﻿284 
  PROFESSOR 
  WILLIAM 
  THOMSON 
  ON 
  THE 
  

  

  Equation 
  (14) 
  will 
  consequently 
  become 
  

  

  \u(l 
  + 
  Et) 
  J 
  J 
  

  

  dv 
  ~ 
  dt 
  .... 
  ^4j, 
  

  

  a 
  result 
  peculiar 
  to 
  the 
  dynamical 
  theory; 
  and 
  equation 
  (16), 
  

  

  k 
  - 
  n 
  - 
  Wpv 
  m-) 
  

  

  which 
  agrees 
  with 
  the 
  result 
  of 
  § 
  53 
  of 
  my 
  former 
  paper. 
  

  

  If 
  V 
  be 
  taken 
  to 
  denote 
  the 
  volume 
  of 
  the 
  gas 
  at 
  the 
  temperature 
  0°, 
  under 
  

   unity 
  of 
  pressure, 
  (25) 
  becomes 
  

  

  E 
  2 
  V 
  

  

  K 
  - 
  N 
  = 
  ., 
  L, 
  -■ 
  (26). 
  

  

  /x(l 
  + 
  E/) 
  ^ 
  ' 
  

  

  52. 
  All 
  the 
  conclusions 
  obtained 
  by 
  Clausius, 
  with 
  reference 
  to 
  air 
  or 
  gases, 
  

   are 
  obtained 
  immediately 
  from 
  these 
  equations, 
  by 
  taking 
  

  

  T 
  E 
  

  

  ^ 
  = 
  J 
  lTEV 
  

  

  d~N 
  

   which 
  will 
  make 
  -5— 
  = 
  0, 
  and 
  by 
  assuming, 
  as 
  he 
  does, 
  that 
  N, 
  thus 
  found 
  to 
  be 
  

  

  independent 
  of 
  the 
  density 
  of 
  the 
  gas, 
  is 
  also 
  independent 
  of 
  its 
  temperature. 
  

  

  53. 
  As 
  a 
  last 
  application 
  of 
  the 
  two 
  fundamental 
  equations 
  of 
  the 
  theory, 
  let 
  

   the 
  medium, 
  with 
  reference 
  to 
  which 
  M 
  and 
  N 
  are 
  denned, 
  consist 
  of 
  a 
  weight 
  

   1 
  — 
  sb 
  of 
  a 
  certain 
  substance 
  in 
  one 
  state, 
  and 
  a 
  weight 
  x 
  in 
  another 
  state 
  at 
  

   the 
  same 
  temperature, 
  containing 
  more 
  latent 
  heat. 
  To 
  avoid 
  circumlocution 
  

   and 
  to 
  fix 
  the 
  ideas, 
  in 
  what 
  follows, 
  we 
  may 
  suppose 
  the 
  former 
  state 
  to 
  be 
  

   liquid, 
  and 
  the 
  latter 
  gaseous 
  ; 
  but 
  the 
  investigation, 
  as 
  will 
  be 
  seen, 
  is 
  equally 
  

   applicable 
  to 
  the 
  case 
  of 
  a 
  solid 
  in 
  contact 
  with 
  the 
  same 
  substance 
  in 
  the 
  liquid 
  

   or 
  gaseous 
  form. 
  

  

  54. 
  The 
  volume 
  and 
  temperature 
  of 
  the 
  whole 
  medium 
  being, 
  as 
  before, 
  de- 
  

   noted 
  respectively 
  by 
  v 
  and 
  t 
  ; 
  we 
  shall 
  have 
  

  

  \(l-x) 
  + 
  jx 
  = 
  v 
  . 
  ... 
  (27), 
  

  

  if 
  A 
  and 
  7 
  be 
  the 
  volumes 
  of 
  unity 
  of 
  weight 
  of 
  the 
  substance 
  in 
  the 
  liquid 
  and 
  

   the 
  gaseous 
  states 
  respectively 
  ; 
  and 
  p, 
  the 
  pressure, 
  may 
  be 
  considered 
  as 
  a 
  

   function 
  of 
  t, 
  depending 
  solely 
  on 
  the 
  nature 
  of 
  the 
  substance. 
  To 
  express 
  M 
  and 
  

   N 
  for 
  this 
  mixed 
  medium, 
  let 
  L 
  denote 
  the 
  latent 
  heat 
  of 
  a 
  unit 
  of 
  weight 
  of 
  the 
  

   vapour 
  ; 
  c 
  the 
  specific 
  heat 
  of 
  the 
  liquid 
  ; 
  and 
  h 
  the 
  specific 
  heat 
  of 
  the 
  vapour 
  

   when 
  kept 
  in 
  a 
  state 
  of 
  saturation. 
  We 
  shall 
  have 
  

  

  Mc?«=L-t^ 
  dv 
  

  

  d 
  v 
  

  

  dx 
  

   N 
  d*t=c(l 
  — 
  x)d 
  t+hxdt+Ii-j- 
  dt. 
  

  

  v 
  J 
  d 
  t 
  

  

  