﻿relation 
  to 
  Pressure 
  and 
  Temperature. 
  221 
  

  

  A 
  and 
  B 
  may 
  be 
  obtained 
  from 
  the 
  equations 
  

   a 
  _/ 
  i*2-,M 
  

  

  From 
  the 
  form 
  of 
  these 
  expressions 
  it 
  will 
  be 
  seen 
  that 
  it 
  

   is 
  inadvisable 
  to 
  select 
  pairs 
  of 
  observations 
  in 
  which 
  the 
  

   temperature 
  interval 
  is 
  small. 
  Further 
  to 
  test 
  this 
  point 
  

   the 
  coefficients 
  of 
  the 
  five 
  cubic 
  equations 
  already 
  investigated 
  

   have 
  been 
  recalculated, 
  substituting 
  for 
  A 
  the 
  values 
  obtained 
  

   by 
  treating 
  each 
  pair 
  of 
  observations 
  independently. 
  

   For 
  the 
  first 
  cubic 
  A 
  = 
  '8888, 
  yielding 
  the 
  equation 
  

  

  470,375 
  » 
  3 
  - 
  14,833,255 
  r 
  2 
  + 
  83,786,976 
  v 
  — 
  125,483,646 
  = 
  0. 
  

  

  The 
  coefficients 
  in 
  this 
  equation 
  only 
  differ 
  slightly 
  in 
  value 
  

   from 
  those 
  previously 
  obtained. 
  The 
  mean 
  roots 
  of 
  the 
  five 
  

   cubics 
  recalculated 
  in 
  this 
  manner 
  are 
  respectively 
  

  

  First 
  cubic 
  4*176 
  

  

  Second 
  „ 
  4*230 
  

  

  Third 
  „ 
  4*329 
  

  

  Fourth 
  „ 
  4*226 
  

  

  Fifth 
  „ 
  4*280 
  

  

  Mean 
  of 
  five 
  roots 
  4- 
  248 
  

  

  (The 
  " 
  weighted 
  " 
  mean 
  is 
  here 
  only 
  4*240.) 
  

  

  Compared 
  with 
  4*266 
  as 
  a 
  normal 
  value 
  this 
  shows 
  a 
  

   deviation 
  of 
  about 
  three- 
  sevenths 
  per 
  cent, 
  in 
  defect. 
  

  

  As 
  a 
  test 
  example 
  isopentane 
  is 
  a 
  very 
  favourable 
  case, 
  

   and 
  generally 
  greater 
  differences 
  in 
  the 
  values 
  of 
  the 
  mean 
  

   roots 
  of 
  the 
  cubic 
  may 
  be 
  expected 
  to 
  occur. 
  The 
  validity 
  

   of 
  this 
  method 
  of 
  finding 
  the 
  critical 
  volume 
  depends 
  upon 
  

   the 
  exactitude 
  with 
  which 
  the 
  law 
  of 
  Cailletet 
  and 
  Mathias 
  

   is 
  fulfilled 
  by 
  the 
  substance 
  under 
  investigation. 
  Regarded 
  

   geometrically, 
  if, 
  on 
  a 
  density-temperature 
  diagram, 
  the 
  

   position 
  of 
  a 
  series 
  of 
  points 
  on 
  the 
  line 
  of 
  mean 
  density 
  

   has 
  been 
  determined 
  by 
  experiment, 
  the 
  assumption 
  is 
  made 
  

   that 
  the 
  series 
  of 
  lines 
  obtained 
  by 
  joining 
  pairs 
  of 
  these 
  

   points 
  will, 
  on 
  being 
  produced, 
  pass 
  through 
  the 
  point 
  

   representing 
  the 
  critical 
  density. 
  Any 
  slight 
  curvature 
  of 
  

   the 
  diameter 
  at 
  the 
  extremity, 
  such 
  as 
  Young 
  has 
  observed 
  

   in 
  many 
  cases, 
  will, 
  to 
  the 
  extent 
  that 
  it 
  occurs, 
  invalidate 
  

  

  