﻿6* 
  Lord 
  Kelvin 
  : 
  The 
  Problem 
  of 
  

  

  atmosphere, 
  and 
  which 
  are, 
  according 
  to 
  the 
  definition 
  given 
  

   in 
  § 
  3, 
  inconsistent 
  with 
  a 
  condition 
  of 
  convective 
  equi- 
  

   librium, 
  we 
  are 
  still 
  forced 
  to 
  conclude 
  that 
  Homer 
  Lane's 
  

   exquisite 
  mathematical 
  theory 
  gives 
  no 
  approximation 
  to 
  the 
  

   present 
  condition 
  of 
  the 
  sun, 
  because 
  of 
  his 
  great 
  average 
  

   density. 
  " 
  This 
  was 
  emphasised 
  by 
  Professor 
  Perry 
  in 
  the 
  

   seventh 
  paragraph, 
  headed 
  ' 
  Gaseous 
  Stars,' 
  of 
  his 
  letter 
  to 
  

   Sir 
  Norman 
  Lockyer 
  on 
  ' 
  The 
  Life 
  of 
  a 
  Star' 
  (Nature, 
  

   July 
  13, 
  1899), 
  which 
  contains 
  the 
  following 
  sentence 
  : 
  — 
  

  

  ' 
  It 
  seems 
  to 
  me 
  that 
  speculation 
  on 
  this 
  basis 
  of 
  perfectly 
  

   gaseous 
  stuff 
  ought 
  to 
  cease 
  when 
  the 
  density 
  of 
  the 
  gas 
  at 
  

   the 
  centre 
  of 
  the 
  star 
  approaches 
  0*1, 
  or 
  one- 
  tenth 
  of 
  the 
  

   density 
  of 
  ordinary 
  water 
  in 
  the 
  laboratory 
  ' 
  "" 
  x 
  ". 
  

  

  § 
  57. 
  According 
  to 
  a 
  promise 
  in 
  the 
  1887 
  paper 
  to 
  the 
  

   Philosophical 
  Magazine 
  " 
  On 
  the 
  equilibrium 
  of 
  a 
  gas 
  under 
  

   its 
  own 
  gravitation 
  only," 
  I 
  now 
  give 
  examples 
  of 
  the 
  

   application 
  of 
  this 
  theory 
  of 
  convective 
  equilibrium 
  to 
  

   spherical 
  masses 
  of 
  argon 
  and 
  of 
  nitrogen 
  ; 
  choosing, 
  for 
  

   illustration, 
  amounts 
  of 
  matter 
  equal 
  to 
  the 
  masses 
  of 
  the 
  

   sun, 
  earth, 
  and 
  moon, 
  with 
  density 
  at 
  the 
  centre 
  O'l 
  in 
  each 
  

   case. 
  

  

  Assuming 
  

  

  t 
  = 
  C®[xC-» 
  {K 
  - 
  1) 
  ] 
  .... 
  (67) 
  

  

  as 
  the 
  solution 
  of 
  (24), 
  which 
  gives 
  central 
  density 
  O'l, 
  we 
  

   find 
  from 
  equation 
  (19) 
  

  

  o-i 
  

  

  -m 
  w. 
  

  

  and, 
  as 
  in 
  this 
  case 
  we 
  suppose 
  the 
  total 
  mass 
  M 
  of 
  the 
  

   nebula 
  to 
  be 
  known, 
  we 
  can 
  determine 
  by 
  applying 
  

   equation 
  (25) 
  above. 
  Thus 
  

  

  M 
  = 
  (K 
  + 
  1 
  ) 
  S; 
  0-^> 
  @ 
  , 
  (g) 
  (69)j 
  

  

  where 
  q 
  denotes 
  the 
  value 
  of 
  x 
  for 
  which 
  ® 
  K 
  (,v) 
  = 
  0. 
  Elim- 
  

   inating 
  A 
  and 
  a 
  by 
  means 
  of 
  equations 
  (22) 
  and 
  (68), 
  we 
  

   obtain 
  

  

  * 
  Quoted 
  from 
  "On 
  Homer 
  Lane's 
  Problem 
  of 
  a 
  Spherical 
  Gaseous 
  

   Nebula," 
  'Nature/ 
  Feb. 
  14, 
  1907. 
  

  

  