﻿a 
  Spherical 
  Gaseous 
  Nebula. 
  7 
  

  

  From 
  equations 
  (68) 
  and 
  (22) 
  we 
  can 
  determine 
  the 
  following 
  

   expressions 
  for 
  A 
  and 
  a 
  : 
  — 
  

  

  -H^r^;m 
  

  

  (71) 
  

  

  K-3 
  

  

  <j) 
  f 
  -1866[-1366.^)] 
  " 
  J 
  f 
  ^^(gT 
  (72). 
  

  

  The 
  radius 
  of 
  the 
  outer 
  boundary 
  of 
  the 
  nebula 
  is 
  given 
  by 
  

  

  B=^ 
  • 
  (73), 
  

  

  where 
  

  

  M 
  -KK-D 
  =q 
  (74 
  ) 
  # 
  

  

  We 
  have 
  therefore 
  ~EL=<rg~ 
  1 
  Q~ 
  i(K 
  ~ 
  1 
  ^, 
  which, 
  by 
  means 
  of 
  

   equations 
  (53) 
  and 
  (55), 
  may 
  be 
  written 
  in 
  the 
  form 
  

  

  2-6527 
  [e^)]V(5)*- 
  • 
  • 
  < 
  75 
  >- 
  

  

  For 
  argon 
  we 
  have 
  & 
  = 
  1§, 
  or 
  k=l'5 
  ; 
  and 
  S 
  = 
  5*767 
  kilo- 
  

   metres 
  ; 
  and 
  for 
  nitrogen 
  we 
  have 
  k 
  = 
  l'4=, 
  or 
  tc 
  = 
  2'5 
  ; 
  and 
  

   S 
  = 
  8*256 
  kilometres. 
  With 
  these 
  values 
  of 
  S 
  and 
  k, 
  inserted 
  

   in 
  the 
  above 
  formulas, 
  we 
  obtain 
  the 
  results 
  shown 
  in 
  the 
  

   following 
  table 
  : 
  — 
  

  

  R 
  

  

  e 
  

  

  

  

  

  Central 
  tem- 
  

  

  

  

  

  Matter 
  

   in 
  nebula. 
  

  

  Total 
  mass, 
  

   that 
  of 
  

  

  Central 
  

   density. 
  

  

  perature 
  in 
  

  

  Centigrade 
  

  

  degrees 
  above 
  

  

  absolute 
  zero. 
  

  

  Central 
  pressure 
  

  

  in 
  metric 
  tons 
  

   per 
  sq. 
  kilometre. 
  

  

  Eadius 
  of 
  

   boundary 
  in 
  

   kilometres. 
  

  

  Adiabatic 
  

   Constant 
  in 
  

   kilometres. 
  

  

  Argon. 
  

  

  Sun. 
  

  

  •1 
  

  

  1105 
  x10 
  s 
  

  

  233 
  XlO 
  u 
  

  

  3-04 
  XlO 
  6 
  

  

  1-08 
  XlO 
  7 
  

  

  „ 
  

  

  Earth. 
  

  

  •1 
  

  

  2-342 
  Xl0 
  4 
  

  

  4-95 
  XlO 
  10 
  

  

  4-42 
  XlO 
  4 
  

  

  2-30 
  XlO 
  4 
  

  

  »J 
  

  

  Moon. 
  

  

  •1 
  

  

  1-243 
  xlO 
  3 
  

  

  263 
  XlO 
  9 
  

  

  1-02 
  XlO 
  4 
  

  

  1-22 
  XlO 
  2 
  

  

  Nitrogen. 
  

  

  Sun. 
  

  

  1 
  

  

  6-383 
  xlO 
  7 
  

  

  1-92 
  XlO 
  14 
  

  

  4-79 
  xlO 
  6 
  

  

  4-82 
  XlO 
  6 
  

  

  ,, 
  

  

  Earth. 
  

  

  •] 
  

  

  1-353 
  XlO 
  4 
  

  

  4-07 
  XlO 
  10 
  

  

  6-97x10* 
  

  

  1-02 
  xlO 
  3 
  

  

  j> 
  

  

  Moon. 
  

  

  •1 
  

  

  7-185 
  xlO 
  2 
  

  

  2-16 
  XlO 
  9 
  

  

  1-61 
  xlO 
  4 
  

  

  543 
  

  

  § 
  58. 
  The 
  curves 
  of 
  figures 
  3 
  and 
  4 
  represent 
  temperature 
  

   and 
  density 
  at 
  different 
  distances 
  from 
  the 
  centres 
  of 
  nebulas 
  

   for 
  which 
  tc 
  has 
  the 
  values 
  1*5, 
  2*5, 
  3, 
  and 
  4. 
  The 
  tem- 
  

   perature 
  curves 
  are 
  drawn 
  from 
  the 
  numbers 
  given 
  in 
  the 
  

   third 
  columns 
  of 
  Tables 
  I. 
  . 
  . 
  . 
  IV. 
  of 
  the 
  Appendix 
  : 
  the 
  den- 
  

   sity 
  curves, 
  from 
  the 
  numbers 
  given 
  in 
  the 
  fourth 
  columns. 
  

  

  