylinder,  construcUon  of  stack,  and  ihe 
condition  of  the  outer  atmosphere.  It  is  tlicrefore  impossible  to  give  rules 
for  computing  the  exact  diameter  of  the  orifices.    All  that  can  be  done  is  to 

five  a  rule  by  which  an  approximate  diameter  can  be  found.  The  exact 
lameter  can  only  be  found  by  trial.  Our  experience  leads  us  to  believe  that 
the  area  of  each  orifice  in  a  double  exhaust-nozzle  should  be  equal  to  1/400 
part  of  the  grate-surface,  and  for  Ringle  nozzles  1/200  of  the  grate-Kiirface. 
These  ratios  have  been  used  io  finding  ibe  diamelers  of  the  nozzles  given  in 
the  following  table.  The  same  sizes  are  often  used  for  either  bard  or  soft 
coal-burners. 


Doable 

Stnirle 

Orate-area 

Grate-area 

Nocsles. 

Nozxies. 

Size  of 

for  Anthra- 
cite Coal,  in 
sq.  in. 

for  Bitumin- 
ous Coal,  In 
sq.  In. 

Diameter 

Cylinders, 
in  inches. 

of  Stacks, 
in  inches. 

Diam.  of 
Orifices,  in 

Diam.  of 
Orifices,  in 

inches. 

inches. 

1«X20 

1601 

1817 

^H 

8 

S  18/16 

18X20 

1878 

1488 

loS 

86/16 

8 

14X20 

21 79 

1666 

iTS 

811/16 

16X22 

2T48 

8097 

1^ 

8  9/16 

16X84 

8415 

8611 

14 

8» 

4    1/16 

17X24 

8866 

2948 

16 

81/16 

4    6/16 

18X24 

4881 

8804 

1694 

11/16 

4l8/I6 

19X24 

4810 

8678 

16S 

20X24 

6887 

4061 

itS 

8M 

6    1/16 

Kxhanst-Bozsles  In  I<oeoiiiotlTe  Boilers.— A  committee  of 
the  Am.  K3-.  Manier  Mechanics'  Assn.  in  1890  reported  that  they  had,  after 
two  years  of  experiment  and  research,  come  to  tlie  conclusion  that,  owing 
to  the  great  diversity  in  the  relative  proportions  of  cylinders  and  boUers, 
together  with  the  difference  In  the  quality  of  fuel,  any  rule  which  does  not 
recognize  each  and  all  of  these  factors  would  be  worthless. 

The  committee  was  unable  to  devise  any  plan  to  determine  the  size  of  the 
exhaust-nozzle  in  proportion  to  any  other  part  of  the  engine  or  boiler,  and 
believes  that  the  best  practice  Is  for  each  user  of  locomotives  to  adopt  a 
nozzle  that  will  make  steam  freely  and  fill  the  other  desired  conditions,  heet 
determined  by  an  intelligent  use  of  the  indicator  and  a  check  on  the  fuel 
account.  The  conditions  desirable  are  :  That  it  must  create  draught  enough 
on  the  fire  to  make  steam,  and  at  the  same  time  Impose  the  least  possible 
amount  of  work  on  the  pistons  in  the  shape  of  back  pressure.  It  should  be 
large  enough  to  produce  a  nearly  uniform  blast  without  lifting  or  tearing 
the  fire,  and  be  economical  in  its  use  of  fuel. 

Fire-brick  Arclies  In  I^ocoinotlTe  Fire-boxes.— A  com- 
mittee of  the  Am.  Ry.  Master  Mechanics*  Assn.  in  1890  reported  strongly  In 
favor  of  the  use  of  brick  arches  In  locomotive  fire-boxes.  Tliey  say :  It  is 
the  unanimous  opinion  of  all  who  use  bituminous  coal  and  brick  arch,  that 
it  is  most  efficient  in  consuming  the  various  gases  composing  black  smoke, 
and  by  impeding  and  delaying  their  passage  through  the  tubes,  and  ming- 
ling and  subjecting  them  to  the  heat  of  the  furnace,  ffreaUy  lessens  %he 
volume  ejected,  and  Intensifies  combustion,  and  does  not  In  the  least  check 
but  rather  augments  draught,  with  the  consequent  saving  of  fuel  and  in- 
creased steaming  capacity  that  might  be  expected  from  such  results.  This 
in  particular  when  u««e(i  In  connection  with  extension  front. 

Size,  I¥el8:ht9  TractlTe  Poprer,  ete.,  of  Dlfi^rent  Slses  of 
LocomotlTes*    (J.  G.  A.  Meyer,  Modern  Locomotlre  Construction,  Aw, 


SIZE,   WEIGHT,  TnACnVE  POWEE,   ETC. 


867 


Mack.^  Aufr.  8, 1885. >— The  tractirA  power  should  not  be  more  or  less  than 
the  adhesion.  In  column  3  of  each  table  the  adhesion  is  given,  and  Rince  the 
adhesion  and  tractive  power  are  expressed  by  the  same  number  of  pounds, 
these  figures  are  obtained  by  finding  the  tractive  power  of  each  engine,  for 
this  purpose  always  using  the  small  diameter  of  driving-wheels  given  in 
column  2.  The  weight  on  drivers  is  shown  in  column  4,  which  is  obtained  by 
multiplying  the  adneeion  by  5  for  all  cUsses  of  engines.  Ck>lumn  5  gives  the 
weights  on  the  trucks,  and  these  are  based  upon  observations.  Thus,  the 
weight  on  the  truck  for  an  eight-wheeled  engine  is  about  one  half  of  that 
placed  on  the  drivers. 

For  Mogul  engines  we  multiply  the  total  weight  bn  drivers  by  the  decimal 
.2,  and  the  procUict  wUl  be  the  weight  on  the  truck. 

For  ten-wheeled  engines  the  total  weight  on  the  drivers,  multiplied  by  Uie 
decimal  .32,  will  be  equal  to  the  weight  on  the  truck. 

And  lastly,  for  consolidation  engmea,  the  total  weight  on  drivers  multi- 
plied by  the  decimal  .16,  will  determine  the  weight  on  tlie  truck. 

In  column  6  the  total  weight  of  each  engine  is  given,  which  is  obtained  by 
adding  the  weight  on  the  drivers  to  the  wei^t  on  the  truck.  Dividing  the 
adhesion  given  in  column  1  by  7Vi  gives  the  tons  of  2000  lbs.  that  the  engine 
i<  capable  of  hauling  on  a  straight  and  level  track  ooiiimn  7,  at  slow  speed. 

The  weight  of  engines  given  in  these  tables  will  be  found  to  sgree  gen- 
erally with  the  actnal  weights  of  locomotives  recently  built,  aluiougn  it 
must  not  be  expected  that  these  weights  will  agree  in  evei7  case  with  the 
actual  weights,  because  the  dilferent  builders  do  not  build  the  engines  alike. 

The  actual  weight  on  trucks  for  eight-wheeled  or  ten-wheeled  engines  wUl 
not  differ  much  from  those  given  in  Uie  tables,  because  these  weights  depend 
greatly  on  the  difference  between  the  total  and  rigid  wheel-base,  and  taese 
are  not  often  changed  bv  the  different  builders.  The  proportion  between 
the  rigid  and  total  wheel-base  is  generally  the  same. 

The  rule  for  finding  the  tractive  power  is : 


j  Square  of  dia.  ot\^\  Mean  effect,  steam  (.  ^  j  stroke  I 
<  _. ,_  .— t..-   f  A-jp^g^  pppgq  jp       f^linfeetf 


1  piston  in  inches 


Diameter  of  wheel  in  feet. 


=  tractive  power. 


ElOUT  WlliE£lJEn   LCM'Ollti^tVKS.           1 

Tu- 

W^mELXD 

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1, 

§ 

11  m 

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In. 

tn. 

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nw. 

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3«U0 

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71]» 

JJXJB 

<M»   (477 

tm* 

ISHtS 

mto     m 

ItirS 

M-U 

mm  w:m 

1060'  tMiW 

f      T*3 

ux^ 

1^7  mi> 

ivm 

13137, 

um,   ]Q» 

ISift 

m^m 

Ufll'  UIM 

t71«« 

61^0 

«10 

t-ixi^ 

IA  »  9m 

iXWO 

\mc 

f6S|0     IS» 

ii>j4 

U-41 

Tt/tJ    38M& 

intx 

mm 

I«H 

1«Mg4 

U-M  ilfftft 

tyitm 

ISI.^ 

IKm      IBSI 

l*xt* 

sts 

^B 

1170 

t7XH 

U-M  ISUa 

Aiaw 

L^fiju  rniw   ysm 

l^cM 

E*H 

mi 

axM 

M-M,Jiri!t 

i««11 

£iHH    £»m1     UW 

I7x»| 

iit"#A 

l«KH  ftvsn 

snio 

wm 

1^ 

VfxH 

Ur^,  14410 

7SIMJ 

UtK94 

41-eft 

nm  &7sta 

mm 

mm 

lesfi 

I 

Mooui.  EMOiKn. 

OONSOUDATIOTr  EMOTincs. 

in. 

In. 

IbB. 

lbs. 

lbs. 

lb«. 

in. 

in. 

Ibf. 

llM. 

.b.. 

lbs. 

llxi« 

SIMO 

4978 

24891 

4078 

29869 

668 

[4X16 

36-38 

7840 

39800 

6272 

4M78 

1048 

12X18 

8$-4I 

6480 

89400 

6480 

38880 

864 

16x18 

36-38 

10126 

60625 

8100 

86726 

1380 

ISxlS 

S7-4I 

7980 

880fr7 

7890 

44996 

086 

K)X24 

48-60 

18060 

14400 

104400 

9400 

UXSO 

»-43 

9046 

4M90 

90tf 

64276 

1906 

BX84 

60-tt 

20909 

i04M4 

167S7 

121271 

1717 

U>xSl 

42-47 

10607 

&903& 

10607 

63642 

1414 

10X24 

4^-6I 

12888 

61440 

12888 

73738 

16S8 

17X84 

4»^64 

12739 

63997 

12739 

76436 

1698 

llxt4 

ftl-M 

18782 

68611 

13782 

82888 

1829 

19x24 

64-60 

14440    72200 

14440 

86640 

1926 

868  LOCOMOTIVES. 

lioadlnff  American  Type*  of  LocomotlTe  for  Wrelght  and 
Passenger  ffervlce. 

1.  The  eight- wheel  or  **  Anierictiii ''  patiseuger  type,  having  four  coupled 
driving-wheels  and  a  four-wlieeled  tniclc  in  front. 

2.  The  "  ten- wheel  '*  type,  for  mixed  traffic,  having  six  coupled  drivers  and 
a  leading  four-wheel  truck. 

8.  The  '*  Mogul  '*  freight  type,  havitig  six  coupled  driving-wheels  and  a 
pony  or  two-wneel  truck  in  fi*oiit. 

4.  The  ''  Ck>n8oiidation  '*  type,  for  heavy  freight  service,  having  eight 
coupled  driving-wheels  and  a  pon}'  truck  in  front. 

Besides  these  there  is  a  great  variety  of  types  for  special  conditions  of 
service,  as  four-wheel  and  six- wheel  switching-engines,  without  trucks;  the 
Forney  type  used  on  elevated  railroads,  with  four  coupled  wheels  under  the 
engine  and  a  four-wheeled  rear  truck  carryine  the  water-tank  and  futfl; 
locomotives  for  local  and  suburban  service  with  fotu*  coupled  driving-wheels, 
with  a  two- wheel  truck  front  and  rear,  or  a  two- wheel  truck  front  and  a 
four-wheel  truck  rear,  etc.  **  Decapod  "  engines  for  heavy  freight  service 
have  ten  coupled  driving-wheels  ana  a  two-wheel  truck  in  front. 

flteam-dlstrlbntlon  for  HlBli-speed  I«oeomofiTea« 

(C.  H.  Quereau,  Eng'g  News,  March  8, 18M.) 

Baianced  Valves.— Ilr.  Philip  Wallls,  in  1886,  when  Engineer  of  Te8t«  for 
the  C,  B.  &  Q.  R.  R.,  reported  that  while  6  H.P.  was  required  to  work  uo- 
tMdanced  valves  at  40  miles  per  hour,  for  the  balanced  valves  it.H  H.P.  only 
was  necessa^. 

Effect  of  Speed  on  Avei-nge  Cylinder-preanire.— Assume  that  a  locomotive 
has  a  train  in  motion,  the  reverse  lever  is  placed  in  the  running  notch,  and 
the  track  is  level;  by  what  is  the  maximum  speed  limited  ?  The  resistancv 
of  the  train  and  the  load  increase,  and  the  power  of  the  locomotive  de 
creases  with  increasing  speed  till  the  resistance  and  power  are  equal,  when 
the  speed  becomes  uniform.  The  power  of  the  engine  depends  on  tb; 
average  pressure  in  the  cylinders.  Even  though  the  cut-off  and  boiler' 
pressure  remain  the  same,  this  pressure  decreases  as  the  speed  increase^: 
oecause  of  the  higher  piston-speed  and  more  rapid  valve-travel  the  steam 
has  a  shorter  time  in  which  to  enter  the  cylinders  at  the  higher  speed.  The 
following  table,  from  indicator-cards  taken  from  a  locomotive  at  Taiying 
speeds,  snows  the  decrease  of  average  pressure  with  increasing  speed: 

Miles  per  hour. 46  51  51        63       54  57       60       66 

Speed,  revolutions 824  S48  S48  S58  268  277  2S»  S-Jl 

Average  pressure  per  eq.  in.: 

Actual 51.5  44.0  47.8  48.0  4t.8  4S.5  87.8  86.3 

Calculated 46.5  46.5  44.7  48.8  41.8  88.5  35.9 

The  ''  average  pressure  calculated  ^*  was  figured  on  the  assumption  that 
the  mean  effective  pressure  would  decrease  iu  the  same  ratio  that  the  speed 
increased.  The  main  difference  lies  in  the  higher  steam-line  at  the  lower 
speeds,  and  consequent  higher  expansion-line,  showing  that  more  steani 
entered  the  cylinder.  The  back  pressure  and  compression-lines  agree  quite 
closely  for  all  the  cards,  though  they  are  slightly  better  for  the  slower 
speeds.  That  the  difference  is  not  greater  majr  safely  be  attributeti  to  the 
large  exhaust-ports,  passages,  and  exhaust  tip,  which  is  5  in.  diameter. 
These  are  matters  of  great  importance  for  higli  speeds. 

Boiler-preMure.—The  increase  of  train  resistance  with  increased  speed  is 
not  as  the  square  of  the  velocity,  as  is  commonly  supposed.  It  is  more  likely 
that  it  incn*ases  as  the  speed  after  about  20  miles  an  hour  is  ivacbed.  As- 
suming that  the  latter  is  true,  and  that  an  average  of  60  lbs.  per  square  inch 
is  the  greatest  that  can  be  realized  in  the  crliuders  of  a  ^iven  eogine  at  40 
miles  an  hour,  and  that  this  pressure  furnishes  just  sufficient  power  to  ke<*p 
the  train  at  this  speed,  it  follows  that,  to  increase  the  speed  to  60  miles,  the 
mean  effective  pressure  must  be  increased  in  the  same  proportion.  To  in- 
crease the  capacity  for  speed  of  any  locomotive  its  power  must  be  increased, 
and  at  least  by  as  much  as  the  speed  is  to  be  increased.    One  wav  to  accom- 

glish  this  is  to  increase  the  boiler-pressure.  That  this  is  generally  realixed, 
>  shown  by  the  Increase  in  boiler-pressure  in  the  last  ten  rears.  For  twenty- 
three  single-expansion  locomotives  described  in  the  railway  Journals  this 
year  the  steam-pressures  are  as  follows:  8,  160  lbs.;  4, 165  lbs.;  1^  170  lbs.: 
18, 180  lbs.;  1,  ISUlbs. 


SOME  LARGE  AMERICAK  LOCOMOTIVES,    1893.     859 

Valve-t7avel.  —  An  Increased  ayerage  cylinder-pressure  may  also  be 
obtaitied  by  iDcreasliifr  the  valve-travel  without  raisins  the  boiler-pressure, 
and  better  results  will  be  obtained  by  increasing  both.  The  longer  travel 
elves  a  higher  steam-pressure  in  the  cylinders,  a  later  exhaust-opening, 
later  exhaust-closure,  and  a  larger  exhaustropening— a^l  necessary  ror  high 
speeds  and  economy.  I  believe  that  a  20-in.  port  and  6)4-ln.  (or  even  7-in.) 
travel  could  be  successfully  used  for  high-speed  engines,  and  that  frequently 
by  so  doing  the  cylinders  could  be  economically  reduced  and  the  counter- 
balance lightened.  Or,  better  still,  the  diameter  of  the  drivers  increased, 
securing  lighter  counterbalance  and  better  steam-distribution. 

Size  of  Drivers,— Economy  will  increase  with  increasing  diameter  of 
drivers,  provided  the  work  at  average  speed  does  not  necessitate  a  cut-off 
longer  than  one  fourth  the  stroke.  The  piston-speed  of  a  locomotive  with 
6i-in.  drivers  at  55  miles  per  hour  is  tiie  same  as  that  of  one  with68-lD. 
drivers  at  61  miles  per  hour. 

Steam-ports.— The  length  of  steam-ports  ranges  from  15  in.  to  2S  in.,  and 
lias  considerable  influence  on  the  power,  speed,  and  economy  of  the  loco- 
motive. In  cards  from  similar  engines  the  steam-line  of  the  card  from  the 
engine  with  28-in.  ports  is  considerably  nearer  boiler-pressure  than  that  of 
the  card  from  the  engine  with  17^-in.  ports.  That  the  higher  steam-line  is 
due  to  the  greater  length  of  steani-port  there  is  little  room  for  doubt.  The 
23-in.  port  proiluced  &31  H.P.  in  an  I8U-in.  cylinder  at  a  cost  of  23.5  lbs.  of 
indicated  water  per  I.H.P.  per  hour.  The  17^  in.  port,  424  H.P.,  at  tlie  rate 
of  22.9  lbs.  of  water,  in  a  19-in.  cylinder. 

Allen  Valve* —Ttmre  is  considerable  difference  of  opinion  as  to  theadvan- 
tagu  of  the  Allen  ported-valve     (See  Eng.  News,  July  6, 1893.) 

Speed  of  Ralliv^ay  Trains.— In  ISHi  the  average  speed  of  trains  on 
the Xtverpool  and  Manchester  Railway  was  twenty  miles  an  hour;  in  1838  it 
WAS  twenty-five  miles  an  hour.  But  by  1840  there  were  engines  on  the  Great 
Western  Railway  capable  of  running  Afty  miles  an  hour  with  a  train,  and 
eighty  miles  an  hour  without.  A  speed  of  66  miles  per  hour  was  made  in 
England  with  the  T.  W.  Worsdell  compound  locomotive.  The  total  weight 
of  the  engine,  tender,  and  train  was  695,000  lbs.;  indicator-cards  were  taken 
showing  1068.6  H.P.  on  the  level.  At  a  speed  of  75  miles  per  hour  on  a 
level,  and  the  same  train,  the  indicator-cards  showed  1040  H.P.  developed. 
(Trans.  A.  S.  M.  E.,  vol.  xiii.,  383.) 

The  limitation  to  the  increase  of  speed  of  heavy  locomotives  seems  at 
present  to  be  the  difficulty  of  counterbalancing  the  reciprocating  parts.  The 
unbalanced  vertical  component  of  the  reciprocating  parts  causes  the  pres- 
sure of  the  driver  on  the  rail  to  vary  with  every  revolution.  Whenever  the 
.speed  is  high,  it  is  of  considerable  magnitude,  and  its  change  in  direction  is 
so  rapid  that  the  resulting  effect  upon  the  rail  is  not  inappropriately  called 
a  "  hammer  blow.^'  Heavy  rails  have  been  kinked,  and  bridges  have  been 
shaken  to  their  fall  under  the  action  of  heaviiv  balanced  drivers  revolving 
at  high  speeds.  The  means  by  which  the  evil  is  to  be  overeome  has  not  yet 
been  made  clear.   See  paper  by  W.  F.  M.  Ooss.  Trans.  A.  8.  M.  E..  vol.  xvi. 

Engine  No.  999  of  the  Mew  York  Central  Railroad  ran  a  mile  hi  82  seconds 
equal  to  112  miles  per  hour,  May  11, 1898. 

Speed  in  miles  \  _  circum.  of  driving-wheels  in  in.  X  no.  of  rev,  per  jnin.  X  60 
pel-  hour      f  -  ^^^ 

=  diam,  of  driving-wheels  in  in.  x  no.  of  rev.  per  min.  X  .003 
(approximate,  giving  result  8/10  of  1  per  cent  too  great). 

BinsifsioNs  OF  some  large  ahikrioan 

LOCOREOTIVKS,   1893. 

The  four  locomotives  described  below  were  exhibited  at  the  Chicago 
Ebcpositlon  in  1898.  The  dimensions  are  from  Engineering  News,  June,  1698. 
The  first,  or  Decapod  engine,  has  ten-coupled  driving-wheels.  It  is  one  of 
the  heaviest  and  most  powerful  engines  ever  built  for  freight  service.  The 
Philadelphia  &  Reading  engine  is  a  new  type  for  passenger  service,  with  four- 
coupled  drivers.  The  Rhode  Island  engiite  has  six  drivers,  with  a  4-wheel 
leading  truck  and  a  2-wheel  trailing  truck.  These  three  engines  have  all 
compound  cylinders.  The  fourth  is  a  simple  engine,  of  the  standard  Ameri- 
can 8  wheel  type,  4  driving-wheels,  and  a  4-wheel  truck  in  front.  This 
engine  holds  the  world's  record  for  speed  (2893)  for  sliort  distances,  haying 
run  »  mile  in  3?  aeconds. 


860 


LOCOMOTIVEa. 


Baldwin. 
N.  Y.,  L.  E. 
ft 
W.  RR. 
Decapod 
Freight. 


Baldwin. 

Pblla. 

& 

Read.  &R. 

Bzpreea 

Panenger. 


Rhode  IsK 

Looomoti'e 

Works. 

Heavy 

Bxpreea, 


N.  Y.  C.  A 
H.  R.  R. 
Empire 

State 
Bzpresa. 
M0.9M. 


Runnlng-Kear: 

Driving- wheeli,  dlAin  .... 

Truck         "  **    

Journals,  drlvtng-azlee... 
truck-  "  ... 
tender-  '*  ... 
Wheel-baae : 

Driving 

Total  engine 

"     tender 

'*  engine  and  tender. . . 
Wt.  In  -working-order: 

On  drivers 

On  truck-wheels 

£ngine,total 

Tender     "  

Eujglne  and  tender,  loaded 
Cylinders  t 

h.p.(«) 

l.p.(«) 

Distance  centre  to  centre. 

Piston-rod,  diam 

Connecting-rod,  length. . . 

Stoam-porta 

{  Ezhaust-ports 

Slide-valves,  out.  lap,  h.p. 
♦'  •*  out.  lap,  l.p.. 
*•  •*  In.  lap,  h.p... 
••  ••  In.  lap, l.p... 
"  max.  travel.. 
••  "  lead,  h.p.. 
"      lead,  l.p. . 

Boiler— Type 

Diam.  of  barrel  Inside. 
Thickness  of  barrel-plates 
Height  from  rail  to  centre 

line    

Length  of  smoke-box 

Working  steam-pressure.. 

Fi  rebox— type 

Length  inside 

Width       **     

Depth  at  front 

Thickness  of  side  plates . . 

"back  plate... 

Thickness  of  crown-sheet. 

'*         "tube       "     . 

Qrate-area 

Stay-bolts,  diam.,  1^  in. 

Tubes— iron 

Pitoh 

Diam.,  outside 

Length  betw^n  tube-plates 
Heatlug-surface  : 

Tubes,  exterior 

Fire-box 

Miscellaneous  t 
Exhaiist-no2xle,  diam. . . . 
8uiokestack,smarst  diam. 
height    from 
rail  to  top 


4  ft.  2  In. 
8  '*   6  " 
0    X 10  In. 
6    xlO  " 
4J<x  9  - 

18  ft.  10  in. 

jr  ••  s  " 

10  "    8  " 
88  ••    4  " 

170,000  lbs. 
»,B00   " 
l«,fi00  •• 
117,500  " 
810,000   •• 

lOxSdIn. 
27x28  - 
7  ft.  6  •* 

4  in. 
y  8  7/10" 

Sixain. 

28Jix8" 


6  In. 

1/10  in. 

6/16  •' 

Straight 

6  ft.  2^  in. 

8ft.0   In. 

180%. 
Wootten 
10'  119/16" 
8  ft.  SM  In. 

6/16  in. 
6/16  " 


80.6  sq.  ft. 
pitch,4l4ln. 

2      " 
11  ft.  11  In. 

2,208.8  ft. 
234.3  *' 

5  in. 
1  ft.  6  •' 

15  "  6^  " 


0  ft  6  in. 

4  "  0  " 
8Ux]2ln. 
68x10" 
4Hx  8  •• 

6  ft.  10  In. 
«  **  4  »• 
16  ••  0  " 
47  "     8  •* 

82,Tt»lbs. 

47,000  •* 
120,700  " 

80,678  " 
210.278  " 

18x24  m. 
22x24  " 

7  ft.  4U  in. 

8ft.0Ml'in. 

24  x1m  in. 

24x4U" 
In. 


6  ft.  e  in. 

2  "  9  " 

8    xr89i<n 

4jix  8     '• 


7fl.  2ln. 
8  '*  4   " 

9      X  ISWin. 
6}4«JO     - 


H: 


(neg)Hiln 

None 

Sin. 

Straight 

4  ft.  BH  in. 

Hill. 


180  lbs. 
Wootten 
9fi.6    in. 

6/10  in. 
6/16  " 
6/16  "^ 

76,8  sq.  ft. 


18  ft  6    In. 


8  ft.    6  in. 
_     ,  »  '*    11  •* 
15  "  0     **  IB  ft, 
80  "  ^  "  47 


88,600  lbs. 

64,800  •* 
148,000  •* 

76,000  " 
218,000  " 

one  21x96 
one  81  k20 

7  ft  1  In. 

S^in. 

10  ft.  8U  in. 

1Ux20and 

lHx26 

8x20  In. 


[fa. 


8^24 

21/lCin. 

l^ln. 

10  ft  0  in. 

1,262  sq.  ft. 
178  *'    •' 

lit.  6°in. 

14  ft.  0%  in. 


Wagon  top 

6^.  2  in. 

Kin- 

8  ft.  11  in. 

6  "     1  " 

200  lbs. 

Radial  stay 

10  ft  0    in. 

6  "  iffi  * 
6/16  in. 


£8sq.ft 
4  In. 
272 

12  ft  8H  in, 


1ft  8  in. 
16  "  2  " 


84.000  lbs 
40,0(10  " 

IM.OOO  " 
80,000  " 

204,000  '* 

10x24  in. 

'lift  6 in.' 

8  ftruS'ln- 
lH>(18in. 

8%xl?" 
1  in. 


1/10  In. 
*6HIn. 


Wagon  top 

4  ft.  9  ii<. 

9/16  in. 

7ft.llHin. 

4  "  8  - 
190  lbs. 
Biichaiifto 
9  f  L  e»fi  iiL 

8  -  iii  •• 

0  "   ^H 

6/16  in. 
5/16  " 

Jl' 

80.7^,  ft, 
4  in. 


2  in. 
12  ft.  0  Id. 

1,697  Rq.  ft 
288^    •    I 

1  fLsSj  in. 
14  *•  10    •• 


DIUENSIONS  OF  AMERICAN  LOCOMOTIVES. 


8G1 


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*8dQnx 

JO  man 


•oo 
S«?5 


«?«!, 


'oiMiiilaomiy 
-a|  *b0  J0d  ojn 


8|88gS8|S8g§SSgSg8g§|SSg8|Sg| 


*9j  'bs  'aoBjjnt 


•?jb8 
*0dvjjn8-8ai 


Is 


3     «    .     t-e-.     ©It'. 


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iiili 


ottti 


'a9«j0jo«gJT 


•Bqi  *S|aaqiii 
1«l»!^Al  mox 


§ii|§|i§l§i§l§§§l§i§§§i§ii§§i 


ipllfTsililllllllllflllillfi 


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XXXMKXKXXX- 


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SSSgp|fsSS«tSiS?iSSel§gSgslsS22g 


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-^^■^'W<V«^-9<-<9<-««9^«>"«>MM^^O-«>9<^'<*0<^9»9t«« 


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I  BjaALia  30  -Oil 
cjii'Sda'Vqjsiajj 

i    JO  jaaaaggpj 


^-^«OQ^-«^<<*^'V«D»tD^O^CO«OOOOOaO«COQO«DOQD-««P 


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862 


LOCOMOTIVES. 


ntmeiiiilons  of  Some  American  IjoeomotlTes.— The  Ubleon 
paKe  861  is  condensed  from  one  given  by  D.  L.  Barnes,  in  his  paper  on 
^'  Distinctive  Featiii-es  and  Advantages  of  American  Locomotive  Practice,'* 
Trans.  A.S.C.E.,  1898.  The  formula  from  which  column  marked  **  Haiio  of 
cylinder- power  to  weight  available  for  adhesion"  is  calculated  as  follows: 
2  X  cylinder  area  x  boiler-pressure  x  stroke 
Weight  on  drivers  X  diameter  of  driving-wheel' 

(Ratio  of  cylinder-power  of  compound  engines  cannot  be  compared  with 
tliat  of  the  single-expansion  engines.) 

Where  the  boiler-pressure  could  not  be  determined  from  the  description 
of  the  locomotives,  as  given  by  the  builders  and  operators  of  thelocoraoiivfs^ 
it  has  been  assumed  to  be  160  lbs.  per  sq.  in.  above  ihe  atmosphere. 

For  compound  locomotives  the  figures  in  the  last  column  of  ratios  are 
based  on  the  capacity  of  the  low-pressure  cylinders  only,  the  volume  of  the 
high-pressure  being  omitted.  This  has  been  done  for  the  purpose  of  com- 
parison, and  because  there  is  no  accurate  simple  way  of  comparing  the 
cylinder-power  of  single-expansion  and  compound  locomotives. 

Dimensions  of  Standard  IjOComoflTes  on  the  N*  T*  ۥ  A 

H.  R.  R.  and  Penna.  R.  R.,  1882  and  1893« 
C.  H.  Quereau,  Eng'g  News,  March  8. 1894. 


N.  Y.  C.  &  H.  R.  R. 


Through 
Passenger. 


1882.    1893. 


Through 
Freight. 


1882.    1898, 


Pennsylvania  R.  R. 


Through       Thromch 
Passenger.      Freight. 


1882.    1898. 


1832.     1893. 


Grate  surface,  sq.  ft 

Heating  surface,  sq.  ft. 

Boiler,  diam.,  in 

Driver,  diam.,  in 

Steam- pressure,  lbs. .   . 
Cylin.,  diam.  and  stroke. 

Valve-travel,  ins 

Lead  at  full  gear,  ins . . . 

Outside  lap 

Inside  lap  or  clearance . 

Steam-ports,  leneth 

"         •*      width 

Type  of  engine 


17.87 

1358 

50 

70 

150 

17X24 


^ 


VI 


15! 
Arri. 


'\^ 


27.3 
1821 

58 
78,86 

180 
19x24 

1/16 
1 
0 
18 

J^ 
Am. 


17.87 
1358 
50 
64 
150 
17X24 

1/16 
Am. 


S9.8 

17.6 

1763 

1067 

58 

50 

67 

62 

160 

125 

19X26 

17X24 

594 

5 

1/16 
3% 

? 

18 

16 

IH 

m 

Mog. 

Am. 

83.2 

1583 
67 
78 
175 

1 

1^ 

Am. 


Indicated  l¥ater  Consumption  of  Single  and  Componud 
IiOcomotlTc  Engines  at  Varying  Speeds. 

C.  H.  Qnereati,  Encf'g  News,  March  8,  1894. 


Two-cylinder  C!ompound. 

Single-expansion. 

Revolu- 
tions. 

Speed, 

miles  per 

hour. 

Water 
per  LH.P. 
per  hour. 

Revolu- 
tions. 

Miles  per 
Hour. 

Water. 

100  to  150 
150  ••  200 
200  "  250 
250  ♦'  8r5 

21  to  31 
81   "  41 
41   "  61 
51   "  56 

18.88  lbs. 
18.9     " 
19.7     *• 
31.4      " 

151 
219 
253 
807 
821 

81 
45 
52 
68 

66 

21.70 
20.91 
20.62 
80.28 
20.01 

It  appears  that  the  compound  engine  is  the  more  economical  at  low  speeds, 
the  economy  decreasing  as  the  speed  increases,  and  that  the  single  engine 
increases  in  economy  with  increase  of  speed  within  oi'dinary  limits,  becom- 
ing more  economical  than  the  compound  at  speeds  of  more  than  50  miles 
per  hour. 

The  C,  B.  &  Q.  two-cylinder  compound,  which  was  about  30]C  less  eco- 
nomical than  simple  engines  of  the  same  class  when  tpstetl  in  passenger 
service,  has  since  oeen  shown  t-o  be  15*  more  economical  in  freight  service 


■dNo. 

Revs. 

MUes 
per  hour. 

I.H.P. 

Card  No. 

Beys. 

Miles, 
per  hour. 

100 

S7.1 

648.8 

V 

804 

70.6 

200 

00.8 

728 

8 

296 

68.6 

190 

44 

651 

9 

800 

00.6 

250 

68 

891 

10 

804 

T0.6 

200 

00 

960 

11 

840 

78.9 

298 

89 

968 

12 

810 

71.9 

ADVANTAGES  OF  COMPOUNDING.  803 

than  the  best  slnele-expanslon  engine,  and  29%  more  economical  than  the 
averaire  record  of  40  siraple  enjcin^s  of  the  same  class  on  the  same  division. 
Indicator-teats  or  a  IjOcomotlTe  at  Hl^lt  Speed*  (Locomo- 
tive Eng'g,  June,  1898.)— Cards  were  taken  by  Mr.  Angus  Sinclair  on  the 
locomotive  drawing  the  Empire  State  Express. 

Results  or  Imdjoator- diagrams. 

I.H.P. 

977 
973 
1,045 
1,059 
1,120 
l,0;j6 

The  locomotive  was  of  the  eight-wheel  tjrpe,  built  by  the  Schenectady 
Ixwomotlve  Works,  with  19  X  24  in.  cylinders,  78-ln.  drivers,  and  a  large 
boiler  and  flre-box.  Details  of  important  dimensions  are  as  follows : 
Heating-surface  of  fire-box.  150.8  sq.  ft.;  of  tubes,  1670.7  sq.  ft.;  of  l)oilfr. 
1821 .5  sq  ft.  Orate  area.  27.8  sq.  ft.  Fire-box:  length,  8  ft.;  wldtli.  8  ''r.  4?^ 
in.  Tubes,  288;  outside  diameter,  2  in.  Ports:  steam.  18  x  IH.  *"• ;  exhaust, 
18x294 in.  Valve-travel,  b\i  in.  Outside  lap,  1  In.;  inside  lap,  1/64  In. 
Jonrnals:  driving-axle,  8U  x  10^  in.;  truck-axle,  6  X  10  in. 

The  train  consisted  of  four  coaches,  weighing,  with  estimated  load,  840,000 
lbs.  The  locomotive  and  tender  weighed  in  working  order  200,000  lbs,, 
making  the  total  weight  of  the  train  about  270  tons.  During  the  time  that 
the  engine  was  first  lifting  the  train  into  speed  diagram  No.  1  was  taken.  It 
shows  a  mean  cylinder-pressure  of  S9  lt>8.  According  to  this,  the  power 
exerted  on  the  rails  to  move  the  train  is  6558  lbs.,  or  24  lbs.  per  ton.  The 
speed  is  87  miles  an  hour.  When  a  speed  of  nearly  60  miles  an  hour  was 
reached  the  average  cylinder-pressure  is  40.7  lbs.,  representing  a  total 
traction  force  of  4520  lbs.,  without  making  deductions  for  iiitemal  friction. 
If  we  deduct  \Q%  for  friction,  it  leaves  15  lbs.  per  ton  to  keep  the  train  going 
ai  the  speed  named.  Cards  6,  7,  and  8  represent  the  work  of  keeping  the 
train  running  70  miles  an  hour.  They  were  taken  three  miles  apart,  when 
the  speed  was  almost  uniform.  The  average  cylinder-pressure  for  the  three 
cards  is  47.6  lbs.  Deductine:  \(i%  again  for  friction,  this  leaves  17.6  lbs.  per 
i4in  as  the  power  exerted  iu  keeping  the  train  up  to  a  velocity  of  70  miles. 
Throughout  the  trip  7  lbs.  of  water  were  evaporated  per  lb.  of  coal.  The 
work  of  pulling  the  train  from  New  York  to  Albany  was  done  on  a  coal  con- 
sumption of  about  3^  lbs.  per  H.P.  per  hour.  The  highest  power  recorded 
wa^  at  the  rate  of  1120  H.P. 

liOeomotlTe-teatlni:  Apparatus  at  tlie  Ijaboratorjr  of 
Pardne  UnlTerelty.  (W.  F.  M.  Uoss,  Trans.  A.  S.  M.  E.,  vol.  xlv.  826.)— 
Vi\**  locomotive  is  mounted  with  its  drivers  upon  supporting  wheels  which 
are  carried  by  shafts  turning  in  fixed  bearings,  thus  allowing  the  engine  to 
be  run  without  changing  its  position  as  a  whole.  Load  Is  supplied  by  four 
friction-brakes  fitted  to  the  supporting  shafts  and  offering  resistance  to  the 
turning  of  the  supporting  wheels.  Traction  is  measured  by  a  dynamometer 
attached  to  the  draw-bar.  The  boiler  is  fired  in  the  usual  way,  and  an 
exhaust-blower  above  the  engine,  but  not  in  pipe  connection  with  il,  carries 
off  all  that  may  be  given  out  at  the  stack. 

A  Standard  Method  of  Conducting  Locomotive- test n  Is  given  in  a  report 
by  n.  Committee  of  the  A.  8.  M.  E.  in  vol.  xiv.  of  the  Transactions,  page  1312. 
'Waate  of  Fuel  In  liOeomotlTea,— In  American  practice  economy 
of  fuel  is  necessarily  sacrificed  to  obtain  greater  economy  due  to  heavy 
train-loads.  D.  L.  Barnes,  in  Eiig.  Mag.,  June,  1894,  gives  a  diagram  showing 
the  reduction  of  eflSciency  of  boilers  due  to  high  rates  of  coniDustion,  from 
which  the  following  figures  are  taken: 

Ll>8.  of  coal  per  sq.  ft.  of  grate  per  hour 12     40     80     120     160     200 

P#^  cent  efficiency  of  boiler 80     75     67       69       51       48 

A  rate  of  12  lbs.  is  given  as  representing  stationary-boildr  practice,  40  lbs. 
is  English  locomotive  practice,  1'20  lbs.  average  American,  and  200  lbs.  max- 
imum American,  locomotive  practice. 

AdTAiitaaee  of  Componndliifl;.— Report  of  a  Committee  of  the 
American  Railway  Master  Mechanics' Association  on  Compound  Locomotives 
(Ant,  Mnch.^  July  8,  1890)  gives  the  following  summary  of  the  advantages 
gained  by  compounding:  (a)  It  has  achieved  a  saving  iu  the  fuel  burnt 
averaging  ISHC  at  reasonable  boiler-pressures,  with  encouraging  poseibilitiea 


864  LOCOHOTITES. 

of  further  improvement  In  pressure  uid  in  fuel  and  water  economy,  (b)  It 
has  leiwenfKl  the  amount  of  watt* r  (dead  weiglit)  to  be  hauled,  ao  that  (c)  the 
tender  and  its  load  are  materially  reduced  m  weight,  (d)  It  has  incre«ae<l 
the  possibilities  of  speed  far  bejroud  60.  miles  |)er  hour,  without  unduly 
straining  the  motion,  f lames,  axles,  or  axle-boxes  of  the  engine,  (e)  It  has 
increaseil  the  haulage-power  at  full  speed,  or,  in  other  words,  has  increasMHl 
the  continuous  HP.  developed,  per  given  weight  of  engine  and  t>oiler.  (/>  In 
some  classes  has  increased  the  starting-power,  (o)  It  has  materially  leaaened 
the  slide-valve  friction  per  H.P.  developed,  (h)  It  has  equalized  or  distrib- 
uted the  turning  force  on  the  crank-pin,  over  a  longer  portion  of  ita  path, 
which,  of  course,  tends  to  lengthen  the  repair  life  of  the  engine.  («)  In  the 
two-cylinder  type  it  has  decreased  the  oil  consumption,  and  has  even  done 
BO  in  the  Woolf  four-cylinder  engine.  ( j)  Its  smoother  and  steadier  dratight 
on  the  fire  is  favorable  to  the  combustion  of  all  kinds  of  soft  coal;  and  the 
sparks  thrown  being  smaller  and  less  in  nnmber,  it  lessens  the  risk  to  pi-op- 
erty  from  destruction  by  dre.  (k)  These  advantoges  and  eeonomtea  are 
gained  without  having  to  improve  the  man  handling  tlie  engine,  less  beine 
Tett  to  his  discretion  (or  careless  indifference)  than  in  the  simple  engine.  (/) 
Valve-motion,  of  every  locomotive  type,  can  be  used  in  iia  best  working  and 
most  effective  poaition.  (m)  A  wider  ehisticity  In  locomotive  design  is  per- 
mitted ;  as,  if  desired,  side-rods  can  be  dispensed  with,  or  articulated  engines 
of  100  tons  weighty  with  indei»endent  trucks,  used  for  sharp  curves  od  moun- 
tain service,  as  suggested  by  Mallet  and  Brunner. 

Of  27  compound  locomotives  in  use  on  the  Phila.  and  Beading  Railroad  Un 
16VS2),  12  are  In  use  on  heavy  moimta in  grades,  and  are  designed  to  be  the 
equivalent  of  22  X  21  in.  simple  consolidations;  10  are  in  somewhat  lighter 
service  and  correspond  to  )iO  x  24  in.  consolidations;  5  are  in  fast  passcmgw 
service.    Theinoutbly  coal  record  shows: 

Cl«.  of  Engine.  Ho.         ^Ul^Si^^ 

Mountain  locomotives \2  V^toMfC 

Heavy  freight  service 10  12^tol7y 

Fast  passenger 5  ih(toll)( 

(Report  of  Com.  A.  R.  M.  M.  Assn.  1802.)  For  a  description  of  the  various 
types  of  compound  locomotive,  with  discussion  of  their  relative  merits,  see 
paper  by  A.  Von  Berries,  of  Germany,  The  Development  of  the  C?ompound 
Locomotive.  Trans.  A.  S.  M.  E.  1893,  vol.  xlv.,  p.  1 172. 

Connterbalancliii:  I«o€oinoUTeii,->The  following  rules,  adopted 
by  different  locomotive- builders,  are  quoted  in  a  paper  by  Prof.  Xauzs 
CTrans.  A.  S.  M.  E.,  x.  802): 

A.  **  For  the  main  drivers,  place  opposite  the  crank-pin  a  weight  equal  to 
one  half  the  weight  of  the  back  end  of  the  connecting-rod  plus  one  half  the 
weight  of  the  front  end  of  the  connecting-rod,  piston,  piston-rod,  and  cross- 
head.  For  balanchig  the  coupled  wheels,  place  a  weignt  opposite  the  crank- 
pin  eiqual  to  one  half  the  parallel  rod  plus  one  half  of  the  weights  of  the 
front  end  of  the  malnrod,  piston,  pislon-rod,  and  cross-head.  The  centres 
of  gravity  of  the  above  weights  must  be  at  the  same  distance  from  the 
axles  OS  the  crank- pin.** 

B.  The  rule  given  by  D.  K.  Clark :  "  Find  the  separate  revolving  weights 
of  crank-piu  boss,  couollng-rods,  and  connecting-rods  for  each  wheel,  abo 
the  reciprocating  weignt  of  the  piston  and  appendages,  and  one  half  the 
conneciing-rod,  divide  the  reciprocating  weight  equally  between  each  whef^l 
and  add  the  part  so  allotted  to  the  revolving  weight  on  each  wheel:  the 
sums  thus  obtained  are  the  weights  to  be  placed  oppofdte  the  crank-pin.  and 
at  the  same  distance  from  the  axiB.  To  find  the  coimterweight  to  be  us^ed 
when  the  distance  of  its  centre  of  gravity  is  known,  multlpiv  the  alM>v« 
weight  by  the  leneth  of  the  crank  in  Inches  and  divide  by  the  given  dis- 
tance.'^ This  rule  differs  from  the  preceding  in  that  the  same  weight  l£ 
placed  in  each  wheel. 

O.  •*  TT  «a -^ — ^-',  in  which  8  s  one  half  the  stroke,  O  =  distance 

from  centre  of  wheel  to  centre  of  gravity  in  counterbalance,  w  •  weight  at 
crank-pin  to  be  balanced,  W  =  weight  in  counterbalanoe,  /  =  eoefflcieut  of 
friction  so  called,  s  5  in  ordinary  practice.  The  reciprocating  weight  is 
found  by  adding  together  the  weights  of  the  piston,  piston-rod,  csross-bead. 
and  one  half  of  the  main  rod.  The  revolving  weight  for  the  main  wheel  is 
found  by  adding  together  the  weights  of  the  crank^pin  hub,  crank-pin,  ons 


PETROLSUM-BUEKIKG   LOCOMOTIVES.  865 

half  of  the  main  rod,  and  one  half  of  each  parallel-rod  connecting  to  this 
wheel;  to  this  add  the  reciprocating  weight  divided  by  the  number  of 
wheels.  The  revolving  weight  for  the  remainder  of  the  wheels  is  found  in 
the  same  manner  as  for  the  main  wheel,  except  one  half  of  the  main  rod  is 
not  added.  The  weight  of  the  cranio  pin  hub  and  the  counterbalance  does 
not  Include  tlie  weight  of  the  spokes,  but  of  the  metal  inclosing  them.  This 
calculation  is  based  for  one  cylinder  and  Its  corresponding  wheels/* 

D.  *'  Ascertain  as  nearly  as  possible  the  weights  of  crank-pfn,  additional 
weight  of  wheel  boss  for  the  same,  add  side  rod,  and  main  connections, 
pts-ton-rod  and  head,  with  cross-bead  on  one  side:  the  sum  of  these  multi« 
plit^  by  the  distance  in  Inch<»  of  the  centre  of  the  ciank-pin  from  the  centre 
of  ilie  wheel,  and  divided  by  the  distance  from  the  centre  of  the  wheel  to 
the  common  centre  of  gravity  of  the  counterweights,  ts  taken  for  the  total 
counterweight  for  that  side  of  the  locomotive  which  is  to  be  divided  among 
the  wheels  on  that  side." 

E.  **  Balance  the  wheels  of  the  locomotive  with  a  weight  equal  to  the 
weights  of  crank -pin,  crank-pin  hub,  main  and  parallel  rods,  brasses,  etc., 
plus  two  thirds  of  the  weight  of  the  reciprocating  parts  (cross-head,  piston 
and  rod  and  packing).'* 

F.  "  Balance  the  weights  of  the  revolving  parts  which  are  attached  to 
each  wheel  with  exactness,  and  divide  equally  two  thirds  of  the  weights  of 
the  reciprocating  parts  between  ali  the  wheels.  One  half  of  the  main  rod  is 
computed  as  reciprocating,  and  the  other  as  revolving  weight.*' 

See  also  articles  on  CoauterbalandngLocomotlves,  in  B.  R.  d  Eng.  Jour., 
March  and  April,  1890»  and  a  paper  by  w.  F.  SI.  Goes,  in  Trans.  A.  S.  M.  E., 
vol  xvl 

lllftxiiiiiun  Bmtt  Load  for  Steel  Tires  on  Steel  Ralle* 
(A.  S.  11.  £.,  vii.,  p.  786.)— Mr.  Ohanute's  experiments  led  to  the  deduction 
that  12,(XX)  lbs.  should  be  the  limit  of  load  for  any  one  driving-wheeL  Hr. 
Angus  Sinclair  objects  to  Mr.  Chanute's  figure  of  12,000  lbs.,  and  savs  that 
a  locomotive  tire  which  has  a  light  load  on  it  is  more  injurious  to  the  rail 
th&n  one  which  has  a  heavy  load.  In  Engli^  practice  8  and  10  tons  are 
safely  used.  Mr.  Oberlin  Smith  has  used  steel  castings  for  cam-rollers  4  in. 
diam.  and  8  In.  face,  which  stood  well  under  loads  or  from  10,000  to  20,000 
lbs.  Mr.  C.  Shaler  Smith  proposed  a  formula  for  the  rolls  of  a  pivot-bridge 
which  may  be  reduced  to  the  form  :  Load  as  1700  x  face  X  Vdiam.,  all  in 
lbs.  and  inches. 

See  dimensiona  of  some  large  American  locomotives  on  pages  860  and  861. 
On  the  *'  Decapod ''  tlie  load  on  each  drivicg*wheei  is  17,000  lbs.,  and  on 
''No.  WO,'' 21 .000  Iba 

Narro^r-ffanse  Ball^raye  In  Xlannfaetnrliiff  l¥orke«— 
A  tramway  of  18  mches  gauge,  neveral  miles  in  leugtli,  is  iu  the  works  of 
the  LancaMhlre  and  Yorkshire  Railway.  Curves  of  IS  feet  radius  are  used. 
The  looomotives  used  have  the  following  dimensions  (Proc.  Inst.  M.  E.,  July, 
1888):  Hie  qylinden  were  6  in.  diameter  with  6  in.  stroke,  and  2  ft.  8U  in. 
centre  to  centre.  The  wheels  were  1<^4  in.  diameter,  the  wheel-base 
S  ft.  9  in.;  the  frame  7  ft.  4U  in.  long,  and  the  extreme  width  of  the  engine 
S  feet.  The  boiler,  of  steel,  S  ft.  Sin.  outside  diameter  and  2  ft.  lotig  between 
tube-plates,  containing  56  lubee  of  1|^  in.  outside  diameter;  the  nre-box,  of 
iron  and  cylindrical,  2  ft.  8  in.  long  and  17  in.  inside  diameter.  The  heating- 
surface  1049  sq.  ft.  in  the  fli^box  and  86  12  in  the  tubes,  total  46.54  sq.  ft.; 
the  grate-area,  1.78  sq.  ft.;  capacity  of  tank,  26^  gallons;  working- preat^ure, 
:70  lbs.  per  sq.  in.;  tractive  power,  say,  1412  lbs.,  or  0.22  lbs.  per  lb.  of  eflTc c- 
tive  preHBUre  per  sq.  in.  on  the  piston.  Weight,  when  empty,  2.80  tons; 
when  full  and  in  working  order,  8.10  tons. 

For  description  of  a  system  of  narrow-gauge  railways  for  manufactories, 
see  circular  of  the  C.  W.  Hunt  Co.,  New  York. 

lillCbt  IjOeomotlTee.— For  dimensions  of  light  ocorootives  used  for. 
mining,  etc.,  and  for  much  valuable  information  concerning  them,  see  cata- 
logue of  H  K.  Porter  &  Co.,  Pittsburgh. 

Petrolenm-bariiliis:  I^ocoinotlTee.    (From  Clark's   Steam-en- 

fine.)— The  combustion  of  petroleum  refuse  in  locomotives  has  been  success 
ully  practised  by  Mr.  Thos.  Urquhart,  on  the  GrazI  and  Tsarltsin  Kailway, 
Southeast  Russia.  Since  November,  1884,  the  whole  stock  of  148  locomotives 
under  his  superintendence  has  been  fired  with  petroleum  refuse.  The  oil  is 
injected  from  a  nozzle  through  a  tubular  opening  in  the  back  of  the  flre-box, 
by  means  of  a  Jet  of  steam,  with  an  induced  current  of  air. 

A  brickwork  cavity  or  *'  regenerative  or  accumulative  combustion-cham- 
ber'*  is  formed  in  the  fire-box,  into  which  the  combined  current  breaks  aa 


866  LOCOMOTIVES. 

spray  agiai'nst  the  rugged  brickwork  slope.  In  this  arntngemeiit  the  brick- 
work is  maintained  at  a  white  heat,  and  combustion  is  complete  and  nmoke- 
less.  The  form,  mass,  and  dlmenRi'ons  of  the  brickwork  are  the  most  im- 
portant elements  in  such  a  combination. 

Ck>mpres8ed  air  was  tried  instead  of  steam  for  injection,  but  no  appreciable 
deduction  in  consumption  of  fuel  was  noticed. 

The  heating-power  of  petroleum  refuse  is  given  as  19.832  heat-miita, 
equivalent  to  the  evaporation  of  90.53  lbs.  of  water  from  and  at  218^  F.,  or  to 
17.1  llts.  at  8^  atmospheres,  or  125  lbs.  per  sq.  in.,  efTective  pressure.  Tho 
highest  evaporative  duty  was  14  lbs.  of  water  under  S}4  atmospheres  per  lb. 
of  the  fuel,  or  nearlv  B2%  efficiency. 

There  is  no  probability  of  any  extensive  use  of  petroleum  as  fuel  Tor  loco- 
motives in  the  United  States,  on  account  of  the  unlimited  supply  of  coal  and 
the  comparatively  limited  supply  of  petroleum. 

Ptrelesa  liOcoinotlTe.— The  principle  of  the  Francq  locomotive  is 
that  it  depends  for  the  Hupply  of  steam  on  its  spontaneous  generation  from 
a  body  or  heated  water. in  a  reservoir.  As  steam  is  generated  and  drawn 
off  the  pressure  falls;  but  by  providing  a  sufficiently  large  volume  of  water 
heated  to  a  high  temperature,  at  a  pressure  correspondingly  high,  a  margin 
of  surplus  pressure  may  be  secured,  and  means  may  thus  be  provided  for 
supplying  the  required  quantity  of  sieam  for  the  trip. 

The  tireless  locomotive  designed  for  the  service  or  the  Metropolitan  Rail- 
way of  Paris  has  a  cylindrical  reservoir  having  segmental  ends,  about  5  fu 
Tin.  in  diameter,  26^  ft.  in  length,  with  a  capacity  of  about  620  cubic  feet. 
Four  fifths  of  the  capacity  is  occupied  by  water,  which  is  heated  by  the  aiil 
of  a  powerful  jet  of  steam  supplied  from  stationary  boilers.  The  water  is 
heated  until  equilibrium  is  established  between  the  boilers  and  the  reser- 
▼oir.  The  temperature  is  raised  to  about  S00<*  F.,  corresponding  to  2&  lbs. 
per  SQ.  in.  The  steam  from  the  reservoir  is  passed  through  a  reducing- 
valve,  oy  which  the  steam  is  reduced  to  the  required  pressure.  It  is  then 
passed  through  a  tubular  superheater  situated  within  the  receiver  at  the 
upper  part,  and  thence  through  the  ordinary  regulator  to  the  cylinders. 
The  ezfiaust-steam  is  expanded  to  a  low  pressure,  in  order  to  obviate  noise 
of  escape.  In  certain  cases  the  exhaust-steam  is  condensed  in  closed 
vessels,  which  are  only  in  part  filled  wiiii  water.  In  the  upper  free  space  a 
pipe  is  placed,  Into  which  the  steam  is  exhausted.  Within  this  pipe  another 
pipe  is  fixed,  perforated,  from  which  cold  water  is  projected  into  the  sur- 
rounding steam,  so  as  to  effect  the  condensation  as  completely  as  may  be. 
Tiie  heated  water  falls  on  an  inclined  plane,  and  flows  off  without  mixing 
with  the  cold  water.  The  condensing  water  is  circulated  by  means  of  a 
centrifugal  pump  driven  by  a  small  three -cylinder  engine. 

In  working  off  the  steam  from  a  pressure  of  8S5  lbs.  to  67  Iba,  530  cubic 
feet  of  water  at  9IXy*  F.lis  sufficient  for  the  traction  of  the  trains,  for  working 
the  circulating-pump  for  the  condensers,  for  the  brakes,  and  for  electric- 
lighting  of  the  train.  At  the  stations  the  locomotive  takes  from  8900  to  9300 
lbs.  of  steam — nearly  the  same  as  the  weight  of  steam  consumed  during  the 
run  between  two  consecutive  charging  Ktationa  There  is  210  cubic  feet  of 
condensing  water.  Taking  the  initial  temperature  at  60°  F.,  the  tempera- 
ture rises  to  about  ISO^F.  after  the  longest  runs  underground. 

The  locomotive  has  ten  wheels,  on  a  base  24  ft.  long,  of  which  six  are 
coupled,  4^  ft.  in  diameter.  The  extreme  wheels  are  on  radial  axles.  The 
cylinders  are  28^  in.  in  diameter,  with  a  stroke  of  2n^  in. 

The  engine  wets^,  in  working  order,  68  tons,  of  wnich  86  tons  are  on  the 
coupled  wheels.  The  speed  varies  from  15  miles  to  26  miles  per  hour.  The 
trains  weigh  about  140  tons. 

€oiiipress«d«atr  I<ocoiiiotlwes«— For  an  aeooont  of  the  Mekarski 
system  of  compressed-air  locomotiTos  see  psge  510  ante. 


BHAFnKG.  867 

SHAFTTNG. 

(Bee  also  Tobsiomal  Stbkngtb;  also  Shafts  op  Stbam-bnoikis.) 
For  diameters  of  shafts  to  resist  torsional  strains  only,  Molesworih  gives 


-/p- 


d  =  i/  ~»  in  which  d  =  diameter  in  inches,  P=  twisting  force  in  pounds 

applied  at  the  end  of  a  lever-arm  whose  length  is  {  in  inches,  IT  =  a  coeffi- 
cient whose  values  are,  for  cast  iron  1500,  wrought  iron  1700,  cast  steel  3S00, 
gun-bronze  460,  brass  425,  copper  380,  tin  220,  lead  170.    The  value  given  for 
cast  steel  probably  applies  only  to  bigh-carbon  steel. 
Thurston  gives: 


For  head   shafts  well 
supported         against  • 
springing  (bearings  close 
to  puUeys  or  gears): 


H.P.  =  _;d:.|;^_^-,  for  iron; 

d^R,   .  _   yi00H.P..  for  cold-rolled 
^•^•-■to"'  V         A'  iron. 


For      line     shafting, , 
hangers  8  ft.  apart: 


For  transmission  sim- 
ply, no  pulleys: 


H.P.  =  ^;d  =  ^?«f£-.forl««, 

H.P.  =  ^;  d  =4y?5-5^»  for  cold-rolled  iron. 

H.P.  =  ^;.  =  |/™.  ,„,.„,„, 

H.P.  =  ^;  d  =:  //?5^,  for  cold-rolled  iron. 

H.P.  =  horse-power  transmitted,  d  s  diameter  of  shaft  in  inches,  R  =  rev. 
olutions  per  minute. 

J.  B.  Francis  gives  for  turned-iron  shafting  d  =  a/ 

Jones  and  LaughUna  give  the  same  formulae  as  Prof.  Thurston,  with  the 
following  exceptions:  For  line  shafting,  hangers  8  ft.  apart: 

cold-rolled  Iron.  H.P.  =  ^.  <*  =  ^  - -f^- 

For  simply  transmitting  power  and  short  counters: 

turned  iron,  H.P.  =  —,  d  =:  a/      ^     ; 


?/100H.P. 


cold-rolled  Iron,  H.P.  =  -^ ,  d  =  A/  -^ — . 

They  also  give  the  following  notes:  Receiving  and  transmitting  pulleys 
should  always  be  placed  as  close  to  lieariiigs  as  possible;  and  it  is  good  prac- 
tice to  frame  short  **  headers  "  between  the  main  tie-beams  of  a  mill  so  as 
to  support  the  main  receivers,  carried  by  the  head  shafts,  with  a  bearing 
close  to  each  side  as  is  contemplated  in  the  formuloB.  But  If  it  Is  preferred, 
or  necessary,  for  the  shaft  to  span  the  full  width  of  the  **  bay  "  without  in- 


868 


8HAFTIVQ. 


termedfate  bearings,  or  for  the  pulley  to  be  placed  away  from  the  bearinira 
towards  or  at  the  middle  of  the  bay,  the  siaee  of  the  Rhaft  must  be  larirely 
increased  to  secure  tlie  stiffnenB  n^cfsaary  to  support  the  load  without  un. 
due  deflection.  Shafts  may  not  deflect  more  than  1/80  of  an  inch  to  each 
foot  of  clear  length  with  safety. 

To  find  the  diameter  of  shaft  neceflsary  to  carry  safely  the  main  pulley  at 
the  centre  of  a  bay:  Multiply  the  fourth  power  of  the  diameter  obiained  by 
above  formulae  by  the  laoirth  of  the  ''  bay,"  and  divide  this  product  by  the 
distance  from  centre  to  centre  of  the  bearhifcs  when  the  shaft  Is  aupported 
as  required  by  the  formula.  The  fourth  root  of  this  quDiieat  will  be  the 
diameter  required. 

The  foilowiog  cable,  computed  by  this  rule,  ia  prsetlcally  correct  and  safe. 


iu. 
2 

m 

4 


Diameter  of  Shaft  necessary  to  carry  the  Load  at  the  Centre  of 
a  Bay,  which  is  from  Centre  to  Centre  of  Betrings 


eififu 


In. 


aft. 


!« 


3J*ft, 


in. 


4  ft. 


aft. 


6  ft. 


aft. 


in. 
4 


10  ft 


As  the  strain  upon  a  shaft  from  a  load  upon  it  is  proportional  to  the 
product  of  the  paru  of  the  shaft  multiplied  into  eacn  other,  therefore, 
should  the  load  oe  applied  near  one  end  of  the  span  or  bay  instead  of  at  the 
centre,  multiply  the  fourth  power  of  the  diameter  of  the  shaft  required  to 
carry  the  load  at  the  centre  of  the  span  or  bay  by  the  product  or  the  two 
parts  of  the  shaft  when  the  load  is  near  one  end.  and  divide  this  product  by 
the  product  of  the  two  parts  of  the  shaft  when  the  load  is  carried  at  the 
centre.    The  fourth  root  of  this  quotient  wili  be  the  diameter  required. 

The  shaft  in  a  line  which  carries  a  receiving-pulley,  or  whi<^  carries  a 
transmitting -pulley  to  drive  another  line,  shouia  always  be  oonsidered  a 
head  shaft,  and  should  be  of  the  size  given  by  the  rules  for  shafts  carrying 
main  puUeva  or  gears. 

Deflection  of  SltaltlnfC*  (Pencoyd  Iron  Works.)— As  the  d«^flectlon 
of  steel  and  iron  is  practically  alike  under  similar  conditions  of  dimensionK 
and  loads,  and  as  shafting  is  usual^  determined  by  its  transverse  stiff  orss 
rather  than  its  ultimate  strength,  nearly  the  same  dimensions  should  be 
used  for  steel  as  for  iron. 

For  continuous  line-shafting  it  is  considered  good  practice  to  limit  the 
deflection  to  a  maximum  of  l/lOO  of  an  inch  per  foot  of  length.  The  weitrhc 
of  bare  shafting  in  pounds  =  2.M^L  =  W,  or  when  as  fully  loaded  with 
pulleys  as  is  customary  in  practice,  and  allowing  40  lbs.  per  Inch  of  width 
for  the  vertical  pull  of  the  belts,  experience  shows  the  load  in  pounds  to  be 
about  ISd'L  =  IV.  Taking  the  modulus  of  transverse  elasticity  at  86,000,000 
lbs.,  we  derive  from  authoritative  formulas  the  following: 

L  m   ^873d«,  d  s  i /^,  for  bare  shafting; 

L  m   r  176d»,  d  =  JU  y:z^  for  shafting  canylng  pul]eys,^tc. ; 

h  being  the  maztmum  distance  in  feet  between  bearings  for  contlnuons 
sharHng  subjected  to  bending  stress  alone,  d  =  diam.  in  mches. 

The  torsional  stress  is  Inverselv  proportional  to  the  velocity  of  rotation, 
while  the  bending  stress  will  not  be  reduced  b)  the  same  ratio.  It  is  there* 
fore  impossible  to  write  a  formula  covering  the  whole  problein  and  sofll- 


HORSB-POWER  AT  DIVVSREKT  SPEEDS. 


86a 


dently  tlmple  for  pnustiCAl  appllcatloD.  but  the  foIlowiBf  ivIm  are  eorrect 
within  the  range  of  velooUfes  usual  in  practice. 

For  coDtinuons  shaftine  so  proportioned  as  to  deflect  not  more  than  l/KW 
of  an  inch  per  foot  of  Mngth,  aUowaace  being  made  for  the  weakening 
effect  of  key-seats. 


(  ^TSOd*.  for  bare  dUAss 
X«  (^  14(kP,  for  Bhaftt  carrybiff  pallef^  •!& 


d  B  dtam.  In  inches,  L  =  length  in  feet,  R  as  rrrs.  per  mfai. 

The  following  tableCby  J.  B.  Fraocts)  gives  the  greatest  admissible  dia- 
taaoea  between  the  bearings  of  continuous  shafts  subject  to  no  transveme 
strain  except  from  their  own  weight,  as  would  be  the  case  were  the  power 
giyen  off  from  the  shaft  equal  on  all  sides,  and  at  an  equal  distance  from 
the  hanger-bearings. 


Dtstance  between 
Bearings,  in  ft. 


Diam.  of  Shaft,  Wroup^t-tron   Steel 
in  Inches.  Shafts.      Shafts, 

t  15.49  16.89 

I  1T.70  18.19 

4  19.48  fiO.02 

6  9C.99  21.57 


Distance  between 
Bearings,  In  ft. 

Diam.of Shaft,  Wrought-lron  Steel 

in  inches.  Shafts.      Shafts. 

6  tS.80          88.9B 

r  ».48          M.1S 

8  M.65  85.S8 

9  t5.6S  96.94 

These  conditions,  however,  do  not  usually  obtain  In  the  transmission  of 
power  by  belts  and  pulleys,  and  tbe  varying  circumstanoes  of  each  case 
render  It  Impracticable  to  give  any  rule  which  would  be  of  value  for  univer- 
sal application. 

For  example,  the  theoretical  requirements  would  demand  tbat  tbe  bear- 
ings be  nearer  together  on  those  sections  of  shafting  where  most  power 
is  delivered  from  the  shaft,  while  oonsiderations  as  to  the  location  and 
desired  contlgultv  of  the  driven  machines  may  render  it  impracticable  to 
separate  the  driving-pulleys  by  the  intervention  of  a  hanger  at  tbe  theo- 
retically required  location.   (Joshua  Rose.) 


H«rae*poiiw«r  Tmnanained  by  Turned  Iron  tnukMng  at 
DUTerent  Speeds. 

As  PniKB  MoYER  OR  Hkad  Shir  CAUmno  Mair  Drivimo-puzxkt  or  Gear, 
WKLL  BITPFORTBP  BY  BKARiHoa.    Formula :  H.P.  s=  d^B  •••  196b 


g^*f 

Number  of  Revohxtions  per  Minute. 

s"! 

eo 

80 

100 

195 

150 

175 

200 

286 

260 

976 

800 

Ins. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H,P, 

H.P. 

H.P. 

^H 

9.8 

8.4 

4.8 

5.4 

6.4 

7.5 

8.6 

O.T 

10.7 

11.8 

12.0 

3 

8.8 

6.1 

6.4 

6 

0.6 

11.9 

12.8 

14-.4 

16 

17.6 

19.2 

fl^ 

5.4 

7.8 

8.1 

10 

19 

14 

16 

18 

90 

29 

94 

9Vb 

7.5 

10 

19.5 

16 

18 

98 

25 

28 

81 

84 

87 

9B2 

10 

18 

16 

90 

94 

96 

89 

86 

40 

44 

48 

a' 

18 

17 

90 

96 

80 

86 

40 

45 

50 

55 

60 

18 

99 

97 

84 

40 

47 

64 

61 

67 

74 

81 

3L^ 

SO 

97 

84 

49 

61 

59 

68 

78 

85 

08 

109 

^» 

98 

88 

49 

69 

68 

78 

84 

94 

106 

115 

196 

4 

80 

41 

61 

64 

76 

89 

109 

119 

127 

140 

158 

4H 

48 

68 

79 

90 

106 

196 

144 

109 

180 

196 

216 

r^ 

80 

80 

100 

196 

150 

176 

200 

296 

250 

275 

800 

«H 

80 

108 

183 

166 

190 

988 

266 

299 

838 

866 

400 

870 


BHAFTIVQ. 


As  SBCXIKD  MoTBRS  or  LlNB-BHArTIK< 

».  BSARIHM  8  VT.  IPABT. 

Formula :  H.P.  =  dflR  -t-  90. 

in  4 

Number  of  Revolutions  per  Minute. 

5^1 

100 

1S5 

150 

175 

200 

225 

250 

876 

800 

825 

850 

InR. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

n 

6 

7.4 

8.9 

10.4 

11.0 

18.4 

14.9 

16.4 

17.9 

19.4 

90.9 

7.8 

9.1 

10.9 

12.7 

14.6 

16.8 

18.2 

80 

81.8 

88.6 

85.4 

^r 

8.9 

11.1 

18.8 

15.6 

17.7 

20 

22.2 

24.4 

26.6 

88.8 

81 

^^ 

10.6 

18.9 

15.9 

18.ft 

81.8 

28.8 

86.5 

89.1 

81.8 

84.4 

87 

s| 

12.0 

16.8 

19 

88 

85 

28 

81 

85 

88 

41 

44 

^i 

15 

18 

28 

80 

89 

88 

87 

41 

44 

48 

62 

A 

17 

SI 

88 

80 

84 

80 

48 

47 

as 

66 

60 

s? 

98 

80 

84 

40 

46 

68 

68 

64 

69 

75 

81 

r 

80 

87 

45 

68 

60 

67 

76 

88 

90 

97 

106 

88 

47 

67 

66 

76 

85 

96 

104 

114 

188 

18S 

SVft 

47 

69 

71 

88 

96 

107 

119 

181 

148 

165 

167 

89a 

68 

78 

88 

102 

117 

182 

146 

162 

176 

190 

806 

4 

71 

80 

lor 

125 

142 

160 

178 

106 

818 

881 

MO 

Fob  Simply  Trahsmittino  Power. 
Formula :  H.P.  ac  d*R  •«-  60. 


fi,.«^ 

Number  of  Revolutions  per  Minute. 

ri 

100 

185 

150 

176 

800 

888 

867 

800 

SS8 

867 

400 

Ins. 

H.P. 

HP. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

1^ 

6.7 

8.4 

10.1 

11.8 

18.5 

15.7 

17.8 

20.8 

22.5 

84.8 

87.6 

H 

8.6 

10.7 

12.8 

15 

17.1 

20 

82.8 

25.8 

28.6 

81.5 

84.9 

H 

10.7 

18.4 

10 

18.7 

81.6 

25 

28 

82 

86 

89 

43 

1^/2 

18.8 

16.5 

19.7 

23 

26.4 

81 

35 

89 

44 

48 

58 

8 

16 

80 

24 

28 

32 

87 

42 

48 

68 

68 

64 

8^ 

19 

24 

29 

88 

88 

44 

61 

57 

68 

TO 

76 

m 

29 

28 

84 

80 

45 

52 

60 

68 

75 

88 

90 

A 

27 

83 

40 

47 

58 

62 

70 

79 

88 

96 

105 

H 

81 

89 

47 

54 

62 

78 

88 

93 

104 

114 

125 

2    ' 

41 

53 

62 

78 

88 

97 

111 

125 

189 

158 

167 

8^ 

54 

67 

81 

94 

108 

126 

144 

169 

180 

196 

816 

^ 

68 

86 

103 

120 

137 

160 

182 

205 

228 

250 

273 

ft5 

107 

128 

160 

171 

IHX) 

228 

257 

885 

818 

848 

Horse-poorer  TransmlUed  by  €oId-roIled  Iron  Shaftlnc 
at  IMITerent  Speeds* 

Ab  Prdib  Movbr  or  Head  Shaft  carrtimo  Main  Driyiko-pullkt  or 
Grab,  well  bdpfobtkd  bt  Bbarimos.    Formula :  H.P.  s  d^B  -*•  75. 


6^^ 

Number  of  Revolutions  per 

Minute. 

r^ 

60 

80 

100 

125 

150 

176 

200 

225 

260 

876 

800 

Ins. 

H.P. 

H.P. 

H.P. 

HP. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

i^ 

8.7 

8.6 

4.5 

5.6 

6.7 

7.9 

0.0 

10 

11 

18 

IS 

4.8 

6.6 

7.1 

8.9 

10.6 

12.4 

14.2 

16 

18 

19 

81 

8 

6.4 

8.6 

10.7 

18 

16 

19 

81 

84 

86 

89 

88 

^4 

9 

12 

15 

19 

28 

26 

80 

84 

88 

48 

46 

$£t 

18 

17 

81 

26 

31 

86 

41 

47 

62 

07 

08 

2m 

16 

88 

87 

86 

41 

48 

66 

es 

70 

76 

82 

8^ 

81 

89 

86 

45 

64 

68 

78 

81 

90 

96 

108 

8^ 

27 

86 

45 

57 

68 

80 

91 

106 

114 

186 

186 

8i 

84 

45 

67 

71 

86 

100 

114 

129 

148 

157 

178 

t\ 

48 

56 

70 

87 

105 

123 

140 

166 

174 

196 

810 

4 

51 

69 

85 

106 

128 

149 

170 

192 

812 

814 

8S6 

4« 

78 

97 

121 

151 

182 

212 

248 

878 

808 

8» 

864 

H0B8E-F0WEB  AT  DIFFERENT  SPEEDS. 


871 


As  SBCOKD  MoTKRS  OB  LlNS-SRAFTINa,  BkARIKOB  8  FT.  APART. 

Formula :  H.P.  =  €PR  ■*•  tO. 


a^i 

Number  of  Revolutions  per  Minute. 

ri 

100 

185 

150 

175 

800 

825 

250 

875 

300 

825 

8S0 

Ids. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

]^ 

6.7 

8.4 

10.1 

11,8 

18.5 

16.2 

16.8 

18.5 

20.2 

81.9 

88.6 

]^ 

8.6 

10.7 

12.8 

15 

17.1 

19.8 

21.5 

83.6 

26.7 

28.0 

81 

]l^ 

10.7 

18.4 

16 

18.7 

81.5 

84.2 

26.8 

29.5 

32.1 

84.8 

89 

iQ 

18.8 

16.5 

19.7 

88 

26.4 

29.6 

82.9 

86.9 

80.6 

48.8 

46 

8 

16 

20 

84 

28 

82 

86 

40 

44 

48 

58 

56 

2W 

10 

24 

29 

88 

88 

48 

48 

68 

57 

62 

67 

^M 

28 

28 

84 

89 

45 

50 

56 

61 

68 

74 

80 

2^2 

27 

88 

40 

47 

58 

60 

67 

ra 

60 

86 

01 

2|^ 

81 

89 

47 

54 

62 

69 

78 

86 

08 

101 

109 

2^ 

41 

52 

62 

78 

88 

93 

104 

114 

125 

185 

145 

3 

54 

67 

81 

94 

106 

121 

184 

148 

162 

175 

ISO 

^ 

68 

86 

108 

120 

187 

154 

172 

188 

806 

288 

840 

85 

107 

128 

150 

171 

1P2 

814 

286 

857 

878 

300 

Fob  Simply  Transmitting  Powbb  and  Shobt  CkXTKnaa. 
Formula :  H.P.  =  d*R  ■«•  80. 


s  - 

Number  of  Revolutions  per  Minute. 

i''l 

100 

185 

160 

175 

800 

238 

267 

800 

888 

807 

400 

IML 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

HP. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

t< 

6.5 

8.1 

0.7 

11.3 

18 

15.2 

17.4 

19.5 

81.7 

88fl 

86 

t'H 

8.5 

.  10.7 

12.8 

15 

17 

19.8 

22.7 

86.6 

88.4 

81 

34 

M 

11.2 

14 

16.8 

19.6 

82.5 

86 

30 

88 

87 

41 

45 

ti 

14.8 

17.7 

81.2 

84.8 

28.4 

88 

38 

48 

47 

52 

57 

r^ 

18 

28 

27 

81 

35 

41 

47 

58 

59 

05 

71 

ii 

82 

27 

83 

88 

44 

51 

58 

65 

78 

TO 

87 

2^ 

26 

88 

40 

46 

53 

62 

71 

80 

88 

97 

106 

^^4 

82 

40 

47 

56 

63 

78 

84 

96 

105 

116 

127 

^ 

88 

47 

57 

66 

76 

89 

101 

114 

187 

189 

158 

a'^ 

44 

65 

66 

77 

88 

103 

118 

133 

148 

163 

178 

iA 

68 

65 

78 

91 

104 

121 

138 

155 

172 

100 

807 

m 

60 

84 

00 

118 

138 

161 

184 

207 

281 

254 

8T7 

8 

00 

112 

185 

157 

180 

210 

240 

870 

300 

830 

860 

Spebd  of  SBAFnNO.~Machine  shops 120  to  180 

Wood-worklnjr 860tod00 

Cotton  and  woollen  mills 800  to  400 

There  are  in  some  factories  lines  1000  ft  long,  the  power  beiDg  applied  at 
the  middle. 

HoUo^r  Sbafts*— Let  d  be  the  diameter  of  a  solid  shaft,  and  did^  the 
external  and  internal  diameters  of  a  hollow  shaft  of  the  same  material. 

Then  the  shafts  will  be  of  equal  torsional  strength  when  d>  =    '   ""    *  , 

A  10-inch  hollow  stiaft  with  internal  diameter  of  4  inches  will  weigh  loj  less 
than  a  solid  10-inch  shaft,  b  ut  its  strength  will  be  onlv  2.569(  less.  If  the  hole 
were  increased  to  5  inches  diameter  the  weight  would  be  2!^  less  tlian  that 
of  the  solid  shaft,  and  the  strenfrth  6J2S)f  less. 

Table  for  I«ayliijg  Out  Sbaflln^:.— The  table  on  the  opposite  page 
rfrom  the  Steven$  Indicator,  April,  1802)  is  used  by  Wm.  Sellers  &  Co.  to 
facilitate  the  laying  out  of  shaf  ilng. 

The  wood-cuts  at  the  head  of  this  table  show  the  position  of  the  hangers 
and  position  of  couplings,  either  for  the  case  of  extension  in  both  directions 
from  a  central  head-shaft  or  extension  in  one  direction  from  that  head-shaft. 


872 


CABLE  FOE  LATINS  OUT  SHAFTIKO. 


^^f^'.^;=»:s?^: 


n^^Ss?£S5^*;f  ? 


c  L^  OD  a  o  ^  w  w^  B  2g  UlJg^SI  ^' 


%1        ^d 


:5^ 


affs^s^S 


I 


.f.a^gi 


:?'  :^ 


23?  2P  3f:ri! 

OJ  M  «  -^  ^  «  O 


w^Ol^??^*- 


iilli!! 


^  ^  ?i  »  «  M  « CO  **  *  c  3" IP  » i«  ^a 


-T  rfl  a  t&  O  ^^CC  O  -*  9*  »  ^*fe^| 
^  ^  ^  n  p«  r«  V4  vv  f 


PROPORTIONS  OF  PULLEYS.  873 


FXJIiIiEYS. 

Proportions  of  Pulleys.  (See  also  Fly-wheels,  pasres  820  to  8S3.)— 
Let  n  =  number  of  arms,  D  =  diameter  of  pulley,  S  =  thickness  of  belt.  /= 
thickness  of  rim  at  edge.  r=  ihicknetis  in  middle,  B  =  width  of  rlm,/S  = 
width  of  belt,  h  -  breadth  of  arm  at  hub,  A,  =  breadth  of  arm  at  rim,  e  = 
UilcknesB  of  arm  at  hub  e^  =  thickness  of  arm  at  rim,  c  =  amount  of  crown- 
ing; dimensions  in  indies. 

Unwin.  Reuleauz. 

B  =  widthof  rim O/BO+0.4)  9/8^  to  5/4^ 

i  =t  thickness  at  edge  of  rim 0.7fi+  .006D      \  ^'i!lsAto^iil'"*^ 

r=       "  "  middle  of  rim 2<  +  c  jfT.!?.,... 

(  For  single     ^/^^ 

belts  =  .smy  IT  w//     ft      „ 

&=  breadth  of  arm  at  hub J  \, 4- j.£  +  ^ 

1  For  double  ]  fSD     4   ^  4  ^  aOn 
\      belts  =  .798y   "^ 

fc,=         ••       ••    "     •*  rim %fc  0.8A 

e  =  thickness  of  arm  at  hub 0.4A  0  SA 

'i=  "        ; rim..      ..  0.4J,  oijWi, 

n=  number  of  arms,   for  a»  ajl°9  \A        ^^ 

single  set,  >'•'  "*"  IBO  *^\*^2^/ 

Z,  =  length  of  hub -I  ?o*2f  ss  than  8.55, )  B  for  sin.-arm  pulleys. 

\,     *:°^  ,         ■  7  :    :       nsoftenJ^A  fa^^double^rm  " 

Jf=  thickness  of  metal  in  hub Ato9^i 

c  =  crowning  of  pulley 1/84B  :;.... 

The  number  of  arms  is  really  arbitrary,  and  may  be  altered  if  necessarv. 
(UnwIn.)  ' 

Pulleys  with  two  or  three  sets  of  arms  may  be  considered  as  two  or  three 
separate  pulleys  combined  in  one,  except  that  the  proportions  of  the  anus 
should  be  0.8  or  0.7  time  that  of  single-arm  pulleys.    (Reuleaux.) 

EXAMPLC— Dimensions  of  a  pulley  00"  diam.,  10"  face,  for  double  belt  XL" 
thick.  ^ 

Solution  by..,.     nAAiee.       fTXlfe 
Unwin 9     8.79  3.58   1.6S   1.01   .65    1.97   10.7   8.8    .07 

Reuleauz 4     5.0    4.0     3.5     3.0         1.85       16       6 

The  following  proportions  are  given  in  an  article  In  the  Amer,  MaehinisL 
authority  not  stated:  ' 

h  =s  .06a5i>+  .6  In.,  h^  a  .042)  +  8185  in.,  e  =  .085D  -J-  .8  In., «,  s  .OlOD  + 
.185  In. 

Thesegive  for  the  above  example:  h  =  4.36  In.,  fc,  =  3.71  In.,  e  =  1  7  in. 
e,  =  1 .09  In.    The  section  of  the  arms  in  all  cases  is  taken  as  elliptical. 

The  following  solution  for  breadth  of  arm  is  proposed  by  the  author* 
As'^ume  a  belt  pull  of  45  lbs.  per  inch  of  width  of  a  single  belt,  that  the 
whole  strain  Is  taken  in  equal  proportions  on  one  half  of  the  arms,  and  that 
the  arm  Is  a  beam  loaded  at  one  end  and  fixed  at  the  other.    We  have  the 

formula  for  a  beam  of  elliptical  section  fP  =  .0988  ^^,  in  whteh  P  =  the 

load,  A  =r  the  modulus  of  rupture  of  the  cast  Iron,  b  =  breadth,  d  =  depth 
and  I  =s  length  of  the  beam,  and/  =  factor  of  safety.  Assume  a  modulus 
of  rupture  of  86.000  lbs.,  a  factor  of  safety  of  10,  and  an  additional  allow- 
ance for  safety  in  taking  2  =  ^  the  diameter  of  the  pulley  Instead  of  ViD 
less  the  radius  of  the  hub.  ^ 

Take  d  =  A,  the  breadth  of  the  arm  at  the  hub,  and  6  s  e  =  0.4A,  the 
thickness.    We  then  have  /P  =  10  x  ^  =  90o|  =  ^^^,  whence 

*  '^  V  ^5»  "=  -^^y  ^'  ^^^^^  *■  practteally  the  same  as  (he  value 
reached  by  Unwin  from  a  different  set  of  assumptions. 


874 


PULLEYS. 


ConTexlty  of  Pulleys.— Authorities  differ.  Morin  giTM  a  rise  equal 
to  1/10  of  the  face ;  Molesworth,  1/24  ;  others  from  %  to  1/B6.  Soott  A. 
Smith  says  the  crown  should  not  be  over  %  inch  for  a  24-inch  face.  Pulleys 
for  shifting  belts  should  be  **  straight/'  that  is,  without  crowning. 

CONE  OR  STEP  PUIil^ETS. 

To  And  the  diameters  for  the  several  steps  of  a  pair  of  cone-pulleys: 
1.  Crossed  Belts.— Let  D  and  d  be  the  diameters  of  two  pulleys  ood 
nected  by  a  crossed  belt,  L  =  the  distance  between  their  oentrea,  and  fi  = 
the  angle  either  half  of  the  belt  makes  with  a  line  Joining  the  centres  of  the 

pulleys  :  then  total  length  of  belt  »  (D  +  d)^  +  (Z>  +  d)^  +  21^  cos  fi. 
p  =  angle  whose  sine  is  ^^.     Cos  /i  =  i/i«  -  (^-y^)  •    The  length  of 

the  belt  Is  constant  when  D  +  ^2  is  constant;  that  is,  in  a  rair  of  step- 
pulleys  the  belt  tension  will  be  uniform  when  the  sum  of  the  alameters  of 
each  opposite  pair  of  steps  is  constant.  Crossed  belts  are  seldom  used  for 
cone-pulleys,  on  account  of  the  friction  ))etween  the  rubbing  parts  of  the 
belt. 

To  design  a  pair  of  tapering  speed-cones,  so  that  the  belt  may  fit 
equally  tight  in  all  positions  :  When  the  belt  is  crossed,  use  a  pair  of  equal 
and  siniilnr  coneK  tapeiing  opposite  ways. 

3.  Open  Belts.— When  the  belt  is  uncrossed,  use  a  pair  of  equal  and 
sliiiiku*  conoids  tapering  opposite  ways,  and  bulging  in  the  middle,  socord- 
ing  to  the  following  formula:  Let  L  denote  the  distance  between  the  axes 
of  the  conoids;  R  the  radius  of  the  larger  end  of  each;  r  the  radius  of  the 
smaller  end;  then  the  radius  in  the  middle,  r^  is  found  as  follows: 


»"•  = 


jg-fr   .  (g-r)» 


6.S!8L 


-.    (Bankine.) 


If  D»  =  the  diameter  of  equal  steps  of  a  pair  of  cone-pulleys,  D  and  d  a 
the  diamdters  of  unequal  opposite  steps,  and  L  m  distance  between  the 
^       DH-d  .  (D-d)* 

If  a  series  of  differences  of  radii  of  the  steps,  i?  ^  r,  be  assumed,  then 
R  -i-T  (R  —  r\^ 

for  each  pair  of  steps  — g—  =  r^  -  -g-jSr"«  •"**  '**®  ""*'*  °'  ••^  ™*y  ^ 
computed  from  their  half  sum  and  half  difference,  as  follows : 

» - ^  +  ^ a.  SjiZ.      •■ «  ^  +  *'      g-** 

*•  —        A        T  a •  •   ™         •>  '      a      • 


A.  J.  Frith  (Trans.  A.  S.  M.  E.,  x.  298)  shows  the  following  appUeatton  of 
Rankine*H  method:  If  we  had  a  set  of  cones  to  design,  the  extreme  diame- 
ters of  which,  including  thickness  of  belt,  were  40^'  and  10^',  and  tlie  ratio 
desired  4,  8,  2,  and  1,  we  would  make  a  table  as  follows,  L  being  100": 


Trial 
Sum  of 
Z)-hd. 

Ratio. 

Trial  Diameters. 

Values  of 

(D.-d)« 

12.66L 

Amount 

to  be 
Added. 

Corrected  Values. 

D 

d 

D 

d 

50 
60 
50 
50 

4 
8 
2 
1 

40 
87.5 
88.338 
25 

10 
12.5 
16.666 
26 

.7165 
.4975 
.ft212 
.0006 

.0000 

.2190 
.4958 
.7165 

40 

87.7190 
88.8886 
8S.716S 

10 

12.7190 
17.1619 
25.7165 

The  above  formulsB  are  approximate,  and  the^  do  not  give  satisfactory 
results  when  the  difference  of  diameters  of  opposite  steps  u  large  and  when 
the  axes  of  the  pulleys  are  near  together,  giving  a  large  belt-angle.  The 
following  more  accurate  solution  of  the  problem  is  given  by  C  A.  Smith 
(Trans.  A.  S.  M.  R.,  x.  S69)  (Fig  152): 

I^y  off  the  centre  distance  C  or  EF,  and  draw  the  circles  D*  and  d,  equal 
to  the  first  pair  of  pulleys,  which  are  always  previously  determined  by 
known  conditions.  Draw  ///  tangent  to  the  circles  i>,  and  dj.  From  B, 
midway  between  E  and  F,  erect  the  perpendicular  BO^  making  the  lengtSi 


CONE  OR  STEP   PULLETS. 


875 


SO  =  .S14C.  With  Q  as  a,  centre,  draw  a  circle  tangent  to  HI.  Generally 
this  circle  will  be  outside  of  the  belt-line,  as  iu  the  cut,  but  when  C  is  short 
and  the  first  pulleys  Di  and  d,  are  large,  it  will  fall  on  the  inside  of  the  belt- 
line.  The  belt-line  of  any  other  pair  of  pulleys  mu^t  be  tangent  to  the  cir- 
cle Q ;  hence  any  Une,  as  JK  or  LM,  drawn  tangent  to  the  cii^cle  O,  will  give 


1 

G                I 

/V 

1         L-""^ 

Mi 

?" 

H 

:Z. 

-c — 

V 

Jd^  j  j 

Fio.  152. 

the  diameters  D,.  d,  or  Z),,  d%  of  the  pulleys  drawn  tangent  to  these  lines 
from  the  centres  E  and  F. 

The  above  method  is  to  be  used  when  the  belt-angle  A  does  not  exc<NKl 
18".  When  it  is  between  IS**  and  SO^  a  slight  modification  is  made.  In  that 
case,  in  addition  to  the  point  Q,  locate  another  point  m  on  the  line  BG  .208  C 
al>ove  B.  Draw  a  tangent  line  to  the  circle  O^  mailing  an  angle  of  IH^  to  the 
line  of  centres  EF,  and  from  the  point  m  draw  an  arc  tangent  to  this  tan- 
gent line.  All  belt-lines  with  angles  greater  than  I  j*  are  tangent  to  this  arc. 
The  following  is  the  summary  of  Mr.  Smith's  mathematical  method: 

A  =  angle  in  degrees  between  the  centre  line  and  the  belt  of  any  pair  of 


a  s  .814  for  belt-angles  less  than  IS"*,  and  .298  for  angles  between  18* 
andSQo; 
B*  =  an  angle  depending  on  the  velocity  ratio; 
C  =  the  centre  distance  of  the  two  pulleys; 
D.  d  =  diameters  of  the  larger  and  smaller  of  the  pair  of  pulleys; 
^  —  an  angle  depending  on  B** ; 

L  =s  the  length  of  the  belt  when  draw^n  tight  around  the  pulleys; 
r  s  D  +  d,  or  the  velocity  ratio  (larger  divided  by  smaller). 


(1)  Sin  il  = 


D  -  d  , 


(2)  tan  B«  = 


aa(r-l). 


(8)  Sin  £o  a  sin  ^^(oos  A  - 


r+1    ' 

4aC    /' 
fi*  -f  £*  when  sin  J^  Is  negative; 


i4)A9B^^E*  when  sin  E^  is  positive 

(6)  d  =  ^^^~\  m  .8188(L  -  20  when  ^  =  0  and  r  »  I; 

(0)  D  =  rd; 

(7)  Z^  =  2Cooa  il  -f  .(M74fid[180  +  (r  -  1)(90  +  A)]. 

Equation  (1)  is  used  only  once  for  any  pair  of  cones  to  obtain  the  constant 
€os  At  by  the  aid  of  tables  of  sines  and  cosines,  for  use  In  equation  Qi), 


876  BELTIHO. 


BELTING-. 

Tlieory  of  Belts  and  Bands.— A  pulley  Is  driven  bj  a  belt  1^ 
means  of  tne  friction  between  tbe  surfaces  in  contact.  Let  7\  be  the  tension 
on  the  drivlnK  side  of  the  belt,  7s  the  tension  on  the  loose  side;  then  S.  =  T^ 
—  3, ,  is  the  total  friction  between  tbe  band  and  the  puU^,  which  is  equal  to 
the  tractive  or  drivlnfc  force.  Let  /  =a  the  coefflcient  of  mctiao«  B  the  ratio 
of  tbe  lenj^h  of  tbe  arc  of  contact  to  the  toogtb  of  the  radius,  a  =  the  anirle 
of  tba  arc  of  contact  in  degrees,  e  s  the  base  of  tbe  Kaperiaa  lofcarithms 
=  3.71IQ8,  m  =s  tbe  modulus  of  the  common  lof^aritbms  =  0.484ii86.  The 
followintr  formulsB  are  derived  by  calculus  (Rankine's  Mach*y  &  Millwork, 
p.  8St :  Carpenter's  Exper.  £og*K,  p.  178): 

If  the  arc  of  coataet  between  the  band  and  the  Q^ey  eKpresssd  In  turns 
and  fractions  of  a  turn  =  n,  ^  =  2jrn;  e^*  =  Ky*-'*^";  that  is,  e^  Js  the 
natural  number  correspondfaiff  to  tbe  common  loi^rithm  2.7:.'88/n. 

The  value  of  the  coelncient  of  friction  /  depends  on  the  state  and  material 
of  the  rubbing  surfaces.  For  leather  belts  on  iron  pulleys,  Morin  found 
/  =  .56  when  dry,  .86  when  wet.  .23  when  greasy,  and .  15  when  oily.  In  calcu^ 
lating  the  proper  mean  tension  for  a  bait,  tbe  amaUest  value,  /  s  .15.  Is 
to  be  taken  if  there  is  a  probability  of  the  belt  becoming  wet  with  oil.  The 
experiments  of  Henry  B.  Towns  and  Robert  Brigss,  however  (Jour.  Frank. 
Inst.,  1866),  show  that  such  a  state  of  lubrication  is  not  of  ordinarf  occur- 
rence; and  that  in  designing  maebinery  we  may  in  most  cases  safely  take 
/  n  0.49.  Reuleaux  takes/  »  0.25.  The  following  table  Rhows  tbe  rallies  of 
the  coefllcient  8.7888/,  by  whfasb  n  is  multiplied  in  the  last  eguatlon,  oori^e^ 
sponding  to  different  values  of  /;  also  the  corresponding  values  of  various 
ratios  among  tbe  loroest  when  the  arc  of  contact  is  half  a  circumference : 
/aO.16  0.85  0.4*  O.06 

2.728^  =  0.41  0.68  1.15  1.68 

Let  9  a  »  and  n  s  H,  then 
r,-*.r,  =  1608 

Ti  +  Ts  -•-  as  »  «.!• 

In  onllnary  practioe  it  is  usual  to  assume  Tg  x  s;  7i  »  28;  T.  +  TV  ••- 
85  s  1  5 .    Thfe  corresponds  to  /  =  0.  ys  nearly . 

For  a  wire  rope  on  cast  iron  /  maybe  taken  as  0.16  near^:  and  If  the 
groove  of  the  pulley  is  bottomed  with  gutta-percha,  0.85.    (Uanklnej 

Oentrlfliipal  Tension  of  Belts.— When  a  belt  or  band  runs  at  a 
high  velocity,  centrifugal  force  produces  a  tension  in  addition  to  tliat  exist- 
ing when  tbe  belt  is  at  rest  or  moving  at  a  low  velocity,  lliis  centrifugal 
tension  diminishes  the  effective  driving  force. 

JEtaukine  says  :  If  an  endless  band,  oit  any  figure  whatsoever,  runs  at  a 
given  speed,  the  centrifugal  force  produces  a  uniform  tension  at  each  cross- 
section  of  the  band,  equal  to  tbe  weigtat  of  a  piece  of  the  band  whose  length 
is  twice  the  height  from  which  a  heavy  body  must  fall,  in  order  to  acquire 
the  velocity  of  the  band.    (See  Cooper  on  Belting,  p.  101.) 

If  To  =s  centrifugal  tension ; 

V  =  velocity  in  feet  per  second; 
g  as  acceleration  due  to  gravity  s  82.8; 
W"  ss  weight  of  a  piece  or  the  belt  1  ft.  long  and  1  sq.  in.  sectional  ares,'- 

Leather  weighing  56  lbs.  per  cubic  foot  gives  IT  ==  56  -f  144  s  .888. 


8.188 

8.788 

8.881 

184 

1.86 

1.81 

1.84 

0.86 

0.71 

BELTIKQ  PBAGTIOB.  877 

BeltliM:  Fraetlee*  Han4y  PommUB  for  B«lUiic«  —  Since 
In  the  pracUoal  application  of  the  aboye  f  oraiulsB  th«  value  of  the  coefficient 
of  friction  must  he  aasumed,  its  aotual  value  varying  within  wide  limits  ilH 
to  IW),  and  since  the  vahies  of  r,  and  T^  also  are  fixed  arbitrarily,  it  Is  cus- 
tomary iu  practice  to  substitute  for  these  theoretical  formula)  more  sim^ 
empirical  lormulsB  and  rules,  some  of  which  are  given  helow. 

Let  d  s  diam.  of  pnUey  in  inches;  nd  s  circumferenoe; 

V  s  velocity  of  belt  in  ft.  per  second;  v  =  yeL  in  ft  per  minute; 
a  e  angle  of  the  arc  of  contact; 

L  s  length  of  arc  of  contact  in  feet  a  nda  h-  (12  x  800);  ^ 
F  B  traotive  force  per  square  inch  of  sectional  area  of  oeltt 
w  s  width  in  inches;  t  =  thickness; 
8  s  tractive  force  per  inch  of  width  m  F-*-  U 
rpBL  s  rers.  per  minute;  rpe.  =  revs,  per  seooua  a  rpm.  -«-  00. 

V  «  ^  X  ipoL ; «  .«0l8d  X  tpm. 

Hoi».power.  H.P.  »  ^  «  ^  -  SS^gP  -  X0O0anW5i«f  X  rpm. 

If  Fs  working  teoaloa  per  square  ioob  k  870 lbs.,  tad  t  a  7/88  inch,  8  = 
QOil».iisar]j,thea 

H.P.  »  ^  a  .lOOrw  =  .doomed  x  rpm.  s  IStOEL.  .       (I) 
If  F  •>  ^  As.  per  square  Inob,  and  f  ai  i/e  inch, «  »  80  Ihe.,  Umb 

H.P.»5^i..O»Fw*.000888«idxrpm.-2L|L^Sl.    .   (^ 

If  the  working  strain  Is  00  lbs.  per  inch  of  width,  a  belt  l  Inch  wide  travel- 
ling S60  ft.  per  minute  will  transmit  1  horse-power.  If  the  working  strain  is 
80  lbs.  per  inch  of  width,  a  belt  1  inch  wide,  travelling  1100  ft.  per  minute, 
will  transmit  1  horse-power.  Numerous  rules  are  given  by  difTerent  writers 
on  belting  which  vary  between  these  extremes.  A  rule  commonly  used  is : 
1  Inch  wide  travelling  1000  ft.  per  min.  »  I.H.P. 

H.P.«j^-.06nD».O00802i«fXrpm.al2i^^-.    .    .    {9> 

This  corresponds  to  a  working  strain  of  38  lbs.  per  Inch  of  width. 

Many  writers  give  as  safe  practice  for  slngTe  belts  in  good  condition  a 
working  tension  of  46  lbs.  per  inch  of  width.    This  gives 

H«P-  «  ^  «  .081«Ffe  s  .000807ifKf  X  tptn.  «  !^  L!f  ""^     .    (4) 

For  double  belts  of  average  thickness,  some  writers  say  that  the  trans- 
mitting effideney  is  to  that  of  single  belts  as  10  to  7,  which  would  give 

H.P.  of  doublebelU  =  ^=s  AmVw=  .00061  t«J X rpm.  ==  "'^  ^'"\  (6) 

Other  authorities,  howeyer,  make  the  transmittlne-power  of  double  belts 
twice  that  of  shigle  belts,  on  the  asvumption  that  the  tiiickness  of  a  double- 
belt  is  twice  that  of  a  single  belt. 

Rules  for  hoi-sc'power  of  belts  are  sometimes  based  on  the  number  of 
square  feet  of  surface  of  the  belt  which  pass  over  the  pulley  in  a  minute. 
8<].  f u  per  min.  a  irv  •♦- 13.  The  above  formulas  translated  into  this  form 
give: 

U)    For  S  a  00  lbs.  per  inch  wide  ;  H.P.  s  40  sq.  ft.  per  minute. 

W     **    Smm   "*  *  "       H.P.  =92      »    "^     " 

(a)**fl[»ia**  "  •*       H.P.  =  88      •*  '• 

<4)      ••    «s«46    ••  •  ••       H.P.  =  01      •*  * 

(i)     ^    amUA**        •*         **      E.P. -48     *«         **  jflouhto hrit»i 


878 


BELTIKQ. 


The  above  fonnuls  are  all  based  on  the  supposition  that  the  arc  of  con- 
tact is  IHQo  For  other  arcs,  the  traosmitting  power  is  approxlnuiteljr  pro 
portional  to  the  ratio  of  the  degrees  of  ar^  to  180*. 

Some  rules  base  the  horse-power  on  tlie  length  of  the  arc  of  contact  in 

obtain  by  substitution  H .  P.  =  -rgg^Q  XLx  tpm.,  and  the  flva  formntaB  then 
take  the  following  form  for  the  several  values  of  8i 


H.P: 


wL  X  rpm. 
275 


(1); 


wLxrpm. 


550 


wL  X  rpm. 
367 


(O; 


H.P.  (double  belt)  = 


wL  X  rpm. 
257 


(5). 


None  of  the  handy  forrauIsB  take  Into  consideration  the  centrifugal  ten- 
sion  of  belts  at  high  velocities.  When  the  velocity  is  over  8000  ft.  per  min- 
ute the  efTect  of  this  tension  becomes  appreciable,  and  It  should  be  takes 
account  of  as  in  Mr.  Nagle's  formula,  which  is  given  below. 

Horse-poiprer  of  m  lieatlier  Belt  One  Indft  irlde.    (Naolb.) 

Formula:  H.P.  «  CVtwiS  -  .012F«>-»  560. 
For /n  .40,0  a  180*,  0«  .715,  to  s  1. 


LArso  Belta.  h^  ^  1^5. 

Rivrreo  Bri^tb,  8  m  40Q. 

n 
Id 

Thick n«»a  la  iDcljee  ^  t. 

1^ 

Thfckntiss  ta  Inches  k  f. 

1/7 

J/6 

3/m 

7/53 

I/i 

a/je 

1/3 

7/32 

1/4 

Vie 

1/8 

a-s 

7/1« 

1  im 

.307 
.50 

JB7 

7B 

.84 

K18 

15 

3tO 

i.e» 

.250 
1,01 

.312 

,B3S 
S.5S 

.a7^ 

m 

10 

3.4? 

««1 

i^,K 

],^ 

.7f> 

.KH 

1.00 

ra-i 

rfifi 

K77 

w 

:2.t!4 

a,ft7 

sai 

S.45; 

fi  ,<> 

4^ 

A  u 

30 

uoo 

i.r 

im 

i.:5 

'i  10 

a.ai 

-^5 

2  7& 

3.10 

!J.flS 

4.SiV 

i.TH 

^.m 

ft,37 

5B 

l.*i 

i.*a 

IM 

J.SH 

■J  Id 

;S.Ag 

'l&t 

3D 

n:J] 

a,7Ti 

I.T4 

6.115 

r».fiT 

e.« 

?» 

m 

t,-l7 

I. TV 

i.03*^.*3:i 

•^.bb 

i.v^^a  44 

35 

3.8i 

4  37 

5.46 

.M^ 

A  &« 

T.« 

)4.1» 

m 

]  m 

1  y; 

■iA^'iti  ^0 

!i.;« 

'J.TOri.Wl 

40 

4  8.^ 

4.05 

6.1U 

0  ^j 

7.it 

9.M 

•5 

40 

1  !XI 

^/-K 

^.iorj.w 

?J3W 

4  i:>4,-»i 

45 

4.8--» 

5  4y 

e.Na; 

7,3i! 

e,4-i 

vm 

10  a 

45 

^jni 

L*^5 

'i  7r^;.i^Ha.G7 

i.&srHO 

m 

5.iifl 

11  m 

7  51 

P,0;; 

0Oit 

tU.Atf  t<iil 

5ft 

<t  -t^ 

-:jl=i 

2,tl43  <H.H  9^ 

4.97hM 

55 

"i.O^l 

9.W 

a  12 

S  Gfi! 

0  ;j 

njni««f 

5,-1 

2  il 

-.81 

ri.ias  W,4  -^ 

OO 

flflOj 

«.ffl 

8.7C 

0.«t 

10  4M 

rt  17  isn 

flO 

2   fnrt 

ri.il] 

^..^,3.&5'(  5] 

U5 

7,09 

7.JJ7 

»'.-J 

B.^ 

Tl,ort 

T?  w  11  :i 

^ 

U.71 

?l.lti?l5.'^'4.1* 

4,T4 

s.s-i'fl.a'i 

70 

7S^ 

»«^ 

10. SJ 

n  G'j 

I3.W  "?,  « 

7D 

■i.Rl 

3  07 

a.6M:i,ao 

i.Hl 

fl,H6.54 

75 

B.ll 

10.13 

10!^4 

12.  JA 

T4.t#1^  tt 

Tr> 

iJ.Wl 

3  ^ 

?t.70  4.4-.V"i  U.i 

C  ai  G.7^ 

m 

7.SC 

8.4t 

10  51 

iLn 

taus 

M.n  m,n 

m 

a.9i 

ij  45  i  ftGI^-W'S  15 

6  44,S?4| 

m 

7.:i^i 

^,6<l 

losir 

1I.^^ 

n  m 

i5.iai7.a 

m 

J.^ 

:i.4T^  JMII.ftj 

r>.2<) 

0  riO'F3.«»;i 

90 

7.71 

^.fci,-> 

11. oe  it,^";n/^i!a,4fii7(i 

90 

3  »7 

3JT;3«M  S5 

rp.yo 

ti.rn)B.ffii 

100 

7«J 

0.JD 

ik37iiit.i3ltaeoisa,»«Efi« 

tiiefL 

P.  b^cotiiefta  tiiaxiriium 

The  H.P.  becoiiirs  a  inlXbcMn  *l 

af»T 

.41  f 

t     IN* 

TtHH! 

=  :j 

!;j:ir 

t.  \*. 

mm. 

ia>. 

1  ft. 

p^r 

ser-.  : 

=  031^^ 

fL  p 

«rtttt] 

n. 

In  the  above  table  the  an^le  of  subtension,  a,  is  taken  at  180*. 

Should  it  be I  90«»|100«»|110«ll90»Ma0»|140»|160»|ie0*|17a»|18t>»,2(W 

Multiply  above  values  by  |  .65  |  .70 1  .76 1 .79 1 .83 1 .87 1  .91 1  .94 1 .97 1    1  li.as 

A*  F«  Naffle's  Formula  (Trans.  A.  a  U.  E.,  toL  IL,  1881.  n.  91. 

Tables  published  in  188aS.) 

..9  -  .012 r»\ 


H.P.  a  CVttc( 


C-l-10-«>Wa; 
a  3  def^rees  of  belt  contait; 
/  s  coefficient  of  friction; 
10  m  width  in  inches; 


t  s  thickness  in  inches; 
V  ss  velocity  in  feet  pet  second; 
S  =  BtTrhij  Upon  bell  ptjr  ti(|uare  inch. 


WIDTH  OP  BELT  FOR  A  GIVEN  HORSE-POWBE.    879 


Taking  fif  at  275  Ibe.  per  sq.  In.  for  laced  belts  and  400  lbs.  per  aq.  in.  for 
lapped  aod  riveted  belts,  the  formula  becomes 

H.P.  a  CVtfiiM  "  .OOOOeiSr*)  for  laced  belta; 
H.P.  s  CVtwi.Tftl  -  SMCHISV*)  for  riveted  belts. 

Values  of  C  «  1  -  10  --OWSVa    (n^o,^.) 


ill 

Degrees  of  contact  m 

a. 

O  V^ 

11  «£ 

90» 

100* 

110» 

1«0» 

130» 

140* 

160» 

ieo» 

170« 

180* 

200* 

.15 

.310 

.280 

.260 

.270 

.288 

.807 

.825 

.842 

.860 

.876 

.406 

.20 

.270 

.805 

.819 

.842 

.864 

.886 

.406 

.428 

.448 

.467 

.908 

.» 

.8S5 

.854 

.881 

.407 

.482 

.457 

.480 

.508 

.524 

.544 

.582 

80 

.876 

.40B 

.488 

.467 

.494 

.520 

.544 

.567 

.600 

.610 

.649 

.35 

.428 

.457 

.489 

.520 

.548 

.575 

.600 

.024 

.046 

.667 

.705 

AO 

.467 

.502 

.586 

.567 

.597 

.624 

.649 

.678 

.695 

.715 

.798 

.45 

.607 

.544 

.579 

.610 

.640 

.667 

.692 

.715 

.787 

.767 

.792 

.55 

.578 

.617 

.652 

.684 

.718 

.789 

.763 

.786 

.806 

.828 

.858 

.80 

.610 

.649 

.684 

.715 

.744 

.769 

.792 

.818 

.882 

.848 

.877 

1.00 

.TW 

.885 

.853 

.877 

.897 

.918 

.9-^7 

.987 

.947 

.056 

.969 

The  following  table  gives  a  comparison  of  the  formulas  already  given  for 
tlie  case  of  a  belt  one  inch  wide>  with  arc  of  contact  180^. 

floraei>poinrer  of  a  Belt  One  Incli  wide,  Are  of  Contact  1 80*. 

CoMPAiusos  or  DirrsBBNT  Formula. 


Form.  1 

H.P.  « 

wv 

650 

Form.  8 

H.P.  « 

wv 

iioo' 

Form.  8 

H.P.  = 

wv 

1000 

ronn.4 

H.P.  as 

wv 
788* 

Form.  5 

dbl.belt 

H.P.  = 

wv 

518* 

Nagl«'8  Form. 
7/88"8inglebelt 

Laced. 

Riveted 

10 
80 
80 
40 
50 
60 
70 
80 
90 

ino 

110 

600 
1800 
1800 
8400 
8000 
8600 
4200 
4800 
5400 
6000 
6600 
7200 

50 
100 
150 
800 
850 
800 
860 
400 
450 
600 
550 
600 

1.09 
8.18 
8.27 
4.86 
5.46 
6.56 
7.63 
8.78 
9.88 
10.91 

.06 
J.09 
1.64 
2.18 
8.78 
8.27 
8.88 
4.86 
4.91 
6.45 

.60 
1.80 
1.80 
8.40 
8.00 
8.60 
4.80 
4.80 
6.40 
6.00 

.88 
1.64 
2.46 
8.27 
4.09 
4.91 
5.73 
6.55 
7.87 
8.18 

1.17 
8.84 

8.51 
4.68 
5.65 
7.08 
8.19 
0.36 
10.58 
11.70 

.78 
1.54 
8.25 
2.90 
8.48 
8.95 
4.29 
4.50 
4.55 
4.41 
4.06 
8  49 

1.14 
2.84 
8.81 
4.88 
6.26 
6.09 
6.78 
7.86 
7.74 
7.96 
7.97 

130 



7.75 

TTldtli  of  Belt  for  a  GlTen  Horse-pow^er.— The  width  of  belt 
lequired  for  any  given  horse-power  may  be  obtained  by  transposing  the  for- 
mulsB  for  horae-power  so  as  to  give  the  value  of  ir.  Thus: 

^        .          ,    ,.,  660H.P.      9.17  H.P.       2101  H.P.        275H.P. 

From  formula  (1), 

From  formula  (8). 

From  formula  (8), 

From  formula  (4), 


From  formula  (6)  ,•  w  » 
•  For  double  bel|8. 


v       ^        V             dxrpm.      Lxrpm.* 
1100  HP.       18.83  H.P.       4808  H.P.        630  H.P. 

V        ^         V            dx  rpm. 
1000  H.P.       16.67 HP.       8820  HP. 

L  X  rpm." 
600  H.P. 

V        ^          V            d  X  rpm. 
788H.P.       18.22  H.P.       2800  HP. 

L  X  rpm.' 
860H.P. 

V        "^          V            d  X  rpm. 
613  H.P.       8.66  HP.       1960  H.P. 

L  X  rpm.' 
897H.P. 

d  X  rpm.     L  X  rpm.* 


880 


BELTIKG. 


Many  authoritiM  vote  formula  (1)  for  doable  belts  and  fornnda  (S)  or  (3)  f  of 

single  oelts. 

To  obtain  the  width  by  Kagrle's  formula,  w  m  y^m.o  ^  Qtijriy  ^  divide 

the  given  horse-power  by  the  figure  in  the  table  oorresponding  to  the  Klven 
thickness  of  belt  and  velocity  In  feet  per  second. 

The  for  inula  to  be  u»ed  in  any  particuXar  case  Is  largely  a 
matter  of  judgment.  A  single  belt  proportioned  according  to  formula  (1 1. 
if  tightly  Rtretctied.  and  if  the  surface  is  in  good  condition,  will  transmit  the 
horse-powercalculatedby  the  formula,  but  one  so  proportioned  is  objec- 
tionable, first,  because  it  requires  so  great  an  initial  tension  that  it  ia  apt  to 
stretch,  slip,  and  require  frequent  restretcbing  and  relacing;  and  seoood, 
because  this  tension  win  cause  an  undue  preesure  on  the  pulley -shaft,  and 
therefore  an  undue  loss  of  power  by  friction.  To  avoid  thew  difficulties, 
formula  (2),  (8),  or  (4,)  or  Mr.  Nag1e*8  toble,  should  be  used;  the  latter  espe- 
cially in  cases  in  which  the  velocity  exceeds  4000  ft.  per  mln. 

Taylor's  Rules  for  Beltiiiff.-F.  W.  Taylor  (Traoa  A.  8.  M.  B^ 
zv.  'Mi)  describee  a  nine  years'  expeiiment  on  belting  In  a  raachlne-shop, 
giving  results  of  testa  of  48  belts  running  night  and  day.  Some  of  these 
belts  were  run  on  cone  pulleys  and  others  on  shifting,  or  fast-and-loose.  pul- 
leys. The  average  net  working  load  on  the  sliifting  belts  was  only  4/10  of 
that  of  the  cone  belts. 

The  shifting  belts  varied  In  dimensions  from  89  ft  7  in.  long,  8.6  in.  wide, 
.25  in.  thick,  to  61  ft.  5  in.  lone,  8.5  in.  wide,  .87  in.  thick.  Tlie  cone  beite 
varied  in  dimensions  from  24  ft.  7  in.  long,  2  In.  wide,  .23  in.  thick,  to  SI  ft. 
10  in.  long,  4  in.  wide,  .87  in.  thick. 

Belt-clamps  were  used  having  spring-balances  between  the  two  pairs  of 
clamps,  so  that  the  exact  tension  to  which  the  belt  was  sublected  wss 
accurately  weighed  when  the  belt  was  first  put  on,  and  each  time  it  was 
tightened. 

The  tension  under  which  each  belt  was  spliced  was  carefully  figured  so  as 
to  place  It  under  an  initial  strain— while  the  belt  was  at  rest  Immediately 
after  tightening— of  71  lbs.  per  inch  of  width  of  double  belts.  This  is  eq[uiv- 
alent.  In  the  case  of 

Oak  tanned  and  fulled  belts,  to  192 lbs.  per  sq.  hi.  section; 
Oak  tanned,  not  fuUed  belts,  to  229  "      *♦     "    *•        *• 
-      t0  253  **      "     **    ••         •* 


Semi- raw-hide  belts* 
Raw-hide  belts. 


to  284 


From  the  nine  years*  experiment  Mr.  Taylor  draws  a  number  of  oonchi- 
siona,  some  of  which  are  given  in  an  abridged  form  below. 

In  using  belting  so  as  to  obtain  the  gi^eatest  economy  and  the  moat  satis- 
factory results,  the  following  rules  should  be  observed: 


A  double  belt,  having  an  arc  of  contact  of 

180*,  win  give  an  effective  pull  on  the  face 

of  a  pulley  per  inch  of  width  of  bell  of. 

Or,  a  different  form  of  same  rule: 

The  number  of  sq.  ft.  of  double  Beit  passing 
around  a  pulley  per  minute  required  to 
transmit  one  horse-  power  is 

Or:  The  number  of  lineal  feet  of  double- 
belting  1  in.  wide  passing  around  a  pulle\' 
per  minute  required  to  transmit  one  horse- 
power is 

Or :  A  double  belt  6  in.  wide,  running  4000  to 
SOiX)  ft.  per  min.,  will  transmit 


Oak  Tanned 

and  Fulled 

Leather  Belts. 


86  lbs. 

80  sq.ft. 

950  ft. 
80H.P. 


Other  Types  of 
Leather  Belts 

and  0-  to  7-plj 
Rubber  Belts. 


80  lbs. 

SO  sq.ft. 

1100  ft. 
25  H.P. 


The  terms  ** initial  tension,"  "effective  pull,**  etc., are  thus  explain«Kl  by 
Mr.  Taylor :  When  pulleyK  upon  which  belts  are  tightene<l  are  at  rest,  bota 
strands  of  the  belt  (the  upper  and  lower)  are  under  the  same  stress  per  in. 
of  width.    By  "  tension,^' '"  iuitial  tension,*'  or  '*  tension  while  at  rest«"  we 


tayloe's  kules  for  beltikg.  881 

me&n  the  stress  per  in.  of  width,  or  sq.  In.  of  aectloo,  to  which  one  of  the 
strands  of  the  belt  is  tightened,  w  hen  at  rest.  After  the  belts  are  In  motion 
and  cransmittioR  power,  the  stress  on  the  slack  side,  or  strand,  of  the  belt 
b<>coines  less,  while  that  on  the  ti^ht  side^or  the  side  which  does  the  pull- 
ing— becomes  greater  than  when  the  belt  was  at  rest.  By  the  term  "  tetal 
load  **  we  mean  the  total  stress  per  in.  of  width,  or  sq.  in.  of  section,  on  the 
tight  side  of  belt  while  in  motion. 

The  diiferenoe  between  the  stress  on  the  tight  side  of  the  belt  and  its  slack 
»iide,  while  in  motion,  represents  the  effective  force  or  pull  which  is  trans* 
mitted  from  one  puller  to  another.  By  the  terms  ''working  load,'*  *'  nel 
working  load,**  or  "effective  pull,"  we  mean  the  diffi'rence  in  the  tension 
of  the  tight  and  alack  sides  of  the  belt  per  in.  of  width,  or  sq.  in.  section, 
while  in  motion,  or  the  net  effective  force  that  is  transmitted  from  one  pul- 
ley to  another  per  in.  of  width  or  sq  in.  of  section. 

The  discovery  of  Messrs.  Lewis  and  Bancroft  (Trans.  A.  8.  H.  E.,  vii.  740) 
that  the  "sum  of  the  tension  on  both  sides  of  the  belt  does  not  remain 
con^taut.'^  upsets  all  previous  theoretical  belting  formule. 

The  belt  speed  for  maximum  economy  should  be  from  4000  to  4500  ft.  per 
minute. 

The  best  distance  from  centre  to  centre  of  shafts  is  from  SO  to  25  ft. 

Idler  pulleys  work  most  satisfactoiily  when  located  on  the  slack  side  of 
tlie  belt  about  one  quarter  way  from  the  drivlrg-pulley. 

Belts  are  more  durable  and  work  more  satisfactorily  made  narrow  and 
tliick,  rather  than  wide  and  thin. 

It  is  safe  and  advisable  to  use:  a  double  belt  on  a  pulley  18  in.  diameter  or 
Barger;  a  trii}le  belt  on  a  puUev  20  in.  diameter  or  larger;  a  quadruple  belt 
on  a  pulley  80  in.  diameter  or  larger. 

As  oeits  Increase  in  width  they  should  also  be  made  thicker. 

The  ends  of  the  belt  should  be  fastenoii  together  by  splicing  and  cement- 
ing, instead  of  lacing,  wiring,  or  using  hooks  or  clamps  of  any  kind. 

A  V-splice  should  oe  used  on  triple  and  quadruple  belts  and  when  idlers 
are  used.  Stepped  splice,  coated  with  rubber  and  vulcanized  in  place,  is  best 
for  rubber  belts. 

For  double  belting  the  rule  works  well  of  making  the  splice  for  all  belts 
up  to  10  in.  wide,  10  in.  long;  from  10  in.  to  18  in.  wide  tlie  Rplice  should  be 
the  same  width  as  the  belt,  18  in.  being  the  greatest  length  of  splice  required 
for  double  belting. 

Bf  Its  should  be  cleaned  and  greased  every  five  to  six  months. 

Double  leather  belts  will  last  well  when  repeatedly  tightened  under  a 
strain  (when  at  rest)  of  71  lbs.  per  in.  of  width,  or  S40  lbs  per  sq.  in.  section. 
Tiiey  will  not  maintain  this  tension  for  any  length  of  time,  however. 

Belt-clamps  having  spring- balances  between  the  two  pairs  of  clamps 
should  be  used  for  weighing  the  tension  of  the  belt  accurately  each  lime  it 
is  tightened. 

The  stretch,  durability,  cost  of  maintenance,  etc.,  of  belts  proportloni^d 
(A)  according  to  the  ordinary  niles  of  a  total  load  of  111  lbs.  per  inch  of 
w  idth  corresponding  to  an  effective  pull  of  66  lbs.  per  inch  of  width,  and  (B) 
according  to  a  more  economical  rule  of  a  total  load  of  C4  lbs.,  corresponding 
to  an  effective  pull  of  26  lbs.  per  inch  of  width,  are  found  to  be  as  follows: 

When  It  is  impracticable  to  accurately  weigh  the  tension  of  a  belt  in  tight- 
ening it.  it  is  safe  to  shorten  a  double  belt  one  half  inch  for  every  10  ft  of 
lengin  for  (A)  and  one  inch  for  every  10  ft.  fur  (B),  If  it  requires  tightening. 

Double  leather  belts,  when  treated  with  great  care  and  run  night  and  day 
at  moderate  speed,  should  last  for  7  years  (A);  18  years  (B). 

The  cost  of  all  labor  and  materials  used  in  the  maintenance  and  repairs  of 
double  belts,  added  to  the  cost  of  renewals  as  they  give  out,  through  a  term 
of  years,  will  amount  on  an  average  per  year  to  87j(  of  t-he  original  cost  of 
the  bells  (A);  14)(  or  less  (B). 

In  figuring  the  total  expense  of  belting,  and  the  manufacturing  cost 
chargeable  to  this  account,  by  far  the  largest  item  is  the  time  lost  on  the 
machines  while  belts  are  being  relaced  and  repaired. 

The  total  stretch  of  leather  belting  exceeds  6j<  of  the  original  length. 

The  stretch  during  the  first  six  months  of  the  life  of  belts  is  30^  of  their 
entire  stretch  (A);  15^  (B). 

A  double  belt  will  stretch  47/100  of  1%  of  its  length  before  requiring  to  be 
tightened  (A);  81/100  of  i%  (B). 

Th^  most  important  consideration  in  making  up  tables  and  rules  for  the 
use  and  care  of  belting  is  how  to  secure  the  minimum  of  interruptions  to 
manufacture  from  this  source. 


883  BELTIKG. 

The  averaffe  double  belt  (A),  when  ninninf?  nf^ht  and  dajr  in  a  machine 
shop,  wiii  cause  at  least  26  interruptions  to  manufacture  dunnjc  its  life,  or  5 
Int'erruplions  per  year,  but  with  {B)  interruptions  to  manufacture  will  not 
average  oftener  for  each  belt  than  one  in  sixteen  months. 

The  oalc-tanned  and  fulled  belts  showed  themselves  to  be  superior  in  all 
respects  except  the  coefficient  of  friction  to  either  the  oaic-tannea.not  fulled, 
tlie  sf  mi-raw-nide,  or  raw-hide  with  tanned  face. 

Belts  of  any  width  can  be  successfully  shifted  backward  and  forward  on 
tight  and  loose  pulleys.  Belts  running  between  6000  and  6000  ft.  per  min. 
and  driving  300  U.F.  are  now  l)eiiig  daily  shifted  on  tight  and  loose  pulleys, 
to  throw  lines  of  shafting  in  and  out  of  use. 

The  best  form  of  beli-shifter  for  wide  belts  is  a  pair  of  rollers  twice  the 
width  of  belt,  either  of  which  can  be  pressed  onto  the  flat  surface  of  the 
belt  on  Its  slack  side  close  to  the  driven  pulley,  the  axis  of  the  roller  making 
an  nngle  of  75^  with  the  centre  line  of  the  belt. 

Remarks  on  IHr*  Taylor's  Rales*  (Trans.  A.  S.  M.  E.,  xr.,  94S.) 
—The  must  notable  feature  m  Mr.  Taylor's  oaper  is  the  great  difference  be- 
tween his  rules  for  proper  proportioning  of  belts  and  those  given  by  earlier 
writers.  A  very  commonly  used  rule  is,  one  horse-power  may  be  transmitted 
by  a  single  lielt  1  in.  wide  running  x  ft.  per  min.,  substituting  for  x  various 
values,  according  to  the  ideas  of  different  engineers,  ranging  umially  from 
650  to  IIUO. 

The  practical  mechanic  of  the  old  school  is  apt  to  swear  by  the  flmire 
600  ns  being  thoroughly  reliable,  while  the  modem  engineer  is  more  apt  to 
use  the  figure  lOOU.  Mr.  Taylor,  however,  instead  of  using  a  figure  from  &oO 
to  1 100  for  n  single  belt,  uses  1)50  to  1100  for  double  belts.  If  we  assume  that 
a  double  belt  is  twice  as  strong,  or  will  carry  twice  as  much  power,  as  a 
shigle  belt,  then  he  uses  a  figure  at  least  twice  as  large  as  that  used  io 
modem  practice,  and  would  make  the  cost  of  belting  for  a  given  shop  twice 
as  large  as  if  the  belting  were  proportioned  according  to  the  most  liberal  of 
the  customary  rules. 

This  great  difference  is  to  some  extent  explained  by  the  fact  that  tha 
problem  which  Mr.  Taylor  undertakes  to  solve  is  quite  a  different  one  from 
thai  which  is  solved  by  the  ordinary  rules  with  their  variations.  The  prob- 
lem of  the  latter  generally  is,  **  How  wide  a  belt  must  be  used,  or  how  nar- 
row a  belt  may  be  used,  to  transmir-  a  given  horse-power  ?"  Mr.  Taylor^s 
problem  is:  **  How  wide  a  belt  must  be  used  so  that  a  given  horse-power 
may  be  transmitted  with  the  minimum  cost  for  belt  repairs,  the  longest  life 
to  the  belt,  and  the  smallest  loss  and  inconvenience  from  stoppuii^  the 
machine  while  the  belt  is  being  tightened  or  repaired  ?^* 

The  difference  between  the  old  practical  mechanic's  rule  Of  a  l-fn.-wide 
single  belt,  600  ft.  per  min.,  transmits  one  horse-power,  and  the  rule  com- 
monly used  by  engineers,  in  which  1000  is  substituted  for  600,  is  due  to  the 
belief  of  the  engineers,  not  that  a  horse-power  could  not  be  transmitted  by 
the  belt  proportioned  by  the  older  rule,  but  that  such  a  proportion  involved 
undue  strain  from  overtightening  to  prevent  slipping,  which  strain  entoiled 
too  much  journal  friction,  necessitated  frequent  tightening,  and  decreased 
the  length  of  the  life  of  the  lielt. 

Mr.  Taylor's  rule  substituting  1100  ft.  per  min.  and  doubling  the  belt  te  a 
further  step,  and  a  long  one,  in  the  same  direction.  Whether  it  will  be  taken 
in  any  case  by  engineers  will  depend  upon  whether  they  appreciate  the  ex- 
tent of  the  losses  due  to  slippage  of  belts  slackened  by  use  under  overstrain, 
and  the  loss  of  time  in  tightening  and  repairing  belts,  to  such  a  degree  as  to 
induce  them  to  allow  the  first  cost  of  the  belts  to  be  doubled  in  order  to 
avoid  these  losses. 

It  should  be  noted  that  Mr.  Tay]or*s  experiments  were  made  on  rather 
narrow  belts,  used  for  transmitting  power  from  shafting  to  machinery,  and 
his  conclusions  may  not  be  applicable  to  heavy  and  wide  belta,  suoias 
engine  fiy-wheel  belts. 

IHISCEIiliANEOUS  NOTES  ON  BBI^TING. 

Formuin  are  useful  for  proportioning  belts  and  pulleys,  but  thev  furnish 
no  means  of  estimating  how  much  power  a  particular  belt  may  be  trans- 
mitting at  any  given  time,  any  more  than  the  slse  of  the  engine  is  a  measure 
of  the  load  it  is  actually  drawing,  or  the  known  strength  of  a  horse  is  a 
measure  of  the  load  on  Uie  wagon.  The  only  reliable  means  of  determining 
the  power  actually  transmitted  is  some  form  of  dynamometer.  (See  Trans. 
A.  STm.  B..vol.xii.p.  707.) 


MISCELLANEOUS  NOTES  ON  BELTING.  883 

If  we  Increase  the  thickness,  the  power  transmitted  oujrht  to  Increase  in 
proportion;  and  for  double  belts  we  should  have  half  the  width  required  for 
a  »luji^le  belt  under  the  game  conditions.  With  large  pulleys  and  moderate 
velocities  of  belt  it  is  probable  that  this  holds  f^ood.  With  small  pulleys, 
however,  when  a  double  belt  is  used,  there  is  not  such  perfect  contact 
between  the  puUey-f ace  and  the  belt,  due  to  the  rigidity  of  the  kttter,  and 
more  work  ts  necessary  to  bend  the  belt^flbres  than  whon  a  thinner  and 
moi-e  pliable  belt  is  used.  The  centrifugal  force  tending  to  throw  the  belt 
from  the  pulley  also  increases  with  the  thickness,  and  for  these  reasons  the 
width  of  a  double  belt  required  to  tranpmii  a  given  horse-power  when  used 
with  small  pulleys  is  generallv  assumed  not  less  than  seven  tenths  the 
width  of  a  single  belt  to  transmit  the  same  power.  (Flather  on  *'  Dynamom- 
eters and  Measurement  of  Power.") 

F.  W.  Tavlor.  however,  flnds  that  great  pliability  is  objectionable,  and 
favors  thick  belts  even  for  small  pulleys:  Tne  power  consumed  in  beuding 
the  belt  around  the  pulley  he  considers  inappi-eciable.  According  to  Kan- 
kine's  formula  for  centrifugal  tension,  this  tension  is  proportional  to  the 
sectional  area  of  the  belt,  and  hence  it  does  not  increase  with  increase  of 
thickness  when  the  width  is  decreased  in  the  same  proportion,  the  sectional 
area  remaining  constant. 

Scott  A.  Smith  (Trans.  A.  S.  M.  E.,  x.  765)  says:  The  best  belts  are  made 
from  all  oak -tanned  leather,  and  curried  with  the  use  of  cod  oil  and  tallow, 
all  to  be  of  superior  quality.  Such  belts  have  continued  in  use  thirty  to 
forty  years  when  used  as  simple  driving-belts,  driving  a  proper  amount  of 
power,  and  having  had  suitable  care.  The  flesh  side  should  not  be  run  to 
tiie  pulley -face,  for  the  reason  that  the  wear  from  contact  with  the  pulley 
should  come  on  the  grain  side,  as  that  surface  of  the  belt  is  much  weaker 
in  its  tensile  strength  than  the  flesh  side;  also  as  the  grain  is  hard  it  is  more 
enduring  for  the  wear  of  attrition;  further,  if  the  grain  is  actually  worn  off, 
then  the  belt  may  not  suffer  in  its  Integrity  from  a  ready  tendency  of  the 
bard  grain  side  to  crack. 

The  most  Intimate  contact  of  a  belt  with  a  pulley  comes,  first,  in  the 
smoothness  of  a  pulley-face.  Including  freedom  from  ridges  and  hollows  left 
by  turning-tools;  second,  in  the  smoothness  of  the  surface  and  evenness  in 
theteztureorbodyof  abe1t;tbird,in  having  the  crown  of  the  driving  and  re- 
ceiving pulleys  exactly  alike,— as  nearly  so  as  is  practicable  in  a  commercial 
sense;  fourth.  In  having  the  crown  of  pulleys  not  over  U"  for  a  24"  face,  that 
is  to  say,  that  the  pulley  is  not  to  be  over  Si"  larger  in  rliameter  in  its  centre; 
fifth.  In  having  toe  crown  other  than  two  planes  meeting  at  the  centre; 
sixth,  the  use  of  any  material  on  or  In  a  belt,  in  addition  to  those  necessarily 
used  in  the  currying  process,  to  keep  them  pliable  or  increase  their  tractive 
quality,  should  wholly  depend  upon  the  exigencies  arising  in  the  use  of 
belts;  non-use  is  safer  than  over-use;  seventh,  with  reference  to  the  lacing 
of  belts,  it  seems  to  be  a  good  practice  to  cut  the  ends  to  a  convex  shape  by 
using  a  former,  so  that  there  may  be  a  nearly  uniform  stress  on  the  lacing 
through  the  centre  as  compared  with  the  edges.  For  a  belt  10"  wide,  the 
centre  of  each  end  should  recede  1/10". 

I<aelliff  of  Belte*— In  punching  a  belt  for  lacing,  ura  an  oval  punch, 
the  longer  diameter  of  the  punch  being  parallel  wlih  the  sides  of  the  belt. 
Punch  two  rows  of  holes  in  each  end,  placed  zigzag.  In  a  8-in.  belt  there 
should  be  four  holes  in  each  end— tvto  In  each  row.  In  a  6-inch  belt,  seven 
holes^four  in  the  row  nearest  the  end.  A  10-inch  belt  should  have  nine 
holes.  The  edge  of  the  holes  should  not  come  nearer  than  %  of  an  Inch  from 
the  sides,  nor~%  of  an  Inch  from  the  ends  of  the  belt.  The  second  row  should 
be  at  least  l^mches  from  the  end.  On  wide  belts  these  distances  should 
be  even  a  little  greater. 

Begin  to  lace  in  the  centre  of  the  belt  and  take  care  to  keep  the  ends 
exactly  In  line,  and  to  lace  both  sides  with  equal  tightness.  The  lacing 
should  not  be  crossed  on  the  side  of  the  belt  that  runs  next  the  pulley.  In 
taking  up  belts.  olMterve  the  same  rules  as  putting  on  new  ones. 

Setting  m  Belt  on  Qnarter-tivlrt*— A  belt  mwvX  run  squarely  on  to 
tne  pullev.  lo  connect  with  a  belt  two  horizontal  shafts  at  right  angles 
with  each  other,  say  an  engine-shaft  near  the  floor  with  a  line  attached  to 
the  ceiling,  will  require  a  quarter-turn.  First,  ascertain  the  central  point 
on  the  face  of  each  pulley  at  the  extremity  of  ti»e  horizontal  diameter  where 
the  belt  will  leave  the  pulley,  and  then  set  that  point  on  the  driven  pulley 
plumb  over  the  corresponding  point  on  the  driver.  This  will  cause  the  heft 
to  run  squarely  on  to  each  pulley,  and  It  will  leave  at  an  angle  greater  or 
less,  according  to  the  size  of  the  pulleys  and  their  distance  trofn  eac|i  other. 


884  BELTINQ. 

In  quarter-twist  belti,  In  order  that  the  belt  mmv  ramain  on  the  fMi11(»t!i. 
the  oeiiti-al  plane  on  each  pulley  must  pass  through  the  point  of  delivery  of 
the  other  pulley.    This  arrangement  doen  not  admit  of  revened  motion. 

To  flnd  the  I^enartn  of  Belt  required  fbr  two  dTea 
Pulleys*^ Whan  the  length  caunot  be  measured  directly  by  a  tap«*-Iine, 
the  following  approximate  rule  may  be  uiied  :  Add  the  diameter  of  the  two 
puUeyH  toffetber,  diride  the  lum  by  2,  and  multiply  the  quotj(«nt  br  SW,  and 
add  the  product  to  twioe  the  distance  between  the  centres  of  the  shafta 
(See  accurate  formula  below.) 

To  And  tlie  Anyle  of  tbe  Are  of  ConUiet  of  ft  Belt.— Divide 
the  difference  between  ihe  radii  of  the  two  pulleys  in  inches  by  the  distance 
between  their  centres,  al80  in  Inches,  and  in  a  table  of  natural  sines  find  tbe 
angle  most  nearly  corresponding  with  tbe  quotient.  Multiply  this  angle  by 
8,  and  add  the  product  to  ISO®  for  the  angle  of  contact  with  the  larger 
pulley,  or  subtract  It  from  180"  for  the  smaller  pulley. 

Or,  let  K  =s  radius  of  larger  pulley,  r  s  radius  of  smaller; 
L  sz  distance  between  centres  of  the  pulleys; 
a  s  angle  whose  sine  is  (R  -  r)  +  L. 

Are  of  contact  with  smaller  pulley  =  180*  -  Sa; 
'*     '*       **  *'    larger  pulley    «=  180*  4-  2a. 

To  And  tlie  I«eii|^li  of  Belt  In  Contaet  ^irltli  tlie  Ptillex.- 

For  tha  Utfger  pulley,  multiply  the  angle  ».  found  aa  above,  by  .0840,  to  the 
product  add  8.1416,  and  multiply  the  sum  by  the  radius  of  the  pulley.  Or 
length  of  belt  in  oontaot  with  the  pulley 

a  radius  X  (»  +  .084»a)  e  radius  X  ir(l  +  ~). 

For  the  smaller  pulley,  length  a  radius  x  (»  -XB41>a)=  radius  X  »(*  "  fi/ 

The  above  rules  refer  to  Open  Belts.  The  accurate  formula  for  lemth 
Of  an  open  belt  Is, 

Length  «  iri?(n- ^)  4- irr(l  -  ^)  +  «L  cos  a 

=  !?(»  4-  .08490)  4-  »■(»  -  .084»a)  4-  2L  cos  a, 

in  whloh  B  t±  radius  of  larger  pulley,  r  s:  radius  of  smaller  pulley. 

L  =  distance  between  centres  of  pulleys*,  and  a  =  angle  whose  sine  li 

(i?-r)-i-r;  cosa-  Vl^  -  (B  -  r)^ -*- L. 
For  Crossed  Belts  the  formula  is 

Length  of  belt  =  ,iz(i  4-  i)  4-  ,r(l  4.  i)  4-  tL  cos  ^. 

=  <«  4-  r)  X  (»  4-  .0349/1)  4-  iL  cos  fl, 


in  which  fi  B  angle  whose  sine  Is  (A  4*  r)  -i-  L\  cos  fi  s  Vl^  -  (i?  +  r>*  •«-  L. 

To  And  tbe  Ijencrtlt  of  Beltirtaen  Closely  Rolled.— The  sum 

of  the  diameter  of  the  roll,  and  of  tbe  eye  in  inches,  x  the  number  of  toroi 
made  bv  tbe  belt  and  by  .l.m  =  length  of  tbe  belt  in  feet 

To  find  the  Approximate  Welglit  of  Belts  —Multiply  the 
leuKth  of  belt,  in  feet,  by  the  width  in  Inches,  and  divide  the  product  by  IS 
for  single,  and  8  for  double  l)elt. 

Belatlons  of  the  Size  and  Speeds  ot  DrlTlnjc  nnd  Brlwee 
Pulleys.— The  driving  pulley  is  called  the  driver,  D,  anothe  driven  pulley 
the  driven,  d.  It  the  number  of  teeth  in  gears  Ir  used  instead  of  diameter,  la 
these  calculations,  number  of  teeth  must  be  substituted  wherever  diameter 
occurs.    B  s=  revs.  i>er  min.  of  driver,  r  =  revs,  per  min.  of  driven. 

Dsi  dr-*-B; 
Dlam.  of  driver  =  diam.  of  driven  x  revs,  of  driven  -i-  revsT  of  driver. 

d  =  DB  -*-  r; 
Diam.  of  driven  =  dlam.  of  driver  x  revs,  of  driver  -»-  revs,  of  driva^ 

/?  =  dr  -f-  Di 
Revs,  of  driver  =  revs,  of  drlveo  x  dlam.  of  driveu  -»-  4i«m.  Qt  driver. 


MISCELLANEOUS  NOTES  ON  BELTING. 


885 


Revs,  of  diiveii : 


:  reVB.  of  drlTer  x  dfam.  of  driver  -*-  diau.  of  driven. 


Snis  of  TIfflit  Belt*.  (Jonee  end  lAUftbHnt.V-ClAmiii  with  i 
screws  sre  often  used  to  put  on  belte  with  extreme  dg^htnees,  and  with  mott 
in jurioiiB  strain  upon  the  leather.  They  should  be  very  judiciously  used  for 
horisontal  belts,  which  should  be  allowed  sufflcient  slackneBs  to  move  with  a 
loose  undulating  vibration  on  the  returning  side,  as  a  test  that  they  have  no 
more  iitratn  imposed  than  Is  necMsary  simply  to  transmit  the  power. 

On  this  subject  a  New  England  cotton-mill  engineer  of  larM  ezperlenoe, 
says:  I  believe  that  three  quarters  of  the  trouble  exnerienced  In  brolren  pul. 
leys,  hot  boxes,  eto.,  can  be  traced  to  the  fault  of  tlgot  belts.  The  enormous 
and  useless  pressure  thus  put  upon  pulleys  must  In  time  break  them,  if  they 
are  made  in  any  reasonable  proportions,  besides  wearing  out  the  whole  out- 
fit, and  caushig  heating  and  consequent  destruction  of  the  bearings.  Below 
are  some  figures  showing  the  power  it  takes  in  average  modem  ttUls  with 
first-class  shafting,  to  dnve  the  shaftbig  alone : 


Whole 
Load, 

Shafting  Alone.   | 

Min, 

No. 

Whole 
Iioad, 
H.P. 

Shafting  Alone. 

Mill, 
No. 

Horse- 
power. 

Percent 
of  whole. 

Horse- 
power, 

Per  cent 
of  whole. 

1 

8 
4 

199 

486 

077 

51 

lll.S 
184 
190 

S5.8 
88.6 
S7.6 
28.1 

S 
6 

I 

759 
885 
670 

en 

m.6 

84.8 
188 

S9.8 
96.8 

These  may  be  taken  as  a  fair  showing  of  the  power  that  Is  required  In 
many  of  our  best  mills  to  drive  shafting.  It  is  unreasonable  to  think  that  all 
that  power  is  consumed  by  a  legitimate  amount  of  friction  of  bearing^ 
and  belts.  I  know  of  no  cause  for  such  a  loss  of  power  but  tight  belts.  These, 
when  there  are  hundreds  or  thousands  in  a  mlu,  easily  multlp^  the  friction 
on  the  bearings,  and  would  account  for  the  figures. 

Sa^  of  Belts.— In  the  location  of  shafts  that  are  to  be  connected  with 
each  other  by  belts,  care  should  be  taken  to  secure  a  proper  distance  one 
from  the  other.  This  distance  should  be  such  as  to  allow  of  a  gentle  ssg  to 
the  belt  when  in  motion. 

A  general  rule  may  be  stated  thus:  Where  narrow  belts  are  to  be  run  over 
sroau  puUeys  15  feet  is  a  good  average,  the  belt  having  a  sag  of  lU  to  9  inches. 

For  larger  belts.  worUng  on  larger  pulleg^s,  a  distance  oCflO  to  25  feet  does 
weU,  with  a  sag  of  2U  to  4  Inches. 

Por  mahi  belts  working  on  very  large  puDeys,  the  dlstanoe  should  be  2S  to 
80  feet,  the  belts  working  well  with  a  sag  of  4  to  6  Inches. 

If  too  great  a  distance  1b  attempted, the  belt  will  have  an  unsteady  fiappkig 
motion,  which  will  destroy  both  the  belt  and  machinery. 

Arransement  of  Belts  and  Pulleys.— If  possible  to  avoid  it.  con- 
nected shafts  should  never  be  placed  one  directly  over  the  other,  as  in  such 
case  the  belt  must  be  kept  very  tight  to  do  the  work.  For  this  purpose  belts 
should  be  carefully  selected  of  well-stretched  leather. 

It  is  desirable  that  the  angle  of  the  belt  with  the  floor  should  not  exceed 
46«.  It  is  also  desirable  to  locate  the  shaftbig  and  machinery  so  that  belts 
should  run  off  from  each  shaft  in  opposite  directions,  as  this  arrangement 
win  relieve  the  bearings  from  the  friction  that  would  result  when  the  belts  all 
ptill  one  way  on  the  shaft. 

In  arranging  the  belts  leading  from  the  main  line  of  shaftbig  to  the 
counters,  those  pulling  in  an  opposite  direction  should  be  placed  as  near 
each  other  as  practicable,  while  those  pulling  in  the  same  direction  should  be 
separated.  This  can  often  be  accomplished  by  changing  the  relative  posi- 
tions of  the  pulleys  on  the  counters.  By  this  procedure  much  of  the  friction 
on  the  Journals  may  be  avoided. 

If  possible,  machinery  should  be  so  placed  that  the  direotkin  of  the  belt 
motion  shall  be  from  the  top  of  the  driving  to  the  top  of  the  driven  puOey, 
when  the  sag  will  increase  the  arc  of  contact. 

The  pulley  slioukl  be  a  little  wider  than  the  belt  required  for  tbe  wortc 


886  BELTING. 

The  motion  of  drirlnfir  sbould  run  with  and  not  a^cainst  the  lane  of  Uie  be]t& 

Tightening  or  guide  pulleys  should  be  applied  to  the  slack  side  of  belts  and 
near  the  smaller  pulley. 

Jones  &  Laughlios,  in  their  Useful  Information,  say:  The  diameter  of  the 
pulleys  should  be  as  large  as  can  be  admitted,  provided  they  will  not  pro- 
duce a  speed  of  more  than  4700  feeL  of  belt  motion  per  minute. 

They  £uso  say :  It  is  better  to  gear  a  mill  with  small  pulleys  and  run  them 
at  a  nigh  velocity,  than  with  large  pulleys  and  to  run  them  slower.  A  mill 
thus  geared  costs  less  and  has  a  much  neater  appearanoe  than  with  large 
heavy  pulleys. 

M.  Arthur  Achard  (Proc.  Inst.  M.  E.,  Jan.  1881,  p.  6S)  says:  When  the  belt 
is  wide  a  partial  vacuum  is  formed  between  the  belt  and  the  pulley  at  a 
high  velocity.  The  pressure  is  then  greater  than  that  computed  from  the 
tennions  in  the  belt,  and  the  resistance  to  slipping  is  greater.  This  has  the 
advantage  of  permitting  a  greater  power  to  be  transmitted  by  a  given  belt, 
and  of  diminishing  the  strain  on  the  shafting. 

On  the  other  hand,  some  writers  claim  that  the  belt  entraps  air  between 
itself  and  the  pulley,  which  tends  to  diminish  the  friction,  and  reduce  the 
tractive  force.  On  this  theory  some  manufacturers  perforate  the  belt  with 
numerous  holes  to  let  the  air  escape. 

Care  or  Belts.— Leather  belts  should  be  well  protected  against  water, 
loose  steam,  and  all  other  moisture,  with  which  they  should  not  come  in  ooo- 
tact.  But  where  such  conditions  prevail  fairly  good  results  are  obtained  by 
using  a  special  dressing  prepared  for  the  purpose  of  water-proofing  leather, 
thougli  a  pof^itive  water-proofing  material  has  not  yet  been  direovered. 

Belts  made  of  coarse,  loose-fibred  leather  will  do  better  service  in  dry  and 
warm  places,  but  if  damp  or  moist  conditions  ejdst  then  the  very  finest  and 
firmest  leather  should  be  used.    (Fayerweath^r  &.  Ladew.) 

Do  not  allow  oil  to  drip  upon  the  belts.    It  destroys  tiie  life  of  the  leather. 

Leather  belting  cannot  safely  stand  above  110^  of  heat. 

Strencib  ol  Belting.— The  ultimate  tensile  strength  of  belting  does 
not  geuerally  enter  as  a  factor  in  calculations  of  power  transmission. 

The  strength  of  the  solid  leather  in  belts  is  from  1:2000  to  fiOOO  lbs.  per  square 
inch;  at  the  lacings,  even  if  well  put  together,  only  about  1000  to  150D.  If 
riveted,  the  joint  should  have  half  the  streneth  of  the  solid  belt.  The  work- 
ing strain  on  the  driving  side  is  generally  taken  at  not  over  one  third  of  ihe 
strength  of  the  lacing,  or  from  one  eighth  to  one  sixteenth  of  the  strength  ' 
of  the  solid  belt.  Dr.  Hartig  found  that  the  tension  in  practice  varied  from 
30  to  53'i  lbs.  per  square  inch,  averaging  873  lbs. 

Adliealon  Independent  of  IMameter.  (Schulta  Belting  Ck>.)— 
1.  The  adhesion  of  the  belt  to  the  pulley  is  the  same — the  arc  or  number  ot 
degrees  of  contact,  aggregate  tension  or  weight  being  the  same— without 
reference  to  width  of  belt  or  diameter  of  pulley. 

2.  A  belt  will  slip  just  as  readily  on  a  pulley  four  feet  in  diameter  as  it  will 
on  a  pulley  two  feet  In  diameter,  provided  the  conditions  of  the  faces  of  the 
puUevH,  the  arc  of  contact,  the  tension,  and  the  number  of  feet  the  belt 
travels  per  minute  are  the  same  in  both  cases. 

8.  A  belt  of  a  given  width,  and  making  any  given  number  of  feet  per 
minute,  will  transmit  as  much  power  running  on  pulleys  two  feet  in  diam 
eter  as  it  will  on  pulleys  four  feet  in  diameter,  provided  the  arc  of  contacL 
tension,  and  conditions  of  pulley  faces  are  the  same  in  both  cases. 

4.  To  obtain  a  greater  amount  of  power  from  belts  the  pulleys  may  he 
covered  with  leather;  this  will  allow  the  belts  to  run  very  slack  and  give  SSii 
more  durability. 

Endless  Belts.— If  the  belts  are  to  be  endless,  they  should  be  put  on 
and  drawn  together  by  '*  belt  clamps  **  made  for  the  purpose.  If  the  oelt  is 
made  endless  at  the  belt  factory,  it  should  never  be  run  on  to  the  pulleys,  le^c 
the  irregular  strain  spring  the  belt.  Lift  out  one  shaft,  place  the  belt  on  the 
pulleys,  and  force  the  shaft  back  into  place. 

Belt  Data*— A  fly-wheel  at  the  Amoskeag  Mfg.  Co.,  Manchester,  N.  H., 
80  feet  diameter,  110  inches  face,  running  61  revolutions  per  minute,  carried 
two  heavy  double-leather  belts  40  inches  wide  each,  and  one  84  inches  wide. 
The  engine  indicated  1950  H.P.,  of  which  probably  1850  H.P.  was  transmitted 
by  the  belts.  The  belts  were  considered  to  be  heavily  loaded,  but  not  over- 
taxed. 

^^^^1^^^^^^  =  888  feet  per  minute  for  1  H.P.  per  inch  of  width. 

Samuel  Webber  {Am.  Mach  ,  Feb.  22,  1804)  reports  a  case  of  a  belt  90 
inches  wide,  %  inch  thick,  running  for  six  years  at  a  velocity  of  8900  feet  per 


TOOTHED-WHEEL  GEARIKG.  887 

mtouto,  on  to  a  pulley  5  feet  d lameter,  and  transmitting  550  H.P.  This  gives 
a  velocity  of  210  feet  per  minute  for  1  H.P.  per  Inch  of  width.  By  Mr.  Nagle'a 
table  of  riveted  beltj<  this  belt  would  be  designed  for  338  H.P.  By  Mr.  Taylor's 
rule  it  would  be  used  to  transmit  only  1*^8  H.P. 

The  above  may  be  taken  as  exam  pies  of  what  a  belt  may  be  made  to  do,  but 
they  sliould  not  be  used  as  precedents  in  designing.  It  is  not  stated  how  much 
power  was  lost  by  the  journal  friction  due  to  over-tightening  of  these  belts. 

Belt  DreMincs.— We  advise  that  no  belt  dressing  should  be  used  ex- 
cept when  the  belt  becomes  dry  and  huskv,  and  in  such  instances  we  recom- 
mend the  use  of  Post's  Belt  Dressing.  Where  this  i&not  used  beef  tallow  at 
blood- warm  temperature  should  be  applied  and  then  dried  in  either  by  ar- 
tiflcial  heat  or  the  sun.  The  oil  of  the  tallow  passes  into  the  leather,  serving 
to  soften  it,  and  the  stearine  is  left  on  the  outside  to  flll  the  pores  and  leave 
a  smooth  surface.  The  addition  of  beeswax  to  the  tallow  will  be  of  some 
service  if  the  belts  are  used  in  wet  or  damp  places.  Belts  which  have  be- 
come dry  and  hard  should  have  an  application  of  Post's  belt  oil  or  neats's- 
foot  oil  of  the  purettt  quality.  Our  experience  convinces  us  that  resin  should 
never  be  used  on  leather  belting  in  any  form.    (Faverweather  &  Ladew.) 

