﻿THE 
  

   LONDON, 
  EDINBURGH, 
  and 
  DUBLIN 
  

  

  PHILOSOPHICAL 
  MAGAZINE 
  

  

  AND 
  

  

  JOURNAL 
  OF 
  SCIENCE. 
  

  

  [SIXTH 
  SERIES.] 
  

  

  JULY 
  1908. 
  

  

  I. 
  The 
  Problem 
  of 
  a 
  Spherical 
  Gaseous 
  Nebula. 
  

   By 
  the 
  late 
  Lord 
  Kelvin. 
  

  

  [Continued 
  from 
  vol. 
  xv. 
  p. 
  711.] 
  

  

  § 
  52. 
  "\\7"E 
  may 
  now 
  apply 
  the 
  above 
  equations 
  to 
  obtain 
  

   T 
  T 
  the 
  complete 
  solution 
  of 
  our 
  problem 
  of 
  § 
  21 
  : 
  — 
  

   to 
  determine 
  for 
  any 
  spherical 
  gaseous 
  nebula 
  of 
  given 
  mass, 
  

   initially 
  in 
  convective 
  equilibrium, 
  exactly 
  what 
  its 
  radius 
  was, 
  

   what 
  its 
  central 
  temperature 
  and 
  density 
  were, 
  and 
  what 
  were 
  

   the 
  temperature 
  and 
  density 
  at 
  any 
  distance 
  from 
  the 
  centre, 
  

   at 
  the 
  time 
  when 
  a 
  stated 
  quantity 
  of 
  heat 
  has 
  been 
  radiated 
  

   into 
  space. 
  Looking 
  to 
  equation 
  (57), 
  we 
  see 
  that 
  throughout 
  

   all 
  approximate 
  equilibrium 
  conditions 
  of 
  a 
  constant 
  total 
  

   mass 
  the 
  relation 
  

  

  <r 
  C-H 
  K 
  -*) 
  = 
  Jt( 
  Sl 
  constant) 
  . 
  . 
  . 
  (62) 
  

  

  holds 
  : 
  and, 
  with 
  this 
  condition, 
  equation 
  (51) 
  shows 
  that, 
  

   during 
  the 
  gradual 
  loss 
  of 
  heat 
  from 
  the 
  nebula, 
  the 
  value 
  

   of 
  z 
  for 
  each 
  stated 
  mass 
  m, 
  concentric 
  with 
  the 
  boundary, 
  is 
  

   constant. 
  We 
  have 
  accordingly 
  for 
  the 
  mass 
  m 
  

  

  '=—, 
  — 
  : 
  f 
  -v 
  • 
  • 
  • 
  • 
  < 
  63 
  >' 
  

  

  where 
  C 
  varies 
  slowly 
  as 
  time 
  goes 
  on. 
  If 
  we 
  suppose 
  C 
  t 
  to 
  

   be 
  the 
  initial 
  central 
  temperature 
  of 
  the 
  nebula, 
  and 
  C 
  2 
  its 
  

   central 
  temperature 
  after 
  a 
  quantity 
  of 
  heat 
  H 
  has 
  been 
  

   lost 
  by 
  radiation, 
  by 
  applying 
  (62) 
  in 
  the 
  equations 
  given 
  

   Phil 
  Mag. 
  S, 
  6, 
  Vol. 
  16. 
  No. 
  91, 
  July 
  1908, 
  B 
  

  

  