﻿AND 
  ITS 
  CONNECTION 
  WITH 
  THE 
  THEORY 
  OF 
  HEAT. 
  435 
  

  

  =^<—>V 
  v 
  ^ 
  

  

  To 
  determine 
  the 
  second 
  part 
  of 
  the 
  integral 
  we 
  have 
  the 
  condition, 
  that 
  the 
  

   quantity 
  of 
  atomic 
  atmosphere 
  enclosed 
  within 
  each 
  surface 
  at 
  which 
  a 
  <p 
  has 
  

   some 
  given 
  value, 
  is 
  invariable 
  ; 
  that 
  is 
  to 
  say 
  

  

  (»*#*V+» 
  v 
  3v 
  + 
  St 
  £ 
  ) 
  fr 
  ftMV 
  /*; 
  '***» 
  =0 
  

  

  Hence 
  

  

  d 
  a 
  <p= 
  

  

  k 
  g.MY 
  e 
  v 
  — 
  

  

  w 
  i 
  

  

  The 
  value 
  of 
  the 
  second 
  part 
  of 
  the 
  integral 
  (23) 
  is 
  now 
  found 
  to 
  be 
  : 
  — 
  

  

  In 
  the 
  double 
  integral, 
  let 
  A 
  = 
  log<> 
  V 
  be 
  put 
  for 
  k 
  (p, 
  G 
  for 
  w, 
  and 
  H 
  for 
  the 
  

   single 
  integral, 
  as 
  in 
  equation 
  (9.) 
  Then 
  the 
  double 
  integral 
  becomes 
  

  

  i/ 
  1 
  H^ 
  = 
  -i|f-b,E, 
  1 
  .(10) 
  

  

  — 
  00 
  

  

  k 
  dH, 
  

  

  G 
  x 
  rfT 
  

  

  Also 
  because 
  p 
  x 
  M 
  V 
  = 
  ^± 
  by 
  eq. 
  (9), 
  and 
  *-&■ 
  = 
  - 
  ( 
  T 
  -*), 
  the 
  second 
  part 
  of 
  

   the 
  integral 
  (23) 
  is 
  found 
  to 
  be 
  

  

  %<r-4(»r£ 
  T 
  +»V&) 
  : 
  0;. 
  ■ 
  • 
  ■ 
  (23 
  BO 
  

  

  Hence, 
  adding 
  together 
  (23 
  A.) 
  and 
  (23 
  B.) 
  we 
  find 
  for 
  the 
  total 
  variation 
  of 
  

   latent 
  heat 
  

  

  ^ 
  ¥<-){*- 
  ^ 
  +*v. 
  (J, 
  + 
  M)} 
  (24) 
  

  

  To 
  express 
  this 
  in 
  terms 
  of 
  quantities 
  which 
  may 
  be 
  known 
  directly 
  by 
  expe- 
  

   riment, 
  we 
  have 
  by 
  equations 
  10 
  and 
  9 
  : 
  — 
  

  

  J 
  XT 
  p 
  

  

  tt 
  » 
  s~ 
  + 
  Q 
  — 
  tf 
  1 
  = 
  0, 
  that 
  is 
  to 
  say, 
  

  

  rflog,H, 
  G 
  1 
  t 
  M 
  t 
  

  

  dV 
  ~K 
  X 
  V 
  KY~hfx 
  P 
  kV 
  

  

  