Belts  should  not  be  soaked  in  water  before  oiling,  and  penetrating  oils 
should  but  seldom  be  used,  except  occasionally  when  a  belt  gets  very  dry 
and  husky  from  neglect.  It  may  then  be  moistened  a  little,  andihave  neat's- 
foot  oil  applied.  Frequent  applications  of  such  oils  to  a  new  belt  render  the 
leather  soft  and  flabby,  thus  causing  it  to  stretch,  and  making  it  liable  to 
run  out  of  line.  A  composition  of  tallow  and  oil,  with  a  little  resin  or  bees- 
wax, is  better  to  use.  Prepared  castor-oil  dressing  is  good,  and  may  i>e 
applied  with  a  brush  or  rag  while  the  belt  is  running.    (Alexander  Bros.) 

Cement  fbr  Clotlt  or  lieatber.  (Molesworth.)— 10  parts  gutta- 
percha, 4  india-rubber,  )i  pitch,  1  shellac,  2  linseed-oil,  cut  amaU,  melted  to- 
gether and  well  mixed. 

Bobber  Beltiufl:.— The  advantages  claimed  for  rubber  belting  are 
perfect  uniformity  in  width  and  thickness;  it  will  endure  a  great  degree  of 
heat  and  cold  without  injury;  it  is  also  specially  adapted  for  use  in  damp  or 
wet  places,  or  where  exposed  to  the  action  of  steam;  it  is  very  durable,  and 
has  great  tensile  strength,  and  when  adjusted  for  service  it  has  the  most  per- 
fect liold  on  the  pulleys,  hence  Is  less  liable  to  slip  than  leather. 

Never  uae  animal  oU  or  grease  on  rubber  beUe^  as  it  will  greatly  injure  and 
soon  destroy  them. 

Rubber  belts  will  be  improved,  and  their  durability  increased,  by  putting 
on  with  a  painter's  brush,  and  letting  it  dry,  a  composition  made  of  equal 
parts  of  red  lead,  black  lead,  French  yellow,  and  litharge,  mixed  with  boiled 
linseed-oil  and  japan  enough  to  make  it  dry  quickly.  The  effect  of  this  « ill 
be  to  produce  a  nnely  polished  surface.  If,  from  dust  or  oiher  cause,  the 
belt  should  slip,  it  should  be  lightly  moistened  on  the  side  next  the  pulley 
with  boiled  linseed-oil.   (From  circulars  of  manufacturers.) 


GEABING. 

TOOTHBD-WHKKIi  OBABING. 

Pttcli*  PIteli-elrelej  ete«— If  two  cylinders  with  parallel  axes  are 
pressed  together  and  one  of^them  is  rotated  on  its  axis,  it  will  drive  the  other 
by  means  of  the  friction  between  the  surfaces.  The  cylinders  may  be  con- 
sidered as  a  pair  of  spur-wheels  with  an  infinite  numl>er  of  very  small  teeth. 
If  actual  teeui  are  formed  upon  the  cvlinders,  making  alternate  elevations 
and  depressions  in  the  cylindrical  surntces,  the  distance  between  the  sxes 
ramaining  the  same,  we  have  a  pair  of  gear-wheels  which  will  drive  one  sn- 
other  by  pressure  upon  the  faces  of  the  teeth,  if  the  teeth  are  properly 
shaped.  In  making  the  teeth  the  cylindrical  surface  may  entirelv  diMip- 
pear,  but  the  position  it  occupied  may  still  be  considered  as  a  cylindrical 
surface,  which  is  called  the  '*  pitch -surf ace,"  and  its  trace  on  the  end  of  the 
wheel,  or  on  a  plane  cutting  the  wheel  at  right  angles  to  its  axis,  is  called 
the  *'  pitch-circle  "  or  **  pitch-line.'*  The  diameter  of  this  circle  is  called  the 
pitch -diameter,  and  the  distance  from  the  face  of  one  tooth  to  the  corre- 
sponding face  of  the  next  tooth  on  the  same  wheel,  measured  on  an  src  of 
the  pltcn-clrcle,  Is  called  the  "pitch  of  the  tooth,''  or  the  circular  pitch. 

If  two  wheels  having  teeth  of  the  same  pitch  are  geared  together  »>  that 
their  pitch-circles  touch,  it  is  a  property  of  the  pitch-circles  that  their  dian^ 
eters  are  proportional  to  the  number  of  teeth  in  the  wheels,  and  vice  versa/ 


OBAEIKO. 


tbns.  If  one  wheel  Is  twice  the  diameter  (meatured  on  the  pltcb«lrcle)  of  the 
other.  It  has  twice  as  many  teeth.  If  the  teeth  are  properly  ehapied  the 
linear  Telocity  of  the  two  wheels  are  equal,  and  the  angular  velocities,  or 
speeds  of  rotation,  are  inversely  proportional  to  the  number  of  teeth  and  to 
toe  diameter.  Thus  the  wheel  that  has  twice  as  many  teeth  as  the  other 
will  revolve  Just  half  as  many  times  in  a  minute. 

The  "  pitch,"  or  distance  measured  on  an  arc  of  the  pitch-circle  from  the 
face  of  one  tooth  to  the  face  of  the  next,  consists  of  two  parts— the  **  thlcic- 
iiess ''  of  the  tooth  and  the  **  space  "  between  it  and  the  next  tooth.  The 
space  is  lamr  than  the  ihtckness  by  a  small  amount  called  the  "  back- 
lash," which  is  allowed  for  imperfections  of  workmanship.  In  flnely  cut 
gears  the  hacklimh  may  be  almost  nothing. 

^/  The  length  of  a  tooth  in  the  dlrec- 

J{*  j^ ^->^^.^ ^ — n    /      tion  of  the  radius  of  the  wheel  Is 

called  the  "depth,"  and  this  Is  di- 
vided into  two  parts:  First,  the 
**  addendum,"  the  height  of  the  tooth 
Above  the  pitch-line;  second,  t^ 
**ded«ndnm/*  the  depth  below  the 

etch  line,  which  Is  an  amount  equal 
the  addendum  of  the  mating  gear. 
Ihe  depth  of  the  space  Is  usually 
o^ven  a  little  ^  clearance "  to  allow 
»r   inaccuracies   of  workmanship, 
especially  in  cast  gears. 
Referring  to  Fig.  158,  p2,  pi  arv  the 

gtch-lines,  aX  the  addendum- line,  W 
e  root-line  or  dedendum-Une,  c2 
'*"•  "^  the  clearance-line,  and  6  the  back- 

lash.  The  addendum  and  dedendom  are  usually  made  equal  to  each  other. 
-..       a     .    ij  I.  No.  of  teeth  8.1416 

Diametral  pitch  =  -  -  - 


Circular  pitch  = 


diam.  of  pitch-circle  in  inches 
diam.x  8.1416  8.1416 


circular  pitch' 


diametral  pitch* 
Some  writers  use  the  term   diametral  pitch  to  mean  j 


No.  of  teeth 

dIam.       __ 
'  No.  of  teeth  ~ 
'^o  ?r.V — f  but  the  first  definition  Is  the  more  common  and  the  more 

8.1410 

eonvenient.    A  wheel  of  13  In.  diam.  at  the  pitch-circle,  with  48  teeth  is  48/ld 
=s  4  diametral  pitch,  or  simply  4  pitch,   The  circular  pitch  of  the  oame 

.      -  ,    12  X  8.1416         __      .  8.1416 
wheel  is -^ =  .7854,  or  — —  s 


.7854  in. 


Relat 

Ion  Of 

Diame- 

piamet 

Circular 

ral  Co  € 

Circular 

Ircolar  PlCcb. 

Diam  3- 

Circular 

Diame- 

Circular 

Diame- 

tral 
Pitch. 

Pitch. 

tral 
Pitch. 

Pitch. 

Pitch. 

tral 
Pitch. 

Pilch. 

tral 
Pltcb. 

1 

8.142  in. 

11 

.286  in. 

8 

1.047 

15/16 

8.831 

m 

2.004 

12 

.262 

^ 

1.267 

1«^6 

8.600 

2 

1.671 

14 

.224 

sr 

1.571 

8.867 

2M 

1.896 

16 

.196 

Vi 

1.6W 

1?^16 

4.180 

si 

1.257 

18 

.175 

12 

1.795 

4.570 

tl 

1.142 

SO 

.167 

1^ 

1.988 

1^16 

6.087 

8 

1.047 

22 

.148 

IH 

8.094 

5.686 

8H 

.606 

24 

.181 

1^/16 

2.185 

Vi^ 

6.288 

4 

.796 

26 

.121 

^n 

2.285 

7.181 

6 

.628 

28 

.112 

1  6/16 

2.894 

5/16 

8.878 

6 

.524 

80 

.105 

1  8/16 

2.513 

10.068 

7 

.449 

82 

.098 

2.646 

^. 

12.566 

8 

.898 

86 

.087 

1« 

2.793 

16.765 

9 

.849 

40 
i      48 

.079 

1  1/16 

2.957 

% 

85.138 

10 

.314 

.065 

1 

8.142 

1/16 

50.266 

ai..^^ 

nl»....1.M  ^t 

..u      cli 

am.  X  3.1 

418     ^..», 

circ.  I 

Mtch  X  N 

0.  of  teeth 

Since  circular  pitch  = 


No.  of  teeth    '    — —  -  8.1416 

which  always  brings  out  the  diameter  as  a  number  with  an  inconvenient 


TOOTHED-WHKEL  GEARING. 


889 


fraction  if  the  pitch  is  In  even  inches  or  simple  fractions  of  an  inch.  By  the 
diametral-pitch  system  this  inconvenience  Is  avoided.  The  diameter  may 
be  in  even  inches  or  convenient  fractions,  and  the  number  of  teetli  is  usually 
an  even  multiple  of  the  number  of  inches  in  the  diameter. 
Diameter  of  Plteh-llne  of  WlieelM  f^ona  10  to  lOO  Teetb 
of  1  In.  Circular  Plteli. 


, 

^ 

.•       -       1 

"  " 

, 

1 

o  'f, 

|d 

2| 

^a 

»l 

¥ 

fl 

1^ 

.J3 

"1 

Diam. 
in. 

Teeth 

§i 

10 

3.183 

26 

8.276 

41 

18.051 

56 

17.825 

71 

22.600 

86 

27.875 

11 

8.501 

27 

8.594 

42 

13.369 

57 

18.144 

72 

22.918 

87 

27.699 

Vi 

8.820 

28 

8.918 

43 

18.687 

58 

18.462 

73 

23.286 

88 

28.011 

13 

4.138 

29 

9.331 

44 

14.006 

59 

18  781 

74 

23.565 

89 

86.829 

14 

4.466 

30 

9.549 

45 

14.824 

60 

19.099 

75 

28.878 

90 

28.648 

15 

4.775 

31 

9.868 

46  1  14.642 

61 

19.417 

76 

24.192 

91 

2K  966 

n 

6.098 

32 

10.186 

47     14.961 

62 

19.735 

77 

24.610 

92 

29.285 

17 

5.411 

33 

10.504 

48 

15.279 

63 

20  054 

78 

24.828 

98 

29.608 

18 

5.780 

34 

10.828 

49 

15.597 

64 

20.372 

79 

25.146 

W 

89.921 

I'J 

6.048 

35 

11.141 

50 

15.915 

65 

20.690 

80 

25.465 

95 

30.239 

SO 

6.866 

86 

11.459 

51 

16.284 

66 

21  008 

81 

25.783 

96 

30.r>.'i8 

21 

6.6R5 

37 

11.777 

52 

16.552 

67 

21.327 

82 

26.101 

97 

30.876 

;S 

7.003 

38 

12.096 

58 

16.870 

68 

21.645 

83 

26.419 

98 

81.194 

23 

7.881 

39 

12  414 

54 

17.189 

69 

21.963 

84 

26.738 

99 

31.512 

24 

7.689 

40 

12.732 

55 

17.607 

70 

22.282 

K) 

27.050 

100 

31.831 

25 

7.958 

For  diameter  of  wheels  of  any  other  pitch  than  1  in.,  multiply  the  flg^ures 
in  the  table  by  the  pitch.  Given  the  diameter  and  the  pitch,  to  find  the  num- 
ber of  teeth.  Diviae  the  diameter  by  the  pitch,  look  in  the  table  under 
diameter  for  the  figure  nearest  to  the  quotient,  and  the  number  of  teeth  will 
be  found  opposite. 

Proportions  of  Teetb.    Circular  Plteli  =  1. 


Depth  of  tooth  above  pitch-line. , 

below  pitch-line. 

Working  depth  of  tooth 

Total  depth  of  tooth , 

Clearance  at  root , 

Thickness  of  tooth 

Width  of  space 

Backlash 

Thickness  of  rim 


.85 
.40 
.70 
.75 
.05 
.45 
.54 
.09 


.80 
.40 
.60 
.70 
.10 
.45 
.55 
.10 


3. 


.37 
.43 
.78 
.80 
.07 
.47 
.53 
.06 
.47 


5. 


.33 

!66 
.75 

!45 
.55 
.10 
.45 


.30 
.40 


.175 
.525 
.05 
.70 


.30 
.35 

.65 

!485 
.515 
.03 
65 


Depth  of  tooth  above  pitch-line... 
*♦      "     below  pitch-line.. 

Working  depth  of  tooth 

Total  depth  of  tooth 

Clearance  at  root 

Thickness  of  tooth 


Width  of  space 
Backlash     


.25  to  .33 
.85  to  .42 


.6   to  .75 


.48  to  .485 

.52  to  .615 
.04  to  .03 


.80 

.35+.  08" 


65-f.08'' 


.48-. 03'^ 

.52+.03" 

.014-. 06" 


.318 
.369 
.637 
.087 
.04  to  .05 

.48  to  .5] 

.52  to  .5 1 
.0   to  .04 


10.» 

iH-P 

1.157-:-/' 

2-t-P 

2.157"^-P 

.157-4-P 

1.51-i-Pto 

1.57-4-P 

1.57 -hP  to 

1.63 -*-P 

0  to  0  6-i-P 

•  In  terms  of  diametral  pitch. 

AoTHORm«8.— 1.  Sir  Wm.  Fairbairn.  2,  8.  Clark,  R.  T.  D.;  "used  by  en- 
gineers in  good  practice."*  4.  Molesworth.  5,  6.  Coleman  Sellers :  5  for 
ca.*<t.  6  for  cut  wheels.  7,8.  Unwin.  9, 10.  Leading  American  manufacturers 
of  rut  (fearK. 

Tbe  Cbordal  Pltcli  (erroneously  called  "true  pitch*'  by  some 
authors)  Is  the  length  of  a  straight  line  or  chord  drawn  from  centre  to 
centre  of  two  adjacent  teeth.    Tbe  term  Is  now  but  little  used. 


890 


GEARING. 


Chordal  plUsh  =  diam.  of  pltch-clrele  X  8<ne  of  yp  ^f  tg^^h'     Chordal 

flitch  of  a  wheel  of  10  In.  pitch  diameter  and  10  teeth,  10  x  sin  18*  =  8.0903 
n.  Circular  pitch  of  same  wheel  =  8.1416.  Chordal  pitch  is  used  with  chaiti 
or  sprocket  wheels,  to  conform  to  the  pitch  of  the  chain. 

Fornmlv  for  Detenulnliiff  tbe  IMmonslons  of  Small  G««rs. 

(Brown  &  Sharpe  Mfg.  Co.) 
P  =  diametral  pitch,  or  the  number  of  teeth  to  one  inch  of  diameter  of 
pitch- circle; 


IT: 
D: 

N: 
V: 

d'  : 

d. 
n  : 


;  diameter  of  pitch  circle. 

:  whole  diameter 

number  of  teeth 

:  velocity 


:  diameter  of  pitch-circle. 

:  whole  diameter 

:  number  of  teeth 

;  velocity , 


^fS!^. 


Smaller 
Wheel. 


These  wbeelf 

run 

together. 


a  =  distance  between  the  centres  of  the  two  wheels; 

6  =  number  of  teeth  in  both  wheels; 

t  =  thickness  of  tooth  or  cutter  on  pitch-circle; 

n  •=  addendum; 
Z>"=  working  depth  of  tooth; 

/  =  amount  added  to  depth  of  tooth  for  rounding  the  comers  and  for 

clearance; 
j)"4-f  =  whole  depth  of  tooth; 

«  =  8.1416. 

p*  =  circular  pitch,  or  the  distance  from  the  centre  of  one  tooth  to  the 
centre  of  the  next  measured  on  the  pitch-circle. 

FormulsB  for  a  single  wheel: 


P=s 


JV-f  2. 


P   = 


P  = 


P'' 


ly  ^ 


DXJL. 

N  +  2  * 

2V 
P' 

~P~' 


D"  =  -p=2.;    «  =  ^: 


N   -  Piy; 
N  =  PD-  2; 
t 

io' 

1.57 
'   P 


=  .S188P'; 
D 


f  : 


JV-f  2' 
•+/  =  Xl+^)=.a685P 


Formulas  for  a  pair  of  wheels: 


br 


Ns 


■.9aPi 
no 

NV 


bv 


v+V* 
bV 


Tar 


piyy 

V 

pjyy. 

n     ' 

NV 

'    »  • 

nv 

"IT' 

2a  V    , 


- — b — • 

"        6        * 

6  . 
'  8P'* 


The  following  proportions  of  gear  wheels  are  recommended  by  Prof.  Cole- 
man Sellers.    {Stevent  Indicator,  April,  1882.) 


TOOTHED-WHEEL  GEARIKO. 


891 


Proportion*  of  GeAr-w^beel*. 


Circular 
Pitch. 

Outside  of 

Pitcb-Une. 

PX.8 

Inside  of  Pitch-Hne. 

Width  of  Space. 

h 
1^ 

For  Cast  or 
Cut  Bevels 
or  for  Cast 

Spurs. 

JPX.4 

For  Cut 
Spurs. 
PX  .85 

For  Cost 
Spurs  or 
Devels. 

For  Cut 

Bevels  or 

Spurs. 

Q 

PX.525 

PX.M 

.»18 

.076 

.100 

.088 

.181 

.128 

12 

.079 

.105 

.092 

.187 

.184 

10 

.81416 

.004 

.126 

.11 

.166 

.16 

.^ 

.118 

.150 

.181 

.197 

.191 

8 

.118 

.157 

.187 

.206 

.2 

7 

.4477 

.184 

.179 

.157 

.286 

.228 

.^ 

.16 

.20 

.176 

.268 

.256 

6 

.157 

.209 

.188 

.275 

.267 

9/16 

.169 

.225 

.197 

.295 

.287 

.^ 

.188 

.25 

.219 

.828 

.819 

5 

.188 

.251 

.22 

.88 

.82 

^ 

.226 

.8 

.268 

.894 

.388 

4 

.7864 

.286 

.814 

.275 

.412 

.401 

^ 

.268 

.85 

.807 

.459 

.446 

1 

.8 

.4 

.85 

.525 

.61 

8 

1.0472 

.814 

.419 

.864 

.55 

.581 

u^ 

.888 

.45 

.894 

.591 

.574 

294 

.848 

.457 

.40 

.6 

.588 

..^. 

.876 

.6 

.438 

.656 

.638 

2^ 

.877 

.508 

.44 

.66 

.641 

I9i 

.418 

.55 

.481 

.722 

.701 

uJHb 

.45 

.6 

.525 

.78J 

.765 

2 

.471 

.628 

.66 

.825 

.801 

1% 

525 

.7 

.618 

.919 

.898 

2^* 

.6 

.8 

.7 

1.06 

1.02 

^H 

2.0944 

.628 

.888 

.788 

1.1 

1.068 

2^ 

.676 

.9 

.7«8 

l.lGl 

1.148 

2L , 

.75 

1.0 

.875 

1.318 

•J. 273 

^ 

.825 

1.1 

.968 

1.446 

1.408 

8 

.9 

1.2 

1.05 

1.575 

1.58 

1 

8.1416 

.942 

1  257 

1.1 

1.649 

1.602 

'^ 

.975 

1.8 

1.138 

1.706 

1  657 

1.06 

1.4 

1.225 

1.888 

1.78B 

Thickuess  of  rim  below  root  =  depth  of  tooth. 

"Wtdtli  of  Teetb.— The  width  of  the  faces  of  teeth  is  Kenerallj  made 
from  ;;  lo  3  tiuieu  the  circular  pilch  —  from  6.28  to  9.43  divided  by  the  diam- 
etral pitch.    There  is  no  standard  rule  fur  width. 

TliH  following  sizes  are  given  in  a  stock  list  of  cut  gears  in  "  Grant's 
Qears: " 

Diameter  pitch 8  4  6  8  12  16 

Face,  inches 8  and  4    3^    1?^  and  2    1)4  and  1^   9i  and  1   H  and  ^ 

The  Walker  Company  give: 
Circular  pitch,  In..      H       %       H       %        1     lU     2     2U      3     4      5      6 
Face.ln... 1^      3^      ^H       SJ       2«    4>5     6     7^      9    U    16    20 

Roles  for  Calcnlatins  tlie  Speed  of  Geam  and  Paiieya.— 

The  r**laiion8  of  the  size  and  speed  of  driving  and  driven  gear  wheels  are 
the  name  as  those  of  belt  pulleys.  In  calculating  for  gears,  multiply  or 
divlile  by  the  •diameter  of  the  pitch-circle  or  by  the  number  of  teeth,  as 
may  be  required.  Iti  calculating  for  pulleys,  multiply  or  divide  by  their 
diameter  in  inches. 

If  /)  =  diam.  of  driving  wheel,  d  =  diam.  of  driven,  R  =  revolutions  per 
minute  of  driver,  r  =  revs,  per  min.  of  driven. 

Rz=rd-t-  D;    r  =  RD-*-d;    D  =  dr -t-  R;    d  =  DR -*■  r. 

If  y  r=  number  of  teeth  of  driver  and  n  =  numt)er  of  teeth  of  driven, 
A"  =  nr  -f-  R\    n  =  NR  -*- r;    R  =  rn  -*-  N\    r  =  RN  -+-  n. 


892  GEABING. 

To  flod  the  number  of  reToluilons  of  the  last  wheel  at  the  end  of  a  tnun 
of  spiir-whettls,  all  of  which  ai*e  in  a  line  and  mesh  into  one  aDOther,  when 
the  revolutions  of  the  fii'Bt  wheel  and  the  number  of  teeth  or  the  dianifier 
of  the  first  and  last  ure  (pven:  Multiply  the  revolutions  or  the  fina  Mheel  by 
its  number  of  tt^ih  or  its  diameter,  and  divide  the  product  by  the  nuiiib«>r 
of  teeth  or  the  diameter  of  the  last  wheel. 

To  find  the  number  of  teeth  in  each  wheel  for  a  train  of  spur -wheels, 
eacli  to  have  a  i^iven  velocity:  Multiply  the  number  of  revolutioiis  of  tlie 
driving-wheel  by  its  number  of  teeth,  and  divide  the  product  by  the  number 
of  revolutions  each  viheel  is  to  maka 

To  And  tlie  number  of  revolutions  of  the  last  wheel  in  a  train  of  wneels 
and  pinions,  uhen  the  revolutions  of  the  first  or  driver,  and  the  diamt^ter, 
th<i  tfeih,  or  the  circumference  of  all  the  drivers  and  pinions  are  fsivfit: 
Multiply  I  he  diameter,  the  circumference,  or  the  number  of  teeth  of  all  the 
d ri vi 1 1|^- wheels  together,  and  this  continu«^d  product  by  the  number  of  r^Mn 
luliaus  of  the  flrst  wheel,  and  divide  this  product  by  the  continued  product 
of  the  diameter,  the  circumference,  or  the  number  of  teetli  of  all  the  driven 
wheels,  and  the  quotient  will  be  the  number  of  revolutions  of  the  last  whtn*!. 

ExAMPUs— 1.  A  train  of  wheels  consists  of  four  wheels  each  13  in.  ditMiiettr 
of  pitch-circle,  and  three  pinions  4,  4,  and  8  in.  diameter.  The  larice  wher<s 
are  the  drivers,  and  the  first  makes  96  revs,  per  inln.  Required  the  spevtl 
of  the  lust  wheel 


.  ^  .^  « =  1296  rpm. 


4X4X8 

2.  What  is  the  speed  of  the  first  large  wheel  If  the  plnlona  are  tbe  driven, 
the  8-in.  pinion  being  the  first  driver  and  making  86  revs,  per  min.? 

86X8X4X4      ,  ^^      .^ 
l-iX  12X12     =*'T""-  ^**- 

ntlllnic  Cutters  for  Interdtftnceable  Cl«ara«— The  Pratt  & 
Whitney  Co.  make  a  series  of  cutters  for  cutting  epicycloidal  teeth.  Tbe 
number  of  cutters  to  cut  from  a  pinion  of  12  teeth  to  a  rack  is  Ui  for  each 
pilch  coarser  than  10.  The  Brown  A  Sfaarpe  Mfg.  Co.  make  a  similar  serleN 
and  also  a  series  for  Involute  teeth,  in  which  eight  cutters  are  made  for 
each  pitch,  as  follows: 

No 1.  9.  8.  4.  6.  6.  7.  8. 

WUl  cut  from       186  66  85  26  21  17  14  12 

to  Back      134  54  84  25  20  1«  IS 

FORMS  OF  THE  TBVTH. 

In  order  that  the  teeth  of  wheels  and  pinions  may  run  together  amoothly 
and  with  a  constant  relative  velocity,  it  is  necessary  that  their  working 
faces  shall  be  formed  of  certain  curves  called  odontoids.  The  eesentisi 
property  of  these  curves  is  that  when  two  teeth  are  in  contact  the  comnioa 
normal  to  ihe  tooth  curves  at  their  point  of  contact  must  pass  through  the 
pitch-point,  or  point  of  contact  of  the  tw  o  pitch  circles.  Two  such  eurres 
ai-e  in  common  use— the  cvlold  and  the  Involute. 

Tlie  Cycloldal  Tooth.  -  In  Fig.  154  let  PL  and  pi  be  the  pitch-cln*lfs 
of  two  i^ear-vv heels;  6'Cand  yc  are  two  equal  generAilng-cirdes,  whose  radii 
should  be  taken  as  nut  greater  than  one  half  of  the  radius  of  the  amalier 
piich-circle.  If  the  circle  gc  be  rolieil  to  the  left  on  the  larger  pitch*circie 
JHL,  the  point  O  will  describe  an  epicvcloid,  oejgh.  If  the  other  generating- 
ciivle  GCbe  rolleil  to  tlie  right  on  FL,  the  jwliit  O  wL'l  describe  a  bypocy- 
cloid  oabcd.  These  two  curves,  which  are  tangent  at  O.  form  the  two  |iarts 
of  a  tooth  curve  for  a  gear  whose  pitch-circle  is  PL,.  The  upper  part  olt  Is 
called  the  face  and  the  lower  part  od  is  called  the  flank,  If  the  same  circled 
be  rolleil  on  the  other  pitch-circle  jj/,  they  will  describe  the  curve  for  a  tooth 
of  ihe  gear  i>i,  which  will  work  properly  with  the  tooth  on  PL, 

The  cyclofUal  curves  mav  be  drawn  without  actual!}'  rolling  the  generat- 
ing-circle,  as  follows:  On  the  line  PL,  from  O,  step  off  and  mark  equal  dis- 
tant es.  OS  1, 2, 3,  4,  etc.  From  1, 2, 3,  etc.,  draw  rauial  lines  toward  the  centre 
of  PL,  and  from  6.  7,  8,  etc.,  draw  radial  Hues  from  the  same  centre,  hut  be- 
yond  PL.  With  tlie  radius  of  tbe  general! ng-circle.  and  with  centres  snc- 
cessively  placed  on  these  radial  lines,  draw  arcs  of  circles  tangent  to  PL  at 
J  ii  8,  6  7  8,  etc.    With  the  dividers  set  t^  ope  of  the  equal  divisions,  as  Q^, 


FORMS  Of  THE  TEETH. 


893 


step  off  la  and  6e;  step  off  two  such  divisions  on  the  circle  from  8  to  &,  and 
from  7  to/;  three  such  divisions  from  8  to  c,  and  from  Stog;  and  so  on,  thus 
locating  the  several  points  obcdH  and  efgkt  and  throu^  these  points  draw 
the  tooth  curves. 

The  curves  for  the  mating  tooth  on  the  other  wheel  may  be  found  in  like 
manner  by  drawing  arcs  of  the  generatiug-circle  tangent  at  equidistant 
points  on  the  pitch  -  circle  p^ 

The  tooth  curve  of  the  face  oh  is  Ihnited  by  the  addendum-line  r  or  rx, 


Fio.  154.? 


and  that  of  the  flank  on  by  the  root  curve  R  or  Rj.  R  and  r  represent  the 
root  and  addendum  curves  for  a  large  number  of  small  teeth,  and  RiT  the 
like  curves  for  a  small  number  of  large  teeth.  The  form  or  apjpearauce  of 
the  tooth  therefore  varies  according  to  the  number  of  teeth,  wlalle  the  pitch- 
circle  and  the  generating-circle  may  remain  the  same. 

In  the  cycloidal  svstem,  in  order  that  a  set  of  wheels  of  different  diam- 
eters but  equal  pitches  shall  all  correctly  work  together,  it  is  necessary  that 
the  generating-circle  used  for  the  teeth  of  all  the  wheels  shall  be  the  same, 
and  it  should  have  a  diameter  not  greater  than  half  the  diameter  of  the  pitch- 
line  of  the  smallest  wheel  of  the  set.  The  customary  standard  size  of  the 
Senerating-circle  of  the  cycloidal  system  is  one  having  n  diameter  equal  to 
le  radius  of  the  pitch-circle  of  a  wheel  having  12  teeth.  (Some  gear- 
makers  adopt  15  teeth.)  This  circle  gives  a  radial  flank  to  the  teeth  of  a 
wheel  having  12  teeth.  A  pinion  of  10  or  even  a  smaller  number  of  teeth 
can  be  made,  but  in  that  case  the  flanks  will  be  undercut,  and  the  tooth  will 
not  be  as  strong  as  a  tooth  with  radial  flanks.  If  in  any  case  the  describing 
circle  be  half  the  size  of  the  pitch-circle,  the  flanks  will  be  radial;  if  it  be 
less,  they  will  spread  out  toward  the  root  of  the  tooth,  giving  a  stronger 
form;  but  if  greater,  the  flanks  will  curve  in  toward  each  other,  whereby  t^e 
teeth  become  weaker  and  difllcult  to  make. 

In  some  cases  cycloidal  teeth  for  a  pair  of  gears  are  made  with  the  gener- 
ating-circle of  each  gear,  having  a  radius  equal  to  half  the  radius  of  its  pitch- 
circle.  In  this  case  each  of  the  gears  will  have  radial  flanks.  This  method 
makes  a  smooth  working  gear,  but  a  disadvantage  is  that  the  wheels  are 
not  interchangeable  with  other  wheels  of  the  same  pitch  but  different  num- 
bers of  teeth. 


894 


GBARIKl}. 


The  rack  In  the  cydoldal  Bystem  is  equlyalent  to  a  wheel  with  an  fnflnits 
number  of  teeth.  The  pitch  is  equal  to  the  circular  pitch  of  the  matiair 
gear.  Both  faces  and  flaulcs  are  cycloids  formed  by  rolling  the  generating- 
circle  of  the  mating  gear-wheel  on  each  side  of  the  straight  pitch-line  of 
the  rack. 


\ 


\ 


Fio.  165. 

Another  method  of  drawing  the  cycloldal  curves  is  shown  In  Fig.  165.  It 
is  known  as  the  method  of  tangent  arcA.  The  generating-circles,  a»  before, 
are  drawn  with  equal  radii,  the  length  of  the  radius  being  lem  than  half  the 
radius  ot  pi,  the  smaller  pitch-circle.  Equal  divisions  1,  2.  3,  4.  etc.,  are 
marked  off  on  the  pitch  circles  and  diviMions  of  the  same  length  KtepptKl  off 
on  one  of  the  generating^! rcles.  as  oaiic,  etc.  From  the  points  1, 2.  8, 4,  5  un 
the  line  po,  with  radii  successively  equal  to  the  chord  distances  ixi^  ob,  oc. 
ixi^  oe,  draw  the  Ave  small  arcs  J^.  A  line  drawn  through  the  outer  edges  of 
these  small  arcs,  tangent  to  them  all,  will  be  the  hypocycloidal  curve  for  the 
flank  of  a  tooth  below  the  pitch-line  pi.  From  the  points  1, 2,  8,  etc.,  on  the 
line  ol,  with  radii  as  before,  draw  the  small  arcs  G.  A  line  tangent  to  thi*»^ 
arcs  will  be  the  epicycloid  for  the  face  of  the  same  tooth  for  which  the  flank 
curve  has  already  been  drawn.  In  the  same  way,  from  centres  on  the  line 
Jt*a.  and  oL,  with  the  same  radii,  the  tangent  arcs  H  and  K  mnj  be  drawn, 
which  will  give  the  tooth  for  the  gear  whose  pitch-circle  ij  PL. 

If  the  generating-circle  had  a  radius  Just  one  half  of  the  radius  of  pi.  the 
bypocyclold  F  \.orld  be  a  straight  line,  and  the  flank  of  the  tootli  would 
have  been  radial. 

Tlie  Involute  Tootli.— Id  drawing  the  involute  tooth  curve,  the 
angle  of  obliquity,  or  the  angle  whic!i  a  common  tangent  to  the  teeth,  when 
they  are  in  contact  at  the  pitch-point,  makej  with  a  line  Joining  the  cenrres 
of  the  wheels,  is  flrst  arbitrarily  determloed.  It  is  customary  to  take  it  at  ih". 
The  pitoh-lines  pi  and  PL  being  drawn  in  contact  at  O,  the  line  of  obliquity 
A  Bis  drawn  through  O  normal  to  a  common  tanrirent  to  the  tooth  curv^.  or 
at  the  given  angle  of  obliquity  to  a  common  tangent  to  the  pitch-cirrlea.    In 


FOUMS   OP  THE  TEETH. 


895 


the  cut  the  angle  is  20*.  From  th6  centres  of  the  pitdi-circles  draw  circles  e 
and  d  tangent  to  the  line  AB.  These  circles  are  called  base-lines  or  base- 
circles*  from  which  the  involutes  F  and  IT  are  drawn.  By  laying  off  conven- 
i«*nt  distances,  0,  1,2,  8,  which  should  each  be  less  than  1/10  of  the  diameter 
of  the  base-circle,  stnall  arcs  can  be  drawn  with  successively  increasing 
radii,  which  will  form  the  involute.    The  involute  extends  from  the  points  P 


Flo.  106. 

and  K  down  to  their  renpectlTe  base-circles,  where  a  tangent  to  the  invo- 
lute t>ecome8  a  radius  of  the  circle,  and  the  remainders  of  the  tooth  curves, 
as  G  and  //,  are  radial  straiKht  lines. 

In  the  involute  syHtem  the  customary  standard  form  of  tooth  is  one 
having  an  angle  of  obliquity  of  15^  (Brown  and  Sharpe  use  14^<*),  an  adden- 
diim  of  about  one  third  the  circular  pitch,  and  a  clearance  of  about  one 
eighth  of  the  addendum.  In  this  system  the  smallest  gear  of  a  set  has  12 
teeth,  this  being  the  smallest  number  of  teeth  that  will  gear  together  when 
made  with  this  angle  of  obliquitv.  In  gears  with  less  than  30  teeth  the 
points  of  the  teeth  nmst  be  slightly  rounded  over  to  avoid  interference  (see 
Grant's  Teeth  of  Gears).  All  involute  teeth  of  the  same  pitch  and  with  the 
same  angle  of  obliquitv  work  smoothly  together.  The  rack  to  gear  with  an 
involute-toothed  wneel  has  straight  faces  on  its  teeth,  which  make  an  angle 
with  the  middle  line  of  the  tooth  equal  to  the  angle  of  obliquity,  or  in  the 
standard  form  the  faces  are  inclined  at  an  angle  of  30^  with  each  other. 

To  draw  the  tteth  of  a  rack  which  is  to  gear  with  an  involute  wheel  (Fig. 
157).~Lec  AB  be  the  pitch-line  of  the  rack  and  AI=ir=ihe  pitch.  Through 


Fio.  157. 


the  pitch-point /draw  ^F at  tlie  given  angle  of  obliquity.  Draw  >4^ and 
I'F  perpendicular  to  EF.  Through  E  and  F  draw  lines  EGG'  and  FH  par- 
allel to  the  pitch-line.  EGO'  will  be  the  addendum-line  and  i/A^  the  flank- 
line.  From  /draw  JK perpendicular  to  AB  eaual  lo  the  greatest  addendum 
in  the  set  of  wheels  of  the  given  pilch  and  obliquity  plus  an  allowance  for 
clearance  equal  to  ^  of  the  addendum.  Through  K,  parallel  to  AB^  draw 
the  clearance-line.  The  fronts  of  the  teeth  are  planes  perpendicular  to  EF, 
and  the  backs  are  planes  inclined  at  the  same  angle  to  ^^  in  the  contrary- 
direction.  The  outer  half  of  the  working  face  ^£niay  be  slightly  curved. 
Mr.  Grant  makes  it  a  circular  arc  drawn  from  a  centre  on  the  pitch-line 


896 


GEARtKG. 


with  a  radius  a  2..  inches  divided  by  the  diametral  pitch,  or  .07  fa.  X  ci^ 

oular  pitch. 
To  Draw  an  Angle  of  15*  without  uging  a  Protractor.—Yrom  C,  on  tha 

line  AC,  with  radius  AC,  draw 
an  arc  AB,  and  from  ^,  with 
the  same  rekdius,  cut  the  arc  at 
B.  Bisect  the  arc  BA  by  draw. 
log  small  arcs  at  D  from  A  and  B 
as  centres,  with  the  same  radius, 
which  must  be  greater  than  ow> 
half  of  AB.  Join  DC,  cutting  BA 
at  E.  The  angle  ECA  is  30*.  Bi- 
sect the  arc  AE  in  like  manner, 
and  the  angle  FCA  will  be  15". 

A  property  of  inrolute-toothed 
wheels  is  that  the  distance  between 
the  axes  of  a  pair  of  gears  may  be 
altered  to  a  considerable  extent 
without  interfering  with  their  ac- 
tion. The  backlash  is  therefore 
variable  at  will,  and  may  be  a<t- 


Fio,  loa 


Justed  by  moving  the  wheels  farther  from  or  nearer  to  each  other,  and  roar 
thus  be  adjusted  so  aa  to  be  no  greater  than  is  necessary  to  prevent  jam- 
ming of  the  teeth. 

Tlie  relative  merits  of  cycloldal  and  involute-shaped  teeth  are  still  a  sub* 
ject  of  dispute,  but  there  is  an  increasing  tendency  to  adopt  the  involoie 
tooth  for  aJl  purposes. 

Clark  (R.  T.  D.,  p.  72M)  says :  Involute  teeth  have  the  disadvantage  of 
being  too  much  inclined  to  the  rctdial  line,  by  which  an  undue  pressure  is 
exerted  on  the  bearings. 


Unwin  (Elements  of  Machine  Design,  6th  ed.,  p.  865)  says :  The  obliquity 
of  action  is  ordinarily  alleged  as  a  serious  objection  to  Involute  wheels.    *~~ 


Its 


importance  has  perhaps  been  overrated. 

George  B.  Qrant  (Am.  Mach,,  Dec.  26, 1885)  says : 

1.  The  work  done  by  the  friction  of  an  involute  tooth  is  always  less  than 
the  same  work  for  any  possible  epicycloldal  tooth. 

S.  With  respect  to  work  done  oy  friction,  a  change  of  the  base  from  a 
gear  of  U  teetn  to  one  of  15  teeth  makes  an  improvement  for  the  epicycloid 
of  less  than  one  half  of  one  per  cent. 

3.  For  the  IS-tooth  svstem  the  involute  has  an  advantage  of  1  1/6  per 
cent,  and  for  the  15-tooth  system  an  advantage  of  9i  per  cent 

4.  That  a  maximum  improvement  of  about  one  p€r  cent  can  be  accom- 
plished by  the  adoption  of  any  possible  non -interchangeable  radial  flank 
tooth  in  preference  to  the  l:2-tootn  interchangeable  system. 

5.  That  for  gears  of  yerv  few  teeth  the  involute  has  a  decided  advantage. 

6.  That  the  common  opinion  among  millwrights  and  the  mechanical  1 4ib- 
lie  in  general  in  favor  of  the  epicycloid  is  a  prejudice  that  is  founded  oa 
long-continued  custom,  and  not  on  an  intimate  knowledge  of  the  propertiet 
of  that  curve. 

Wilfred  Lewis  (Proc.  Engrs.  Club  of  Phila.,  vol.  x..  1803)  says  a  strong 
reaction  In  favor  of  the  involute  system  is  in  progress,  and  he  believes  thai 
an  involute  tooth  of  22U**  obliquity  will  finally  supplant  all  other  forms. 

Approximation  By  Olrcnlar  Arcs.— Having  found  the  form  o! 
the  actual  tooth-curve  on  the  drawing-board,  circular  arcs  maybe  found  b) 
trial  which  will  give  approximations  to  the  true  curves.  :snd  these  may  tM 

E 


Fie.  1681 


FORMS  OF  THE  TEETH. 


897 


ned  tn  completing  the  drawing  and  the  pattern  of  the  gear-wheels.  The 
■oot  of  the  curve  is  connected  to  the  clearance  by  a  flllet,  which  should  be 
i&  la.rgn  aspossible  to  give  increased  strength  to  the  tooth,  provided  it  ia  doe 
arsce  enough  to  cause  interference. 

Molesworth  eives  the  following  method  of  conatruction  by  circular  arcs : 

From  the  raaial  line  at  the  edge  of  the  tooth  on  the  pitch-line,  lay  oft  the 
ine  UK  At  an  angle  of  75°  with  the  radial  line;  on  this  line  will  be  the  cen- 
tres of  the  root  AB  and  the  point  EF.  The  lines  struck  from  these  centres 
ire  shown  in  thick  lines.  Circles  drawn  through  centres  thus  fotmd  will 
^ive  the  lines  in  wliioh  the  remaining  centres  will  be.  The  radius  DA  for 
linking  the  root  AB  i»  =  pitch  +  the  thickness  of  the  tooth.  The  radius 
JE  for  striking  the  point  of  the  tooth  EF  =  the  pitch. 

George  B.  Grant  says :  It  is  sometimes  attempted  to  construct  the  curve 
)y  some  handy  method  or  empirical  rule,  but  such  methods  are  generally 
ikorrhless. 

Stepped  Creara*— Two  gears  of  the  same  pitch  and  diameter  mounted 
;ide  L»y  »ide  on  the  same  shaft  will  act  as  a  single  gear.  If  one  gear  is  keyed 
>D  tlie  shaft  so  that  the  teeth  of  the  two  wheels  are  not  in  Une,  but  the 
«eih  of  one  wheel  slightly  in  advance  of  the  other,  the  two  gears  form  a 
iiepped  gear.  If  mated  with  a  similar  stepped  gear  on  a  parallel  shaft  the 
lumber  of  teeth  in  contact  will  be  twice  as  great  as  in  an  ordinary  gear, 
K  hich  will  increase  the  strength  of  the  gear  and  its  smoothness  of  action. 

X'wistedTeetli.— If  agreat  number  of  very  thin  gears  were  placed 
A>gether,  one  Klightly  in  advance  of  the  other,  thev  would  still  act  as  a 
iCepped  gear.  Continuing  the  subdivision  until  the 
hickuess  of  each  separate  gear  is  infinitesimal,  the 
:aces  of  the  teeth  instead  of  being  in  steps  take  the 
:orin  of  a  spiral  or  twisted  surface,  and  we  have  a 
wisted  gear.  The  twist  may  take  any  shape,  and  if  it  is 
n  one  direction  for  half  the  width  of  the  gear  and  in  the 
>pi>osite  direction  for  the  other  half,  we  have  what  is 
EDOwn  as  the  herring-bone  or  double  helical  tooth.  The 
>bliquity  of  the  twisted  tooth  if  twisted  in  one  direction 
uiuaes  an  end  thrust  on  the  shaft,  but  if  the  herring- 
>oae  twist  is  used,  the  opposite  obliquities  neutralize 
iach  other.  This  form  of  tooth  is  mucn  used  in  heavy 
x>lling-niill  practice,  where  great  strength  and  reeisUnce 
«  shocks  are  necessary.  They  are  frequently  made  of 
it«el  castings  (Fig.  160).    The  angle  of  the  tooth  with  a  ^.„    tit^ 

ine  parallelto  the  axis  of  the  gear  is  usually  80».  *  ^^^  l^. 

SplTAl  Geam.— If  a  twisted  gear  has  a  uniform  twist  it  Ijtieoomes  a 
(piraJ  gear.  The  line  in  which  the  pitch-surface  intersects  the  face  of  the 
ooth  is  part  of  a  helix  drawn  on  the  pitch-surface.  A  spiral  wheel  may  be 
nade  with  only  one  helical  tooth  wrapped  around  the  cylinder  several 
iines.  in  which  it  becomes  a  screw  or  worm.  If  it  has  two  or  three  teeth 
iu  wrapped,  it  is  a  double-  or  triple-threaded  screw  or  worm.  A  spiral-gear 
iieKldng  into  a  rack  is  used  to  drive  the  table  of  some  forms  of  planing- 
iiacbine. 

l^V^orm-c^Artnn:*— When  the  axes  of  two  spiral  gears  are  at  right 
angles,  and  a  wheel  of  one,  two,  or  three  threads  works  with  a  larger  wheel 
>f   uiany  threads,  it  becomes  a  worm-gear,  or  endless  screw,  the  smaller 


FiQ.  161. 

«vheel  or  driver  being  called  the  worm,  and  the  larger,  or  driven  wheel,  the 
lA'orm-wheel.  With  this  arranzenient  a  hisrh  velocity  ratio  may  \^  obtained 
w  ith  a  single  pair  of  wheels.    For  a  one-ihrt>aded  wheel  the  velocity  ratio  is 


898 


GEARIKO. 


the  number  of  teeth  in  the  worm-wheel.  The  worm  and  wheel  are  com- 
monly 80  constructed  that  the  worm  will  drive  the  wheel,  but  the  wheel  viJI 
not  drive  the  worm. 

To  find  the  diameter  of  a  toorvi-wheel  at  the  throat,  number  of  teeth  and 
pitch  of  the  worm  belnK  £^1^^":  Add  8  to  the  number  of  teeth,  multiplj  the 
sum  bv  0.8188,  and  by  the  pitch  of  the  worm  in  inches. 

To  find  the  number  of  teeth,  diameter  at  throat  and  pitch  of  worm  bf^iof^ 

iriven:   Divide  8.1416  times  the  diameter  by  the  pitch,  and  subtract  2  from 

tiie  quotient. 

In  FiK.  161  ab  is  the  diam.  of  the  pitch-circle«  cd  is  the  diam.  at  the  throat. 

ExAMPUB.— Pitch  of  worm  ^  in.,  number  of  teeth  70,  required  the  diam. 

at  the  throat.    (70  +  2)  X  .81ffl  X  .25  =  6.78  in. 

Teetli  of  Bevel-nrlieels*  (Rankine^s  Machinery  and  Millwork.v- 
The  teeth  of  a  bevel -wheel  have  acting:  surfaces  of  the  conicsl  kind,  geo- 
erated  by  the  motion  of  a  line  traversing  the  apex  of  the  conical  pitch 
surface,  while  a  point  in  it  is  carried  round  the  traces  of  the  teeth  upon  s 
spherical  surface  described  about  that  apex. 

The  operations  of  drawing  the  traces  of  the  teeth  of  bevel-wheels  exact  I  r. 
whether  bv  involutes  or  by  rolling  curves,  are  in  every  respect  analoirou^  b 
those  for  drawing  the  traces  of  the  teeth  of  spur-wheels;  except  that  in  tie 
case  of  bevel- wheels  all  those  operations  are  to  be  performed  on  the  surface 
of  a  sphere  described  about  the  apex,  instead  of  on  a  plane,  substitutiPi: 
poles  for  centres  and  great  circles  for  straight  lines. 

In  consideration  of  the  practical  difficulty,  especially  in  the  case  of  lanrs 
wheels,  of  obtaining  an  accurate  spherical  surface,  and  of  drawing  upon  r 
when  obtained,  the  following  approximate  method,  proposed  originally  bj 
Tredgold,  is  generally  used: 

Let  O,  Fig.  162,  be  the  common  apex  of  the  pitch-cones,  OBI  OB"!,  of  a 
pair  of  beyel*wheelfl;  QCt  OC,  the  axes  of  those  cones;  01  their  line  of  con- 
tact. Perpendicular  to  OI  draw 
AIA\  cutting  the  axes  in  A,  A'; 
make  the  outer  rims  of  the  patterns 
and  of  the  wheels  oortlons  of  the 
cones  ABl  A'B'I,  of  which  the  nar- 
row zones  occupied  by  the  teeth  will 
be  sufficiently  near  for  practical  par- 
poses  to  a  spherical  surface  de8cnb(>d 
about  O.  As  the  cones  ABI,  A'Rl 
cut  the  pitch -cones  at  right  angles  in 
the  outer  pitch -circles  IB,  1B\  ihpr 
niav  be  called  the  normal  cones.  To 
find  the  traces  of  the  teeth  upon  U» 
normal  cones,  draw  on  a  flat  surfact^ 
circular  arcs,  ID,  Ijy,  with  the  radii 
AL  A' I;  those  arcs  will  be  the  d<^ 
velopments  of  arcs  of  the  pitch- 
^,  circles  IB,  IB*  when  the  conical  sur- 

faces ABl,  A*  B' I  are  spread  out  flat.  Describe  the  traces  of  teeth  for  the 
developed  arcs  as  for  a  pair  of  spur-wheels,  then  wrap  the  developed  ar« 
oil  the  normal  cones,  so  as  to  make  them  coincide  with  the  pitch-circles,  and 
trace  the  teeth  on  the  conical  surfaces. 

For  f  ormuleB  and  instructions  for  designing  bevel-gears,  and  for  much  other 
valuable  information  on  the  subject  of  gearing,  see  "  Practical  Treatise  oa 
Gearing,"  and  '*  Formulas  in  Gearing,"  published  by  Brown  &  Sharpe  Mfjj 
Co.:  and  »' Teeth  of  Gears,"  by  George  B.  Grant,  Lexington,  Mass.  The 
student  may  also  consult  Rankine's  Machinery  and  Millwork,  Reuleaiu'« 
Constructor,  and  Unwinds  Elements  of  Machine  Design.  See  also  article  oa 
Gearing,  by  C.  W.  MacCord  In  App.  Cyc.  Mech.,  vol.  II. 

Aunular  and  DUTerentlal  Oearfn^.  (S.  W.  Baloh.,  Am,  Mach., 
Aug.  24,  1898.)— In  internal  gears  the  sum  of  the  diameters  of  the  describine 
circles  for  faces  and  flanks  should  not  exceed  the  difference  in  the  pitch 
diameters  of  the  pinion  and  its  internal  gear.  The  sum  may  be  equal  to  this 
difference  or  it  may  be  less;  if  It  is  equal,  the  faces  of  the  teeth  of  each 
wheel  will  drive  the  facts  as  well  as  the  flanks  of  the  teeth  of  the  other 
wheel.  The  teeth  will  therefore  make  contact  with  each  other  at  two  points 
at  the  same  time. 

Cycloldal  tooth-curves  for  interchangeable  gears  are  formed  with  describ- 
ing circles  of  about  ^  the  pitch  diameter  of  the  smallest  gear  of  the  series. 
To  admit  two  such  circles  between  the  pitch-circlee  of  the  pinion  and  internal 


EFPICIEKCT  OP  GEAMNO. 


899 


(tear  the  number  of  teeth  In  the  Internal  Rear  should  exceed  the  number  In 
th«  pinion  by  12  or  more,  if  the  teeth  are  of  the  customary  proportions  and 
curvaiure  used  in  interchangeable  gearing. 

Ver>'  of  len  a  less  difference  is  desirable,  and  the  teeth  may  be  modified  in 
several  ways  to  malce  this  possible. 

nrat.  The  tooth  curves  resulting  from  smaller  describing  circles  may  be 
employed.  These  will  give  teeth  which  are  more  rounding  and  narrower  at 
their  tops,  and  thei-efore  not  as  desirable  as  the  regular  forms. 

Second.  The  tips  of  the  teeth  may  be  rounded  until  they  clear.  This  \a  a 
cut-and-try  method  which  aims  at  modifying  the  teeth  to  such  outlines  as 
smaller  describing  circles  would  give. 

Thii-d.  One  of  the  describing  circles  may  be  omitted  and  one  onlv  used, 
which  may  be  equal  to  the  difference  between  the  pitch -circles.  This  will 
permit  the  meshing  of  gears  differing  by  six  teeth.  It  will  usually  prove 
inexpedient  to  put  wheels  in  inside  gears  that  differ  [by  much  less  than  12 
teeth. 

If  a  regular  diametral  pitch  and  standard  tooth  forms  are  determined  on, 
the  diameter  to  which  the  internal  gear-blank  is  to  be  bored  is  calculated  by 
subtracting  2  from  the  number  of  teeth,  and  dividing  the  remainder  by  the 
diametral  pitch. 

The  tootn  outlines  are  the  match  of  a  spur-gear  of  the  same  number  of 
teeth  and  diametral  pitch,  so  that  the  spur-gear  will  fit  the  internal  gear  as 
a  punch  fits  its  die,  except  that  the  teeth  of  each  should  fail  to  bottom  in 
the  tooth  spaces  of  the  other  by  the  customary  clearance  of  one  tenth  the 
thickness  of  the  tooth. 

Internal  gearing  is  particularly  valuable  Tvhen  employed  in  differential 
action.  This  is  a  mechanical  movement  in  which  one  of  the  wheels  is 
mounted  on  a  crank  so  that  its  centre  can  move  in  a  circle  about  the  centra 
of  the  other  wheel.  Means  are  added  to  the  device  which  restrain  the  wheel 
on  the  crank  from  turning  over  and  confine  it  to  the  revolution  of  the  crank. 
The  ratio  of  the  number  of  teeth  in  the  revolving  wheel  compared  with 
the  difference  between  the  two  will  represent  the  ratio  between  the  revolv- 
ing wheel  and  the  crank-shaft  by  which  the  other  is  carried.  The  advan- 
tage in  accomplishing  the  change  of  speed  with  such  an  arrangement,  as 
compared  with  ordinary  spur- gearing,  lies  in  the  almost  entire  absence  of 
friction  and  consequent  wear  of  the  teeth. 

But  for  the  limitation  that  the  difference  between  the  wheels  must  not  be 
too  small,  the  possible  ratio  of  speed  might  be  increased  almost  Indefinitely, 
and  one  pair  of  differential  gears  made  to  do  the  service  of  a  whole  train  of 
wheels.  If  the  problem  is  properly  worked  out  with  bevel-gears  this  limita- 
tion may  be  completely  set  aside,  and  external  and  internal  bevel-gears, 
differing  by  but  a  single  tooth  if  need  be,  made  to  mesh  perfectly  with  each 
other. 

Differential  bevel-gears  have  been  used  with  advantage  in  mowing-ma- 
chines. A  description  of  their  construction  and  operation  Is  given  by  Mr. 
Balch  in  the  article  from  which  the  above  extracts  are  taken. 

EFFICIENCY  OF  GEARING. 

A.n  extensive  series  of  experiments  on  the  efficiency  of  gearing,  chiefly 
worm  and  spiral  gearing,  is  described  by  Wilfred  Lewis  in  Trans.  A.  8.  M.  E., 
vii.  273.  The  average  results  are  shown  in  a  diagram,  from  which  the  fol- 
lowing approximate  average  figures  are  taken  : 

Effxcirnct  of  Spub,  Spiral,  and  Worm  Oearfng. 


Gearing. 

Pitch. 

Velocity  at  Pitch  line  in  feet  i>er  mm. 

8      1        10 

40 

100 

aoo 

Spur  pinion 

45» 
80 
20 
15 
10 

7 

5 

.90 
.81 
.75 
.67 
.61 
.51 
.48 
.84 

.935 

.87 

.815 

.75 

.70 

.615 

.58 

.48 

.97 

.98 

.89 

.845 

.805 

.74 

.72 

.60 

.96 

.955 

.98 

.90 

.87 

.82 

.766 

.70 

.965 

Soiral  oiiiion 

.965 

.945 

M                tt 

.92 

•i         <» 

.90 

Spiral  pinion  or  worm 

.86 

.815 

.765 

900 


GBARtKG. 


The  experiments  showed  the  adrantSLge  of  spur-j^earing-  orer  all  otlh*r 
kinds  in  both  dambUity  and  efficiency.  Toe  variation  from  the  mean  results 
rarely  exceeded  6%  In  either  direction,  so  lon^  ae  no  cuttinf?  occurred,  but 
the  Tariation  became  much  greater  and  very  irrefirular  as  soon  as  cutting 
began.  The  loss  of  power  varies  with  the  speed,  the  pressure,  the  tempera- 
ture, and  the  condition  of  the  surfaces.  Tlte  ezceiisive  friction  of  worm  and 
spiral  gearing  is  largely  due  to  thee  nd  thrust  on  the  collara  of  the  shafts 
Oniis  may  be  considerably  reduced  by  roller-bearings  for  the  collars. 

When  two  worms  with  opposite  spirals  run  in  two  spiral  worm-gears  that 
also  work  with  each  other,  and  tlie  pressure  on  one  gear  is  opposite  that  on 
the  other,  there  is  no  thrust  on  the  shaft.  Even  with  light  loads  a  worm 
will  begin  to  heat  and  cut  if  run  at  too  high  a  speed,  the  limit  for  safe  work- 
ing being  a  velocity  of  the  rubbing  surfaces  of  200  to  800  ft.  per  mhiute,  the 
former  t>eing  preferable  where  the  gearing  has  Co  work  continuously.  The 
wheel  teeth  will  keep  onol,  as  they  form  part  of  a  casting  having  a  large 
radiating  surface;  but  the  worm  itself  is  so  small  that  its  heat  is  dissipated 
slowly.  Whenever  the  heat  generated  increases  faster  than  it  can  be  con- 
ducted and  radiated  away,  tlie  cutting  of  the  worm  may  be  expected  to  be- 
gin. A  low  efficiency  for  a  worm*gear  means  more  than  the  loss  of  power, 
since  the  power  which  is  lost  reappears  as  heat  and  may  cause  the  rapid 
deiitmetion  of  the  worm. 

Unwin  (Elements  of  Machine  Design,  p.  294)  says :  Tie  efficiency  is  greater 
Che  less  the  radius  of  the  worm.  Generally  the  radius  of  the  worm  =  1.5  to 
8  times  the  pitch  of  the  thread  of  the  worm  or  the  circular  pitch  of  the 
worm-wheel.  For  a  one-threaded  worm  the  efficiency  is  only  2/5  to  J^; 
for  a  two-threaded  worm,  4/7  to  t/5;  for  a  three-threaded  worm,  H  to  H> 
Since  so  much  work  is  wasted  in  friction  it  is  not  surprising  that  the  wear 
is  excessive.  The  following  table  gives  the  calculated  efficiencies  of  worm- 
wheels  of  1, 2,  a,  and  4  threads  and  ratios  of  radius  of  worm  to  pitch  of  teeth 
of  from  1  to  0,  sssumiDg  a  coefficient  of  friction  of  0.15 ; 


No.  of 
Threads. 

Badins  of  Worm  t-  Pitch. 

1 

IM 

1« 

^H 

2 

^ 

8 

4 

6 

1 

.50 

.44 

.40 

.66 

.83 

.28 

.25 

.30 

.14 

9 

.67 

.68 

.57 

.68 

.SO 

.44 

.40 

.38 

.35 

9 

.75 

.70 

.67 

.68 

.60 

.55 

.50 

.48 

.83 

4 

.80 

.76 

.78 

.70 

.C7 

.68 

.67 

.50 

.40 

1 


KHOTH  OF  GEAR-TKBTK. 

The  streui^th  of  gear-teeth  and  the  lM>r8e-power  that  may  be  transmitted 
by  them  depend  upon  so  many  variable  ana  uncertain  factors  that  it  is  noc 
sooprlsing  tnat  the  formulas  and  rules  gfiven  by  diflPerent  writers  show  a 
wloe  vaiwtion.  In  1879  John  H.  Cooper  {Jour.  I^ank.  Jn«f.«  Jaly,  1879) 
found  that  there  were  then  in  existence  about  48  well-established  rules  for 
horse-power  and  working  strength,  differing  from  each  other  fai  extreme 
cases  about  500^.  In  1886  Prof.  Wm.  Harkness  (Proc.  A.  A.  A.  8.  1886), 
from  an  examination  of  the  bibliography  of  the  subject,  begintiitig  la  1796, 
found  that  according  to  the  constants  and  formulee  used  by  various  authore 
there  were  differences  of  15  to  1  in  the  power  which  could  be  transmitted 
by  a  given  pair  of  gearsd  wheels.  The  various  elements  which  enter  into 
tlie  constitulion  of  a  formula  to  represent  the  working  strength  of  a  toothed 
wheel  are  the  following:  1.  The  strength  of  the  metal,  usually  cast  iron,  which 
Is  an  extremely  variable  quantity.  2.  The  shape  of  ttie  tooth,  and  espec- 
ially the  relation  of  its  thieknese  at  the  root  or  point  of  least  strength  to  the 
jAtih  and  to  the  length.  3.  The  point  at  which  the  load  is  taken  to  be  ap- 
plied, assumed  by  some  authors  to  be  at  the  pitch'line,  by  others  at  the 
extreme  end.  along  the  whole  face,  and  by  still  others  at  a  single  outer 
comer.  4.  The  consideration  of  whether  rbe  total  load  is  at  any  Ume  re- 
ceived by  a  single  tooth  or  whether  it  is  divided  between  two  teedt.  5.  The 
Infloence  of  velocity  in  causing  a  tendency  to  break  the  teeth  by  shock.  6. 
The  factor  of  safety  assumed  to  cover  all  the  uncertainties  of  the  other  ele- 
ments of  the  problem. 


STRBKOtH  OF  OfiAU-tEKtS. 


doi 


Prof.  Hurknpiw,  an  a  rmult  of  htii  inv^sttgation,  found  tlist  all  the  fortnulie 
Ob  th«  subject  might  be  expressed  in  one  of  three  forms,  vis.: 

Horse-power  =  CVpJ^    or    CFp«,    or    CPp'/; 

in  which  C  is  a  coelflcient,  V  =  velocity  of  pitch-line  In  feet  per  second,  p  s 
pitch  In  inches,  and  /  s  face  of  tooth  in  incnes. 

From  an  examination  of  precedents  he  proposed  the  following  formula 
for  cast-iron  wheels: 


H.P.. 


0.910Fp/ 


He  found  that  the  teeth  of  chronometer  and  watch  morements  were  sub- 
ject to  stresses  four  times  as  great  as  those  which  any  engineer  would  dare 
to  use  In  like  proportion  upon  cast-iron  wlieels  o^  large  size. 

It  appears  that  all  of  the  earlier  rules  for  the  strength  of  teeth  neglected 
the  consideration  of  the  variations  In  their  form;  the  breakitis  strengih,  as 
said  by  Mr.  Cooper,  being  based  upon  the  thickness  of  the  teeth  at  the  pitch- 
line  or  circle,  as  if  the  thickness  at  the  root  of  the  tooth  were  the  same  in 
all  cases  as  it  Is  at  the  pitch-line. 

Wilfred  Lewis  (Froc.  EngYs  Club,  PhlU.,  Jan.  ISOS;  Anu  Mack.,  June  22, 
1898)  seems  to  have  been  the  first  to  use  the  form  of  the  tooth  in  the  con- 
struction of  a  working  formula  and  table.  He  assumes  that  in  well-con- 
structed machinery  the  load  can  be  more  properly  taken  as  well  distribuied 
across  the  tooth  than  as  concentrated  in  one  comer,  but  that  it  cannot  be 
safely  taken  as  concentrated  at  a  maximum  distance  from  the  root  less 
than  the  extreme  end  of  the  tooth.  He  assumes  tliat  the  whole  load  is 
taken  upon  one  tooth,  and  considers  the  tooth  as  a  beam  loaded  at  one  end. 
and  from  a  series  of  drawings  of  teetli  of  the  involute,  cydoidaL  and  radial 
flauk  sysletns,  determines  the  point  of  weakest  cross-section  of  each,  and 
the  ratio  of  the  thickness  at  that  section  to  the  pitch.  He  thereby  obtains 
the  general  formula, 

in  which  W  is  the  load  transmitted  by  the  teeth,  in  pounds;  s  is  the  safe 
working  stress  of  the  material,  taken  at  8000  lbs.  for  cast  iron,  when  the 
working  speed  is  100  ft.  or  less  per  minute;  p  =  pitch;/  =  face.  In  inches; 
y  =  a  factor  depending  on  the  form  of  the  tuoth,  whose  value  for  diflPerent 
1  is  given  in  the  following  table: 


Factor  for  Strength,  y.    \ 

Factor  for  Strength,  y. 

No.  of 
Teeth. 

No.  of 
Teeth. 

Involute 

Involute 

Radial 
Flanks. 

Involute 

Involute 

Radial 
Flanks. 

Vy*  Obli- 

150 and 

20°  Obli- 

15»  and 

quity. 

Cycloidal 

quity. 

Cycloidal 

18 

.078 

.067 

.058 

27 

.111 

.100 

.064 

i3 

.083 

.070 

.053 

80 

.114 

102 

.065 

14 

.088 

.or» 

.054 

34 

.118 

.KM 

.066 

15 

.092 

.075 

.055 

88 

.122 

.107 

.067 

16 

.004 

.077 

.056 

43 

126 

.110 

.068 

17 

.006 

.080 

.057 

50 

:80 

.112 

.060 

18 

.008 

.083 

.058 

60 

134 

.114 

.070 

JO 

.100 

.087 

.050 

75 

.138 

.116 

.071 

20 

.102 

.090 

.060 

100 

.142 

.118 

.072 

31 

.104 

.00) 

.061 

150 

146 

.120 

.078 

28 

.106 

.004 

.062 

800 

.:50 

122 

.074 

25 

.106 

.007 

.068 

Back. 

.154 

.124 

*075 

Safe  Working  Stress,  a 

Speed  of  Teeth  in 
ft.  per  minute. 

100  or 
less. 

COO 

800 

600 

000 

1200 

1800 

"aoob" 

5000 

2400 

Cast  iron 

8000 
20000 

6000 
16000 

4800 
12000 

4000 
10000 

8000 
7500 

»(00 
6000 

1700 

Steel 

4300 

902  OfiARIKG. 

The  yalues  of  «  in  the  above  table  are  giTen  by  Mr.  Lewis  tentalivelj,  in 
t)ie  absence  of  sufficient  data  upon  which  to  base  more  definite  values*  bat 
ther  have  been  found  to  give  satisfactory  results  in  practice. 

Mr.  Lewis  Kives  the  following  example  to  Illustrate  the  use  of  the  tables: 
Lot  it  be  required  to  And  the  working  strengtli  of  a  12- toothed  pinion  of  1- 
inch  pitch,  Scinch  face,  driving  a  wheel  of  60  teeth  at  100  feet  or  less  per 
minute,  and  let  the  teeth  be  of  the  SO-degree  Involute 
form.  In  the  formula  TTs  «p/y  we  have  for  a  cast-iron 
pinion  8  =  8000,  pf  s=  8.fi,  and  y  =.078;  and  multiplying  these 
I  values  together,  we  hsve  W  s  1560  pounda  For  the  wheel 
I  we  have  y  =  .184  and  W  =  8880  pounds. 

The  cast-Iron  pinion  is.  therefore,  the  measure  of 
strength:  but  If  a  steel  pinion  be  substituted  we  have 
t  =  saO.OOO  and  W  s  8000  pounds.  In  which  combination 
the  wheel  is  the  weaker,  and  it  therefore  becomes  the 
measure  of  strength. 

For  bevel-wheels  Mr.  Lewis  gives  the  following,  refer- 
ring to  Fig.  16B:    Z>  =  large  diameter   of  bevel;    d  = 
small  diameter  of  bevel;  p  =■-  pitch  at  large  diameter; 
n  =  actual  number  of  teeth;  /  =  face  of  beve.;  N  =  for- 
Fko.  168.  mative  number  of  teeth  =  n  x  secant  a,  )r  the  number 

corresponding  to  radius  R  ;  y  =  factor  depending  upon 
•hape  of  teeth  and  formative  number  N\  W=  working  load  on  teetb. 

^  =  *P^y  SDHD  -  d)'  o^™©**"*™?^^*  W=:9p/y^, 

which  gives  almost  identical  results  when  d  is  not  less  than  9i  !>*  a*  is  the 
case  in  good  practice. 

In  Am,  Mach.^  June  88, 1808,  Mr.  Lewis  gives  the  following  formulsp  for 
the  working  strength  of  the  three  systems  of  gearing,  which  agree  very 
closely  with  those  obtained  by  uee  of  the  table: 

For  involute,  «0«  obliquity,  W  =  tp/ (.154  -  —  ) ; 
For  Involute  16*,  and  qyolddal,  W  s  <p/(  .184  -  •^) ; 
For  radial  flank  system,  TTb  «p/f  .078  ->  - —  J ; 

in  which  the  factor  within  the  parenthesis  corresponds  to  y  in  the  genera) 
formula.    For  the  horse-power  transmitted,  Mr.  Lewis's  general  formula 

W  =  »p/y,  =  ^•QQQHP'^  niay take  the  form  H.P.  =  2^»  ^  ''•iteh  v  =s 

V  ss,uuu 

velocity  in  feet  per  minute;  or  since  t7  =  dir  x  rpm.  -•- 18  s  .8618d  X  rpm.«  is 
which  d  =  diameter  in  inches  and  rpm.  =  revolutions  per  minute, 

It  must  be  borne  in  mind,  however,  that  in  the  case  of  machines  which 
consume  power  intermittently,  such  as  punching  and  shearing  machines, 
the  gearing  should  be  designed  with  reference  to  the  maximum  load  IT, 
which  can  be  brought  upon  the  teeth  at  any  time,  and  not  upon  the  average 
horse-power  transmitted 

Comparison  of  tlie  Harkness  and  I«eirla  Formnlns*- 
Take  an  average  case  in  which  the  safe  working  strength  of  the  material, 
8  =  6000,  V  =  300  ft.  per  min.,  snd  y  =  .100,  the  value  in  Mr.  Lewis's  table 
for  an  Involute  tooth  of  15*^  obliquity,  or  a  cycloidal  tooth,  the  number  of 
teeth  in  the  wheel  being  87. 

^'^'  ^  ^m  "       88.000      -  IT  "  1-W'^vv; 

if  Fls  taken  In  feet  per  second. 
Prof.  Harkness  gives  H.P.»    Q-^^^^P/   .     If  the  F  in  the  denominator 
Vl  +  0.66r 


STRENGTH  OF   GEAR-TEETH. 


903 


be  taken  at  S»0-<-60  =  3>i  feet  per  second,  i^l-f  0.66r=  ^'SAGT  =  hTS, 
and  H.P.  =  ^Vp/=  .blXpfV,  or  about  523^  of  the  result  given  by  Mr.  Lewis's 

formula.  This  is  probablv  as  close  an  agreement  as  can  be  expected,  since 
Prof.  Harkness  derived  his  formula  from  an  investigation  of  ancient  prece- 
dents and  rule-of-thumb  practice,  largely  with  common  cast  gears,  while 
Mr.  Lewis's  formula  was  derived  from  considerations  of  modern  practice 
with  machine-moulded  and  cut  gears. 

Mr.  Lewis  takes  into  consideration  the  reduction  In  working  strength  of  a 
tooth  due  to  Increase  In  velocity  by  the  figures  in  his  table  of  the  values  of 
the  safe  working  stress  a  for  diiierent  speeds.  Prof.  Harkness  gives  expres- 
slon  to  the  same  reduction  by  means  of  the  denominator  of  his  formula, 
y  1-|-  0.65  r.  The  decrease  in  strength  as  computed  by  this  formula  Is 
somewhat  less  than  that  given  in  Mr.  Lewis's  table,  and  as  the  figures  given 
In  the  table  are  not  based  on  accurate  data,  a  mean  between  the  values  given 
by  the  formula  and  the  table  Is  probably  as  near  to  the  true  value  as  mny 
be  obtaineil  from  our  present  knowledge.  The  following  table  gives  the 
▼alnes  for  diflPerent  speeds  according  to  Mr.  Lewis's  table  and  Prof.  Hark- 
ness's  formula,  taking  for  a  basis  a  working  stress  «,  for  cast-irou  8000,  and 
for  sieel  20,000  lbs.  at  speeds  of  100  ft.  per  minute  and  less: 


V  =  speed  of  teeth,  ft.  per  min. . 
r=     "  •*     ft.  per  sec.. 


Safe  stress  s,  cast-iron,  Lewis. . . 

Relative  do.,  n-*-  8000 

c^l-<-4'l4-0.e5F.... 

Relative  val.  C-4-.098. 

s.  =  8000  X  (c -H  .098) 

Mean  of  s  and  Sj,  cast-iron  =  «« . 

;•     **       •'  for  steel  =  «<. 

Safe  stress  for  steel,  Lewis 


100 

800 

300 

600 

900 

1200 

1800 

2400 

\% 

m 

5 

10 

15 

20 

80 

40 

8000 

6000 

4800 

4000 

8000 

2400 

2000 

1700 

1 

.76 

.6 

.6 

.376 

.8 

.26 

.2126 

.6980 

.5621 

.4860. 86S0 

.3050 

.2672 

.2208 

.1924 

1 

.811 

.700  .526 

.480 

.885 

.818 

.277 

8000 

64S8 

5600  4206 

8612 

8080 

2544 

2216 

8000 

6200 

5200  4100 

8300 

2700 

2800 

2000 

80000 

15500  18000  lOsXX) 

8100 

6800 

6700 

4900 

20000 

15000 

12000 

10000 

7500 

6000 

6000 

4800 

Comparing  the  two  formulae  for  the  case  of  <  =  8000,  corresponding  to  a 
speed  of  100  ft.  per  min.,  we  have 


650  660  -'«l«P/y* 


Harkness:  H.P.  =  1  -*-  VI -f  0.66 r  x  .910rp/  =  .695  x  .91  X  l«p/=  1.051;j/' 

I-wta:        H.P.=  ^ 

In  which  y  Tarles  according  to  the  shape  and  number  of  the  teeth. 

For  radial-flank  gear  with  12  teeth  y  »  .062:  24.24p/v  s=  1.260p/ ; 

For  20*  involute,  19  teeth,  or  16«»  In  v.,  27  teeth  y  =  .100;  2i.2ip/y  =  2.42^/; 
For  16«  Involute,  800  teeth  y  s  .150;  24.24p/y  =  8.6S6p/. 

Thus  the  weakest- shaped  tooth,  according  to  Mr.  Lewis,  will  transmit  20 
|>er  cent  more  horse- power  than  is  given  by  Prof.  Haikness's  formula,  in 
which  the  shape  of  itie  tooth  is  not  considered,  and  the  average-shaped 
tooth,  according  to  Mr.  Lewis,  will  imnKmit  more  than  double  the  horse- 
power given  by  Prof.  HarknessV  fonnula. 

Comparison  of  Other  Formulae.— Mr.  Cooper,  in  summing  up 
his  exaiiiiiiaiioii.  KfJfcieti  un  old  b:ii»rliKh  rule,  which  Mr.  Lewis  considers  as 
a  paanably  coirect  expresj«i«>n  of  good  general  averages,  vis. :  X  =  2000p/, 
X  =  breaking  load  of  tooth  in  poundx,  p  =  pitch,  /  =  face.  If  a  factor  of 
safety  of  10  be  taken,  this  would  give  for  safe  working  load  W  =  fiOOpf. 

George  B.  Grant,  in  hlH  Teeth  of  Gears,  page  88.  takes  the  breaking  load 
at  8500p/,  and,  with  a  fwtor  of  safety  of  10,  gives  W  =  850p/. 

Nystrom's  Pocket-Book,  20ih  ed.,  1881 ,  says  :  **  The  strength  and  durability 
of  cast-iron  teeth  require  that  thev  shall  transmit  a  force  of  80  lbs.  per  inch 
of  pitch  and  per  inch  breadth  of  face."  This  is  equivalent  to  TT  =  SC^p/,  or 
only  40^  of  that  given  by  the  English  rule. 

F.  A.  Halsey  (Clark's  Pocket  Book)  gives  a  table  calculated  from  the 
formula  H.P.  =  p/d  x  rpm.  -«-  850. 

Jones  &.  Loughllns  give  H.P.  =  p/d  x  rpm.  ■+■  650. 

These  formulie  transformed  give  W=  ViSpf  and  W  s  218p/,  respectiveljc 


904  GEAEIKG. 

Unwtn,  on  the  lissumptionjhat  the  load  acts  on  the  corners  of  the  teeth, 
derives  a  formula  p  =  KVw,  in  which  IT  is  a  coefficient  derived  from  ex- 
istiiiK  wiieels.  its  values  beinjf :  for  slowly  moving  Rrearinfl:  not  subject  to 
much  vibration  or  shook  K=  .04:  in  ordinary  miil-geariug.  running  at 
greater  speed  and  subject  to  considerable  vibration,  JC  =  .05;  and  in  wheels 
nubjected  to  excesslvft  vibration  and  shock,  and  in  mortise  gearing,  K=  .Oti. 
Reduced  to  the  form  W=  Opt  assuming  that/  =  «p,  Uiese  values  of  K  give 
W  =  a62p/.  -iOOp/,  and  189p/,  respectively. 

Unwiu  also  gives  the  folloiviug  formula,  based  on  the  assumption  that  the 

pressure  is  distributed  along  the  edge  of  the  tooth :   p  «  ^^l/y  *^^ 

where  JT,  =  about  .0707  for  iron  wheels  and  .0848  for  mortise  wheels  when 
the  breadth  of  face  is  not  less  than  twice  the  pitch.  For  the  case  of  /  =  to 
and  the  given  values  of  JSTj  this  reduces  to  W  =  UMpf  and  IF  =  I8»p/, 
i*espectively. 

Box,  in  his  Treatise  on  Mill  Gearing,  gives  H.P.  =        ioqq  ^t  *"  which  n 

=  number  of  revoliitions  per  minute.  This  formula  differs  from  the  mnre 
modern  forranlee  in  making  tlie  H  P.  vary  as  p«/,  instead  of  asp/,  and  in 
tills  respect  it  is  no  doubt  incorrect. 

Making  the  H.P.  vary  as  i^dn  or  as  \^,  instead  of  directly  as  r,  makes 
the  velocity  a  factor  of  the  working  strength  as  in  tlie  Harkness  and  Lewis 

formulae,  the  relative  strength  varying  as  -^— ,  or  as~7p,  which  for  different 
velocities  is  as  follows  : 

Speedof  teethlnft.  permin.,v  =100  300  800  600  900  1200  1800  9400 
Relative  strength  =  1     .707    .574    .406   .88S    .880     .e86     .904 

Showing  a  somewhat  more  rapid  reduction  than  is  given  by  Mr.  Lewis. 

For  the  purpose  of  ct^mnaring  different  formulae  they  may  in  general  be 
reduced  to  either  of  the  following  forms  ; 

H.P.  =  Cpfv,       H.P.  =  Cjp/d  X  rpm.,        W  =  cp/, 

in  which  p  =  pitch,  /=  face,  d  =  diameter,  all  in  inches ;  v  =  velocity  in 
feet  per  minute,  rpm.  i-evoUitions  per  minute,  and  C,  C|  and  c  coefflcieola. 
The  lormulee  for  transformation  are  as  follows : 

HP-   ^^  -  ^X  dxrpm.. 
^'^'  "  8;3000  ■"         lii6,050 

„     88,000  H.P.     126,060  H.P.      ^^  r^n  ^      ^    ^•^'  H.P.  W 

^^-—^ =  dxrpm.   -^-^^-P-^-P>^  =  -cir°C.«IXrpm.='^- 

Cx  =  .2618(7;    c  =  88.000C;    C  =  8.82(7, ,  =  ^^;    o  =  126,0000,. 

In  the  Lewis  formula  (7  varies  with  the  form  of  the  tooth  and  with  the 
speed,  and  is  equal  to  «y-»-  88,000,  in  which  y  and  s  are  the  values  taken  from 
tlie  table,  and  c  =  8y, 

WO 

In  the  Harkness  formula  C7  vailes  with  the  speed  and  is  equa'.  to  A/fXo'<^ 

(F  being  in  feet  per  second),  =  — ' 

In  the  Box  formula  C  varies  with  the  pitch  and  also  with  the  velocity, 

and  equal,  ""  ^^  """■  =  .(Km  -^.    c  =  88,0000  =  774 -^r 

For  V  =  100  ft.  per  min.  C  =  77.4p  ;   for  u  =  600  ft.  per  minute  c  &3r81.6p. 
In  the  other  formulce  considered  (7,  Ct  ,  and  c  are  con8tant4t.    Reducing 
the  several  rormulae  to  the  form  W  s  cpf,  we  have  the  following : 


FRICTIONAL  GEARING,  905 

Comparison  of  Diffcrent  Fork  .  ljb  for  Strength  of  Gbar-tbetb. 

Safe  workinfir  pressure  i>er  inch  pitch  and  per  inch  of  face,  or  value  of  c  in 
formula  W  =  cpfi 

V  ss  100  ft.     v  =  COO  ft. 
per  min.        per  min. 
Lewis:  Weak  form  of  tooth,  radial  flank,  18  teeth. ..  c  e=   416  S06 

Metlium  tooih,  in  v.  15®,  or  cycloid,  87  teeth.,  c  =   800  400 

Strong  form  of  tooth,  or  cycloid,  800  teeth. . .  c  =  1200  600 

Harkness:  Average  tooth c  =   347  184 

Box:  Tooth  of  llnch  pitch c  =     77.4  81.6 

•*     **  8  inches  pitch c  =   288  96 

Various,  in  which  c  is  Independent  of  form  and  speed:  Old  English 
rule,  c  =3  200;  Grant,  c  =  350;  Nystrom,  c  =  80;  Halsey.  c  =  138;  Jones  & 
Laughlins,  c  =  218;  Unwiu,  c  =  262,  200,  or  189,  according  to  speed,  shock, 
and  vibration. 

The  value  given  by  Nystrom  and  those  given  by  Box  for  teeth  of  Rmall 
pitch  are  so  much  smaller  than  those  given  by  the  other  authoi-ities  that  they 
may  be  rejected  as  having  an  entirely  unnecessary  .suri)liis  of  strengtli.  The 
values  given  by  Mr.  Lewis  seem  to  rest  on  the  most  logical  baais.  the  form  of 
(he teeth  as  well  as  the  velocity  being  considered;  and  since  ihey  are  said  to 
have  proven  satisfactory  in  an  extended  machine  practice,  they  may  be  con- 
sidered reliable  for  geai-s  that  are  so  well  made  that  tne  pressure  bears 
along  the  face  of  the  teeth  instead  of  upon  the  comers.  For  rough  ordi- 
nary work  the  old  English  rule  W  =  SOQp/  is  probably  as  good  an  any,  ex 
cept  that  the  figure  200  may  be  too  high  for  weak  forms  of  tooth  and  for 
high  speeds. 

The  formula  Tr=  200p/ Is  equivalent  to  H.P.  =  ^^^  1^^'  =  ^»  ^^ 

HP.  =  .001.'S873p/d  X  rpm.  =  .006063p/v. 

Maximum  Speed  of  eemrlnir.— A.  Towler,  Ena*g^  April  19,  1889, 
p.  888,  fcives  llie  maxiniuni  speeds  at  which  it  was  possible  under  favorable 
conditions  to  ran  toothed  gearing  safely  as  follows: 

Ft,  per  mia 

Ordinary  cast-iron  wheels 1800 

Helical       *♦       •*        "     8400 

Mortise       '*       •'         *♦ 2400 

Ordinary  cast-steel  wheels 8600 

Helical       "       **        •' 8000 

Special  cast-iron  machine-cut  wheels 8000 

Prof.  Coleman  Sellers  {Stevens  Indicator,  April,  1892)  recommends  that 
gearing  be  not  run  over  1200  ft.  per  minute,  to  avoid  great  noise.  The 
Walker  Company,  Cleveland,  O.,  say  that  2900  ft.  per  min.  for  iron  gears  and 
SOtH)  ft.  for  wood  and  iron  hnorti.se  gears)  ure  excessive,  and  slionld  be 
avoiiied  if  posaible.  The  Corliss  engine  at  the  Philadelphia  Exhibition  (1S76) 
had  a  fly  wheel  :J0  ft.  in  diameter  running  35  rpm.  geared  into  a  pinion  12  ft. 
diani.    The  speed  of  the  pitch-line  was  S-'iOO  ft.  per  min. 

A  Heavy  ]flaehliie-cat  Spnr*cear  was  made  in  1891  by  the 
Walker  Company,  Cleveland,  O.,  for  a  diamond  mine  in  South  Africa,  with 
dimensions  as  follows:  Number  of  teeth,  192;  pitch  diameter,  80^  6.66";  face, 
30";  pitch,  6":  bore,  27";  diameter  of  hub,  9'  2";  weight  of  hub,  15  tons;  and 
total  weight  of  gear,  669^  tons.  The  rim  was  made  in  12  segnients,  the  joints 
of  ilie  segments  being  fastened  with  two  bolts  each.  The  spokes  were  bolted 
to  the  middle  of  the  seGrments  and  to  the  hub  with  four  bolts  in  each  end. 

Prletlonal  Gearine*— In  frictlonal  gearing  the  wheels  are  toothless, 
and  one  wlifel  drives  the  oiher  by  means  of  the  friction  between  the  two 
surfaces  which  are  pre^ssed  together.  They  may  be  used  where  the  power 
to  be  transmitted  Is  not  very  great;  when  the  speed  is  so  high  that  toothed 
wheels  would  be  noisy;  when  the  shafts  require  to  be  frequently  put  into 
and  out  of  gear  or  to  have  their  relative  direction  of  motion  reversed;  or 
when  it  is  desired  to  change  the  velocity-ratio  while  the  machinery  is  in  mo- 
tion, as  in  the  case  of  disk  friction-wheels  for  changing  the  feed  In  machine 
tools. 

Tjet  P  =  the  normal  pressure  in  pounds  at  the  line  of  contact  by  which 
two  wheels  are  pressed  together.  T  =  tangential  resistance  of  the  driven 
wheel  at  the  line  of  contact,  /  =  the  coefficient  of  friction,  V  =  the  velocity 
of  the  pitch-surface  !n  feet  |)er  second,  and  H.P.  =  horse-power ;  then 
T  may  be  equal  to  or  less  than  fP\  H.P.  =  TV-*-  550.    The  value  of/  for 


906 


HOISTIKG. 


metal  on  metal  may  be  taken  at  .15  to  .20;  for  wood  on  metal,  JS5  to  .90;  axA 
for  wood  on  compressed  paper,  .20.  The  tani^ntial  driving  force  T  may  l« 
as  hif^h  as  80  lbs.  per  inch  width  of  face  of  the  driving  surface,  but  this  is  ac- 
companied by  great  pressure  and  friction  on  the  Journal-bearings. 

Ill  frictional  grooved  gearing  circumferential  wedge-shaped  grooves  are 
cut  in  the  faces  of  two  wheels  in  contact.  If  P  =  the  force  pressing  the 
wlieels  together,  and  N  =  the  normal  pressure  on  all  the  grooves,  F  —  N 
(sin  a  -{-/cos  a),  in  which  2a  =  the  inclination  of  the  sides  of  the  grooves 
and  the  maximum  tangential  available  force  T  —  fN.  The  inclination  of  the 
sides  of  the  grooves  to  a  plane  at  risrht  angles  to  the  axis  is  usuallv  80*. 

Frlctlonal  Grooved  Gearlne,— A  set  of  friction-gears  for  trans- 
mittiiig  150  H.P.  is  on  a  steam- dre<1ge  described  in  Proc.  Insr.  M.  E.,  July. 
1888.  Two  grooved  pinions  of  54  tn.  diam.,  with  9  grooves  of  19!^  in.  pitch  and 
angle  of  40"  cut  on  their  face,  are  geared  into  two  wheels  of  l27i^  in  diam. 
similarly  grooved.  The  wheels  can  be  thrown  in  and  out  of  gear  by  leverc 
operating  eccentric  bushes  on  the  large  wheel-shaft.  The  circumferential 
speed  of  the  wheeln  is  about  500  ft.  per  min.  Allowing  for  engine  fricUon, 
if  half  the  power  is  transmitted  through  each  set  of  gears  the  tangential 
force  at  the  lims  is  about  8960  lbs. ,  requiring,  if  the  angle  is  40**  and  the  co- 
efficient of  friction  0  18.  a  pressure  of  75'i4  lbs.  i)etween  the  wheels  and 
pinion  to  prevent  slipping. 

The  wear  of  the  wheels  proving  excessive,  the  gears  were  replaced  by  spur- 
gear  wheels  and  brake-wtieels  with  steel  brake-bands,  which  arrangement 
has  proven  more  durable  than  the  grooved  wheels.  Mr.  Daniel  Adamson 
states  that  if  the  frictional  wheels  had  been  run  at  a  higher  speed  the  results 
would  have  been  better,  and  says  they  should  run  at  least  80  ft.  per  second. 


HOISTING. 

Approximate  IFelclit  and  Streiifftli  of  Cordage. 

and  Lo«:kp(>rL  Block  Co.)— 8ee  also  pagew  389  to  845. 


(Boston 


Size  In 
Circum- 
ference. 

Size  in 
Diam- 
eter. 

Manila, 
In  lbs. 

Strength 

of  Manila 

Rope, 

in  lbs. 

Size  In 
Circum- 
ference. 

Sisein 
Diam- 
eter. 

Manila, 
inlbe. 

Strength 

of  ManiU 

Rope, 

in  lbs. 

inch. 

inch. 

Inch. 

inch. 

a 

U 

18 

4,000 

49i 

19/16 

72 

22,500 

2V4 

16 

5,000 

5 

^H 

80 

85,000 

2^ 

18/IC 

20 

6,250 

6H 

m 

97 

80,250 

2^ 

H 

24 

7,500 

6 

2 

118 

36,000 

8 

1 

28 

9,000 

0^ 

^H 

188 

48,250 

8^ 

11/lG 

88 

10,500 

7 

^ 

158 

49.000 

^H 

88 

12,250 

7^ 

184 

56,250 

3^ 

IM 

45 

14,000 

8 

8^  1 

Sll 

64.000 

4 

ir 

51 

16,000 

m 

gu 

9»6 

78,250 

1^ 

58 

18,062 

9 

8 

862 

61,000 

m 

65 

20.250 

ITorklne  SStrenelb  of  Blocks.    (B.  &  L.  Block  Ck>.) 


Regular  Mortise -blocks  Single  and 
Double,  or  Two  Double  Iron* 
strap{)e(l  Blocks,  will  hoist  about- 


Wide  Mortise  and  Extra  Heavy 
Single  and  Double,  or  Two  Double, 
Iron-strapped  Blocks,  will  hoisi 
about— 


inch. 

lbs. 

inch. 

lbs. 

^ 

250 

8 

8,000 

6 

850 

10 

6,000 

7 

600 

18 

12,000 

8 

1,200 

14 

84,000 

9 

2,000 

16 

88.000 

10 

4,000 

18 

50,000 

12 

10,000 

80 

90,000 

14 

16,000 

Where  a  double  and  triple  block  are  i 

used  together. 

a  certain  extra  Droixx^ 

tioned  amount  of  weight  can  be  safely  hoisted',  as  larger  books  are  uisedl 

PROP   ETIONS  OF   HOOKS. 


907 


ComparatlTe  ISfllclency  In  Clialii* blocks  botli 
Holstlne  and  liO'werinc 


(Teats  by  Prof.  R.  H. 

Thurston,  Hoisting,  March,  1898.) 

Work  or  HoramNO. 

Work  of  Lowcring. 

Load  of  2000  lbs.       | 

Load  of  2000  lbs.,  lowered  7  ft.  In  each  case. 

1 

§ 

1? 

1 

Exclusive  of  Factor  of  Time. 

Inclusive  of 
Time. 

1 

9  g 

1' 

111 

ill 

i 

a 

9 

E 

|& 

80.50 

79.50 

1.00 

82.5C 

8.00 

227. 

1.816 

1.00 

0.75 

1.000 

68.00 

82.00 

.40 

6-».44 

14.00 

486. 

6,104 

8.88 

1  20 

.186 

69.00 

81.00 

.89 

80  OC 

92.80 

196. 

18,090 

10.00 

1.50 

.060 

71.80 

28.80 

.86 

88. OC 

92.60 

168. 

15.556 

8.60 

8.50 

.(m 

78.96 

28.04 

.83 

48.0( 

78.30 

17.5 

1.282 

0.71 

280 

.880 

75.66 

24.81 

.81 

ft8.0C 

56.60 

870. 

20,942 

11.60 

1.80 

.a36 

77.00 

28.(X) 

.29 

44. 8C 

55.00 

810. 

17,050 

9.40 

8.75 

.029 

8 

81.03 

18.97 

.84 

61.00 

48.50 

426. 

80,000 

11.80 

8.75 

.018 

No.  1  wasWdston^s  triplex  block;  No.  8,  Weston's  diflPerentlal;  No.  4, 
Weston's  imported.  The  others  were  from  different  makers,  whose  names 
ar(>  not  given.    All  the  blocks  were  of  one-ton  capacity. 

Proportions  of  Hooks.— The  followinfr  formulae  are  griven  by 
Henry  K.  Towne,  in  his  Treatise  on  Cranes,  as  a  result  of  an  extensive 
experimental  and  mathematical  investi* 
flatten.  They  apply  to  hooks  of  capaci- 
ties from  350  lbs.  to  20,000  lbs.  Each  size 
of  hook  is  made  from  some  commercial 
sine  of  round  iron.  The  basis  in  each 
case  is.  therefore,  the  size  of  iron  of 
which  the  hook  is  to  be  made,  indicated 
by  A  in  the  diagram.  The  dimension  D 
is  arbitrarily  assumed.  The  other  di- 
mensions, as  giy*fii  by  the  formuiaB,  ai'e 
those  which,  while  preservinK  a  proper 
bearing-face  on  the  interior  »u  the  hook 
for  the  ropes  or  chains  which  may  be 
passed  throuf^h  it,  g^ive  the  greatest  re- 
sistance to  spreading  and  to  ultimate  ' 
rupture,  which  the  amount  of  material 
in  the  original  bar  admits  of.  The  sy ni  • 
bol  A  is  used  to  indicate  the  nominal  ca- 
pacity of  the  hook  in  tons  of  ;:000  lbs. 
The  formulae  which  determine  the  lines 
of  the  other  parts  of  the  hooks  of  the 
several  sizes  are  as  follows,  the  measure- 
ments being  all  expressed  in  inches: 


Fig.  164. 


D  =  .5  A  -H  1.85 
^  =  .64  A  -i- 1.60 
F  =  .88  A  4-   .86 


O  =  .75D. 

O  =  .808  A  -f   .66 

g  =  .64   A  -f  1.60 


H=  1. 08  A 
/=  1.83^ 
J  =  1. 20  A 

K  =  1.18^ 


L  =  1.05^ 
M  =    .50^ 
N  =    .85«  -  .10 
U=    .866^ 


The  dimensions  A  are  necessarily  based  upon  the  ordinary  merchant  sizet^ 
of  round  iron.    The  sizes  which  it  has  been  found  best   to  select  are  the 
following: 
Capacity  of  hook: 

%         H       M  ll^li       884668        10  tons. 

Dimension  A: 

H     11/18     94     1 1/18     IM      19^     1»     3     8^     8H     S»     ^  in. 


908  HOtSTtKO. 

Experiment  has  tbown  that  hooks  made  accordtne  to  the  above  foitnule 
will  give  way  first  by  opening  of  the  jaw,  which,  however,  will  not  occur 
except  with  a  load  much  in  excess  of  tiie  nominal  capacity  of  ttie  hoolc. 
This  yielding  of  the  hook  when  overloaded  becomes  a  source  of  safetj^,  as  it 
constitutes  a  signal  of  danger  which  cannot  easily  be  overlooked,  ana  which 
must  proceed  to  a  considerable  length  before  rupture  will  occur  and  the 
load  be  dropped. 

POWBR  OP  nOISTING-BNGlIIES. 

Horse-power    required   to    raise   a  liOad  at   a   Qtven 

speed.  -  H.P.  =  9r£«L5^1^JlLy>i.  x  speed  in  ft.  per  m»n.    To  this  add 

25)(  to  50j(  for  friction,  contingencies,  etc.  The  gross  weight  Includes  the 
weight  of  cage,  rope,  etc.  In  a  shaft  with  two  cages  balancing  each  oUier 
use  the  net  load  4-  weight  of  one  rope,  instead  of  the  gross  weight. 

To  find  the  load  whidi  a  given  pair  of  engines  will  siart.—u&t  A  =  area 
or  cylinder  in  square  inches,  or  total  area  of  both  cyUnders.  if  there  are  two: 
P  =  mean  effective  pressure  in  cylinder  In  lbs.  per  sq.  In.;  8=  stroke  of 
cylinder  in  inches;  C  —  ciixsumference  of  hoisting-drum  in  inches;  L  =  load 
lifted  by  hoisting- rope  in  lbs.;  F=  friction,  expressed  as  a  dimioutioo  of 

the  load.    Then  L  =  — ^ F. 

An  example  In  GoWy  Engr.,  July,  1891,  is  a  pair  of  hoisting-engiiies  94"  x 
40",  drum  12  ft.  diam..  average  steam-pressure  in  cylinder  ==:  99.5  Ib«.:  A  = 
904.8;  P=  5d.5;  5  a  40;  Cs  4(S.4.  Theoretical  load,  not  allowing  for  friction. 
A  PiS  -H  C  =  9689  lbs.  The  actual  load  that  could  just  be  lifted  on  trial  was  79R8 
lbs.,  making  friction  loss  F  s  1601  lbs.,  or  SO  +  per  cent  of  the  actual  load 
lifted,  or  If^  of  the  theoretical  load. 

The  above  rule  takes  no  account  of  the  resistance  due  to  inertia  of  the 
load,  but  for  all  ordinary  cases  in  which  the  acoeleratioo  of  speed  of  the 
cage  is  moderate,  it  is  covered  by  the  allowance  for  friction,  etc.  The  re< 
sistance  due  to  inertia  is  equal  to  the  force  required  to  gfTe  the  load  the 
velocity  acquired  in  a  given  time,  or,  as  shown  In  Mechanics,  equal  to  the 

product  of  the  mass  by  the  acceleration,  or  B  ss  — ,  in  which  B  =  resist- 
ance in  lbs.  due  to  Inertia;  W  =  weight  of  load  in  lbs. ;  V=  maximum  veloG- 
ity  in  feet  per  second;  T  =s  time  in  seconds  taken  to  acquire  the  velocity  r*; 
g  =  .%.16. 

Effect  of  Slaek  Rope  upon  Strain  tn  Bolstlnff.— A  series  of 
tests  with  a  dynamometer  are  published  by  the  Trenton  Iron  Co.,  which 
show  that  a  dangerous  extra  strain  may  be  cansed  by  a  few  inches  of  slack 
rope  In  one  case  the  cage  and  full  tubs  weighed  UJSOO  lbs.;  the  strain  when 
the  load  was  lifted  gently  was  11,529  lbs.;  with  3  in.  of  slack  chain  it  was 
10.0-35  lbs ,  with  6  in.  slack  S».750  lbs.,  and  with  9  in.  slack  S7,990  lbs. 

I#lnilt  of  Deptb  for  Hoisting;.— Taking  the  weight  of  a  cast-steel 
hoisting-rope  of  1^  inches  diameter  at  'i  lbs.  per  running  foot,  and  its  breek* 
ing  strength  at  84,000  lbs.,  it  should,  theoretically,  sustain  itself  antfl  42<U00 
feet  long  before  breaking  from  its  own  weight.  Bat  taking  Uie  usual  factor 
of  safety  of  7.  then  the  safe  working  length  of  such  a  ro]>e  would  be  only 
GOOO  feet.  If  a  weight  of  8  tons  is  now  hung  to  the  rope,  which  ia  equivalent 
to  that  of  a  cage  of  moderate  capacity  with  Its  loaded  cars,  the  maximum 
length  at  which  such  a  rope  could  be  used,  with  the  factor  of  safety  of  7,  is 
8000  feet,  or 

2sp.f.fl000=?^^        .-.««  8000  feet- 

This  limit  may  be  greatly  iDCreased  by  using  special  steel  rope  of  higher 
strength,  by  using  a  smaller  factor  c^  safety i  and  by  uslsfp  taper  r(i^>e8. 
(See  paper  by  H.  A.  Wheeler,  Trans.  A.  I.  M.  E.,  aix.  Iw.) 

Ijarse  Ilolstlni;  Records*— At  a  colliery  in  North  Derbyshire  dur- 
ing the  first  week  in  June,  1890,  6809  tons  were  raised  from  a  depth  of  fiOi 
yards,  the  time  of  winding  being  from  7  a.m.  to  8.30  p.m. 

At  two  other  Derbyshire  pits,  17D  and  140  yards  in  depth,  the  speed  of 
winding  and  changing  has  been  brought  t^)  such  perfection  that  tubs  are 
drawn  and  changed  three  times  in  one  minute.    (Proc.  Inst.  M.  B.,  ISM.) 


POWER  OF   H018T1KG-ENGIKES.  909 

At  the  Kotttnffham  Colliery  near  Wilkesbarre,  Pa.,  In  Oct.  18M,  70.168  tons 
urere  shipped  in  24.16  dayii,  the  average  hoist  per  day  being  1818  mine  cars. 

The  depth  of  hoist  was  470  feet,  and  all  coal  came  from  oi>e  openlog.  The 
engines  were  fast  motion,  22  x  48  inches,  conical  drums  4  feet  1  inch  long,  t 
feet  diameter  at  small  end  and  0  feet  at  large  end.    {Bng^g  Netca,  Nov.  1891.) 

Pnenmaeic  HolaUng.  (H.  A.  Wheeler,  Tnuts.  A.  I.  M.  E.,  xix.  107.)- 
A  pneumatic  hoist  was  Insttilled  hi  1876  at  Eplnac,  France,  consisting  of  two 
continuous  air-tight  iron  cylinders  extending  from  the  bottom  to  the  top  of 
the  shaft.  Within  the  cviinder  moired  a  piston  from  which  was  hung  the 
cage.  It  was  operated  by  exhausting  the  air  from  above  the  pteton,  the 
lower  side  being  open  to  the  atmosphere.  Its  use  ▼'as  discontinued  on  ac- 
count of  the  failure  of  the  mine.  Mr.  Wheeler  gives  a  descHption  of  the  sys- 
tem, but  criticises  it  as  not  being  equal  on  the  whole  to  boistiog  by  steel  ropes. 

Pneumatic  hoisting-cylinders  using  compressed  air  have  been  used  at 
blast-furnaces,  the  weighted  piston  counterbalancing  the  weigtitof  the  cage, 
and  the  two  being  connected  by  a  wire  rope  passing  over  a  pulley-sheave 
above  the  top  of  the  cylinder,  in  the  more  modem  furnaces  steam-engine 
faoisij*  are  generally  used. 

€oiiiiterlMiUi.neliic  of  IVlBdlnc-enffiBea*  (H.  W.  Hughes,  Co- 
lumbia Coll.  ^y.)— Engines  iiiiinlng  un(>alanced  are  subject  to  enonnons 
Tartotions  in  tiie  toad;  for  let  W  •=■  weight  of  cage  and  empty  tubs,  say  6870 
)bs. ;  c  =  weight  of  coal,  say  4480  lbs.;  r  =:  weight  of  hoisung  rope,  say  6000 
Ibe. ;  r*  =  we^ht  of  counterbalance  rope  hanging  down  pit,  say  60UO  lbs.  The 
weight  to  be  lifted  will  be: 

If  weight  of  rope  Is  unbalanced.        If  weight  of  rope  Is  balanced. 

At  beginning  of  lift: 

TV'.fc-i-r- Worl0,4801ba  TT-f  c-f  r-C^T-f  Kjy 

At  middle  of  lift: 

At  end  of  lift: 
Wr+c-(Fr-fr)orininiMl6a01be.  TT+c-f  r'-ClT+r), 

That  counterbalancing  materially  affects  the  size  of  winding-engines  is 
#hown  by  a  formula  given  by  Mr.  Robert  Wilson,  which  is  based  on  the  fact 
4hat  the  greatest  work  a  winding-engine  has  to  do  is  to  get  a  given  mass  into 
a  certain  velocity  uniformly  accelerated  from  rest,  and  to  raise  a  load  the 
distance  passed  over  during  the  time  this  velocity  is  being  obtained. 

Ust  W  =  tlie  weight  to  t)e  set  in  motion:  one  cage,  coal,  number  of  empty 
tubs  on  cage,  one  winding  rope  from  pit  head-gear  to  bottom, 
and  one  rope  from  banltlng  level  to  bottom. 

V  =  greatest  velocity  attained,  uniformly  accelerated  from  rest; 

g  =  gravity  ==  3S.2; 

t  =  time  in  seconds  during  which  v  is  obtained; 

L  =  unbalanced  load  on  engine; 

S  =  ratio  of  diameter  of  drum  and  crank  circles; 

P  s  average  pressure  of  steam  in  cylinders; 

N=  number  of  cylinders; 

8  =  space  passed  over  by  crank-pin  during  time  f ; 

C  =:%,  constant  to  reduce  angular  space  passed  through  by  crank,  to 
.    tlte  distance  passed  through  by  the  piston  during  the  time  t; 

A  a  area  of  one  cylinder,  without  margin  for  friction.  To  this  an  ad- 
dition for  friction,  etc.,  of  engine  is  to  be  made,  varying  from  10 
to  80j<  of  ^. 


or 
4480 
lbs. 


VL  Where  kMul  Is  balanced. 


Fjysc. 

9d.  Where  load  Is  unbalanced: 

The  formula  is  the  same,  with  the  addition  of  another  term  to  aUow  for 
the  variation  in  the  lengths  of  the  ascending  and  descending  ropes.  In  this 
case 


DIG 


HoisTiira. 


hi  =  reduced  length  of  rope  In  t  attached  to  ascendlnff  CBfft^ 
ht  =■  iucreatted  length  of  rope  in  t  attached  to  deacendhig  cage; 
w  =  weight  of  rope  per  foot  in  pounds.    Then 

PNSC. 

Applying  the  above  formula  when  designing  new  engines,  Mr.  Wilaon 
found  that  30  inches  diameter  of  cyUnders  would  produce  equal  results,  womi 
balanced,  to  those  of  the  36-inch  cylinder  in  use,  the  latter  being  unbal- 
anced. 

Counterbalancing  may  be  employed  in  the  following  methods : 

(fi)  Tapering  Hope.->At  the  initial  sUM^  the  tapering  rope  enables  us  to 
wind  from  grbater  depths  than  is  possible  with  ropes  of  uniform  section. 
The  thickness  of  such  a  rope  at  any  point  should  only  be  such  as  to  safely 
bear  the  load  on  it  at  that  point. 

With  tapering  ropes  we  obtain  a  smaller  difference  between  the  Initial  and 
final  load,  but  the  difference  is  still  considerable,  and  for  perfect  equaliza- 
tion of  the  load  we  must  rely  on  some  other  resource.  The  theory  or  taper 
ropes  is  to  obtain  a  rope  of  uniform  strength,  thinner  at  the  cage  end  where 
Uie  weight  is  least,  and  thicker  at  the  drum  end  where  it  is  greatest. 

(b)  The  Counterpoise  System  consists  of  a  heavy  chain  working  up  and 
down  a  staple  pit,  the  motion  being  obtained  by  means  of  a  special  small 
drum  placeid  on  the  same  axis  as  the  winding  drum.  It  is  so  arranged  that 
the  chain  hangs  in  full  length  down  the  staple  pit  at  the  commencement  of 
the  winding;  in  the  centre  of  the  run  the  whole  of  the  chain  rests  on  the 
bottom  of  the  pit,  and,  finally,  at  the  end  of  the  winding  the  counterpoise 
has  been  rewound  upon  the  small  drum,  and  Is  In  the  same  condition  as  it 
was  at  the  commencement. 

(c)  Loaded-xoagon  System.— A  plan,  formerly  much  employed,  was  to 
have  a  loaded  wagon  miming  on  a  short  incline  in  place  of  this  heavy  cbain: 
the  rope  actuating  this  wagon  being  connected  in  the  same  manner  as  tne 
above  to  a  subsidiary  drum.  The  incline  was  constructed  steep  at  the  oom« 
mencement,  the  inclination  gradually  decreasing  to  nothing.  At  the  begin' 
ning  of  a  wind  the  wagon  was  at  the  top  of  the  incline,  and  during  a  portion 
of  the  run  graduallv  passed  down  it  till,  at  the  meet  of  cages,  no  |puil  was 
exerted  on  the  engine— the  wagon  by  this  time  being  at  the  bottom.  In  tiie 
latter  part  of  the  wind  the  resistance  was  all  against  the  engine,  owing  to 
its  having  to  pull  the  wagon  up  the  incline,  and  this  resistance  lncrea«i«d 
from  nothing  at  the  meet  of  cages  to  its  greatest  quantity  at  the  condusiou 
of  the  lift. 

id)  Tlie  Endless-rope  System  is  preferable  to  all  others,  if  there  is  sufn 
cient  sump  room  and  the  shaft  is  free  from  tubes,  cross  timbers,  and  other 
impediments.  It  consists  in  placing  beneath  the  cages  a  tall  rope,  similar 
in  diameter  to  the  winding  rope,  and,  after  conveying  this  down  the  pit,  it  is 
attached  beneath  the  other  cage. 

(e)  Flat  Ropes  Coiling  on  /fe«Zs— This  means  of  winding  allows  of  a  cer- 
tain equalization,  for  the  radius  of  the  coil  of  lascending  rope  continues  to 
increase,  while  that  of  the  descending  one  continues  to  diminish.  Conse- 
quently, as  the  resistance  decreases  in  the  ascending  load  the  leverage 
mcreases,  and  as  the  power  increases  in  the  other,  the  leverage  diminishes. 
The  variation  in  the  leverage  is  a  constant  quantity,  and  la  equal  to  the 
thickness  of  the  rope  where  it  is  wound  on  the  drum. 

By  tlie  above  means  a  remarkable  uniformity  in  the  load  may  be  ob- 
tained, the  only  objection  being  the  use  of  flat  ropes,  which  weigh  heavier 
and  only  last  about  two  thirds  the  time  of  round  ones. 

(/)  Conical  Ih*um«.— Results  analogous  to  the  preceding  may  be  obtained 
by  using  round  ropes  coiling  on  conical  drums,  which  may  either  lie  smooth, 
with  the  successive  colls  lying  side  by  side,  or  they  may  be  provided  with  a 
spiral  groove.  The  objection  to  these  forms  is,  that  perfect  equalization  is 
not  obtained  with  the  conical  drums  unless  the  sides  are  very  steep,  and  con- 
sequently there  is  great  risk  of  the  rope  slipping ;  to  obviate  this,  scroll 
drums  were  proposed.  They  are,  however,  very  expensive,  and  the  latersl 
displacement  of  the  winding  rope  from  the  centre  line  of  pulley  becomes 
very  great,  owing  to  their  necessary  large  width. 

(g)  37tc  Koepe  System  of  Winding.— An  iron  pulley  with  a  single  circular 
groove  takes  the  place  of  the  ordinary  drum.  The  winding  rope  passes 
from  one  cage,  over  its  head-gear  pulley,  round  the  drum,  and,  after  pass 


CBAKBS.  911 

foflT  over  the  other  head-eear  pulley,  Is  connected  with  the  second  cage.  The 
winding  rope  thus  encircleB  about  half  the  periphery  of  the  drum  in  the 
same  manner  as  a  driving-belt  on  an  ordinary  pullt^y.  There  is  a  balance 
mpe  beneath  the  cages,  iMissinsr  round  a  pulley  in  the  sump;  the  arrantre- 
m  -lit  may  be  likened  to  an  endless  rope,  the  two  cages  being  simply  points 
of  attachment. 

BBIiT-CONTBTORS. 

Orain-elevators*  —  American  O rain-elevators  are  described  in  a 
paper  by  E.  Lee  Heidenreich,  read  at  the  International  Engineering  Con- 
gress at  Chicago  (Trans.  A.  S.  C.  E.  1H93).    See  also  Trans.  A.  8.  M.  E.  vii.  660. 

Bands  for  carrjrlnff  Oraln.  —  Flexible-rubber  bands  are  exten- 
sively used  for  carrying  gram  in  and  around  elevators  and  warehouses.  An 
article  on  the  grain-storage  warehouses  of  the  Alexandria  Dock.  Liverpool 
(Proc.  Inst.  M.  E.,  July,  1801),  describes  the  performance  of  these  bauds, 
aggregating  three  miles  In  length.  A  band  16m(  inches  wide,  r.nt)  feet  long, 
running  9  to  10  feet  per  second  has  a  canying  capacity  of  fiO  tons  per  hour. 
See  ai»o  paper  on  Belts  as  Grain  Conveyors,  by  T.  W.  Hugo,  Trans.  A.  S. 
M.  E..  vi.  400. 

Carrylns-bands  or  Belts  are  used  for  the  purpose  both  of  sorting 
cotil  and  of  removing  impuiities.  These  carrying-bands  may  be  said  to  be 
confined  to  two  descriptions,  namely,  the  wire  belt,  which  consists  of  an 
endless  length  of  woven  wire;  and  the  steel-plate  belt,  which  consists  of 
two  or  three  endless  chains,  carrying  steel  plates  varying  in  width  from  6 
inches  to  14  inches.    (Proc.  Inst.  M.  £.,  July,  1890.) 

CRANZ38. 
ClaMtfl<satlon  of  Cranes.    (Henry  R.  Towne,  Trans.  A.  S.  M.  E.,  Iv. 

288.    Revised  in  Hoisting,  published  by  The  Yale  &  Towne  Mfg.  (3o.) 

A  Hoist  is  a  machine  for  raising  and  lowering  weights.  A  Crane  is  a 
hoist  with  the  added  capacity  of  moviug  the  load  In  a  horizontal  or  lateral 
direction. 

Cranes  are  divided  into  two  classes,  as  to  their  motions,  viz..  Rotary  and 
-Bectilineai-y  and  into  four  groups,  as  to  their  source  of  motive  power,  viz.: 

Hand. — When  operated  by  manual  power. 

Pouvr.— When  driven  by  power  derived  from  line  shafting. 

Steam,  Electric.  Hydraulic^  or  Pneumatic.— When  driven  by  an  engine  or 
motor  attached  to  the  crane,  and  operated  by  steam,  electricity,  water,  or 
air  transmitted  to  the  crane  from  a  ftxed  source  of  supply. 

Locomoftve.— When  the  crane  is  provided  with  its  own  boiler  or  other 
generator  of  power,  and  is  self-propelling ;  usually  being  capable  of  both 
rotary  and  rectilinear  motions. 
.  Rotary  and  Rectilinear  Cranes  are  thus  subdivided : 

RoTART  Cranes. 

(I)  fi^f{7<nj^crane«.~HaviDg  rotation,  but  no  trolley  motion. 

(3)  Jt6-crane«.~HaviDg  rotation,  and  a  trolley  travelling  on  the  jib. 

(8)  (7oiumn-crane«. ^Identical  with  the  Jib-cranes,  but  rotating  around  a 
fixed  column  (which  usually  supports  a  floor  above). 

(4)  Pt//ar-crane«.— Having  rotation  only;  the  pillar  or  column  being  sup- 
ported entirely  from  the  foundation. 

(5)  Pillar  Jt6-crane«.— Identical  with  the  last,  except  in  having  a  jib  and 
trolley  motion. 

(6)  2><fn*icfc-ot'ane«.— Identical  with  jib-cranes,  except  that  the  head  of  the 
mast  is  held  in  position  by  guy -rods,  instead  of  by  attachment  to  a  roof  or 
ceiline. 

(7)  m(Zfcino-craue«.— Consisting  of  a  pillar  or  jib^srane  mounted  on  wheels 
and  arranged  to  travel  longitudinally  upon  one  or  more  rails. 

(8)  I«ocomo<tve-crane«.— Consisting  or  a  pillar  crane  mounted  on  a  truck, 
and  proviaed  with  a  steam-engine  capable  of  propelling  and  rotating  the 
crane,  and  of  hoisting  and  lowering  the  load. 

Rbctilinbar  Crambs. 

(9)  Bridge-cranes.— HavIus:  a  fixed  bridge  spanning  an  opening,  and  a 
trolley  moving  across  the  bridge. 

(10)  Trarn-craneA.— Consisting  of  a  tnick,  or  sliort  bridge,  travelling  lon- 
gitudinally on  overhead  rails,  and  without  trolley  motion. 

(II)  TVavcfUf'nt^crane*.— Consisting  of  a  bridge  moving  longitudinally  on 
overhead  tracks,  and  a  trolley  moving  transversely  on  the  bridge. 


912  HOISTING. 

(12)  (/an/riec.— OonsIstiDS  of  ao  overhead  bridge,  carried  at  each  eod  br  a 
treKtle  travellinfc  on  longitudinal  tracks  on  the  ground,  and  having  a  trolley 
moving  transversely  on  the  bridge. 

(]8)  Rotary  Bridge-a'anes.—Comblniuf^  rotarv  and  rectilinear  movements 
and  oonsistuig  of  a  bridge  pivoted  at  one  end  to  a  central  pter  or  post, 
and  supported  at  the  other  end  on  a  circular  track  ;  provided  with  a  trolley 
moving  transversely  on  the  bridge. 

For  descriptions  of  these  several  forms  of  cranes  see  Townees  "Treatise 
on  Cranes.** 

Stresses  In  Granes«~nee  Stresses  in  Framed  Structures,  p.  440,  ante, 

Posltton  of  tlie  Inclined  Brace  In  a  jrib-crane«— The  ntost 
economical  arrangement  is  that  in  which  the  inclined  brace  intersects  the 
jib  at  a  distance  from  the  mast  equal  to  four  fifths  the  eflteciive  radius  of 
the  crane.    (Hoiating.) 

A  Ijarse  TraTelllnc*erane,  designed  and  built  by  the  Morgan 
Engineering  Co.,  Alliance,  O..  for  the  12-incn-gun  shop  at  the  Wasblogtoo 
Navy  Yard,  is  described  in  American  MachiniMt,  Jane  18,  1890.  Capacity, 
150  net  tons;  distance  between  centres  of  inside  rails,  60  ft.  6  in.;  maximum 
cross  travel,  44  ft.  2  in.;  effective  lift,  40  ft.;  four  speeds  for  main  hoist,  1,  2, 
4,  and  8  ft.  per  min. ;  loads  for  these  speeds,  ISO,  75, 87^,  and  1^  tons  respec- 
tively ;  traversing  speeds  of  trolley  on  bridge,  85  and  50  ft.  per  minute ; 
speeds  of  bridge  on  main  track,  90  and  60  ft.  per  minute.  Square  shafts  are 
employed  for  driving. 

A  l50-<on  Pillar^erane  was  erected  in  1808  on  Finnieston  Quay, 
Glasgow.  The  jib  is  formed  of  two  steel  tubes,  each  89  in.  diam.  and  90  ft. 
long.  Tlie  radius  of  sweep  for  heavy  lifts  is  dR  ft.  The  jib  and  its  load  are 
counterbalanced  by  a  balance-box  weighted  with  100  tons  of  iron  and  steel 
punchings.  In  a  test  a  180- ton  load  was  lifted  at  the  rate  of  4  f  ^  per  minute, 
and  a  complete  revolution  made  with  this  load  in  5  minutes.  Eng*g  News, 
July  80,  1893. 

OonipreBsed-air  TraTelllnv-«ranes«— Compressed-air  ovex^iead 
travelling-cranes  have  been  built  by  the  Lane  &  Bodley  Co.,  of  Cincinnati. 
They  are  of  80  tons  nominal  caiMicity,  each  about  50  ft.  span  and  400  ft.  length 
of  travel,  and  are  of  the  triple-motor  type,  a  pair  of  simple  reversing-engines 
being  used  for  each  of  the  necessary  operations,  the  pair  of  engines  for  the 
bridge  and  the  pair  for  the  trolley  travel  being  each  5>lnch  bore  by  7>lnch 
stroke,  while  the  pair  for  hoisting  is  7-inch  bore  by  0-inch  stroke.  Air  is 
furnished  by  a  comi)ressor  having  steam  and  air  cylinders  each  10- in.  diam. 
and  18-in.  stroke,  which  with  a  boiler-pressure  of  about  80  pounds  gives  an  alr^ 

Sreasure  when  required  of  somewhat  over  100  pounds.  The  air-compressor 
I  allowed  to  run  continuously  without  a  governor,  the  speed  being  regulated 
by  the  resistance  of  the  air  in  a  receiver.  From  a  pipe  extending  from  the 
receiver  along  one  of  the  supporting  trusses  communication  is  continuously 
maintained  with  an  auxiliary  receiver  on  each  traveller  by  means  of  a  one- 
inch  hose,  the  obiect  of  the  auiiliary  receiver  being  to  provide  a  supplv  of 
air  near  the  engines  for  immediate  demands  and  independent  of  the  hose 
connection,  which  may  thus  be  of  small  dimension.  Some  of  the  advantages 
said  to  be  possessed  by  this  type  of  crane  ai-e:  simplicity:  absence  of  all  mov- 
ing parts,  excepting  those  required  for  a  particular  motion  when  that  motion 
is  in  use;  no  danger  from  fire,  leakage,  electric  shocks,  or  freezing;  ease  of 
repair;  variable  speeds  and  reversal  without  gearing;  almost  entire  absence 
of  noise;  and  moclerate  cost. 

^nay-cranen.— An  illustrated  description  of  several  varieties  of  sta- 
tionary and  travelling  cranes,  with  results  of  experiments,  is  gt^en  in  a 
paper  on  Quay-cranes  in  the  Port  of  Hamburg  by  Chas.  Nehls,  Trans.  A.  B. 
C.  K..  Chicasro  Meeting,  1893. 

Hydraulle  Cranes,  Acenmnlators,  etc*— See  Hydraulic  Press* 
ure  Transmission,  page  618,  ante. 

Sleclrfc  Cranes.— Travelling-cranes  driven  by  electric  motoiv  have 
largely  supplanted  ciunes  driven  by  square  shafts  or  flying-ropes.  Eadtk  of 
the  three  motions,  viz.,  longitudinal,  traversing  and  hoisting,  Is  usually  ae> 
complished  by  a  separate  motor  carried  upon  the  crane. 

mUAK-ROPB  nAI7IiAGB« 

Methods  for  transporting  coal  and  other  products  by  means  of  wire  ropc^ 
though  varying  from  each  other  in  detail,  may  be  grouped  in  five  c' 
I.  The  Self-acting  or  Gravity  Inclined  Plane. 
II.  TheSUnpIe  Engme- plane. 


WIRE-ROPE  HAULAGE.  S13 

tn.  The  Tail-rope  System. 
IV.  The  Endless-rope  System. 
V.  The  Cable  Tramway. 

The  follow! njf  brief  description  of  these  systems  !b  abridged  from  a 
Mtmphlet  on  Wire-rope  Haulage,  by  Wm.  Hlldenbrand,  C.E.,  published  by 
John  A.  RoebIine*8  Song  Co.,  Trenton,  N.  J. 

I.  Tbe  Seir-actlnc  Inclined  Plane.— The  motive  power  for  the 
self-acting  inclined  plane  is  gravity;  consequently  this  mode  of  transport- 
ing coal  finds  application  only  in  places  where  the  coal  is  conveycki  from  a 
higher  to  a  lower  point  and  where  the  plane  has  sufficient  grade  for  the 
loaded  descending  cars  to  raise  the  empty  cars  to  an  upper  level. 

At  the  head  of  tiie  plane  there  is  a  drum,  which  Is  generally  constructed 
of  wood,  having  a  diameter  of  seven  to  ten  feet.  It  is  placed  high  enough 
to  allow  men  and  cars  to  pass  under  it.  Loaded  cars  coming  from  the  pit 
are  either  singly  or  in  sets  of  two  or  three  switched  on  the  track  of  tne 
plane,  and  their  speed  in  descending  is  regulated  by  a  brake  on  the  drum. 

Supporting  rollem,  to  prevent  the  rope  dragging  on  the  ground,  are 
p:enerally  of  wood,  ft  to  6  inches  In  diameter  and  18  to  24  inches  long,  with 
H-  to  ^-Inch  iron  axles.  The  distance  between  the  rollers  varies  from  15  to 
So  feet,  steeper  planes  requiring  less  rollers  than  those  with  easy  grades. 
Considering  only  the  reduction  of  friction  and  what  is  best  for  the  preserva- 
tion of  rope,  a  general  rule  may  be  given  to  use  rollers  of  the  greatest 
possible  diameter,  and  to  place  them  aa  close  as  economy  will  permit. 

The  smallest  angle  of  inclination  at  which  a  plane  can  oe  maae  self-acting 
will  be  when  the  motive  and  resistins^  forces  balance  each  other.  The 
motive  forces  are  the  weights  of  the  loaded  car  and  of  the  descending  rope. 
The  resisting  forces  consist  of  the  weight  of  the  empty  car  and  ascending 
rope,  of  the  rolling  and  axle  friction  of  the  cars,  and  of  the  axle  friction  of 
the  supporting  rollers.  The  frirtlou  of  the  drum,  stiffness  r  f  rope,  and 
resistance  of  air  may  be  neglected.  A  general  rule  cannot  be  given,  because 
a  change  in  the  length  of  the  plane  or  in  the  weight  of  the  cars  changes  the 
proportion  of  the  forces;  also,  because  the  coefficient  of  friction,  depending 
on  tne  condition  of  the  road,  construction  of  the  cars,  etc.,  is  a  very  uncer- 
tain factor. 

For  working  a  plane  with  a  ^inch  steel  rope  and  lowering  from  one  to 
four  pit  cars  weighing  empty  1400  lbs.  and  loaded  4000  lbs.,  the  rise  in  100 
feet  necessary  to  make  the  plane  self-acting  will  be  from  about  5  to  10  feet, 
decreasing  aa  the  number  of  cars  increase,  and  increasing  as  the  length  of 
plane  increases. 

A  gravity  inclined  plane  should  be  slightly  concave,  steeper  at  the  top 
than  at  the  bottom.  The  maximum  deflection  of  the  curve  should  be  at  an 
inclination  of  45  degrees,  and  diminish  for  smaller  as  well  as  for  steeper 
Inclinations. 

II.  Tlie  Simple  Ensrlne-plane.— The  name '*  Engine-plane  "Is 
ICiven  to  a  plane  on  which  a  load  is  raised  or  lowered  by  means  of  a  single 
wire  rope  and  stationary  ateam-englne.  It  is  a  cheap  and  simple  method  of 
conveying  coal  underground,  and  therefore  Is  applied  wherever  circum- 
stances permit  it. 

Under  ordinary  conditions  such  as  prevail  In  the  Pennsylvania  mine 
region,  a  train  of  twenty -five  to  thirty  loaded  cars  will  descend,  with  reason- 
able velocity,  a  straight  plane  5000  feet  long  on  a  grade  of  1^  feet  in  100, 
while  it  would  appear  that  2^  feet  In  100  is  necessary  for  the  same  number 
of  empty  cars.  For  roads  longer  than  5000  feet,  or  when  containing  sharp 
curves,  the  grade  fshould  be  correspondingly  larger. 

III.  Tlie  Tail-rope  Syeteni.— Of  all  methods  for  conveying  coal 
underground  by  wire  rope,  the  tail-rope  system  has  found  the  most  applica- 
tion. It  can  be  applied  under  almost  any  condition.  The  road  may  be 
straight  or  curved,  level  or  undulating.  In  one  continuous  line  or  with  side 
branches.  In  general  principle  a  tail-rope  plane  is  the  same  as  an  engine- 
plane  worked  in  both  directions  with  two  ropes.  One  rope,  called  the  '*  main 
rope,*' serves  for  drawing  the  set  of  full  cars  outward;  the  other,  called 
the  *'  tail-rope,*'  is  necessary  to  take  back  the  empty  set,  which  on  a  level 
or  undulating  road  cannot  return  by  gravity.  The  two  drums  mav  be 
located  at  the  opposite  ends  of  the  road,  and  driven  by  separate  engines, 
but  more  frequently  they  are  on  tiie  same  shaft  at  one  end  of  the  plane. 
In  the  first  case  each  rope  would  require  the  length  of  the  plane,  but  m  the 
second  case  the  tail  rope  must  be  twice  as  long,  being  leu  from  the  drum 
around  a  sheave  at  the  other  end  of  the  plane  and  back  again  to  its  starting- 


914  HOISTING. 

point.  When  the  main  rope  draws  a  set  of  full  cars  out,  the  tail-rope  drum 
runs  loose  on  the  shaft,  and  the  rope,  being  attached  to  the  rear  car.  un- 
winds itself  stead  ilv.  Going  in,  the  reverse  takes  place.  Each  drum  is 
provided  with  a  brake  to  check  the  speed  of  the  train  on  a  down  i^rade  and 
prevent  its  overrunning  the  forward  rope.  As  a  rule,  the  tail  rope  is 
strained  less  than  the  main  rope,  but  in  cases  of  heavy  grades  dipping  out> 
ward  it  is  possible  that  the  strain  in  the  former  may  become  as  large,  or 
even  lai-ger,  than  in  the  latter,  and  in  the  selection  of  the  sizes  reference 
should  be  had  to  this  circumstance. 

IT.  The  Eiidle8B*rope  System*— The  prhicipal  features  of  this 
system  are  as  follows: 

1.  The  rope,  as  the  name  indicates,  is  endless. 

ft.  Motion  is  given  to  the  rope  by  a  single  wheel  or  drum,  and  friction  is 
obtained  either  by  a  grip- wheel  or  by  passing  tiie  rope  several  times  around 
the  wheel. 

3.  The  rope  must  be  kept  constantly  tight,  the  tension  to  be  produced  by 
artifloial  means.  It  is  done  in  placing  either  the  return-wheel  or  an  extra 
tension  wheel  on  a  carriage  and  connecting  it  with  a  weight  hanging  over  a 
pulley,  or  attaching  it  to  a  fixed  post  by  a  screw  which  occasionally  can  be 
shortened. 

4.  The  cars  are  attached  to  the  rope  bv  a  grip  or  clutch,  which  can  take 
hold  at  any  place  and  let  go  again,  starting  and  stopping  the  train  at  will, 
without  stopping  the  engine  or  the  motion  of  the  rope. 

5.  On  a  single-track  road  the  rope  works  forward  and  backward,  but  on  a 
double  track  it  is  possible  to  run  it  always  in  the  same  direction,  the  full 
cars  going  on  one  track  and  the  empty  cars  on  the  other. 

This  method  of  conveying  coal,  as  a  rule,  has  not  found  as  general  an  in- 
troduction AS  the  tail-rope  system,  proliablv  because  its  efficacy  is  not  so 
apparent  and  the  opposing  difflculties  require  greater  mechanical  skill  and 
more  complicated  appliances.  Its  advantages  are,  first,  that  it  requires 
one  third  less  rope  than  the  tail-rope  system.  This  advantage,  however, 
is  partially  counterbalanced  by  the  circumstance  that  the  extra  tension  io 
the  rone  requires  a  heavier  size  to  move  the  same  load  than  when  a  main 
and  tall  rope  are  used.  The  second  and  principal  advantage  is  that  it  is 
possible  to  start  and  stop  trains  at  will  without  signalling  to  the  engineer. 
On  the  other  hand,  it  is  more  difficult  to  work  curves  with  the  endless  sys- 
tem, and  still  more  so  to  work  different  branches,  snd  the  constant  stretch 
of  the  rope  under  tension  or  its  elongation  under  changes  of  temperature 
frequentnr  causes  the  ro(>e  to  slip  on  the  wheel,  in  spite  of  every  attention, 
causing  delay  In  the  transportation  and  injurr  to  the  rope. 

T.  HTlre-rope  Traimraya.— Tho  methods  of  conveying  products  on 
a  suspended  ix)pe  tramway  find  especial  application  in  places  where  a  mine 
is  located  on  one  side  of  a  river  or  deep  ravine  and  the  loading  station  on 
the  other.  A  wire  rope  suspended  between  the  two  stations  forms  the  track 
on  which  material  in  properly  constructed  ** carriages'*  or  *' buggies"  ts 
transported.  It  saves  the  construction  of  a  bridge  or  trmtlework,  and  is 
practical  for  a  distance  of  2000  feet  without  an  intermediate  support. 

There  are  two  distinct  classes  of  rope  tramways: 

1.  The  rope  is  stationary,  forming  the  track  on  which  a  bucket  holding 
the  material  moves  forward  and  backward,  pulled  by  a  smaller  endless 
wire  rope. 

2.  The  rope  is  movable,  forming  Itself  an  endless  line,  which  serves  at 
the  same  time  as  siipportlng  track  and  as  pulling  rope. 

Of  these  two  the  first  method  has  found  more  general  application,  and  is 
especially  adapted  for  long  spans,  steep  inclinations,  and  heavy  loads.  The 
second  method  is  used  for  long  distances,  divided  into  short  spans,  and  is 
only  applicable  for  light  loads  which  are  to  be  delivered  at  regular  intervals. 

For  detailed  descriptions  of  the  several  systems  of  wire-rope  transporta- 
tion, see  circulars  of  John  A.  R^ebling's  Sons  Co.,  The  Trenton  Iron  Co.,  and 
other  wire-rope  manufacturers.  See  also  paper  on  Two-rupe  Haulage 
Systems,  by  R.  Van  A.  Norris,  Trans.  A.  S.  M.  E.,  xil.  (J-26. 

In  the  Bleichert  System  of  wire-rope  tramways,  in  which  the  track  rope  is 
stationary,  loads  of  1000  pounds  each  and  upward  are  carried.  While  the 
avernge  spans  on  a  level  are  from  150  to  200  feet,  in  crossing  rivers,  ravines, 
etc.,  spans  up  to  1500  feet  are  fiequently  adopted.  In  a  tramway  on  this 
system  at  Granite.  Montana,  the  total  length  of  the  line  is  9730  feet,  with  a 
fall  of  Vii5  feet.  The  descending  loads,  amounting  to  a  constant  weight  of 
about  11  tons,  develop  over  14  horse-power,  which  is  sufficient  to  haui  <dm 
empty  buckets  as  well  as  about  50  tons  of  supplies  per  day  up  the  line,  ai:d 


SUSPEXSIOK^  CABLEWAYS   OR  CABLE   HOISTS.       915 


also  to  run  the  ore  crusher  and  elevator.    It  is  capable  of  delivering  %0 
tons  of  mateiial  in  10  liours. 

Snapeniiloii  Cablenrays  or  Cable  Holst-coiiTeyora* 

(Trenton  Iron  Co.) 

In  quarrying^,  rock-cuttlnf?,  strippiiifif.  piling,  dam-building,  and  many 
other  operations  where  it  is  necessary  to  hoist  and  convey  large  individual 
loads  economically,  it  frequently  happens  that  thi^  application  of  a  system 
of  derricks  is  impracticable,  by  reason  of  the  limited  area  of  their  efficiency 
and  the  room  which  they  occupy. 

To  meet  such  conditions  cable  hoist^onveyors  are  adapted,  as  they  can  be 
operated  In  clear  spans  up  to  1500  feet,  and  in  lifting  individual  loads  up  to 
15  tons.  Two  types  are  made— one  in  which  tlie  lioisting  and  conveying  ai,-e 
done  by  separate  running  ropes,  and  the  other  applicable  only  to  Inclines, 
in  which  the  carriage  dcwoends  by  gravity,  and  but  one  running  rope  is  re- 
quired. The  moving  of  the  carriage  in  the  former  is  effected  by  means  of 
an  endless  rope,  and  these  are  commonly  known  as  "  endless-rope  "  hoist- 
conveyors  to  aistlnguish  them  from  the  latter,  which  are  termed ''  inclined  '* 
h<>ist-conveyors. 

The  general  arrangement  of  the  eadless-rope  hoist-conveyors  consists  of  a 
main  cable  passing  over  towers,  A  frames  or  masts,  as  may  be  most  conve* 
Dient,  and  anchored  flrmly  to  the  ground  at  eacli  end,  the  requisite  i€<nsion 
In  the  cable  being  maintained  by  a  turnbuckle  at  one  anchorage. 

Upon  this  cable  travels  the  carriage,  which  is  moved  back  and  forth  over 
the  line  by  means  of  the  endless  rope.  The  hoisting  is  done  by  a  separate 
rope.  tK>th  ropes  being  operated  by  an  en<;ine  specially  designed  for  the 

gurpose,  whicn  may  be  located  at  either  end  of  the  line,  and  is  constructed 
1  such  a  way  that  the  hoisting-rope  is  coiled  up  or  paid  out  automatically 
as  the  carriage  is  moved  in  and  out.  Loads  may  hts  picked  up  or  discharged 
at  any  point  along  the  line.  Where  sufficient  inclination  can  be  obtained  In 
the  main  cable  for  the  carriage  to  descend  by  gravity,  and  the  loading  and 
unloading  is  done  at  fixed  pomtii,  tlie  endless  rope  can  be  dispensed  with. 
The  carriage,  which  is  similar  In  construction  to  the  carriage  used  In  the 
endless-rope  cableways,  is  arrested  in  its  descent  by  a  stop-block,  which 
may  be  clamped  to  the  main  cable  at  any  desired  point,  the  speed  of  the 
descending  carriage  being  under  control  of  a  bralce  on  the  engine-drum. 

Stress  In  noUtlnjE-ropes  on  Inellned  Planes. 

(Trenton  Iron  Co.) 


1^1 

^1 

asS 

hit 

o| 

bU 

Ui 

o| 

sU 

Pl 

m 

iH 

« 1 

fl 
<1 

B 

MI'S 

ft. 

ft. 

ft. 

6 

2«68' 

140 

55 

28*49' 

1006 

no 

47°  44' 

1516 

10 

6»43' 

240 

60 

80O68' 

1067 

120 

{iO"  !«' 

1578 

15 

8»8a' 

836 

65 

88«02' 

1128 

130 

5'2«»  26' 

1620 

90 

ll'IO' 

432 

70 

35«00' 

1185 

140 

64«S«' 

1663 

S5 

14«08' 

687 

75 

860  58' 

1288 

150 

.56«19' 

1699 

80 

16»  42' 

618 

80 

88"  40^ 

1287 

160 

58"  00' 

1780 

35 

19»  18' 

700 

85 

40«  22' 

1332 

170 

59«33' 

1758 

40 

21 M9' 

78-2 

90 

42«»00' 

1375 

180 

60"  r,7' 

1782 

45 

84'»  14' 

860 

05 

48»  32' 

1415 

190 

6v»"  15' 

1804 

60 

26«34' 

0:» 

lUO 

45"  00' 

1450 

200 

63"  'J7' 

182-3 

The  above  table  Is  based  on  an  allowance  of  40  lbs.  per  ton  for  rolling  fric- 
tion, but  an  additional  allowance  must  be  made  for  stress  due  to  the  weight 
of  the  rope  proportional  to  the  length  of  the  plane.  A  factor  of  safety  of  5 
to  7  should  be  taken. 

In  hoisting  the  slack-rope  should  be  taken  up  gently  before  beginning  the 
lift,  otherwtee  a  severe  extra  strain  will  be  brought  on  the  rope. 

A  Double-suspension  Cable^cay.  carrying  loads  of  15  tons.  ei*ected  near 
WiUiamsport.  Fa.,  by  the  Trenton  Iron  Co..  is  described  by  E.  G.  Spilsbnry 
in  Trans.  A.  I.  M.  E.  xx.  766^  The  span  is  733  feet,  crossing  the  Susquehanna 
Biver.  Two  steel  cables,  each  -i  in.  diam..  are  used.  On  these  cables  runs  a 
carriage  supported  on  four  wheels  and  moved  by  an  endless  cable  1  inch  in 
diam.    The  load  consists  of  a  cage  carrying  a  railroad-car  loaded  with  lum* 


91G 


HOISTING. 


ber.  the  latter  weiichinic  about  12  tons.  The  power  to  fumished  bj  a  50-H.P. 
eDfdne.  and  the  trip  across  the  river  is  made  in  about  three  mtnutMHL 

A  hoUUne  cable vray  on  the  endless-rope  sTst«^m,  erected  by  the  Udf^er- 
wood  Mfff.  Co.,  at  the  Austin  Dam,  Texas,  hod  a  single  span  ISSO  ft.  in 
length,  with  main  cable  2^  in.  diam.,  and  hoisting-rope  i^  in. diam.  LfOads 
of  7  (o  8  tons  were  handled  at  a  speed  of  600  to  800  ft.  per  minute. 

Another,  of  still  looRer  span,  1G50  ft.,  was  erected  by  the  same  company  at 
Holyoke,  Mass.,  for  use  in  ttie  construction  of  a  dam.  The  main  cable  is 
the  SHIott  or  locked  wire  cable,  having  a  smooth  exterior.  In  the  construc- 
tion of  the  Chicago  Drainage  Canal  twenty  cableways.  of  700  ft.  span  and  8 
ions  capacity,  were  used,  the  towers  travelling  on  rail«. 

Tensloii  required  to  Prevent  Slipping  of  Rope  on  Drum* 
CTrenton  Iron  Co.)— The  amount  of  artificial  tension  to  be  applied  in  an 
endless  rope  to  prevent  slipping  on  the  driving-drum  depends  on  the  char- 
acter of  the  drum,  the  condition  of  the  rope  and  number  of  lape  which  it 
makes.  If  T  and  S  represer.v  respectively  the  tensions  in  the  taut  and  alack 
lines  of  the  rope;  W,  the  necessary  weight  to  be  applied  to  the  tail-aheave; 
J2,  the  resistance  of  the  oars  and  rope,  allowing  for  friction ;  n,  the  number 
of  half-laps  of  the  rope  on  the  driving-drum;  and/,  the  coefficient  of  fno* 
tiou,  the  following  relations  must  exist  to  prevent  supping: 

T=$ef'\    Wz^T-^a,    and    R  =  T  -  8; 


from  which  we  obtain 


e/»»-l 


fn  which  e  v  2.71828,  the  base  of  the  Naperian  system  of  logarithnu. 
The  following  are  some  of  the  values  of/ : 

Dry.       Wet       Oreaoy. 

Wire-rope  on  a  grooved  iron  drum l^A)         .065  .070 

Wire-rope  on  wood.fllled  sheaves 285         .170  .140 

;cVire-rope  on  rubber  and  leather  filling..     .495         .400  ja06 

The  values  of  the  coefficient  -^ ,  corresponding  to  the  above  values 

€/"'  -  1 

of/,  for  one  up  to  six  half-laps  of  the  rope  on  the  driving-drum  or  sheaves, 
are  as  follows: 


/ 

fi 

=  Number  of  Half-laps  on  Driving-wheel. 

1 

S 

8 

4 

6 

« 

.070 

9.180 

i.QrtS 

A.iil 

2.418 

1.989 

1.720 

.085 

7.586 

3.8.3.<) 

2.629 

2.047 

1.714 

1.505 

.180 

5.845 

2.777 

1.953 

1.670 

1.858 

1.832 

.140 

4.6iS8 

2.418 

1.729 

1.416 

1.249 

1.151 

.170 

3.888 

8.047 

1.505 

1.268 

1.149 

1.065 

.805 

3.212 

1.762 

1.838 

1.165 

1.068 

1.048 

.»« 

2.881 

1.592 

1.215 

1.110 

1.051 

1.064 

.400 

1.796 

1.176 

1.047 

1.018 

1.004 

l.OOt 

.495 

1.538 

1.003 

l.OiO 

1.0O4 

1.001 

The  importance  of  keeping  the  rope  drv  is  evident  from  these  figures. 

When  the  rope  is  at  rest  tlie  tension  is  alBtributed  equaliv  on  the  two  lines 
of  the  rupe,  but  when  running  there  will  be  a  difference  in  the  tensions  of 
the  taut  and  slack  lines  equal  to  the  resistance,  and  the  values  of  T  and  JS 
may  be  readily  computed  from  the  foregoing  formulsB. 

T»per  Bopee  of  rnlform  Tensile  Strength •->The  tme  form 
of  rope  is  not  a  i-egular  taper  l>ut  follows  a  logarithmic  curve,  the  irirth 
rapidly  increasing  towai-d  the  upper  end.  Mr.  Chas.  D.  West  gives  Uie  fol- 
lowing formula,  based  on  a  breaking  strain  of  80.000  lbs.  per  sq.  in.  of  the 
rope,  core  included,  and  a  factor  of  safety  of  10:  log  O  =  P/9Q80  4-  log  g.  in 
which  F  =  length  in  fathomH,  and  O&nd  g  the  girth  in  inches  at  any* two 
sections  iP  fathoms  apart.  The  girth  u  is  first  calcuU»r4id  for  a  safe  strain  ' 
of  8000  IbK,  per  sq.  in.,  and  then  G  is  obtained  by  the  formula.  For  a 
mi^theinatical  inv^stlgatioq  »ee  The  Ungineety  A^ril,  i8iK),  p.  8G7. 


TRANSMISSION  OF  POWBB  BY  WIRE  BOPB.        917 


TBANSMIS8ION  OF  POWER  BT  WIRE  BOPB. 

The  following  notes  have  been  furnished  to  the  author  by  Mr.  Wm.  Hewitt, 
Vice-President  of  the  Trenton  Iron  Co.  (See  also  circulars  of  the  Trenton 
Iron  Co.  and  of  the  John  A..  Roebliner's  Sons  Co.,  Trenton,  N.  J.;  "Trans- 
mission of  Power  by  Wire  Ropes,"  by  A.  W.  Stahl,  Van  Nostrand's  Science 
Series,  No.  28;  and  Keuleaujc's  Constructor.) 

The  force  transmitted  should  not  exceed  the  difference  between  the 
elastic  limit  of  the  wires  and  the  bending  stress  as  determined  by  the  fol- 
lowing tables,  taking  the  elastic  limit  of  tempered  steel,  »uch  as  is  used  iu 
the  best  rope,  at  57,000  lbs.  per  sq.  in.,  and  that  of  S^-edish  iron  at  half  this, 
or  88,fi00  lbs.    (The  el.  lim.  of  fine  steel  wires  may  be  higher  than  fi7,000  lbs.) 

Elaseie  lilmtt  of  Wire  Bopes, 


7- Wire  Rope. 

Diam.  of 
Wires. 

Aggregate 
Area  of  Wires. 

Elasiic  Limit. 
Steel. 

Elastic  Limit. 
Iron. 

diam.,  in. 

ins. 
.028 

sq.  in. 
.<W5862 

lbs. 
1,474 

lbs. 
7«7 

"a" 

.085 

.040409 

2,808 

M5« 

.042 

.068189 

8.817 

1,659 

7/16 

.049 

.079201 

4,514 

2,257 

H 

.056 

.099785 

5,688 

8,844 

9/16 

.06S85 

.15*855 

7,845 

8,672 

k 

.070 

.161635 

9,218 

4,607 

nyifl 

.076 

.190582 

10,860 

6,480 

k 

.063 

.227«46 

12.958 

6.477 

H 

.097 

.810378 

17,691 

8,846 

1 

.111 

.406480 

28,167 

11,688 

t9-Wire  Rope. 

.% 

.017 

.025876 

.031 

.03W85 

H 

.094 

.061578 

The  elastic  limit  of  19-wire 

7/16 

.039 

•      .075>!99 

rope  may  be  taken  the  same 

L^ 

.033 

.097604 

as  for  7-wire  rope  since  the 

9/16 

.0875 

.125909 

ultimate    strength    of     the 

.042 

.157941 

wires    Is    7   to   10  per  cent 

11/16 

.046 

.189158 

greater. 

k 

.090 

.223839 

% 

.058 

.801198 

1^ 

.067 

.401925 

The  working  tension  may  be  greater,  therefore,  as  the  bending  stress  is 
less;  but  since  the  tension  m  the  slack  portion  of  the  rope  oannot  be  les.s 
than  a  certain  proportion  of  the  tension  in  the  taut  portion,  to  avoid 
slipping,  a  ratio  exists  between  the  diameter 
of  sheave  and  the  wires  composing  the  rope, 
corresponding  to  a  maximum  safe  working  A 
tensioti.  This  ratio  depends  upon  the  num-  ^1 
ber  of  laps  that  the  rope  makes  about  the 
sheaves,  and  the  kind  of  filling  in  the  rim;*  or 
the  character  of  the  material  upon  which  the 
rope  tracks. 


Tbe  sbeaves  (Fig.  165)  are  usually  of 
cast  iron,  and  are  made  as  light  as  passible 
consistent  with  the  requisite  strength.  Vari- 
ous materials  have  been  used  for  filling  the 
bottom  of  the  groove,  such  as  tarred  oakum. 


J  lute    yarn,  hard    wood,    india-rubber,  and  £ 
eather.     The  filling  which    gives    the  best  £ 


satisfaction,  however,  in  ordinary  transmis- 
sions oonsiats  of  segments  of  lesther  and 
blocks  of  India-rubber  soaked    in    tar  and 


Section 
of  Rlnu 


Beetton  i 
of  Arm.  ' 


Fio.  165. 


packed   alternately  in  the  {groove.     Where  the  working  tension  is  very 


918        TRAKSMISSIOK  OF  POWER  BY  WIRE  BOPB. 


f^reat,  however,  the  wood  fllliDgis  to  be  pieferi-ecl,  as  In  the  case  of  long  dis> 
tnnce  tmiisiiiissions  where  the  rope  makes  several  laps  about  the  sheaves, 
aud  is  run  at  a  comparatively  slow  speeii. 

Bendlnc:  Stresses,  7-TIFIre  Rope* 

Ka 
k  =  ^ . 

2.06y-f  27.54 

k  =  Bending  stress;  JE  =  Modulus  of  elasticity  =  28,500,000; 
a  =  Aggregate  area  of  wires;  R  =  Radius  of  bend;  B  =  Diam.  of  wires 
(lbs.  and  inches). 


Diam.  Bend.     24 

86 

48 

60 

T2 

84 

3,fllG 
4,^M7 
6  <ir»ri 

2,233 

3an9 
4,os; 

108 

3,M1 
4.TS.*- 

1&,M]  1 
Sl.fUS! 

1^0  1  182 

Diam.  Rope. 
5/16 

# 

11/18 

810 
1,569 

645 
1.060 
1,822 
2,878 
4,053 

411 
800 
1,377 
2,178 
8,070 
4,486 
6,278 

642 
1,106 
1,751 
2,470 
3,613 
5,060 
6.459 
8,:J88 

1.1  fi5 

2,'^: 

5,112 

ll.lGfl 
lG,i.^l 

10  IS'l 

1 

.... 

14!458  M,1T? 

i!S,3t4  24,0->l 
S4,1W  31,151 

it? 

34.5^3 

ii 

( 

Bendlnc:  Stresses,  19- Wire  Rope* 

.  _  Ea    

2.06^  +  45.9 


Diam.  Bend. 

12 

24 

86 

48 

60 

72    1    84 

W    \   IDS 

120 

Diam.  Rope- 

H 

5/10 

t 
•1 

11/16 
1 

965 
1,774 

495 
920 
1.366 
2,389 
8,4y5 
5,089 

621 
924 
1,620 
2,376 
8.468 
4,847 
6,201 
8,101 
12,528 

698 
1,22G 
1,800 
2,6311 
3,68ti 
4,81  s 
6,166 
9.55*i 
14,011 

KIIH' 

4  lir; 

2,485 
8,257 
4.173 

8.591 
6.583 
8.566 

7.598 

:   .it  6.481 

16,500 
22.239 

9,937 

jl 



13,872  11,966 
18,713  16.168 
25.850  21.897 
32,403  28.008 

10,528    9,887 
14.909  12.682 
19.272  17,809 
24,662  22.080 
80,957,27,664 
39.208  85.048 
47,689  42,606 
57,183  fil.lAO 

15  645 

1^ 

19  906 

1^ 

35,140 
44,476 

26  005 



31,»J9 
88,.VM 

2H 



::::::::::: 



72,908166,002 

TRANSMISSION   OF   POWEB  BY  WIRE  ROPE.         919 


IIoni«*Poi;rer  Transmitted*  -The  general  formula  for  the  amount 
of  poirer  capable  of  being:  crun^niltted  is  as  follows: 

H.P.  =  [cd«  -  .000006  (w  +  ^i  +  i7,)]v; 
in  which  d  =  diameter  of  the  rope  in  inches,  t;  =  velocity  of  the  rope  in  feet 
per  second,  to  =  weight  of  the  rope,  (/•  =  weight  of  tlie  terminal  sheaves 
and  shafts,  g^  =  weight  of  the  intermediate  slieaves  and  shafts  (all  in  Ib8.)« 
and  c  =  a  constant  depending  on  the  material  of  the  rope,  the  flliing  in  the 
grooves  of  the  sheaves,  and  the  number  of  laps  about  the  sheaves  or  drums, 
a  single  lap  meaning  a  half-lap  at  each  end.  The  values  of  c  for  one  up  to 
six  laps  for  steel  rope  are  givvn  in  the  following  table: 


Number  of  Laps  about  Sheaves  or  Drums. 

c  =  for  steel  rope  on 

1 

S 

S 

4 

« 

6 

Iron 

5.61 
6.T0 
9.29 

8.81 
9.93 
11.96 

10.62 
11.51 
18.70 

11.65 
12.26 
12.91 

12.16 
12.66 
12.97 

12.56 

Wood 

12  83 

Rubber  and  leather 

13.00 

The  values  of  c  for  Iron  rope  are  one  half  the  above. 

