﻿572 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  V, 
  a 
  measurable 
  state, 
  condition, 
  or 
  mode 
  of 
  existence 
  of 
  the 
  body, 
  whose 
  

   tendency 
  to 
  increase 
  is 
  represented 
  by 
  

  

  P, 
  a 
  force, 
  depending 
  on 
  the 
  condition 
  V, 
  the 
  energy 
  Q, 
  and 
  permanent 
  pro- 
  

   perties 
  of 
  the 
  body 
  ; 
  so 
  that 
  

  

  P 
  d 
  V 
  is 
  the 
  increment 
  of 
  a 
  form 
  of 
  potential 
  energy, 
  corresponding 
  to 
  a 
  

   small 
  increment 
  d 
  V 
  of 
  the 
  condition 
  V. 
  

  

  Let 
  d 
  S 
  be 
  the 
  quantity 
  whereby 
  the 
  increment 
  of 
  potential 
  energy 
  P 
  d 
  V 
  

   falls 
  short 
  of 
  the 
  quantity 
  of 
  actual 
  energy 
  of 
  the 
  form 
  Q, 
  which 
  is 
  converted 
  

   into 
  the 
  potential 
  form, 
  by 
  the 
  change 
  of 
  condition 
  d 
  V. 
  

  

  Then, 
  as 
  in 
  Equation 
  69 
  

  

  f\ 
  "D 
  

  

  an 
  equation 
  from 
  which 
  all 
  those 
  in 
  the 
  previous 
  articles 
  are 
  deducible, 
  and 
  which 
  

   comprehends 
  the 
  whole 
  theory 
  of 
  the 
  mutual 
  conversion 
  of 
  the 
  actual 
  form 
  of 
  

  

  energy 
  Q, 
  and 
  the 
  potential 
  form 
  / 
  P 
  d 
  V, 
  whatsoever 
  those 
  forms 
  may 
  be, 
  when 
  

  

  no 
  other 
  form 
  of 
  energy 
  interferes. 
  The 
  application 
  of 
  these 
  principles 
  to 
  any 
  

   form 
  or 
  any 
  number 
  of 
  forms 
  of 
  actual 
  and 
  potential 
  energy, 
  is 
  the 
  subject 
  of 
  a 
  

   paper 
  read 
  to 
  the 
  Philosophical 
  Society 
  of 
  Glasgow, 
  on 
  the 
  5th 
  January 
  1853, 
  and 
  

   published 
  in 
  the 
  Philosophical 
  Magazine 
  for 
  February 
  1853. 
  

  

  Sub-Section 
  2. 
  — 
  Properties 
  of 
  Temperature. 
  

   (53.) 
  Still 
  abstaining 
  from 
  the 
  assumption 
  of 
  any 
  mechanical 
  hypothesis, 
  

   let 
  us 
  proceed 
  a 
  step 
  beyond 
  the 
  investigation 
  of 
  the 
  foregoing 
  articles, 
  and 
  in- 
  

   troduce 
  the 
  consideration 
  of 
  temperature 
  ; 
  that 
  is 
  to 
  say, 
  of 
  an 
  arbitrary 
  function 
  

   increasing 
  with 
  heat, 
  and 
  having 
  the 
  following 
  properties. 
  

  

  Definition 
  of 
  Equal 
  Temperatures. 
  

  

  Two 
  portions 
  of 
  matter 
  are 
  said 
  to 
  have 
  equal 
  temperatures, 
  when 
  neither 
  

   tends 
  to 
  communicate 
  heat 
  to 
  the 
  other. 
  

  

  Corollary. 
  

  

  All 
  bodies 
  absolutely 
  destitute 
  of 
  heat 
  have 
  equal 
  temperatures. 
  

   The 
  ratio 
  of 
  the 
  real 
  specific 
  heats 
  of 
  two 
  substances, 
  is 
  that 
  of 
  the 
  quantities 
  

   of 
  heat 
  which 
  equal 
  weights 
  of 
  them 
  possess 
  at 
  the 
  same 
  temperature. 
  

  

  Theorem. 
  

  

  The 
  ratio 
  of 
  the 
  real 
  specific 
  heats 
  of 
  any 
  pair 
  of 
  substances, 
  is 
  the 
  same 
  at 
  all 
  

   temperatures. 
  

  

  For, 
  suppose 
  equal 
  weights 
  of 
  a 
  pair 
  of 
  homogeneous 
  substances 
  to 
  be 
  in 
  con- 
  

   tact, 
  containing 
  heat 
  in 
  such 
  proportions 
  as 
  to 
  be 
  in 
  equilibrio. 
  Then, 
  let 
  additional 
  

  

  