﻿relation 
  to 
  Pressure 
  and 
  Temperature. 
  219 
  

  

  approximation, 
  significant 
  figures 
  have 
  been 
  retained 
  in 
  

   excess 
  of 
  the 
  number 
  probably 
  sufficient 
  for 
  accuracy. 
  

  

  First 
  Cubic. 
  — 
  The 
  first 
  cubic 
  equation 
  calculated 
  by 
  this 
  

   method 
  was 
  obtained 
  from 
  data 
  at 
  temperatures 
  60° 
  (J. 
  and 
  

   120° 
  C, 
  giving 
  the 
  equation 
  

  

  469,319 
  i* 
  3 
  - 
  14,784,759 
  v 
  2 
  + 
  83,569,800 
  v 
  -123,986,496 
  = 
  0. 
  

  

  This 
  cubic 
  has 
  three 
  positive 
  roots, 
  of 
  which 
  the 
  values 
  are 
  

   approximately 
  

  

  2-397, 
  4-260, 
  24-846. 
  

  

  Second 
  Cubic, 
  from 
  data 
  at 
  10° 
  0. 
  and 
  100° 
  C. 
  

  

  403.175r 
  3 
  --20,326,881iy 
  + 
  129,983,430r 
  -- 
  215,643,367 
  = 
  0. 
  

  

  The 
  roots 
  of 
  this 
  equation 
  are 
  approximately 
  

  

  2-892, 
  4-277, 
  43'24. 
  

  

  Comparing 
  these 
  results, 
  we 
  infer 
  that 
  the 
  extreme 
  roots 
  

   of 
  the 
  cubic 
  equation 
  are 
  irrelevant 
  and 
  that 
  the 
  mean 
  root 
  

   gives 
  the 
  true 
  critical 
  volume. 
  In 
  the 
  equations 
  which 
  

   follow 
  only 
  the 
  mean 
  root 
  has 
  been 
  calculated. 
  

  

  Third 
  Cubic, 
  from 
  data 
  at 
  10° 
  C. 
  and 
  60° 
  C. 
  

  

  123,112*V— 
  10,765,884 
  r 
  u 
  2 
  + 
  73,280,079 
  «> 
  - 
  126,317,603=0. 
  

  

  Mean 
  root, 
  4*260. 
  

  

  Fourth 
  Cubic, 
  from 
  data 
  at 
  60° 
  C. 
  and 
  100° 
  C. 
  

  

  254,067 
  r 
  3 
  -9,637,135 
  r 
  2 
  + 
  57,457,144 
  1? 
  — 
  89,824,667 
  = 
  0. 
  

  

  Mean 
  root, 
  4*231. 
  

  

  Fifth 
  Cubic, 
  from 
  data 
  at 
  10° 
  C. 
  and 
  30° 
  C. 
  (Low 
  

   temperatures 
  and 
  a 
  smaller 
  temperature 
  interval.) 
  

  

  30,185 
  y 
  3 
  -4,057,493 
  r 
  2 
  + 
  28,301,939 
  r 
  -48,996,154 
  = 
  0. 
  

  

  Mean 
  root, 
  4*315. 
  

   Summarizing 
  these 
  results, 
  we 
  get 
  for 
  v 
  : 
  — 
  

  

  First 
  cubic 
  . 
  . 
  

  

  . 
  4-260 
  

  

  60° 
  and 
  120° 
  C. 
  

  

  Second 
  cubic 
  

  

  . 
  4-277 
  

  

  10° 
  and 
  100° 
  C. 
  

  

  Third 
  cubic 
  

  

  . 
  4-260 
  

  

  10° 
  and 
  60° 
  C. 
  

  

  Fourth 
  cubic 
  

  

  . 
  4-231 
  

  

  60° 
  and 
  100° 
  C. 
  

  

  Fifth 
  cubic 
  . 
  . 
  

  

  . 
  4315 
  

  

  5)21-343 
  

   4-2686 
  

  

  10° 
  and 
  30° 
  C. 
  

  

  as 
  against 
  Young 
  

  

  's 
  value, 
  4*266 
  

  

  c.c. 
  

  

  

  Q2 
  

  

  

  