When  more  than  three  laps  are  made,  the  character  of  the  surface  in 
contact  is  immaterial  as  far  as  slippage  is  concerned. 

From  the  above  formula  we  have  the  general  rule,  that  the  actual  horae- 
potver  capable  of  being  tranamittird  by  any  wire  rope  approximately  equals 
c  timea  the  aqunre  of  the  diameter  of  the  rope  in  inchea,  leas  six  millionths 
th^  entire  weight  of  all  the  moving  parts^  multiplied  by  the  speed  of  therope^ 
in  feet  per  second. 

Instead  of  grooved  drums  or  a  number  of  sheaves,  about  which  the  rope 
makes  two  or  more  laps.  It  is  sometimes  found  more  desirable,  especially 
where  space  is  limited,  to  use  grip-pulleys.  The  rim  is  fitted  with  a  con- 
tinuous series  of  sieel  Jaws,  which  liite  the  rope  in  contact  by  reason  of  the 
pressure  of  the  same  against  them,  but  as  soon  as  relieved  of  this  pressure 
they  open  readily,  offering  no  re^istnuce  to  the  egress  of  the  rope. 

In  the  ordinary  or  "  flying  "  trann'misHion  of  power,  where  the  rope  makes 
a  single  lap  about  sheaves  lined  with  rubber  and  leather  or  wood,  the  ratio 
between  the  diameter  of  the  sheaves  and  the  wires  of  the  rope,  corresitond- 
ing  to  a  maximum  safe  working  tension,  is  one  resulting  iu  a  working  ten- 
sion of  one  third  and  bending  stress  of  two  thirds  of  the  elastic  limit  of  the 
material.    The  diametei-s  of  sheaves  are  as  follows: 

IMameteraof  mntmnm  Sbeaveii  In  Ineliesy  Correspond tn^ 
to  a  Rfazlmuni  Safe  l¥orklnfl;  Tension, 


Diameter 
of  Rope. 

Steel. 

Iron. 

In. 

7-Wlre. 

12.Wire. 

19^Wire. 

7.Wire. 

12-Wire. 

19-Wire. 

6^6 

19 

14 

12 

40 

30 

24 

24 

J8 

14 

50 

88 

80 

29 

22 

17 

60 

45 

36 

7% 

34 

25 

20 

TO 

53 

42 

38 

29 

23 

80 

60 

48 

9^6 

43 

32 

26 

90 

68 

54 

48 

36 

29 

100 

75 

60 

11^6 

53 

40 

82 

no 

88 

66 

58 

48 

35 

120 

90 

72 

fs 

67 

50 

40 

140 

105 

84 

1 

77 

67 

46 

leo 

I'M 

96 

Assuming  the  sheaves  to  be  of  equal  diameter,  and  of  the  sizes  in  the 
above  table,  the  horse-nofver  that  may  be  transmitted  by  a  steel  rope  making 
a  single  lap  on  wood-filled  sheaves  is  given  in  the  table  on  the  next  page. 


920        TRAKSM1S8I0N  OF  POWER  BY  WIRE  ROPB. 


Tlie  transmtsBfon  of  greater  horsepowers  than  250  is  Impracticable  with 
filled  sheaves,  as  the  tension  would  be  so  great  that  the  filling  would 
quiclclj  out  out,  and  ihe  adhesion  od  a  metallic  surface  would  be  insiufflcieiit 
where  ihe  rope  makes  but  a  single  lap.  In  this  case  it  becomes  neoessaiy 
to  use  theBeuleaux  method,  in  which  the  rope  is  given  more  than  one  lap, 
as  referred  to  below,  under  the  caption  "  Long-distance  Transmissions.** 

Horse-ponrer  Traniiiiiltt«d  by  a  Steel  Rope  on  'Wood-filled 
SlieaveB. 


Diameter 

Velocity  of  Rope  lir  Feet  per  Second. 

of  Rope. 
In. 

10 

20 

80^ 

40 

50 

60 

70 

80 

00 

100 

H 

4 

8 

13 

17 

21 

25 

28 

32 

37 

40 

5/16 

7 

13 

»J0 

26 

33 

40 

44 

51 

67 

W 

% 

10 

19 

28 

38 

47 

56 

64 

78 

80 

S9 

7/16 

18 

26 

38 

61 

68 

75 

88 

99 

100 

121 

H 

17 

3i 

51 

67 

83 

99 

115 

130 

144 

1S9 

9/16 

22 

43 

66 

66 

106 

128 

147 

167 

1M4 

aJ3 

% 

27 

63 

79 

104 

ISO 

155 

179 

203 

225 

547 

11/16 

32 

68 

95 

126 

157 

186 

217 

245 

^ 

88 

76 

las 

150 

186 

228 

62 

104 

156 

206 

1 

68 

135 

202 

Tke  horse-power  that  may  be  trarumitted  by  iron  ropes  is  one  half  of  the 
above. 

This  table  gives  the  amount  of  horse-power  transmitted  by  wire  ropes 
under  maximum  safe  working  tensions.  In  using  wood-lined  sheaves,  therv^ 
fore,  it  is  well  to  make  some  allowance  for  the  stretching  of  the  rope,  and 
to  advocate  somewhat  heavier  equipments  than  the  above  table  would  give; 
that  Ih,  if  it  is  desired  to  transmit  20  horse-power,  for  insrance,  to  put  in  a 
plant  that  would  transmit  25  to  30  horse-power,  thus  avoiding  the  necessity 
of  having  to  take  up  a  cnmp.iratively  small  amount  of  stretch.  On  rubl>er 
and  leather  filling,  no  we  ver,  the  amount  of  power  capable  of  being  tran!^ 
milled  is  40  per  cent  greater  than  for  wood,  so  that  this  filling  is  generaliv 
used,  and  in  this  case  no  allowance  need  be  made  for  stretch,  as  suvo 
sheaves  will  likely  transmit  the  power  given  by  the  table,  under  all  possible 
deflections  of  the  rope. 

Under  ordinary  conditions,  ropes  of  seven  wires  to  the  strand,  laid  about 
a  hemp  core,  are  best  adapted  to  the  transmission  of  power,  but  eoiidiiious 
often  occur  where  12-  or  19-wire  rope  is  to  be  preferred,  as  stated  below. 

Deflectlonii  of  the  Rope.^The  tension  of  the  rope  Is  measured  hv 
the  amount  of  sag  or  dettectU»n  at  the  centre  of  the  span,  and  the  defiectioo 
corresponding  to  the  maximum  safe  working  tension  is  determined  by  the 
following  formulae,  in  which  S  represents  the  span  in  feet: 

Steel  Rope.  Iron  Rope. 

Def.  of  still  rope  at  centre,  in  feet. ...  /i  =  .00004S«        h  = . 00O08S« 
•'  driving     "        "  "     ....  /i,  =  .000025S«        ii,  =  .00Oa5.S« 

••         slack         "       '*  ■*....  /i,=  .0000875S«      A,=  OOOlTSif* 

ItfiiultKi  of  Span*— On  spans  of  less  than  sixty  feet,  it  Is  impossible  to 
splice  the  rope  to  such  a  degree  of  nicety  as  to  give  exactly  the  required  de- 
fleciion.  an«l  a.s  the  rofw  is  fiirther  subject  to  a  certain  amount  of  stretch,  it 
becomes  necessary  in  such  cases  to  apply  mechanical  means  for  produeintr 
the  proper  tension,  in  order  to  avoid  frequent  splicing,  which  is  very  objec- 
tionable :  but  care  should  always  be  exercised  in  using  auch  tigfateniui: 
devices  that  they  do  not  become  Uie  means,  in  unskilled  hands,  of  over- 
straining the  rope.  The  rope  also  is  more  sensitive  to  every  irregularity  io 
the  sheaves  and  the  fluctuations  in  the  amount  of  power  transmitted,  and 
is  apt  to  sway  to  such  an  extent  beyond  the  narrow  limits  of  the  required 
deflections  as  to  cause  a  jerking  motion,  which  is  very  Injurious.  For  xhH 
reason  on  very  short  spans  it  is  foiuid  desirable  to  us«  a  considerabiv 
heavier  rope  than  that  actually  required  to  transmit  the  i^H>wer:  or  in 
other  words,  insteati  of  a  7-wire  rope  corresponding  to  the  conditions  of 
lunximum  tension,  it  is  better  to  use  a  19-wire  rope  of  the  same*  slae  wirf^, 
and  to  run  this  under  a  tension  considerably  below  the  maximum.  In  this 
way  is  obtained  the  ad\  anta;?es  of  increased  weight  and  no  stretch,  without 


THAKSMISSIOX  OF  POWER  BY   WIRE  ROPE.        921 

having  to  um  larger  sheates,  while  the  wear  will  be  (jtreAter  in  proportion  to 
the  increased  surface. 

In  deteniiiniug  the  maximum  limit  of  span,  the  contour  of  the  ground 
and  thM  available  height  of  the  terminal  ahea^ee  must  be  taken  Into  eon- 
slderation.  U  in  customary  to  transmit  the  power  through  the  lower  portion 
of  the  rope,  as  in  this  case  the  greatest  deflection  in  this  portion  occurs 
wiien  the  rope  is  at  rest.  When  running,  the  lower  portion  rises  and  the 
upper  portion  sinks,  thus  enabling  obstructions  to  be  avoided  which  other- 
wise would  have  to  be  removed,  or  make  ii  neeeesary  to  erect  very  high 
towers.  The  maximum  limit  of  span  in  this  case  is  determined  by  tlie  max- 
imum deflection  that  may  be  given  to  the  upper  portion  of  the  rope  when 
running,  which  for  sheaves  of  10  ft.  diameter  is  about  000  feet. 

3Iuch  greater  spans  than  this,  however,  are  practicable  where  the  contour 
of  the  ground  is  such  that  the  upper  portion  of  the  rope  may  be  the  driver, 
and  there  is  nothing  to  interfere  with  the  proper  deflection  of  the  under 
portion.  Some  very  long  transmissions  of  power  have  been  effected  in  this 
way  without  an  intervening  support^  one  at  LiOckport,  N.  Y.,  having  a  clear 
span  of  1700  feet. 

Lons-dlaianea  Tranamlaalottfl*— When  the  distance  exceeds  the 
limit  for  u  clear  span,  inu*rniediate  supporting  sheavee  are  used,  with  plain 
grooves  (not  filled),  and  as  a  rule  the  taut  portion  of  the  rope  requires  fewer 
than  the  slack  portion.  The  sise  of  these  sheaves  will  depend  on  the  angle 
of  the  bend,  gauged  by  the  tangents  to  the  ciurves  of  the  rope  at  the  points 
of  inflection.  If  the  curvature  due  to  the  tension,  regardless  of  the  sise 
of  the  sheave,  is  less  than  that  of  the  minimum  sheave  correHponding 
to  a  maximum  safe  working  tension,  the  intermediate  sheaves  should  be 
equal  in  size  to  the  terminal  sheaves  or  minimum  sheave  corresponding  to 
the  rope  used  (see  table  of  minimum  sheaven).  but  if  it  is  greater,  smaller 
intermediate  sheaves  may  be  used.  (See  Bending  Curvature  of  Wire 
Ro[>es,  below.) 

In  very  long  transmissions  of  power,  requiring  numerous  intermediate 
supports,  it  is  found  impracticable  to  run  the  rope  at  the  high  speeds  main- 
tained in  *'  flying  transmissions.*'  The  rope  therefore  is  run  under  a  higher 
working  tension,  made  practicable  by  wrapping  it  several  times  about 
grooved  terminal  drums,  with  a  lap  about  a  sheave  on  a  take-up  or  counter- 
weigh r^^d  carriafire,  which  preserves  a  constant  tension  in  the  slack  portion. 

Inclined  TransmlMtons*— When  the  terminal  sheaves  are  not  on 
the  same  elevation,  the  tension  at  the  upper  sheave  will  be  greater  than  that 
at  the  lower,  but  thi»  difference  is  so  slight,  in  most  cases,  that  it  may  be 
ignored.  The  span  to  be  considered  is  the  horizontal  distance  between  the 
sheaves,  and  the  principles  governing  the  limits  of  span  will  hold  good  in 
this  case,  so  that  for  very  steep  inclinations  it  becomes  necessary  to  resort 
to  tightening  devices  for  maintaining  the  requisite  tension  in  the  rope.  The 
limiting  case  of  inclined  transmissions  occurs  when  one  wheel  Is  directly 
above  the  other.  The  rope  in  this  case  produces  no  tension  whatever  on 
the  lower  wheel,  while  the  upper  is  subject  only  to  the  weight  of  the  rope, 
which  is  usually  so  insigniflcant  that  it  may  be  neglected  altogether,  and 
tiirbteninfiT  sheaves  are  therefore  an  absolute  necesKUv. 

Bending;  CurrAtnre  of  "Wire  Ropes.— the  curvature  due  to 
any  bend  in  a  wire  rope  Is  dependent  on  the  tension,  and  is  not  always  the 
same  as  the  sheave  In  contact,  but  may  be  greater,  which  explains  how  it  is 
that  large  ropes  are  fi*equently  run  around  comparatively  small  sheaves 
without  detriment,  since  It  is  possible  to  place  these  so  close  that  the  bend- 
ing angle  on  each  will  be  such  that  the  resulting  curvature  will  not  over- 
strain the  wires.  This  curvature  may  be  ascertained  from  the  formula 
and  table  on  the  next  page,  which  give  the  theoretical  radii  of  curvature  in 
inches  for  various  sizes  of  ropes  and  different  angles  for  one  pound  tension 
in  the  rope.  Dividing  these  figures  by  the  actual  tenidon  in  pounds,  gives 
the  radius  of  curvature  assumed  by  the  rope  in  cases  where  this  exceeds  the 
curvature  of  the  sheave.  The  rigidity  of  the  rope  or  internal  friction  of 
the  wires  and  core  has  not  been  taken  Into  account  In  these  figures,  but  the 
effect  of  this  is  insignificant,  and  it  Is  on  the  safe  side  to  ignore  ft.  By  the 
**  angle  of  bend  *'  is  meant  the  angle  between  the  tangents  to  the  curves  of 
the  rope  at  the  points  of  inflection.  When  the  rope  is  straight  the  an^le  is 
ISO*.  For  angles  less  than  100*  the  radius  of  curvature  In  meet  oases  will  tie 
lees  than  that  corresponding  to  the  safe  working  tension,  and  the  proper 
size  of  sheave  to  use  in  Kuch  cases  will  be  governed  by  the  table  heaae<l 
"Diameters  of  Minimum  Sheaves  Corresponding  to  a  Hoximiim  Safe 
Working  Tension.^' 


923 


HOPE-DRIVING. 


Badlns  of  Corratnre  of  ITlre  Rope*  In  Inclie*  for 
1-lb.  Tension* 

Fonnula  :  R  =  JiZ*n  •«•  6.25C  oor  ^B  ;  in  which  R  ss  radius  of  curralare: 
£  ss  modulus  of  etasiiclty  s  28,900,000;  i  sr  diameter  of  wires;  n  =  now 
of  wires  ;  0  =.  angle  of  bend;  t  s  working  stress  Obs.  and  ins.). 

Divide  by  stress  in  pounds  to  obtain  radius  in  inches. 


Diam. 
of  wire. 


160» 

16o« 

4,226 

5,628 

11,090 

14,758 

«,<^74 

29.688 

48.184 

57,451 

71,816 

95.541 

na,768 

150.016 

169,185 

2«,012 

12,914 

17,179 

29,7tJ2 

39,594 

6-2,813 

82,899 

116,'^ 

154,641 

199,%23 

205,173 

8*^.556 

4-.»6,4:i9 

504,402 

671,041 

170* 

172» 

174» 

8,421 

10,940 

14,593 

22,005 

26.781 

85,628 

45,412 

54,417 

72,580 

86,040 

102,688 

186,869 

148,085 

175,182 

233,492 

224,667 

880,607 

874,010 

886,982 

427,689 

570,050 

25,727 

81.125 

41,485 

59,297 

:5,98S 

101.282 

124,151 

167,-)T0 

210.018 

281.503 

291,917 

889.085 

397,129 

497,998 

668.767 

688,674 

797.607 

1,063.217 

1,004,965 

1,216,817 

1,620,518 

176« 


178* 


21.884 
58,429 
108,767 
206,251 
860,150 
660.872 
854,868 

62,212 
151.884 
814,948 
588,470 
996,880 
1,594.«B 
2,480,151 


43.7oS 
106,841 
5n7,fiOS 
410,440 
700,193 
1,121.574 
1,709,4» 

]d4.4ti6 
308.r.1 
0S9.SIU 
1,164.099 
1,990.478 
8,188.359 
4,8&0,56I 


ROPB-DBIVING. 


The  tranfmifssioD  of  power  by  cofton  or  msnila  ropes  is  a  competitor  with 
gearing  and  leather  belting  when  the  amount  of  power  is  lar^e,  or  tlie  dis- 
tance between  the  power  and  the  work  is  comparntlvely  great.  The  follow- 
ing is  condensed  from  a  paper  by  C.  W.  Hunt,  Trans.  A.  S.  M.  E.,  xiL  230: 

But  few  accurate  data  are  available,  on  account  of  the  Inne  period  re- 

Suired  in  each  ex|>eriment,  a  rope  lasting  from  three  to  six  years.    Inst&Iia- 
Ions  which  have  been  successful,  as  well  as  those  In  which  the  wear  of  the 
rope  was  dentrnctive.  Indicate  that  200  lbs.  on  a  rope  one  inch  In  diameter 
te  a  safe  and  economical  working  strain.    When  the  strain  is  materially 
Increased,  the  wear  is  rapid. 
In  the  following  equations 
C  =  circumference  of  rope  In  inches;     o  =  gravity; 
D  =  saK  of  tlie  rope  in  inches;  Ju  =  hoi-se-power; 

F  =  centrifugal  force  in  pounds;  L  =  distance  between  pulleyslu  feet; 

jp  =  pounds  per  foot  of  rope;  u;  =  working  strain  in  pounds; 

R  s  force  in  pounds  doing  useful  work; 
S  =  strain  In  pounrls  on  the  rope  at  the  pulley ; 
T  =  tension  in  pouuds  of  drivinrr  side  of^the  rope; 
t  =  tension  in  pounds  on  slack  side  of  the  rope; 
V  =  velocity  of  the  rope  in  feet  i>er  second; 
W  =  ultimaU)  breaking  strain  in  pouuds. 


Tr=720C>; 


P=  ,082C«; 


:20C«. 


This  makes  the  normal  working  strain  equal  to  1/80  of  the  breaking 
strength,  and  about  1/25  of  the  strength  at  the  splice.  The  actual  strains 
are  ordinarily  much  greater,  owing  to  Uie  vibrations  in  running,  as  well  as 
from  imperfectly  adjusted  ten.«ion  mechanism. 

For  this  invest igalioii  we  assume  that  the  strain  on  the  driving  side  of  a 
rope  is  equal  to  200  lbs.  on  a  rope  one  inch  in  diameter,  and  an  equivalent 
strain  for  other  sises,  and  that  the  rope  is  in  motion  at  various  velocities  of 
from  10  to  140  ft.  per  second. 

The  centrifugal  force  of  the  rope  in  running  over  the  pulley  will  reduce 


EOPE-DRIVING.  923 

th«*  arooant  of  force  available  for  the  transmission  of  poirer.    The  centrifu* 
KrI  force  F  =  P»*  -h  g. 

At  a  spL*ed  of  about  80  ft.  per  second,  the  centrif URal  force  increases  faster 
tliuQ  the  power  from  increased  velocity  of  the  rupe,  and  at  about  140  ft.  per 
HecoDd  equals  the  assumed  allowable  tension  of  the  rope.  Computintc  this 
force  at  various  speeds  and  then  subtracting  it  from  the  assumea  maximum 
t4*D8ion,  we  have  the  force  available  for  the  transmission  of  power.  The 
whole  of  this  force  cannot  be  used,  because  a  certain  amount  of  tension  on 
the  slack  side  of  the  rope  is  needed  to  fn^e  adhesion  to  the  pulley.  What 
tension  should  be  given  to  the  rope  for  this  purooee  is  unueriain,  as  there 
are  no  experiments  which  give  accurate  data.  It  is  known  from  considerable 
experience  that  when  the  rope  runs  in  a  groove  whose  sides  are  inclined 
toward  each  other  at  an  angle  of  4S<*  there  is  sufficient  adhesion  when  the 
ratio  of  the  tensions  7-i-  f  =  2. 

For  the  present  purpose,  T  can  be  divided  into  three  parts:  1.  Tension 
doing  useful  work;  2.  Tension  from  centrifugal  force;  8.  Tension  to  balance 
the  strain  for  adhesion. 

The  tension  t  can  be  divided  into  two  parts:  1.  Tension  for  adhesion; 
2.  Tension  from  centrifugal  force. 

It  is  evident,  however,  that  the  tension  required  to  do  a  given  work  should 
not  be  materially  exceeded  during  the  life  of  the  rope. 

There  are  two  methods  of  putting  ropes  on  the  pulleys;  one  In  which  the 
rofMM  are  single  and  spliced  on,  being  made  very  taut  at  first,  and  less  so  as 
the  rope  lengthens,  stretching  until  it  slips,  when  it  is  respliced.  The  other 
method  is  to  wind  a  single  rope  over  the  pulley  as  many  turns  as  needed  to 
obtain  the  necessary  horsepower  and  put  a  tension  pulley  to  give  the  neces- 
sary adhesion  and  also  take  up  the  wear.  The  tension  t  required  to  trans- 
mit the  normal  horse-power  for  the  ordinary  speeds  and  sizes  of  rope  is  com- 
puted by  formula  (1),  below.  The  total  tension  Ton  the  driving  side  of  the 
rope  is  assumed  to  be  the  same  at  all  speeds.  The  centrifugal  force,  as  well 
as  an  amount  equal  to  the  tension  for  adhesion  on  the  slack  side  of  the  rope, 
must  be  taken  from  the  total  tension  T  to  ascertain  the  amount  of  force 
available  for  the  tnansmission  of  power. 

It  is  assumed  that  the  tension  on  the  shick  side  necessary  for  giving 
adhesion  Is  equal  to  one  half  the  force  doing  useful  work  on  the  driving  side 

ar—  F\ 
at  the  rope;  hence  the  force  for  useful  work  is  H  =  -^^ — g — •';  and  the  ten- 
sion on  the  slack  side  to  give  the  required  adhesion  is  yf^T  —  F),    Hence 

,.(£:i£)  +  ,. (,) 

The  sum  of  the  tensions  Tand  t  is  not  the  same  at  different  speeds,  as  the 
^nation  (1)  indicates. 

AS  F  varies  as  the  square  of  the  velocity,  there  is,  with  an  increasing 
npeed  of  the  rope,  a  decreasing  useful  force,  and  an  increasing  total  tension, 
r,  on  the  slack  side. 

With  these  assumptions  of  allowable  strains  the  horse-power  will  be 

^-      3X550 ^ 

Transmission  ropes  are  usually  from  1  to  19^  inches  In  diameter.  A  com- 
putation of  the  horse-power  for  four  sizes  at  various  speeds  and  under 
r»r(1inary  conditions,  based  on  a  maximum  strain  equivalent  to  200  lbs.  for  a 
nype  one  inch  in  diameter,  is  given  in  Fig.  160.  Tlie  horse-power  of  other 
sizes  is  readily  obtained  from  these.  The  maximum  power  is  transmitted, 
under  the  assumed  oonditions,  at  a  speed  of  about  80  feet  per  second. 

The  wear  of  the  rope  is  both  internal  and  external ;  the  Internal  is  caused 
by  the  movement  of  the  fibres  on  each  other,  under  pressure  in  bending 
(»ver  the  sheaves,  and  the  external  is  caused  by  the  slipping  and  the  wedg- 
ing in  the  grooves  of  the  pulley.  Both  of  these  causes  of  wear  are,  within 
the  limits  of  ordinary  practice,  assumed  to  be  directly  proportional  to  the 
K{>eed.  Hence,  if  we  assume  the  coefficient  of  the  wear  to  be  /c,  the  wejtr 
will  be  kv,  in  which  the  wear  increases  directly  as  the  velocity,  but  the 
horne-power  that  can  be  transmitted,  as  equation  (2)  shows,  will  not  vary  at 
the  same  rate. 

The  rope  is  supposed  to  have  the  strain  T  constant  at  all  speeds  on  the 
driving  Bide,  ana  m  direct  proportion  to  the  area  of  the  cross-section;  hence 


924 


BOPE-DRIVING. 


the  catenary  of  the  driving  aide  ia  not  affected  bj  the  speed  or  bj  the  diam- 
eter of  the  rope. 

The  deflection  of  the  rope  between  the  pulleys  on  the  slack  side  vari^ 
with  each  change  of  the  load  or  change  of  the  spc»d,  as  the  tension  equatioo 
(1)  indicates. 

The  deflection  of  the  rope  Is  computed  for  the  assumed  value  of  T  and  t 


4J 

— 

— 

rr 

? 

*^ 

•^ 

n 

n 

r- 

r 

.u 

Hope   ontvifiQ^ 

> 

s 

10 

4 

/ 

y^ 

\ 

la 

i/ 

' 

w 

r 

\ 

1 

IJjfL 

^ 

">! 

St 

- 

'V 

r 

^ 

St 

L^ 

:^ 

^ 

*% 

ou 

4 

' 

g 

^ 

" 

^ 

S 

^ 

- 

^ 

V 

~^ 

^ 

^ 

V 

A  w-^ 

w 

feS 

3^:^^^ 

at 

- 

~1 

^>^^1^ 

h 

"^ 

1 

5f^ 

^ 

— 

S{ 

V 

J 

-^# 

^ 

rll 

.>^l^J2-, 

> 

r 

s 

, 

\, 

< 

?;^^S 

\ 

\ 

1* 

-- 

L^ 

2^r^ 

- 

— 

\ 

i. 

\ 

14 

VS, 

^>  >  - 

irf' 

^ 

n 

- 

\ 

y 

. 

\\ 

u 

10 

-^% 

^9^ 

> ' 

^ 

\i 

LO 

2 

- 

- 

p 

^ 

i 

4 

a 

^/^^ 

1>T^ 

^i 

— 

i~ 

1 

1 

1^ 

i 

< 

1 

0 

'4> 

w 

4 

i>    s 

Q 

G 

0 

Tl 

D 

s 

Q 

J 

(k 

1 

A 

LlO 

v^ 

m-Tm- 

Valodtjr  of  I>rTin|f  Rope  In  fe«t  per  second. 
FiO.  166. 

by  the  parabolic  formula  S  m  -r-jr-  +  PD^  8  being  the  assumed  strain  Ton 

the  driving  side,  and  f,  calculated  by  equation  (1),  on  the  slack  side.    Tbe 
tension  t  varies  with  the  speed. 

Horse-poiver  of  Tranamlaslon  Rope  at  Various  Speeds. 

Computed  from  formula  (2),  given  above. 


Speed  of  the  Rope  In  feet  per  minute. 

1^^ 

1500 

dooo 

2500 

8000 

3500 

4000 

4500!  6000 

6000 

7000 

8000 

m 

^ 

1.45 

1.0 

8.8 

2.7 

S 

8.2 

8.4)    8.4 

8.1 

2.2 

0 

20 

2S 

8.2 

3.6 

4.2 

4.6 

6.0 

6.8     5.3 

4.9 

8.4 

0 

24 

i 

8.8 

4.3 

52 

5.8 

6.7 

7.2 

7.71    7.7 

7.1 

4.9 

0 

31) 

4.5 

6.9 

7.0 

8.2 

0.1 

9.8 

10.8!  10.8 

9.8 

6  0 

0 

36 

1 

6.8 

7.7 

9.2 

10.7 

11.9 

12  b 

18.6,  13.7 

12.5 

8.8 

0 

42 

iH 

9.2  t  12.1 

14.8 

16.8 

18.6 

20.0 

21.2'  21.4 

19.6 

is. 8 

0 

54 

iC? 

13.1  '  17.4 

20.7 

28  1 

26.8 

28.F 

80.6  80.8 

28.2 

19.8 

0 

60 

1^ 

18         23.7 

28.2 

82.8 

86,4 

39.2 

41.5!  41.8 

87.4 

27.6 

0 

?i 

2 

23.2     30.8 

30.8 

42.8 

47. G   51. t 

54.4!  54  8 

50 

85.2 

0 

84 

The  following  notes  are  from  the  circular  of  the  C.  W.  Hunt  Co.,  Nev 
York: 

For  a  temporary  Installation,  when  the  rope  is  not  to  be  long  In  us^,  it 
might  be  advisable  to  increase  the  work  to  double  that  given  in  the  table. 

For  convenience  in  estimating  the  necessary  clearance  on  the  driving  and 
on  the  slack  sides,  we  insert  a  table  showing  tlie  sas  of  the  rope  at  diflTerf nt 
speeds  when  transmitting  the  horse-power  given  in  the  preceding  table. 
When  at  rest  the  sag  is  not  the  same  as  when  running,  being  greater  or  Die 
driving  and  less  on  the  slack  sides  of  the  rope.  The  sag  of  the  driving  side 
when  transmitting  the  normal  iiorse-power  is  the  same  no  matter  what  sizo 
of  rope  is  used  or  what  the  speed  driven  at,  because  the  assumption  is  th.-xt 
the  strain  on  the  rope  shall  be  the  same  at  all  speeds  when  transmitting  tb« 


SAG  OP  THE  ROPE  BETWEEN   PULLEYS. 


925 


a»mmed  horse -power,  but  on  the  slAok  eide  the  etmlDs,  and  oonaequently 
the  MMC.  YM'y  with  the  speed  of  the  rope  and  also  with  the  horse  power. 
The  (able  gives  the  saff  for  three  speeds.  If  the  actual  safe  Is  less  than  given 
in  the  table,  the  rope  Is  strained  more  than  the  work  requires. 

This  table  is  only  approximate,  and  is  exact  onlv  when  the  rope  fs  runninff 
at  Its  normal  speed,  transmitting  its  full  load  and  strained  to  the  assumed 
amount.  All  of  these  conditions  are  varying  in  actual  work,  and  the  table 
must  be  used  as  a  guide  only. 

S«c  of  tlie  Rop«  betureen  Palleya. 


Distance 
between 
Pulleys 
in  feet. 


40 

60 
SO 
100 
120 
140 
160 


Driving  Side. 


All  Speeds. 


Ofeet  4  inches 

0  •*  10  " 

1  "  5  " 
8  •»  0  ** 

2  "  11  " 
8  "  10  " 
6  "  t  " 


Slack  Side  of  Rope. 


80  ft.  per  sec. 

©0  ft.  per  sec. 

40  ft.  per  sec. 

Ofeet  7 Inches 

Ofeet  9 inches 

0  feet  11  inches 

1   *•     5     " 

1   "     8     •* 

1    "    11      " 

«   !•     4     " 

8   ••    10     " 

8  "     8     •• 

8  ••     8     •• 

4  "     6     " 

6   ••     «     " 

6  "     8     •• 

6   «      8     " 

7   **     4     ** 

7  "     8     «« 

8   "      9      •* 

AM       g       t« 

0   "     8     " 

11    "      8      " 

14    "      0      " 

The  size  of  the  pulleys  has  an  important  effect  on  the  wear  of  the  rope-' 
the  larger  the  sheaves,  the  less  the  fibres  of  the  ropo  slide  on  each  other,  and 
consequently  there  is  less  internal  wear  of  the  rope.  Tiie  pulleys  should  not 
be  less  than  forty  times  the  diameter  of  the  rope  for  economical  wear,  and 
as  much  larger  as  it  is  possible  to  make  them.  ThiH  rule  applies  also  to  the 
idle  aud  tension  pulleys  as  well  as  to  the  main  driving  pulley. 

The  angle  of  the  sides  of  the  grooves  in  which  the  rope  runs  varies,  with 
different  engineers,  from  45'  to  60^,  It  is  very  important  that  the  sides  of 
these  gix>ove8  should  be  carefully  polished,  as  the  fibres  of  the  rope  rubbing 
on  the  metal  as  it  comes  from  the  lathe  tools  will  gradually  break  fibre  by 
flbre,  and  so  give  the  rope  a  short  life.  It  ia  also  necesury  to  carefully  avoid 
all  sand  or  blow  holes,  as  they  will  cut  the  rope  out  with  surprising  rapidity. 

Much  depends  also  upon  the  arrangement  of  the  rope  on  the  pulleys,  es- 
pecially where  a  tension  weight  Is  used.  Experience  shows  that  the 
increasetl  wear  on  the  rope  from  bending  the  rope  first  in  one  direction  and 
then  in  the  other  is  similar  to  that  of  wire  rope.  At  mines  where  two  cages 
are  used,  one  being  hoisted  and  one  lowered  by  the  same  engine  doing  the 
same  work,  the  wire  ropes,  cut  from  the  same  coil,  are  usually  arranged  so 
that  one  rope  Is  k>ent  continuously  in  one  direction  nnd  the  other  rope  is  bent 
first  in  one  direction  and  then  in  the  other,  in  winding  on  the  drum  of  the 
engine.  The  rope  having  the  opposite  bends  wears  much  more  rapidly  than 
the  other,  lasting  about  three  quarters  as  long  as  its  mate.  This  difference 
in  wear  snows  In  manihi  rope,  both  in  transmission  of  power  and  in  c<>al< 
hoisting.  The  pulleys  should  be  arranged,  as  far  as  possible,  to  bend  the 
rope  in  one  direction. 

The  wear  of  the  rope  is  independent  of  the  distance  apart  of  the  shafts, 
sincA  the  wear  takes  place  only  on  the  pulleys;  hence  in  transmitting  power 
any  distance  within  the  limits  of  rope -driving,  the  life  of  the  ro).)e  will  be 
the  same  whether  the  distance  is  small  or  great,  but  the  first  cost  will  be  in 
proportion  to  the  distance. 

Tension  on  thb  Slack  Part  of  ths  Ropb. 


Speed  of 

Diameter  of  the  Rope  and  Pounds  Tension  on 

the  Slack  Rope. 

Etope,  in  feet 
per  second. 

H 

H 

H 

54 

1 

1W, 

1H 

m 

2 

90 

10 

27 

40 

71 

no 

m 

216 

288 

30 

14 

29 

42 

56 

74 

115 

170 

226 

296 

40 

15 

81 

4f. 

60 

79 

123 

181 

240 

8)5 

50 

16 

88 

49 

65 

85 

m 

195 

259 

839 

60 

18 

86 

.53 

71 

93 

145 

214 

285 

873 

70 

19 

89 

59 

T8 

101 

168 

236 

810 

406 

80 

ei 

43 

64 

8fi 

111 

173 

255 

840 

4« 

90 

24 

48 

70 

93 

122 

190 

279 

872 

487 

926 


BOPB-DKIYINa. 


For  large  amounts  of  power  it  is  common  to  use  a  number  of  ropes  lyini; 
side  by  side  in  grooves,  each  spliced  separately.  For  light«r  drives  some 
engineers  use  one  rope  wrapped  as  iiianv  times  around  the  puMeyK  as  is 
necessary  to  get  ihe  horse-power  required,  with  a  tension  pulley  to  take  up 
the  slack  as  the  rope  wears  when  first  put  in  use.  The  weight  put  upon  this 
tension  pulley  should  be  carefully  adjusted,  as  the  overstraining  of  the  rope 
from  this  cause  is  one  of  the  most  common  errors  in  rope  driving.  We 
therefore  f^ve  a  table  showing  the  proper  strain  on  the  rope  for  the  various 
sizes,  from  which  the  tension  weight  to  transmit  ihe  horse-power  in  tht; 
tables  is  easily  deduced.  This  strain  can  be  still  further  rttduced  if  ilie 
horse-power  transmitted  is  usually  less  than  the  nominal  work  which  the 
rope  was  proportioned  to  do,  or  if  the  angle  of  groove  in  the  pulleys  is 
acute. 

DlAlllETER  or  PULLKYS  AMD  WkIOBT  OF  RoPK. 


Diameter  of 

Smallest  Diameter 

Length  of  Rope  to 

Approximate 

Rope, 

of  Pulleys,  in 

allow  for  Splicing, 

Weight,  in  lbs.  pen 

In  inches. 

inches. 

in  feet. 

foot  of  rope. 

w 

SO 

6 

.12 

I'S. 

84 

6 

.18 

% 

30 

7 

.24 

'  '4t 

86 

8 

.82 

1 

42 

9 

.49 

M 

10 

.60 

|i2 

«0 

12 

.83 

]a^ 

72 

18 

1.10 

2 

84 

14 

1.40 

'r 

'r 

% 

T 

,!^' 

2" 
13 

58 

44 

88 

83 

28 

« 

121 

145 

170 

193 

228 

stVi 

860 

480 

500 

600 

675 

'.SO 

86 

43 

BO 

60 

67 

78 

2G8 

242 

280 

847 

.380 

446 

28 

34 

41 

49 

54 

68 

With  a  given  velocity  of  the  driving-rope,  the  weight  of  rope  required  for 
transmitting  a  given  horse-power  is  the  same,  no  matter  what  size  rope  i^ 
adopted.  The  smaller  rope  will  require  more  parts,  but  the  weight  will  t>e 
the  «sme. 

Rllscellaneoiiii  Note*  on  Rope-drlTins*— W.  H.  Booth  commu- 
nicates to  the  Avier.  Machinist  the  following  daui  from  English  practice  with 
cotton  ropes.  The  calculated  figures  are  based  on  a  total  allowable  tension 
on  a  19^-inch  rope  of  600  lbs.,  and  an  initial  tension  of  1/10  the  total  allowed 
stress,  which  corresponds  fairly  with  practice. 

Diameter  of  rope 1J4" 

Weight  per  foot,  lbs 6 

Centrifugal  tension  =  F«  divided  by    64 
for  F=  80  ft.  per  sec,  lbs.  100 

Total  ten?ion  allowable 300 

Initial  tension 80 

Net  working  tension  at  80  ft. velocity  170 
Horse-power  per  rope     "        "  24 

The  most  usual  practice  in  Lancashire  is  summed  up  roughly  'u\  the  fol- 
lowing  figures:  19;j-inch  cotton  ropes  at  5000  ft.  per  minute  velocity  =  .V)  H.l\ 
per  rope.  The  most  common  sizes  of  rope  now  used  are  15^  and  \%  in.  The 
maximum  horse-pov^er  for  a  given  rope  is  obtained  at  ahoi it  80  to  83  feet 
per  second.  Aix)ve  that  speed  the  power  is  reduced  by  centrifugal  tension. 
At  a  npeed  of  sjSOO  ft.  per  minute  four  rt)pe8  will  do  about  the  same  work  as 
three  at  5i)00  ft.  per  in  in. 

Cotton  ropes  do  not  require  much  lubrication  In  the  sense  that  it  is  re- 
quired by  ropes  made  of  the  rough  fibre  of  manila  hemp.  Mertrly  a  slight 
surface  dressing  is  all  that  is  required.  For  small  ropes,  common  In  spin- 
ning machinery,  from  ^  to  9^  inch  diameter,  it  is  the  custom  to  prevent  the 
fluffing  of  the  ropes  on  the  sui'face  by  a  light  apnlicatitm  of  a  mixture  of 
black-lead  and  molasses.— but  only  enough  &ould  oe  usecl  to  Ia>'  the  fibres,— 
put  upon  one  of  the  pulleys  in  a  series  of  light  dabs. 

Reuleaux's  ConKtructor  gives  as  the  "  specific  capacity  "  of  hemp  rope  in 
actual  practice,  that  is,  the  horse-power  transmitted  per  square  inch  of 
cross-section  for  each  foot  of  linear  velocity  per  minute,  .004  to  .002,  the 
cross  sect  ion  being  taken  as  that  due  to  the  full  outside  diameter  of  the 
rope.  For  a  1^-in.  rope,  with  a  cross-section  of  2.405'-q.  In.,  at  a  velocity  of 
f>OU0  ft.  per  iiiin.,  this  gives  a  hor8e-{)ower  of  from  24  to  48,  as  against  41.8 
h^  Mr.  |lunt*s  table  and  49  bv  Mr.  Booties. 


MlSCELLAKEOUS  NOTES  ON  HOPE-DEIVING.        927 

Reuleauz  g^ives  formulee  for  calculating  sources  of  loss  in  hemp-rope 
transmission  due  to  (1)  journal  friction,  (2)  stiffness  of  ropes,  and  (8)  creep 
of  ropes.  Tlie  constants  in  these  forraulsB  are,  however,  uncertain  from 
lack  of  experimental  data.  He  calculates  an  average  case  ffiving  loss  of 
power  due  to  journal  friction  =  4%,  to  stiffness  7.9%^  and  to  creep  6^,  or  I6.8]t 
in  all,  and  says  this  is  not  to  be  considered  hteher  than  the  actual  loss. 

Spencer  Miller,  in  a  paper  entitled  **  A  Problem  in  Continuous  Rope-drlv- 
tnff ''  (Trans.  A.  S.  C.  E.,  1897),  reviews  the  difHculties  which  occur  in  rope- 
driving,  with  a  continuous  rope  from  a  large  to  a  small  pulley.  He  adopts 
the  angle  of  45^  as  a  minimum  angle  to  use  on  the  smaller  pulley,  and 
recommends  that  the  larger  pulley  be  grooved  with  a  wider  angle  to  a  degree 
such  that  the  resistance  to  slipping  is  equal  in  both  wheels.  Bv  doing  this 
the  effect  of  the  tension  weight  is  felt  equally  throughout  all  the  slack 
strands  of  the  rope-drive,  hence  the  tight  ropes  pull  equally.  It  is  shown 
that  when  the  wheels  are  grooved  alike  the  strains  in  the  various  ropes  may 
differ  greatly,  and  to  such  a  degree  that  danger  is  introduced,  for  while  one- 
half  the  tension  weight  should  represent  the  maximum  strain  on  the  slack 
rope,  it  is  demonstrated  in  the  paper  that  the  actual  maximum  strain  may 
be  even  four  or  six  times  as  great. 

in  a  drive  such  as  is  recommended,  with  a  wide  angle  in  the  large  sheave 
with  the  larger  arc  of  contact,  the  conditions  governing  the  ropes  are  the 
same  as  if  the  wheels  were  of  the  same  diameter;  and  where  the  wheels  are 
of  the  same  diameter,  with  a  proper  tension  weight,  the  ropes  pnll  alike.  It 
is  claimed  ihat  by  widening  the  angle  of  the  large  sheave  not  only  is  there 
no  power  lost,  but  there  is  actually  a  great  gain  in  power  transmitted.  An 
example  is  given  in  which  it  is  shown  that  in  that  Instance  the*  power  trans- 
mitted is  nearly  doubled.  Mr.  Miller  refers  to  a  ^SO-horse-power  drive  which 
^as  been  running  ten  years,  the  large  pulley  being  grooved  60**  and  the 
smaller  45<*.  This  drive  was  designed  to  use  a  1^-in.  manila  rope,  but  the 
gi-ooves  were  made  deep  enough  so  that  a  ^-in.  rope  would  not  bottom.  In 
order  to  determine  the  value  of  the  drive  a  common  ^-in.  rope  was  put  in 
at  first,  and  lasted  six  years,  working  under  a  factor  of  safety  of  only  14. 
He  recommends,  however,  the  employment  in  continuous  rope-driving  of  a 
factor  of  safety  of  not  less  than  20. 

The  Walker  Company  adopts  a  curved  form  of  groove  instead  of  one  with 
straight  sides  inclined  to  each  other  at  45".  The  curves  are  concave  to  the 
rope.  The  rope  rests  on  the  sides  of  the  groove  in  driving  and  driven  pul- 
leys. In  idler  pulleys  the  rope  rests  on  the  bottom  of  the  groove,  which  is 
semicircular.  The  Walker  Company  also  uses  a  '*  differential '*  drum  for 
heavy  rope^lrives.  in  which  the  grooves  are  contained  each  in  a  separate 
ring  which  is  free  to  slide  on  the  turned  surface  of  the  drum  in  case  one  rope 
pulls  more  than  another. 

A  heavy  rope-drive  ou  the  separate,  or  English,  rope  svstem  is  described 
and  illustrated  in  Poioer,  April.  1898.  It  is  In  use  at  the  India  Mill  at  Darwen, 
England.  This  mill  was  originally  diiven  by  gears,  but  did  not  prove  success- 
ful, and  rope-driving  was  resorted  to.  The  85,000  spindles  and  preparation 
are  driven  by  a  3000-horse-power  tandem  compound  engine,  with  cylinders 
23  and  44  inches  in  diameter  and  ?<2-inch  strofce,  running  at  54  revolutions 
per  minute.  The  fly-wheel  is  80  feet  in  diameter,  weighs  65  tons,  and  is 
arranged  with  80  grooves  for  l^^-inch  ropes.  These  ropes  lead  off  to  recelv- 
ing-pulleyK  upon  the  several  floors,  so  that  each  floor  receives  its  power  direct 
from  the  fl^-wheel.  The  speed  of  the  ropes  is  5089  feet  per  minute,  and  five 
7-foot  receivers  are  used,  the  number  of  ropes  upon  each  being  proportioned 
to  the  amount  of  power  required  upt>n  the  several  floors.  I^mbeth  cotton 
ropes  are  used.  (For  much  othnr  information  on  this  subject  see  "  Rope- 
Driving,*'  by  J.  J.  Flather,  John  Wiley  &  tions,  1895.) 


928 


yHTOTlOK  AND  LUBRICATIOK, 


FBICmOW  AND  LtrBRIOATIOW. 


Prletlon  Is  defined  by  lUnktne  as  tliafc  forc«  whtcTi  actn  b«tir«en  two 
bodies  at  their  surfdoe  of  contact  bo  ap  to  t^ist  tbefr  tslidinfc  on  ^ach  other, 
and  which  depends  on  the  force  with  which  the  bodies  Afe  pr0ssi<d  lojff  !hf  r. 

Coettolent  of  Friction.— The  ratio  of  the  fot-ce  required  to  t*ti<i<?  a 
body  along  a  horizontal  plane  surface  to  the  weli^ht  of  the  bodj'  is  enlkKl  ihe 
coefflclent  of  friction.  It  is  equivalent  to  the  tauKent  of  the  angle  of  repaid, 
which  is  the  ani^le  of  inclination  to  the  horixontal  of  an  inclined  p(BD«  r.n 
which  the  body  will  Just  overcome  IM  tendency  to  slide.  The  BbRle  us  UKuaiiy 
denoted  by  9,  and  the  coefficient  by/.  /  =  tan  #. 

PHotion  of  tto«t  and  of  flloflon.— The  force  rsqnlred  to  c^tart  a 
body  sliding  is  called  the  filctlon  of  i'CHt,  and  the  force  required  to  coutfoue 
its  Rlldlnsr  after  havlntr  start4»d  Is  called  the  friction  of  motion. 

Rolling  Friction  Is  the  force  required  to  roll  a  cylindrical  or  spheri- 
cal body  on  a  plane  or  on  a  curved  surface.  It  depends  on  the  nature  of  tl}« 
snrfaces  and  on  the  force  with  which  they  are  pressed  together,  but  is 
esRentiatlv  different,  from  ordinary,  or  sliding,  friction. 

Prictlon  of  Soilda.—Rennie*s  experiments  0^'^  on  fricttoa  of  solids, 
usually  Unlubrlcated  and  dry,  led  to  the  following  conclusions: 

1.  The  laws  of  sliding  friction  differ  with  the  character  of  th«  bodipt 
rubbing  together. 

2.  Tlie  friction  of  fibrous  material  is  increased  by  Increased  extent  of 
surface  and  by  time  of  contact,  and  Is  dlminlttbed  by  pressure  atid  speed. 

8.  With  wood,  metal,  and  stones,  within  the  limit  of  abrasion,  ftii-tioi} 
varies  only  with  the  pressure,  and  is  Independent  cf  the  extent  or  surfac«>. 
time  of  contact  and  velocity. 

4.  The  limit  of  abrasion  Is  determined  by  the  hardness  of  the  softer  of  the 
two  rubbing  parts. 

&.  Friction  is  greatest  with  soft  and  least  with  hard  materials. 

6.  The  friction  of  lubricated  surfaces  Is  determined  by  (he  nature  of  tb« 
lubricant  rather  than  by  that  of  the  solids  themselves. 

Priction  ot  Mett.   (Rennie.) 


Prejiure. 

Values  of/. 

Wrought  iron  on 

Wroufrht  on 
Cast  Iron. 

Bteelon 

Braes  on 

Wrought  Iron. 

Cast  Iron. 

Cast  Iron. 

187 

.35 

.88 

.80 

.28 

224 

.27 

.29 

.28 

836 

.81 

.88 

•8ft 

.31 

448 

.88 

.87 

.85 

.21 

660 

.41 

.87 

86 

.28 

672 

Abraded 

.88 

.40 

.88 

784 

Abraded 

Abraded 

.88 

I<AW  Of  trnlubricatea  Priotion.— A.  M.  Wellington,  Sfig''o  Setn. 
April  7, 1888,  siate.s  that  the  most  Important  and  the  best  determined  of  all 
the  laws  of  unlubrlcated  friction  may  be  thus  expressed: 

The  coefTldent  of  unlubrlcated  friction  deci'eases  materially  with  veloclt}-, 
is  very  much  greater  at  minute  velocities  of  0  +,  falls  very  rapidly  with 
minute  Increases  of  such  velocities,  and  continues  to  fall  much  less  rapkllr 
with  higher  velocities  no  to  a  certain  varying  point,  following  closely  the 
laws  which  obtain  with  lubricated  friction. 

Friction  of  Steel  Tires  Sliding  on  Steel  Rsdls.  (Westing 
house  &  Gallon.) 

Speed,  miles  per  hour 10        15       25       88       45       50 

Coefficient  of  friction 0.110    .087    .080    .061     .047    .040 

Adhesion,  lbs.  per  ton  (;i240 lbs.)     246       195      17»      128     114       90 


?WOTIO», 


930 


Rollinif  FFletlon  !•  a  ooosequeiuM  of  the  irregiilaritieg  of  form  and 
the  rouKbueBs  of  Rurface  of  bodies  rolling  one  over  the  other.  Its  lawa 
are  not  yet  deflqltely  eeti^ibllsbed  in  consequence  of  the  uiiceitahity  which 
exists  in  experiment  as  to  how  much  of  the  resistance  is  due  to  rouj?nneas  of 
surfnoe.  hovr  much  to  orlf^nal  and  permanent  irregularity  of  form,  and  bow 
much  to  diHtortion  under  thn  load-    (Tliumton.) 

CoeflleteuM  of  Rollins  PrlcUoii.--If  R  =  resistance  applied  at 
the  eiivumftrrence  of  tiie  whe«I7  W  a  toiai  weight,  r  =x  radius  of  tne  wheel, 
and  /  s  a  coefilcient,  R  =  fW-t-  r,  /  is  very  variable.  Coulomb  gives  .06 
for  wood,  .005  for  metal,  where  W  in  in  pounds  and  r  in  feet.  Tredgold 
made  the  value  of /for  iron  on  Iron  ,0W. 

For  wagons  on  soft  soil  Morin  found  /  =s  .0Q5,  and  on  hard  smooth  roads 

A  Committee  of  the  Society  of  Arta  (Clark,  R.  T.  D.)  reported  a  loaded 
omnibuf  to  exhibit  a  r««istance  on  various  loads  as  below: 

Pavement  Speed  p^rhour.  Coeffiolent.  Resistance. 

Granite    2.87miltta,  .007  17.41  per  ton. 

Asphalt 8.60     *•  ,0I«1  8T.U 

Wood 8. 34     ••  .0198  41. W 

Macadam,  gravelled 8.45     **  .0190  44.43       " 

granite,  new..       8.51     "  .0451  101,09       " 

Tliurston  gives  the  value  of /for  ordinary  railroAds,  .008,  well-laid  railroad 
track,  .008;  best  possible  railroad  track.  .001. 

The  few  experiments  that  have  been  made  upon  the  coefficients  of  rolling 
friciioD.  apart  from  axle  friction*  are  too  incomplete  to  serve  as  a  basis  for 
practical  rules.    (Tmnfwine). 

l.awn  of  Fluia  FHetlOB«-For  all  fluids,  whather  liquid  or  gaseous, 
the  resifiaiice  is  U)  independent  of  the  pressure  between  the  masses  in 
contact;  g?)  directly  proportional  to  the  artra  of  rubbing-surface;  (8)  pro- 
portional to  the  square  of  the  relative  velocity  at  moderate  and  high  speeds, 
and  to  the  velocity  nearly  at  low  speeds;  (I)  independent  of  the  nature  of 
the  surfaces  of  the  solid  against  which  the  stn^am  may  flow,  but  dependent 
to  somt*  extent  upon  their  degree  of  roughness;  (5)  proportional  to  the  den- 
sity of  the  flukl,  and  related  in  some  way  to  ita  visoosity,    (Thurston.) 

The  Friction  of  Lubricate($  8urfacf$  approximates  to  that  of  solid  fric- 
tion as  the  Journal  is  run  dry,  and  to  tbat  of  fluid  friction  as  it  is  flooded 
with  oil. 

Angploa  of  Repoao  snd  Coofllcfoiit*  of  Frlotton  of  Bolld* 
lug;  JHaleriala.    (Prom  Rankine's  Applied  lAeoiiauius.) 


/  =  tan*. 


1 
tan«* 


Dry  maaoory  and  briokwork 
Masonry  and  brickwork  with 

dampmortar  .,, 

Timber  on  stone.... 

Iron  on  atone .,. 

Timber  on  timber ,,,. 

"      "metala. .., 

Metals  on  metals 

Masonry  on  dry  clay , 

"        •*  moist  clay.  ... 

Earth  on  earth 

"      **    dry  sand,  clay, 

and  mixed  earth. 

Sarth  on  earth»  damp  clay. . 
•»     '•     »•      wet  clay.... 
"     **     '•        shingle  and 
gravel    


81*  to  850 


86*  to  18M* 

1»^»  XqXJU 

8r  to  ilMr 

14«  to  8UO 

18^« 
U*  to  45« 

ttl*to87« 
450 
XT 

80«to46« 


.6  to  ,7 

.74 
about  .4 
.7  to  .8 
,6  to  .2 
.6  to  .9 
.35  to. 15 
.51 

.25  to  1.0 

.86  to  .75 
1.0 
.81 

.81 


1.97  to  1.4 

1.85 

3.5 
1.48  to  8.3 

2  to  6 
1,67  to  5 
4  to  6.67 

1.96 
8. 

4tol 

9.68  to  1.88 

8.88 
1.8810  0.9 


Frtctton  of  motion. --The  following  is  a  table  of  the  angle  of  repose 
B,  Uw  coefficient  of  friction  /  ^  tan  9,  and  its  reciprocal,  1  •^/Tfor  the  ma- 
terials  of  mechaoiam«4sondens««d  from  the  tables  of  General  Morin  (1881), 
and  other  aouroea,  as  given  by  Kanlcine: 


930 


raiCTION  AND  LUBRICATIOK. 


No. 

Surfaces. 

'• 

/. 

IH-/. 

1 

Wood  on  wood,  dry .... 

14°  to  26U^ 
llU'toa^ 

.25tx>  .6 

4  to  2 

2 

'*      "       "     soaped.. 

.2   to  .04 

5to25 

3 

Metals  on  oak,  dry 

26U<»  to  81" 

.6  to  .6 

2tol.C7 

4 

• wet 

18K*  to  14» 

.24  to  .86 

4.17  to  8.96 

6 

6 

••       "     "     soapy..  . 
"       "  elm,  dry 

11H<»  to  W 

.2 
.2  to  .25 

5 
5  to  4 

7 

Hemp  on  OH k,  d ry 

280 

.58 

1.89 

8 

"      "    "      wet 

15»  to  li^' 

.38 

8 

9 

Leather  on  oak 

.27  to  .38 

8.7  to  8.86 

10 
11 

"        •*  metals, dry.. 
"        "       "       wet.. 

.56 
.36 

1.79 
2.78 

13 

a       .4     groasy 

13» 

.88 

4.85 

18 

"       "     oUy... 

8H' 

.15 

6.67 

14 

Metals  on  metals,  dry... 

8H»  to  11« 

.15  to  .2 

6.67  to  5 

15 

wet... 

16^- 

.8 

8.33 

16 

Smooth   surfaces,  occa- 

sionally greased 

4«»  to  4Hi* 

.07to.08 

14.8  to  12.5 

17 

Smooth     Burfacfs,    con- 

tinuously greased 

S* 

.05 

80 

18 

Smooth    surfaces,    best 

results 

Bronze  on  lignum  vltes, 

1  Ji»  to  «• 

.08  to  .036 

19 

constantly  wet 

Sof 

.05? 

Coefflelentii  of  Friction  of  JToarnals,    (Morin.) 


Material. 

Unguent. 

Lubrication. 

Intermittent. 

Continuous. 

Cast  Iron  on  cast  Iron. ... | 

Cast  Iron  on  bh)nze | 

Cast  iron  on  lignura-vitee . . 

Oil,  lard  tallow. 
Uuctuous  and  wet. 
Oil,  tard,  tallow. 
Unctuous  and  wet. 
Oil,  lard. 

Oil.  lard,  tallow. 

Oil,  lard. 
Unctuous. 
OliTe-oll. 
Lard. 

.07  to  .08 

.14 
.07  to  .06 

.16 

.08  to  .054 

.08  to  .OM 

.09 

Wrought  iron  on  cast  iron  J 
**          **    "bronze.,  j 

Iron  on  lignum  YitsB -j 

Bronze  on  bronze \ 

.07  to  .08 

.11 
.19 
.10 
.09 

.03  to  .054 

Prof.  Thurston  says  concerning  the  above  figures  that  much  better  results 
are  probably  obtained  in  good  practice  with  ordinary  machinery.  Those 
here  given  are  so  greatly  modified  byVarfations  of  speed,  pressure,  and  tem- 
perature, that  they  cannot  be  taken  a*«  correct  for  general  purposes. 

ATeragre  Coelliclents  of  Friction.  Journal  of  cast  iron  in  bronze 
bfaring;  velocity  720  feet  per  minute;  t«*mp6rature  70*  F.;  intermittent 
feed  through  an  oil-hole.    (Thurston  on  Friction  and  Lost  Work.) 


Oils. 

Pressures,  pounds  per  square  inch. 

8 

16 

88 

48 

Sperm,  lard,  neat*s-foot,etc. 
Olive,  cotton -seed,  rape,  etc. 

Cod  and  menhaden 

Mineral  lubricating-olls.  . . 

.l.'iO  to  .250 
.160  "  .288 
.248  "  .278 
.154    "  .261 

.188  to  .192 
.107  "  .245 
.124   ♦♦  .167 
.145  **  .288 

.086  to  .141 
.101  "  .168 
.097  "  .108 
.086  "  ,1781 

.077  to  .144 
.079  ••  .181 
081    •*  .123 

.094  **  .8a 

With  fine  steel  Journals  running  in  bronze  bearings  and  continuous  lubrk 
cation,  coefflcientR  far  below  those  above  given  are  obtained.  Thus  with 
sperm-oil  the  coelTlcient  with  50  lbs.  per  square  inch  pressure  was  .0034;  with 
200  lbs.,  .0051;  with  300  lbs..  .0057. 


PRICTIOW.  931 

» 

For  ?ery  lotr  pressures,  as  In  spindles,  the  coefficients  are  much  higher. 

Thus  Mr.  Woodbury  found,  at  a  temperature  of  100«  and  a  Telocity  of  600 

feet  per  minute. 

Pressures,  Ihs.  per  so.  in 1  8  8  4  5 

Coefficient 88       .27       .28       .18       .17 

These  high  coefficients,  however,  and  the  great  decrease  in  the  coefficient 
at  increased  pressures  are  limited  as  a  practical  matter  only  to  the  smaller 
pressures  which  exist  especially  In  spinning  machinery,  where  the  pressure 
is  so  light  and  the  flim  of  oil  so  thick  tliat  the  viscosity  of  the  oil  is  an  import- 
ant part  of  the  total  f riotlonal  resistance. 

Bxperlments  on  Friction  of  a  JTonrnal  I^nbrlcat^d  by  an 
Oll-bath.  creported  by  the  Committee  on  fViotion,  l'i*oc.  Inst.  M.  E.. 
Nov.  1888)  show  that  tlie  absolute  friction,  that  Is.  the  absolute  tangential 
force  per  tiauare  inch  of  bearing,  required  to  resist  the  tendency  of  the  brass 
to  go  round  with  the  journal,  is  nearlv  a  constant  under  all  loads,  within  or- 
dinary worlcing  limits.  Most  certainly  it  does  not  increase  in  direct  propor- 
tion to  the  load,  as  It  should  do  according  to  the  ordinary  theorv  of  solid 
friction.  The  results  of  these  experiments  seem  to  show  that  the  friction  of 
a  perfectly  lui>ricated  journal  follows  the  laws  of  liquid  friction  nmch  more 
closely  than  those  of  solid  friction.  They  show  that  under  these  circum' 
stances  the  friction  is  nearly  independent  of  the  pressure  per  square  Inch, 
and  that  It  increases  with  the  velocity,  though  at  a  rate  not  nearly  so  rapid 
as  the  square  of  the  velocity. 

The  experiments  on  friction  at  different  temperatures  indicate  a  great 
diminution  in  the  friction  a^  the  temperature  rises.  Thus  in  the  case  of 
lard-oil,  talcing  a  speed  of  450  revolutions  per  minute,  the  coefficient  of  fric- 
tion at  a  temperature  of  1^20"  Is  only  one  third  of  what  it  was  at  a  tempera- 
tnrH  of  60. 

The  journal  was  of  steel.  4  Inches  diameter  and  6  Inches  long,  and  a  gnn- 
metal  bras<«.  embracing  somewhat  less  than  half  the  circnmfei-ence  of  the 
ioumal,  rested  on  its  upeer  side,  on  which  the  load  was  applied.  When  the 
bottom  of  the  journal  was  immersed  in  oil,  and  the  oil  therefore  carried 
under  the  brass  by  rotation  of  (he  journal,  the  greatest  load  carried  with 
raoe-oil  was  ftTS  lbs  per  soiiare  Inch,  and  with  mineral  oil  625  lbs. 

In  experiments  with  ordinary  lubrication,  the  oil  being  fed  in  at  the  cen- 
tre of  the  top  of  the  brass,  and  a  distributing  groove  being  cut  in  the  brass 
parallel  to  the  axis  of  the  journal,  the  bearing  would  not  run  cool  with  only 
100  lbs.  per  square  Inch,  tlie  oil  beintr  pressed  out  from  the  bearing-surface 
aiiii  ttirouKh  the  oil-hole.  Instead  of  being  carried  in  by  it.  On  introducing 
tiie  oil  at  the  sides  through  two  parallel  grooves,  the  lubrication  appeared 
to  be  satisfactory,  but  the  bearing  seized  with  380  lbs.  per  square  inch. 

When  the  oil  was  introduced  through  two  oil-holes,  one  near  each  end  of 
the  brass,  and  each  connected  with  a  curred  groove,  the  brass  refused  to 
talce  its  oil  or  ruu  cool,  and  seized  with  a  load  of  only  200  lbs.  per  square 
inch. 

With  an  oil  pad  under  the  journal  feeding  rape-oil.  the  bearing  fairly  car- 
ried 551  lbs.  Mr.  Tower's  conclusion  from  these  experiments  Is  that  the 
fricli(»n  depends  on  the  quantity  and  uniformity  of  distribution  of  the  oil, 
and  mav  lie  anything  between  the  oil-baih  results  an<l  seizing,  according  to 
the  perfection  or  imperfection  of  the  lubrication.  The  lubrication  may  b« 
very  small,  giving  a  coefficient  of  l/IOO;  but  it  appeared  as  though  it  could 
not  be  dimhji«*hed  and  the  friction  Increased  much  beyond  this  point  with- 
out imminent  rislc  of  healing  and  seizing.  Tlie  oil-bath  probably  n»presents 
the  most  perfect  lubrication  possible,  and  the  limit  beyond  which  friction 
cannot  lie  reduced  by  lubrication :  and  the  experiments  show  that  with  speeds 
of  from  100  to  200  feet  per  minute,  by  pronerly  proportioning  the  bearingr- 
surfa<?e  to  the  load,  it  is  possible  to  recfiice  tne  coefficient  of  friction  to  as  low 
as  1/1000.  A  coefficient  of  1/1500  Is  easily  attainable,  and  probably  is  fre- 
quently attained.  In  ordinary  engine-bearings  In  which  the  diret*tion  of  the 
force  is  rapidly  alternating  and  the  oil  given  an  opportimity  to  get  between 
the  surfaces,  while  the  duration  of  the  force  in  one  dli-ection  is  not  sufficient 
to  allow  time  for  the  oil  film  to  be  squeezed  out. 

Observations  on  the  behavior  of  the  apparatus  gave  reason  to  believe  that 
with  perfect  lubrication  the  speed  of  minimum  friction  was  from  100  to  150 
feet  per  minute,  and  that  this  sjieed  of  minimum  friction  tends  to  l>e  higher 
with  an  Increase  of  load,  and  also  with  less  perfect  lubrication.  By  the 
speed  of  minimum  friction  is  meant  that  speed  in  approaching  which  from 
roBt  the  friction  diminishes,  and  above  which  the  friction  increases. 


932 


FRICTION  AND  LUBRICATION, 


Coeflletents  of  Friction  of  JTonmal  with  OU-b«Ui.— Ab. 

Btraut  of  rettiilu  of  Tower's  exptirimvnta  <>u  friction  (Prao.  lojui.  M.  £.,  Not. 

1588).    Journal,  4  in.  diam.,  6  in.  long;  temperature,  90*  P- 


Lubricant  in  Bath. 

Nominal  Load,  in  pounds  per  square  inch. 

625 

530 

415  1  810     205     158     100 

CoefBcienU  of  Friction. 

Lard-oil : 
157  ft.  per  min 

.0009 
.0017 

.0014 
.0022 

seized 

.001 
.0015 

.001$ 
.0018 

.0012 
.0021 

:S8J? 

.0015 
.0021 

.0009 
.0010 

.0012 
.003 

.0014 
.0029 

.0028 
.004 

.0011 
.0019 

.0006 
.0016 

.0014 
.0024 

.0058 
.0088 

.0099 
.0099 

.0020  .0097 
.0042.005$ 

.0084.0088 
.0066.0068 

.0016  .0019 
.0027   0067 

.0014  .002 
.0024  .004 

.0042 

471     •»          •»  

.009 

Mineral  grease : 
157ft  nermin 

.001 
.002 

0076 

471     "         " 

Sperm-oil : 
157  ftk  per  min.. .  

.0151 
.008 

471      -          "  

Rape-oil : 

157  ft.  permin 

471     **         ** 

(578  ib.) 
.001 

.OOM 

.004 
.007 

Mineral-oil : 
157  f  t.  per  min 

471     " 

.0C18 

.0021 

.0085  

.004 
.007 

Rape-oil  fed  by  syphon  lubricator: 
lo7  ft.  per  miu 

.0098 
.0077 

.0106 

.0125 

814     »•         »•  

.0162 

Rape-oil,  pad  under  journal: 
157  ft  Der  min 

.0099 

814     " 



.0078 

.OISIS 

Comparative  friction  of  different  lubricants  under  same  circumstances, 
temperature  90«,  oil-bath t 

8perm-oil lOOpercent.   1   Lard 135  percent. 

Bape-oU 106       "  Olive-oil 185       " 

MiueraloU 129       "  |   Mineral  grease 217       ** 

Coetlketentm  oT  FrietlOA  of  Btotlon  and  of  Rest  or  m 
JTournal*— A  casi-iron  Journal  in  stee)  boxes,  tested  by  Prof.  Thurston  at 
a  speed  of  rubbing  of  150  feet  per  minute,  with  lard  and  with  sperm  oil, 
gave  the  following: 

Pressures  per  sq.  in.,  lbs 60  100  250  600  750        1000 

Coeff.,  with  sperm 018        .008        .005         .004        .0043       .000 

'•    lard 02        .0187      .0086       .0058       .0066      .012S 

The  coefficients  at  starting  were: 

Withsperm 07  .186         .14  .16         .185 

Withllrd 07  .11  .11  .10        .12 


.18 
.12 

The  coefficient  at  a  speed  of  150  feet  per  minute  decreases  witb  Increase 
of  pre8«ure  until  500  lbs.  per  sq.  in.  Is  reached;  above  this  it  increases.  The 
coemcient  at  rest  or  at  startiog  increases  with  the  pressure  throughout  the 
range  of  the  tej»ts.  _  -«,,.. 

Valae  of  Antl-fMotlon  Metala.  (Denton.)— The  variouit  white 
metals  available  for  lining  brasses  do  not  afford  coefficients  of  friction 
lower  than  can  be  obtained  with  bare  brass,  but  they  are  leas  liable  to 
•*overh»*ating,'*  because  of  the  superiority  of  such  material  over  bronse  In 
ability  to  permit  of  abrasion  or  crushing,  without  ezoesslve  increase  of 
friction.  .  .  ,  •*,_,.  ^        ^ 

Thurston  rFriction  and  Lost  Work)  says  that  gun-bronze,  Babbitt,  and 
other  soft  white  alloys  have  substantially  the  same  friction:  in  other  words, 
the  friction  is  determined  by  Uie  nature  of  the  unguent  and  not  by  that  of 
the  rubbing- surfaces,  when  the  latter  are  in  good  order.  Tlie  soft  metals 
run  at  higher  temperatures  than  the  bronze.  This,  however,  does  not  nec- 
essarily indicate  a  serious  defect,  but  simply  deficient  conductivity.  The 
value  of  the  white  alloys  for  bearings  lies  mainly  in  their  ready  reduction 
to  a  smooth  surface  after  any  local  or  general  injury  by  alteration  of  either 
surface  or  form. 


MOUIN^S  LAWS  OF   FRICTION.  933 

Cm«t«lron  for  Bearlnc*-  (Joshua  Rose.)— Cast  iron  appears  to  be  ac 
exi:fpiiou  to  the  tretieral  rule,  that  the  harder  the  metal  the  jcreater  the 
resistance  lo  wear,  because  cast  iron  Is  softer  in  its  texture  and  easier  to 
cut  with  steel  tools  than  steel  or  wrought  iron,  but  in  some  situations  it  is 
far  more  durable  than  hardened  steel;  thus  when  surroimded  by  steam  it 
will  wear  better  than  will  any  other  metal.  Thus,  for  instance,  experience 
has  demonstrated  that  piston-riugs  of  cast  iron  will  wear  smoother,  better, 
and  equttlly  as  lonir  as  those  of  steel,  and  Ioniser  than  those  of  either 
wrouKiit  iron  or  brass,  whether  the  cvlinder  in  which  it  works  be  oompoaed 
of  brass,  steel,  wrought  iron,  or  cast  iron;  the  latter  being  the  more  note* 
worthy,  Hince  two  surfaces  of  the  same  metal  do  not,  as  a  rule,  wear  or 
worlc  well  tofrether.  So  also  slide- valves  of  brass  are  not  found  to  wear  so 
long  or  so  suioothly  as  those  of  cast  iron,  let  the  metal  of  which  the  seating 
is  composed  be  whatever  it  may;  while,  on  the  other  hand,  a  cast  iron  slide* 
valve  will  wear  longer  of  itself  and  cause  less  wear  to  its  seat,  if  the  latter 
is  of  cast  iron,  then  if  of  steel,  wrouglit  iron,  or  brass. 

Frletlon  of  Hetalfl  under  Sieam^presfliire,— The  friction  of 
bra-s  upon  iron  under  steam-pressure  is  double  that  of  iron  upon  iron. 
lO   H.  Babcock,  Trans.  A.  8.  M.  B..  i.  151.) 

IHIorlit^s  <<  Laura  of  Frtetlon.*'— 1.  The  friction  between  two  bodies 
iii  directly  proportiooed  to  the  pressure;  i.6.,  the  ooefilcient  is  constant  for 
all  pressures. 

i.  The  coefficient  and  amount  of  friction,  pressure  being  the  same,  is  in- 
dependent of  the  areas  in  contact. 

8  The  coetBcient  of  friction  is  independent  of  veloci^,  although  static 
friction  (friction  of  rest)  is  greater  than  the  friction  of  motion. 

Eiig'q  News,  April  7, 1888,  comments  on  these  '*law8**  as  follows  :  From 
1881  till  about  1876  there  was  no  attempt  worth  speaking  of  to  enlarge  our 
knowledge  of  the  laws  of  fHction,  which  during  all  that  period  was  assumed 
to  be  complete,  although  It  was  really  worse  tlian  nothing,  since  it  was  for 
the  most  part  wholly  false.  In  the  year  first  mentioned  Morln  began  a  se- 
ries of  experiments  which  extended  over  two  or  three  yearn,  and  which 
resulted  in  the  enunciation  of  these  three  "  fundamental  laws  of  friction," 
no  one  of  which  is  even  approximately  true. 

For  fifty  years  these  laws  were  aoeepted  as  axiomatic,  and  were  quoted  as 
such  without  question  in  eveiy  scientiiSo  work  published  during  that  whole 
period.  Now  that  they  are  so  thoroughly  discredited  it  has  been  attempted 
to  explain  away  their  defects  on  the  ground  that  ther  cover  only  a  very  lim- 
ited range  of  pressures,  areas,  velocities,  etc,  and  that  Morin  himself  only 
announced  them  as  true  within  the  range  of  hm  conditions.  It  is  now  dearfy 
established  that  there  are  no  limits  or  conditions  within  which  any  one  of 
thvm  even  approxhnates  to  exactitude,  and  that  there  are  many  conditions 
under  which  they  lead  to  the  wildest  kind  of  error,  while  many  of  the  con- 
stants were  as  Inaccurate  as  the  laws.  For  example,  in  Morin 's  "  Table  of 
Coefficients  of  Moving  Friction  of  Smooth  Plane  Surfaces,  perfectly  lubri- 
cated,'' which  may  be  found  in  hundreds  of  text-books  now  In  use.  the  coeffi- 
cient of  wrought  iron  on  brass  Is  given  as  .075  to  .106.  which  would  make  the 
rolling  friction  of  railway  trains  15  to  20  lbs.  per  ton  instead  of  the  8  to  6  lbs. 
which  it  actually  is. 

General  Morin,  in  a  letter  to  the  Secretary  of  the  Institution  of  Mechanical 
Engineers,  dated  March  15. 1879,  writes  as  follows  concerning  his  experiments 
on  friction  made  more  than  forty  years  before:  '*  The  results  f umisnod  hy  my 
experiments  as  to  the  relations  between  pressure,  surface,  and  speed  on  the 
one  hand,  and  sliding  friction  on  the  other,  have  always  been  regarded  by 
m vself.  not  as  mathematical  laws,  but  an  close  approximations  to  the  truth, 
within  the  limits  of  the  data  of  the  experiment?  themselves.  The  same  holds, 
in  my  opinion,  for  many  other  lawH  of  practical  mechanics,  such  as  those  of 
rolling  resistance,  fluid  resistance,  etc.'' 

Prof  J.  K.  Denton  {St*'V4'n8  Indicator^  July,  1800)sa3rs:  It  has  been  gen- 
erally assumed  that  fricti<m  tietween  lubricated  surfaces  follows  the  simple 
law  that  the  amount  of  the  friction  is  some  fixed  fraction  of  the  pressure  be- 
tween the  surfaces,  such  fraction  being  independent  of  the  intensity  of  the 
pres<*ure  per  square  inch  and  the  velocity  of  rubbing,  between  certain  limits 
of  practice,  and  that  the  fixed  fraction  referred  to  is  represented  by  the  co- 
efllcienis  of  friction  given  by  th  •  experiments  of  Morin  or  obtained  from  ex- 
perimental data  which  represent  conditions  of  practical  lubrication,  such  as 
those  given  in  Webber's  Manual  of  Power. 

By  Uie  experiments  of  Thnrston,  Woodburv,  Tower,  etc.,  however.  It 
appears  that  the  f rictton  between  lubricated  metallic  surfaces,  such  as  ma« 


934  FRICTIOK  AKD  LtTBRtCATIOIT. 

chine  beftrioKe,  is  not  directly  proportional  to  the  pressure,  is  not  ilid^peti- 
dent  of  the  speed,  and  that  the  coefficients  of  Monn  and  Webber  are  about 
tenfold  too  great  for  modem  journals. 

Prof.  Denton  offers  an  explanation  of  this  appctfent  contradiction  of  an- 
thorities  by  showing,  with  laboratory  testlnff-machlne  data,  that  Moriu's 
laws  hold  for  bearings  lubricated  by  a  restricted  feed  of  lubricant,  such  as 
is  afforded  by  the  oil-cups  common  to  machinery;  whereas  the  modem  ex- 
periments have  been  made  with  a  surphia  feed  or  superabundance  of  lubri- 
cant, such  as  is  provided  only  in  railroad -car  journals,  and  a  few  special 
cases  of  practice. 

That  the  4ow  coefficients  of  friction  obtained  under  the  latter  oonditlons 
are  realised  in  the  case  of  car- journals,  is  proved  by  the  fact  that  the  tem- 
perature of  car-boxes  remains  at  lOO^*  at  ftiigh  velocities:  and  experiment  shows 
that  this  temperature  is  consistent  only  with  a  coefficient  of  friction  of  a 
fraction  of  one  per  cent.  Deductions  from  experiments  on  train  resistanoe 
also  Indicate  the  same  low  d^ree  of  friction.  But  these  low  co-efficients  do 
not  account  for  the  internal  friction  of  steam-engines  as  well  as  do  the  co- 
efficients of  Morin  and  Webber. 

In  American  Machinist,  Oct.  88, 1890.  Prof.  Denton  says:  Morin^s  measure- 
ment of  friction  of  lubricated  journals  did  not  extend  to  light  prpssures. 
They  apply  only  to  the  conditions  of  general  shafting  and  engine  worlc. 

He  clearly  understood  that  there  was  a  frictional  resistance,  due  soldy  to 
the  viscosity  of  the  oil,  and  that  therefore,  for  very  light  pressures,  the  laws 
which  he  enunciated  did  not  prevail. 

He  applied  his  dynamometer«i  to  ordinaiy  shaft-journals  without  special 
preparation  of  the  rubbing-surfaces,  and  without  resorting  to  artificial 
methods  of  supplying  the  oil. 

Later  experimenters  have  with  few  exceptions  devoted  themselves  exclu- 
sively to  the  measurement  of  resistanoe  praeticallv  due  to  viscosity  aione. 
They  have  eliminated  the  resistance  to  which  Monn  oonflned  his  measure- 
ments, namely,  the  friction  due  to  such  contact  of  the  rubbing-surfaces  aa 
prevail  with  a  very  thUi  film  of  lubricant  between  comparatively  rough  sur- 
faces. 

Prof.  Denton  also  says  (Trans.  A.  S.  M.  E..  x.  51H):  "  I  do  not  believe  there 
is  a  particle  of  proof  in  any  investigation  of  friction  ever  made,  that  Morin 's 
laws  do  not  hold  for  ordinary  pmctlcal  oil-cups  or  restricted  rates  of  feed." 

liAurs  of  Friction  of  irell»labrlcated  Journals.— John 
Goodman  (Trans.  Inst.  C.  E.  1886.  Eny'g  Meics.  Apr.  7  and  14,  18S8>,  review- 
ing the  results  obtained  from  the  testing-machines  of  Thurston,  Tower,  and 
Stroudley,  arrives  at  the  following  laws: 

Laws  of  Friction:  Wbll-lttbrioatsd  Subpaoes. 
(Oil-bath.) 

1.  The  coefficient  of  friction  witli  the  surfaces  efficiently  lubricated  is  from 
1/5  to  1/10  that  for  <lrv  or  scantily  hibricated  surfaces. 

2.  The  coefficient  of  friction  for  moderate  pre.s8ures  and  speeds  varies  ap- 
proximately inversely  as  the  normal  pressure:  the  frictional  resistanoe  va- 
nes as  the  area  In  contact,  the  normal  pressure  remaining  constant. 

8.  At  yerj  low  journal  speeds  t  .e  coefficient  of  friction  is  abnormally 
high;  but  as  the  speed  of  Rlidlng  increases  from  about  10  to  lOO  ft.  per  min., 
the  friction  diminishes,  and  again  rises  when  that  speed  is  exceedeo,  varying 
approximately  as  the  square  root  of  the  speed. 

4.  The  coefficient  of  friction  varies  approximately  inversely  as  tbetemper- 
atiu^  within  certain  limits,  namely,  just  before  abrasion  takes  place. 

The  evidence  upon  which  these  laws  are  based  is  taken  from  various  mod- 
em experiments.  That  relating  to  Law  1  is  derived  from  the  "  Firet  Report 
on  Friction  Experiments/*  by  Mr.  Beauchamp  Tower. 


^  Method  of  Lubrication. 

Coefficient  of 
Friction. 

Comparative 
Friction. 

Oil-bath 

.00139 

.0098 

.0090 

1.00 

Siphon  lubricator 

7.06 

Fad  under  journal 

6.48 

With  a  load  of  298  lbs.  per  sq.  in.  and  a  journal  speed  of  814  ft.  per  mio. 
Mr.  Tower  found  the  coefficient  of  friction  to  be  .0016  with  an  oil-bath,  and 


LAWS  OF  FRICTION. 


935 


.0097,  or  slz  ttmefl  as  much,  with  a  pad.  The  w&j  low  ooefBdents  ob- 
tained by  Mr.  Tower  will  be  accounted  for  by  Law  2,  as  he  found  that  the 
frjctional  resistance  per  square  inch -under  varying  loads  is  nearly  constant, 
as  below: 

Ix>ad  in  lbs.  per  sq.  in 629     468     415     863     310     258     SOS     153    iOO 

FricUonal  resist,  per sq.  in.  .416    .514    .498    .472    .464    .438    .48      .458  .46 

The  ft-ictlonal  resistance  per  square  inch  is  tlie  product  of  the  coefBcient 
of  friction  into  the  load  per  square  inch  on  horisontal  sections  of  the  brass. 
Hence,  if  this  product  be  a  constanr.  the  one  factor  must  vary  inversely  as 
the  other,  or  a  high  load  will  give  a  low  coefBcient,  and  vice  versa. 

For  ordinary  lubrication,  the  coeflRcient  is  more  constant  under  varying 
loads:  the  frictional  resistance  then  varies  directly  as  the  load,  as  shown  by 
Mr.  Tower  in  Table  VIII  of  his  report  (Proc.  Inst.  M.  E.  1868). 

With  respect  to  Law  8,  A.  M.  WelliDgton  (Trans.  A.  S.  C.  E.  1884).  in  ex- 
periments oo  Journals  revolving  at  very  Tow  velocities,  found  that  the  friction 
was  then  very  great,  and  nearly  constant  under  varying  conditions  of  the 
labrication,  load,  and  temperature.  But  as  the  speed  increased  the  friction 
fell  slowly  and  regularly,  and  again  returned  to  the  original  amount  when 
the  velocity  was  reduced  to  the  same  rate.  This  is  shown  in  the  following 
table: 
Speed,  feet  per  minute: 

0+      2.16     3.83     4.86     8.82     21.42     86.87     58.01      80.28     106.08 
Coefficient  of  friction: 

.118      .094      .070      .069      .055       .047        .040        .085       .080        .026 

It  was  also  found  by  Prof.  Kimball  that  when  the  Journal  velocity  was  in- 
creased from  6  U)  110  ft.  per  minute,  the  friction  was  reduced  70jl\  in  another 
case  the  friction  was  reduced  67%  when  the  velocity  was  increased  from  1  to 
100  ft.  per  minute;  but  after  that  point  was  reached  the  coefficient  varied 
approximately  with  the  square  root  of  the  velocity. 

The  following  results  were  obtained  by  Mr.  Tower: 


Feet  per  minute. . . 

209 

262 

814 

866 

419 

471 

Nominal  Load 
per  sq.  in. 

Coeff.  of  friction.. 
ti         it 

.0010 
.0018 
.0014 

.0012 
.0014 
.0015 

.0013 
.0015 
.0017 

.0014 
.0017 
.0019 

.0015 
.0018 
.0021 

.0017 
.002 
.0024 

520  lbs. 
468  " 
415   " 

The  variation  of  friction  with  temperature  is  approximately  in  the  inverse 
ratio.  Law  4.    Take,  for  example,  Mr.  Tower's  results,  at  262  ft.  per  minute: 


Temp.  F. 

110« 

100<» 

w 

80* 

TOO 

60«» 

Ooserved 

Calculated.... 

.0044 
.00451 

.0061 
.00618 

.006 
.00608 

.0078 
.00788 

.0092 
.00964 

.0119 
.01262 

This  law  does  not  hold  good  for  pad  or  siphon  lubrication,  as  then  the  co- 
efficient of  friction  diminishes  more  rapidly  for  given  increments  of  tem- 
Kerature,  but  on  a  gradually  decreasing  scale,  until  the  normal  temperature 
as  been  reached;  this  normal  temperature  increases  directly  as  the  load 
per  sq  in.  This  is  shown  in  the  following  table  taken  from  Mr.  Stroudley*s 
experiments  with  a  pad  of  rape  oil : 


Temp.  F 

lOS^ 

110«»  j  115« 

120« 

126» 

130» 

135» 

140» 

1450 

Coefficient 

.022 

.0180,  .0160 
.OOiO'  .0020 

.0140 
0020 

.0125 
.0015 

.0115 

.ooiol 

.0110 
.0005 

.0106 
.0004 

.0102 

Decrease  of  coeff. . 

.0002 

In  the  Galton-We8tlnghou.se  experiments  it  was  found  that  with  velocities 
below  100  ft.  per  min.,  and  with  low  pressures,  the  frictional  resistance 
varied  directly  as  the  normal  pressure;  but  when  a  velocity  of  100  ft.  per 
min.  was  exceeded,  the  coefficient  of  friction  greatly  diminished;  from  the 
same  experiments  Prof.  Kennedy  found  that  the  coefficient  of  friction  for 
high  pressures  was  sensibly  less  than  for  low. 

Alloivable  Pressures  on  B«arlnff-siirfkces«  (Proc.  Inst.  M.  E., 
May,  1888.)— The  Committee  on  Friction  experimented  with  a  steel  ring  of 


W6  FRICTION  AND  LUBBICATION. 

notonffular  Motion.  proMod  between  two  cant-iron  diaki,  the  •mraUr  bear- 
inff-mirf»oa6  of  which  were  covered  with  jrun -metal,  and  were  19  in.  inside 
diameter  and  H  in.  ouu^ide.  The  two  disks  w«re  rotated  togethert  and  the 
steel  ring  was  prevented  from  rotating  bv  means  of  a  lever,  the  boldinip 
torce  of  which  was  raeasurea.  When  oiled  thr(^igh  grooves  cut  in  each  face 
of  the  ring  and  tested  at  from  50  to  130  revs,  per  min.,  it  was  found  that  a 
pressure  of  75  lbs.  per  sq.  in.  of  bearing-surface  was  as  much  as  it  would 
bear  safely  at  the  highest  speed  without  seising,  although  it  carried  90  lbs. 

ger  sq.  in.  at  the  lowest  speed.  The  ooeiUcient  of  friction  is  also  much 
igher  than  for  a  cylindrical  bearing,  and  Uie  friction  follows  the  law  of  the 
friction  of  solids  much  more  nearly  than  that  of  liquids.  Tliis  is  doubtleoa 
due  to  the  much  less  perfect  lubrication  applicable  to  this  form  of  bearing 
oompared  with  a  cylindrical  one.  The  ooemoient  of  f ricUon  appears  to  be 
about  the  same  with  the  same  load  at  all  speeds,  or,  in  other  words,  to  be 
independent  of  the  speed:  but  it  seems  to  diminish  somewhat  aa  the  load  is 
'ocreased,  and  may  oe  stated  approximately  as  1/UO  at  16  lbs.  per  aq.  In., 
diminishing  to  1/80  at  75  lbs.  per  sq.  in. 

The  high  coefncients  of  friction  are  explained  by  the  difficulty  of  lubricat- 
ing a  collar-bearing.  It  is  similar  to  the  slide- block  of  an  engine,  which  can 
caiTv  only  about  one  tenth  the  load  per  sq,  in,  that  can  be  oarried  by  the 
cranlc-pins. 

In  experiments  on  cylindrical  ioumals  it  has  been  shown  that  wheo  a 
cvltndrical  Journal  was  lubricated  from  the  side  on  which  the  pressure  bore, 
100  lbs.  per  sq.  in.  was  the  limit  of  pressure  that  It  would  carry;  but  when  it 
came  to  be  lubricated  on  the  lower  side  and  was  allowed  to  drsg  the  oil  in 
with  it,  600  lbs.  per  sq.  in.  was  reached  with  impunity:  and  if  the  GOO  lbs.  per 
sq.  in.,  which  was  reckoned  upon  the  full  diameter  oi  the  bearing,  came  to 
be  reckoned  on  the  sixth  part  of  the  circle  that  was  taking  the  groater  pro- 
portion of  the  load,  it  followed  that  the  pressure  upon  thai  part  of  the  circle 
amounted  to  about  ISOO  lbs.  per  sq.  in. 

In  connection  with  these  experiments  Mr.  Wieksteed  states  that  fn  drill- 
ing-machines the  pressure  on  the  collars  is  frequently  as  high  as  8M  lbs.  per 
sq.  in.,  but  the  speed  of  nibbing  in  this  case  is  lower  than  it  was  in  any  of 
the  experiments  of  the  Besearch  Committee,  In  machines  working  very 
slowly  and  intermittently,  as  in  testing-machines,  very  much  higher  pres* 
surea  are  admissible. 

Mr.  Adamson  mentions  the  case  of  a  heavy  upright  shaft  carried  upon  a 
._._..... ^ ^.    -    .^^^.Jq  J. ...    _ 


small  footstep- bearing,  where  a  weight  of  at  ]oo»t  80  tons  was  carried  on  a 
■haft  of  5  in.  diameter,  or,  say,  SO  sq.  in.  area,  giving  a  pressure  of  1  ton  per 
a.  in.  The  speed  was  190  to  *200  revs,  per  min.  It  was  neoessary  to  force  the 


sq.  In.  Tbe  speed  was  190  to  soo  revs,  per  mm.  it  was  neoessary  to  force  loe 
oil  under  the  bearing  by  means  of  a  bump.  For  heavy  horizontal  shafts, 
snch  as  a  fly-wheel  shaft,  carrying  100  tons  on  two  journals,  his  practice  for 
getting  oil  into  the  bearings  was  to  flatten  the  jouraal  along  one  side 
throughout  its  whole  length  to  the  extent  of  about  an  eighth  of  an  In^  in 
width  for  each  inch  in  diameter  up  to  8  in.  diameter;  above  that  siae  rather 
less  flat  in  proportion  to  the  diameter.  At  flrst  sight  it  appeared  alarming 
to  get  a  continuous  flat  place  coming  round  in  every  revolution  of  a  heavily 
loaded  shaft;  yet  it  carried  the  oil  effectually  into  the  bearing,  which  ran 
much  better  in  consequence  than  a  truly  cylindrical  journal  without  a  flat 
«ide. 

In  tbrust-oearings  on  torpedo-boats  Mr.  Thornycrof  t  allows  a  preasurs  of 
never  more  than  50  lbs.  per  sq.  in. 

Prof.  Thurston  (Friotion  and  I^ost  Work,  p.  940)  says  7000  to  8000  lbs. 
pressure  per  square  inch  is  reached  on  the  slow-working  and  raraly-moved 
pivots  of  swing  bridges. 

Mr.  Tower  says  (Proc.  Inst.  M.  E.,  Jan.  1884):  In  eocentrlc-pins  of  punch- 
ing and  shearing-machines  very  high  pressures  are  sometimes  used  without 
seising.    In  addition  to  tbe  alternation  in  the  direction,  tbe  pressure  is  ap- 

eied  for  only  a  very  short  space  of  time  in  these  machines,  so  that  the  oil 
IS  no  time  to  be  squeeaed  out. 

In  the  discussion  on  Mr.  Tower's  paper  (Proc.  Inst.  H.  E.  1885)  it  was 
stated  that  it  is  well  known  from  practical  experience  that  with  a  constant 
load  on  an  ordinary  journal  it  is  difficult  and  almost  impossible  to  have  more 
than  aOO  lbs.  per  square  inch,  otherwise  the  bearing  would  get  hot  and  the 
oil  go  out  of  ft;  but  wheo  the  motion  was  reciprocating,  so  that  the  load  was 
alternately  relieved  from  the  journal,  as  with  crank-pins  and  similar  jour* 
nals,  much  higher  loads  might  be  applied  than  even  700  or  800  lb0.  per  Bqnsre 


FRICTION   OF  CAR-JOURNAIi  BRASSES.  037. 

Mr.  Qoodmao  fProc.  iDst.  C.  B.  1886)  found  that  the  total  friotlooal  i^ 
sli^iooe  is  materially  reduced  by  diroluivhfiiK  the  width  of  the  braw. 

The  lubricatioD  i»  mont  efQcient  in  reducing  (he  friotion  when  the  braai 
BubcendR  an  auRle  of  from  1;!0»  to  60<>.  The  fflm  ia  probably  at  it«  best  be- 
tween the  angles  80"  and  i]0<'. 

In  the  oase  of  a  brass  of  a  raU«ray  azle-bearini;  where  an  oU-f{rooTe  ie  cut 
aloni;  its  crown  and  an  oll-bole  ia  dnUed  throiw^h  the  top  of  the  bra.**  into  it, 
the  wear  is  invariably  on  the  off  aide,  which  ia  probably  due  to  the  oil  eeoap- 
inK  as  soon  as  it  reaches  the  crown  of  the  braaa,  and  so  leavinK  the  oiBT  me 
almost  dry,  where  the  wear  cooaequently  enauee. 

In  railway  axles  the  braas  weo  m  always  on  the  forward  side.  The  same  ob- 
servation has  been  made  in  marine  engrine  journals,  whioh  alwi^s  wear  in 
exactly  the  reverse  way  to  what  they  mifirht  be  expected.  Mr.  Stroudlay 
thinks  this  peculiarity  is  due  to  a  fllm  of  lubi'ioant  belni;  drawn  in  flx>m  the  un- 
der side  of  the  journal  to  the  aft  part  of  the  brass,  which  effectually  lubri- 
cates and  prevents  wear  on  that  side;  and  that  when  the  lubricant  reaeb«B 
the  forward  side  of  the  braas  it  is  so  attenuated  down  to  a  wed4^  shape  that 
there  is  insufficient  lubrication,  and  greater  wear  oonseqiiently  follows. 

Prof.  J.  G.  Denton  (Am.  Mack.,  Oct.  80,  1800)  says:  Besarding  the  prea- 
sure  to  wnioh  oil  is  subjected  in  railroad  oar-9er?ioe,  it  is  probably  more  severe 
than  in  any  other  olaas  of  praotioe.  Oar  brasses,  when  used  bore,  are  ao  im- 
perfectly fitted  to  the  journal,  that  during  the  ear^  stagee  of  their  use  the 
area  of  bearing  may  be  but  about  one  square  inch.  In  this  caae  the  pressure 
per  square  inch  is  upwards  of  0000  lbs.  But  at  the  slowest  apeeds  of  freight 
servioe  the  wear  of  a  brass  is  so  rapid  that,  within  about  thirty  minutes  the 
area  ia  either  iocreased  to  about  three  inches,  and  is  thereby  able  to  reUere 


the  oil  so  that  the  latter  can  successfully  prevent  overiieating  of  the  journal, 
or  elaa  overheating  takes  place  with  any  oil,  a»id  measures  of  relief  must  be 
taken  which  eliminate  the  question  of  differeacea  of  luhrioating  power 


among  the  different  lubrioante  available.  A  braaa  which  has  been  run  about 
fifty  miles  under  isooo  lbs.  load  may  have  extended  the  area  of  beariog-aurfaoe 
to  about  three  square  inches.  The  pressure  is  then  about  1700  Iba.  per  aquare 
inch  It  may  be  assumed  that  this  is  an  average  minimum  area  for  career- 
vice  where  no  violent  and  unmanageable  overheating  has  occurred  during  the 
use  of  a  brass  for  a  abort  time.  This  area  will  wy  slowly  inoreaae  with  any 
lubricant. 

C.  J.  Field  iPowm-^  Feb.  1688)  says:  One  of  the  moat  vital  points  of  an  en- 
gine for  electrical  eer?ioe  is  that  of  main  bearings.  They  ahould  have  a  anr- 
faoe  Telocity  of  not  exceeding  a50  feet  per  minute,  with  a  mean  bearing- 
pressure  per  square  inch  of  projected  area  of  journal  of  not  more  than  H> 
Iha.  This  ia  considerably  within  (he  safe  limit  of  oool  performance  and  easy 
operation.  If  the  bearings  are  deaigned  in  this  way,  it  would  admit  the  uae 
of  greaae  on  all  the  main  wearing-surface,  which  in  a  large  type  of  engines 
for  this  claas  of  work  we  think  aUviaable. 

011«presflur6  In  «  Bearinc^— Hr.  Beauchamp  Tower  (Proe.  IniL 
M.  K  ,  Jan.  188&>  made  experiraenta  with  a  braaa  bearing  4  Inotaea  diameter 
by  6  inchea  long,  to  determine  the  pressure  of  the  oil  between  the  braaa  and 
the  journal.  The  bearing  was  half  immersed  in  oil,  and  had  a  total  load  of 
KJi)8  lbs.  upon  it.    The  journal  rotated  150  revolutions  per  minute.    The 

Sressure  of  the  oil  was  determined  by  drilling  small  boles  in  the  bearing  at 
ifforent  points  and  connecting  them  by  tubes  to  a  Bourdon  gauge.  It  was 
found  that  the  pressure  varied  from  310  to  0^  lbs.  per  square  inch,  the  great- 
est pressure  being  a  little  to  the  "  off  '*  side  of  the  centre  line  of  the  top  of 
the  oearing,  in  the  direction  of  motion  of  the  journal.  The  sum  of  the  up- 
ward force  exerted  by  these  pressures  for  the  whole  lubricated  area  was 
nearly  equal  to  the  total  pressure  on  the  bearing.  The  speed  was  reduced 
from  l.nO  to  tiO  revolutions,  but  the  oil-preasure  remained  the  same,  ahowing 
that  the  brass  waw  as  completely  oil-borne  at  the  lower  speed  as  at  the 
higher.  Toe  following  was  the  observed  friction  at  the  lower  speed: 
Nominal  load.  lbs.  per  square  inch ...  449  888  Sll  89 
Coemdent  of  friction 00182    .00168    .00^47    .0044 

The  nominal  load  per  square  inch  is  the  total  load  divided  by  the  product  of 
the  diameter  and  length  of  the  journal.  At  the  same  low  speed  of  ^  revo- 
liitiouH  ner  minute  it  was  increased  to  670  lbs.  per  square  Inch  without  any 
signs  or  heating  orReizing. 

Friction  of  Car-Jonrnnl  Braaaes.  (J.  E.  Denton,  Trans.  A.  8.  M. 
E  ,  acii.  405  >— A  new  brass  dressed  with  an  emery-wheel,  loaded  with  iSOOOlba., 
may  have  an  actual  bearing-surface  on  the  journal,  as  shown  by  the  polish 


.938  FRICTION  AND   LUBRICATION. 

of  a  portion  of  the  surface,  of  only  1  square  Inch.  With  this  preasure  of  SOOO 
IhB.  per  square  inch,  the  coefficient  of  friction  roay  be  G%,  ana  the  brass  may 
be  overheated,  scarred  and  cut  but,  on  the  contrary,  it  may  wear  down  evenly 
to  a  smooth  bearinsr.  Rivinfc  a  highly  polished  area  of  contact  of  8  square 
inches,  or  more,  inside  of  two  hours  of  running,  (gradually  decreasing  the 
pressure  per  square  inch  of  contact,  and  a  coefficient  of  friction  of  leas  than 
0.5^.  A  reciprocating  motion  in  the  direction  of  the  axis  is  of  importance 
in  reduciug  the  friction.  With  such  polished  surfaces  any  oil  will  lubricate, 
and  the  coefficient  of  friction  then  depends  on  the  viscosity  of  the  oil.  With 
H.  pressure  of  1000  lbs  per  square  inch,  revolutions  from  170  to8S0  per  minute, 
and  temperatures  of  76«  to  118°  F.  with  both  sperm  and  parraffine  oils,  a  co- 
efficient of  as  low  aaO.U%  has  been  obtained,  the  oil  being  fed  continuously 
by  a  pad. 

Experiments  on  Overbeatlns:  of  Bearinfl^n.— Hot  Roxes. 
(DentonJ— Tests  with  car  brasses  loaned  from  liOO  to  4600  lbs.  per  square 
inch  gave  7  cases  of  overheating  out  of  Si  trials.  The  tests  show  now  jmrely 
a  matter  of  chance  is  the  overheating,  as  a  brass  which  ran  hot  at  6000  lbs. 
load  on  one  day  would  run  cool  on  a  later  date  at  the  same  or  higher  pres- 
sure. The  explanation  of  this  apparently  arbitrary  difference  of  behavior  is 
that  the  accidental  variations  of  the  smoothness  of  the  surfaces,  almost  in- 
finitesimal in  their  magnitude,  cause  variations  of  friction  which  are  alwav^ 
tending  to  produce  overheating,  and  it  Is  solely  a  matter  of  chance  wbf>Q 
these  tendencies  'preponderate  over  the  lubricating  influence  of  the  oil. 
There  is  no  appreciable  advantage  shown  by  sperm-oil,  when  there  Is  do  ten- 
dency to  overheat— that  is,  parafflne  can  lubricate  under  the  highest  pres- 
sures which  occur,  as  well  as  sperm,  when  the  surfaces  are  within  the  condi- 
tions affording  the  minimum  coefficients  of  friction. 

Sperm  and  other  oils  of  high  heat-resisting  qualities,  Uke  vegetable  oil  and 
petroleum  cylinder  stocks,  only  differ  from  me  more  volatile  lubricants, 
uke  parafflne,  in  their  ability  to  reduce  the  chances  of  the  oontinuAl  acci- 
dental infinitesimal  abnudon  producing  overheating. 

The  effect  of  emery  or  other  gritty  substance  In  reducing  overheating  of  a 
bearing  is  thus  explained: 

The  effect  of  the  emery  upon  the  surfaces  of  the  bearings  ia  to  cover  the 
latter  with  a  series  of  parallel  grooves,  and  apparently  after  such  grooves 
are  made  the  presence  of  the  emery  does  not  practically  increase  the  friction 
over  the  amount  of  the  latter  when  pure  oil  only  is  between  tbe  surfaces. 
The  infinite  number  of  grooves  constitute  a  very  perfect  means  of  insuring 
a  uniform  oil  supply  at  every  point  of  the  bearings.  As  long  as  grooves  in 
^he  journal  match  with  those  in  the  brasses  the  friction  appears  to  amount 
to  only  about  \0%  to  Ibi  of  the  pressure.  But  if  a  smooth  journal  Is  placed 
between  a  set  of  brasses  which  are  grooved,  and  pressure  be  applied,  the 
journal  crushes  the  grooves  and  tiecomes  brazed  or  coated  with  braes,  and 
then  the  coefficient  of  friction  becomes  upward  of  40%.  If  then  emeiy  is 
applied,  the  friction  is  made  very  much  less  by  its  presence,  because  the 
grooves  are  made  to  match  each  other,  and  a  uniform  oil  supply  prevails  at 
every  point  of  the  bearings,  whereas  before  the  application  of  the  emery 
many  spots  of  the  latter  receive  no  oil  between  them. 

Moment  of  Friction  and  UTork  of  Frietlon  of  Slldliic* 
•nrHacea,  etc. 

Moment  of  Fric-  Energy  lost  by  Frictioo 
tlon,  inch-lbs.  in  ft.-lbs.  per  min. 

Flat  surfaces fWS 

Shafts  and  journals H/^<<  MIB/Wdn 

Flat  pivots HfWr  A746fWm 

Collar-bearing HfW^^l ""  **'!  .1745/Trn*'*' ~  *''' 

rj"  —  ri»  rj'  —  r,' 

Conical  pivot J^/TTrcoseca  .  1745/H>n  cosec  a 

Conical  journal %fWraeca  .l74bfWmeeca 

Truncated-cone  pivot HfW^-^^^-  .1745/tr''**  7  ''*' 

^•'       r,  sino  '       r,  sina 

Hemispherical  pivot fWr  .26\SfWr 

Tractrlx,    or  Schiele's   "  anti- 
friction "  pivot fW  .^IS^fTr. 


PITOT-BEABIKGS.  939 


In  the  above   /  :t:  coefficient  of  friction ; 

W  =  weieht  on  Journal  or  pivot  in  pounds; 
r  =  radius,  d  =  diameter,  in  inches; 
S  =  space  in  feet  throuf^h  which  sliding  takes  place; 
ri  =  outer  radius,    r*  =  inner  radius; 
n  =  Dumber  of  revolutions  per  minute; 
a  =  the  half-angle  of  the  coue,  i-e.,  the  angle  of  the  slope 
with  the  axis. 

To  obtain  the  horse-power,  divide  the  quantities  in  the  last  column  by 

33,000.    Horse-power  absorbed  by  friction  of  a  shaft  =  4^2^^. 

DSjOUoU 

The  formula  for  energy  lost  by  shafts  and  journals  is  approximately  true 
for  looiMsly  fitted  beariugs.  Prof.  Thurston  shows  that  the  correct  formula 
varies  accordiDg  tn  the  character  of  fit  of  the  bearing;  thus  for  loosely 
fitted  Journals,  if  CT  s  the  energy  lost, 

U  =  -^r^Wn  inch-pounds  =  :«?1^^  foot-lbs. 

For  perfectly  fitted  journals    X7  =  ^MfvrWn  Inch-lbs.  =  .3325/irdn,  ft.-Ibs. 

For  a  beariufr  in  which  the  journal  is  so  grasped  as  to  give  a  uniform 
pressure  throughoot,  U  =  fvh'Wn  inch-lbs.  =  A\\2fWdn,  ft.-lbs. 

Resistance  of  railway  trains  ana  wagons  due  to  friction  of  trains: 

Pull  on  draw-bar  = '' — — —  poands  per  gross  ton, 

In  which  2?  Is  the  ratio  of  the  radius  of  the  wheel  to  the  radius  of  Journal. 

A  cylindrical  Journal,  perfectly  fitted  into  a  bearing,  and  carrying  a  total 
load,  distributes  the  pressure  due  to  this  load  unequally  on  the  bearing,  the 
maximum  pressure  being  at  t)ie  extremity  of  the  vertical  radius,  while  at 
the  ^extremities  of  the  horizontal  diameter  the  pressure  is  zero.  At  any 
point  of  the  bearing-surface  at  the  extremity  of  a  radius  which  makes  an 
angle  9  with  the  vertical  radius  the  normal  pressure  is  proportional  to  cos  B. 
It  p  =  normal  pressure  on  a  unit  of  surface,  io  =  total  load  on  a  unit  of 
length  of  the  journal,  and  r  =  radius  of  journal, 

wco8«  =  1.67rp,    pz^l'L^^, 
'^      '^        l,57r 

PITOT-BEABINGS. 

Tlie  Selilele  Curve.— W.  H.  Harrison,  in  a  letter  to  the  Am.  Machin- 
ist^ 1801,  savs  the  Schieie  curve  is  not  as  good  a  form  for  a  bearing  as  the 
segment  of  a  sphere.  He  says:  A  millstone  weighing  a  ton  frequently 
bears  its  whole  weight  upon  the  fiat  end  of  a  hard-steel  pivot  lyL"  diameter, 
or  one  square  inch  area  of  bearing;  but  to  carry  a  weight  of  SOOO  lbs.  he 
advises  an  end  bearing  about  4  inches  diameter,  made  in  Uie  form  of  a  seg- 
ment of  a  sphere  about  ^  inch  in  height.  The  die  or  fixed  bearing  should 
be  dished  to  fit  the  pivot.  This  form  gives  a  chance  for  the  bearing  to 
atljust  itself,  which  It  does  not  have  when  made  fiat,  or  when  made  with  the 
ScFiiele  curve.  If  a  side  bearing  Is  necessary  it  can  be  arranged  farther  up 
the  shaft.  The  pivot  and  die  should  be  of  steel,  hardened;  cross-gutters 
should  be  in  the  die  to  allow  oil  to  flow,  and  a  central  oil-hole  should  be 
modd  in  the  shaft. 

The  advantage  claimed  for  the  Schlele  bearing  is  that  the  pressure  is  uni- 
formly distributed  over  its  surface,  and  that  it  therefore  wears  uniformly. 
Wilfred  Lewis  (/Im.  Mach.^  April  19,  1894)  says  that  its  merits  as  a  thrust- 
bearing  have  been  vastly  overestimated;  that  the  term  *•  anti-friction " 
applied  to  it  is  a  misnomer,  since  its  friction  Is  greater  than  that  of  a  flat 
step  or  collar  of  the  same  diameter.  He  advises  that  fiat  thrust-bearings 
should  always  be  annular  in  form,  having  an  inside  diameter  one  half  of 
the  external  diameter 

Friction  of  «  Flat  PlTot-bearlng:.  -The  Research  Ck)mmittee 
on  Friction  (Proc.  Inst.  M.  E.  1H91)  experimented  on  a  step-bearing,  flat- 
ended,  S  in.  diam..  the  oil  being  forced  into  the  bearing  through  a  nole  in 
Its  centre  and  distributed  through  two  radial  grooves,  insuring  thorough 
lubrication.    The  step  was  of  steel  and  the  hearing  of  manganese-bronze. 


940  FRICTION  AND  LUBRICATIOIT. 

At  revolutions  per  min 60  128  194  290         S53 

The  coefficient  of  fiiotionvuiedj         .OlSl       .005S       .0051       .0044      .00^^ 

between  >and.Oc&l       .Olia       .010^       .OKS      .0167 

Wiih  a  white-metal  bearing?  at  128  revolutions  the  coeffldfnt  of  friciion 
was  a  little  lar^rer  than  with  the  manj^anese-bronze.  At  the  hi};her  itpfeds 
the  coefficient  of  friction  was  less,  owing  to  the  more  perfect  lubrication,  as 
shown  by  the  more  rapid  circulation  of  the  oti.  At  1^  revolutiouK  tlie 
bronze  bearlni?  heated  and  seized  on  one  occasion  with  a  load  of  :ieO  pounds 
and  on  another  occasion  with  SCO  pounds  per  ttquare  inch.  The  white-metal 
beartng:  under  similar  conditions  heated  and  seized  with  a  load  of  2A0 
pounds  per  square  inch.  The  steel  footstep  on  manKanese-bronce  was  after- 
wards tried,  lubricating  with  three  and  with  four  radial  gi*oove9;  but  the 
friction  was  from  one  and  a  half  tiiues  to  twice  as  great  as  with  only  the  two 
grooves.    (8ee  also  Allowable  Pressures,  page  936.) 

HercarT-lMith  Pivot.— A  nearly  frictionless  step-bearing  may  be 
obtained  by  Hoaiing  the  bearing  with  its  superincumbent  weight  upon  mer- 
cury.  Such  an  apparatus  is  used  in  the  liglithouses  of  La  Heve,  Havre.  It 
is  thus  described  in  Eno'g^Julv  14,  1888,  p.  41: 

The  optioal  apparatus,  weighing  about  1  ton,  rests  on  a  circular  caat-iron 
table,  which  is  supported  by  a  vertical  shaft  of  wrought  iron  'i.'M  in. 
diameter. 

This  is  kept  in  position  at  the  top  by  a  bronze  ring  and  outer  iron  support, 
and  at  the  bottom  in  the  same  way,  while  it  rotates  on  a  removable  6te<^l 
pivot  resting  in  a  steel  socket,  which  Is  fitted  to  the  base  of  the  support.  '1  c 
the  vertical  shaft  there  is  rigidly  fixed  a  floating  cast-iron  ring  17.1  in.  rliam 
eter  and  11.8  in.  in  depth,  which  is  plunged  into  and  rotatea  in  a  mercury 
bath  contained  in  a  fixed  outer  drum  or  tank,  the  clearance  between  the 
vertical  surfaces  of  the  drum  and  ring  being  only  0.2  in.,  so  as  to  reduce  as 
much  as  pos^ble  the  volume  of  mercury  (about  220  lbs.),  while  Uie  horizou' 
tal  clearance  at  the  bottom  is  0.4  in. 

BALL-BBABINGS,  FRICTION  BOLLEB8,  KTC. 

A.  H.  Tyler  {Ena^g,  Oct.  20,  1896,  p.  48S),  after  experiments  and  com- 
parison with  experiments  of  others  arnves  at  the  following  conclusions: 

That  each  ball  must  have  two  points  of  contact  only. 

The  balls  and  race  must  be  of  glass  hardness,  and  of  abeolute  truth. 

The  tjalls  should  be  of  the  lai'gest  possible  diameter  which  the  space  at 
disposal  will  admit  of. 

Any  one  ball  should  be  capable  of  carrying  the  total  load  upon  the  beariiig. 

Two  rows  of  balls  are  always  sufficient. 

A  ball-bearing  requires  no  oil,  and  has  no  tendency  to  heat  unless  over- 
loaded. 

Until  the  crushing  strangth  of  the  balls  is  being  neared,  the  f  rictional  re- 


sistance Is  proportional  to  the  load. 
The  friciional  resistance  Is  ir 


Inversely  proportional  to  the  diameter  of  the 

balls,  but  in  what  exact  proportion  Mr.  Tyler  is  unable  to  say.  Probably  it 
varies  with  the  square. 

The  reslHiance  is  independent  of  the  number  of  balls  and  of  the  speed. 

No  rubbing  action  will  take  place  between  the  balls,  and  devices  to  guard 
against  it  ai-e  unnet'essary,  and  usually  iujurlous. 

The  above  will  show  tliat  the  ball-bearing  Is  most  suitable  for  high  speeds 
and  light  loads.  On  the  spindles  of  wood-carving  machines  some  make  a& 
much  as  80.000  revolutions  per  minute.  They  run  perfectly  cool,  and  never 
have  any  oil  upon  ihem.  For  heavy  loads  the  balls  ahould  not  he  less  than 
two  thirds  the  diameter  of  the  shaft,  and  are  better  if  made  equal  to  it. 

Ball-bearliicrii  hare  not  been  found  satisfactory  for  thrust -blocks,  for 
the  reason  Hp|>ai-eiitly  that  the  tables  crowd  together.  Better  results  have 
been  ohiaineii  from  coned  ix>llers.  A  combined  system  of  rollers  and  ballii 
is  d«HMl»>ed  in  En<j\y,  Oct.  6.  1893,  p.  429. 

Friotlon-rollem.  —If  a  Journal  instead  of  revolving  on  ordinary 
bearings  >>e  supported  on  friction-rollers  the  force  required  to  make  the  jour- 
unl  revolve  will  be  reduced  in  nearly  the  same  proportion  that  the  diameter 
of  the  axles  of  the  rollers  is  less  than  the  diameter  of  the  rollers  tlieinselve;:. 
In  exi>eriments  by  A.  M.  Wellinirton  with  a  Journal  S^  in.  dlam.  supported 
on  rollers  8  In.  diam.,  whose  axles  wei-e  1%  in.  dlam.,  the  friction  in  starting 
from  rest  was  H  ^^^  friction  of  an  ordinary  83^ in.  bearing,  but  at  a  car 
speed  of  10  miles  per  hour  It  was  J4  that  of  the  ordinary  bearing.  The  ratio 
of  the  dlam.  of  the  axle  to  diam.  of  roller  was  1^^:  6,  or  as  1  to  4.6. 


FBICTION   OF  STEAM- ENGINES.  941 

BeaHncs  for  Very  Hlffb  RotaitTe  Speeds.  (Proc.  Inst.  M.  E., 
Oct.  IMHH.  p.  43V.)— In  the  Parsons  steam-turbine,  which  has  a  speed  of  as 
hifCb  as  18,000  iev.  per  niin.,  as  it  is  impossible  to  secure  absolute  accuracy 
of  balance,  tlie  bearinsrs  are  of  special  construction  so  as  to  ailow  of  a  certain 
very  srnall  amount  of  lateral  freedom.  For  this  purpose  the  bearing  is  sur- 
rouodel  by  two  sets  of  steel  washers  1/16  inch  thicic  and  of  different  diam- 
eters, the  larger  fitting  close  in  the  casing  and  about  1/82  Inch  clear  of  the 
l)earing.  and  the  smaller  fitting  close  on  the  bearing  and  about  l/&*a  inch 
clear  of  the  casing.  These  are  arranged  alternately,  and  are  pressed 
together  by  a  spiral  spring.  Consequentiy  any  lateral  movement  of  the 
liearing  causes  Uiem  to  slide  mutually  against  one  another,  and  by  their 
friction  to  checlc  or  damp  any  vibrations  that  may  be  bet  up  in  the  spindle. 
The  tendency  of  the  spindle  is  then  to  rotate  about  its  axis  of  mass,  or  prin- 
cipal axis  as  it  is  called;  and  the  bearings  are  thereby  relieved  from  exces- 
sive pressure,  and  tho  machine  from  undue  vibration.  The  finding  of  the 
centre  of  gyration,  or  rather  allowing  the  turbine  itself  to  find  its  own 
centre  of  gyration,  is  a  well-known  device  in  oti»er  branches  of  mechanics: 
CM  In  the  instance  of  the  centrifugal  hydro^xtracior,  whei«  a  mass  very 
much  out  of  balance  is  allowed  to  find  its  own  centre  of  gvration;  the  faster 
it  ran  tlie  more  steadily  did  it  revolve  and  the  less  was  the  vibration.  An* 
other  Ulustraiiuji  is  to  be  found  in  the  spindles  of  spinning  machinery, 
which  run  at  about  10,000  or  11.000  revolutions  per  minute:  they  are  made 
of  hardened  and  tempered  steel,  and  although  of  very  small  dimensions,  the 
outside  diameter  of  tee  largest  portion  or  driving  whorl  being  periiaps  not 
more  than  1)4  in.,  it  is  found  impracticable  to  run  them  at  that  speed  in 
what  might  oe  called  a  hard-and-fast  bearing.  Thev  are  therefore  run  with 
Home  elastic  substance  surrounding  the  bearing,  such  as  steel  springs,  hemp, 
or  cork.  Any  elastic  substance  is  sufficient  to  absorb  the  vibration,  and 
permit  of  absolutely  steady  running. 

FHICTION  OF  STBAH-BNGINBS. 

Distribution  of  the  Frtetlon  or  Knstnes,— Prof .  Thurston  In 
{lis  "  Fiiclion  and  Lost  Work/' gives  the  following: 

12  8 

Mainbearings 47.0            j».4  ».'o 

Pistonandrod 2S.9             S5.0  81.0 

Crank^pin 6.8               5.1)  .«  n 

Cross-head  and  wrist-pin 6,4              4.1  f  "•" 

Valveandrod 2.6             86.4t  «« n 

Eccentric  strap 6.8              4.0)  '"•" 

Link  and  eccentric 9.01 

100.0  ioO.O  100.0 

No.  1,  Straight-line, «"  X  1«",  balanced  valve;  No. «,  Stralght-llne.  6"  X  «", 
unbalanced  valve;  No.  3,  7"  x  10",  tensing  traction  locomotive  valve-gear. 

Prof.  Thurston's  tests  on  a  number  of  different  styles  of  engines  indicate 
ihat  the  friction  of  any  engine  is  practically  constant  under  all  loads. 
Crrans.  A.  8.  M.  B.,  viii.  §6;  iz.  74.) 

In  a  Siraight-line  engine,  8"  x  14",  I.H.P.  from  7.41  to  57.54,  the  friction  H. 
P.  varied  irreguiariy  between  1.97  and  4.02,  the  variation  being  independent 
of  the  load.  With  60  H. P.  on  the  brake  the  I.H.P.  was  only  516,  the  friction 
being  only  8.6  H.P.,  or  about  6%. 

In  a  compound  condensing-engine,  tested  from  0  to  lOd.6  brake  H.P.,  gave 
I.H.P.  from  14.98  to  117.8  H.P.,  the  friction  H.P.  varying  only  from  14.9:2  to 
17.48.    At  tlie  maximum  load  the  friction  was  15.2  H.P.,  or  18. 9<. 

The  friction  increases  with  increase  of  the  boiler-presstire  ri<om  90  to  70 
lbs.,  and  then  becomes  constant.  The  friction  generally  iucreases  with  in- 
creane  of  speed,  but  there  are  exceptions  to  this  rule. 

Prof.  Denton  (Hteveiis  Indicator,  July,  1890),  comparing  the  calculated 
friction  of  a  number  of  engines  with  the  friction  as  determined  by  measure- 
meui,  finds  that  in  one  case,  a  75-ton  ammonia  ice-mnchine,  the  friction  of 
the  compressor,  17^  H.P.,  is  accounted  for  by  a  coefficient  of  friction  of  7V0 
on  all  the  external  tiearings,  allowing  6<(  of  the  entire  friction  of  the  machine 
for  the  frictioo  of  pistons,  stufttng-boxes.  and  Talves.  In  the  case  of  the 
Pawtucket  pumplng-engine,  estimatrngthe  friction  of  the  external  bearings 
with  a  coefncient  of  friction  of  6^  and  that  of  the  pistons,  valves,  and  stuff- 
ing-boses  as  in  the  case  of  the  ice-machine,  we  have  the  total  friction 
ilisiribated  as  follows  i 


942  FKICTION  AND  LUBUICATIOK. 

Horse-  Per  cent 

power,  of  Whole. 

Crank-plnn  and  effect  of  piston-thrust  on  main  shaft . .    0.71  1 1 .4 

Weight  of  fly- wheel  and  main  shaft 1.95  82.4 

Steam-valvea 0.28  3.7 

Eccentric 0.07  1.9 

Pistons 0.4«  7.2 

Stuffing-boxes,  six  altogether  0.72  11.3 

Air-pump 2.10  82.8 

Total  friction  of  engine  with  load . .  .* 6.21         100.0 

Total  friction  per  cent  of  indicated  power  . . .    4.27 

The  friction  of  this  engine,  though  very  low  in  proportion  to  the  Indicated 
power,  is  satisfactorily  accounted  for  by  Morin^s  law  used  with  a  coffflcient 
of  friction  of  b%.  In  both  cases  the  main  items  of  friction  are  those  due  to 
the  weight  of  the  fly-wheel  and  main  shaft  and  to  the  piston- thrust  od 
crank-pins  and  main-shaft  bearings.  In  the  Ice-machine  the  latter  Items 
are  the  larger  owing  to  the  extra  crank -pin  to  work  the  pumpe,  tihil» 
in  the  Pawtucket  engine  the  former  preponderates,  as  the  crank-thrusts  are 
partly  absorbed  by  tne  pump-pistons,  and  only  the  surplus  effect  acts  on 
the  crank -shaft. 

Prof.  Denton  describes  in  Trans.  A.  8.  M.  E.,  x.  892,  an  apparatus  hy 
which  he  measured  the  friction  of  a  piston  packing- ring.  When  the  p«rts 
of  the  piston  were  thoroughly  devoid  of  lubricant,  the  coeiBcient  of  friction 
was  found  to  be  about  7^0;  with  an  oil-feed  of  one  drop  in  two  miiiut4-K  thr 
coefficient  was  about  9/%;  with  one  drop  per  minute  it  was  about  9%.  Tlif>*» 
rates  of  feed  gave  unsatisfactory  lubrication,  the  piston  groaning  at  ih>> 
ends  of  the  stroke  when  run  slowly,  and  the  flow  of  oil  left  upon  the  surfartrs 
was  found  by  analysis  to  contain  about  SOjC  of  iron.  A  feed  of  two  drops  \^r 
minute  reduced  the  coefficient  of  friction  to  about  1^,  and  gave  practicallr 
perfect  lubrication,  the  oil  retaining  its  natural  color  and  purity. 

Ii17BBI€ATION. 

raeaanrement  of  the  DnraMIlty  of  Liibrlcaiits,  cJ.  E.  Th-n 
ton.  Trans.  A.  S.  M.  E.,  xi.  1013.)— Practical  differences  of  diiraitiliiy  of  lubri- 
cants depend  not  on  any  differences  of  inherent  ability  to  resist  being  "  worn 
out**  by  rubbing,  but  upon  the  rate  at  which  they  flow  through  and  away 
from  the  beariiig«surfaces.  The  conditions  which  control  thfe  flow  are  so 
delicate  in  their  influence  that  all  attempts  thus  far  made  to  measure  dura- 
bility of  lubricants  may  be  said  to  have  failed  to  make  distinctionR  of  lubri- 
cating value  having  any  practical  significance.  In  some  kinds  of  service  the 
limit  to  the  consumption  of  oil  depends  upon  the  extent  ro  which  dust  or  oi  Iter 
refuse  becomes  mixed  with  it.  as  in  railroad-car  lubrication  and  in  tlie  ca.M' 
of  agricultural  machinery.  The  economy  of  one  oil  over  another,  ao  far  m 
the  quality  used  is  concerned— that  is.  so  far  as  durabilltv  is  concerned  — i!< 
slmpiv  proportional  to  the  rate  at  which  it  can  insinuate  itself  into  and  flow 
out  or  minute  orifices  or  cracks.  Oils  will  differ  in  their  ability  to  do  this 
first,  in  proportion  to  their  viscosity,  and,  second,  in  proportion  to  the  ca- 
pillary properties  which  they  may  possess  by  virtue  of  the  pariicuUtr  Ingre- 
dients used  in  their  composition,  where  the  thickness  of  film  between  rub* 
bing-surfaces  must  be  ao  great  that  Iars:e  amounts  of  oil  pasa  through 
l>eai-ing8  in  a  given  time,  and  the  surroundings  are  such  as  to  permit  oil  ro 
be  fed  at  high  temperatures  or  applied  by  a  method  not  requiring  a  perferf 
fluidity,  it  is  probable  that  the  least  amount  of  oil  will  be  used  when  the  ris* 
coaity  Is  as  great  as  in  the  petroleum  cylinder  stocks.  When,  however,  the 
oil  must  flow  freely  at  ordinary  temperatures  and  the  feed  of  oil  v 
restricted,  aa  in  the  caae  of  crank-pin  bearings,  it  is  not  practicable  to  f«-ed 
such  heavy  oila  in  a  satisfactory  maimer.  Oils  of  less  viscoelty  or  of  • 
fluidity  approxi mating  to  larrl-oil  nuist  then  be  used. 

RelaUFe  Value  of  Ijnbrlcants.  (J.  E. Denton.  Am.Mach.^  Oct  SS, 
1890.)— Tlie  three  elements  which  deterniiue  the  value  of  a  lubricant  are  ibe 
cost  due  to  conaumptioi)  of  lubricants,  the  cost  spent  for  coal  to  overcome 
the  f fictional  resistance  caused  by  use  of  the  lubricant,  and  the  coat  due  to 
the  metallic  wear  on  the  Journal  and  the  brasses.  In  cotton-milia  the  ofA 
of  the  power  is  alone  to  be  considei-ed ;  in  rolling-mills  and  marine  enKimfli 
the  coat  of  the  quantity  of  lubricant  used  is  the  only  important  factor:  hut 
In  railroads  not  only  do  both  these  elements  enter  the  problem  aa  tangiiils 


LUBRICATION.  943 

factors,  but  the  cofit  of  the  wearing  away  of  the  metallic  parts  enters  in  ad- 
dition, and  furth(*niii>re,  the  latter  w  the  greateRt  element  of  cost  in  thee 


The  anallflcatlona  of  a  Good  liUbrlcant,  an  laid  down  by 
W.  H.  Bailey,  in  Proc  Inst.  C.  £.,  vol.  xlv.,  p.  37)!,  are:  1.  SufQcient  body 
to  keep  the  Kiirfaces  free  from  contact  under  maximum  prestsure.    i.  The 

{;reat«st  possible  fluidity  consistent  with  the  foregoiiiE  condition.  3.  The 
uwest  possible  coefficient  of  friction,  which  in  t>ath lubrication  would  be  for 
tliiid  friction  approximately.  4.  The  greatest  capacity  for  storing  and 
carrying  away  neat.  6.  A  high  temperature  of  decomposition.  6.  Power 
to  resist  oxidation  or  the  action  of  tlie  atmosphere.  7.  Freedom  from  cor- 
rosive action  on  the  metals  upon  which  used. 

Best  I«abrie«ntii  for  DUTerent  Purposes.    (Thurston.) 

Low  temperatures,  as  In  rock-drills  j  j  ,^v^^  «i«4k..«i  i„K.4n.»in<.  ^n. 
driven  by  compressed  air:  }  ^^^^^  mineral  lubricaUng-oila. 

Very  great  pressures,  slow  speed. .   ]  ^^5fS,£**P*'°"*'  *"^  ""^^^  "^"** 

Heavy  pressures,  with  slow  speed. . .  ]  "^^j.^^' *°^  **"*•  **"°^»  ^^^  ^^**^' 

Heavy  prassures  and  high  speed . . . .  {  ^^^^jj^  castor-oll,  and  heavy  min- 

Light  pressures  and  high  speed \  ^^^.'^^^^f  petroleum,  olive,  rape. 

rk...i{n«>..«r  «^^^M».^^  J  Lard-oil,  tallow-oil,  heavy  mineral  oils. 

Onlinary  machinery ]     and  the  heavier  vegelible  oils. 

Steam -cylinders Heavy  mineral  oils,  lard,  tallow. 

watches  and  other  delicate  m~lut- j  CXfaSSTISf.r.SiL'eSr'Xl'a 
•  (    oils. 

For  mixture  with  mineral  oils,  sperm  is  best;  lard  is  much  used;  olive  and 
cotton -seed  are  srond. 

Amoant  of  OH  needed  to  Ron  an  Enfl^lne*— The  Vacuum  Oil 
Co.  in  IfU^,  in  response  to  an  inquiry  as  to  cost  of  oil  to  run  a  lOOOH.P. 
Corliss  engine,  wrote:  The  cost  of  running  two  engines  of  equal  size  of  the 
same  make  Is  not  alwavs  the  same.  Therefore  while  we  could  furnish 
flguree  showing  what  it  is  costing  some  of  our  customers  having  Corliw 
engines  of  1000  H.P.,  we  could  only  give  a  general  Idea,  which  in  itself 
might  be  considerably  out  of  the  way  as  to  the  protuible  cost  of  cylinder- 
and  engine-oils  per  year  for  a  particular  engine.  Such  an  engine  ought  to 
run  readily  on  less  than  8  drops  of  600  W  oil  per  minute.  If  8000  drops  are 
figured  to  the  quart,  and  8  drops  used  per  minute,  it  would  take  about 
two  and  one  half  barrels  (52.$  gallons)  of  (XX)  W  cylinder-oil,  at  (J5  cents  per 
gallon,  or  about  $66  for  cylinder-oil  per  year,  running  6  days  a  week  and  10 
hours  a  day.  Engine -oil  would  be  even  more  difflcnlt  to  guess  at  what  the 
cost  would  be,  because  it  would  depend  upon  the  number  of  cups  required 
on  the  engine,  which  varies  somewhat  according  to  the  style  of  the  engine. 
It  would  doubtless  be  safe,  however,  to  calculate  at  the  outside  that  not 
more  than  twice  as  much  engine-oil  would  be  required  as  of  cylinder-oil. 

The  Vacuum  Oil  Co.  in  1892  published  the  following  results  of  practice 
with  "  600  W  "  cylinder-oil: 

n^-i:^fl  A»n««^«in^  o«i<*{n<>  J  20  and  83  x  48;  83  revs,  per  mln.;  1  drop  of  oil 
Corliss  compound  engine,^     per  min.  to  1  drop  in  two  mlnut^.       ^ 

"       triple  exp.      "         20,  83,  and  46  X  48;  1  drop  every  2  minutes. 
D^  .„_  » ,,-„  44       j  20  and  36  X  86:  143  revs,  per  mln. ;  2  drops  of  oil 

rorter-Aiien  -j     p^^.  |^,„    educed  afterwards  to  1  drop  per  mln. 

P  ,,  It       j  16  X  25  X  16;  240  revs,  per  min.;  1  drop  every  4 

"**"  "J     minutes. 

Results  of  tests  on  ocean-steamers  communicated  to  the  author  by  Prof. 
Denton  in  1892  gave:  for  1200-H.P.  marine  engine.  5  to  6  English  gallons  (6  to 
7.2  U.  8.  gals.)  of  engine-oil  per  24  hours  for  external  lubrication;  and  for  a 
1500-H.P.  marine  engine,  triple  expansion,  running  75  revs,  per  min.,  6  to  7 
English  gals,  per  24  nours.  The  cylinder-cil  consumption  is  exceedingly 
variable,— from  1  to  4  K&\a.  per  day  on  different  engines,  including  cylinder- 
oil  used  to  swab  the  piston-rods. 

4|aantlty  of  Oil  used  on  a  liocomotlve  Crank -pin  .—Prof. 
Denton,  Trans.  A.  8.  M.  K.,  xi.  1020,  says:  A  very  economical  case  of  practical 
oil-consumption  ia  when  a  locomotive  main  crank-pin  consumes  about  six 


944  FRICTION  AlffD  LUBRICATION", 

cubic  inches  of  oil  In  a  thousand  miles  of  Mrvlee.  This  is  equivalent  to  a 
consumption  of  one  milli;?ram  to  seventy  !>quare  inches  of  surface  rubbed 
over. 

rrhe  Examl nation  of  IiiibrleatlnK*olls.  (Prof.  Thos.  B.  Still- 
man,  steveut  Indicator,  July,  iHOOj^Tlie  generally  accepted  conditions  of 
a  good  lubricant  are  as  follows: 

1.  "  Body  **  enouirh  to  prevent  the  surf  aces,  to  which  it  is  applied,  from 
coming  in  contact  with  each  other.    (ViRcoRity.) 

9.  Freedom  from  corrosive  acid,  either  of  mineral  or  animal  origin, 

8.  As  fluid  as  poswible  consistent  with  **  body." 

4.  A  minimum  coefficient  of  friction. 

5.  High  "flash'*  and  burning  points. 

6.  Freedom  from  all  materials  liable  to  produce  oxidation  or  '*  gumming." 
The  examinations  t^  be  made  to  verify  Uie  above  are  both  cbemicai  and 

mechanical,  and  are  usually  arranged  in  the  following  order ; 

1.  Identification  of  the  oil,  whether  a  simple  mineral  oil.  or  animal  oil,  or 
a  mixture.  8.  Density.  3.  Viscosity.  4.  Flash -point  6.  Burning -point. 
6.  Acidity.    7.  Coefficient  of  friction.    8.  Cold  test. 

Detailed  directions  for  making  all  of  the  above  taste  are  given  In  Prof. 
Stillman'fi  article. 

'Weitgiktu  of  Oil  per  Gallon*— The  following  are  approximately  the 
weights  per  gallon  of  different  kinds  of  oil  cPenn.  R.  R.  Specifications): 

Lard-olI,  tallow-oil,  neat's- foot  oil,  bone -oil,  colsa -oil,  mustard-seed  oil. 
rape-seed  oil,  parafflne-oll,  500*  flre-test  oil,  engine-oil,  and  cylinder  lubricant, 
7H  pounds  per  gallon. 

Well-oil  and  passenger-car  oil,  7.4  pounds  per  gallon;  navy  gperm-oll,  7. '4 
pounds  per  gallon;  signal-oil.  7.1  pounds  oer  gallon;  800»  burning -oil,  6.9 
pounds  p«r  gallon:  and  ISiO'  bnming-oil,  6.6  pounds  per  gallon. 

Penna.  R.  R,  Speclfleatlon*  for  Petroleam  Prodncta. 
189 5 •■—Five  different  grades  of  petroleum  products  will  be  used. 

The  materials  detiired  under  this  specification  are  the  products  of  the 
distillation  and  refining  of  petroleum  unmixed  with  any  other  sub* 
stances. 

1Q0«  Fire-test  0«7.-~This  grade  of  oil  will  not  be  accepted  If  sample  (1)  la 
not  "  water-white  *'  in  color:  (2)  flashes  below  130**  Falirenheit;  (6)  bums 
below  If)  1<*  Fahrenheit;  (4)  is  cloudy  or  sbipment  lias  cloudy  barrels  when 
reoeived,  from  the  pres<^nce  of  kIus  or  suspended  matter;  (5)  beoomea 
opaque  or  shows  cloud  wheu  the  sample  has  been  10  minutea  at  a  tempera* 
ture  of  0«  Fahrenheit. 

900"  Fire^leMt  Oil.^Thi*  grade  of  oil  will  not  be  accepted  if  sample  (i)  is 
not  **  water- white '*  in  color;  (9)  flashes  below  U9^  Fahrenheit;  (8)  burns 
below  ^8'  Fahrenheit;  (4)  is  oluudy  or  shipment  has  cloudy  barrels  when 
received,  from  the  presence  of  glue  or  suspended  matter;  (.'>)  becomee 
opaque  or  shows  cloud  when  the  sample  has  been  10  miautoa  at  a  tampera* 
ture  of  &2*>  Fahrenheit;  (6)  shows  pi-ecipitatlon  when  some  of  the  sample  i« 
heated  to  450«  F.  The  precipitation  test  is  made  by  having  about  two  floid 
ounces  of  tlie  oil  in  a  six-ounce  beaker,  with  a  thermometer  suspended  in 
the  oil,  and  then  heating  slowly  until  the  thermometer  shows  the  required 
temperature.  .  The  oil  changes  color,  but  must  show  no  precipitation. 

Purnj^ne  and  Jieutrai  0<w.— These  grades  of  oil  will  not  be  accepted  if 
the  sample  from  shipment  (1)  is  so  dark  in  color  that  printing  with  long, 
primer  type  cannot  be  read  with  ordinaiy  daylight  through  a  layer  of  the 
oil  %  inch  thick;  (2)  flashes  below  il^«  F.;  (3)  has  a  gravity  atOO"  F.,  below  24«» 
or  above  35"*  Baum^;  (4)  from  October  ut  to  May  1st  ha»  acold  test  above 
10®  F.,  au'l  from  May  Jst  to  October  iKt  has  a  cold  test  above  8i"  F. 

The  color  toht  is  made  by  having  a  layer  of  the  oil  of  the  prescribed  thick- 
nerts  in  a  proper  glnss  vessel,  and  then  putting  tbeprintiug  on  one  side  of  the 
▼easel  and  rending  it  through  the  layer  of  oilwith  the  back  of  the  obserrer 
towaril  the  sourco  of  linht. 

Well  Oi/.'-This  grade  of  oil  will  not  be  accepted  if  the  sample  from 
shipment  (1)  flaiihes,  from  May  1st  to  October  1st,  below  «IW»  F.,  or, 
from  Oitober  1st  to  May  1st.  below  JWd"  F.:  (2)  has  a  gravity  at  80*  F., 
below  )i)i»  or  above  31**  B«um6:  (8)  fi*om  October  1st  to  May  1st  has 
a  cold  test  above  lO^  F.,  and  from  May  1st  to  October  lat  has 
a  cold  test  above  S^o  F.;  (4)  shonrs  any  precipitation  when  5  cubic 
centimetres  are  raized  with  95  c.  o.  of  gasoline.  The  precipitation  test 
is  lo  exclude  tarry  and  suspended  matter.  It  is  made  by  putting  Oft  o.o.  of 
89*  B  gasoUiie,  which  must  not  be  above  60"  F.  iu  temperature,  into  a  100  c.  o. 


SOLID   LUBRlOAKrS.  948 

graduate,  then  ailJine  the  prescribed  amount  of  oil  and  shaking  tlioroufirhly. 
Allow  to  stand  len  minutes.  With  satisfactory  oil  no  separated  or  pi'eclp> 
itated  material  can  be  seen. 

50(y*  Fire-test  0(7.— Thid  l^Tftde  Of  Oil  Will  nOt  1M  Accepted  if  sample  from 
shipment  (1)  flashes  below.  494"  F.;  {•!)  shows  precipiiation  with  gasoline 
when  tested  as  described  for  well  oil. 

Printed  directions  for  deterininine  flashing  and  burning  tests  and  for 
making  cold  tests  and  taking  gr&mv  are  furnished  by  the  railroad  com- 
pany.   The  speciflcations  of  1889  contamed  the  following: 

150*  I*ire'teat  Oil.— The  flashing  and  burnlns  points  ai'e  determined  by 
heating  the  oil  in  nn  open  \es8el,  not  less  than  12*  per  minute,  and  applyinif 
Iho  test -flame  ev(>hy  7*.  iHJginning  at  123'»  Fahrenheit.  The  cold  lest  may  be 
conveniently  made  by  luivingnn  ounce  of  the  oil,  in  a  four-ounce  sample 
bottle,  with  a  thermometer  sui^peuded  in  the  oil,  and  exposing  tliis  to  a 
freezing  mixture  of  ice  and  salt.  It  Is  advisable  to  stir  with  the  thermome- 
ter while  the  oil  is  cooling.  The  oil  must  remain  transparent  in  the  freesiug 
ntltiui'e  ten  minutes  after  it  has  cooled  to  zero. 

300*'  Fire-te»i  OW.— The  flashing  and  burning  points  are  determined  the 
same  Alt  for  i.'U)*  flre-test  oil,  except  that  the  oil  is  hvated  ]&*>  per  minute, 
test- flame  being  applied  first  at  'iAi!^  Fahrenheit.  The  cold  test  is  made  the 
sama  as  above,  except  that  ice  and  water  are  used. 

Pav(tJJHM~oil.—*l\\%  flashing-point  is  determined  same  as  for  800°  flrc>test 
oil.  The  cold  test  Is  determined  as  follows:  A  couple  of  ounces  of  oil  is  put  In 
a  four-ounce  sample  bottle,  and  a  thermometer  placed  in  it.  The  oil  is  then 
frozen,  a  freezing  mixture  of  ice  and  salt  being  used  if  necessary.  When  ih« 
oil  has  become  hard,  the  bottle  is  removed  from  the  freezing  mixture  and  the 
frozen  oil  allowed  to  soften,  being  stirred  and  thoroughly  mixed  at  the  same 
time  by  nieans  of  the  thermometer,  until  the  mass  will  run  from  one  end  of 
the  bottid  to  the  other.  The  reading  of  the  thermometer  when  this  is  the 
ca!<e  i»  regarded  as  the  cold  test  of  the  oil. 

WAl  Oll.^ToT  summer  oil  the  flashing-point,  Is  determined  the  fti\me  as  for 
parafllne^oil;  and  for  winter  oil  the  same,  except  that  the  test-flame  U  ap- 
plied first  at  103*  Fahrenheit.  The  cold  test  Is  made  the  same  as  fOr  par- 
afiSne-oil. 

500*  fire  teat  Oil.— tn  the  flashing-test  the  flame  is  first  applied  at  438*  P. 

SOIilD   LUBBIGANTS. 

Grapblte  in  a  condition  of  powder  and  used  as  a  aolid  lubricant^  so 
called,  to  distinguish  it  from  a  liquid  lubricant,  has  bean  found  to  do  well 
where  the  latter  has  failed. 

Renuie,  In  16M,  says :  *'  Graphite  lessened  frictioh  in  all  cases  where  it 
was  used."  General  Morln.  at  a  later  date,  concluded  from  experiments 
that  it  could  be  used  with  advantage  under  heavy  pressures;  and  Prof. 
Ttiurston  found  it  well  adapted  for  use  under  both  light  and  heavy  prefwures 
when  mixed  with  certain  oils.  It  is  especially  valuable  to  prevent  abrasion 
and  cutting  under  heavy  loads  and  at  low  velocities. 

8o«patoii6«  also  called  taks  and  steatite,  in  the  form  of  powder  and 
mixed  with  oil  or  fat,  is  sometimes  used  as  a  lubricant.  Graphite  or  soap- 
stone,  mixsd  with  soap,  is  used  on  aurfaoos  of  wood  working  against  either 
Iron  or  wood. 

Flbre-irrapbtte«-^A  new  self-lubiicating  bearing  known  as  flbre- 
grapnice  is  ilescribed  by  John  H.  Cooper  in  Trans.  A.  8.  M.  K.,  xiii.  374,  ns 
the  Invention  of  P.  H.  Holmes,  of  Gardiner,  Me.  This  bearing  material  is 
composed  of  selected  natural  graphite,  which  has  been  finely  divided  and 
fre«d  from  foreign  and  gritCy  matter,  to  which  is  added  wood-fibre  or  other 
growth  mixed  in  water  in  various  proportions,  according  to  the  purpose  to 
be  served,  and  then  solidifled  by  pressure  in  specially  prepared  moulds  ; 
after  removal  from  which  the  bearings  are  first  thoroughly  dried,  then  satu- 
rated with  a  drying  oil.  and  fiually  subjected  to  a  current  of  hot,  dry  air  fur 
the  purpose  of  ozidising  t^e  oil.  and  hardening  the  mass.  When  flnishfd, 
they  may  be  "  machined  ^'  to  size  or  shape  with  the  same  CaoUity  and  means 
emnloyed  on  metals.     (Holmes  Fibre^Uraphite  Mfg.  Co.,  Philadelphia.) 

n^tallne  is  a  solid  oompound,  usually  oontaining  graphite,  made  In  the 
form  of  small  oylindets  which  are  fitted  permanently  into  boles  drilled  Id 
the  surface  of  tlis  bearing.  The  bearing  thus  fitted  runs  without  any  otiier 
lubrication. 


946  THE  FOUKD&t. 


THE    FOUJNDBY. 

CVPOIiA  PBAOTICB. 

The  following  notes,  with  the  accoinpanyinR  table,  are  taken  from  an 
article  by  Simpson  Bolland  Id  American  Macfiinist^  June  80, 1692.  The  table 
shows  heights,  depth  of  bottom,  quantity  of  fuel  on  bed,  proportion  of  fuel 
and  Iron  in  charfces.  diameter  of  main  blast-pipes,  number  of  tuyeres,  blast- 

Eressure,  sizes  of  blowers  and  power  of  engines,  and  melting;  capacity  per 
our,  of  cupolas  from  S4  inches  to  84  inches  m  diameter. 

Capacity  of  Cupola.— The  accompanying  table  will  be  of  serTice  in  deter- 
mining the  capacity  of  cupola  needed  for  the  production  of  a  given  quantity 
of  iron  in  a  specified  time. 

First,  ascertain  the  amount  of  iron  which  is  likely  to  be  needed  at  each 
cast,  and  the  length  of  time  which  can  be  devoted  profitably  to  its  disposal: 
and  supposing  that  two  hours  is  all  that  can  be  spared  for  that  purpose,  and 
that  ten  tons  is  ihe  amount  which  must  be  melted,  find  in  the  column.  Melt- 
ing  Capacity  per  hour  in  Pounds,  the  nearest  figure  to  five  tons  per  hour, 
which  is  found  to  be  10.760  pounds  per  hour,  opposite  to  which  in  the  column 
Diameter  of  Cupolas,  Inside  Lining,  will  be  found  48  inches  ;  this  will  be  the 
size  of  cupola  required  to  furnish  ten  tons  of  molten  iron  in  two  hours. 

Or  suppose  that  the  beats  were  likely  to  average  6  tons,  with  an  occasional 
increase  up  to  ten,  then  it  might  not  be  thought  wise  to  incur  the  extra  ex- 
pense consequent  on  working  a  48- inch  cupola,  in  which  case,  by  following 
the  directions  given,  it  will  be  found  that  a  40-Inch  cupola  would  answer  the 
purpose  for  6  tons,  but  would  require  an  additional  hour's  time  for  meltin.g 
whenever  the  10  ton  heat  came  along. 

The  Quotations  in  the  table  are  not  supposed  to  be  all  that  can  be  melted 
in  the  nour  by  some  of  the  very  best  cupolas,  but  are  simply  the  amounts 
which  a  common  cupola  under  ordinary  circumstances  may  be  expected  to 
melt  in  the  time  specified. 

Height  of  Cupola.— Bj  height  of  cupola  is  meant  the  distance  from  the 
base  to  the  bottom  side  of  the  charging  hole. 

Depth  of  Bottom  of  Ottpo/a.— Depth  of  bottom  is  the  distance  from  the 
sand-lwd,  after  it  has  been  formed  at  the  bottom  of  the  cupola,  up  to  the 
under  side  of  the  tuveres. 

All  the  amounts  for  fuel  are  based  upon  a  bottom  of  10  inches  deep,  and 
any  departure  from  this  depth  must  be  met  by  a  corresponding  change  in 
the  quantity  of  fuel  used  on  the  bed  ;  more  in  proportion  as  the  depth  is 
increased,  and  less  when  it  is  made  shallower. 

Amount  of  Fuel  Required  on  the  Bed.— The  column  "  Amount  of  Fuel  re- 
quired on  Bed.  in  Pounds"  is  based  on  the  supposition  that  the  cupola  is  a 
straight  one  all  through,  and  that  the  bottom  is  10  inches  deep.  If  the  bot- 
tom be  more,  as  in  those  of  the  CoUiau  type,  then  additional  fuel  will  be 
needed. 

Tlie  amounts  being  given  in  pounds,  answer  for  both  coal  and  coke,  for. 
should  coal  be  used,  it  would  reach  about  1,5  inches  above  the  tuyeres  ;  the 
same  weight  of  coke  would  bring  it  up  to  about  22  inches  above  the  tuyeres, 
which  is  a  reliable  amount  to  stock  with. 

Firnt  Charge  of  Iron.— The  amounts  given  in  this  column  of  the  table  are 
safe  figures  to  work  upon  in  every  instance,  yet  it  will  always  be  in  order, 
after  proving  the  abilitV  of  the  l>ed  to  carry  the  load  quoted,  to  make  a  slow 
and  gradual  increase  of  the  load  imtil  it  is  fully  demonstrated  Just  how  muc^ 
burden  the  bed  will  carry. 

Succeeding  Charges  of  Fuel  and  lron.—\w  the  columns  relating  to  succeed* 
ing  charges  of  fuel  and  iron,  it  will  be  seen  that  the  highest  proportions  are 
not  favored,  for  the  simple  reason  that  successful  melting  with  any  greater 
proportion  of  iron  to  fuel  is  not  the  rule,  but,  rather,  the  exception.  When- 
eirer  we  see  that  iron  has  been  melted  in  prime  condition  in  the  proportion 
of  12  pounds  of  iron  to  one  of  fuel,  we  may  reasonably  expect  that  the  talent, 
material,  and  cupola  have  all  been  up  to  the  highest  degree  of  excellence. 

Diameter  of  Main  Blast -pipe. —The  table  gives  the  diameters  cMf  main 
blast-pipes  for  all  cupolas  from  24  to  84  inches  diameter.  The  sixes  given 
opposite  each  cupola  are  of  sufficient  area  for  all  lengths  up  to  100  feet. 


CUPOLA  PRACTICE. 


947 


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948 


THE   FOUNDRY. 


3ViyerM /or  (7upoIa.~Two  oolumos  are  devoted  to  the  number  and  Blzen  of 
tuyeres  requisite  for  the  guccewf  ul  worklnir  of  each  cupola ;  one  fd^^s  the 
number  of  pipes  6  inches  diameter,  and  ihe  other  gives  the  number  and 
dimensions  t)f  rectangular  tuyeres  which  are  their  equivalent  In  area. 

From  these  two  columns  any  other  arrangement  or  disposition  of  tuyeres 
may  be  made,  which  shall  answer  in  their  totality  to  the  areas  given  in  the 
table. 

When  cupolas  exceed  60  Inches  In  diameter,  the  Increase  in  diameter 
should  begin  somewhere  above  the  tuyeres.  This  method  is  necessary  in  all 
common  cupolas  above  60  inches,  because  it  is  not  possible  to  force  the  blast 
to  the  middle  of  the  stock,  effectively,  at  any  greater  uiameter. 

On  no  coHRideration  must  the  tuyere  area  be  reduced:  thus,  an  84 -inch 
cupola  must  have  tuyere  area  equal  to  31  pipes  6  inches  diameter,  or  16  flat 
tuyeres  16  inches  by  13^  inches. 

If  it  is  found  that  the  given  number  of  flat  tuyeres  exceed  in  circumference 
that  of  the  diminished  part  of  the  cupola,  thev  can  be  shortened,  allowing 
the  decreased  length  to  be  added  to  the  depth,  or  they  may  be  built  in  on 
end;  by  so  doing,  we  arrive  at  a  modified  form  of  the  Blakeney  cupola. 

