﻿220 
  Mr. 
  E. 
  Haioh 
  on 
  Orthobaric 
  Volumes 
  in 
  

  

  <- 
  

  

  Taking 
  Young's 
  value 
  for 
  the 
  critical 
  volume 
  as 
  a 
  standard, 
  

   the 
  greatest 
  deviation 
  is 
  in 
  the 
  case 
  of 
  the 
  fifth 
  cubic, 
  where 
  

   the 
  temperatures 
  are 
  both 
  low, 
  and 
  the 
  law 
  of 
  Cailletet 
  and 
  

   Mathias 
  holds 
  less 
  exactly. 
  The 
  deviations 
  from 
  the 
  norm 
  

   are 
  not 
  always 
  in 
  the 
  same 
  direction 
  and 
  we 
  may 
  infer 
  that 
  

   the 
  critical 
  volume 
  will 
  probably 
  lie 
  between 
  the 
  greatest 
  

   and 
  least 
  of 
  the 
  mean 
  roots 
  of 
  the 
  several 
  cubic 
  equations, 
  

   and 
  that 
  the 
  mean 
  of 
  their 
  sum 
  will 
  be 
  a 
  close 
  approximation 
  

   to 
  its 
  actual 
  value 
  *. 
  A 
  value 
  for 
  the 
  critical 
  volume 
  having 
  

   been 
  obtained, 
  the 
  critical 
  temperature 
  can 
  be 
  deduced 
  from 
  

   the 
  law 
  of 
  Cailletet 
  and 
  Mathias, 
  and 
  hence 
  also 
  the 
  critical 
  

   pressure 
  from 
  the 
  dual 
  equation. 
  

  

  The 
  number 
  of 
  substances 
  for 
  which 
  the 
  critical 
  constant^ 
  

   can 
  be 
  directly 
  determined 
  by 
  experiment 
  is 
  very 
  small, 
  and 
  

   the 
  method 
  here 
  described 
  may 
  therefore 
  be 
  useful 
  in 
  

   obtaining 
  approximate 
  values 
  for 
  these 
  important 
  constants 
  

   in 
  cases 
  where 
  experimental 
  observations 
  can 
  only 
  be 
  made 
  

   at 
  temperatures 
  falling 
  considerably 
  below 
  the 
  critical 
  

   point. 
  

  

  Regarded 
  as 
  a 
  test 
  of 
  the 
  applicability 
  of 
  the 
  cubic 
  equation 
  

   to 
  determine 
  the 
  critical 
  volume, 
  the 
  foregoing 
  investigation 
  

   is 
  open 
  to 
  the 
  objection 
  that 
  the 
  value 
  of 
  A 
  which 
  has 
  been 
  

   employed 
  has 
  been 
  obtained 
  from 
  the 
  complete 
  series 
  of 
  

   liquid 
  and 
  vapour 
  densities 
  observed 
  between 
  10° 
  C. 
  and 
  a 
  

   temperature 
  verging 
  closely 
  upon 
  the 
  critical 
  temperature. 
  

   If 
  observations 
  are 
  confined 
  within 
  a 
  more 
  limited 
  range, 
  ir 
  

   is 
  conceivable 
  that 
  somewhat 
  different 
  values 
  of 
  A, 
  B 
  may 
  

   be 
  obtained, 
  and 
  the 
  values 
  of 
  the 
  roots 
  of 
  the 
  cubic 
  corre- 
  

   spondingly 
  affected. 
  To 
  this 
  objection 
  it 
  may 
  be 
  replied 
  

   that 
  Young's 
  investigations 
  have 
  shown 
  that 
  in 
  the 
  case 
  

   of 
  normal 
  substances 
  such 
  deviations 
  are 
  only 
  of 
  small 
  

   magnitude, 
  and 
  hence 
  no 
  great 
  alteration 
  in 
  the 
  value- 
  el' 
  

   the 
  coefficients 
  of 
  the 
  terms 
  in 
  the 
  cubic 
  equation 
  will 
  be 
  

   thereby 
  produced. 
  In 
  the 
  hypothetical 
  case 
  in 
  which 
  it 
  is 
  

   assumed 
  that 
  we 
  have 
  at 
  our 
  disposal 
  only 
  a 
  small 
  number 
  

   of 
  experimental 
  observations, 
  falling 
  within 
  a 
  restricted 
  

   range 
  of 
  temperature, 
  mean 
  values 
  of 
  A 
  and 
  B 
  may 
  be 
  

   determined 
  from 
  the 
  whole 
  series 
  of 
  available 
  observations 
  

   or, 
  taking 
  each 
  pair 
  of 
  observations 
  independently, 
  values 
  of 
  

  

  * 
  Perhaps 
  ;i 
  preferable 
  method 
  would 
  be 
  to 
  (t 
  weigh! 
  " 
  the 
  results 
  by 
  

   multiplying 
  each 
  mean 
  rool 
  1>\ 
  the 
  corresponding 
  interval 
  of 
  temperature 
  

   and 
  divide 
  ili«' 
  total 
  thus 
  obtained 
  by 
  the 
  sum 
  of 
  these 
  temperature 
  

   intervals. 
  A.pplied 
  to 
  the 
  live 
  roots 
  given 
  above 
  this 
  method 
  Leads 
  to 
  

   ill' 
  •• 
  weighted 
  " 
  mean 
  \ 
  alue 
  r 
  1*205. 
  

  

  