﻿232 
  Mr, 
  J. 
  Rose-Innes 
  on 
  Lord 
  Kelvin 
  s 
  Absolute 
  

  

  to 
  the 
  Joule-Thomson 
  effect. 
  It 
  may 
  be 
  regarded 
  as 
  a 
  

   correction 
  necessary 
  owing 
  to 
  the 
  deviation 
  of 
  the 
  substance 
  

   from 
  a 
  perfect 
  gas. 
  It 
  is 
  this 
  quantity 
  which 
  is 
  calculated 
  

   and 
  tabulated 
  so 
  as 
  to 
  give 
  us 
  the 
  means 
  of 
  arriving 
  at 
  the 
  

   absolute 
  scale. 
  We 
  notice 
  that 
  in 
  order 
  to 
  calculate 
  this 
  

   term, 
  we 
  require 
  to 
  know 
  the 
  value 
  of 
  t, 
  the 
  very 
  quantity 
  

   we 
  are 
  seeking 
  to 
  find. 
  Sufficiently 
  accurate, 
  however, 
  for 
  

   the 
  purpose 
  of 
  calculating 
  this 
  small 
  term, 
  will 
  be 
  the 
  value 
  

   of 
  t 
  found 
  by 
  means 
  of 
  a 
  first 
  approximation. 
  

  

  Thermodynamic 
  Correction 
  for 
  Const 
  ant 
  -volume 
  

   Gas- 
  Thermometer. 
  

  

  We 
  will 
  now 
  compare 
  the 
  indications 
  of 
  a 
  gas-thermometer 
  

   kept 
  at 
  constant 
  volume 
  with 
  the 
  thermodynamic 
  scale 
  of 
  

   temperature. 
  

  

  Let 
  us 
  start 
  as 
  before 
  with 
  the 
  differential 
  equation 
  

  

  ~di\t)~7 
  d 
  ~~ 
  J 
  2 
  ' 
  

   Integrate 
  this 
  between 
  the 
  limits 
  t 
  and 
  oo 
  and 
  we 
  have 
  

  

  i 
  1A_B 
  

   t 
  ~2~t 
  2 
  V 
  

  

  v 
  

   where 
  P 
  is 
  the 
  value 
  of 
  -, 
  as 
  v 
  and 
  t 
  are 
  made 
  to 
  grow 
  

  

  indefinitely 
  large 
  with 
  p 
  constant. 
  To 
  determine 
  the 
  form 
  of 
  

  

  P 
  we 
  must 
  appeal 
  to 
  experiment. 
  We 
  know 
  that 
  when 
  a 
  

  

  gas 
  is 
  made 
  to 
  expand 
  to 
  larger 
  and 
  larger 
  volumes 
  it 
  obeys 
  

  

  Boyle's 
  law 
  more 
  and 
  more 
  closely 
  ; 
  hence 
  we 
  infer 
  that 
  

  

  v 
  

   when 
  v 
  and 
  t 
  are 
  made 
  indefinitely 
  large, 
  the 
  value 
  of 
  - 
  must 
  

  

  L 
  

  

  vary 
  inversely 
  as 
  the 
  pressure. 
  We 
  may 
  therefore 
  write 
  

  

  P 
  = 
  ^ 
  

   P 
  

  

  where 
  is 
  a 
  constant 
  characteristic 
  of 
  the 
  gas. 
  

  

  Writing 
  in 
  this 
  value 
  we 
  have 
  as 
  the 
  complete 
  solution 
  

  

  C 
  *> 
  = 
  1A_B 
  

  

  p 
  "t 
  " 
  2 
  t 
  2 
  t' 
  

   Multiply 
  this 
  hy 
  pt, 
  and 
  transpose, 
  

  

  ^ 
  = 
  «-4t- 
  B 
  )- 
  

  

  If 
  we 
  neglect 
  the 
  Joule-Thomson 
  effect 
  we 
  have 
  as 
  a 
  first 
  

   approximation 
  pv 
  = 
  Ct, 
  or 
  t=^, 
  which 
  is 
  the 
  value 
  for 
  t 
  in 
  

  

  