Another  important  point  in  this  connection  is  to  arrange  ihe  tuyeres  in 
such  a  manner  as  will  concentrate  the  fire  at  the  melting-point  into  the 
smallest  possible  compsss,  so  that  the  metal  In  fusion  will  have  lees  space 
to  traverse  while  exposed  to  the  oxidizing  influence  of  the  blast. 

To  accomplish  thi8,  recourse  has  been  had  to  the  placing  of  additional 
rows  of  tuyeres  in  some  Instan  es— the  '*  Stewart  rapid  cupola  **  having 
three  rows,  and  the  *'  Colliau  cupola  furnace  "  having  two  rowa,  of  tuyeres. 

B/n«^;»'eMure.— Experiments  show  that  about  SO.OOO  cubic  feet  of  air  are 
consumed  in  melting  a  ton  of  iron,  which  would  weigh  about  840U  pounds 
or  more  than  both  iron  and  fuel.  When  the  proper  quantity  of  air  is  sup- 
plieii,  the  combustion  of  the  fuel  is  pnrfect.  snd  carnonic-acid  gas  is  tlie 
result.  When  the  supply  of  air  is  insufficient,  the  combustion  is  imperfect, 
and  carbonic-oxide  pas  is  the  result.  The  amount  of  heat  evolved  In  these 
two  coses  is  as  15  to  4}^,  showing  a  loss  of  over  two  thirds  of  the  heat  by  im- 
perfect combustion. 

It  is  not  always  true  that  we  obtain  the  most  rapid  melting  when  we  are 
forcing  Into  the  cupt^la  the  largest  quantity  of  air.  Some  time  Is  required 
to  elevate  the  temperature  of  the  air  supplied  to  ihe  point  that  it  will  enter 
Into  combu«tlon.  If  more  air  than  this  is  supplied,  Ir.  rapidly  absorbs  heat, 
reduces  the  temperature,  and  retards  combustion,  and  tlie  fire  in  the  cupola 
may  be  extinguished  wjtli  too  much  blast. 

Slag  in  CnpnI(ut.—\  certain  amount  of  slag  Is  necessary  to  protect  the 
molten  iron  which  has  fallen  to  the  bottom  from  the  action  of  the  blast;  if 
it^va»  not  there,  the  iron  would  suffer  fmm  decarbonlzation. 

When  slag  from  anv  cause  forms  in  too  great  abundance,  it  should  be  leil 
away  by  Inserting  a  iiole  a  liitle  below  the  tuyeres,  through  which  it  will 
find  its  way  as  the  iron  rises  in  the  bottom. 

In  the  event  of  clean  iron  and  fuel,  slag  seldom  forms  to  any  appreciable 
extent  in  small  heats  ;  this  renders  any  preparation  for  its  withdraw  al  un* 
necessary,  but  when  the  cupola  is  to  be  taxed  to  its  utmost  capacity  it  is 
then  incumbent  on  the  melter  to  flux  the  charges  all  through  the  beat,  car* 
rying  it  away  In  the  manner  directed. 

The  best  flux  for  this  purpose  is  the  chips  from  a  white  marble  yard. 
About  0  pounds  to  the  ton  of  iron  will  give  good  results  when  all  is  dean. 

Wlien  fuel  is  bad.  or  iron  is  dirty,  or  both  together,  it  becomes  imperative 
that  the  slag  b«*  kept  nmning  all  the  time. 

Fitel  for  Ciipotas.— The  best  fuel  for  melting  Iron  is  coke,  because  It  re- 
quires less  bla«;t,  makes  hotter  Iron,  and  melts  faster  than  coal.  When  coal 
must  be  UFed,  care  xhouM  be  exercised  in  its  selection.  All  anthracites 
which  sre  bright,  black,  hard,  and  free  from  slate,  will  melt  iron  admiraiiiv. 
The  Pi/e  of  the  coal  used  affects  the  melting  to  an  appreciable  extent,  and. 
for  the  best  results,  small  cupolas  should  oe  charged  with  the  sixe  called 
•*egg,''a  still  larger  grade  for  medium-sized  cupolas,  and  what  is  called 
*'  lump ''  will  answer  for  all  large  cupolas,  when  care  is  taken  to  pack  it 
carefully  on  the  charees. 

Charfflns  a  Cnpola.— Chas.  A.  Smith  (Am.  Mnch  ,  Feb.  13,  IKin  gives 
the  following :  A  2«-in.  cupola  should  have  from  SOO  to  400  pounds  of  coke 
on  bottom  bed:  a  .36.in.  cupola.  700  to  800  pounds;  a  48-in.  cupola,  1.500  lbs.; 
and  a  60-in.  cupola  should  have  one  ton  of  fuel  on  bottom  bed.  To  every 
pound  of  fuel  on  the  bed,  three,  and  sometimes  four  pounds  of  metal  can  be 
added  with  safety,  if  the  cupola  has  proper  blast;  in  after-charges,  to  evei7 


CUPOLA  PBACTIOE. 


949 


pouad  of  fuel  add  8  to  10  pounds  of  metal;  any  well'Constructed  cupola  will 
stand  ten. 

F.  P.  Wolcott  (Am.  Mach.,  Mar.  5, 1891)  gives  the  followiii«:  as  the  practice 
of  the  Col  well  Iron-works,  Cai'teret,  N.  J.:  *'  We  melt  daily  from  twenty  to 
forty  tons  of  iron,  with  an  averapre  of  11 .3  pounds  of  iron  to  one  of  fuel.  In 
a  :i6-in.  cupola  seven  to  nine  pounds  is  good  melting,  but  in  a  cupola  that 
lines  up  4S  to  GO  inches,  anything  less  than  nine  pounds  shows  a  defect  in 
arrangement  of  tuyeres  or  strength  of  blast,  or  in  charging  up.'' 

'*  The  Moulder's  Te3ct-book,"  by  Thos.  D.  West,  gives  forty-alx  reports  in 
tabular  form  of  cupola  practice  in  thirty  States,  reaching  from  Maine  to 
Oregon. 

Cupola  Cliargea  In  StoTe-ronndriea.  {Irwi  Age,  April  14, 1603.) 
No  two  cupolas  are  charged  exactly  the  same.  The  amount  of  fuel  on  the 
bed  or  between  the  charges  differs,  while  varying  amounts  of  iron  are  used 
in  the  charges.  Below  will  be  found  charging>ltot4  from  some  of  the  prom- 
inent stove-foundries  In  the  country : 


lbs. 

-Bed  of  fuel,  coke 1,S00 

First  cbai-ge  of  iron 5.000 

All  other  charges  of  iron . .  1 ,000 
First  and  second  charges 
of  coke,  each  200 


lbs. 
Four  next  charges  of  ooke, 

each 150 

81  z  next  charges  of  coke,  each  120 
Nineteen  next  charges  of  coke, 

each 100 


Thus  for  a  melt  of  18  tons  there  would  be  S120  lbs.  of  coke  used,  giving  a 
ratio  of  7  to  1.  Increase  the  amount  of  iron  melted  to  24  tons,  and  a  ratio  of 
8  pounds  of  Iron  to  1  of  coal  is  obtained. 


lbs. 

-Bed  of  fuel,  coke  1,600 

First  charge  of  iron 1,800 

First  charge  of  fuel ISO 

All  other  charges  of  iron, 
each 1,000 


lbs. 
Second  and  third  charges  of 

fuel lao 

All  other  charges  of  fuel,  each     100 


For  an  18-ton  melt  6060  lbs.  of  coke  would  be  necessary,  giving  a  ratio  of 
7.1  lbs.  of  iron  to  1  pound  of  coke. 


lbs. 

All  other  charges  of  iron 2,000 

AU  other  charges  of  ooke ISO 


lbs. 

C-Bed  of  fuel,  coke  1,600 

First  charge  of  Iron 4,000 

First  and  second  charges 
of  coke 200 

In  a  melt  of  18  tons  4100  lbs.  of  coke  would  be  used,  or  a  ratio  of  8.5  to  1. 

lbs.    I  lbs. 

JD— Bed  of  fuel,  coke 1,800       All  charges  of  coke,  each 200 

First  charge  of  iron 6,600  |   All  other  charges  of  Iron ...... .  2,IP0O 

In  a  melt  of  18  tons,  8900  lbs.  of  fuel  would  be  used,  giving  a  ratio  of  9.4 
pounds  of  iron  to  1  of  coke.    Very  high,  indeed,  for  stove-plate. 

lbs.    I  lbs. 

K— Bed  of  fuel,  coal  1,900  I  All  other  charges  of  iron,  each  2,000 

First  charge  of  iron 6,000  I  All  other  charges  of  coal,  each     176 

First  charge  of  coal 200  | 

In  a  melt  of  18  tons  4700  lbs.  of  coal  would  be  used,  giving  a  ratio  of  7.7 
lbs.  of  iron  to  1  lb.  of  coal. 

Tlieseare  aufllcieut  to  demonstrate  the  varying  practices  existing  among 
different  stove-foundries.  In  all  these  places  the  iron  was  proper  for  stove- 
plate  purposes,  and  apparently  there  was  little  or  no  difference  in  the  kind 
of  work  in  the  sand  at  the  different  foundries. 

Results  of  Increased  Brlvlns*  (Erie  City  Iron-works,  1891. )-> 
May— Dec.  1890:  60-in.  cupola.  100  tons  clean  castings  a  week,  melting  8  tons 
per  hour;  iron  per  pound  of  fuel,  7^  lbs. ;  percent  weight  of  good  castings  to 
iron  charged,  75^.  Jan.-May,  1891 :  Increased  rate  of  melting  to  1 1)^  tons  per 
hour;  iron  per  lb.  fuel,  9^;  per  cent  weight  of  good  castings,  75;  one  week, 
1314  tons  per  hour,  10.3  lbs.  iron  per  lb.  fuel;  per  cent  weight  of  good  cast- 
ings, 76.8.  The  increase  was  made  by  putting  in  an  additional  row  of  tuveres 
and  using  stronger  blust,  14  ounces.  Ooke  was  us^d  as  fuel.  (W>  0*  Webbert 
Trans.  A.  &  U.  £.  xii.  1046.) 


950 


THE  FOUNDRY. 


Bnllklo  flMeel   Pressnre-blowers.    Speeds   and  Capaeltlea 
m»  applied  to  Cupola*. 


■s 

1 

S 

o 

8 

^ 

i 

^la 

8 

1. 

cIs 

Is 

gO.5 

1^^ 

III 

i^ 

s 

it 

Ill 

m 

4 

4 

20 

8 

4782 

1645 

606 

9 

5030 

1617 

717 

5 

6 

25 

8 

4209 

2821 

773 

10 

4726 

2600 

867 

6 

8 

80 

8 

8660 

3093 

951 

10 

4108 

8671 

1067 

7 

14 

85 

8 

8244 

4218 

1486 

10 

3842 

4777 

1068 

8 

18 

40 

8 

2948 

5425 

2199 

10 

3310 

6083 

2469 

9 

26 

45 

10 

2785 

7818 

8208 

12 

3260 

8308 

8523 

10 

86 

55 

10 

2105 

11295 

4938 

12 

2113 

12878 

5431 

11 

45 

65 

12 

1952 

16955 

7707 

14 

2116 

18357 

8358 

iiH 

55 

72 

12 

1647 

22607 

10276 

14 

1797 

25176 

11144 

13 

76 

84 

12 

1625 

256^ 

11744 

14 

1775 

28019  12736 

In  the  table  are  given  two  different  speeds  and  pressures  for  each  size  of 
blower,  and  the  quantity  of  iron  that  may  be  melted,  per  hour,  with  each. 
In  all  cases  it  is  recommended  to  use  the  lowest  pressure  of  blast  that  will  do 
the  worlc.  Run  up  to  the  speed  given  for  that  pressure,  and  regulate  quan- 
tity of  air  by  the  blast-gate.  The  tuyere  area  should  be  at  least  one  ninth 
of  the  area  of  cupola  in  square  iuches,  with  not  less  than  four  tuyeres  at 
equal  distances  around  cupola,  so  as  to  equalise  the  blast  throughout.  Va- 
riations in  temperature  affect  the  working  of  cupolas  materially,  hot 
weather  requiring  increase  in  volume  of  air. 
(For  tables  of  the  Sturtevant  blower  see  pages  519  and  520.) 
liOBB  In  meltlns  Iron  In  Cupolan.— O.  O.  Valr,  Am.  Mach.^ 
Uarch  5,  1891,  gives  a  i-ecord  of  a  45-in.  Colliau  cupola  as  follows: 

Ratio  of  fuel  to  iron,  1  to  7.42. 

Good  castings 21,814  lbs. 

Newscrap 8,005  ** 

Millings 200  ** 

Loss  of  metal.... 1,481  " 

Amount  melted 86,000  lbs. 

Loss  of  metal,  &.69%.    Ratio  of  loss,  1  to  17.55. 

Use  of  Softeners  In  Foundry  Practice.  (W.  Graham,  Iron  Affe, 

June  27.  18S9.)— In  the  foundry  lite  ()roblem  is  to  have  the  right  proportions 
of  combined  and  graphitic  carbon  in  the  rettulting  casting;  this  is  done  by 
getting  the  proper  proportion  of  silicon.  The  variations  in  the  proportions 
of  silicon  atforu  a  reliaole  and  inexpensive  means  of  producing  a  cast  iron 
of  any  required  mechanical  character  which  is  possible  with  the  material 
employed.  In  this  way,  by  mixing  Kuitable  irons  in  the  right  proportions, 
a  required  grade  of  casting  can  be  made  more  cheaply  than  by  using  irons 
in  which  the  necessary  proportions  are  already  found. 

If  a  strong  machine  casting  were  required,  it  would  be  necessaryto  keep 
the  phosphorus,  sulphur,  and  manganese  within  certain  limits.  Professor 
Turner  found  that  cast  iron  which  possessed  the  maximum  of  the  desired 
qualities  contained,  graphite,  2.59^;  silicon,  1.42j(;  phosphorus,  0.393e;  sul- 
phur,  O.OOjf ;  manganese,  0.58%. 

A  strong  casting  could  not  be  made  if  there  was  much  increase  In  the 
amount  of  phosphorus,  sulphur,  or  manganese.  Irons  of  the  above  percent- 
ages of  phospiiorus,  sulphur,  and  manganese  would  be  most  suitable  for  this 
purpose,  but  they  could  be  of  different  grades,  having  different  percentages 
of  silicon,  comi){ned  and  graphitic  carbon.  Thus  hard  irons,  mottled  and 
white  irons,  and  even  steel  scran,  all  containing  low  percentages  of  silicon 
and  high  percentages  of  combined  carbon,  could  be  employed  if  an  iron 
having  a  lar^e  amount  of  silicon  were  mixed  with  them  in  sufficient  amount. 
This  would  bring  the  silicon  to  the  proper  proportion  and  would  cause  the 
conihineil  carbon  to  be  forced  into  the  graphitic  state,  and  the  resultiog 


SHRINKAGE  OF  CASTINGS. 


951 


eastinir  would  be  aoft.    High-silicon  irons  used  in  this  way  are  called  "  soft- 
eners." 
The  following  are  typical  analyses  of  softeners: 


Ferro-silicon. 

Softeners,  American. 

Scotch 
Irons,  No.  1. 

Foreign. 

American. 

Well- 
ston. 

Globe 

Belle- 
fonte. 

Eg- 
linton 

Colt* 
ness. 

Silicon 

Combined  C. 
Graphitic  C. 
Manganese . . 
Phosphorus. . 
Sulphur  

10.66 
1.64 
0.52 
8.86 
0.04 
0.03 

9.80 
0.60 
1.12 
1.95 
0.21 
0.04 

12.08 
0.06 
1.68 
0.T6 
0.48 

Trace 

10.84 
0.07 
1.98 
0.58 
0.4R 

Trace 

6.W 
2.67 

o'.w 

Trace 

5.89 
0.80 
385 
1.00 
1.10 
0.08 

8to6 
0.85 
8. 

0.58 
0.85 
0.08 

8.15 
0.81 
8.76 
2.80 
0.68 
0.08 

8.59 

i'.TO* 
0.86 
0.01 

(For  other  analyses,  see  pages  871  to  878.) 

Ferro-silicons  contain  a  low  percentage  of  total  carbon  and  a  high  per- 
centage of  combined  carbon.  Carbon  is  the  most  important  constituent  of 
cast  iron,  and  there  should  be  about  9.4%  total  carbon  present.  By  adding 
ferro-silicon  which  contains  only  2%  of  carbon  the  amount  of  carbon  iu  the 
resulting  mixture  is  lessened. 


ini;  as  high  a  percentage  of  combined  carbon  as  0.70^  to  overcome  the  bad 
effects  of  coraoined  carbon  iu  other  irons. 

The  Scotch  irons  generally  contain  much  more  phosphorus  than  is  desired 
in  irons  to  be  employed  in  making  the  strongest  castings.  It  is  a  mistake  to 
mix  with  strong  low -phosphorus  irons  an  iron  that  would  increase  the 
amount  of  phosphorus  for  the  sake  of  adding  softening  qualities,  when  soft- 
ness can  be  produced  by  mixing  irons  of  the  same  low  pnosphorus. 
(For  further  discussion  of  the  influence  of  silicon  see  page  865.) 
Sbrinkase  of  CaatlnffS.— The  allowance  necessary  for  shrinkage 
▼aries  for  different  kinds  of  metal,  and  the  different  conditions  under  which 
they  are  cast.  For  castings  where  the  thickness  runs  about  one  inch,  cast 
under  ordinary  couditions,  the  following  allowance  can  be  made: 


For  cast-iron,  >^ 
**    brass,       8/; 
"    steel, 
*'    mal.  iron, 


r„      inch  per  foot.  For  ssinc,  5/16  Inch  per  foot. 

8/16 "    tin,  1/18    **       ♦•     " 

"      "  "    aluminum,  8/16    "      •*      " 

*•      "  "    Britannia,  1/38    "       **      " 


Thicker  castings,  under  the  same  conditions,  will  shrink  less,  and  thinner 
ones  more,  than  this  standard.  The  quality  of  the  material  and  the  manner 
of  moulding  and  cooling  will  also  make  a  difference. 

Numerous  experiments  by  "W.  J.  Keep  (see  Traos.  A.  S.  M.  E.,  toI.  xvi.) 
showed  that  the  shrinkage  of  cast  iron  of  a  given  section  decreases  as  the 
percentage  of  silicon  increases,  while  for  a  given  percentage  of  silicon  the 
shrinkage  decreases  as  the  section  is  increased.  Mr.  Keep  gives  the  follow- 
ing table  showing  the  approximate  relation  of  shrinkage  to  size  and  per- 
centage of  silicon: 


Sectional  Area  of  Citing. 

Percentage 

1 

of 

H"o 

1"  0 

1"  X  8" 

2"  □ 

8"  D 

4"  D 

Sflicon. 

1              1 

Shrinkage  in  Decimals  of  an  inch  per  foot 

of  Length. 

1. 

.183 

.158 

.146 

.130 

.113 

.108 

1.6 

.171 

.145 

.133 

.117 

.098 

.087 

2. 

.159 

.183 

.121 

.104 

.065 

.074 

8.5 

.147 

.181 

.108 

.098 

.073 

.060 

8. 

.186 

.106 

.095 

.077 

.069 

.045 

8.6 

.188 

.096 

.088 

.066 

.016 

.083 

958 


tttfi  JOUJ^DftY. 


Mr.  Kmp  alM  liVM  the  followfug: "  Apt>fox(ttiAt«  key  toY  fftgulattn^  font!' 
diy  mixtures"  so  as  to  produce  a  shrinkage  of  ^  in.  per  ft.  in  castiDgs  of 
difiereDt  sections: 

8fse  of  casting: U  1  S  8  4     In.  sq. 

Silicon  required,  percent.....  8.i»       8.75       ft9S       1.75       1.95  percent. 

Bhritikaffe  of  a  ^-in.  test-bar.    .105       .135       .145       .155       .165  in.  per  ft. 

ir«tcht  or  CASttnsa  d«t«niilned  firom  Weicbt  of  Pattern. 

(Rosens  Pttttern-makerV  Assistant.) 


A  Pattern  welichinK  One  Pound, 
made  of-^ 


Mahogany— Kassau . . . . 
Honduras 
Spanish    . 

Pine, red... 

•*    white 

'*    yellow............ 


Will  weigh  when  cast  in 


cast 
Iron. 

Zinc. 

Copper. 

Yellow 
Brase. 

Gun- 
metal. 

Ihs. 

IhB. 

lbs. 

lbs. 

lbs. 

10.7 

10.4 

18.8 

13.8 

1^.5 

l».9 

18.7 

15.9 

14.6 

15. 

8.5 

8.8 

10.1 

9.7 

9.9 

18.5 

18.1 

14.9 

14.8 

14.6 

16.7 

16.1 

19.8 

19.0 

19  5 

14.1 

18.6 

16.7 

16.0 

ie.5 

Rloiilcllna  Sand*  (From  a  paper  on  '*  The  Mechanical  Treatment  ot 
Moulding  8and."  by  Walter  Bsgshaw,  Proc.  Inst.  M.  K.  1891.)— The  chemical 
oomposition  ot  sand  will  affect  tlie  nature  of  the  casting,  no  matter  whsi 
treatment  it  undergoes.  Stated  ttenerally,  good  sand  is  coni|H>sed  of  IM  parti; 
Blllca,  5  parts  alumina,  and  traces  of  magnesia  and  oxide  of  iron.  Sand  con- 
taining much  of  the  metallic  oxides,  and  especially  lime,  is  to  be  avoided. 
Qeographlcal  position  is  the  chief  factor  governing  the  selection  of  sand: 
and  whether  weak  or  strong,  its  deficiencies  are  made  up  for  by  the  skill  <»f 
the  moulder.  Kor  this  reason  the  same  sand  Is  often  used  for  both  heavy  and 
light  castings,  the  proportion  of  coal  varying  according  to  the  nature  of  the 
casting.  A  common  mixture  of  facing-sand  consists  of  six  parts  by  weight 
of  old  sand,  four  of  new  sand,  and  one  of  coal-dust.  Floor->and  requires 
only  half  the  above  proportions  of  new  sand  and  coal-dust  to  renew  it.  Ger- 
man founders  adopt  one  part  by  measure  of  new  sand  to  two  of  ol«l  sand; 
to  which  is  added  coal-dust  In  the  proportion  of  one  tenth  of  the  bulk  for 
large  castihiss,  and  one  twentieth  for  small  castings.  A  few  founders  mix 
street-sweepings  with  the  coal  In  order  to  get  porosity  when  the  metal  in 
the  mould  is  llKely  to  be  a  long  time  before  setting.  Plumbago  is  eftt^ctive  in 
preventing  destruotion  of  the  sand ;  but  owing  to  its  refractoiy  nature,  it 
must  not  be  dusted  on  in  such  quantities  as  to  close  Uie  pores  and  prevent 
free  exit  of  the  gases.  Powdered  French  chalk,  soapstone,  and  other  sub- 
stances are  sometimes  used  fur  facina  the  mould;  but  next  to  plumbago,  oak 
charcoal  takes  the  best  place,  notwithstanding  ita  liability  to  float  occasion- 
ally and  give  a  rough  casting. 

For  the  treatment  of  sand  in  the  moulding-shop  the  most  primitive  method 
Is  that  of  hand-riddling  and  treading.  Here  the  materials  are  roughly  pro- 
portioned by  volume,  and  riddled  over  an  Iron  plate  in  a  flat  heap,  wnere 
the  mixture  Is  trodden  into  a  cuke  by  stamping  with  the  feel ;  it  Is  turned 
over  with  the  shovel,  and  the  process  repeated.  Tough  sand  can  lie  obtained 
in  this  manner,  itn  toughness  l)eing  usually  tested  by  squeezing  a  handful 
into  a  ball  and  then  breaking  it :  but  the  process  Is  slow  and  tedious.  Other 
things  being  equal,  the  chief  characteristics  of  a  good  mouldlng-juind  &n 
toughness  and  porosity,  qualities  that  depend  on  the  manner  of  mixing  as 
well  as  on  uniform  ramming. 

TonKhnesA  of  Sand.— In  order  to  test  the  relative  toughness,  sand 
mixed  in  variouH  ways  Was  pressed  under  a  Uniform  load  into  oars  1  in.  sq. 
and  about  12  In.  long,  ana  ench  bar  was  made  to  projeot  further  and 
further  over  the  edge  of  a  table  until  Its  end  broke  off  by  its  own  weight. 
Old  sand  from  the  shop  floor  had  very  irregular  cohesion,  breaking  at  all 
lengths  of  projections  from  \i  in.  to  1^  In.  New  sand  In  Its  natural  state 
held  together  until  an  overhang  of  2^  in.  was  reached.  A  mixture  of  old 
sand,  new  sand,  and  coal-dust 
Mixed  under  rollers broke  at  8     to  dU  in.  of  overhang. 

"      in  the  centrifugal  machine *'      **  2      **  8M  "    " 

"      through  a  riddle ,.       "      "  1J<  **  •>«  **    "        " 


8PEED  OF  CtJTXIKa-TOOLS  IK  LATHES,  ETO.       D53 


Showlnir  M  A  mean  of  the  tests  onlj  sifght  dffferenoefl  between  tbe  last 
three  methods,  but  In  favor  of  machtne-work.  Id  many  Instances  the  frac- 
lurps  were  so  uneven  that  minute  mcAfiiirements  were  not  taken. 

Dimensions  of  Fonndrr  Iiadlea«^The  following  table  elves  the 
diniens  ons.  inside  the  lining,  of  ladles  from  25  lbs.  to  16  tons  eapacltv.  All 
the  ladles  are  supposed  to  have  straight  sides.    {Am,  Mtich.^  Aug*  4, 1808.) 


Capadry. 

Diam. 

Depth. 

Capacity. 

Diam. 

in. 
80 
17 
18U 

log 

10^^ 
9 
8 
7 

Depth. 

16  tons 

in. 
64 
63 
49 
46 
48 
89 
84 
81 
27 

In. 
66 
63 
60 
48 
44 
40 
85 
88 
28 
85 
88 

N*^'* 

Ji  - :::::::: 

800  pounds.... 
250  "  .... 
200  '•  .... 
160  ••  .... 
100        «• 

75          •        .... 

50         -        .... 

85         *• 

in. 
80 

14     ••     

17 

12     ••     

10     *•      

18U 

^    ••      

G     "     

lOU 

4     ••     

8     *•     

?     "     

IVb-* 

0 

1  -  :::;:;::;. 

THE   MACHTNE-SHOP. 


flPBBD  OP   crTTINtt-TOOliS    IN   I.4THE8,    MlIililNO 
MACHINES,  BT€.  ^ 

Rt*lation  of  diameter  of  rotating  tool  or  piece,  number  of  revolutions, 
and  cutting-Hpeed  : 
Let  d  ^  diam.  of  rotating  piece  in  inches,  n  ^  No.  of  revs,  per  min.; 
8  a  speed  of  circumference  in  feet  per  minute; 


«-^-.26IW„;    n^^Ag: 


8.823 
d    • 


da 


8.825 


Approximate  rule :  No.  of  revs,  per  mIn.  b  4  X  speed  in  ft.  per  mIn.  -»> 
diam.  in  Inches. 

Speed  of  Cut-tor  liftthes  and  Planers.  (Prof.  Coleman  Sellers, 
Stitven*'  Indicator^  April,  J 692. h-i^tucs  may  oe  turned  at  high  speed  like 
wood. 

Bronze.^ A.  speed  of  18  feet  per  minute  can  be  u<9ed  with  the  soft  alloys— 
sa^  8  to  1,  while  for  bard  mixtures  a  slow  speed  is  required— say  6  feel  per 
minute. 

Wrouyht  Iron  can  be  turned  at  40  feet  per  minute,  but  planing-machines 
that  are  used  for  both  cast  and  forged  iron  are  operated  at  18  feet  per 
minute. 

Machinery  3^eeZ.— Ordinary,  14  feet  per  minute;  oar-axles,  etc.,  9  feet  per 
minute. 

Wheel  r/rM.^6  feet  per  minute:  tbe  tool  stands  well,  but  many  prefer 
to  run  faster,  say  8  to  10  feet,  and  grind  the  tool  more  frequently. 

L(ithe8,'-Tt%e  speeds  obtainable  by  means  of  the  cone-pulley  and  the  back 
gearing  are  in  geometrical  progression  from  the  slowest  to  tbe  fastest.  In 
a  well-proportioned  machine  the  speeds  hold  the  name  relation  through  all 
the  steps.  Many  lathes  have  the  Kame  speed  on  the  Mlowest  of  the  cone  and 
the  faAtest  of  the  back-gear  speeds. 

The  Speed  of  Counter-shaft  of  the  lathe  is  determined  by  an  assumption 
of  a  slow  speed  with  the  back  gear,  say  6  feet  per  minute,  on  the  lai:gest 
diameter  that  the  lathe  will  swing. 

ExAXPLB.— A  80-incb  lathe  will  swing  80  Inches  s,  say,  90  inches  circumfer- 
ence =  7'  6^';  the  lowest  triple  gear  Khould  give  a  speed  of  5  or  6  per  minute. 

In  turninjc  or  planing,  if  the  cutting-speed  exceed  80  ft.  per  minute,  so 
much  heat  will  be  produced  that  the  temi^er  will  be  drawn  from  the  tool. 
The  speed  of  cutting  U  also  governed  by  the  thiukuess  of  the  shaving,  and 
by  the  hardness  and  tenacity  of  the  metal  which  is  being  cut;  for  instance, 
in  cutting  mild  steel,  with  a  traverse  of  %  in.  iier  revolution  or  stroke,  and 
with  a  shaving  about  ^  in.  thick,  the  speed  or  cutting  must  be  reduced  to 
about  8  ft.  per  minute.   A  good  average  cuitiug-speed  for  wrought  or  caal 


954 


THE  MACHIKE-8H0P. 


Iron  is  SO  ft,_per  mtimte,  whether  for  the  lathe,  planing',  shapinsr,  or  slotting 
machine.    (Proc.  Inst.  M.  E.,  April,  1888,  p.  sMS.) 

Table  of  €attliis»apee4a« 


Feet  per  minute. 

Diameter, 

1 

inohes. 

5 

10   1 

»  1 

20 

86 

80 

85 

40 

45         60 

Revolutions  per  minute. 

H 

76.4 

168.8 

229.8 

305  6 

882.0 

468.4 

534.8 

611.2 

687.6 

764.0 

I 

50  P 

101  9 

152.8 

208.7 

254.6 

305.6 

366.6 

407.4 

458.3 

500.^ 

4 

38.-2 

76.4 

114.6 

152.8 

191.0 

829.2 

867.4 

305.6 

843  8 

Sfri.O 

1 

30.6 

61.1 

91.7 

122.2 

152.8 

188.4 

213.9 

244.5 

275.0 

305.6 

3 

25.5 

60.9 

76.4 

101.8 

1873 

152.8 

178.2 

203.7 

229.1 

254  D 

fi 

21  .S 

43.7 

65.5 

87.8 

109.1 

180.9 

152.8 

174  6 

196.4 

8l^.3 

1 

19.1 

88.8 

67.8 

70.4 

96.6 

114.6 

133.7 

152.8 

171.9 

191.0 

1^ 

17.0 

84.0 

60.9 

67.9 

84.9 

101.8 

118.8 

185.8 

152.8 

169.7 

m 

15.3 

30.6 

45.8 

61.1 

76.4 

01.7 

106.9 

182.2 

137.6 

152  8 

^H 

13  9 

27.8 

41.7 

65.6 

60.6 

FS.3 

97.2 

111.1 

125.0 

138.9 

1^ 

12.7 

85.5 

88.2 

60.9 

68.6 

76.4 

89.1 

101.8 

114.5 

li7.:J 

m 

10  9 

81.8 

887 

48.7 

64.6 

65  5 

76.4 

87.3 

98.2 

109  i 

8 

9.6 

19.1 

88.7 

88.8 

47.8 

67.3 

66.9 

764 

86.0 

»5.5 

fgLi 

8.5 

17.0 

25.5 

81  0 

42.5 

60.9 

60.4 

67.9 

76.4 

84.9 

2L  , 

7.6 

15  8 

829 

80.6 

38.2 

45.8 

63.5 

61.1 

68  8 

76.4 

9^ 

6.9 

18.9 

20.8 

27.8 

34.7 

41.7 

48.6 

55.6 

68.5 

68.5 

8 

6.4 

IS. 7 

19,1 

85.5 

31.8 

38  2 

44.6 

w.n 

57.3 

IV^.T 

SH 

6.5 

10.0 

16.4 

81.8 

27.8 

82.7 

382 

4.s.r 

49.1 

.%4.6 

4^ 

4.8 

9.6 

14.8 

10.1 

88.9 

28.7 

83.4 

38  J 

43.0 

47. S 

A% 

4.2 

8.6 

12.7 

17.0 

81.2 

25.5 

29.7 

34  0 

88.2 

4-,'5 

tr 

8.8 

7.6 

11.5 

16.3 

19.1 

82.9 

86.7 

306 

a4.4 

88.1 

^Vi 

3.6 

6.9 

10.4 

18,9 

17.4 

20  8 

84.3 

27.8 

31.i 

84.7 

fT 

8.8 

6.4 

9.6 

12.7 

16.9 

19.1 

22. JJ 

25.5 

28.6 

81. K 

7 

8.7 

6.5 

8.2 

10.9 

13.6 

16.4 

19  1 

21.8 

84.6 

27  3 

8 

2.4 

4.8 

7.2 

0.6 

11.9 

14.3 

16.7 

19.1 

81..%     S3  9 

0 

2.1 

4.2 

6.4 

8.6 

10.6 

12.7 

14.8 

17.0 

19.1 

21.8 

10 

19 

8.8 

6.7 

7.6 

0.6 

11.5 

13.3 

15.3 

17.2 

19  t 

n 

1.7 

8.6 

6.2 

6.9 

8.7 

10,4 

12.2 

18.9 

15.6 

17.4 

18 

1.6 

8.2 

4.8 

64 

8U 

9.6 

11  1 

12.7 

14.3 

1.'>.9 

13 

1.5 

89 

4  4 

69 

7.8 

8.8 

10  3 

11.8 

18.2 

14.7 

34 

1.4 

8.7 

4.1 

6.6 

6.8 

8.2 

9.5 

10.9 

12.3 

.  13.6 

15 

1.3 

2.6 

8.8 

6.1 

6.4 

7.6 

8.9 

10.2 

11.5 

12.7 

16 

1.2 

8.4 

3.6 

4.8 

6.0 

78 

8.4 

9.5 

10.7 

11.9 

18 

l.l 

2.1 

8.2 

4.2 

6.8 

6.4 

7.4 

8.6 

9.5 

10.6 

80 

1.0 

1.9 

8.9 

38 

4.8 

5.7 

6.7 

7.6 

8.6 

96 

»3 

.9 

1.7 

8.6 

8.5 

4.3 

6.8 

6.1 

6.0 

7.8 

8.7 

84 

.8 

1.6 

8.4 

8.2 

4.0 

4.8 

6.6 

6.4 

7.8 

8.0 

26 

.7 

1.5 

2.2 

2.9 

3.7 

4.4 

6.1 

6.9 

6.6 

7.8 

28 

.7 

1.4 

2.0 

2.7 

8.4 

4.1 

4.8 

6.5 

6.1 

68 

80 

.6 

1.8 

1.9 

2.6 

8.8 

8.8 

4.5 

5.1 

5  7 

6.4 

86 

.5 

1.1 

1.6 

8.1 

8.7 

88 

8.7 

4.2 

4.8 

53 

42 

.6 

.9 

1.4 

1.8 

8.3 

2.7 

8.2 

3.6 

4.1 

4.5 

48 

.4 

.8 

1.2 

1.6 

8.0 

8.4 

8.8 

3.2 

3.6 

4.0 

M 

.4 

.7 

1.1 

1.4 

1.8 

8.1 

86 

8.8 

8.8 

8.5 

60 

.3 

.6 

1.0 

1.3 

1.6 

1.9 

8.8 

8.5 

8.9 

8.2 

Speed  of  Cattlns  irlth  Turret  I«athes«— Jones  &  Lanison  Ma- 
chine Co.  give  the  following  cuulog-speeds  for  use  with  their  flat  turret 
lathe  on  diameters  not  exceeding  two  inches: 

Ft.  per  minute 


'Tool  steel  and  taper  on  tubing. ^..,       lO 

Machinery 15 

Very  soft  steel 20 

Cut  which  reduces  the  stock  to  U  of  Its  original  diam . .  'itQ 
Cut  which  reduces  the  stock  to  9S  of  its  original  diam. .  25 
Cut  which  reduces  the  Mt(H;k  to  %  of  its  original  diam . .  80  to  33 

t  Cut  wliich  re<)  uces  tlie  stock  to  15/16  of  its  original  diaai.  40  to  45 
Turning  very  soft  macliinery  steel,  light  cut  and  cool  work.. 60  to  60 


Threading 

Turning 

machinery 

steel 


GEARING   OF  LATHE8.  955 

Forms  of  netal-ciittlnfi:  Tools.— "  fTuffe,"  the  German  EofH- 
oeei-s'  Pockel-book,  gives  the  following  ciitUng-anglee  for  using  least  power: 

Top  Ralco.       Angle  of  Cutting-edge. 

Wn>ughtiron 8*  61* 

Castiron 4»  6l» 

Bronse 4*  (»• 

The  American  MtuhiniBt  comments  on  these  flguresas  follows:  We  are 
not  able  to  give  the  best  nor  even  the  generally  used  angles  for  tools, 
because  these  vary  so  much  to  suit  different  drcumstaDces.  such  as  degree 
of  hardness  of  the  metal  being  cut«  quality  of  steel  of  which  the  tool  is 
made,  depth  of  cut,  kind  of  Anish  desired,  etc.  The  angles  that  cut  with 
the  least  expenditure  of  power  are  easily  determined  by  a  few  experiments, 
but  the  best  angles  must  be  determined  by  goo<1  judgment,  guided  by  expe* 
rience.  In  nearly  all  cases,  however,  we  think  the  best  practical  angles  are 
greater  than  those  given. 

F'or  illustrations  and  deeciipUonfi  of  various  forms  of  cutting-tools,  see 
articles  on  Lathe  Tools  in  App.  Cyc  App.  Mech.,  vol.  ii.,  and  In  Modern 
Mechanism . 

Cold  CliIselB.— Angle  of  cutting-faces  (Joshua  Rose):  For  cast  steel, 
about  65  degrees;  for  gun-metal  or  brass,  about  60  degrees;  for  copper  and 
soft  metals,  about  80  to  85  degrees. 

Bale  for  CtoaHns  I«atlicB  for  Serew-entttni:.  (Garvin  Ma- 
chine Co.)— Read  from  me  lattie  uidex  the  number  of  threads  per  inch  cut 
by  equal  gears,  and  multiply  it  by  any  number  that  will  give  for  a  product 
a  trear  on  the  index;  put  this  gear  upon  the  stud,  then  multiply  the  number 
of  threads  per  inch  to  be  cut  by  the  same  number,  and  put  the  resulting  gear 
upon  the  screw. 

ExAMPLC—To  cut  IIU  threads  per  Inch.  We  find  on  the  index  that  48  Into 
48  cuts  6  threads  per  inch,  then  6  X  4  =  ;i4.  gear  on  stud,  and  IIM  x  4  s  46, 
gear  on  screw.  Any  multipUer  may  be  used  so  long  as  the  products  include 
gears  that  belong  with  the  lathe.  For  instance,  instead  of  4  as  a  multiplier 
we  may  use  6.  Thus,  0  X  6  =  86,  gear  upon  stud,  and  11H  x  6  a  69,  gebf 
upon  screw. 

Bales  tor  Calenlattnff  Simple  and  Comnoand  GeariiUT 
ivhere  tliere  tm  no  Index.  (Am  AfocA.)— If  the  lathe  is  simple- 
geared,  and  the  stud  runs  at  the  same  speed  as  the  spindle,  select  some  giear 
for  the  screw,  and  multiply  its  number  of  teeth  by  the  number  of  threads 
per  inch  in  the  lead-screw,  and  divide  this  result  by  the  number  of  threads 
per  inch  to  be  cut.  This  will  give  the  number  of  teeth  in  the  gear  for  the 
stud.  If  this  result  is  a  fractional  number,  or  a  number  which  Is  not  among 
the  gears  on  hand,  then  try  some  other  gear  for  the  screw.  Or,  select  the 
gear  for  the  stud  first,  then  multiply  its  number  of  teeth  by  the  number  of 
threads  per  inch  to  be  cut,  and  divide  by  the  number  of  threa<is  per  inch  on 
the  lead-screw.  This  will  give  the  number  of  teeth  for  the  gnar  on  the 
screw.  If  the  lathe  is  compound,  select  at  random  all  the  dnving-gears, 
multiply  the  numbers  of  their  teeth  together,  and  this  product  by  the  num- 
ber of  threads  to  be  cut.  Then  select  at  random  all  the  driven  gears  except 
one;  multiply  the  numbers  of  their  teeth  together  and  this  product  by  the 
number  of  threads  per  inch  in  the  lead-screw.  Now  divide  the  first  result  by 
the  second,  to  obtain  the  number  of  teeth  in  the  remaining  driven  gear.  Or, 
select  at  random  all  the  driven  gears.  Multiply  the  numbers  of  their  teeth 
together,  and  this  product  by  the  number  of  threads  per  inch  in  the  lead- 
screw.  Then  select  at  random  all  the  driving-gears  except  one.  Multiply 
the  numbers  of  thetr  teeth  together,  and  this  result  by  the  number  of  threads 
per  inch  of  the  screw  to  be  cut.  Divide  the  first  result  by  the  last,  to  obtain 
the  number  of  teeth  in  the  remaining  driver.  When  the  gears  on  the  com- 
pounding stud  are  fast  together,  and  cannot  be  changed,  then  the  driven  one 
has  usually  twice  as  many  teeth  as  the  other,  or  driver,  in  which  case  in  the 
calculations  consider  the  lead-screw  to  ha  twice  as  many  threads  per  inch 
as  it  actually  nas«  and  then  ignore  the  compounding  entirely.  Some  lathes 
are  so  constructed  that  the  stud  on  which  the  first  driver  is  placed  revolves 
only  half  as  fast  as  the  spindle.  This  can  be  ignored  in  the  calculations  by 
doubling  the  number  of  tnreads  of  the  lead-screw.  If  both  the  last  condi- 
tions are  present  ignore  them  in  the  calculations  by  multiplying  the  number 
of  threads  per  inch  in  the  lead -screw  by  four.  If  the  thread  to  be  cut  is  a 
fractional  one,  or  if  the  pitch  of  the  lead-screw  is  fractional,  or  if  both  are 
fractional,  then  reduce  the  fractions  to  a  common  denominator,  and  use 
die  numerators  of  these  fractions  as  if  thev  equalled  the  pitch  of  the  screw 


966 


THB  MACHINE-SHOR 


to  he  cut,  and  of  the  lead-screw,  refq^ectlvelj.  Then  use  that  part  of  the  rale 
^ven  iit>ov«f  which  applies  to  the  lathe  in  question.  For  inittaiice,  Kuppoae 
It  is  desired  to  cut  a  thread  of  25/82-iDch  pitch,  and  the  I<*ad-screw  lias  4 
threads  per  Inch.  Then  the  pilch  of  the  lead-screw  will  be  U  htcb.  which  is 
equal  to  8/-13  iuih.  We  now  have  two  fraction,  25/J2  and  8/32,  and  tlte  two 
screws  will  be  iu  the  proportion  of  25  to  8,  and  the  firears  cnn  be  flared  by 
the  above  rule,  assuming  the  number  of  threads  to  btf  cut  to  be  8  per  inch, 
and  those  on  the  lead-screw  to  be  :^  per  inch.  But  this  Utter  number  may 
be  further  modified  by  conditions  named  above,  such  an  a  reduced  speed  of 
the  stud,  or  fixed  compound  ffvars.  In  the  iniumoe  given,  if  the  lead-screw 
had  been  fiy%  threads  per  inch,  then  its  pitch  being  4/10  incli,  we  have  the 
fractions  4/10  and  2i/^  which,  reduced  to  a  common  denominator,  are 
64/160  and  ie6/ltiO,and  the  gems  will  be  the  same  as  if  the  lead-ecrew  had  VA 
tlneads  per  inch,  and  the  screw  to  be  out  64  threads  per  inch. 

On  tills  subject  consult  also  '*  Formulas  in  Gearing."  published  by  Brown 
&  Sharpe  Mf^.  Co..  and  Jamiesnn^s  Applied  Mechanics. 

€h«nKa^eara  for  fk;reir«eatUnc  liatliea^^Tbera  is  a  lack  of 
unitormity  auione  lathe-buUders  as  to  the  cbanRe-gears  provided  for  screw* 
cutting.  W.  R.  Macdonald.  in  Am.  Mach,^  April  7,  1892,  proposes  the  follow- 
ing series,  by  which  98  wholo  threads  (not  fractional)  may  ba  cut  by  changes 
of  only  nine  gears: 


i 

Spindle. 

Wboto  Threads. 

& 

80 

40 

60 

00 
4 

70 

1X0 

ISO 

180 

fX> 

6 

4  4/5 

8  3/T 

8  8/11 

1  11/18 

8 

88 

44 

90 

is 

9 

7  1/5 

6 

6  1/7 

8  8/11 

8  10/18 

84 

48 

40 

24 

16 

la 

9  8/6 

8 

6  6A 

4  4/11 

8    9/18 

86 

52 

50 

80 

SiU 

15 

•  •• . 

30 

8  4/7 

6  6/11 

4    8/18 

88 

66 

60 

86 

S4 

18 

14  2/5 

10  2/7 

6  6/11 

6    7/18 

80 

72 

to 

42 

88 

81 

16  4/5 

14 

7  7/11 

6    6/18 

88 

78 

110 

66 

44 

81 

26  2/5 

22 

18  6/7 

, . . , ,  , . 

n 

10    8/11 

8 

86 

190 

?a 

48 

86 

28  4/5 

24 

20  4/7 

18  1/11 

11    1/12 

8 

80 

80 

180 

78 

bi 

89 

81  1/5 

26 

J2  3/7 

14  2/11 

18 

10 

21 

48 

Ten  geai-s  are  sufficient  to  out  all  the  ustuil  threads,  with  the  esoeption  of 
perhaps  11  Vt,  the  standard  pipe-throad;  in  ordinary  practice  any  fractional 
thread  between  11  and  12  will  be  near  enough  for  the  oustomary  shorl  pipe* 
threat! :  if  not,  the  addition  of  a  single  gear  will  give  it. 

In  this  table  the  pilch  of  tlie  lead-screw  is  18*  and  it  may  be  objected  to  as 
too  fine  for  the  purpose.  This  may  be  rectified  by  nuking  the  real  piu-h  6 
or  any  other  desiralile  pitch,  and  ttstabllshiug  the  proper  ratio  between  the 
laihe  spindle  and  the  gear-stud. 

metric  Sore  wihreftda  may  ba  cut  oo  lathes  with  inch-divided  lead- 
ing-screws, by  the  use  of  change-wheels  with  SO  and  187  teeth;  lor  127 
oentl metres  =  bo  inches  (127  X  0.39^7  =  49.9999  in.). 

Bale  for  SettlDK  the  Taper  In  •  Ijatba.  Um.  Jldc^KNo 
rule  oaa  be  given  which  will  produce  exact  results,  owing  to  the  fact  that 
the  centres  enter  the  work  an  indefluite  distance.  If  it  were  not  for  this  cir- 
cunihiauce  the  following  would  be  an  exact  rule,  and  it  is  an  approximation 
as  it  is.  To  Hud  the  distance  to  set  the  centre  over:  Divide  the  difference  hi 
the  diameters  of  the  large  and  small  end  of  the  taper  by  8,  and  multiply  this 
qnotieni  by  the  ratio  \\htch  the  total  length  of  the  shaft  bears  to  the  length 
of  the  tapereil  portion.  Example:  Suppose  a  shaft  three  feet  long  is  to  have 
a  tayter  turned  on  the  end  one  foot  long,  the  Urge  end  of  the  taper  being  two 

inches  and  the  small  end  one  Inch  diameter.      7*-  ■  X  -  =  IJi  Inches. 

Eleetrle  BrUlinK-machlnea  -Speed  of  Drlllinc  Bolea  tn 
Steel  FJates.  U'roc.  Inst.  M.  E.,  Aug.  1887.  p.  829  h-ln  drilling  holes  in 
the  siiell  of  the  S.B.  "Albania,''  after  a  very  small  amount  of  practice  the 
men  working  the  machines  drilled  the  ^-Inch  holes  in  the  shell  with  greet 
rapidity,  doing  the  work  at  the  rate  of  one  hole  every  08  stvonds,  inclosU-n  of 
the  lime  occupied  in  altering  the  position  of  the  maonlnes  by  means  of  differ* 
ential  pnllej*blocks,  which  were  not  convenieaily  arrangcil  as  slings  foi 
this  purpose.  Repeated  trials  of  these  drilling-machines  have  also  shown 
that,  when  ushtg  elroirical  energy  in  both  hOMing^o  magneu  and  mptor 


UILLIKChCUTTEBS. 


967 


Amounting^  to  abont  ^  H.P.,  thej  have  drilled  holeg  of  1  inoh  dlanMter 
throui?h  1^  loch  thickness  of  solid  wrougrht  iron,  or  throu^rb  IK  tseh  of  mild 
sreel  in  two  plates  of  13/16  inch  each,  lakinir  ezacClr  194  mln.  for  each  hole. 
Speed  of  Drills.  (Morse Twisudrill  and  Machine  Connpanv.)— The  fol- 
lowiDK  table  ici^es  the  revolutions  per  minute  for  drills  from  1/16  la.  to  8  In. 
diameter,  aa  usually  applied: 


Diameter 
of 

Speed  for 
Wrought 

^^ 

Speed 
for 

Diameter 
of 

Speed  for 
Wrought 

Speed 
for 

«?r 

Drills,  in. 

Iron  and 
Steel. 

Cast 
Iron. 

Brass. 

Drills,  iD. 

Iron  and 
Steel. 

Cast 
Iron. 

Brass. 

1/16 

1712 

2888 

8544 

1  1/16 

78 

108 

180 

H 

8» 

1191 

1779 

11^. 

6$ 

lOt 

170 

im 

571 

794 

1181 

64 

07 

161 

897 

669 

855 

11/,. 

68 

80 

150 

5% 

SIS 

4fiS 

684 

66 

84 

118 

SMS 

877 

670 

IH 

68 

81 

186 

7/16 

227 

828 

489 

1I/I6 

60 

77 

180 

% 

188 

867 

418 

1^ 

46 

74 

m 

^2* 

168 

8.18 

867 

1  «/16 

44 

71 

117 

147 

S14 

830 

1^ 

40 

66 

118 

11/16 

183 

104 

.300 

I  11/16 

88 

68 

109 

112 

168 

865 

1  ts/W 

87 

61 

106 

13716 

108 

16S 

244 

86 

m 

101 

96 

144 

iUl 

M6/16 

88 

65 

90 

16/16 

89 

184 

218 

80 

68 

06 

76 

116 

191 

2 

31 

51 

00 

One  inch  to  be  drilled  in  soft  cast  Iron  will  usually  require:  for  M<io. 
drill.  160  revolutions;  for  Win.  drill,  140  revolutions;  for9^-in.  drill,  100 
revolutions:  for  1-io.  drill,  i)?>  revolutions.  These  speeds  should  seldom  be 
exceeded.  Feed  per  revolution  for  ^-In.  drill,  .006  ioch:  for  H-lP.  drill, 
.007  inch;  for  ^-in.  drill  .010  inch. 

The  rates  of  feed  for  twist  drills  are  thus  given  by  the  same  company; 
Diameter  of  drill 1/16      M         H      H         H 1  IH 

Revs,  per  Inch  depth  of  hole.  185      125       120  to  140       1  Inob  feed  per  mln, 

SIII«l4lNG-OI7TTBB8. 

Qeorge  Addy,  (Proc.  Inst.  M.  E.,  Oct.  1890.  p.  587),  gives  the  following: 
JLnmXjM^m  of  Bieel.— The  following  are  analyses  of  miUlng-cucter 

blanks,  made  from  best  quality  crucible  cast  steel  and  from  self -hardening 

•»  Ivanhoe  '*  steel : 

CruoibleCast  Steel,         Ivanhoe  Steel, 

per  cent.  per  cent. 

Carbon 1.2  1,67 

Silioon 0.119  0.26S 

Phnephorus 0.018  0.061 

Manganese •       0.86  8.667 

Sulphur 0.08  0.01 

Tungsten 4.66 

Iron,  by  diiference 96.20  90.81 

100.000  100.000 

The  first  analysis  is  of  a  cutter  14  Id.  diam..  1  In.  wide,  which  gave  very 
good  service  at  a  cuttlng-speed  of  60  ft.  per  mln.  Large  miUfng-cutterM  are 
sometimes  built  up,  the  cutting-edges  onlv  being  of  tool  steel.  A  cutter  22  In. 
diam.  by  5>i  in.  wide  has  been  made  In  tnls  way,  the  teeth  being  clamped 
between  two  cast-iron  flanges.  Mr.  Addy  recommends  for  this  form  of 
tooth  one  with  a  cutting-angle  of  70«,  the  face  of  the  tooth  being  set  10"  back 
of  a  radial  line  on  the  cutter,  the  clearance -angle  being  thus  10*.  At  the 
Clarence  Iron -works,  Lieeds,  the  face  of  the  tooth  Is  set  10»  beck  of  the  rndtiU 
line  for  cutting  wrought  Iron  and  80"  for  steel. 

Pitcb  of  Tcetb.— For  obtaining  a  suitable  pitch  of  teeth  for  milling* 
cutters  of  various  diameters  there  exists  no  standard  rule,  the  pitch  being 
nsuall/  decided  In  an  arbitrary  manner,  according  to  IndiTidnal  taste. 


958  THE  KACHINE*3H0P. 

For  esUmatiiiR  Uie  pitch  of  teeth  fn  a  cutter  of  an  j  diameter  from  4  tn.  to  15 
In.,  Mr.  Addy  has  worked  out  the  following  rule,  which  he  has  found  capa- 
ble of  giying  good  results  in  practice: 


Pitch  in  inches  :=  V(diam.  in  inches  x  8)  X  0.0QS5  =  .177  Vdiam. 

J.  H.  Qray  gives  a  rule  for  pitch  as  follows:  The  number  of  teeth  in  a 
milling-cutler  ought  to  be  lOo  times  the  pitch  in  inches;  tliat  is,  if  there 
were  vl  teeth,  the  pitch  ought  to  be  0.S7  in.  The  rules  are  practically  the 
same,  for  if  a  =;  diam.,  n  =  No.  of  teeth,  p  =  pitch,  c  =  circumference,  c  = 

pn\    d=^  =  ?^  =  81.88p«;    p  =  V^WUd  =  .177  i^;  No,  of  teeth,  n,  = 

8.14d  -+-  p. 

NuniD^r  of  Teeth  In  mile  or  Cutters*  (Joshua  Rose.)— The  teeth 
of  cutters  must  obviouslv  be  spaced  wide  enough  apart  to  admit  of  the  enier?  - 
wheel  grinding  one  tooth  without  touching  the  next  one,  and  the  front  faces; 
of  the  teeth  are  always  made  in  the  plane  of  a  line  radiating  from  the  axis  of 
the  cutler.  In  cutters  up  to  8  in.  in  diam.  it  is  good  practice  to  provide  8 
teeth  per  in.  of  diam.,  wnlle  in  cutters  above  that  diameter  the  spaciUK 
may  be  coarser,  as  follows: 

Diameter  of  cutter,  6  hi. :  number  of  teeth  in  cutter,  40 
7  "  »*        •*     * 45 

il  tt  it  Q   it  It  ft  u         it  ti  KQ 

Speed  of  Cutters.— The  cutting  speed  for  milling  was  originally  fixed 
very  low;  but  experience  has  shown  that  with  the  improyements  now  id 
use  it  mav  with  aoTantage  be  oonsiderably  increased,  especially  with  cuttere 
of  large  diameter.  The  following  are  recommended  as  safe  speeds  for  cut- 
ters of  6  in.  and  upwards,  provided  there  is  not  any  great  depth  of  material 
to  cut  away: 

Steel.     Wrought  iron.  Cast  iron.       Brass. 

Feet  per  minute 88  48  60  ISiO 

Feed,  inch  per  mhi...      Vi  I  1%  9^ 

Should  it  be  desired  to  remove  any  large  quantitv  of  material,  the  same 
cutting-speeds  are  still  recommended,  but  with  a  flner  feed.  A  simplt*  rtile 
for  cutting-speed  is:  Number  of  revolutions  per  minute  which  the  cutter 

rdle  should  make  when  working  on  cast  iron  =  240,  divided  by  the  diam- 
of  the  cutter  in  inches. 

Speed  or  BKillins-cnttere.  (Proc.  Inst.  M.  E.,  April,  1883,  p.  248.)- 
The  cutting-speed  whicn  can  be  employed  in  milling  is  much  greater  than 
that  which  can  be  used  in  any  of  the  ordinary  operations  of  turning  in  the 
lathe,  or  of  planing,  shaping,  or  slotting.  A  milling-cutter  with  a  plentiful 
supply  of  oil,  or  soap  and  water,  can  be  run  at  from  80  to  100  ft.  per  min  . 
when  cutting  wrought  iron.  The  same  metal  can  only  be  turned  in  a  lathe, 
with  a  tool-holder  having  a  good  cutter,  at  the  rate  of  SO  ft.  per  min.,  or  at 
about  one  third  the  speed  of  milling.  A  milliug-cutter  will  cut  cast  steel  at 
the  rate  of  25  to  30  ft.  per  min. 

The  following  extracts  are  taken  from  an  article  on  speed  and  feed  of 
milling-cutters  in  Evg'g,  Oct.  22, 1881 :  Milling-cutters  are  successfully  em- 
ployed on  cast  iron  at  a  speed  of  250  ft.  per  min. ;  on  wrought  Iron  at  from 
80  ft.  to  100  ft.  per  min.  The  latter  materials  need  acopious  supply  of  good 
lubricant,  such  as  oil  or  soapy  water,  lliese  rates  or  speed  are  not  ap- 
proached by  other  tools.  The  usual  cutting- speeds  on  the  lathe,  planiD^. 
shaping,  and  sloitins:  machines  rarely  exceed  about  one  third  of  those  given 
above,  and  freauently  average  about  a  fifth,  the  time  lost  in  back  strokes  not 
being  reckoned. 

The  feed  in  the  direction  of  cutting  is  said  by  one  writer  to  vary,  in  ordi- 
nary work,  from  40  to  70  revs,  of  a  4-in.  cutter  per  in.  of  feed.  It  must  always 
to  an  extent  depend  on  the  character  of  the  work  done,  but  the  above  gives 
shavings  of  extreme  thinness.  For  example,  the  circumference  of  a  4-in. 
cutter  being,  say,  12)^  in.,  and  having,  say,  60  teeth,  the  advance  corre- 
sponding to  the  passage  of  one  cutting-tooth  over  the  surface,  in  the  coarser 
of  the  above-named  feed-motions,  is  1/40  x  1/fiO  =  1/MOO  in. ;  the  flner  feed 
gives  an  advance  for  each  tooth  of  only  1/70  X  1/60  =s  1/4900  in.  Such  fine 
feeds  as  these  are  used  only  for  light  finishing  cuts,  and  the  same  author- 
ity recommends,  also  for  finishing,  a  cutter  about  9  in.  in  circumference,  or 
nearly  8  in.  in  diameter,  which  sliould  be  run  at  about  60  revs,  per  nitn.  to 
cut  tough  wrought  steel,  120  for  ordinary  cast  iron,  about  80  for  wrought 


MILLING-MACHINES.  959 

Iron,  and  from  140  to  180  for  the  Tarious  qualtitlee  of  ftun-metal  and  braau 
With  cuctere  smaller  or  largi^r  the  rates  of  revolution  are  Increased  or 
ditniiiisbed  to  accord  with  the  following  table,  which  i^ves  these  rates  of 
cuttiog-speeds  and  shows  the  lineal  speed  of  the  cutting-edge: 

Steel.    Wrought  Iron.    Cast  Iron.    Qun-metaL    Brass. 
Feet  per  minute...       46  00  00  105  180 

Thfse  speeds  are  intended  for  rerj  light  finishing  cuts,  and  they  must  be 
reduced  to  about  one  half  for  heavy  cutting. 

The  following  results  have  been  found  to  be  the  highest  that  could  be  at- 
tained in  ordinary  workahop  routine,  having  due  oonsiidei-ation  to  economv 
and  the  time  taken  to  change  and  grind  the  cutters  when  they  become  dull: 
Wrought  iron— a6  ft.  to  40  ft.  per  min.;  depth  of  cut.  1  in.;  feed,  <^  in.  per 
mill.  Sort  mild  steel— About  ao  ft.  per  min.;  depth  of  cut,  ^  in.;  feed,  9^ 
)ugh  gun-metal— 80  ft.  per  min. ;  depth  of  cut,  y^  in. ;  feed,  91 


in.  per  min.    Tough  gun-metal— 80  ft.  per  min. ;  depth  of  cut,  )4  i;    , 

in.  per  min.    Cast-iron  gear-wheels— 9bV4  ft.  i>er  min.;  depth  of  cut,  ^  in.; 

feed.  ^  in.  per  min.    Hard,  close-grained  cast  Iron— JK)  ft.  per  min.;  depth 


of  cut,  8^  in..*  feed,  6/16  In.  p^r  min.  Gun-metal  Joints,  58  ft.  per  mm.; 
depth  of  cut,  194  in.;  feed,  %  in.  per  min.  Steel  -  bars— :21  ft.  per  min.;  depth 
of  cut,  1/32  in.;  feed,  ^  in.  per  min. 

A  stepped  milling-cutter,  4  in.  In  diam.  and  12  in.  wide,  tested  under  two 
conditionsof  speed  in  the  same  machine,  gave  the  following  results:  The 
cutter  in  both  Instances  was  worked  up  to  its  maximum  speedbefore  it  gave 
way,  the  oblect  being  to  ascertain  definitely  the  relative  amount  of  work 
done  by  a  high  speed  and  a  light  feed,  as  compared  with  a  low  speed  and  a 
heavy  cut.  The  machine  was  used  single-geared  and  double-geared,  and  in 
both  cases  the  width  of  cut  was  10^  in. 

Single-gear,  42  ft.  per  min.;  5/16  in.  depth  of  cut;  feed,  1.8  tn.  per  rain.  =± 
4.16  cu.  in.  per  min.  Double-gear.  19  ft.  per  min.;  ^  in.  depth  of  cut;  feed, 
^  in.  per  min.  =  2.40  cu.  in.  per  min. 

Extreme  Results  irltb  JHlillns-macliIneB.  —  Horace  L. 
Arnold  {Am.  Mach.,  Dec.  28, 1893)  gives  the  following  results  in  fiat-surface 
milling,  obtained  in  a  Pratt  &  Whitnev  milling-machine :  The  mills  for  the 
flat  cut  were  V  diam.,  12  teeth,  40  to  50  revs,  and  i'U,"  feed  per  min.  One 
single  cut  was  run  over  this  piece  at  a  feed  of  O'' per  min.,  but  the  mills 


tr'  feed  per  min.:  Surface  speed,  64  ft.  per  min.;  feed  per  tooth,  0.016";  cuts 
per  inch,  66^. 

At  a  feed  of  4^"  per  min.  the  mills  stood  up  well  in  this  job  of  cast-bx»n 
surfacing,  while  with  a  9''  feed  they  required  grinding  after  surfacing  one 
piece;  in  other  words.  It  did  not  damage  the  mill-teeth  to  do  this  job  with 
123  cuts  per  in.  of  surface  finished,  but  they  would  not  endure  66^  cuts  per 
inch.  In  this  cast-iron  milling  the  surface  speed  of  the  mills  does  not  seem 
to  be  the  factor  of  mill  destruction:  it  is  the  Increase  of  feed  per  tooth  that 
prohibits  increased  production  of  finished  surface.  This  is  precisely  the  re- 
verse  of  the  action  of  single-pointed  lathe  and  planer  tools  in  general:  with 
such  tools  there  is  a  surface-speed  limit  which  cannot  be  economically  ex- 
ceeded for  dry  cuts,  and  so  long  as  this  surface-speed  limit  is  not  reached, 
the  cut  per  tooth  or  feed  can  be  made  anvthing  up  to  the  limit  of  the  drlv- 
ing  power  of  the  lathe  or  planer,  or  to  tne  safe  strain  on  the  work  itself, 
which  can  in  many  cases  be  easily  broken  by  a  too  great  feed. 

In  wrought  metal  extreme  figures  were  obtained  In  one  experiment  made 
in  cutting  key  ways  5/16''  wide  by  ^"  deep  in  a  bank  of  8  shafts  l^"  diam. 
at  once,  on  a  Pratt  &  Whitney  No.  8  column  miiling-machine.  The  8  mills 
were  successfully  operated  with  45  ft.  surface  sp^Ml  and  19^  in.  per  min. 
feed;  the  cutters  were  5"  diam.,  with  28  teeth,  giving  the  following  figureSt 
in  steel:  Surface  speed,  45  fL  per  min.;  feed  per  tooth,  O.OiOsli";  cuts  per 
iuch,  60,  nearly.  Fed  with  the  revolution  of  mill.  Flooded  with  oil,  that  is, 
a  large  stream  of  oil  running  constantly  over  each  mill.  Face  of  tooth 
radial.  The  resulting  keyway  was  described  as  having  a  heavy  wave  or 
cutter-mark  in  the  bottom,  and  it  was  said  to  have  shown  no  signs  of  being 
heavy  work  on  the  cutters  or  on  the  machine.  As  a  result  of  the  experiment 
it  was  decided  for  economical  ttleady  work  to  run  at  17  rev8.,  with  a  feed  of 
4"  per  min..  fiooded  cut,  work  fed  with  mill  revolution,  giving  the  following 
flKures:  Surface  speed,  22^  ft.  per  min.;  feed  per  tooth,  0.0061'';  cuts  per 
inch,  119. 


y60  THE  MACHIKE-SHOP. 

An  etperiment  In  milling  a  wrotigtatlron  eonnectltiff-rod  of  a  locomotfre 
on  a  Pratt  &  Whltner  double-head  inniinr-tnachine  In  described  In  the  Iron 


Age,  Aug.  87, 1891.  The  aiiiount  of  metal  removeil  at  one  cut  meaKtir»*d  3U 
In.  wide  by  1  3/10  In.  de<*p  In  the  groove,  and  acrosB  the  top  U  in.  deep  by  4*1 
in.  wide.    This  represented  a  section  of  nearlr  4^  sq.  in.    This  was  done  at 


the  rate  of  194  i"-  P^^  i^iQ*  Nearly  8  cu.  in.  of  metal  were  cut  up  into  chips 
every  minute.  The  surface  left  by  the  cutter  was  very  perfect.  The  cutter 
moved  in  a  direction  contrary  to  that  of  onlinary  practice;  that  is,  it  cut 
down  from  the  upper  surface  Instead  of  up  from  the  bottom. 

mUlns  <<wftli»)  or  <««i:ftlnst»»  the  Feed^-Tesrs  made  with 
the  Brown  A  Sharpe  No.  5  milling-machine  (described  by  H.  L.  Arnold,  in 
Am.  Mach.,  Oct.  18,  18(M)  to  determine  the  relative  advantage  of  running 
the  milling-cutter  with  or  against  the  feed—**  with  the  feed  **  meaning  that 
the  teeth  of  the  cutter  strike  on  the  top  surface  or  ** scale'*  of  cast-iron 
work  in  process  of  being  milled,  and  ** against  the  feed  ^*  meaning  that  the 
teeth  begin  to  cut  In  the  clean,  newly  cut  surface  of  the  work  and  cut  up- 
wards toward  the  scale— showed  a  decided  advantage  in  favor  of  ninniof? 
the  cutter  asnainst  the  feed.  The  result  is  directly  opposite  to  that  obtained 
In  tests  of  a  Pratt  &  Whitney  machine,  by  experts  of  the  P.  &.  W.  Co. 

In  the  tests  with  the  Brown  &  Sharpe  machine  the  cutters  used  were  6 
inches  face  by  4^  and  8  inches  diameter  respectively,  15  teeth  In  each  mill. 
4^  revolutions  per  minute  in  each  case,  or  nearly  50  feet  per  minute  surface, 
speed  for  the  ^Inch  and  83  feet  per  minute  for  the  8-Inch  mill.  The  revo- 
lution marks  were  0  to  the  inch,  tpving  a  feed  of  7  inches  per  minute,  and  a 
cut  per  tooth  of  .011^'.  When  the  machine  was  forced  to  the  limit  of  its 
driving  the  depth  of  cut  was  11/33  inch  when  the  cutter  ran  in  the  "  old  " 
way,  or  against  the  feed,  and  only  ^  inch  when  it  ran  in  the  **  new  *'  way, 
or  with  the  feed.  The  endurance  of  the  milling-cutters  was  much  greater 
when  they  were  run  In  the  *•  old  *'  way. 

Splntl  in  lllfttK-entters.— There  Is  no  rule  for  finding  the  angle  of 
the  spiral;  from  1U<^  to  15*>  is  usually  considered  sufficient;  irmuch  fiTiDat«*r 
the  end  thrust  on  the  spindle  will  be  Increased  to  an  extent  not  desirable  for 
some  machines. 

miling-K^n  tiers  ixrUli  Inserted  Teeth.— When  It  is  reqnfred  to 
use  milling-cutters  of  a  greater  diameter  than  about  8  In.,  It  is  preferable  to 
Insert  the  teeth  in  a  disk  or  head,  so  as  to  avoid  the  expense  of  making 
solid  cutters  and  the  difficulty  of  hardening  them,  not  merely  becauw  of 
the  risk  of  breakage  In  hardening  them,  but  also  on  account  of  the  difficulty 
In  obtaining  a  uniform  degree  of  hardness  or  temper. 

HEilllnir  •  machine  versus  Plsner.  —  For  comparative  data  of 
work  done  by  each  see  paper  by  J.  J.  Gram.  Trans.  A.  8.  M.  E.,  Ix.  tS/9.  He 
•ays :  The  advantages  of  the  milling  machine  over  the  vlaner  are  many, 
among  which  are  the  following :  Exact  dupllcatiou  of  work;  rapidity  of  pro- 
duction —  the  cutting  being  continuous;  cost  of  production,  as  several 
machines  can  be  operated  by  one  workman,  and  he  not  a  skilled  mechanic; 
and  cost  of  Cools  for  producing  a  given  amount  of  work. 

POWBB  UVlflVMUVa^  FOB  StACHIBIB  TOOI<9. 

Beslstnnee  overcome  In  Cnttlnfc  IS eial*  (Trans.  A.  8.  M.  E., 
vfii.  800. >— Some  experiiuenrs  made  at  the  works  of  William  Sellers  A  Co. 
showed  that  the  resistance  In  cutting  steel  in  a  lathe  would  vary  from 
180,000  to  700,000  pounds  per  square  inch  of  section  removed,  while  for 
east  iron  the  resistance  Is  about  one  third  as  much.  The  power  required  to 
remove  a  given  amount  of  metal  depends  on  the  shape  of  the  cut  and  on 
the  shape  and  the  sharpness  of  the  tool  used.  If  the  cut  is  neariy  squan*  is 
sectloo.  the  power  required  Is  a  minimum;  if  wide  and  thin,  a  maximum. 
Tt»  duinesB  of  a  tool  affects  but  little  the  power  required  for  a  heavy  cuL 

BleaTjr  "Work  on  a  Planer.— Wm.  Sellers  &  Co.  write  as  folknn 
to  the  Anterican  Machinist :  The  XiSV'  planer  table  is  geared  to  run  18  ft.  per 
minute  under  cut,  and  72  feet  per  minute  on  the  return,  which  Is  equivaleot, 
without  allowance  for  time  lost  in  reversing,  to  continuous  cut  of  14.4  f«t 
per  minute.  Assuming  the  work  to  be  28  feet  long,  we  may  take  14  feet  ti 
the  continuous  cutting  speed  per  minute,  the  .8  of  a  foot  being  much  more 
than  sufficient  to  cover  time  loss  in  reversing  and  feeding.  The  machine 
carries  four  tools.  At  %"  feed  per  tool,  the  surface  planed  per  hour  would 
be  85  square  feet.  The  section  of  metal  cut  at  ^'*  depth  would  be  .75"  x 
.l'<25"  X  4  s  .875  square  inch,  which  would  require  approximately  80,000  Ita. 


POWER  BEQTJIBED  FOB  MACHINE  TOOLS. 


961 


freegure  to  remove  IL  The  weiffht  of  metal  removed  per  hour  would  be 
4  X  12  X  .375  X  /^  X  00  =  106S.8  lbs.  Our  earlier  form  of  86"  planer  has 
ivmoved  with  one  tool  on  ^,'*  cut  on  work  900  lbs.  of  meukl  per  hour,  and 
the  120"  uiachiiie  has  more  than  Ave  times  its  capacity.  The  total  pulling 
power  of  the  planer  is  4.S,000  lbs. 

Horse-poirer  Required  to  Run  Ijathea.  (J.  J.  Flather,  Am, 
JtfacA.,  April  ;i3,lti01.)~Tnt»  power  required  to  do  useful  work  varies  with 
the  depth  and  breadth  of  chip,  with  the  shape  of  tool,  and  with  the  nature 
and  ileosity  uf  metal  operated  upon;  and  the  power  required  to  run  a  ma- 
cliiue  empty  is  often  a  variable  quantity. 

For  instance,  when  the  niacliine  is  new,  and  the  working  parts  have  not 
b«'coine  worn  or  fitted  to  each  other  as  tliey  will  be  after  running  a  few 
months,  the  power  irquired  will  be  greater  than  a*iU  be  tha  case  after  the 
running  parts  have  become  better  fitted. 

Another  cause  of  variation  of  the  power  abfiorbed  is  the  driving-belt;  a 
tight  belt  will  increase  the  friction,  hence  to  obtain  the  greatest  efRclency 
or  a  machine  we  should  use  wide  belts,  and  run  them  juMt  tight  enough  to 
prevent  slip.  The  belts  should  also  be  soft  and  pliable,  otherwise  power  is 
consumed  in  bending  them  to  the  curvature  of  the  pulleys. 

A  third  cause  is  the  variation  of  Journal-f  riot  ion,  due  to  slacking  up  or 
tightening  the  cap-screws,  and  also  the  end-thrust  bearing  screw. 

Hartig's  investigations  show  that  it  requires  less  total  power  to  turn  off  a 
given  weight  of  metal  in  a  given  time  than  it  does  to  plane  oft  the  same 
amount;  and  also  that  the  power  Is  less  for  large  than  for  small  diameters. 

The  following  table  gives  the  actual  horse-power  required  to  drive  a  lathe 
empty  at  vary  nig  numbers  of  revolutions  of  main  spindle. 

HORSB-FOWBE  FOB  SlUI<L  LATBIB. 


Without  Back  Gears. 

With  Back  Gears. 

Revs,  of 
Spindle 
per  min. 

H,P. 

required 
to  drive 
empty. 

Revs,  of 

Spindle 

per  min. 

H.P. 

required 

to  drive 

empty. 

Bemarks. 

188.79 

210.06 
869.00 

.146 
.197 
.810 

14.6 
24.88 
88.48 

.126 
.141 
.874 

80"  FItohburg  lathe. 

47.4 
125.0 

188 

.169 
.860 
.838 

4.84 
18.8 
19.8 

.188 
.187 
.830 

Smallla  the  iX^W%  Chern* 
nits.    Germany.     New 
machine. 

54.6 
122 
18S 

.906 
.339 
.456 

6.61 
14.8 
88.1 

.157 
.806 
.949 

\7W  lathe  do.     New 
machine. 

18.8 
54.6 
8-».« 

.066 
.810 
.326 

8.81 
6.72 
10.8 

.085 
.063 
.087 

86"  lathe  do. 

If  H.P.o  =  horse-power  necessary  to  drive  lathe  empty,  and  N^  numbm* 
of  revolutions  per  minute,  then  the  equation  for  average  small  laibes  is 
H.P.o  =  0.093 -f  0.00l2iV. 

For  the  power  necessary  to  drive  the  lathes  empty  when  the  back  gears 
are  in,  an  average  equation  for  lathes  under  80"  swing  is 

H.P.o  =  0.10 -f0.006Jf. 

The  larger  lathes  vary  so  much  in  construction  and  detail  that  no  general 
rule  can  be  obtained  which  will  give,  even  approximately,  the  power  re- 
quired to  run  them,  and  although  the  average  formula  nhows  that  at  least 
0.005  horsepower  Is  needed  to  start  the  Hmall  lathes,  there  are  many  Amer- 
ican lathes  under  80"  swing  working  on  a  consumption  of  less  than  06 
horse- power. 


962 


THE  HACHINE-SHOP. 


The  amount  of  power  required  to  remoTe  metal  In  a  machine  la  determin- 
able within  more  accurate  limits. 

Referring  to  Dr,  Hartig'g  researches,  H.P.i  =  CTT,  where  C  Is  a  constant, 
and  W  the  weight  of  chips  removed  per  hour. 

Average  values  of  O  are  .030  for  cast-iron,  .082  for  wroughtrlron,  .047  for 

The  size  of  lathe,  and,  therefore,  the  diameter  of  work,  haa  no  apparent 
effect  on  the  cutting  power.  If  the  lathe  be  heavy,  the  cut  can  be  increased, 
and  consequently  the  weight  of  chips  increased,  but  the  value  of  C  appears 
to  be  about  the  same  for  a  given  metal  through  several  varying  sizes  of 
lathes. 


Hoaax-FowiB  BsquiRKD  to  bbmote  Cast  Iron  in  a  90-ihch  Laths. 
(J.  J.  Hobart) 


6 

1 

S5 

^ 

« 

d 

1 

I 

u 

M 

% 

1 

S8 

2 

16 

17 

2 

4 

1 

1 

Tool  used. 


Side  tool 

Diamond 

Round  nose 

Left  •  hand    round 

nose 

Square -faced  tool 

V' broad 


itl 

B 

^1 
*^  a 

?5 

^1 

1? 

11 

Be 
111 

ill 

g?S-a 

|5 

g?^ 

^^ 

^Sa 

•§^ 

< 

< 

< 

< 

> 

87.90 

.125 

.015 

.842 

18.80 

.035 

80.50 

.125 

.015 

.218 

10.70 

.030 

42.61 

.125 

.015 

.353 

14.95 

.023 

26.20 

.125 

.015 

.287 

9.22 

.026 

25.82 

.016 

.125 

.265 

9.06 

.02S 

25.27 

.048 

.048 

.200 

10.89 

.018 

25.64 

.125 

.015 

.946 

8.99 

.027 

The  above  table  shows  that  an  average  of  .26  horse-power  is  required  to 
turn  off  10  pounds  of  cast-iron  per  hour,  from  which  we  obtain  the  average 
value  of  the  constant  C  =  .024. 

Most  of  the  cuts  were  taken  so  that  the  metal  would  be  reduced  \i,"  in 
diameter;  with  a  broad  surface  cut  and  a  coarse  feed,  as  In  No.  5,  the  power 
required  per  pound  of  chips  removed  in  a  given  time  was  a  maximum;  the 
least  power  per  unit  of  weight  removed  being  required  when  the  chip  was 
square,  as  in  No.  6. 

Horse-power  required  to  rbvoti  Metal  ik  a  29-nfCH  Laths. 
(R  H.  Smith.) 


II 

HetaL 

II 
1 

5 

a 

5 
la 

III 

II 

I 

Cast  Iron 

12.7 

.05 

.046 

.105 

5.49 

.019 

Cast  iron 

11.1 

.186 

.046 

.217 

12.96 

.017 

Cast  Iron 

12.86 

.04 

.088 

.098 

8.66 

.027 

Wrought  Iron 

0.6 

.08 

.046 

.050 

2.49 

.028 

Wrought  iron 

9.1 

.06 

.046 

.188 

4.72 

.029 

Wrought  iron 

7.9 

.14 

.046 

.186 

9.56 

.019 

Wrought  iron 

9.35 

.045 

.038 

.092 

2.99 

.031 

Steel 

6.00 

.02 

.046 

.048 

1.08 

.012 

Steel 

5.8 

.04 

.046 

.066 

2.00 

.012 

4 

Steel 

5  1 

0« 

.046 

.106 

2.64 

040 

POWER  REQUIRED  FOB  MACHINE  TOOLS.  963 

The  small  values  of  C,  .017  and  .010,  obtained  for  cast  fron  are  probably 
due  to  two  reasons:  the  iron  was  soft  and  of  fine  quality,  known  as  pulley 
metal,  requlrlDsr  less  power  to  cut;  and,  as  Prof.  Smith  remarks,  a  lower 
cuttinsr-speed  also  takes  less  horse-power. 

Hardness  of  metals  and  forms  of  tools  vary,  otherwise  the  amount  of 
chips  turned  out  per  hour  per  horse-power  would  be  practically  constant,  the 
hitrher  cuttinfir-speeds  decreasing  but  sligrhtly  the  visible  work  done. 

Taking  into  account  these  variations,  the  weight  of  metal  removed  per 
hour,  multiplied  by  a  certain  constant,  is  equal  to  the  power  necessary  to  do 
the  work. 

This  constant,  according  to  the  above  tests,  is  as  follows : 

Cast  Iron.  Wrought  Itx>o.  SteeL 

Hartig 080  .002  .047 

Smith .088  .088  .049 

Hobart 084 

Average 080  .000  .044 

The  power  necessary  to  run  the  lathe  empty  will  vary  from  about  .00  to  .3 
H.P.,  which  should  be  ascertained  and  added  to  the  useful  horse-power,  to 
obtain  the  total  power  expended. 

Ponrer  iis«d  by  Blactaine-tools.  (R.  E.  Dinsmore,  from  the  Elec- 
trical World.) 

1.  Shop  shafting  2  S/W  X  180  ft.  at  160  revs.,  carrying  SO  pulleys 

from  6''  diam.  to  86'',  and  running  80  Idle  machine  belts 1 .88  H.P. 

2.  Lodge-Davis  upright  back-geared  drill-press  with  table,  2S^' 
swing,  drilling  %"  hole  in  cast  iron,  with  a  feed  of  1  In.  per 

minute 0.78H.P. 

8.  Morse  twist-drill  grinder  No. :;!,  carrying  2"  x  ^i"  wheels  at  8800 

revs 0.29  H.P. 

4.  Pease  planer  80''  X  S6'^  table  6  ft.,  planing  cast  Iron,  cut  )4" 

deep,  planing  6  sq.  in.  per  minute,  at  9  reversals 1 .06  H.P. 

6.  Shaping-machine  &"  stroke,  cutting  steel  die,  6"  stroke,  ^" 

deep,  shaping  at  rate  of  1 . 7  square  inch  per  minute 0.87  H.P. 

6.  Engine-lathe  17"  swing,  turning  steel  shaft  3%"  diam.,  cut  3/16 

deep,  feeding  7.98  inch  per  minute 0.48  H.P. 

7.  Engine-lathe  81"  sw^ing,  boring  cast-iron  hole  5"  diam.,  cut  3/16 

diam.,  feeding  0.8"  per  minute 0.88  H.P. 

8.  Sturtevant  No.  2,  monogram  blower  at  1800  revs,  per  minute, 

no  piping 0.8  H.P. 

0.  Heavy  pUner  28"  X  88"  X  14  ft.  bed,  stroke  8",  cutting  steel, 
28  reversals  per  minute 8.2  H.P. 

The  table  on  the  next  page  compiled  from  various  sources,  principally 
from  Hartig's  researches,  by  Prof.  J.  J.  Flather  {Avi.  Mach.,  April  12, 1894), 
may  be  used  as  a  guide  in  estimating  the  power  i-equired  to  run  a  given 
machine;  but  it  must  be  understood  that  the»e  values,  although  determined 
by  dyuamoraetric  measurements  for  the  individual  machines  designated, 
are  not  necessarily  representative,  as  tlie  power  required  to  drive  a  machine 
itself  is  dependent  largely  on  its  particular  design  and  construction.  The 
character  of  the  work  to  be  done  may  also  affect  the  power  required  to 
operate;  thus  a  machine  to  be  used  exclusively  for  brass  work  mav  be 
speeded  from  lOjC  to  lb%  higher  than  if  it  were  to  be  used  for  iron  work  of 
similar  size,  and  the  power  required  will  be  proportionately  greater. 

Where  power  is  to  be  transmitted  to  the  machines  by  means  of  shafting 
and  countershafts,  an  additional  amount,  varying  from  80|;e  to  60)(  of  the  total 
power  absorbed  by  the  machines,  will  be  necessary  to  overcome  the  friction 
of  the  shafting. 

Horse-poorer  required  to  driTe  ShafUns.— Samuel  Webber. 
In  his  *•  Manual  of  Power  "  gives  among  numerous  tables  of  power  required 
to  drive  textile  machinery,  a  table  of  results  of  tests  of  shafting.  A  line  of 
2>^"  shafting,  348  ft.  long,  weighing  4098  lbs.,  with  pulleys  weighing  5331  lbs., 
or  a  total  of  9489  lbs.,  supported  on  47  bearings,  816  revolutions  per  minute, 
requii-ed  1.858  H.P.  to  drive  it.  This  gives  a  coefficient  of  friction  of  5.58j(. 
In  seventeen  tests  the  coefllcieut  ranged  from  8.84j(  to  11 .4](,  averaging 
5.7;W. 


964 


THE  KACniK&-SHOP. 


HoraenN^^v'er  He^aii^a  to  DrlTe  HaeldiMVT* 


Obaarved  Hone-power. 


Name  of  Machine. 


'  swing,  B.  a. 


Small  screw-cutting  latbe  13] 
8crew*cuttlng  lathe  17^",  B. 
Screwcutcing  lathe 'M"  (Fitotiburg),  B.  Q 
Screw-cutting  lathe  SO^',  B.  G 


Lathe,'*)"  face  plate,  will  8wrng*l(J8"'/T.  Q.' 
Large  facing  lathe,  will  twhjg  Ol",  T.  O 


Wheel  lathe  60"  swing.  

Small  ihaper  (stroke  4",  traverse  11") 

Small  Hhaper«  Richards  (M^"  x  29") 

Shaper  (16"  stroke  Qould  &  Eberliardt) 

Large  shaper,  Richards  (29"  x  91") 

Crank  planer  (capacity  88"  x  S7"  x  S6U"  stroke). 

Planer  (capacity  »'X  86"  X  11  feet) 

Large  planer  (capacity  W  X  W"  X  87  feet 

Small  drill  press 

TTpright  slot  drilling  mach.  (wiU  drill  f^'*  dlam.).. . 

Medium  drill  press 

Large  drill  press 

Radial  drffl  6  feet 


Radial  drffl«  feet  BWlog 

ftadial  drills  feet  swing 

Radial  driU  press Tt. 

aiottar  (8"  ^oke) 

Siotter  (9U"  stroke) 

Stotter  (ly' stroke) 

Universal  milling  maoh  (Brown  &.  Sharpe  No.  1).. . . 

Milling  machine  (IS"  cutter-head,  IS  cutters) 

Small  head  traversing  mlUiog  machine  (cutter-head 


11"  diameter,  16  cutters) 

Gear  cutter  wiU  cut  20"  diameter 

Eoriaoiital  boring  machine  for  iron,  88^"  swing. . . . 

Hydraulic  shearing  machine 

Large  plate  shears— knives  S8"  long,  8"  stroke 

Large  punch  press,  over-reach  28",  8"  stroke,  t^" 

stock  can  be  punched 

Small  punch  and  shear  combM,  7U"  knives.  !>{"  str. 
Circular  saw  for  hot  Iron  (SOU"  diameter  of  saw). . . 
Plate-bending  rolls,  diam.  oil  roUs  18",  length  9^  ft. 
Wood  planer  18U"  (rotary  knives,  2  horn  2^ vert 

Wood  planer  24"  (rotary  knives) 

Wood  planer  17U"  (rotary  knives) 

Wood  planer  28''^  (rotary  Knives) 

Wood  planer  28"  (DaniePs  pattern) 

Wood  planer  and  matcher  (capacity  U}i  x  4^"). .. 

Circular  saw  for  wood  (28"  diameter  of  saw) 

Circular  saw  for  wood  (85"  diameter  of  saw) 

Band  saw  for  wood  (84"  band  wheel) 

Wood-raortlsing  and  boring  machine 

Hor'I  wood-boring  and  mortising  machine,  drill  4' 

diam..  mortise  6^  deep  X  llH"  long 

Tenon  and  mortising  machine 

Tenon  and  mortising  machine.  

Tenon  and  mortising  machine 

Bdge-molder  and  shaper.    (Vertical  spindle) 


Wood-molding  mach.  (cap.  7J4  x  2^).    Hor.'  spindle 
Grindstone  for  tools,  81 ''diam.,  6"  face.    "" 


,         .     V<docity 

680  ft.  per  minute 

Grindstone  for  stock,  42"  X12".    Vel.  1680  ft.  per  min, 
Rmery  wheel  11^"  diameter  X  14".    Saw  grinder. 


Total 
Work. 


0.41 

0.867 

0.47 

0.462 

0.S3 

0.91 

0.16 
0.24 
0.68 
1.14 
0.24 
084 
1.47 
0.68 
0.41 
1.88 
1.24 
0.58 
0.67 
1.08 
0.28 
0.44 
0.95 
0.28 
0.66 

0.18 
0.28 

0.98 

1.92 
7.12 

4.41 
0.79 
4.12 
2.70 
4.84 
8.(0 
4.63 
5.00 
8.20 
6.91 
8.23 
5.64 
0.96 
0.49 

8.68 
2.11 
2.78 
2.25 
2.00 
2.45 

1.55 
8.11 
0.66 


Running  Light. 


0.18: 0.15*-O.84t 
0.207;  0.16^.406 
0.12;  O.IS  to  0.81 
0.05;  0.08  to 0.33 
0.187;  0.12to0.66 
0.87;  0.89  to  0.81 
0.28  to  3.40 
0.06«  to  0.e6 
0.07;  a07  to  0.13 
0.21  ;a01  to  0.47 
0.26;  0.15  to  0.;3 
0.12;  0.12  to  0.4C 

0.«7 

0.60 

0.80 
0.15;  0.15  to  0.43 

0.62 

0.62 

0.44;0.1»-0.44t 

0.80;  0.12*^.biit 

0.46 
0.09;  0.05  tOd.es 
0.32;  0.15  to  0.65 
0.57;  0.48  too  91 
0.01:000^-0.13 
0Jt6;  0.26  to  0.55 

0.10 
0.11 

0.12;  0.10-0.12*; 

0.10  to  0.25t 

087 

0.67 

1.00 
0.16 
0.61 
.54 
3.85 
1  tt 
1.25 
0.74J-0-17I 
1.45 
4.18 
0.70 
1.16 
0,1« 
0.84 

1.67;  0.C5  to  3.0 
l.tt 
0.61 
2.17 
1.80 
2.00 

0.32 
C.94 
0.40 


♦  With  back  gears,    t  Without  back  gears.    $  For  surface  cutters.    fWlth 
Bide  cutters.    B.  G.,  back-geared.    T.  G..  triple-geared. 


ABBASIVB  rUOC ESSES. 


965 


Itors««power  consumed  tn  Macblne««liopa*--How  much 
powf  1*  U  i-«qulr<*d  to  driv«»  oitliuai'y  iimobitie-tuoialf  and  how  many  men  can 
be  employed  per  horse-power?  axe  quoKiiuos  which  it  in  imponsible  to  auawer 
by  any  fixed  rule.  The  power  Taries  ijeatly  according  to  the  conditions  tn 
each  shop.  The  followioff  table  gi?en  bv  J.  J.  Flather In  his  work  on  Djrna- 
mometers  gives  an  idea  ol  the  variation  in  several  large  works.  Tlie  peroen- 
tage  of  the  total  power  required  to  drive  the  shafting  varies  from  15  to  80, 
and  the  number  of  men  eniployed  per  total  H.P.  varies  from  0.68  to  O.Oi. 

Home-po'wers  Friction;  Men  Employed* 


Name  of  Firm. 


lAneABodley E.&W.W, 

J.  A.Fay&  Oo W.  W 

Union  Iron  Works EL,M.  M 

Frontier  Iron  A  Brass  W'ks  M.  E.,  etc, 

Taylor  Mfg.  Co £. 

Baldwin  Loco.  Works L. 

W.  Sellers  &  Co.  <one  de- 
partment)        H.  U. 

Fond  Machine  Tool  Co  . . .        M.  T. 
Pratt  ft  Whitney  Co. . . 
Brown  &  Sharpe  Co. . . 

Yale  A  Towne  Co 

Ferraoute  Machine  Ca 

T.  B.  Wood's  Sons 

Bridgeport  Forge  Co  . . 

Singer  Mfg.  Co 

Howe  Mfg.  Co 

Woixsester  Maoh.  Screw  Oo 
Hartford        •*          " 
NicbolBon  File  Co 


Averages 1^46.4 


Kind 

of 
Work. 


C.ftU 

P.  &D. 

P.  &S. 

H   F. 

S.M. 

M.S. 


Horse-power. 


11 


15 
06 

8 

«000 


58 
100 
400 

25 

96 

ssoo 
loe 

180 
120 
280 
136 

8S 

12 
150     75 

laoo 

8S0 
40 
400   100 
850 


75 


300 


50 


-ft* 


1500 
80 
850 
400 


8.«7 
3.00 
4.00 
O.fO 
2.42 
1.04 


182 

800 
1600 

150 

880 
4100 

800 

432 
725 

0008. 
7005 

002 

80  2 

180    .86 

85008.60 


36.6^818.3  2.96   5.18 


I 

i 


8.58 
5.f4 

8.89 

8.80 

4.8T 
4.11 


10.26 
8.76 


1.78 


Abbreviations:  E..  engine:  W.W.,  wood-working  machinery;  M.  M.,  min- 
ing machineir;  M.  £.,  manne  engines;  L.,  locomotives;  H.  M.,  heavy  ma- 
chinery; M.  T.,  machine  tools:  C  &  L.,  cranea  and  locks;  P.  &  D.,  presses 
and  dies;  P.  &  S.,  pulleys  and  shafting;  H.  F.,  heavy  forgirigs;  8.  M.,  sewings 
machines;  M.  S„  machine-screws:  F.,  files. 

J.  T.  Henthorn  states  (Trans.  A.  8.  M.  £.,  vl.  468)  that  tn  print-mills  which 
he  examined  the  friction  of  tho  shafting  and  engine  was  in  7  caws  below 
90%  and  in  85  cases  betwi^en  20|t  and  80^  in  11  casen  from  90%toi»%  and  In  8 
cases  above  85^,  the  average  being  26.9%.  Mr.  Barras  in  eight  cotton-mills 
found  the  range  to  be  between  l¥%  and  25.7^,  the  average  being  82jt.  Mr. 
Flather  believes  that  for  shops  using  heavy  machinery  the  percentage  of 
power  required  to  drive  the  shafting  will  avemge  from  40%  to5l^  of  the  total 
power  expended.  This  presupposes  that  under  the  head  of  shafting  are 
uicluded  elevators,  fans,  and  blowers. 

AKRA8ITB  PROCBSSBS* 

Abrasive  cutting  is  performed  by  meaim  of  stones,  sand,  emerr.  glass, 
oorundum,  carborundum,  crocus,  rouge,  chilled  globules  of  Iron,  ami  in  some 
caseH  by  soft,  friable  iron  alone.  (See  paper  by  John  Richards,  read  before 
the  Technical  Society  of  the  Pacific  0>aKt,  Am.  Mach.t  Aug.  80, 1891,  and 
Eng.  db  M.  Jow^  Ja&  »  and  Aug.  15. 1801.  i 


966  THE  MACHINE-SHOP. 

Tlie  **  Cold  Sa^v*"— For  sawtnK  any  Bection  of  Iron  trblle  cold  thci 
cold  saw  is  sometimes  used.  This  consists  simply  of  a  plain  soft  6t<^l  or 
iron  disk  without  teeth,  about  48  Inches  diameter  and  8/16  inch  thiclc.  The 
velocity  of  the  circumference  Is  about  16,000  feet  per  minute.  One  of  the^e 
saws  will  saw  through  an  ordinary  steel  rail  cold  in  about  one  minute.  In 
this  saw  the  steel  or  iron  is  ground  off  by  the  friction  of  the  disk,  and  is  not 
cut  as  with  the  teeth  of  an  ordinary  saw.  It  has  generally  been  found  more 
profitable,  however,  to  saw  iron  with  disks  or  band-saws  fitted  with  cuuing- 
leeth,  which  run  at  moderate  speeds,  and  cut  the  metal  as  do  the  teeth  of  a 
milling-ciuter. 

Bees«'s  FoslnfE^dlsk.— Beese^s  fusing-disk  is  an  application  of  the 
cold  saw  to  cutting  iron  or  steel  in  the  form  of  bars,  tubes,  cylinders;,  etc.. 
in  which  the  piece  to  be  cut  is  made  to  revolve  at  a  slower  rate  of  speed 
than  the  saw.  By  this  means  only  a  small  surfsce  of  the  bar  to  be  cut  is 
presented  at  a  time  to  the  circumference  of  the  saw.  The  saw  Is  about  the 
same  size  as  the  cold  saw  above  described,  and  is  rotated  at  a  velocity  of 
about  85,000  feet  per  minute.  The  heat  generated  by  the  friction  of  this  saw 
against  the  smaH  surface  of  the  bar  rotated  against  It  is  so  gi-eat  that  the 
particles  of  Iron  or  steel  in  the  bar  are  actually  fused,  and  the  **  sawdust  ** 
welds  as  it  falls  into  a  solid  mass.  This  disk  will  cut  either  cast  iron,  wrought 
li-on.  or  steel.  It  will  cut  a  bar  of  steel  19^  inch  diameter  in  one  minute.  In- 
cluding the  time  of  setting  it  in  the  macnme,  the  bar  being  rotated  about 
aOO  turns  per  minute. 

Cattlnn:  Stone  y^rtth.  Wire*— A  plan  of  cutting  stone  by  means  of  a 
wlr»^  cord  has  been  tried  m  Europe.  While  retaining  sand  as  the  cutting 
agent,  M.  PauUn  Gay,  of  Marseilles,  has  succeeded  in  applying  it  by  mechan- 
ical means,  and  as  continuously  as  formerly  the  sand-blast  and  band-saw. 
with  both  of  which  appliances  his  system— that  of  the  "helic<»idal  wire 
cord  ^*— has  considerable  anali^^.  An  engine  puts  in  motion  a  continuous 
wire  cord  (varying  from  five  to  seven  thirty-seconds  of  an  inch  in  diameter, 
according  to  the  work),  composed  of  three  mild-steel  wires  twisted  at  a  cer- 
tain pitch,  that  is  found  to  give  the  best  results  In  practice,  at  a  speed  of 
from  15  to  17  feet  per  second. 

The  Sand-blast.— Ill  the  sand-blast,  invented  by  B.  F.  Tllghman,  of 
Philadelphia,  ana  first  exhibited  at  the  American  Institute  Fair,  New  York, 
in  1871,  common  sand,  i>owdered  quartz,  emery,  or  any  sharp  cutting  mate* 
rial  is  blown  by  a  jet  of  air  or  steam  on  glass,  metal,  or  other  comparatirely 
brittle  substance,  by  which  means  the  latter  is  cut,  drilled,  or  euKraved 
To  protect  those  portions  of  the  surface  which  It  is  desired  sliall  not  lje 
abraded  it  is  only  necessary  to  cover  tliem  with  a  soft  or  tough  material, 
such  as  lead,  rubber,  leather,  paper,  wax,  or  rubber-paint.  (See  description 
in  App.  Cyc.  Mech. ;  also  U.  S.  report  of  Vienna  Exhibition,  1873,  vol.  lii.  Si 6.) 

A  "  jet  of  sand  ^*  impelled  by  steam  of  moderate  pressure,  or  even  b^'  the 
blast  of  an  ordinarv  fan,  depolishes  glass  in  a  few  seconds;  wood  is  cut  quite 
rapidly;  and  metals  are  given  the  so-called  "frosted"  surface  with  great 
rapidity.  With  a  Jet  issuing  from  under  800  pounds  pressure,  a  hole  was 
cut  through  a  piece  of  corundrum  1V4  inches  thick  in  2o  minutes. 

The  sand-blast  has  been  applied  to  the  cleaning  of  metal  castings  and 
sheet  metal,  the  graining  of  zinc  plates  for  lithographic  purposes,  the  frost- 
ing of  silverware,  the  cutting  of  figures  on  stone  and  glass,  and  the  cutting 
of  devices  on  monuments  or  tombstones,  the  recuiting  of  files,  etc.  The 
time  required  to  sharpen  a  worn-out  14-lnch  bastard  file  is  about  four 
minutes.  About  one  pint  of  sand,  paased  through  a  No.  180  sieve,  and  four 
hoi-se-power  of  OO-lb.  steam  are  required  for  the  operation.  For  clear. n;; 
castings  compressed  air  at  from  8  to  10  pounds  pressure  per  square  Incii  is 
employed.  Chilled-iron  globules  instead  of  quarts  or  flint-sand  are  used 
witti  good  results,  both  as  to  speed  of  working  and  cost  of  material,  when 
the  operation  can  be  carried  on  under  proper  conditions.  With  the  exp**ii« 
diture  of  2  horse-power  in  compressing  air,  S  square  feet  of  ordinary 
scale  on  the  surface  of  steel  and  iron  plates  can  be  removed  per  minute. 
Tiie  sui*face  thus  prepared  is  ready  for  tinning,  galvanizing,  plating,  bronz- 
ing, painting,  etc.  By  continuing  the  operation  the  hard  skin  on  the  surface 
of  castings,  which  Is  so  destnictive  to  the  cutting  edges  of  milling  nnd 
other  tools,  can  be  removed.  Small  castings  are  placed  in  a  ^o^t•  cf  slowlv 
rotating  barrel,  open  at  one  or  both  ends,  through  which  the  blast  is 
directed  downward  against  them  as  they  tumble  over  and  over.  No  portion 
of  the  surface  escapeii  the  action  of  the  sand.  Plain  cored  work,  such  as 
valve-bodies,  can  Ite  clean  ini  peifectly  both  Inside  and  out.  100  lbs.  of  cast- 
ings can  be  cleaned  in  from  10  io  15  niinutes  with  a  blast  created  by  2  horse- 


EMERT-WHEELS  AND  GBINDSTOKES. 


967 


power.    The  same  weifirht  of  small  for^n^  and  stampings  can  be  scaled  In 
from  80  to  90  minutes.— /rou  Age,  March  8, 1894. 

Eia[EBT-WHEEI.S  AND  GRINDSTONES. 

Tlfte  Selection  of  Emersr-nrtaeels*— A  pamphlet  entitled  **  Emery* 
wheels,  their  Selection  and  Use,"  published  by  the  Brown  &  Sharpe  Mf|?. 
Co.,  after  callinf?  attention  to  the  fact  that  too  much  should  not  be  expected 
of  one  wheel,  and  commenting  upon  the  importance  of  selecting  the  proper 
wheel  for  the  work  to  be  done,  says : 

Wheels  are  numbered  from  coarse  to  line:  that  Is,  a  wheel  made  of  No. 
60  emery  Is  coarser  than  one  made  of  No.  100.  Within  certain  limits,  and 
othet  things  being  equal,  a  coarse  wheel  Is  less  liable  to  change  the  tem- 
perature of  the  work  and  lees  liable  to  glaze  than  a  fine  wheel.  As  a  rule, 
the  harder  the  stock  the  coarser  the  wheel  required  to  produce  a  given 
fliiish.  For  example,  coarser  wheels  are  required  to  produce  a  glren  sur- 
face upon  hardened  steel  than  upon  soft  steel,  while  finer  wheels  are  re- 
quired to  produce  this  surface  upon  brass  or  copper  than  upon  either 
hardened  or  soft  steel. 

Wheels  are  graded  from  soft  to  hard,  and  the  grade  is  denoted  by  the 
letters  of  the  alphabet,  A  denoting  the  softest  grade.  A  wheel  is  soft  or 
hard  chiefly  on  account  of  the  amount  and  character  of  the  material  com- 
bined in  its  manufacture  with  emery  or  corundum.  But  other  character- 
istics being  equal,  a  wheel  that  Is  composed  of  fine  emery  Is  more  compact 
and  harder  than  one  made  of  coarser  emery.  For  Instance,  a  wheel  of  No. 
100  emerr,  grade  B,  will  be  harder  than  one  of  No.  00  emery,  same  grade. 

The  softness  of  a  wheel  is  generally  its  most  Important  charactenstlc.  A 
soft  wheel  is  less  apt  to  cause  a  change  of  temperature  in  the  work,  or  to 
become  glazed,  than  a  harder  one.  It  is  best  for  grinding  hardened  steel, 
cast-iron,  brass,  copper,  and  rubber,  while  a  harder  or  more  compact  wheel 
is  better  for  grinding  soft  steel  and  wrought  iron.  As  a  rule,  other  things 
being  equal,  the  haraer  the  stock  the  softer  the  wheel  required  to  produce 
a  given  finish. 

Generally  speaking,  a  wheel  should  be  softer  as  the  surface  in  contact 
with  the  work  Is  Increased.  For  example,  a  wheel  1 /Id-Inch  face  should  be 
harder  than  one  U-inch  face.  If  a  wheel  Is  hard  and  YieAtA  or  chatters,  It 
can  often  be  made  somewhat  more  effective  by  turning  off  a  part  of  its 
cutting  surface;  but  it  should  be  clearly  understood  that  while  this  will 
sometimes  prevent  a  hard  wheel  from  heating  or  chattering  the  work,  such 
a  wheel  will  not  prove  as  economical  as  one  of  the  full  width  and  proper 
grade,  for  it  should  be  borne  in  mind  tliat  the  grade  should  always  bear  rhe 
proper  relation  to  the  width.  (See  the  pamphlet  referred  to  for  other  in- 
formation. See  also  lecture  by  T.  Dunkin  Paret.  Preset  of  The  Tanite  Co., 
on  Emery-wheels.  Jour.  Frank.  Inst.,  March,  1890.) 

Speed  of  Emery "nrheeln*— The  following  speeds  are  reoommended 
by  different  makei-s : 


^S 

Revolutions  per  minute.        1 

-4 

SI 

Revolutions  per  minute. 

u 

pi 

0 

¥. 

E6 

1-1 

z^ 

15 

4 

ill 

§8 

*^?J 

fe« 

_&_ 

&^ 

- 

"^ 

}^» 

& 

6^ 

1 

Itf.OOO 

10 

1,050 

2.160 

2,200 

2,200 

iH 

12,500 

V4,466 



12,000 

12 

1.600 

1,800 

1,800 

1,850 

2 

ft.500 

10.800 



10.000 

14 

1,400 

1,570 

1,600 

1,600 

2H 

7.600 

8.640 



8,r,oo 

16 

1,200 

1,850 

1,400 

1,400 

3 

6,400 

7,«K) 

7,400 

7,400 

18 

1,060 

1,222 

1,260 

1,250 

4 

4,800 

6,400 

5,400 

6,4.'iO 

20 

950 

1,080 

1,100 

1,100 

5 

8.800 

4,H20 

4.400 

4,400 

22 

875 

1.000 

1,000 

1,000 

6 

8.'^ 

3,600 

3,600 

8,600 

24 

800 

917 

925 

925 

7 

2.700 

8,080 

^,'^oo 

8,150 

26 

750 

600 

825 

8 

2.400 

2,700 

2,700 

2.750 

30 

676 

733 

600 

785 

9 

2,150 

2,400 

2.400 

2,4.')0 

:^ 

5.50 

611 

400 

560 

•'We  advise  the  regular  speed  of  5500  feet  per  minute.'*    (Detroit  Emery- 
wheel  Co.) 
"Experience  has  demonstrated  that  there  is  no  advantage  in  running 


968 


THE  XACBINE-SBOP. 


16 

t* 

SO 

M 

t« 

30 

86 

i« 

40 

46 

•* 

60 

70 

*i 

80 

00 

** 

100 

aolld  emeiy-wbeoto  at  a  higher  rate  (ban  6500  feet  per  minuU  peripheral 

speed.*'    (Springfield  E.  W.  Mf|r.  Co.) 

**  Althoufi^h  there  is  no  exactly  defined  limit  at  which  a  wheel  must  be  run 
to  render  it  effective,  experience  has  demonstrated  that,  taking  into  account 
safety,  durability,  and  liability  to  heat,  6600  feet  per  minute  a(  the  periphery 
Rives  the  best  results.  All  flrst-daas  wheels  have  the  number  of  revolutions 
necessary  to  fi^ive  this  rate  marked  on  their  labels,  and  a  column  of  fif  uros 
in  the  pnce-list  gives  a  coiTespondiog  rate.  Above  this  speed  all  wheels 
are  unsafe.  If  run  much  below  it  they  wear  away  rapidly  in  proportion  to 
what  they  accomplinh/*    (Northampton  E.  W.  Oo.) 

Ctr»de«  of  Bmeryc—The  numbers  representinic  the  grades  of  emery 
run  from  8  to  VM).  iind  tbe  decree  of  smoothnees  of  surface  they  leave  may 
be  compared  to  that  It^f  t  by  files  as  follows: 

8  snd   10  represent  the  cut  of  a  wood  rasp. 

"   "     ^  ••         .4     .»    «»  a  coarse  rough  Ale. 

u        u     »»    »»  0Q  ordinary  rough  flleb 
M        »     •»    •»  a  bastard  file. 
**        •*     "    *•  a  second-cut  file. 
»•        "     ••    "  a  smootli         »» 
"        ••     "    "  a  superfine      •* 
1«0  P  and  FF      ••        ••     ••    ♦•  a  dea<i-smooth  file. 

Speed  ofPoltalilnir-wbeeto* 

Wood  covered  with  leather,  about  7000  f  t.  per  mlDuU 

**  "  **     a  hair  bi-ush,  about 2500  rev«.  for  lartest 

•*  •*       lH"to8"diam.,hairl"fcolM"long,ab.  4600   "      « eniallest 

Walrus*hide  wheels,  about 8000  ft.  per  minutt* 

RacT'Wheels,  4  ^o  8  in.  diameter,  shout 7000  "     "         ** 

SAfe  Speeds  for  Grlndstonea  and  Smeryvivlieelaf^O.  D. 
Hiscoz  (Iron  Agn,  April  7, 18K2),  by  an  application  of  the  foriiiuiafor  ct»Dtrif- 
ugal  force  in  fly-wheels  (see  Fly -wheels),  obtains  the  figures  for  strains  in 
grindstones  and  emery-wheels  which  ai-e  given  in  the  tablee  helow.  Bis 
formuleB  are: 
Stress  per  sq.  in.  of  section  of  a  grindstone      =  (.7071  DxJf)*X  .00007B6 

••       "    ** an  emery-wheel  s  (.7071/>  X  ^)»  X  OOOlOttB 

Z>  ^  diameter  in  feet,  N  =  revolutions  per  minute. 

He  takes  the  weight  of  sandstone  at  .078  lb.  per  cubic  Inch,  and  that  of  an 
eniery-wheel  at  0.1  lb.  per  cubic  inch;  Ohio  stone  weighs  about  .061  lb.  and 
Huron  stone  about  .080  lb.  per  cubic  inch.  The  Ohio  stone  will  bear  a  s»i«tHl 
at  the  periphery  of  2500  to  3000  ft.  per  min.,  which  latter  should  never  be 
exceeded.  The  Huron  stone  can  be  ti-usted  up  to  4000  ft.,  when  properly 
clamped  between  flanges  and  not  excessively  wedged  in  setting.  Apart 
from  the  speed  of  grindstonee  as  a  cause  of  bursting,  probably  the  majoritj 
of  accidents  have  really  been  caused  by  wedging  them  on  the  shaft  and  over 
wedging  to  true  them.  The  holes  being  square,  the  excessive  driving  oi 
wedges  to  true  the  stones  starts  cracks  in  tne  comers  that  eventually  run 
out  until  the  centrifugal  strain  becomes  greater  than  the  tenacity  of  tlic 
remaining  solid  stone.  Hence  the  necessity  of  great  caution  in  the  use  oi 
wedges,  as  well  as  the  holding  of  large  quick-running  stones  between  large 
flanges  and  leather  washers. 

Slralns  in  Orlndstonea* 

Limit  of  VsijoorrT  and  Approxihatv  acttual  Strain  per  SqrARB  Inch  oi 

Sectional  Arsa  for  Qrindstones  of  Mediuv  Tbnsilb  Strbkoth. 


Diam- 

Revolutions per  minute. 

eter. 

100 

160 

200 

250 

800 

350 

400 

feet. 
4^ 

lbs. 
1.58 
S.47 
8.57 
4.86 
6.85 
8.04 
0.03 
14.30 
19.44 

lb8. 
8.57 
5.57 
8.04 
10.93 
14.30 
1808 
2-^.34 
33.17 

lbs. 
6..% 
9.88 
14.28 
19.44 
27.37 
34.16 

lbs. 

0.98 
15.49 
22.34 
80.38 

lbs. 
14.80 
28.80 
83.16 

lbs. 
18.36 
28.64 

lbs. 
25. 4« 
89.75 

5^ 

6 

7 

Approximate  bresking  strain  tei 
times  the  strain  for  sise  opposiu 
the  bottom  figure  in  each  column. 

EMERY-WHEELS  AKD   GRINDSTONES. 


9C9 


Thi)  flfCuraB  at  the  bottom  of  columns  desiKnate  the  limit  cf  Telocity  (in 
revolutions  per  minute),  at  the  head  of  the  cohmmfi  for  stones  of  rbe  diam- 
eter in  the  nrst  column  opposite  the  designatluK  flRure. 

A  general  rule  of  safety  for  any  size  grindstone  that  has  a  compact  and 
strong  grain  is  to  liuiit  the  peripheral  velocity  to  47  feet  per  second. 

There  is  a  large  variation  In  the  listed  speeds  of  emerj-wheelA  by  different 
mAl(er»'-40nO  as  a  minimum  and  5600  maximum  feet  per  niinule,  while 
othet-8  claim  a  maximum  Rpeed  of  aO.OOO  feet  per  minute  as  the  safe  siieed 
of  their  beet  emerv-wheels.  Rim  vrheels  and  iron  centre  wheels  are  special* 
ties  that  require  the  maker's  guarantee  and  assignment  of  speed. 

Strains  In  Bmery-nrlieels. 

Actual  Strain  pkr  S^uark  IhXB  of  Sbctiok  in  Emkry-wheels  at  thb 

Vblocitiks  at  Head  op  CoLuincs  for  Sizes  in  First  Column. 


ii 

Revolutions  per  minute. 

600 

800 

1000 

1200 

1400 

1600 

1800 

2000 

2200 

2400 

2600 

4 
0 



22.67 
51.18 
00.71 
141.90 

27.48 
61.86 
109.76 
171.71 

32.64 
78.6-2 
180.62 

88.81 
86  40 

8 
10 

'i8.46 
24.80 
82.57 
41.41 
60.08 
61.81 
78.62 
86.86 
115.04 
165.64 

48.iX) 
67.86 
78.62 
90.28 
109.41 
180.88 
162.85 

22.87 
85.47 

51.12 
68.70 
90.24 
115,03 
141.22 
171.23 

32  65 

51.08 
7:}.  62 
99.21 
130.31 
165.65 

44.45 
60.51 
100.21 

58.05 
00.81 
180.88 

78.47 
114.94 
165.66 

1f»8.80 

12 

..     .. 

Diam 

1ft 

177.80 

Revs,  per 

18 

min. 

90 

in. 

2800 

9^ 

8000 

24 

**  ' 

4 

6 
6 

44.48 
100.21 
177.80 

51.12 

no 

115.08 

36 



Joshua  Rose  (Modem  Machine-shop  Practice)  says:  The  average  speed  of 
grindstones  in  worksliops  may  be  given  as  follows: 

Circumferential  Speed  of  Stone. 

For  grinding  machinists*  tools,  about 900  feet  per  minute. 

"       carpenters'     **        **     600   '»     "        " 

The  speeds  of  stones  for  fUe-grlnding,  and  other  similar  rapid  grinding  la 
thus  given  in  the  "  Qrindera*  Ltot.** 

Diam.  ft 8       7U       7       6U       6       5U       6       4U       4     8U      8 

R0VS.  permtn.  185  144  154  166  180  m  218  240  270  808  860 
The  following  table,  from  the  Mechanical  W^orW.  Is  for  the  diameter  of 
atones  and  the  number  of  revolatlons  they  should  run  per  minute,  (not  to  be 
exceeded),  with  the  diameter  of  change  of  shirt-pulleys  required,  varying 
each  shift  or  change  8^  inches,  2^  Inches,  or  2  Inches  m  diameter  for  each 
reduction  of  6  inchet*  In  the  diameter  of  the  stone. 


Shift  of  Pulleys,  in  inches. 

Diameter 

Revolutions 

of  Stone. 

«« 

^ 

2 

ft.    in. 

£       0 

185 

40 

86 

82 

V       6 
7       C 

144 
154 

^ 

38?i; 

8lVi 

SO 
28 

6        J 

166 

«^ 

20^ 

26 

U 

180 

80 

27 

84 

o       6 

196 

2r^ 

249i 

22 

6       0 

216 

25 

2-4! 

80 

4       6 

240 

^14 

m. 

18 

4       0 

270 

20 

18 

16 

8       6 
8       0 

808 
860 

\^ 

i^ 

14 
It 

1 

8 

8 

4 

5 

970 


THE  MACHINE-SHOP. 


Columns  3,  4,  and  5  are  given  to  show  that  If  we  start  an  8-foot  stone  with, 
say,  a  countershaft  pulley  driTing  a  40-inch  pulley  on  the  grindstone  spindle, 
and  the  8tone  makes  the  right  number  (185)  of  revolutions  per  minute,  the 
reduction  in  the  diameter  of  the  pulley  on  the  grindliig-stone  spindle,  when 
the  stone  has  been  reduced  6  inches  in  diameter,  will  require  to  be  also  re- 
duced v}4  inches  in  diameter,  or  to  shift  from  40  inches  to  37^  inches,  and  so 
on  similarly  for  columns  4  and  6.  Any  other  suitable  dimensions  of  pulley 
may  be  used  for  the  stone  when  eight  feet  in  diameter,  but  the  number  of 
inches  in  each  shift  named,  in  order  to  be  correct,  will  have  to  be  propor- 
tional to  the  numbers  of  revolutions  the  stone  should  run,  as  given  in  column 
8  of  the  table. 

Varieties  of  Grindstones. 

(Joshua  Rose.) 

For  Obindimo  Machinists'  Tooia. 


Name  of  Stone. 


Nova  Scotia, 

Bay  Chaleur  (New 

Brunswick), 
Liverpool  or  Melting , 


Kind  of  Grit. 


Texture  of  Stone. 


All  kinds,  from 
finest  to  coarsest 

Medium  to  finest 

Medium  to  fine 


All  kinds,  from 
hardest  to  softest 

Soft  and  sharp 

Soft,  with  sharp 
grit 


Color  of  Stone. 


Blue  or  yellowish 

Uniformly    light 

blue 
Reddish^. 


For  Wood-workino  Tools. 


Wickersley 

Liverpool  or  Melting. 

Bar  Chaleur  (New  f 

Brunswick),  f 

Huron.  Michigan  . . . 


Medium  to  fine 
Medium  to  fine  •) 

Medium  to  finest 
Fine 


Very  soft 
Soft,  with  sharp 
grit 

Soft  and  sharp 

Soft  and  sharp 


Grayish  yellow 
Reddish 

Uniform  light  blue 
Uniform  light  blue 


For  Grinding  Broad  Surfaces,  as  Saws  or  Iron  Flatbs. 


Newcastle 

Independence.. 
Massillon 


Coarse  to  med^m 

Coarse 

(hoarse 


The  hard  ones 
Hard  to  medium 
Hard  to  medium 


Yellow 

Grayish  white 
Tellowish  white 


TAP  DBII^IiS. 

Taps  for  MaclUne-sere^rs.    (The  Pratt  A  Whitney  Co.) 


Approx. 

Approx. 

Diameter, 

Wire 

No.  of  Threads 

Diameter, 

Wire 

No.  of  Threads 

fractions 

Gauge. 

to  inch. 

fractions 

Gauge. 

to  inch. 

of  an  inch. 

of  an  inch. 

No.  1 

60,78 

No.  18 

80.24 

2 

48,  56,  64 

H 

14 

16,  18,  80.  88,  84 

40,  48.  56 

16 

18,  80,  84  ^ 

7/64 

88,  88,  40 

l^ 

16 

16,18,80,88 

80,  82,  86,  40 

18 

16,18,80 

9/84 

30,  32,  36,  40 

19 

16^18.80 

24,  30,  32 

5/16 

20 

16,  18,  20 

6/92 

8 

24,  80.  32,  36,  40 

88 

16,18 

9 

24,  28.  SO,  82 

H 

SI 

14,  16.  18 

S/16 

10 

20,  22,  24,  30.  82 

86 

16 

11 

22.  24 

88 

16 

T/M 

12 

20.  22.  34 

80 

16 

The  Morse  Twist  Drill  and  Machine  Co.  gives  the  following  table  showing 
the  diffei^nt  sizes  of  drills  that  tihoiild  be  used  when  a  suitable  thread  is  ;u 
be  tapped  in  a  hole.    The  sizes  given  are  practically  correct. 


TAl'  ouaLS. 


971 


J 


^t 


II 

t 


« 


i; 


^1 


:  i  :  i  i«  : 


li!!l 


•:|: 


;«! ! 


^|s^ 


ssss 


OOCOaOQO    •••••••••••    -tOaOiOid^   •    i    •    'lOiOiOiO 

t- fe*  fe*  t- 1«  «•  fe«  C>  «0  «0  «  «0  CD  «0  O  CD  lO  lO  lO  lO  lO  iO  lO  lO '«  "«•  ^  ^^ 


li 


:o  :k  :  •  :s : :  :g  i ;  i : :  i : :  i  i :  i  i : ; 


-ni; 


iiX:i:fS 


llHi 


-e^iO  t-o»0' 


^^^^^^i?^^-*^  ■  i'l?^  :  :  :  :  :  : 


»«Deoo'V^^Tf?i9i'?}'?*oo«-i*-<oooo9»a:o»a»Qcaoooao 


rt   „   r-   ^    r-i   0)i-iC>   cIf-iO*   C*  —  «    ^i-«?0 


972 


THK  MACHINE-SHOP. 


TAPBB  BOIiTS,  PINS,  BEAMRB8,  ET€. 

Taper  Bolts  for  I<oooiiioUTeB.— Bui t- threads,  U.  6.  standard, 
except  stay-bolttf  and  boilernscuds,  V  threads,  13  per  ioob;  valves,  coeJcH,  and 
plU|^,  V  tlireads,  14  per  iaoh,  atid  Hi-iuoh  taper  per  1  inch.  Standard  boIi 
tnwr  1/16  inch  per  foot. 

Taper  Beamers.— The  Pratt  A  Whitney  Oo.  makes  standard  taper 
reamei-8  for  locomotive  work  taper  1/16  inch  per  foot  from  )4  inch  di&m.; 
4  in.  length  of  flute  to  2  in.  diam.:  16  in.  lenrtb  of  flute,  diameters  advancing 


by  leths  and  82ds.    j^^ 

r>r  foot,  are  made  In  14  sizes  of  diameters,  0.135  to  1.009  in.;  length  c 
5/16  in.  to  IS  in. 


P.  &  W.  Cp.B  standard  taper  pin  reameiis  taper  ^  '"• 


Stakdikd^apbr  Sookbt. 

No. 

Diameter 

Small  End, 

inches. 

Diameter 

Large  End, 

inches. 

Diam!7a'ge 
end,  inches 

s 

III 

Total 
L'ngth. 

Taper 

0.S65 
0.578 
0.779 
1.026 
1.486 
8.117 

0.526 
0.749 

?:§ 

1.796 
S.S66 

0.475 
0.699 
0.980 
1.231 
1.746 
2.500 

85/16 

6 
7M 

3 

5 
6 

10 

I2^ 

0.900 
0.602 
0.603 

o.im 

0.6:« 
0.635 

Standard  Steel  Taper*pins*— The  following  eiaes  aie  made  by 
The  Pratt  &  Whitney  Co.: 
Number: 

0  18345678910 


.809      .841      .409     .498     .691      .706 
19/64    11/88    18/88     yi     19/88    88/38 


iS    '4    •I' 


.898 


.sn 


Diameter  large  end: 

.156  .178  .198  .819  .850 
Approximate  fractional  sizes: 

5/88  ll/IM  8/16  7/88  ^ 
Lengths  from 

Diameter  small  end  of  standard  taper-pin  reamer:t 
.135  .146  .162  .183  .itOS  .8l0  .879  .881 
Standard  Steel  Mandrels.  (The  Pratt  £  Whitney  CoV- These 
mandrels  are  mode  of  lool-steel,  hardened,  and  ground  true  on  their  cen- 
tres. Centres  are  also  ground  to  true  60»  cones.  The  ends  are  of  a  form 
best  adapted  to  resist  Injury  likely  to  be  caused  by  diiving.  They  are 
slightlv  taper.  Sizes,  ^  in.  diameter  by  8^  iu.  long  to  8  io.  diam.  by  149^  in. 
long,  diameters  advancmg  by  16tha. 

PITNCHBS  AND  JDIES,  PRESSES,  ETC. 

Clearance  betiveen  Puneli  and  Die.  —For  computing  the  amount 
of  clearance  that  a  die  «bould  liave,  or,  iu  other  words,  the  difference  in 
size  between  die  and  punch,  the  general  rule  is  to  make  the  diamerer  of 
die-hole  equal  to  the  aiameter  of  the  punch,  plus  3/10  the  thlckneas  of  the 
plate.  Or,  D  =s  d-{-  .8f,  in  which  D  =  diameter  of  die-bole,  d  =  diameter  of 
punch,  and  t  =  thickness  of  plate.  For  very  thick  plates  some  mechanica 
prefer  to  make  the  die-hole  a  little  smaller  than  called  for  by  the  above  rule. 
For  ordinary  boiler-work  the  die  is  made  from  1/10  to  8/10  of  the  thickness 
of  the  plate  larger  than  the  diameter  of  the  pnnch;  and  aouie  boiler-makers 
advocate  making;  the  punch  fit  the  die  accurately.  For  punching  nuts,  the 
punch  flte  in  the  die.    (Am.  MavhinUt.) 

Kennedy's  Spiral  Puncb.  (The  Pratt  &  Whitney  Co.>--B.  Martell, 
Chief  SSui-veyor  of  Uoyd's  Uegister,  reported  tests  of  Kennedy's  spiral 
punches  In  which  a  %-inch  spiral  punch  penetrated  a  ^-inch  plaie  at  a  pre*- 
sure  of  82  to  25  tons,  while  a  flat  punch  required  88  to  85  tons.  Steel  boiler- 
plates punched  with  a  flut  punch  gave  an  average  tensile  strength  of  58^79 

*  Lengths  vary  by  )4,"  each  «ize.  t  Taken  Hi"  from  extreme  end.  Each 
size  overlaps  smaller  one  about  ^",    Taper  M''  ^  ^^  ^oot. 


PORClKa  AND  SHRINKING  FITS.  973 

lbs.  per  square  inch,  and  an  elongation  In  tiro  inches  acroM  the  bole  of  5.9fi^ 
\f\n\e  plau«  punched  with  a  spiral  punch  gare  e8«090  Ihs.,  and  10.B%  elonipi- 
tion. 

The  spiral  shear  form  is  not  recommended  for  puaohes  for  use  in  metal  of 
a  thickness  greater  tlian  the  diameter  of  the  punch.  This  form  is  of  great* 
eftt  benefit  when  the  thickness  of  metal  worked  is  less  than  two  thirds  the 
diameter  of  punch. 

Slse  of  IBlanks  «sed  la  tl&e  Dnnnrlnc^pres**  Oberlin  Smith 
(Jour.  Frank,  insc,  Nov.  IbW)  gives  three  methods  Of  finding  the  siaa  of 
blanks.  The  first  is  a  tentative  method,  and  consists  simply  7n  a  series  of 
experiments  with  various  blanks,  until  the  proper  one  is  found.  This  is  for 
use  mainly  in  complicated  cases,  and  when  the  cutting  portions  of  the  die 
and  punch  can  be  finally  sized  after  the  other  work  is  done.  The  second 
method  is  by  weighing  the  sample  piece,  and  then,  knowing  the  weight  of 
the  sheet  metal  per  square  inch,  computing  the  diameter  of  a  piece  having 
the  required  area  to  equal  the  sample  in  weight.  The  third  method  is  by 
computation,  and  the  formula  is  a:  =  Vd^  -f  4dk  for  sliarp-comered  cup, 
where  x  =  diameter  of  blank,  d  =  diameter  of  cup,  h  =  height  of  cup.  For 
round-cornered  cup  where  the  comer  is  small,  say  radius  of  corner  less  tlian 
^4  height  of  cup,  the  formula  is  «  =  (  i^d^  +  4dA)  —  r,  about;  r  being  the 
radius  of  the  comer.  This  is  based  upon  the  assumption  that  the  thiclcness 
of  the  metal  is  not  to  be  altered  by  the  drawing  operation. 

PreMore  attainable  by  the  Vme  of  the  Arop*presB.  (ft.  H. 
Thurston,  Trans.  A.  S.  M.  £.,  v.  68.)— A  set  of  copper  cyUuUers  was  prepared, 
of  pure  Lake  Superior  copper;  tbej  were  subjected  to  the  action  of  pfvsses 
of  different  weights  and  of  different  heights  of  fall.  Companion  specimens 
of  copper  were  compressed  to  exactly  the  same  amount,  and  measures  were 
obtained  of  the  loads  producing  compression,  and  of  the  amount  of  work 
done  in  producing  the  compression  by  the  drop.  Comparing  one  with  the 
otlier  it  was  foond  that  the  work  done  with  the  hammer  was  wi  of  the  work 
which  should  have  been  done  with  perfect  efAciency.  That  is  to  say,  90ji  of 
the  work  done  In  the  testlng-nmohiiM  was  equal  to  that  due  the  weight  of 
the  drop  falltaig  the  given  distance. 

PomuU:  Ueu  pr««ur«  in  pound.  =  W"8h»  "^  <»~P  X  toll  x  «mcteHy 

compression. 

For  pressures  per  square  inch,  divide  by  the  mean  area  opposed  to  crush- 
ingaction  durine  the  operation. 

Floir  of  Metals.  (David  Townsend,  Jour.  Frank.  Inst..  March,  1878.) 
<.-Iu  puQChiug  holes  7/16  inch  diameter  through  iron  blocks  \H  Inches  thick. 
It  was  found  that  the  core  punched  out  was  only  1 1/16  inch  thick,  and  its 
volume  was  only  about  SS%  of  the  volume  of  the  hole.  Therefore,  fy  of  the 
xneul  displaced  by  punching  the  hole  flowed  into  the  block  itself,  IncreaslDg 
its  dimensions. 

FORCINO  ANB  SHRINKING  FITS. 

Forcing:  Pita  of  Pins  and  Axles  byHydraallc  Pressare. 

^A  4-ioeh  axle  is  turned  .015  inch  diameter  larger  thau  the  hole  into  which 
it  is  to  be  fitted.  They  arepressed  on  by  a  pressure  of  80  to  85  tons.  (i<ec- 
ture  by  Ooleman  Sellers,  1872.) 

For  forcing  the  crank-pin  into  a  locomotive  driving-wheel,  when  the  pin- 
hole is  perfectly  true  and  smooth,  the  pin  should  be  pressed  In  with  a  pres- 
sure of  0  tons  for  every  inch  of  diameter  of  the  wheel  fit.  When  the  hole  is 
not  perfectly  trae,  which  may  be  the  result  of  shrinking  tlte  tire  on  the 
wheel  centre  after  the  hole  for  the  crank^in  has  been  bored,  or  if  the  hole  Is 
not  perfectly  smooth,  the  pressure  may  have  to  be  increased  to  9  tons  for 
every  inch  of  diameter  of  the  wheel-fit.    {Am.  Machinigt.) 

Shrtnkace  Flts.--Io  1866  the  American  RaUway  Master  Mechanics' 
Association  recommended  the  following  shrinkage  allowances  for  tires  of 
standard  looomotivea.  The  tires  are  uniformly  heated  by  gas»flames.  slipped 
over  the  cast-iron  centres,  and  allowed  to  cool.  The  centres  are  tamed  to 
the  standard  sizes  given  below,  and  the  tires  are  bored  smaller  l»y  the 
amount  of  the  shrinkage  designated  for  eeob : 

Diameter  of  centre,  in  . . .       88       44       fiO       R6       08       00 
Shrinlcage  allowance,  in  .     .040     .047    .058    .000    .060    .070 

This  shrinkage  allowance  is  apjiroximately  1/SO  inch  per  foot,  or  1/960.  A 
common  allowance  is  1/1000.    Taliiiig  the  modulus  of  elasticity  of  steel  at 


974  THE  KACfilKE-SHOP. 

80,000.000,  the«train  caused  by  shiinkase  would  be  80.000  lbs.  per  square  inch, 
which  is  well  within  the  elastic  limit  of  machinery  steel. 

SCBBW8,  SCBBWVTHBEADS,  ETC.* 

Kllleiency  of  a  Sereiw.^Let  a  =  anjcle  of  the  thread,  that  is.  the 
angle  whose  tangent  Is  the  pitch  of  the  screw  divided  by  the  crircuinferetice 
of  a  circle  whose  diameter  Is  the  hiean  of  the  diameters  at  the  top  and 
bottom  of  the  thread.    Then  for  a  square  thread 

Bancicncy  =  ,V"/T°  ^ 
^      l-h/cotana* 

in  which  /  is  tlie  coefHctent  of  friction.  (For  demonstration,  see  Cotterfll  and 
8lade,  Applied  Mechanics,  p.  146.)  Since  cotan  =  1  h-  tan,  we  may  substitute 
for  cotan  a  the  reciprocal  of  the  tangent,  or  if  p  =  pitch,  and  c  =  mean  cir- 
cumference of  the  screw, 

Efficiency  = ^, 

£ZAiit*LC.~Efficlency  of  square-threaded  screws  of  ^  in.  pitch. 

Diameter  at  bottom  of  thread.  In ....      1  8                  3                   4 

**    top        "      "        "....    IJf  ^               «H               4Ji 

Mean  circumference "      "        ''....  8.W7  7.009  10.21  M.-i't 

Cotangent  a  s  c -«- p =7.864  14.14  20.42  26  ;o 

Tangent  a  =  p -I- e =  .1278  .0661  .0490  .0  75 

Efficiency  if /s  .10 =65  9%  4t.2%  9^.7%  i7.'^ 

"/=.16 =    46%  Sl.7%  9iA%  !».•/; 

The  efficiency  thus  increases  with  tlie  steepness  of  the  pitch. 

The  above  formulsB  and  examples  are  for  square-threaded  screv^«,  and 
oonsider  the  friction  of  the  screw-thread  only,  and  not  the  friction  ^f  the 
ooHar  or  step  by  which  end  thrust  is  resisted,  and  which  further  reduo**8  thn 
efficiency.  The  efficiency  is  also  further  reduced  by  giving  an  Inclination  to 
the  8ide  of  the  thread,  an  in  the  V-threaded  screw.  For  discussion  of  this 
subject,  see  paper  by  Wilfred  L«ewi8,  Jour.  Frank.  Inst.  1880;  also  Traus. 
A.  S.  M.  E.,  vol.  xii.  T84. 

Efllclencjr  of  Screnr-bolto.— Mr.  Lewis  gives  the  following  approx- 
imate formula  for  ordinary  screw-bolts  (V  threads,  with  collars):  p  = 
J)Itch  of  screw,  d  =  outside  diameter  of  screw,  F  =  force  app]ic»d  at  clrcum- 
erence  to  lift  a  unit  of  weight,  E  =  efficiency  of  screw.  For  an  averaga 
case,  in  which  the  coefficient  of  friction  may  be  assumed  at  .15, 

F_P-f  d  j?.-_E_. 

^-     8rf    '  ^-^ZfT 

For  bolts  of  the  dimennions  given  above,  ^-in.  pitch,  and  outside  diam- 
eters 1^,  2^,  8U,  and  4^  in.,  the  efficiencies  according  to  this  formul* 
would  be,  respectively,  .25,  .167.  .125.  and  .10. 

James  McBride  (Trans.  A.  S.  M.  E..  xil.  781)  describes  sn  experiment  with 
an  ordinary  2-in  screw-bolt,  with  a  V  thread,  4%  threads  per  Inch,  raising 
aweight  of  7500  lbs.,  the  force  being  applied  by  turning  tne  nut.  Of  tli« 
power  applied  89.8^  was  absorbed  by  friction  of  the  nut  on  its  supporting 
washer  and  of  the  threads  of  the  bolt  in  the  nut  The  nut  was  not  faced, 
and  had  the  flat  side  to  the  wa.slier. 

Prof.  Ball  in  his  "  Experimental  Mechanics  "  says:  '^Experiments  6howe<l 
in  two  cases  resi.)ectively  about  %  and  9^  of  the  power  was  lost." 

Trautwine  says:  "  In  practice  the  friction  of  the  screw  (which  under 
heavy  loads  becomes  very  great)  make  the  theoretical  calculations  of  but 
little  value." 

Weisbach  ftfiys:  "The  efflciVncy  Is  from  195<  to  90%V 

Efllclency  of  a  JDiflerentlal  Screnr.— A  correspondent  of  the 
American  Machinist  describes  an  experiment  with  a  dilierentlal  8crew> 

Eunch,  consisting  of  an  outer  screw  2  m.  diam.,  3  threads  per  in.,  and  an 
mer  screw  1^  in.  dlam.,  3^  threads  per  Inch.  The  pitch  of  the  outer  screw 

*  £*or  U.  S.  Standard  Screw-threads,  see  page  201 


KEYS.  975 

^'ing  W  In.  and  that  of  the  Inner  screw  S/7  In.,  the  punch  would  ad- 
Tance  in  one  revolution  ^  —  2/7  =  1/21  in.  Efxperiments  were  made  rode« 
tenriine  the  force  requireil  to  punch  an  ll/16-in.  hole  in  iron  ^  in.  thick,  the 
force  beiuff  applied  at  the  end  of  a  lever- arm  of  4T9ii  in.  The  leverage  would 
b«  47^  X  ^  X  21  =  6300.  The  mean  force  applied  at  the  end  of  the  lever 
wasi  95  Ihs..  and  the  force  at  the  punch,  if  there  was  no  friction,-  would  be 
6800  X  95  =  596,fi00  lbs.  The  force  required  to  punch  the  iron,  as8umlnfc  a 
shearing  resistance  of  50,000  lbs.  per  sq.  in.,  would  be  50,000  x  11/16  x  «  x 
l^  =  27,000  lbs.,  and  the  efficiency  of  the  punch  would  be  27,000  ■*•  598,500  = 
only  4.5)(.  With  the  lai^r  screw  only  used  as  a  punch  the  mean  force  at 
the  end  of  the  lever  was  only  82  lbs.  The  leverage  in  this  case  was  479^  x 
2v  x  8  =  900,  the  total  force  referred  to  the  punch,  including  friction,  900  x 
82  =  73,800,  and  the  efficiency  27,000  +  78,800  =  86.7^.  The  screws  were  of 
tool-steel,  well  fitted,  and  lubricated  with  lard-oil  and  plumbago. 

Ponreirs  Heur  Screiir-tliread*— A.  M.  Powell  (Am.  Mach.,  Jan.  91, 
1895)  has  designed  a  new  screw-thread  to  replace  the  square  form  of  thread, 
giving  the  advantages  of  greater  ease  in  making  fits,  and  provision  for  *'  take 
up  "  in  case  of  wear.  The  dimensions  are  the  same  as  those  of  square- 
thread  screws,  with  the  exception  that  the  sides  of  the  thread,  instead  of 
being  perpendicular  to  the  axis  of  the  screw,  are  inclined  14^<>  to  such  per- 
pendicular: that  is.  the  two  sides  of  a  thread  are  Inclined  29<>  to  each  other. 
The  formulfB  for  dimensions  of  the  thread  are  the  following:  Depth  of 
thread  =  ^  -«-  pitch;  width  of  top  of  thread  =  width  of  space  at  bottom  = 
.3707  +  pitch;  thickness  at  root  of  thread  =  width  of  space  at  top  =  .6293  -h 
pitch.    The  term  pitch  is  the  number  of  threads  to  the  Inch. 

PBOPOBTIONINe  PARTS  OF  MACHINES  IH  A  8BRIE9 
OF  SIZBS. 

{Stevens  Indicator,  April,  1893.) 

The  following  method  was  used  bv  Ooleman  Sellers  while  at  William  Sellers 
&  Co.^s  to  get  the  proportions  of  the  parts  of  machines,  based  upon  the 
size  obtained  in  building  a  large  machine  and  a  small  one  to  any  series  of 
machines.  This  formula  is  used  In  getting  up  the  proportion-book  and  ar- 
ranging the  set  of  proportions  from  which  any  machine  can  be  constructed 
of  intermediate  size  between  the  largest  and  smallest  of  the  series. 

Rule  to  Eatablisb  Constmctioii  Form  alas.— Take  difference 
between  the  nominal  sizes  of  the  largest  and  the  smallest  machines  that 
have  been  designed  of  the  same  construction.  Take  also  the  difference  be- 
tween the  sisses  of  similar  parts  on  the  largest  and  smallest  machines  se- 
lected. Divide  the  latter  by  the  former,  and  the  result  obtained  will  be  a 
"factor,"  which,  multiplied  by  the  nominal  capacity  of  the  intermediate 
machine,  and  increased  or  diminished  hy  a  constant  "  increment,'^  will  give 
the  size  uf  the  part  required.  To  find  the  *'  increment  :*'  Multiply  the  nomi- 
nal capacity  orsome  known  size  by  the  factor  obtained,  and  subtract  the 
result  from  the  sise  of  the  part  belonging  to  the  machine  of  nominal  car 
pacity  selected. 

ExAMPLB.— Suppose  the  size  of  a  part  of  a  7S-in.  machine  Is  8  in.,  and  the 
corresponding  part  of  a  42-in.  machine  is  \%,  or  1.875  in.:  then  72  -  4'i  = 
ao,  and  8  in.  -  1%  in.  =  m  in.  =  1.125.  1.125  -h  80  =  .0875  =  the  "  factor," 
and  .0875  X  42  =  1.675.  Then  1.875  -  1.575  =  .8  =  the  '*  Increment "  to  bo 
added.  Let  Z>  s  nominal  capacity;  then  the  formula  will  read:  x  = 
D  X  .0875  4-  .8. 

Pi'oof:  42  X  .0875  -h  .8  =  1.875,  or  i%.  the  size  of  one  of  the  selected  parts. 

Some  prefer  the  formula:  aZ>  -f  c  =  ;r.  In  which  D  =  nominal  capacity  In 
inches  or  In  pounds,  c  Is  a  constant  Increment,  a  Is  the  factor,  and  x  =  the 
part  to  be  found. 

KEYS. 

SiMS  or  Keys  for  nUl-searlns.  (Trans.  A.  8.  M.  E.,  xlii.  229.)— E. 
O.  Parkhurst's  rule :  Width  of  key  =  ^dlam.  of  shaft,  depth  =  1/9  diam.  of 
■haft:  taper  U  In.  to  the  foot. 

Custom  in  Michigan  saw-mills :  Keys  of  square  section,  side  =  H  diam.  of 
shaft,  or  as  nearly  as  may  be  in  even  sixteenths  of  an  inch. 

J.  T.  Hawkinses  rule  :  Width  =  ^  diam.  of  hole;  depth  of  side  abutment 
in  shaft  =  V^  diam.  of  hole. 

W.  S.  HuHon's  rule :  ^-inch  key  for  1  to  1^  in.  shafts,  6/16  key  for  I^  to 
IK  in.  sliafts,  H  In.  key  for  IH  to  1^^  In.  shafts,  and  so  on.  Taper  %  in.  to 
the  foot.    Total  thickness  at  large  end  of  splice,  4/5  width  of  key. 


976 


THE   MAGHINE-SHOP. 


Unwfti  (BlemeDtfl  of  Maohfne  OMign)  gives :  Width 
neas  =  ^d  -«-  ^  in..  In  which  d  =  dijim.  of  shaft  in  Inches. 


Md  +  Mln.   Thick, 
when  wheels  or 


pulleys  transniittiog  only  a  small  amount  of  power  are  kejed  on  large  shafts, 
he  says,  these  dimensions  are  exoeesive.  In  that  case,  if  H.P.  s  horse- 
power transmitted  by  the  wheel  or  pulley.  N  s  revs,  per  min,  P  =  force 
acting  at  the  circnmfereooe,  in  lbs.,  and  R  =  radius  of  pulley  in  inches,  take 


Prof.  Coleman  Bellers  {Steveti*  JndieatoTn  April,  1803)  gives  the  following : 
The  aixe  of  keys,  both  for  shaftlnr  and  for  machine  tools,  are  the  propor- 
tions  adopted  by  William  Sellers  St  Co.,  and  rigidly  adhered  to  during  a  pe- 
riod of  nearly  forty  years.  Their  practice  in  makmg  keys  and  fitting  them 
ia,  that  the  keys  shall  always  bind  tight  sidewlse,  but  not  top  and  bottom ; 
that  is,  not  necessarily  touch  either  at  the  bottom  of  the  key-aeat  in  the 
shaft  or  touch  the  top  of  the  slot  cut  in  the  gear-  wheel  that  Is  fastened  to 
the  shaft ;  but  in  practice  keys  used  in  this  manner  depend  upon  the  fit  of 
the  wheel  upon  the  shaft,  being  a  forcing  fit,  or  a  flt  that  is  so  tight  as  to  re- 
quire screw'presf ure  to  put  the  wheel  in  plaoe  upon  the  shaft. 

fitze  of  Keys  for  SliaDttiiff. 

Diameter  of  Shaft,  in.  Size  of  Ke 

IM  17/16      111/16 5/16  X  j 

115/16    2«/16 7/16 X  k 

87/16 »/16x  IZ 

8  11/16    2  15/16    8  3/16     8  7/16 11/16  x  || 

8  16/16    4  7/16     4  16/16 18/16x2 

5  7/16     5  16/16    6  7/16 16/16x1 

6  15/16    7  7/16     7  15/16    8  7/16    8  16/16..  1  1/16x1^ 
Length  of  key-seat  for  coupling  =  l^  X  nominal  diameter  of  shaft. 

StjM  of  Keys  for  Haehine  Tools. 


y,to. 


Diam.  of  Shaft,  in. 
15/16   and  under. 


Siaeof  Key, 
in. 


16 


1  to  1  8/16, 
IM  to  1  7/16 

lU  tol  11/16 b/16 

iS  to2  8/16... 7/16 

2Mto8  11/16 0/16 

294  to8  lVi0 11/16 


Diam.  of  Shaft,  in.       ®'*?„*''g^*^- 

4    to  6  7/16 ia/ii 

6^to   6  16/16 16/16 

7     to  8  15/16 1  1/16 

0     tolO  16/16 1  8/16 

11      to  12  15/16 1  5/16 

18     to  14  15/16 1  7/16 


John  Richards,  In  an  article  In  0cu8(er*»  MiiTas^ne,  writes  as  follows:  Tliers 
ara  two  kinds  or  system  of  keys,  both  proper  and  neceitsary,  but  widely  dif- 
ferent In  nature.  1.  The  common  fastening  ker,  usually  made  in  width  one 
fourth  of  the  shaft's  diameter,  and  the  depth  five  eighths  to  one  third  the 
width.  These  keys  are  tapered  and  Qt  on  all  sides,  or,  as  it  is  commonly  d^ 
scribed,  "  bear  all  over.*'  They  perform  the  double  function  In  most  ca^es 
of  driving  or  transmitting  and  fastening  the  keyed«on  member  against 
movement  eudwise  on  the  shaft.  Such  keys,  when  properly  made,  drive 
as  a  strut,  diagonally  from  corner  to  corner. 

2.  The  other  kind  or  class  of  keys  are  not  tapered  and  flt  on  their  sides 
only,  a  slight  clearance  being  left  on  the  back  to  insure  against  wedge  action 
or  radial  strain.    Tliese  keys  drive  by  shearing  Ktrain. 

For  fixed  work  where  there  is  no  sliding  movement  such  kevs  are  com- 
monly made  of  square  section,  the  sides  only  being  planed,  so  the  depth  Is 
more  than  the  width  by  so  much  as  is  cut  away  in  finishing  or  fitting. 

For  sliding  bearings,  as  In  the  case  of  drttUng-machfne  spindles,  the  depth 
should  be  increased,  and  in  cases  where  there  Is  heavy  strain  there  should 
be  two  keys  or  feathers  instead  of  one. 

The  following  tables  are  taken  from  proportions  adopted  in  practical  use. 

Flat  keys,  as  In  the  first  tabl«*,  are  employed  for  fixed  work  when  the 
parts  are  to  be  held  not  only  against  torsional  strain,  but  also  against  move- 
ment endwise  ;  and  in  case  of  heavy  strain  the  strut  principle  being  the 
strongest  and  mo«t  secure  against  movement  when  there  is  strain  each  way. 
as  in  the  case  of  engine  cranks  and  first  movers  generally.   The  obieotions 


HOLDlKG-POWBtl  OF  KfiYS  AlSTD  SEt-SCllfiWS. 


to  the  system  for  oeoeral  use  are,  straining  the  work  out  of  truth,  the  care 
and  ei[pense  required  Id  Attliiff,  and  destroy! og  the  evidence  of  good  or  bad 
fitting  of  the  keyed  Joint.  When  a  wheel  or  other  part  Is  fastened  with  a 
tapering  key  of  this  Kind  there  Is  do  meaos  of  knowing  whether  the  work  Is 
well  fitted  or  not.  For  this  reason  such  keys  are  not  employed  by  machiue- 
tool^makera,  and  in  the  case  of  accurate  work  of  any  kind,  lodeed,  cannot 
be,  because  of  the  wedging  strain,  and  also  the  difficulty  of  Inspeoting  ootn* 
pleted  work. 

I.  DtiiKKStONS  o»  Flat  Kkts,  tir  Ikches. 


Diam.  of  shaft 

Breadth  of  keys  . . 
Depth  of  keys 


i/ii 


6/lJ 
3/16 


7/ld 
9/32 


b% 


8 

7% 


5 

11/16 


e 

18/!« 


8 


II.  DmnraioMs  or  SqoAiia  Kbtb,  nv  Ikcbm. 


Diam.  of  shaft. . . 
Breadth  of  keys. 
Depth  of  keys — 


5/82 
8/16 


H 


5/16 


'l8/83 
7/16 


17/82 
0/16 


11/16 
H 


m.  DiMKVSIOMe  OF  SXJDlNO  FBATBBR-KEYS,  IN  iNOBttl. 


Diam.  of  shaft... 
Breadth  of  keys.. 
Depth  of  keys 


7/16 


5/18 
7/16 


11 


^.6 


»/is 
H 


P.  Pryibll  furnishes  the  following  table  of  dimensions  to  the  Am.  Machin- 
ist, He  says :  On  special  hea?y  work  and  very  sbort  hubs  we  put  in  two 
keys  In  one  shaft  90«  apart.  With  special  long  hubs,  where  we  cannot  UM 
keys  with  noses,  the  keyp  should  be  thicker  than  the  standard. 


Diameter  of  Shafts,    Width,  Thick- 
inches,  inches,  ness,  in. 


tol  1/16 
1^        to  1  ft/16 
1  7/16    tol  11/16 
1  15/16  to  8  8/16 
8  7/16    to  8  n/16 
a  16/16  to  8  8/16 


3/16 
6/16 


8/16 
?/16 

Pl8 


Diameter  of  Shafts,    Width, 
inches.  Inches. 


8  7/16   to  8  11/16 
8  16/10  to  4  8/16 
4  7/16   to  4  11/16 
4^        toSfl 
6t|        tojnl 


Thick- 
ness, in. 


16/16 


Keys  longer  than  10  inches,  say  14  to  IV^  1/W  thicker;  keys  longer  than 
10  inches,  say  18  to  HO",  %"  thicker;  and  so  on.  Special  short  hubs  to  have 
two  keys. 

For  description  of  the  Woodruff  system  of  keying,  see  circular  of  the 
Pratt  &  Whitney  Co. ;  also  Modern  Mechanism,  page  465. 

