﻿relation 
  to 
  Pressure 
  and 
  Temperature. 
  203 
  

  

  Dividing 
  both 
  sides 
  of 
  equation 
  (1) 
  by 
  6, 
  and 
  rearranging 
  

   the 
  terms, 
  we 
  obtain 
  the 
  more 
  concise 
  but 
  less 
  suggestive 
  form 
  

  

  {-+G- 
  l 
  )£ 
  + 
  &K*- 
  1 
  ) 
  

   . 
  + 
  {* 
  + 
  G- 
  i 
  )& 
  + 
  £>K*- 
  1 
  ) 
  

  

  = 
  16 
  (3) 
  

  

  It 
  will 
  be 
  observed 
  that 
  the 
  left-hand 
  side 
  of 
  the 
  equation 
  

   is 
  now 
  an 
  invariant 
  function 
  of 
  the 
  variables, 
  and 
  is 
  also 
  

   symmetrical 
  with 
  respect 
  to 
  <£, 
  -v/r. 
  Putting 
  

  

  we 
  have 
  

  

  and 
  hence 
  

  

  F(^,f) 
  + 
  F(f,^) 
  = 
  16 
  .... 
  (4) 
  

  

  or 
  briefly 
  X 
  = 
  16. 
  

  

  Both 
  forms 
  of 
  the 
  fundamental 
  equation 
  can 
  of 
  course 
  be 
  

   expressed 
  in 
  terms 
  of 
  any 
  other 
  system 
  of 
  units 
  by 
  sub- 
  

   stituting 
  

  

  />o 
  ( 
  o 
  t 
  t 
  

  

  where 
  r, 
  z« 
  represent 
  the 
  volumes 
  of 
  unit 
  mass 
  in 
  the 
  vapour 
  

   and 
  liquid 
  phases 
  respectively, 
  t 
  the 
  absolute 
  temperature, 
  

   p 
  the 
  vapour-pressure, 
  and 
  jo 
  , 
  £ 
  , 
  r 
  the 
  critical 
  values 
  of 
  the 
  

   pressure, 
  temperature, 
  and 
  volume. 
  

  

  Equation 
  (1) 
  thus 
  transformed 
  becomes 
  

  

  (£ 
  + 
  ( 
  1 
  _i)(V.£) 
  + 
  ?V)(««.i) 
  

  

  CPo 
  V 
  t 
  J\vu 
  p 
  J 
  v 
  2 
  j 
  \v 
  J 
  

  

  = 
  16* 
  

  

  

  

  It 
  is 
  obvious 
  from 
  its 
  form 
  that 
  this 
  equation 
  is 
  one 
  of 
  

   great 
  generality, 
  and 
  the 
  degree 
  of 
  concordance 
  with 
  

   experimental 
  results 
  is 
  shown 
  in 
  the 
  tables 
  given 
  below. 
  

  

  In 
  compiling 
  these 
  tables 
  the 
  values 
  of 
  the 
  invariant 
  

   function, 
  which 
  forms 
  the 
  left-hand 
  side 
  of 
  equation 
  (3), 
  

   have 
  been 
  calculated 
  for 
  various 
  substances 
  from 
  the 
  ex- 
  

   perimental 
  data 
  supplied 
  by 
  the 
  researches 
  of 
  Young, 
  

   Ramsay, 
  and 
  their 
  collaborators. 
  

  

  For 
  the 
  sake 
  of 
  comparison, 
  tables 
  for 
  methvl 
  alcohol 
  and 
  

  

  P 
  2 
  

  

  