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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
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19
.00108814
6G0
.00151515
5
.00187981
790
.00121/582,
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.OOI169ft9
920
.00108696
1
.00151*6
6
.00137741
1
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6
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2
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7
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7
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3
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9
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5
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730
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6
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860
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6
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1
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6
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1
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6
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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
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5
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090
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6
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2
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7
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8
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8
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4
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9
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4
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740
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B
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870
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5
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e
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1
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1 ^
.00124009
1
.00114811
6
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7
.00147710
2
.00134771
7
.00123916
2
.00114679
7
.00106724
8
.00147498
3
.00134589
8
.00123762
8
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8
00I0601O
g
.CO 14727 5
4
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.00134228
1 8
.00128609
4
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9
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68U
.00147059
6
1 810
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5
.00114286
940
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1
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6
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11
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6
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1
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2
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7
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8
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8
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8
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8
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4
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9
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1 54
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750
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3
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3
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9
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6
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1 2
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830
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960
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7 .00j:w:i78:
2
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8
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900
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6
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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
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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
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e
.00101215
.000949668
18
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8
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8
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19
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4
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9
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99i]
.00101010
.000947867
1120
.000892867
6
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1260
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.00100906
.000046070
1
.000892061
6
.000843170
1
.000799860
00100606
.000946074
2
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7
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8
.000798;'28
.00100706
.000945180
8
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8
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8
.000798085
.00100601
.000944287
4
.000889680
9
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4
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.00100602
1()6C
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6
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1190
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5
00071*6818
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6
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1
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6
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.00100801
.000941.620
7
.000687311
8
.OOOi'38926
7
.000795645
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8
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8
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8
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00100100
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9
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4
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9
.OOO". 94281
lOOC
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1180
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5
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1260
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000938086
1
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6
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1
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2
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7
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2
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8
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8
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8
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4
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9
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4
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1200
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7
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8
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8
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8
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9
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4
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9
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1011
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1140
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5
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1270
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.000969120
.000929868
1
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6
.0008V9187
1
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.000968142
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a
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7
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8
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8
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4
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9
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4
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loec
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6
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1210
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5
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6
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11
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6
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7
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12
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7
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.000923361
8
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18
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8
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9
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14
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9
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ICtiO
.000980892
.000921659
1150
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15
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1280
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.000970488
.000920610
1
.000868810
16
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1
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0000:6474
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2
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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
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5
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.000974659
1 .0U0916590
6
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1
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6
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.000078710
2 .000915761
7
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2
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7
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s
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8 .000914913
8
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3
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8
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9
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4I.0U09HO77
9
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4
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9
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KM
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5
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1160
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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
UW2 1
289.419
6665.7
' i
302 378
755TG U
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
'4
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
5^^ggg^.|fH2?^^««fg^^jr;?.-^fl^
je«<oxc«iAao<-<
^ ~»»asaS88S8a5?*8S51SS888EeeSg3E5S$!§
>-• «o^ • floli ^ "^ ** ^ w sTct ^2 •-1 n Vw 00 o» »- •-I ©* •^«6 i-ft r-*w-^ 5i^ ^T^'ob'
1^ «««a!S9S883S8??^S5SSgS8SKl5f5£S$sSfe8
fMi^ooeeoio
^ "••S«S2s^«SS^§gi^gSSg3S§?fSP5o5£5S68
«-<4teo^iOttc*Qoa»o^e«eo^tc«Dt>Qoa»0'«2»eo'^
8»S{S$^3^^^gS8»SiS
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
i^
2206.2
9744.0
K
7«9.9
69784
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
12448
68.
8824.8
77952
88.
81643
899388
».
8642.1
12770
H
8992.0
80178
^
81904
804881
H
8887.8
18108
64.
9160.8
88448
84.
32167
810340
j4
8784.0
18442
^
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
2874.8
14494
56. ^
9852.0
91958
86.
83285
888089
n
8988.5
14866
H
10029
94488
H
88506
888888
S
2970.6
15284
67.
10907
96967
87.
83779
844798
SI.
8019.1
15599
H
10887
99541
^
24058
850771
8068.0
15079
68.
10568
102161
88.
84888
856819
L ,
8117.8
16866
H
10751
104826
H
S4606
862985
£
8166.9
16758
59.
10936
107536
89.
24885
869122
«.
8817.0
17157
H
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
18817
H
11882
181794
H
26802
401109
H
8478.8
19248
62.
ijore
124789
92. "
86590
407781
-,
8586.7
19685
H
12278
127882
^
86880
414405
r
8578.5
80129
68.
12469
130925
98.
27172
421161
84.
8681.7
80580
H
18668
134067
^
27464
427991
g
8685.8
21087
64.
18868
137259
94.
27759
484894
878B.8
81501
^
13070
140601
H
28055
441871
85.
8848.5
82449
65.
13278
143794
95.
28858
448920
M
8050.2
88485
H
18478
147138
H
88652
466047
86.
4071.5
66.
13685
150538
96.
28958
463848
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
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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
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66.8
100.2
138.6
167.0
800.4
838.8
867.8
800.6
838
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66.6
99.9
188. 2
166.6
199.8
888.1
866.4
290.7
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3.3.2
664
99.6
132.8
166.0
199.8
832.4
865.6
298.6
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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
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32.9
65.3
98.7
131.6
164.5
197.4
830.8
868.8
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328
32.8
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98.4
181.2
164.0
196.8
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868.4
896.8
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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
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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
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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
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2846
5028
8882
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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
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6
7
8
9
Diff.
170
1
9
3
Sa0449
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5528
0704
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6781
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8604
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8548
1215
8757
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6637
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1724
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6799
9299
1979
4617
7041
9660
2234
4770
7202
9800
2488
6028
7544
2742
6276
7795
256
268
252
0050
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2790
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7?28
250
249
248
246
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4526
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4772
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2610
6061
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245
248
242
241
389
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9
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8882
6287
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6477
8877
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2125
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2868
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2
3
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1976
4846
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6937
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288
237
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284
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6T72
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1877
3606
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8296
1609
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6232
8625
288
232
280
229
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8
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271842
4158
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2074
4889
6692
2306
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PsopomxoNAi* Pabtb.
Diff,
2B5
254
258
252
261
250
249
248
2f7
246
944
248
242
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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
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49.2
49.0
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47,8
47.0
47.4
47 2
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46.8
46.6
46.4
46.9
46.0
45.8
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76.6
76.2
75.9
75.6
75.3
75.0
74.7
74.4
74.1
73.8
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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
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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
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1158
0126
1267
0041
1881
; 0865
' 1496
0460 1 0688
0607
1836
0611
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114
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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
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6122
5235
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5
5461
5574
5686
5799
5912
6024
6187
6250
6362
6475
6
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6700
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6025
7037
7149
7988
7874
7486
75r.9
7
7711
7823
7935
8047
8160
8272
6884
8496
8G06
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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
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0817
6027
7087
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7586
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7805
7914
8024
8184
S248
8858
6462
8572
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7
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8900
0(X)9
9110
0228
9387
0446
9556
9065
9774
8
9888
9092
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0210
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0428
0587
0646
0755
0864
109
GOOOn
106i
U91
1290
1406
1617
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1734
1848
1951
400
2060
2109
2277
2386
2404
2008
2711
2819
2828
8096
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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
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7884
7991
8098
8206
8312
8419
107
8526
8638
8740
8ft47
8064
9061
9167
9274
0381
0488
9504
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9808
9914
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1086
0128
1192
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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
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f
8
4
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7
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f ^ oesa j 9024.
