﻿R. 
  deSaussure 
  — 
  Graphical 
  Thermodynamics. 
  47 
  

  

  the 
  equation 
  to 
  the 
  isothermals 
  being: 
  <ps 
  = 
  KTE, 
  the 
  integra- 
  

   tion 
  gives 
  : 
  

  

  EH 
  = 
  KTE 
  (log 
  <p 
  + 
  2 
  log 
  s) 
  

   Hence 
  : 
  

  

  EH 
  X 
  = 
  KT^Iog 
  g> 
  D 
  s\ 
  -log 
  <p 
  c 
  s\) 
  

   -EH 
  = 
  KT 
  E(log 
  cp 
  B 
  s\ 
  - 
  log 
  <p 
  A 
  8\) 
  

  

  But 
  the 
  equation 
  to 
  the 
  adiabatics 
  being 
  : 
  (ps~ 
  = 
  constant, 
  we 
  

   have 
  also 
  : 
  <f 
  c 
  s 
  2 
  c 
  = 
  ^b^b 
  an 
  -d 
  ^vA 
  = 
  <Pa 
  s 
  \i 
  so 
  that 
  by 
  dividing 
  : 
  

  

  t,~t 
  

  

  which 
  can 
  be 
  written 
  : 
  

  

  5CzS- 
  T 
  izZt 
  

  

  Thus, 
  the 
  demonstration 
  of 
  the 
  theorem 
  consists 
  simply 
  in 
  

   the 
  analytical 
  measurement 
  of 
  areas, 
  and 
  the 
  reason 
  of 
  it 
  is 
  

   that 
  the 
  heat 
  of 
  transformation 
  H, 
  which 
  is 
  the 
  unknown 
  

   quantity, 
  is 
  represented 
  graphically 
  by 
  areas. 
  This 
  is 
  not 
  the 
  

   case 
  in 
  the 
  usual 
  graphical 
  methods, 
  and 
  Carnot's 
  Theorem 
  can 
  

   only 
  be 
  demonstrated 
  indirectly, 
  by 
  showing 
  first 
  that 
  the 
  eco- 
  

   nomical 
  coefficient 
  of 
  Carnot's 
  cycle 
  is 
  independent 
  of 
  the 
  

   nature 
  of 
  the 
  substance, 
  then 
  computing 
  its 
  value 
  for 
  a 
  perfect 
  

   gas. 
  One 
  can 
  object 
  to 
  this 
  method 
  that 
  a 
  perfect 
  gas 
  is 
  only 
  

   a 
  theoretical 
  substance, 
  having 
  no 
  real 
  existence. 
  

  

  The 
  use 
  of 
  the 
  coordinates 
  cf> 
  and 
  5, 
  does 
  not 
  imply 
  any 
  

   hypothesis 
  upon 
  the 
  nature 
  of 
  the 
  motion 
  constituting 
  heat, 
  as 
  

   $ 
  and 
  s 
  can 
  be 
  regarded 
  simply 
  as 
  two 
  auxiliary 
  variables, 
  with- 
  

   out 
  attributing 
  to 
  them 
  any 
  special 
  significance. 
  

  

  Another 
  advantage 
  of 
  expressing 
  the 
  thermodynamic 
  func- 
  

   tion 
  in 
  terms 
  of 
  <\> 
  and 
  s, 
  is 
  that 
  each 
  one 
  of 
  the 
  specific 
  heats 
  

   of 
  the 
  substance 
  can 
  be 
  obtained 
  separately 
  from 
  said 
  function, 
  

   while 
  the 
  ordinary 
  form 
  of 
  the 
  thermodynamic 
  function 
  

   F(P, 
  V, 
  T)= 
  furnishes 
  only 
  the 
  difference 
  between 
  the 
  two 
  

   specific 
  heats 
  (C 
  — 
  c). 
  Finally, 
  if 
  heat 
  is 
  really 
  a 
  vibratory 
  

   motion 
  of 
  the 
  particles 
  of 
  matter, 
  the 
  state 
  of 
  this 
  vibration 
  

   at 
  any 
  time 
  is 
  obtained 
  from 
  the 
  experimental 
  data, 
  by 
  solving 
  

   the 
  thermodynamic 
  function 
  with 
  respect 
  to 
  <f> 
  and 
  s. 
  

  

  