﻿230 
  Mr. 
  J. 
  Bose-innes 
  on 
  Lord 
  Kelvins 
  Absolute 
  

  

  HcilCG 
  

  

  jk 
  #!+ 
  e 
  c 
  

  

  

  = 
  (t 
  -f) 
  v 
  ° 
  (l 
  , 
  «J*Pi 
  + 
  *o\ 
  

  

  If 
  ^ 
  and 
  £ 
  are 
  taken 
  as 
  the 
  boiling-point 
  and 
  freezing- 
  

   point 
  of 
  water 
  respectively, 
  then 
  this 
  equation 
  gives 
  us 
  the 
  value 
  

   of 
  the 
  freezing-point 
  t 
  in 
  terms 
  of 
  the 
  interval 
  t 
  x 
  — 
  1 
  ; 
  it 
  is 
  

   usual, 
  as 
  pointed 
  out 
  by 
  Lord 
  Kelvin, 
  to 
  take 
  the 
  interval 
  

   h 
  — 
  tQ 
  as 
  containing 
  100 
  degrees 
  (he. 
  cit. 
  p. 
  175). 
  It 
  is 
  

   evident 
  that 
  we 
  should 
  have 
  obtained 
  the 
  same 
  value 
  for 
  t 
  if 
  

   6 
  had 
  been 
  constant 
  throughout 
  the 
  range 
  of 
  temperature 
  

  

  t 
  to 
  t 
  1 
  , 
  and 
  equal 
  to 
  - 
  1 
  — 
  — 
  5 
  . 
  This 
  shows 
  that 
  the 
  proper 
  

  

  mean 
  cooling-effect 
  is 
  simply 
  the 
  arithmetic 
  mean 
  of 
  the 
  

   cooling 
  effects 
  at 
  the 
  boiling-point 
  and 
  freezing-point. 
  The 
  

   following 
  table 
  gives 
  us 
  the 
  value 
  of 
  the 
  freezing-point 
  de- 
  

   rived 
  from 
  experiments 
  on 
  the 
  three 
  gases. 
  

  

  Uncorrected 
  estimate 
  

  

  of 
  temperature 
  of 
  Corrected 
  

  

  freezing-point. 
  Correction. 
  estimate. 
  

  

  Hydrogen 
  . 
  . 
  . 
  273*13 
  -'13 
  273*00 
  

  

  Air 
  272-44 
  -72 
  273-16' 
  

  

  Carbonic 
  acid 
  . 
  . 
  269-5 
  4-35 
  273*85 
  

  

  The 
  first 
  column 
  of 
  figures 
  is 
  taken 
  from 
  Lord 
  Kelvin's 
  

   paper 
  (loc. 
  cit. 
  p. 
  177). 
  

  

  Thermodynamic 
  Correction 
  for 
  a 
  Constant 
  -pressure 
  

   Gas 
  Thermometer. 
  

  

  Suppose 
  now 
  we 
  have 
  a 
  temperature 
  t 
  lying 
  above 
  both 
  

   t 
  l 
  and 
  t 
  , 
  and 
  fixed 
  by 
  some 
  definite 
  physical 
  phenomenon. 
  

   We 
  require 
  to 
  know 
  exactly 
  how 
  it 
  lies 
  with 
  respect 
  to 
  t 
  

   and 
  t 
  ± 
  . 
  

  

  We 
  start 
  as 
  before 
  with 
  the 
  differential 
  equation 
  

  

  d 
  /v\ 
  JK 
  (a, 
  fi 
  > 
  

  

  dt\t)~ 
  1T\¥ 
  ~¥y 
  

  

  We 
  may 
  put 
  this 
  

  

  d 
  / 
  v 
  \ 
  __ 
  A 
  B 
  

  

  