9144
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06
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1186
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^ 2431 f 2517
1741
1887
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8086
8178
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2689
2775
2861
3947
8038
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3463
8540
8636
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7740
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7911
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8061
8166
88
0401
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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
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1807
8650
1B02
1976
2060
2144
2329
8813
3897
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2^734
2818
2902
29H6
8070
8154
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88
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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
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0299
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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
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2310
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8601
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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
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8658
4134
4n4
5298
5871
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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
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1880
1928
2506
8088
8660
4250
4830
5400
5987
6561
7111
7n7
9440
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0585
1150
1727
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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
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8319
8924
0497
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0642
1218
1784
S354
2923
8401
7815
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0018
0619
0218
0817
1416
8018
8606
8204
8799
4882
4086
6578
6160
0760
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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
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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
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7
8
9
800
1
2
8
4
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6
7
8
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6491
7064
7017
8179
8741
9002
0602
8B0«n
0080
1587
2006
2651
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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
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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
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9002
0149
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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.
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[No.864L.9BL
N.
810 908486
1 I 9091
2 9666
910001
0004
1168
1090
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8814
4848
4878
6400
6027
6464
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7S06
8000
8866
9078
9001
900198
0646
1166
1086
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2796
8944
8709
4S79
4796
6818
6888
6848
6887
7870
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9410
9080
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1466
8688
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9010
0144
0678
1211
1748
2275
8806
8837
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4896
4996
5458
5080
0507
7088
7566
8068
8007
0180
0176
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1218
1788
2268
2r?7
8296
8814
4881
4848
6364
5879
6804
6006
7498
7986
8447
8959
9470
9081
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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
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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
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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
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7248
7766
8208
8810
0840
0602
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8677
8800
0896
9000
0884
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1420
1940
2406
2065
8606
5054
5670
6065
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7114
7627
8140
6052
9108
9074
0166
0094
1204
1712
0411
0914
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2009
2541
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3602
4182
4000
0180
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6243
6770
7295
7820
8845
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0892
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1580
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1908
2518
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8555
4079
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5106
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0215
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0746
3254
1763
0460
1010
1580
2060
2670
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4124
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5167
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1062
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2102
2622
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1104
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1114
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2074
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pROPORTioNAi. Parts.
Dili.
1
2
8
4
6
6
7
8
9
58
62
51
60
6.8
5.2
5.1
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10.6
10.4
10.2
10.0
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15.6
15.3
15.0
21.2
20.8
20.4
20.0
30.5
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25.0
81.8
81.2
3().6
30.0
87.1
86.4
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4
5
6
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LOOAtlltttMS OF irtJHBEBS.
No 900 L. 864.1
[No.M4L.9ni
N.
064948
47!ffi
6307
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4260
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7548
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8950
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1278
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4051
4512
4972
4291
4778
5255
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6216
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9089
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0043
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1460
1948
2417
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4807
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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
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7
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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
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6n7
0763
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6000
0946
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7087
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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
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8600
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86S7 , 8688
8728
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8810
6665
8911
8050
9002
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9003 0138
0184
9290
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9321
9360
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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
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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"
^1
II
Sf
s .
II
II
11
St c
II
1
5j
n
*S9
^:4
II
ll
3Jit
m
li
SJ
Hi
c
aifl
bit
....
If
IS
13*
iMi
lit
130
Mil
ll
t£
41
m
Ul
Lta
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 '
~iW
It
fill
h
E-
£":
''^ ^ a
Ih
c;
— c
3"
s
4(t
9i
»>
1H»
la
«l
^
ll-t0
"
3-^
IHI
\9X
is
113
M
(in
u
Fkl
IS- 1ft
HO
IM
w
irj7
fkU
]»i
3>
Wl
7H
101
403
iW
1BA
rtfl
la*
&4
t^
«
in
3S
7,
l&-t«
in
-•TV
lift
n^\ K,1
ii«
^
litf
.y,
1,^
44
10
t
Mi
Hi?
1^4
.i>i^ niy
sety
Ki
m
fiy
IMJ
Tn
l!l
3*
«^
m
«i
1 t-H
i*i
410
ir,l
j;] i;tj
ail
111
-IhI
Mti L^-il
m
W
134
ti
t 1-4
m
&1Q
IW
IM l«9
ami
IJI
I'l i^
107
M
lit
117
«
113
r ■
m
I ^^
«S7
&A5 HK
w>
in
IMI
III, :hs
13^
»
]«9
137
SI
lit7
4»
tti
i 1 «
...H JPfl
w*
aM
i-ii ITS
4]il
411?
3ft
»U
HI
ft
M
M
117
1 34
:£H
.??•
4;^ 183
&CT7, 5Sii:
fit 14A
31ft
HA
m
^3
ft
IS?
....
4"
1*7
17-«
, ..d
,+.*
fiik
.11
lot
iV
m
»7
1«*
«1
■
t*^.
...
.,»
....
tVi
Ml
m
4#t
t«l
i J^
*.t*
....
kl.1
«...
,. + -
TF-.
-.#.
...4
*-..
m
4i»
t9»
iMB
t 1-1
r...
....
»...
i...
+ ..«
-+-►
....
ait
IM
ISI
m
Kl-i
—*
*...
.,..
....
***■
....
1*T*
314
^*"
1
I"""
»» ,
*,..
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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3S88fi«88S8Sia88«8nSS«
Dm Bl^SIONS, WBIOHT, RESISTANCE OF COPPEB WIRE. 219
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MATBBIALS.
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iiiliiiliiilSiliilis8S§§eS3§gisSSisis.Rssfle8
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asssissgsgsiiiiiiiiiiililsisiiiiiiiiiiiiiil
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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
§
10
IS
14
18 IH
fO
SS
24
se
£8
sa
f.
^
ftp
£7
4£
50
87
4^
32
27
31
\ 1
5ii
f VriUUlA* >Cr ^ —
n '
2
S
71
Ui
m
41}
57
4:^
40
43
3H
w ^ eafi^ to Ad In tons of
?|
:s
m
fri
5G
50
44
^
£000 ponnd^;
B
eo
Tfl
71
C4
57
!^r»
44
a == orosu-s^cUon of coL-
I
»T
au
«1
TS
m
5G
50
unin;;
'.ii
lOt
04
80
7B
70
ea
D7
I ^ unpiupport^J lengib
In Jtic'Iihs;
gi
1
)13
KW
y7
^
7R
71
G4
m
1SS
lie
117
100
107
10!
07
88
fi6
70
7fl
71
d = iJlaTDt^trr ji] IncfaifH.
04
10
I
m
1S3
114
10S
945
EB
SO
7a
m
145
1^
ISO
137
107
97
m
eo
m
15fl
UO
iml
128
117
107
07
m
1
147
n9
ni
in
IIS
im
90
i ^
so]
II
m
IC3
155
lie
V^
120
lie; \m
07
RO
iS
I7«
nt^
ido
140
13tt
U7i 117
]m
GN«|
3M
]g5
185
174
Itl^
l!»
13.^1 137
h7\ IftV
f
]U
1P[
174
105
1S5
115
J35
12:
ii^ irie w
It
]|i
ir.9
H*l
1BI
170
150
14^
!87
% 117 10H
tn
aiT
307
li^
185
373
101
N^
Irjtt, lifT, 117
I^
234
*iii4
&!]:;
aoo
1S7
373
101
J4U' IK 1^
IH
^10
1^^
Ifl]
174
lej
IM
144
1 J.R4i IW' llfi
107
11 1
-m
^n
Jfh;
^&I
IliiO
!C«
iTiH
l47| 137: 127
117
J k^
230
^k)
*J-JO
-m
m
1H4
i;a
I(W 14tt l.SH
1L!S
I^
■,^5«
2iH
si^r
1^
21^
m
iNi
l7^^ Ihl
149
1,^
14
T|i
SSI
th23
an
^
Iffi
1^
la^ 157
147
137
les
iS
f53
*J1^
S^J
:^^I f07, 195
lUt 171
IflO
na
13ft
M
*;3
ce3
351
2^^ 234' 'ill
198 IKI
ir^i
101
150
m '
i!!03
ayj
aoo
iir.5
*41i irir
iriUJ 18rt
m
lui
1CI
^H
;^5
^v.
