﻿relation 
  to 
  Pressure 
  and 
  Temperature. 
  217 
  

  

  value 
  o£ 
  the 
  ratio 
  on 
  the 
  right-hand 
  side 
  o£ 
  the 
  equation 
  is 
  

   the 
  same 
  from 
  whatever 
  set 
  of 
  observations 
  the 
  values 
  of 
  

   the 
  coefficients 
  are 
  obtained. 
  Hence 
  

  

  H^p 
  — 
  E^ 
  H 
  2 
  ^q— 
  K 
  2 
  

  

  L^-M^ 
  + 
  Ni 
  ~ 
  IW-M 
  2 
  * 
  +N 
  2 
  ' 
  

  

  from 
  which 
  we 
  obtain 
  the 
  cubic 
  equation 
  

  

  (H 
  1 
  L 
  2 
  - 
  H.LOt'o 
  3 
  - 
  (HA- 
  H^ 
  + 
  K 
  t 
  L 
  2 
  - 
  K 
  2 
  Lt> 
  2 
  

   + 
  (H 
  1 
  N 
  2 
  -H 
  S 
  N 
  1 
  + 
  K 
  1 
  M 
  2 
  -K 
  2 
  M 
  1 
  > 
  -(K 
  1 
  N 
  2 
  -K 
  2 
  1S 
  T 
  1 
  ) 
  = 
  0. 
  (8) 
  

  

  In 
  the 
  cases 
  which 
  have 
  been 
  examined 
  this 
  cubic 
  has 
  

   three 
  real 
  and 
  positive 
  roots, 
  but 
  only 
  the 
  mean 
  root 
  is 
  

   common 
  to 
  all 
  the 
  cubics 
  relating 
  to 
  the 
  same 
  substance. 
  

   As 
  this 
  method 
  of 
  obtaining 
  the 
  critical 
  volume 
  is 
  new, 
  

   it 
  will 
  be 
  well 
  to 
  examine 
  its 
  application 
  in 
  detail, 
  taking 
  for 
  

   the 
  purpose 
  a 
  normal 
  substance 
  whose 
  properties 
  are 
  well 
  

   known. 
  

  

  Isopentane. 
  

  

  From 
  Young's 
  paper 
  (" 
  Thermal 
  Properties 
  of 
  Isopentane") 
  

   the 
  following 
  data 
  of 
  five 
  experimental 
  determinations 
  are 
  

   taken 
  : 
  — 
  

  

  T 
  

  

  (Centigrade). 
  

  

  t 
  

   (Abs. 
  temp.). 
  

  

  p, 
  in 
  mm. 
  

  

  u, 
  in 
  c.c. 
  

   (from 
  curve). 
  

  

  v, 
  in 
  c.c. 
  

   (from 
  curve). 
  

  

  10° 
  

  

  283° 
  

  

  3904 
  * 
  

  

  1-5885 
  

  

  607-5 
  

  

  30° 
  

  

  303° 
  

  

  815-5* 
  

  

  1-6413 
  

  

  303-0 
  

  

  60° 
  

  

  333° 
  

  

  2036-5 
  t 
  

  

  1-7329 
  

  

  127-9 
  

  

  100° 
  

  

  373° 
  

  

  5345-5 
  t 
  

  

  1-8940 
  

  

  4945 
  

  

  120° 
  

  

  393° 
  

  

  8018 
  t 
  

  

  2-0037 
  

  

  32-20 
  

  

  * 
  Dynamical 
  method. 
  

  

  t 
  Mean 
  of 
  experimental 
  values. 
  

  

  The 
  relation 
  between 
  the 
  liquid 
  and 
  vapour 
  densities 
  is 
  

   expressed 
  by 
  the 
  equation 
  

  

  1 
  1 
  A 
  

  

  U 
  V 
  

  

  Bt 
  

  

  whe 
  

  

  re 
  

  

  A 
  = 
  -8872 
  or 
  8872 
  x 
  10' 
  

  

  -6 
  

  

  B 
  = 
  -000908 
  or 
  908 
  X 
  10' 
  

   Phil 
  Mag. 
  Ser. 
  6. 
  Vol. 
  16. 
  No. 
  92. 
  Aug. 
  1908. 
  

  

  Q 
  

  

  