﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  

  

  187 
  

  

  The 
  sixth 
  column 
  contains 
  the 
  common 
  logarithms 
  of 
  the 
  volume 
  of 
  one 
  

   pound 
  of 
  steam 
  of 
  saturation 
  corresponding 
  to 
  the 
  same 
  temperatures. 
  

  

  The 
  seventh 
  column 
  contains 
  the 
  differences 
  of 
  the 
  successive 
  terms 
  of 
  the 
  

   sixth 
  column, 
  which 
  are 
  negative; 
  for 
  the 
  volumes 
  diminish 
  as 
  the 
  pressures 
  

   increase. 
  

  

  By 
  the 
  ordinary 
  method 
  of 
  taking 
  proportional 
  parts 
  of 
  the 
  differences, 
  the 
  

   logarithms 
  of 
  the 
  volumes 
  corresponding 
  to 
  intermediate 
  pressures, 
  or 
  the 
  loga- 
  

   rithms 
  of 
  the 
  pressures 
  corresponding 
  to 
  intermediate 
  volumes, 
  can 
  be 
  calculated 
  

   with 
  great 
  precision. 
  Thus, 
  let 
  X 
  + 
  h 
  be 
  the 
  logarithm 
  of 
  a 
  pressure 
  not 
  found 
  in 
  

   the 
  table, 
  X 
  being 
  the 
  next 
  less 
  logarithm 
  which 
  ^s 
  found 
  in 
  the 
  table 
  ; 
  let 
  Y 
  be 
  

   the 
  logarithm 
  of 
  the 
  volume 
  corresponding 
  to 
  X, 
  and 
  Y— 
  k 
  the 
  logarithm 
  of 
  the 
  

   volume 
  corresponding 
  to 
  X 
  + 
  h 
  ; 
  let 
  H 
  be 
  the 
  difference 
  between 
  X 
  and 
  the 
  next 
  

   greater 
  logarithm 
  in 
  the 
  table, 
  as 
  given 
  in 
  the 
  fourth 
  column, 
  and 
  K 
  the 
  corre- 
  

   sponding 
  difference 
  in 
  the 
  seventh 
  column 
  ; 
  then 
  by 
  the 
  proportion 
  

  

  n 
  : 
  K 
  :: 
  h 
  : 
  k 
  

  

  either 
  Y-k 
  may 
  be 
  found 
  from 
  X 
  + 
  h, 
  or 
  X 
  + 
  h 
  from 
  Y—k. 
  

  

  In 
  the 
  fifth 
  and 
  eighth 
  columns 
  respectively, 
  are 
  given 
  the 
  actual 
  pressures 
  

   and 
  volumes 
  corresponding 
  to 
  the 
  logarithms 
  in 
  the 
  third 
  and 
  sixth 
  columns, 
  to 
  

   five 
  places 
  of 
  figures. 
  

  

  In 
  the 
  ninth 
  column 
  are 
  given 
  the 
  values 
  of 
  the 
  quantity 
  denoted 
  by 
  P 
  t 
  V 
  t 
  

   in 
  the 
  formulae, 
  which 
  represents 
  the 
  mechanical 
  action 
  of 
  unity 
  of 
  weight 
  of 
  

   steam 
  at 
  full 
  pressure, 
  or 
  before 
  it 
  has 
  begun 
  to 
  expand, 
  in 
  raising 
  an 
  equal 
  

   weight. 
  Those 
  values 
  are 
  expressed 
  in 
  feet, 
  being 
  the 
  products 
  of 
  the 
  pressures 
  

   in 
  the 
  fifth 
  column 
  by 
  the 
  volumes 
  in 
  the 
  eighth, 
  and 
  have 
  been 
  found 
  by 
  multi- 
  

   plying 
  the 
  absolute 
  temperature 
  in 
  centigrade 
  degrees 
  by 
  153*48 
  feet. 
  Interme- 
  

   diate 
  terms 
  in 
  this 
  column, 
  for 
  a 
  given 
  pressure 
  or 
  a 
  given 
  volume, 
  may 
  be 
  approxi- 
  

   mated 
  to 
  by 
  the 
  method 
  of 
  differences, 
  the 
  constant 
  difference 
  for 
  5° 
  centigrade 
  

   being 
  767*4 
  feet 
  ;. 
  but 
  it 
  is 
  more 
  accurate 
  to 
  calculate 
  them 
  by 
  taking 
  the 
  product 
  

   of 
  the 
  pressure 
  and 
  volume. 
  

  

  When 
  the 
  pressure 
  is 
  given 
  in 
  other 
  denominations, 
  the 
  following 
  logarithms 
  

   are 
  to 
  be 
  added 
  to 
  its 
  logarithm, 
  in 
  order 
  to 
  reduce 
  it 
  to 
  pounds 
  avoirdupois 
  per 
  

   square 
  foot 
  : 
  — 
  

  

  For 
  Millimetres 
  of 
  mercury, 
  

  

  Inches 
  of 
  mercury, 
  .... 
  

  

  Atmospheres 
  of 
  760 
  millimetres, 
  . 
  

   Atmospheres 
  of 
  30 
  inches, 
  

   Kilogrammes 
  on 
  the 
  square 
  centimetre, 
  

   Kilogrammes 
  on 
  the 
  circular 
  centimetre, 
  

   Kilogrammes 
  on 
  the 
  square 
  metre, 
  

   Pounds 
  avoirdupois 
  on 
  the 
  square 
  inch, 
  

   Pounds 
  avoirdupois 
  on 
  the 
  circular 
  inch, 
  

   VOL. 
  XX. 
  PART 
  I. 
  

  

  0-44477 
  

   1-84960 
  

   3-32559 
  

   3-32672 
  

   3-31136 
  

   3-41627 
  

   1-31136 
  

   2-15836 
  

   2-26327 
  

   3d 
  

  

  