﻿a 
  Spherical 
  Gaseous 
  Nebula. 
  5 
  

  

  being 
  radiated 
  from 
  it 
  into 
  space. 
  The 
  abscissas 
  represent 
  

   distance 
  from 
  the 
  centre. 
  The 
  ordinates 
  in 
  figure 
  1 
  repre- 
  

   sent 
  temperature 
  reckoned 
  from 
  absolute 
  zero; 
  OTj.-.OTs, 
  

   being 
  proportional 
  to 
  1, 
  T052, 
  1-108, 
  M69, 
  1*235 
  : 
  figure 
  2 
  

   gives 
  the 
  corresponding 
  density 
  curves. 
  

  

  § 
  54. 
  The 
  remarkable 
  result 
  we 
  have 
  arrived 
  at 
  for 
  P 
  gases 
  

   (for 
  which 
  alone, 
  as 
  we 
  have 
  seen, 
  convective 
  equilibrium 
  

   can 
  be 
  realised), 
  that 
  the 
  internal 
  energy 
  of 
  a 
  given 
  mass 
  in 
  

   approximate 
  convective 
  equilibrium 
  increases 
  through 
  gradual 
  

   loss 
  of 
  heat 
  by 
  radiation 
  into 
  space, 
  was 
  first 
  suggested 
  as 
  a 
  

   possibility 
  by 
  Homer 
  Lane 
  ; 
  the 
  suggestion 
  being 
  given 
  in 
  

   his 
  paper 
  referred 
  to 
  in 
  § 
  2. 
  To 
  understand 
  it 
  more 
  fully, 
  

   go 
  back 
  to 
  equation 
  (62), 
  and 
  observe 
  that 
  in 
  the 
  case 
  of 
  

   P 
  gases 
  <r 
  is 
  continually 
  diminishing, 
  while 
  the 
  globe 
  is 
  

   shrinking 
  through 
  loss 
  of 
  heat. 
  The 
  adiabatic 
  constant 
  A, 
  

   which 
  determines 
  the 
  relation 
  between 
  temperature 
  and 
  density 
  

   throughout 
  the 
  fluid 
  at 
  any 
  instant, 
  must 
  therefore 
  also 
  con- 
  

   tinually 
  diminish 
  as 
  time 
  goes 
  on 
  [see 
  (22) 
  above]. 
  Thus, 
  

   we 
  find 
  from 
  equation 
  (19) 
  that, 
  although 
  the 
  density 
  and 
  

   temperature 
  of 
  the 
  gas 
  near 
  the 
  centre 
  of 
  the 
  sphere 
  are 
  

   increasing, 
  as 
  we 
  see 
  from 
  figures 
  1 
  and 
  2, 
  and 
  the 
  total 
  

   energy 
  is 
  increasing, 
  in 
  reality 
  the 
  temperatures 
  at 
  places 
  

   of 
  the 
  same 
  density 
  are 
  continually 
  diminishing. 
  And 
  this 
  

   diminution 
  of 
  temperature 
  at 
  places 
  of 
  the 
  same 
  density 
  

   causes 
  a 
  diminution 
  of 
  the 
  elastic 
  resistance 
  of 
  the 
  gas 
  to 
  

   compression 
  which 
  allows 
  the 
  gravitational 
  forces 
  to 
  effect 
  a 
  

   contraction 
  of 
  the 
  gaseous 
  mass. 
  

  

  § 
  55. 
  It 
  seems 
  certain 
  that, 
  as 
  the 
  condensation 
  illustrated 
  

   in 
  figures 
  1 
  and 
  2 
  continues 
  with 
  increasing 
  total 
  energy, 
  a 
  

   time 
  must 
  come 
  when 
  the 
  resistance 
  to 
  compression 
  of 
  the 
  

   matter 
  in 
  the 
  central 
  regions 
  must 
  become 
  much 
  more 
  than 
  

   in 
  accordance 
  with 
  the 
  laws 
  of 
  perfect 
  gases 
  ; 
  and 
  after 
  that 
  

   occurs, 
  the 
  cooling 
  at 
  the 
  surface, 
  with 
  continual 
  mixing 
  of 
  

   cooled 
  fluid 
  throughout 
  the 
  interior 
  mass, 
  must 
  ultimately 
  

   check 
  the 
  process 
  of 
  becoming 
  hotter 
  in 
  the 
  central 
  regions, 
  

   and 
  bring 
  about 
  a 
  gradual 
  cooling 
  of 
  the 
  whole 
  mass. 
  

  

  § 
  56. 
  The 
  application 
  of 
  the 
  above 
  theory 
  of 
  approximate 
  

   convective 
  equilibrium 
  to 
  the 
  sun, 
  regarded 
  as 
  a 
  mass 
  of 
  

   matter 
  in 
  the 
  monatomic 
  state, 
  requires 
  that 
  the 
  law 
  of 
  

   increase 
  of 
  density 
  from 
  the 
  surface 
  inwards 
  should 
  be 
  such 
  

   that 
  the 
  density 
  at 
  the 
  centre 
  is 
  about 
  six 
  times 
  the 
  mean 
  

   density 
  (see 
  Appendix, 
  § 
  16). 
  The 
  mean 
  density 
  of 
  the 
  sun 
  

   is 
  about 
  1*4, 
  the 
  density 
  of 
  water 
  being 
  taken 
  as 
  unity. 
  

   From 
  this 
  fact 
  itself 
  it 
  seems 
  certain 
  that 
  the 
  sun 
  is 
  not 
  

   gaseous 
  as 
  a 
  whole. 
  Disregarding, 
  therefore, 
  the 
  high 
  velo- 
  

   cities 
  which 
  we 
  know 
  to 
  exist 
  in 
  portions 
  of 
  the 
  sun's 
  

  

  