﻿Method 
  of 
  Graduating 
  a 
  Thermometer. 
  229 
  

  

  than 
  Lord 
  Kelvin's 
  ; 
  there 
  is 
  nothing 
  astonishing 
  in 
  this 
  as 
  

   it 
  contains 
  two 
  disposable 
  constants 
  instead 
  of 
  only 
  one. 
  

   But 
  it 
  tins 
  the 
  following 
  further 
  advantages 
  : 
  — 
  

  

  (i.) 
  It 
  includes 
  the 
  three 
  cases 
  of 
  air, 
  hydrogen, 
  and 
  

   carbonic 
  acid 
  under 
  one 
  form, 
  and 
  therefore 
  enables 
  us 
  to 
  treat 
  

   them 
  all 
  in 
  one 
  common 
  investigation. 
  

  

  (ii.) 
  It 
  renders 
  more 
  manageable 
  the 
  differential 
  equation 
  

   concerned 
  in 
  the 
  thermodynamic 
  scale 
  of 
  temperature, 
  and 
  

   leads 
  to 
  simpler 
  algebraic 
  results 
  after 
  integration. 
  

  

  This 
  last 
  proposition 
  we 
  must 
  now 
  proceed 
  to 
  prove. 
  It 
  

   is 
  shown 
  by 
  Lord 
  Kelvin 
  that 
  when 
  a 
  gas 
  passes 
  through 
  a 
  

   porous 
  plug 
  we 
  must 
  have 
  

  

  dv 
  JK 
  n 
  

  

  where 
  t 
  and 
  v 
  denote 
  the 
  temperature 
  and 
  volume 
  of 
  the 
  eras 
  

   respectively, 
  K 
  its 
  specific 
  heat, 
  6 
  the 
  cooling 
  effect 
  per 
  atmo 
  

   of 
  differential 
  pressure, 
  II 
  the 
  value 
  of 
  one 
  atmo, 
  and 
  J 
  the 
  

   value 
  of 
  Joule's 
  mechanical 
  equivalent 
  (Reprinted 
  Papers, 
  

   vol. 
  iii. 
  p. 
  179). 
  Hence 
  

  

  ldv__v_ 
  JK 
  6 
  

  

  t 
  dt 
  ~t 
  2 
  ~~ 
  n 
  ¥ 
  

  

  Jt\t) 
  z 
  n 
  \¥~¥ 
  s 
  ' 
  

  

  Estimate 
  of 
  the 
  Absolute 
  Value 
  of 
  the 
  Freezing-point 
  

  

  of 
  Water. 
  

  

  Integrate 
  the 
  last 
  equation 
  between 
  the 
  limits 
  t 
  and 
  tu 
  and 
  

   we 
  obtain 
  

  

  h 
  t 
  n 
  \2t 
  2 
  w 
  \t 
  TjJ 
  

  

  jKfi 
  n/f/i 
  i\ 
  A 
  \ 
  

  

  n 
  U 
  tJlAl 
  + 
  y'-Pf 
  

  

  nu 
  tj 
  2 
  ' 
  

  

  where 
  X 
  and 
  O 
  are 
  the 
  values 
  of 
  6 
  at 
  the 
  temperatures 
  t 
  and 
  

   t 
  respectively. 
  1 
  

  

  Multiply 
  the 
  equation 
  by 
  t 
  t 
  x 
  and 
  we 
  get 
  

  

  