HOIiDINfi-POWBR  OF  KBYS  ANB  8B1>8€BBW8* 

Teats  of  the  Btoldliic-power  of  Set-screws  In  Piillef  s« 

jO.  Lanza,  Trans.  A.  S.  M.  ET,  x.  230.)— Tht-se  teKts  were  made  by  using  a 
pulley  fastened  to  the  shaft  by  two  set-screws  with  the  shaft  keyed  to  the 
holders;  then  the  load  required  at  the  rim  of  the  pulley  to  cause  it  to  slip 
was  determined,  and  this  being  multiplied  by  the  number  6.037  (obtained  by 
adding  to  the  radius  of  the  pulley  one-half  the  diameter  of  the  wire  ropf, 
and  dividing  the  sum  by  twice  the  radlua  of  the  shaft,  since  there  were  two 
set-screws  In  action  at  a  time)  gives  the  holding-power  of  the  set-screws. 
The  Mt-screws  used  were  of  wrought-iron,  %  of  an  Inch  In  diameter,  and  ten 
threads  to  the  h)ch;  the  shaft  used  was  of  steel  and  rather  hard,  the  set- 
screws  making  but  little  Inipretwion  upon  it.  They  were  set  up  with  a 
force  of  ib  lbs.  at  the  end  of  a  ten-inch  monkey-wrench.  The  set-screws 
UMed  were  of  four  kinds,  marked  respectively  A,  B,  0,  and  D.  The  results 
were  as  follows : 


978  DtKAMOMSTERS, 

A,  ends  perfectly  flat,  9/16-in.  diameter,     1412  to  2294  lbs.;  average  2004. 

B,  radius  of  rounded  ends  about  U  inch,  2747  *'  9079  **  '*       2912. 

C,  **      "         *'  *•  »*     H    **       1902  '*  8079    "  '*        2573. 
D  ends  cup-shaped  and  case-hardened,      1903  '*  2958   **           **       2470. 

Remarks.— A.  The  set-screws  were  not  entirely  normal  to  the  shaft ;  hence 
they  bore  less  In  the  earlier  trials,  before  they  had  become  flattened  by 
wear. 

B.  The  ends  of  these  set-screws,  after  the  first  two  trials,  were  found  to 
be  flattened,  the  flattened  area  havine  a  diameter  of  about  ^  inch. 

C.  The  ends  were  found,  after  the  first  two  trials,  to  be  fiattened,  an  in  B. 

D.  The  first  test  held  well  because  the  edses  were  sharp,  then  the  holdinf^- 
power  fell  off  till  they  had  become  flattened  In  a  manner  similar  to  B,  when 
the  holding-power  Increased  again. 

Testa  of  the  CEoldlnp-poiirer  of  Keys.  (Lanza.)— The  load 
was  applied  as  in  the  tests  of  set-screws,  the  shaft  being  flrmly  keyed  to  the 
holders.  The  load  required  at  the  rim  of  the  pulley  to  shear  the  keys  w&i 
determined,  and  this,  multiplied  by  a  suitable  constant,  determined  in  a  sim- 
ilar way  to  that  used  in  the  case  of  set-screws,  gives  us  the  shearing  strength 
per  square  inch  of  the  keys. 

The  keys  tested  were  of  eight  kinds,  denoted,  respectively,  by  the  letters 
A.  B,  C,  D,  E,  F,  Q  and  H,  and  the  results  were  as  follows  :  A,  B,  D  and  F. 
each  4  tests;  E,  8  teste ;  C,  Q,  and  H,  each  2  tests. 

A,  Norway  iron,  r^>",         40,184  to   47,700 lbs.;  average,  42,726. 

B,  refined  iron.  ir'.           86,482''    89,254;              *•          88,059. 

C,  tool  steel,  1"  J          I                           91,844  &  100,056. 

D,  machinery  St* .  1.  V        m  i?>/«2",      64,680  to   70,186;             "          66.875. 

E,  Norway  iron,  fiii'  A  a^'  -  7/16'',        86,850"    87,222;             »*          87,086. 

F,  cast-iron,  2";  >;i"KlO/*r',                 80,278*'    86,944;             "          88.0M. 

G,  cast-iron.  1J4  %'*  >   T  t(5",               87,2:22  &   88,700. 
H,  cast-iron,  1'^  29,814  &   88,9r8. 

In  A  and  B  some  crushing  took  place  before  shearing.  In  E,  the  keys  be- 
ing only  7/16  in.  deep,  tippM  slightly  in  the  key-way.  In  H,  in  the  flrst  testi 
there  was  a  defect  in  the  key -way  of  the  pulley. 


DYNAMOMETERS. 

Dynamometers  are  instmroents  need  for  raeaanring  power.  They  are  of 
several  classes,  as :  1.  Traction  dynamometers,  used  for  detemifnmg  the 
power  required  to  pull  a  car  or  other  vehicle,  or  a  plough  or  harrow. 
2.  Brake  or  absorption  dvnamometers,  in  which  the  power  of  a  rotating 
shaft  or  wheel  is  absorbed  or  converted  into  heat  by  the  friction  of  a  brake; 
and.  8.  Transmission  dynamometers,  in  which  the  power  in  a  rotating  shaft 
is  measured  during  its  transmission  through  a  belt  or  other  connection  to 
another  shaft,  without  beinar  absorbed. 

Traction  Dynamometers  generally  contain  two  principal  parts: 
(1)  A  springer  series  of  springs,  through  which  the  pull  is  exerted,  the  ext^'n- 
sionof  the  spring  measuring  the  amount  of  the  pulling  force;  and  (2)  a  paper, 
covered  drum,  rotated  either  at  a  uniform  speed  by  clockwork,  or  at  a  si>e«!d 
proportional  to  the  speed  of  the  traction,  through  gearing,  on  which  the  ex< 
tension  of  the  spring  is  registered  by  a  pencil.  From  the  average  height  of 
the  diagram  drawn  by  the  pencil  above  the  zero-line  the  average  pulling 
force  in  pounds  is  obtained,  and  this  multiplied  by  the  distance  traversed, 
in  feet,  gives  the  work  done,  in  foot-pounds.  The  product  divided  by  the 
time  In  minutes  and  by  8:^,000  gives  the  horse-power. 

The  PronT  brake  is  the  typi^^l  form  of  absorption  dynamometer. 
(See  Fig.  167,  from  Flather  on  Dynamometers  and  the  Measurenaent  ot 
Power.) 

Primarily  this  consists  of  a  lever  connected  to  a  revolving  shaft  or  pulley 
in  such  a  manner  that  tbe  friction  induced  between  the  surfaces  in  contact 
will  tend  to  rotate  the  arm  in  the  direction  in  which  the  shaft  revolves.  This 
rotation  is  counterbalanced  by  weights  f,  hung  in  the  scale-pan  at  the  end 
of  the  lever.  In  order  to  measure  the  power  for  a  given  number  of  revolu- 
tions of  pulley,  we  add  weights  to  the  scale-pan  and  screw  up  on  bolts  bby 
until  the  friction  induced  balances  the  weishte  and  the  lever  is  maintained 


THE  ALDEX  ABSOBPTXON-DYKAHOHBTBB.  979 

Id  Its  horisontal  position  while  the  reyolutfoiiB  of  shaft  per  minute  remain 
constant. 

For  small  powers  the  beam  Is  Renerally  omitted— the  friction  being  mea- 
Bured  by  weigrhtlnff  a  band  or  strap  thrown  over  the  pulley.  Ropes  or  cords 
are  often  used  for  the  same  purpose. 

Instead  of  hanf^hif^r  weiiprbts  in  a  scale-pan,  as  in  Fi|(.  167,  the  friction  may  be 
weif^hed  on  a  platform-scale;  in  this 
case,  the  direction  of  rotation  being 
the  same,  the  lever-arm  will  be  on  the 
opposite  side  of  the  shaft. 

Ill  a  modification  of  this  bralce,  the 
brake- wheel  is  keyed  to  the  shaft, 
and  its  rim  is  provided  with  inner 
flanges  which  form  an  annular  trough 
for  the  retention  of  water  to  keep  the 
ptiUey  from  heating.  A  small  stream 
of  water  constantly  discharges  Into 
ttie   trough  and   revolves  with  the  Piq   ^fgj 

pulley— the  centrifugal  force  of  the 

panicles  of  water  overcoming  the  action  of  gravity;  a  waste-pipe  with  its 
end  flattened  is  so  placed  in  the  trough  that  it  acts  as  a  scoop,  snd  removes 
all  surplus  water.  The  brake  consists  of  a  flexible  strap  to  which  are  fitted 
blocks  of  wood  forming  the  rubbing-surface;  the  ends  of  the  strap  are  con- 
nected by  an  adjustable  bolt-clamp,  by  means  of  which  any  desired  tension 
may  be  obtained. 

The  horse -power  or  work  of  the  shaft  is  determined  from  the  following: 

Let  W  =  work  of  shaft,  equals  power  absorbed,  per  minute; 

P  =  unbalanced  pressure  or  weight  In  pounds,  acting  on  lever-arm 

at  distance  L; 
L  =s  length  of  lever-arm  In  feet  from  centre  of  shaft; 
V  =  velocity  of  a  point  in  feet  per  minute  at  distance  L,  if  arm  were 

allowed  to  rotate  at  the  speed  of  the  aliaft; 
N  =  number  of  revolutions  per  miuute; 
H.P.  =  horse-power. 

Then  will  Wz=PF=  9nLNR 

Since  H.P.  =  FF-*-  83,000,  we  have  H.P.  =  ftwLNP-t-  88,000. 

If  L  B  ^.  we  obtain  H.P.  =  -ir^.  83 + 2«  Is  practically  6  ft.  8  In.,  a  value 

vften  used  in  practice  for  the  length  of  arm. 

If  the  rubbing-surface  be  too  small,  the  resulting  friction  will  show  great 
Irregularity— probably  on  account  of  insufllcient  TubricatioD— the  Jaws  be- 
ing allowed  to  seise  the  pulley,  thus  producing  shocks  and  sudden  vibra- 
tions of  the  lever-arm. 

Soft  woods,  such  as  bass,  plane-tree,  beech,  poplar,  or  maple  are  all  to  be 

E referred  to  the  harder  woods  for  brake-blocks.  The  rubbing-surface  sliould 
e  well  liihrioAted  with  a  heavy  grease. 

The  Alden  AbaorpUon-dynamometer.  (O.  I.  Alden,  Trans. 
A  8.  M.  E.,  vol.  zi.  958;  also  xii,  700  and  xiii.  4:29. »— This  dvnamometer  is  a 
f  liction-brake,  whfeh  Is  capable  in  quite  moderate  sizes  of  absorbing  large 
prtwers  with  unusual  steatiiness  ana  complete  regulation.  A  smooth  cast- 
iron  disk  Is  keyed  on  the  rotating  shaft.  This  is  enclosed  in  a  casMron 
shell,  formed  of  two  disks  and  a  ring  at  their  circumference,  which  Is  free 
to  revolve  on  the  shaft.  To  the  interior  of  each  of  the  sides  of  the  shell  is 
fitted  a  copper  plate,  enclosing  between  itself  and  the  side  a  water-tight 
aiiace.  Water  under  pressure  from  the  city  pipes  is  admitted  into  each  of 
tnese  spaces,  forcing  the  copper  plate  against  the  central  disk.  The 
cliamber  enclosing  the  disk  is  filled  with  oiL  To  the  outer  shell  is  fixed  a 
weighted  arm,  which  resists  the  tendency  of  the  shell  to  rotste  with  the 
shaft,  caused  by  the  friction  of  the  plates  against  the  central  disk.  Four 
brakes  of  this  tvpe,  56  in.  diam.,  were  used  in  testing  the  experimental 
locomotive  at  Purdue  University  (Trans.  A.  8.  M.  E.,  xili.  4*Z9).  Each  was 
designed  for  a  maximum  moment  of  10,500  foot-pounds  with  a  water-press- 
ure of  40  lbs.  per  sq.  in. 

The  area  in  effective  contact  with  the  copper  plates  on  either  side  is  rep- 
re!iente<l  by  an  annular  surface  having  its  outer  radius  equal  to  28  inches, 
and  Its  inner  radius  equal  to  10  inches.  The  aTtparent  cm-ffit  ient  of  friction 
lielween  th«*  plates anii  the  disk  was  3>^<. 


980 


DTNAHOHETEBS. 


W.  W.  B«*ainont  (Proo.  Iiist.  C.  E.  1889)  has  deduced  a  formula  hr  meaDii 
of  which  the  relative  capacity  of  brakes  can  be  compared,  fudging  rrom  the 
amount  of  horse^power  ascertained  by  their  ose. 

If  TTk  width  of  rubblns-iiurfaoe  on  brake-wheel  in  Inches;  V:=:.  Tel.  of 
point  on  circum.  of  wheel  In  feet  per  minute;  K  b  ooeffldent;  then 

K  =  WV  -¥  H.P. 

Capacity  of  FrIction*l^rmkes*— Prof.  Blather  obtains  the  values 
of  K  given  in  the  last  column  of  the  subjoined  table : 


o 


81 
10 
90 
40 
88 
ISO 
84 
180 
475 
12ft 
850 
40 
125 


h 

Brake- 

t 

pulley. 

iT  . 

^.1 
|l 

160 

7 

148.6 

7 

149 

7 

180 

10.5 

160 

10.5 

150 

10 

142 

12 

100 

24 

75.2 

24 

290 
2R0f 

84 

290r 

13 

t 


88" 
88.88^' 

82" 
82" 

88.8i'' 
125.1" 
191" 


87«" 


Deslcn  of  Bnikei 


Royal  Air.  Soc.,  compensating 

McLaren,  compensating 

*'  water-cooled  and  comp 
Oanrett, 

ki  *i  k«       «• 

Schoenheyder,  water-cooled 

Balk 

Gately  &  Kletsch,  water-cooled . . . 
Webber,  water-cooled  

Weetinghouse,  water-cooled 


-a 
> 


785 
058 
802 
741 
749 
888 
1885 
200 
84.7 

466 
847 


The  above  calculations  for  eleven  brakes  give  values  of  IT  varying  from 
84  7  to  1885  for  actual  horse-powers  tested,  the  avenge  being  K  s  65fi. 

Instead  of  assuming  an  aversge  coelllcieut.  Prof.  Flather  proposes  the 
following : 

Water-cooled  brake,  non-compensating,  K  =  400;  TT  =  400  H.P.  •♦•  V. 

Water-cooled  brake,  compensating,  K  ss  760;  TT  s  750  H.P.  •*•  V. 

Noncoolliig  brake,  with  or  without  compensating  device,  K  s  900; 
W^  =  900  H.P.  -^  F. 

Tranuniaslon  Dynamometem  are  of  rarious  forms,  as  the 
Batchelder  dynamometer,  in  which  the  power  Is  transmitted  through  a 
**  train-arm  *'  of  bevel  gearing,  with  Its  modlflcatlons,  as  the  one  described 
by  tht*  author  in  Trana  A.  I.  M.  E.,  vlli.  177,  and  the  one  described  by 
Samuel  Webber  in  Trans.  A.  S.  M.  E..  z.  514:  b<>lt  dynamometers,  as  the 
Tatham:  the  Van  Winkle  dynamometer,  in  which  the  power  Is  iransmlttfyl 
from  a  revolving  shaft  to  another  in  line  with  it,  the  two  almost  touching, 
through  the  medium  of  coiled  springs  fastened  to  arms  or  disks  keyed  to 
the  shafts;  the  Braokett  and  the  Webb  cradle  dynamometers,  used  for 
measuriii?  the  power  required  to  run  dynamo-electric  machines.  Descrip- 
tions of  the  four  last  named  are  given  in  Flather  on  Dynamometers. 

Much  information  on  various  forms  of  dynamometers  will  be  found  in 
Trans.  A.  8.  M.  E.,  vol.  vli.  to  zv.,  Inclusive,  Indexed  under  Dynamometers 


OPERATIOKS  OF  A  fiEFHIQERATIKG-JlACHlNF.     981 


ICB-MASma  OB  BEFBIGSBATING  KACHXlfBQ. 

Refereiiee0«— An  elaborate  discussion  of  the  theraiodynamic  theory  of 
the  HciioD  of  the  various  fluids  used  In  the  production  of  cold  was  published  bj 
M.  Ledoux  In  the  AntKiles  den  Mines,  and  translated  in  Van  yoiitrand''9  Magn- 
ziue  in  ld79.  This  work,  revised  and  additions  made  in  the  light  of  recent  ex- 
perience by  Professors  Den  ton,  Jacobus,  and  Riesenberfcer,  was  reprinted  in 
1892.  (Van  Koatrand'8  Science  Series,  No.  40.)  The  work  la  largreiy  niaihe- 
maticai.  but  It  ateo  contains  much  information  of  immediate  practical  value, 
from  which  tome  of  the  matter  given  below  is  taken.  Other  referencee  are 
Wood's  Thermodynamics,  Chap.  V.,  and  numerotis  papers  by  Prof essors 
AVood,  Detiton,  Jacobus,  and  Llnde  In  Trans.  A.  8.  vi.  jC..  vols.  x.  toxiv.; 
Johnson's  Cyclopiedia,  article  on  Refrigeratinjr-machines;  also  Bhig^g,  June 
l».  July  S  and  9, 1886;  ApHl  1, 1887;  June  15.  IflA;  July  81,  Aur  SR.  1880;  Sept. 
1 1  and  Dec.  4, 1891 ;  May  6  and  July  8, 1802.  For  properties  of  Ammonia  and 
Sulphur  Dioxide,  see  papers  by  Professors  Wood  and  Jacobus,  Trans.  A.  8. 
M.  B.,  vols.  X.  and  xll. 

F<tr  illusrrated  articles  describing  refrfgerating-machines,  see  Am.  Mach., 
May  29  and  June  28.  1890,  and  M/rs.  Recoi'd  JJct.  7, 1892;  also  cacalo^uee  of 
bundem,  as  Frick  A  Co.,  Waynesboro,  Pa. ;  De  La  Vergne  Befrigarating>ma- 
chine  C'o  ,  New  York;  and  others. 

Operations  of  a  RefHserating^-inacbiiie.— Apparatus  designed 
for  refrigerating  is  based  upon  ilie  following  series  of  operations: 

Compress  a  gas  or  vapor  by  means  of  some  external  force,  then  relieve  it 
of  its  heat  so  as  to  diminish  its  volume;  next,  cause  this  compressed  gas  or 
vapor  to  expand  so  as  to  produce  mechanical  work,  and  thus  lower  Its  tem- 
perature. Tiie  absorption  of  heat  at  this  stage  by  the  ras,  in  resuming  its 
orlginiil  condition,  constitutes  the  refrigerating  effect  of  the  apparattis. 

A  refrlgerat  Ing-mnchine  is  a  heat-engino  reversed. 

From  this  similarity  between  heat-motors  and  f reexlng-machlnee  It  results 
that  all  the  equations  deduced  from  the  mechanical  theory  of  heat  to  deter- 
mine the  perfoimance  of  the  first,  apply  equally  to  the  second* 

The  efllciency  depends  upon  the  duierence  between  the  extremes  of  tem- 
perature. 

The  useful  effect  of  a  refrigeratlng-machlne  depends  upon  the  ratio 
between  thn  heat-unlts  eliminated  and  the  work  expended  In  compressing 
and  expanding. 

This  result  is  Independent  of  the  nature  of  the  body  employed. 

Unlike  the  heat^motors,  the  freesing-machine  possesses  the  greatest  effi- 
ciency when  the  range  of  temperature  is  small,  and  when  the  final  tempera- 
ture IS  elevated. 

If  the  temperatures  are  the  same,  there  is  no  theoretioal  advantage  in  em- 
plovtng  a  gas  rather  than  a  vapor  in  order  to  produce  cold. 

The  choice  of  the  intermediate  body  would  be  determined  by  practical 
<K)n9klerattons  based  on  the  physical  characteristics  of  the  body,  such  as  the 
greater  or  less  facility  for  manipulating  it,  the  extreme  pressures  required 
for  the  best  effects,  etc. 

Air  offers  the  double  advantage  that  It  Is  everywhere  obtainable,  and  that 
we  can  vary  at  will  the  higher  pressures,  independent  of  the  temperature  of 
the  refrigerant.  But  to  produce  a  given  userul  effect  the  apparatus  must 
be  of  larger  dimensions  than  that  required  by  Hqueflable  vapors. 

The  maximum  pressure  Is  determined  by  the  temperature  of  the  con- 
denser and  the  nature  of  the  volatile  liquid:  this  pressure  is  often  very  high. 

When  a  change  of  volume  of  a  saturated  vapor  Is  made  under  constant 
pressure,  the  temperature  remains  constant.  The  addition  or  subtraction  of 
neat,  which  produces  the  chansre  of  volume,  is  represented  by  an  Increase  or 
a  diminution  of  the  quantity  of  liquid  mixed  with  the  vapor. 

On  the  other  hand,  wh^^n  vapors,  even  If  saturated,  are  no  longer  in  con- 
tact with  their  liquids,  and  receive  an  addition  of  heat  either  through  com- 
pression by  4  mechanical  force,  or  from  some  external  source  of  heat,  they 
comi)ort  themselves  nearly  in  the  same  way  as  permanent  gases,  and  be- 
come superheated. 

It  results  from  this  property,  that  refrlgeratlng«machlnes  using  a  Hquefl- 
able gas  will  afford  results  differing  according  to  the  method  of  worclng, 


982       ICE-HAKIKG   OR  BEFRIOERATINO   MACHIli^ES. 


and  dependinii:  upon  the  Ktate  of  the  km,  whether  It  remains  constantly  satp 
urated,  or  in  Kuperbeated  during  a  part  of  the  cycle  of  working. 

The  temjperature  of  the  condenser  Is  determined  by  local  conditions.  The 
interior  vvnl  exceed  by  9"  to  18**  the  temperature  of  the  water  furnished  to 
the  exterior.  This  latter  will  vary  from  about  53*  F.,  the  temperature  of 
water  from  considerable  depth  below  the  surface,  to  about  96*  F.,  the  tem- 
perature of  surface-water  In  hot  climates.  The  volatile  liquid  employed  in 
the  machine  ouRht  not  at  this  temperature  to  have  a  tension  above  that 
which  can  be  readily  managed  by  tiie  apparatus. 

On  the  other  hand,  if  the  tension  of  the  kah  at  the  minimum  temperature 
is  too  low,  it  becomes  necessary  to  give  to  the  compression-cylinaer  lar^ 
dimensions.  In  order  that  the  weight  of  vapor  compressed  by  a  single  stroke 
of  the  piston  shall  be  sufficient  to  produce  a  notably  useful  efTect. 

These  two  conditions,  to  which  may  be  added  others,  such  as  those  de- 
pending upon  the  greater  or  less  facility  of  obtaining  the  liquid,  upon  the 
dangers  incurred  in  its  use,  either  from  its  inflammability  or  unhealthfut- 
ness,  and  Anally  upon  its  action  upon  the  metals,  limit  the  choice  to  a  small 
number  of  substances. 

The  gases  or  vapors  generally  available  are:  sulphuric  ether,  sulphurous 
ozlile,  ammonia,  methyiic  ether,  and  carbonic  acid. 

The  following  table,  derived  from  Regnault,  shows  the  tensions  of  the 
vapors  of  these  substances  at  different  temperatures  between  —  2d*  and  -{- 

Pressares  and  Boillnc-points  of  liiqulda  aTailable  for 
Use  in  UemKeratinff-maelkineii. 


Temp,  of 
Ebullition. 

Tension  of  Vapor,  in  lbs.  per  sq.  in.,  above  Zero. 

Falfr. 

Sul- 
phuric 
Ether. 

Sulphur 
Dioxide. 

Ammonia. 

Methyiic 
Ether. 

Carbonic 
Add. 

Pictet 
Fluid. 

-40 

10.88 

18.88 

16.95 

21.51 

27.04 

83.67 

41.58 

60.91 

61.85 

74.55 

89.81 

105.99 

]i5.08 

146.64 

170.88 

197.  as 

2-i7.76 

-81 

-  18 



6.56 
7.88 
9.27 
11.76 
14.75 
18.81 
28.58 
27.48 

88  36 

89  98 
47.68 
66.39 
66.37 
77.64 
90.8-2 

11.15 
18.85 
17.06 
SO  84 
85.87 
80.41 
86.84 
48.18 
50.84 
69  66 
69.85 
80.88 
92.41 

"251  ie" 
898.9 
840.1 
898.4 
453.4 
530. 4 
6iM.8 
676.9 
766.9 
864.9 
971.1 
1085.6 
1M7.9 
1888.3 

-    4 
5 
14 
28 
82 
41 
50 

77 
86 
95 

1.80 

1.70 

2.19 

8.79 

8.55 

4.45 

6.54 

6.84 

«.38 

10.19 

1881 

14.76 

IT. 59 

18.5 
16.8 
19.3 
.*»2.9 
^.9 
81.8 
86.8 
41  7 
48.1 
».6 
64.1 
73  "i 

104 

R2.9 

The  table  shows  that  the  use  of  ether  does  not  readily  lead  to  the  produc- 
thin  of  low  temperatures,  becaune  its  pressure  becomes  then  very  feeble. 

Ammonia,  on  the  contrary,  is  well  adapted  to  the  production  of  low  tem- 
peiutures. 

Methyiic  ether  yields  low  temperatures  without  attaining  too  great  pres- 
sures at  the  temperature  of  the  condeuser.  Sulphur  dioxide  readily  alTords 
temperatures  of—  14  to  —  6,  while  its  pressure  Is  only  8  to  4  atmosphert^ 
at  the  ordinaiy  temperature  of  the  condenser.  These  latter  substances  then 
lend  themselves  conveniently  for  the  production  of  cold  by  means  of 
mechanical  force. 

The  ''Pictet  fluid'*  is  a  mixture  of  97<  sulphur  dioxide  and  9%  carbonic 
acid.  At  atmospheric  pressure  it  affords  a  temperature  14*  lower  than 
sulphur  dioxide. 

Carbonic  acid  is  as  yet  (1895)  In  use  but  to  a  limited  extent,  but  the  rela- 
tively  greater  compactness  of  compressor  that  It  i-equires,  and  its  Inoffensive 


THB  AHHOKIA  ABSOBPTIOX-MACUIKE.  983 

character,  are  leadintr  to  its  reoommendatioD  for  service  on  shipboard,  where 
economy  of  space  is  important. 

Certain  ammonia  plants  are  operated  with  a  surplus  of  liquid  present  dur- 
ing compression,  so  that  superheating  is  prevented.  This  practice  is  known 
as  the  ^'  cold  system  **  of  compression. 

Nothing  definite  is  known  regarding  the  application  of  methylic  ether  or 
of  the  petroleum  product  chymogene In  practical  ref rigeraiing  service.  The 
inflammability  of  the  latter  and  the  cumbrousness  of  the  compressor 
rennlred  are  objections  to  its  utie. 

^^lee-meUliiff  BflTeet."— It  is  agreed  that  the  term  "Ice-melting 
effect  '*  means  the  cold  produced  in  an  insulated  bath  of  brine,  on  the  as- 
sumption that  each  142.3  B.T.U.*  represents  one  pound  of  ice,  this  being  the 
latent  beat  of  fusion  of  ice,  or  the  heat  required  to  melt  a  pound  of  ice  at 
89«  to  water  at  the  same  temperature. 

The  performance  of  a  machine,  expressed  in  pounds  or  tons  of  **  ice-melt- 
ing  capacity,'*  does  not  mean  that  the  refrigerating-raHcbine  would  make 
the  same  amount  of  actual  ice,  but  that  the  cold  pi*oduced  is  equivalent  to 
the  effect  of  the  melting  of  ice  at  82"  to  water  of  the  same  temperature. 

In  making  artificial  ice  the  water  frozen  is  generally  about  70"  F.  when  snb- 
niitted  to  the  ref  rigerating  effect  of  a  machine;  second,  the  ice  is  chilled  from 
1'i"  to  SO*  below  its  freezing-point;  third,  there  is  a  dissipation  of  cold,  from 
the  exposure  of  the  brine  tank  and  the  manipulaliun  of  the  ice-cans:  there- 
fore the  weight  of  actual  ice  made,  multiplied  by  its  latent  heat  of  fusion. 
142.2  thermal  units,  represents  only  about  three  fourths  of  the  cold  produced 
in  the  brine  by  the  refrigerating  fluid  per  I.H.P.  of  the  engine  driving  the 
compressing-pumps.  Again,  there  is  considerable  fuel  consumed  to  operate 
the  brine-circulating  pump,  the  condensing-water  and  feed-pumps,  and  to 
reboil,  or  purtfy,  the  condensed  steam  from  which  the  ice  is  frozen.  This 
fuel,  together  with  that  wasted  in  leakage  and  drip  water,  amounts  to  about 
one  half  that  required  to  drive  the  main  steam-engine.  Hence  the  pounds 
of  actual  ice  manufactured  from  distilled  water  is  Just  about  half  the  equiv- 
alent of  the  refrigerating  effect  produced  in  the  brine  per  indicated  horse- 
power of  the  steam-cylinders. 

When  ice  Is  made  directly  from  natural  water  by  means  of  the  **  plate 
fiystem,"  about  half  of  the  fuel,  used  with  distilled  water,  is  saved  by  avoid- 
ing the  reboiling.  and  using  steam  expansively  in  a  compound  engine. 

Kther-iiiaelklnea,  used  in  India,  are  said  to  have  produced  about  6 
lbs.  of  actual  ice  per  pound  of  fuel  consumed. 

The  ether  machine  is  obsolete,  because  the  density  of  the  vapor  of  ether, 
at  the  necessary  working-pressure,  requires  that  tbe  compressing-cylinder 
fihall  be  about  6  times  larger  than  for  sulphur  dioxide,  and  17  times  largek* 
than  for  ammonia. 

Alr^BiAclilnefl  requlro  about  1.2  times  greater  capacity  of  compress- 
ing cylinder,  and  are,  as  a  whole,  more  cumbersome  than  ether  macninen, 
but  they  remain  in  use  on  ship-board.  In  using  air  the  expansion  must  take 
place  in  a  cylinder  doing  work,  instead  of  througli  a  simple  expansion-cock 
which  is  used  with  vapor  machines.  The  work  done  in  the  expansion-cylln- 
der  is  utilized  In  assisting  the  compressor. 

Ammonia  CompreMion-machtnea.— "Co2d  "  vs.  '"'Dry  "  SysiemB 
rtf  Comm-e»8ioH.— In  the  '*  cold  **  system  or  "  humid  **  system  some  of  the 
ammonia  entering  the  compression-cylinder  is  liquid,  so  that  the  heat  de- 
veloped in  the  cvunder  is  absorbed  by  the  liquid  and  the  temperature  of  the 
Ammonia  thereby  confined  to  the  boiling-point  due  to  the  condenser-pres- 
sure.   No  Jacket  is  therefore  required  about  the  cylinder. 

In  the  "  dry  "  or  *'  hot ''  system  all  ammonia  entering  the  compressor  is 
gAseous,  and  the  temperature  becomes  by  compression  several  hundred  de- 
grees greater  than  the  boiling-point  due  to  the  condenser-pressure.  A  water- 
jacket  is  therefore  necessary  to  permit  the  cylinder  to  be  properly  lubri- 
cated. 

Relative  Performance  of  Ammonia  Compreaaion-  and 
Abaorptlon-maciiinea,  aaanminic  no  ITater  to  be  Bn- 
trainea  ivitlk  tlie  Ammonia-^as  in  the  Condenser.  (Denton 
and  Jacobus,  Trans.  A.  S.  M.  E..  xiii.)— It  is  assumed  in  the  calculation  for 
both  machines  that  1  lb.  of  coal  imparts  10,000  B.T.U.  to  the  boiler.    The 

«  The  latent  heat  of  fusion  of  ice  is  144  thermal  units  (Phil.  Mag.,  1871, 
zli.,  18S);  but  it  i»  customary  to  use  H2.  (Prof.  Wood.  Trans.  A.  S.  M.  E., 
zl.  834.) 


d$4      lOE-llAKtKG  OH  ttEFHlOKRATlfiTG  KAOHttTES. 


onndenfled  Rteam  from  the  generator  of  the  abeorption«mfictaioe  in  aMomed 
to  be  returneil  to  the  boiler  at  the  temperature  of  the  steam  enteriu^  the 
generator.  The  engine  of  the  compreMion-inachine  fa  aaaunied  lo  ezhaiist 
through  a  feed- water  heater  thai  heats  the  feed-water  to  91  ;i*  F.  The  trnruie 
is  assumed  to  consume  36^  lbs.  of  water  per  hour  per  horse-power.  The 
flsures  for  the  oompreseion- machine  inolude  the  effect  of  friction,  which  is 
taken  at  16j(  of  the  net  work  of  compression. 


Condenser. 


61.2 
690 
69.0 
69.0 
80.0 
86.0 
86.0 
86.0 
10»  0 
104.0 


I 

i 

i 

u 


110.6 

106.0 

106.0 

106.0 

170.8 

170.8 

170.8 

170.8 

«<7. 

227  7 


Refriee  rat- 
ing Ooilfl. 


5 
5 
6 

fl 
5 

-29 

6 

-89 


u 


88.7 
88.7 
83.7 
16.9 
83.7 
88.7 
16.9 
10.0 
88.7 
16.9 


61.2 
59.0 
180.0 
69.0 
86.0 
180.0 
86.0 
180.0 
104.0 
104.0 


Pounds  of  Ice-melting  Effect 
per  lb.  of  Goal. 


Compress. 
Machine. 


B  O 

r 


88.1 
80.8 
89.8 
98.4 
25.0 
25.0 
16.5 
16.5 
19.6 
18.6 


II 


71.4 
74.6 
74.6 
48.9 
46.9 
46.9 
80.8 
80.8 
86.8 
96.8 


Absorption- 
machine.* 


Hi 


88.1 
88.8 
89.8 
86.8 
85.4 
86.9 
88.8 
84.1 
88.4 
81.4 


is 


83.5 
88.9 
85.1 
81.6 
98.6 
99.9 
96.5 
97.0 
26.1 
88.4 


fill 

III 

hi 


907 
881 
1000 
968 
966 
1086 
1009 
1008 
1041 


Tbe  AmmonlA  Absorptlon-macliine  comprises  a  generator 
which  contains  a  ooncentraieti  solution  of  ammonia  in  water;  this  gener- 
ator  is  heated  cither  directly  by  a  fire,  or  indirectly  by  pipes  leading  from  a 
steam-boiler.  Tbe  condenser  communicates  with  the  upper  part  of  the  grn* 
erator  by  a  tube;  it  is  cooled  externally  by  a  current  of  cold  water.  The 
cooler  or  brine-lank  is  so  constructed  as  to  utilise  the  cold  produced;  the  up* 
per  part  of  it  U  in  comnmnication  with  the  lower  part  of  the  coiideiiiier. 

An  absorption-chamber  is  filled  with  a  weak  solution  of  ammonia;  a  tube 
puts  this  chamber  in  communication  with  the  cooling-tank. 

The  absorption- chamber  communicates  with  the  boiler  by  two  tabes:  one 
leadH  from  the  botUim  of  the  generator  to  the  top  of  the  chamber,  the  other 
leads  from  the  bottom  of  the  chamber  to  the  top  of  the  generator.  Upon 
the  latter  is  mounted  a  pump,  to  force  tbe  liquid  from  the  absorption  cham- 
ber, where  the  pressure  ismaintalued  at  about  one  atmosphere,  iii:o  Uie  gen- 
erator, where  the  pressure  is  from  8  to  19  atmoepheree. 

To  work  the  apparatus  the  ammonia  solution  In  the  generator  is  flmt 
heated.  This  releases  the  gas  from  the  solution,  and  the  pressure  rise^. 
When  it  reaches  the  tension  of  the  saturated  gas  at  the  temperature  of  the 
condenser  there  is  a  liquefaction  of  the  gas.  and  also  of  a  small  amount  of 
steam.  By  means  of  a  cock  the  flow  of  the  liquefied  gas  into  the  refrigerate 
ing  coils  contained  in  the  cooler  is  regulated.  It  is  here  vaporized  by  ab- 
sorbing the  heat  from  the  substance  placed  there  to  toe  cooled.  AS  tmn  as  it 
is  vaporised  it  is  absorbed  by  the  weak  solution  in  the  absorbing-chamber. 

Under  the  influence  of  the  heat  in  the  boiler  the  solution  is  unequally  sat* 
iirati'd,  the  stronger  solution  being  uppermost. 
^    The  weaker  portion  is  conveyed  by  the  pipe  entering  the  top  of  the  absorb- 
ing-chamber, tne  flow  t>eiug  regulated  by  a  cock,  while  the  pump  sends  an 
equal  quantity  of  strong  sohition  from  the  chamber  back  to  tbe  boiler. 

*  5jl  of  M-ater  entrained  in  the  ammonia  will  lower  the  economy  of  theab* 
sorption -machine  about  15%  to  20%  below  the  figures  given  in  the  table. 


SULPHUR-DIOXIDB  MACHINES. 


985 


The  working  of  the  apparatus  depends  upon  the  adjustment  and  regula- 
tion of  the  flow  of  the  ga^  and  Ifquicf;  by  these  means  the  pressure  Is  varied, 
and  consequently  the  temperature  in  the  cooler  may  be  controlled. 

The  working  Is  similar  to  that  of  compression-machines.  The  absorption- 
chamber  Alls  the  office  of  aspirator,  and  the  generator  plays  the  part  of 
compressor. 

The  mechanical  force  producing  exhaustion  is  here  replaced  by  the  aflftnity 
of  water  for  ammonia  gns;  and  the  mechanical  force  required  for  compree- 
sion  is  replaced  by  the  neat  which  seven  this  affinity  and  sets  the  gas  at 
liberty. 

(For  discussion  of  the  efficiency  of  the  absorption  system,  see  Ledouz*8 
work;  paper  by  Prof.  Linde,  and  discussion  on  the  same  by  Prof.  Jacobus, 
Trans.  A.  B.  H.  £.,  xiv.  1416,  1486;  and  papers  by  Denton  and  Jacobus, 
Trans.  A.  8.  M.  B.  x.  709;  xili.  507. 

Snlplftar-IHoxlde  l!IIachine««^Result8  of  theoretical  calculations 
are  given  in  a  table  by  Ledoux  showing  an  ice-melting  capacity  per 
hour  per  horse-power  ranging  from  134  to  63  lbs.,  and  per  potmd  of  coal 
ranging  from  44.7  to  81.1  lbs.,  as  the  temperature  corresponding  to  the 
pressure  of  the  vapor  in  the  condenser  rises  from  60^  to  104*  F.  The  theo- 
retical results  do  not  represent  the  actual.  It  is  necessary  to  take  into  ac- 
count the  loss  occasioned  by  the  pipes,  the  waste  spaces  in  the  cylinder,  loss 
of  time  in  opening  of  the  valves,  the  leakage  around  the  piston  and  valves, 
the  reheating  by  the  external  air,  and  finally,  when  the  ice  is  being  made, 
the  quantity  of  the  ice  melted  in  removing  the  blocks  from  their  moulds. 
Manufacturers  estimate  that  practically  the  sulphur-dioxide  apparatus  using 
water  at  55<>  or  60*  F.  produces  fi6  lbs.  of  ice,  or  about  10,000  neat-units,  per 
hour  per  horse-power,  measured  on  the  driving-shaft,  which  is  about  66%  of 
the  theoretical  useful  effect.  In  the  commercial  manufacture  of  ice  about 
7  lbs.  are  produced  per  pound  of  coal.  This  includes  the  fuel  used  for  re- 
boiling  the  water,  which,  together  with  that  wasted  by  the  pumps  and  lost 
oy  radiation,  amounts  to  a  considerable  portion  of  that  used  by  the  engine. 

Prof.  Denton  says  concerning  Ledoux'a  theoretical  results:  The  figures 
given  are  higher  than  those  ootained  In  practice,  because  the  effect  of 
Hiiperheating  of  the  gas  during  admission  to  the  cylinder  is  not  considered. 
This  superheating  may  cause  an  increase  of  work  of  about  Sbi.  There  are 
other  losses  due  to  superheating  the  gas  at  the  brine-tank,  and  in  the  pipe 
leading  from  the  brine-tank  to  the  compressor,  so  that  in  actual  practice  a 
sulphur-dioxide  machine,  working  under  the  conditions  of  an  absolute 


'pr^ure  in  the  condenser  of  66  lbs.  per  sq.  ir.  and  the  corresponding  tem- 
perature of  77*  F.,  will  give  about  ad  lbs.  of  ice-melting  capacity  per  pour  ' 
of  coal,  which  is  about  00%  of  the  theoretical  amount  neglecting  friction,  or 


TOj^  inc^ding  friction.  The  following  tests,  selected  from  those  made  by 
Prof.  SchrSter  on  a  Pictet  ice-machine  having  a  compression-cylinder  11.8 
In.  bore  and  24.4  in.  stroke,  show  tlie  relation  between  the  theoretical  and 
actual  ice-melting  capacity. 


Temp,  in  degrees  Fahr. 
corresponding  to       ' 
pressure  of  vopor. 

Ice-melting  capacity  per  pound  of  coal. 

No.  of 
Teat. 

Oondenser. 

Suction. 

Theoretical 

friction 
included.* 

Actual. 

Per  cent  loss  due  to 
cylinder  super- 
heating, or  differ- 
ence between 
cols.  4  and  5. 

11 
12 
13 

14 

77.3 
76.2 
76.« 

80.6 

28.5 

14.4 

-2.6 

-16.9 

41.3 
31.2 
23.0 
16.6 

38.1 
24.1 
17.5 
10.1 

19.0 
22.8 
23.9 
89.2 

Tbe  R^flrlceratiiii:  Colla  of  a  Pictet  ice-machine  described   by 
Ledoux  had  79  sq.  ft.  of  surface  for  each  100.000  theoretic  negative  heat-units 

Sroduced  per  hour.    The  temperature  corresponding  to  the  pressure  of  the 
ioxide  in  the  coils  is  lOA^  F.,  and  that  of  the  bath  (calcium  chloride  solu- 
tion) In  which  they  were  immersed  i»  19  4®. 

♦  Friction  taken  at  figure  observed  in  the  test,  which  ranged  from  23j<  to 
S6%  of  the  work  of  the  steam-cylinder.     * 


DS6       ICE-MAKIKG   OB  BEFKIGBRATIKG  MACHIK£& ' 


-oiox  JO  admm '.2  aOe  ^upnnB 
-811  *iC)pBd«o^api9ui~«9I  JO 
aox  J9d    uo^VM  -  JSaisa^pnoQ 

i 

uow 
-s>!J.i  11!M^  jdpaiiXo-uiTOig 
JO  JH  •>»<*  jnoq  jad  [woo 
JO  *8q|  8  aafiunesv  *i«oo  jo 
•qi   J9d  ^)|0«d«o  >)up|9ui-aoi 

i 

*9a9ui90vid 
-sia   n«»8!«T  JO   !joo^  oiqno 
a 9a    ^)p«€li^     j)a|iidui-90l 

<i 

Hi 

5| 

Is 

•nopoMJ  qi!M 

'J9AO€r 

-9SJOH  Jod  Jnoq  J9ci 

•uonou  J  qiijii  • 
'aoissaidmc^  jo    o» 
VOAlJoqi--^jj9«i 

ill 

g 

1 

i 
2 

li 

1 

•J9MOd        ^ 

mv»iQ  pa^nojpui      S 
JO  'aopoiJji  M»IM    :; 

OOQOS 

•iiono|j^?noqqiii\    ^ 

i 

at 

•p9dOT9A 

»^X    JO  J9quinK 

•J9Ba9paoo         - 
V»     p9>0WJ48qv     !»TOH    ^ 

- 

SS9 

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-moo   8B0    JO    %1{^\9J^      * 

1 

ill 

1   ^ 
*uoi889Jdaioo  JO 

*8l|O0-dun«49SlJJ          " 

-9H  uf  9anssaj<i  d^niosqy     "'* 

It 

J0<3 
-pu 

tijioo 

l«AJO 

od»M 

JOQ    9Jn)UI9dUI9J, 

1 

S88 
1 

AMMONIA  COMPRESSION-MACHIKES. 


987 


*&inoq  fs  Of  iCipod 
gox  Jod  otinum  joj 


'iCi|Otid«o  am 
-9Idia-90i  JO  uox  JL^d 


uojaftl  JO  -3 J  na  j^>j 


lodoidovidsta 


1^ 

teW 


•ao!JOiJi[  q?IM 


-non 


•norpiJ.i  qilM 


'nopi 


I 


-pn|oa)  'popuadxa 


•aopoijji 
^noq^IM'pepaddxca 
VOM  JO    qi -^j  49J 


§SS3SS8 


iliilll 


-  aci  —  c?*'? 


l^iiii^fe 


^^e»aoapi'>C 


^iiiii 


-JdMod-tavd^g  p9)iK> 
-!pai  JO  'aonaij^  qq|A 
'ao}8sajduioo    jo    ^40j^ 


•uopop^  inoq^fM 
*uo|88ajdaioo     jo    sfJOAi 


■ja  aanii.iaaijj»a  jo  opwa 


ni    io#jj3 


•jj»8aapaoo 
raojj  iCvAiv  pdfjjvj  ^v^n 


'ao{8B9jdaioo 
JO  paa   9«   ejn^Bjoduidj, 


'josagp 
-aoQ  in  ainssajfi  »)ii[u8qy 


I  Si 

lit 


'jasoopnoo  uj  jo<Ii?a 
JO  '889J^   o^  9nQ    duia^  ! 


O  ^«  (DOC  OOQO 


ssagu^ss 


g^s^s^s 


?ii§ii§ 


c^siSiis 


^«  ©i  r- «  i-i  .-• 


t>.Oooao^«D 


siiiiii 

-88888S 


"^'CO  fc«  00  OD  Ok  O 


'vevcoaooto) 


Ss§%gg^ 


-  <a  o  1^  00  S  S 


988      IC£-K/kKIKQ  OR  B£FRIGERATING  HACHIKES. 


The  foUowlofi:  is  a  comparison  of  the  theoreUcal  ice-mdhiiig  capadty  of  an 
amniOQia  compre88ioB  machine  with  that  obuUnAd  in  soine  of  Prof. 
Bchrdcer's  tests  on  a  Llnde  machine  having  a  oonipreesiOM-cjIinder  9.9-ln. 
bore  and  16.&  in.  strolce,  and  alao  in  tests  by  Prof.  Denton  on  a  maciiine 
having  two  single-acting  compression  cylinders  19  in.  x  80  in.: 


Temp,  in  Degrees  F. 

Correspoamng  to 
Pressure  of  Vapor. 


on  cyiinaers  is  in.  x  au  m.: 

Ice-mettlng  Capacity  per  lb.  of  Coal, 
'    assummg  » lbs  per  hour  per 
Horse-power. 


No. 

of 

Test. 


Condenser. 


Suction. 


Theoretical, 

Friotion  ♦  in- 

Aceoal. 

cluded. 

50.4 

40.6 

87.6 

80.0 

80.4 

89.0 

JB.8 

16.1 

87.4 

84.8 

21 .« 

17.6 

18.8 

14.6 

PerOsot 
of  Loss  Due  le 

Cylinder 
Superheating. 


2  I  4 


78.8 
70.5 
60.8 
68.6 

84.9 
88.7 
84.6 


26.6 

34.8 

0.5 

-11.8 

15.0 
-  8.8 
-10.8 


19.4 
20.9 
99.9 
89.4 

n.T 

19.0 
»i.9 


Beflrlfferailiiff  ]II«chln««  nains  Vapor  of  ITater.  (Ledons.) 
~ln  these  machines,  Boiiieiimes  cult«d  vacuum  macliines,  water,  at  ordi 
nary  temperatures,  is  injected  into,  or  placed  In  connection  wiUi,  a  chamber 
in  which  a  strong  vacuum  is  maintained.  A  portion  of  the  water  Taporln**, 
the  heat  to  cause  the  vaporization  being  supplied  from  the  water  not  vapor- 
ized,  so  that  the  latter  is  chilled  or  f  rosea  to  ice.  If  brine  is  uscsd  instead  of 
pure  water.  Its  temperature  may  be  reduced  below  the  freezin^r  p<wnt  of 
water.  The  water  vapor  is  compressed  from,  say,  a  pressure  of  one  tenth 
of  a  pound  pet*  square  inch  to  one  and  one  half  pounds,  and  dipcharged  Into 
a  condenser.  It  is  tlien  condensed  and  removed  bv  means  of  an  ckrdinary 
alr-pumu.  The  principle  of  action  of  such  a  machine  is  the  same  as  that 
of  volatile-vapor  machines. 

A.  theoretical  calculation  for  ice-making,  assuming  a  lower  temperature 
of  82«  F.,  a  pressure  in  the  condenser  of  1^  lbs.  per  square  inch,  and  a  ct^ 
consumption  of  3  Uis.  per  I.H.P.  per  hour,  gives  an  ice-melting  effect  of  JM.5 
lbs.  per  pound  of  coal,  neglecting  friction.  Ammonia  for  ice-malcing  qotkII- 
tions  gives  40.9  lbs.  The  volume  of  the  compressing  cylinder  is  about  190 
times  the  theorettnal  volume  for  an  ammonia  machine  for  the*ie  conditions. 

RelatlTe  Bfllclencjr  of  a  Refrl««ratinf(  IWaehlne.— Tifie  effi- 
ciency of  a  refrigerating  machine  is  sometimes  expressed  as  the  Quotient  of 
the  quantity  of  neat  received  by  the  ammonia  from  the  brine,  that  i5.  the 
quantity  of  useful  work  done,  divided  by  the  heat  equivalent  of  the  naeckan- 
ical  work  done  in  the  compressor.  Thus  in  column  1  of  the  table  of  perfonn- 
ance  of  the  75-ton  machine  (page  098)  the  heat  given  by  the  brine  to  the 
ammonia  per  minute  is  14,770  B.T.U.  The  horse-power  of  the  ammonia  cylin- 
der 16  05.7.  and  its  heat  equivalent  =  65.7  X  33,000  ^  778  =  8796  B.T.U.  Then 
14,770  -i-  278(>  =  5.804,  eiBciency.  The  apparent  paradox  that  the  efllciencv 
is  greater  than  unity,  which  is  Impossible  in  any  machine,  is  thus  explained. 
The  working  fluid,  as  ammonia,  receives  heat  from  the  brine  and  reject* 
heat  into  the  condenser.  (If  the  compressor  is  jacketed,  a  portion  Is  rejected 
into  the  jacket-water.)  The  heat  lejectod  into  the  condenser  is  greater  than 
that  received  from  the  brine;  the  difference  (plus  or  minus  a  small  diflrer«»oce 
radiated  to  or  from  the  atmosphere)  Is  lieat  received  by  the  ammouia  fr»>in 
the  compressor.  The  work  to  be  done  by  tiie  compressor  is  not  the  mechan- 
ical equivalent  of  the  refrigeration  of  the  brine,  but  only  that  neceasary  to 
supply  the  difference  between  the  hent  rejecf-ed  by  the  ammonia  Into  the  con- 
denser and  I  hat  receivcnl  from  the  brine.  If  cooling  water  colder  t-ban  the 
brine  were  available,  the  brine  might  transfer  its  heat  directly  into  the  cool- 
ing water,  and  there  would  be  no  ne^d  of  ammonia  or  of  a  compressor;  but 


♦  Friction  taken  at  figures  observed  iu  the  tests,  which  range  from  14jf  to 
20JC  of  the  work  of  tlie  steam-cvlinder. 


BFFICIBNOY  OF  BBFEIOBRATIliO-MAOHIKES.       989 


since  miob  oo)4  Wi|ter  in  no(  AVftUnble,  ihf  brin«  mJecta  its  heat  into  (be 
colder  ammonia,  and  then  the  coiupretisor  is  required  to  heat  the  ammonia 
to  »uch  a  temperatQM  that  it  may  rejeot  haat  into  the  cooling  water. 

The  efflcleupy  of  ck  refrigerating  plant  referred  to  the  ftmount  of  fuel 
couaumed  19 


Ice-melting   fiapiicltj ) 
per  pound  oi  ruel     f 


( pounds  oiroqiated  per  hour 
X  speciflo  he^t  X  rwjgu 
of  temperature 


1 


foil 


brine  or  other 
olrouUttittg  fluid. 


ltt.8  X  pouudsof  fuel  used  perliour. 
The  ifle^malt^og  oftpMity  |a  evproMed  iw  fcaiows; 


[  of  brine  QirpvlAtfid  per  bour. 


( ^  X  pounds 
Tonsfof  fiOOOIbs.)      )     i      X  »pec*flo  b«»t 

paolty  per  M  hours  |  14;I.D  X  HOOO 

The  analogy  between  a  heat-engine  and  a  refMprsriltlng- machine  is  as  fol- 
lows: A  steam-engine  receives  heat  from  the  boiler,  eonveris  a  part  of  it 
into  mechanical  work  in  the  cylinder,  and  throws  away  the  difference  into 
the  condenser.  The  ammonia  in  a  compression  refrigerating  machine  re- 
ceives  heat  from  the  brine-tan li  or  oold-rpom,  receives  an  additional  amount 
of  heat  from  the  mechftnioal  work  done  in  the  oompvesslon- cylinder,  and 
throws  away  the  supi  into  the  condenser.  The  efficiency  of  the  steam-engine 
=  work  done  •*■  heat  received  Ivoai  boiler.  The  elHolenoy  ef  the  ref riKenit* 
iiig-roaehiqe  b  heat  received  from  the  brine-tank  or  ocad-room  -*-  haat  re- 
(^ulred  to  produQe  (be  worK  in  the  oompreask>n-cyliuder.    Iq  the  ammonia 


Wwm  Water  *"»  ewnprnrfeo.  H^t  reetired 

Hmi  rajvetcd  fron  brioe 

OlAPHilM  OP  AMMONIA  C0MPIICII8I0N  MAQHINC. 


absoratlott-amianitus.  the  ammonia  receives  best  from  the  brln»4ank  and 
additional  heat  from  the  boiler  or  generator,  and  relects  the  sum  Into  the 
condenser  and  into  (he  cooling  water  supplied  to  the  absorber.  The  elll- 
c)9nc7  s  bea^  received  froir^  the  brine  -t-  beat  received  from  t|)e  boiler. 


990      ICB-MAKING  OR  RBFEIGBRATING  MACHINES, 

TBST-TRIAIiS  OF  RBPBIGERATING-MACCIINBS. 

(G.  L(nde,  Trans.  A.  S.  M.  E.,  xiv.  1414.) 

The  purpose  of  the  test  Is  to  determine  the  ratio  of  consumption  and  pro* 
ductlon,  so  that  there  will  have  to  be  measured  both  the  refrigerative  effect 
and  the  heat  (or  mechanical  work)  consumed,  also  the  coolinf^  water  The 
refrigerative  effect  is  the  product  of  the  numberof  heat^units  (Q)  abstracted 

To  —  T 
from  the  body  to  be  cooled,  and  the  quotient  — = — ;  in  which  Te  =  abso- 
lute temperature  at  which  heat  is  transmitted  to  the  cooling  water,  and  T  = 
absolute  temperature  at  which  heat  is  taken  from  the  body  to  be  cooled. 

The  determination  of  the  quantity  of  cold  will  be  possible  with  the  proper 
exactness  only  whea  the  machine  is  employed  during  the  test  to  refrigerate 
a  liquid;  and  if  the  cold  be  found  from  the  quantity  of  liquid  circulated  per 
unit  of  time,  from  Its  range  of  refrigeration,  and  froui  it«  specific  heat. 
Sufficient  exactness  cannot  oe  obtained  by  the  refrigeration  of  a  curi^nt  of 
circulating  air,  nor  from  the  manufacture  of  a  certain  quantity  of  ice,  nor 
Irom  a  calculation  of  the  fluid  circulating  wltiiin  the  machine  (for  instance, 
the  quantity  of  ammonia  circulated  by  the  compressor).  Thus  the  refrig- 
eration of  brine  will  generally  form  the  basis  for  tests  making  any  pretension 
to  accuracy.  The  degree  of  refrigeration  should  not  be  greater  than  neces- 
sary for  allowing  the  range  of  temperature  to  be  measured  with  the  neces- 
saiy  exactness;  a  range  of  temperature  of  from  5°  to  6^  Fahr.  will  suffice. 

The  condenser  measurements  for  cooling  water  and  its  temperatures  will 
bepossible  with  sufficient  accuracy  only  with  submerged  condensers. 

The  measurement  of  the  quantity  of  brine  circulated,  and  of  the  cxwiing 
water,  is  usually  effected  by  water-meters  inserted  into  the  condulta.  If  the 
necessary  precautions  are  observed,  this  method  is  admissible.  For  quite 
precise  tests,  however,  the  use  of  two  accurately  gauged  tanks  must  be  ad 
vised,  which  are  alternately  filled  and  emptied. 

To  measure  the  temperatures  of  bdne  and  cooling  water  at  the  entrance 
and  exit  of  refrigerator  and  condenser  respectively,  the  employment  of 
specially  constructed  and  frequently  standardized  therroomecers  ia  intlis- 
pensable;  no  less  important  is  the  precaution  of  using  at  each  spot  simul- 
taneously two  thermometers,  and  of  changing  the  position  of  one  such 
thermometer  series  from  inlet  to  outlet  (and  vice  versa)  after  the  expiration 
of  one  half  of  the  test,  in  order  that  possible  errors  may  tie  compensated. 

It  is  Important  to  determine  the  specific  heat  of  the  brine  used  in  each 
instance  for  its  corresponding  temperature  range,  as  small  differences  in  the 
composition  and  the  concentration  may  cause  considerable  variations. 

As  regards  the  measurement  of  consumption,  the  programme  will  not  have 
any  special  rules  in  cases  where  only  the  measurement  of  steam  and  cooling 
water  is  undertaken,  as  will  be  mainly  the  case  for  trials  of  absorption-ma- 
chines. For  compression-machines  the  st^am  consumption  depends  both 
on  the  quality  of  the  steam-engine  and  on  that  of  the  refrigeiating-niaehine. 
while  it  is  evidently  desirable  to  know  the  consumption  of  the  former  sep- 
arately from  tliat  of  the  latter.  As  a  rule  steam-engine  and  compressor  are 
coupled  directly  together,  thus  rendering  a  direct  measurement  olT the  power 
absorbed  by  the  ref  rigerating-machine  impossible,  and  it  will  have  to  suffice 
to  ascertain  the  indicated  work  both  of  steam-engine  and  compressor.  Bv 
further  measurin.;  the  work  for  the  engine  running  empty,  andby  connpar- 
ing  the  differences  in  power  between  steam-engine  and  compressor  resulting 
for  wide  variations  of  condenser-pressures,  the  effective  consumption  of 
work  Le  for  the  refrigerating-machtne  can  be  found  very  closely.  In  pen- 
oral,  it  will  suffice  to  use  the  indicated  work  found  in  the  steam-cylinder, 
especially  as  from  this  observation  the  expenditure  of  heat  can  be  directly 
determined.  Ordinarily  the  use  of  the  indicated  work  in  the  compressor- 
cylinder,  for  purposes  of  comparison,  should  be  avoided;  firstly,  because 
there  are  usually  certain  accessory  apparatus  to  be  driven  (B;^tators,  etc.). 
belonging  to  the  refrigerating-machiue  proper;  and  secondly,  because  the 
external  friction  would  be  excluded. 

Keat  Balanee.— We  possess  an  important  aid  for  checklnj^  the  cor- 
rectness of  the  results  found  in  each  trial  b\-  forming  the  t>alance  in  each 
case  for  the  heat  received  and  rejected.  Only  such  tests  should  be  re- 
garded as  correct  beyond  doubt  which  show  a  sufficient  conformity  in  the 
heat  balance.  It  is  true  that  in  certain  instances  it  may  not  be  easy  to 
aci'ount  fully  for  the  transmission  of  heat  between  the  several  parta  of  the 
machine  and  its  environment  by  radiation  and  convection,  but  ^^neral^ 


TBMPERATURE  BAKGE.  991 

^partlcul&rly  for  compression -machfnes)  It  will  be  possible  to  obtafn  for  the 
heat  reoeiyed  and  rejected  a  balance  exhibltinfc  small  discrepancies  only. 

Beport  of  Test.— Reports  intended  to  be  used  for  oompaiison  with 
the  fli^iree  found  for  other  machines  will  therefore  have  to  embrace  at  least 
the  following  observations : 
Refrigerator*, 

Quantity  of  brine  drenlated  per  hour 

Brine  temperature  at  Inlet  to  refrigerator 

Brine  temperature  at  outlet  of  refrigerator i 

Specific  gravity  of  brine  (at  64*  Fahr.)    

Specific  heat  of  brine 

Heat  abstracted  (cold  produced) Qt 

Absolute  pressure  In  the  refrigerator 

Condenser  : 

Quantity  of  cooling  water  per  hour 

Temperature  at  Inlet  to  condenser 

Temperature  at  outlet  of  condenser t 

HoAt  abstracted Qi 

Absolute  pressure  in  the  condenser 

Temperature  of  gases  entering  the  condenser 


COMPBBSSTON-MACBINK. 

CompretBor : 

Indicated  work Lt 

Temperature  of  gases  at  inlet.. 

Temperature  of  gases  at  exit . . 
Steam-engine : 

Feed-water  per  hour 

Temperature  of  feed-water. . . . 

Absolute  steam-preesure  before 
steam-engine 

Indicated  work  of  steam-engine 
Le 

0>nden8ing  water  per  hour .... 

Temperature  of  da 

Total  sum  of  losses  by  radiation 

and  convection ±  Q^ 

Heat  Balance : 

Qe  +  ALo^Qt±Qt. 


AB0ORPTION-MACHINS. 
Still  : 

Steam  consumed  per  hour 

Abs.  pressure  of  heating  nteam. 
Temperature     of      condensed 

steam  at  outlet... 

Heat  imparted  to  still Q'e 

Absorber : 
Quantity  of  cooling  water  per 

hour 

Temperature  at  inlet 

Temperature  at  outlet 

Heat  removed  Qt 

Pump  for  Ammonia  Liquor: 
IndicAted  work  of  steam-engine 
Steam-consumption  for  pump.. 
Thermal  equivalent  for  work  of 

pump ALp 

Toul  sum  of  losses  by  radiation 

an4  convection ±  Q^ 

Beat  Balance  : 

«•  +  «'•  =  «,  +  «t±Qt. 
For  the  calculation  of  efficiency  and  for  comparison  of  various  tests,  the 
actual  efficiencies  must  be  compared  with  the  theoretical  maximum  of  effi- 
ciency \-¥f)  max.  =        _      corresponding  to  the  temperature  range. 

Temperature  BanKe«  —  As  tempere,tures  (T  and  To)  at  which  the 
heat  is  abstracted  in  the  refrigerator  and  imparted  to  the  condenser, it  is  cor- 
n>ct  to  select  the  temperature  of  the  brine  leaving  the  refrigerator  and  that 
of  the  cooling  water  leaving  the  condenser,  because  it  in  in  principle  impos- 
sible to  keep  the  refrigerator  pressure  hieher  than  would  correspond  to  the 
lowest  brine  temperature,  or  to  reduce  tne  condenser  pressure  below  that 
corresponding  to  the  outlet  temperature  of  the  cooling  water. 

Prof.  Unde  shows  that  the  maximum  theoretical  efficiency  of  a  com- 
pression-machine may  be  expressed  by  the  formula 

g  __     T 

AL  ^  To"  T' 

In  which  Q  =  qoantltv  of  heat  abstracted  (cold  produced); 

AL  =  thermal  equivalent  of  the  mechanical  work  expended; 
L  =  the  mechanical  work,  and  A  =  1  •*'779\ 
T=  absolute  temperature  of  heat  abstraction  (refrigerator); 
Tfl  =       **  **  **      '*     rejection  (condenser). 

If  tt  =  ratio  between  the  heat  equivalent  of  the  mechanical  work  AL^  and 
the  quantity  of  heat  Q^  which  must  be  imparted  to  the  motor  to  produce 
the  work  L,  then 


992      ICE-MAKIKO  OE  RBFRIGEHATIKG  MACHIKE8. 


AL 


It  follows  that  the  expenditure  of  heat  (^  neceBatLry  for  the  prodaction  of 
the  quantity  of  cold  Q  In  a  compression -machine  will  be  the  smaller,  the 
BmAller  the  difference  of  temperature  Tc.  -  T. 

Meteriiiff  tb«  Aiiui&oiii««->For  a  complete  test  of  an  ammonia  re- 
frlKerating-machiue  it  is  advisable  to  measure  the  quantity  of  ammonia  cir- 
culated, as  was  done  in  the  test  of  the  75-ton  mac  nine  deecribed  by  Prof. 
Denton.    (Trann.  A.  8.  M.  E.,  xii.  830.) 

PBOPEBTIB8  OF  817IiPH17R  DIOXIDB  Alfll 
AMHONIA  GAS. 

liedonx's  Table  for  Saturated  Snlphnr-dloxlde  Gaa« 

Heat-units  expressed  in  B.T.U.  per  pound  of  sulphar  dioxide. 


Temperature 
of  Ebullition 
in  deg.  F. 

liai 
< 

Total  Heat 
from82oF. 

Heat  of  Liquid 
reckoned 

Heat  Eqiriva^ 
lent  of  Exter- 
nal Work. 
APu 

Increase  of 
Volume  dur- 
ing Evapo- 
ration. 
11 

Deg.  F. 

Lbs. 

B.T.U. 

B.T.U. 

B.T.U. 

B.T.U. 

B.T.U. 

Co.  ft 

Lbs. 

-28 

5.66 

167.48 

-19.56 

176.99 

18.59 

168.89 

18.17 

.076 

-18 

7.23 

158.64 

-16.80 

174.95 

18.88 

161.18 

10.27 

.097 

-  4 

9.27 

189.84 

-18.05 

172.89 

14.06 

158.84 

8.12 

.123 

6 

11.76 

161.08 

-  9.79 

170.82 

14.26 

156.66 

6.60 

.153 

14 

14.74 

168.20 

-  6.58 

168.73 

14.46 

154.27 

6.25 

.190 

88 

18.31 

163.86 

-  8.27 

166.68 

14.66 

151.97 

4.29 

.233 

82 

22.63 

161.61 

0.00 

164.51 

14.84 

149.68 

8.M 

.282 

41 

27.48 

165  65 

8,27 

162  88 

15.01 

147.87 

2.98 

.340 

60 

83.25 

166.78 

6.65 

160.28 

15.17 

145.06 

8.45 

.407 

5d 

89.08 

167.90 

9.83 

158.07 

16.82 

142.75 

2.07 

.4« 

66 

47.61 

168.99 

18.11 

155.89 

16.46 

140.48 

1.75 

.570 

77 

56.89 

170.09 

16.89 

153.70 

15.59 

188.11 

1.49 

.669 

86 

66.86 

17117 

19.69 

151.49 

15.71 

185.78 

1.27 

.780 

96 

77.64 

172.24 

22.98 

149.26 

15.88 

188.45 

1.09 

.906 

104 

90.81 

173.80 

26.28 

147.02 

15.91 

181.11 

91 

1.046 

6 

10 

15 

90 

41 

60 

59 

68 

6296 

.6280 

.6100 

.9tt3 

Benslty  of  Liquid  Ammoiiia.  (DAndreff,  Trans.  A.  S.  M.  E., 
X.  041.) 

At  temperature  C -10      —5         0 

»»  F +14        88       82 

Density. 6492      .6489     .6864 

These  may  be  expressed  very  nearly  by 

t  B  0.6864  -  0.0014««  OenUgrade; 
a  =  0.6608  -  0.000777P»  Fahr. 

Ijatent  Heat  of  Brax  oration  of  Ammonia*    (Wood,  Trans. 

A.  8.  M.  E.,  X.  641.) 

;^s:  555.6  ~0.618r  -0.0002197>(inB.T.UMFahr.deg.): 

Ledoux  found  he  =  588.88  -  0.54997  -  0.0001178T>. 

For  experimental  values  at  different  temperatures  determined  by  Prof. 
Denton,  see  Trans.  A.  S.  M.  £.,  zli.  866.  For  calculated  valuea,  ««« 
vol.  X.  646. 

Beneity  of  Ammonia  Oa««'Theoretlaal,  0.6804;  experlmentaL 
0.5U6.    Regnanit  (Trans.  A.  S.  M.  E..  x.  688). 

Specific  Heat  of  liiqald  Ammonia*    (Wood«  Trans.  A.  8.  M.  E . 
X  645  >— The  speoiflo  heat  is  nearly  constant  at  different  temperatures,  aci 
about  equal  to  that  of  water,  or  unity.    From  0^  to  100^  F.,  it  is 
c  =  1 .096  -  .00187,  nearly. 

In  a  later  paper  by  Prof.  Wood  (Trans.  A.  a  M.  B.,  zli.  186)  he  glvesa  higher 
value,  viz.,  c  =  1.12136  +  O.OOWSSr. 


PROPERTIES  OF  AMMONIA  VAPOB. 


993 


L.  A.  EUeati  and  Wm.  D.  Ennig  (Jour,  jnranklin  Irut.,  April,  ISSfif)  sAve  the 
RsnltH  of  iiino  determinations,  made  between  OP  and  20®  C^  which  raum 
from  0.tW8  to  I  .OM,  averag^W  1.0906.  Von  Strombeck  (Jotu;  Franklin  Iiut.^ 
Dec.  1890)  found  the  specific  heat  between  6'^*  and  81''  C.  to  be  1.2^870. 
Ludekini?  and  Starr  (Am.  Jour.  Science,  iii,  4.>,  800;  obtained  0.886.  Prof. 
Wood  deduced  from  thermodynamic  equations  c  =  1.093  at  -  84^  F.  or 
-  38«  C,  and  Ledouz  In  like  manner  finds  c  =  1.0058  -f  .0036S8e«  C.  Elleau 
and  Ennis  give  Ledoux's  equation  wiih  a  new  constant  derived  from  their 
experiments,  thus  c  x*  0.96M  +  O.0OM58t«  O. 

Properties  of  die  Saturated  Vapor  of  Ammonia. 
(Wood's  Thermodynamics.) 


■ 

Preasora, 

Heat  of 

Volume 

Volume 

Weight 

A-OBi 

rsuvv. 

Vaporlxa- 
tlon,  ther- 
mal units. 

of  Vapor 
perlS., 
cu.  ft. 

of  Liquid 
per  Ij., 
cu.  ft. 

of  acu. 

If- 

Abso- 
lute, F. 

^r 

LbB.per 
sq.m. 

ft.  of 
Vapor, 

-    40 

4«0.e6 

1540.7 

lo.eo 

679.67 

24.879 

.0284 

.0410 

-   85 

495.66 

1778.6 

19.81 

676.09 

91.819 

.02.36 

.0468 

-   30 

480.66 

9085.8 

14.18 

678.69 

18.697 

.0987 

.0585 

-   25 

485.66 

98^.5 

16.17 

670.68 

16.446 

.0288 

.0606 

-   90 

440.66 

9057.6 

18.46 

667.67 

14.507 

.0240 

.0689 

-   15 

445.66 

8099.5 

20.99 

664.64 

19.834 

.0949 

.0770 

-    10 

450.66 

8428.0 

93.80 

561.61 

11.884 

.0943 

.0878 

-     6 

466.66 

8877.9 

96.98 

558.56 

10.195 

.0944 

.0968 

0 

460.66 

4873.6 

80.87 

555.50 

9.027 

.0246 

.1106 

h    6 

466.66 

4920.5 

84.17 

552.43 

8.060 

.0947 

.1239 

. 

.   10 

470.66 

6592  9 

88.84 

649.86 

7.299 

.0249 

.1383 

. 

-   15 

473.66 

6182.4 

49.98 

546.26 

6.499 

.0950 

.1544 

. 

-  90 

480.66 

6905.8 

47.95 

643.15 

6.849 

.0959 

.1719 

. 

-  95 

485.66 

7695.9 

68.48 

540.03 

6.960 

.0968 

.1896 

, 

•  80 

490.60 

a')56.6 

69.41 

536.99 

4.768 

.0954 

.9100 

, 

-  89 

495.66 

9488.9 

66.98 

633.78 

4.813 

.0866 

.9810 

. 

-  40 

500.66 

10519 

78.00 

680.68 

8.914 

.0957 

.9666 

. 

.   45 

505.66 

11616 

60.66 

697.47 

8.559 

.0959 

.9809 

. 

.   50 

510.66 

19811 

88.96 

694.80 

8.949 

.0961 

.8086 

. 

-    55 

515.66 

14109 

97.98 

621.19 

9.968 

.0268 

.8381 

_ 

-   60 

6S0.66 

15494 

107.60 

517.93 

2.704 

.0265 

.3696 

. 

■   65 

595.66 

16908 

118.06 

614.78 

9.476 

.0266 

.4088 

. 

-  70 

680.66 

18606 

199.91 

611.59 

9.971 

.0268 

.4408 

. 

-  75 

585.66 

90!ia6 

141.95 

606.29 

9.067 

.0970 

.4798 

_ 

-  80 

640.66 

92199 

154.11 

506  05 

1.920 

,Qm 

.6906 

. 

■  86 

645.66 

24178 

167.86 

601.81 

1.770 

.0973 

.5660    : 

. 

-  90 

550.66 

96800 

183.8 

498.11 

1.689 

.0974 

.6128 

_ 

-  96 

655.66 

98666 

196.87 

496.99 

1.610 

.0277 

.6628 

. 

-100 

560.06 

3096C 

915.14 

499.01 

1.896 

.0979 

.7153 

. 

-106 

566.1J6 

88550 

982.98 

488.78 

1.296 

.0261 

.7716 

. 

-110 

570.66 

86984 

951.97 

485.49 

1.208 

.0283 

.8819 

. 

-115 

576.66 

89188 

979.14 

489.41 

1.110 

.0286 

.8937 

- 

-190 

580.66 

42«7 

998.40 

478.79 

1.045 

.0987 

.9560 

. 

-126 

586.66 

48688 

816.16 

476.45 

0.970 

.0289 

1.0309 

. 

-  130 

590  60 

48978 

840.49 

479.11 

0.906 

.0291 

1.1049 

. 

-186 

605.66 

59696 

865.16 

466.76 

0.845 

.0293 

1.1834 

. 

-140 

eoo.66 

56488 

999  98 

466.80 

0.791 

.0295 

1.2649 

. 

-145 

605.66 

60550 

4-;».49 

462.01 

0.741 

.0297 

1  3496 

. 

-150 

610.66 

64883 

480.90 

458.69 

0.606 

.0299 

1.43SR 

i. 

-156 

615.66 

69811 

481.54 

456.29 

0.669 

.0802 

1.5387 

- 

-160 

6;>0.66 

74066 

514.40 

451  81 

0.618 

.0804 

1.6343 

^ 

-166 

9&.W 

79071 

649.04 

448.30 

0.577 

.0806 

1.7333 

Haeelilc  Heat  of  Anunonla  Taper  at  tlie  Saturation 
Point*  (Wood,  Trans.  A.  6.  H.tE.,  x.  644.)— For  the  range  of  temperatiirea 
ordinarily  used  in  engineeering  practice,  the  specific  heat  of  saturated  am- 
monia is  negative,  and  the  saturated  vapor  will  condense  with  adiabarlc  ex- 
pansion, and  the  liquid  will  evaporate  with  the  compression  of  the  vapor^ 
and  when  all  is  vaporized  will  superheat. 

Regnault  {Rel.  des.  Exp.,  ii.  162)  gives  for  specific  beat  of  ammoDi»«tt9 
O.eoSo.    (Wood,  Trans.  A.  S.  M.  E.,  xii.  133J 


994      ICE-MAKING   OR  REFRIGERATING   MACHINES. 


Properties  of  Brine  used  to  absorb  RelHcenUUis  Bflbct 
of  AmmonUl.  (J.  E.  Denton,  Trans,  a.  8.  H.  E  ,  z.  iM.)— A  solution  of 
Iiiverpool  salt  in  well-water  having  a  specific  gravity  of  1.17,  or  a  weight 
per  cubic  foot  of  73  lbs.,  will  not  sensibly  thicken  or  congeal  at  0*  Flahren- 
heit. 

The  mean  specfflc  heat  between  90«  and  16<>  Fahr.  was  found  by  Denton  to 
be  0.805.  Brine  of  the  same  specific  gravity  has  a  specific  heat  of  0.806  at 
<»•  Fahr,  according  to  Naumann. 

Naumann*8  values  are  as  follows  (Lehr-  und  Handbueh  der  Tkermochcwue, 
1882): 

Specific  heat 791      .806*     .863      .805      .081      .083      .978 

Specific  gravity.    1.187    1.170     1.108    1.073    1.044    1.088    I.OIS 
*  Interpolated. 

Oblorlde-of-ealcluiii  solution  has  been  used  instead  of  brine.  Ac- 
cording to  Naumann,  a  solution  of  1.0356  sp.  gr.  has  a  specific  heat  of  .057. 
A  solution  of  1.163  sp.  gr.  in  the  test  reported  in  Eng^g^  July  23, 1887,  gave  a 
specific  heat  of  .837. 

ACTUAIi  PBRFOBIHANCES  OF  I€E-]IIAKIlf« 
nACKINBS. 

The  table  given  on  page  006  is  abridged  from  Denton,  Jacobus,  and  Riesen- 
berger's  translation  of  Ledoux  on  Ice-making  Machines.  The  following 
shows  the  class  and  sixe  of  the  machines  tested,  referred  to  by  letters  in  the 
table,  with  the  names  of  the  authorities: 


Authority. 

Dimensions    of   Compres. 
Bion-cylinder  in  inches. 

Bore. 

Stroke. 

A.  Ammonia  cold-compression.. 

B.  Pictetfiuiddry-compression. 
C  Bell-Goleman  air 

SchrGter. 

j  Renwick  ft 
1  Jacobus. 
Denton. 

0.0 
11.8 
88.0 

10.  . 

13.0 

16.5 
84.4 

P.  Closed  cycle  air ...♦---t- 

18.0 

E.  Ammonia  dry-compression.. 

F.  Ammonia  absorption 

80.0 

Perlbrmanee  of  a  TS^ton  Anunoiila  Compreoslon- 
maeblne*  (J.  £.  Denton,  Trans.  A.  8.  M.  E.,  xii,  836.)— The  machine  had 
two  single-acting  compression  cylinders  13"  X  30",  and  one  Coriiss  steam - 
cylinder,  double-acting,  18"  x  86".  It  was  rated  by  the  manufacturers  as  a 
50-ton  machine,  but  it  showed  75  tons  of  ice-refrigerating  effect  per  S4  hours 
during  the  test. 

The  most  probable  figures  of  performance  in  eight  trials  are  as  follows : 


*s 

Ammonia 

Pressures, 

lbs.  above 

Atmosphere. 

Brine 
Tempera- 
tures, 
Degrees  F. 

Capacity  Tons 
Refrigerating 
Effect  per  24 
hours. 

Efficiency  lbs.  of 
Ice  per  lb.  of 
Coal  at  8  lbs. 
Coal  per  hour 
perH.P. 

Water-consump- 
tion,  gals,    of 
Water  permin. 
per  ton  of  Ca- 
pacity. 

Ratio  of  Aciual 
Weights  of 
Ammonia  cir- 
culated. 

6 

t 

i 

Con- 
densing 

Suc- 
tion. 

Inlet. 

Outlet. 

Si 

1 

8 
7 
4 
6 
3 

151 
161 
147 
163 
105 
185 

38 

27.6 

18.0 
8.3 
7.6 

15.7 

86.76 
86.86 
14.39 
6.37 
6.40 
4.63 

28.86 
38.46 
3.39 
308 
-3.33 
8.32 

70.8 

70.1 

43.0 

86.48 

87.30 

37.3 

83.60 
88.37 
16.37 
14.10 
17.00 
18,30 

0.80 

1.00 

0.88 

1.1 

8.00 

1.85 

1.0 

1.0 

1.70 

1.08 

1.91 

8.50 

1.0 

1.0 

1.66 

1.93 

1.88 

8  57 

The  principal  results  in  four  tests  are  given  in  the  table  on  page  098.  The 
fuel  economy  under  different  conditions  of  operation  is  ^own  in  the  fol- 
lowing table : 


PfiltfORMAi^CES  OB  ICK-MAKIKG  MACHINES.       995 


%i 

r 

28 
7 
28 

Pouudg  of  Ice>ineltiiig  Effect  with 
Eufifinea— 

B.T.U.  per  lb.  of  Steam 
^       with  Engines— 

NoD-con- 
densiug. 

Non-com- 
pouud  Con- 
densing. 

Compound 
Con- 
densing. 

a 
8-2 

1 

"iT 

800 
725 
470 

i 

f 

li 

24 
H 

94.5 
22 

11 

2.90 
1.69 
4.1U 
2.11.5 

£8 

|l 

150 
150 
105 

la-. 

30 
17.5 
48 
«7.5 

8.61 
2  11 
5.18 
8.81 

87.5 
21.6 
54 
84.5 

4.51 
2.58 
6.50 
4.16 

398 
240 
591 
876 

640 
860 
923 
591 

Tlte  noil -condensing  engine  is  assumed  to  require  25  lbs.  of  steam  per 
horse-power  per  hour,  the  non-compound  condensing  20  lbs.,  and  the  com- 
densing  16  lbs.«  and  the  boiler  efTlciency  is  assumed  at  8.3  lbs.  of  water  per 
lb.  coal  under  working  conditions.  The  following  conclusions  were  derived 
from  the  investigation : 

1.  The  capacity  of  the  machhie  is  proportional,  almost  entirely,  to  the 
weight  of  ammonia  circulated.  This  weight  depends  on  the  suction- 
pressure  and  the  displacement  of  the  compressor-pumps.  The  practical 
suction-pressures  range  from  7  lbs.  above  the  atmosphere,  with  which  a 
temperature  of  0^  F.  can  be  produced,  to  28  lbs.  above  tke  atmosphere,  w  ith 
which  the  tempers  tures  of  refrigeration  are  confined  to  about  28*>  F.  At  the 
lo«irer  pressure  only  about  one  half  as  much  weight  of  ammonia  can  be  cir- 
culated as  at  the  upper  pressure,  the  proportion  oelng  about  in  accordance 
with  the  ratios  of  the  absolute  pressures,  22  and  42  lbs.  respectively.  For  each 
cubic  foot  of  piston-displacement  per  minute  a  capacity  of  about  one  sixth 
of  a  ton  of  **  refrigerating  effect "  per  84  hours  can  be  p/oduced  at  the  lower 
pressure,  and  of  about  one  third  of  a  ton  at  the  upi>er  pivsKure.  No  other 
elements  pn^ctically  affect  the  capacity  of  a  machine,  provided  the  cooling, 
surface  in  the  brine-tank  or  other  space  to  be  cooled  is  equal  to  about 
86  sq.  ft.  per  ton  of  capacity  at  28  lbs.  bacic  pressure.  For  example,  a  d  iffer- 
enceof  lOOjC  in  the  rate  of  oirculatioD  of  brine,  while  producing  a  prnpur- 
tional  difference  in  the  range  of  temperature  of  the  latter,  made  no  practical 
difference  in  capacity. 

The  brine-tauk  was  10^  X  18  X  10^  ft.,  and  contained  8000  lineal  feet  of 
1-in.  pipe  as  cooling-surface.  The  condensing-tanlc  was  18  X  10  x  10  ft.,  and 
contained  6000  lineal  feet  of  1-in.  pipe  as  cooling-surface. 

8.  The  economy  in  coal-consumption  depends  mainly  upon  both  the  suc- 
tion pressures  and  condensing-pressures.  Maximum  economy^  with  a  given 
type  of  engine,  where  water  must  be  bought  at  average  city  prices,  is 
obtained  at  28  lbs.  suction -pressure  and  about  150  lbs.  condenslng-pressure. 
Under  these  conditions,  for  a  non-condensing  steam-engine,  consuming  coal 
at  the  rate  of  3  lbs.  per  hour  per  I.H.P.  of  steam-cylinders,  84  lb«.  of  ice- 
refrigerating  effect  are  obtained  per  lb.  of  coal  consumed.  For  the  same 
condensing-pressure,  and  with  7  lbs.  suction-pressure,  which  affords  tem- 
peratures or  0°  F.,  the  possible economv  falls  to  about  14  Ibn.  of  *'  refrigerat- 
ing effect  ^^  per  lb.  of  coal  consumed.  The  condenning-prassure  is  determined 
by  the  amount  of  condensiug-water  supplied  to  liquefy  the  ammonia  in  tlie 
condenser.  If  t  he  latter  is  about  1  gallon  per  minute  per  ton  of  refrigerating 
effect  per  24  hours,  a  conden»inff-pressure  of  150  lbs.  results,  if  the  initial  tem- 
perature of  the  wat-er  is  about  56*  F.  Twenty-five  per  cent  less  water  causes 
the  condensiiig-prfasure  to  increase  to  190  lbs.  The  work  of  compression  is 
thereby  increased  about  20j(,  and  the  resulttng  "economy"  is  reduced  to 
al>out  18  lbs.  of  "  i<ie  effect "  per  lb.  of  coal  at  28  lbs.  suction-pressure  and 
11  5  at  7  lbs.  If,  on  the  other  hand,  the  supply  of  water  is  made  8  gallons 
per  minute,  the  eondensing-nressure  may  be  confined  to  about  105  lbs.  The 
work  of  compression  is  thereby  reduced  about  25^,aud  a  proportional  increase 
of  economy  results.  Minor  alterations  of  economy  depend  on  tlie  initial 
temperature  of  the  condensing- water  and  variations  of  latent  heat,  but  these 
are  confined  within  about  b%  of  the  groi«8  result,  the  main  element  of  control 
being  the  work  of  compression, a.s affected  by  the  backpressure  and  con- 
denfflng-pressure,  or  both.  If  the  steam  engine  supplying  the  motive  power 
may  use  a  condenser  tc  secure  a  vacuum,  an  increase  of  economv  of  25)6  ia 
available  over  the  above  tlgures,  maldfig  the  lbs.  of  ''ice  effect  '^  per  lb.  ot 


ICE-MAKIKG   OR   REFRIGERATIKG  MACHINES. 


r  IM)  lbs.  coiidensinr-prewure  and  88  lbs.  suction -pressure  80.0,  and 
s.  suction-pressure,  17.0.  It  Is,  boWever*  ibipracticable  to  use  a  con- 
in  cities  wbero^ water  is  bought.  The  latter  must  be  practically 
cost  to  be  available  for  this  purpose.  In  this  case  it  may  bs  assitnted 
iter  will  also  be  available  for  condensing  the  ammonia  to  obtain  as 
ondenslng-pressure  as  about  100  lbs.,  and  the  economy  of  the  rtfrig- 
-maohiiie  becOtnee,  for  88  lbs.  back-pressure,  48.0  lbs.  of  ''  ice  effect '' 
of  coal,  or  for  7  lbs.  back-pressure,  87.6  lbs.  of  ice  effebt  par  lb. 
If  a  compouud  co&densing-enffine  can  be  used  with  a  steani-cOn- 
on  per  hour  per  horse-power  of  Id  lbs.  of  water,  the  economy  of  the 
ratinx-macliine  may  be  ^  higher  than  the  flirUres  laft  named,  mAk- 
'Zi  lbs.  back  pressure  a  refrigerating  effect  of  M.O  lbs.  per  lb.  <tt  cofU, 
7  lbs.  back  pressure  a  ref  liberating  effect  of  84.0  lbs.  per  lb.  of  coaL 
Actual  Perform  ft  nee  of  loc*iiiakiii|r  JJlttetilnca. 


Lperature  of  air  at  entrance  and  exit  of  «xpaii8lou-oylinder« 

I  basis  of  8  lbs.  of  coal  per  liour  per  H.P.  Gf  steam-eyllnder  of  com- 

i-ma(*hine  and  an  evaporation  of  11.1  Iba.  of  water  per  pound  of 

tible  from  and  at  '^18°  F.  in  the  absorption-macbiiie. 

cent  of  theoretical  with  no  friction. 

I  due  to  beating  during  aspii^tioii  of  gas  in  the  compreflBlon-<y Under 

■adiation  aod  superheating  at  brine-tank. 

lal,  incladlDg  reaftstaoee  due  to  inlet  and  eiLlt  valtes. 


^£llPO&MAKC£S  OF   iC£-MAKING  MACHINES.       99t 

III  cfaMfi  A,  a  QeniMK  mAchitie,  the  ioe-neltiiiK  oapaciiy  raqj^es  ikT»ift  46.29 
to  16.14  lbs.  of  ice  per  |K)und  of  coal,  according  as  the  suction  pressure 
varies  from  about  4S  to  8  lbs.  above  the  atmosphere,  this  preKsnre  beinf?  the 
condition  which  mainly  controls  the  economy  of  compression-machines. 
These  results  aix*  equiTHlent  to  realizing  from  72%  to  b7%  of  theoretically  per- 
fect performances.  The  higher  per  cents  appear  to  occur  with  the  higher 
suciionpreesures,  indteatiirjr  a  greater  loss  from  cylinder-heating  (a phe- 
nomenon the  reverse  of  cylinder  condensation  in  steam-engines),  as  the 
range  of  the  temperature  ot  the  gas  in  the  compression -cylinder  is 
greater. 

In  E,  as  Ain«rfoan  conipresaioti-machine,  operating  on  the  *'  dry  system," 
the  percentage  of  theoretical  effect  realized  ranges  from  69. 5j^  to  62.6j(. 
The  friction  losses  are  higher  forihe  American  machine.  The  latter's  higher 
efficiency  may  be  attributed,  therefore,  to  more  perfect  displacement. 

The  largest  **  ice-melt4ug  capacity  "  in  the  American  machine  is  S4.16  lbs. 
This  corresponds  to  the  highest  suction-pressures  used  in  American  practice 
for  such  recrlgeratioB  as  Is  required  in  beer-storage  ceUans  using  Uie  direct- 
expansion  system.  Tlie  conditions  most  nearly  oorres|X)ndiog  to  American 
brewery  practice  in  the  German  tests  are  those  in  Une  5,  whicji  give  an  '*  ioe- 
melting  oapacitv  '*  of  19.07  lbs. 

For  the  manufacture  of  artificial  Ice,  the  conditions  of  practice  are  those 
of  liffies  3  and  4,  and  Ikies  25  and  ii6.  In  the  former  the  condensing  pnessura 
used  requires  mot«  expense  for  cooling  water  than  is  common  la  American 
practice.  The  Ice-melting  cajMioity  is  therefore  greater  to  tJie  tierniaB  ma> 
chine,  being  HM  and  16.14  lbs.  against  17.65  and  14.58  for  the  American 
apparat^is. 

Cl^ss  B.  Sulphur  Dioxide  or  Pictet  Machkies.— No  records  are  available 
for  determination  of  the  "  loe-melting  capacity  "  of  machines  using  pure 
sulphur  dioxide.  This  fluid  is  <n  use  In  American  machines,  but  in  Europe 
it  has  given  way  to  the  ^'  Pictet  fluid,"  a  mixture  of  about  V!%  of  sulphur 
dioxide  and  9%  of  carbonic  add.  The  presence  of  the  carbonic  acid  affords 
a  temperature  about  14  Fabr.'degrees  lower  than  is  obtained  with  pure  sul* 
phur  dioxide  at  atmospheric  pressure.  The  latent  heat  of  this  mixture  has 
never  been  determined,  but  is  assumed  to  be  equal  to  that  of  pure  sulphur 
dioxide. 

For  brewery  refiigerating  conditions,  line  17,  we  have  26.^  lbs.  "  ice- 
melting  capacity,"  and  for  ice-making  conditioas,  line  38,  the  ''ice-melt- 
ing capacity"  is  17.47  lbs.  These  figures  are  practically  as  economical 
as  those  for  anmkonla,  the  per  cent  of  theoretical  effect  realised  ranging 
from  65.4  to  67.8.  At  esttremely  low  temperatures,  —15*  Fahr.,  lines  14  and 
18,  thf  percent  realized  i.s  as  low  as  42.5. 

Cyllnder-beatlfii;*— In  compression-machines  employing  volatile 
vapors  tihe  principal  cause  of  the  difference  between  the  theoretical  and  the 
practical  result  is  tlie  heating  of  the  ammonia,  by  tlie  warm  cylinder  walls, 
during  Its  eotranoe  into  the  compressor,  thereby  expanding  it,  so  that  to 
compress  a  pound  of  ammonia  a  greater  number  of  revolutions  must  be 
made  bv  the  compi^essing-pumps  than  corresponds  to  the  density  of  the 
ammoniagas  as  it  issues  from  the  brine-tank. 

Testa  of  Anuttonla  AI>aorptl«B-«ii»eblBe  used  tai  storage-ware- 
houses under  approaches  to  the  New  York  and  Brooklyn  Bridge.  (Eng'g, 
July  22,  1887.)— Tne  circulated  fluid  consisted  of  a  solution  of  chloride  of  cal- 
cium of  1  163  sp.  gr.    Its  speciflc  heat  was  found  to  he  .827. 

The  efficiency  of  the  apparatus  for  24  hours  was  found  by  taking  the 
product  of  the  cubic  feet  of  brine  circulating  through  the  pipes  by  the  aver- 
age difference  in  temperature  In  th»'  ingoing  and  outgoing  currents,  as 
observed  at  frecfuent  intervals  bv  ihe  speciflc  heat  of  tlie  ortne  (627)  and  its 
weight  per  cubic  foot  (73.48).  The  flnal  product,  applying  all  allowances  for 
corrections  from  various  causes,  amounted  to  6,216,816  heat-utkits  as  the 
amount  abstracted  In  24  hours,  equal  to  the  melting  of  43,566  lbs.  of  ice  in  ' 
the  same  time. 

The  theoretical  heating-power  of  the  coal  used  4n  24  hours  was  27.600,000 
beat-units;  hen<^  the  efficiency  of  th«  apparatus  was  Z\%.  This  is  equivalent 
to  an  ice -melting  effect  of  16.1  lbs.  per  lb.  of  coal  iiaving  a  heating  value  of 
10,000  B.T.U.  per  lb. 

A  test  of  a  85-fon  absorption  viachine  in  New  Haven,  Conn.,  by  Prof. 
Denton  (Trans.  A.  S.  M.  E  ,  x.  792),  gave  an  ice-melting  effect  of  20.1  lbs.  per 
lb.  of  coal  on  a  basis  of  boiler  economy  equivalent  to  8  lbs.  of  steam  per 
LU.P.  in  a  good  non-condensing  steam-engine.  The  ammonia  was  worked 
between  188  and  28  n>B.  pressure  above  t  he  atmosfdiei'e.  _ 


99d     ICE-MAKIKG  Ott  UEFRIGB&AtiKO  MACfitKBS. 


Perfomtaiice  of  a  7B»ton  KefHceimttns^iiaeliliie. 


u 

111 

15 

fii 

B 

Ci 

^'11 

^>»2  • 

5  S£ 

ES*| 

B  S     £ 

so*** 

|ll 

[Maxim 

1     Econ 

Brine 

Back 

Hi 

Av.  hli^h  ammonia  press,  above  atmos 

151  lbs. 

156  lbs. 

147  lbs. 

16IIba. 

Av.  back  ammonia  presn.  above  atmos 

Av.  temperature  brine  inlet 

28  " 

8.2  " 

18  " 

27.6  " 

88.78» 

6.2T» 

14.29» 

Av.  temperature  brine  outlet 

88.86* 

2.(M» 

2.«9» 

28  45* 

Av.  ranfire  of  temperature    

7.9» 
2281 

4.24'» 
2178 

12.00* 
948 

7.91» 

Lbs.  of  brine  circulated  per  minute 

2874 

Av.  temp,  condensing- water  at  inlet 

44.6RO 

56.66« 

46.9» 

54. 00* 

Av.  temp,  condensing- water  at  outlet 

88.86« 

86.4» 

85.46« 

8«.86« 

Av.  range  of  temperature  ... 

89.01* 
442 

28.';B«» 
815 

88.5e« 
257 

28.80* 

Lbs.  water  circulated  p.  min.  thro*  cond'ser 

601.5 

Lbs.  water  per  min.  througli  Jackets 

25 

44 

40. 

14 

Range  of  tempnrature  in  jackets 

84.0* 

16.2« 

16.4- 

29.1« 

Lbs.  ammonia  circulated  per  min 

♦28.17 

14.68 

16.67 

28.39 

Probable  temperature  of  liquid  anmionia, 
entrance  to  brine-tank 

♦71. 80 

♦68» 

♦68.7* 

76.7» 

Temp,  of  amm.  corresp.  to  av.  back  press. 

-f-14» 

-  8» 

-  5'» 

14« 

Av.  temperature  of  gas  leaving  brine-tanks 

84. 20 

14. ?» 

80« 

29.2» 

Temperature  of  gas  entering  compressor. . 

♦39» 

W 

10.18* 

34» 

Av.  teihperatura  of  gas  leaving  compressor 

2I8« 

aB8« 

289» 

221- 

Av.  temp,  of  gas  entering  condenser 

Temperature  due  to  condensing  pressure.. 

200* 

218<» 

ao9«» 

168« 

84.5« 

84.0» 

aj-s* 

88.0- 

Heat  given  ammonia: 

By  brine,  B  T.U.  per  miniute 

147T8 

7186 

8824 

1464? 

By  cmnpressor,  B.T.U.  per  minute 

2780 

2820 

2516 

aoao 

By  atmosphere.  B  T.U.  per  minute.  . . . 

140 

147 

167 

141 

Total  heat  rec.  by  amm.,  B.T.U.  per  min. 

17702 

9658 

11400 

17708 

Heat  taken  from  ammonia: 

By  condenser,  B.T.  U.  per  min 

17242 

006 

9066 
712 

9010 
656 

ITVO 

By  jackets,  B.T.U.  fwr  min 

By  atmosphere,  B.T.U.  per  min ...     . . 
Total  heat  rej.  by  amm..  B.T  U.  per  min. . . 
Dif.  of  heatrec'd  and  rej.,  B.T.U.  per  min. 

406 

182 

888 

250 

252 

1803:! 

10106 

10816 

18017 

830 

458 

407 

309 

%  work  of  compression  removed  by  jackets. 

J^ 

81  Jf 

8W 

19f 

Av.  revolutions  per  min 

56.00 

9i.n 

67.7 
27.17 

57.88 
27.88 

58.69 

Mean  eff.  press,  steam-cyl.,  lbs.  per  sq.  in . . 

82.97 

Mean  eff.  press,  amm.-cyl.,  lbs.  per  sq.  In . . 

65.9 

58.8 

59.86 

70.54 

Av.  H.P.  steam-cylinder /. 

86.00 

65.7 

23.0 

71.7 
54.7 
24.0 

•ra.G 

59.87 
20.0 

H8.63 

Av.  H.P.  ammonla-C5'linder 

71  20 

Friction  in  per  cent  of  steam  HP 

19.67 

Total  cooling  water,  gallons  per  min.  per 
ton  per  »4  hours 

0.76 

1  185 

0.797 

0.990 

Tons  ice-melting  capacif  v  per  24  hours 

74.8 

86.48 

44.64 

74.56 

Lbs.  ice-refrigerating  eff.  per  lb.  coal  at  8 

lbs.  per  H.P.  per  hour 

24.1 

14.1 

17.27 

28.87 

Cost  coal  per  ton  of  ice-refrfgerating  effect 

at  $4  per  ton 

90.166 

$0.!288 

$0,281 

$0,170 

Cost  water  per  ton  of  ice-refrigerating  effect 

at  $1  per  1000  cu.  f t 

$0,128 
$0,294 

S0.200 
$0,488 

$0,186 
$0,467 

$0,169 
$0,889 

Total  cost  of  1  ton  of  ice-refrigerating  eff... 

Figures  marked  thus  (♦)  ar-e  obtained  by  calculation;  all  other  figures  are 
obtained  from  experimental  data  ;  temperatures  are  in  Fafaraoh^t  degrees 


ARTIFICIAL  ICB-MANUFACTURB. 


999 


Ammonia  Compresston-maelilne* 

Actual  Results  obtained  at  the  Munich  Tests. 
(Prof.  Linde,  Trans.  A.  S.  M.  E.,  xiv.  1419.) 


No.  of  Test. 


Temp,  of  refrig- 1  Inlet,  deg.  P 

erated  brine     )  Outlet,  t  deg.  F. . . 

Specific  heat  of  brine 

Quantitj  of  brine  circ.  per  h.,  cu.  ft. 

Cold  produced,  B.T,U.  per  hour 

Quant,  of  cooling  water  per  h..  c.  ft. 
I.U.P.  in  steam-ensdne  cylinder  (i». 
Cold    pro- )  Per  I.H.P.  In  comp.-cyL 

ducedper VPer I.H.P.  in  steam-cyl. 

h.,  B.T.U. )  Per  lb.  of  steam 


48.194 
87.054 
0.861 
1.089.88 
842,909 
388.76 
15.80 
24,818 
21 .70S 
1,100.8 


88.844 

22.885 
0.851 
906.84 
268,950 
260.88 
16.47 
18,471 
16,026 
785.6 


3 


13  W« 

«m 

IT^-U' 

1&7  :^ 

15. as 

12.770 
11,107 
6C4.3 


0.279 
0.B3: 

10,140 


28,251 

0.851 

230.  aw 

Sl7.7ii 

21.61 

ll,l&t 

10,!W 


Means  for  Applying  tlie  Cold.  (M.  C.  Bannister,  Liverpool 
Eng'g  Soc'y,  1890. )— The  most  useful  means  for  applying  the  cold  to  various 
uses  is  a  saturated  solution  of  brine  or  chloride  of  magnesium,  which 
remains  liquid  at  5"  Fahr.  The  brine  is  first  cooled  by  being  circulated  in 
contact  with  the  refrigerator-tubes,  and  then  distributed  through  coils  of 
pipes,  arranged  either  in  the  substances  requiring  a  reduction  of  tempera- 
ture, or  in  the  cold  stores  or  rooms  prepared  for  them;  the  air  coming  in 
contact  with  the  cold  tubes  is  immediately  chilled,  and  the  moisture  in  tho 
air  deposited  on  the  pipes.  It  then  falls,  making  room  for  warmer  air,  and 
so  circulates  until  the  whole  room  is  at  the  temperature  of  the  brine  in  the 
pipes. 

In  a  recent  arrangement  for  refrigerating  made  bv  the  Linde  British  Re- 
1  rigeration  Ca,  the  cold  brine  is  circulated  through  a  shallow  trough,  in 
which  revolve  a  number  of  shafts,  each  geared  together,  and  driven  by  me- 
chanical means.  On  the  shafts  are  fixed  a  number  of  wrought-iron  disks, 
partly  immersed  in  the  brine,  which  cool  them  down  to  the  brine  tempera- 
ture as  they  revolve;  over  these  disks  a  rapid  circulation  of  air  is  passed  by 
a  fan,  being  cooled  by  contact  with  the  plates;  then  it  is  led  into  tne  cham- 
bers requiring  refrigeration,  from  which  it  is  again  drawn  by  the  same  fan; 
thus  all  moisture  and  impurities  are  removed  from  the  chambers,  and  de- 
posited in  the  brine,  producing  the  most  perfect  antiseptic  atmosphere  yet 
invented  for  cold  storing;  while  ihe  maximum  efficiency  of  the  brine  tem- 
perature was  always  available,  the  brine  t>eing  periodically  concentrated  by 
suitable  arrangements. 

Air  has  alao  been  uted  as  the  circulating  medium.  The  ammonia-pipes 
refrigerate  the  air  in  a  cooling-chamber,  and  large  wooden  conduits  are  used 
to  convey  it  to  and  return  it  from  the  rooms  to  be  cooled.  An  advantage  of 
this  system  is  that  by  it  a  room  may  be  refrigerated  more  quickly  than  by 
brine-coils.  The  returning  air  deposits  Its  moisture  in  the  form  of  snow  on 
the  aomionia-pipes,  which  is  removed  by  mechanical  brushes. 

ARTIFICIAIi  ICB-niANUFACTURE. 

Under  summer  conditions,  with  condensing  water  at  70«,  artificial  ice-ma- 
chines use  ammonia  at  about  190  lbs.  above  the  atmo^here  condenser- 
pressure,  and  15  lbs.  suction-pressure. 

In  a  compression  type  of  machine  the  useful  circulation  of  ammonia, 
allowing  for  the  effect  of  cylinder- heating,  is  about  18  lbs.  per  hour  per  in- 
dicated horse-power  of  the  steam -cylinder.  This  weight  of  ammonia  pro- 
duces about  3^  lbs.  of  ice  at  15°  from  water  at  70*>.  If  the  ice  is  made  from 
distilled  water,  as  in  the  '*can  system,^'  the  amount  of  the  latter  supplied 
by  the  boilers  is  about  88^  greater  than  the  weight  of  Ice  obtained.  This 
exi^ss  represents  steam  escaping  to  the  atmosphere,  from  the  re- boiler  and 
steam-condenser,  to  purlfv  the  distilled  water,  or  free  it  from  air;  also,  the 
loss  through  leaks  and  drips,  and  loss  by  melting  of  the  ice  In  extracting  it 
from  the  cans.  The  total  steam  consumed  per  horse-power  is,  therefore, 
about  32  X  1.88  =  43.0  lbs.  About  7.0  lbs.  of  this  covers  the  steam -consump- 
tion of  the  steam-engines  driving  the  brine  circulating-pumps,  the  several 


1000  IC£-HAKIKa  OR  REFRIGERATING  MACHIITES. 

cold-water  pumps,  and  leakaite,  drips,  etc.  Oonsequently,  the  main  steam - 
engine  must  consume  86  lbs.  of  steam  per  hour  per  I.H.  P..  or  else  live  steam 
must  be  condensed  to  supply  the  required  amount  of  distilled  water.  Thero 
is,  therefore,  nothing  to  be  gained  by  uslns  steam  at  high  rates  of  expansion 
in  the  8team-«*uKines,  In  making  artiflcial  ice  from  distilled  water.  If  the 
cooling  water  for  the  ammonia-coils  and  steam-condenser  Is  not  too  bard  for 
use  In  the  boilers,  it  may  eater  the  latter  at  about  175**  F..  by  restricfinic  the 

S[uantity  to  1  ^  gallons  per  minute  per  ton  of  ice.    With  good  coal  8V^  lbs.  of 
eed  -water  may  then  be  evaporated,  on  the  average,  per  lb.  of  coal. 

The  icK  made  per  pound  of  coal  will  then  be  32  -«-  (43.0  -h  8.5)  =  6.0  lbs. 
This  corresponds  with  the  results  of  average  practice. 

If  ice  Is  manufactured  by  the  "plate  system,**  no  distilled  water  is  osed 
Tor  freezing.  Hence  the  water  evaporated  by  the  boilers  may  be  reduced  to 
the  amount  which  will  drive  the  steam-motors,  and  the  latter  may  use  steam 
expansively  to  any  extent  consistent  with  the  power  required  to  compress 
«he  ammonia,  operate  the  feed  and  filter  pumps,  and  the  hoisting  machinery. 
The  latter  may  require  about  ISijl  of  the  power  needed  for  compressing  the 
aiumonia. 

If  a  compound  condensing  steam-engine  is  used  for  driving  the  com- 
pressors, the  steam  per  indicated  steam  horse-power,  or  per  9S  lbs.  of  net 
ice,  may  be  14  lbs.  per  hour.  The  other  motors  at  50  lbs.  of  steam  per  horse- 
power will  use  7.5  lbs.  per  hour,  making  the  total  consumption  per  steam 
horsepower  of  the  compressor  21.5  lbs.  Taking  the  evaporation  at  8  lbs., 
the  feed- water  tempei'ature  being  limited  to  about  110*,  ibe  coal  per  horse^ 

Kwer  is  2.7  iba.  per  hour.  The  net  ice  per  lb.  of  coal  is  then  about  8d  -i-  ii.7  = 
8  lbs.  The  best  results  with  '*  plate-system  **  plants,  u.sing  a  compound 
sream-englne.  have  thus  far  afforded  about  10^  lbs.  of  ice  per  lb.  of  co«L 

In  the  "  plate  system  **  the  ioe  gradually  forms,  in  from  8  to  10  days,  to  a 
thickness  of  about  14  inches,  on  the  hollow  plates,  10  X  14  feet  in  area,  in 
which  the  cooling  fluid  circulates. 

In  the  "  can  system  *'  the  water  is  f  roaen  in  blocks  weighing  about  800  Ibfi. 
each,  and  the  freezing  is  completed  in  from  40  to  48  hours.  The  freeslng- 
tank  area  occupied  ny  the** plate  system"  is,  therefore,  about  twelve 
times,  and  the  cubic  contents  about  four  times  as  much  as  required  In  the 
**  can  system." 

The  Investment  for  the  ** plate"  Is  about  one-third  greater  than  for  the 
"can  "  system.  In  the  latter  system  Ice  is  being  drawn  throughout  the  $4 
hours,  and  the  hoistinsr  is  done  by  hand  tackle.  8<>me  **can  "  plants  are 
equipped  with  pneumatic  hoists  and  on  large  hoists  «*Ieciric  cranes  are  used 
to  aitvantage.  In  the  *'  plate  system  "  the  entire  dally  product  is  dra\>  n, 
cut,  and  stored  in  a  few  hours,  the  hoisting  being  performed  by  power. 
The  distribution  of  cost  is  as  follows  for  the  two  systems,  taking  the  cost 
for  the  *'can  "  or  distilled- water  system  as  100,  which  represents  an  aetuAl 
cost  of  about  $1 .26  per  net  ton: 

Oan  Rystem.    Plate  System. 

rioisting  and  storing  ioe 14.2  8.8 

Engineers,  firemen,  and  coal-passer 15.0  ]S.d 

Coal  at  $8.50  per  gross  ton 42.2  80.0 

Water  pumped  directly  from  a  natural  source 

at  5  cts.  per  1000  cubic  feet 1.3  8.8 

Interest  and  depreciation  at  10% 24.6  32.7 

Repairs. 8.7  8.4 

100.00'  75.4 

A  compoun<i  condensing  engine  Is  assumed  to  be  used  by  the  *'  plate  sys^ 
tern." 
Teat  or  the   Neir  York  Hycela  Ice-maklns*  PIant*~<By 

Messrs.  Hupfel,  Griswoid.  and  Mackenzie;  Stevens  Jiulieator^  Jan.  1891.) 
The  final  results  of  the  tests  were  as  follows: 

Ket  ice  made  per  pound  of  coal,  in  pounds 7.18 

Pounds  of  net  ice  per  hour  per  horsepower 87.8 

Ket  ice  manufactured  i)er  day  (li2  hours)  in  tons 97 

Av.  pressure  of  ammonia-gas  at  condenser,  lbs.  per  sq.  in.  ab.  atmos.  185.2 

Average  back  pressure  of  anim.-gas,  lbs.  per  sq.  in.  above  atmos... .  15.8 

Average  t(>mperature  or  brine  in  freezing-tanks,  degrees  F 19.7 

Total  number  of  cans  filled  per  week     4389 

Ratio  of  cooling-surf aoe  of  coils  ia  briue-touk  to  ofw-surfaoe 7  to  10 


MARINE  ENGINEERIKG.  1001 

Ratio  of  brine  In  tanks  to  water  In  cans 1  to  1.2 

Ratio  of  circtilatfnff  water  at  condensers  to  distilled  water 26  to  1 

Pounds  of  water  evaporated  at  boilers  per  pound  of  coal 8.085 

Total  horse-power  developed  by  compressor-engines 444 

Percentage  of  ice  lost  in  removing  from  cans 2.2 

APPBOXIMATB  DIVISION  OF  BTBAM  IN  FBR  CENTS  OF  TOTAL  AMOUNT. 

Compressor-engines GO.l 

Live  steam  admitted  directly  to  condensers 19.7 

Steam  for  pumps,  agitator,  and  elevator  engines , 7.6 

Live  steam  for  reboiiing  distilled  water 6.6 

Steam  for  blowers  furnishing  draught  at  boilers ....       6.6 

Sprinklers  for  removing  ice  from  cans 0.6 

The  precautions  taken  to  insure  the  purity  of  the  Ice  are  thus  deacribed: 
The  water  which  Anally  leaves  the  condenser  Is  the  aocumulation  of  the 
exhausts  from  the  various  pumps  and  engines,  together  with  an  amount  of 
live  steam  injected  into  it  directly  from  the  boilers.  This  last  quantity  is 
used  to  make  up  any  deficit  in  the  amount  of  water  necessary  to  supply  the 
ioe-cans.  This  water  on  leaving  the  condensers  is  violently  reboiled,  and 
afterwards  cooled  by  rtmning  through  a  coil  surface-cooler.  It  then  passes 
through  an  oil-separator,  after  which  it  runs  through  three  charcoal-fl Iters 
and  deodorizers,  placed  in  series  and  containing  28 feet  of  charcoal.  It  next 
passes  into  the  supply-tank  in  which  there  is  an  electrical  attachment  for 
detecting  sale.  Nitrate-of-silver  tests  are  also  made  for  salt  daily.  From 
this  tank  it  is  fed  to  the  ioe-cans,  which  are  carefully  covered  so  that  the 
water  cannot  poesibly  receive  any  Impurittes. 

MARINE  ENGINEEBING. 

Rules  for  IHeasiirlnir  IMmensioiis  and  Obtaining:  Ton- 
nac^  of  VesselB*  (Record  of  American  &  Foreign  Shipping.  American 
Bureau  of  Shipping,  N.  T.  1800.)— The  dimensions  to  be  measured  as  follows: 

I.  Length.  iS.—From  the  fore  side  of  stem  to  the  after  side  of  steni'poflt 
measured  at  middle  line  on  the  upper  deck  of  all  vessels,  except  those  hav- 
Ing  a  continuous  hurrksane-deck  extending  right  fore  and  aft.  in  whieh  the 
/ength  i4  to  be  measured  on  the  range  of  deck  immediately  below  the  hurri« 
eane-deck. 

Vessels  having  clipper  heads,  raking  forward,  or  receding  stems,  or  rak-> 
ing  stern-posts,  the  length  to  be  the  dfstance  of  the  fore  side  of  stem  from 
aft-side  of  stem  poet  at  ihe  deep-load  water-line  measured  at  middle  line. 
(The  inner  or  propeller  post  to  be  taken  as  stern-post  in  screw-steamers. 

II.  Breadth,  B.~To  be  measured  over  the  widest  frame  at  its  widest  part; 
to  other  words,  the  moulded  breadth. 

III.  Depth,  />.— To  be  measured  at  the  dead-flat  frame  and  at  middle  line 
of  vesseL  It  shall  be  the  distance  from  the  top  of  floor-plate  to  the  upper 
Bide  of  upper  deck-beam  in  all  vessels  except  those  having  a  continuous 
}iurricane-deck,  extending  right  fore  and  aft,  and  not  intended  for  the 
American  coasting  trade,  in  which  the  depth  is  to  be  the  distance  from  top 
of  floor-plate  to  midway  between  top  of  hurricane  deck-beam  and  the  top 
of  deck-beam  of  the  deck  immediately  lielow  hurricane-deck. 

In  vessels  fitted  with  a  continuous  hurricane  deck,  extending  right  fore 
and  aft.  and  intended  for  the  American  coasting  trade,  the  depth  Is  to  be 
the  distance  from  top  of  floor-plate  to  t.op  of  deck-beam  of  deck  immedi- 
atelv  below  hnrricane-d<»ck. 

Rule  for  Obtaining  Tonnace,— Multiply  together  the  length, 
breadth,  and  depth,  and  their  product  ^  .76;  divide  the  Ifist  product  by  100; 

the  quotient  will  be  the  tonnage,    >^ ^     ^  '      =  tonnage. 

X%e  IT*  S*  Cuiitom-bouiie  Tonnage  liair,  May  6,  1864,  provides 
th«t  '•  the  register  tonnage  of  a  vessel  shall  be  her  entire  internal  cubic 
capacity  in  tons  of  100  cubic  feet  each.*'  This  measurement  includes  all  the 
apace  between  upper  decks,  however  many  there  may  be.  Explicit  dlrec- 
ttona  for  makintr  the  measurements  are  given  in  the  law. 

Xlie  Dliialae«nient  of  a  Tesiiel  (measured  in  tons  of  2240  lbs.)  is 
the  weight  or  the  volume  of  water  wiiich  it  displaces.  For  sea-water  it  is 
equal  to  the  volume  of  the  vessel  beneath  the  water-line,  in  cubic  feet, 
divided  by  35,  which  figure  is  the  number  of  cubic  feet  of  sea-water  at  60* 


1002  XABINE  ENOINEERIKG. 

F.  In  a  ton  of  2940  lbs.  For  fresh  water  the  divisor  Is  85.08.  The  (J.  8.  re^o 
Ister  tonnage  will  equal  the  displacemftnt  when  the  entire  Internal  cubio 
capacitT  bears  to  the  displacement  the  ratio  of  100  to  85. 

The  displaoement  or  grross  tonnage  is  sometimes  ^ppr^TlmiiitWy  ^stima  tfil 
as  follows:  Let  L  denote  the  length  in  feet  of  the  boat,  B  Its  extreme 
breadth  in  feeu  and  D  the  mean  draught  in  feet;  the  product  of  these  three 
dimensions  will  give  the  volume  of  a  parailelopipedon  in  cubic  feet^  Puu 
ting  V  for  this  volume,  we  have  T  =  JL  X  JS  X  i). 

Tub  volume  of  displacement  may  then  1m  expressed  as  a  peroentoffe  nf 
the  volume  F,  linown  as  the  '*  Mock  coefficient,"  This  percentage  varies  for 
different  classes  of  ships.  In  racing  yachts  with  very  deep  keels  it  varies 
from  iM  to  88;  in  modem  merchantmen  from  55  to  75;  for  ordinary  small 
boats  probably  60  will  give  a  fair  estimate.  The  volume  of  displaoement  in 
cubic  leet  divided  by  85  gives  the  displaoement  in  tons. 

Coeflelent  of  Pl]ieneM*-A  term  used  to  express  the  relation  be- 
tween the  displaoement  of  a  ship  and  the  volume  of  a  rectangular  prism  or 
box  whose  lineal  dimensions  are  the  length,  breadth,  and  draught  of  the 

■***•  n     85 

Coefficient  of  ftnenen  ss  ?  v  Bx  ty'^^^g  ^^  displaoement  in  tons 

of  85  cubic  feet  of  sea-water  to  the  ton,  Lthe  length  between  perpendlculani, 
B  the  extreme  breadth  of  beam,  and  TTthe  mean  draught  of  waCAr,  all  lo 
feet. 

Goeflelent  of  TF«ter*ltiies«— An  expression  of  the  relation  of  the 
displacement  to  the  volume  of  the  prism  whose  section  equals  the  midship 
secUon  of  the  ship,  and  length  equal  to  the  length  of  the  ship. 

Coefficient  of  ^'^^^^^  .^^iu^uier^^rBecUonxI.'  *"^ 
gives  the  following  vfthies: 

OoeffioleDt  OoeffldeBt  of 

ofFineneas.  Water-lines. 

Finely-shaped  shipa. • 0.55  0.68 

Fairly-shaped  ships 0.61  0.07 

Ordinary  merchant  steamera  for  speeds  of  10  to 

11  knots 0.65  O.Tt 

Cargo  steamers,  0  to  10  knots •         0.70  0.T6 

Modem  cargo  steamers  of  laige  siie 0.78  0.88 

Bealatanee 

water  may 
ment,  mid 

etc    The  I ^ 

ment  of  the  water  at  the  bow  and  its  repUcement  at  the  stem,  with  the 
consequent  formation  of  waves,  fid.  The  friction  between  the  wetted  stir- 
face  of  the  ship  and  the  water,  known  as  skin  resisrance.  A  oommon  ap< 
proximate  formula  for  resistance  of  vessels  is 

Resistance  s  speed*  x  ^^displacement*  x  a  eonstanti  or  12  s  S*l^  x  C, 
If  D  s  displaoement  In  pounds,  8  a  speed  In  feet  per  minute,  R  ss  resist- 
ance in  foot-pounds  per  minute,  R  s  CS*i)i.  The  work  done  In  overcom- 
ing the  reslfttanoe  through  a  distance  equal  to  8  IbBxSss  CS^lAi  and 
it  J?  is  the  efficiency  of  the  propeller  and  machinery  oombined,  the  Indicated 

bo^e-power  LH.P.  =  -^^^j^. 

If  S  =  speed  in  knots,  D  =  displacement  in  tons,  and  Oa  oonstant  whkb 
includes  all  the  constants  for  form  of  vessel,  efficiency  of  mechanism,  etc, 

I.H.P.  =  ^. 

The  wetted  surface  varies  as  the  cube  root  of  the  square  of  the  displace- 
ment; thus,  let  L  be  the  length  of  edge  of  a  cube  Just  immersed,  whose  dit-  : 
placement  is  D  and  wetted  surface  W.    Then  D  ss  lA  or  Xi  ss  ^^3,  and  I 
VP«5XL*»5X(  {/^)*.    That  Is,  VT  varies  as  Z)i 


MAEIKE  KHGIK££RIKQ« 


1003 


Another  approximate  formula  is 
LH.P. 


area  of  tmmerged  midship  aection  X  8* 

K  * 


The  luefulness  of  these  two  forrauIsB  depends  upon  the  accuracy  of  the 
«OH»lled  "constants  '*  Cand  JT,  which  vary  with  the  sise  and  form  of  the 
ship,  and  probably  also  with  the  speed.  Seaton^ves  the  foltowini^^,  which 
may  be  taken  roughly  I 
pressed: 


r  as  the  valaee  of  C  and  iC  under  the  conditions  ez- 


Qeneral  Description  of  Ship. 


Speed, 

Value 

Value 

knots. 

Of  a 

of  K, 

IB  to  17 

240 

680 

IB  -  17 

190 

600 

18  »•  16 

840 

650 

11  »*  18 

900 

700 

11  "  13 

240 

650 

9  *'  11 

960 

700 

18  "  15 

800 

680 

11  "  la 

840 

660 

9  "  11 

860 

TOO 

11  "  18 

880 

680 

9  **  11 

860 

680 

11  "  1« 

880 

600 

9  ••  11 

840 

640 

9  "  11 

880 

«00 

11  ••  18 

800 

650 

10  **  11 

810 

680 

9  "  10 

880 

090 

9  »•  10 

800 

600 

Ships  over  400  feet  long,  finely  shaped . . 
*•       800       " 

»*  »4  4t 

n  4»  «« 

Ships  over  800  feet  long,  fairly  shaped*.  *. 
Ships  over  860  feet  long,  finely  shaped . ! 

«4  4*  »t 

44  44  »4  " 

Ships  orer  860  feet  long,  fairly  shaped . . 

Shipe  over  800  feet  long,  finely  shifted. . 

Ships  oyer  800  feet  long,  fairly  shaped  . 
Ships  under  800  feet  long,  finely  shaped 

•4  44  44 

Ships  under  800  feet  long,  fairly  shaped 


Coeflctent  of  Perfonnance  of  VeMels*— The  quotient 


^(displacement;*  X  (speed  in  Iniots)* 

tons  of  coal  in  84  hours 

gives  a  quotient  of  performance  which  represents  the  oomparatlve  cost  of 
propulalOD  in  coal  expended.  Sixteen  vessels  with  three-stage  ezpansion- 
englnee  in  1690  gave  an  average  ooeflicient  of  14,810,  the  range  being  from 
18,18010  10,700. 

In  1881  aeventeen  vessels  with  two-stage  expansion-engines  gave  an  aver- 
age coeflksient  of  11.710.  In  1881  the  length  of  the  vessels  tested  ranged  from 
800  to  890,  and  in  1890  from  895  to  400.  The  speed  in  knots  divided  by  the 
square  root  of  the  length  in  feet  in  1881  averaged  0.589;  and  in  1890,  0.579; 
ranging  from  0.580  to  0.641.   (Proc.  Inst.  M  E.,  July,  1891,  p.  889.) 

nofoeta  of  tbe  Commoii  Formula  for  Realataneo*— Modem 
experiments  throw  doubt  upon  the  truth  of  ihe  siatemeut  that  the  resistance 
varies  as  the  square  of  the  speed.  (See  Robt.  Maosel's  letters  In  Engineer- 
ing^ 1891 ;  also  his  paper  on  The  Mechanical  Theory  of  SteamshlpPropulsion, 
read  before  Section  G  of  the  Ilngineerlng  Congress,  Chicsgo,  1888.) 

Seaton  says:  In  small  steamers  the  chief  resistance  is  the  skin  resistance. 
In  very  fine  steamers  at  high  speeds  the  amount  of  power  required  seems 
excessive  when  compared  with  that  of  ordinary  steamers  at  ordinary  speeds. 

In  torpedo-launches  at  certain  bi^h  speeds  the  resistance  increases  at  a 
lower  rate  than  the  square  of  the  speed. 

In  ordinary  sea-going  and  river  steamers  the  reverse  seems  to  be  the  case. 

Rankiae'a  Formvla  for  total  resistance  of  vessels  of  the  *'  wave* 
line  '*  type  is: 

B  =  ALBVHl  +  4  sin«  •  +  8in4  0), 

fln  which  equation  tf  is  the  mean  angle  of  greatest  obllquitv  of  the  strean^ 
lines,  .^  Is  a  constant  multiplier.  B  the  mean  wetted  girth  of  the  surface  ev 
posed  to  friction,  L  the  length  in  feet,  and  V  the  speed  in  knots.  The  power 
demanded  to  impel  a  ship  is  thus  the  product  of  a  constant  to  be  determined 
by  experiment,  the  area  of  the  wetted  surface,  the  cube  of  the  speed,  and  the 


1004 


MAklKS  fiKGIKfifiRiH e.  • 


quantity  in  the  iMti'en thesis,  which  Is  known  «a  the  '**CDellleieiit  «f  i  „ 
tation."  The  last  term  of  the  coefficient  may  be  neglected  in  calculatinjr  the 
resistance  of  ships  M  too  tmall  to  be  pnMStleally  impoitant.  In  applying  the 
formula,  the  mean  of  the  squares  of  the  sines  of  the  angles  of  maximum 
obliquity  of  the  water-lines  Is  to  be  taken  for  sin>  B,  and  the  rule  will  then 
nwdttitis: 

to  obtatn  tiM  resletaBoe  of  a  fihfp  of  ffood  form,  in  p«o«d8,  multiply  the 
iMtttli  ift  feet  by  the  imsaa  immensed  girth  and  by  thetioencioiitof  auf;in«^n> 
tatioii^  and  tlven  take  tiM  inroduet  of  this  ^augwentod  surfaoe,"  as  Rankine 
termed  it,  by  the  square  of  the  speed  in  knots,  and  by  the  proper  oonacatit 
coefficient  selected  from  tbeXoUowiog; 

f^or deaA. painted  vessels,  iroft  hulls Am  fii 

Tot  cleaa  coppered  vessels Ass  .000  to  .006 

^or  moderately  rough  iron  vessels ^  s  .011  4 

Vhe  net,  at  effedtive.bonw- power  demanded  will  be  ouite  closely  obtained 
by  tnultkplyiVig  the  reststanoe  oaloulated,  as  above,  by  the  speed  in  knots  and 
dividing  by  ft26.  ^The  ftn>6e»  or  indicated,  power  is  obtained  by  multiplyinfr 
the  last  quMitit;^  by  tae  reciprocal  of  tlie  <enoiency  «ff  the  naclitnery  and 
propeller,  wliich  usually  shouki  be  aiK>ut  0.6.  Bankine  uses  as  a  divlbor  in 
thf8case200U>9M. 

five  form  of  tSie  veswel,  even  when  designed  by  skilful  and  experienced 
naval  architects,  will  dften  vary  to  such  an  extent  as  to  cause  the  above  con- 
sttkttt  coeffiielents  to  tat^  somewhat^  smd  the  raaHt«  of  vairfatioB  with  good 
tdrtoB  is  fevittd  to  be  fiK>m  0^  to  1.5  the  figures  given. 

Foir  well««1iap6d  iron  vessele,  an  apptvMnate  fommla  for  the  bone^fM^wer 

re^Ulre^  is  &.P.  tt  ~g^  in  which  ^  is  tha  ^'cMigiMntod  amims^''    The  ex- 

pNMion  ^r=r  hie  been  called  by  Bankine  the  coefficient  of  propuUion,    In 

tbcjlulsen  Rit«r  «t«amer  "  Maiy  PowiaU,"  ^bccordlng  to  Thuntoa,  this 
coeffictcnrt  wbr  bs  high  as  1S8,{)00. 

The  ezprefiBfOfi  •  ,.  ^   has  been  called  fte  locomotive  performance,    (See 

Rank{ne*8  Treatise  on  SMptenfiding,  18M;  Thnrston^s  Manual  of  the  Steam- 
engine,  part  ii.  p.  16;  also  .paper  by  F.  T.  Bowtea,  U.S.N.,  Proc.  U.  S.  Naval 
Institute,  1883.) 

aankiae's  tnethod  fercakMlaUag  theresiatanoe  is  «aidfey  SeaAon  to  fdve 
more  «ooura(e  and  reliable  resaka  than  chose  obtoi«wd  l^y  the  older  ruW, 
but  4e  IsorltkMfled  as  4setng  difficult  and  iBconveMeac  of  ajiH'kstion. 

Br.  Ktrk^a  Uletbod.— This  method  is  generally  used  on  tiie  Clyde. 

Tlie  geueivl  idea  proposed  'by  Dr.  K*rk  is  to  reduoe  aU  shifw  to  90  defUnifte 
•ad  siwiple  a  form  that  tliey  may  be  easily  coivipai«d;  and  the  «aasi]1t«de  of 
oertain  features  of  this  fonm  shall  detemine  the  auitability  of  the  ship  foe 
■peed,«tev 

The  form  consists  of  a  middle  body,  which  isarectaagatau*  parallelopiped, 
and  fore  body  and  after  ho^sr,  ifviaaEia  iiwriag  iaoaceloB  Crtansles  for  teat^ 
as  shown  In  Fig.  168. 


FiQ.  ica 


^Is  is  4ttLlIed  a  blook  model,  and  Is  such  that  its  length  is  equal  to  U>at  of 
the  ship,  the  depth  is  equal  to  the  mean  draught,  the  capacity  equal  to  the 
displacesaent  volume,  and  its  area  of  section  equal  to  the  area  of  im< 


XARIKE  EKGIKKERINO.  1000 

ntennd  ititdahlp  teoUorii  The  dImeoBiQifti of  the  blMsk  model  sui/ be  obtained 
te  follows: 

Ij^A&m  HB»  leagtii  of  fore-  or  after-body  m  Fi 
OH  m  Wttgth  of  middle  body  b  if; 

KL  m  mean  draught  ■■•£>; 

M^      area  of  immersed  midship  section       ^ 

ggm ■■ — jr — '  *-*• 

YOlttme Of  block  »t(r^M)xBxH; 

Midship  MoUon  It  BxH; 

DiBplacement  in  tons  ts  volume  In  oublc  ft  -^^  IK. 

AB^AQ  +  QH^  F-\-  M  =  displacement  X  85  -•-  (B  X  ff  X 

'Ule  wetted  surface  of  the  block  is  nearly  equal  to  that  of  the  ship  of  the 
Acme  length,  beam  and  draught;  usually  Sjl  to  OH  gtfeater.  In  eJtceediAgiy 
fine  hoUow-line  shipa  It  may  ba  ^  gi'eatet*. 

Area  of  bottom  of  block  m{F-^M}KBl 
Araaofidde6M8Mxfi: 

▲E«a  of  sides  of  ends  =  4|/i^«  +  (|.)*x  fl\ 

Tangent  of  half  abgle  of  entraiMe  m  <^  m  jm^. 

Prom  this,  by  a  table  of  natural  tatagents,  the  angle  Of  entrance  may  be 
obtained: 

AAgle  of  Entrance     Fore-b<Kiy  hi 
of  the  Block  Model,  parts  of  length. 
Oceau-tiotiur  steAtnefa.  14  kbots  and  upwards     ifl*  to  !«•  .t  to  .ao 

•♦  "         IB  to  14  knots,  r It    loia  .ttio.8 

**         cargo  steamers,  lO  to  19  Ittiots. .     80  to  «i  .ta  to  .26 

IS.  il.  ]lttiltifbra*»  MetlioA  ofCiiletilAttii*  HT^tted  SttrfiaeM 

Is  giveii  in  a  paper  by  Ain;hibald  Denny,  h^g^o.  Bent. Hi,  i($M.  Iberoilovrlng 
is  his  formula,  wliicii  gites  closely  accurate  reauite  fbf  medium  draughtSi 
beams,  ahd  fluenesses: 

S  -  (X,  X  D  X  1.7)  +  (!» X  *  X  C>, 

in  which  S  »  wetted  surface  in  square  f^et; 

L  ss  length  between  pei'petidiculam  in  fortt 
D  ab  mlddla  draught  la  feet: 
B  SB  beam  in  feet ; 
O  B  block  coefflvient. 

The  formula  may  alte  be  cn»r«fised  In  the  form  S  m  L(h7D  +  BO. 

In  the  case  of  twin-screw  ships  having  projecting  shaft-casings,  or  In  the 
case  of  a  ship  having  a  deeu  keel  or  bilge  keelR,  an  addttion  must  be  made 
for  sueh  prajeetione.  The  formula  gives  results  which  are  in  genemi  much 
more  accurate  than  those  obtained  by  Kirk's  method.  It  ttnderestimati^ 
thH  surfaoe  When  the  beam,  draught,  or  block  coefficients  afs  esoeisive;  but 
the  error  is  small  except  in  the  osse  of  abnormal  forma,  auch  as  stem-wheel 
steameri  having  very  excessiva  beams  (nearly  one  fourth  the  leugth).  and 
aUo  Tsry  full  block  coaffldents.  The  formula  gives  a  surface  about  ^  too 
small  for  (tuch  formn. 

rro  Ptiid  «h«  IllAl««t«4l  HofM-ttow^T  itonk  t]l»  ITeUvd 
0ttrfke«k  i6eatou.)-^lii  ordinary  cases  tha  horse^power  per  lOU  feet  af 
wetted  surface  may  be  found  by  assuming  that  the  rate  for  a  speed  of  10 
knotH  is  ft,  and  that  th^  quantiry  varies  as  the  cube  of  the  speed.  For  exam- 
ple: To  find  tha  Bunioer  of  I.H.P.  neoesaary  to  drive  a  ship  at  A  speed  of  15 
knott,  having  a  fretted  skin  of  block  model  of  ltt,:iUO  sqitare  feeit 

ttie  mte  oer  100  feet  e=  (15/10)*  x  5  k  14.875. 
Then  LH.P.  i^equired  =  lft.876  x  162  •=  2734, 


1006 


MARINE.  ENGINEERIKG. 


When  the  ship  ts  ezceptionallv  well-proportioned,  the  bottom  quite  clean 
and  the  efficiency  of  the  machinery  hiffh,  as  low  a  rate  as  4  LH.P.  per  I0(i 
feet  of  wetted  skin  of  block  model  may  be  allowed 

The  eross  indicated  horne-power  Includes  the  power  necessary  to  over- 
come the  friction  and  other  resistance  of  the  enf^itte  itself  and  the  shafting, 
and  also  the  power  lost  in  the  propellor.  In  other  words,  I.H.P.  is  no  meas- 
ure of  the  resistance  of  the  snip,  and  can  only  be  relied  on  as  a  means  of 
deciding  the  size  of  engines  for  speed,  so  Ionic  as  the  efficiency  of  the  enfrine 
and  propellor  is  known  definitely,  or  so  lonf:  as  similar  engines  and  propellers 
are  employed  In  ships  to  be  compared.  The  former  is  difficult  to  obtain, 
and  it  is  nearly  impossible  in  practice  to  know  how  much  of  the  power  shovo 
in  the  cvlinders  is  employed  usefully  In  overcoming  the  resistance  of  the 
ship.  The  following  example  is  given  to  show  the  variation  in  the  elBciencj 
of  propellers: 

Knots.       I3.P. 

H.M.S."  Amazon,**  with  a  4-bladed  screw,  gave. 12.064  with  IMO 

H.M.S.  "  Amason,*^  with  a  2-bIaded  screw.  Increased  pitch, 

and  less  revolutions  per  minute 18.806     *'     1663 

H.M.S. '' Iris,'' with  a  4-bladed  screw 16.677     ••     7503 

H.M.S.  *"  Iris,*'  with  2-bladed  screw,  increased  pitch,  less 

revolutions  per  knot 18. .^87     •'     TUX 

Relative  Horae-poirer  Required  for  miTereiit  Speeda  el 
Vessels.  (Horse-power  for  10  knotv  =  1.)— The  horse-power  is  taken  usuallv 
to  vary  as  the  cube  of  the  speed,  but  in  different  vessels  and  at  difTertnic 
speeds  it  may  vary  from  the  2.8  power  to  the  3.5  power,  depending  upor  tb« 
lines  of  the  vessel  and  upon  the  efficiency  of  the  engines,  the  propeller,  etc. 


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14. &e 

17,87 

'11 .1,' 

S2t 

.{r.m 

■."If?  %-.'i 

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^.653  3  t»0K;ft.4#9 

7.4W 

9.tHrhJ.Dt 

15.07 

J9.80 

■^]v 

S' 

j>i  til 

■Jlr;    :",;  ■,' 

1    ]  ru'> 

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8. 

10  65  13*2 

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S*'l       .<!    S( 

■y\:-  .."■1' 

:    I  :  1  ,.  i 

■.'.fi;iS:4  X*0?!!6JK5 

K.57-1 

11.53  15.09 

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flJM* 

r^. 4711(1,47 

stl.88 

m^ 

^m 

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.  ".ii,  1  71-,  n  iih'i^Mfi 

13.4Wl7.9e 

23.41 

mm 

r.3* 

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.17(1 

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14,80  t».e2 

fia.TC 

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m.' 

Example  in  Use  of  the  Table.— A  certain  vessel  makes  14  knots  t-vefi 
with  587  I.H.P.  and  16  knots  with  900  I.H.P.  What  I.H.P.  will  be  required  at 
18  knots,  the  rate  of  increase  of  horse-power  with  increase  of  speed  remain. 
ing  constant  ?  The  first  step  is  to  find  the  rate  of  increase,  thus:  14^  :  IG' :: 
687:900. 

X  log  16  -  a;  log  14  =  log  900  -  log  687; 

0^0.204190  -  0.146188)  s  2.964948  --  9.768688, 

whence  x  (the  exponent  of  S  in  formula  H.P.  oc5^  z=  8  9. 

From  the  table,  for  S**  and  16  knots,  the  I  H.P.  is  4.6  times  the  I.H.P.  at 
10  knots, .'.  H.P.  at  10  knots  =  900  -h  4.6  =  200. 

From  the  table,  for8*  >  and  18  knots,  the  I.H.P.  is  6.660  times  the  I.H  P  at 
10  knots:  .-.  H.P.  at  18  knots  =  9(K)  X  6.669  =  1812  H  P. 

Resistance  per  Korse-power  ror  IMITereiit  Speeds.  (Oif 
hui*Ke-power  =  88.U00  lbs.  resistance  overcome  through  1  ft.  in  1  min.) — Tir 
resistances  per  horse-power  for  various  speeds  are  as  follows:  For  a  snee^  d 
1  knot,  or  6080  feet  per  hour  =  101^  ft.  per  min.,  83,000  -h  101^  =  896.658  lits 
per  horse-power;  and  for  any  other  speed  396.668  lbs.  divided  by  the  spet^l 
in  knots;  or  for 


1  knot  395.66  lbs. 
9  knoU  162.88    '* 
8     '*      108.65    •» 
4     ••       81.41    " 
A     "       66.18    " 


6  knots  54.28  lbs. 

7  »'      46.69    " 

8  "      40.71    •• 

9  ••      86.18    »• 
10     ••      89.67    '• 


11  knots  S0.61  lbs. 

12  "  27.14  ** 
18  ••  26.05  ** 
14  "  98.96  - 
16     *•      91.71    " 


16  knota  ao.SS  Ih& 

17  ••      19.16   • 

18  "      18.09   ' 

19  "      17  14    ' 
90     ♦*      16  2b 


MARINE   EKGINEEKINa. 


1007 


Rennlta  of  Trials  or  Steam-veaaels  ofTariona  Stses. 

(From  Seftton'8  Marine  Engineering.) 


Length,  perpendleulan . 

Brettdth,  exuvme 

Mean  draught  water. 

IMsplaoemeu  t  (tons).. ....  ... 

Area  Immeraed  mid,  section . 
^j  r  Wotted  skin.. 

SI 


Length,  fore-body. . 

Angle  of  entrance. 
Displacement  X  85 


Length  X  Imm.  mid  area"* 

8peed(knots) 

Indicated  horse-power. 

I.H.P.  per  100  ft.  wetted  slcin . 
I.H.P.  per  100  ft.  wetted  skin,  re- 
duced to  10  knots 

Dlxfl* 

LH.P.  

Immersed  mid  area  X  ffl 

lht;  *•• 


90'  0" 
10'  6" 
a*  6" 
89.78 
84? 
908 

46' 0* 

18»40' 

0.481 

88  01 
460 
50.0 

4.78 

888 

566? 


00  tH 
I 


171'  9" 
18*  V 

99 
8796 

78*00" 

]1»80' 

0.676 

15.8 
708 
81.04 

5.87 

198 

445 


4 


180' 0' 
81'  0" 
8'  10" 

870 

148 
8754 

48' 6" 

S8»60' 

0.608 

10.74 
871 
9.88 

7.97 

178.8 

405 


I 


286'  0" 
84'  8" 
6*  0" 
800 
800 
8288 

148' 0' 

18»  81- 

0.481 

17.90 
1490 
18.18 


8.56 


898.7 


688 


4 


880'  0" 
89'  0" 
WO" 
1500 
840 
10,076 

79'  6' 

17»0" 

0.671 

10.04 
508 
5.00 


866 


600 


CUf 


8 


«^'0" 
85' 0" 
18' 0" 
1900 
886 
15,788 

129'0" 

ll«86' 

0.605 

17.8 
4751 
80.00 

5.88 
188 
899 


s 


ii 

CD  h 

i 

m? 

»!: 

wW 

aoo'  0" 

46' 0" 
18'  8" 
8890 
700 
18,168 

800' 0" 
46' 0" 
18'  8" 
8^90 
700 
18,168 

870'  0" 
41' 0" 

18'  11" 

4685 

666 

88,688 

898   0" 
89   0" 
81'  4" 
5767 
788 
86,885 

135'  6" 

186' 6" 

188'  0" 

118'  0" 

160  16' 

16»16' 

16«4' 

16«80' 

0.548 

0.548 

0.668 

0.698 

18.578 

T7I4 

48.46 

15.746 

8958 

81.78 

18.80 
8500 
11.04 

18.064 

1758 
6.7 

6.684 

5.58 

4.80 

8.88 

188.7 

818.8 

898 

880 

581.4 

600.5 

680 

785 

^1 

si 


length,  perpendiculars.. 

Breadth,  extreme 

Mean  draught  water.  . . . , 

Displacement  (tons) 

Area  Imm.  mid.  section, 
f  Wetted  skin , 


Length,  fore-body. 

Angle  of  entrance. 
Displacement  x  85 


Length  X  Imm.  mid  area 

Speed  (knots)  

Indicated  hoine-power 

I.H.P.  per  100  ft.  wetted  skin . . . . 
I.H.P.  per  100  ft.  wetted  skin,  re- 
duced to  10  knots 

d1x5» 


LH.P.  

Immersed  mid  area  X 
LHlPi 


270' 0" 
48' 0" 

18'  10" 

8057 

688 

16,008 

101' 0' 

18«  44' 

0.689 

14.966 
4015 
25.08 

7.49 
175.8 
587.5 


450'  0" 
46'  8" 
88'  7" 
8600 
986 
88,578 

129'  0" 

mio* 

0.714 

15.045 
4900 
15.04 

4.48 
889.8 
648.6 


1008 


MABINB  EKGINEEBUiQ. 


Besnlts  of  ProsreMlTe  Speed  Trials  In  Typical  Teaaels. 

{Eng'g,  April  15,  1888,  p.  469.) 

li 

4 

4 

u 

III 

Length  (In  feet 
Breadth"     *' 
Draught  (mean 
Displacement  ( 
LHLP.-lOknot 

18     *• 

It                 2Q          U 

) 

185 
14 

V  1" 
106 
110 
860 
870 

IISO 

1 

8.36 
7.91 
10.27 

280 
87 
8' 8" 
785 
450 
1100 
8500 
8500 

866 

41 
16*  6" 
8800 
700 
8100 
6400 
lOOOO 

800 
48 

16' 8" 
8880 
800 
2400 
6000 
9000 

860 
60 

88' 9" 
7800 
1000 
8000 
7300 

IIOOO 

875 
05 
85'  9" 
9100 
1500 
4000 
9000 
18600 

625 

68 

>  on  trial 

tons) 

81'  8" 
11560 

B..........    ... 

sooo 

4600 

10000 

14500 

Speed 

10 
14 
18 
» 

Ratio  of 
speed* 

2.'744 
5.88* 

8. 

Ratio  Of  H.P.S 

1 

8.44 

5.56 

7.78 

1 
8 

0.14 
14.14 

1 
8 

7.6 
11.85 

1 

8 

7.5 
11 

1 

8.67 
6. 
8.49 

1 

8.3 
5 
7.85 

Admiralty  coeff.       f  10  knots. 

200 
282 

147 
156 

181 
SOB 
100 
186 

884 

259 
181 
159 

879 
885 
217 

196 

880 
847 
896 

an 

996 
288 
878 

865 
804 
897 
881 

The  figures  for  I.H.P.  are  "  round.*'  The  "  Medusa's  "  figures  for  80  knots 
are  from  trial  on  Stokes  Bay,  and  show  the  retarding  effect  of  shallow  water. 
The  figures  for  the  other  ships  for  80  knots  are  estimated  for  deep  water. 

More  accurate  methodi  than  those  above  given  for  cetlmating  the 
horse-power  required  for  any  proposed  ship  are:  1.  Estimations  calculated 
from  the  results  of  triala  of  *'  similar"  Teasels  driven  at  '*  corresponding*' 
speeds:  "  similar  *'  voKseU  being  those  that  have  the  same  ratio  of  length  to 
breadth  and  to  draught,  and  the  same  coefficient  of  fineness,  and  **  corre- 
sponding" speeds  those  which  are  pi'oportional  to  the  square  roots  o( 
tne  lengths  or  the  respective  vessels.  Proude  found  that  the  reeistances  of 
such  vessels  varied  almost  exactly  as  wetted  surface  x  (speed)*. 

8.  The  method  employed  by  ifie  British  Admiralty  and  by  some  CIvde 
shipbuilders,  viz.,  ascertaining  the  resistance  of  a  model  of  the  vessel,  12  to 
80  ft.  long,  in  a  tank,  and  calculating  the  power  from  the  results  obtained. 

Speed  on  Canals.— A  great  loss  of  speed  occurs  when  a  stesm-veswl 
passes  from  open  water  into  a  more  or  less  restricted  channel.  The  average 
speed  of  vessels  in  the  Suez  Canal  in  1888  was  only  5M  statute  miles  per  hour. 
{Eiiu'g.  Feb.  15,  1P84,  p.  189.) 

Kstlmated  JMnplaeement,  Borae-poirerf  ete*~The  table  on 
the  next  page,  calculated  by  the  author,  will  be  found  convenient  for  mak* 
lug  approximate  estimates.  . 

The  figures  in  7th  column  are  calculated  by  the  formula  H.P.  =  S*2>i  -•-  c. 
in  which  c  =  200  for  vessels  under  200  ft.  long  when  C  =  .65,  and  810 
when  G  =  .55;  c  a  200  for  vessels  200  to  400  ft.  long  when  C7  as  .75,  8^0  when 
C7  =  .65,  840  when  C  =  .55;  c  =  280  for  vessels  over  400  ft.  long  when  C  s  .75, 
250  when  C  =  .65,  260  when  C  =  .55. 

The  figures  in  the  8th  column  are  based  on  5  H.P.  per  100  p>q.  ft.  of  wetted 
surface. 

The  diameters  of  screw  in  the  9th  column  are  from  formula  Z>  ^ 
8.81  {/I.H.P.,  and  in  the  10th  column  from  formula  D  =  8.71  |/I.H.P, 

To  find  the  diameter  of  screw  for  any  other  speed  than  10  knots,  revolu- 
tions being  100  per  minute,  multiply  the  diameter  given  in  the  table  bj  the 
5th  root  of  the  cube  of  the  given  speed  -+- 10.  For  any  other  revolutions  per 
minute  than  100,  divide  by  the  revolutions  and  multiply  by  100. 

To  find  the  approximate  horse -power  for  any  other  speed  than  10  knots, 
multiply  the  horse-power  given  in  the  table  by  the  cube  of  the  ratio  of  the 
given  speed  to  10,  or  by  the  relatl?e  figure  from  table  on  p.  1006.       ^» 


HAIltKB  ££iQlKfiBtltKQ. 


IMImated  lHs»laeeiB|eiit«  BlovM«poir«r,  «Ce.«  of  Stei 

TesselB  of  TanouB  Slses. 

1  _»^ 

4e^ 

l^i 

1  Diaplue- 

,    £<Uin«t«d  Horto- 

DUnuorSenw 

u- 

2^ 

II 

1    nilmt. 
LBDXC 

W«Ucd  Sorikc* 
Ia.7D+BC) 

power  at  10  knoti. 

knot*  iptvd  u 

Cik. 

Calc.  irom 

reTt,  par  mJm 

li 

/I'sl 

«8~ 

■q.fk. 

fronDb. 

Wattad 

IfPltoh-,  IfP 

o  «  - 

tOH. 

plftcm't. 

Sarfa««. 

Dtam. 

1.4 

12 

1.5 

.65 

.85 

48 

4.8 

2.4 

4.4 

16 

1.5 

;  .55 

1.13 

64 

5.2 

3.2 

4.6 

2 

.66 

2.88 

96 

8.9 

4.8 

6.1 

90] 

1.5 

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1.41 

80 

6.0 

4.0 

4.7 

2 

.66 

2.27 

120 

10.8 

6.0 

6.8 

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3.5 

1.6 

'  .86 

1.96 

104 

7.6 

6.2 

5 

4.5 

2 

.66 

4.01 

152 

12.6 

7.6 

5.6 

80 

2 

.66 

8.77 

168 

11.6 

8.4 

6.4 

2.5 

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6.96 

224 

18.2 

11.2 

6.9 

40| 

4.5 

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.66 

6.66 

235 

15.1 

11.8 

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2.5 

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11.1 

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24.9 

16.3 

6.8 

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.55 

14.1 

420 

27.8 

21.0 

6.4 

8 

3.5 

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26 

566 

43.9 

27.9 

7.1 

fiOJ 

S 

8.5 

.65 

86.4 

621 

42.2 

81.1 

7.0 

10 

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.65 

44.6 

798 

62.9 

89.9 

7.6 

to] 

10 

4 

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44 

861 

59.4 

48.1 

7.5 

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4.5 

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1082 

85.1 

54.1 

8.1 

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4.5 

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67.9 

1140 

79.2 

57.0 

7.9 

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5 

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104.0 

1408 

111 

704 

8.5 

90] 

13 

6 

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91.9 

1408 

97 

70.4 

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6 

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160 

1854 

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98.7 

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102 

1566 

104 

78.3 

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5.5 

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153 

1910 

143 

95.5 

8.9 

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6 

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219 

2295 

208 

116 

9.6 

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5.5 

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145 

2046 

131 

102 

8.8 

120- 

16 

6 

.66 

214 

2472 

179 

184 

9.4 

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6.5 

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801 

2946 

250 

147 

10 

16 

6 

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211 

2660 

169 

188 

9.2 

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6.5 

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806 

8185 

227 

160 

9.8 

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.75 

420 

3766 

312 

188 

10.6 

17 

6.5 

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878 

8264 

206 

168 

9.6 

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896 

8880 

269 

194 

10.1 

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7.5 

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540 

4560 

868 

228 

10.8 

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806 

4128 

257 

806 

10.1 

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7.6 

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558 

4869 

387 

248 

10.6 

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5688 

466 

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11.8 

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4800 

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6970 

878 

299 

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11.6 

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7250 

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9460 

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875 

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12.8 

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1175 

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12.5 

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894 

13.6 

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14.4 

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14.5 

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34875 

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15.4 

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29600 

1454 

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10400 

35200 

1966 

1760 

15.1 

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22 

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14143 

41200 

2543 

2060 

15.9 

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56 

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9680 

36245 

1747 

1812 

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60 

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2266 

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49665 

2998 

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42900 

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50220 

2656 

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22731 

58020 

3480 

2901 

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1010  MAEtKfi  fiNQlKKERlKG;' 

TBE  SCBVUr-PBOPELI^BR. 

The  **  pitch  *'  of  a  propeller  is  the  distance  which  any  point  in  a  blade, 
describing  a  helix,  wlfi  travel  in  the  direction  of  the  axis  during  one  revolu- 
tion, the  point  being  assumed  to  move  around  the  axis.  The  pitch  of  a 
propeller  with  a  uniform  pitch  is  equal  to  the  distance  a  propeller  will 
advance  during  one  revolution,  provided  there  is  no  slip.  In  a  case  of  this 
kind,  the  term ^' pitch*'  is  analogous  to  the  term  "pitch  of  the  thread**  of 
an  ordinary  single-threaded  screw. 

