﻿DYNAMICAL 
  THEORY 
  OF 
  HEAT. 
  281 
  

  

  subjected 
  to 
  a 
  uniform 
  pressure 
  in 
  all 
  directions, 
  which 
  lead 
  to 
  various 
  remarkable 
  

   conclusions. 
  Such 
  of 
  these 
  as 
  are 
  independent 
  of 
  Joule's 
  principle 
  (expressed 
  by 
  

   equation 
  (2) 
  of 
  § 
  20), 
  being 
  also 
  independent 
  of 
  the 
  truth 
  or 
  falseness 
  of 
  Carnot's 
  

   contrary 
  assumption 
  regarding 
  the 
  permanence 
  of 
  heat, 
  are 
  common 
  to 
  his 
  theory 
  

   and 
  to 
  the 
  dynamical 
  theory 
  ; 
  and 
  some 
  of 
  the 
  most 
  important 
  of 
  them,* 
  have 
  

   been 
  given 
  by 
  Carnot 
  himself, 
  and 
  other 
  writers 
  who 
  adopted 
  his 
  principles 
  

   and 
  mode 
  of 
  reasoning 
  without 
  modification. 
  Other 
  remarkable 
  conclusions 
  on 
  

  

  the 
  same 
  subject 
  might 
  have 
  been 
  drawn 
  from 
  the 
  equation 
  -rj— 
  -j— 
  =0, 
  express- 
  

  

  CI 
  Z 
  C1 
  1) 
  

  

  ing 
  Carnot's 
  assumption 
  (of 
  the 
  truth 
  of 
  which 
  experimental 
  tests 
  might 
  have 
  

   been 
  thus 
  suggested) 
  ; 
  but 
  I 
  am 
  not 
  aware 
  that 
  any 
  conclusion 
  deducible 
  from 
  

   his 
  assumption 
  besides 
  that 
  which 
  Carnot 
  gives 
  regarding 
  the 
  motive 
  power 
  of 
  

   heat 
  through 
  finite 
  ranges 
  of 
  temperature, 
  has 
  yet 
  been 
  actually 
  obtained 
  and 
  

   published. 
  

  

  45. 
  The 
  recent 
  writings 
  of 
  Carnot 
  and 
  Clausius 
  contain 
  some 
  of 
  the 
  conse- 
  

   quences 
  of 
  the 
  fundamental 
  principle 
  of 
  the 
  dynamical 
  theory 
  (expressed 
  in 
  the 
  

   first 
  fundamental 
  proposition 
  above) 
  regarding 
  physical 
  properties 
  of 
  various 
  

   substances 
  ; 
  among 
  which 
  may 
  be 
  mentioned 
  especially 
  a 
  very 
  remarkable 
  dis- 
  

   covery 
  regarding 
  the 
  specific 
  heat 
  of 
  saturated 
  steam 
  (investigated 
  also 
  in 
  this 
  

   paper 
  in 
  § 
  58 
  below), 
  made 
  independently 
  by 
  the 
  two 
  authors, 
  and 
  a 
  property 
  of 
  

   water 
  at 
  its 
  freezing 
  point, 
  deduced 
  from 
  the 
  corresponding 
  investigation 
  re- 
  

   garding 
  ice 
  and 
  water 
  under 
  pressure 
  by 
  Clausius 
  ; 
  according 
  to 
  which 
  he 
  finds 
  

   that, 
  for 
  each 
  j^ 
  cent, 
  that 
  the 
  solidifying 
  point 
  of 
  water 
  is 
  lowered 
  by 
  pressure, 
  

   its 
  latent 
  heat, 
  which, 
  under 
  atmospheric 
  pressure 
  is 
  79, 
  is 
  diminished 
  by 
  *081. 
  

   The 
  investigations 
  of 
  both 
  these 
  writers 
  involve 
  fundamentally 
  various 
  hypo- 
  

   theses 
  which 
  may 
  be 
  or 
  may 
  not 
  be 
  found 
  by 
  experiment 
  to 
  be 
  approximately 
  

   true 
  ; 
  and 
  which 
  render 
  it 
  difficult 
  to 
  gather 
  from 
  their 
  writings 
  what 
  part 
  of 
  

   their 
  conclusions, 
  especially 
  with 
  reference 
  to 
  air 
  and 
  gases, 
  depend 
  merely 
  on 
  the 
  

   necessary 
  principles 
  of 
  the 
  dynamical 
  theory. 
  

  

  46. 
  In 
  the 
  remainder 
  of 
  this 
  paper, 
  the 
  two 
  fundamental 
  propositions, 
  ex- 
  

   pressed 
  by 
  the 
  equations 
  

  

  « 
  £N 
  1^ 
  . 
  . 
  . 
  . 
  (2)o 
  f§20 
  

  

  are 
  applied 
  to 
  establish 
  properties 
  of 
  the 
  specific 
  heats 
  of 
  any 
  substance 
  whatever 
  ; 
  

   and 
  then 
  special 
  conclusions 
  are 
  deduced 
  for 
  the 
  case 
  of 
  a 
  fluid 
  following 
  strictly 
  

   the 
  " 
  gaseous 
  laws" 
  of 
  density, 
  and 
  for 
  the 
  case 
  of 
  a 
  medium 
  consisting 
  of 
  parts 
  

  

  * 
  See 
  above, 
  § 
  22. 
  

   VOL. 
  XX. 
  PART 
  II. 
  4 
  G 
  

  

  