﻿COSMICAL 
  PHYSICS 
  JEANS 
  173 
  

  

  the 
  " 
  coefficient 
  of 
  opacity 
  " 
  of 
  the 
  matter. 
  By 
  comparison 
  with 
  the 
  

   kinetic 
  theory 
  formula 
  e"^'^ 
  for 
  the 
  reduction 
  in 
  strength 
  of 
  a 
  

   shower 
  of 
  moving 
  molecules, 
  we 
  see 
  that 
  the 
  " 
  free 
  path 
  " 
  of 
  the 
  

   radiation 
  must 
  be 
  taken 
  to 
  be 
  1/k^. 
  When 
  we 
  use 
  this 
  value 
  for 
  the 
  

   free 
  path 
  of 
  radiation 
  and 
  calculate 
  carrying 
  capacities 
  in 
  the 
  way 
  

   already 
  explained, 
  the 
  carrying 
  capacity 
  of 
  both 
  nuclei 
  and 
  electrons 
  

   is 
  found 
  to 
  be 
  insignificant 
  in 
  comparison 
  with 
  that 
  of 
  the 
  radia- 
  

   tion. 
  The 
  nuclei 
  and 
  electrons 
  may 
  have 
  the 
  greater 
  amount 
  of 
  

   energy 
  to 
  carry, 
  but 
  the 
  distance 
  over 
  which 
  they 
  carry 
  it, 
  their 
  free 
  

   path, 
  is 
  far 
  less 
  than 
  that 
  of 
  the 
  radiation, 
  and 
  their 
  speed 
  of 
  trans- 
  

   port 
  is 
  also 
  less, 
  since 
  radiation 
  transports 
  energy 
  with 
  the 
  velocity 
  

   of 
  light. 
  In 
  this 
  way 
  it 
  comes 
  about 
  that 
  practically 
  the 
  whole 
  trans- 
  

   port 
  of 
  energy 
  from 
  the 
  interior 
  of 
  a 
  star 
  to 
  its 
  surface 
  is 
  by 
  the 
  

   vehicle 
  of 
  radiation. 
  

  

  This 
  general 
  principle 
  was 
  first 
  clearly 
  stated 
  by 
  Sampson 
  in 
  

   1894 
  (Mem. 
  R. 
  A. 
  S., 
  51, 
  p. 
  123), 
  but 
  his 
  detailed 
  applications 
  were 
  

   vitiated 
  by 
  his 
  using 
  an 
  erroneous 
  law 
  of 
  radiation. 
  Twelve 
  years 
  

   later, 
  Schwarzschild 
  independently 
  advanced 
  the 
  same 
  idea 
  (Gott. 
  

   Nach., 
  1906, 
  p. 
  41) 
  ; 
  he 
  showed 
  how 
  the 
  temperature 
  of 
  any 
  element 
  

   of 
  a 
  star's 
  interior 
  must 
  be 
  determined 
  by 
  the 
  condition 
  that 
  it 
  

   received 
  just 
  as 
  much 
  radiation 
  as 
  it 
  emitted, 
  and 
  gave 
  accurate 
  

   equations 
  of 
  radiative 
  equilibrium 
  which 
  have 
  formed 
  the 
  basis 
  of 
  

   every 
  subsequent 
  discussion 
  of 
  the 
  problem. 
  

  

  THE 
  CONFIGURATION 
  OF 
  A 
  STAR 
  IN 
  EQUILIBRIUM 
  

  

  As 
  a 
  consequence 
  of 
  radiation 
  completely 
  outstripping 
  the 
  mate- 
  

   rial 
  carriers 
  in 
  the 
  transport 
  of 
  energy 
  to 
  the 
  star's 
  surface, 
  the 
  build 
  

   of 
  a 
  star 
  is 
  entirely 
  determined 
  by 
  the 
  values 
  of 
  k, 
  the 
  coefficient 
  of 
  

   opacity 
  in 
  its 
  interior. 
  If 
  this 
  coefficient 
  is 
  everywhere 
  zero, 
  the 
  

   star 
  is 
  entirely 
  transparent, 
  and 
  so 
  can 
  not 
  retain 
  any 
  heat 
  ; 
  we 
  now 
  

   have 
  a 
  star 
  of 
  zero 
  temperature 
  and 
  therefore 
  of 
  infinite 
  extent. 
  

   If, 
  on 
  the 
  other 
  hand, 
  the 
  coefficient 
  of 
  opacity 
  is 
  everywhere 
  infinite, 
  

   the 
  star 
  is 
  completely 
  opaque, 
  so 
  that 
  all 
  radiation 
  accumulates 
  where 
  

   it 
  is 
  generated 
  until 
  the 
  star's 
  temperature 
  becomes 
  infinite, 
  and 
  we 
  

   have 
  a 
  star 
  of 
  infinite 
  temperature 
  but 
  of 
  infinitesimal 
  radius. 
  It 
  

   is, 
  of 
  course, 
  the 
  intermediate 
  values 
  which 
  are 
  of 
  practical 
  interest, 
  

   but 
  the 
  two 
  extreme 
  cases 
  just 
  mentioned 
  show 
  how 
  the 
  whole 
  build 
  

   of 
  a 
  star 
  depends 
  on 
  the 
  value 
  of 
  the 
  opacity 
  coefficient 
  k. 
  So 
  much 
  

   is 
  this 
  the 
  case 
  that 
  all 
  attempts 
  to 
  investigate 
  the 
  build 
  of 
  stars 
  

   before 
  the 
  value 
  of 
  this 
  coefficient 
  was 
  known 
  can 
  only 
  be 
  regarded 
  

   as 
  speculation. 
  

  

  TJie 
  first 
  attempt 
  to 
  evaluate 
  it 
  theoretically 
  bj'^ 
  Eddington 
  in 
  

   1922 
  (Mon. 
  Not. 
  R. 
  A. 
  S., 
  83, 
  p. 
  32) 
  proved 
  unsuccessful 
  and 
  was 
  

  

  