Let  P  =  pitch  of  screw  in  feet,  R  =  number  of  revolutions  per  second. 
V  =s  velocity  of  sti^am  from  the  propeller  =  P  x  -B, «  =  velocity  of  the  ship 
in  feet  per  second,  F  -  v  s  slip,  A  =  area  in  square  feet  of  section  of  stream 
from  the  screw,  approximately  the  area  of  a  circle  of  the  same  diameter, 
AX  V  =  volume  of  water  projected  astern  from  the  ship  in  cubic  feet  per 
second.  Taking  the  weight  of  a  cubic  foot  of  sea- water  at  04  lbs.,  and  the 
force  of  gravity  at  8S,  we  have  Trom  the  common  formula  for  force  of  acod- 

eratlon,  via.:  F=  Ut  =  —  -^^  or  J*=  — «i»  when  *  =  1  second,  v^  being 

t        g   t  g 

the  acceleration. 

fAAV 
Thrust  of  screw  in  pounds  s  -55— (F  ^  v)  =  2AViV  —  v), 
o* 

Rankine  (Bnles,  Tables,  and  Data,  p.  275)  gives  the  following:  To  calculate 
the  thrust  of  a  propelling  instrument  ijet,  paddle,  or  screw)  in  pounds, 
multiply  together  the  transverse  sectional  area,  in  square  feet,  of  the  stream 
driven  astern  by  the  propeller;  the  speed  of  the  stream  relatively  to  the  9tap 
in  knots;  the  real  sIk),  or  part  of  that  speed  which  is  impressed  on  that 
stream  by  the  propeller,  also  in  knots;  and  the  constant  5. w  for  sea- water, 
or  5.5  for  fresh  water.  If  ;9  =  speed  of  the  screw  in  knots,  »  =  speed  of  ship 
in  knots,  A  =  area  of  the  stream  in  square  feet  (of  searwater). 

Thrust  in  pounds  =  Ax  S(S  -  s)  X  5.60. 

The  real  dip  is  the  velocity  (relative  to  water  at  rest)  of  the  water  pro- 
jected stemward;  the  apparent  »lip  is  the  difference  between  the  speed  of 
the  ship  and  the  speed  of  the  screw;  i.e.,  the  product  of  the  pitch  of  the 
screw  by  the  number  of  revolutions. 

This  apparent  slip  is  sometimes  negative,  due  to  the  working  of  the  screw 
In  disturfcHBd  water  which  has  a  forward  velocity,  following  the  ship.  Nega- 
tive apparent  slip  is  an  indication  that  the  propeller  is  not  suited  to  the 
ship. 

The  apparent  slip  should  generally  be  about  8jt  to  10]C  at  full  speed  In  well- 
formed  vessels  with  moderately  fine  lines;  in  blulT  cargo  tKMits  it  rarely 
exceeds  b%. 

The  effective  area  of  a  screw  Is  the  sectional  area  of  the  stream  of  water 
laid  hold  of  by  the  propeller,  and  is  generallv,  if  not  always,  greater  than 
the  actual  area,  in  a  ratio  which  in  good  ordinary  examples  is  1.2  or  there- 
abouts, and  is  sometimes  as  high  as  1.4;  a  fact  probably  due  to  the  stiffness 
of  the  water,  which  communicates  motion  laterally  amongst  its  particles. 
(Rankine'B  Shipbuilding,  p.  80.) 

Prof.  D.  S.  Jacobus,  Trans.  A.  S.  M.  E.,  zi.  1028,  found  the  ratio  of  the  ef- 
fective to  the  actual  disk  area  of  the  screws  of  different  vessels  to  be  as 
follows : 

Tug-boat,  with  ordinary  true-pitch  screw 1 .48 

"  **    screw  having  blades  projecting  backward 57 

Ferryboat  "  Bergen,"   with  or-  \  at  speed  or  12.09  stat.  miles  per  hour.  1 .58 

dinary  true-pitch  screw  »     "  **  18.4      "       *'        "       **      1.48 

Steamer  *'  Homer  Ranisdell,"  with  ordinary  true-pitch  screw 1  20 

Size  of  Scre¥F«— Seaton  sajs:  The  sise  of  a  screw  depends  on  so  many 
thing;^  that  it  is  very  difficult  to  lay  down  any  rule  for  guidance,  and  mncn 
must  always  be  left  to  the  experience  of  the  designer,  to  allow  for  all  the 
circumstances  of  each  particular  case.  The  following  rules  are  given  for 
ordinary  cases.    (Seaton  and  Rouuthwaite*s  Pocket-book): 

]A|000 

P  =  pitch  of  propeller  In  feet  =  _,■,-- -,  In  which  8  =  speed  in  knots, 

a(10v  --  X) 

R  s=  revolutions  per  minute,  and  x  =3  percentage  of  apparent  slip 
For  a  slip  of  lOjf,  pitch  =  — ^. 


THE    SCREW  PKOPELLBB. 


1011 


X>  B  diameter  of  propeller  =  K 


^ ,  K  being  acoefflcientKiven 


/     IHP. 
in  the  table  below.     If  iT  «  20.  D  a  a0000i/~5:^ 


/l  H  P 
Total  developed  area  of  blades  s  Ci/   'J  ■',  In  which  C  is  a  coefficient 

to  be  taken  from  the  table. 
Another  formula  for  pitch,  given  in  6eaton*8  Marine  Engineering,  is 

C    t /T  R  p 

^^"rV      ni    »  *"  which  C  s  737  for  ordinary  veeeela,  and  600  for  slow- 


speed  cargo  Teasels  with  full  lines. 
Thickness  of  blade  at  root 


X  Ir,  in  which  d  s  diameter  of  tail- 
shaft  in  inches,  n  ss  number  of  blades,  b  s  breadth  of  blade  in  inches  where 
It  Joins  the  boss,  measured  parallel  to  the  shaft  axis;  ik  =  4  for  cast  iron,  1.5 


for  cast  steel,  8  for 


Thickness 


[,  8  for  gun-metal,  1.6  for  high-class  bronze, 
of  blade  at  tip:  Cast  iron  MD  -f  .4  in.;  caa 


of  propeller  in  feet. 


tip: 
big 


cast  steel  .06i> 


gun-metal  .06Z)  -f  Jii  in. ;  high-class  bronze  SiriD  +.  3  In.,  where 


1.06i>-f-.4i 
D  s  diame 


Propeller  CoelBeleiita. 


Description  of  Vessel. 


Bluff  cargo  boats 

Cargo,  moderate  lines.  . 

Pass,  and  mail,  fine  lines. 
..       tt       it       ti      it 

*»       *»       •*     very  fine. 
Naval  ve^ls,     |*       || 
Torpedo-boats.   **       " 


^  . 

^.9^' 

i 

ui 

C5 

ill 

II 

> 

8-10 

One 

17    -17.6 

19    -17.5 

10-18 

18    -19 

17    -15.5 

1S-I7 

t4 

19.5-20.5 

15    -18 

13-17 

Twin 

20.5-^1^ 

14.5-12.6 

17-22 

One 

21    -22 

12.5-11 

17-2« 

Twin 

22    -23 

10.5-9 

16-ia 

21    -22.5 

11.5-10.6 

16-22 

♦* 

22    -^.5 

8.5-7 

20-26 

One 

8 

25 

7-6 

i 

P 


Cast 
CI. 
G.M. 


iron 
or  8. 
orB 


B.  or  F.  S. 


C.  I.,  cast  iron;  O.  M.,  gun-metal;  B.. 


From  the  formulas  D  ^  20000 


4/^ 

V  (Px 


bronze;  S.,  steel 
737 


Rf 


and  P 


F.  8.,  forged  steel. 
•/I.H.P. 


ro«    yx.ti.r.   -_   _       ^ 


I.H.P.  =38I^I.H.P. 


!  100,  we  obtain  D  =  ^400  x 

!  1.4D  and  R  =  100,  then  D  =  f^l45.8  X  I.H.P.  =  2.71  f^I.H.P. 


and  R  -. 

If  P  = 

From  these  two  formulsa  the  figures  for  diameter  of  screw  in  the  table  on 
page  1009  have  been  calculated.  They  may  be  used  as  rough  approximntions 
to  the  correct  diameter  of  screw  for  any  given  horse-power,  for  a  speed  of 
10  knots  and  100  revolutions  per  minute. 

For  any  other  number  of  revolutions  per  minute  multiply  the  figures  in 
the  table  by  lOO  and  divide  by  the  given  number  of  revolutions.  For  any 
other  speed  than  10  knots,  since  the  I.H.P.  vuies  approximately  as  the  cube 
of  the  speed,  and  the  diameter  of  the  screw  as  the  5th  root  of  the  I.H.P., 
multiply  the  diameter  given  for  10  knots  by  the  5th  root  of  the  cube  of  one 
tenth  of  the  given  speed.    Or,  multiply  by  the  following  factors: 

For  speed  of  knots: 

4    5    6    7    8    9   11   12   18   14   15   16 


^{8 -f  10)9 


«8.077  .660  .796  .807  .875  .9^  1.050  ^UG  1.170  l.??4  1.^  1.387 


1012 


XABINE  EXOINEERIKQ. 


8p^: 

s  1.876  1,488  1.470  1.615  1.661  1.605  1.648  1.091  1.738  1.774  1.815  1.855 

For  more  toeurate  deterrainationa  of  diameter  and  piteh  of  acrew.  tb« 
formulae  and  coefflcfentfi  friven  by  Seaton,  quoted  alK>v«*,  should  be  used. 

Efficiency  of  tlie  ProMllAr.—According  to  Rankine,  if  the  slip  of 
the  water  ba  «^  ita  welif  ht  M^,  tii«  lusiiitanoe  R,  and  th*  apeed  of  the  ship  «, 


»-^« 


Uvi 


Wbv 

;       »     I  • 


This  ImpelHnir  action  must,  to  aeonre  maximum  effloleiicy  of  propeller,  bo 
effected  by  an  instrument  which  takes  hold  of  the  fluid  without  shock  or 
disturbance  of  the  surroundine  mass,  and,  by  a  steady  acoeteratioii,  s1t««  i% 
the  required  flnal  velocity  of  discharge.  The  Telocity  of  the  propeller  ovei^ 
comlnff  the  rvsiftaoce  A  wQiUd  th«n  be 


i±.fe±D.,+», 


and  Ih9  wotk  psffonned  would  be 


<"+!)  =  ^+ 


the  first  of  the  last  two  teruis  being  useful,  the  second  the  minimum  lost 
work;  the  latter  being  the  wasted  energy  of  the  water  tiirown  backward. 
The  eUteiency  is 


E^V'*^(v-{.0; 


and  this  is  the  limit  attainable  with  a  perfect  propelling  instrument,  which 
limit  is  approached  the  more  nearly  a$  the  conditions  above  prescribed  are 
the  more  nearly  fulfllled.  The  efficiency  of  the  propelling  instrument  ia 
probably  rarely  much  above  0,60,  and  tiever  above  D.80. 

In  designing  the  tjcrew-propeller,  as  was  shown  by  1>r.  Freude,  the  best 
apg)e  for  tlte  surface  is  that  of  45<*  with  the  plane  of  the  disk;  biifeasall 
parts  of  the  blade  cannot  be  given  the  same  angle,  it  should,  where  practi- 
cable, be  so  proportioned  that  the  **  pltcb^ngle  at  the  oentre  of  effon" 
should  be  made  45**,  The  miucimpm  possible  efl^oiency  iy  then,  aooording 
to  Froude,  TTjJ, 

In  order  that  the  water  should  be  taken  on  without  ^hock  and  di9(^iarged 
with  maximum  backward  velocUy,  the  acrew  must  hATe  an  axiaUy  increas- 
ing pitch* 

The  true  screw  is  by  far  the  more  ususl  form  of  propeller,  in  all  steamers, 
both  merchant  and  naval.  (Thureton,  Manual  of  tne  Steaxn-engiQet  PArt  ii-t 
p.  176.) 

Tlie  combined  efficiency  of  screw,  shaft,  engine,  etc.,  is  generelly  takes 
at  50^.  In  some  castts  it  may  r«aoh  W  Qr  (BM,  Bapktne  takes  the  effecUve 
H.P.  to  equal  the  I.H.P.  -h  1,68. 


Pltelfc-ratto 

and  Slip  for  ISerewe  ofSUindapd  Fomn. 

Pitch-ratio. 

Real  Slip  of 
Screw. 

Pitchratlo. 

Real  Blip  of 
Sci^w 

.8 

15.55 

1,7 

21  *S 

16.33 

1.8 

^•1 

1:? 

16.88 

1.0 

17.55 

2.0 

18.3 

3.1 

18.9 

3.3 

B4.0 

19.6 

2,3 

Ui 

20.1 

3.4 

^.    '•*  ...  .. 

80.7 

8.6 

64 — 

THS  PADDLK«WHE8L.  1013 

Renults  of  R«eeiit  BesMirelies  on  the  effloioBey  of  acrew-prooek 

lei-s  Hi-ti  surnnmnzed  by  8.  W.  Baruabv,  in  a  paper  read  before  leetioa  G  oi 
the  KnirtneeriDe  Confin'eAS,  Chicafro,  1»^.  He  suites  that  the  followiiig  gen- 
eral pi-incipleis  nave  bf^en  established: 

(a)  There  Is  a  defluite  amount  of  real  slip  at  which,  and  at  which  only, 
niaximum  efficiency  can  be  obtained  wlih  a  screw  of  any  f^ven  type,  and 
this  amount  varies  with  the  pitch-ratio.  The  slip-ratio  proper  to  agivea 
i-atio  of  pilch  to  dianeler  has  been  diaeovered  and  tabulated  for  a.  acf^^ 
of  a  stavdArd  type,  as  below  (see  table  on  page  lOai^; 

(6)  Screws  of  large  pitch-ratio,  besides  being  leas  elQcleBl  la  themaelvea, 
add  to  the  reaistanoe  of  the  hull  by  an  amount  baariDg  aonie  proportion  to 
their  distance  from  it,  and  to  the  amount  of  rotation  left  In  the  race. 

(c)  The  beet  ptteh^atio  Itas  probably  between  1.1  and  l.S. 

id)  The  fuller  the  lloea  of  the  Tesne),  the  less  the  piteh-ratio  ahould  be. 

(e)  Ooarse-pitched  screws  ahould  be  plaeed  furiner  from  the  stern  than 
flii^pitched  onee. 

(/>  Apparent  oegattye  ellp  Is  a  natural  result  ef  abnormal  proportions  of 
pmpeliera. 

(g)  Three  blades  are  to  be  preferred  for  high-speed  Yeasels.  but  when  the 
diameter  is  unduly  restricted,  four  or  even  more  may  be  advantageously 
employed. 

(A)  An  efBcient  form  of  blade  ia  an  ellipse  having  a  minor  a^is  equal  to 
four  tenths  the  major  axis. 

(t)  The  pitch  of  wide-bladed  screws  should  increase  from  forward  to  aft, 
but  a  uniform  pitch  gives  satisfactory  results  when  the  blades  are  narrow, 
and  tlie  amount  of  the  pitch  variation  should  be  a  fuiietlon  of  the  vidth  of 
the  blade. 

( i')  A  considerable  inolinatlon  of  screw  shaft  prod ueee  vibration,  and  with 
rlgnt-handed  twin-screws  tumhig  outwards,  if  the  shafts  are  InoUned  at 
all,  it  should  be  upwai'ds  and  outwards  from  the  propellers. 

For  results  of  experiments  with  screw«pi*opellerf,  see  F.  C.  Marshall,  Proc. 
Inst.  M.  £.  1881;  R  E.  Froude,  Trans.  Institution  of  Naval  Architects,  1886; 
G.  A.  Calvert,  Trans.  Institution  of  Naval  Architects  1887;  and  S.  W.  Bar- 
iiaby,  Proc.  Inst.  Civil  Eng'rs  1890,  vol.  cfl. 

One  of  the  moat  important  results  deduced  from  experiments  on  model 
screws  is  that  they  appear  to  have  praetloally  equal  efflolenciee  throughout 
a  wide  range  both  in  pitch-ratio  ana  In  surface-ratio;  so  that  great  latitude 
is  lert  to  the  designer  fh  regard  to  the  form  of  the  propeller.  Another  lm« 
portant  feature  is  that,  although  these  experiments  are  not  a  direct  guide  to 
the  selection  of  the  most  efftcient  propeller  for  a  particular  ship,  they  sup- 
ply the  means  of  analyzing  the  performances  of  screws  flttiftd  to  veoMls,  and 
of  thus  indirectly  determining  what  are  likely  to  be  the  best  dimensions  of 
screw  for  a  vessel  of  a  class  whose  results  are  known.  Thus  a  great  ad- 
vance has  been  made  on  the  old  method  of  trial  upon  the  ship  liaelf,  whieh 
was  the  origin  of  almost  every  conceivable  erroneous  view  respecting  the 
Bcrew-propeUer.    (Proc.  InsL  M.  B.,  July*  1891.) 

THB  PADBI^B-mrHllBL. 

Paddle-wlieela  wltb  H.«<ltal  Floats.  (Beaton's  Marine  En- 
gioeering.)— The  efTective  diameter  of  a  radial  wheel  is  usually  taken  from 
the  centres  of  opposite  floats;  but  it  Is  di|Scult  to  say  what  Is  absolutely 
that  diameter,  as  much  depends  on  the  form  of  float,  the  amount  of  dip, 
and  the  waves  set  in  motion  by  the  wheel.  The  slip  of  a  radial  wheel  Is 
from  15  to  ao  per  cent,  depending  on  the  siae  of  float 

Area  of  one  float  w  -^-^  x  G. 

D  is  the  efPective  diameter  in  feet,  and  C  Is  a  multfpllep,  varying  from 
0.25  in  tugs  to  0.175  In  fast-ruonliig  light  steamers. 

The  breadth  of  the  float  is  usually  about  ^  Its  length,  and  its  thiolcnesv 
about  yi  its  breadth.  The  number  of  floats  varies  directly  with  the  dlam,- 
eter,  and  there  should  be  one  float  for  every  foot  of  diameter. 

(For  a  discussion  of  the  action  of  the  radial  wheel,  see  Thurston,  Manual 
of  the  Steam-engine,  part  II.,  p,  182.) 

Featliertiiff  Paddle  •  ^wlieela.  (Seaton.)  —  The  diameter  of  a 
feathering-wheel  is  found  as  follows  :  The  amount  of  slip  varies  from  19  to 
20  per  cent,  although  when  the  floats  are  small  or  the  resistance  great  it 


1014  MARINE  ENGINEERING. 

is  as  high  as  S5  per  cent;  a  well-deelgned  wheel  on  a  well-fonned  ship  should 
not  exceed  15  per  cent  under  ordinary  ciroumstanceB. 

If  K  is  the  speed  of  the  ship  in  knou,  jS  the  percentage  of  slip,  and  R  the 
revolutions  per  minute, 

Diameter  of  wheel  at  centres  =    ,  ^-      p  » 

9.14  X  A 

The  diameter,  however,  must  be  such  as  will  suit  the  structure  of  the 
ship,  so  that  a  modification  may  be  necessary  on  this  account,  and  the 
revolutions  altered  to  suit  it. 

The  diameter  will  also  depend,  on  the  amount  of  *'  dip  "  or  Immersion  of 
float. 

When  a  ship  Is  working  always  in  smooth  water  the  immersion  of  the  top 
edge  should  not  exceed  ^  the  breadth  of  the  float;  and  for  general  service 
at  sea  an  immersion  of  Hi  the  breadth  of  the  float  is  suflScient.  If  the  ship 
is  intended  to  carry  cargo,  the  immei*8ion  when  light  need  not  be  more  than 
2  or  3  inches,  and  should  not  be  more  than  the  breadth  of  float  when  at  the 
deepest  draught;  indeed,  the  efficiency  of  the  wheel  falls  off  rapidly  with 
the  immersion  of  the  wheel 

I  H  P 
Area  of  one  float  =        '      X  C 

C  is  a  multiplier,  vanning  from  0.8  to  0.85;  D  is  the  diameter  of  the  wheel 
to  the  float  centres,  in  feet. 

The  number  of  floats       =  U(i>  -f  S). 

The  breadth  of  the  float  =  0.86  x  the  length. 

The  thickness  of  floats    =^  1/12  the  breadth. 

Diameter  of  gudgeons     =  thickness  of  float. 
Seaton  and  Kounthwaite*8  Pocket-book  gives: 

Number  of  floats  =  --^, 

Vr 

where  R  is  number  of  revolutions  per  minute. 

Area  of  one  float  (in  square  feet)  =  ^'y^^^^^^  ^» 

where  N  =s  number  of  floats  in  one  wheel. 

For  vessels  plying  always  in  smooth  water  K  =  1200.  For  seorgoing 
steamers  K  =  1400.  For  tugs  and  such  craft  as  require  to  stop  and  start 
frequently  In  a  tide-way  K  =  1600. 

It  will  be  quite  accurate  enough  if  the  last  four  flgures  of  the  cube 
(D  X  R)*  be  taken  as  ciphers. 

For  illustrated  description  of  the  feathering  paddle-wheel  see  Seaton *« 
Marine  Engineering,  or  Seaton  and  Rounth  waiters  Pocket-book.  The  diam- 
eter of  a  feathering -wheel  is  about  one  half  that  of  a  radial  wheel  for  equal 
efflciencv.    (Thurston.) 

Blllclenejr  of  Padd]e-iv]ieela«>-CompuUtions  by  Prof.  Thurston 
of  the  efficiency  of  propulsion  by  paddle-wheels  give  for  light  river  steamers 
with  ratio  of  velocity  of  the  vessel,  t;,  to  velocity  of  the  paddle -float  at 

centre  of  pressure,  F,  or  ^^  =  - ,  with  a  dip  =  3/20  radius  of  the  wheel,  and 

a  slip  of  25  per  cent,  an  efficiency  of  .714 ;  and  for  ocean  steamers  with 

the  same  slip  and  ratio  of  •=,  and  a  dip  =  H  radius,  an  efficiency  of  .e85. 

JET-PBOPITMION. 

Numerous  experiments  have  been  made  in  driving  a  vessel  by  the 
reaction  of  a  Jet  of  water  pumped  through  an  orifloe  in  the  stem,  but 
they  have  all  resulted  in  commercial  failure.  Two  Jet- propulsion  steamers, 
the  "  Waterwitch,'*  1100  tons,  and  the  * 'Squirt,*^  a  small  torpedo-boat, 
^ere  built  by  the  British  Qovemment.  The  former  was  tried  in  1867,  and 
gave  an  efficiency  of  apparatus  of  only  18  per  cent.  The  latter  gave  a  spee<l 
of  12  knots,  as  against  17  knots  attained  by  a  sister-ship  having  a  screw  and 
equal  steam-power.  The  mathematical  theory  of  the  efficiency  of  the  jet 
was  discussed  by  Baukine  in  The  Engineer^  Jan.  11, 1867,  and  he  showed  thnt 
the  greftter  the  qui^ntity  of  water  operated  on  by  a  jet-propeller,  the  greater 


B£0£1{T  FHACtiOE  IK  HAEIKE  ENGIKES.       1015 

JB  the  efficiency.  In  deflaoce  both  of  the  theory  and  of  the  results  of  ecu-Uer 
experiments,  and  also  of  the  opinions  of  many  naval  engineers,  more  than 
$;»0,000  were  spent  in  1888-60  In  New  York  upon  two  experimental  boats,  the 
'*  Prima  Vista  *^  and  the  "  Evolution/'  in  which  the  Jet  was  made  of  very  small 
size,  in  the  latter  case  only  ^inch  diameter,  and  with  a  pressure  of  2600 
lbs.  per  square  inch.  As  had  been  predicted,  the  vessel  was  a  total  failure. 
iSee  article  by  the  author  in  Mechanics,  March,  1881.) 

The  theory  of  the  Jet-prop«;ller  is  similar  to  that  of  the  screw-propeller. 
If  ^  =  the  area  of  the  Jet  in  square  feet,  F  its  velocitv  with  reference  to  the 
orifice.  In  feet  per  second,  v  =  the  velocity  of  the  snip  in  reference  to  the 
earth,  then  the  thrust  of  the  jet  (see  Screw-propeller,  ante)  hiiAViV-^  v). 
The  work  done  on  the  vessel  Is  %AV(V->-  v)v,  and  the  work  wasted  on  the 
rearward  pro^tlon  of  the  Jet  is  hi  X  2^F(F  -  «)>.     The  efficiency  is 

iAViv'-T+AriV-v,^  =  FTi-  ™* •^"-*'" ""-^ "-"'' '''"•" 

F  s  V,  that  is,  when  the  velocity  of  the  Jet  with  reference  to  the  earth,  or 
F  —  v,  s  0;  but  then  the  thrust  of  the  propeller  is  also  0.  The  flnreater  the 
value  of  Fas  compared  with  v,  the  less  the  efficiency.  For  F  =  Wv,  as  was 
proposed  in  the  "  Evolution,"  the  efficiency  of  the  jet  would  be  less  than  10 
per  cent,  and  this  would  be  further  reduced  by  the  friction  of  the  pumping 
mechanism  and  of  the  water  in  pipes. 

The  whole  theory  of  propulsion  may  be  siunmed  up  in  Rankine*s  words: 
**That  propeller  is  the  best,  other  things  being  equal,  which  drives  astern 
the  largest  body  of  water  at  tne  lowest  velocity.^* 

It  is  practically  impossible  to  devise  any  system  of  hydraulic  or  jet  propul- 
sion which  can  compare  favorably,  under  these  conditions,  with  the  screw 
or  the  paddle-wheel. 

Reaction  of  a  Jet*— If  a  Jet  of  water  issues  horizontally  from  a  ves- 
sel, the  reaction  on  the  side  of  the  vessel  opposite  the  orifice  Is  eoual  to  the 
weight  of  a  column  of  water  the  section  of  which  Is  the  area  of  tne  orifice, 
and  the  height  is  twice  the  head. 

The  propelling  force  in  Jet-propulsion  Is  the  reaction  of  the  stream  Issuing 
from  the  orifice,  and  it  Is  the  same  whether  the  Jet  is  discharged  under 
water.  In  the  open  air,  or  against  a  solid  wall.  For  proof ,  see  account  of 
trials  by  C.  J.  Everett,  Jr.,  given  by  Prof.  J.  Burkltt  Webb,  Trans.  A.  S.  M. 
£.,  xiL  901. 

BEOENT  PBACnCB  IN   BrARINE   ENOINES. 

{From  a  paper  by  A.  Blechynden  dn  Marine  Engineering  during  the  past 
Decade,  Proc.  Inst.  M.  E.,  July,  1891.) 

Since  1881  the  three-stage-ezpanslon  enslne  has  become  the  rule,  and  the 
boiler-pressure  has  been  increased  to  100  lbs.  and  even  as  high  as  2m  lbs. per 
square  inch.  Four-stage-expansion  engines  of  various  forms  have  also  been 
adopted. 

Forced  nranslit  has  become  the  rule  In  all  vessels  for  naval  service, 
and  is  comparatively  common  in  both  passenger  and  cargo  vessels.  By  this 
means  it  is  possible  considerably  to  augment  the  power  obtained  from  a 
given  boiler;  and  so  long  as  It  Is  kept  within  certain  limits  it  need  result  in 
no  injury  to  the  boiler,  but  when  pushed  too  far  the  Increase  is  sometimes 
purchased  at  considerable  cost. 

In  r^^rd  to  the  economy  of  forced  draught,  an  examination  of  the  ap- 
pendeatable  (page  1018)  will  show  that  while  the  mean  consumption  of  coal 
in  those  steamers  working  under  natural  draught  is  1.578  lbs.  per  indicated 
horse-power  per  hour,  it  is  only  1.886  lbs.  in  those  fitted  with  forced  draught. 
This  is  equivalent  to  an  economy  of  ISjt.  Part  of  this  economy,  however, 
may  be  due  to  the  other  heat-saving  appliances  with  which  the  latter 
steamers  are  fitted. 

BoUers*— As  a  material  for  boilers,  iron  Is  now  a  thing  of  the  past, 
though  it  seems  probable  that  it  will  continue  yet  awhile  to  be  the  material 
for  tubes.  Steel  plates  can  be  procured  at  18^  square  feet  superficial  area 
and  l^i  inches  thick.  For  purely  boiler  work  a  punching-maehlne  has  be- 
come obsolete  in  marine-engine  work. 

The  increased  pressures  of  steam  have  also  caused  attention  to  be  directed 
to  the  furnace,  and  have  led  to  the  adoption  of  various  artifices  in  the  shape 
of  corrugated,  ribbed,  and  spiral  fiues,  with  the  object  of  giving  increased 
strength  against  collapse  without  abnormally  Increasing  the  thickness  of 
the  plate.   A  tliick  furnace- plate  is  viewed  by  many  engineers  with  graat 


1016  KAEIKIS  £KaiH£K&XKG. 

susplcioD;  and  the  advlaenof  the  Board  of  Trade  have  fired  Uie  limit  of 
thlcknen  for  fumace-platfes  at  %  inch ;  but  whether  thia  limitation  will 
stand  In  the  light  of  prolonged  experience  remaiuR  to  be  seen.  It  Is  a  fact 
generaliv  accepted  that  the  conditions  of  the  surfaces  of  a  plate  are  far 
greater  factors  in  its  resistance  to  the  transmission  of  heat  than  either  the 
material  or  the  thickness.  With  a  plate  free  from  lamination,  thick ne^ 
being  a  mere  secondary  element,  it  would  appear  that  a  furnace-plate  mif?ht 
be  iuoreased  from  M  iucli  to  ^  ii  ch  thickness  witliout  increasing  its  n^sist- 
anoe  more  than  lyi^.  80  convinced  have  some  engineers  become  of  the 
soundness  of  this  view  that  they  have  adopted  flues  ^  inch  thick. 

Ptatoii'TalTea*— Since  higher  steam -pressures  have  become  common, 
pifitou-valves  have  become  the  rule  for  the  high-preosure  cylinder,  and  arv 
not  unusual  for  the  intermediate.  When  well  designed  they  have  the  great 
advantage  of  being  almost  free  from  friction,  so  far  as  the  valve  itself  is 
concernM.  In  the  earlier  plHton-valves  it  was  customary  to  fit  spring 
rings,  which  were  a  frequent  source  of  trouble  and  absorbed  a  laifre  amount 
of  power  in  friction;  but  in  recent  practice  it  has  become  usual  to  fit  spring- 
less  adjustable  sleeves. 

For  low-pressure  cylinders  piston-valves  are  not  in  favor:  if  fitted  with 
spring  rings  their  friction  is  about  as  great  as  and  occasionally  gi^sater  than 
that  of  a  well-balanced  slide-valve;  while  if  fitted  with  springless  rings  there 
is  always  some  leakage,  which  is  irrecoverable.  But  the  tarse  port-clear- 
ances uiseparable  from  the  use  of  piston -valves  are  most  objectionable: 
and  with  triple  engines  this  is  especially  so,  because  with  the  custoniarr 
late  cutK»ir  it  becomes  difficult  to  compress  sufficiently  for  insuring  econo- 
my and  smoothness  of  working  when  in  "  full  gear,'*  without  some  special 
device. 

Staaiii«plpea«— The  failures  of  copper  steam-pipes  on  large  vesseh 
have  drawn  serious  attention  both  to  the  material  and  the  modes  of  con- 
struction of  the  pipes.  As  the  brazed  joint  is  liable  to  be  imperfect,  it  is 
proposed  to  substitute  solid  drawn  tubes,  but  as  these  are  not  made  of  lante 
sizes  two  or  more  tut>es  may  be  needed  to  take  the  place  of  one  brazed  tub<«. 
Reinforcing  the  ordinary  brazed  tubes  by  serving  them  with  steel  or  copper 
wire,  or  by  hooping  them  at  intervals  with  steel  or  iron  bands,  has  been 
tried  and  found  to  answer  perfectly. 

Auxiliary  Supply  of  Freali  mrafer— BraponitorB.— To  makt* 
up  the  losses  of  water  due  to  escape  oF  steam  from  safeiy-valvt* s,  leakag<e  At 
glands,  joints,  et<:.,  either  a  reserve  supply  of  fresh  water  is  carried  in  tank», 
or  the  supplementary  feed  is  distilled  from  sea-water  by  special  apparatus 
provided  for  the  purpose.  In  practice  the  distillation  is  effected  by  pa8>^ng 
steam,  say  from  the  first  receiver,  through  a  nest  of  tubes  inside  a  still  or 
evaporator,  of  which  the  steam-space  is  connected  either  with  the  sectn.'i 
receiver  or  with  the  condenser.  The  temperature  of  the  steam  inside  tbf 
tubes  being  higher  than  that  of  the  steam  either  In  the  second  receiver  or  -!i 
the  condenser,  the  result  is  that  the  water  inside  the  still  is  evaporated,  and 
passes  with  the  rest  of  the  steam  into  the  condenser,  where  it  is  conden»H] 
and  serves  to  make  up  the  loss.  This  plan  localizes  the  trouble  of  the  kU- 
posit,  and  frees  it  from  its  dangerous  character,  because  an  evaporator  can- 
not become  overheated  like  a  boiler,  even  though  it  be  neglected  until  it 
salts  up  solid;  and  if  the  same  precautions  are  taken  in  woricing  the  evapo- 
rator which  used  to  be  adopted  with  low-pressure  boilers  when  they  wen» 
fed  with  salt  water,  no  serious  trouble  should  result. 

UTelr'a  Feed-water  Heater.— The  principle  of  a  method  of  heatin? 
feed -water  introduced  by  Mr.  James  Weir  and  widely  adopted  in  tht 
marine  service  is  founded  on  the  fact  that,  if  the  feed -water  as  it  Is  dravo 
from  the  hot-well  be  raised  in  tempei-ature  by  the  heat  of  a  portion  of  steam 
introduced  into  It  from  one  of  the  steam-receivers,  the  decrease  of  the  c**^ 
necessary  to  generate  steam  from  the  water  of  the  higher  temperature  bear^ 
a  greater  ratio  to  the  coal  required  without  feed-heating  than  the  power 
which  would  be  developed  in  the  cylinder  by  that  portion  of  steam  vroul  1 
bear  to  the  whole  power  developed  when  passing  all  the  steam  through  alj 
the  cylinders.  Suppose  a  triple-expansion  engine  were  working  under  th<* 
following  conditions  without  feed-heating:  boiler-pressure  150  lbs.:  I.H.P.  in 
high-pressure  cylinder  89S,  in  intermediate  and  low-pi-essnre  cylinders  to- 
gether 790,  total  1168.  The  temperature  of  hot-well  ]00«  F.  Then  with  fee<j- 
heating  the  same  engine  might  work  as  follows:  the  feed  might  be  heated  10 
280®  P.,  and  the  percentage  of  steam  from  the  first  receiver  required  to  heat 
it  would  be  lO.Ojt:  the  I.H.P.  in  the  h.p.  cylinder  would  be  as  before  899.  aiul 
in  the  three  cyliuders  it  would  be  1103,  or  9Sgi  of  the  power  developed  wtihoitt 


BECBNT  PRACTICE  IN  MARINE   ENGINES.       1017 


feed-heatinfir.  Meanwhile  the  heat  to  be  added  to  each  pound  of  the  feed- water 
at  ZiOF"  F.  for  conYertingr  it  into  steam  would  be  1006  units  against  11^  units 
HMth  feed  at  100"  F.,  equivalent  to  an  expenditure  of  only  &.4%  of  the  heat 
required  without  feed-lieatine.  Hence  tbe  expenditure  of  heat  in  relation 
to  power  would  be  89.4  ■*-  93.0  =r  96.4)(,  equivalent  to  a  heat  economy  of  Z.Bi, 
If  the  steam  for  heatinfp  can  be  taken  n-om  the  low-pressure  receiver,  the 
economy  is  about  doubled. 

Passenfi^er  Steamers  fitted  irlth  Twin  Screws. 


Vessels. 

1 

Cylinders,  two  sets 

1-^ 

jj 

Diameters. 

Stro. 

City  of  New  York  ? 

*»    "   Paris          r 

Majestic  ( 

Teutonic  \ 

Normannla 

Feet 
6S6 

666 

600 

468^ 

440 

416 
460 

Feet 
68M 
68 

S^ 

61 

.48 
54« 

Inches 
45,  71,  118 

48,  68,  110 

40,  67,  106 

41,  66,  101 

83,  61,  82 

84,64,  86 
84«.  57«,  92 

In. 
60 

60 

66 
66 

54 

61 
60 

Lbs. 
160 

190 

160 
160 

160 

160 
170 

I.H.P. 

ao,ooo 

18,000 
ll,i)00 

Columbia 

B:mpresB  of  India  ) 

^*        "Japan- 

"  China 
Orel  

12,500 
10,185 
10  000 

Scot 

iije-Mj 

Comparative  Results  of  urorkln 
187i{,  1881,  and 

K  of  ntarlne  Engtnes, 
1891.                              ' 

Boilera,  Engines,  and  Coal. 

1872. 

1881. 

1891. 

Boiler-pressure,  lbs.  per  sq.  in  

62.4 
4.410 
55.67 
876 

2.110 

77.4 
8.917 
69.76 
467 
1.828 

158.5 

Heating-surface  per  norse-power,  sq.  ft 

Revolutions  per  minute,  revs 

8.275 
03.75 

Piston-speed,  feet  per  min 

589 

Coal  per  horse-power  per  hour,  lbs 

1  522 

UTeticlit  of  Three  -  sta^e  -  expansion  fin^lnes  In  Nine 
Steamers  in  Relation  to  Indicated  Horse-poiver  and 
to  rylinder*capacit7. 


c 

Weijrhtof 
Machinery. 

Relative  Weight  of  Machinery. 

1 

e  5 

p 

Per  Indicated  Horse- 

fi-®^ 

s->,. 

Type  of 

i 

i 

power. 

ii 

gq     o 

Boiler-ro 

per  100  sq 

of  Heatf 

surface 

Machinery, 

Engine- 
room. 

"IbsT 

Boiler- 
room. 

Total 

tons. 

tons. 

tons. 

lbs. 

lbs. 

tons. 

tons. 

1 

681 

662 

1343 

226 

220 

446 

1.80 

3.75 

Mercantile 

« 

638 

619 

12W 

259 

251 

510 

1.46 

4.10 

n 

134 

128 

262 

207 

198 

405 

1.23 

8.23 

»* 

4 

38.8 

46.2 

85 

170 

208 

373 

1.29 

8.30 

*♦ 

5 

719 

695 

1414 

167 

162 

329 

1.41 

8.44 

•i 

6 

75.2 

107.8 

183 

141 

202 

843 

1.87 

8.87 

tt 

7 

44 

61 

105 

77 

108 

185 

1.22 

2.72] 

Naval 
horizontal 

8 

7^.5 

109 

182.5 

78 

116 

194 

1.11 

2.78 

do. 

9 

2ea 

429 

691 

62.5 

102 

165       0.82    1    2.70 1 

Naval 
vertical 

1018 


MAHimC  ENGIKEERIUfG. 


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CONSTRUCTION  OF  BUILDINGS. 


1019 


I^ImeiiMlonii,  ladlcated  Horse  -  power,  and  Cylinder « 
eapaeltjr  of  Three -eiacfe- expansion  Buslnen  In  Nine 
Sieamers. 


Ota;' 

Cillndera, 

^  s 

"o  - 

4t 

1^ 

II 

Hftfttlng-sur^ 
face. 

II 

1 
Diameters,  fUtruku 

1 

Total. 

Fter 

LH.P, 

Iti^f.            Ins, 

rev«. 

llHl. 

I.  HP, 

€U.  ft. 

M.  ft. 

1«^- 

I 

fflnirl* 

JO      1^    IDO'     :- 

fli.s 

160 

CT51 

r/jj 

39      fil      07,    m 

tlT/g;     IfW 

BiWS 

4SII 

15,107 

a. 73 

■* 

^    S8    ai 

4:! 

H,1 

leo 

1450 

ITO 

3.01-4 

3  T3 

iL 

17      atJii^  4^ 

S4 

»} 

1» 

SIO 

J» 

1.403 

a  75 

TlTill 

^^      M      H-i 

51 

88 

IttO 

Bdsi5 

eoii 

LU19CJ 

3,10 

r* 

tS      LM      3S 

t!7 

na 

ISO 

1104 

55 

3,300 

36B 

SlQute 

;jo     m     4r» 

*^4 

IPI 

i4r» 

r-jw 

3fl.S 

ii,t^ 

).:« 

Twin 

S3^  49      T4 

Jl 

ItW.ft 

140 

aics 

OflJi 

8,9-J» 

l.dT 

" 

as 

1+5 

uw 

mm 

3ig 

15.*fiJ 

I M 

CONSTBUCTION   OP  BUHiDINQS.* 

(Extract  from  th«»  Building  Laws  of  the  City  of  New  York,  1898.) 
"Walle  of  ITarelioaees,  Stores,  Factories,  and  Stables.^ 

85  feet  or  less  in  width  between  walls,  not  less  than  li  in.  to  height  of  40  ft.; 
If  40  to  60  ft.  in  height,  not  less  than  16  in.  to  40  ft.,  and  18  In.  thence  to  top; 
60  to  80    «♦  »^        "      »»       "    20     "      85       "       16 

75  to  85    »•  ••        »»•*••    84     •»     80  ft. ;  20  In.  to  60  ft.»  and  16  in. 

to  top; 
65  to  100  ft.  in  height,  not  less  than  28  in.  to  25  ft ;  84  in.  to  50  ft. ;  20  in' 

to  75  ft.,  and  16  in.  to  top: 
Over  100  ft.  in  height,  each  additional  25  ft.  in  height,  or  part  thereof,  next 
above  the  curb,  shall  be  increased  4  inches  in  thiclciiess,  the  upper  100 
feet  remaining  the  same  as  specified  for  a  wall  of  that  weight. 
If  walls  are  over  25  feet  apart,  the  bearing-walls  shall  be  4  incnes  thicker 
than  above  specified  for  every  12^  feet  or  fraction  thereof  that  said  walls 
are  more  than  *J5  fe«>t  apart. 

Strenfftli  of  Floors,  BooA,  and  Supports* 

Floors  calculated  to  bear 
safely  per  sq.  ft.,  in  addition 
to  their  own  weight. 
Floors  of  dwelling,  tenement,  apartment-house  or  hotel,  not 

lessthan TOlbs. 

Floors  of  offlce-building,  not  less  than..' 100  ** 

'*        public-assembly  building,  not  less  than 120   *' 

^        store,  factory,  warehouse,  etc.,  not  less  than 150   ** 

Roofs  of  all  buildings,  not  lei>s  than 50  ** 

Every  floor  shall  be  of  sufficient  strength  to  bear  safely  the  weight  to  be 
Imposed  thereon,  in  addition  to  the  weight  of  the  materials  of  which  the 
floor  is  composed. 

Colnmus  and  Posts*— The  strength  of  all  columns  and  posts  shall 
be  computed  according  to  Gordon's  formulsB,  and  the  crushing  weights  in 
pounds,  to  tlie  square  inch  of  section,  for  the  following-named  materials, 
shall  be  taken  as  the  coefficients  in  said  forinuleB,  namely:  Cas'  iron,  80.U00; 
*The  limitations  of  space  foibid  any  extended  treatment  of  this  subject. 
Much  valuable  information  upon  it  will  be  found  in  Trautwine's  Civil  Kiifd- 
neer's  Pocket-book,  and  in  Kidder's  Architect's  and  Builder'H  Pocket-book. 
The  latter  in  its  preface  mentions  the  following  works  of  reference:  ''  Notes 
on  Building  Construction,**  3  vols.,  Rivingtons,  publishers,  B>ston;  "Building 
Superintendence,"  byT.  M.Clark  (J.  R.  Osgood  &  Co.,  Boston.);  **The 
American  House  Carpenter,"  by  R.  Q.  Hatfield:  "  Graphical  Analysis  of 
Roof-trusses."  by  Prof.  C.  E.  Greene;  "The  Fii-e  Protection  of  Mills,"  by  C. 
J.  H.  Woodburv:  "  House  Drainage  and  Water  Service,"  by  James  C. 
Bayles;  **The  BulIder^s  Guide  and  Estimator's  Price- bock,"  and  "  Plaster- 
ing Mortars  and  Cements,'*  by  Fred.  T.  Hodgson;  '* Foundations  and  Con- 
cret<»  Works."  and  "Art  of  Building."  by  E.  Dobsoii.  Weale's  Series.  London. 
J.  H.  Woodbury:  "  Honse  Drainage  and  Water  Service,"  by  James  C, 
Bayles;  "The  Builder's  Guide  and  Estimator's  Price-boolc,"  and  "Plaster- 
ing Mortars  and  Cements,"  by  Fred.  T.  Hodgson;  "Foundations  and  Con- 


1020  OOlfSTRUCnOK  OF  BUILmNOS. 

wrought  or  rolled  Iron,  40,000;  rolled  ttoel,  48,000;  white  pine  aiwl  spnioe, 
8600;  pitch  or  GeorgiA  pine,  5000;  American  oak,  flOOO.  The  breaklnff  straaKth 
of  wooden  beams  and  girders  shall  be  computed  according  to  tlie  forcnulfe 
In  which  the  constants  for  transverse  strains  for  cential  iood  ahall  be  as 
follows,  namely:  Hemlock,  400;  white  pine,  450;  spruce,  450;  pitch  orQeorgte 
pine,  5oO;  American  ouk,  000;  and  for  wooden  beams  and  girders  carrying  a 
uniformly  distributed  load  the  constanta  will  be  doubled.  The  factors  of 
safety  shall  be  as  one  to  four  for  all  beams,  girders,  and  other  pieces  subject 
to  a  transverse  strain;  as  one  U)  four  for  all  postSi  columns,  and  otiier 
yertloal  supports  when  of  wi^ught  iit^n  or  rolled  steel;  as  one  to  five  for 
other  materials,  subject  to  a  compressive  strain;  as  one  to  six  for  tie- 
rods,  tie-beams,  and  other  pieces  subject  to  a  tensile  strain.  Good,  solid, 
natural  earth  shall  be  deemed  to  safely  sustain  a  load  of  four  tooa  to  the 
superficial  foot,  or  as  otherwise  determined  by  the  suparintandent  of  build- 
ings, and  the  width  of  footing-courses  shall  be  at  least  sufficient  to  me«i  this 
requirement.  In  oomputing  tlie  width  of  wails,  a  cubic  foot  of  brickwork 
shall  be  deemed  to  weigh  115  lbs.  Sandstone,  white  marble,  gmnite,  and 
other  kinds  of  building-stone  shall  deemed  to  weigh  lOO  lbs.  per  oubic  foot. 


The  safe-bearing  load  to  apply  to  good  brickwora  sliall  ha  takan  at  8  tons 
per  superficial  foot  when  good  lime  mortar  is  used,  11 U  tons  per  superficial 
foot  when  good  lime  and  oement  niortai*  mixed  is  used,  and  lb  Ions  par  sup- 


erficial foot  when  Rrood  cement  mortar  is  used. 

Fire-proof  Blill<t|ng«— Iroa  ftiid  Sl^^l  Colamiu^— All  cast- 
iron,  wrouglit'iron,  or  tx>iieit-steel  oolumns  shall  be  made  true  and  sraooih 
at  both  ends,  and  shall  rest  on  iron  or  steel  bed-plates,  and  have  iron  or 
steel  cap-plates,  which  shall  also  be  made  tntc  All  Iron  or  steel  trimmer- 
beams,  headers,  and  tail-beams  shall  be  suitably  framed  and  connected  to- 
gether.  and  the  iron  girders,  columns,  beams,  trusses,  and  all  othar  ironwork 
of  all  floors  and  roofs  shall  tie  strapped,  bolted,  anchored,  and  connected  to- 
gether, and  to  the  walls,  in  a  strong  and  substantial  manner.  Where  beams 
are  framed  into  headers,  the  angle^rons,  which  aro  bolted  to  the  tall-beams, 
shall  have  at  least  two  ijolts  for  all  beams  over  7  inches  in  depth,  and  thr«e 
bolts  for  all  beams  19  inches  and  over  in  depth,  and  thece  bolts  shall  not  bi 
less  than  ^  inch  in  diameter.  Each  one  of  such  angles  or  knees,  when  boliei  I 
to  girders,  shall  have  the  same  number  of  bolts  as  stated  for  the  other  l«*g 
The  angle-iron  In  no  case  shall  be  less  in  thickness  than  the  header  or  trim- 
mer to  which  it  is  bolted,  and  the  width  of  angle  in  no  csae  shal!  be  lesa  than 
one  third  the  depth  of  beam,  excepting  that  no  angle-knee  shall  be  1«88  than 
»^  inches  wide,  nor  required  to  be  more  than  6  inches  wide.  All  wrought- 
iron  or  rolled-steel  beams  8  inches  deep  and  uuder  shali  have  bearings  equal 
to  their  deptli,  if  resting  on  a  wall;  9  to  li  inch  beams  shall  have  a  bearing 
of  10  inches,  and  all  beams  more  than  li  inches  in  depth  shall  have  bearin^^ 
of  not  less  than  18  inches  if  resting  on  a  wall.  Where  beams  rest  on  ittm 
supports,  and  are  properly  tied  to  the  same,  no  greater  bearings  shall  be  re- 

auired  than  one  tliird  of  the  depth  of  the  beams.  Iron  or  steel  floor-beams 
tiall  be  so  arranged  as  to  spacing  and  length  of  beams  that  the  load  to  bs 
supported  by  them,  together  with  the  weights  of  the  materials  used  to  ttie 
construction  of  the  said  floors,  shall  not  cause  a  deflection  of  the  said  beams 
of  more  than  1/30  of  an  inch  per  linear  foot  of  span;  and  they  shall  be  tit^ 
totrether  at  intervals  of  not  uiore  than  eight  times  the  depth  oi  the  beam. 

Under  the  ends  of  all  iron  or  steel  beams,  where  they  rest  on  the  walls,  a 
stone  or  oast  iron  template  shall  be  built  into  the  walls.  Bald  template  sliall 
be  8  inches  wide  in  12-inch  walls,  and  in  all  walls  of  greater  thickness  saiil 
template  shall  be  10  inches  wide;  and  such  templates,  If  of  stone,  shall  not  1« 
in  any  case  less  than  fl^  inches  in  thickness,  and  no  template  ahall  be  k«s 
than  13  inches  long. 

No  cast  iron  post  or  column  shall  be  used  In  may  building  of  a  leas  average 
thickness  of  shaft  than  three  quarters  of  an  inch,  nor  shall  it  have  an  ud- 
supported  length  of  more  tlian  twenty  times  its  least  lateral  dimensions  or 
diameter.  No  wrought-iron  or  rolled-steel  Qolumn  shall  have  an  unsupported 
length  of  more  than  thirty  times  its  least  lateral  dimension  or  diameter,  nor 
shall  its  metal  bt^  less  than  one  fourth  of  an  Inch  in  thioknesa. 

l4lMtela9  Beartiig:a  and  Suppori««^All  iron  or  steal  lintels  shall 
have  bearings  proportionate  to  the  weight  to  be  imposed  thereon,  but  no 
lintel  used  to  span  any  opening  more  thau  10  feet  in  width  shall  have  a  besr- 
ing  less  than  ]'J  inches  at  eaoli  end,  if  resting  on  a  wall  (  but  if  rseting  on  an 
iron  post,  such  lintel  shall  have  a  bearing  of  at  least  0  ioohea  at  each  end, 
by  the  thickness  of  the  wall  to  he  imported 

9$riM>ift  on  Gtrdora  upd  liiire^.^^||e<i  iron  or  pteel  beam  gli> 


STBlirGTH   OF  FLOOBS.  1031 

d6f8.  or  rlyeted  Iron  or  aCeel  plate  ^rden  lued  as  lintols  or  as  glrden, 
carrying  a  wall  or  floor  or  both,  shall  be  ao  proportioiied  that  the  loadt 
which  may  come  upon  them  shall  cot  produce  sti^aina  in  tension  or  oom* 
presuUon  upon  the  flanges  of  more  than  18,000  lbs.  for  iron,  nor  more  than 
16.000  lbs.  for  steel  per  square  inch  of  the  mm  seotton  of  each  of  such 
flati^eM,  nor  n  shearing  strain  upon  the  web-plate  of  more  than  flOOO  lbs.  per 
square  inch  of  aeciion  of  such  web-plate,  it  of  iron,  nor  more  than  llXN) 
pound!  tf  of  steel;  but  no  web- plate  shall  be  less  than  ^  Inoh  In 
ttiicknetu.  Riveu  in  plate  girders  shall  not  be  less  than  9^  inch  in  diameter, 
and  shall  not  be  spaced  more  than  C  Inches  apart  in  any  case.  They  shall  be 
BO  gpac<sd  that  their  shearing  strains  sliall  not  eicoeed  9000  lbs.  per  square 
innh.  on  their  diameter,  multiplied  by  the  thickness  of  the  platee  through 
which  they  pass.  The  riveted  plate  girdera  shall  be  proportioned  upon  the 
supposition  that  the  bending  or  chord  strains  are  resisted  entirely  by  the 
upper  and  lower  flanges,  and  that  the  shearing  strains  are  insisted  entirely 
by  the  web-plate.  No  part  of  the  web  shall  be  estimated  as  flange  area,  nor 
more  than  one  half  of  that  portion  of  the  angle-iron  which  lies  against  the 
web.  The  distance  between  the  centres  of  gravity  of  the  flange  areas  will 
b«  considered  as  the  effective  depth  of  the  girder. 

The  building  laws  of  the  City  of  New  York  contain  a  great  amount  of  de- 
tail in  addition  to  the  extracts  above,  and  penalties  are  provided  for  viola- 
tion. See  An  Act  creating  a  Department  of  Buildings,  etc.,  Chapter  279,' 
Laws  of  1808.  Pamphlet  copy  published  by  Baker,  Voorhies  &  Co.,  New 
York. 

JHAXIinvnt  I«OAB  ON  FI«OORS. 

(Eng^g,  Nov.  18,  180;2.  p.  044.)~Mazimum  load  per  square  foot  of  floor 
surface  due  to  the  weight  of  a  dense  crowd.  Considerable  variation  Is 
apparent  In  the  figures  given  by  many  authorities,  as  the  following  table 
shows: 

A»thoriU«  "^fi^^'aTf"*^ 

French  practice,  quoted  by  Traut wine  and  Stoney 41 

Hatfield  C*  Transverse  Strains,**  p.  80)  70 

Mr.  Page,  London,  quoted  by  Trautwiae • 84 

Maximum  load  on  American  hisrhway  bridges  according  to 

Waddeirs  general  speolflcatfons 100 

Mr.  Nash,  architect  of  Buckingham  Palace. 180 

Kxperlments  by  Prof.  W.  N.  Kemot,  at  Melbourne i       ^&  i 

Ejroerlments  by  Mr.  B.  B.  Stoney  (**  On  Stresses,"  p.  617). . . .  147 .4 

The  highest  results  were  obtained  by  crowding  a  number  of  persons  pre* 
T  iouslv  weighed  into  a  small  room,  the  men  being  tightly  packed  so  as  to 
1  eseinble  such  a  crowd  as  frequently  occurs  on  the  stairways  and  platforms 
'>f  a  theatre  or  other  public  building. 

STRKNGTH  OF  FI^OORS. 

(From  circular  of  the  Boston  Manufacturers*  Mutual  Insurance  Oo.) 

The  following  tables  were  prepared  by  C.  J.  H.  Woodbury,  for  determining 
Rafe  loads  on  floors.  Care  should  be  observed  to  select  the  figure  giving  the 
fcreatest  poaaible  amount  and  concentration  of  load  as  the  one  wnich  may 
be  put  upon  any  beam  or  set  of  floor-beams;  and  in  no  case  should  bf«iiis  be 
Ruhjected  to  greater  loads  than  those  specified,  unless  a  lower  factor  of 
safHtv  is  warranted  under  the  advice  of  a  competetit  engineer. 

Witenever  and  wherever  solid  beams  or  heavy  timbers  are  made  use  of  in 
the  Gonstruction  of  a  factory  or  warehouse,  they  should  not  be  painted,  var- 
nished or  oiled,  filled  or  encased  in  impervious  concrete,  air-proc#f  plastering, 
DP  metal  for  at  least  three  years,  lest  fermentation  should  destroy  them  by 
what  is  called  **dry  rot.** 

It  Is,  on  the  whole,  safer  to  make  floor-beams  In  two  parts,  with  a  small 
3pen  space  between,  so  that  proper  ventilation  may  be  secured,  even  if  the 
outside  should  be  inadvertently  painted  or  filled. 

These  tables  apply  to  distributed  loads,  but  the  first  can  be  used  In  respect 
:o  floors  which  may  carry  oonoentrated  loads  by  using  half  the  figure  given 
n  the  table,  since  a  beam  will  bear  twice  as  much  load  when  evemy  distrib- 
it^'d  over  Its  length  as  it  would  If  the  load  was  concentrated  In  the  centre 
>f  the  span. 

The  weight  of  the  floor  should  be  deducted  from  the  flgure  given  in  the 
able,  in  order  to  ascertain  the  net  load  which  may  be  placed  upon  any  floor. 
The  weight  of  spruce  may  be  taken  at  36  lbs.  per  cubic  foo^  and  that  of 
>outhern  pine  at  48  lbs.  per  cubic  foot. 


1023  OOKSTRUCnON  OF  BUILDINGS, 

Tftble  I  was  computed  upon  a  worklni;  modulus  of  rupture  of  Southern 
pine  at  SI 60  lbs.,  using  a  factor  of  safety  of  six.  It  can  also  be  applied  to 
ascertaining  the  strength  of  spruce  beams  if  the  figures  given  in  the  table 
are  multiplied  by  0.78;  or  In  designing  a  floor  to  be  sustained  by  spruce 
beams,  multiply  the  required  load  oy  1.28,  and  use  the  dimensions  as  given 
by  the  table. 

Theses  tables  are  computed  for  beams  one  inch  in  width,  because  the 
strength  of  beams  increases  directly  as  the  width  when  the  beams  are  broad 
enough  not  to  cripple. 

£xAMPLB.^Required  the  safe  load  per  square  foot  of  floor,  which  may  be 
safely  sustained  by  a  floor  on  Southern  pine  10  x  14  Inch  beams,  8  feet  on 
centres,  and  20  feet  span.  In  Table  I  a  1  X  14  inch  beam,  90  feet  span,  will 
sustain  118  lbs.  per  toot  of  span;  and  for  a  beam  10  Inches  wide  the  load 
would  be  1180  lbs.  per  foot  of  span,  or  147^  lbs.  per  square  foot  of  floor  for 
Southern-pine  beams.  From  this  should  be  deducted  the  weight  of  the  floor, 
which  would  amount  to  17^  lbs.  per  square  foot,  leaving  ISO  lbs.  per  square 
foot  as  a  safe  load  to  be  carried  upon  such  a  floor.  If  the  beams  are  of 
spruce,  the  result  of  147U  lbs.  would  be  multipUed  by  0.78.  reducing  the  load 
to  115  lbs.  The  weight  of  the  floor,  In  this  instance  amounting  to  16  lbs., 
would  leave  the  safe  net  load  as  00  lbs.  per  square  foot  for  spruce  beanos. 

Table  U  applies  to  the  design  of  floors  whose  strength  must  be  in  excess 
of  that  necessary  to  sustain  the  weight,  in  order  to  meet  the  conditions  of 
delicate  or  rapidly  moving  machinery,  to  the  end  that  the  vibration  or  dn- 
tortion  of  the  floor  may  be  reduced  to  the  least  practicable  limit. 

In  the  table  the  limit  is  that  of  load  which  would  cause  a  bending  of  the 
beams  to  a  curve  of  which  the  average  radius  would  be  r^50  feet. 

This  table  is  based  upon  a  modulus  of  elasticity  obtained  from  obaerva* 
tlons  upon  the  deflection  of  loaded  storehouse  floors,  and  is  taken  at  2,OUU.000 
lbs.  for  Southern  pine;  the  same  table  can  be  applied  to  spruce,  whose 
modulus  of  elasticity  is  taken  as  1.300,000  lbs.,  if  six  tentlis  of  the  load  for 
Southern  pine  is  taken  as  the  proper  load  for  spruce;  or,  in  the  matter  cf 
designing,  the  load  should  be  increased  one  and  two  thirds  times,  and  the 
dimension  of  timbers  for  this  increased  load  as  found  in  the  table  should  be 
used  for  spruce. 

It  can  also  be  applied  to  beams  and  floor- timbers  which  are  supported  at 
each  end  and  In  the  middle,  remembering  that  the  deflection  of  a  l>eam 
supported  in  that  manner  is  onlv  four  tenths  that  of  a  beam  of  equal  rpan 
which  rests  at  each  end;  that  Is  to  say,  the  floor- planks  are  two  and  one 
half  times  as  stiff,  cut  two  bays  In  length,  as  they  would  be  if  cut  only  one 
bay  in  length.  When  a  floor-plank  two  bays  in  length  is  evenly  loaded, 
three  sixteenths  of  the  load  on  the  plank  is  sustained  by  the  beam  at  each 
end  of  the  plank,  and  ten  sixteenths  by  the  beam  under  the  middle  of  the 
plank;  so  that  for  a  completed  floor  three  eiKbtbs  of  the  load  would  be  sus- 
tained by  the  beams  under  the  joints  of  the  plank,  and  Ave  eighths  of  the  load 
by  the  beams  under  the  middle  of  the  plank:  this  Is  the  reason  of  the  impor- 
tance of  breaking  joints  In  a  floor-planic  every  three  feet  in  order  that  each 
beam  shall  receive  an  identical  load.  If  it  were  not  so,  three  eighths  of  the 
whole  load  upon  the  floor  would  be  sustained  by  every  other  beam,  and  five 
elgiiths  of  the  load  by  tiie  corresponding  alternate  beams. 

Hepeating  the  former  example  for  the  load  on  a  mill  floor  on  Southern- 

fine  beams  10  X  1^  inches,  and  20  feet  span,  laid  8  feet  on  centres:  In^Table 
[  a  1  X  14  inch  l)eani  sliould  recei've  61  lbs.  per  foot  of  span,  or  n  Iba.  per 
sq.  ft.  of  floor,  for  Southern-pine  beams.  Deducting  the  weight  of  the  floor, 
1«  V4  lbs.  per  sq.  ft.,  leaves  57  lbs.  per  sq.  ft.  as  the  advisable  load. 

If  the  beamrt  are  of  spruce,  the  result  of  76  lbs.  should  be  multiplied  by  0.6, 
reducing  the  load  to  45  lbs.  Tlie  weight  of  the  floor,  in  this  instance  amount- 
ing to  16  lbs.,  would  leave  the  net  load  as  29  lbs.  for  spruce  beams. 

If  the  beams  were  two  spans  in  length,  they  could,  under  these  conditions, 
support  two  and  a  half  times  as  much  load  with  an  equal  amount  of  deflec- 
tion, unless  such  load  shouM  exceed  the  limit  of  safe  load  as  found  by  Table 
I,  Rs  would  be  the  ca.se  under  the  conditions  of  this  problem, 

3K111  Columns*— Timber  posts  offer  more  resistance  to  flre  than  iron 
pillars,  aiKi  have  generally  displaced  them  in  millwork.  Experiments 
made  on  the  testing-machine  at  theU.  S.  Arsenal  at  Watertown,  Mass, 
show  that  sound  timber  posts  of  the  proportions  customarily  used  in  mill- 
work  yield  by  direct  crushing,  the  strength  being  directly  as  the  area  at  the 
smallest  part.  The  columns  yielded  at  about  4500  lbs.  per  square  inch,  oon- 
flrming  the  general  practice  of  allowing  600  lbs.  per  square  inch,  as  a  safe 
load.  Square  columns  are  one  fourth  stronger  than  round  ones  of  the  t 
diameter. 


STRENGTH   OF   FLOORS. 


1023 


!•  S«ft  IHstrlbiiied  Loads  upon  Sontbem-plne  Beams 
One  Ineb  In  Wldtlu 

(C.  J.  H.  Woodbury.) 
at  the  load  is  concentrated  at  the  centre  of  the  span,  the  beams  wUl  bub- 
tain  half  the  amount  as  given  in  the  table.) 


1 

Depth  of  Beam  in  inches. 

1 

2       8 

4       5   1   6 

7 

8       9      10 

11 

12     18 

14 

15 

16 

Loii 

id  in  pounds  per  foot  of  Span. 

5 

88 

m 

iU 

2jn 

Mti 

4  Til 

614 

t;h 

950 

6 

27 

IS^l 

m 

]r57 

•,^lll 

:i:j: 

4S 

540 

ekf7 

ttOT 

2(» 

44 

m 

1t^ 

I7)i 

vw 

314 

i^u: 

4»0 

tm 

706 

fe^ 

8 

Ifi 

,^ 

60 

^N 

in:* 

y^i 

340 

ao4 

3^ 

451 

MO 

0^ 

7^ 

9 

27 

47 

74 

]!►: 

I4n 

100 

MO 

S« 

8Qfi 

4*7 

acu 

5H1 

667 

730 

10 

iVI 

a8 

1^1 

r«i- 

i3,S 

1!M 

104 

Ml 

9W 

^0 

406 

470 

EMO 

M4 

11 

H2 

W 

^1 

»r 

13T 

101 

IDS 

S40 

386 

335 

888 

446 

60^ 

U 

SJ7 

42 

<» 

as 

107 

las 

107 

SMK 

S40 

2S2 

»27 

575 

474 

18 

}» 

.^t 

TO 

9U 

115 

142 

irs? 

«05 

£740 

27H 

aiO 

3S4 

14 

Rl 

44 

m 

7H 

^ 

(^ 

I4S 

170 

207 

^0 

276 

314 

15 

K7 

as 

5a 

QH 

&j 

107 

1^ 

154 

IW 

2U(t 

SMO 

273 

ie 

34 

4fi 

r^o 

76 

94 

iia 

185 

1.^ 

1B4 

211 

240 

\7 

80 

41 

53 
4T 

74 

JOl 

ISO 
107 

140 
1'45 

m 

115 

1W7 
167 

217 

18 

100 

19 

4^ 

54 
44 

66 

m 

71 
66 

SO 
7« 

101 

130 
US 
107 

ISO 
135 

170 

20 

1 

154 

21 

m 

22 

5« 

m 

71 

B4 

97 

112 

127 

23 

45 

65 

65 

i  4 

m 

1<»3 

llfl 

24 

60 

60 

7(> 

WJ 

91 

107 

23 

4fi     55] 

flri 

75 

NS 

TIB 

II.  Distributed  Loads  upon  Sontbem-plne  Beams  s 
elent  to  produce  Stanilard  lilmlt  of  Bellectlon. 

(C.  J.  H.  Woodbury.) 


1 

Depth  of  Beam  in  inches. 

i. 

1 

2     8   1   4   1   5   1    6 

7       8       9 

10  1  11      12     18  1  14     15 

16 

Il 

Load  in  pounds  per  foot  of  Span. 

&- 

5 
6 
7 
8 
9 
10 
11 

3 
2 

10 
7 
5 

4 

23 
16 
12 
9 
7 
6 

44 

81 
28 
17 
14 
11 
9 

77 
58 
89 
80 
24 
19 
16 
13 
11 

122 
85 
62 
48 
38 
80 
25 
21 
18 
16 
14 

182 
126 
93 
71 
56 
46 
88 
82 
27 
28 
20 
18 
16 

259 
180 
132 
101 
80 
65 
54 
46 
88 
88 
29 
25 
22 
20 
18 

247 
181 
139 
110 
89 
73 
62 
53 
45 
40 
85 
81 
27 
25 
22 
20 

241 

185 
146 
118 
98 
82 
70 
60 

46 
41 
87 
83 
30 
27 
24 
22 

240 
190 
154 
127 
107 
91 
78 
68 
60 
58 
47 
48 
88 
85 
82 
29 
27 
25 

805 
241 
195 
161 
V» 
116 
100 
87 
76 
68 
60 
54 
49 
44 
40 
87 
34 
81 

301 
244 
20-J 
169 
144 
124 
108 
95 
84 
75 
68 
61 
65 
50 
40 
42 
89 

800 
248 
208 
178 
153 
133 
117 
104 
83 
88 
75 
68 
62 
57 
52 
48 

801 
253 
215 
186 
162 
147 
126 
112 
101 
91 
83 
75 
69 
68 
58 

.0300 
.0432 
.0588 
.0768 
.0972 
.1200 
.1452 

12 
18 
14 

.1728 
.2028 
.2352 

15 

.2700 

in 

.8078 

17 

.8468 

18 

.3888 

19 

.4332 

20 
21 

.4800 
.5292 

22 
23 

.5808 
.6348 

24 
25 

.6912 
.7500 

1024  ELECTRICAL   EXGIN-EETIING. 

ELECTRIOAIi  ISNOTSHSEBING. 

8TAN1»AR1»S   OF  IIIJBASIJREJHBNT. 

C.G.S.  (Centimetre*  Gramme,  Second)  or  **  Albsolnte" 
System  of  Pbyslcal  Ulemsnrements  t 

Unit  of  space  or  distance  =  1  centimetre,  cm.; 

Unit  of  mass  =  1  fframme,  gm. ; 

Unit  of  time  s  1  second,  s.; 

Unit  of  velocity  =  space  -h  time  :=.-  1  centimetre  In  1  second; 

Unit  of  acceleration  -=  cliange  of  1  unit  of  velocity  In  1  second ; 

Acceleration  due  to  g:ravityf  at  Paris*  =  961  centimetres  in  1  second; 

Unit  of  force  =:  1  dyne  =  |^  gramme  =  '^^^  lb.  =  .000008847  lb. 

A  dyne  Is  that  force  which,  acting  on  a  mass  of  one  gramme  during  one 
second,  will  give  it  a  velocity  of  one  centimetre  per  second.  The  weight  of 
one  gramme  in  latitude  40*  to  45*  is  about  980  dynes,  at  the  equator  978  dyness 
and  at  the  poles  nearlv  964  dynes.  Taking  the  value  of  o,  the  acceleratioa 
due  to  gravity,  in  British  measures  at  8S.185  feet  per  second  at  Fails,  and  tlM 
metre  =  80.87  inches,  we  have 

1  gramme  a  82.165  x  12  •«-  .8987  =  961 .00  dynes. 

Unit  of  work   s  1  erg    ss  1  dyne-centimetre  =  .00000007378  foot-pound ; 
Unit  of  power  =  1  watt  s=  10  million  ergs  per  second, 
s=  .7878  footpound  per  second, 

=  —^  =  ^of  1  horse-power  =  .00184  H.P. 

C.G.S.  Unit  of  magnetism  »  the  quantity  which  attracta  or  repels  aa 
equal  quantity  at  a  centimetre's  distance  with  the  force  of  1  dyne. 

C.O.S.  Unit  of  electrical  current  =  the  current  which,  flowing  through  a 
length  of  1  centimetre  of  wire,  acts  with  a  force  of  1  dyne  upon  a  unit  of 
magnetism  distant  1  centimetre  from  every  point  of  the  wire.  The  ampere, 
the  commercial  unit  of  current,  Is  one  tenth  of  the  CG.S.  unit. 

Tlio  Practical  ITialts  used  in  Bleetrleal  Calonlatloas  are: 

Ampeie^  the  unit  of  current  strength,  or  rate  of  flow,  represented  by  C. 

VoU,  the  unit  of  electro-motive  force,  electrical  pressure,  or  difference  of 
potential,  represented  by  E. 

Ohm,  the  unit  of  resistance,  represented  by  R. 

Coulomb  (or  ampere-iiiecoud),  the  unit  of  quantity,  Q, 

Ampere-hour  =  8603  coulombs,  Q'. 

Watt  (ampere-volt,  or  volt -ampere),  the  unit  of  power,  P. 

Jovle  vvoltcoulomb),  the  unit  of  energy  or  work,  W, 

Farad,  the  unit  of  capacity,  represented  by  K, 

Henry,  the  unit  of  induction,  represented  by  L, 

Using  letters  to  represent  the  unite,  the  relations  between  them  may  bf 
expressed  by  the  following  formulsB,  in  which  t  represents  one  second  sod 
T  one  hour: 

C=|,      Q^Ct,     q^^CT,     «  =  §.      W=QE,     P^CB, 

Ah  these  relations  contain  no  coefficient  other  than  unity,  the  letters  nuir 
represent  any  quantities  given  in  terms  of  those  units.  For  example,  if  R 
represents  the  number  of  volts  electro-motive  force,  and  R  the  number  of 
ohms  resistAnce  in  a  circuit,  then  their  ratio  E-t-  R  will  give  the  number  of 
amperes  current  strength  In  that  circuit. 

The  above  six  formulae  can  be  combined  by  substitution  or  eliminatloo, 
so  as  to  give  the  relations  between  any  of  the  quantities.  The  most  iinpor* 
tant  of  diese  are  the  following  : 

g  =  |f,    E^^t,      W=CEt  =  ^t=C*Rt  =  Pt, 

P^^^c-R^K^9IL 


STANDARDS  OF  HEABUBEMEKT.       1025 

ThA  definitions  of  these  units  as  aaopted  at  the  InternatioDal  Electrical 
C'oni^reRs  at  Chicago  in  18S6,  and  as  established  hy  Act  of  Congress  of  the 
United  States,  July  U,  181)4,  are  as  follows: 

The  ohm  is  substantially  equal  to  10*  (or  1,000,000,000)  unlu  or  resistance 
of  the  C.O.8.  system,  and  is  represented  by  the  resistance  offered  to  an  un- 
wary inic  electric  current  by  a  column  of  mercury  at  92^  F.,  14.453{1  grammes 
in  mass,  of  a  constant  cross-sectional  area,  and  of  the  length  of  lOu.3  centi- 
metres. 

The  ampere  is  1/10  of  the  unit  of  current  of  the  C.O.8.  system,  and  is  the 
practical  equivalent  of  the  unrarying  current  which  when  passed  through 
a  solution  of  nitrate  of  silver  in  water  in  ac(K>rdance  with  scacdard  specl- 
ficjitions  depoMits  silver  at  the  rate  of  .001118  gramme  per  second. 

The  volt  is  the  electro-motive  force  that,  steadily  applied  to  a  conductor 
whose  resistance  is  one  ohm,  will  produce  a  current  oi:  one  ampere,  and  is 
practically  equivalent  to  1000/1484  (or  .6074)  of  the  electro-motive  force  be- 
tween the  poles  or  electrodes  of  a  Clark's  cell  at  a  temperature  of  15^  C, 
and  prepared  in*  the  manner  described  In  ihe  standard  specifications. 

The  coulomb  is  the  quantity  of  electricity  transferred  by  a  current  of  one 
ampere  in  one  second. 

The  farad  is  the  capacity  of  a  condenser  charged  to  a  potential  of  one 
volt  by  one  coulomb  of  electricity. 

Tlie  joiUe  is  equal  to  10.000,000  units  of  work  in  the  C.O.8.  system,  and  is 
practically  equivalent  to  the  energy  expended  in  one  second  by  an  ampere 
lu  an  ohm. 

The  watt  is  equal  to  10,000,000  units  of  power  in  the  C.O.S.  system,  and  ia 
practically  equivalent  to  the  work  done  at  the  rate  of  one  Jouie  per  second. 

The  henry  is  the  induction  In  a  circuit  when  the  electro-motive  force  in- 
duced in  this  circuit  is  one  volt,  wliile  the  Inducing  current  varies  at  the  rate 
of  one  ampere  per  second. 

The  oliro,  volt,  etc.,  as  above  defined,  are  called  the  ^Mntemational  *^  ohm, 
volt,  etc.,  to  distinguish  them  from  the  **  legal  *'  ohm,  B.A.  unit,  etc. 

The  value  of  the  ohm,  determined  by  a  committee  of  the  British  Associa- 
tion In  1863,  called  the  B.A.  unit,  was  the  resistance  of  a  certain  piece  of 
copper  wire  preserved  in  London.  The  so-called  '*  legal  '*  ohm,  as  adopted 
at  the  International  Congress  of  Electricians  in  Paris  in  1884,  was  a  correc> 
tioa  of  the  B.A.  unit,  and  was  defined  as  the  resistance  of  a  columu  of 
mercury  1  sauare  millimetre  in  section  and  106  centimetres  long,  at  a  tem- 
perature of  JQ*  F. 

1  legal  ohm  ss  1.0112  B.A.  units,    1  B.A.  unit  =  0.0689  legal  ohm; 

1  intemational  ohm  =  1.0136    ''       ^        1    •'       **     =  0.0866  Int.  ohm; 

1  •»  **     =  1.0028  legal  ohm,    1  legal  ohm  =  O.WTT  "     *• 

Derived  Units. 
1  megohm       =  1  million  ohms; 
1  microhm       =  1  millionth,  of  an  ohm; 
1  milliampere  =  1/lOOOof  an  ampere; 
1  micro-farad  =  1  millionth  of  a  farad. 
Relations  or  VAaious  Units. 

I  ampere a  1  coulomb  per  second; 

1  volt-ampere =s  l  watt  =  l  volt-coulomb  per  second; 

(   s=  .7378  fooUpound  per  second, 

IwaU <  8  .0009477  heauunits  per  second  (Fahr.), 

(  s  1/746  of  one  horse-power; 
(   s=  .7878  foot-pound, 

1  joule 5   =  work  done  by  one  watt  in  one  second, 

I   =  .0000477  heat-unit; 
1  British  thermal  unit =  1056.2  joules: 

1=s  787.3  foot-pound  per  second, 
=  .0477  heai-units  per  second, 
s  1000/746  or  1. 8 106  horse- powers; 
1  kilowatt-hour,  (  ss  l.StOS  horse-power  hours, 

1000  volt-ampere  hours,  <  =  2,664,200  foot-pounds, 

1  Britltih  Board  of  Trade  unit,  (  =  iiVi  heat-uuitK; 

1  horsp-nower  i  =  ""^^  ^'*^^  =  ^^  volt-amperes, 

morse-power ^  =  83,000  footpounds  per  minute. 

The  ohm,  ampere,  and  volt  are  defined  in  terms  of  one  another  as  follows: 
Ohm,  the  resist ance  of  a  conductor  through  which  a  current  of  one  ampero 
will  pass  when  the  electro-motive  force  is  one  volt.    Ampere,  the  quantity 


1036 


ELECTRICAL   ENGIKEEBIKG. 


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PLOW  OF  WATER  AND  ELECTEIOTT. 


1037 


of  cuTTpnt  which  will  flow  through  a  resistance  of  one  ohm  when  the  electro* 
moiive  force  is  one  volt.  Volt,  the  electro-motive  force  requii^ed  to  cause  a 
current  of  onf*  ampere  t^  flow  tbrougrh  a  resistance  of  one  ohm. 
ITnlts  oftbe  Illanietle  Circuit.— (See  Electro- maRnets.  page  1088.) 
For  IHetliods  ormalKliiff  Electrical  Illeasiireiiiente*  Test- 
inff,  ete»9  see  Munroe  &  Jamieson*s  Pocket-Book  of  Electrical  Rules, 
Tables,  and  Data;  8.  P.  Thompson's  Dynamo-Electric  llachinery;  and  works 
on  Electrical  En8:ine«>rin(?. 

RqalTalent  Electrical  and  necbanlcal  tTnlts.—Cr.  Ward 
Leonard  published  In  The  Electrical  Btufineer.  Feb.  25, 1895,  a  table  of  use- 
ful equivalents  of  electrical  and  mechanical  units,  from  which  the  table  on 
pafre  1095  Is  taken,  with  some  modifications. 

ANAIiOOIES  BETWEEN  THE  FLOW  OF  WATER  AND 
ELEOTRICITT. 

Water.  Elictricttt. 

Head,  difference  of  level,  In  feet. 
Difference  of  pressure  per  sq.  in..  In  - 
lbs. 


{ 

Resistance  of  pipes,  apertures,  etc., 
increases  with  lensth  of  pipe,  with 
contractions,  roughness,  etc.;  de- 
creases with  increase  of  sectional  • 
area.  The  law  of  Increase  and  de- 
crease is  expressed  by  complex 
formuln.    See  Flow  of  Water. 

Itate  of  flow,  as  cubic  ft.  per  second, 
gallons  per  minute,  etc.,  or  volume 
divided  by  the  time.  In  the  mining: 
regions  sometimes  expressed  in 
"  miners^  Inches." 

Quantity,  usually  measured  In  cubic ' 
feet  or  gallons,  but  is  also  equiva- 
lent to  rate  of  flow  X  time,  as 
cubic  feet  per  second  for  so  many 
hours. 


Work,  or  energy,  measured  in  foot- 
pounds; product  of  weight  of  fall- 
ing water  into  height  of  fall;  in 
pumping,  product  of  quantity  in 
cubic  feet  into  the  pressure  in  lbs. 
per  square  foot  against  which  the 
water  is  pumped. 


Volts;  electro-motive  force ;  differ- 
ence of  potential  or  of  pressure;  E. 
or  E.M.F. 

Ohms,  resistance,  R.  The  resistance 
Increases  directly  as  the  length  of 
the  conductor  or  wire  and  Inversely 
as  its  sectional  area,  R«c  l-t-8. 
It  varies  with  the  nature  or  quaUty 
of  the  conductor. 

Conductivity  is  the  reciprocal  of  spe- 
cific resistance. 

Amperes;  current;  current  strength: 
intensity  of  current;  rate  of  flow;  1 
ampere  s  1  coulomb  per  second. 

.  volts       ^      B    „    ^^ 

Coulomb,  unit  of  quantity,  Q,  =  rate 
of  flow  X  time,  as  ampere-seconds. 
1  ampere-hour  =  8600  coulombs. 


Joule,  volt-coulomb,  TT,  the  unit  of 
work,  =  product  of  quantity  by  the 
electro-motive  force  =  volt-ampere- 
second.    1  Joule=  .7878  foot-pound. 

If  C  (amperes)  =  rate  of  flow,  and 
E  (volts)  31  difference  of  pressure 
between  two  points  in  a  circuit, 
energy  expended  =  CEt,  =  CRt, 
since  E  =  CR, 


Watt,  unit  of  power,  P,  s  volte  x 
amperes,  ss  current  or  rate  of  flow 
X  difference  of  potential. 

1  watt  =  .7878  foot-pound  per  second 
s=  1/745  of  a  horse-power. 


Power,  rate  of  work.  Hor8e-power,ft.- 

Ibs.  of  work  done  in  1  mln. -1-88,000. 
Id   falling  water,  pounds  falling  in 

one  second  -*-  550.  In  water  flowing 

in  pipes,  rate  of  flow  in  cubic  feet 

Ser  second  X  pressure  resisting  the 
ow  in  lbs.  per  sq.  ft.  -*-  550. 

Aaalomr  bet^nreen  tbe  Ampere  and  tlie  nUner^s  Incli. 
(T.  O^Connor  Sloane.)— The  miner^s  inch  is  defined  as  the  quantity  of  water 
which  will  flow  through  an  aperture  an  inch  square  In  a  board  two  inches 
thick,  under  a  head  ot  water  of  six  inches.  Here,  as  in  the  case  of  the  am- 
pere, we  have  no  reference  to  any  abstract  quantity,  such  as  gallons  or 
pounds.  There  is  no  reference  to  time.  It  is  dimply  a  rate  of  flow.  We 
may  consider  the  head  of  water,  six  inches,  as  the  representative  of  elect  ri- 
tual pressure;  i.e.,  one  volt.  The  aperture  restricting  the  flow  of  water  may 
be  assumed  to  represent  the  resistance  of  one  ohm;  the  flow  through  a  re- 
sistance of  one  ohm  under  the  pressure  of  one  volt  is  one  ampere;  the  flow 
through  the  resistance  of  a  one-Inch  hole  two  inches  long  under  the  pressure 
of  six  Inches  to  the  upper  edge  of  the  opening  is  one  miner's  inch. 

Tbe  ininer*s  inch-second  is  the  correct  analogue  of  the  ampere-second;  the 
one  denotes  a  specific  quantity  of  water,  0.1M  gallon;  the  other  a  apedflo 
quantity  of  electricity,  a  coulomb* 


10^8  BLECTBlCAt   liKGtKEBlltNa. 

BliEGVRlCAI.  RliSlSTAlfCB. 

^  liAira  of  Electrical  Rcslatance.— The  resistance,  A.  of  any  eon. 
dnctor  Tarfes  directljr  as  its  teagtfi,7,  and  inversely  as  its  sectional  area, «, 

orS«  i.. 

s 
Example.— If  one  foot  oi  copper  wire  .01  Ib.  diameter  has  a  resdstaace  rf 

.108'<!3  ohm,  what  wUl  be  the  resistaoce  of  a  mile  of  wire  .a  ia.  diam.  at  ilie 
same  temperature  ?  The  sectional  areas  betag  proportional  to  the  sqiiam 
of  the  diameters,  the  ratio  of  the  areas  is  ^  :  .01«  ir  900  to  1.  The  lengths 
are  as  5280  to  1.  The  resistances  being  directly  as  the  lengths  and  inversrtv 
as  the  tectional  areaa»  the  resistance  of  the  second  wire  to  .KWa  x  aSBD  4 
900  =  .6<^  ohm. 

Conductance,  c.  Is  the  inverse  of  resistance,  i?  s  -i,     c  s  -4r.  If  c  and  r. 

.represent  the  oonductaacea,  and  B  and  B^  the  respective  resistance  of  tiro 
subHtances  of  the  same  length  and  section,  then  c:c»:  :  R»:  B. 

K«iilTaleiit  ConAaetars.— With  two  conductors  of  leagth  I,  L.  of 
ooBductanoes  c,  c^,  and  sectional  areas  s,  «i«  we  hava  the  same  rimiafsnci. 

find  one  may  be  substituted  for  tlie  other  wlien  —  =  -il-. 

The  specMe  resistance,  also  called  resistivity,  a,  ol  a  material  of  anit 
leugiii  and  section  Is  Its  resistance  as  compared  with  the  resistance  of  a 
standard  conductor,  such  as  pure  copper.  Cooduotlvfty,  or  speeillc  con- 
ductance, is  the  reciprocal  of  resisUvity.  ^^ 

sc*  s 

If  tw^o  wives  have  lengtiis  I,  l^,  areas  t,  Sj.  and  qpeciflc  resistances  a,  a,*  their 
aauialiwiBtaaMBareAs^,  jr,s^,  aad   |.  a  ii^. 

Klectrteal  Gondvctlwlty  #f  DMteveat  lEetala  mmd.  AIlon« 

--Laaare  Weiler  presented  to  the  Soci^t^  Internationale  des  Elect riclemii he 
results  of  bis  ezpenmeuta  upon  the  relative  electrical  conductivity  of  certain 
metals  and  alloys^  aa  here  appended  : 


1.  Puresltver 100 

Sl  Pureeopper lOO 

&  Refined    and    CTystaQIsed 

copper 99.9 

4.  Tclefrraphtosflicfotisbronas   9$ 
6.  Alloy  of  copper  and  silver 

•.  Pure  ptold 78 

T.  Bilicidc  of  copper,  4jr  81. . . .  75 

8.  Siiicideof  copper,  lay  a...  84.7 

0.  Pure  aluminum 54.!?* 

10.  Tin  with  TSJT  of  sodhim ...  46.9 

11.  Telephonic  sillctouB  bronze  85 
r2.  Copper  with  W  of  toad ....  SO 

13.  Purs  zinc S9.9 

14.  Tttlepfaooie        phosphcr  - 

broDse 29 

15.  Silieious  brass,  25^  sine. . . .    »,4» 
IS.  Brass  with  8Ctf  of  ziac 21.6 


17.  Phosphor  tin 17.7 

18L  Alloy  of  gold  and  silver 

^       (6*1 W.« 

J &.  Swedish  iron le 

20.  Pure  Banca  tin  . . .  15  « 

81.  Antimoniai  copper 1^7 

28.  Atuniinum  bronae  (lQ|t) . . .  I2.C 

28.  Slemeas  steel 12 

^.  Pure  platinum 10  6 

29.  Conper  with  I9fi  of  nickeL.  10. ft 

26.  Cadmium  amalgam  OH).  10.2 

27.  Dronier  mercurial  bronae..  10.  U 

28.  Arsenical  copper  ( 10%) 9.1 

8».  Pure  lead g.,-* 

SO.  Bronse  with  SCIjr  of  tin 9A 

91.  Pare  nickel 7. SI 

88.  Ffiosphor^bronze,  lOjif  tin  ..  6.5 

«3.  Fhosphorcopper,  99(  phoe..  4.9 

84.  AnUttoay s.8 


The  above  eoasparattve  resistances  may  be  reduced  to  ohms  on  the  bajCi 
that  a  whp»  of  soft  copper  one  ramiii>eti'e  in  dfameter  at  a  temperature  or .  * 
C.  has  aresMstance of  .0S029  latenmtional  ohms  per  metre;  or  a  wli-e  .001  i. .  U 
dtfUtt.  has  a  reslstaaca  of  0,S»  international  ohi^^  per  foot.  *  "^  •«" » '  "» 

•This  firare  is  too  low.  J.  W.  Richards (j€Wfr. /^V»nfc.  /»««.,  Mai  Ife.;i 
givcB  for  hAKd-dravm  aluminum  of  pnriry  98.5. 99.0,  99.5.  and  99.7«  resuev 
tively  a  coaductirrHy  of  50,  50, «.  and  k  to  W.  copprr  being  WOjf.  STIKS 
Sl^If  S^J'^'VSJ?  90i;**«ms  thai  lis  purest  ahtmhram  haa  a  conductfvfty  of 
©v©r64.6;(.    (JEny'y  iVw«,  Dec.  17, 1896.)  ' 


BtiECtRtCAL   nESlSTAXCE. 


1O20 


S«lMlTe  CondncilTttlM  or  Dlfl^rent  ISIctals  at  O**  and 
lOO*"  €•    (Matttii««fteuj 


Ootlductivities. 

Metals. 

Oonduetlvities. 

ttetate. 

At  (TC. 

AtlOO«C. 
a  2ja«  p. 

At  0«C. 
"  82"»F. 

At 100»  0. 

fUlvAr  ha.t-A 

100 
99.05 
77.96 
S9.02 
JB.72 
18.00 
16.80 

71.86 
70.27 
M.90 
80.67 
16.77 

Tin 

W.S6 
8.82 
4.76 
4.62 
1.60 
1.S46 

8.67 

Copper,  hard.... 

Gold,  hard  

Zinc,  prefified.... 

Lead  

sIm 

Anenlo 

8.88 

Antimony 

Mercury,  pure. . 
Bismuth  

diS 

Platinum,  soft. . . 
Iron,  soft 

0  878 

Conductors  and  Insalatora  In  Order  oftbelr  Value. 


Ck>liductor8. 
All  metals 

Well- burned  charcoal 
Plumbafco 
Acid  solutiona 
Saline  solutlong 
Metallic  ores 
Animal  fluids 

LA7\ng  Tej^etable  substances 
Moist  earth 
Water 


Insulators 
Dry  Air 
Shellac 
Parafftn 
Amber 
Basins 
Sulphur 
War 
Jet 
Glass 
Mica 


(Noncond  uctors). 
KbODlte 
Gutta-percha 
India-rubber 
811k 

Dry  Paper 
Parchment 
Dry  Lf^ather 
Porcelain 
Oils 


According  to  Culley,  the  rwlstanca  of  distilled  water  Is  6764  million  times 
as  frreat  as  that  of  copper. 

Reslvtanee  Varies  ^nrltb  Temperatare.— For  every  deffr^  Cen- 
tigrade the  resistance  of  copper  increases  about  0.4^,  or  for  every  degree  F. 
0.2s222^.  "Thus  a  pteee  of  copper  wire  having  a  resistance  of  10  ohms  at  9iS^ 
would  have  a  reslRtance  of  ll.ll  ohms  at  84°  F. 

The  following  table  shows  the  amount  of  resistance  of  a  few  suhfttances 
used  for  various  elMstrlcal  purposes  by  which  1  ohm  \t  increased  by  a  rlM 
of  temperature  !•  F.,  or  l*  C. 

Rise  of  It.  of  1  Ohm  when  Heated-— 


Material. 

PlaUnoid 00018 

Platlnnm-rilver 00018 

German  silver  (see  below) 00094 

Gold,  silver OOaSO 

Oairtiroii onoi4 

Ck)pp€r 00828 


1°  C. 
.00021 
.00091 
.00044 
.00065 
.00080 
.00400 


Annealing*— The  degree  of  hardness  or  softness  of  a  metal  or  alloy 
affecta  its  resistance.  Resistance  is  lessened  by  annealing.  Matthiestien 
gives  the  following  relative  conductivities  for  copper  and  silver,  the  com- 
parison  being  made  with  pure  silver  at  ]00*>  C. : 


Metal.  Temp.  C.      Hard. 

Copper 11*  96.81 

Silver 14.8o  95.88 


Annealed.        Ratio. 
97.a3  1  to  1.087 

103.38  1  to  1.084 


Dr.  Siemens  compared  the  conductivities  of  copper,  silver,  and  brass  with 
pure  mercury  at  0«  C,  with  the  following  results: 

Metal.                                    Hard.  Annealed.              Ratio. 

Copper 52.-.W  55.253  ltol.058 

Silver 66.298  64.880  1  to  1.145 

Brass 11.489  13.503  1  to  1.180 

Edward  Weston  (Proc.  Electrical  Congress^  1898.  p.  179)  says  that  the  re- 
sistance of  German  silver  depends  on  its  composition.  Matthiessen  givei*  It  as 
nearly  l8  limes  that  of  copper,  with  a  temperature  coeffleientof  .0004438  per 
degree  C.    Weston,  however,  has  found  eopper-nickel*zinc  alloys  (German 


1030  ELECXBIGAL   KNGINEEBUTG. 

•llVer)  which  had  a  redstAnoe  of  nearly  88  titnes  that  of  <^per,  and  a  twn- 


880<*C. 

Standard  of  Realvtaiiee  or  Copper  Wire.  (Trans.  ▲.  I.  E.  E., 
Sept.  aitd  Not.  1890.)— Matthiesneii's  standard  Is:  A  bard-drawo  copper  wire 
1  metre  Iodk,  welehine  1  gramme  has  a  resistance  of  0.1460  B.A.  unit  at 
iy*  C.  (1  B.A.  unit  =  0.9889  leRal  ohm  =  0.9668  intemalional  ohm.)  Resist- 
ance  uf  hard  copper  » l.OSiiO  times  that  of  soft  copper.  Relative  oonductiog 
power  (Matthiessen):  silver,  100;  hard  or  unann<saled  copper,  99.05;  soft  or 
Jin^ealed  copper,  10».81.  Conductivity  of  copper  at  other  temperatureB  than 
0*  C,  Cf  =  Co(l  -  .00887*  -f-  .0O00090O9<«). 

The  I'esistance  is  the  reciprocal  of  the  conductivity,  and  is 
/?!  =  «o(>  +  -OOBSre  -f  .00000597<»). 

The  shorter  formula  R^  =  i?o(1  +  .004060  la  commonly  used. 

A  committee  of  the  Am.  Inst.  Electrical  Engineers  recommend  the  follow- 
ing as  the  most  correct  form  of  the  Matthiessen  standard,  taking  8.80  as  the 
sp.  gr.  of  pure  copper : 

A  sort  copper  wire  1  metre  long  and  1  mm.  diam.  has  an  electrical  resist- 
ance of  .08064  B.A.  unit  at  0*>  C.  From  this  the  resistance  of  a  soft  copper 
Mire  1  foot  long  and  .001  in.  diam.  (mil-foot)  is  found  to  be  O.TiH)  B.A.  units 
atO»C. 

SUndard  Resistance  at  0«C.  B. A.  Units.     Legal  Ohms.   ^ohJS!^ 

Metre-millimetre,  soft  copper 08067  .08084  .09089 

Cubic  centimetre    **        *'       000001616       .000001698       .000001588 

MU-foot  *•         •*       9.780  9.618  9.690 

1  mil-foot,  of  soft  copper  at  10».88  O.  or  80».4  P. . .  10  Q.VTT 

♦*     *'    "  »*        "  16*.5        "    59«.9F...  10.80  10.175 

"       "     ••    "         ••        "  88«.9       *•    76«     F...  10.68  10.606 

For  tables  of  the  renatance  of  copper  wire,  see  pages  818  to  280,  also 
pp.  1084,  loa-s. 

Taking  Matthie8sen*8  standard  of  pure  copper  as  iOOfC.  Rome  refined  metal 
haK  exhibited  an  electrical  conductivity  equivalent  to  108i%. 

Matthiessen  found  that  impurities  In  copper  sufficient  to  decrease  Its 
density  from  8.94  to  8.90  produced  a  marked  increase  of  electrical  resistance. 

DIRECT  EI<ECTRI€  CURRENTS. 

Obm's  lia^iir*— This  law  expresses  the  relation  between  the  three  fun- 
damental units  of  resistance,  electrical  pressure,  and  current.    It  is : 

_  ^      electrical  pressure     ry       ^        v  «x,»»        ^    ^      S 

^"^"*  = resistance        ^    ^=B^    ''^•"^    ^=^*'  and   «  =  ^ 

In  terms  of  the  units  of  the  three  quantities. 

Amperes  =  ^ — ;    volts  =  amperes  x  ohms;    ohms  =     ^^        . 
ohms'  amperes 

Examples:  Simvle  Circuit».—\.  If  the  source  has  an  effective  electrical 
pressure  of  100  volts,  and  the  resistance  is  two  ohms,  what  is  the  current  ? 

C  =  ^  =  -g-  =  60  amperes. 

3.  What  pressure  will  give  a  current  of  50  amperes  through  a  resistance  of 
8  ohms  ?    fe=C7R  =  60x8=100  volts. 
8.  What  resistance  is  required  to  obtain  a  current  of  60  amperes  when  the 

pressure  is  100  volts  r    i?  =  ~  =  --r-  =  8  ohms. 
C        oU 

The  following  examples  are  from  R  E.  Day's  *'  Electric  Light  Arithmetic:*' 
1.  The  internal  resistance  of  a  certain  Brush  dynamo-machine  hi  10.9  ohms, 
and  the  external  resistance  is  78  ohms;  the  electro-motive  force  of  the  ma- 
chine being  889  volts.  Find  th^'  tit  length  of  the  current  flowing  in  the  c^ncoit. 
£*  =  889;    fi  =  73  -f  10.9  =  88.9  ohms; 
C  *s  E -%- R  =  889 -t-  88.9  ss  10  amperes. 


BLECTBIC  CURRBKT8.  1031 

S.  Three  are  lamps  in  series  have  a  combined  reelstanoe  of  0.86  ohms,  while 
the  resistance  of  the  leading:  wires  is  1.1  ohm.  and  that  of  the  dynamo  is  2.8 
ohms.  Find  wliat  must  be  the  electro-motive  force  of  the  machine  when 
the  strength  of  the  current  produced  is  14.8  amperes. 

£  B  2.8  +  0.86  +  1.1  =  18.S6  ohms;   C  »  14.8  amperes; 
Jff  =  C  X  fi  »  1S.86  X  14.8  =  106.8  YOlts. 

8.  Calculate  from  the  following  data  the  average  resistance  of  each  of 
three  arc  lamps  arranged  in  series.  The  electro-motive  force  of  the  machine 
Is  244  volts  and  its  resiKtanoe  is  3.7  ohms,  while  that  of  the  leading  wires  is  8 
ohms,  and  the  strength  of  current  through  each  lamp  is  21  amperes. 

If  X  repretient  the  average  resistance  in  ohms  of  each  lamp,  then  the  total 
resistence  of  the  circuit  is  /2  s  &r  +  3  +  8.7. 

But  by  Ohm*s  law  /{  s  iS  •«-  C,  .*.  8x  +  6.7  s=  844/81  s  11.61  ohms,  whence 
;r  s=  1.07  ohms,  nearly. 

4.  Three  Maxim  incandescent  lamps  were  placed  in  series.  The  average 
resistance,  when  hot,  of  each  lamp  was  80.8  ohms,  and  that  of  the  dynamo 
ajad  leading  wires  11.8  ohms.  What  electro-motive  force  was  required  to 
maintain  a  current  of  1.8  amperes  through  this  circuit  ? 

In  this  case  we  have 

B  =  8  X  80.8  +  11.8  »  180.1  ohms,  and 
Cs  1  J)  ampere; 
and  therefore,  by  Ohm^s  law, 

JB  =  6*  X  i?  =  1.8  X  180.1  =  1M.0  volta 

5.  The  resistance  of  the  arc  of  a  certain  Brush  lamp  was  8.8  ohms  when  a 
current  of  10  amperes  was  flowing  through  it.  What  was  the  electro-motive 
force  between  the  two  terminals  i 

£  =  C  X  17  =  10  X  8.8  =  88  volts. 

6.  Twenty-flve  exactly  similar  galvanic  cells,  each  of  which  had  an  aver- 
age internal  resistance  of  16  ohms,  were  joined  up  in  series  to  one  Incandes- 
cent lamp  of  70  ohms  resistance,  and  produci^d  a  current  of  0.118  amperes. 
What  would  be  the  strength  of  current  produced  by  a  series  of  80  such  cells 
through  8  lamus.  each  of  80  ohms  resistance  f 

The  data  or  the  first  part  of  the  problem  enable  us  to  determine  the 
average  electro- motive  force  of  each  cell  of  the  battery.  Let  this  be  repre- 
eented  by  K\  then  we  have 

25.B;=  CXR=  .118X  (a5X  15 -f  TO)  =  .112  X  445; 

.^  J,  :.:ll?|il««o  volts,  nearly. 

Then  from  the  data  In  the  second  part  of  the  problem,  we  have,  by  Ohm's 
law, 

^  =  «,xn  +  2x9>  =  5To=  oi"-!-"- 

IHvlded  Circuits.— ir  the  circuit  has  two  paths,  the  to«al  current  in 
Doth  diviileM  itSflT  iuvernely  as  the  resistances. 

If  R  and  R^  are  the  resistances  of  the  two  branches,  and  Cand  Ci  the  cur- 
rents, Cx  R=  CiX  Ri,  and  ^=  -jj .  whence 

n      ^iBl.     n        ^'^  .     D       C",  R,       „        CR 
0=-^;    6',=  -^;    R^^\   «.  =  ^. 

In  the  case  of  the  double  circuit,  one  circuit  is  said  to  be  In  thunt  to  the 
other,  or  the  circuits  are  in  multiple  arc,  in  multiple,  or  In  parallel. 

Condnetom  In  Series*— If  conductors  are  arranged  one  after  the 
other  they  are  said  to  (»«  in  series,  and  the  total  resistance  is  the  sum  of 
their  raveral  resistance's.  /?  =  B,  -f  i?,  4-  R%. 

Internal  Resistance.— in  a  simple  circuit  we  have  two  resistanoes, 
tnat  of  the  circuit  B  and  that  of  the  internal  parts  of  the  source  of  electro- 


1034  ELBGTRICAL  ENQIKEEKING. 

motive  force,  called  internal  resiBtance,  r.    The  formula  of  Ohm^s  Uw  wh<v 

B 
the  Inteiual  resistance  is  considered  is  C  =:  p  .    , 

Total  or  Joint  ResAvtance  of  Tvro  ]iraiiekea»~Let  C  be  the 

total  current,  and  Ci,  C^  tlie  currents  in  branches  wiiose  resistances  respectr 

lvelyarel?,.i?a.    Then  C=  C,  +  C,;  C=  ^;  C,  =  ^-;  C,  = -^;  or,  if  £  = 

It  xf]  /(• 

til  H  R 

U  0  =  "S"  =  K-  4-  -5-.  whence  R  =  p  '   *  ,  which  is  the  joint  re«i8tanoe  <rf 

J?i  and  i^.. 
Similarly,  the  joint  resistances  of  three  branches  have  resistances  respect^ 

.vely  of  «.,  fi„  »..  I.  Jt  =  ^^^^&^j^^. 

When  the  branch  resistances  are  equal,  the  foiTuula  beoomes 

where  Rx  =  the  resistance  of  one  branch,  and  n  =  the  number  of  bnmcfaes. 

KlrenboflT^fl  I^aiv*.— 1.  The  sum  of  the  currents  in  all  the  wires  which 
meet  in  a  point  is  nothing. 

2.  The  sum  of  all  the  products  of  the  currents  and  resistances  in  all  the 
branches  forminfir  a  closed  circuit  is  equal  to  the  sum  of  all  the  electrical 
pressures  in  the  same  circuit. 

When  E  =  Ex -\- E^  +  Et,  etc.,  and  (7  =  Ci  +  C,  -f  Ca,  etc.,  and  R  is  ih^ 
total  resistance  of  RxR^R^^  etc.,  then 

^1  +  JPa  +  K»i  etc.  =  CiR,  +  C^R%  +  C,i?|,  etc. 

Ponrer  of  tke  Clrcalt.— The  power,  or  rate  of  work,  fn  watts  = 
current  in  amperes  X  eleoiro-moti ve  force  in  volts  ^C'xJC.    Since  C  s S-t-R, 

watts  s  ^  s  electro-motive  force'  -*-  resistance. 

Example.— What  H.P.  is  required  to  supply  100  lamps  of  40  ohms  resist- 
ance each,  reauirlnjf  an  electro-motive  force  of  60  volts  ? 

E*      00* 
The  number  of  volt-amperes  for  each  lamp  **  "S"  =  1q  »  *  volt-ampere  = 

60' 
.00184  H.P.;  therefore  45  X  100  x  .00184  =  18  H.P.  (electrical)  veiy  neariy. 

If  the  loss  in  the  dynamo  is  20  per  cent,  then  12  H.P.  is  80  per  cent  of  the 

12 
actual  H.P.  required;  which  therefore  **  55  =  ^^  H.P. 

Heat  Generated  hf  a  Ciirreiit.— Joule's  law  shows  that  the  beat 
developed  in  a  conductor  is  directly  proportional,  1st,  to  its  resistance;  Sd, 
to  the  square  of  the  current  strength:  and  3d,  to  the  time  during  which  the 
current  Bows,  or  H  =  C*Rt    Since  C=  E-^R, 

X*  ]B*        jnt 

C*Rt  =  ^CRt  =  ECt^  B^t  =  ^. 

Or,  heat  =  cnrrent*  X  resistance  x  time 

=  electro  -motive  force  x  current  X  time 
=  electro-motive  force*  X  time  ■*-  resistance. 

E 
Q  =  quantity  of  electricity  flowing  =  Ct  =  ^i. 

H  =  EQ;  or  heat  =  electro-motive  force  x  quantity. 

The  electro- motive  force  here  is  that  causing  the  flow,  or  the  difference  in 
potential  between  the  ends  of  the  conductor. 

The  electrical  unit  of  heat,  or  **  joule  *'  =  10*  ergs  s  tieat  generated  in  one 
second  by  a  current  of  1  ampere  flowing  through  a  resistance  of  one  ohm  s 
.239  gramme  of  water  raised  1"  C.  H  =  C*Rt  x  .280  gramme  calortea  = 
C^Rt  X  .0009478  British  thermal  units. 

In  electric  lighting;  the  energy  of  the  current  is  converted  into  beat  in  the 
lamps.  The  resistance  of  the  lamp  is  made  great  so  that  the  required 
quantity  of  heat  may  be  developed,  while  in  the  wire  leading  to  and  Croa 


ELBOTBIC  ovfiBiurrs. 


1033 


the  lamp  the  resistance  Is  made  as  small  as  is  commercially  practicable,  so 
that  as  little  energy  as  possible  mav  be  wasted  in  heatinf;  the  wire.  The 
tranaformatioDg  oreDei*g3r  from  the  fuel  burned  in  the  boiler  to  the  electric 
light  are  the  following: 

Ueat  energy  is  transformed  into  mechanical  energy  by  means  of  the  boiler 
and  engine. 

HechMnical  energy  is  transformed  into  electrical  energy  in  the  dynamo. 

Electrical  energy  is  transformed  into  heat  in  the  electric  light. 

The  heat  generated  in  a  conductor  is  the  equiralent  of  the  energy  causing 
the  ilow.  Thus,  rate  of  expenditure  of  energy  in  watts  =  electro-motive 
force  in  volts  X  current  in  amperes  =  EC^  and  the  energy  In  joules  s  watts 
X  time  in  seconds  =  ECt.    Heat  zz  C*Rt  =  ECt. 

Heatlns  of  Conductors*  (From  Kapp*s  Electrical  Transmission 
of  Energy.)— It  becomes  a  matter  of  great  importance  to  determine  before- 
hand what  rise  in  temperature  is  to  be  expected  in  each  given  case,  and  if 
tliat  rise  should  be  found  to  be  greater  than  appears  safe,  provision  must  be 
made  to  Increase  the  rate  at  which  h^at  is  carried  off.  Tnis  can  generally 
be  done  by  increasing  the  superficial  area  of  the  conductor.  Say  we  have 
one  circular  conductor  of  1  square  inch  area,  and  find  that  with  1000  amperes 
flowing  it  would  become  too  hot.  Now  by  splitting  up  this  conductor  Into 
10  separate  wires  each  one  tenth  of  a  squai'e  inoh  cross-seotlonal  area,  we 
have  not  altered  the  total  amount  of  energy  transformed  into  heat,  but  we 
have  increased  the  surface  exposed  to  the  cooling  action  of  the  surrounding 
air  in  the  ratio  of  1  :  VlO,  and  therefore  the  ten  thin  wires  can  dissipate  more 
Uian  three  times  the  heat,  as  compared  with  the  single  thick  wire. 
HeatlDi:  of  Wlrea  of  Subaqneona  and  Aerial  Cables  (In* 
salated  ^nrlth  Qntta-perclia).  (Prof.  Forbes.) 
Diameter  of  cable  -4-  IManieter  of  conductor  s  4. 

Temperature  of  air  =  30*  C.  =  («•  F. 
t  =  exceiss  of  temperature  of  conductor  over  air. 


Diameter  in  centi- 
metres and  mils. 

Curi-ent  In  amperes. 

Cm. 

Mils. 

f  =  1«»C. 

f  =  9»C. 

f  =  25«  C. 

t  =  49»  C. 

<  =  81<'C. 

=  1.8*  F. 

=  16.2»  F. 

=  45*  F. 

=  92  2«  F. 

=  145.8*  F. 

.1 

40 

8.7 

11.0 

17.8 

24.0 

29.6 

.9 

80 

9.1 

27.0 

48.8 

59.0 

72.5 

.3 

120 

15.0 

44.4 

72.1 

97.3 

119 

.4 

180 

21.2 

62.5 

102 

137 

168 

.5 

.   200 

27.4 

81.0 

181 

177 

218 

.6 

240 

83.7 

100 

164 

219 

288 

.7 

880 

40.1 

119 

192 

259 

819 

.8 

810 

46.4 

m 

228 

801 

309 

.9 

850 

62.9 

157 

253 

842 

420 

1.0 

890 

59.8 

175 

285 

884 

472 

2  0 

780 

124 

867 

595 

803 

968 

3.0 

1180 

189 

659 

908 

1225 

1006 

4.0 

1570 

254 

758 

1221 

1646 

9091 

5.0 

1970 

819 

945 

1584 

2068 

2528 

6.0 

2860 

385 

1188 

1846 

8491  • 

3058 

7.0 

2760 

450 

1330 

2158 

2846 

8.')75 

8.0 

8150 

514 

1525 

2472 

.  8335 

4004 

9.0 

8540 

580 

1716 

2785 

8755 

4611 

10.0 

8940 

645 

1909 

8097 

4178 

5130 

Prof.  Forbes  states  that  an  insulated  wire  carries  a  greater  current  without 
overheating  than  a  bare  wire  if  the  diameter  be  nnt  too  great.  Assuming 
the  diameter  of  the  cable  to  be  twice  the  diam.  of  the  conductor,  a  greater 
cnrrentcan  be  carried  in  iiisnlated  wires  than  in  bare  wires  up  to  r9  inch 
diam  of  conductor.  If  diam.  of  oaWlt*  =  4  times  diam.  of  conductor,  tliis  is 
the  ca.se  up  to  1.1  Inch  diam.  of  conductor. 

Copper-^iirire  Table.— Tlie  table  on  pa^es  1034  and  1035  is  abridged 
from  one  computed  by  the  Committee  on  Units  and  Standards  of  the  Ameri- 
can Institute  of  Electrical  Engineers  (Trans.  Oct.  1893). 


1034 


ELECTRICAL   EKGINEEBIXG. 


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ELECTRIC  CURRENTS.  1035 

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1036  ELECTRICAL  EKGlKEEttlKQ. ' 

The  data  from  which  the  foregoing  table  has  been  computed  are  as  foUotrs: 
MaithietMen*!  standai-d  resiatlvity,  Matlhlefc8e&*s  temperature  coeAci^vits, 
specific  grarlty  of  copper  sa  8.80.  Beftistance  in  terms  of  the  intemaUanal 
(mm. 

Matthiessen^s  standard  1  metre-gi-amme  of  hard-drawn  copper  s=  0.14® 
B.  A.  U.  ^  0"  C.    Ratio  of  resistivity  hard  to  soft  copper  1  .QSBm, 

Matthiessen's  standard  1  metre-gramme  of  soft-drawn  copper  =  0.14d65 
B.  A.  U.  ^  0"  C.    One  B.  A.  U.  ss  0.9866  intematlonal  ohm. 

Matthiessen^s  standard  1  metre-gramme  of  soft-drawn  copper  =b  0.1417S 
international  ohm  ^  0*>  C. 

Temperature  coefficients  of  resistance  for  20«  C,  W  C,  and  80»  C,  l.OTIWfi, 
1.30625,  and  1.33681  respectively.  1  foot  =i  O.S0480fi»  metre,  1  pound  = 
45S.59S96  grammes. 

Bl«atliiic  of  €ol]»*— To  calcnlate  the  heating  of  a  coil,  glTen  the  cool- 

Ing  surface  and  Its  resistance.    (Forbes.) 

Let  p  =  the  resistance  of  a  coil  in  ohms  at  the  permissible  teinperatnr« 

(the  resistance  (cold)  must  be  increased  by  1/5  of  its  value  to  give  p/: 

8  =  the  surface  exposed  to  the  air  measured  in  square  oenU metres 

(1  square  cm.  =  .156  square  inch;  1  sq.  in.  =  6.45  square  cm.}; 
t  =  the  rise  in  temperature,  centigrade  scale; 
C  =  the  current  In  amperes. 

.iiC^P  s=  heat  generated  s  etS. 
where  e  is  McFarlane's  constant,  varying  from  .OOOS  to  .OQOZ.    The  latter 
▼aiue  may  be  taken.    If  50*>  C.  be  the  peruiissible  rise  in  temperature. 


,^^--^^=..^. 


BxAVPLK.— The  resistance  of  the  field-magnets  of  a  dynamo  is  1.5  ohms 
cold,  and  the  surface  exposed  to  the  air  is  1  square  metre;  find  the  cnrrem 
to  heat  it  not  more  than  50«  C.  

Here S  =  10,(X)0;  p  =  1.8 ohms;  and  C  =  Xbkf      *       =  88.8 amperes. 

For  the  heating  of  coils  of  fleld-magnets  Carl  Hiring  gives  1  watt  of 
energy  diRsipatpn  for  every  228  square  inches  of  cooling-surface  for  escli 
degree  F.  of  difference  between  the  temperature  of  the  coll  and  the  sur- 
rounding air. 

W=CE-  l/2i^TS  =  0.0044T6TS,  in  which  W'=  watts  lost  in  coil,  r=r 
degrees  Fahr.,  and  8  =  square  inches. 

C=  Qt^^  is  the  greatest  current  which  can  be  used  in  the  magnet  colls  of 

a  shunt  machine  having  a  certain  pressure  in  order  that  they  do  not  heal 
above  a  certain  t  em  perature.  Thus  for  a  rise  of  temperature  of  60*  F.  above 
the  surrounding  ain 

C  s=  ^g  :r  .234  J .    Substltating  for  B  ita  equivalent  OR,  we  get 

If  80^  F.  is  the  maximum  difference  of  temperature, 
C 


-mE  -  '^E  -  '^Y  R' 


The  formula  can  be  used  for  series  machines  when  C  is  known,  for  writinf 

C*R  =  1/22ATS,    wegetfi  =  g^. 
With  a  permissible  rise  of  SO**  F.  or  80<>  F.,  we  have  respectively. 

The  surface  area  of  the  coil  in  square  inches  may  be  found  from 
_  2Mir       22SiCE  _  92aC*B 
r     ~       T     ~       T    ' 


SLEGTRIO  GURRBKTS. 


1037 


For  a  rige  of  tempemtore  of  90°  F.  or  80*  F.,  re«peekhr«Iy,  tbe  rarfAM  will 
be 


S  =  -=^  =  A.46W;    and  8  =     ^     : 


^  2.8Tr. 


ir«aloii  #r  Wir«i«— W.  H.  Freece  irivea  a  formula  for  thecarrent  re* 

qnired  to  fuse  wires  of  different  metals,  viz. :  C  =  ad^^  in  which  d  Is  tbe 
ciiameter  in  Inches  and  a  a  coefficient  whose  value  for  different  metals  is  as 
follows:  Copper  10814;  aluminum  7585;  platinum  517:3;  German  silver  5990; 
platinoid  4750;  iron  8148;  tin,  1849:  lead,  1879;  alloy  of  2  lead  and  1  tin,  1818. 

IHametem  of  Various  Wires  ivbleli  irlll  be  Fased  by  a 
Slwett  Cmrrenu 

Formula,  d=(^^;  a  =  1643  for  tin  =s  1879  for  lead  =  10844  for  copper  = 

S148  for  iron. 


Tin  Wire. 

Lead  Wive. 

Copper  Wire. 

Iron  Wire. 

Current, 

In 
amperea. 

SSSi 

1%~S. 

SSSii. 

1%~S. 

Diam. 
Inobea. 

I'^rs. 

ffiSi. 

IWS. 

1 

.0072 

88 

.0081 

82 

.0021 

.0047 

36 

2 

.0118 

20 

.0128 

S9 

.OOM 

so" 

.0074 

32.5 

8 

.0149 

26.5 

.0168 

25.6 

.0044 

37 

.0097 

30 

4 

.0181 

26 

.0208 

24 

.0058 

85.6 

.0117 

28.6 

5 

.0810 

28.5 

.0^86 

28.5 

.0069 

84 

.0186 

27.6 

10 

.0834 

19.5 

.0875 

18.5 

.0008 

80 

.0010 

28.5 

15 

.0487 

17 

.0401 

10 

.0120 

28 

.0988 

21 

SO 

.0629 

16 

.0505 

16 

.0150 

26 

.0848 

19 

85 

.0614 

14,5 

.0690 

13 

.0181 

25 

.0898 

18 

80 

.0694 

13 

.0779 

12 

.0205 

24 

.0450 

17 

85 

.0769 

12.5 

.0864 

11.6 

.0227 

23 

.0496 

16 

40 

.0640 

11.5 

.0944 

11 

.0248 

22 

.0545 

15.5 

49 

-0000 

11 

.lOtf 

10 

.0268 

91.5 

.0680 

15 

BO 

.oon 

10.5 

.1095 

9.5 

.0288 

21 

.ooei 

14 

60 

.1101 

9 

.1287 

8.5 

.M25 

90 

.0714 

18 

90 

.1290 

8.6 

.Wl 

7.5 

.0860 

19 

.0791 

12 

80 

.1884 

7.5 

.1499 

7 

.0394 

18 

.0864 

11.5 

90 

.1443 

7 

.1831 

6 

.0426 

17.5 

.0985 

11 

too 

.1548 

6.5 

.1789 

6.5 

.0457 

17 

.1008 

10 

120 

.1748 

5.5 

.1964 

4.5 

.0616 

16 

.1188 

9 

140 

.1987 

4.8 

.2176 

8.5 

.0572 

15 

.1255 

8 

160 

.2118 

4 

.2379 

8 

.0636 

14 

.1872 

7.6 

180 

.2291 

3 

.2578 

2 

.09r6 

13.5 

.1484 

7 

9D0 

.«S7 

2 

.2?B0 

1.5 

.0^25 

18 

.1592 

6 

250 

.2851 

1 

.3:?03 

0 

.0841 

11.5 

.1848 

5 

800 

.8320 

0 

.3617 

00 

.0950 

10.5 

.2086 

4 

Cvnrevt  In  Aaii 


iperes  Bo^olredl  to  Fuse  Wlr< 
to  tbe  Fornmla  C  =  adi- 


>••  Aecordlns 


<^^^. 

Diameter, 
inches. 

di- 

Tin. 
a  =  1642. 

Lead 
a  =  1379. 

a'^J^ 

Iron, 
a  =  3148. 

12 

.680 

.028627 

37.15 

81.20 

281.8 

71.22 

14 

.ON 

.016191 

26.60 

22.82 

166.8 

60.90 

16.5 

.048 

.010516 

17.27 

14.50 

iar.7 

88.10 

19 

.036 

.006831 

11.22 

9.419 

69.97 

21.50 

21 

.028 

.004685 

7.692 

6.461 

48.00 

14.76 

28 

.022 

.003263 

5.357 

4.499 

33.43 

10.27 

25 

.018 

.002415 

3.965 

3.330 

24.74 

7.602 

27 

.0148 

.001801 

2.956 

2.488 

18.44 

5.667 

2H 

.0124 

.001381 

2.267 

1  904 

14.15 

4.347 

29 

.0108 

.001122 

1.843 

1.548 

11.50 

8.588 

1038  ELBCTUrCAL   ENGINEERING. 

BliBCTBIC  TBANSmSSIOir,  DtBBCT  CVBlKBmrS. 

Grosa-aectlon  of  IBTIre  Beqiiired  for  n  GItoh  Curr^mU— 

Constant  Current  (Series)  Syatem.^The  croBB-wctional  area  of  copper 
neoeasary  in  any  circuit  for  a  given  constant  current  depends  on  the  differ- 
ence between  the  pressure  at  the  generatina:  station  and  the  nMucimom 
pressure  required  by  ali  the  apparatus  on  the  circuit,  and  on  the  total  lencrtb 
of  the  circuit.  The  following  fomiuIsB  are  given  in  **  Practical  EUectrical 
Engineering:'* 

If  F*  =  pressure  in  volts  at  generators; 

V  =  sum  of  aU  the  pressures  (in  volts)  required  by  apparatuB  supplied 

in  the  circuit: 
n  =  total  length  (going  and  return)  of  circuit  in  miles; 
C  =  current  in  amperes; 
r  a:  resistance  of  1  mile  of  copper-conductor  of  1  square  inch  sectional 

area  in  ohms; 
a  s  required  cross-sectional  area  of  copper  in  square  ineheB, — 

nrC 


If  we  take  the  temperature  of  the  conductor  when  the  oarrent  haa  been 
flowing  for  some  time  through  it,  as  W  F., 

rr- 0.0455  ohm,    and     a  =  ^'^^f. 

It  generally  happens,  however,  that  we  are  not  tied  down  to  a  particnlar 
value  of  V,  as  the  pressure  at  the  generators  can  be  varied  by  a  few  volts  to 
suit  requirements.  In  this  case  it  is  usual  to  fix  upon  a  current  densily  and 
determine  the  cross-sectional  area  of  copper  in  accordance  with  it. 

If  D  s  current  density  in  amperes  per  square  inch  determined  upon, 

'  =  §■ 

The  ciurent  density  is  frequently  taken  at  1000  amperes  to  the  square  inch, 
but  should  in  general  be  determined  by  eoonomical  considerations  for 
every  case  in  question. 

Conatant  Preaanre  (Parallel  8ystem).~To  determine  tiie  loss  Id 
pressure  in  a  feeder  of  given  size  in  the  case  of  two-wire  parallel  distributioo. 

Let   a  s  cross-sectional  area  of  copper  of  one  conductor  of  the  feeder  fai 
square  inches; 
n  =  length  of  feeder  (going  and  return)  in  miles; 
C  =  current  in  amperes; 
V  ^  V  =i  loss  of  pressure  in  feeder  in  volts; 

r  s  resistance  of  1  mile  of  copper  conductor  of  1  square  Inch  see 
tional  area  in  ohnu. 

a 
If  the  temperature  of  the  conductor  with  this  current  flowiDg  In  It  is 
assumed  to  be  80«  F., 

«««.    ,-  J     TT  0.0455»iC 

r  =  0.0466  ohm,    and     F  -  v  = . 

o 
E 
Sltort-clreulUiis«— From  the  law  C=  ^  it  is  seen  that  with  any  pres- 

sure  E  the  current  C  will  become  very  great  it  Rln  made  very  small.  In 
short-circuiting  the  resistance  becomesemall  and  the  current  therefore  gi^st 
Hence  the  dangers  of  short-circuiting  a  current. 


ELECTBIC  TUAKSMISSIOK. 


1039 


Beonomy  of  Electric  TransmUalon.  <R.  G.  Blaine,  Eng^g. 
June  5,  1881.)— Sir  W.  Thomson's  rule  for  the  most  economical  section  of 
conductor  is  that  for  which  the  **  annual  interest  on  capital  outlay  is  equal 
to  the  annual  cost  of  energy  wasted.** 

Tables  have  been  compiled  bv  Professor  Forbes  and  others  in  accordance 
with  modifications  of  Sir  W.  Thomson's  rule.  For  a  Riven  entering  horse- 
power the  question  is  merely  one  as  to  what  current  density,  or  how  many 
amperes  per  square  inch  of  conductor,  should  be  employed.  Sir  W.  Thom- 
son's rule  gives  about  388  amperes  per  square  inch,  and  Proressor  Forbes's 
tables— for  a  medium  cost  of  one  electrical  horse-power  per  hour—give  a 
current  density  of  about  860  amperes  per  square  inch  as  most  economical. 

When  a  given  horse-power  is  to  be  delivered  at  a  given  distance,  the  case 
is  somewhat  different,  and  Professors  Ay rton  and  Perry  (Electrician^  March, 
1886)  have  shown  that  in  that  case  both  the  current  and  resistance  ars 
variables,  and  that  their  most  economical  values  may  be  found  from  the  fol- 
lowing formula: 


cr  =  ^(1  + Bin  ♦). 


.  J*«       Bin» 
'  nto  (1  -f  sin  ^)*  * 


in  which  C  ss  the  proper  current  in  amperes;  r  =  resistance  in  ohms  per 
mile  which  should  be  given  to  the  conductor;  P  =  pressure  at  entrance  in 
volts;  n  s  number  of  miles  of  conductor;  to  =  power  delivered  in  watts; 
^  =  such  ao  angle  that  tan  ^  =  nt-*-P,  t  being  a  constant  depending  on 
the  price  of  copper,  the  cost  of  one  electrical  horse-power,  interest,  etc.:  it 
may  be  taken  as  about  17. 

In  this  case  the  current  density  should  not  remain  constant,  but  should 
diminish  as  the  length  increases,  being  in  all  cases  less  than  that  calculated 
bv  Sir  W.  Thomson's  rule. 

EXAHPUB.— If  the  current  for  an  electric  railway  is  sent  in  at  9CN)  volts,  100 
hoFMe-power  being  delivered,  find  the  waste  of  power  in  heating  the  con- 
ductor, the  distance  being  6  miles  and  there  being  a  return  conductor. 

Here  n  =  10,  t  =  17,^=900;  tan  ^  =  170  ••- 800  s  .86,  ^  =  iO^  2^.  sic  ^  = 
.6477. 

Hence  most  economical  resistance 


900* 


.6477 

''"'10X74600  ^1.6477*' 

or  .1879  ohm  in  Its  total  length. 


.01879  ohm  per  mile, 


74800 
The  most  economical  current,  C  =  -^f^  X  1.6477  =  614.88  amperes,  and  W, 


the  power  wasted  in  heat,  = 


C*R 


200 
614.68*  X  .1879 


=s  C4.76  horse-power. 


746  ~  746 

The  following  tables  show  the  power  wasted  as  heat  in  the  conductor. 


HoRSB-powBR  Wastbd  IN  Traitsxittino  Power  Elbotbtoallt  to  a  Qiten 
dibtancb,  the  entering  powbr  bbino  fixbd.  pressure  at  entrance, 
800  Volts.    Current  Density,  880  Amperes  per  Square  Inch. 


Horse-power  Wasted,  the 

Horse-power 
sent  in.* 

Distance  to  which  the 

Power  is  Transmitted  being 

one  Mile  (there  being  a 

Horse-power  Wasted. 
Distance  Five  Miles. 

Beturn  Conductor). 

10 

1.668 

8.818 

80 

8887 

16  686 

40 

6.654 

88.87 

60 

8.818 

41.59 

80 

18.806 

66.64 

100 

16.686 

83.18 

800 

88.278 

166.86 

*  That  is,  horse-power  at  the  generator  terminals. 


1040 


ELBOTRICAL  ENGINBBEIiarO. 


Pbbssubb  at 

EimuNGB,  9000  VoLTa 

Horse- 
power 
seutln. 

Hone-power 

Wasted.  Distance 

One  Mile  (there 

beiiif;  a  Return 

Conductor). 

Horse-            Horse- 
power           _power 
Wasted.  Dis-      'Wasted. 
UDce  Five     Distance  Ten 
Miles.              Miles. 

Wasted. 

Disranoe 

Twenty  Miles. 

100 
900 
400 
600 
800 
1000 
9000 

1.668 
8.8:87 
6.664 
8.818 
18.808 
16.686 
88.978 

8.818 
16.6S6 
88.979 
41.59 
66.M 
83.18 
166.86 

16.686 
88.979 
66.54 
8S.18 
188.08 
166.86 
8S8.79 

88.97 
08.54 
183.08 
106.86 
960.17 
389.79 
665.44 

It  will  be  seen  from  these  numbers  that  when  the  current  denalMr  is  fixed 
the  power  wasted  is  proportional  to  the  entering  horse-power  and  the  length 
of  the  conductor,  and  is  inversely  proportional  to  the  potentiaL  For  a 
copper  conductor  the  rule  may  be  simply  stated  as 

Tr=  16.6858^  Xi, 

E  being  the  horse-power  and  P  the  pretsure  at  entrance,  and  I  the  length  of 

the  conductor  in  miles. 

HoBSK-Powaa  Wasikd  in  Elbctbig  Tiuirsiasaiov  to  a  Qivbv  Dibtakcs, 

THE  POWBB  TO  BB  DbLIVBRBD  AT  TBB  DISTANT  BND  BBINO  FIZBD.      pRCSr 
8UBB   AT   ENTRANGB,  200   VoUTSl     CVBRBNT  AND   BbBUTANCB   CaMHTI^ATBD 

bt  Atbton  and  Fbbbt^b  Rulbb. 


Horse-power  Wasted, 

the  Distance  to  which 

Horse-power 

Horse-power 

Horse-power 

the  Power  is  Transmitted 

Wasted. 

Wasted. 

Delivered. 

being  One  Mile  (there 

Distance  Five 

Distance  Tw 

being  a  Return 

MUes. 

BlUeB. 

Conductor). 

10 

1.678 

6.476 

8.090 

90 

8.889 

19.069 

17.»4 

40 

6.704 

95.004 

84.48 

60 

8.88 

82.38 

48.10 

80 

13.408 

61.808 

68.96 

100 

16.76 

64.86 

86.90 

200 

33.58 

129.59 

179.4 

Pbbbsurb  at  Extrakcb,  20Q0  Voltb. 


'oSwSSdL'"     Wwted.  :Dtet*nce 


Horae-power 

Wasted.    Distance 

Ten  Miles. 


It  H  =  horse-power  sent  in,  to  =  power  delivered  in  vatts,  C  =  current  in 
amperes,  r  =  resistance  in  ohras  per  mile»  F  s  preasure  »t  eotraoce  io 

vulis,  uud  II  =  number  of  miles  of  conductor, 

(w+C»»)-f-74e  =H;    w  =  746J5f-C»r;    ^ 


TABLB  OP  BLKCTRICAL  HOnSB-POWERS. 


10-il 


id  the  formulae  for  best  current  and  resistance  become 
(7- (14-8ln^);    r  =  -7r- 


gin» 


n{74»U  -  C*r  '^  i  -f-ain  ^' 


n  4-  Bin  ^* 


Energy  wasted  as  heat  in  watts  per  mile  =  C*r  = 

Horae-power  wasted  per  mi]e=  TT,  =        '  "    . . 

(^  s  angle  whone  tangent  =  nt-t-P^  and  the  valae  of  t  corresponding  to  a 
irrent  density  of  880  amperes  per  sq.  in.  is  16.086.) 


TABIiB  OF  EliBCTBIOAIi   BOBSB-POWBB8. 

lauU :  VolU  x^Amperes  ^  ^  p      ^    ^  vdt-ampeie  =  .0018406  ] 
Read  amperes  at  top  and  rolts  at  side,  or  vice  verMo, 


Yolta  or  Amperes. 


g 

1 

10 

90 

"1 

40 

60 

80 

70 

80 

90 

100 

110 

180 

.' 

.00134 

.013A 

.0968 

J 

.0638 

.0570 

.0804 

.0838 

.1079 

J208 

.1841 

.1476 

.1800 

2.00968 

.0968 

.0538 

.0804 

.1079 

.1341 

.1600 

.1877 

.9146 

.9413 

.9681 

.9049 

.3817 

3    MHOS 

.04001 

.0604 

.12061 

.1609 

JOll 

.9413 

J8815 

.«17 

.8619 

.4099 

.4494 

.4898 

4  .00696 

.0636 

.1079 

.1609,    .91461 

.9681 

.3217 

.8753 

.4990 

.4898 

.6388 

.6898 

.6434 

5.00S70 

.0670 

.1341 

.9011 

.9681 

.8361 

.4092 

.4892 

J369 

J0S9 

.8768 

.7378 

.8043 

S.OOWi 

.0804 

.1608 

.9413 

.8917 

.4098 

.4896 

J830 

.8434 

.7939 

.8043 

.8847 

.9889 

7 

.00B38 

.8838 

J877 

J816 

.3768 

.4809 

.8830 

.8668 

.7607 

.8445 

.8884 

1.089 

8 

.01072 

.1072 

JU46 

.8217 

.4290 

6382 

.8434 

.7807 

.8679 

.0858 

1.078 

1  180 

l!987 

9 

.01906 

.1906 

.9413 

.3819 

.4888 

.8082 

.7939 

.8446 

.9652 

1.086 

1.906 

1.897 

1*448 

10 

.01341 

.1341 

JI881 

.40S9     .6889 

.8703 

J043 

.0883 

1.079 

1.906 

LS41 

1.476 

1.600 

11 

.01475 

.1475 

.9949 

.4424     .6888 

.7378 

.8847 

1.032 

1.180 

1.397 

1.476 

1.699 

1.700 

ri'.oiw* 

.1600 

.8217 

.4826     .84.^ 

.8043 

.9662 

1.126 

1.287 

1.448 

1.100 

1.760 

1.800 

131.01743 

Aia 

.8486 

.6C98     .81170 

.8713 

1.014 

1.920 

1.394 

1.608 

^•2S 

1.917 

9.091 

U,. 01877 

.1S77 

.3768 

.6830     .7607 

.8384 

1.126 

1.314 

1.601 

1.680 

i.8n 

9.064 

19B9 

15.019011    ,«]] 

.4Aa 

J088     .8043 

1.006 

um 

1.408 

1.808 

1.810 

1011 

9.919 

9.418 

16  .OSltf    .91i» 

.4»0 

.84341    .8879 

1.079 

1.987 

1.601 

i.n8 

1.030 

1M6 

1380 

1674 

17'.0«7»    .«7» 

.4668 

.88371    .9116 

1.130 

1.387 

1.685 

1498 

1061 

1970 

9.607 

9.T86 

18.0841S    .8418 

.4896 

.7939'    .9669 

1.206 

1.448 

1.689 

1930 

1179 

8.413 

9.664 

9.896 

19  .02M7,  .8547 

.6094 

.7641    1.019 

1.273 

1.6(88 

1.783 

2.087 

1999 

1547 

9.801 

3.066 

2U  .026H1I  .9881 
911.088151  .9816 

.6362 

.8043   1.072 

1.348 

1.809 

1.877 

2.146 

1413 

1681 

9.949 

3.917 

.6630 

.8446'  1.198 

1.408 

1.880 

1.971 

9.969 

1633 

9.S16 

3.007 

8.878 

g:!^:SS 

.6898 

.8847,  1.180 

1.476 

1.788 

8.064 

9.360 

1164 

1840 

194A 

8.698 

.8188 

.9949!  1.233 

1.549 

1.860 

8.168 

9.407 

1776 

1888 

8.801 

8.700 

24.03817    .8917 

.8434 

.9869 

1.987 

1.060 

1.080 

1268 

9.674 

1896 

1917 

3630 

8.M1 

25.03351    .8361 

.8703 

1.006 

1.341 

1.676 

9.011 

8.346 

1681 

1010 

1361 

1686 

4:S9 

961.03486    .8686 

.8971 

1.048 

1.386 

1.748 

9.001 

2.440 

9.788 

1137 

1486 

1834 

4.189 

271.03819    .a61» 

.7939 

1.088 

1.448 

L810 

9.179 

9.534 

1805 

1967 

1619 

3.981 

4.343 

281.03753    JKCk 

.7607 

1.198 

1.601 

i.8n 

9Jtt8 

2.627 

8.008 

8.378 

1763 

4.189 

4.604 

»l.03887    .sat 

.7776 

1.166 

1.565 

1.044 

9.339 

8.721 

3.110 

1499 

1887 

4.276 

4.866 

30>.010sa    .Mtt 

.8043 

1.906 

1.608 

9.011 

2.413 

2.815 

8.917 

1619 

4.098 

4.424 

4.898 

3lL041S«    .4168 

.8311 

1.247 

1.688 

9.078 

9.493 

2.900 

8.S94 

1740 

4.166 

4.671 

4.887 

38  .M290   .4980 

.8679 

1.987 

1.T16 

9.146 

9.674 

8.008 

3438 

1861 

4.990 

4.719 

6.1a 

33.044«4    .4424 

.8847 

1.327  ,  1.789 

9.219 

9.654 

.1.097 

3.639 

1986 

4.424 

4.866 

6.808 

34  .r)46ri8 

.6568 

.0115 

1.887 

1.883 

9.978 

9.736 

3.190 

1646 

4.102 

4.858 

5.013 

5. 489 

35  0I692 

.4889 

.9884 

1.408 

L877 

9.348 

9.815 

3.284 

1763 

4.293 

4.009 

6.161 

6.880 

36.04896 

.4898 

.9668 

L448 

1.990 

S.41S 

9.886 

S.378 

1861 

4.313 

4.898 

6.308 

6.791 

37  .m960 

.498« 

.9020 

1.488 

LB84 

9.480 

9.876 

3.479 

1868 

4.484 

4.960 

6.466 

6.068 

38.0MM 

.8804 

1.019 

1  598 

2,038 

9.547 

3.066 

3.S66 

4.076 

4.586 

5.094 

6.603 

0.113 

39  .iW-Btt 

.5£i8 

1.046 

1.668 

2.091 

2.614 

3.137 

3.660 

4.189 

4.706 

5.X28 

5.761 

6.274 

40|.05J6a 

.8362 

1.079 

1.609 

9.146 

2  681 

3.217 

8.763 

4.980 

4.826 

6.362 

5.898 

6.434 

41i.0.'>4M 

.5496 

1.099 

1.849 

9.198 

2.748 

3.298 

3.847 

4.897 

4.946 

1496 

6.046 

150C 

4'ii.()him 

.5630 

1.186 

1.688  '  2.2.52 

2.815 

3.378 

3.941 

4.604 

6.067 

1880 

6.193 

6.768 

43|. 05764 

.6764 

1.168 

1.729 

9.306 

9.889 

3.468 

4.0S5 

4.811 

6.187 

5.704 

1341 

8.017 

44I.O58OT 

.6896 

1.180 

1.769 

2.369 

L949 

8.630 

4.199 

4.719 

1388 

1888 

8.488 

7.078 

46.O0OK 

.8038 

1.906 

1.810 

9.4IS 

3.016 

3.619 

4.923 

4.896 

6.480 

1089 

1886 

7.239 

4«'.0616( 

.6166 

1.933 

1.860 

2.467 

8.083 

3.700 

4.318 

4.033 

6J60 

1188 

6.783 

7.400 

47I.Q630Q 

.8860 

1.980 

1.890 

2.820 

3.160 

3.780 

4.410 

6.040 

5.670 

1300 

6.930 

7.600 

4M  («4.S4 

.6434 

1.287 

1.930 

2.674 

3.917 

3.861 

4.604 

5.148 

6.791 

1434 

7.078 

7.721 

49  .O05«> 

.6668 

1.314 

1.970 

2  627 

.^284 

3.941 

4.598 

5.955 

6.919 

1568 

7.826 

7.888 

60;.0670J 

.6709 

1.341 

8.011 

*"' 

S.S61 

4.022 

4.692 

6.368 

1038 

1703 

7.373 

8.043 

J 

1042  ELECtRtCAL   ftKOmfiERmG. 

TABLB  OF  ELECTBICAIi  nOB8E-POWEBS-(Cbnemu^) 


II 

Voltii  or  Amperes. 

k 

1      1     10 

90 

90 

40 

60 

60 

70 

80 

90 

100 

110 

UO 

65 

.07!r7jl     .7878 

1.476 

9.919 

9.949 

3.686 

i.494 

6.161 

6.898 

6.635 

7jn 

t.llO 

tw 

22 

:^i  .wSliMS 

9.413 

SL917 

4.099 

4.826 

&630 

6.434 

7J30 

8L04« 

S.«47 

96S< 

6» 

9.614 

3.486 

4.367 

6.288 

6.099 

6.970 

7J49 

8.71* 

9.684 

10.  tf 

70 

•OOSHfl     .98841  1.877 

2.816 

3.763 

4.609 

6.630 
6.082 

6.668 

7.607 

8.446 

9.384 

10.39 

lis 

76 

.1006A    1.006     8.011 
.10794'    1.072  9.146 
.11394     1.139    2.279 

3.016 

4.021 

5.027 

7.087 

8.043 

9.048 

10.06 

11.00 

lt.« 

80 

8.917 

4.990 

6.362 

6.434 

7.607 

8.579 

9.688 

10.72 

ll.M 

121? 

86 

3.418 

4.558 

6.ev7 

6.836 

7.976 

9.116 

10.20 

11.30 

12.83 

U«7 

90 

.190061    1.900   9.413 

8.610 

4.896 

6.039 

7.239 

8.446 

9.669 

10.86 

19.06 

IS.tJ 

14ti 

96 

.12735'    1.273   2.647 

3.820 

6.004 

6.367 

7.641 

8.914 

10.18 

U.46 

12.73 

14.01 

ISS 

100 

.13106     1.341    2.681 

4.022 

6.362 

6.708 

8.043 

9.364 

10.79 

19.06 

13.41 

14.75 

16« 

900 

.96810     8.681*  6.362 

8.0iS 

10.79 

13.41 

16.09 

18.77 

91.46 

84.13 

96.81 

29.40 

38  IT 

800 

.40815     4.02S   8.043 

12.06 

16.09 

90.11 

24.13 

98.16 

32.17 

3810 

4a92 

44.94 

48a 

MO 

.63020     6.382  10.72 

16.09 

91.46 

90.81 

88.17 

37.53 

42.90 

48.26 

68.09 

68.9lt;  64.Ji 

500 

.67086:    6.70313.41 

20.11 

96.81 

33.51 

40.22 

46.98 

63.62 

60.32 

07.03 

73.73   80  49 

too 

.80430 

8.013  16.09 

94.13 

32.17 

40.29 

48.26 

66.30 

64.34 

72.39 

80.43 

tt.47    9t« 

700 

.93836 

9.384 

18.77 

28.16 

37.63 

46.92 

6&30 

66.68 

76.07 

84.46 

t3.84|  10S.9 

1114 

800 

1.0724 

10.78 

21.46 

32.17 

42.90 

63.68 

64.34 

75.07 

86.79 

96.62 

107.9 

lU.O 

12L7 

900 

1.9066 

19.06 

94.18 

36.19 

48.96 

60.32 

72.39 

84.45 

96.62 

108.6 

190.6 

139.7 

14U 

1,000 

1.3406 

13.41 

96.81 

40.92 

53.09 

67.03 

80.43 

93.84 

107.9 

190.6 

IM.l 

147.6 

lOM 

9,000 

2.6810 

90.81 

68.09 

80.43 

107.9 

134.1 

160.9 

187.7 

S14.6 

94I.S 

968.1 

tH.9 

3SI.7 

3,000 

4.0915 

40.29 

80.43 

190.6 

160.9 

901.1 

94I.S 

281.6 

381.7 

361.0 

402.2 

44S.4 

AtU 

4,000 

5.3620 

53.69 

107.9 

160.9 

914.6 

908.1 

321.7 

876.8 

499.0 

482.6 

636.9 

MO.  8 

013.1 

6,000 

6.7025 

67.03 

134.1 

901.1 

968.1 

335.1 

402.9 

469.9 

636.9 

608.2 

670.3 

7W.3 

DMi 

e.000 

8.0430   80.48 

160.9 

241.3 

321.7 

402.9 

488.6 

663.0 

643.4 

723.9 

804.3 

n4.7 

086J 

7,000 

9.3835   93.84 

187.7 

981.6 

376.8 

M9.9 

663.0 

6S6.8 

760.7 

844.6 

988.4 

1099 

lUB 

8.000 

10.794  107.9 

914.6 

321.7 

42W.0 

536.9 

643.4 

760.7 

867.9 

966.9 

1079 

1I» 

1J87 

9,000 

12.066  120.6 

241.3 

381.9 

489.6 

603.9 

793.9 

844.6 

966.9 

1086 

1906 

1397 

1448 

10.000 

13.406   134.1 

968.1 

409.9 

636.9 

•70.3 

804.3 

988.3 

1079 

1906 

1341 

U7S 

1009 

Virtre  Table.—The  wire  table  on  the  following  page  (from  a  circular  of 
the  Westini^iioiise  El.  &  Mfg.  Ck>.)  shows  at  a  fflance  the  size  of  wire  nece*- 
aarj  for  the  transmission  of  any  fciven  current  orer  a  known  distance  with 
a  ^ven  amount  of  drop,  for  lOO-volt  and  500-voIt  circuits,  with  Tarying 
losses.    The  formula  by  which  this  table  has  been  calculated  Is 


DXIWO 


R, 


in  which  D  equals  the  Tolts  drop  in  electro-motive  force,  C  the  current,  L  the 
distance  from  the  dynamo  to  the  point  of  distribution,  and  R  the  line  resist 
ance  in  ohms  per  thousand  feet. 

ExAMPLB  1.— Required  the  size  of  wire  necessary  to  carry  a  cuirent  of  60 
amperes  a  distance  of  650  feet  with  a  loss  of  b%  at  100  volts. 

Referring  ro  the  table,  under  60  amperes,  we  And  the  given  distance,  650 
feet.  In  the  same  horizontal  line  and  under  fi^  drop  at  100  volts,  we  find  Na 
000  wire,  which  is  the  size  required. 

Example  2.— What  size  will  be  required  for  10  amperes  2000  feet,  with  a 
drop  of  \0i  at  500  volts. 

Under  10  amperes  find  1930— the  nearest  figure  to  9000— and  in  the  same 
horizontal  hne  under  lOji  at  500  volts  find  No.  11,  the  size  required. 

Wirlnir  FornmlaB  for  Ineotndeacent  lilglitlns.  (W.  D. 
Weaver,  Elec.  World,  Oct.  16,  1802.)— A  formula  for  calculatbg  wiring 
tables  is 

.      2150^  rjc    «        J      21S0LO 


aEP 


aB 


where  A  —  section  in  circular  mils;  W  =  watt  rating  of  lamps;  B  =  vc^ 
age;  L  =  distance  to  centre  of  distribution,  in  feet;  N  =  number  of  la>mps; 
a  -  percentage  of  drop;  C  =  current  In  amperes. 

ExAMPLB.— Volts,  60;  amperes,  100;  feet  to  centre  of  distribution,  100; 
drop,  fifi. 

8150  X  100  X  100      „,.  ,^    ,       , 
;r;rsr =  216,000  circular  mils, 

or  about  0000  B.  &  8.  gauge. 


ELECTRIC  TRAKSHTSSIOM'. 


104 


i 

g 
a 

8 

8 

« 

s 

s 

S 

9 

E 

E 
< 

i 

£ 

1 

^1 

-IS 

II 

g38SS^a 

jssafisissss*'-* 

i! 

o 

SiSISIS; 

^as^^ltFrssssiss 

aSESS  2I*»s 

1 

i 

1  |s«°-" 

:4iia«*^tf*OJ^^ieve 

3§a83  gasss  sssits 

g§£g§  3S2SK  cti3K« 

in%i  SSSS9  «3='« 

1 

^§Si§S  SSSSS  ^^'St 

o 

|pi?il  gS5£S  5iS8S 

£CS3 

iSSLS    SsUi»» 

4lai5  sSg§g  sssit  ssnea 

1 

pg§a  SSS^g  ^SSgs  iissfls    . 

b 

liiss  nus 

Bjgags  ssdn« 

1 

Si 

•sgg  asssa 

SflliSS 

9 

lllli  Niii  m 

Ills  Bissa 

S1IS22 

8 

mn  f.Us%  fiu^  SSSS3 

asjsss  ^ 

S 

lilil  ||igi  iiri=  sssss- 

5^«SS 

llill  lipi  mu 

tBi^^ 

Si^S^SS 

£ 

lllli  ISftg  i! 

iilll  liiis  si 

iMa 

«l^8^ 

£iEiSK3s  saa— 

s 

!33S  SSils 

83SJ8fc    B£:2S« 

f 

lllli  IlISi 
lllli  llilf 

SSU3  SggSS 

SS5SS  aai;^^;^ 

£ 

|gS$s  SSSifS 

SSSSB    »»-r^2 

B 

1  > 

1 

1 

1 

ID    1 

— 

H 

i 
! 

1 

o 
« 
« 

-»»***•    S::3^3    SSL:S2    S 

m^ia^f^m    *2-2*i    sS2i:;S   SiH 

«»«..i^«    ...Ki^S    -2223    2'^^S8 

9_aage"     *t«'*ei5     ^.«]*ffl-     ^-j.*«- 

uaag 

^    SiS*    ^•'«-**>    ••--*asto    SS!2i3 

SSJSSR 

1    - 1|  s • 

-ssM 

aaa^s  sts 

1    i  i8 — 

'••fs^a 

saaa-r  aa« 

ll^ 

o* 

■^•rt-* 

««i>««t 

2=253   S5USS 

1044 


ELKCTUICAL   ENGINEEBING. 


The  horse-power  and  efficiency  of  a  motor  bejne  given,  the  sise  of  ihe  cod- 
ductiDg  wire  in  circular  mils  can  be  found  from  the  following  formula: 


A  =r 


lflO,400,000  X  H.P.  X  L 
aB^  X  efficiency 


EzAMPLV.— Horse-power,  10;   Tolta,  500;   drop,  dift\  feed  to  dfstribatins 
'  point,  600:  efficiency  of  motor,  76)t. 


lgO,4OQ.O0O  X  10  X  goo 


17,109  circular  mils,  or  about  No.  8  B.  &  S. 


3X600X500X75 

Cost  of  Copper  for  IjOiis«dlstanc«  Tranonlasloift. 

(Westinghouse  El.  A  Mfg.  Ck>.) 

Cost  or  Ck>ppBR  required  roR  tbb  Dbuvkby  or  On  Mbchavigal  Horic- 
POWER  ikT  Motor  SBArr  with  1000,  9000,  3000,  4000, 5000,  amd  10,000  Volts 
AT  Motor  Terminaub,  or  at  TsRMiKAiii  or  LowxaiMO  TRAiiBroaiuEK&. 

tiOfls  of  energy  in  conductors  (dropX  equals  90%, 

Distances  equal  one  to  twenty  milee. 

Motor  efficiency  equals  W%- 

Length  of  conductor  per  mile  of  single  distance,  11,000  feet,  to  aJlow  for 
sag. 

Cost  of  copper  taken  at  16  cents  per  pound.  (This  figure  is  too  high. 
An  approximate  figure  now,  1897,  is  18  cents  per  pound.) 


Miles. 

1000  ▼. 

2000  ▼. 

8000  T. 

4000  V. 

5000  T. 

10,000  T. 

•?s 

•2S 

^'B 

f0.18 

$0.06 

90.08 

8.38 

2.06 

0.08 

0.58 

0.88 

^.08 

18.70 

4.66 

2.06 

1.17 

0.76 

0.19 

88.30 

.     8.82 

8.70 

8.06 

1.88 

O.SS 

68.06 

18.00 

6.78 

8.85 

8.06 

0.58 

74.90 

18.70 

8.82 

4.68 

8.00 

0.7S 

109.00 

25.50 

11.80 

6.87 

4.06 

1.02 

183.26 

88.30 

14.80 

8.82 

5.88 

1.83 

168.60 

42.90 

18.70 

10.60 

6.74 

1.69 

206.19 

52.05 

28.14 

18.01 

8.88 

8.08 

251.90 

68.00 

88  00 

15.76 

10.06 

8.52 

299.80 

75.00 

88.80 

18.70 

12.00 

8.00 

852.00 

88.00 

89.00 

88.00 

14.08 

8.S2 

408  00 

102.00 

45.80 

85.50 

16.88 

4.06 

468.00 

117.00 

52.00 

29.85 

18.78 

4.68 

583.00 

133.00 

59.00 

83.80 

81.82 

5.38 

600.00 

150.00 

67.00 

87.60 

84.00 

e.oo 

675.00 

169.00 

75.00 

42.80 

87.00 

6.75 

760.00 

188.00 

83.60 

47.00 

80.00 

7.50 

20 

833.00 

208.00 

92.60 

68.00 

88.88 

8.83 

Welffht  of  Copper  reqntred  Ibr  Long-distance  Tmns- 
mlaalon.— W.  F.  C.  fiasson  (Ti-ans.  Tech.  Socy.  of  the  Pacific  Coast,  tql 
X,  No.  4)  gives  the  following  formula: 


W: 


.§H.P.<l??,^W.^ 


where  IT  is  the  weight  of  copper  wire  in  pounds;  D,  the  distance  in  mOes: 
E.  the  E.M.F.  at  the  motor  in  hundi'eds  of  volts;  H.P.,  the  horse-power 
delivered  to  the  motor;  £,,  the  per  cent  of  line  loss. 

