﻿170 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  — 
  ^' 
  "*' 
  = 
  381-64 
  metres 
  = 
  1252 
  feet 
  per 
  centigrade 
  degree, 
  } 
  

   or 
  6956 
  feet 
  per 
  degree 
  of 
  Fahrenheit's 
  scale, 
  J 
  

  

  This 
  quantity 
  we 
  shall 
  denote 
  by 
  K 
  w 
  . 
  It 
  is 
  the 
  mechanical 
  equivalent 
  of 
  the 
  

   ordinary 
  thermal 
  unit. 
  

  

  I 
  have 
  already 
  pointed 
  out 
  (in 
  Article 
  2. 
  of 
  the 
  First 
  Section) 
  the 
  causes 
  

   which 
  tend 
  to 
  make 
  the 
  apparent 
  value 
  of 
  the 
  mechanical 
  equivalent 
  of 
  heat, 
  in 
  

   Mr 
  Joule's 
  experiments, 
  greater 
  than 
  the 
  true 
  value. 
  The 
  differences 
  between 
  

   the 
  result 
  I 
  have 
  just 
  stated, 
  and 
  those 
  at 
  which 
  he 
  has 
  arrived, 
  do 
  not 
  seem 
  

   greater 
  than 
  those 
  causes 
  are 
  capable 
  of 
  producing, 
  when 
  combined 
  with 
  the 
  un- 
  

   certainty 
  of 
  experiments, 
  like 
  those 
  of 
  Mr 
  Joule, 
  on 
  extremely 
  small 
  variations 
  

   of 
  temperature. 
  

  

  (15.) 
  Besides 
  the 
  conditions 
  of 
  constant 
  volume 
  and 
  constant 
  pressure, 
  there 
  

   is 
  a 
  third 
  condition 
  in 
  which 
  it 
  is 
  of 
  importance 
  to 
  know 
  the 
  apparent 
  specific 
  

   heat 
  of 
  an 
  elastic 
  fluid, 
  namely, 
  the 
  condition 
  of 
  vapour 
  at 
  saturation, 
  or 
  in 
  con- 
  

   tact 
  with 
  its 
  liquid. 
  

  

  The 
  apparent 
  specific 
  heat 
  of 
  a 
  vapour 
  at 
  saturation, 
  is 
  the 
  quantity 
  of 
  heat 
  

   which 
  unity 
  of 
  weight 
  of 
  that 
  vapour 
  receives 
  or 
  gives 
  out, 
  while 
  its 
  temperature 
  

   is 
  increased 
  by 
  one 
  degree, 
  its 
  volume 
  being 
  at 
  the 
  same 
  time 
  compressed 
  so 
  as 
  to 
  

   bring 
  it 
  to 
  the 
  maximum 
  pressure 
  corresponding 
  to 
  the 
  increased 
  temperature. 
  

  

  It 
  has 
  been 
  usually 
  taken 
  for 
  granted, 
  that 
  this 
  quantity 
  is 
  the 
  same 
  with 
  the 
  

   variation 
  for 
  one 
  degree 
  of 
  temperature, 
  of 
  what 
  is 
  called 
  the 
  total 
  heat 
  of 
  evapor- 
  

   ation. 
  Such 
  is, 
  indeed, 
  the 
  case 
  according 
  to 
  the 
  theory 
  of 
  Carnot 
  ; 
  but 
  I 
  shall 
  

   shew 
  that, 
  according 
  to 
  the 
  mechanical 
  theory 
  of 
  heat, 
  these 
  two 
  quantities 
  are 
  

   not 
  only 
  distinct, 
  but 
  in 
  general 
  of 
  contrary 
  signs. 
  

  

  I 
  shall, 
  for 
  the 
  present, 
  consider 
  such 
  vapours 
  only 
  as 
  may 
  be 
  treated 
  in 
  prac- 
  

   tice 
  as 
  perfect 
  gases, 
  so 
  as 
  to 
  make 
  the 
  first 
  of 
  the 
  Equations 
  (20.) 
  applicable. 
  

  

  It 
  has 
  been 
  shewn 
  that 
  the 
  logarithm 
  of 
  the 
  maximum 
  elasticity 
  of 
  a 
  vapour 
  

   in 
  contact 
  with 
  its 
  liquid 
  may 
  be 
  represented 
  by 
  the 
  expression 
  

  

  lo 
  g 
  P=«-£— 
  ^- 
  

  

  The 
  coefficients 
  a, 
  (3, 
  7, 
  being 
  those 
  adapted 
  for 
  calculating 
  the 
  common 
  loga- 
  

   rithm 
  of 
  the 
  pressure, 
  I 
  shall 
  use 
  the 
  accented 
  letters 
  a', 
  ft, 
  y, 
  to 
  denote 
  those 
  

   suited 
  to 
  calculate 
  the 
  hyperbolic 
  logarithm, 
  being 
  equal 
  respectively 
  to 
  the 
  for- 
  

   mer 
  coefficients 
  x 
  2-3025851.° 
  

  

  Then 
  for 
  vapour 
  at 
  saturation, 
  

  

  g-A+% 
  ■■■■ 
  <w 
  

  

  Making 
  this 
  substitution 
  in 
  the 
  general 
  Equation 
  (21.), 
  we 
  find 
  the 
  following 
  value 
  

   for 
  the 
  apparent 
  specific 
  heat 
  of 
  perfectly 
  gaseous 
  vapour 
  at 
  saturation 
  : 
  — 
  

  

  