﻿2 
  Lord 
  Kelvin 
  : 
  The 
  Problem 
  of 
  

  

  above, 
  we 
  easily 
  find 
  (with 
  suffixes 
  1 
  and 
  2 
  referring 
  to 
  

   the 
  initial 
  and 
  final 
  conditions 
  respectively) 
  the 
  following 
  

   results: 
  — 
  . 
  . 
  

  

  Co 
  . 
  /Co\ 
  ) 
  

  

  h 
  — 
  Q^h 
  ; 
  P2 
  — 
  \ 
  jr. 
  r 
  1 
  

  

  -m 
  

  

  

  r 
  2 
  = 
  -Q/i', 
  R2 
  = 
  q-Ri 
  . 
  . 
  . 
  (64); 
  

  

  l 
  2 
  =§Ii 
  ; 
  W 
  2 
  =gw, 
  

  

  in 
  which 
  t 
  2 
  , 
  h, 
  p 
  2 
  , 
  pi, 
  r 
  2 
  , 
  r 
  l5 
  all 
  refer 
  to 
  points 
  on 
  the 
  spherical 
  

   surface 
  enclosing 
  a 
  stated 
  mass 
  m. 
  The 
  total 
  heat 
  lost 
  by 
  

   radiation 
  may 
  now 
  be 
  written 
  — 
  

  

  H=(W 
  2 
  -W 
  1 
  )-(I 
  2 
  -Ii)=^^ 
  i 
  (W 
  1 
  -I 
  1 
  ) 
  . 
  (65); 
  

  

  and 
  for 
  an 
  infinitesimal 
  change 
  in 
  the 
  condition 
  of 
  the 
  whole 
  

   mass 
  at 
  any 
  time 
  this 
  becomes 
  

  

  8H 
  = 
  ^(W-I) 
  .... 
  (66). 
  

  

  § 
  53. 
  These 
  are 
  interesting 
  results. 
  Remembering 
  that 
  

   I 
  1= 
  =/c/3.Wi, 
  we 
  see 
  by 
  (65) 
  and 
  (^66) 
  that 
  the 
  central 
  tem- 
  

   perature 
  of 
  a 
  globe 
  of 
  gas 
  P 
  in 
  equilibrium 
  increases, 
  through 
  

   gradual 
  loss 
  of 
  heat 
  by 
  radiation 
  into 
  space. 
  We 
  then 
  see 
  

   also 
  by 
  (64) 
  that 
  the 
  internal 
  energy 
  of 
  a 
  globe 
  of 
  gas 
  P, 
  

   continuing 
  in 
  a 
  condition 
  of 
  approximate 
  equilibrium 
  while 
  

   heat 
  is 
  being 
  radiated 
  away 
  across 
  its 
  boundary, 
  would 
  go 
  

   on 
  increasing, 
  and 
  the 
  work 
  done 
  by 
  the 
  mutual 
  gravitation 
  

   of 
  its 
  parts 
  would 
  go 
  on 
  increasing, 
  till 
  the 
  gas 
  in 
  the 
  central 
  

   regions 
  became 
  too 
  dense 
  to 
  obey 
  Boyle's 
  Law. 
  At 
  the 
  

   same 
  time 
  the 
  radius 
  of 
  the 
  globe 
  would 
  diminish. 
  In 
  other 
  

   words, 
  the 
  repulsive 
  power 
  which 
  the 
  globe 
  of 
  gas 
  P 
  pos- 
  

   sesses 
  by 
  virtue 
  of 
  its 
  internal 
  energy, 
  while 
  in 
  approximate 
  

   equilibrium, 
  is, 
  owing 
  to 
  gradual 
  loss 
  of 
  energy 
  by 
  radiation, 
  

   at 
  each 
  instant 
  just 
  insufficient 
  to 
  exactly 
  balance 
  the 
  attractive 
  

   force 
  due 
  to 
  the 
  mutual 
  gravitation 
  of 
  its 
  parts. 
  The 
  globe 
  

   is 
  therefore 
  compelled 
  to 
  contract 
  : 
  and, 
  as 
  the 
  heat 
  due 
  to 
  the 
  

   contraction 
  is 
  not 
  radiated 
  away 
  so 
  quickly 
  as 
  it 
  is 
  produced, 
  

   the 
  shrinkage 
  of 
  the 
  globe 
  is 
  accompanied 
  by 
  augmentation 
  

   of 
  its 
  internal 
  energy. 
  

  

  In 
  figures 
  1 
  and 
  2 
  curves 
  are 
  shown 
  illustrating 
  five 
  

   successive 
  stages, 
  numbered 
  1, 
  2, 
  3, 
  4, 
  5 
  respectively, 
  in 
  the 
  

   history 
  of 
  a 
  constant 
  mass 
  of 
  any 
  monatomic 
  gas 
  (#=1*5 
  ; 
  

   k 
  = 
  l'i) 
  in 
  approximate 
  convective 
  equilibrium 
  while 
  heat 
  is 
  

  

  