241
231 213
SiW IW
182
171
150
150
11
iH
'3sr
2Ta 263
250 S;iS
22a; 210: 197
18?
173
loa
111
^)9
iKW-^l ii^i
m\ 2%i
m^
227/ 211
IS^
IHO
174
m
»^^
J^IO 301
m\ 271
255
240 235
yu
lOS
Its
'^
30] 'JP^*
^7ri S^2
348
m
St^i
2iip
107
lt*5
im-
im 8J0
2^1 2??2
S67
251
330
tj:>
212
K'9
m
S|5
am
»Hl' 300
?HS
270
Sf^
2:5:1
22:*
212
3r;fi
?j^A ^r
S-it
m
29fl
2:y
'Xi
UTA
10^
V l
jwi
3rn fMw
!M4
3>H ftlH
20'-
yna
i!r^
llJ
415
,199' 3**"i
30C 3(0; :t33
317
;^iOo
285
f0i
in
435^ 4iO
40 ^ ZH^\ 373
^l^7
■W
3safl
1
^r.l, 4<7
431
414 3117
SSjI
vm
347
s
41-HJ 47;^
4W3
•iH^' 4211
40-^
3.<l
afi7
*f*
r,i7 iro
■HI
4r^i! 413
42.-. 4W
:-^^r
^
.«
m
401
44*-' i^i
4lHl 4fio
!i*4
ts^
511
40 <
47M; 1(51
443 1 4eo
40ff
541
5^; I
fiW'J 4!^«
470' 4'?
m
m
ft«l
Srt'J' GIH
524
Wl' 4H5
4(«
i
G2fl f^S
5.S0!
&70 f.^0
r^l
**:
r^ns, 6iy
n^tf,
t;UI nT[l
r>:>9
G!H; 071
or.(>
(^20 60H
W
1
7;i4 70:j
C8t
(i:^o oi; 014
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
I I
I I
£ I
•3
&
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
o
O
I
IS
e
I
s
8
s
S
IB
H
1^
9 £
Sl«S!»Sh5l«5l«5l«Sh5l»5l<» Si'
nnuiiuflun
»; S K 5 S «:_ s;. ^
ft,
-7(0 .h7«> - 12
tl
■i
iplhplL^-Sii
11^
THi« '^"' etioo ^'^ 'v 00 ^'eo 051
I II N M n tl II M
II-
ft
u
I I
8 I
I
2^1
I'll
i li I - I «3
» «l I ft 1 ll
SI §8 I & 't
•8
I
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
68.1
728800
'•
**
50
1 IT] 0 t6i5 65
483.4
16.04
6.78
1.04
64.6
687600
**
•'
45
Ij i^Ki 46;5.65
455.8
15.09
6.87
1.07
60.8
648200
'•
••
4^
l^^^S0.4l'5.60
441.7
14.02
6.95
1.08
63.0
628800
B9
12
85
IkK .19 0.44 5.09
288.3
10.07
4.71
0.99
38 0
405800
*•
*•
81.5
fL3fi 0.85 5.00
215.8
950
4.83
1.01
36.0
883700
Bll
10
40
IL76 0.76 5.10
158.7
9.50
3 67
0.90
81.7
388500
••
*•
85
K\«9 0 604.95
146.4
8.52
377
0.91
89.8
812400
»»
**
80
^.Hi 0 4514.80
184.2
7.65
8.90
0.08
26.8
286300
'*
**
S5
:.3:0.8l4.fM'>
128 1
6.89
4.07
0.97
24.4
260500
B13
9
SR
10.89 0.7fl^ t;
111.8
7.81
3. .29
084
24.8
265000
*•
**
80
8.8a 0.57 J. til
101.9
6.42
8.40
0.85
22.6
241500
M
•*
88
7..35'0.41 4.4-1
91.9
5.65
8.64
0.88
20.4
817900
•♦
**
21
6.8l!0.2fl 4.*t1
84.9
6.16
8.67
0.90
18.9
201300
615
8
85.5
7.500.64 4 r
68.4
4.75
8.02
0.80
17.1
182500
"
**
23
6.76 0.4.^ 1.1-
64.5
4.89
3.09
0.81
16 1
172000
•*
it
805
6.m0.9L4.ijj
60.6
4 07
8 17
0.62
16.1
161600
*»
*•
18
6.38 0.27 4.00
66.9
3.78
8.27
0.84
14.2
151 roo
BIT
7
80
5 880.468.87
42.2
3.24
2.68
0.74
12.1
128C00
*•
*•
1T.5
6.15 0.35 8.76
89.2
2.94
2.76
0.76
11.2
119400
M
••
15
4.4i 0.25 3.66
86.2
2.67
2.86
0.T8
10.4
110400
B19
6
17W
5.07 0.488.58
26.2
2.36
2.27
0.68
8.7
93100
»4
»•
149i
4.340.838.45
24.0
2.09
2.35
0.69
8.0
86300
**
•»
ISki
3.610.23 8.33
21.8
1.85
2.46
0.72
7.3
77.')00
Bi\
5
14^
4.310.60 3.29
16.2
1.70
1.87
0.63
6.1
W600
••
*•
1254
3.600.36 3.15
13.6
1.45
1.94
0.63
5 4
581C0
•'
*•
\oi
2.87 0.?1 3.00
12.1
1.23
205
0.65
4.8
51600
Bsa
4
3.09 0.412.83
7.1
1.01
1.62
0.57
8.6
38100
'*
**
9.5
2.790.31280
6.7
0.93
1.65
0.58
3.4
36000
•'
•♦
8.5
2.500.262.73
6.4
0.85
1.69
0.68
8.8
33900
"
*'
7.5
2.21 0.19 2.60
6.0
0.77
1.64
0.69
3.0
31800
BT7
8
7.5
2.210.36 2.62
2.9
0.60
1.16
0.62
1.9
20700
"
•'
6.5
1.910.262.42
2.7
0.63
1.19
0.62
1.8
19100
"
"
5 5
1.fi8
0.17
2.33
2 5
0.46
1.2:1
0.53
1.7
17600
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
<
i
1
1
!*
9
10
11
12
H
a-
1
i
1
£.2 3
Radius of Gyration,
Neutral Axis Coin-
cident with Centre
Lln« of Web.
s6d
pi
III
Itl
in.
lb*.
i*]. in.
(R. '
fn.
/
J'
r
r*
8
c
Bi
.?0
100
'^vJl
n.H8
7,:fS
1&5S.S
f^ZM
7.50
1.84
165 G
176C100
95
!^ 91
flWi
1.21
leoft B
rjO.78
7.58
1.85
160 7
1718900
••
»»
90
-ii^-i:
0 74
7.14
Wi7.M
4W.98
7.67
1 86
166 8
l66lGi)0
•»
85
'a.ihJ
(LUfl
7 im
I&08 7
47.Ti5
7 77
1.37
150 9
1G09100
»•
"
80
;!a 7^
n,iifl
7 00
N*S<3.,^
4^81
7.86
1.89
146.7
1.5'»4:{UO
B4
ir.
m
iS.41
1,18
B.rr
WHJ.."^
.W96
5.68
1.31
120.1
1280700
95
*J7.flt
I.W
ff.iS7
87ir U
4ft «7
5.60
1.82
116.4
1241500
»■
»•
90
^1 47 0, DM
rtJss
fM.1.4
4ft.fll
5.85
1.88
112.7
120-i300
••
85
mArfiO^m
fi.4!^
HIT. 8
4:1.57
6.72
1.82
109.0
1168000
••
•»
80
2^.S1U HI
(HO
7I»f>5
41 70
6.78
1.82
lOG.l
118i:«0
Br.
i:>
75
tji.Ofitl.HH
ft *J5i
nm .'2
anjvs
5 60
1.18
9-».2
96800(1
70
WMU 7«
fi.lfl
ma n
^flOO
6.68
1.19
88.5
M:»iO
•»
'»
05
llM:rn.W
'1.30
5?W,0
J.'7,4v'
5 77
i.ao
84.8
UU4600
»»
»»
flO
]T.6T.0.r>11
(i.<)0
COOJJ
ar».fl6
6.87
1.21
81.2
86G100
RS
u
56
Hi iHti.si
rr.61
3il 0
17 4»i
4.45
1.04
M.5
670U00
50
U.7I n TO
■^49
:Wi .*]
ir, 5^
4.54
1.05
50.6
580200
»»
45
]:l.'iUl.r>Ji1
ri J!7
■>r^7
N.N9
4.65
1.06
47.6
5071100
*'
"
«
1] ^1
M II'.