ThuB.  to  transmit  800  horse-power  ten  miles  with  10  per  cent  Iocs,  and 
have  3000  volts  at  the  motor,  we  have 


W 


^0X10  ^  200  y  (100 
80X30^         ^ 


10) 


10 


X2C6.5r=  58,800  lbs. 


BLBCXKIC  IBA1«6J1I6S10N. 


1043 


Cost  of  Ooppbr  rkquiked  to  dbuvkr  One  Mkobanical  Horsk-powbr  ai 
MoTOR-sHAPr  WITH  Varyino  Pkrckhtagm  op  Loss  in  Cohductors.  upox 

TBK  AS8UMPnOK    THAT    THE    POTENTIAL  AT  MoTOR  TSKMINAUS  IB  IH  £ACB 

Cask  30UU  Volts.*  (Westiughouse  El.  &  Mfg.  Co.) 

Distances  equal  one  to  twenty  miles. 

Motor  efllclencj  equals  90%. 

Ijemgih  ot  conductor  per  mile  of  siugla  distance,  11,000  feet,  to  allow  for 


Cost  of  copper  equals  16  cents  per  pound. 

Miles. 

W 

15J< 

90% 

86j< 

W 

fO.KS 

$0.88 

fO.88 

10.17 

$0.18 

8.06 

1.31 

0.U8 

0.60 

0.54 

4,68 

2.85 

8.08 

1.A6 

1.81 

$M 

5.85 

8.70 

8.77 

9.15 

18.00 

8.80 

5.78 

4.88 

8.87 

18.70 

11.75 

8.88 

6.88 

4.86 

95.50 

16.00 

11.80 

8.45 

6.60 

88.90 

21.00 

14.80 

11.00 

8.60 

48.20 

86.60 

18.76 

14.00 

10.90 

58.05 

88.78 

88.14 

17.81 

18.60 

68.00 

88.75 

88  00 

81.00 

16.80 

75.00 

47.80 

83.80 

84.90 

1940 

88.00 

56. SO 

89.00 

29.80 

88.80 

108.00 

64.80 

46.:i0 

88.90 

86.40 

117.00 

78.75 

58.00 

88.90 

80.80 

188.00 

88.80 

59.00 

44.80 

84.50 

150.00 

94.75 

67.00 

50.00 

89.00 

160.00 

106.00 

75.00 

86.80 

48.80 

188.00 

118.00 

83.50 

68.50 

48.70 

90 

808.00 

181.00 

98.60 

60.89 

54.00 

KIBciency  of  LongHllaCiuiee  Tmnsmlaalon.  (F.  R.  Hart. 
I\jwer^  V%h.  iMI8.)-~Th«*  uieobauical  efficiency  ot  a  Kystem  is  the  ratio  of  the 
power  delivvreU  to  tbe  dvoauio-electric  macnines  ot  one  end  of  tbe  line  to 
the  power  delivered  by  the  electric  motors  at  Uie  distant  end.  The  com- 
xuerciai  efflcienuy  of  a  dynamo  or  motor  varieH  with  its  load.  Under  the 
most  favorable  couditious  we  must  expect  a  loss  of  say  9%  in  the  dynamo 
and  9%  in  tite  motor.  The  loss  in  transmission,  due  to  fall  in  electiical  pres- 
sure or  "drop'*  in  the  line,  is  governed  by  the  size  of  the  wires,  the  other 
conditions  remaining  tlie  same.  For  a  long-distauce  transmission  plant 
thid  will  vary  from  5^  upwards.  With  a  loss  of  5%  in  the  line  the  total 
efflcitfOOT  of  transmission  will  be  slightly  under  79%.  With  a  loss  of  \9%  in 
the  line  it  will  be  hlightly  under  7b%.  We  may  call  HOj(  the  practical  limit  of 
the  efficiency  with  the  apparatus  of  to  day.  Tlie  methods  for  longdistance 
transmission  may  be  divided  iiitu  three  general  classes :  (1)  continuous  cur- 
rent:  (i)  alternating  ciiirent;  and  (3)  regenerating  or  "motor-dynamo** 
systems. 

There  are  many  factors  which  govern  the  selection  of  a  system.  For  each 
problem  considered  there  will  be  found  certain  fixed  and  certain  unfixed 
conditions.  In  general  the  fixed  factors  are:  (1)  capacity  of  source  of 
power;  (;ij)  cost  or  power  at  source;  (8)  cost  of  power  by  othoF meant  at  point 
of  delivery;  (4)  danger  considerations  at  motors;  (5)  operation  conditionw; 
(6)  construction  conditions  (length  of  line,  character  of  country,  etc.).  The 
partly  fixed  conditions  are:  (7)  power  which  must  be  delivered,  i.e.,  the  effl- 
cieucy  of  the  system:  (8)  size  and  number  of  delivery  units.  The  rarlable 
conditions  are:  (9)  initial  voltage;  (10)  pounds  of  copper  on  line;  (11)  origi- 
nal cost  of  all  apparatus  and  construction;  (18)  expenses,  operating  (fixed 
charges,  interest,  depreciation,  taxes,  insurance,  etc.);  (13)  liability  of  trouble 
and  stoppages;  (14)  danger  at  station  and  on  line;  (15)  convenience  in  oper- 
ating, making  changes,  extensions,  etc.  Assuming  that  the  cost  of  dyna- 
mos, motors,  etc.,  will  be  approximately  the  same  whatever  the  initial 
pressure,  the  great  variation  in  the  cost  of  wire  at  diffei'ent  pressures  is 
shown  by  Mr.  Hart  in  the  following  figures,  giving  the  weights  of  copper 
re(}uired  for  transmitting  100  horse-power  5  miles : 


1046 


ELECTRICAL  ENGIKEERINQ. 


8,000 
10,000 


Drop  10  per  cent. 
16,800  lbs. 
7,400  " 


Drop  30  per  cent. 

8,400  lbs. 

8,700    •' 

8jO    '• 


The  subdivisions  of  each  of  the  general  methods  of  transmiso^ion  ar^' 
tabulated  as  follows: 


Continuous 
current 


Alternating 
current 


2.wire 


3- wire 


Low 
voltage 

High 
voltage 


Regenerating 
systems 


Multiple-wire 
Alternating  single  phase 


(  One  machine. 

1  Machines  in  paralleL 

(  One  machine. 

<   Machines  in  parallel. 

(   Machines  in  series. 

J  2  machines  in  series. 

(  Machines  In  multiple  seriea 

Machines  in  series. 
S  Without  conversloDS. 
I  With  conversions. 
(   Without  conversions. 
1   "With  conversions. 


Alternating  multiphase 

Alt<>rnating  continuous. 

Alternating  converter;  line  converter;  aliemating:  con- 
tinuous. 
Continuous-continuous. 
Partial  reconversion  of  any  system. 

The  relative  advantages  of  these  systems  vary  with  each  particular  trans* 
mission  problem,  but  in  a  general  way  may  be  tabulated  as  below. 


System. 

Advantages. 

Disadvantages. 

(  Low  voltage. 

9  iirlrr.  ^ 

Safety,  simplicity. 

Expense  for  copper. 

« 

/  High  voltage. 

Economy,  simplicity. 

Danger,     difficulty     of 
building  machines. 

.2 

o 

8- wire. 

Low  voltage  on  machines 
and  saving  in  copper. 

Low  voltage  at  machines 
and  saving  in  copper. 

Not  saving   enough    in 
copper  for  long    Jlv 

u 

Multiple- wire. 

Unces.    Necessity  for 
"  balanced ''  system. 

Single  phase. 

Economy  of  copper. 

Cannot  start  under  loaii. 

a 

£ 

2 

Multiphase. 

Economy  of  copper,  syn- 
chronous speed  unnec- 
essary;  applicable   to 
very  long  distances. 

Beanires  more  than  two 

< 

Motor-dynamo. 

High- voltage    transmis- 
sion.   Low-voltage  de- 
livery. 

Expensive. 
Low  efDclency. 

A  Graphical  method  of  calculating  leads  for  wiring  for  electric 
lighting  is  described  by  Carl  Hering  in  Trans.  A.  I.  E.  E.,  1891.  He  furnishes 
a  chart  containing  three  sets  of  diagonal  straight -line  diagrams  so  con- 
nected that  the  examples  under  the  general  formula  for  wiring  may  be 
solved  without  calculation  by  simply  locating  three  points  in  succession  on 
the  chart. 
Systems  of  Blectrlcal  Dlstrlbntlon  In  Common  Use.   (Chss. 

T.  Scott,  Proc.  Engi*a.  Soc'y  of  Western  Penna.,  1895.) 
I.  Continuous  or  Direct  Citrrknt. 
A.  Constant  Potential. 

110  Volts.— Disiances  less  than,  say,  1500  feet. 
For  incandeKcent  lamps. 
For  arc-lumps,  usually  2  in  series. 
For  motors. 


ELECTRIC   TRANSMISSIOK.  1041 

S80  Volte.— Distances  less  than,  say,  8000  feet. 

For  incandescent  lamps,  usually  2  in  series. 

For  orC'lamps,  usually  4  in  series. 

For  motors. 
880  Volts,  a-wire.— Disvances  less  than,  say,  8000  feet. 

For  incandescent  lamps. 

For  arc-lamps,  utiually  2  in  series  on  each  branch. 

For  motors  llO  or  a»  volts,  usually  2-.'0  volts. 
fiOO  Volts.— Distaaoes  less  than,  say,  SiKX)  feel. 

For  incandescent  lamps,  usually  6  in  series. 

For  arc-lamps,  usually  10  in  series. 

For  motors,  stationary  and  street-car. 

£.  Cmutant  Current.  ..^         ,.    ,  ,       .  w. 

Usually  about  10  amperes,  the  volts  increasing  to  several  thou- 
sand,  as  demanded. 
For  arc-lampe« 
For  motors. 

II;  AlOBBKATma  CURBSNT. 

A,  Constant  Potential. 

Ordinai'ily ,  about  16,000  or  7200  alternations  per  minute.   Primary 
circuit,  1000  or  SOOO  volU ;  secondary  circuit,  50  or  100  volts. 

For  incandescent  lamps. 
•     For  arc-lamps. 

For  small  motors. 
Multiphase  Syetems. 

For  lighting. 

For  motors. 

For  rotary  transformers  for  giving  direct  current. 

B.  Constant  OwTent 

Usually  10  amperes. 
For  aro-lamps. 
Bfliel«ncy  of  a,  Combined  Bngliie  and  Dynamo.  —  A  oom- 

Sound  double -crank  WUlans  engine  mounted  on  a  single  base  with  a 
ynaraoof  the  Edison -Hopklnson  type  was  tested  in  1890,  with  results  as 
follows :  The  low-pressure  cylinder  is  14  in.  diam.,  16  in.  stroke;  steam- 
-.pressure  190  lbs.  It  is  coupled  to  a  dynamo  constructed  for  an  output  of  475 
amperes  at  110  volts  when  driven  at  480  revolutions  per  minute.  Tlie  arma* 
ture  is  of  the  bar  construction,  is  plain  shunt-wound,  and  is  fitted  with  a 
commutator  of  hard-drawn  copper  with  mica  insulation.  Four  brushes  are 
•carried  on  each  rocker-arm. 

Resistance  of  magnets 16.        ohms 

Resistance  of  armature 0.0065     ** 

I.H.P 88.8 

E.H.P 7«.8 

Total  efficiency  86.7percent 

Consumption  of  water  per  I.H.P.  hour .  81 .6  pounds 

Consumption  of  water  per  E.H.P.  hour 25         " 

The  engine  and  dynamo  were  worked  above  their  full  normal  output, 
which  fact  would  tend  to  slightly  increase  the  efficiency. 

The  elt^ctrical  losses  were :  Loss  in  magnet  coils.  766  watts,  equal  to  1.4](; 
loss  in  armature  coil,  1886  watts,  equal  to2.6)(;  so  that  the  electrical  efficiency 
of  the  machine  due  to  ohmic  resistance  alone  was  06)(.  The  remainder  of 
the  losses,  a  little  over  8  horse-power,  is  due  to  friction  of  engine  and 
dynamo,  hystert^Ris,  and  the  like. 

Electrical  Bmclency  of  a  Ctoncrator  and  Motor.— A  twelve- 
mile  iransniissiou  of  power  at  Bodie,.  Cal..  is  described  by  T.  H.  Leggett 
(Trans.  A.  I.  AI  E.  1804).  A  single-phase  alternating  cuirent  is  used.  The 
ipenerator  is  a  Westinghouse  ISO  K.  W.  constant-potential  13-pole  machine, 
speed  860  to  870  revs,  per  min.  The  motor  is  a  synchronous  constant^po- 
tential  machine  of  120  horse-power.  It  is  brought  up  to  speed  by  a  lO-H.P. 
Tes(la  starling  motor.  Tests  of  the  electrical  emcleucy  of  the  generator  and 
motor  gave  the  following  results ; 


1048 


ELECTRtCAL  ENOINBERING. 
Test  on  Qknkrator. 


Amperes 

Volts. 

Watts. 

8elf-«xclted  fteld  

15.8 

18.2 

00 

78 

M8 

8eparately-excft«d  field 

1419.6 

Resistance  o^  armature,  1.6618  ohms. 
C/?,  losR  in  armaiure 

664.7? 

Total  loss  in  machine , 

3082  3i 

Load 

20 

UH 

eaeso 

Apparent  electrical  efficiency  of  generator,  05.559)(. 
Tbst  oh  Motor. 


.\m  penes 

Volts. 

Watts. 

Self-excited  field 

52 

62.4 

8241.8 

Resistance  of  armature,  1.4  ohms. 

aen.o 

Total  loss  In  machine 

8804.08 

Load 

20 

8110 

6«0OO 

Apparent  electrical  efliciency  of  motor,  96.6889(. 

Billclency  of  an  Bl«ctrlcal  Pnmplng^plaiiU  (Bug,  «t  M. 
Jour.,  Feb.  7,  1891.)— A  pumping-plaiit  at  a  mine  at  Normanton,  Entpland, 
was  tested,  with  results  given  below: 

Above  ground  there  is  a  pair  of  2(U^  x  48-in.  engines  running  at  20  rers.  per 
min.,  driving  two  seriee  dynamos  givmg  690  volts  and  59  amperes.  The  cur- 
rent from  each  chnamo  is  carried  into  tlie  mine  by  an  insulated  cable  about 
3000  feet  long.  There  they  are  connected  to  two  fi0h.p.  motors  which  oper- 
ate a  pair  of  differential  ram<pumps,  witli  rams  6  in.  and  4^  io.  diam.  and 
M  in.  stroke.  The  total  head  against  which  the  pumps  operate  is  890  fe«-t 
Connected  to  the  same  dynamos  there  is  also  a  set  of  gearing  for  driving  a 
hauling  plant  on  a  oonlinuous-rope  system,  and  a  set  of  three-throw  ram- 
pumps  with  6*inch  rams  and  18-inch  stroke  can  also  be  thrown  into  gear. 
The  connections  are  so  made  that  either  motor  can  opei:ate  any  or  all  Uiree 
of  the  sets  of  machinery  just  described.  Indicator-diagrams  gave  Uie  foh 
lowing  results: 

Friction  of  engine  ...  6.9  H.P.      9.4]f 

Belt  and  dynamo  friction 4.8   '*  6.H 

Leads  and  motor 6.7   **  9A% 

Motor  belt,  gearing  and  pumps  empty 10.2   '*         U.ifjl 

Load  of  117  gallons  through  800  feet 81.5    "         i»A% 

Water  friction  in  pumps  and  rising  main U.9  *'         17.^ 

78.0  H.P.  lOO.OjC 

At  the  time  when  these  data  were  obtained  the  total  efllctency  of  the  plant 
was  43.1^,  but  in  a  larer  test  It  rose  to  47^. 

Bererencen  on  Ponrer  Dlstrlbntton.—Kapp,  Eieotric  Tmnsmis- 
sfon  of  Energy;  Badt,  Electric  Transmission  Handbook;  Martin  and  Wetzler, 
The  Electric  Motor  and  its  Applications;  Hospitalier,  Polyphased  Electrls 
Currents. 

BI<«€TBI€  RAILWAYS. 

Space  will  not  admit  of  a  proper  treatment  of  this  subject  in  this  work. 
Consult  Crosbv  and  Bell,  The  Electric  Railway  In  Theory  and  Practice, 
price  $3  50:  Fairchild,  Street  Railways,  price  $4  00;  Merrill,  Reference 
Book  of  Tables  and  Formulea  for  Street  Railway  Engineers,  price  $1.00. 

Teat  of  a  Street  Rallipray  Plant*— A  test  of  a  small  electric-rail- 
way plant  i.s  rt- ported  by  Jesse  M.  Smith  in  Trans.  A.  8.  M.  E.,  vol.  xv.  The 
following  are  some  of  the  results  obtained: 


ELECTRIC   RAILWAYS.  1049 

'riction  of  engine,  air-pump,  and  boiler  feed-pump ;  main  belt  off    0.22 1.  H.P. 
'rict  ton  of  engine,  air  and  feed  pumps,  and  dynamo,  brushes  off.  11.84 1.H.P, 

Viction  of  dynamo  and  belt 2.12 1.H.P. 

*ower  consumed  by  engine,  air  and  feed  pumps  and  dynamo, 

with  brushes  on  ana  main  circuit  open 14.84 1.H.P. 

*ower  required  tocharge  fields  of  dynamo S.OOI.H.P. 

L&ied  capacity  of  engine  and  dynamo  each     160 1.H.P. 

'ower  developed  by  engine min.  21 .27;  max.  141 .4:  mean,  70.1 1.H.P. 

'ol ts  deTeloped  by  dynamo range,  480  to  520;  average,  601  volts 

Linperes  developed  by  dynamo max.  200;  rain.  4.7;  average.  67  amperes 

Lve rage  watts  delivered  by  dynamo 38,567  Watts 

Average  electrical  horse-power  delivered  by  dynamo 46  E.ILP. 

Average  I.H.P.  del'd  to  pulley  of  dynamo,  estimating  friction  of 

armature  shaft  to  be  the  same  as  friction  of  belt 50.8 1. H.P. 

kTerage  commercial  efficiency  of  dynamo 45  -i-  50.8  =  n.fS&% 

Average  number  of  cars  in  use  durmgtest 2.80car8. 

<}uinber  of  single  trips  of  cars , 64 

Average  number  of  passengers  on  cars  per  single  trip. .  16.2 

iVeight  of  cars  14,500  lbs. 

^Ist.  total  weight  of  cars  and  persons 15,000  lbs. 

\.verage  weight  in  motion 45,050  lbs. 

Average  electrical  horse-power  per  1000  lbs.  of  weight  moved. .  0.06  E.H.P. 
\.Terage  horse-power  developed  by  engine  per  1000  lbs.  of  weight 

moved 1.62I.H.P. 

^.verage  watts  required  per  car 11,615  watts 

^vei-age  electrical  horse-power  per  car 16.54  E.H.P. 

Average  horse-power  developea  in  engine  per  car 24 .26  LH.P. 

Lengthofroad  10.5  miles. 

Average  speed,  including  all  stops,  21  miles  in  1 .5  hours  =  14  miles  per  hour. 
A^verage  speed  between  stops,  21  m.  in  1.866  hours  =15.88  miles  per  hour. 

BliECTBIG  lilGHTING. 

MAi9  Of  Incandescent  Lamps.  (JCVip'g,  Sept.  1, 1808,  p.  283.V--7n>m 
experiments  made  by  MesKrs.  SlemenH  and  Halske,  Berlin,  it  appears  that 
th«)  average  life  of  incandescent  lamps  at  different  expenditure  of  watts  per 
candle-power  is  as  follows: 

Watts  per  candle-power 1.5        2        2.5         8  8.6 

Life  of  lamp,  hours 45        200       450       1000       1000 

Ijife  and  BIBciency  Tests  of  Lamps.  (P.  O.  Oossler,  £Zec. 
Worlds  Sept.  17,  1892.)— Lamps  burning  at  a  voltage  above  that  for  which 
they  are  rated  give  a  mu<!h  greater  illurainatiug  power  than  16  candles,  but 
at  the  same  time  their  life  is  very  considerably  shortened.  It  has  been  ob- 
served that  lamps  received  from  the  factory  do  not  average  the  same  candle- 
power  and  efficiency  for  different  invoices;  that  is,  lamps  which  are  received 
In  one  invoice  are  usually  quite  uniform  throughout  that  lot,  but  they  vary 
considerably  from  lamps  made  at  other  times. 

The  following  flgures  show  the  different  illuminating-powers  of  a  16.c.p., 
50- volt,  52-watc  lamp,  for  various  voltages  from  25  to  80^ volts: 
Volts: 
25       84.8       40         48         60       58.5      55.6      50.5       62       68.2     72.5       80 
Amperes: 
.561       .774      .808     .068     1.055    1.007    1.161    1.236     1.29     1.410    1.484     1.68 
Candles: 
.4        2.47       5.1       12.6      15.8      20.5      28.4      39.3      50.7     74.5     103.2     141 
Watts: 
14.09    26.94    85.93    46.84    52.75    57.57    64.55    73.98    79.98    9C.78    107.5    126.4 

Watts  per  c.p.: 
85.1     10.81     7.04      8.68      8.84      2.81      2.30      1.90      1.58      1.80     1.04      .90 

mr«et-ltclitlnff.  (H.  Robinson,  M  I.C.E.,  Eng'g  Nevm,  Sept.  12, 1891  .> 
—For  street-lighting  the  arc-lamp  is  the  most  economical.  The  sinallesB 
size  of  aro-lamp  at  present  manufacture<i  requires  a  ciurent  of  about  5 
amperes;  but  for  steadiness  and  efficiency  it  is  desirable  to  use  not  less  than 
6  amperes.  (Qood  8-anipere  lamps  are  now  on  the  market.  1897.)  The 
candle-power  of  arc-lamps  varies  considerablv.  according  to  the  angle  at 
which  it  is  measured.  The  greatest  intensity  with  continuous-current  lamps 
is  found  at  an  angle  of  about  40*  below  tlie  horisoutal  line.    The  f ollowiDg 


1050 


ELECTRICAL  ENGINEERINa. 


table  (irives  ihe  Approximate  candle-power  at  various  angles.  The  helj^bt  of 
the  lamps  should  be  nrrangred  so  as  to  gire  an  angle  of  not  len  than  T*  to 
the  most  distant  point  it  is  intended  to  serve. 

Llgbtlns^power  of  Arc-lamps* 


-Candle-power. - 


In^m^JL     HorlMntal    ^^  A°«*«    ^^  ^^^^    ^*  ^°K^®    Marfmum  at 
m  Amperes,    uonrontai      ^^^  ^^  j^o.         of  goo.      Angle  of  40». 

6  98  175  907  822  460 

8  1S6  SCO  850  646  780 

10  220  490  405  770  1100 

The  following  data  enable  the  coefficient  of  minimum  Ughthis-power  b 

streets  to  be  determined: 

Let  P  =  candle-power  of  lamps; 

L  =  maximum  distance  from  lamp  in  feet; 

H  -  heiKht  of  lamp  in  feet; 

JT  =  a  coefficient. 

The  light  falling  on  the  unit  area  of  pavement  varies  inversely  as  the  sauar^ 

of  the  distance  from  the  lamp,  and  is  directly  proportional  to  the  angle  ai 

which  it  falls.    This  angle  is  nearly  proportional  to  the  height  of  the  lamp 

divided  by  the  distance.    Therefore 


or   X  =  ^. 


The  usual  standard  of  gas-lighting  is  represented  by  the  amount  of  ll^b' 
falling  on  tlie  unit  area  of  pavement  50  feet  away  from  a  13-c.p.  gas-lani  v 
feet  high,  which  gives  a  coefficient  as  follows: 

X=-y,'' =  0.000864. 

The  minimum  standard  represents  the  amount  of  light  on  a  unit  area  'Jj 
feet  away  from  a  a4-c.p.  lamp,  9  ft.  high,  and  gives  the  coefficient  .0017* 

Adopting  the  first  oi  the  above  coefficients.  Mr.  Robinson  calculates  that 
the  before-mentioned  sizes  of  arc-lights  will  give  the  same  standard  oi 
light  at  the  height«  and  distances  t^tated  in  Table  A.  Table  B  gives  the 
corresponding  distances,  assuming  the  minimum  standard  to  be  adopted. 


Table  A. 

Tablb  B. 

Hgt.  of  Lamps. 

20  ft. 

25  ft.  |30  ft.  85  ft. 

Height 

90ft.|25ft.  |30ft|S5fl 

Current  in 
Amperes. 

Max.  distances  served 
from  lamp,  in  ft. 

Amperes. 

from  Lamp^ 

6 

8 
10 

160 

1R5 

•:or) 

175 
909 
225 

100 
990 
243 

202 
985 
960 

6 
8 
10 

180 
150 
170 

144 

165 
190 

165 
180 
5205 

The  distances  the  lamps  are  apart  would,  of  course,  be  double  the  Ax^- 
lances  mentioned  in  Tables  A  and  B.  One  arc-lamp  will  talce  the  plact*  •  ' 
from  3  to  6  gas-lamps,  according  lo  the  locality,  arrangement, and  stanilari 
of  licrht  adopted.  A  scheme  of  arc-lighting,  based  on  the  substitution  of  en' 
arc-light  on  the  avers jtp  for  3V^  to  4  gas -lamps,  would  double  the  minin' •-'- 
standard  of  light,  while  the  average  standaixi  would  be  increased  10  oi  it 
times. 

Candle-poirer  of  the  A.rc-llfflit*  (Elibu  Thomson,  El.  Worid. 
Feb.  28, 1891.)— With  the  long  arc  the  maximum  Intensltv  of  the  light  is  fn.»^p: 
40^  to  W*  downward  from  the  horizontal.  The  spherical  candle-power  i^ 
only  a  fraction  of  the  rated  c.p.,  which  is  generally  taken  at  the  maximum 
obtainable  in  the  best  direction.  For  this  reason  the  term  9000  c.p.  has  little 
si^iiiUcauce  i<A  iuaicuim»;  me  iiiuiii.ri.t.iij<-|Miiier  of  an  arc.  It  Is  now  gentrr 
ally  taken  to  mean  an  arc  with  10  ainpoit^s  and  nut  le^  than45volis  betwrfu 
the  carbons,  or  a  450- watt  arc.  The  9ualiiy  of  the  carbons  will  detenniDd 
whether  the  450  watts  are  expended  m  ubiainiug  the  most  light  or  not.  or 
-whether  that  light  will  have  a  iimximum  iuteusiiy  at  one  angle  or  another 


ELECTRIC   WELDING.  lOdi 

within  certain  limits.  The  lar8:er  the  current  passlnj?  in  an  arc,  the  less  is 
its  I  eMistance.  Well-developed  arcs  with  4  amperes  will  haTe  about  11  ohms, 
with  10  amperes  4.5  ohms,  and  with  100  amperes  .46  ohm. 

It  is  not  unusual  to  run  from  50  to  60  lij^iits  in  a  series,  each  deroandinfp 
from  45  to  iM)  volts,  or  a  total  of,  say,  .3000  volts.  In  going  beyond  this  the 
difYlcuities  of  insulation  ara  ernatly  iiicrease<l. 

Reference  Books  on  Eleetrlc  I<lfflitlni;.>-Noll,  How  to  Wire 
Duildiugs,  $1.00;  Hedges,  Continental  Electiic-iiKht  Central  Stations,  $6.00; 
!•  leming.  Alternating  Current  Transformers  in  Theory  and  Practice,  i  volrt., 
$s  00;  Atkinson.  Elements  of  Electric  Lighting,  $1.50;  Algave  and  Boulard, 
Klectric  Light:  its  History,  Production,  and  Application,  $5.00. 

ELECTRIC    WEIiDING. 

The  apparatus  most  generally  used  consists  of  an  alternating-current 
<1\  iiamo,  reeding  a  comparatively  hJgh-pot«?ntial  current  to  the  primary  coil 
of  an  induction-coil  or  transformer,  the  secondary  of  which  is  made  so 
l.iT>;e  in  section  and  so  short  in  len^^th  as  to  supply  to  the  work  currentti 
nni  exceeding  two  or  three  volts,  and  of  very  large  vohime  or  rate  of  flow. 
The  welding  clamps  are  attached  to  the  secondary  terminals.  Other  forms 
of  apparatus,  such  as  dynamos  constructed  to  yield  alternating  currents 
direct  fi-om  the  armature  to  the  welding -clamps,  are  used  to  a  limited 
extent. 

The  conductivity  for  heat  of  the  metal  to  be  welded  has  a  decided  Influ- 
ence  on  the  heating,  and  in  welding  iron  its  comparatively  low  heat  conduc- 
tion a.ssiMts  the  work  materially.  (See  papera  by  Sir  F.  Bramwell,  Proc. 
In-^t.  C.  E.,  part  iv.,  vol.  cil.  p.  1;  and  EUhu  Thomson,  Trans.  A.  I.  M.E.,  xix. 
877) 

Fre<l.  P.  Royce,  Iron  Age^  N<»v.  28, 1892.  gives  the  following  figures  show* 
ing  the  amount  of  power  required  to  weld  axles  and  tires: 

AXLE- WELDING. 

Seconds. 

1 -Inch  round  axle  requires  25  H.P.  for 45 

1-inch  square  axle  requires  30  H.P.  for 48 

1^-inch  round  axle  requires  35  H.P.  for 60 

1^-inch  square  axle  requires  40  H.P.  for 70 

2-inch  round  axle  requires  75  H.P.  for 95 

2-inch  square  axle  requires  90  H.P.  for 100 

The  slightlv  increased  time  and  power  required  for  welding  the  square 
axle  is  not  only  due  to  the  extra  metAl  iu  it,  but  iu  part  to  the  care  which  it 
is  best  to  use  to  secure  a  perfect  alignment. 

TIRE -WELDING. 

Seconds. 

1  X  3/lG-inchUre  requires  11  HP.  for 15 

IW  X  «^inch  tire  requires  28  H.P.  for 25 

ILjx^-inch  tire  requires  20  H.P.  for f» 

IH  X  H-inch  tire  requires  28  H.P.  for 40 

2x  Ji-lnchtirereciuires29H.P.  for 55 

2  X  94  inch  Ure  requires  42  H.P.  for 62 

The  time  above  given  for  welding  Is  of  course  that  required  for  the  actual 
application  of  the  current  only,  and  does  not  include  that  consumeti  by 
placing  the  axles  or  tires  iu  the  machine,  tiie  removal  of  the  upset  and 
other  finishing  processes.  From  th»*  data  thus  submitted,  the  cost  of  welding 
can  be  readily  figured  for  any  locality  where  the  price  of  fuel  and  cost  oC 
labor  are  known. 

In  almost  all  cases  the  cost  of  the  fuel  used  under  the  boilers  for  produc- 
ing power  for  electric  welding  is  practically  the  same  as  the  cost  of  fuel 
used  in  forges  for  the  same  amount  of  work,  taking  into  consideration  the 
liflference  m  price  of  fuel  used  in  either  case. 

Prof.  A.  B.  w.  Kennedy  found  that  2^-inch  iron  tubes  J4  inch  thick  were 
A'elded  in  61  seconds,  the  net  horsepower  required  at  this  speed  being  23.4 
(say  33  indicateii  horse-power)  per  square  Incli  of  section.  Brass  tubing  rer 
quired  21 .2  net  horse-power.  About  80  total  indicattni  horse-power  would  !« 
retjulred  for  the  welding  of  angle-irons  3  X  8  >  Vii  >"t;h  iu  from  two  to  three 
minuteM.  Copper  requires  about  80  h<)rse-i)ower  per  .square  inch  of  section, 
and  an  inch  bar  can  be  welded  in  25  seconds.  It  takes  about  90  WJConUs  tQ 
weld  a  steel  bar  2  inches  iu  diameter. 


1052  ELECTIUCAL   EXGINEERING. 

KliECTRIC   BIEATBBS. 

Wherever  a  oomparativel^  smnll  amount  of  heat  is  desired  to  be  auto 
matically  and  uniformly  maintained,  and  started  or  stopped  on  the  instant 
without  waste,  there  is  the  province  of  tiie  electric  heater. 

The  elementary  form  of  heater  is  some  form  of  resistance,  such  as  coils 
of  thin  wire  introduced  into  an  electric  circuit  and  surrounded  with  a  sub- 
stance, which  will  permit  the  conduction  and  radiation  of  heat,  and  at  ibd 
same  time  serve  to  electrically  insulate  the  resistance. 

This  resistance  should  be  proportional  to  tlie  eteciro-motiTe  force  of  the 
current  used  and  to  the  equation  of  Joule's  law : 

fl=C>l?f  X0.34, 

where  Ois  the  current  In  amperes;  R,  the  resistance  in  ohms;  f,  the  Ume  in 
seconds;  and  A.,  the  heat  in  gram -centigrade  unita. 

Since  the  resiRtance  of  metals  increases  as  their  temperature  increase«s  a 
thin  wire  heated  by  current  passing  through  it  will  resist  more,  and  grow 
«iotter  and  hotter  until  its  rate  of  loss  of  heat  by  conduction  and  radiation 
equals  the  rate  at  which  beat  is  supplied  by  the  current.  In  a  short  wire, 
before  heat  enough  can  be  dispelled  for  commercial  purposes,  fusion  will 
beffin;  and  in  electric  heaters  it  is  necessary  to  use  either  long  lengths  of 
thin  wire,  or  carbon,  which  alone  of  all  conductors  resists  fusion.  In  the 
majority  of  heaters,  coils  of  thin  wire  are  usfd,  separately  embedded  ia 
some  substance  of  poor  electrical  but  good  thermal  conductivity. 

The  Consolidated  Car-heating  Co.'s  electric  heater  consists  of  a  galvanised 
Iron  wire  wound  in  a  spiral  groove  upon  a  porcelain  insulator.  Each  heater 
Is  ao*^  in.  long,  8^  in.  high,  and  6^  in.  wide.  Upon  it  is  wound  808  ft  of 
wire.    The  weight  of  the  whole  is  t^%  ibs. 

Each  heater  is  designed  to  absorb  1000  watts  of  a  500- volt  current.  Six 
heaters  are  the  complement  for  an  ordinary  electric  oar.  For  ordinary 
weather  the  heaters  may  be  combined  by  the  switch  In  different  ways,  so 
that  Ave  different  intensities  of  heating-surface  are  possible,  besides  the 
position  in  which  no  heat  is  generated,  the  current  being  turned  entirely  uS. 

For  heating  an  ordinary  electric  car  the  Consolidated  Co.  state*  tliat 
from  2  to  12  amperes  on  a  fiOO-volt  circuit  is  sufficient.  With  the  outside 
temperature  at  SiO*  to  30*,  about  6  amperes  will  suffice.  With  aero  or  lower 
temperature,  the  full  12  amperes  is  required  to  heat  a  car  effectively. 

Compare  these  figures  with  the  experience  in  steam-heating  of  railway- 
cars,  as  follows : 

1  B.T.U.  =  0.29084  watt-hours. 

6  amperes  on  a  500-volt  circuit  =  8000  watts. 

A  current  consumption  of  6  amperes  will  generate  8000  -i-  OJS9064  =  10,315 
B.T.U.  per  hour. 

In  steam- car  heating,  a  passenger  coach  usuallv  requires  from  60  Ibe.  of 
Bteam  in  freezing  weather  to  100  lbs.  in  zero  weather  per  hour.  Suppofiioe 
the  steam  to  enter  the  pipes  at  20  lbs.  pressure,  and  to  be  dischaiiged  at  dOU^ 
F.,  each  pound  of  steam  will  give  up  968  ELT.U.  to  the  car.  Then  the 
equivalent  of  the  thermal  imits  delivered  by  tm  electrical-heating  system  in 
pounds  of  steam,  is  10,815  -t-  983  =  10^,  nearly. 

Thus  the  Consolidated  Co.^s  estimates  for  electric-heating  provide  the 
equivalent  of  10)^  lbs.  of  steam  per  car  per  hour  in  freezing  weather  and  i\ 
lbs.  in  zero  weather. 

Suppose  that  by  the  use  of  good  coal,  careful  firing,  well  designed  boilers, 
and  triple-expansion  engines  we  are  able  in  daily  practice  to  gt'uerate 
1  H.P.  delivered  at  the  fly-wheel  with  an  expenditure  of  23^  lbs.  of  coal  i>6r 
hotu'. 

We  have  then  to  convert  this  energy  into  electricity,  transmit  it  by  wire 
to  the  heater,  and  convert  it  into  heat  dv  passing  it  through  a  resistanoe-c^ul. 
We  may  set  the  combined  efficiency  of  the  dynamo  and  line  circuit  at  »:.*. 
and  will  suppose  that  all  the  electricitv  is  converted  into  heat  in  the  resis^t- 
ance-coils  of  the  radiator.  Then  1  brake  H.P.  at  the  engine  =  0.85  electrical 
H.P.  at  the  resistance-coil  =  1,688,000  ft.-lbs.  energy  per  hour  =  2180  beat- 
units.  But  since  it  requii-ed  2^  lbs.  of  coal  to  develop  I  brake  H.P.,  it  fel- 
lows that  the  heat  given  out  at  the  radiator  per  pound  of  coal  burned  in  the 
boiler  furnace  will  be  2180  -4-  2^  =  872  H.U.  An  ordinary  steam-heating 
system  utilizes  9652  H.U.  per  lb.  of  coal  for  healing:  hence  the  efficiency 
of  the  electric  system  va  to  the  efficiency  of  the  sieam-heating  system  as  87^ 
to  9652,  or  about  1  to  H.    {Kng'f/  JVejrs,  Aur.  9,  '90;  Mar.  30, '!«;  May  15,  1«..» 


ELECTRICAL  ACCUMULATORS  OR  STORAGE-BATTERIES,  105  J 


EI«ECTBI€AI«  ACCUlHUIiATOBS  OB  8TOBAOH- 
BATTEBIES. 

Stnrage-batterieB  may  be  divided  into  two  classes:  tie.,  those  in  wklch  the 
active  iiiateriai  is  formed  from  the  substance  of  the  element  itself,  either 
hv  direct  chemical  or  electro -chemical  action,  and  thoae  in  which  the 
cneinical  formation  is  accelerated  by  the  application  of  some  easily  reduci- 
ble salt  of  lead.  Elements  of  the  former  ^pe  are  usually  called  Plants,  and 
those  of  the  latter  **Faure,"  or  **  pasted." 

Faraday  when  electrolyzing  a  solution  of  acetate  of  lead  found  that  per- 
oxide of  lead  was  produced  at  the  positive  and  metallic  lead  at  the  negatiTe 
pole.  The  surfaces  of  the  elements  in  a  newly  and  fully  charged  Plants  cell 
consists  of  nearly  pure  peroxide  of  lead,  PbO*,  and  spongy  metallic  lead, 
Pb,  respectively  on  the  positive  and  negative  plates. 

During  the  dtschars^e,  or  if  the  cell  be  allowed  to  remain  at  rest,  the  sul- 
phuric acid  (H,S04)Tn  the  solution  enters  into  combination  with  the  per- 
oxide and  spongy  lead,  and  partially  converts  it  into  sulphate.  The  actd 
being  continually  abstracted  from  the  electrolyte  as  the  discharge  proceeds, 
the  aensity  of  the  solution  becomes  less.  In  the  charging  operation  this 
action  is  revertied,  as  the  reducible  sulphates  of  lead  which  have  been 
formed  are  apparently  decomposed,  the  acid  being  reinstated  in  the  liquid 
and  therefore  causing  an  increase  in  its  density. 

The  difference  of  potential  developed  by  lead  and  lead  peroxide  immersed 
in  dilute  HsSOj  is,  as  nearly  as  mav  be,  two  volts. 

A  lead-peroxide  plate  gradually  loses  its  electrical  energy  by  local  action, 
the  rate  of  such  loss  varVing  according  to  the  circumstances  of  Its  prepara- 
tion and  the  condition  of  the  cell.  Various  forms  of  both  Plants  and  Faun 
batteries  are  illustrated  in  ''  Practical  Electrical  Engineering.'* 

In  the  Faure  or  pasted  cells  lead  plates  are  coated  with  minium  or 
litharge  made  into  a  paste  with  acidulated  water.  When  dry  these  plates 
are  placed  in  a  bath  of  dilute  H,S04  ^nd  subjected  to  the  action  of  the 
current,  by  which  the  oxide  on  the  positive  plate  is  converted  into  peroxide 
of  lead  and  that  on  the  negative  plate  reduced  to  finely  divided  or  porous 
lead. 

Gladstone  and  Tribe  found  that  the  initial  electro-motive  force  of  the 
Faure  cell  averaged  2.25  volts,  but  after  being  allowed  to  rest  aome  little 
time  it  was  reduced  to  about  2.0  volts. 

The  following  tables  give  the  elements  of  several  sizes  of  "chloride**  ac- 
cumulators made  i)y  the  Electric  Storage  Battery  Co.,  Philadelphia.  Type 
G  is  furnished  in  cells  containing  from  11  to  125  plates,  and  type  H  from  21 
plates  to  any  greater  number  desired.    The  voltage  of  cells  of  all  sixes  is 


TYPE  ■'  B." 
SKxe  of  Plrit-eA,  fl  X  3  In. 


Kumber  of  platf^s.  ,,♦*..,►.     , . . 
I>iaciiiii'gf^  \  For  H  iuyurm  . .  ^ 

in  aiu-<     "  5     "      ,....,,, 

peivs:  [  ''3  '*  ...,,.., 
K'lrmal  i-liutve  ralu  .„...».... 
TftVlijht  of  ench  eltiinpnt,  lbs  . , 
Outfiide  mt?a^ur<5mfiit  t  Width  «  1 

of    rubber    jar    lu  J  Length,  a, 

Ineh4>n;  (  ItHght,  h 

Outside  measurement  i  Wjdlh.* 

of     giasa     jar      in<I^ogai. 

1nch<«s:  ( Ili'i^ht. 

ITeight  at  acid  in  g}Sis^  jjsira  In 

lbs 

Weight  of  iic:jd  in  rubber  jars 

in  Iba */.,.» 

Wfi^ht  of  L-ell  complete,  with 

acid,  ill  rubber  jJLrH  ju  IbN,  ,,. 
Ilfijght  of  ceil  overall  In  inches. 


TYTE   '*C. 

sue  of 

FJates,  4x4 

in. 


3 

n 

it 

1 

8 

6 

^ 

2 

4y, 

& 

7 

m 

& 

4 

&h 

^ 

»k 

I 

m 

H 

1 

i 

en 

8 

JO 

10^ 
10 


TYPE  "D." 
^Ize  of  plates,  G  x  ti  tn. 


5 

ft 

7 
iQ 

& 
H 

3 

m 
mm 


4 

m 

D 


im 


D  U 

ID  12W 

to  \im 

5  I  e 


7 


m 


IS 

15 

IS 

m 

T 

m 


m 
m 


1054 


ELECTRICAL   ENGINEERING. 


TYPE  "  V  " 
Size  of  Platos,  7%'x  7^  in. 


Number  of  plates... 
Dischargee  (  For  8  lioure 

in   am-<     "  5     *' 

peres:     (     "8     ** 
Normal  charge  rate.. . . 
WeiKht  each  element. 

lbs 

•  •  (Width,  in.,  |  nib- 
*'g-^Len}?th,  *'  [-  her 
lIlHfiKht.  ;'  (  jar. 

O  I  <  I^nRth,  "  V  1 55 
2  I  Height,  "  \  'ttT' 

Weight  of  acid  in  glass 
jars  in  lbs 

Weight  of  acid  in  rub- 
ber jars  in  lbs 

Weight  of  cell  com- 
plete, with  acid,  in 
rubber  jar  in  lbs. .  . 

Height  of  cell  over  all, 
in  inches 


Ti 

7 

0 

HI 

15 

iKi 

M 

^l 

m 

X 

:W 

40 

10 

15 

t^ 

'^ 

il 

n 

'<] 

i 

5 

htij 

H^ 

^H 

n 

11 

11 

0^* 

f^ 

im 

UH 

11t^ 

IT 

21 

•^ 

C^ 

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M 

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i3 


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71 

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11 

u 

84 


91 
144 


TYPE  "  F." 
Size  of  Plates, 
10^  X  VH  in. 


9 
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61 


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15 

17 

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70 

80 

84 

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19 
90 
126 
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339    376    413 

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19      19     ;i9 


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IS 

♦  D  =  addition  per  plate  from  '25  to  125  plates;  approximate  as  to  dimen- 
sions and  weights. 

slightly  above  two  volts  on  open  circuit,  and  during  discharge  varies  from 
that  point  at  the  beginning  to  1.75  at  the  end. 

Accumulators  are  largely  used  In  central  lighting  and  power  stations,  in 
oflnce  buildings  and  other  large  isolated  plants,  for  ihe  purpose  of  absorbing 
the  energy  of  the  generating-|)lant  during  times  of  light  load,  and  for  giving 
it  out  during  times  of  heavy  load  or  when  the  generating.plant  is  idle.  The 
advantages  of  their  use  for  such  purposes  are  thus  enumerated: 

1.  Reduction  in  coal-coiisumption  and  general  operating  ex})enses,  due  to 
the  generating  michinery  being  run  at  the  point  of  greatest  economy  while 
in  service,  and  being  shut  down  entirely  during  hours  of  light  toad,  the  bat- 
tery supplying  the  whole  of  the  current, 


ELECTRICAL  ACCUMULATORS  OR  STORACJE-EATTEUIES.  IOjC 

2.  The  possibility  of  obtaining  good  regulation  in  pressure  daring  fluetua> 
tions  in  load,  especially  when  the  day  load  consists  largely  of  elevators  and 
Birnilar  disturbing  elements. 

8.  To  meet  sudden  demands  which  arise  unexpectedly,  as  in  the  case  of 
darkness  caused  by  storm  or  thunder-showers;  also  In  case  of  emei^ncy 
due  to  accident  or  stoppage  of  generating-plant. 

4.  Smaller  generating-plant  required  where  the  battery  takes  the  peak  of 
the  load,  which  usually  only  lasts  for  a  few  hours,  and  yet  where  no  battery 
is  used  necessitates  sufficient  generators,  etc.,  being  installed  to  provide  for 
the  maximum  output,  which  In  many  cases  Is  about  double  the  normal 
our  put. 

Tney  are  also  in  common  use  for  furnishing  current  for  electric  motors 
for  a  ?reac  variety  of  purpoeea,  and  as  a  siibstitute  for  primary  electric 
batteries. 

For  a  very  full  description  of  various  forms  of  storage-batteries,  see 
"  Practical  iSlectrical  Engineering,"  part  zil.  For  theory  of  the  battery  and 
practice  with  the  Julien  battery,  see  paper  on  Electrical  Accumulators  bj' 
P.  n.  Saloin.  Trans.  A.  I.  M.  K.,  xviii.  848. 

Use  of  Storase-baUerles  In  Poirer  and  I^lelit  Stations* 
(Iron  Aue,  Nov.  a,  1H93.)— The  storage-batteries  in  the  Kdison  station,  m 
Fifty-third  Street,  New  York,  relieve  the  other  stations  at  the  hours  of  heavy 
load,  by  delivering  into  the  mains  a  certain  amount  of  current  that  would 
otherwise  have  to  come,  and  at  greater  loss  or  *'  drop,^*  from  one  or  another 
of  the  stations  connecting  with  the  network  of  mains.  Hence  the  load  may 
be  varied  more  or  less  arbitrarily  at  these  stations  according  to  the  propor- 
tion of  load  that  the  larger  stations  are  desired  or  able  to  carry. 

The  battery  consists  of  140  cells  each  of  about  1000  ampere-hour  capacity, 
weighing  some  750  lbs.,  and  of  about  48  inches  in  length,  21  inches  in  width, 
and  15  inches  in  depth.  The  battery  has  a  normal  discharge  rate  of  about 
200  amperes,  but  can  be  discharged,  if  necessary,  at  500  amperes. 

A  test  made  when  the  station  was  running  only  12  hours  per  day,  from 
noon  to  midnight,  showed  that  the  battery  furnished  about  28.2^ of  the  total 
energy  delivered  to  the  mains.  The  maximum  rate  of  discharge  attained 
by  the  battery  was  about  270  amperes.  Thus,  in  this  case,  we  have  an  ex- 
ample of  a  battery  which  is  used  for  the  purpose:  1.  Of  giving  a  load  to 
station  machinery  that  would  otherwise  be  idle.  2.  Utilizing  the  stored 
energy  to  increase  the  rate  of  output  of  the  station  at  the  time  of  heavy 
load,  which  would  otherwise  necessitate  greater  djmamo  capacity. 

Tbe  IVorklnc  Current,  or  Enersy  EtBclency,  of  a  storage- 
cell  is  the  ratio  between  the  value  of  the  current  or  energy  expended  in  the 
charging  operation,  and  that  obtained  when  the  cell  is  discharged  at  any 
specified  rate. 

In  a  lead  storage  cell,  if  the  surface  and  quantity  of  active  material  be 
accurately  proportioned,  and  if  the  discharge  be  commenced  immediately 
after  the  termination  of  the  charge,  then  a  current  efficiency  of  as  much  as 
989(  may  be  obtained,  provided  the  rate  of  discharge  is  low  and  well  regu- 
lated. In  practice  it  is  found  that  low  vates  of  discharge  are  not  economical, 
and  as  the  current  efficiency  always  decreases  as  the  discharge  rate  In 
creases,  it  is  found  that  the  normal  current  efficiency  seldom  exceeds  90j(, 
and  averages  about  85^. 

As  the  normal  discharging  electro-motive  force  of  a  lead  secondary  cell 
never  exceeds  2  volts,  ana  as  an  electro-motive  force  of  from  2.4  to  2.5  volts 
is  required  at  Its  poles  to  overcome  both  its  opposing  electro-motive  force 
and  its  Internal  resistance,  there  is  an  initial  loss  of  *M%  between  the  energy 
required  to  charge  it  and  that  given  out  during  its  discharge 

As  the  normal  discharging  potential  is  continually  being  reduced  as  the 
rate  of  discharge  increases,  it  follows  that  an  energy  efficiency  of  80^  cau 
never  be  realiased.  As  a  matter  of  fact,  a  maximum  of  7i%  and  a  mean  of 
eo%  IS  the  usual  energy  efficiency  of  lead-sulphuric-acid  storage-oella. 


1056  ELECTRICAL  ENGINEERING. 

BliECTBO-CHBlHICAIi  EQUIVAIiENTS. 


Elements. 

• 

i 

t 

St 

< 

> 

3 

1^ 

11^ 

Itll 

C 

If 

!3 

El.KCTRO-POSITIVB. 

Hvd  roiren 

Na, 
Al, 

An, 

Cua 
Cu, 

P 

Sn4 

Fe, 

]?»« 
Zn, 

0, 

1.00 
89.04 
22.99 
27.3 
28.94 
106.2 

ior.66 

68.00 
68.00 
199.8 
199.8 
117.8 
117.8 
55.9 
55.9 
58.6 
64.9 
206.4 

15.96 
35.37 
126.53 
79.75 
14.01 

1.00 
89.04 
23.99 
9.1 
11.97 
654 

107.66 
81.5 
63.00 
99.9 

199.8 
29.45 
68.9 
18.64t 
27.95 
29.3 
82.45 

103,2 

7.98 
85.87 
128.53 
79.75 

4.67 

.010^ 

.40539 

.23873 

.09449 

.12480 

.67911 

1.11800 
.32709 
.65419 

1.08740 

2.07470 
.30581 
.61162 
.19356 
.29035 
.30425 
.33696 

1.07160 

.08286 
.86728 
1.81890 
.82812 
.04849 

96298.00 
2467.50 
4188.90 
1068.30 

804.03 
1473.50 

894.41 
8068.60 
1625  80 

968.99 

481.90 
8270.00 
1685.00 
5166.4 
8445.50 
3SW6.90 
2967.10 

988.26 

0.08738 

Potassium... 

Sodium  

Aluminum 

SX^."";::::.::.;:: 

1.45950 

0.344^  IS 
0.44T4T 
2.444ai 

Silver 

Copper  (cuprlc) 

**       (cuprous) 

Mercury  (mercuric).. . . 

**        (mercurous).. 

Tin  (stannic)    

4.02500 
1.177U0 
2.85500 

8.73450 

7.4»O0 
1.10090 

"    (stannous) 

Iron  (ferric).. 

**    (ferrous) 

8.201HO 
0  69GS1 
1.044^ 

Nickel 

Zinc 

1.09530 
1.21830 

Lead 

Oxygen 

8.85780 

Chlorine 

Iodine 

Bromine 

Nitrogen 

*  Valency  is  the  atom-lizing  or  atom-replacing  power  of  an  elemeot  com- 
pared with  hydrogen,  whose  valency  Is  unity. 

t  Atomic  weight  Is  the  weight  of  one  atom  of  each  element  compared  with 
hydrogen,  whose  atomic  weight  is  unity. 

t  Becqueret's  extension  of  Faraday 'slaw  showed  that  the  electro-cfaemical 
equivalent  of  an  element  is  proportional  to  Its  chemical  equivalent.  The 
latter  is  equal  to  Its  combining  weleht,  and  not  to  atomic  weight  -*-  valencr, 
as  defined  by  Thompson,  Hospitaller,  and  others  who  have  copied  their 
tables.  For  example,  the  ferric  salt  is  an  exception  to  Thompson's  rule^  as 
are  sesqui-salts  in  general. 

EIiBCTBOI«YSIS. 

The  separation  of  a  chemical  compound  into  its  constituents  by  means  of 
an  electnc  current.  Faraday  gave  the  nomenclature  relating  to  electroly- 
sis. He  called  the  compound  to  be  decomposed  the  Electrolyte,  and  the  pro- 
cess Electrolysis.  The  plates  or  poles  of  the  battery  he  called  Electrodes. 
The  plate  where  the  greatest  pressure  exists  he  called  the  Anode,  and  the 
other  pole  the  Cathode.    The  products  of  deconipoaition  he  called  Ions. 

Lord  Rayleigh  found  that  a  current  of  one  ampere  will  deposit  0.017^ 
grain,  or  0.001118  gramme,  of  silver  per  second  on  one  of  the  plates  of  a  sil« 
ver  voltameter,  the  liquid  eniployea  being  a  solution  of  silver  nitrate  con- 
taining from  15^  to  'J0%  of  the  salt. 

The  weight  of  hydrogen  similarly  set  free  by  a  current  of  one  ampere  is 
.00001038  gramme  per  second. 

Knowing  the  amount  of  hydrogen  thus  set  free,  and  the  chemical  equiva- 


ELECTROLYSIS.  1057 

lents  of  the  constituents  of  other  substances,  we  can  calculate  what  wetrht 
of  their  elements  will  be  set  free  or  deposited  in  a  given  time  bj  a  given 
current. 

Thus  the  current  that  liberates  1  gramme  of  hydrogen  will  liberate  8 
g-rainmes  of  oxygen,  or  107.7  grammes  of  silver,  the  numbers  8  and  107.7 
being  the  chenifcal  equivalents  for  oxygen  and  silver  respectively. 

To  find  the  weight  of  metal  deposited  by  a  given  current  in  a  given  time, 
find  the  weight  of  hydrogen  liberated  by  the  given  current  in  the  given 
time,  and  multiply  by  the  chemical  equivalent  of  the  metal. 

Thus:  Weight  of  silver  deposited  in  10  seconds  by  a  current  of  10  amperes 
=  weight  of  hydrogen  liberated  per  second  X  number  seconds  X  curren* 
strength  X  107.7  =  .00001038  X  10  X  10  X  107.7  =  .11178  gramme. 

Weight  of  copper  deposited  in  1  hour  by  a  current  of  10  amperes  s 

.00001038  X  8800  X  10  X  81.6  =  11.77  grammes. 

Since  1  ampere  per  second  liberates  .00001068  gramme  of  hydrogen, 
strength  of  current  In  amperes 

weight  in  grammes  of  H.  liberated  per  second 
^  .00001088 

-     weight  of  element  liberated  per  second 
~  .00001038  X  chemical  equivalent  of  element' 

The  table  on  page  1067  (from  •'Practical  Electrical  Engineering '*)  is  cal- 
culated upon  Lord  Rayleigh's  determination  of  the  electro-chemical  equlva- 
lentit  and  Koscoe's  atomic  weights. 

KLECTRO-MAGIVETS. 

Vniim  of  Electro-mai^netle  Bfeasaremento. 

C.Q.B.  unit  of  force  =  1  dyne  s  1.01986  milligrammes  in  localities  in  which 
the  acceleration  due  to  gravity  is  981  centimetres,  or  83.185  feet,  per  second. 

CCS.  unit  of  energy  =  1  erg  =  energy  required  to  overcome  the  resist* 
ance  of  1  dyne  at  a  speed  of  1  centimetre  per  second.    1  watt  =  10'  ergs. 

Unit  magnetism  =  that  amount  of  magnetic  matter  which,  If  ooncentrated 
In  a  point,  will  repel  an  equal  amount  of  magnetic  matter  concentrated  la 
another  point  one  centimetre  distant  with  the  force  of  one  dyne. 

Unit  strength  of  field  s=  that  flow  of  magnetic  lines  which  will  exert  unit 
mechanical  force  upon  unit  pole,  or  a  density  of  1  line  per  square  centi- 
metre. 

The  following  deflnitlons  of  practical  units  of  the  magnetic  circuit  are 
given  In  Houston  and  Kennelly*s  **  Electrical  Engineering  Leaflets.** 

OUbert,  the  unit  of  magneto-motive  force;  such  a  H.M.F.as  would  be 

produced  by  —  or  0.7968  ampere-turn. 

If  an  air-core  solenoid  or  hollow  anchor-ring  were  wound  with  100  turns 
of  Insulated  wire  carrying  a  current  of  6  amperes,  the  M.M.F.  exerted  would 
be  500  ampere-turns  =  628.5  gilberts. 

Weber,  the  unit  of  magnetic  flux;  the  flux  due  to  unit  M.M.F.  when  the 
reluctance  Is  one  oersted. 

GauM,  the  unit  of  magnetic  flux-density,  or  one  weber  per  normal  square 
centimetre. 

The  flux-density  of  the  earth*s  magnetic  field  in  the  neighborhood  of 
New  Torlc  Is  about  0.6  gauss,  directed  downwards  at  an  inclination  of  about 
72«. 

Oerxtedy  the  unit  of  magnetic  reluctance;  the  reluctance  of  a  cubic  centi- 
metre of  an  alrpump  vacuum. 

Reluctance  is  that  quantity  In  &  magnetic  circuit  which  limits  the  flux 
under  a  given  M.M.F.  It  corresponds  to  the  resistance  in  the  electric  cir- 
cuit. 

The  relucfMty  of  any  medium  Is  its  speclflc  reluctance,  and  In  the  C.G.S. 
system  Is  the  reluctance  offered  by  a  cubic  centimetre  of  the  body  between 
opposed  parallel  faces.  The  reluctivity  of  nearly  all  substances,  other  than 
the  magnetic  merals.  is  sensibly  that  of  vacuum,  is  equal  to  unity,  and  19 
independent  of  the  flux  density. 

Pei-m^ability  la  the  reciprocal  of  magnetic  reluctlTlty. 


1058  ELECTUICAL    ENGINEEiaXG. 

The  fundamental  equation  of  the  mag^netic  circuit  is 

Weber.  =  55!^, 
oersteds 

or,  mafcnetic  flux  =  inaflrDeto-mottve  force  •♦>  mai^etlc  reluetaiios. 

From  this  equation  we  have 

Gilberts  =  webers  X  oersteds;  oersteds  =  gilberts  -»-  weber& 

There  are  therefore  two  ways  of  increasing  the  magnetic  flux:  1.  by  in* 
creasing  the  M.M.F.;  2.  by  decreasing  the  reluctance. 

Lines  and  Loops  of  Force*— In  discussing  magnetic  and  electrical 
phenomena  it  is  couTeniionally  assumed  that  the  attractions  and  repulsions 
as  shown  by  the  action  of  a  magnet  or  of  a  conductor  upon  iron  fllings  are 
due  to  **  lines  of  force  **  surrounding  the  magnet  or  conductor.  Tlie  "  num- 
ber of  lines  '*  Indicates  the  magnitude  of  the  forces  acting.  As  the  iron 
filings  arrange  themselves  in  concentric  circles,  we  may  assume  that  tbt; 
forces  may  be  represented  by  cloee  curves  or  **  I09PS  of  force."  The  follow, 
ing  assumptions  are  made  concerning  the  loops  of  force  in  a  conductive 
circuit: 

1.  That  the  lines  or  loops  of  force  in  the  conductor  are  parallel  to  tlie  axis 
of  the  conductor. 

8.  That  the  loops  of  force  external  to  the  conductor  are  proportional  in 
number  to  the  current  in  the  conductor,  that  is,  a  definite  current  generates 
a  definite  number  of  loops  of  force.  These  may  be  stated  as  the  strength  of 
field  in  proportion  to  the  current. 

8.  That  the  radii  of  the  loops  of  force  are  at  right  angles  to  tlie  axis  of 
the  conductor. 

The  magnetic  force  proceeding  from  a  point  is  equal  at  all  points  on  the 
surface  of  an  imaginary  sphere  described  by  a  given  radius  about  that 
point.  A  sphere  of  radius  1  cm.  has  a  surface  of  4v  square  centimetres.  If 
T  =  total  field  strength,  expressed  as  the  number  of  lines  of  force  emanat- 
ing from  a  pole  containing  if  units  of  magnetic  matter, 

F=iwM;    M^iF-t-iw. 

Hagnetio  moment  of  a  magnet  =  product  of  strength  of  pole  Jf  and  its 

length,  or  distance  between  its  poles  L,    Magnetic  moment  ss  — . 

If  £  s  number  of  lines  flowing  through  each  square  centimetre  of  cross- 
section  of  a  bar-magnet,  or  the  "  specific  induction,"  and  A  =  cross  section, 

LAB 
Magnetic  moment  s  — r — . 

If  the  bar-msgnet  be  suspended  in  a  magnetic  field  whose  Induction  is  H, 
and  so  placed  that  the  lines  of  the  field  are  all  horizontal  and  at  right  angles 
to  the  axis  of  the  bar,  the  north  pole  will  be  pulled  forward,  that  is,  in  the 
direction  in  which  the  lines  flow,  and  the  south  pole  will  be  pulled  in  the 
opposite  direction,  the  two  forces  producing  a  toreional  moment  or  torque, 

Torque  =  MLH  =  LABH  ■*■  4v,  in  dyneK»ntimetres. 

Magnetic  attraction  or  repulsion  emanating  from  a  point  varies  inTersely 
as  the  square  of  the  distance  from  that  point.  The  law  of  iuverae  squares, 
however,  is  not  true  when  the  magnetism  proceeds  from  a  surface  of  ap- 
preciable extent,  and  the  distances  are  small,  as  in  dynamo«lectnc 
machines.    (For  an  analogy  see  '*  Radiation  of  Heat,"  page  467.) 

Streni^li  of  an  Electro«ma|irnet«— In  an  electric  magnet  made  by 
coiling  a  current-carrying  conductor  around  a  core  of  soft  iron,  the  space 
in  which  the  looi>8  of  force  have  Influence  is  called  the  magnetic  field,  and 
it  is  convenient  to  assume  that  the  strength  of  the  field  Is  proportional  to 
the  number  of  loops  of  magnetic  force  surrounding  the  maf^net.  Under 
this  assumption,  if  we  take  a  given  current  passing  through  a  given  number 
of  conductor-turns,  the  number  of  magnetic  loops  will  depend  upon  the 
resistance  of  the  magnetic  circuit,  just  as  the  current  with  a  given  press- 
ure in  the  conductive  circuit  depends  upon  the  resistance  of  the  circuit. 

The  following  laws  express  the  most  important  principles  concerning 
electro-magnets : 

(1)  Tlie  magnetic  intensity  (strength)  of  an  electro-magnet  Is  nearly  pro- 
portional to  the  strength  of  the  magnetizing  current,  provided  the  core  is 
not  saturated. 


ELECTRO-MA.QNETS.  1059 

(2)  The  RiAgiietic  streng^th  ft  proportional  to  the  number  of  turns  of  wire 
in  the  msLfpieiitlne  coil;  that  is,  to  the  number  of  ampere  turns. 

(8)  The  ma^etic  strength  is  independent  of  the  thickness  or  material  of 
the  conducting  wires. 

These  laws  may  be  embraced  in  the  more  general  statement  that  the 
strength  of  an  electro -magnet,  the  size  of  the  magnet  being  the  same,  is 
proportional  to  the  number  of  its  ampere  turns. 

Porce  In  the  Gap  betureen  Tw^o  Poles  of  a  ]IIa«net.— If 
P  a  force  exerted  by  one  of  the  poles  upon  a  unit  pole  in  tlie  gap,  and  in  = 
density  of  lines  in  the  field  (that  is,  that  there  are  m  absolute  or  C.Q.8.  units 
on  each  square  centimetre  of  the  polar  surface  of  the  magnet),  the  polar 
surface  being  lar^e  relative  to  the  breadth  of  the  gap,  P  =  2vt}t.  The  total 
force  exerted  upon  the  unit  pole  by  both  north  and  south  poles  of  the 
magnet  is  2P  =  4vm,  in  dynes  =  £,  or  the  induction  in  lines  of  force  per 
square  centimetre.  It  S  =  number  of  square  centimetres  in  each  polar 
surface.  SB  =  total  flow  of  force,  or  field  strength  =  F;  Sni  =:  total  pote 
strength  =  A/,  spread  over  each  of  the  polar  suriaces.  We  then  have  F  = 
4ir3f,  as  before:  that  is,  the  total  field  is  4v  times  the  total  pole  strength. 

Total  attractive  force  between  the  two  opposing  poles  of  a  magnet,  when 
SJB* 
the  distance  apart  is  small,  =  —j—^  in  dynes. 
Oir 

This  formula  may  be  used  to  determine  the  lifting-power  of  an  electro- 
magnet,  thus: 

A  bent  magnet  provided  with  a  keeper  is  8  cm.  square  on  each  pole,  and 
the  induction  B  =  ^,000  lines  per  square  centimetre.    The  attractive  force 

D  X  20000^ 
of  each  limb  on  the  keeper  in  dynes  =   a^.  o  *a  »  or  ^  kilogrammes  for 

o  X  0.1* 

The  nacnetic  Circuit.— In  the  conductive  circuit  we  have  C  s  •^; 

is 

-,  ^       electro*motive  force        volts 

Current  =  ri =  -r • 

resistance  ohms 

In  the  magnetic  circuit  we  have 
Number  of  lines,  or  loops,  of  force,  or  magnetism 

Current  X  conductor  turns Ampere  turns 

Besistance  of  magnetic  circuit  "  Resistance  of  magnetic  circuit* 

Or,  in  the  new  notation,  webers  =  — — 7-^— • 

'  oersteds  ^ 

Let  2<r=  No.  of  lines  of  force,  Rm  =  total  magnetic  resistance.  At  a 
At 
ampere  turns,  then  N  =  -5—. 

The  magnetic  pressure  due  to  the  ampere  turns  =  ja^'^C  =  1.2672\!;^ 

,.         «      X                J   ^                            u           »T       ^^rC       1.267!rC 
where  r=  turns  and  C  =  amperes,  whence  i\r=  -^ —  =  — ^ . 

If  Rm  s=  total  magnetic  resistance,  and  Ra,  Ra,  Rf  the  magnetic  resist* 
ances  of  the  air-spaces,  the  armature,  and  the  field-magnets,  respectively, 

«»  =  iea  +  B^  +  R,;    and    y=^/g^j,^. 

Betermlnlnc  the  Polarity  of  Electro-macnets*— If  a  wire 
is  wound  around  a  magnet  in  a  right-handed  helix,  the  end  at  which  the 
current  flows  Into  the  helix  is  the  south  pole.  If  a  wire  is  wound  around  an 
ordinary  wood  screw,  and  the  current  flows  around  the  helix  in  the  direc- 
tion from  the  head  of  the  screw  to  the  point,  the  head  of  the  screw  is  the 
south  pole.  If  a  magnet  ia  held  so  that  the  south  pole  is  opposite  the  eye  of 
the  observer,  the  wire  being  wound  as  a  right-handed  helix  around  it,  the 
cm  rent  flows  in  a  right-handed  direction,  with  the  hands  of  a  clock. 


1060  ELECTRICAL  ENGIKEERIKa. 

BTNA]!IO-KI«B0TBI€  MACHINBS. 

There  aro  three  clamea  of  dynamo-electHo  machJoes,  viz,: 

1.  Qenerators,  for  the  conversion  of  mechanical  into  electrical  eneiK7. 

3.  Motors,  for  the  conversion  of  electrical  into  mechanical  energy. 
Generators  and  motors  are  both  subdivided  into  direct-current  and  alter- 

natine-current  machines. 

8.  Transformers,  for  the  conversion  of  one  character  or  voltage  of  current 
into  another^  as  direct  into  alternating:  or  alternating^  Into  direct,  or  from 
one  voltage  into  a  higher  or  lower  voltage^ 

Kinds  of  Djnaino-eleetrte  Klaeliliieft  as  regards  Mas* 
ner  of  Wln€llii|c»    (Houston's  Electi-ical  Dictionary.) 
\    1.  Dynamo-electnc  Machine.-^A.  machine  for  the  conversion  of  mechan- 
ical energy  into  electrical  energy  by  means  of  magneto-electric  Induction. 

2.  Compound-tcound  Dynamo.— The  fleld-magnets  are  excited  by  more 
than  one  circuit  of  coils  or  bv  more  than  a  single  electric  source. 

8.  Closed-coil  Dynamo.— Hh»  armature-colls  are  grouped  iu  sectionn  com* 
municating  with  successive  bars  of  a  collector,  so  as  to  be  connected  cod* 
tinuously  together  in  a  closed  circuit. 

4.  Open-coil  Dynamo.— Th^  armature-coils,  though  connected  to  the  suc- 
cessive bars  of  the  commutator,  are  not  connectedcontlnuously  in  a  closed 
circuit. 

6.  Separate-coil  Dynamo.— The  field-magnets  are  excited  by  means  of 
coils  on  tlie  armature  separate  and  distinct  from  those  which  furnish  cur^ 
rent  to  the  external  circuit. 

6.  Separately-excited  Dynamo. — ^The  field-magnet  colls  have  no  connec- 
tion with  the  armature-coils,  but  receive  their  current  from  a  separate 
machine  or  source. 

7.  Series-wound  Dynamo.— The  field-current  and  the  external  circuit  are 
connected  in  series  with  the  armature  circuit,  so  that  the  entire  armature 
current  must  pass  through  the  field-coils. 

Binee  in  a  series-wound  dynamo  the  armature-coils,  the  field,  and  the  ex- 
ternal-series circuit  are  in  series,  any  increase  in  the  resistance  of  the  ex- 
ternal circuit  will  decrease  the  electro- motive  force  from  the  decrease  in 
the  magnetizing  currents.  A  decrease  In  the  resistance  of  the  external  cir- 
cuit will,  in  a  like  manner,  increase  the  electro-moUve  force  from  the  in- 
crease in  the  magnetizing  current.  The  use  of  a  regulator  avoids  these 
changes  in  the  electro-mouve  force. 

8.  Series  and  Separat^y-excited  Oompound'Wound  Dynamo.— There  are 
two  separate  circuits  in  the  field-magnet  cores,  one  of  which  is  connected 
In  series  with  the  field-magnets  and  the  external  circuit,  and  the  other  with 
some  source  by  which  it  is  separately  excited. 

9.  Shiint-wound  Dynamo.— The  fleld-magnet  coils  are  placed  in  a  shunt 
to  tl^  armature  circuit,  so  that  only  a  portion  of  the  current  generated 
iMisses  through  the  field-magnet  coils,  but  all  the  difference  of  potential  of 
the  armature  acts  at  the  terminals  of  the  field-circuit. 

In  a  shunt-dynamo  machine  an  increase  in  the  resistance  of  the  external 
circuit  increases  the  electro-motive  force,  and  a  decrease  in  the  resistance 
of  the  external  circuit  decreases  the  electro-motive  force.  This  is  Just  the 
reverse  of  the  series-w^ound  dynamo. 

In  a  shunt-wound  djniamo  a  continuous  balancing  of  the  current  occurs. 
The  current  dividing  at  the  brushes  between  the  field  and  the  external  cir- 
cuit in  the  inverse  proportion  to  the  resistance  of  these  circuits,if  the  resist- 
ance of  the  external  circuit  becomes  greater,  a  proportionately  greater 
current  passes  through  the  field-magnets,  and  so  causes  the  electro-motive 
force  to  become  greater.  If,  on  the  contrary,  the  resistance  of  the  external 
circuit  decreases,  less  current  passes  through  the  field,  and  the  electro- 
mi^tive  force  is  proportionately  decreased. 

10.  Series- ana  Snunt-wouna  Compound-wound  Dynamo.— The  field-mag- 
nets are  wound  with  two  separate  coils,  one  of  which  is  in  series  with  Uie 
armature  and  the  external  circuit,  and  the  other  in  shunt  with  the  arma> 
ture.    This  is  usually  called  a  compotmd-wound  machine. 

11.  Shunt  and  Separately^exdted  Oompound'^UHmnd  Dyiumo,^Thb  field 
k  excited  both  by  means  of  a  shunt  to  the  armatmre  drcoit  and  hy  a  cm^ 
rent  produced  by  a  separate  source. 

Carrent  Generated  by  a  Dynamo-eleetrlo  niaclkiiie*— Unit 
current  in  the  C.G.S.  system  is  that  current  which,  fiowing  in  a  thin  wire 
forming  a  circle  of  one  centimetre  radius,  acts  upon  a  tmit  pole  placed  in 
the  centre  with  a  force  of  Sir  dynes.  One  tenth  of  this  unit  is  the  iinii  of 
ourrent  used  in  practice,  called  the  ampere. 


DYNAMO-ELECruiG   MAC1IIXE8.  1061 

A  wire  through  which  a  current  passes  has,  when  placed  in  a  magnetic 
JI«ld,  a  tendency  to  move  perpendicular  to  itself  and  at  rlrht  aneles  to  the 
lines  of  the  field.  The  force  producing  this  tendency  Is  P  =  IcB  dvnes,  in 
which  /  a  length  of  the  wire,  c  ss  the  current  In  C.O.8.  unttB,  and  B  the  tor 
ductioD  in  the  field  in  lines  per  square'oentimetre.    , 

If  the  current  C  Is  taken  m  amperes,  P  s  ICBIO^* 

If  Pji  Is  taken  In  kilogrammes, 

Pjt  =  ^^  =  10.1W7ZCB10-*  kilogrammes. 

SziMTLE.— The  mean  strength  of  field,  £,  of  a  dynamo  is  6000  O.G.8.  lines; 
a  current  of  100  amperes  flows  through  a  wire;  the  force  acts  upon  10  centi- 
metres  of  the  wire  rs  10.18S7  X  10  X  100  X  6000  X  10"  •=  .5007  kilogrammes. 

In  the  *'  English  "  or  Kapp's  system  of  measurement  a  total  flow  of  6000 
C.Q.8.  lines  is  taken  to  equal  one  English  line.  Calling  Bs  the  Induction  in 
English,  or  Kapp's,  lines  per  square  inch,  and  B  the  induction  in  O.O.S.  lines 
per  square  centimetre,  Bs=  o-t-  980.04;  and  taking  l"  in  inches  and  Pp  in 

pounds,  Pp  ss  681  (T'BflO'*  pounds. 

Torque  of  an  Ajnnatiii<e.~i)>  In  the  last  formula.^  the  force  tendhig 
to  move  one  wire  of  length  l'\  which  carries  a  current  of  C  amperes  through 
the  field  whose  induction  is  Bg  English  lines  per  square  inch.  The  current 
through  a  drum-armature  splits  at  the  commutator  into  two  branches, 


radius  of  the  armature  to  the  centre  of  the  couductors,  expressed  in  feet) 
then  the  torque  =  HPpir,  a  ^  X  531  X  Cl"Bjg  X  10"*  X  tr  foot^pouods  of 
moment,  or  pounds  acting  at  a  radius  of  1  foot. 

E:zAMPLB.>-Let  the  length  I  of  an  armature  a  20  In.,  the  radius  =  6  in.  or 
.5  ft.,  number  of  conductors  s  120,  of  which  <  a  80  are  under  the  influence 
of  the  two  pole- pieces  at  one  time,  the  average  Induction  or  magnetic  flux 
thrv-ugh  the  armature-fleld  ^j^  a  6  English  lines  per  square  inch,  and  the 
current  passing  through  the  armature  a  400  amperes;  then 

Torque  ■J4X681X400X«OX6x80X.5X  lO'*  =  424.8. 

The  work  done  in  one  revohition  a  tonne  X  circumference  of  adrde  el 
t  foot  radius  a  424.8  X  6j88  a  ^70  foot-pounds. 
Lei  the  roTolntions  per  minute  a  600,  then  the  horse-powcr 

^awoxeoQ^      ^ 

88000        -««»»^* 

Klectro-iiiotlTe  Force  of  tlie  Armature  01r«alt«— Ftom  the 

boree-power,  calculated  as  above,  together  with  the  amperes,  we  can  obtain 
the  KM.F.,  for  CE  a  H.P.  x  746,  whence  E.M.F.  or  £  a  R.p.  x  746  •«-  C. 

If  H.P.,  as  above,  a  40.5,  and  C  a  400,  S  a  ^^'^  ^^  «  75.6  volts. 

The  E.H.F.  may  also  be  calculated  more  directly  by  the  following  formuln 
given  bjr  Gisbert  Kapp: 

C  a  Total  current  through  armature;  c,  current  through  single  armature 

conductor; 
ea^  BJf .F.  in  armature  In  volts; 

r  s  Number  of  active  conductors  counted  all  around  armature; 

p  a  Number  of  pairs  of  poles  (p  a  1  in  a  two-pole  machine); 
n  a  Speed  in  revolutions  per  minute; 
^  a  Total  induction  in  C.G-S.  lines; 
Z  m  Total  induction  in  English  lines. 

.Jv5.io-«    K    ^ 

eO  r  f or  two-pcde 


Electro-motive 
force 


•„  «  pZntlO' 


P^gQ^O-*   1  for  mulUpolar  machines  with 
series-wound  armature. 


1Q63  BTiKCTniCAL  ENGINEERIXO. 


[  Knogramme-motTM  as  1.61B^yO10-*  >  for  two-pole  ma- 

l>oique -{   Foot-pounds m7MZrOlO'^      ^  chines. 

I   Kilogramme-metres  b  ZJiSFrcp  10~^®    I  for  multipolar  ma- 

I  Fbot-pounds =  14,10ZrcpiO'^    J  chines. 

&ZAMPLB.—r  =  190,  n  s  500,  length  of  armature  I  ss  80  in  ,  diameter 
d  =  1-2  in.,  cross-section  =  SO  x  12  =  S40  sq.  in..  Induction  per  sq.  in.  ^.s 
6  Unes  per  sq.  in.,  toUl  induction  ^  a  240  X  5  s  1:;»0;  then  ' 

E  =  .^mlO-«  s  laOO  X  120  X  500  X  10-«  s  7S  voitBL 

A  formula  for  horse-power  given  by  Kapp  is 

H.P.  =  1/746  ZmnW^^Ca 

«=  1A46  2a6miVifalO-«Cb. 

Cb  =  current  in  amperes,  n  =  revs,  per  rain.,  2ab  s=  8ecti<wal  area  of  an» 
atiire-core,  m  =  average  density  of  lines  per  sq.  in.  of  armature-core.  Nt  =s 
total  number  of  external  wires  counted  all  around  the  circumference,  t  =s 
numlier  of  wires  correspondirg  to  one  plate  in  the  commutator,  N  =  nuin> 
ber  of  plates,  Z  =  iabm  =  total  number  of  English  lines  of  force. 

Kapp  says  that  experience  has  shown  that  the  density  of  lines  m  in  ihe 
core  cannot  exceed  a  certain  limit,  which  is  reached  when  the  core  is  fiatii- 
rated  with  magnetism.  This  value  ia  reached  when  m  =  TO.  A  fair  a veragre 
▼alue  in  modern  dynamos  and  motors  is  m  ss  30,  and  (he  area  ab  must  b* 
taken  as  that  actually  filled  by  iron,  and  not  the  gro&s  area  of  the  core,  do 
Snglish  lines  per  sq.  in.  =  18,600  C.Q.S.  lines  per  square  centimetre.  Sil- 
vanus  P.  Thompson  says  it  is  not  advisable  in  continuoua^^urreut  machines 
to  push  the  nuignetization  further  than  B  s  17,000  C.G.S.  lines  per  square 
centimetre. 

Thompson  gives  as  a  rough  average  for  the  magnetic  field  in  the  gap-«:pace 
of  a  dynamo  or  motor  6900  lines  per  sq.  cm.,  or  40,000  lines  per  sq.  in.,  and 
the  drag  per  inch  of  conductor  .00354  lb.  for  each  ampere  of  current  carried. 

JJ    p     w   ao  QM 

Pounds  average  drag  per  conductor  =s        '^  ^^^  in  which  C  is  the 

number  of  conductors  around  the  armature. 

.  Streni^li.of  tlie  RKasnetlo  Field.— Kapp  gives  for  the  total  num- 
ber of  lines  of  force  (i^pp's  lines  s  O.Q.S.  lines  •+■  6000)  in  the  magnetic  dr- 

jr 
cuit.    Z  ss  =r — r-^ — r-s=»  Jtt  which  Z=s  number  of  magnetic  lines,  Jl  s  the 

iSo  +  KA  +  KF 

exciting  pressure  due  to  the  ampere  turns  =  AwTO^  Ra.  Ra,  and  Rf.  =  re- 
spectively the  resistances  of  the  air-spaces,  the  armature,  and  the  field-mate 

Kapp  gives  the  following  empirical  values  of  fio,  Ra^  and  Rp^  for  dynamos 
and  motors  made  of  well-annealed  wrought  iron,  with  a  permeabllitj  of  ^  a 
940: 

Ra^im^^    RA  =  ^;   Rr^^^i 

in  which  «  =  distance  across  the  span  between  armature<core  and  polar 
surface,  b  =  breadth  of  armature  measured  parallel  to  axis.  X  =  length  of 
arc  embraced  by  polar  surface,  so  that  Kb  =  the  polar  area  out  of  which 
magnetic  lines  issue,  a  =  radial  depth  of  armature-core,  so  that  ab  =  <!ec- 
tion  of  armature-core  (space  actually  occupied  by  iron  only  being  reckoned), 
AB  =  area  of  field-magnet  core,  I  =  length  of  magnetic  circuit  within  ar- 
mature, L—  length  of  magnetic  circuit  in  field  magnet;  all  dimensions  in 
inches  or  square  inches. 

0  8  JT 
For  cast-iron  magnets,  Z  s rrc — '-^ ^^ 

1800—  -\ — -  -I-  --- 
A6  ^  a&  ^  AB 

For  double  horse-shoe  magnets  of  wrought  iron, 
Z  ^    X  

«        1440''i  +  ~H  +  it' 


DTNAMO-ELKCTRIC   MACHINES.  1063 

^    ^       ,,  Z 0.8X 

and  of  cast  iron,  g   = ^~    ^ j^. 

Thme  formiiln  apply  only  to  cases  in  which  the  iDtensI^  of  maffoetintion 
is  not  too  fcrtfBt — Ray  up  to  10  Kapp*8  lines  per  square  Inch. 

Silvan  us  P.  Thompson  frfves  the  followinpr  method  of  calculatinf?  the 
Rtrenf^h  of  the  Held,  or  the  magnetic  flux,  J/F,  or  the  whole  number  of 
magnetic  lines  flowitif^  in  ttie  circuit  In  C-G.S.  lines: 

The  nia«:iietic  resistance  of  any  magnetic  conductor  Is  proportional  direct- 
ly to  its  length  and  invei-sely  to  Us  cross-section  and  its  permeability. 

HaKnetic  resistance  s=  -p ,  In  which  L  as  length  of  the  magnetic  circuit 

passing  through  any  piece  of  iron,  8  ss  section  of  the  magnetic  circuit 
passi-«g  through  any  piece  of  iron,  fi  s  permeability  of  that  piece  of  iron. 

Ill  a  dynamo-machine  in  which  the  reiHstances  are  three,  viz.:  1.  The  field* 
magnet  cores;  2.  The  armature-core;  3.  The  gape  or  alr-spacee  between 
them,— 

let  Lm,  .<?m,  fim  refer  to  the  field -magnet  part  of  the  drcuit; 
L<u,  Scat  tma  refer  to  the  air-space  part  of  the  circuit; 
£0,  <Sa,  Ma  refer  to  the  armature  part  of  the  circuit; 

the  lengths  across  each  of  the  air-spaces  being  LtUt  And  the  exposed  ana  oC 
polar  surface  at  either  pole  being  Saa, 

Total  magneUc  resistance  a  ~^  +  J^    +  ^^ 
lUgneCIo  flux,  or  total  mmiber  «»f  magnetio  Aiea^ « 

Lm      .       La»      .     Xg. ' 
Smy^m       ikiaiui$  "'"  Sofia 

3V9  B  turns  of  wlr<Hi,  ur  number  of  turns  in  the  spiral; 
C  =  current  in  amperes  passing  throuErh  spiral. 

AppUeatloii  to  Heaijgnlnfl:  of  Dynamosu  (S.  P.  Thompson.V- 
Suppose  in  designing  a  dynamo  it  Das  been  liecided  what  will  be  a  conven- 
ient speed,  how  many  conductors  shall  be  wound  upon  the  armature,  and 
what  quantity  of  magnetic  lines  there  must  be  in  the  field,  It  then  becomes 
necessary  to  calculate  the  sizes  of  the  iron  parts  and  the  quantity  of  excita- 
tion to  be  provided  for  by  the  fleldmagnet  coils.  It  i»eing  Icnown  what  MF 
is  to  be,  the  problem  Is  to  desitrn  the  machine  so  os  to  get  the  required 
value.  Experience  shows  that  In  every  type  of  dynamo  there  is  magnetio 
leakage;  also,  that  it  is  not  wise  to  push  the  saturation  of  the  armature-core 
to  more  than  16,000  lines  to  the  square  centimetre  at  the  most  highly  satu- 
rated part,  and  that  the  Induction  in  the  fleld-niagnet  ought  to  be  not 
greater  than  this,  even  allowing  for  leakage.  Leakage  may  amount  to  ^ 
of  the  whole:  hence,  if  the  magnet-cores  are  made  of  same  quality  of  iron 
as  the  armature -cores,  their  cruss-section  ought  to  be  at  least  5/4  as  great 
as  that  of  the  armature-core  at  its  narrowest  point.  If  the  field-magnets 
are  of  cast  iron,  the  section  ought  to  be  at  least  twice  as  gi-eat. 

Now.  Ha  (theliiduciion  in  the  armature-core)  =  Ma-*- 8a  (or  magnetic  flux 
through  armature  H- croK8-8eciin!ial  area  of  the  armature;  hence.  If  this 
is  flxed  at  1G,0(X)  Jines  per  centimeire  of  cross-sect  ion,  we  at  once  get  Sa  = 
Ma-*-Ba  This  Axes  the  cross- section  of  the  armature-core.  (Example:  K 
Ma  =s  4,000,000  of  lines,  then  there  must  be  a  cross-section  equal  to  '.itO 

,,       ^        -       4.000,000       ,^^ 
square  centimetres  for  -^z^^-  =  250.) 

IO,UUU 

Magnetic  Lenf/th  of  At-vuitiire  Circuit.— The  size  of  wires  on  the  arma- 
ture is  fixed  by  ihe  i:umber  of  amperes  which  it  nmst  carry  without  risk. 
Kememl>ering  that  only  lialf  th»^  current  (in  ring  or  drum  armatures)  passes 
ilirougli  any  one  coil,  and  as  the  number  is  supposed  to  have  been  fixed  be- 
forehand, this  practically  settles  tlie  quantity  of  copper  that  must  be  put  on 
the  armature,  and  experience  dictates  that  the  core  stiould  l>emade  so  large 
that  ttie  thicKness  of  tlie  external  winding  Ao^»  not  exceed  1/6  of  the  radial 
depth  of  tiie  iron  core.  Tills  settles  the  size  of  the  armature -core,  from 
which  an  estimate  of  /xx,  the  average  length  of  path  of  ttie  magnetic  lines 
in  the  core,  can  be  made. 


10U4  ELECTKICAL  BNGINEERINQ. 

Length  and  Section  or  Surface  Area  of  ^xr-«pac«.— Experience  farther 
dictates  the  requisite  clearance,  and  the  advantage  of  making  the  pole- 
pieces  subieud  an  arc  (in  two -pole  machines)  of  at  least  185*  each,  ao  as  to 
gain  a  larg^e  polar  area.    This  settles  Lom  and  Saa. 

Length  of  Field-magnet  Iron  Corea,  etc.—AA  shown  above,  the  minimum 
value  of  Sm  is  settled  by  leakage  and  materials;  Lm  therefore  remains  to 
be  decided.  It  is  clear  that  the  magnet-cores  must  be  long  enough  lo  allow 
of  the  requisite  magnetizing  coils,  but  should  not  be  longer.  As  a  rul«, 
they  are  made  so  stout,  especially  in  the  yoke  part,  that  they  do  not  add 
much  to  tiie  magnetic  resistance  of  the  circuit,  then  a  little  extra  iengUi  as 
sumed  in  the  calculation  does  not  matter  much.  It  now  only  remains  to 
calculate  the  number  of  ampere- turns  of  excitation  for  which  it  will  be 
needful  to  proTide. 

It  will  now  be  more  convenient  to  rewrite  the  formula  of  the  magnetic 
circuit  as  follows: 

Ja    -^    -1-2     ^^      I      ^    I 
A  X  Tmw  =  Jfo y;^ ; 

where  A  =  amperes  of  current  passing  through  the  fleld>mag*iet  coils; 
Tmw  =  total  turns  of  the  magnet  wire; 
X  =  leakage  coefficient  (say  5/4). 

Or,  aa  before, 

A  X  Tmw 


Jfa=  1.257 


kRm  ■{- Bos  +  Ra' 


where  Bm,  Ru,  Ra  stand  for  the  magnetic  resistance  of  magnets,  idr- 
space,  and  armature,  respectively. 

But  we  cannot  use  this  formula  yet,  because  the  values  of  t».  in  it  depend  on 
the  degree  of  saturation  of  the  iron  In  the  various  parts.  These  have  to  be 
found  from  the  Hopkinson  tables,  given  below;  and,  indeed,  it  is  preferable 
first  to  rearrange  the  formula  once  more,  by  dividing  it  Into  its  aeparaie 
members,  ascertaining  separately  the  ampere-turns  requisite  to  force  the 
required  number  of  magnetic  lines  through  the  separate  parts,  and  then 
add  them  together. 

1.  Ampere- turns  required  for  magnet-cores  =  K  ^  X  —-*'  1.257. 

8.  Ampere -turns  required  for  air-spaces        =  —^  X  2-^  -i- 1 .857. 

a.  Ampere-turns  required  for  armature-core  =  -^  X  ~  -•♦  1 .257. 

Now  A^  is  the  value  of  B  in  the  magnet-cores,  and  reference  to  the  taUt 

of  permeability  will  show  what  the  corresdonding  value  of  ttm  must  be. 

Bimilarly,-^^  will  afford  a  clue  to  |ia.    When  the  total  number  of  ampere- 

lurns  to  be  allowed  for  is  thus  ascertained,  the  sise  and  length  of  wire  will 
be  determined  bv  the  permissible  rise  of  temperature,  and  the  mode  of 
exciting  the  fleld-magnets,  whether  in  series,  or  as  a  shunt  machine,  or 
with  a  compound-winding. 

PermeabllltF*— Materials  differ  in  regard  to  the  resistance  they  offer 
to  the  paKsage  of  lines  of  force;  thus  iron  is  more  permeable  thac  air.  The 
permeability  of  a  substance  is  expressed  by  a  coefficient  fuwhicli  denottm 
Its  relation  to  the  permeability  of  air,  which  is  taken  as  1.  It  H  =  nunibei 
of  magnetic  lines  per  squai-e  centimetre  which  will  pass  through  an  ai-^- 
space  between  the  poles  uf  a  magnet,  and  B  the  number  of  lines  which  will 
pass  through  a  certain  piece  of  Iron  in  that  space,  then  fi  s=  B  -*-  H.  The 
permeability  varies  with  the  quality  of  the  iron,  and  the  degi*ee  of  satiirs- 
tion,  reaching  a  practical  limit  for  soft  wrought  iron  when  B  s  about  18,0X1 
and  for  cast  Iron  when  B  =  about  10^000  C.G.S.  lines  per  aquare  o^atUn^tre. 


DYKAMO-ELBCTRIC  MACHINES. 


10C5 


The  foUowingr  values  are  given  by  Thompson  as 

calculated  from  Hopkin- 

■on*^B  expeiiments: 

Annealed  Wrought  Iron. 

Gray  Cast  Iron. 

B 

^ 

M 

B 

H 

M 

5,000 

8 

3,600 

4,000 

6 

800 

g.ooo 

4 

8,850 

'^^Sffi 

10 

600 

10,000 

5 

8,000 

6,000 

81.5 

879 

11,000 

6.5 

1,688 

"^'SK 

48 

188 

12,000 

8.6 

1.418 

8,000 

80 

100 

18,000 

18 

1,088 

*'SJ2 

187 

71 

14,000 

17 

888 

10,000 

188 

58 

16,000 

88.5 

686 

11,000 

898 

87 

16,000 

68 

806 

17,000 

105 

161 

18,000 

800 

90 

19.000 

890 

54 

PermUolble  Amp«ra«e  and  PermlMlble  I>eplh  of  Wind- 
Ins  for  Mmsnets  wllli  CoUon-coTered  l¥lre«— Walter  S.  Dix 
{ELShioineer^Veo.  81, 1892)  given  the  foUowing  formula: 


w 


TXL 
V      M 

where  C  =  current; 

W  =  emissirity  In  watts  per  square  Inch; 
ODmf  =  ohms  per  mil -foot ; 
M  =  circular  mils  ; 
T  =  turns  per  linear  inch : 
L  =  number  of  layers  in  depth. 
The  emisslvity  Is  taken  at  .4  watt  per  sq.  in.  for  stationary  magnets  for  a 
rise  of  temperature  of  85°  C.  (68°  F.).    For  armatures,  according  to  Esson^s 
experiments,  it  is  approximately  correct  to  say  that  .9  watt  per  sq.  in.  will 
be  dissipated  for  a  rise  of  85°  C. 

The  Insulation  allowed  is  .007  inch  on  No.  0  to  No.  11  B.  &  S.;  .005  inch 
on  No.  12  to  No.  84  ;  and  .0045  inch  on  No.  85  to  No.  81  single  ;  twice  these 
values  for  insulation  of  double-covered  wires.  Fifteen  per  cent  is  allowed 
for  imbedding  of  the  wires. 

Formnln  of  Efllctency  of  JBjwtmnkom* 

CS.  P.  Thompson  in  "  Munro  and  Jamleson's  Pocket-Book.") 

Dotal  Electrical  Energy  (per  second)  of  any  dynamo  (expreesed  in  watts) 
is  the  product  of  the  whole  E.M.F.  generated  by  armature-colls  into  the 
whole  current  whichpAAses  throusrh  the  armature. 

UaefiU  Electrical  llnergy  (per  second),  or  useful  output  of  the  machine,  Is 
the  product  of  the  useful  part  of  the  E.M.F.  (I.e.,  that  part  which  is  avail- 
able at  the  terminals  of  the  machine)  Into  the  useful  part  of  the  current 
(I.e.,  that  part  of  the  current  which  flows  from  the  terminals  Into  the  exter- 
nal circuity. 

Economic  Coefficient  or  "  electrical  efficiency  "  of  a  dynamo  Is  the  ratio 
of  the  useful  energy  to  the  total  energy. 

Commercial  Efficiency  of  a  dynamo  is  the  ratio  of  the  useful  energy  or 
output  to  the  power  actually  absorbed  by  the  machine  in  being  driven. 

Let  Ea  =  total  E.M.F.  generated  in  armature; 
JSe  =s  useful  E.M.F.  available  at  terminals; 
Ca  =  total  current  generated  in  armature; 
Cg  rz.  current  sent  round  sliunt-coiis; 
C«  s  useful  current  supplied  to  external  circuit; 
Etk  =  resistance  of  armature-coils; 
Em  s  resistance  of  magnet-coils  in  main  circuit  (teriet); 
R%  =  resistance  of  magnet-cotls  in  shunt; 
tu  s  resistanoe  of  external  circuit  (lamps,  mains,  etoJx 


1066 


BLECTUICAL  EKGINEEKIKO. 


Wa  =  Watts  EORt  in  armature; 
Wm=  Watts  lost  ill  magnet-coils; 
Vt  =  lost  volts; 

Te  =  total  electrical  energy  (per  second); 
Ue  =  us4*fiil  electiical  output; 

c  =  economic  coefflclent; 

p  =  commercial  efflciency  (percentage). 

When  only  one  circuit  (series  machine)  C«  =  C«. 

In  shunt  machines  Cs  should  not  be  more  than  bjC  ot  Ck.  Also, 
C  =  C#  4-  C: 

In  all  dynamos,  Ra  ought  to  be  less  than  1/40  as  great  as  the  workini; 
value  of  K«. 

In  series  (and  compound)  machines,  Rm  should  be  not  greater  than  R^ 
and  preferably  only  %  as  great. 

In  shunt  (and  compound)  machines,  Ra  should  be  not  less  than  300  times 
as  great  as  Jia  and  preferably  1000  to  1200  times  as  great. 


Series  Machine. 

Shunt  Machine. 

w. 

C2K. 

ClRa 

^m 

Cl^m 

ClR,=Bl^R, 

Vl 

CaRa 

CA 

T. 

KCa  = 

KC.= 

C^(K.+  i?,„  +  /?e) 

rir  1  ''•''' ^ 

"^rVJ 

V, 

E.C.^CIR, 

E,C,=  CIR, 

e 

E                 R, 

CIR, 

K      ^«+«»+i?. 

ClRe-hClRa+ClR^ 

P 

lOOxB^C^-H 

(n.P.X748) 

lOOX^e^e-* 

(H.P.X746) 

N.B.  Horse-potver 
is  converted    into 
wrJbts  (so  as  to  com- 
pare with  electric 
output  of  the  ma- 
chine) by  multiply- 
ing by  746. 

♦This  will  be  a 
tnazimurn  when  Re 
in  a  mean  propor- 
tional between  Rm 
and  R„, 

Cooopound  Machine 
(Sliort  Shunt). 


CIR^+CJR, 


100x£;Ce-KH.P.x74<0 


In  well-constructed  com- 
pound machines  the  difTer- 
ence  between  **  short  shunt** 
and  *'  long  shunt'*  is  very 
slight,  as  An  is  so  small. 


Alternatlnfl:  Cnrrentii,  IVInlUpliaae  Currents,  Tranv- 
formers,  etc.— The  proper  discussion  of  these  subjects  would  take  niort» 
space  than  cnn  be  atTordeti  in  this  work.  Consult  S.  P.  Thompsou''s  **  Dy- 
namo-Electric Machinery,"  Bedell  and  Crehore  on  **  Alternating  Currents.'' 
Fleming  on  "  Alternating  Currents,"  and  Kappon  **  Dynamos,  Alternators 
and  Transformers.'* 

The  Blectric  Motor.— The  electric  motor  Is  the  same  machine  as 
the  (lynamo,  but  with  the  nature  of  its  operation  reversed.  In  the  dynamo 
mechanical  energy,  such  as  'rom  a  belt,  is  converted  into  electric  current; 
in  the  motor  the  current  entering  the  machine  is  converted  into  mechanical 
energy,  which  may  be  taken  off  by  a  lielt.  The  difference  in  the  action  of 
the  machine  as  a  dynamo  and  ns  a  motor  is  thus  explained  by  Prof.  P.  B 
Crocker,  (Cassier'a  Mag,,  March,  1895): 


DYKAMO-ELECTUIC   MACUINES. 


1067 


In  tho  case  of  the  dynamo  there  exists  only  one  E.M.F.,  whereas  In  the 
motor  there  miist  always  be  two. 

One  kilowatt  dynamo,  C  ^  E  -^  R\  10  amperes  =  100  volts  -*- 10  ohms. 


One  kilowatt  motor,  C  s 


«i 


-;  10  amperes  = 


100  volts  -  00  volts 
1  ohm 


CIs  the  current:  B,  the  direct  E.M.F.;  e.  the  counter  E.M.F.;  R.  ihe  total 
resiaiancH  of  the  circuit;  /?,,  the  resiRtance  of  the  armature.  The  current 
and  diivct  E.M.F'.  are  the  same  in  the  two  caaet«,  but  the  repistanoe  is  only 
one  tenth  as  much  in  the  case  of  the  motor,  the  difference  being  replaced 
by  the  counter  E.M.F. ,  which  acts  like  resistance  to  reduce  the  current.  In 
the  case  of  the  motor  the  counter  E.M.F.  represents  the  amount  of  the 
eleclrical  energy  converted  into  mechanical  energy.  The  so-called  electri- 
cal efficiency  or  conversion  factor  =  counter  E.M.r.  -♦-  direct  E.M.F.  The 
actual  or  commercial  efficiency  Is  son^ewhat  less  than  this,  owing  to  fric- 
tion, Foucault  currents,  and  hvsteresis. 

For  full  di5)cu8sioDs  of  the  theory  and  practice  of  electric  motors  see  S. 
P.  Thompson's  "Dynamo-Electric  Machinery,"  Kapp's  "  Electiic  Trens- 
mission  of  Energy,^^  Martin  and  Wetzler's  *'The  Electric  Motor  and  its 
Applications,'*  Cox's  **  Continuous  Current  Dynamos  and  Motors,"  and 
Crocker  and  Wheeler's  "Practical  Management  of  Dynamos  and  Motors." 

STANDARD  BBI.TED  MOTORS  AND  GENERATORS. 

(Crocker-Wheeler  Electric  Co.,  1808.) 


Otitput* 

Effl- 

Onl»yn  [limen- 
BinuH  in  hticlif^. 

Si»e  rif 

.. 

. . — — 

— 

citftjcy. 

* 

Nut  Oyer 

All. 

Pulley. 

0 

_* 

1 

Motor.    ' 

Dynamo. 

1 

i 

►1 

J 

i 

1 

[ 

i 

1 

1 

p: 

i 

^ 

i^ 

1 

2*^ 

S«5 

400 

aoo 

4rrfi88 

99 

.wnoo 

133 

7.t»i 

^^ 

38 

;}o 

45 

Vifi 

1,V> 

4tiU 

lSO 

IWK5 

V> 

11300 

^ 

tViH 

07 

ia 

!!3 

49 

%m 

100 

ttW 

WJ 

GTiiiHS 

'."i-i 

11000 

W^i 

B144 

iEJ 

lU 

45 

Ih 

7S 

1V.'5 

GO 

(;;:.  im 

•^■^ 

o.'yoo 

fi'JJi 

<fl>t 

1!0 

U 

4& 

SO 

ha 

n.vi 

Art 

70(1  ^'J 

yikt 

4:xn) 

61^ 

4GL4 

J  J 

n 

J2 

45 

35 

31 

700 

:Jl.fi 

T.'H^  >s 

^.(1 

U*A) 

40U 

37V4 

IB 

1] 

ih 

ri 

i!fl 

::jO 

'j;.rj 

Hr-  Kit 

f^U 

"J40<1 

?« 

aa 

1« 

d 

45 

n 

ir. 

W)0 

vi 

etH'^^iV,  S8  " 

ir)io 

M 

3^^ 

SIM 

t1 

R 

15 

10 

'J 

10 

m) 

10 

TOiNUfCj  ' 

K7 

fWO 

S0M 

^]h 

Q 

r 

45 

'H 

S 

"^j 

am 

7.& 

lOWlKS 

m 

7«0 

as 

» 

0 

4.5 

5 

b 

u-yj 

r> 

1100  83 

85 

510 

esM 

ml 

7 

B 

15 

S 

3 

?1 

aTft 

s 

nr'iBa 

^H 

410^ 

^ 
^ji 

1^4ft 

ft 

<^4 

t5 

s 

'3 

*I 

Iixm 

2 

vsm ;.% 

8i 

38B 

15*4 

s 

1 

45 

1 

't 

1 

tOOQ 

1 

13<X)TG 

HI 

306 

itrk 

1ft 

nu 

4 

HU. 

45 

H 

<j 

n 

IJUl) 

.ri 

iik'K> 

07 

;^ 

lOO 

l^*i 

10 

s 

!J  ^ 

45 

H 

2 

i;^7J5 

;i5 

tioi 

rnO 

73 

70 

la 

'^ 

^ 

3 

5i^j 

45 

1  II 

12 

1% 

leoi 

JJ 

;MX> 

55     |{{J 

iJ7 

m 

G^j 

m 

I 

4$ 

APPENDIX. 


STRENGTH  OF  TIRIBER. 


S«f«  lioads  In  Tons,  Vnlformly  IHstrlbnted,  for  White- 
oak  Beams. 

(In  accordance  with  the  Building  Laws  of  Boston.) 

TT,  safe  load  in  tons  of  2000  lbs.;  P,  extreme 
flbre-stress  =  1000  lbs.  per  sq.  in.  for  white 
oak;  B^  breadth  in  inches;  A  depth  in  inches; 
!.,  distance  l;>etween  supports  in  inches. 


Formula  :  W  = 


4PBD* 


o  a 
cc 


2xfl 

2x  H 
2k  10 
2x  V* 
3%G 
3xH 
.3*10 
3xVi 
.3  X  H 

.3x  n 

4>r    '3 

4>  '  I 
4>   ■  ■ 

4>   !H 


iJifttancr 


r  Supports  itt  feet. 


O.fiT 
1,19 

1  &.'» 

uoo 

4  (MJ 
7,11 


..... 


to    11     le     14     Iti     16 


0  SOO 

1  39  ] 

y  (X)  3 

O.T5'0 
1.33|1 

2.0Sll 


l.iHM 


4.CKI 
r,.44 
7. It 
!t.00 


0.-16 
1  ni 

(iT|0.fl7 

lOi'J.l.Hi; 

.3(501  I«ls 
.aOti.M.fi 


J?l'''7i 


— r 

.  ss  n 

Otl3 
.33  ]. 

.hitO. 

&r.  1. 

.714 
.00  & 

I, 


au 


51  0 

14 
41 


TG 


0.^.-70.25 


l^jl 
71 

IllSf 

,0(Jrl 


0.44 
0.15S* 

1  m> 

0  37 

0  ^ 

1  CH 

1.50 

.*  ts 
1 .3U 

e.w 

.504 


0.400 
0H»  II 


JM     IV    SI     sa 


0.3,1 

or* 

ti.37 
i.j^ 

!  7fi 
4.00 


0.S4O. 
O.HJO. 
0,7«  0. 

,M'O.M  0. 
ft^:0,70  <> 
1, 


.'-^|1,H 

7-i  Kfifl 

,171  OG 

.^^'2  07 

.7Vi^.43]3 


0  44 
0,64 


0.« 
0.«7 

o.oe 

1.3[ 
1.71 
O.StJ 

aoM.sa 

W)  I  74 
47  [j!,^ 


le 


o.« 
o.ea 

0.41 

0.64 
0.93 
1,25 
1.64 
0.B5 

a,77 


For  other  kinds  of  wood  than  white  oalc  multiply  the  fl{;iire.s  in  the  table 
by  a  figure  selected  from  th«>8e  given  below  (whicn  represent  the  safe  stress 

f>er  square  inch  on  beams  of  different  kinds  of  wood  according  to  the  build- 
ng  laws  of  the  cities  named)  and  divide  by  1000. 


Hemlock. 

Spruce. 

White 
pine. 

Oak. 

Yellow 
Pine. 

New  York 

Boston 

.      800 

900 
750 

900 
750 
900 

1100 
lOOOt 
1080 

1100* 
1850 

Chicago 

1440 

*  Georgia  pine. 


t  White  oak. 


1069 


1070 


APPENDIX. 


MATHE9IATICS. 

Formula  for  Interpolation* 

^     ,   ,         iw     .  (n-1)(n-2)^        in. 


l)(n  -  2Kn  -  3) 


<*.+-. 


i.a        "'  '  1.2.3 

a,  =  the  first  term  of  the  series;  n,  number  of  the  required  terra;  o,,,  the 
required  term;  dj,  d^,  d^.  first  terms  of  successive  orders  of  difrerences 
between  ai,  09.  as,  a4.  successlTe  terms. 
Example.— Required  the  log  of  40.7,  logs  of  40,  41,  42,  43  being  given  as 

Termsai.rt,.  a„a4:    1.6081    1.6128    1.6232    1.6885 
1st  dlflTereiices:  .0107      .0104      .0108 

2d         "  -  .0003    -  .0001 

8d         "  +  .0002 

For  log.  40  n  =  1 ;  log  41  n  =  8;  log  40.7  n  =  1.7,  »  -  1  =  0.7.  n  —  8  =  -  0,3 
n  -  8  =  -  .1.3. 

(0.7)(  -0.3)(  -  .OOaS)   ,   (0.7)(  -  0.3)(  -  1.3X.0«g) 

6 


=  1.G021  -f  0.7(.0107)  4- 


.0003)   ^   (0.7)(. 


=  1.6021  4-  .00749  +  .000081  +  .000009  =  1.6096  +. 

maxima  and  Minima  ivlthout  the  Calculns,— In  the  equation 
y  =  a  4-  &x  4-  cx^,  in  which  a,  6,  and  c  are  constants,  either  positive  or  nt-f^- 
ative,  if  c  be  positive  2^  is  a  minimum  M'hen  ;r=-b-f-2c;ifcbe  negative  y 
is  a  maximum  when  x  =  -  b-i-2c.  In  the  equation  y  =  a-{-bx  -^  c/x,  y  is 
a  minimum  when  bx  s  c/x. 

Application.— The  cost  of  electrical  transmission  is  made  up  (1)  of  fixed 
charges,  such  as  superintendence,  repairs,  cost  of  poles,  etc.,  which  may  be 
represented  by  o;  (2)  of  interest  on  cost  of  the  wire,  which  varies  with  th<? 
sectional  area,  and  may  be  represented  by  bx;  and  (8)  of  cost  of  the  energy 
wasted  in  transmission,  which  varies  inversely  with  the  area  of  the  wire,  or 
c/x.  The  total  cost,  y  =  a  +  bx-\-  c/x,  is  a  minimum  when  item  2  =s  item 
8,  or  bx  =  c/x. 


RIVETKD  JOINTS. 

Preesore  Required  to  DriTe  Hot  RiTeta.— R.  D.  Wood  &  Co.. 

Philadelphia,  give  the  following  table  {Itm): 

Power  to  Drive  Rivets  Hot. 


Size. 

Girder- 

Tank- 

Boiler- 

Size. 

Girder. 

Tank- 

Boiler- 

work. 

work. 
tons. 

work. 

work. 

work. 

work. 

in. 

tons. 

tons. 

in. 

tons. 

tons. 

tons. 

9 

15 

20 

^H 

88 

60 

75 

TO 

12 

18 

25 

V/.. 

45 

70 

100 

u 

15 

22 

83 

^i 

60 

85 

185 

2i 

80 

45 

1^ 

75 

100 

150 

1 

30 

45 

60 

The  above  in  based  on  the  rivet  passing  through  only  two  thicknesses  cf 
plate  which  together  exceed  the  diameter  of  the  rivet  but  little,  if  any. 

As  the  plate  thiclcuess  increases  the  power  required  increases  approxi* 
mately  in  proportion  to  the  square  root  of  the  increase  of  thickness.  Thus, 
if  the  total  thickness  of  plate  is  four  limes  the  diameter  of  the  rivet,  we 
should  require  twice  the  power  given  above  in  order  to  thoroughly  fill  the 
rivet-holes  and  do  good  work.  Double  the  thickness  of  plate  would  increase 
the  necessary  power  about  40<. 

It  takes  about  four  or  five  times  as  much  power  to  drive  rivets  cold  as  to 
drive  them  hot.  Thus,  a  machiu«^  that  will  drive  94-in.  rivets  hot  will  usually 
drive  9^-in.  rivets  cold  (steel).  Baldwin  Locomotive  Works  drive  H-in.  soft- 
iron  rivets  cold  with  15  tons. 


HEATING   AND    VENTILATION. 


1071 


HEATING  AND  TENTIIiATION. 

Table  of  Capacities  for  Hot-blant  or  Pleniun  Heatlni; 
nrlth  Fans  or  Blowers. 


(Computed  by  F. 

R.  Stni,  American  plower  Co.»  Detroit, 

Mich.) 

i  . 

1 
1 

E 

d 

e 

K 

L 

55 

■5.5 

1^ 

2 

1= 

ill 

111 

III 

92 

a 

m 

X 

W 

4^  1 

360 

S>ii 

6>IQ 

4U\900 

1,021.01111 

0a> 

7.7 

1760 

590 

m 

4a 

aao 

a 

8.500 

QIO.OOO 

1,J35.0CO 

0.45 

Til 

90 

M 

saso 

4 

10,500 

0;i(>,000 

K,%50J»0 

\i.M 

mi 

100 

60 

S5a 

5 

la.MO 

Tao.ouu 

l,tH&.OCM) 

\\» 

'• 

1050 

tio 

m 

330 

0 

i5,H(:ii) 

&4fl,0lRJ 

B,a:)5.0tJ0 

i;.6--> 

ij£ea 

ii» 

7i 

i\Q 

S 

10,800 

laiw.ooo 

:i.tNJiJ,i)0O 

ai. 

1650 

MIT 

«4 

m 

10 

iWJ/JOO 

i,r,TV,i>oi> 

3.la7l>,000 

iiy.i 

2800 

m 

9.1 

150 

13 

a;i,ocw 

l,i>80.mi 

4,-H7i>.00a 

*;.7 

»7T0 

IHU 

lOH 

1^ 

L-i 

li.t^j 

u,4im,uw 

^jao.ouo 

46  a 

SIM 

SftP 

130 

1^ 

IB 

»Kgoo 

3.0(»;ttl0 

7.B7b.im 

&3.5 

4140 

1 

s 
I 

1 

i  -a 

o 

1 

■3 

1 
1 

'3 

~  3 

IB 

'it 

It* 

m 

St" 

if 

Hi 

1 

II 
U 

=  1 

1 

K 

1 
1 

ffl 

H 

P 

Hi 

m 

TO 

1J40 

WTtff 

nn 

2 

3^ 

fiiS 

Ifi 

R.700 

n,fl7 

8."J00 

Hi> 

a,  14  J 

l',w 

4 

>J 

4S 

fi*5 

IK 

IftJtX) 

la.oTi 

10,000 

(») 

S.fllO 

KWW 

4H  2^ 

fia 

ru5 

iTi 

la.t^TO 

11. T7* 

VJ.fiOO 

100 

a.t:rf> 

ISill 

5    1  -M 

ea 

iwri 

li" 

15,800 

17.55 

i&,noo 

iiui    ajrri 

2m 

r^H  3 

HO 

IL-OO 

a4 

iy,wo 

saj.t'O 

1H,UU0 

laol    i3w 

;.n»!X) 

tj      » 

100 

IMKJ 

M 

ai.oof) 

27  MO 

S3,H00 

140       M^i 

!191W 

T       a^j 

1:^ 

muri 

^,7 

,aajt)o 

ric  M« 

?^1,400 

ItU} 

H.ajO 

rrf)-:!i 

8       4 

1G7 

^£>(I5 

73 

4L700 

40.30 

att.eo'i 

ISO 

10,4TO 

Ot^Tj 

0       414     'Jll 

31  OS 

90 

fi!,>,iW)U 

f>»  40 

&0,fHll 

i.W 

J  J. 

tM 

7 

*&J 

]i:> 

5 

1 

tf5U 

r,f^ 

liJH 

( 

ia/joo 

70.**:i 

60,G0a 

Temp«'rature  <»f  fresh  air,  0" ;  of  air  from  coils,  ISO";  of  steam,  227".  Pres- 
sure of  Kteam,  5  lbs. 

Peripheral  velocitv  of  fan-tips,  4000  ft.:  number  of  pipes  deep  In  coil,  24; 
depth  of  coil,  60  inches;  area  of  coils  approximately  twice  free  area. 

TTATER-WHEEIiS. 

IVater-poiirer  Plants  Operating  nnder  Hlffh  Pressores.— 

The  followiiijf  notes  are  contributed  by  ihe  Peiton  Water  Wheel  Co.: 

The  C«)nsolidatt=d  Virfrfnia  &  C<>l.  Mining  Co.,  Virjflnia,  Nev..  has  a  3  ft. 
8teel-disl<  Peiton  wheel  operatin^under  2100  ft.  fall,  equal  to 011  lbs.  persq  in. 
It  runs  At  a  peripheral  velocity  of  10.804  ft.  per  minute  and  has  a  capacitv 
of  over  too  II. P.  The  rigidity  with  which  water  under  such  a  high  pressure 
as  this  leaves  th«  nozzle  U  shown  in  the  fact  that  it  is  Impossible  to  cut  the 


1072 


APPENDIX. 


stream  with  an  axe,  however  heary  the  blow,  as  it  will  rebound  just  as  it 
would  from  a  steel  rod  travelling  at  a  high  rate  of  speed. 

The  London  Hydraulic  Power  Ck>.  has  a  large  number  of  Pelton  wheels 
from  13  to  18  in.  diameter  running  under  pressure  of  about  1000  lbs.  per.  »q. 
in.  from  a  system  of  pressure-mains.  The  I8-in.  wheels  weighing 80  lbs.  hare 
a  capacity  of  over  20  H.P.    (See  Blaine's  *'  Hydraulic  Machmery.**) 

Hydraulic  Power-hoist  of  Milwaukee  Mining  Co  ,  Idaho.— One  cage  travels 
up  as  the  other  descends;  the  maximum  load  of  5500  lbs.  at  a  speed  of  409 
ft.  per  min.  is  carried  by  one  of  a  pair  of  Pelton  wheels  (one  for  each  cage). 
Wheels  are  started  and  stopped  by  opening  and  closing  a  small  bydrauHe 
valve  at  the  engineer's  stand  which  operates  the  larger  valves  by  hydraulic 
pressure.  An  air-chamber  takes  up  the  shock  that  would  otherwise  occur 
on  the  pipe  line  under  the  pressure  due  to  860  ft.  fall. 

The  Mannesmann  Cycle  Tube  Works,  North  Adams,  Mass.,  are  using  four 
Pelton  wheels,  having  a  fly-wheel  rim,  under  a  pump  pressure  of  600  lbs.  per 
sq.  in.  These  wheels  are  direct-connected  to  the  rolls  through  which  the 
ingots  are  passed  for  drawing  out  seamless  tubing. 

The  Alaska  Gold  Mining  Co..  Douglass  Island,  Alaska,  has  a  S2-ft.  Pelton 
wheel  on  the  shaft  of  a  Riedler  duplex  compressor.  It  is  used  as  a  fly- 
wheel as  well,  weighing  25,000  lbs.— and  develops  600  H.P.  at  75  revolutions. 
A  valve  connected  to  the  pressure-chamber  stnrts  and  stops  the  wheel 
automatically,  thus  maintaining  the  pressure  in  theair-receiver. 

At  Pachuca  in  Mexico  five  fVelton  wheels  having  a  capacity  of  800  H.P. 
each  under  800  ft.  head  are  driving  an  electric  transmission  plant.  These 
wheels  weigh  less  than  600  lbs.  each,  showing  over  a  horse-power  per  pound 
of  metal. 

FormnUe  for  Calculating  the  Po'wer  of  Jet  DTater- 
^rlieels.  such  as  the  Pelton  (F.  JC  Blue).— HP  =  horse-power  dt-livered; 
a  =  62.86  lbs.  per  cu.  ft.;  E=  eflBclency  of  turbine;  q  =  quantity  of  water, 
cubic  feet  per  minute;  h  =  feet  effective  head;  d  =  inches  diameter  of  jet; 
p  =  pounds  per  square  inch  effective  head;  c  =  coefficient  of  discharge  from 
nozzle,  which  may  be  ordinarily  taken  at  0.9. 


HP: 


S=-«»«»«9'^  = 


.00486J5'qrp  =.00496£ic<f*  VA»  =  .0174£W»  i'p*. 


q  =     529.2  J^  =  229—  =  S.62ccn   VH  =  8.90cd«  ^p. 


d«  = 


Eh 
Ec  Vh* 


Ep 


HP 


=  57.4 ~  =  .881 

EcVp* 


=  .25- 


cVh  cVp 


GAS  FUEL. 


ATera^e  Volumetric  Compoaitlon*  EnereT*  etc.*  of  'Vwkjrf' 
oua  Gaaes.    (Contribut<?d  by  R.  D.  Wood  &  Co.,  PhiladHlphia;  IW.) 


Natural 
Qas. 

Coal- 
gas. 

Water- 
gas. 

Producer-ga.s. 

Air. 

Anthra. 

Bitum. 

CO 

0.50 
2.18 
92.6 
0.81 
0.26 
3.61 
0.34 

6.0 
46.0 
40.0 

4.0 

0.5 

1.5 

0.6 

1.5 
32.0 
735,000 

5 

45.0 
45.0 
2.0 

27.0 

12.0 

1.2 

27.0 
12.0 
2.5 
0.4 
9.5 
55.8 
0.8 

H    

CH. 

c.iL 

O 

Vapor 

4.0 
2.0 
0.5 
1.5 
45.6 
322,000 

25 

2.5 
57.0 
0.8 

trace 

79 
2t 
trace 

Lbs.  in  1000  cu.  ft.. 

H.  U.  in  1000  cu.  ft. 

Cu.f  t.  from  each  lb. 

of  coal  approx... 

45.6 
1.100,000 

65.6 
137,455 

85 

65.9 
156,917* 

75 

76.1 
200t 

*  The  real  enerery  of  bituminous  produces^gas  when  used  hot  ia  far  io 
excess  of  that  indicated  by  the  above  table,  on  account  of  the  hydrocarbonjs 
which  do  not  show,  as  they  are  condensed  in  the  act  of  collecting  the  gas 
for  analysis.  In  actual  practice  there  is  found  to  be  about  bQ%  more  effective 
energy  in  bituminous  gas  than  in  anthracite  gas  when  used  hot  enough  te 
prevent  condensation  In  the  flues. 

t  Cubic  feet  of  air  requhred  to  bum  1  lb.  ot  coal  with  \ 


STEA-M-BOlLEftS.  1073 

STEAM-BOILEBS. 

Steam-boiler  Const ruetlon.  (Extract  from  the  Rules  and  Speol- 
teatious  of  tlie  Hartford  Steam  Boiler  Inspection  &  Insurance  Co.,  1896.) 

Cylindrical  boiler  shells  of  Are  box  steel,  and  tube-beads  of  best  iSaoge 
(t  eel.    Limits  of  tensile  strength  between  55,000  and  6*<i,000  lbs.  per  sq.  in. 

Iron  rivets  in  steel  plates,  3H,uuu  lbs.  shearing  strength  per  sq.  in.  in 
liugle  shear,  and  fiBjf  more,  or  70.300  lbs.,  in  double  Hhear. 

Each  shell-plate  must  bear  a  test-coupon  which  shall  be  sheared  off 
ind  tested.  Each  coupon  must  fulfil  the  above  requirements  as  to  tensile 
(trength,  but  must  have  a  contraction  of  area  of  not  less  than  56%  and 
in  elongation  of  26)C  In  a  length  of  8  in.  It  must  also  stand  bending  180® 
when  cold,  when  red  hot,  and  after  being  heated  red  hot  and  quenched  in 
;old  water,  without  fracture  on  outside  of  bent  portion. 

Crow-foot  bituses  are  required  for  boiler-heads  without  welds,  and  if  of 
ron  limit  the  strain  to  7600  lbs.  per  sq.  in.,  and  stay-bolts  must  not  be  sub- 
jected to  a  greater  strain  than  6000  lbs.  per  sq.  in. 

The  thickness  of  double  butt-straps  6/10  the  thickness  of  plates.  In  lap- 
joints  the  distance  between  the  rows  of  rivets  is 9^  the  pitch.  In  double- 
'iveted  lap-joints  of  plates  up  to  ^  in.  thick  the  efficiency  is  70;(  and  in 
:riple-riveted  lap-joints  75^  of  the  solid  plate. 

In  triple-riveted  double-strapped  butt-seams  for  plates  from  ^iin.to}^  in. 
thick,  the  efficiency  ranges  from  88]t  to  86%  of  the  solid  plate. 

In  high-pressure  boilers  the  holes  are  required  to  be  drilled  in  place;  that 
is,  all  holes  may  be  punched  M  in.  less  tlian  full  size,  then  the  courses  are 
rolled  up,  tube-heads  and  joint-covering  plates  bolted  to  courses,  with  all 
tioles  together  perfectly  fair.  Then  the  rlveUholes  are  drilled  to  full  size, 
ELiid  when  completed  the  plates  are  taken  apart  and  the  burr  removed. 

The  rule  for  the  bursling.pressure  of  cylindrical  boiler-shells  is  the  follow- 
ing: Multiply  the  ultimate  tensile  strength  of  the  weakest  plate  in  the  shell 
by  its  thiclcness  in  inches  and  by  the  efficiency  of  the  joint,  and  divide  result 
by  the  semi-diameter  of  shell ;  the  quotient  is  the  bursting-pressure  per 
square  inch.  This  pressure  divided  by  the  factor  6  gives  the  allowable 
working  pressure. 

BOIIiKB  FEBDINO. 

OraTity  Boller-feedem.— If  a  closed  tank  be  placed  above  the 
level  of  the  water  in  a  boiler  and  the  tank  be  filled  or  partly  filled  with 
water,  then  on  shutting  off  the  supply  to  the  tank,  admitting  steam  from 
the  boiler  to  the  upper  part  of  the  tank,  so  as  to  equalize  the  steam -pressure 
in  the  boiler  and  in  the  lank,  and  opening  a  valve  in  a  pipe  leading  from  the 
tank  to  the  boiler  the  water  will  run  Into  the  boiler.  An  apparatus  of  this 
kind  may  be  nia<ie  to  work  with  practically  perfect  efficiency  as  a  boiler- 
feeder,  as  an  injector  does,  when  the  feed-supplv  is  at  ordinary  atmospheric 
temperature,  since  after  the  tank  is  emptied  of  water  and  the  valves  in  the 
pipe><  connecting  it  with  the  boiler  are  closed  the  condensation  of  the  steam 
remaining  in  the  tank  will  create  a  vacuum  which  will  lift  a  fresh  supply  of 
water  into  the  tank.  The  only  loss  of  enencT  la  the  cycle  of  operations  is 
the  radiation  from  the  tank  and  pipes,  which  may  be  made  very  small  by 
pi*oper  covering. 

NV  hen  the  feed-water  supply  Is  hot,  such  as  the  return  water  from  a  heat* 
ing  system,  the  gravity  apparatus  may  be  made  to  work  by  having  two 
receivers,  one  at  a  low  level,  which  receives  the  returns  or  other  feed-supply, 
and  the  other  at  a  point  above  the  boilers.  A  partial  vacuum  being  created 
in  the  upper  tank,  steam-pressure  is  applied  above  the  water  in  the  lower 
tank  by  which  it  is  elevated  Into  the  upper.  The  operation  of  such  a 
machine  may  be  made  automatic  by  suitable  arraneement  of  valves.  (Bee 
circular  of  the  Scott  Boiler  Feedor,  made  by  the  Q.  &  C.  Co.,  Chicago.) 

FKEB-WATBB  HBATBB8. 

Capacity  o    Feed-ivater  Heatera*— The  following  extract  from 

a  letter  by  W.  R.  BillingH,  treasurer  of  the  Taunton  Locomotive  Manufactur- 
ng  Co.,  builders  of  the  Wain  w  right  feed- water  heater,  to  Eitgineering  Record^ 
February,  1898,  is  of  interest  in  showing  the  relation  of  the  heating  surface 
of  a  heater  to  the  work  done  by  it: 

*'  Closed  feed- water  heaters  are  seldom  provided  with  sufficient  surface  to 
raise  the  feed  temperature  to  more  than  200<>.    The  rate  of  heat  t 


Difference  between 
flnal  tempera-  ^ 
turesof  water  and 
&team 


hour  bv  each  sq.  ft 
of  surface  for  eacL 
decree  of  avera^^* 
difference  iu  temprr- 
attires. 


1074  APPENDIX. 

mission  mav  be  measured  by  the  number  of  British  thermal  units  which 
pass  through  a  square  foot  of  tubular  surface  in  one  hour  for  each  deere>* 
of  difference  in  temperature  between  the  water  and  the  steam.  The  uiffi- 
culties  wliich  attend  experiments  in  this  direction  can  only  be  appreciat<rd 
by  those  who  have  attempted  to  make  such  experiments.  Ceriatn  resuliJi 
have  been  reached,  however,  which  point  to  what  appears  to  be  a  reasonable 
conclusion.  One  set  of  experiments  made  ouite  recently  ^ave  certain  resulis 
which  may  be  set  fortli  in  the  table  herewith. 

ST 67  B.T.U.l  Transmitted     in     o» 

6«" 7»      ** 

8«»" 89      " 

ll"'' 114      " 

!.•)•" 1S»      *• 

.18«" 139      " 

"  In  other  wortls,  when  the  water  was  brought  to  within  5*  of  the  temp*»r 
ature  of  ihe  heating  medium,  heal  was  transmitted  through  the  t-ulies  aithf 
rate  of  67  B.T.U-  per  square  foot  for  each  degree  of  difference  in  temperanim*  I 
in  one  hour.  When  the  amount  of  water  flowing  through  the  heater  was  v)  I 
largely  increased  as  to  make  it  impossible  to  get  the  water  any  nearer  Ihaa 
within  I&*>  of  the  tem|)erature  of  the  steam,  the  heat  was  transmitted  at  th<" 
rate  of  13d  B.T.U.  per  sq.  ft.  of  surface  for  each  d^ree  of  difference  in 
temperature  in  one  hour.  Note  Iiere  that  even  with  the  rate  of  transmissi^vi 
as  low  as  67  B.T.U.  the  water  was  still  5**  from  the  temperature  of  the 
steam.  At  what  rate  would  the  heat  have  been  transmitted  if  the  watrr 
could  have  been  brought  to  within  2*'  of  the  temperature  of  the  steam,  or  to 
rilO*  when  the  steam  is  at  212«  ? 

'  'For  comnieraial  purposes  feed-water  heaters  are  given  a  H.P.  rating  which 
allows  about  one-third  of  a  square  foot  of  surface  per  H.P.— a  boiler  H.P. 
being  30  lbs.  of  water  per  hour.  If  the  flgures  given  in  the  table  above  are 
accepted  assubstautiaily  correct,  a  heater  which  is  to  raise  8000  lbs.  of  water 
per  hour  from  60<*  to  207*,  using  exhaust  steam  at  212*  as  a  heating  medium, 
should  have  nearly  84  sg.  ft.  of  heating  surface— that  Is,  a  100  H.P.  feed- water 
heater  which  is  to  mamtain  a  constant  temperature  of  not  less  than  iXf,", 
with  water  flowing  through  It  at  the  rate  of  8000  lbs.  per  hour,  should  hare 
nearly  a  square  foot  of  surface  per  H.P.  That  feed-water  heaters  do  not 
carry  this  amount  of  heating  surface  Is  well  known. ^^ 

THE  STBAM-ENGINE. 

Current  Practice  In  Enerlne  Proportions,  1897  (Compare 
pages  792  to  8i7.)— A  paper  with  this  title  by  Prof.  John  H.  Barr.  in  Trans. 
A.  8.  M.  E..  xviii.  787.  gives  the  results  of  an  examination  of  the  proportions  of 

¥arts  of  a  great  number  of  single-cylinder  engines  made  by  different  buildeni. 
he  engines  classed  as  low  speed  (L.  S.)  are  Corliss  or  other  lon^^-stroke 
engines  usually  making  not  more  than  100  or  125  revs,  per  min.  Those 
classed  as  high  "peed  (H.  S.)  have  a  stroke  generally  of  1  to  1^  diameters 
and  a  speed  of  200  to  300  revs,  per  min.  The  results  are  expressed  iu  for- 
mulas of  rational  form  with  empirical  coefficients,  and  are  here  abridged  as 
follows : 

Thickness  of  Shell,  L.  S.  only.— «  =  CD  +  B;  D  =  dlam.  of  piston  In  in.; 
B  =  0.8  in. ;  C  varies  from  0.4  to  0.6,  mean  =  0.5. 

Flanges  and  Cylinder-heads.— I  to  1.5  times  thickness  of  shell,  mean  l.S. 

Cylinder'head  Studs.— lio  studs  less  than  9i  in.  nor  greater  than  1^^  in. 
diam.  Least  number,  8,  for  10  in  dlam.  Average  number  =  0.7D.  Average 
diam.  =i>/40-f  ^in. 

Ports  ami  Pipes.— a  =  area  of  port  (or  pipe)  in  sq.  In. ;  A  =  area  of  piston, 
sq.  in.;  V=  mean  piston-speed,  ft.  per  min.;  a  =  AV/C,  in  which  C=  mean 
velocity  of  steam  tlirough  the  ])ort  or  pipe  In  ft.  per  min. 

Ports,  H.  S.  (same  ports  for  steam  as  for  exhaust).>-C=  4600  to  6600,  mean 
5600.  For  ordinary  piston-speed  of  600  ft.  per  min.  aTzKA;K=  .09  to  .18, 
mean  .11. 

Steam-ports,  L.  8.— (7=  5000  to  9000,  mean  6800;  IT  =  .08  to  .10,  mean  .09. 

Exhaust-ports.  L.  S.— C  =  1000  to  7000.  mean  6500;  K  =  .10  to  .125,  mean  .11. 

Steam-pipes,  H.  S.—U  =  5800  to  7000.  mean  6600.  If  d  =  diam.  of  pipe  and 
D  =  diam.  of  piston,  d  =  .*29/)  to  .82 A  mean  .80/). 

Stenm-pipes,  L.  Q.—C  =  ."iOOO  to  8000.  mean  6000;  d  =  .27  to  .85D.  mean  .S2Z>. 

£:xhatutpipes,  H.  S.— 0  =  2500 to 5500, mean 4400;  d  =  .88 to .50D,  mean  .87 D. 

Exhaust-pipes,  L.  S.— C  =  3800  to  4700,  mean  8800;  d  =  .85  to  .45D,  mean  .40I>, 


LOCOMOTIVES. 


1075 


race  of  rutons.—F  =  face ;  D  =  diameter.  F  =  CD.  H.  S. :  C  =  .30  to  .60 
mean  .48.    L.  S.:  C  =  .35  to  .45,  mean  .32. 

Pi»tonrods.—d  =  diam.  of  rod;  D  =  diam.  of  piston;  L  =  stroke,  in.; 
d  =:C  VdL    H.  S.:  C  =  .12  to  .175,  mean  .145.    L.  S.:  C=  .10  to  .18,  mean  .11. 

Chnnecth^g-rods.—H.  S.  (generally  6  cranks  long,  rectangular  section): 
6  =  breodili;  h  =  height  of  section;  Li  =  leng^th  of  connecting^-rod ;  D  =  diam. 
of  piston;  b  =  C  V^W,  (7=  .043  to  .07,  mean  .057;  h  =  Kb\K  =2.fi  to  4.  mean 
2.7.  L.  S.  (generally  5  cranks  long,  circular  sections  only):  C  =  .082  to  .105, 
mean  .0U2. 

CroBs-head  Slides. — ^Maximum  pressure  in  lbs.  per  sq.  in.  of  shoe,  due  to 
the  vertical  component  of  the  force  on  the  connecting-rod.  H.  S.:  10.5  to  38, 
mean  27.    L.  S  :  29  to  83,  mean  40.  ' 

Cross-head  Pins.  -I  =  length;  d  =  diam.;  projected  area  =  ri  =  di  —  CA; 
A  =  area  of  piston;  I  =  Kd.  H.  S.:  C  =  .06  to  .11,  mean  .08;  iC  =  1  lo  2, 
mean  1.25.    L.  S.:  C  =  .054  to  .10,  mean  .07;  K=  1  to  1.6,  mean  1.8. 

Crank-pin.— HP  =  horse-power  of  engine;  L  =  length  of  stroke:  I  =  length 
of  pin;  I  =  CX  HP/L  +  ^;  d  =  diam.  of  pin;  ^  =  area  of  piston;  dl  =  KA, 
H.  S.:  C  =  .13  to  .46.  mean  .30;  B  =  2.5  in.;  K  =  .17  to  .44,  mean  .24.  L.  S.: 
C  -  .4  to  .8,  mean  .6;  B  =  2  in.;  X"  =  .065  to  .115,  mean  .09. 

Crankshaft  Main  Joumal.-d  =C^HP~-^1f\  d  =  diam.;  /  =  length;  J\'  = 
revs,  per  min.;  protected  area  =  MA\  A  =  area  of  piston.  H.S.:  C  =  6.5  to 
8.5,  mean  7.8;  iC  =  2  to  3,  mean  2.2;  Jtf  =  .87  to  .70,  mean  .46.  L.  S. :  C  =  6  to  8, 
mean  6.8;  K=  1.7  to  2.1,  mean  1.9;  M  =  .46  to  .64,  mean  .56. 

Piston-9peed.—n.  S.:  530  to  600,  mean  600;  L,  S.:  600  to  850,  mean  600. 

Weight  of  Reciprocating  Parts  (piston,  piston-rod,  cross-head,  and  one- 
half  of  connecting-rod).-- Pr  =  CD*  -+-  LN^\  D  =  diam.  of  piston;  L  —  length 
of  stroke,  in.\  N  =  revs  per  min.  H.  8.  only:  C  =  1,200,000  to  2,300,000,  mean 
1.860.000. 

Belt-s^irfare  per  I.H.P.— «  =  CHP+  B;  8  =  product  of  width  of  belt  in 
feet  by  velocity  of  belt  in  ft.  per  min.  H.  S.r  C  =  21  to  40  mean  28;  B  =  1800. 
L.  S.:  S  =  C  X  HP;  C  =  80  to  42,  mean  =  85. 

Flff  wheel  (H.  8.  only).— Weight  of  rim  in  lbs.:  W=CxHP-f  D,«iV»;D,  = 
diam.  of  wheel  in  in.;  C  =  65  X  10»o  to  2  X  fO"  mean  =  12  x  lO",  or 
1.200,000,000,000. 

IVeujht  of  Engine  per  I.H.P.  in  lbs.,  including  fly-wheel.— Tr=  C  X  H.P. 
H.  S.:  (7  =  100  to  135,  mean  115.     L.  S.:  C  -  135  to  240,  mean  175. 

l¥ork  of  Steam-torblnes.  (See  p.  79].)— A300-H.P.  De  I^val  steam- 
turbine  at  the  IJih  Street  station  of  the  Hklison  Electric  Illuminating  Co.  in 
New  York  City  in  April,  1H96,  showed  on  a  test  a  steam-consumption  of 
19.275  lbs.  of  steam  per  electrical  H.P.  per  hour,  equivalent  to  17.348  llis.  per 
brake  H.P.,  assuming  an  efflciency  of  the  dynamo  of  90%.  The  steam- 
pressure  was  145  lbs.  gauge  and  the  vacuum  26  in.  It  drove  two  100-K.W. 
dynamos.  The  turbine-disk  was  29.5  in.  diameter  and  its  speed  9000  revs, 
per  min.  The  dynamos  were  geared  down  lo  750  revs.  The  total  equip- 
ment, including  turbine,  gearing,  and  dynamos,  occupied  a  space  13  ft.  8  in. 
long,  6  ft.  5  in.  wide,  and  4  ft.  3  in.  high. 
•  The  "  Turbinia,*'  a  ton>edo-t)oat  100  ft.  long,  9  ft.  beam,  and  44^  tons 
displacement,  was  driven  at  81  knots  per  hour  by  a  Parsons  steam-turbine 
in  1897,  developing  a  calculated  I.H.P.  of  15;6  and  a  thrust  H.P.  of  916,  the 
steam -pressure  at  the  engine  being  130  lbs.  and  at  the  boilers  200  lbs.  The 
vacuum  was  13><j  lbs.  The  revolutions  averaged  2100  per  minute.  The 
calculated  steam-consumption  was  15.86  lbs.  per  I.H.P.  per  hour.  On 
another  trial  the  *"  Turlnnia  '*  developed  a  speecl  of  32^  knots. 

Relative  Coitt  of  Dlflerent  Sizes  of  Steam-ens^lnes. 
^(Froin  cutalogue  of  the  Bnekeyi?  Engine  CV)..  Part  111.) 


Horse-power 
Cost  per  H.P,  | 


.•iO 

75 

100  125 

l.W 

20O!2.'5O 

20 

1T>4 

IG  15 

14Mi 

13^1  13 

300    850    400  I  500 
12^Il2.6  12.6|12.8 


600 
13H 


700,800 
14      15 


liOco.'noTivics. 

JBeslstance  of  Trains, —The  Baldwin  liocomotive  Works  contribute 
the  following  notes  to  tiie  text  on  pages  852  to  802. 

"  On  iHige  852,  we  think  the  resistances  ' »/ '  for  Increasing  ppeeds  were 
originally  intended  to  be  adde4  to  a  coefhcient  for  the  total  frictional 


1076 


APPENDIX. 


refli^tance,  for,  if  we  assume  a  straight,  level  track  aod  a  speed  of  5  miks 
per  hour,  then  according  to  the  formula  the  total  resistance  per  too  would 
oe  8^  lbs.  This  is  less  than  we  are  actually  able  to  obtain  under  mcqt^t 
farorable  conditions,  and  we  know  that  hi  some  cases,  for  instance,  in  iniD«> 
construction,  the  frictional  resistance  has  been  shown  to  be  as  much  aa 
60  U)8.  per  ton  at  slow  speed.  This  resistance  should  be  approximate  to  suit 
the  conditions  of  each  IndiTidual  case,  and  thenncreased  resistances  due  to 
speed  added  thereto. 
*'  On  page  853,  in  the  formula 

uP  -  W(.0005c  ±  .0001»m)  =  U  +  .O0OS6C  ±  .00019m, 

the  journal  and  rolling  resistances  of  engine  and  tender  at  different  speeds 
are  not  accounted  for,  unless  the  author  includes  them  in  the  coemcienc 
*«,*  under  the  supposition  that  the  tractive  power  will  be  in  proportion  ut 
the  total  weight  or  engine  and  tender  at  different  speeds.  As  the  propor- 
tion of  driver,  or  adhesive  weight,  to  the  total  weight  of  engine  and  tender 
varies  considerably  in  different  classes,  we  think  this  rather  indefinite.  If 
the  coefficient  *  u  '^  were  made  to  embrace  only  the  resistances  of  Uie  worlc- 
ing  parts,  and  the  coefficient  *  I  *  (after  the  modiflcation  suggested  above), 
were  applied  to  the  weight  of  engine  and  tender,  we  think  the  formula 
would  he  more  generally  applicable.  For  instance,  in  the  formula  assumts 
as  before,  a  straight,  level  track:  then  TF(.005c  ±  .00010m)  would  reduce  to 
0,  and  the  total  weight  of  engine  and  tender  would  disappear  entirely, 
except  in  their  indirect  influence  upon  coefficient '  it.* 

*' Approximate  Formula  for  Tratn  Besietanee.  (See  Holmes  on  the  Steam 
Engine,  pages  141  to  148.) 

**  Page  860,  *  Exhaust  NoxxUa.*  Refer  to  the  Annual  Report  of  the  Ameri- 
can Railway  Master  Mechanics'  Association  for  1896,  which  gives  some  io- 
teresting  dala  on  the  subject. 

*'  Page  866.  *  Boilera,^  Refer  to  Holmes  on  the  Steam  Engine,  pages  871 
to  377,  and  888  to  389,  and  also  to  the  Master  Mechanics'  Report  for  1807. 


pages  218  to  S283,  for  a  very  important  list  of  data  and  formul». 
*'  Page  864,  *  Counterbalaiicing.^    RAf«r  tn  rhn  MMtMr  MAnh&r 


Report 


_  ^ Refer  to  the  Master  Mechanics* 

for  1H96,  pages  148  to  15G,  for  some  interesting  formulae. 

*•* Formuloi  for  Curves. 
Approximate  Formula  for  Radius.  Approximate  Formula  for  Swing. 

_         .7646  TT  WT       _ 


(t)  cb     M^  ° 


o 


R  =  radius  of  min.  curve  in  feet. 
P  —  play    of    drivinflr-wheels    In 

decimals  of  1  ft. 
W=  rigid  wheel-base  in  feet. 


W  s=  rigid  wheel  bis  . 
T  =  total 

R  =  radius  of  curve. 
3  =  swing  on  each  side  of  centre.'' 


Performance  of  a  Slf^h-speed  liocomotl-re.— The  Baldwin 
compound  locomotive  No.  10-^.  on  the  Phila.  &  Atlantic  City  Ry.,  in  July  and 
August,  1807,  made  a  record  of  which  the  following  is  a  summary: 

On  July  2d  a  train  was  placed  in  service  scheduled  to  make  the  run 
between  the  terminal  cities  m  1  hour.  Allowing  8  minutes  for  ferry  from 
Piiiladelphia  to  Camden,  the  lime  for  the  55^  miles  from  the  latter  point  to 
Atlantic  (?ity  was  52  minutes,  or  at  the  rate  of  64  miles  per  hour.  Owing  to 
the  inability  of  the  ferry-boats  to  reach  C!amden  on  time,  tlie  train  always 
left  late,  the  average  detention  being  upwards  of  2  minutes.  This  loss  was 
invariably  made  up,  the  train  arriving  at  Atlantic  City  ahead  of  time.  S 
minutes  on  an  average,  every  day.  For  the  52  da3rs  the  train  i-an,  from  July 
Sd  to  August  31 8t, //te  average  time  coiummed  on  the  run  toaa  48  mtnii/^.<i, 
equivalent  to  a  uniform  rate  of  speed  from  start  to  stop  of  69  miles  per  hour. 
On  July  14th  the  run  from  Camden  to  Atlantic  City  was  made  in  46^  min., 
an  average  of  71.6  milen  per  hour  ftr  the  total  distance.  On  2S  days  the 
train  consisted  of  5  cars  and  on  30  days  it  was  made  up  of  6,  the  weight  of 


LOCOMOIIVES. 


1077 


cars  being  as  follows :  combination  car,  57,200  lbs. ;  coaches,  each,  59,200  lbs. ; 
Pullman  car,  85,500  lbs. 

The  general  cUmeosioiis  of  the  locomotive  are  as  follows :  cylinders,  IS  and 
22  X  26  in.;  height  of  drivers,  84^  in.;  total  wheel-base,  26  ft.  7  in.;  driving- 
wheel  base,  7  ft.  3  in.;  length  of  tubes,  14  ft.;  diameter  of  boiler,  58^  in.; 
diameter  of  tubes,  l^  in.;  number  of  tubes,  278;  length  of  fire-box,  118^  in.; 
width  of  flre-boz,  90  in.;  heating-surface  of  flra-boz,  186.4  sq.  ft.;  heating- 
surface  of  tubes,  1614.9  sq.  ft;  total  heating-surface,  1835.1  sq.  ft.;  taiik 
capacity,  4000  gallons;  boiler-pressure,  200  lbs.  per  sq,  in.;  total  weight  of 
engine  and  tender,  227,000  lbs. ;  weight  on  drivers  (about),  78,600  lbs. 

liOComotlFe  lilnk  IHotloii.— Mr.  F.  A.  Halsey,  in  his  work  on 
*'  Locomotive  Link  Motion,"  1896,  shows  that  the  location  of  the  eccentric- 
rod  pins  back  of  the  link-arc  and  the  angular  vibrations  of  the  eccentric- 
rods  introduce  two  errors  in  the  motion  which  are  corrected  by  the  angular 
vibration  of  the  connecting-rod  and  by  locating  the  saddle-stud  back  of  the 
link-arc.  He  holds  that  it  is  probable  that  the  opinions  of  the  critics  of  the 
locomotive  link  motion  are  mistaken  ones,  and  tnat  it  comes  little  short  of 
all  that  can  be  desired  for  a  locomotive  vaJve  motion.  The  increase  of  lead 
from  full  to  mid  gear  and  the  heavv  compression  at  mid  gear  are  both 
advantages  and  not  defects.  The  cylinder  problem  of  a  locomotive  is  en- 
tirely different  from  that  of  a  stationary  engine.  With  the  latter  the 
problem  is  to  determine  the  size  of  the  cylinder  and  the  distribution  of 
steam  to  drive  economically  a  given  load  at  a  given  speed.  With  locomotives 
the  cylinder  is  made  of  a  size  which  will  start  the  neaviest  train  which  the 
adhesion  of  the  locomotive  will  permit,  and  the  problem  then  is  to  utilize 
that  cylinder  to  the  best  advantage  at  a  greatly  increased  speed,  but  under 
a  greatly  reduced  mean  effective  pressure. 

Kegative  lead  at  full  gear  has  been  used  in  the  recent  practice  of  some 
railroads.  The  advantages  claimed  are  an  increase  In  the  power  of  the 
engine  at  full  gear,  since  positive  lead  offers  resistance  to  the  motion  of  the 

f)iston  :  easier  riding;  reduced  frequency  of  hot  bearings;  and  a  slight  gain 
n  fuel  economy.  Mr.  Halsey  gives  the  practice  aa  to  lead  on  several  roads 
as  follows,  showing  great  diversity  : 


New  York,  New   Haven   & 

Hartford     

Maine  Central 

Illinois  Central 

Lake  Shore 

Chicago  Great  Western  — 
Chicago  &  Northwestern. . . 


Full  Gear 
Forward,  In. 


1/16  pes. 

0 
1/32  pos. 
1/16  neg. 

0 
3/16  neg. 


Full  Gear 
Back,  in. 


Mneg. 
Mneg. 


9/64  X 
0 


Reversing 
Gear,  in. 


J4po8. 

"  abt."3/Y6" 

5/16  pos. 

8/16  to  9/16 

54  pos. 


The  link-chart  of  a  locomotive  built  in  1897  by  the  Schenectady  Locomotive 
Works  for  the  Northern  Pacific  By.  is  as  follows: 


Lead. 

Valve  Open. 

Cut-off. 

Forward 

Rearward 

Forward 

Rearward 

Forward 

Rearward 

Stroke,  in. 

Stroke,  in. 

Stroke,  in. 

Stroke,  in. 

Stroke,  In. 

Stroke,  in. 

-  H 

-  J6 

1  % 

1  % 

2:^9/16 

S^ 

-  1789 

-  1782 

1  7/16 

1  7/16 

21 

21 

+  1/88 

+  1/82 

1  1/16 

1  1/16 

19 

19 

3/82 

8/32 

23/82 

23/82 

16 

16 

J^« 

0« 

H 

•         ^ 

13 
10 

18^ 
10 

5/82  8. 

6/32  8. 

6/16 

6/16 

8 

8 

6/82 
5/82  f. 

6/32 
5/82  f . 

^ 

7^2 

6 

4 

4  1/16 

Cylinders  20  x  26  in.,  driving-wheels  09  in.,  six  coupled  wheels,  main  rods 
126^  m.,  rtidius  of  link  40  in.,  lap  1^  in.,  travel  6  in.,  Alien  valve. 


1078 


APPENDIX. 


6BARIN6. 

Elllcleney  of  ^Form  Gearlner*  (See  also  page  806  )— Worm  |?ear- 
inic  U8  a  iiieHiiK  of  iranHinUting  power,  ha8  until  receiitij,  greuerallj  be<'n 
looked  upon  with  BUKpicion,  its  efflciencv  beings  considered  necessarUj  low 
and  its  life  short.  Recent  experience,  however,  indicates  that  when  pro|>- 
erly  proportioned  it  is  both  durable  and  reasonably  efflcienl.  Mr.  F.  A. 
Halscy  discusses  tlie  subject  in  Am.  Machinist^  Jan.  18  and  SO.  lt!!96.  He 
quotes  two  formulas  for  the  efficiency  of  worm  gearing  due  to  Prof.  John 
H.  Barr : 


_  taii^o  (1  —  /  tan  a) 
^-  tan"a+7       ' 

in  which  E  =  efficiency 


.0) 


^  = 


tanuQ  —/tana) 


approx., 


(•2) 


tan  a + ^r 

an((]e  of  thread,  being  angle  between  thread 
and  a  line  perpendicular  to  the  axis  of  the  worm;  f  =  coefficient  of  friction. 

