﻿30 
  B. 
  de 
  Saussure 
  — 
  Graphical 
  Thermodynamics. 
  

  

  Whence 
  by 
  integration 
  : 
  

  

  qjs 
  2 
  = 
  constant 
  

  

  Such 
  is 
  the 
  general 
  equation 
  to 
  the 
  adiabatic 
  lines 
  for 
  any 
  sub- 
  

   stance. 
  These 
  lines 
  are 
  of 
  the 
  third 
  degree 
  and 
  belong 
  to 
  the 
  

   hyperbolic 
  species. 
  

  

  10. 
  Clausius? 
  Theorem. 
  — 
  Equation 
  (9) 
  can 
  be 
  written 
  : 
  

  

  Jfcffl 
  = 
  *»(** 
  +2^) 
  

  

  9 
  

  

  Or 
  again, 
  by 
  the 
  aid 
  of 
  the 
  relation 
  : 
  <ps 
  = 
  KTE 
  : 
  

   dH 
  vr/dq) 
  ds\ 
  

   1 
  \cp 
  s 
  } 
  

  

  Whence, 
  for 
  a 
  finite 
  transformation 
  : 
  

  

  B 
  

  

  J~Y 
  = 
  K 
  ( 
  lo 
  S 
  WB-log 
  cpA) 
  

   When 
  the 
  path 
  is 
  a 
  closed 
  cycle, 
  A 
  = 
  B 
  ; 
  in 
  this 
  case 
  

  

  /' 
  

  

  = 
  

  

  Graphical 
  representation 
  of 
  the 
  Specific 
  Heat. 
  

  

  11. 
  Let 
  Jff 
  be 
  the 
  initial 
  state 
  of 
  the 
  substance 
  (fig. 
  3) 
  ; 
  and 
  

   suppose 
  an 
  elementary 
  path 
  MM' 
  to 
  be 
  described 
  in 
  a 
  certain 
  

   3 
  direction. 
  Amongst 
  the 
  infinite 
  num- 
  

  

  ber 
  of 
  directions 
  around 
  M, 
  some 
  are 
  

   of 
  special 
  interest 
  : 
  

  

  1st. 
  The 
  direction 
  of 
  the 
  isothermal, 
  

   whose 
  equation 
  is 
  : 
  <ps 
  = 
  <p 
  s 
  ; 
  <p 
  and 
  s 
  

   denoting 
  the 
  coordinates 
  of 
  point 
  M. 
  

   This 
  equation 
  has 
  been 
  derived 
  from 
  

   the 
  condition 
  : 
  T 
  = 
  constant 
  or 
  dT= 
  0. 
  

   2d. 
  The 
  direction 
  of 
  the 
  adiabatic, 
  

   whose 
  equation 
  is 
  

   from 
  the 
  condition 
  

  

  All 
  the 
  other 
  directions 
  of 
  special 
  

   interest 
  are 
  found 
  in 
  the 
  same 
  way 
  by 
  

   equating 
  to 
  zero 
  one 
  of 
  the 
  differential 
  

   quantities 
  entering 
  the 
  equations. 
  Thus, 
  

   we 
  shall 
  obtain 
  : 
  

  

  3d. 
  The 
  direction 
  and 
  equation 
  of 
  the 
  path 
  described 
  by 
  the 
  

   substance 
  when 
  its 
  volume 
  is 
  maintained 
  constant, 
  by 
  putting 
  

   dY 
  = 
  or 
  Y 
  = 
  constant 
  ; 
  substituting 
  to 
  "Fits 
  value 
  in 
  terms 
  

   of 
  <p 
  and 
  s 
  as 
  given 
  in 
  equations 
  (8), 
  gives 
  for 
  the 
  equation 
  to 
  

   the 
  curve 
  of 
  constant 
  volume 
  passing 
  through 
  M 
  : 
  

  

  g(<p, 
  s 
  )=g( 
  ( 
  Po, 
  s 
  o) 
  

  

  ps' 
  2 
  =<p 
  s' 
  2 
  , 
  derived 
  

   dK 
  = 
  0. 
  

  

  