•N.H IJ
1-1 H|
4.77
1.08
448
4;8100
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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^ r. d Ci .^1 ca X ■*■
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i
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^- ^ JO! -^ aC ^ ^ T^ ~ 7# *C3t *rt "» S ~ ff •^ ^ tl *f i - ^ TC 1, -
S E it SS ^ TC ^ "•■ '^ ^ ■'- ij ' ~ "' Si t - '^ C 2? *• S ■^' ?v *.
•5 *? <•■* TS 3 irt <: '/ -*^ ^ — TtJ is *,. '^ r^ T^ 5 A 5t ^ T— t# o * -
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P&OPEBTIBS OF ROLLED STRUCTURAL STBBL. 277
Properties of Standard C1iaiiB«Li— Steel*
1
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t
4
6
6
^
8
9
10
n
18
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1^1
Moment of Inertte,
Neutral Axlg Faral-
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of Web.
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14.71
0.723.T*
402.7
11.92
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53.7
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376.1
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11.76
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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,
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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
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3.5
104.2
19.9
8.66
211700
21.80
6.41
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3.5
69.8
14.5
8.88
154200
19.23
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8.5
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11.7
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124800
18.25
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12.30
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2.5
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1.86
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Carneicle T
Shapes.
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1.08
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1.66
10.7
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1.54
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0.79
24800
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3.54
1.61
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1.23
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4990
8TBEK0TH OF MATBBIAL8.
279
Cmmegie T Hhwtpem— (Continued),
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0 M
iKO
t%
Xijjl IJM
O.&iO 44
0.11
0,11
^m:s
O.lHl
0 117
0 fi!
NUf
ih
Xl^l 3 0
0.87:0.10
0.10
O.lt*
D,?irj
41,10
u.\%
^ ;^i
010
^M
XlG' 3fi4
O.ISC0,3.^
am
O.JO
LMid
0 (h
0.10
t> rn
7K't
lUy.m ITS
0 51 0 Jis; 0.07
O.OB
0 m
O.iNi
o,iC
iKn\
C4KI
0 IDO.aB 0.1*4
0 iO
0,:n
n IKit
0 i\[
0.t!U
4i.1l
1^1 V 4i: IM 0/tJH^tst iLt*l
i) ill
0J!»
OJJfi
0 IJT
or.
ilfO
i^viM
'J.N
o.ooi'i.w! n.iw
0 10 ti.^ta
i\ on
».0T
0,si7
Tt5f>
iHxiM
t,(w
o.r*
0 ti8 o.oo
0 iv; ti ^r
II. 0^
0 o^
fl "^fi
r^o
IX lis
M^
i).i:i
iJ.r^i 0 ua
0,{JH 0 IH
f>.<<i
M,0'J
o,iy
fij.>r>
1 XI
1 IS
o,W
o..ii* (i.at
0,10 ILMJ
0 m
0 04
0,'JJ
J170
1 XI
n.sT
0^
o.a» »* o-i
u o;i o,.;o
0.11 1
0 <t!
o/.il
V70
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
i§§
« « d « et
§11 I
^'r^oo-* *v « «' • «r
« 9 «»
ts 1$ ^ ^^ts t ts
I- i» i* •Oflojg 5j fltf
|Usigiiiii|i|i§| III § I III 1 1
1
2 «
l«^-«8r«?...?f .X .f? « ?s?¥tfi
.a?ofxak?aD««ac^oo» ? « » o» ?
00 OD «D
51
I ^ ^^ ^09 « « ^<o 00 <e ^00 « ^00 ^00 « o^oi^ie
il
-Iss^sls !•$ S lf??SSS
ll
liWfsf^issl^gsssslfsosflff^s^ls
•■.«D
I Tl -H -J
im z s s 5s
0(c :3»9i;o
W lO — « « ^
bawtf H<QD«»i-»Q« fcWoCfoJMlH xD> o ^
li
!!
II
-I
5©
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
*s
^
*i
1?
^
^
«i
^
4J
t
1
1
1
1
1
1
1
i
1
t
>
»
>
B
f
n
>
K
f
n
>
K
feeb
feet.
feet
feet.
feet
feet.
feet
feet
feet
feet.
feet
feet.
p.Hec
?.8ec.
3. sec.
p. sec.
p.sec.
p.sec.
*^.»
OOIG
2.62
84
17.9
55
47.0
76
89.8
97
146
.SO
.008$
8.U4
86
19.0
56
48.8
77
92.2
98
149
.75
.OOK
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
.024
4.49
88
22.4
50
54.1
80
99.5
105
171
1.50
.085
18
5.08
89
28.6
60
56.0
81
102.0
110
188
1 75
.048
19
5.61
40
24.9
61
57.9
82
104.5
115
205
2
.062
90
6.22
41
96.1
62
59.8
88
107.1
120
224
2.5
.097
21
6.85
43
27.4
68
61.7
84
100.7
180
268
8
.140
22
7.52
48
28.7
64
68.7
85
112.8
140
804
35
.190
28
8.21
44
30.1
65
65.7
86
115.0
150
850
4
.248
24
8.94
45
81.4
66
67.7
87
11^7
175
476
4.5
.814
25
9.71
46
82.9
67
60.8
88
120.4
200
622
5
.388
26
10.5
47
34.3
68
71.9
89
123.2
800
1399
6
.560
27
11.8
48
9!i.S
60
74.0
90
125.9
400
2488
.761
28
12.2
49
87.3
70
76.2
91
128.7
500
3887
d
.904
29
18.1
60
38.9
71
78.4
92
131 6
600
5597
9
1.26
80
14.0
51
40.4
7T8
80.6
08
184.5
700
7618
10
1.65
81
14.9
68
42.0
73
82.9
94
137.4
800
9952
11
1.88
82
15.9
58
48.7
74
85.1
95
140.8
900
12698
tt
2.24
S8
16.9
54
45.8
75
87.6
96
148.8
1000
155^7
486
HB0HAHI08,
Wmmwm ■•AiMt ^^i^i^^^gsSgS^^^ * ^^^r Vmmnm m
&
I
i
1
4i
1
1
1
►
1
?
1
i>
feet.
feet
p.sea
feet.
feet
p.«ec.
Feet.
feet
p.see.
feet.
feet
ixaeo.
feet.
feet
p.8f«.
i^
fV^
.005
.57
.29
5.01
1 20
8.79
5.
17.0
20.
08.0
79
08.1
.010
.80
.40
5.07
1.82
8.07
.9
18.0
.5
80.0
to
60.5
.015
.98
.41
l:JS
1.24
8.04
.4
18.7
94.
09.0
74
00.0
.oao
1.18
.42
1.26
9.01
.0
10.0
.0
09.7
70
09.0
.025
1.87
.48
5.26
1.28
9.08
.0
10.3
26
40.1
70
00.0
.030
1.80
.44
5.82
1.80
9.15
0.
