﻿164 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  Consequently, 
  for 
  the 
  imperfectly 
  gaseous 
  state, 
  

  

  (*s) 
  

  

  \ 
  

  

  

  V 
  

  

  • 
  • 
  (12.) 
  

  

  + 
  &r 
  + 
  *&)J*^) 
  

  

  dV 
  _ 
  k 
  / 
  n 
  d 
  d? 
  

  

  dr 
  ~ 
  

  

  (8.) 
  It 
  is 
  to 
  be 
  observed 
  that 
  the 
  process 
  followed 
  in 
  ascertaining 
  the 
  nature 
  

   of 
  the 
  function 
  U 
  is 
  analogous 
  to 
  that 
  employed 
  by 
  M. 
  Carnot 
  in 
  his 
  theory 
  of 
  

   the 
  motive 
  power 
  of 
  heat, 
  although 
  founded 
  on 
  contrary 
  principles, 
  and 
  leading 
  

   to 
  different 
  results. 
  

  

  Carnot, 
  in 
  fact, 
  considers 
  heat 
  to 
  be 
  something 
  of 
  a 
  peculiar 
  kind, 
  whether 
  a 
  

   condition 
  or 
  a 
  substance, 
  the 
  total 
  amount 
  of 
  which 
  in 
  nature 
  is 
  incapable 
  of 
  

   increase 
  or 
  of 
  diminution. 
  It 
  is 
  not, 
  therefore, 
  according 
  to 
  his 
  theory, 
  con- 
  

   vertible 
  into 
  mechanical 
  power 
  ; 
  but 
  is 
  capable, 
  by 
  its 
  transmission 
  through 
  

   substances 
  under 
  particular 
  circumstances, 
  of 
  causing 
  mechanical 
  power 
  to 
  be 
  

   developed. 
  He 
  supposes 
  a 
  body 
  to 
  go 
  through 
  certain 
  changes 
  of 
  temperature 
  and 
  

   volume, 
  and 
  to 
  return 
  at 
  last 
  to 
  its 
  primitive 
  volume 
  and 
  temperature, 
  and 
  con- 
  

   ceives, 
  in 
  accordance 
  with 
  his 
  view 
  of 
  the 
  nature 
  of 
  heat, 
  that 
  it 
  must 
  have 
  given 
  

   out 
  exactly 
  the 
  same 
  quantity 
  of 
  heat 
  that 
  it 
  has 
  absorbed. 
  The 
  transmission 
  of 
  

   this 
  heat 
  he 
  regards 
  as 
  the 
  cause 
  of 
  the 
  production 
  of 
  an 
  amount 
  of 
  mechanical 
  

   power, 
  depending 
  on 
  the 
  quantity 
  of 
  heat 
  transmitted 
  and 
  on 
  the 
  temperature 
  at 
  

   which 
  the 
  transmission 
  has 
  taken 
  place. 
  According 
  to 
  these 
  principles, 
  a 
  body, 
  

   having 
  received 
  a 
  certain 
  quantity 
  of 
  heat, 
  is 
  capable 
  of 
  giving 
  out 
  not 
  only 
  all 
  

   the 
  heat 
  it 
  has 
  received, 
  but 
  also 
  a 
  quantity 
  of 
  mechanical 
  power 
  which 
  did 
  not 
  

   before 
  exist. 
  

  

  According 
  to 
  the 
  theory 
  of 
  this 
  Essay, 
  on 
  the 
  contrary, 
  and 
  to 
  every 
  con- 
  

   ceivable 
  theory 
  which 
  regards 
  heat 
  as 
  a 
  modification 
  of 
  motion, 
  no 
  mechanical 
  

   power 
  can 
  be 
  given 
  out 
  in 
  the 
  shape 
  of 
  expansion 
  unless 
  the 
  quantity 
  of 
  heat 
  

   emitted 
  by 
  the 
  body 
  in 
  returning 
  to 
  its 
  primitive 
  temperature 
  and 
  volume 
  is 
  less 
  

   than 
  the 
  quantity 
  of 
  heat 
  originally 
  received 
  : 
  the 
  excess 
  of 
  the 
  latter 
  quantity 
  

   above 
  the 
  former 
  disappearing 
  as 
  heat, 
  to 
  appear 
  as 
  expansive 
  power, 
  so 
  that 
  the 
  

   sum 
  of 
  the 
  vis 
  viva 
  in 
  those 
  two 
  forms 
  continues 
  unchanged. 
  

  

  