Eq.  (1)  applies  lo  the  worm  thread  only,  while  ("J)  applies  to  the  worm  and 
step  conibnied,  on  the  assumption  that  tiie  mean  friction  radius  of  the  two 
is  equal.  Eq.  (1)  gives  a  maximum  for  K  when  tan  a  =  ^1  -|-  /«-/...  (S) 
and  eq.  (2)  a  maximum  when  tan  a  =  V^  -f-  4/*  -  2/.  .  .  .  (4)  Using  a  value 
.iX>  for/  gives  a  value  for  a  in  (H)  of  43**  34'  and  In  (4)  a  value  of  Sst*  49'. 

On  plotting  equations  (1)  and  (2)  the  curves  show  the  striking  influence  of 
the  piicli-uugle  upon  the  efficiency,  and  since  the  lost  work  is  expended  in 
friciion  and  wear,  it  is  plain  why  worms  of  low  angle  should  be  snort-livetl 
anil  those  of  high  angle  loog-lived.  The  following  table  is  taken  from  Mr. 
Hulsey's  plotted  curves : 

RELATION    BRTWERN  THREAD-ANOLB  SPEED  AND  EFFICtFNCT  OF  WOBIf    OBaRS. 


Velocity  of 

Pitch-line, 

feet  per 

minute. 


3 
5 
10 
30 
40 
100 
200 


Angle  of  Thread. 


20 


30 


40 


45 


Efficiency. 


35 
40 
47 
5J 
60 
TO 
76 


52 

66 

73 

56 

69 

76 

62 

74 

79 

67 

78 

83 

74 

83 

87 

82 

88 

91 

85 

91 

92 

76 
79 
82 
85 
88 
91 
92 


80 
82 
86 


91 
92 


The  experiments  of  Mr.  Wilfre»l  I^mIs  on  worms  show  a  very  satisfac- 
tory correspondence  with  the  theory.  Mr.  Halsey  gives  a  collect  ion  of  data 
coraprlsiug  10  wurms  doing  heavy  duty  and  having  pitch-angles  raugn  e 
lielween  4°  3U'  anil  45<*.  which  show  that  every  wonn  having  an  angle  above 
12*»  30*  was  successful  in  regard  to  durability,  and  every  worm  below  9* 
was  unsuccessful,  the  overlapping  region  being  occupied  by  worms  some  of 
which  were  successful  and  some  unsuccessful.  In  several  cases  worms  of 
one  pitch-angle  iiuil  been  replaced  by  worms  of  a  different  angle,  an  increase 
m  the  angle  leading  in  every  case  to  better  results  and  a  decrease  to  poorer 
results  He  concludes  with  the  following  table  from  experiments  by  Mr. 
James  Christie,  of  the  Pencoyd  Iron  Works,  and  gives  data  connecting  the 
load  upon  the  teeth  with  the  pitch-line  velocity  of  the  worm  : 

LIMITING  8PKEDB  AND  PRESSURES  OF  WORM  OEARIKO. 


Revolutions  per  minute 

Velocity  at  pitch-line  in  feet 

per  minute 

IJiniiing  pressure  in  pounds. 


Single-thread 
Worm  1"  Pitch, 
21  Pilch  Diam. 


128 


96 
1700 


201  j  2« 

150;  205 
i:i00  1100 


425 


3S0 
7U0 


Double- 
thread 
Worm  2" 
Pitch,  21 
Pitch  Diam. 


128   201 

961  160 
1100,1100 


278 

205 

1100 


Double- 

thread 

Worm2i" 

Pitch,  4i 

Pitch  Diam. 


201 1  27^.2 

235I  319 
1100]  700 


425 


49!) 
4t)0 


MBT  OP  AUTHOMTDES  QUOTED  IN  THIS  BOOK. 


When  a  name  is  quoted  but  once  or  a  few  times  only,  the  page  or  paves 
are  given.  The  names  of  leading  writers  of  tezi-books,  who  are  quoted  rre< 
qnentlyf  have  the  word  "various"  affixed  in  place  of  the  pajre-number. 
The  list  is  somewhat  incomplete  both  as  to  names  and  pa^  numoers. 


Abel.  F.  A.,  642 

Abendroth  &  Root  Mfg.  Co.,  107, 196 

American  Screw  Co.,  SiOO 

Achard,  Arthur,  886,  919 

Addy,  George,  057 

Addyston  npe  and  Steel  Co.,  187, 188 

Alden,  G.  I.,  079 

Alexander,  J.  8.,  629 

Allen,  Kenneth,  riOS 

Alien,  Leicester,  5S2 

Andrews,  Thomas,  884 

Ansonia  Brass  and  Copper  Co.,  8S7 

Arnold,  Horace  L.,  950 

Ashcroft  Mfg.  Co.,  755J,  775 

Atkinson,  J.  J..  582 

Ayrton  and  Perry,  1040 

Babcock,  G.  H.,  624,  038 

Babcock  &  WUcox  Co.,  588,  636 

Baermann^.  H.,  188 

Bagshaw,  Walter,  052 

Bailey,  W.  H.,  048 

Baker,  Sir  Benjamin,  280, 847,  402 

Balch.  S.  W.,  898 

Baldwin,  Wm.  J.,  541 

Ball,  Frank  H.,  751 

Barlow,  W.  H.,  884 

Barlow,  Prof.,  888 

Bamaby,  a  W.,  1018 

Barnes,  D.  L.,  681,  861,868 

Barms,  Geo.  il.,  686 

Bauer,  Chas.  A.,  907 

Bauschinger,  Prof.,  880 

Bazin,  M.,  563,  587 

Beardslee,  L.  A..  288, 877 

Beaumont,  W.  W.,  979 

Becuel,  L.  A.,  644 

Begtrup,  J.,  848 

Bennett,  P.  D.,  864 

Bernard,  M.  &  B.,  880 

Birkinbine,  John,  606 

Bjorling,  P.,  678 

Blaine,%.  0.^16.  1069 

Blauvelt,  W.  H.,  680, 649 

Blechynden,  A.,  1016 

Bodmer,  G.  K,  768 

Bolland,  Simpson,  046 

Booth,  Wm.  H.,  928 

Box,  Thomas,  475 

Briggs,  Robert.  194,  478,  589,  672 

British  Board  of  Trade,  264,  866, 700 

Brown,  A.  G.,  V23.  724 

Brown,  E.  H.,  888 

Brown  &  Sharpe  Mfg.  Oo^  219, 890 

Browne,  Ross  B.,  597 

Brush,  Cha&  B.,  660 

Buckle,  W^  OU 


Buel,  Richard  H.,  606,  884 
Buffalo  Forge  Co.,  519, 589 
Builders*  Iron  Foundry,  874 
Burr.  Wm.  A.,  566 
Burr,  Wm.  H.,247,  250,  290,  881 

Calvert,  F.  Crace,  886 

Calvert  &  Johnson,  469 

Campbell,  H.  H.,  808.  459,  660 

(^Ampredon,  Louis,  4(^ 

Caniegle  Steel  Co..  177,  272,  277,  891 

Carpenter,  R.  C.  454,  615,  718,  etc. 

Chad  wick  Lead  Works,  201,  615 

Chamberlain,  P.  M.,  474 

Chance,  H.  M.,  681 

Chandler,  Chas.  F..  582 

Chapman  Valve  Mfg.  Co.,  108 

Chauvenet,  S.  H.,  870 

Chase,  Chas.  P.,  812 

Chevandier,  Eugene,  640 

Christie,  James.  804 

Church,  Irving  P..  415 

Church,  Wm.  Lee.  784.  1050 

Clapp,  Geo.  H.,  897,  408,  651 

Clark,  Daniel  Kiunear,  various 

Clarke,  Edwin,  740 

Claude],  455 

Clay,  F.  W.,  201 

Clerk,  Dngald,  847 

Cloud,  John  W.,  851 

Codman.  J.  E.,  198 

Coffey,  B.  H.,  810 

Coffin.  Freeman  C,  209 

Coggswell,  W.  B.,  554 

Cole,  Romalne  C,  820 

Coleman.  J.  J.,  470 

Cooper,  John  H.,  876,  000 

Cooper,  Theodore,  262,  263.  869 

Cotterill  and  Slade,  482,  974 

Cowles,  Eugene  H.,  329, 831 

Cox,  A.  J.,  )19Q 

Cox,  E.  T.,  629 

Cox,  William,  575 

Coxe,  Eckley  B.,  682 

Craddock,  Thomas,  473 

Cramp,  E.  8.,  405 

Crimp,  Santo,  564 

Crocker,  F.  B.,  1070 

Cummins,  Wm.  Russell,  77S 

Daelen,  R.  M.,  617 
Dagger,  John  H.  J.,  889 
Daniel,  Wm.,  493 
D'Arcy,  563 
Davenport,  R.  W.,  0W 
Day.  R.  E^IOOO 
Dean,  F.  W^  606, 689 

1079 


1080 


LIST  OF  AUTH0B1TI£8. 


DtiDtou,  J^men  E..  73CL  781, 781, 989 

Dirn^inohe,  it.  E.,  m 
Dix,  Wftlterfi..  ^-OB.  1066 
Dndf^tit  KiIauiiffiLiurluff  Co.,  844 
Douald,  J.T-,^t85 
Doiiltiii,  B.,  Jr,»4ei,?a8 
Dudltjy,  Cbaa.  B.,^,  888 
Dudky,  F.  H„  401,  m 
Dudley,  W.  D.,  1157 

Dujibar,  J«H,,79a 
DuniTid,  Prof,*  58 
DwelMbaiiTtT^-Dery,  BUS 

Efcleston,  Thomas,  236,  841 
Emeiy,  Cbas.  E^  608, 818, 808 
Eneelhardt,  F.  E..  488 
Ellis  and  Rowland,  677 
English,  Thos.,  758 
Ericsson,  John,  288 
£;ytelwein,  684 


Fwu 


,>ir  Win.,  «4(l,  964, 808, 854 


Falrley,W.,53l.  Saa 
Pulk^^nau.  A  ,600 
FauniTiK,  J.T.,Ga4,670 
Favrti  aoti  ^illHJrmamj,8ai 
Felton.  C.  E.,\^^ 
Fernow,  B*  E.,  640 
Field.  C.  J„  m  9&T 
FittB,  James  H.,  HiA 
Flather,  J.  J..iM11.W# 
Flynn,  P.  J.,  403^MV^ 
Foley,  Neiftofi.  7uO 
Forbes,  Pnjf.  1(138 
rorney,  M.  JiT,  e^"* 
FoPByth,  WmH,C30 
Foster,  R.J.  iBfjl 
FmiidSH  J.  B.  5Hfl»  739;  887 
FrftjEOPt  P<»rslror>S54 
Fi^^mnrt,  J,  R.,^S1,  &S4 
Frith,  A.  J.,  874 
Fulton,  John,  687 

Ganguillet  &  Kutter,  688 
Oantt,  H.  L.,  406 
Garrison,  F.  L.,  826, 881. 408 
Garvin  Blachine  Go.,  060 
Gause,  F.  T.,  601 
Gay,  Paulln,  966 
Gilt,  J.  P.,  667 
Gilmore,  E.  P.,  241 
Glaisber,  483 
Glasffow,  A.  O.,  654 
Goodman.  John,  934 
Gordon,  F.W.,  689, 740 
Gordon,  247 
Goss,  W.  F.  M.,  868 
Gossler,  P.  G.,  1061 
Graff,  Frederick,  885 
Graham.  W.,  960 
Grant,  George  B.,  898 
Grant,  J.  J.,  960 
Grashof,  Dr.,  284 
Gray,  J.  McFarlane,  681 
Gray,  J.  M.,  958 
Greene,  D.  M.,  667 


Grelg  and  IByUi,  8li 
Grosseteste,  W.,  710 
Gniaer,  L.«  888 

Hadfleld,R.A^8Bl,400 

Halpin,  Druitt,  788,  854 

Halsey,  Fred'k  A.,  490, 817 

Harkuess,  Wm.,  900 

Harrison,  W.  H.,  969 

Hart,  F.  k,  1047 

Hartig,  J.,  961 

Hartman,  John  M.,  884 

Hartnell,  Wilson,  848.  818, 888 

Hasson,  w.  F.  O.,  1047 

Hawksley,  T.,  485,  518, 584 

Hazen,  H.  Allen,  494 

Henderson,  G.  R.  847,  851 

Henthom,  J.  T.,  d65 

Hering,  Carl,  1046 

Herschel.  Clement,  688 

Hewitt,  G.  a,  630 

Hewitt,  Wm.,  917 

Hildenbrand,  Wm.,  918 

Hill,  John  W.,  17 

Hiscox,  Q.  D.,  968 

Hoadley,  John  C,  461, 888 

Hobart,  J.  J.,  062 

Hodgkinson,  246 

Holley,  Alexander  L.,  877 

Honey,  F.  R,  47,  68 

Hoopes  &  Townsend,  210 

Houston,  Edwin  J.,  1061 

H-— ^-"  ^  "— tinlfj,  1068 

Hkvm^mJ,  ^Ni.jj.T-0  K.,  ^"42,  882,  886 

Howden,  .Jaicieei,7H 

Howt?,  yifurj  M.,  ^02,  407,  451,  531 

How*?,  Mal^erii  A^tTO,  81S 

Howlftod.  A,  fi,  SW 

HiiiWjq,  J^jlm  Q.,  466 

Hueh(*fi,  I>.  K,  896 

HiJKlkt^-*^.  H.  W.,  909 

HiiglR"*.  Tbsjtt.  E.,  917 

Hinnphrevp,  Akx,  C.  668 

Hiiiisk^ki  r,  Syiiii]  d.  897 

Hum,  Alfrw!  R,  'Jl6,  817,  892,  558 

H^\r^.  ^ '"-'--    v.,  S-10,  928 

Huston,  Charles,  888 

Hutton,  Dr.,  64 

Huyghens,  58 

Ingersoll-Sergeaot  Drill  Go.,  508 
Isherwood,  BenJ.  F.,  478 

Jacobus,  D.  S.,  511.  689, 728, 780 

Johnson,  J.  B^  800,  814 

Johnson,  W.  B.,  475 

Johnson,  W.  R.,  290 

Jones,  Horace  K..  887 

Jones  &  Lamson  Machine  Oo.,  954 

Jones  &  Laugfalins,  867, 885 

Kapp,  GIsbert,  1088 
Keep,  W.  J.,  366,  951 
Kennedy,  A.  B.  W.,  855, 525, 764 
Kemot,  Prof.  494 
Kerr,  Walter  C,  781 
Kiersted,  W^  292 
Kimball,  J.  1^.,  499, 682, 687 
Kinealy.J.  H,,587 


UST  OP  AUTHOBITIES. 


1081 


Kirk.  A.  C,  705 
Kirk,  Dr.,  1004 
Kirkaldy,  David,  296 
Kopp,  d.  O.  C,  47^ 
KuichlinfT,  £.«  078 
Kutter,  WO 

I^ndreth,  O.  H.,  718 

Langley.  J.  W.,  400,  410.  419 

Lanza,  Qaetano,  SlO,  860,  864,  977 

La  Rue.  Benj.  F..  948 

Leaviit.  E.  D.,  788 

Le  Chacelier,  M.,  458 

Le  Conte,  J.,  665 

I^edoux.  M.,  981 

Ijt^ggettj  T.  H.,  1040 

Leonard,  H.  Ward,  1096 

Leonard,  8.  H..  666 

Lewis,  Fred.  H..  186. 180, 897 

i^wis,  I  N    498 

LewlR,  Wilfred,  858,  868, 878, 890 

Unde,  G.,  960 

Lindenthal,  Uustav,  886 

Lloyd's  BeglBter,  £64,  866, 700 

Loss,  H.  v.,  800 

Love.  B.  G.,  666 

Lovett,  T.  D.,  856 

Lyne,  Lewis  F.,  718 

McBride.  James,  074 

VlacCord,  0.  W..  898 

4acdonald,  W.  R ,  956 

ttacgovern,  E.  E.,  545 

tfackay,  W.  M..  642,  644 

Mahler,  M.,  688 

tfain,  Chas.  T.,  690.  780, 790 

tf annesrnann,  L.,  838 

tfanning.  Chas.  H.,  675,  888 

darks.  Will.  D.,  7W,  811 

4aAt«r  Car  Builders*  Asfloe.,  870 

tf  acu»s.  W.  F.,  890 

datthlessen,  1041 

Haver,  Alfred  .M..  466 

tlehrtens,  G.  G..  M,  405 

ieler,  B.  D.,  M8 

deissoer,  O.  A.,  870 

rlelviile,  Geo.  W.,  674 

iendenhall,  T.  CSS 

ierrinian,  Mangfleld,  841,  960,  968 

ietcair,  William.  840,  418 

leyer,  J.  Q.  A.,  796,  856 

f  eystre,  F.  J.,  47« 

liller,  Metcalf  &  Parkin,  418 

liller.  T.  Spencer,  S44,  0*27 

litchell,  A.  £.,855,866 

loles worth.  Sir  G.  L.,  562,  668 

lolyneux  and  Wood,  786 

loore,  Gideon  E..  658 

lorln.  485.  980,  WS 

[orison.  Geo.  S..  881,  898 

[orrell,  T.  T.,  407 

lorris.  Talker  &  Oo.,  190, 196 

I  urn  ford,  E.  R.,  1006 

Luryue,  Daniel,  581 

affle,  A.  F.,  808.  606,  878 

aiijfi*.  -471.  6«9 

ason  .Alfif.  Co..  4  8.648 

atiunat  Pipe  Beudiiuc  Co,*  198 


Nau.J.B.,867,400 

Newberrv,  J.  8.,  694 

Newcomo,  Simon,  489 

Kew  Jersey  Steel  &  Iron  Co.,  958, 810 

Newton,  Sir  Isaac,  475 

Nichoi,  B.  C,  473 

Nichols.  986 

Norris.  R.  Van  A.,  881 

Norwoik  Iron  Works  Co.,  488, 601 

Nystrom,  John  W.,  865 

Ordway,  Prof.,  460 

Paret,  T.  Dunkin,  067 

Parker,  W.,  S54 

Parsons.  H.  de  B.,  861 

Possburg,  Btnil,  466 

Pattinson,  John,  6^ 

Pe*l<*t,  M,,  4T1.  4'r»,  Tai 

Pt'hoD  Warpj*  Whet- i  Co,,  101, 874, 686 

Ptijct?.  W,  D,  sm 

Pt^mroyrt  I  rati  Work«.  179,  989,  868 

Pen  1 1  HI,  Arthur,  555 

R^nJiRylvttniii  R.  K.  Co.,  807,  875,  800 

PlitleyfH|jhia  En^tieerinK  Works,  696 

PliiJhtic'k,  P.  H,446 

P)iirii|iS  W.  B,,  6^9 

PhaMiii  Bridfire  Co.,  aea 

PliLt'Qii  Iron  to  I  l&l,  2S7 

Pier^?e.  C.  a.  1^ 

PliTt-e,  H.  M  ,511 

Pin Hburx  Tf«t ing  Laboratory,  848 

Piatt.  Juliii,  (J17 

Poetiek,  F,  A.,  50S 

Porter,  Cha*.  T,. fl6*  797, 880 

Poitei'.  K  C,  64i5 

Poti»vi]ie  IroD  &  Steel  Co..  960 

Poulllm,  455 

Pourcel,  A,lf  Xftj>dre,  404 

Poupftrcllit,  M.,  (587 

Powell.  A.  M  ,»?& 

Pifirt  A  Whrtciey  Co.,  694  OW 

Prtce,  U.  a,  1^^ 

Prony,  564 

Pl7ibil,P.,077 

Quereaii,aH.,86S,889 

Ramsey,  Erakine,  688 

Rand  Drill  Co.,  490.  506 

Randolph  A  Clowes.  198 

Rankine,  W.  J.  M.,  various 

Ransome,  Ernest  L.,  ^1 

Raymond.  R  W.,  031, 660 

Reese.  Jacob,  966 

Retmanit,  M.,  various 

Reiohhf  Im.  E.  P.,  661 

Kennie,  John,  9-i8 

Reiileaiiz.  various 

Richards.  Prank.  488.  401, 600 

Richards.  John.  905,  976 

Richards.  Windsor,  404 

Riedler,  Prof.,  507 

Rites.  F.  M.,  788.  818 

RobertH- Austen,  Prof.,  461 

Robinson,  H.,  1051 

Robinson,  S.  W.,  588 

Rockwoo<I,  O.  [.,  781 

John  A.  RoebUnx^s  Soot*  06.,  914, 991 


1082 


LIST  OF  AUTHOfilTIES. 


RoeIk<n%C.  R.,  865 
Roney,  W.  R.,  711 
Roots,  P.H.i  F.  M.,5M 
Roee,  Joshua,  414,  809,  970 
Rotbwell,  R.  Pm  687 
Rowland,  Prof.,  456 
Royce,  Fred.  P.,  1058 
Rudiarer,  E.  A.,  671 
RugRles.  W.  B.,  Jr.,  861 
Russell,  S.  Bent,  667 
Rust  and  Coolidge,  290 

Sadler,  P.  P.,  639 
Saint  Venant,  1288 
Salom.P.O.,  406, 1056 
^Sandberg,  C.  P.,  884 
Baunders,  J.  L.,  544 
Saunders,  W.  L.,  605 
Scheffler,  F.  A.,  681 
SchrOter,  Prof..  788 
Schutte,  L.,  &  Co.,  S87 
Seaton,  various 
Sellers,  Coleman,  890,  958, 975 
Sellers,  Wm.,  804 
Sbarplefls,  S.  P.,  811, 688 
SbeltoD,  F.  H.,  668 
Shock,  W.H.,  807 
Simpson,  66 
Sinclair,  Anfiis,  868 
Sloans,  T.  O'Connor,  1087 
Smeaton,  Wm.,  498 
Smith,  Ciiaa.  A^  687, 874 
Smith,  C.  Shaler,  856,  805 
Smith,  Hamilton,  Jr.,  666 
Smith,  Jesse  M.,  1050 
Smith,  J.  Bucknall,  885,  806 
Smith,  Oberlin,  865,  978 
Smith,  R.  H.,  968 
Smith,  Scott  A.,  874 
Snell,  Henry  I.,  614 
Stahl,  Albert  W.,  699 
Stanwood,  J.  B.,  808, 800, 818, 818 
Stead,  J.  £.,  409 
Steams,  Albert,  465 
Stein  and  Scbwara.  410 
Stephens,  B.  F.,  898 
Stillman,Tbo8.  B..044 
Stockalper,  E.,  408 
Stromeyer,  C.  E.,  896 
Struthers,  Joseph,  451 
Sturtevant,  B.  F.,  Co.,  487. 698 
Stut.  J.  C.  H.,  844 
StyfTe,  Knut,  888 
Suplee,  H.  H.,  769,  778 
Suter,  Geo.  A.,  684 
Sweet,  John  £.,826 

Tabor,  Harris,  751 
Tatham  &  Bros.,  801 
Taylor,  Fred.  W..  880 
Taylor,  W.  J.,  646 
Theiss,  Emil.  818 
Thomas,  J.  W.,  869 
Thompson.  Silvanus  P.,  1064, 1066 
Thomson,  Ellbu,  1058 
Thomson,  Sir  Wm.,  461,  1080 
Thurston,  R.  H.,  various 
TilRbman,  B.  F.,  966 
Tompkins,  C.  R.,  885 


Tr-rrfttitv-,  H.  0.,  401 
Turrpy.  Joseph,  SSa.  Si30 
TiH't^r.  E^tfaiRimrtij*,  asi,  084 
Tow  ne,  Htriirv  R  .  ^576,  W,  911 

Tjfl  lit  wine,  J.  C,  ^iK  US.  811.  488 

TraiiTwlue,  J.  a,  Jr.  S55 

TrtM]  ton  Iron  Co.,  tfia,  S^  880,  91S 

Tribe,  James,  765 

Trots,  E .  458- 

TrowbridKe,  John,  467 

Trowbridge,  W.  P.,  478,  518, 788 

Tult,J.  £.,616 

Tweddell,  R.  H..  619 

Tyler,  A.  H.,  940 

Uchatius,  Qen'l,  881 
Unwin,  W.  Cawthome,  various 
Urquhart,  Thos.,  645 
U.S.  Testing  Board,  808 

Vacuum  Oil  Co.,  948 
Vair,  O.  O.,  950 
Violette.  M..  640, 648 
Vladomtroff,  L.,  816 

Wade,  Mftjur,  ffij,  S71 

Walles,J.  w.,^^^^ 

Walker  Mf*c.  Co..  905 

Wallis,  PhiUp,  m^ 

Warren  Fcuudry  &  Mach.  Co.,  189 

Weaver,  W.  D..  \(m 

Webber,  SAmueJ.  5eu  M^ 

Webber,  W.  0„  608 

Webster,  W.  R.  389 

Weidematm  ^  Fivb^z.  400 

Weightmad.  W.  H,T&! 

WeisbadL  t^r  JuUils,  various 

Wellington .  A.  >L,  s^eo.  9;^  985 

We8t,Clm!i.  D.,  910 

West.ThoiruiPi  D.,  StiSi 

Westlngh.'iise  Jt  (^a]tH'>n,  988 

Westlngl-.  .^■■^■  El.  :       ig.  Co.,  10<8 

Weston,  luiward,  ]0%» 

Whitham,  Jay  M.,  47S,  TOO,  708, 810 

Whitney,  A.  J.,  889 

WilleU,  J.  R,  688,  640 

Williamson,  Prof.,  68 

Wilson,  Robert,  Hk 

Wheeler,  H.  A.,  906 

White,  Chas.  F.,  714 

White,  Maunsel.  408 

Wohler,  888,  840 

Wolcott,  F.  P.,  949 

Wolff,  Alfred  R ,  494,  517,  6S8. 888 

Wood,  De  Volson,  various. 

Wood,  H.  A.,  9 

Wood,  M.  P.,  886.  889 

Woodhury.  C.  J.  H.,  587,  081 

Wootten,  J.  £..  865 

Wright,  C.  R.  Alder,  881 

Wright*  A.W.,88e 

Yarrow,  A.  F.,  710 
Yarrow  &,  Co.,  807 
Yates,  J.  A^  287 

Zahner,  Robert*  490 
T,8«7 


INDEX. 


\bbrevIatlOD8, 1 

Ibrasive  processes,  86B 

Ibscissas,  09 

Absolute  zero,  461 

^bsorptioD     refrigerating -machines, 

Accelerated  motion,  497 
Loceleration.  438 

worlc  of,  480 
Accumulators,  electric,  10&8 
Ldiabatic  compression  of  air  (table), 

90*2 
curve,  742 
expaiiKion,  74:) 
formuls,  SOI 
Jr,  4S1-5-47 

and  vapor,  weisrhts  of,  484 
comprtMsed,  4^  499 
compressed,  for  railways,  510 
compressors,  604 
compressors,  steam,  S04 
horse-power  required  to  compress, 

601 
density  and  pressure,  481 
lift-pump,  614 
loss  of  presKure,  487, 4Vi 
manometer,  481 
pressure  through  pipes,  488 
properties  of,  481 
pumps,  839 
pyrometer,  453 
specldc  heat  of,  484 
thermometer,  454 
l^ebra,  88 
Ikfebraicat  signs,  1 
UlKation,  10 
lloj-s,  319-388 
aluminum,  328 
aluiiiinum-silicon-lron,  880 
antimouy,  336 
bismuth.  38^ 
caution  as  to  strength,  8V 
composition  of.  3*J5 
copper-nickel,  326 
copper-tin,  319 
copper-tin-zinc,  828 
copper-zinc,  321,  925 
copper-zinc  iron,  3M 
for  bearings,  338 
fusible,  83:) 
manganese-copper,  381 
ftteels,  407 

cAriation  of  strength,  888 
white-metal,  336 


Alternating  currents.  1066 
Altitude  by  barometer,  488 
Aluminum,  167 

alloys  of,  819, 328 

brass,  829 

bronze,  328 

Uronze  wire,  2S5 

hardened.  330 

properties  and  uses,  817 

steel,  409 

wire,  825 
Ammonia  ice-machines.  968 

vapor,  properties  of.  VHH 
Amperage    permissible   in   magnete 
106G,  1068  -»     •-• 

Analyses  of  alloys  (see  Alloys) 

of  axbesios,  236 

of  coals  (ncre  Coals) 

of  fire-clay.  284 

of  magnesite,  v35 

of  steel  (»ee  Steel)) 

of  water,  568 
Analytical  geometry,  09 
Anemometer,  491 
Angle,  the  economical,  447 
Angle-bars,  sices  and  wel«(hts,  179 

weight  and  strength.  2T9f« 
Angles,  plotting  without  protractor,  5S 

problems  in,  87,  8.S 
.A-iigular  velocity,  425 
Animal  power,  433 
Annealing,  effect  on  conductivity,  109 

iron,  effect  of,  on  magnetic  cap«4dty» 
396 

non-oxidizing  process  of,  887 

of  steel,  394.  413 
Annuities,  15-17 
.Annular  gearing,  898 
Anthracite,  analyses  of,  624 

gHS,  647 

space  occupied  by,  625 

value  of  sizes  of.  632 
Anti  friction  metals,  939 
Antimony.  167 

alloyR,  386 
Apothecaries'   measure  and  weighty 

18,  19 
.\rc  lamps,  lighting  power  of,  105S 
Arches,  tie-rods  for,  281 
Area  of  circles.  1C3,  108 

of  irregular  figures,  55,  66 
Arithmetic,  2 

Arithmetical  progre^ssion,  11 
Armature  circuit,  E.  M.  F.  of,  1061 

1083 


1084 


INDEX. 


jL8besto6, 986 

Asphalrum  ooatinfl:  for  Iron,  8S7 
A^ynlptote8  of  hvperbola,  71 
Atmosphere,  moisture  io,  408 

prefwure  of,  -181 
Atomic  weight  of  elements,  168 
Automatic  cut-oil  eugines,  753 
AToirdupols  weight,  19 
Azl«9fl,  steel,  speciflcaiions  for,  401 

strength  of,  .iM 

Babbitt  metals,  886 

fiaboock  &  Wilcox  boilers,  tests  with 

diilferent  coals,  686 
Bagasse  as  fuel,  648 
Balance,  to  weigh  on  an  incorrect,  10 
Ball  bearings,  040 
Bands  and  belts,  theory  of,  870 
Bands  for  carrjlng  grain.  Oil 
Barometric  readings,  488 
Barrels  (tee  Cables),  64 

Ko.  of,  in  tanics,  100 
Bars,  Low  moor  iron,  207 
Basic  Bessemer  steel,  strength,  809 
Baum6'8  hydrometer,  105 
Basin's  experimentH  on  weirs,  687 

formula,  flow  of  water.  56il 
Beams  and  channels.  ^78-279 
Beams,  ooefHcients  for  special  forms, 
S70 

flexure  of,  967 

of  uniform  strength,  271 

■afe  load  of  pine,  10b»,  1060 

safe  loads,  260 

strength  of,  268 

tie-rods  for,  281 

wooden,  10*28,  1060 
Bearing-metal  alloys,  888 
Bearing-metals,  anti-trlction,  089 
Bearings  (tee  Journal-bearings) 

ball,  040 

oaat-iron,  088 

for  high  speeds,  041 

oil-pressure  in,  037 

overheating  of,  088 

pivot,  030 

pressure  allowed,  085 

roller,  040 
Bed-plates  of  engines,  817 
Belt  cement,  887 

oonveyors.  Oil 

dresslngv,  h87 
BelUng,  876-887 

formula  for,  877 

rubber.  887 

rules  for,  880 
Belts,  adhesion  of,  886 

care  of ,  886 

C9entrif ugal  tension  of,  876 

endless,  8»6 

evil  of  tight,  bS5 

horse-power  of,  878 

lacing  of,  888 

open  and  crossed,  874, 884 
>     setting  a  twist,  888 

Sise  of,  885 

width  for  given  H.P.,  870 
Bends  and  curves,  effect  of,  on  flow  of 
water.  578 


Bends,  valves,  etc.,  resistance  to  flo 

in,  488,  679 
Bessemer  steel,  801 
Bessemerised  cast  Iron,  87.> 
Bevel-wheels,  808 
Binomials,  theorem,  88.  85 
Birmingham  gauge,  28 
Bismuth,  167 

alloys,  839 
Bituminous  coal  {see  Coals) 
Blastrf  urnace  boilers,  689 
Blocks  or  pulleys,  488 

strength  of.  006 
Blowers,  steel  pressure.  05O 
Blowers  and  fans,  511-{i:.>0 

capacity,  517 

centrifugal,  518 

comparative  efOciency,  516 

experiments  with,  514 

for  cupolas,  510,  060 

positive  rotary,  528 

steam-jet,  5'«>7 
Blowing-engines,  596 
Blue  heat,  effect  on  steel,  30& 
Board  measure.  20 
Boiler  compounds,  717 

explosions,  720 

feed-pumps,  605.  786 

furnaces,  neight  of,  771 

heads,  706 

heads,  strength  of.  284-28C 

heads,  wrought-irou,  285 

scale,  559 

ship,  and  tank  plates,  800 

testa,  niles  for,  600 

tubes,  106 

tubes,  holding  power  of,  307 
BoUer8(«ee  Bteani-boilers),  677-741 

for  steam-heatiug,  58S 

locomotive,  855 
Boiling-point  of  water,  500 
Boiling-points,  455 

resistance  to,  468 
Bolts  and  nuts,  200,  211 

track,  210 

weightof,  210.  211 
Bolts,  holding  power  of,  200 

initial  strain,  2»9 

Iran  for,  906 

strength  of,  202 
Brackets,  cast-iroo.  strength  of,  SS9 
Brass  alloys.  825 

composition  of  rolled,  903 

sheet  and  bar,  208 

tubing,  106-9000 

wire  and  platen,  209 
Brick,  Are,  sbses  of.  983, 884 

strength  of,  302,  812 
Bricks,  absuration  of  water  by,  819 

magnesia,  SS5 
Brickwork,  weight  of.  108 
Bridge  iron,  durability.  tt«<5 

members,  working  8ti*ain,  2ffi 

proportionlag  materials  in,  381 

trusses,  448 
Brine,  resistance  to  boiling.  468 

specific  gravity,  etc.,  464,  094 
Bronse  (aee  Aliovs),  310-831 

aluminum,  820 


IKDE^. 


1085 


bronze,  ancient,  8S8 

(ieoxidized,  927 

iiiaiiganese,  8S1 

phosphor,  8S7 

propeller-blade,  800 

Tobin,  887 

▼ariation  of  ■trength,  831 
z^uilding;  construction,  laws  of,  1010 

inatt'riiUs,  coefHcient  of  fricilon,  ft29 

materials,  sizes  aud  weights,  170.  ItA 
buoyancy,  650 
liurr  truss,  443 

:;ables,  chain,  806 

electric,  insulated,  1088 

strength  of.  888 

suspension-bridge,  SSO 
:?able-ways,  suspension,  915 
lra«1mlum,  167 
::;alculus,  differential,  72 
Jaioric  engines,  851 
::alorimeter8,  steam,  738 
i^alorimetric  tests  of  coal,  680 
:;am,  the,  488 

::anals,  speed  of  vessels  on,  1008 
iJanvas,  strength  of,  803 
;3arbon,  burned  out  of  steel.  402 

effect  of,  on  strength  of  steel,  889 
:?ar-axles,  steel  for,  401 
:;ar- heating  by  steam,  538 
Jaslcs,  64 
i^astings,  iron,  analyses  of,  878 

strength  of.  297 

shrinkage  of,  961 

steel,  405 

weighi  of,  from  pattern,  953 
?ast  iron,  866-875 

and  steel  mixtures,  875 

bad,  875 

chemical  elements,  865 

columns,  strength  of,  350 

durability,  886 

hollow  columns,  350 

malleable,  875 

piiM*s,  18&-190 

solid  columns,  250 

specific  gravity,  874 

speeiflcations,  874 

strength  of,  869,  874 

tests,  869 
Datenary,  construction  of,  51 

the  wire  rope.  919 
Cement,  weight  of,  170 

for  belu,  ^7 

mortar,  strength  of,  818 

Portland,  803 
Centigrade  and  Fahrenheit  table,  449 
Centre  of  gravity,  418 

of  gyration,  480 

of  oscillation,  431 

of  percussion,  431 
Centrifugal  fans,  511 

force,  438 

force  ill  fly-wheels,  830,  832 

tf  iKioii  or  belts,  876 
tViti  rif  *igal  pumps,  606 

efflcif  ncy  of.  608 

tests  of,  609 

ventilators,  521 


Oera-perduta  process,  alloys  for,  836 
Chain-blocks,  907 
Chain-cables,  808,  840 
Chains,  crane,  283 

weight  aud  strength,  807,  889 
Channel-beams,  sizes  and  weight,  13^ 

180 
Channel-irons,  tests  of,  S97 
Channels,  steel,  strength  of,  277 
Charcoal,  640 

alMOrption,  641 

composition,  642 

making,  resulu*,  641 

piif  iron,  866,  874 

weight  of,  ITO 
Chemical  elements,  168 
Chimneys.  781-741 

brick,  787 

for  ventilation,  588 

protection  from  lightning,  787 

shafts,  weak.  789 

stability  of,  788 

size  of,  784 

SI  eel.  740 

sheet-iron,  741 

table  of  sizes  of,  785 
Chords  of  circles,  57 
Chrome  steel,  409 
Ciix:le,  equation  of,  70 

measures  of ,  57, 68 
Circles,  problems,  89, 40 

tables  of,  108, 10& 
Circular  arc,  length  of,  67, 66 

iircs,  tables  of,  114. 115 

functions  in  calculus,  78 

measure,  20 

ring,  69 
Cireuiating-pump.  889 
Circumference  of  circles,  108,  106,  IIS 
Cisterns,  cylindrical,  121, 13b 
Clearance  in  steam«engiiies,  731, 792 
CohIs,  analyses  of,  634-081 

calorimetrlc  tests,  686 

classification,  6iM 

evaporative  power  of,  686 

foreign,  681 

heating  value  of,  68i 

navigaUon,  Welsh,  689 

Ohio,  63  7 

Peuusylvania,  634 

relative  value  of.  683 

Southern  and  Western,  638 
Coal  gas,  illuminating,  651 

hoisting,  848 

products  of  disailation  of,  689 

washing,  688 

V  eathering  of,  687 
Co  I  tings  for  iron,  etc.,  887 
(  o  efficient  of  elasticity,  387, 814 

of  fineness,  1003 
C<  •efficients  for  beams,  270 

or  friction,  938-983 

«f  a  propeller,  1011 

of  water-lines,  1003 

of  performance  of  vessels,  lOOb 
Coiled  pipes,  199 
ColiH,  heathig  of ,  1066 
Ct.ke.  687 

manufacture,  by-products,  689 


1086 


IXDEX« 


Ookiogv  experiments  In,  687 

Cold,  effect  of,  on  iron  aod  steel,  883 

rolling,  effect  of,  808 
Gold-diumng  steel.  805 
Oold-sawing  Iron.  966 
OoUapse,  resiRtauce  of  hollow  cylin- 
ders to,  '264 
Oolumns,  built,  296 

cast-iron,  strenRth  of.  260 

cast-iron,  weight  of.  185 

eccentric  loading,  -.'51 

Merrl man's  furmuln,  259 

sieel,  261 

strength  of,  246-260,  1019 

stresses,  252 

tvrought-iron,  255,  260 

wrought-iron,  tests  or,  805 
Combined  stresses,  282 
Combination,  10 
Combustion,  heat  of,  456,  621 

gases  of,  622 

rate  due  to  height  of  chimney,  738 

theory  of,  620 
Composition  of  forces,  415 
Compound  engines,  761-768 

engines,  condensing.  788 

engines,  diameter  of  cyhnder,  768 

engines,  economy  of,  7iV 

engines,  efficiency  of,  784 

engines,  non-condeuHing.  784 

engines,  receiver-space.  766 

engine,  two-  v«.  three-cylinder,  781 

engines,  work  of  nteani  in,  707 

engines,  velocity  of  steam  in,  772 

interest,  14 

locomotives,  862,  863 

numbers,  5 

units  of  weight  and  measure,  27 
Compressed  air,  488,  499 

cranes,  912 

drills  driven  by,  506 

efficiency  of,  508 

engines,  efficiency  of,  506 

formulSB,  501 

for  underground  pumps.  611 

mean  effective  pressui  e  for,  502 

motors,  507 

practical  resuUs  with.  505 

shops  operated  by,  509 

system  in  Paris,  507 

tramway^  5a0 

transmission,  488 

utilization  in  motors.  507 
Compressed  steel,  410 
Compression  and  expnnsion  of  air,  503 

in  steam-engines,  ih\ 

unit  strains  in  structures.  380 
Compression  and  ttu-sion,  stresses,  288 
Compresftive  strength,  244 

of  Iron  bars,  301 
Compressors,  air,  503 
Conoenser,  evaporutive  surface,  844 

increase  of  power  by,  846 
Condensers,  839-846 

elector,  810 

jet.  839 

surface,  840 
Oondenf(f>r-tubes,  transmission  of  heat 
in,  478 


Condenslog  water,  continuous  use  ct 

844 
Conduction  of  heat,  468 
Conductivity,  electrical,  1028 

of  steel,  inflaenoe  of  compositioii  c? 
408 
Conductors,  electrical,  1029 
Cone,  measures  of,  61 

pulleys,  874 
Conic  sections,  71 
Conoid,  parabolic,  63 
Connecting-rods,  799 

Upered,  801 
Conservation  of  energy.  433 
Construction  of  buUdinnFB,  1019 
Convection  of  heat,  471 
Conveyors,  belt,  911 
Cooling  of  air  for  ventilation,  531 
Coordinate  axes,  69 
Copper,  167 

at  high  temperatures,  strength  c' 

bails,  hollow,  S89 

nicicel  alloys.  886 

round  bolt,  203 

strength  of,  800 

tin  alloys,  819 

telegraph  wires,  221 

tubing.  200 

wire  and  plates,  909 

wire,  tables  of.  218-220 

wire,   resistanoe  of  hot  and  c*ku. 
1084,1035 

wire,  cost  of.  for  long-distance  tnc 
mission,  1044 

zinc  alloys,  821 
Cordage,  841,  844.  906 
Cork,  properties  of.  816 
Corrosion  of  iron,  Zf*6 

of  steam-boilers,  716.  719 
Corrosive  agents  In  atmosphere.  9% 
Corrugated  iron.  181 

furnaces,  266,  702.  709 
Cosecant  of  an  angle.  65 
Cotiine  of  an  angle,  65 
Cosines,  tables  of,  150 
Cost  of  coal  for  steam-power,  7¥9 

of  steam-power,  790 
Cotangent  of  an  angle.  65 
Counterbalancing  engines,  7T9 

locomotives,  864 

of  winding-engines,  909 
Couples,  418 

Coverings  for  steam-pipes.  470. 471 
Cox*s  formula  for  loss  of  head.  575 
Crane,  chain,  282 

electric,  912 

simple,  a,  440. 441 
Cranes,  classification  of,  911 

compressed-air,  9l8 

stress  in.  440 
Crank  angles,  880 

Mi-ms.  805.  806 

pins,  80U801 

pins,  steel  for,  400 

shaft,  torsion  and  flesure,  81« 

Hhafts,  813 
Cross-head  guides,  798 

pins.  804 


INDEX. 


1087 


Cracible  steel,  410 

CnishinR  strength  of  maaoiiTy  mate* 

rials,  SU 
Cubature  of  volumes  of  revolution,  75 
Cube  root,  8 

Cubes  and  cube  roots,  table  of,  86 
Cubic  measure,  18 
Cupola,  capaoity  of,  9S0 

ctiarginfc  of,  945 
Cupolas,  blast-pipes  for,  619 

blowers  for,  6l9 

practice,  946 
Current  motors,  699 
Currents,  electric,  1030 
Cutting  stone  with  wire.  966 
Cycloid,  construction  of,  49 

differential  equation  of,  79 

measure  of.  W 
Cycloidal  teeth  of  Rears,  692 
Cylinder  condensation,  762,  768 
Cylinders  and  pipes,  contents  of,  190, 
131 

ensdne,  dimensions  of,  792 

hollow,  resistance  of,  264 

hollow,  strenfcth  of,  'JS7,  288 

measures  of,  61 

under  tension,  269 
Cylindrical  ring,  62 

Dangerous  steam-boilers,  720 

Dam,  stability  of  a.  417 

D'Arcy*s  formula,  flow  of  water,  668 

Decimal  equivalents  of  fractions,  3,  4 

Decimal  gauge,  32 

Decimals,  8 

squares  and  cubes  of,  101 
DecK-beams,  sises  and  weights,  177 

strength  of,  278 
Delta  metal,  225,  826 
Denominate  numbers,  5 
Deoxidized  bronze.  827 
Derricics,  stresses  in,  441 
Diametral  pitcti,  888 
Differential  calculus,  72 

forms,  integrals  of,  78,  79 

gearing.  096 

pulley,  489 

screw,  489 

screw,  efficiency  of,  974 

windlass,  489 
Discount  and  interest,  18 
Disk  fans,  air  removed  by,  626 

efficiency  of,  625 

experiments  with,  624 
Displacement  of  vessels,  1001, 1008 
Draught  of  chimneys,  781 
Drawing-presses,  blanks  for,  078 
Drilling  holes,  Bpeed  of,  956 

machines,  electric,  956 
Drills,  speed  of  twist,  957 

tap,  970 
Drop-press,  pressure  of.  973 
Drunks  for  hoisting-ropes,  917 
Drying  and  evaporation,  462 

in  vacuum,  466 
Dry  measure.  18 
Ductility  of  metals,  169 
Dust  explosions,  642 

fuel,  642 


Durability  of  iron,  885 
Durand*s  rule  for  areas.  56 
Duty  trials  of  pumping-eufrines,  609 
Dynamo  and    engine,   efficiency  of, 
1047 

electric  machines,  1060 
Dynamos,  designing  of,  1068 

efficiency  of,  1064 
Dynamometers,  978 

transmission,  980 

Earth  fllllng,  weight  of,  170 

Earths,  weight  of,  170 

Ek^centric  loading  of  columns.  254 

Eccentrics,  steam-engine,  816 

Economizers,  fuel,  715 

Edison  or  circular  mil  wire  gauge. 

29,80 
Efficiency  of  a  machine,  482 

of  boilers,  688,  689 

of  electric  transmission,  1047 

of  pumps,  608.  606 

of  steam-engines.  749.  775 
Effort,  definition  of,  429 
Ejector  condensers,  840 
Elastic  limit,  286 

resilience,  270 

resistance  to  torsion,  iSi 
Elasticity,  modulus  of,  2^17,  814 
Electric  sccumulators,  105:) 

conductivity  of  steel,  4U8 

generator,  efficiency  of,  1047 

heating,  546, 1062 

lighting,  1049 

motor,  1066, 1067 

pumping-plant,  1048 

railways,  1048 

transmission,  1038 

transmission,  economy  of,  I0S9 

welding,  1061 
Electrical  engineering,  1024 

horse-powers,  table  of,  1041 

resistance,  10*^8 

standards  of  measuremen*^,  1024 

units,  1024 
EUectrlcity,    analogy    with    flow   of 
water,  1027 

beating  by,  546, 1052 
EUectro-chemical  equivalents,  1056 
Electro-magnetic  measurements,  1067 
Electro-magnets.  1067 

polarity  of,  1059 
Electrolysis.  1056 
Elements,  chemical,  163 

of  machines,  486 
Ellipse,  construction  of,  45 

equation  of,  70 

measures  of,  59 
Ellipsoid,  68 

Elongation,  measure  of,  213 
Emery,  grades  of,  9C8 

wheels,  967-969 

wheels,  speed  and  selection,  96f 

wheels,  strains  in,  96*J 
Endless  screw,  440 
Energy,  conservation  of,  482 

of  recoil  of  guns,  481 

or  stored  work,  4'^ 

sources  of,  432 


1088 


INDEX. 


Eni^ne  frames  or  bed-plates,  817 
EiiRiues  («ef  Steam-enKiDee) 

blowing,  6i26 

gM,  847 

ffasoline,  8S0 

hoistinfc,  006 

hot-air,  »51 

marine,  8iz<»s  of  steaio-plpes,  074 

naphtha,  851 

petroleum,  860 

Hteam,  74^-847 

triple-ezpanalOD  steam,  769 

winding:.  909 
Epicycloid,  50 
Equalization  of  pipes,  491 
Equation  of  paymentB,  14 
Equations,  algebraic,  84 
Equilibrium  of  forces,  418 
Equivalent  orifice,  588 
tCrosion  bv  flow  of  water,  665 
^▼aporating  by  exhaust-steam,  465 
Evaporation  and  dryiUR,  46i 

by  the  multiple  system.  465 

from  open  channels,  468 

from  reservoirs,  468 

latent  heat  of,  461 

salt-making,  468 

table  of  factors  of,  095 

total  heat  of.  463 
Evaporators,  fresh-water,  1016 

Weir's,  847 
Evolution,  7 

Ezhaust-steam  for  heating,  780 
Exhausters,  steam-jet.  6si7 
Expansion  by  heat,  459 

of  Iron  and  steel,  8ti5 

of  steam,  742 

of  steam,  real  ratios  of,  750 

of  wood,  811 
Explosive  energy  of  steam-boilers,  730 
Exponentft,  theory  of,  86 
Exponential  functions.  In  calculus,  78 
External  conduction,  rate  of,  470 
Eye-bars,  tests  of,  804,  898 

Factor  of  safety,  814 

in  steam-boilers,  700 
Factors  of  evaporation,  tables,  695 
Fahrenheit  and  Centigrade  uible,  450 
Failures  of  steel,  408 
Falling  bodies,  4^-4*26 
Fans  and  blowers,  capacity,  517 

centrifugal,  518 

efficiency,  &iO 

efficiency  of  ventilation  by,  538 

pressure,  518 

properties  of,  613 
Feed-pumps,  848 

Feed-water,  cold,  strains  caused  by, 
727 

heater,  Weir*s,  1016 

Jieaters,  727,  1078 


purifying,  654 
riore-grapnli 


Fibre-graphlie.  045 

Fifth  roots  and  fifth  powers,  108 

Fink  roof-truro,  446 

Fire,  temperature  of,  682 

Firebrick,  nizes  of,  28).  234 

Fire-clay,  analysis  of,  234 


Fire-engines,  capacities  of,  860 

Fireless  locomoave,  8b0 

Fire-proof  buildings,  1020 

Fire-streams,  571) 

Flagging,  transverse  stTength  of,  813 

Flanges,  pipe,  10«.  108 

Flat  plates  In  steam-boilers,  TCI,  709 

plates,  strength  of,  288 
Flexure  of  beams,  867 
Flooring  material,  weight  of,  S81 
Floors,  strength  of,  1019,  lOKl 
Flow  of  air  in  pipes.  485 

of  air  through  orifices,  484 

of  compressed  air,  480, 498 

of  gas  in  pipes,  657 

of  metals,  OtS 

of  steam  in  pipes.  609 

of  water  from  orifices.  556,  5B4 

of  water  in  house  service- pipes,  5iC 

of  water  over  weirs,  580 
Flowing  water,  horse-power  of.  £80 

measurement,  662 
Flues,  collapse  of,  266 

corrugated,  British  rules,  266,  708 

corrugated,  U.  8.  rules.  709 

(mre  auo  Tubes  and  Boilers) 
Fly-wheels,  fl]7-8M 

arms  of,  620 

centrifugal  force  in,  820 

diameter  of,  Sil 

strains  in  rims,  888 

thickness  of  rims,  828 

wire-wound,  824 

wooden,  828 
Flynn's  formula,  flow  of  water,  56S 
Foot,  decimals  of,  in  fractious  of  iocb, 
118 

pound,  unit  of  work,  488 
Force  of  a  blow,  480 

centrifugal.  428 

expression  of,  489 

moment  of,  416 

of  acceleration,  427 

representation  of,  415 

unit  of,  415 
Forced  draught  in  marine  practice 

1015 
Forces,  composition  of,  416 

equilibrium  of,  418 

parallel,  417 

parallelogram  of,  416 

parallelopipedon  of,  410 

polygon  of.  416 

resolution  of,  415 
Forcing  and  shrinking  fits,  073 
Forging,  broken  anchor,  297 

hydrauUc,  618,  020 

iron.  897 

locomotive.  807 

tool-steel,  418 
Foundry,  the,  946-056 

iron,  analysis,  871 

iron,  chemistry  of,  870 

Irons,  grades,  8*8 

practice,  960 
Fractions,  S 

Francis*8  formula  for  weirs,  386 
Freezing  of  water.  660 
French  measures  and  weights,  S1-8S 


INDEX. 


1089 


Friction  and  lubrication,  93S-M5 

brakes,  960 

car- journals.  987 

Morin'alawof,  983 

of  air  in  passages,  581 

of  steam-engines,  941 

pivot-bearings,  980 

rollers,  940 

work  of,  988 
Frictional  heads,  flow  of  water,  577 
Fuel,  6:i0.651 

analysis  of  gases,  822 

bagasse  as,  848 

economisers,  715 

gas,  646 

miscellaneous  solid,  642 

peat  or  turf,  648 

pressed.  646 

rise  of  temperature,  688 

sawdust,  648 

straw  as,  643 

theory  of  o«mbu8tion  of,  680 

temperature  of  fire,  6sU 

weight  of,  170 

wet  tan  bark,  648 
Fuels,  classification  of,  688.  084 
Furnace,  downward-draught,  68S,  718 

kinds  of,  for  different  coals,  685 

formulsB,  703 
Furnaces,  corrugated,  866, 70fiL  709 

for  boilers,  711 

gas-fuei,  651 

use  of  steam  in,  650 
Fusible  allOTS,  8S3 

plugs  for  Doilers,  710 
FusibaitY  of  metals,  169 
Fusing-disk.  Beese's,  966 
Fusii»<  of  wires  by  electric  currents, 

temperatures,  455 

g,  value  of,  494 

Gallons  and  cubic  feet,  table,  188 
Galvanic  action,  corrosion  by,  8ti6 
Galvanized  wire  rope,  888 
Gas.  ammonia.  998.  998 

calorific  emiivalents,  654 

engines,  847 

engines,  efficiency  of,  848 

engine  test,  840 

fired  steam-boilers.  714 

flow  of,  in  pipes.  657 

for  small  furnaces,  651 

fuel,  646,  1078 

illuminating,  651 

illuminating,  fuel  value  of,  656 

natural,  649 

pipe,  sizes  and  weights,  188,  194 

producers,  649,  650 

sulphur-dioxide,  998 

water.  648-658 
Bases,  absorption  of.  480 

Avogndro's  law,  479 

expansion  of,  by  heat,  459 

flow  of,  480 

heat  of  combustion  of,  456 

law  of  Charles,  479 

Mariotte's  law,  479 

properties,  816 


Gases,  specific  heat  of,  458 

weight  and  specific  gravity  of,  168 

waste,  use  under  boilers,  689,  690 
Gasoline-engines,  850 
Gauges,  wire  and  sheet-metal,  88^38 
Gear,  reversing,  816 

teeth,  strength  of,  900-906 

wheels,  properties  of.  891 
Gearing,  annular  and  differential,  896 

comparison  of  formulas,  90ei,  908 

cycloidal  teeth,  89Bi 

dimensions  of,  890 

efficiency  of,  899 

frictional,  905 

involute  teeth,  894 

of  lathes,  955 

speed  of,  906 

spiral.  899 

strength  of,  900 

toothed-wheel,  439,  887-006 

twisted  teeth.  897 

width  of  teeth,  891 

worm,  897.  1078 
Geometrical  problems,  87 

progression,  11 

propositions,  53 
German  silver,  886,  S88 

silver,  strength  of,  300 
Girder,  Iron  plate,  >t07 
Girders  for  boilers,  708  ' 

strains  on,  1080 
Glass,  skylight,  184 

sti-ength  of,  308 
Gold,  167 

Gordon's  formula,  847 
Governors,  836 
Grain,  weight  of,  170 
Granite,  strength  of,  318 
Grate-  and  heating-surface  of  a  boiler* 

678 
Graphite  as  a  lubricant,  945 

paint,  889 
Gravity,  acceleration  due  to,  484 

centre  of,  418 

specific,  163 
Greatest  conmion  measure,  8 
Greenhouse-heating  by  hot  water,  549 

by  steam,  541 
Green's  fuel-economizers,  718 
Grindstones,  968.  970 

safe  speeds.  968 

strains  in,  968 

varieties,  970 
Gyration,  centre  and  radius  of,  847. 
249,  480,  481 

Haulage,  wire-rope,  018 
Hawley  down-draught  furnace,  712 
Hawsers,  steel,  228,  230 
Heads  of  boilers,  706 

unbraced.  885 

wrought-iron,  285 
Heat.  448-478 

boiling-points,  456 

conduction  of,  468 

convection  of,  471 

equivalent,  mechanical,  456 

expansion  by,  4.^9 

generated  by  electric  currents,  1032 


1090 


IKDEX. 


Heat.  latent,  461 

latent,  of  evaporation,  463 

Jatent,  of  fusion,  461 

meltine-poinut,  455 

of  combustion,  466 

radiation  of,  467 

■peciflc.  467 

storing  of,  788 

transmission,  in   condenser  tubes, 
478 

transmitting  power  of  substances, 
478 

unit,  456,  660 
Heaters,  feed-water,  727 
Heating  a  buUding  to  70°  F.,  546 

and  ventilation,  528-546 

blower  system  of,  545, 1071 

by  electricity,  646,  lOHZ 

by  exhaust  steam,  780 

by  hot  water,  542 

greenhouse  by  steam.  541 

of  electric  conductoiR,  1088 

of  large  buildings,  684 

surface  of  boilers,  678 
Heine  boiler,  test  wiih  different  coals, 

688 
Helical  springs,  capsclty,  340 

for  locomouves,  358 

steel,  847 
Helix,  60 

Hobson^s  hot-blast  pyrometer,  458 
Hodgkinson^s  formula,  :;!4ti 
Hoisting,  906-916 

coal,  848 

engines,  power  of,  003 

pneumatic,  909 

rope,  840 

rope,  stress,  915 

weight  and  strength.  906 
Hollow  cylinders,  collapse  of,  2C4 
Hooks,  hoisiing,  907 
Horse-gin,  484 

work  of  a,  484 
Horae-power,  439 

constants,  757,  758 

electrical,  1041 

of  flowing  water,  680 

of  steam-boilers.  677.  G79 

of  steam-engines,  755 

power-hours.  4**>9 
Hose,  friction  losses  in,  ^ 
Hot-air  engines,  851 
Hot  boxes,  experiments  on.  938 
Hot  water,  diameter  of  pipes.  548 

rules  for  heating  bv,  M4 

velocity  of  flow,  542 
Howe  truss,  445 
Humiditv  in  atmosphere,  483 
Hydraulic  apparatus,  610 

engine,  619 

formulae,  557 

machinery,  friction  of,  616 

pipe,  191 

ram,  efllciency  of.  614 

ram.  water  delivered  by,  615 

riveting-machines,  618 
Hydraulics,  flow  of  water,  556-588 

forging,  618 

grade-line,  578 


Hydraulics,  power,  617 

pressure  transmission,  616 

ram,  614 

speed  of  hoisting  by.  617 

tnickness  of  cylinders,  617 
Hydrometer,  165 

Hygrometer,  dry-  and  wet-bnlb,  4€3 
Hyperbola,  equation  of.  71 

construction  of,  49 
Hyperbolic,  loearithms  156 

curve  in  indicator-diagrams,  7Z^ 
Hypocydoid,  60 

I-beams,  sixes  and  weights,  177 

properties  of,  8713 

spacing  of,  276 
Ice  and  snow,  550 
Ice-making  machines,  961-1001 

manufacture,  990 
Illuminating  gas.  651 

fuel  value  of.  759 
Impact  of  bodies,  481 
Incandescent  lamps,  1040 
Inches  and  fractions,  decimals  of  a 

foot,  112 
Inclined  plane,  487 

planes,  hauling  on,  018,  915 

planes,  motion  on,  4S8 
Incrustation  and  Fcale.  551,  716 
India  rubber,  tests  of.  316 
Indicated  horse- power,  756 
Indicator  diagrams,  754,  759 

errors.  766 

pendulum  rigs.  759 

tests  of  locomotives,  86S 

water-consumption.  700 
Indirect-beating  surface,  59f 
Inertia,  415 

moment  of,  247.  419 

of  railroad  trains,  868 
Injectors,  725 

Inspection  of  steam-boilers,  790 
Insulators,  electrical,  1039 
Integral  calculus,  70 
Integrals,  integration,  73,  74 

of  differential  forms,  78,  79 
Intenslfler.  hydraulic,  619 
Interest  and  discount,  18 

compound,  14 
Interpolation,  formula  for,  107O 
Involute  gear-teeth,  804 

construction  of,  68 
Involution,  6 
Iridium.  167 
Iron,  167 

bars,  sizes  of,  170  | 

bars,  strength  of,  897 

bars,  weight  of,  171 

bridges,  885  , 

corrosion  of.  885  I 

durability  of.  886 

forgings,  locomotive.  897  i 

manganese  plating,  9^ 

preservative  coatings  for,  889  ' 

shearing  strength  of,  806 

stay-bolt,  879 
Iron  and  steel  boilerplate.  8SJi 

clAS<)iflcation  of.  :364 

cold-rolling  of,  898 


IHDSX. 


1091 


Iron  and  steel,  expansion  of,  886 

inoxldizable  surfaces,  886 

rustless  coatings,  886 

sheets,  weight  of,  88,  174 

spectflcatioDs,     PennsylYania  Bail- 
road,  878 

strength  of,  896-4K)0 

strength  at  high  temperature,  88S 

strength  at  low  temperature,  868 
Irregular  figure,  area  of,  65,  56 

solid,  volume  of,  64 
Irrigation  canals,  564 
laotnermal  expansion,  743 

Japanese  alloys,  336 
Jet  condensers,  889 

propulsion  of  vessels,  1014 
Jets,  vertical  water,  679 
Joints,  riveted,  854-868 

double-riveted.  858 

efficiency  of,  859 
Joule*s  equivalent,  456 
Journal-bearings,  810-815 

bearings,  caiiuiron,  988 

friction,  900-089 
Journals,  engine,  810-815 

Kerosene  for  scale  in  boilers,  ^718 
Keys  and  set-screws,  977 

for  mill'gearing,  975 

holding  power  of,  977 
Kinetic  energy,  429 
King-post  truss.  44^2 
Kirkaldy*s  tests  of  materials,  296 
Knot,  or  nautical  mile,  17 
Knots  in  ropes,  344 
Kutter's  formula,  559 

lacing  of  belts,  888 
Ladles,  foundry,  sizes  of,  958 
Latent  heat,  461 

heat  of  evaporation,  461 

heat  of  fusion,  459>461 
Lathes,  change  gears,  956 

cutting  speeds,  954 

H.  P.  required,  961 

rule  for  setting  taper  in,  966 
Lap  and  lead  of  a  valve,  8'.i9-838 
Lead,  167 


pipe.  200, 201 
>akag 


Leakage  of  steam  in  engines,  761 
Least  common  multiple,  2 
Leather,  strength  of.  30*^ 
Le  Chatelier's  pyrometer,  451 
Levelling  by  barometer,  4tii 
Lever,  the  bent,  486 
Levers,  435 

Lignites.  Western.  681 
Lime,  weight  of,  170 
Limestone,  strength  of,  318 
Limit  gauges  for  screw-threads,  205 
Lines  of  force,  1068 
Link  motion,  884, 1077 
Links,  engine,  816 

Lintels,  bearings  add  supports,  1020 
Liquation  of  alloys,  828 
Liquid  measure,  18 
Liquids,  expansion  of.  461 
weight  and  specific  gravity,  164 


Locomotive,  flreless,  806 
Locomotives,  851-866, 1075 

American  types,  868 

compounding,  advantages,  868 

counterbalancing.  864 

dimensions  of,  ^9^.86^ 

fire-brick  arches,  856 

forgings,  297 

free-steaming,  855 

Cte-surface,  boller,855 
:  motion,  1077 

performance,  1076 

petroleum-buminff,  865 

size  of  cylinders,  854 

size  of  boilers,  866 

tests  of,  863 

tractive  power.  856 

waste  of  fuel,  868 

water-consumption,  868 

Wootten*s,  855 
Logarithmic  curve,  71 

sines,  etc.,  162 
Logarithms,  hyperbolic,  156 

differential  or,  77 

of  numbers,  127-155 
Logs,  lumber,  etc.,  weight  of,  888 
Loop,  thA  steam,  676 
Loss  of  head  in  pipes,  573 
Lowmoor  iron  bars,  297 
Lubricating-oils,  examiaation  of,  944 
Lubricants,  amount  of  oil  to  run  a» 
engine,  943 

relative  value,  948 

solid,  945 
Lumber,  weight  of,  888 

Machines,  elements  of,  485 
Machine-shop,  the,  953-978 

shop  practice,  968 

shops,  power  used  in,  966 

screws,  206,  809 

tools,  power  required  for,  960-96^ 

tools,  power  used,  968 

tools,  proportioning  sixes  of,  976 
Maclaurin's  theorem,  76 
Magnesia  bricks,  285 
Magnesium,  ItfR 
Magnetic  balance,  896 

capacity  of  iron,  effect  of  annealini^ 
on,  896 

circuit,  1059 

circuit,  units  of,  1067 

field,  strength  of,  1062 
Magnets,  electro-,  1067 
Malleability  of  metals,  169 
Malleable  ca<ttings.  rules  for,  376 

cast  iron,  375 
Mandrels,  sizes  of,  978 
Manganese,  168 

bronze,  831 

infiuence  of,  on  cast  Iron,  868 

infiuence  of,  on  steel,  889 

plating  of  Iron,  887 

steel,  407 
Mannesmann  tubes,  290 
Manometer,  air,  481 
Man -power,  483 
Manure  as  fuel,  648 
Man-wlie«l,  461 


1092 


INDEX. 


Marble,  strengrth  of,  808 
Marine  enpneeriug,  1001-1018 

engine,  horae-power  of,  7«6 

engine  practice,  1015 

engine,  feed-pump  for,  84S 

engine,  thiclcneH8  of  cylinder,  799 

engine,  three^stage  ezpanaion,  1017- 
lObO 

engine,  triple^xpanalon.  816 

engine,  ratio  of  cylinders,  766,  778 
Marriotre'B  law.  479,  742 
Masonry  materials,  strength  of,  818 

materials,  weight  and  sp.  gr.,  100 
Mass.  487,  489 
Materials.  163-885 

strensch  of,  886-418 
Maxima  and  minima,  76 

without  the  calculus,  1070 
Mtouures  and  weights,  17 

of  work,  power,  and  duty,  |S7 
Measurement  of  air,  491 

of  elongation,  848 
Mechanical  equivalent  of  hest,  456 

powers  («ee  Elements  of  Machines), 
485 

stokers,  711 
Mechanics,  415-447 

elements  of,  485 
Mekaralci  compressed-air  tramway,  510 
Meliing-polnts  of  substances.  465 
MeinphiH  bridge,  strains  on  steel,  881 
Mf  UHuration,  54 
Mercurial  thermometer,  448 
Mercury,  168 

bath  pivot,  940 
Merrlnian*s  formula  for  columns.  960 
Mesur6  and  NouePs  pyrometer,  458 
Mecaline,  945 
Metals,  flow  of,  978 
'  properties  of,  167 

speciflc  gravity  of,  164 

table  for  calculating  weight  of,  169 
Metric  conversion  tables,  88-^ 

measures  and  weights,  81,  88 
Meters,  water,  579 
Mil.  circular.  18,  :.'9 
31illing  cutters.  957 

cutters  for  gears.  898 

machines,  results  with,  959 

pitch  of  teeth,  957  « 

speed,  958 
Mill  power.  589 
Miner's  inch,  18 

inch  measurement,  IS85 
Mine- ventilating  fans,  581 

ventilation.  Ml 
Modulus  of  elasticity.  287,  314 
Moisture  in  steam.  i88 
Mi>iesworth'8  formula,  flow  of  water, 

568 
Moment  of  force,  416 

of  inertia.  847,  419 

statical,  417 
Momentum,  4^ 
M»i  m*s  laws  of  friction,  983 
Mortar,  strength  of,  3l8 
Motion,  forniulfiB  for,  4'^ 

Newton's  lawHof.  415 

on  inclined  planes,  488 


31otion.  perpetual,  489 

retarded,  484 
Motor,  electric,  1066, 1067 
Motors,  comprt^HHeil-air,  007 
Moulding-sand.  958 
Movmg  strut,  486 
Mules,  power  of.  485 
Multiphase  currenOi,  1070 
Muabet  steel,  409 

Nails.  818. 816 

screws,  etc..  holding  power,  26&-89) 
Naphtha-engines,  861 
Napier's  rule  for  flow  of  steam.  669 
Natural  gas,  649 
Nautical  measure,  17 
Newton's  laws  of  motion,  4X5 
Nickel.  168 

alloys,  886,  888 

Rieel.  406 

Kteel,  tests  of,  408 
No^Ezles,   measurement  oi    wAter  by, 

584 
Nuisandboltfl,809,811 

Ohm.  definition  of.  1085 
Oiun's  law,  1080 
Oil,  flre-test,  944 

lubricating.  944 

needed  for  engineis  943 

parafflne,  944 

well,  945 

weight  per  gallon.  944  ^ 

Open-hearth  steel.  891 
Ores,  weight  of,  170 
0>ci nation,  centre  of,  481 
Oxen,  power  of,  485 
Ordinates,  69 

V,  value  of,  57 

I'Ackingrings,  engines, 796 

Paddle-wheels,  1018 

Paint,  qualities  of.  887 

Painting  wood  and  iron  structures,  M 

Parabola,  construction  of,  48 

equation  of,  79 
Parabolic  conoid,  68 
Parallel  forces,  417 
Parallelogram,  54 

of  forces,  416 
Parentheses,  88  i 

Partial  payments,  15  ' 

Peat  or  turf,  M8 

Pelton  water-wheel,  597  | 

Pendulum,  488 

conical,  488 
Percussion,  centre  of.  488 
Perforated  plates,  excess  Btrength  << 
859 

strength  of,  864 
Permutation.  10 
Perpetual  motion.  438 
Petroleum.  645 

as  fuel.  645,  &I6 

burning  locomotive,  865 

dii^tiliates  of,  645 

engines.  850 

Lima.  645 

metallurgical  fuel,  646 


INDEX. 


1093 


Petroleum    products,    spedflcatlons, 

944 

value  of,  64fi 
Pliosphor-brouze,  ft27,  884 

springs,  8&3 

wire,  :e» 
Phosphorus,  influence  of,  on  cast-iron, 

iufluence  of,  on  sreel,  889 
Piezometer,  the,  SSZ 
Pij?  iron,  analysis  of,  871 

chemistry  of,  870 

fl^radliifc  of,  865 

iDfluenoe  of  silicon,  etc.,  on,  366 

testa  of.  869 
Pillars,  strenftth  of.  246 
Pipe  fittings,  cast-iron,  187 

flanges.  198 

lead,  200,  201 

riveted,  197 

sheet-iron  hydraulic,  191 

spiral  riveted.  197 
Pipes,  air-bound,  579 

and  cylinders,  contents  of,  120, 121 

cast-iron,  8ti*ength  of.  251 

cast-iroo,  thickness  of.  188, 190 

cast-iron,  weight  of,  185,  1^6 

coilHd,  199 

effect  of  bends  in,  488,  578,  672 

flow  of  air  in,  485 

flow  of  gas  iu,  667 

flow  of  steam  in,  669 

flow  of  water  in.  557 

loss  of  Itead  in,  578 

riveted,  safe  prefMiiri^fi  in,  707 

steam,  for  steam -heating.  640 

steam,  »izn  for  englnex,  678 

table  for  (<|ti)tlizfng,  491 

water,  rivetr*!,  'J9'y 

wrought-jron  and  f(t<*el,  194,  295 
Piston-rods,  796>798 
Piston  packiog.rings,  796 

valves,  884 
Pistons,  steam-engine,  795 
Pitch,  diametral,  888 

of  gears,  887 

of  riveU,  867-859 

of  screw  propellers,  1018 
Pitot  tube  gauge.  583 
Pivor-beariiigs,  939 
Plane  surfaces,  mensuration.  54 
yiane,  inclined  (tee  Inclined  Plane) 
t'laner.  heavy  work  960 

cutting  speed  of,  954 
Plate  girder,  2ii7 
Plate  iron,  weight  of.  175 

steel,  classiHoation.  899 
Plates,  brass  and  copper,  902 

riveted  steel,  299 

single-riveted.  857 

square  feet  in,  128 

strength  of,  for  boilres,  706 
Platinum,  168 

wire,  226 
Pneumatic  hoisting.  909 

postal  transmission,  509 
Polyedrons,  82 
Polygon  of  forces,  416 
Polygons.  con8trr««tlon  of.  42 


Polygons,  table  of,  65 

tables  of  angles  of,  44 
Population  of  the  United  States,  19 
Portland  cement,  802 
Postal  transmission,  pneumatic,  509 
Potential  energy,  429 
Poweirs  screw-ihread,  975 
Power,  animal,  488 

of  a  fall  of  water,  588 

of  ocean  waves.  599 

rate  of  work,  429 

stations,  electric.  1050 
Powers  of  numbers,  7,  88 
Pratt  truss,  448 
Pressed  fuel,  632 
Presses,  punches,  etc.,  972 
Prism,  measures  of ,  60 
Prismoid,  61 

rectangular,  61 
Prismoidal  formula,  62 
Problems  geometrical,  87*42 

in  circles,  39.  40 

in  lines  and  angles,  87,  88 

in  polygons.  42 

in  triangles,  41 
Producer-gas,  649 
Progression,    arithmetical    and    geo 

metrical,  1 1 
Prony  brake.  979 
Propeller,  coefficients  of,  1011 

blade,  800 

efficiency  of,  1012 

shafts,  strength  of,  299 
Proportion.  5 
Pultoy,  differential,  489 
Pulleys,  878-875 

arrangement  of,  874 

arms  of,  8S0 

convexity  of,  874 

or  blocks,  488 

size  and  speed  of,  684,  891 
Pulsometer,  612 
Pumping -engine,  tests  of,  788 
Pumping-englnes,  duty  trials,  60ft 

leakage  tests.  61 1 

measurement  of  discharge,  684 

triple-expansion,  782 
Pumps,  601-614 

air  lift,  614 

boiler-feed.  G05,  726 

capacity  of.  601 

centrifugal,  606.  609 

circulating.  842 

direct-acting,  608 

duplex.  604 

efficiency  of,  608,  rag 

home-power  of,  601 

jet,  614 

piston- speed  of,  G05 
*  sizes  of,  G08 

speed  of  water  through,  602 

Bteam-cyiinde,*s  of,  b02 

suction  of.  602 

vacuum.  612 

valves  of.  605,  606 
Punched  plates,  strength  of,  864 
Punches  and  dies.  972 
Punching  and  drillitig  steel.  895- 

steel,  effect  of.  894 


1094 


IKDEX. 


Purifying  feed-water,  564 
Pyramid,  W 
Pyrometers,  461-458 
I^rrometry,  448-454 

Quadratic  equations,  85 
Quadrature  of  a  plane  flRure,  74 

of  surfaces  of  revolution,  75 
Quadruple-expansion  engines,  7TS 
Quantitative   measurement  of  heat, 

455 
Quarter-twist  belts,  88S 
Queen-post  truss,  443 

Radiating  and  reflective  power,  468 

surface,  rules  for,  586 
Badiation  of  heat.  467 
Radiators,  transmission  of  heat  by, 

475-477,  546 
Radius  of  gyration,  £47,  420.  421 

of  oscillation,  421 
Railroad  axles,  888 

trains,  resistance  of,  851 
Rail-steel,  specifications,  401 
Rails,  maximum  safe  load  on,  665 

steel,  strength  of,  2H6 
Railway  trains,  speed  of,  869 
Railways,  narrow-gauge,  866 
Ram,  hydraulic.  614 
Ratio  and  proportions,  6 
Reamers,  taper,  972 
Recalescence  of  steel,  402 
Keceiver-space  In  engines,  766 
Reciprocals  of  nmnbers,  80 

use  of,  86 
Red  lead  as  a  preservative,  889 
Reduction,    descending  and  ascend- 
ing. 6 
Reflection  of  heat,  466 
Refrigerating-machines,  961-1001 

air-machines,  988 

actual  performance,  994 

ainnionia-absorption,  984 

ammonia-compression,  988-987 

ether-machines.  988 

heat  balance.  990 

ice-melting  effect,  963 

liquids  for.  982 

pipe  coils  for,  985 

properties  of  brine,  994 

properties  of  vapor.  998 

relative  efficiency.  988 

sulphur-dioxide,  985 

temperaturt*  range,  991 

test  trials.  990 

use  of  water-vapor,  988 
Registers  and  air-ducts,  689 
Regnault's  experiments  on  steam,  661 
Resilience,  288 

elastic.  270 
Resistance,  electrical,  1028 

electric,  of  copper  wire,  1030 

electric,  of  steel,  403 

of  ships,  1002 

of  trains.  851 

to  repeated  stresses,  288 
Resolutiou  of  forces,  415 
Retarded  motion.  424 
Hhoiubus  and  rhomboid.  58 


RWe 


Rivet  iron  and  steel,  888 
Riveted  iron  pipe,  IIT? 
Riveted  lap-Joiata,  doaUe,  8h 

proportions.  ZS8 

^eted  Joints.  299.  808,  S54-:M8 

drilling  v».  punching  of  bole&,  8S5 

Fairbium's  experiments,  861 

results  of  research.  856 
Riveted  pipes,  flow  of  water  in,  574 

plates,  single,  857 

steel  plates,  297 
Riveting,  efllclency  of  different  m^tt 

od8,856 
Riveting-machines,  hvdraulic,  618 

of  steam-boilers.  700 

of  steel  plates,  884 

SresBures.  862 
ets,  diameter  of,  860 

power  to  drive,  1070 

sises,  etc.,  211 
Rivet-steel,  401 

Roads,  resistance  of  carriBges  on.  4£ 
Rock-drills,  air  required  by,  506 
Roof -coverings,  weight  of,  184 

trusses,  446 
Rooflng  materials.  181, 184 
Rope-driving,  92S-927 

diameter  of  pulleys,  928 

sag  of  rope,  925 

various  speeds,  924 

weight  of  rope,  996 

wire,  226-281 
Rope,  charcoal-wire,  828 

locked-wire.  881 

steel-wire  hawsers,  828 

wire,  281 
Ropes,  801,  888,  906 

flat,  889 

splicing,  841,  845 

strengia  of,  888 
Rotary  olowers,  626 

steam-engines,  791 
Rotation,  accelerated,  480 
Rubber  belting,  887 

vulcanized,  816 
Rule  of  three.  6 
Rustless  coatings  for  Iron,  886 


Safety,  factors  of,  81 4  i 

Safety-valves,  721 

Salinometer,  strength  of  brines.  4M    j 
Salt,  manufacture  of,  468 

solubility  of,  464  j 

weight  of.  170  I 

Sand-blast,  966  j 

moulding,  958  | 

Sawdust  as  fuel,  648 
Sawing  metal,  966  j 

Scale  and  incrustation,  651  ' 

in  steam-boilers.  716  I 

Schiele's  anti-friction  curve,  fiC         | 

pivot-bearing,  989 
Screw,  487 

differential.  489  J 

endless.  440 

propeller,  1010 

thread,  Poweirs,  975 

threads.  904,  206 

tlireads,  English,  206 


INPBZ. 


1097 


eam-pIpM,  nwthtml,  VK 

;>lpes,  •iao  off,  fvr  «ii|^imb,  679 

;>ipes,  valvMiDt  876 

;>ipe8,  wire-wouDd«  67Q 

;>oww,  ooBt  of,  780 

;>ower,  cost  of  ooal  for,  780 

luperfaeatod,  001 

lupply  maliiB,  688 

mole  of  propertiM  of,  OBO 

:einperaU]ro,  preMvre,  etc„ 

;urbizi<>8, 781, 1076 

reBSols,    dimeiiaions,  borae-power, 

«to.,  1000-1008 
ressels,  coeffloieQt  of  perfomumee, 

1008 
resaels,  trials  of,  1007 
Mrater  In,  effeot  of,  on  economy  of 

«iijcines,  181 
tvorf  of.  In  a  aingla  cylinder,  746, 

748 
Bol,  88^14 
lluminum,  400 

jrfiatirBoa  and  propertioB  of,  880 
End  Iron,  dMrttlration,  804 
uinealing,  418 
u  blue  heal,  8BS 
uEles,Sg8 

beams,  safe  load,  988 
Bessemer,  880-W8 
blooms,  wetehtof,  178 
bridiee  links,  897 
Bastings,  409 
eastings,  strength  of,  990 
chrome,  408 
oold-drawtng  of^  805 
columns,  856-801 
somposition  of,  880 
compressed,  410 
cnicible,  410 

effect  U  haquMerf  ng,  419 
effect  of  heat  on,  41  si 
effect  of  nicking,  40a 
effect  of  oxygen  on,  801 
electric  oonductlTlty  of,  406 
failures  of.  408 
for  car-axies,  401 
ror  rails,  401 
bardening  of  soft,  809 
manganese,  407 
MuBhet.408 
Dickei7407 

open-hearth,  801, 803 
p1at«s,  987, 400 

plates,  Bessemer,  strength  of,  880 
plates,  rfreted,  900 
propoUer  shafts,  988 
rails,  strength  of.  986 
recalesoence  of,  409 
segrefcation  in,  404 
Bbeariog  strength,  808 
soft,  bardoaillg  of,  8B6 
■peclflo  graviiT  of,  406,411 
specifications  for,  807 
spring,  999 

■trength  of,  887-881, 888 
Biniaunl,  939, 409 
struts,  989 
tempering,  419,  414 
tires,  Btrengtii  of,  986 


Steel,  trsaiiiMBl  of,  8M 


ugsten, 
einslrt 


slructares,  406 
▼ariatlon  in  strength  of,  886 
water-pipes,  986 
working  stresses  for,  880 

Stoker,  under-feed,  719 

Stokers,  mechanical,  711 

Stone,  sfarength  of.  309, 819 

Stotie-outtiug  with  wire,  006 

Stones,  etc.,  weight  and  sp.  gr.,  160 

Storage-batteries,  1006 

Storing  steam-heat,  980 

Strains  oliowed  la  bridge  membem, 


unit,  in  structural  Iron  and  steel,  878 
Straw  as  fuel;  646 
Stream,  horse-power  of  %  889 
Streams,  measuremeat  oC.  684 
Strength  of  boiler-heads,  985 

of  bolts,  999 

of  columns,  946.  950-961 

compressive,  944 

of  flat  plates,  989 

of  glasi,  808 

of  ma^^nry  matoriali,  819 

of  materials,  966^14 

of  materials,  Kirkaldj's  tests,  886 

of  stayed  surfhces,  986 

of  structural  shapes.  978-980 

of  thnber,  809,  lOnTlOOO 

of  unstayed  snrfaess,  884 

of  water-plpa,  851 

tensile,  2& 

tonribnal,  981 


Stress  and  strain,  986 

dne  to  temperatureJW 
Stresses,  combined,  989 


bridge  1 

effect  of,  968 

in  framed  structures,  440 

in  steel  plating.  987 

of  columns,  m 

practice  in  Ghicago,  861 

sudden  effect  of,  941 
Structural  Iron,  strains  fa,  878 

shapes,  elements  of,  948 

shapes,  properties  of,  979 

shapes,  siaes  and  welgfacs,  177 

steel  in  the  World's  Fair  bi 
886 

steel,  tredtment  of,  884 
Structures,  framed,  440 
Stmt,  the  moving,  486 
Struts,  strebgth  of,  940 

working  f ormulsB  for,  980 

wrought-iron,  959 
Sugar  manufacture,  648 

soluftions,  conosntration  of,  465 
Sulphate  ^  V^mm,  solubility,  464 
Sulphur -dioxide     refrigerating  •ma- 
chines, 966 
Sulphur,  influenoe  of,  on  cast  Iron, 
867 

influence  of,  on  steel,  889 
Surface  condensers,  840-844 
Surfaces,  unstayed  flat,  984 
Suspension  cable  ways,  916 


1098 


INDBX. 


T  Bhapea,  Bted,^ttD«lT8 
Tail-rope  iiystein  of  haalage,  ttS 
Tuibarka8fuel«648  \ 

Tangent  of  an  angle,  65  \ 

Tangents,  sines,  etc.)  table  of,  IM    ' 
Tank-platea  SOO 
Tanks,  cylindrical..  181,  IW 

reetangulAr,  grallons  in,  1S5 
Tannato  of  soda  for  boUer-ecale,  718 
Tap-drills,  «ro,  071 
Taper  bolts,  pins,  reamers,  979 
Taper,  in  Uthes,  966 
Tapered  wire  ropes,  016 
Tavlor's  rules  for  belting,  880 

theorem^  7j5 
^Tserbars,  878 

Teee.  Pencoyd^  siaes  Mid  weights,  180 
Teeth  of  gean,  forms  of,  80S 

propoi«ionB<>f,  860 
Telegrapb-wlte,  Jil7-9tl,  8M 
Telescope,  pyrometer,  458 
Temperature,  absolute,  461 

effect  on  strength,  800, 868 
in  iron,  etc^  868 


Temperatures  in  furnaces,  451 

judged  by  col6r.  464 
Tempering  steel,  414 
Teuaeitr  of  metals,  160 

of  metals  at  diflteeufe  temperatures, 
800,188 
Tensile  strength,  948 

strength,  tnci^sase  by  twisting,  841 
Tension  and  flexure,  aueases,  i«i 
Terra-cotta,  181 

Testing  materials,  precautions  in,  248 
Tast-pteces.  comparlsMt  of  small  and 

standard  sUapes,  848 
Tests  of  materials,  806 
Thermal  unit,  British,  456,  660 
Thermodynamics,  478 
Thermometers,  448 
ThreeHsyllDder  engine,  815 
Three-stage  engine,  771 
Tidal  power.  Utilisation  of,  600 
Tie-rods  for  brick  arches,  881 
Tiles,  sixes  and  weights,  181 
Timber  measure,  80, 81 

strength  Of,  800 
Time,  measure  of,  80 
TiHtltt 

roofing,  181, 188 
Tires,  steel,  strength  of,  80S 
Tobin  bronse,  837,  884 
Toggle-joint.  486 
Tonnage  of  Teesels,  10, 1001 
Tool-sieel.  heating,  418 
Tools,  metal-cutting,  855 
Toothed-wheeled  gearing,  480 
Toothed  wheels,  proportions  of,  680 
Torsion,  elastic  resistance,  888 
.  of  shafts,  806 
Torque  of  an  armature,  1061 
Torsional  strength,  861 
Tower  spherical  engine,  793 
Track  bolis,  810 

spikes,  818 
Tractive  power  of  locomotives*  857 
Tractrlz,  or  Schiele's  curve,  50 


Trains,  resflrtanoe  of,  881.  flS8 
Tramiitay,  eompresscd-alr,  510 
Tramways,  wire-rolw,  914 
Transformers,  1066 
Transmission  by  hydraall^  presson 
617-6«) 

by  wire  rope,  917-889 

eleetric  1068 

electric,  eflleieney  of,  lOfS  ^ 

of  heat,  471-478 

of  power  by  ropes,  9i8-OT7 
Transporting  power  of  water,  088 
Transverse  strength,  968 
Trapeaivm,54 
Trapesoid,  54 

Trapezoidal  rule,  66  ! 

Triangle,  mensuratloo  of,  54 
Ttiangles,  problems  in,  41 

solution  of.  68 
Trigonometrical  funetloms  65-67 

functions,  table,  159 
Trigonometiy,  plane,  85 
Triple  effect,  multiple  syscena,  461 
Triple-expansion  engine,  780 
Troy  weight,  10 
Truss,  Howe  and  Wflima,  445 

king-post,  448 

queen-po«*t,  449 

Pratt  or  Whipple,  448 
Trusses,  roof,  40 
Tubes,  boiler,  hokUnrpoww,  dOf 

for  steam-boilers,  108,  904,  SQO 

Mannesmann,  988 

or  flues,  collapse  of,  885 

seamless  brass,  196 

strength  of,  966 

weights  of,  169  « 

wrought-iron,  198 
Tubing,  brass,  198 
Tungsten-alt^miiram  aBora,  881 

steel,  409 
Turbines,  steam,  791 
Turbine-wheels,  501 

wheels,  tests  of,  608 
Turf  or  peat,  648 
Tumbuckles,  siaes.  911 
Turret  lathes,  cutting  speed,  954 
Twin-screw  vessels,  1017 
Twist-driU  gauge,  99 
Twist-drills,  siaes  and  qMsda,  957 
Twisted  iron  bars,  941 
Type-metal,  886 

Unit  of  heat,  485 
United  SUtes.  popalatlon  of,  19 
Unstayed  surfacea,  strength  ot  M 
Upsetting  of  steel,  894 

Vacuum  pumps,  619 
Valve-diagrama,  8K 
Valve,  lap  and  tmvel  of,  891 

motion,  89B 

rods,  815 

slide,  891 

seats,  area  ttnyNnAi,  MS 
Valves,  engine,  setdngoC,  9M 

in  steam-pipes,  6i5 

of  pumps,  605,  608 
Vapors,  propertlea  pf,  488 


IKDEX. 


1095 


\crew  threads,  metric*  9S6 

threads,  standard,  for  bolts,  207 

threads.  United  States.  904 
(crew-bolts,  efficiency  or,  974 
screws  and  screw-threads,  974 

holding  power  of,  290 

machine,  906,  2U9 
iecant  of  an  angle,  65 
Sectors  and  segments,  S9 
>ediment  In  steam-boilers,  717 
;eeger's  flre-clay  pyrometer,  458 
Segments  of  a  circle,  table,  116 
>egregatlon  in  steel  ingots,  404 
;«)parators,  steam,  7^ 
k)t-8crew8,  holding  power  of,  977 
hewers,  grade  of,  S<w 
>hafc-bearings,  810 

governor,  888 
Uiafting.  867-872 

deflection  of,  868 

H.P.  to  drive,  9<I8 

table  for  laying  out,  873 
>haft8,  engine,  8U6-815 

fly-wheel,  809 

hollow.  871 

propeller,  strength  of,  815 

sceel  propeller,  z99 

twisting  resistance,  281,  806 
ihapes  of  test-specimens,  )US 
)hearing,  effect  of,  on  steel,  894 

strength  of  iron,  806 

strength  of  woodft,  819 

resistance  of  rivets,  863 

unit  strains,  880 
(hear-poles,  stresses  in,  442 
iheet  brass,  weight  of,  908 

copper,  weight  of,  909 

iron  and  steel,  weight  of,  89, 174 

metal,  tensile  strength  of,  800 
»hella.  spherical  strength  of,  986 
thingles,  siaes  and  weight,  188 
•hipping  measure,  19, 1001 
hip-plates,  899 
liips,  resistance  of,  1009 
hocks,  resistance  to,  940,  911 
hot,  lead,  90A 
hrinkage  of  castings,  961 

hrinklng  flts,  978 

igna  of  trigonometrical  functions,  66 

arithmetical,  1 
i  I  icon- bronze  wires,  999,  898  / 
ilicon,  influence  of,  on  cast  Iron,  865 

influence  of  on  steel,  889    / 

ilver,  168  J 

implex  gas-engine,  test,  ftiS 

impsoirs  rule,  66  I 

ine  of  an  angle,  65  } 

iiies,  cosines,  etc.,  table  of,  959 

etc.,  logarithmic,  169  I 

inking'iunds,  17 

iplion,  the,  681 

lAie,  sizes  and  weights,  183    ' 

lide-vftlve,  85M-885 

diagrams,  8;2&-833' 

lap  and  travel  of,  C31 

noke-preveiitlon,  7l5S 

inokestack  guys,  9a!S 

low  and  ice,  660 

capstone  as  a  lubricant, /M5 


Softeners,  use  of,  in  foundiy,  960 
Softening  hard  water,  555 
Soft  steeU  hardening,  898 
Solders,  888 
Solid  bodies,  mensuration  of,  GO 

of  revolution,  69 

measure,  18 
Speciflc  gravitv,  168 

gravity  of  alloys,  890,  898 

gravity  of  cast  iron,  874 

gravity  of  gases,  166 

gravity  of  steely  408,  411 

gravity  of  stones,  biick,  etc.,  166 

heat,  457 

heat  of  air,  484 
Speciflcations  for  azles,  steel,  4C0 

for  car-axles,  401 

for  cast  iron.  874 

for  crank-pin  steel,  400 

for  oils,  944 

for  plate  steel,  899, 400 

for  rail-steel,  401 

for  rivets,  401 

for  spring-steel,  400 

for  steel,  897 

for  steel  castings,  406 

for  steel  rods,  4U0 

for  wrought  iron.  878 
Speed  of  cutting-tools,  958,  954 

of  vessels.  1006 
Sphere,  measures  of,  61 
Spheres,  table  of,  118 

weights  of.  160 
Spherical  polygon,  area  of,  61 

segment,  69 

shells,  strength  of,  986 

steam  engine,  798 

triangle,  area  of,  61 

Eone,  69 
Spheroid,  68 
Spikes,  holding  power,  989 

sizes  and  weights,  919, 918 
Spindle,  surface  and  volume,  68,  64 
Spiral,  construction  of,  60 

gears,  897 

riveted  pipe,  198 

measures  of,  GO 
Splicing  of  ropes,  841 

wire  ropes,  845 
Spring-steel,  999 

locomotive,  400 

speciflcations,  400 

strength  of,  999 
Springs,  capacity  of,  849 

elliptical,  859 

for  governors,  888 

formula  for,  847,  858 

helical  stseUM7 

lambiat^d  steel,  849 

phospbttr-bronze,  863 

tables  of,  849,  858 

torsional  force,  359 
Spur  gear,  machine-cut,  905 
Square  measure,  18 

root,  8 
Squares  and  cubes  of  decimals,  101 

and  square  roota,  table  of,  86 
Stability,  417. 
Stand-pipes,  l(lesign  of,  S99-394 


1096 


INDEX. 


Statical  moment,  417 
Stay-bolt,  irun,  879 
Stay-bolts  for  boilers*  TIO 
Stayed  surfaces,  btreii»f i  li  of,  286 
Stays  for  boilers,  708,  710 
iteam,  «50-«76 
boiler,  water-tube,  688,  689 
boilers,  677-740 
boilers,  air-space  In  grate,  681 
boilers,  allowable  pressures,  706 
boilers,  economy  of,  W'i 
boilers,  efSciency  of,  i>85,  688 
boilers,  explosive  etierxy  "f*  720 
boilers,  factor  of  evaporation,  695 
boilers,  factor  of  safety,  7uO 
boilers,  feediuR,  1074 
boilers,  forced  draught,  714 
boilers,  flues  and  *)aKsage8.  680 
boilers,  gas-fired,  714 
boilers,  grate-surface  of.  678.  680 
boilei-s,  heating  air^upply  to.  687 
boilers,  heating-surface  of,  678 
boilers,  height  of  chimney  for,  786 
boilers,  horse-power  of.  b77 
boilertt,  hydraulic  test  of,  700 
boilers,  incrustation  and  scale,  716 
boilers,  materials  for,  700 
boilers,  measure  of  duty  of,  678 
boilers,  performance  or.  681 
boilers,  Philadelphia  inspection  rule, 

708 
boilers,  proportions  of,  678 
boilers,  rules  for  construction,  iXX), 

1078 
boilers,  safe  working  pressure,  707 
boilers,  strength  of,  700 
boilers,  tests  of,  685 
boilers,  tests,  rules  for.  690-695 
boilers,  tests  with  different   coals, 

686.668 
boilers,  tubulous,  686 
boilers,  using  waste  gases,  689 
boilers,  use  of  zinc  in,  7^ 
domes  on  boilers,  711 
dry.  identification  of,  730 
engine  constants,  756-758 
engine  cylinders.  79*^-^95 
engine,  spherical,  79*<i 
enginen.  74-.i-847 
entwines   at    Columbian  Exhibition. 

774 
engines,  calculation  of  mean  effec- 
tive prosMUre,  744 
engines,  compound.  761 
engines,  Corliss,  773 
engines,  Corliss  condf'nslng.  780 
engines,  cost  of  different  sizett,  1075 
engines,  counterbalancing.  788 
engines,  cylinder-condensation,  7V3 
engines,  dimensions  of  parts  of,  79..'- 

»17,  1074 
engines,  economy  at  various  speeds, 

;s6  , 

engines,  economic  perf(>rmance,  775 
engines,  economy  of  vmrious  sizes, 

7(15,  7H6  . 

en>fiiie»»,     economy     v\th     varying 

,|..ads,  784  . 

eiiguieb.  effect  of  comyTession.  7.M 


Steam-engines,    effect    of    wnter 

steam,  781 
engines,  efDciency  of,  749 
engines,   eftici**ncy  of  uon-oon deny- 
ing compound,  184 
engines,  feed-w  ater  consumpcion  cf. 

7^8,  760.  775 
engines,  frames  of,  817 
engines,  frfcliou  of,  941 
engines,  foundation  of,  7B8 
engines,  leakage  of  sieani  in,  76! 
engines,  limitation  of  speed.  787 
engines  in  ele<aric  stations,  7^ 
engines,  marine,  1015 
engines,  mean  effeciive  press^ure  to, 

75S 
enfrines,  measures  of  duty,  746 
engines,  most  economicai  point  of 

cut-ofi,  7^ 
engines,  non-condenalng,  778 
engines,  performance  of.  775- 7S9 
engines,  pisu>n<«peedB  of,  7>7 
engines,    power-plant    at    Worlds 

Fair,  774 
engines,  presenting  vibratioD^  >^» 
engine   proportions   of  cyliudrr<(. 

7(» 
engines,  puttinit  on  centre,  (9* 
engines,  quadruple-^fxpansion,  77^ 
engines,  relative  econuuiy  of,  7>u 
engines,  rotary,  791 
fjngines,  steam -consumption,  7iO 
engines,  three-cylinder,  8l5 
engines,  three-stage  expansion.  VT.:, 

1019 
:  engines,  triple-expansion.  7C9 
engines,  tnple-expansioii,   annuUr 

ring  method,  769 
engines,  trlple-expansion,  diamt^^ 

cylinders,  778 
engines,    triple-expansion,    doot^ 

'  tandem,  778 
er^gioes,  triple-expansion,   noo^:« 

(Reusing,  7f  9 
engines,    triple-expansion,    prop^ 

ticHiing  cylinders,  77i 
engines,    triple-expatialon.    iels:i«' 

ectinomy,  781 
engiifes,  triple-expansion.  »au«c^ 

of  clanks.  77S 
engines,  two-  v§.  three-cylinder.  >". 
engines,  vertical  higli-^pet^l.  777 
enginek  water-consiimpiiou,  7iO 
expansive  wurking  uf ,  itxi 
fluw  of  1 668 
flow  ofl  in  pipes,  669 
heat,  storing.  789 
heatindt.  686-540 
heating  greenhouse.  541 

tacketj  infiiience  oi,  7^7 
et  blqfwers,  SaK 
oop,  r)76 

loss  off  pressure  in  pipes,  671 
meant  pressures,  743 
moistVire  in,  7'^  1 

pipe  ceoverings,  469  I 

pi|ies,  (KlBuper,  674.  67i> 
pipes,  lo^  front  uncovered,  676         ' 
iiineM.  maldne.  lUlti 


\ 


INDEX. 


1099 


apora  used    la    refrigvmtlngvwa* 

chines,  96*^ 
arniMhofl,  WT 

elocitles,  parallelogTMnof,  4M 
eloclty.  AOKular,  4& 
eotUaUDfc-OQCts,  dlachaiite  of,  580 
fans,  5l7-tt» 

eotilation  and  heating,  6S8-546 
blower  system  of,  045 
by  a  steam- Jet-  bit 
efflcieocy  of,  688 
of  large  buiidinn,  684 
entilators  for  mliiee,  6tt 
i)Qturi  meter,  688 
ersed  sine  of  an  arc.  85 
easels  (see  Steam-vessels) 
ertical  high-speed  engines,  777 
ibrations  of  engines,  prerenting,  780 
ifi*viva,4:iS 
olt,  definition  of,  1085 

Warehouse  floors,  1010 

barren  girder,  446 

^ashers.  sises  of,  212 

^ater,  647-654 

analyses  of,  668 

boiling-point,  660 

buoyancy  of,  660 

comoarison  of  heads  and  pressures, 

compressibiHty  of,  661 

erosion  by  flowing,  666 

expansion  of,  047 

flow  in  channels,  604 

flow  of,  666-468 

flow  of,  experiments,  606 

Bowof,in  pipes, Ubl«8,658,660, 607-670 

freesing-poiut,  690 

ga8,6«,6U 

hardneHS  of,  668 

Ice  and  snow,  660 

Impurities  of,  661 

pipes.  896 

power,  68R 

power,  value  of,  60O 

pressure  engine,  010 

pressure  of.  640 

loftening  of  hard,  566 

ipeciflo  heat  of,  660 

transporting  power  of,  685 

velocities  in  channels,  606 

ireiflrhtof,27,547 

wheel,  jet,  power  of,  1078 

nrheei,  the  Pelton,  607,  1071 

aves,  power  of  ocean,  800 

eathering  of  coal,  687 

edge,  the,  487 

rolume  of  a,  01 

eight  of  bars,  rods,  plates,  etc.,  100 

>f  brickwork,  100 

>f  brass  and  copper,  106-808 

>r  bolts  and  nuts,  S0»-311 

>f  cast-iron  pipes  and  columns,  185- 

108 
>f  cement,  170 
>f  flat  rolled  Iron,  179 
>f  fuel,  170 
>f  iron  bars,  171 
»f  iron  and  steel  sheets,  88, 174 


Weight  of  ores,  earths,  et^.-,  170 

of  plate  Iron,  179 

of  roofing  materials,  181-184 

of  steel  blooms,  170 

of  structural  shapes,  177-180 

of  tin  plates^  188 

of  wrought-iron  pipe,  104-107 

of  various  materials,  100 
Weights  and  measures,- 17 

of  air  and  vapor,  484 
Weir  table,  567 

[  Weirs,  flow  of  water  over,  586 
Welding,  electric,  1061 

of  steel,  884.  896 
Welds,  strength^f  ,800 
Wheel  and  axle,  480 
Whipple  truss,  448 
White-metal  alloys,  886 
Whitworth  compressed  steel,  410 
Wiboi>ch  air-pyrometer,  468 
Wind.  408 

pressure  In  storms.  405 
Winding-engines,  000 

of  magneU,  1088 
Windlass,  480 

differential.  480 
Windmills,  406 
Wind-pressures,  408 
Wire  cables,  8» 

copper  and  brass,  908 

copper,  tables  of,  818-880, 1084 

diilerent  metals,  885 

Elated,  881 

iron  and  steel,  817 

iron,  siae,  strength,  etc..  816 

nails.  814,  816 

piano.  894 

plougn-eteel,  894, 886 

rope,  896.  881 

rope  haulage,  012 

ropes,  durability  of,  010 

ropes,  splicing,  845 

ropes,  strength  of,  801 

ropes,  tapered,  816 

rope  transmission,  017-068 

rope  tramways,  014 

stone-cutting,  086 

strength  of,  801,  808 

tablefor  100  and  500  volts,  1044 

table,  hot  and  cold  wires,  1084, 1085 

telegraph,  917, 881,  S9M 

weight  of,  910 

wound  fly-wheels,  894 
Wiring     formula    for    incandescent 

lighting,  1049 
Wires,  current  required  to  ftise,  1087 
WOhler^s  experiments,  988 
Wood  as  fuel,  088 

composition  of,  040 

compression  strength  of,  811 

expansion  of,  811 

heating  value  of,  080 

shearing  strength  of,  818 

specific  gravity  of,  165 

streM^th  of,  809,  800,  810,  818,  1088, 

weight  of,  166,  988 
Wooden  fiy-wheels,  888 


1100 


IKPEX. 


WoodstoiM  or  xyloUtti,  8l« 
Woolf  type  of  compound  c 
Wootten^looomotiva,  8B6 
Work,  enenor,  power,  4^ 
Work  of  nooderaUoD,  480 

of  men  and  >ntmaln,  488 

unit  of,  488 
Worin-geifcM40 

Wrought  iron,  877-879 
bolts,  streoifth  of,  888 
ohemlBtry  of,  877 
oolumns,  SfiO,  880 
■pecUlcattonB,  898, 839 


7«. 


Wrooffht  iroii,  streBgUi  of;  897,  ; 

■truts,859 
water-pipe,  888 

ZjrloUtli  or  woodstone,  SM 

Yield-point,  887 

Z-bara.  properties  of,  iNO 

sises  and  weiglits»  178 
ZIoc,  188 

tubtaw,  900 

use  cm!,  in  steam-boUert,  ¥98 
Zeuner  Talve-disgnun,  887 
Zero  absolute,  461 


ALPHABETICAL  IMDEI  TO  ADYERTISEIEITS. 

PAOK 

ABKNDROTH  A  ROOT  MANUFAI'TURING  COMPANY 18 

ALLI8  COMPANY,  THE  KDWARD  P 21 

AMBRICAN  BRIDOB  COMPANV 8 

AMERICAN  KNOINE  COMPANY 80 

AMERICAN  STOKER  COMPANY                  11 

ATLAS  PORTLAND  CEMENT  COMPANY  27 

BACON,  EARLE  C 14 

BOSTON  BELTING  COMPANY 18 

BOSTON  BLOWER  COMPANY 26 

BROWN  HOISTING  MACHINERY  CO..  INCORPORATED,  THE 14 

BULLARD  MACHINE  TOOL  COMPANY.  THE 7 

CHAPMAN  VALVE  MANUFACTURING  COMPANY 26 

CINCINNATI  MILUNG  MACHINE  COMPANY,  THE ft 

CRIPPEN,  H.  D 28 

FAYERWEATHER  &  LADEW 10 

FILER  AND  STOWELL  COMPANY,   THE 20 

(iARVIN  MACHINE  COMPANY,  THE  ..       .  5 

GENERAL  ELECTRIC  COMPANY,  THE 2 

GREEN  FUEL-ECONOMIZER  COMPANY.  THE  12 

GRIFFING  IRON  COMPANY,   A.  A            22 

HARTFORD  STEAM  BOILER  INSPECTION  AND  INSURANCE  COM- 

PANY 12 

HKNDEY  MACHINE  COMPANY,  THE « 

HUNT  COMPANY,  ROBERT  W 10 

INDUSTRIAL  WATER  COMPANY  90 

INOERSOLL-8ERGEANT  DRILL  COMPANY,  THE 8 

JOHNS  MANUFACTURING  COMPANY,  H.  W W 

KEUFFKL  &  ESSER  COMPANY 28 

LTDGERWOOD  MANUFACTURING  COMPANY 8 

LUNKENHEIMER  COMPANY,  THE 28 

MAURER&  SON.  HENRY 12 

MONARCH  MANUFACTURING  COMPANY.  THE    27 

MORSE  TWIST  DRILL  AND  MACHINE  COMPANY 25 

NATIONAL  METER  COMPANY 1« 

NATIONAL  TUBE  COMPANY 2 

NORTON  EMERY  WHEEL  COMPANY 24 

NORWALK  IRON  WORKS  COMPANY,  THE » 

PELTON  WATER-WHEEI.  COMPANY 1« 

PHOSPHOR  BRONZE  8M  ELTl  NG  COM  PANY ,  UMITED 27 

PRATT  &  WHITNEY  COMPANY 4 

QUEEN  A  CX)MPANY,  INCORPORATED S» 

RAND  DRILL  COMPANY 9 

RIDER-ERICSSON  ENGINE  CX)MPANY 18 

ROEBUNG'S  SONS  COMPANY,  JOHN  A 16 

SELLERS  A  COMPANY.  INCORPORATED,  WILLIAM 4 

SIMMONS  COMPANY,  JOHN 19 

SMITH  &  COMPANY.  EDWARD 17 

STIRLING  COMPANY,  THE    18 

TAUNTON  LOCOMOTIVE  MANUFACTURING  COMPANY 22 

TRENTON  IRON  COMPANY 16 

VACUUM  OIL  COMPANY 8 

WOOD  &  COMPANY,  R.  D 17 

WHITLOCK  COIL  PIPE  COMPANY,  THE 24 

WHITON  MACHINE  COMPANY.  THE  D.  E 28 

YALE  &  TOWNE  MANUFACTURING  COMPANY,  THE 1 


CLASSIFIED  INDEX  TO  ADVERTISEMENTS, 

COMPEBSBORS   AMD   BOCK-ORILLB.  PAOK 

Ciippen,D.H » 

^^^[ngereoll-Sergeant  Drill  Co  ..  8 

Norwalk  Iron  Works  Co.,  The 9 

RandDrillOo 9 

Am ALTTicAL  Laboratory.    Hunt  &  Co.,  Robert  W 10 

▲8BI8TOS  PiPB  AND    BOJLBR    COVBRINOS,   PACKINGS,    BUILDINO    PAPBRS, 

RooFXMOB.  Faints,  ctc. 

Johns  Mfg.  Co.,  H.  W 19 

Bbarimos,  Amti-frictional. 

Phosphor  Bronse  Smelting  Co.,  Limited 87 

BBLTIMO  AMD  HOSB. 

Boston  Belting  Co 18 

Fftjrerweather  &  Ladew 10 

Blowers.— Boston  Blower  Co 88 

Boiler  Imsfeotion  and  Imsdramcb. 

Hartford  Steam  Boiler  Inspection  and  Insurance  Co 18 

Boilers,  Steam. 

Abendroth  &  Root  Mfg.  Co 18 

Stirling  Co..  The IS 

BoilerTubks.     National  Tube  Co 8 

Boiler  Water,  Softenino  and  Purification. 

Industrial  Water  Co  ? 

Bbabs  and  Iron  Steam  Specialties. 

QrifflDg  Iron  Co.,  A.  A 88 

Lunkenheiuier  Co.,  The 88 

Monarch  Mfg.  Co.,  The 87 

BiaDOES.    American  Bridge  Co 8 

Ckment,  American  Portland.    Atlas  Portland  Cement  Co 87 

Chain  Hoists.    Yale  ft  To wne  Mfg.  Co.,  The 1 

Chucks,  Milling  Cutters,  Rbambrs,  Spring  Cutters,  Taps,  etc. 

Morse  Twist  Diill  and  Machine  Co ; .  25 

Whiton  Machine  Co.,  The  D.  E J« 

CONDENSORS,  WaTER  TUBB  HSATBRS,  ETC. 

Orifflng  Iron  Co.,  A.  A 88 

Taunton  Locomotive  Mfg.  Co 88 

Whitlock  Coil  Pipe  Co.,  The    84 

Crambs— Steam,  Electric.  Hand-Power,  Travelling,  etc. 

Brown  Hoisting  Machinery  Co.,  Incorporated,  The 14 

Yale  &  Towne  Mfg.  Co.,  The  1- 

Crusbers,  Ore,  Rock,  Stone.     Bacon,  Earle  C 14< 

Drills,  Power  and  Hand. 

Crippen,  D.  H 85 

Ingeraoll -Sergeant  Drill  Co 8 

Norwalk  Iron-Works  Co.,  The 9' 

Rand  Drill  Co 9- 

Drills,  Twist.    Morse  Twist  Drill  and  Machine  Co  85> 

Electrical  Qemeratobs,  Motors,  Arc  and  Incandescent  Lamps,  Sup- 
plies, ETC.    General  Electric  Co..  The 8 

Emery  and  Corundum  Wheels.    Norton  Emery  Wheel  Co 84 

Enginebrino  Outfit. 

Keuif  el  &  Esser  Co  88 

Qaeen  &  Co.,  Incorporated 88 

Enoin kerb.  Consulting.     Hunt  &  Co.,  Robert  W 10 

Engineers  amd  Contraotobs. 

Allls  Co.,  The  Edward  P 81 

American  Bridge  Co...  8 

Bacon,  Earle  C 14 

Bmoimes. 

Allls  Co.,  The  Edward  P «t 

AmericaD  Engine  Co 80 

Bacon,  Earle  C 14 

FHer&Stowell  Co.,  The 80 

CN«an8,  Qas.    Natloiial  Metar.Oo 16- 

Emqimbs,  Pumpimo. 

AUis  Co.,  The  Edward  P 81 

Rider-Ericsson  Engine  Oo 18 

Enoimb  Stop  8rBim.^Monareh  Mfg.  Co.,  The 87 

FeedmWatbb  Heatbbs,  Sepabatobb,  Traps,  Exhaust  Heads,  arc. 

Grlfflng  Iron  Companr.  A.  A 8f 

Taunton  LooomotlFe  Mfk.  Co. 8t 

WhttlockOoU  PipeCo.,The 84 

Fire  Brick.  Tiles,  Slabs,  Cupola  Limimos,  Ci^y  Retorts,  arc. 


CLABSIFIBD  INPBXITO  ADVEBTISSUSMTS. 

FCBL-BCOMOMIZIIU.  PAOI 

American  Stoker  Co II 

Green  Fuel-EconomiMr  Co.,  The i: 

FURNAOU. 

American  Stoker  Co II 

Qreen  Fuel-Economiser  Co.,  The II 

BoisTXifO  Macbinebt— Elbtatobs,  Covtbtobb,  btc. 

Bacon,EarleC H 

Brown  HoistfnK  Machinery  Co.,  Incorporated,  The 14 

Lidgerwood  Mf{?.  Co s 

Chapman  Valve  Mfg.  Co 2< 

Wood«Co.,R.D 1< 

XN8PBCT0R8  OF  Matbriala.    Hunt  &  Co.,  Robort  W 16 

Insolatiom.    Smith  ft  Co.,  Edward ]• 

Lbathbr  Bbltino.    Fayerweather  &  Ladew lu 

LuBRicAim.    Vacuum  Oil  Co t 

Macbinb  Tools  and  Bouts. 

Bullard  Machine  Tool  Co.,  The ' 

Cincinnati  Milling  Machine  Co 5 

Hendey  Machine  Co « 

Pratt  &  Whitney  Co i 

Sellers  A  Co.,  William  (Incorporated) 4 

Mbtal  Coatings.    Smith  ft  Co.,  Edward IT 

Mbtaluc  Structures.    American  Bridge  Co ' 

Mbtbrs.    National  Meter  Co 16 

3I1LLINO  Machines,  Shapbrs,  Planbrs,  Lathes,  etc. 

Billiard  Machine  Tool  Co.,  The T 

Cincinnati  Milling  Machine  Co.,  The i 

Ganrin  Machine  Co. 5 

Hendey  Machine  Co € 

Pratt  &  Whitney  Co 4 

Sellers  ft  Co.,  William  (Incorporated) 4 

MiNiNO  Machinery.    Bacon,  Earle  C 14 

Oils.    VacuumOilCo 6 

Packino— Piston,  Valve,  Joint.    Boston  Belting  Co IS 

Paints.    Smith  ft  Co.,  Edward i: 

PHOSPHER  Bronze,  Ingots,  Castings,  Wire,  Sheet,  etc. 

Phosphor  Bronze  Smelting  Co.,  Limited s: 

Phtsioal  Laboratory.    Hunt  ft  Co.,  Robert  W 10 

Pipb-bendisg,  Coils,  ETC.    Whitlock  Coil  Pipe  Co.,  The S4 

PXPB,  Water  ft  Gas. 

Abeodrothft  Root  Mfg.  Co 13 

National  Tube  Co  « 

Simmons  Co..  John  19 

WoodftCo,R.D IT 

Pipe  and  Boiler  Coverings,  Pacbings,  etc.     Johns  Mfg.  Co.,  H.  W  . . . .  :• 
Pumping  Machinery. 

Allls  Co..  The  Edward  P tl 

Filer  ft  Sto well  Co.,  The «0 

National  Meter  Co 16 

Rider-Ericsson  Engine  Co l'^ 

Radiators.    Grilling  Iron  Co.,  a.  A a 

Scale-prevention.    Industrial  Water  Co 7 

Smobb-prbvention. 

American  Stoker  Co II 

Green  Fuel-Economizer  Co I^ll 

Btbam  Specialties,  and  Engineering  Appllances. 

Grifflng  Iron  Co.,  A.  A tt 

Lunkenheimer  Co.,  The S3 

(Steel  AND  Iron  Construction.    American  Bridge  Co S 

Steel  por  Tools. 
SuRVBTiNG  Instruments. 

Keuffel  ft  Esser  Co 9^ 

8ueen  ft  Co..  Incorporated .^ K 

RiNnERs.    Norton  Emery  Wheel  Co. 84 

Tramways— Wire  Rope.    Trenton  Iron  Co IS 

Turbine  Watrr-whbblb.    Pelton  Water-Wheel  Co.,  The 16 

Valves— Gas,  Water,  and  Steam.     Wood  ft  Co.,  R.  D 17 

Chapman  Valve  Mfg.  Co «5 

Varnishes.    Smith  ft  Co.,  Edward 18 

Water-supply.    Rider-Ericsson  Engine  Co 18 

Water-Whebls.    Pelton  Water- Wheel  Co 16 

WntE  Rope  and  Tblborapb  abo  Tblbpmonb  Wire.  ,_ . 

RoMbling*8  Sons  Co.,  John  A iJBr  It- 


The  Yale  &  Towne  Mfg.  Company. 

Chain  Blocks 


Weston's  Patents. 


Differential:  rs.T.SSr.'i. 

Duplex:    ForiemnluM. 


Tripl 


Av*  For  constant  use 
VA«  gQd  b^gj  economy. 


A  descriptive  Catalogue  of  50  pages,  full 
of  technical  data  of  interest  to  Engineers, 
will  be  sent  on  request. 


'  Differential." 


Duplex.' 


'Triplex. 


FOR  SALE  BY  ALL  DEALERS. 


GENERAL  OFFICES' 

&-11.13  MurraV  St.,  New  York  City. 

Works:  Stsmford  and  Brsnford,  Conn. 

9191-19- 50- 27500 


NATIONAL     TUBE    COMPANY, 

MANUFACTURERS   OF 

LAP-  AND  BUTT-WELDED  WROUGHT  PIPE 

('/•  INCH  TO  80  INCHES  DIAMETER.) 

Charcoal-Iron  and  Mild-Steel  Boiler-Tnbes 

FOR 

Marine,  Locomotive,  and  Stationary  Boilers. 

SEAMLESS  TUBES. 
TROLLEY  POLES.  OIL-  AND  WATER-WELL  TUBULAR  MODS. 

LOCAL  SALES  OFFICES: 
BOSTON,  NEW  YORK,  PHILADELPHIA,  PITTSBURG,  CHICAGO. 

SAN  FRANCISCO. 
FOREIGN  SALES-OFFICE  :    LONDON,  ENGLAND. 

TBE  ilTimliiif s 

GENERATORS  OF  ALL  SIZES 

Direct-connected  or  belt  driven  with  steam  or 
hydraulic  power. 

MOTORS  OF  EVERY  KIND 

For  railway  or  street  car  service,  mills,  factories, 
machine  shops,  pumps,  ventilation,  and  general 
mining  use. 

ARC  AND  INCANDESCENT  LAMPS 

On  direct  or  alternating  current  circuits  for  street, 
store,  and  house  illumination, 

ELECTRICAL  SUPPLIES 

With  insulation  of  the  ^  highest  resistance  for 
equipping  or  renewing  small  or  large  plants,  for 
measuring  current,  and  for  every  other  purpose. 

miM  offlcti  la  ill  i»f«  oitui.     GMiral  Offlci,  SCRENECTIDT,  R.  Y. 

3 


We  caa  supply  ptomptly  any 
ordinary  order  for  Steel  Bridges, 
Btfildlngs,  Roots,  Tnoses,  Cobmins, 
Girders,  Beams,  Channets,  Ang^ 
Plates,  etc 

Stee!  Frame  Work  for  MiUs, 
Factories,  Public  Slarkets,  Sheds, 
Shops,  Power-Hotfses,  Piers,  etc 

liiicis;lcaLiLi 

Engineers  t  Manufactufers, 
Contractoi's 


Metallic  Structures 
of  Every  Description 


Branch  Offices  and  Works  t 


Albany.  N.  Y. 

Athens,  Pa. 

Boston,  Mass. 
,  Buffalo,  N.  Y. 

Baltimore,  Md. 

Butte,  Mont. 
i  Columbus,  Ohio. 
)  Chicago,  III. 
f  Canton,  Ohio. 

Cleveland,  Ohio. 

Denver,  Colo. 

L-2i-iia 


Duluth,  Minn. 
East  Berlin.  Conn. 
Elralra,  N.  Y. 
Groton,  N.  Y. 
Ilorseheads,  N.  Y. 
Lafayette,  Ind. 
Milwaukee.  Wis. 
Minneapolis,  Minn. 
New  Orleans,  La. 
Pencoyd,  Pa. 
Philadelphia,  Pa. 


Pittsburg,  Pa. 
Rochester,  N.  Y. 
Seattle,  Wash. 
San  Francisco,  Cal. 
Salt  Lake  City.  Utah. 
Sydney,  N.  S.  W. 
Trenton,  N.  J. 
Wilmington,  Del. 
Youngstown.  Ohio. 
London,  England. 


WM.  SELLERS  4t  CO. 

(INCORPORATED), 

PHILADELPHIA,   U.  S.  A. 

IMPROVED  LABOR-SAVING  MACHINE  TOOLS 
For   Railway  and   Machine-shop   Equipneot. 

HIGH-SPEED   TRAVELING    AND   SWING-CRANES. 

TURNTABLES    FOR    LOCOMOTIVES  AND   SHOP- 
CARS. 

INJECTORS  FOR  ALL  CONDITIONS  OF  SERVICE. 

SHAFTING  IN  ALL  ITS  DETAILS  FOR  THE  ECO- 
NOMICAL TRANSMISSION  OF  POWER. 

GRINDING-MACHINES  FOR  TOOLS  AND  DRILLS. 

IMPROVED  HYDRAULIC  TESTING-MACHINES, 
Under  Patents  of  A.  H.  Emery. 

Etc. 

PRATT  &  WHITNEY  CO., 

HARTFORD,   CONN.,    U.   $.   A., 

MACHINE    TOOLS 

roR 

GENERAL  AND  RAILWAY  MACHINE-SHOP  SERVICE. 

Modern  Machine  Tools  for  the  MaoufaCtare,  on  tiie  Intarefaftngeable 
B/stem,  of  Locomotive  Work.  Bicycles,  Eleotffeal  Apparatus*  Type-wrltfeg 
Machines,  Guns,  and  Sewing  Machines,  including  all  Small  Tools,  Qaogt-s, 
and  Fixtures. 

UthK,  Mllllflg  MaeUHS,  Scm  aid  Tamt-Htad  Chneldig  MadlMS. 

Specially  designed  Machinery  and  Tools  for  the  Manufacture  of  Brtiss 
Goods,  Agricultural  Implements,  etc.,  and  for  ever^  purp99^  where 
Accurate,  Rapid  and  Beonofnieal  Production  is  esaeotial. 

U.  S.  Standard  Taps,  Dies,  and  Gauges.  Standard  CvUndrical  Size  and 
Caliper  Gauges,  Reamers  of  e?ery  kind,  rlain,  Spirally  Fluted,  and  Inaerted- 
Tooth  Milling  Cutters  of  ereir  sise  and  style. 
^  Send  for  Illustrated  Catalogues  and  Prices.    Oorfwpondenoe  invited. 

NEW  YORK:  136-138  Liberty  St. 
BOSTON:  144  Pearl  St. 
CHICAGO:  4a  5o.  Clinton  St. 
BUFFALO:  Cor.  Seneca  and  Wells  5ts. 
PHILADELPHIA:  J.  W.  Cregar  Aicency,  «•  The  Bourse." 

4 


MILLING  MACHINES, 

Plain  and  Universal. 


Largest  producers 
in  the  world  of  this 
type  of  machines. 

Latest  designs. 

IMachines  guaran" 
teed  to  meet  most 
exacting  require- 
ments as  to  efFici* 
ency  and  accuracy* 

Write  for  Complete  Cata- 
logue: also  Treatiee  on 
Milling  Machines, 


THE  CINCINNATI  MILLING  MACHINE  CO., 

CINCINNATI.  OHIO,  U.  8.  A. 


No.  14  Improved  Plain  Miller. 


COMPLETE    UNB 

•     OF 

MULma 

MACHINES 

UNIVERSAL,  PLAIN, 
VERTICAL,  DUPLEX, 
COMPOUND.   HAND. 
PROFILERS,  ROTARY, 
LINCOLN, 
all  with  Numerous 
Attachments. 

Write  tor  llluttnttd 
Catalogm. 


THE  GARVIN  MACHINE  CO.. 


Factory  and  Main  Office, 


NEW  YORK  CITY. 


The  Hendey  Hachine  Company, 

TORRINGTON,  CONN., 

MANUFACTURERS  OF 

MACHINE  TOOLS. 

SPECIALTIES: 

The  Hendey-Norton  Lathes 

AND 

Hendey  Pillar  Shapers. 

THE    DOCTRINE   OF   VACUUM   OIL. 

We  shall  always  work  on  the  lines  we  have  fol- 
lowed for  thirty  years  :  inventing  and  making  oils  to 
put  friction  down  as  low  as  it  can  be  put  down  by 
oil,  with  no  regard  to  the  cost  of  making  the  oil, 

We  shall  always  teach,  as  we  have  been  teaching 
for  ten  years,  that  the  proper  service  of  oil  so  far 
exceeds  its  cost  that  the  best  is  the  cheapest,  ten  to 
one,  sometimes  perhaps  fifty  or  even  a  hundred 
to  one. 

The  only  question  is  how  fast  the  man  most 
nearly  concerned  will  act  on  the  fact — we  mean  the 
consumer. 

We  make  a  few  cents  a  gallon.  He  makes  a  few 
dollars  a  gallon. 

VACUUM   OIL  COMPANY.  Rochester.  N.  Y. 


e 


^^ 


42inch  Mill.    Weight  11,000  lbs. 

THE  BULLARD  MACHINE  TOOL  CO.. 

BIMDGEPOK.X,    CONN., 

MAKE  A  SPECIALTY  OF  V 

Boring  and  Turning  Mills, 

From  30-  to  76-inch  Capacity. 


IN  PREPARATION. 

STEAM    BOILER    ECONO-MY. 

A  TREATISE  ON  THE  THEORY  AMD  PRACTICE  OF  FUEL 
ECONOMY  IN  THE  OPERATION  OF  STEAM  BOILERS. 

By,  WILLIAM   KENT. 
JOHN   WILEY   &   SOliS,  4345  E.  19lh  St,  New  York. 


Air  Compressors. 


EVERY  STYLE 
AND  TYPE 
SUITED   TO 


ROCK  DRILLS, 

stone  Channelifti 
Coal  Cuttirs, 
ThePohleAirUftPup, 


MINING  OPERATIONS, 

MACHINE-SHOP   PRACTICE. 
PUMPING   WATER, 

QAS   COMPRESSION, 
STREET    RAILWAYS, 
PNEUMATIC  T(M>LS, 


AND  ALL  OTHER  COMPRESSED-AIR  USES- 


The  INOERSOLL- 
SbRQEANT 
DRILL  CO., 

NEW  VORK, 


LiDGERWOOD    HOISTING 
■    ENGINES 

Are  built  to  gauge  on  the  Duplicate 
Part  System.     Quick  delivery  assured. 

STANDARD '^o^^W?' 

16,000  in  use. 
Steam  and  Electric  Hoists. 

Cableways 

Hoisting  and 
Conveying  Devices 

For  Mining,  Qoarrying, 
Logging,  Dam  Construc- 
tion, etc. 

LIDGERWOOD  MT'Q  CO., 

Send  Cor  Catalogue.  96  Liberty  St.,  NoW  YOfk. 


8 


THE  NORWALK  AIR  COMPRESSOR 

*  OF  STANDARD  PATTERN 

is  built  with  Tand«m 
Compound  Air  Cylind. 
ort.  CoHiM  Air  Volvos 
CD  the  intake  cylinders 
insure  small  clearance 
spaces.  Tho  Intorooolor 
between  the  cylinders 
saTcs  power  by  remoT- 
ing  the  heat  of  compres- 
sion before  the  work  is 
done,  not  after,  and 
the  compressing  is  all 
done  by  a  straight  pull 
and  push  on  a  continu- 
ous piston  rod.  Tho 
Compressor  is  self-eon. 

are  reduced  to  a  minimum,  and  the  machine  is  ecoiomi^^  an'd^fficient! 
Special  machines  for  high  pressures  and  for  liquefying  gases.  Compound  and 
X  riple  Steam  Ends. 

M  catalog,  explaining  its  man/ points  of  superiority,  is  sent  free  to 
business  men  and  engineers  who  apply  to 

THE  NORWALK  IRON  WORKS  CO., 

SOUTH    NORWALK.   CONN. 


AIR  COMPRESSORS  Tsp^"^ 


MCY    HRII  \  <s   ™  OUARRIES.  MINES, 
llUU^  UnlLLO   AND  CONTRACT  WORK. 


^  RAND   DRILL  COMPANY, 

128    BROADWAY,  NEW   YORK. 


JNO.  J.  CONE  ROBERT  W.  HUNT  JA&  C.  HALLSTEO 

A.  W.  FIERO  D.  W.  M'NAUQHER 

Robert  W.  Hunt  &  Co. 
Bureau  of  Inspection,  Tests  and  Consultation, 

71  BROADWAY,  1121  THE  ROOKERY,  MONONQAHELA  BANK  BUXS^i 

NEW  YORK.  CHICAGO.  PtTTSBUROK 

INSPECTION  OF 

RAILS  AND  FASTENINGS,  CARS,  LOCOMOTIVES,  PIPE,  ETC. 

BRIDGES,  BUILDINGS  AND  OTHER  STRUCTURES. 

CHEMICAL  AND  PHYSICAL  LABORATORIES. 

REPORTS  AND  ESTIMATES  ON  PROPERTIES  AND  PROCESSES. 

WESTERN  AGENTS  FOR  RHEILE  BROS.  TESTING-MACHINES. 


LEATHER  BELTING. 

HOYT  SSJSa'.'..  BELTS 

are  all  stamped  with  this  trademark : 

0\]H  Fl^i^ 


We  guarantet 
to  replace  or 
make  good  to 
you  ail  Hoyt 
Belts  which 
prove:  defec- 
tive. 


*Aui  fAhP^*^ 


FAYERWEATHER  &  LADEW;  Sole 
NEW  YORK,  CHICAQO,  BOSTON. 

Asenclee  In  all  principal  oltlee* 


The  American  Under=Feed  Stoken 

t    Pmrtlcmlan  mnd  Cmtmlogue  on  Appiicatioa. 

11     BROADWAY,     Bowling  Qften   Otflcw.     NEW    YORK, 


Burns  efficiently  tlie  cheapest  grades  of  fuel  without  smoke> 

GREEN'S  FUEL  ECONOMIZER 

FOR    STEAM    BOILERS. 


wHfc— <"  »fP9tf  •€  wrkm.    A  larm  T*laaie  ef  waier  mlwmi9  la  reMrre  at  tka 
^apM«tiT«  v%t  r^mdj  IWr  lauMdlatc  dellTery  U  the  WOen. 

Slocteeza.  3Px*l0e   Adieclaas. 

MOLK  MAMJBR8  IX  THE  VHItED  BTATE8, 

TOs  r.RRn  pnvT  izrmAinTviP  m  nf  VflffAAVfln  i  ? 


OROANIZKO,    I860. 


THOROUGH    INSPECTIONS 

AND 

Wnturunee  o^oitMl  Loss  or  J>ainago   to  Property  aiul  £•••  of 

Lifo  and  Injury  to  Persons  caused  by 

Steam  Boiler  Explosions 

J.  M.  ALLEN,  Prwident. 

WM.  B.  FRANKLIN,  YIoe-PTMideiit. 

F.  B.  ALLEN.  Second  Vice-Pretident. 
J.  B.  PIERCE,  Secretary. 

L.  B.  BRAIN  1!:RD,  TreMarer. 

L.  F.  MIDDLEBROOK,  Asst  SecrsUiy. 

ESTABLISHED  1856. 

HENRY   MAURER   dt   SON, 

MANUFACTURERS  OF 

FlilEBKl£S,liIlli,GIIFOLIIIJin|ilS, 

Clay  Retorts  for  Qas  Works- 

Office,  420  East  23d  Street, 

^    ^     Works,  MMrM",  N.  i.  NFW     VHRIC 

;P.  0.,  T«l«9r«pk,  Md  R.  R,  ttetiM.)  H  C  YY       T  ^-THrV. 

19 


The 


STIRLINe'^BOILER 


Safe 

Economical 

Durable 


All  surfaces  under  pressure,  cylindrical  in  form  and 

made  entirely  of  wrought  metal. 

One  manhole  in  each  drum  gives  access  to  all  parts 

of  the  interior. 

THE  STIRLING  CO. 

OCNERAL  OFFICE*: 

Pullman  Building,  CHICAGO 


AOCNCICS  IN   ALL 

PiiiNciML  Cmcs. 


IMPROVED  ROOT  WATER-TUBE 
BOILER 


HMHCST  ECONOMY— IfCST  ADAPTED  TO  HIGH  PRCSSURBS 
ABSOLUTELY    DRY    STEAM  — PCRFCCT   WORKMANSHIP 

ABENDROTH  ft  ROOT  iFQ.  00.,  NEW  YORK 

IP 


MACHINERY  FOR  HANDLING 

COAL,  ORE,  oT^R  MATERIAL 

ON  DOCKS,  CARS,  AND  VESSELS.   ^ 

MACHINERY  FOR  HANDUNQ  STRUCTURAL  WORK. 

Marine   Plates,  etc.,  in  Ship-building  Yards.  Overhead 
Tramrail  Systems,  Trolley  Blocks,  etc. 

m  CMis  m 

THE  BROWN  HOISTING  MACHINERY  CO., 

INCORPORATED, 

CLEVELAND.   OHIO,    U.   S.   A. 

KAiiteni  Office:  Pittsburgh  Olflc«:  ^"C^EffS  *SS!J» 

,6^r-rsS^.  cm.,..  B«..d.n,.  ^«^^«CS^- 

EARLE  C.  BACON 


UreiDefBrBDyiiDi 

HOimNB  MINES 

and  WINCHES  FOR  EVERY  POSSIBLE  DUTY. 

CRUSHING  ROLLS.  ORE  WASHERS.^^^^^ 
GRAVITY  DRUMS,  MINE  MACHINERY.  BOILERS  &ENGINES 
SCREENS  and  ELEVATORS  for  Ore  and  Rock. 

»'"''' lilCRIISlIEIlS 


inwiEmY  lunnna  utilmes  if 
HOISTINGp  ORUSHjNG 

MINING  MAOHINERY 
COMPLETE  MimilG  I CRUSHMG  PlilTS's 

14 


Jjok 


w^lREROpfi 

"*  \?F  FOR  mi  PURPOSES  3- 

TlNTON-ffl-C^' 

^TRENTON. N. J, '^ 

f!0QP£ltKElWgBBeiBafllRtlH6  SLIP 

CHICAGO    O 


~MADHDCK  eiOCJ 


Mm 


/WIRE  ROPE 

a    Worki4,t;Tre5ton.N4  J;; 

^'    V     ^     \i7  LIBERTY  5T.  NEW  YORK    v^ /, -' 
\    "3*^  ZSpfltMONTSlS^HFRAKOS^O    A-/ 


The  Pelton  •  • 
Water=WheeI 


is  conceded  to  be  one 
of  the  most  useful  as 
well  as  illustrious  in- 
ventions of  this  or 
any  other  country. 
By  means  of  it,  water 
is  converted  into 
power  in  so  simple  and  economical  a  way  that  machinery  may 
be  said  to  be  almost  dispensed  with.  Thousands  of  these 
wheels  are  sent  out  every  year  to  all  parts  of  the  world,  and 
in  no  instance  do  they  fail  to  meet  the  most  sanguine  expecta- 
tions of  purchasers.  Adapted  to  heads  from  tWRty  feel  up 
to  the  highest  in  any  case  obtainable. 

Electric  Power  Transmission. 

PELTON  WHEELS  afford  the  most  reliable  and  eScient 
power  for  such  service,  and  are  running  the  majority  of  sta- 
tions of  this  character  in  the  United  States,  as  well  as  most 
foreign  countries. 

Highest  Efficiency  and  Absolute  Regulation 

guaranteed,  covering  the  most  extreme  variations  of  load.  Cat- 
alogues furnished  on  application.     Address,  giving  conditions, 

PELTON  WATER-WHEEL  C0.'%IWl*y%."a13c 


THE  ORBATBST 


,  WATER  METER 

RECORD  EVER  MADE. 

280,000 

Crown,  Empire,  Nash,  Qem 

METERS  IN  USE. 
National  Meter  Company, 

NEW  YORK.      CHICAOO,      BOSTON,      LONDON, 
AUaUST.  1900.  _  I«  -  - 


R.  D.  WOOD  &  CO., 

ENQINEER8.  IRON-FOUNDEBS,  AND  MACHINISTS, 

400  Oiestnut  St,  Philadelphia,  Pa. 

CAST-IRON    PIPE. 

MATHEWS'   FIRE-HYDRANTS. 

GATE    VALVES. 

VALVE    INDICATOR-POSTS. 

GAS-HOLDERS   AND   GAS    MACHINERY. 

^HYDRAULIC    RIVETERS. 
INTENSIFIERS,  PUNCHES,  AND  SHEARS. 

TURBINES.  CENTRIFUGAL  AND  HIGH  DUTY  FUMPS. 

Our 

Durable  Metal  Coating 

protects  iron  and  steel  structures, 
bridges,  buildings,  water-towers,  etc., 
against  the  destructive  action  of  the 
weather,  corrosive  gases,  dampness, 
water,  salt  drip  from  refrigerator  cars, 
etc.,  in  the  best  possible  manner.  It  is 
also  an  exceptionally  perfect 

Insulator 

against  electric  currents,  electrolysis,  etc. 
EDWARD  SMITH  &  CO., 

VARNISH  MAKERS  AND  COLOR  GRINDERS. 
45  BROADWAY,  NEW  YORK. 

17 


R  GOODS 


BELTING.  j| 

HOSE  fof  all  pufpoics* 

PACKINGS  in  great  variety. 
GASKETS^  VALVES, 
Rubber<overed  Rollers* 

MANUFACTURED   BY 


ws)\^m 


:  JAMES    BENNETT   FORSYTH, 
MFO.   AOT.  A  OEN.    MOR. 


BOSTt>N  : 
:  SM  Deronnhlrif  Pt. 


NEW  YORK: 

KM  R*.i(lc  St. 


CHICAGO  : 
109  Madikon  St. 


GEORGE  H.  FORSYTH, 

AMT.  MOR. 
ST.  LOIIS  :         BUFFAIX* 
11  N.  Sixth  St.         M  P»«rl  M. 


I.   m  r 


DOMESTIC  WATER=SUPPLY 


Without  Depending  on  the  Wind 

THE  IMPROVED  RIDcR 

AND  IMPROVED  ERICSSON 

HOT-AIR  PUMPING- 

ENGINES 

In  use  for  twenty-five  yenrs. 

More  than  20,000  sold. 

Specified  by  the  Leading  Engi- 
neers of  this  country. 


Catalogue  on  appllcatiott  to 
est  store. 


RIDER-ERICSSON  ENGINE  CO., 

aa  CORTLANDT  ST.,  NEW  YORK.      86  LAKE  5T.,  CHiCAOO. 

339  FRANKLIN  5T.,  BOSTON.  40  N.  7th  5T.,  PHILADBLPmA. 


A5BE 

I.  .'ELT 

'STEAM  PIPES 

BOILERS.&C  «c.   .. 


ISTOS 

C0VERLNJQ5 

THEH'ERFECr 


lAFPUCAllONSlWPlE 
ailNtXPEN51VL 

h.W,  JOHN' 

IfEltTrOflK  CHICAGO    PH| 

M  AH"' 

|rOOFIN'g?T  MATE  RIALS 


KLl  LIKE. 
"     ^FIRLPROOK 

s  M  Fo  ca. 

I  LA  DEL  PHI  A      a05.T0W 

"uOUIt^  PAINTS  A  STAINS 
E  L  eCTRlC  At.  MAT  E  R I  At  S. 


OrriCG  &  SALESROOM  S" 

loe-iio  Centre  sf^ 

ptar^J^I^I}    NfiWYORK 


Mjuwcie  aitiQMni^t 


19 


AMERICAN-BALL  DUPLEX 
COMPOUND  ENGINE 

AND 

DIRECT-CONNECTED 
GENERATOR. 

The  latest  develop- 
ment in  practical 
steam-engineering. 

The  highest  econ- 
':!:^omy  of  steam  with 
.^^'the  simplest  possi- 
_  "--^  ble  construction. 

Complete  electric  and   steam    equipments   fur- 
nished of  our  own  manufacture. 

AMERICAN  ENGINE  CO., 
New  York  Qffice-95  Liberty  St.    Bound  Brook,  N.  J. 

THE  FILER  UTOW[LLc«- 

MILWAUKEE,  WIS. 


HEAVY  DUTY  CORLISS  ENGINES. 

Best  Design.  Best  Efficiency.  Best  Workmanship. 

Eastern  Representative,  T.  W.  PHILLIPS,  4  Market  Square,  Proridence,  R.  L 

20 


The  Edw.  P.  AUis  Co., 

MILWAUKEE,  WIS. 


sSolcBtdUenof  the: 


"Reynolds  -  Corliss"  Engine. 


1890  Frame,  **Reyuolclf(-CorliM*'  Engine. 

PUMPING,      BLOWING      AND 
HOISTING    ENGINES 


SAW  MILL,  FLOUR  MILL,  AND 
MINING    MACHINERY. 


V. 


BUNDYRETURN  STEAM-TRAR 


V    RETURNS  TO   BOILER    THE   WATERS 
X   OF    CONDENSATIOM    FROM    ALL   V 
H    .XSOURCES    AT    PRACTICAILT  V^ 
Z  O        XNO  COST  FOR  RUNNING  X 


Q_X  RE^ 

I—  « 

i    Z  O 
O  E  O 

-■  ;= »-  ^ 


oo  o    r 
g--o 


y      SENT    ON    30    OArs       ' 
'trial.      tF    NOT    SATrSFlED 
r      RETURN     AT     OUR     EXPENSE 

X     A,    A.    gRlFFING     IRON    CO; 

N£W  VOHK     eOSTON  .  PHiLADELPHlA  .  JERSEY   CITV 


SEND  FOR  96-PAQE   OATALOQUE   K. 

THE  WAINWRIGHT 

Water  Tube    Even- 
Flow   Heater 

gives  a  high  rate  of  heat  transmission  for  two 
reasons:  high  velocity  of  flow,  and  a  corrugated 
heating  surface. 

Are  you  familiar  with  our 

Expansion   Joints    and 
Surface  Condensers? 

TAUNTON    LOCOMOTIVE   MFG.    CO., 

TAUNTON.  MASS.,   U.  S.  A. 


THE 

LUNKENHEIMER 

COMPANY. 

Main  Offic««  and  Works: 

CINCINNATI,  U.  S.  A. 

Branches: 

New  York :  26  Cortlandt  Street. 
London :  35  Great  Dover  Street. 

Originators  and  Patentees  of 
superior  Brass  and  Iron  En- 
gineering Appliances  for  Steam, 
Water,  Gas,  Air,  Oils,  etc.; 
Valves,  Whistles,  Injectors,  Lu- 
bricators, Oil  and  Grease  Cups, 
etc.,  in  endless  variety. 

SPECIFY  THEM.    WRITE  FOR  CATALOG. 


J^mif 


UNIFORM  QUALITY,  QUICK-CUTTING, 

WONDERFUL    DURABILITY,   WATERPROOF, 

NO  DUST,  NO  ODOR. 


NORTON 

EMERY 

WHEELS 


ILLUSTRATED  CATAL06UE  FREE. 


WALKER  UNIVERSAL  TOOL  AND  CUHER  6RINDER. 


NORTON    EMERY  WHEEL  CO., 

WORCESTER,  MASS, 

Cable  Address:  WHITLOCK,   HARTFORD. 

The  Whitlock  CoU  Pipe  Co., 

HARTFORD,    CONN., 

MANUFACTURERS  OF 

Wrought  Iron  O  /^  1 1    C    of  every 
Ammonia   k^\J  I  ^O  description. 

COPPEft  COIL         ^^SBm^        '"'"'•  ^'>*ss. 

FE£D  WATER HEAT£HS.  ^^KK^^^'fO  COPPER  CO/LS  OF 

CONDENSERS.        ^^^MM       ''"  '""^^  '''"* 

SEPARATORS.        "^mM^    fleatii«  aid  CMlii«. 


U,  Square,  am)  S  Bends  made  of  Standard  Pipe, 

For  175  lbs.  Working  Pressure! 

THE   WHITLOCK   COIL   PIPE   CO., 
HARTFORD,  CONN. 

24 


Morse  Tfist  Drill  and  Hacbine  Co., 

NEW  BEDFORD,  MASS..  U.  S.  A., 

MANUFACTURERS   OF  * 

Arbors.  Beach,  Stetson,  and  Center  Drill  Chucks. 
Counterbores  and  Countersinks.  Increase  Twist  and 
Constant  Angle  Drills.  Drills  with  Oil  Holes.  Drills 
with  Grooved  Shanks.  Dies.  Gauges.  Mandrels. 
Metal-slitting  Saws.  Milling  Cutters.  End  Mills. 
Shell  End  Mills.  Taper  Pins.  Adjustable  and  Ex- 
pansion Reamers.  Reamers  with  Oil  Holes.  Screw 
Plates  with  Dies.  Sockets.  Sleeves.  Taps  and 
Tap  Wrenches. 

We  a/so  make  Special  Tools  and  Machines 
and  solicit  your  correspondence. 

A  copy  of  our  laiett  Caialogue  sant  f^ee  to  any  addratt. 


CHAPMAN  VALVE  MFG.  CO., 

WORKS  AND  MAIN   OFHCE  : 

INDIAN  ORCHARD,  MASS. 

BRANCH   OmCES: 

BOSTON,   NEW  YORK,   PHILADELPHIA,   BALTIMORE, 
ALLENTOWN,  PA.;  CHICAGO,  ST.  LOUIS,  SAN  FRAN- 
CISCO,  LONDON,   ENGLAND;    PARIS,   FRANCE;   AND 
JOHANNESBURG,  SOUTH  AFRICA. 


VALVES 


MADE  IN  ALL  SIZES  AND 
FOR  ALL  PURPOSES  AND 
PRESSURES. 


coftftEsnHoeiicE  soucitsd. 


APPARATUS    FOR    THE 


Softening    and    Purification 
of  Boiler  Water 

Before  it  enters  the  Feed-Water  Heater,  so  that  it 
will  NEITHER  SCALE,  CORRODE,  nor  FOAM, 


For  pariiouiart 
add  rasa 


INDUSTRIAL  WATER  COMPANY,  '^.r^l-SIr 


THE  JACKSON  HAND-POWER  ROCK  DRILL, 

Handled  and  operated 
by  one  man,  will  per- 
form work  of  three 
men  drlllins:  with  ham- 
mers and  bits. 

GUARANTEED 

AGAINST 

BREAKAGE. 


H.   D.  CRIPPEN, 


52  Broadway,  Ne«»  York. 


FOR    FORTY   YEARS 

Whiton  has  been  making  chucks— strong,  honestly  built  chucks  that  have 
never  failed  to  meet  the  requirements  for  which  they  were  designed. 

In  all  these  forty  years  he  has  kept  just  a  little  ahead  in  the  march  of 
improvement  and  the  Whiton  line  of  to-day  covers  every  possible  chuck 
need  in  the  best  possible  way.  | 

Would  the  catalog  Interest  you  ? 

THE  D.  E.  WHITON  MACHINE  CO.,  new  London,  conn. 

Sole  European  Agani:   Selig,  Sonnanthal  &  Co. 
Sole  German  Agent:    E.  Sonnenthal,  Jr. 


FAN  AND  PRESSURE  BLOWERS, 
EXHAUST  FANS  FOR  ALL  USES. 

I  Hot  Blast  Heating  Apparatus,  Dry 
Kiln  Outfits,  Steam  Fans,  Forges, 
High    and    Low   Pressure    Engines. 

S£liD  FOR  C/ROUL/iRS, 

BOSTON    BLOWER    CO.. 

HYDE    PARK,    MASS. 
26 


THE" 


MONARCH 


M  "Safe, 

Swift, 
T  IflUllflllVII  Sure." 

ENGINE-STOP  SYSTEM. 

Over  500  of  thesf  systems  *"  use  on  many  of  the  lorgo«t  plants  in  this  country. 
With  the  usf  of  the  MO.SAKCH  SYSTEM  it  i«  im|io8Klble  for  an  engrine  to  run  away; 
fUfrine  can  alw  be  gtoppcd,  in  ca.«»e  of  einerKimoy.  from  any  portion  of  the  i)lant  by 

ri-(>^sing  an  electric  button.   No  connection  with  the  governor,   tt  closes 

the  throttle,    investigate.    Wi-lte  for  New  Illustrated  IJWl  Catalogue.    Jui<t  Out. 

THE  MONARCH  MANUFACTURING  CO., 

WATERBURY,   CONN. 

L.  W.   SWEET  (N.   A.   a    E-),   General   Masagea. 


ATLAS 

PORTLAND 

CEMENT 

Is  the  Standard  American  Brand. 


Used  by  all  the  leading  Engineers  and 
Contractors  throughout  the  United  States, 
and  preferred  by  the  U.  S.  Qovemment. 


ATLAS  PORTLAND  CEMENT  CO., 

143  LIBERTY  ST.,  NEW  YORK. 


RtGTRADt  MASKS     JhE  pKOSPHOR  BRONZE  SMELTINGCO^UMITED, 

£200  WASHINGTON  Ave.  Philadelphia, 

\  ELEPHANT  BRAND  PHOSPHOR  BRONZE" 

_  INGOTS,CASTINGS,W!RERODS.SHEETS,ETC. 
Mu//<>t-ihi*m-'  — DELTA    METAL^ — 

v'Ov  CASTINGS.  STAMPINGS  A^D  rcRGlNGS, 


PYROMETERS 

FOR   ALL    TECHNICAL    PURPOSES. 

The  Queen  Mercurial  Pyrometer,  for  stack  Temper 

atures,  reading  to  1000°  K. 

The  Queen   Metallic   Pyrometer,  for  oven  Temper- 

atures,  reading  to  1500"  F. 

The   Queen-Chatelier   Pyrometer,   for  Furnace  Tea.. 

peratures,  with  direct  reading  scale  to  3000'  F. 

r.JjLtj:,x^t  ^^  ot7;?!:reter  (:i{';4i:r '-" 

QUEEN  ^t  CO.,  Inc. 

S9  Fifth  Avenue,  ,oio  Chestnut  Street 

NEW  YORK,  PHILADELPHIA. 

KEUFFEir&  ESSER  CO. 

127   FULTON  STREET, 

yjtJW  YORK. 

3»iic1im:  111  UAdlson  St.,  Chloa«o;  708  Loeut  St.,  StLoul^^ 

Manufacturv's  and   lmport«re  of 

DRAWING  MATERfALS, 

MATHEyATICAL  AND 

SURVEYIII8  IMSTRUf — -      1 

Paraflmn,  Key,  and  Arrow  Brand  Drawing  Instniments.  '^ 

l>aragon,  Anvil,  Universal,  and  Dvplez  Drawing  Papers. 
SUndard  Profile  and  Cross-section  Papers  and  Boolcs. 

Helios,  Columbia,  etc.,  Blue  Print  Papers  and  Cloth, 
Madura  Brown  Print  Papers  and  Cloths. 

Nigroslne  and  Umbra  Positive  Black  Process  Papers. 
-rw    ^    .    J!^- *P-Co-;»  Patent  AdlusUMe  and  Duplex  Slide  Rules. 
Tiiacher*s  Calculatinsr  Instrument.    Paragon  Scales,  with  White  Edges. 
Patent  Triangular  Scales.  Triangles,  T  Squares, 

Curves,  Railroad  Curves,  Drawing  Boards,  and  Tabiaa. 
«.-*.  «     ^    r,      Columbia  and  Kallos  Indelible  Drawing  Inks. 
High  grade  Engineer's  TranslU  and  Y  Levels,  latest  and  most  Improved. 
Surveying  and  Prismatic  Compasses,  Aneroid  Baroavtcrs,  etc. 
excelsior  Steel  and  MeUillc  Tapes. 

Surveyor's  Chains,  Rods,  Poles,  etc 

Catalogue  stnt  /r«*  en  a^piicaticn.     WriU  /or  cur  JU$m/kUi  "  /^/^/r/w/- 
ing  /rem  Trmcingt,^*      O 


•^'•■'lUfc.