10.7
20
40.0
n
70.4
.005
1.50
.46
5.88
1.82
9.21
.8
20.0
97
41.7
78
70.0
.040
l.QO
.46
5.44
1.84
it
9.48
.4
20.0
98
49.0
70
71.8
.045
1.70
.47
5.60
1.86
.0
200
80
40.9
80
71.0
.OAO
1.70
.46
5.50
1.88
.0
2d.O
80
48.0
81
79.0
.055
1.88
.49
5.61
1.40
9.49
7.
21.0
01
44.7
00
79.0
.000
1.97
.60
5.67
1.42
0.8>7
.9
21.0
00
46.4
00
70.1
.009
2.04
.51
5.78
1.44
9.62
.4
21.8
OS
46.1
04
73.6
.070
2.12
.58
5.78
1.40
9.70
.0
88.:
84
46.8
85
74.0
.075
2.00
.58
5.84
1.40
9.77
.0
98.4
85
47.4
86
74.4
.oeo
2.27
.54
5.90
1.50
9.82
8.
88.7
06
48.1
87
74.8
.065
2.04
•H
0.05
l.»!fi
0.00
.9
28.0
87
48.8
80
75.8
.090
9.41
.50
0.00
1.54
0.96
.4
28.8
08
40.4
89
75.7
.099
0.47
.57
0.06
i.6i
10.0
.0
28.5
80
00.1
90
70.1
.MO
2.54
.58
0.11
i.oS
10.1
.0
28.8
40
oo.r
91
70.5
J05
2.00
.59
6.16
1.60
10,2
10.0
9.
24.1
41
S:J
92
70.9
.110
0.00
.00
0.81
1.60
.9
94.8
42
OS
77.4
«U5
2.72
.62
6.82
1.70
J.75
\0A
10.6
.4
94.0
40
62.0
94
77.0
.120
2.78
.64
6.40
.0
9i.O
44
68.2
05
7P.8
.125
2.01
.60
6.58
1.8(^
10.8
.0
95.1
45
60.0
60
70.0
.180
2.89
.68
6.61
1.90
11.1
10.
25.4
46
64.4
97
79.0
.14
8.00
,70
6.71
2.
11.4
.5
20.0
IS
60.0
08
70.4
.15
0.11
.78
0.81
»1
U.7
11.
26.0
65.0
99
«.8
.10
8.21
.74
0.90
9.2
11.9
13.0
.6
27.2
49
60.1
100
80.9
.17
8.81
.76
0.09
9.0
18.
27.8
60
60.7
125
80.7
.10
8.40
.78
7.00
9.4
12.4
*5
20.4
01
67.0
liO
90.8
:IS
8.60
.SO
7.18
8.5
18.0
13.
28.9
60
57.8
m
100
8.59
.82
7.20
2.0
12.0
.9
295
58
58.4
896
114
.81
8.08
.84
7.80
0.7
18.9
14.
80.0
54
60.0
229
120
.22
8.;o
.86
T.44
2.8
18.4
.0
ft>.0
65
09.0
250
120
.20
8.85
.88
7.50
2.9
la.t
15.
81.1
66
00.0
275
188
.84
8.93
.00
7.01
0.
13.0
.5
81 .6
m
60.0
800
189
.29
4.01
.09
7.69
0.1
14.1
10.
82.1
58
6M
850
150
.20
4.09
.94
7,78
0.9
14.0
.0
32.6
00
61.6
400
100
.27
4.17
.26
7,06
09
14.0
17.
S3.1
00
62.1
450
170
.28
4.25
.98
7.94
8.4
14.0
.5
88.6
01
62,7
600
170
.20
4.82
1.00
8.08
8.0
15.0
18.
34.0
^
6C.2
560
188
.80
1:S?
1.00
8.10
0.6
15.9
.5
81.5
08
68.7
000
lor
.81
1.04
8.18
07
15.4
19.
85.0
04
64.2
700
212
.82
4.64
1.06
8.26
8.8
15.0
.5
85.4
05
04.7
800
987
.38
4.61
1.08
8.84
09
15.0
io.
80.0
06
60.2
900
941
•¥
4.68
1.10
8.41
4.
16.0
.0
86.8
07
66.7
1060
954
.$&
IS
1.12
8.49
.9
16.4
11.
00.8
S
60.1
»00
050
.80
1.14
8.07
.4
16.0
.5
87.2
S?:?
1000
480
.87
4.88
1.16
8.01
.6
17.9
12.
87.0
??
lono
807
.82
4.04
1.18
8.72
.0
17.0
.5
80.1
67.6
507
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.
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410
210.
-84
-8fl.7
32
0.
98
86.7
164
78.8
880
110.
896
146.7
420
215.6
-88
-86.1
88
4-0.8
99
87.9
165
78.9
281
110.6
897
147.8
480
281.1
-^
—85.6
84
1.1
100
87.8
166
74.4
282
111.1
898
147.8
440
aM.7
-81
-35.
35
1.7
101
88.8
167
75.
288
111.7
899
148.8
450
8888
-4J0
-34.4
86
S.9
109
88.9
168
75.6
884
118J8
800
148.9
460
887.8
— M
-88.9
87
8.8
108
89.4
160
76.1
835
llt.8
801
149.4
470
248.8
-«8
-33.8
88
8.8
104
40.
170
TO.7
836
11S.8
802
160.
480
2489
— 1.*7
-83.8
89
8.0
105
40.6
171
77.2
887
118.0
808
16a6
490
254.4
->»
-8J.a
40
4.4
106
41.1
172
778
288
114.4
801
161.1
000
-.■60.
-«
-81.7
41
6.
107
41.7
178
78.8
289
ll8i
806
161.7
510
265.6
—•^4
-81.1
49
6.6
108
499
174
78.9
240
116.6
606
169.8
880
271.1
-28
-80.6
48
0.1
109
42.8
176
79.4
841
116.1
807
159.8
580
276.7
-•J«
—80.
44
6.7
no
48.8
176
80.
242
116.7
808
158.8
640
282.8
-ai
-99.4
46
7.9
111
48.9
m
80.6
848
]l7Ji
809
168.9
660
887.8
-80
-98.9
46
7.8
119
44.4
178
81.1
844
810
154.4
660
298.8
-19
-98.8
47
8.8
118
45.
179
81.7
846
II0.8
811
155.
670
898.9
-18
-97.8
48
8.0
114
45.6
180
82.8
840
118.9
119.4
SiS
166.6
680
804.4
-17
-97.9
49
9.4
115
46.1
181
82.8
847
166.1
890
H10.
-16
-86.7
60
10.
116
46.7
189
88.8
848
614
156.7
600
815 6
-15
-96.1
51
10.6
118
47.2
188
88.9
249
isolo
815
1W.8
610
S21.1
-14
-95.6
62
11.1
47.8
184
84.4
850
181.1
S?
167.8
680
326.7
-W
-25.
68
11.7
119
48.8
186
86.
881
181.7
168.8
630
833.2
-la
-24.4
54
19.2
180
48.9
186
86.6
858
128j»
818
158.9
640
837.8
—11
-28.9
65
19.8
191
49.4
187
86.1
853
819
168.4
660
348.3
—10
-98.8
66
18.8
189
60.
1R8
86.7
854
126b 8
880
100.
660
848.9
- g
-29.8
67
13.0
128
60.6
189
87.8
856
188.0
881
160.6
670
354.4
- 8
-29.2
68
14.4
194
61.1
100
87.8
856
m.4
882
161.1
680
860.
-7
—21.7
59
15.
120
61.7
191
88.8
857
196.
888
161.7
690
365 6
— «
-21.1
60
15.6
126
62.2
108
88.9
858
186.6
884
168.8
700
871.1
-6
-20.6
61
16.1
127
62.8
198
89.4
880
186.1
886
168.8
710
8:6.7
- 4
-20.
