﻿902 
  Dr. 
  Kleeman 
  : 
  Relations 
  between 
  Critical 
  Constants 
  

   by 
  the 
  well-known 
  ther 
  mo 
  dynamical 
  relation, 
  

  

  L+i)(vi 
  — 
  V2) 
  = 
  T(i;i-t'2)j7j, 
  

  

  where 
  vi 
  and 
  v.2 
  are 
  the 
  volumes 
  o£ 
  one 
  gram 
  of 
  the 
  substance 
  

   in 
  the 
  gaseous 
  and 
  the 
  liquid 
  states 
  respectively, 
  p 
  and 
  T 
  

   denoting 
  the 
  pressure 
  and 
  temperature. 
  For 
  all 
  liquids 
  at 
  

   corresponding 
  states, 
  Vi 
  and 
  Va 
  are 
  both 
  the 
  same 
  fraction 
  of 
  

   the 
  critical 
  density, 
  or 
  

  

  and 
  therefore 
  ^'l 
  — 
  ^2 
  = 
  - 
  , 
  

  

  pc 
  

  

  where 
  a 
  is 
  the 
  same 
  constant 
  for 
  all 
  liquids 
  at 
  corresponding 
  

   states. 
  Thus 
  

  

  pc 
  pc 
  d\ 
  

   Combining 
  this 
  with 
  (1) 
  we 
  get 
  

  

  W{XCafp^ 
  a 
  __rp^ 
  dp 
  

  

  7?l3 
  ^ 
  p^ 
  pad 
  I 
  

  

  or 
  

  

  Ta 
  " 
  mf 
  - 
  T 
  '^dT 
  

  

  Dividing 
  each 
  side 
  of 
  the 
  equation 
  by 
  T 
  and 
  integrating, 
  wa 
  

   obtain 
  

  

  Expressing 
  the 
  density 
  and 
  temperature 
  in 
  terms 
  of 
  the 
  

   critical 
  density 
  and 
  temperature^ 
  p 
  = 
  upo 
  and 
  T=^Tc, 
  the 
  

   integral 
  becomes 
  

  

  PcH^CaY 
  T 
  

  

  -0 
  «/3' 
  

  

  dl3 
  

  

  The 
  part 
  A\ithin 
  the 
  brackets 
  is 
  the 
  same 
  for 
  all 
  liquids 
  at 
  

   corresponding 
  states, 
  it 
  may 
  be 
  denoted 
  by 
  N. 
  

   The 
  integrated 
  equation 
  becomes 
  

  

  TlG+{P-^\tc4'^=p. 
  

  

  