﻿the 
  Absolute 
  Scale 
  of 
  Temperature. 
  367 
  

  

  which 
  is 
  directly 
  integrable. 
  Substituting 
  the 
  value 
  of 
  

   K 
  P 
  — 
  K 
  v 
  , 
  it 
  becomes 
  

  

  "dvp 
  

  

  in 
  which 
  ~- 
  is 
  a 
  constant 
  for 
  any 
  given 
  volume, 
  viz. 
  p 
  {3 
  

  

  where 
  p 
  means 
  the 
  pressure 
  at 
  the 
  freezing-point, 
  and 
  /3 
  the 
  

   coefficient 
  of 
  pressure. 
  

  

  Integrating 
  for 
  constant 
  v, 
  we 
  get 
  

  

  logT= 
  rf 
  — 
  logp+ 
  const. 
  .... 
  (iv.) 
  

  

  iVp6 
  

   V 
  

  

  on 
  the 
  assumption 
  that 
  K 
  P 
  e 
  is 
  independent 
  of 
  the 
  temperature. 
  

   Hence 
  to 
  find 
  T 
  we 
  have 
  

  

  log 
  (1 
  + 
  100/T 
  ) 
  = 
  x 
  J^ 
  lv 
  log 
  ( 
  Pm 
  / 
  P 
  o) 
  = 
  YZ^f 
  v 
  lo 
  S 
  (1 
  + 
  10( 
  W- 
  W 
  * 
  

  

  The 
  assumption 
  involved 
  is, 
  of 
  course, 
  not 
  strictly 
  true. 
  

   e 
  is 
  a 
  function 
  of 
  the 
  temperature, 
  and, 
  according 
  to 
  Joule 
  

   and 
  Thomson's 
  experiments, 
  it. 
  may, 
  for 
  some 
  gases 
  at 
  least, 
  

   be 
  taken 
  as 
  inversely 
  proportional 
  to 
  the 
  square 
  of 
  the 
  absolute 
  

   temperature. 
  It 
  would 
  therefore 
  be 
  more 
  exact 
  to 
  express 
  e 
  

  

  * 
  To 
  express 
  the 
  equation 
  (v.) 
  in 
  terms 
  of 
  powers 
  of 
  rj 
  we 
  have 
  

  

  T 
  1 
  1 
  

  

  fioo 
  = 
  (Pm\i-r, 
  =(1 
  + 
  100/3) 
  i-« 
  = 
  (1+100/3) 
  

  

  where 
  r\ 
  is 
  written 
  for 
  K 
  P 
  e/v 
  to 
  save 
  space. 
  Expanding, 
  

   T 
  100 
  /T 
  = 
  (l+100/3)[l+100/3( 
  J7 
  +7 
  7 
  2 
  + 
  . 
  . 
  .) 
  

  

  +—§-^(-1+0+...) 
  

  

  100 
  3 
  /3 
  3 
  

   + 
  -^(+2^-^+...) 
  

  

  , 
  100 
  4 
  /3 
  4 
  

  

  or 
  

  

  l 
  + 
  100/T 
  = 
  (l+100/3)[l 
  + 
  100^(0-852 
  . 
  . 
  .7/ 
  + 
  0-99 
  . 
  . 
  . 
  ^ 
  2 
  +. 
  . 
  .)] 
  

   = 
  1+100/3 
  [1+1-16377 
  + 
  1-35V 
  . 
  . 
  .], 
  

   l/T 
  =/3[l 
  + 
  l-16377+l-3o,, 
  2 
  . 
  . 
  .]. 
  

  

  The 
  term 
  rj 
  2 
  is, 
  however, 
  of 
  no 
  consequence, 
  even 
  in 
  the 
  case 
  of 
  carhon 
  

   dioxide. 
  

  

  2 
  2 
  

  

  