69
16.7
198
68.8
194
90.
260
186.7
m
168.8
780
382.8
- 8
—19.4
C8
17.2
129
63.0
196
90.6
861
18t8
887
168.9
730
887.8
-S
-18.9
64
17.8
180
54.4
196
91.1
862
mi
888
164.4
740
89.38
-1
-18 3
65
18 8
181
65
i»r
91.7
863
889
165.
750
•S989
0
-17.8
66
18.0
182
65.6
106
92.2
864
126.9
880
166.6
780
404 4
+ 1
—17.2
67
194
188
66.1
199
99.8
865
189.4
881
106.1
770
410.
tf
-16.7
68
90.
184
66.7
200
93.8
266
180.
888
166.7
780
415.6
8
-16.1
69
20.6
185
67.2
201
98.9
867
180.6
838
187.8
790
421 1
4
-15.6
70
81.1
136
67.8
202
94.4
868
181.1
181.7
884
107.8
900
426 7
6
—15.
71
91.7
137
68.8
208
95.
861»
885
168.8
810
4»>.2
6
-14.4
72
2d.9
188
68.9
204
95.6
870
laSJB
886
168.9
8BW
487.8
7
-13.9
73
92.8
189
69.4
208
96.1
271
188.8
887
169.4
830
443.3
8
-13.8
74
88.8
140
60.
206
96.7
872
138.8
886
170.
840
44S.9
9
-ia.8
75
93.9
141
60.6
207
97.8
878
188.9
889
170.6
650
454.4
10
-14.2
78
84.4
142
61.1
208
97.8
874
184.4
840
171.1
860
460.
11
-11.7
77
25.
148
61.7
209
98.8
875
186.
841
171.7
870
4C5 6
18
-11.1
;8
25.6
144
62.9
210
98.9
276
186.6
848
178.8
880
471.1
18
-10.6
79
96.1
145
62.8
211
99.4
877
186.1
848
171.8
800
478.7
14
-10.
60
26.7
146
68.8
219
100.
878
186.7
187i
644
178.8
900
488.8
15
-9.4
81
87. 2
147
68.9
218
100.6
279
846
178.9
010
487.8
18
-8.9
82
87.8
148
64.4
214
101.1
280
846
174.4
930
498.8
17
— 8.8
88
88.8
149
65
215
101.7
281
188.6
847
176.
980
498.9
18
-7.8
84
88.9
150
65.6
jtfia
108.2
9a2
1M.9
848
178.6
940
504.4
19
-7.9
85
89.4
151
66.1
217
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,
2
0
10
90
80 1 40
60
60
70 •
80
90
100
sq.ft.
sq. ft.
sq.ft.
sq. ft. sq ft.
sq.ft.
sq.ft.
sq.ft.
sq.ft.
sq.ft.
ra. ft.
H
40
60
62
58
65
57
50
61
68
66
68
1
87
88
82
06
98
101
106
108
119
116
121
1)4
186
140
144
149
163
158
ISi
169
175
1K2
1b9
iQ
186
80:3
909
214
222
226
248
859
961
971
«
840
850
870
880
886
406
4)8
^
449
465
488
fi
U6
661
577
696
618
638
648
701
7-J7
1^
785
807
885
856
868
912
041
074
1060
1046
1066
f<
1060
1099
1188
1166
1208
1241
1888
1827
1874
1425
14^
1885
I486
1478
1871
1580
1571
1621
1654
1788
1795
1861
1936
t^
1767
1617
1827
1086
2058
8120
8108
2272
885C
IS445
818ft
8844
8809
8876 1 8454
9581
8574
2718
2606
29U7
8019
8
8140
8228
8341
8424 8552
8648
8763
8897
4086
4184
4344
T
4«i6
4886
4588
6080
4806
4064
6188
5S08
5406
6700
5920
8
6A60
£744
5918
6284
6484
6616
6082
7180
7444
7736
9
7068
7484
7708
7952
8206
8482
8774
8088
0424
0780
10
8740
8876
9286
9616
8816
10124
10296
12666
10862
11220
iwa
12076
11
10658
10860
11180
I15I8 11879
12862
isioe
18576
14078
M620
U
18860
18818
18864
18606 14806
14568
15052
16588
16144
167»J
17476
13'
14T48
16168
16616
16090 116501
17126
17687
18807
18061
19638
20420
14
17104
17584
18108
18656 19282
19866
20688
21282
21984
22800
286H0
15
196:i4
;i0195
S0789
21419 22089
^>2801
2:j561
24373
25244
26179
27168
16
2«l;»
28978
83648
24820 25136
25936
26464
27?28
28720
29776
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
o»
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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
S
zR
5
6
.51
lOOtoLV)
100 to 150
7
1^
2
4
tS
^
10
.09
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
''^Hi
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
'i\Z
3
8
7
18^
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
8H
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
,c Li
•^t^
.8
53
P
2i
a":
CO
h
1
lU
1
26
.008
66
10
10
10
8000
l.GO
.sooo
l^
a
m
70
.06
eso
12
12
12
4200
2.15
6800
2L^
a
100
.08
S66
15
15
16
7000
S.-^O
8810
JH
8
260
.15
500
18
18
18
10000
5.00
10000
4
450
.87
680
84
^4
24
18000
7.60
900()«
6
5
700
.JW
108-2
30
:w
30
25000 , 10.. ^>()
20<x)r*
6
6
1200
.CA
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.
i
s
* ^
ill
H?lglit ill Fe«t mid Hi.'valutK>Ji}t ptf laiaut^.
d
e
. t'
-£
•u a
11
■a "5
go.
ls
3!;
1
Sf
C'
5' 10'
13 IC'
20'
S5'
30*
5S'
1!4
!i
S
a
70
isjn
rm 6C5
T?0 F8.-1
0W
1015
ir^
1«O0 ' ]|^
£
e
5 1
4
lOll
i-fl
:>iik tMiD
(Wrf) T!^>
STiO
&".
ioy5
1100 ' i
S
'!^
7
6
25(1
4^")
MX)
500
oto
7U%
TtR>
B*«l
9J5
lliQO
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t
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570
c^>
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945
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a
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515.')
410
451
^^^
fiT?i
810
715
7B,^j
BJ6
«
m
11
9
11^
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400
440
5ro
&T0
m*
m
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JO
1-2
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^onc
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■.►70
8W
S30
mn
4S5
^75
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6«
10 *5K
IS
m
SMI
ii;^l
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300!
