﻿214 
  Mr. 
  E. 
  Haigh 
  on 
  Ortliobaric 
  Volumes 
  in 
  

  

  §2. 
  On 
  the 
  Determination 
  of 
  Critical 
  Constants 
  from 
  Obser- 
  

   vations 
  at 
  Temperatures 
  considerably 
  below 
  the 
  Critical 
  Point. 
  

  

  The 
  invariant 
  form 
  of 
  the 
  dual 
  equation 
  may 
  be 
  directly 
  

   employed 
  as 
  a 
  test 
  to 
  ascertain 
  whether 
  given 
  values 
  assigned 
  

   to 
  the 
  critical 
  constants 
  of 
  a 
  normal 
  substance 
  form 
  a 
  con- 
  

   sistent 
  system. 
  If 
  these 
  values 
  are 
  substituted 
  in 
  the 
  

   function 
  

  

  {^(f-O^vHCl- 
  1 
  ) 
  

  

  +{£*e- 
  i 
  )£ 
  + 
  *}(s- 
  i 
  > 
  

  

  the 
  result 
  must 
  approximate 
  to 
  the 
  constant 
  value 
  16. 
  From 
  

   the 
  fact 
  that 
  every 
  experimental 
  determination 
  of 
  ortliobaric 
  

   volumes 
  at 
  a 
  known 
  vapour-pressure 
  and 
  temperature 
  gives 
  a 
  

   relation 
  between 
  the 
  values 
  of 
  the 
  three 
  critical 
  constants, 
  a 
  

   still 
  more 
  important 
  deduction 
  may 
  be 
  drawn. 
  The 
  law 
  of 
  

   Cailletet 
  and 
  Mathias 
  makes 
  it 
  possible 
  to 
  express 
  the 
  critical 
  

   temperature 
  in 
  terms 
  of 
  the 
  critical 
  volume. 
  The 
  critical 
  tem- 
  

   perature 
  being 
  thus 
  eliminated, 
  an 
  equation 
  is 
  obtained 
  

   connecting 
  the 
  two 
  remaining 
  critical 
  constants 
  in 
  which 
  the 
  

   critical 
  pressure 
  occurs 
  only 
  to 
  the 
  first 
  power. 
  From 
  two 
  

   such 
  equations 
  the 
  critical 
  pressure 
  is 
  easily 
  eliminated, 
  

   giving 
  finally 
  a 
  cubic 
  equation 
  in 
  v 
  of 
  the 
  form 
  

  

  where 
  P, 
  Q, 
  R, 
  S 
  are 
  functions 
  of 
  the 
  orthobaric 
  volumes, 
  

   vapour-pressures, 
  and 
  temperatures 
  obtained 
  from 
  any 
  two 
  

   determinations. 
  

  

  Let 
  u 
  u 
  u-2 
  be 
  the 
  volumes 
  of 
  unit 
  mass 
  of 
  liquid, 
  and 
  v 
  x 
  , 
  v 
  2 
  

   the 
  volumes 
  of 
  unit 
  mass 
  of 
  saturated 
  vapour, 
  determined 
  

   respectivelv 
  at 
  vapour-pressures 
  pi, 
  p 
  2i 
  and 
  temperatures 
  t^ 
  t. 
  2 
  . 
  

   Let 
  A, 
  B 
  be 
  constants 
  in 
  the 
  linear 
  function 
  of 
  the 
  tempera- 
  

   ture 
  which 
  expresses 
  the 
  sum 
  of 
  the 
  densities, 
  r. 
  e. 
  

  

  

  a 
  

  

  + 
  - 
  = 
  A-Bt 
  

  

  V 
  

  

  or 
  briefly 
  

  

  

  =/• 
  

  

  Be 
  also 
  

  

  2 
  

  

  =A-r>/„. 
  

  

  or 
  

  

  =;■(-:> 
  

  

  