﻿10 
  Lord 
  Kelvin 
  : 
  The 
  Problem 
  of 
  

  

  With 
  properly 
  chosen 
  scales 
  of 
  ordinates 
  and 
  abscissas, 
  the 
  

   curves 
  shown 
  may 
  represent 
  the 
  condition 
  of 
  any 
  gaseous 
  

   mass, 
  corresponding 
  to 
  any 
  of 
  the 
  solutions 
  (26) 
  above. 
  

   Thus, 
  with 
  scales 
  so 
  chosen 
  that 
  OR 
  K 
  = 
  R 
  = 
  cr^~ 
  1 
  C""^' 
  c 
  ~ 
  1) 
  , 
  and 
  

   OT 
  = 
  C, 
  each 
  curve, 
  TR*, 
  represents 
  the 
  temperature 
  reckoned 
  

   from 
  absolute 
  zero 
  ; 
  and 
  with 
  OD 
  K 
  =(SC/A) 
  K 
  , 
  each 
  curve, 
  

   D 
  K 
  ~R,c, 
  represents 
  the 
  density, 
  in 
  a 
  nebula 
  composed 
  of 
  gas 
  

   for 
  which 
  k 
  has 
  one 
  of 
  the 
  values 
  given 
  above, 
  when 
  the 
  

   central 
  temperature 
  is 
  C. 
  

  

  Each 
  curve 
  shown 
  meets 
  the 
  axis 
  of 
  R 
  at 
  a 
  finite 
  angle 
  ; 
  

   this 
  angle 
  being 
  so 
  small 
  for 
  the 
  density 
  curves 
  that 
  they 
  

   appear 
  to 
  meet 
  OB 
  tangentially. 
  

  

  APPENDIX. 
  

  

  By 
  George 
  Green. 
  

  

  § 
  1. 
  In 
  order 
  to 
  determine 
  the 
  conditions 
  of 
  temperature, 
  

   pressure, 
  and 
  density, 
  at 
  any 
  distance 
  from 
  the 
  centre 
  of 
  a 
  

   spherical 
  mass 
  of 
  gas 
  in 
  convective 
  equilibrium, 
  held 
  together 
  

   by 
  the 
  mutual 
  gravitation 
  of 
  its 
  parts, 
  it 
  is 
  necessary 
  to 
  find 
  

   a 
  solution 
  of 
  the 
  equation, 
  

  

  dH 
  _ 
  _^ 
  m 
  

  

  dx 
  2 
  ~ 
  x 
  4 
  ' 
  W 
  ' 
  

  

  In 
  this 
  equation, 
  

  

  x 
  is 
  inversely 
  proportional 
  to 
  r, 
  the 
  distance 
  of 
  any 
  point 
  

   from 
  the 
  centre 
  of 
  the 
  sphere 
  : 
  

  

  R] 
  

  

  t 
  is 
  the 
  temperature 
  of 
  the 
  gas 
  at 
  any 
  point 
  of 
  a 
  spherical 
  

   surface, 
  of 
  radius 
  r 
  : 
  

  

  t 
  K 
  is 
  proportional 
  to 
  the 
  density 
  where 
  t 
  is 
  the 
  tem- 
  

   perature 
  : 
  

  

  Hiyj 
  

  

  -j- 
  is 
  proportional 
  to 
  the 
  mass 
  of 
  gas 
  within 
  the 
  surface 
  

   of 
  radius 
  r 
  : 
  

  

  dx 
  

  

  'dt 
  c 
  2 
  m~J 
  

  

  and 
  k 
  is 
  equal 
  to 
  1/(^—1), 
  where 
  k 
  is 
  the 
  ratio 
  of 
  specific 
  

   heats 
  of 
  the 
  gas 
  considered 
  (see 
  §§ 
  22 
  ... 
  24 
  of 
  the 
  

   above 
  paper). 
  

  

  