3'JO
ss.^
455
475
600
535
TO
IJ
*
14
u
4-WO
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la^
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i'«i
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318
840
300 1«
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7T)IX>
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330 ,15
IS
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145
leo
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390 m
^l
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l^^
15(>
JTO
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iiH
eyo
«Bl> 1M
30
ariorto
a-s
]m
lift
m
14«
165
ISS
B04
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BO
rl.'JWXJ
05
ine
n>
lr»
14f*
165
l!^5
804
21S 3Q
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
42, 471 ft->
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
.SHH
.4*^96 .6444
.S.'3S«2
1.0T40
1.s;H88
1 W^
1.711^4
] ii.)i
1™
'2»0
.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
I.SVOlk
a 51S0 3 7771
hAmi
O.aifil
7.rp541
P t5l3t
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
!4.4eo
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
3.^
a.r-fltN
5JS*;W 7 77r^'>
30 3(57
13 169
15,fi5l
18,143
JfO.TSS
^.396
34
i.^r^n
B.^-iOeO fl.'3!S3M
11.005
13 756
J6.508
19.^
^MQ
24.763
Hft
i 9]%^
5>!,I10 t5 74<l^
iKoaa
14.5^
17 493
20,409
S9.3e4
96.S40
30
3 0H4Ji
(i 1090 9,a^4
13 3:«
15.433
18 507
SI 591
»4,67fi
!«T,T60
37
3,'2rj8'2
6 ;>i«4 9.rr47
tajBi
10.391
19,549
3S.806
se.ofie
9».m
3«
3 43fl7
6.&731 10 310
13.747
17.184
20.630
u.m
OT.4ii
80.90
ao
;i.«^W
7ANO0 lO.NOO
14 4B0
]8.KM>
31 .7i,'0
25.340
^,9ao
^.«flD
40
s.sriHO
7.aifii>n 434
15 2^
19.0*9
33 848
3fl.^
a0 4M
8i.m
41
4 onoH
H.noiu I'i.ooe
Ifi.OOS
30 004
34.006
31*. 006
j«.006
36 4W7
43
4.IB«.t
8.3«&e 13 E^^
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
44
4J5077
9 -21:4 18.83^1
IB 431 '33.088
:£7.046
8S.S54
86 Ml
41.469
4&
4 Hm
9 t;.190l4.4:»»
19.3TB 24 098
38 917
aa.Ttr
88.656
4a.3T»
44
^.m\i
10 073 Ifi 108
30,144
£5,180
ao.319
35.968
«0.i80
4&.m
4T
5.i'i71
lO.fvia n 77^
31 aio
30 387
dl.515
M.eot
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
SL439
50
li.ftri(X)
11.900 \7^^
SiH.eOO
29.750
85.TO0
41,650
47.600
53.1150
51
UJWI
ViMX 1^.571
a4.7fl2
3O,0t-}2
ST,14«
43.333
49,623
55,713
m
fi 4!iv>
iif.871 jQ.mr
3.V743
33,17«
38.613
45.CH9
51.464
5T.W0
m
e.ftwi
13 .CI 30.050
30 74^
31437
40.113
46.79fi
53,488
80lt9
hi
f..9ll>l
13 K.H) 'JO W-H)
37.7BO
34.700
41.640
48.581
E6 5»1
64.461
55
T.ia-l.S
]i.mt
!>| 55W
28.79a
arenas
43.197
50.397
57,596
6(796
!kt
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
ii3. IW
30 090
l^.f^
4fi,:t96
54 128
61.861
69 594
5«
saim
1(1.013
SIOIW
}&im
40.032
48 088
56.014
64 061
73.067
5t>
K*>«49
TO 570
,?-l.8.M
'I3J39
^1 4314
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
■ad|d')8nvt(
-xa JO »Bf8
§§§§§1
!§§§§§§
8!SSS*°nSS'°S^^S •**^
II i illllllii
Naeooeookf-ir^f-iM
•9d(d
mv9i9 JO 9zrS
KUonniOAOH
«5S3iiis§5S82S|g|8 § 128 i-ags
ssgsssgs
u| j»|ouiv)G
MMMM MM M M KKMM KM M
M M MM-
M M M M M Mm
'pvoq uinui
-jxnH a HI
iiill ;
g§3§i
l§ i iSiSgSgii
•Avao
-uoaa lunia
•fxwM d'HI
§i§§§p§is§§gi§3§§ § gsii isssigiiis
e 5.
•^- II
•pioi^aA
ad— = ' >
1
S
■g - 5 - s «
w
fr
«> - :. ;: . 'I
Icl&ii
O'^aj.c'iJ
Bd— = 5 = = = = >{« ■
: >B= = s = : 5 = :
£.1
" = &=
J 8 -si
.88g
c
I- a ill: <= * * it a^5
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.
C€*l rQn«lfnT4tr»ri
. PI 4 ttir.
per H.P. i<T hi>ur;
10 Koi*rw j^
\ Vt*r.
• l.5t\
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m.m.
HM^
;
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LDQg TulLL
man.
P
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Ton.
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1
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31.000
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O.rnBli 3^I.^K^| V.iiffJ
4IMNI
la.iwi-
rto.inl iii,iXM
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.
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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
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7980
880fr7
7890
44996
086
K)X24
48-60
18060
14400
104400
9400
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9046
4M90
90tf
64276
1906
BX84
60-tt
20909
i04M4
167S7
121271
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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.
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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¬ 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
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mv»iQ pa^nojpui S
JO 'aopoiJji M»IM :;
OOQOS
•iiono|j^?noqqiii\ ^
i
at
•p9dOT9A
»^X JO J9quinK
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-
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-moo 8B0 JO %1{^\9J^ *
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ill
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*uoi889Jdaioo JO
*8l|O0-dun«49SlJJ "
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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.
a
4
6
8
1
]Q IS
1
!4
in
IS
£0
22
n
m
aa
V
HPtt
1
"^
1
«V»*
.0709
.'im .S35
L 1.6(3fl
:?.5G5
3.r^|5.185
tt.B6^
9,0l)6ll.&i
14. &e
17,87
'11 .1,'
S2t
.{r.m
■."If? %-.'i
! T iv;i:
^.653 3 t»0K;ft.4#9
7.4W
9.tHrhJ.Dt
15.07
J9.80
■^]v
S'
j>i til
■Jlr; :",; ■,'
1 ] ru'>
^ 74*14. 0afi|6.fl32
8.
10 65 13*2
1?-5H
^].9&
S*'l .<! S(
■y\:- .."■1'
: I : 1 ,. i
■.'.fi;iS:4 X*0?!!6JK5
K.57-1
11.53 15.09
i&.a4
24.SJI
»14
^' iSm
jyj
.!!-
■'/iT. I MI"S.!^;j
flJM*
r^. 4711(1,47
stl.88
m^
^m
S^^ Mm
,is.s
,■!.
. ".ii, 1 71-, n iih'i^Mfi
13.4Wl7.9e
23.41
mm
r.3*
&■* * (MW
.17(1
,41V'-
\.]:iliA.'^Vi7^^mQ.m
14,80 t».e2
fia.TC
U 14
11 «
A'* » oioa
107
J5S
J i.**y.i
-i.U7l&.m\7 Kg4[ll.3l
l5.7Baj.4a
2a.»
m,!^
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
.56
1.41
80
6.0
4.0
4.7
2
.66
2.27
120
10.8
6.0
6.8
24]
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
.65
6.96
224
18.2
11.2
6.9
40|
4.5
2
.66
6.66
235
15.1
11.8
6.7
2.5
.65
11.1
826
24.9
16.3
6.8
60]
8
.55
14.1
420
27.8
21.0
6.4
8
3.5
.65
26
566
43.9
27.9
7.1
fiOJ
S
8.5
.65
86.4
621
42.2
81.1
7.0
10
4
.65
44.6
798
62.9
89.9
7.6
to]
10
4
.65
44
861
59.4
48.1
7.5
12
4.5
.65
7t).2
1082
85.1
54.1
8.1
80]
12
4.5
.65
67.9
1140
79.2
57.0
7.9
14
5
.65
104.0
1408
111
704
8.5
90]
13
6
.56
91.9
1408
97
70.4
8.3
16
6
.66
160
1854
147
98.7
9
I
13
5
.55
102
1566
104
78.3
8.4
100-^
15
5.5
.65
153
1910
143
95.5
8.9
17
6
.75
219
2295
208
116
9.6
14
5.5
.55
145
2046
131
102
8.8
120-
16
6
.66
214
2472
179
184
9.4
18
6.5
.76
801
2946
250
147
10
16
6
.56
211
2660
169
188
9.2
14oJil8
6.5
.65
806
8185
227
160
9.8
i «
7
.75
420
3766
312
188
10.6
17
6.5
.56
878
8264
206
168
9.6
IM-^ 19
7
.66
896
8880
269
194
10.1
21
7.5
.75
540
4560
868
228
10.8
20
7
.55
806
4128
257
806
10.1
180-J ti
7.6
.66
558
4869
387
248
10.6
24
8
.75
741
5688
466
284
11.8
22
7
.66
484
4800
867
240
10.1
200 •!
