﻿566 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  Sub-Section 
  1. 
  — 
  Properties 
  of 
  Expansive 
  Heat. 
  

  

  (47.) 
  To 
  shew 
  more 
  clearly 
  the 
  nature 
  of 
  the 
  questions, 
  towards 
  the 
  decision 
  

   of 
  which 
  these 
  experiments 
  are 
  a 
  step, 
  I 
  shall 
  now 
  briefly 
  review 
  the 
  fundamental 
  

   principles 
  of 
  the 
  theory 
  of 
  heat, 
  and 
  the 
  reasoning 
  on 
  which 
  they 
  are 
  based 
  ; 
  and 
  the 
  

   object 
  of 
  this 
  being 
  illustration 
  rather 
  than 
  research, 
  I 
  shall 
  use 
  algebraical 
  symbols 
  

   no 
  farther 
  than 
  is 
  absolutely 
  necessary 
  to 
  brevity 
  and 
  clearness, 
  and 
  shall 
  follow 
  

   an 
  order 
  of 
  investigation, 
  which, 
  though 
  the 
  same 
  in 
  its 
  results 
  with 
  that 
  pursued 
  

   in 
  the 
  previous 
  sections 
  of 
  this 
  paper, 
  is 
  different 
  in 
  arrangement. 
  

  

  By 
  a 
  mind 
  which 
  admits 
  as 
  an 
  axiom, 
  that, 
  in 
  the 
  present 
  order 
  of 
  things, 
  

   physical 
  power 
  cannot 
  be 
  annihilated, 
  nor 
  produced 
  out 
  of 
  nothing, 
  the 
  law 
  of 
  the 
  

   mutual 
  convertibility 
  of 
  heat 
  and 
  motive 
  power 
  must 
  be 
  viewed 
  as 
  a 
  necessary 
  

   corollary 
  from 
  this 
  axiom, 
  and 
  Mr 
  Joule's 
  experiments, 
  as 
  the 
  means 
  of 
  deter- 
  

   mining 
  the 
  relative 
  numerical 
  value 
  of 
  those 
  two 
  forms 
  of 
  power. 
  By 
  a 
  mind 
  

   which 
  does 
  not 
  admit 
  the 
  necessity 
  of 
  the 
  axiom, 
  these 
  experiments 
  must 
  be 
  

   viewed 
  also 
  as 
  the 
  proof 
  of 
  the 
  law. 
  

  

  This 
  law 
  was 
  virtually, 
  though 
  not 
  expressly, 
  admitted 
  by 
  those 
  who 
  intro- 
  

   duced 
  the 
  term 
  Latent 
  Heat 
  into 
  scientific 
  language 
  ; 
  for 
  when 
  divested 
  of 
  ideas 
  

   connected 
  with 
  the 
  hypothesis 
  of 
  a 
  subtle 
  fluid 
  of 
  caloric, 
  and 
  regarded 
  simply 
  as 
  

   the 
  expression 
  of 
  a 
  fact, 
  this 
  term 
  denotes 
  heat 
  which 
  has 
  disappeared 
  during 
  

   the 
  appearance 
  of 
  expansive 
  power 
  in 
  a 
  mass 
  of 
  matter, 
  and 
  which 
  may 
  be 
  made 
  

   to 
  reappear 
  by 
  the 
  expenditure 
  of 
  an 
  equal 
  amount 
  of 
  compressive 
  power. 
  

  

  (48.) 
  Without 
  for 
  the 
  present 
  framing 
  any 
  mechanical 
  hypothesis 
  as 
  to 
  the 
  

   nature 
  of 
  heat, 
  let 
  us 
  conceive 
  that 
  unity 
  of 
  weight 
  of 
  any 
  substance, 
  occupying 
  

   the 
  bulk 
  V 
  under 
  the 
  pressure 
  P, 
  and 
  possessing 
  the 
  absolute 
  quantity 
  of 
  thermo- 
  

   metric 
  heat 
  whose 
  mechanical 
  equivalent 
  is 
  Q, 
  undergoes 
  the 
  indefinitely 
  small 
  

   increase 
  of 
  volume 
  d 
  V 
  ; 
  and 
  let 
  us 
  investigate 
  how 
  much 
  heat 
  becomes 
  latent, 
  or 
  

   is 
  converted 
  into 
  expansive 
  power, 
  during 
  this 
  process 
  ; 
  the 
  thermometric 
  heat 
  

   being 
  maintained 
  constant, 
  so 
  that 
  the 
  heat 
  which 
  disappears 
  must 
  be 
  supplied 
  

   from 
  some 
  external 
  source. 
  

  

  During 
  the 
  expansion 
  d 
  V, 
  the 
  body, 
  by 
  its 
  elastic 
  pressure 
  P, 
  exerts 
  the 
  me- 
  

   chanical 
  power 
  P 
  d 
  V. 
  Part 
  of 
  this 
  power 
  is 
  produced 
  by 
  molecular 
  attractions 
  

   and 
  repulsions 
  ; 
  and 
  although 
  this 
  part 
  may 
  be 
  modified 
  by 
  the 
  influence 
  of 
  heat 
  

   upon 
  the 
  distribution 
  of 
  the 
  particles 
  of 
  the 
  body, 
  it 
  is 
  not 
  the 
  direct 
  effect 
  of 
  

   heat. 
  The 
  remainder 
  must 
  be 
  considered 
  as 
  directly 
  caused 
  by 
  the 
  heat 
  pos- 
  

   sessed 
  by 
  the 
  body, 
  of 
  which 
  the 
  pressure 
  P 
  is 
  a 
  function 
  ; 
  and 
  to 
  this 
  portion 
  of 
  

   the 
  power 
  developed, 
  the 
  heat 
  which 
  disappears 
  during 
  the 
  expansion 
  must 
  be 
  

   equivalent. 
  

  

  To 
  determine 
  the 
  portion 
  of 
  the 
  mechanical 
  power 
  P 
  d 
  V 
  which 
  is 
  the 
  effect 
  of 
  

   heat, 
  let 
  the 
  total 
  heat 
  of 
  the 
  body, 
  Q, 
  be 
  now 
  supposed 
  to 
  vary 
  by 
  an 
  indefinitely 
  

  

  