25
8
.66
748
6970
878
299
10.8
28
0
.76
1060
7960
526
868
11.6
28
8
.66
880
7250
888
863
10.9
280-
88
10
.66
I486
9460
592
478
11 9
36
12
.75
2814
11850
875
598
12.8
82
10
.66
1509
10380
648
619
11.7
800-
36
12
.66
2407
18140
806
667
12.6
40
14
.75
3600
17140
1175
857
13.6
38
12
.55
2608
14455
769
728
12.5
9S0J
42
14
.65
8822
17885
nil
894
13.6
46
16
.75
5520
21505
1.^68
1060-
14.4
44
14
.65
38T2
19200
1028
960
13.8
400-!
48
16
.65
6705
23380
1461
1168
14.2
(
52
18
.75
8023
27W0
2006
1392
15.8
50
16
.56
5657
24515
1221
1226
13.7
450-^
54
18
.65
8128
29565
1616
1478
14.5
1
68
20
.75
11157
34875
8171
1744
15.4
52
18
.55
7354
29600
1454
1480
14.2
60oi
56
iO
.65
10400
35200
1966
1760
15.1
60
22
.75
14143
41200
2543
2060
15.9
(
56
20
.55
9680
36245
1747
1812
14.7
660-<
60
22
.66
13483
42735
2266
2187
16 6
64
24
.75
18103
49665
2998
2483
16.4
(
60
22
.55
124 J6
42900
20G5
2145
15.2
600 "I
64
24
.65
17115
50220
2656
2511
15.4
68
26
.75
22731
58020
3480
2901
16.9
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
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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.
o
c
if
r^^2
i£H
all
2^.
CB k 00
sii
J— S *
* X * = - ,; s 2
a
5
:85
^^B
=7^S
stfl:
gcoS
2||
0l3
fill*
Silvia
§4:
>*
S'i§S
S8 '^
C , 1) t *=
t & .
u ** ii
2*1-
II
4
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^
;s?ii
5 a a> > -S-N
- ir
efeo
•»f8?
!"§
.11
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.
Its.
n OS
I
o
e
g
2^1
iiiiii^§3ss»s||ii=g§§ig||||§g8s§isgs3s=|i$!
iiiiiiiiiiiiiiiiiiiiiiiiiiiissssip
eooeodooeee'ooedooodeooodooeeeooeoooooooocc
iiiiiliiiiiiiiiiiliiiilliiilliiiiiiililM
dddddddddddddddddddddddddddddddddodddodedc
iP§§i§esga9SSj|ssassss^gS£S8sg2!-ss&2s3s«»fi»'
iiiiiiiliiiiiiiiiilliiiliiiiiiiiiiliiilili
tllllililliillilliiiiiiiiiiiiililipiyiii
00» t^« « « -Jc» of rf t^«0 • lO lO ^^ « « « « «* Ot *H1 ^ »^ M r< ^
s
a
s
9
« « o» • «e te 0> M* M of ^"^ »^
iiliilMipiiiPMiiiiiiiiiiiiiiiiiiiiillg
§§|l§.§§§§.||P.||P.|§§8.|lfl.|lil|i^ll|SS§iiS§l
In
imMmmmmmmmnniMUMi
9 00 9dsi<ic>tic>o^o<>«>oci^^<i9d^<>^^^^^^o<>t»c>^o^o«>^9o
OS
I t
s s 9 a a a s
0>H MW^iO «t««Dak
s s s a s ss »
\di,
i ° —
■I IV
ELECTRIC CURRENTS. 1035
fiiiiiiiiliiiiliiiiiiiiiiiiiiiisisiiiis
..JliiiiiiiiiiiiiiiiiniMMisMM^
O
iliiiiliiiliiiliiiiiiliiiipirsMliiH^
d«dddd«»dddo'«»ddddde>ddddd<>deed»d«*o««>e>eddc»r^
lit
if
0%
fed
u
iSS§SSSSISSssss«s?s3&ss«»oe«o«»^^«
o>HMM«tMWioiaoeoB
««.«.oSSaBf:8K5lS8SftSr32:8S89SS§18Ss§iSSIS83sSl
H
iii3§iii§§!iliiiiiiliil||ii|ilillM^^^
•i&ac&S!=9fi93s3i*Tl
lliiiiliiiiliililiiiiiiiiiillliiliiill^
OOOOOOOO do 09000 9990 09099090 00090 0 00000000
hi
»ot«iooeSemSot3So8 f!^S
|2.||8.i.|lil5ili?liSII2SSSS35S8se*8S««sa=sss
I 10
iiiiiililiiiiiiiiiiiiiiiiiiiliihliiiiiif
dddddededddddddedddddddddooeddddeddbdddde
s as SI a ss ss Si ss s ssa a as as
O05
& ss aa a a 85 a as. a as « aa aaass aas
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^
0
n^
31
43
M
HH
II lU
i3
NH^'^
71
8H
11
u
84
91
144
TYPE " F."
Size of Plates,
10^ X VH in.
9
53
I
II
12^
16Vi
61
18
15
17
60
70
80
84
i9«
113
IJO
140
l(»
60
70
80
19
90
126
ISO
90
li»R 145 165 I1A4
1' 15 jl5
1^-. 171^179-4
U'. 2 ...
K ;^5^
.V :o
&1 04 ,114
■iif4
15
1^
339 376 413
I
19 19 ;i9
Si«n of rimun, lS]li X I'H ^n-
Bif^ of PiaU!«,
15^ X 3* in.
Nuiulier of platiw. , . , .
n
T3
If* 1 17
S5
Us
I)*
tl
i3
^
1'J6 1 D*
UJHt-harge 1 Fiir tt hm.
lihi
i'j(i
l'li> IGD
dJil
IT J J a
1(1
400
44()
lao
i!4§f>:-j0
in am- -. " S '*
uu
i(i«
\M '^24
s:-h;
i::j<l
U
£.60
^ilft
ftTt ;a*7-j
".•8
tJO'f
sfni
V'SO -SJO
INI.>
Ui^i
20
8IK)
(CO
!I60 UOBO
40
Normal char[ft* rat p.. .
100
I JO
140 ItkP
'3IU
U4()
10
-«00
4fO
480
■MSli
tw
'WrHiB'hl tjf *'ach ek-
niij!f>t, (h«*... „.,
^ISJ
m^
a(Nj -ill
50H
'JS3S
^.4
790
ao6
Mt
4T4I
s-^
Oulsidi.^ ; WiiUh
IM^
\m
18^20
^^
III]
%
i»^
^m
28^
MU
•8
of tftJlk iu i i^"t^^'"
19*i
im
im'^m
Al^
:!1^
^1J4
«IM
21 H
^m
iiiL-ht:^. illeijrhr
i'ih
^£^
mi,^i
JS-fii
m4
^m
^^^
4f?*
4Bi^ ..
Weijfht of aful -ii
J
jjouiKirt
"VVint^bt nf wll. com
m
ITfl
197 itia
;rtfcj
l^K
D.fV
51 fi
:v,vi 59(1
S5IS
19.2
J
id^'te, iTilb uuid m
■
k*n^Minwl tank in
i
jkjuihIh: .....-._.
im J
\i'j
sai
685
99-2
4^
itfl
leas
1769 IW4
?*aii
68
Hrigtititf ci»n overfill
Inches . .
tj<i
Sfi
2G
^20
L^
:^
....
4J&
4$ 45
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
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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
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700
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T.'H^ >s
^.(1
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37V4
IB
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ri
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aa
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d
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n
ir.
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vi
etH'^^iV, S8 "
ir)io
M
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t1
R
15
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TOiNUfCj '
K7
fWO
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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.