﻿Gravitational 
  Matter 
  in 
  any 
  part 
  of 
  the 
  L 
  

  

  /averse, 
  

  

  sixteenth 
  magnitude. 
  Newcomb 
  estimated 
  from 
  thirty 
  to 
  

   fifty 
  million 
  as 
  the 
  number 
  of 
  stars 
  visible 
  in 
  modern 
  

   telescopes. 
  Young 
  estimated 
  at 
  100 
  million 
  the 
  number 
  

   visible 
  through 
  the 
  Lick 
  telescope. 
  This 
  larger 
  estimate 
  is 
  

   only 
  one 
  tenth 
  of 
  our 
  assumed 
  1000 
  million 
  masses 
  equal 
  to 
  

   the 
  sun, 
  of 
  which, 
  however, 
  900 
  million 
  might 
  be 
  either 
  non- 
  

   luminous, 
  or, 
  though 
  luminous, 
  too 
  distant 
  to 
  be 
  seen 
  by 
  us 
  

   at 
  their 
  actual 
  distances 
  from 
  the 
  earth. 
  Remark, 
  also, 
  that 
  

   it 
  is 
  only 
  for 
  facility 
  of 
  counting 
  that 
  we 
  have 
  reckoned 
  our 
  

   universe 
  as 
  1000 
  million 
  suns 
  ; 
  and 
  that 
  the 
  meaning 
  of 
  our 
  

   reckoning 
  is 
  that 
  the 
  total 
  amount 
  of 
  matter 
  within 
  a 
  sphere 
  

   of 
  3*09. 
  10 
  16 
  kilometres 
  radius 
  is 
  1000 
  million 
  times 
  the 
  sun's 
  

   mass. 
  The 
  sun's 
  mass 
  is 
  1*99. 
  10 
  27 
  metric 
  tons, 
  or 
  1*99. 
  10 
  83 
  

   grammes. 
  Hence 
  our 
  reckoning 
  of 
  our 
  supposed 
  spherical 
  

   universe 
  is 
  that 
  the 
  ponderable 
  part 
  of 
  it 
  amounts 
  to 
  1*99.10 
  42 
  

   grammes, 
  or 
  that 
  its 
  average 
  density 
  is 
  1'61.10~ 
  23 
  of 
  the 
  

   density 
  of 
  water. 
  

  

  Let 
  us 
  now 
  return 
  to 
  the 
  question 
  of 
  sum 
  of 
  apparent 
  areas. 
  

   The 
  ratio 
  of 
  this 
  sum 
  to 
  47r, 
  the 
  total 
  apparent 
  area 
  of 
  the 
  

   sky 
  viewed 
  in 
  all 
  directions, 
  is 
  given 
  by 
  the 
  formula 
  * 
  : 
  

  

  a= 
  -p(-)j 
  provided 
  its 
  amount 
  is 
  so 
  small 
  a 
  fraction 
  of 
  

  

  unity 
  that 
  its 
  diminution 
  by 
  eclipses, 
  total 
  or 
  partial, 
  may 
  be 
  

  

  neglected. 
  In 
  this 
  formula, 
  N 
  is 
  a 
  number 
  of 
  globes 
  of 
  

  

  radius 
  a 
  uniformly 
  distributed 
  within 
  a 
  spherical 
  surface 
  

  

  of 
  radius 
  r. 
  For 
  the 
  same 
  quantity 
  of 
  matter 
  in 
  W 
  globes 
  

  

  of 
  the 
  same 
  density, 
  uniformly 
  distributed 
  through 
  the 
  same 
  

  

  W 
  ( 
  a 
  \ 
  3 
  

   sphere 
  of 
  radius 
  r, 
  we 
  have 
  ^- 
  = 
  I 
  — 
  ) 
  and 
  therefore 
  

  

  °L=-. 
  With 
  N=10 
  9 
  , 
  r=3'09.10 
  16 
  kilometres; 
  and 
  a 
  

  

  a 
  od 
  

  

  (the 
  sun's 
  radius) 
  =7.10 
  5 
  kilometres 
  ; 
  we 
  had 
  a=3*87.10~ 
  13 
  . 
  

   Hence 
  a' 
  = 
  7 
  kilometres 
  gives 
  a' 
  = 
  3 
  , 
  87.10~ 
  s 
  ; 
  and 
  <x"=l 
  centi- 
  

   metre 
  gives 
  a" 
  = 
  1/36*9. 
  Hence 
  if 
  the 
  whole 
  mass 
  of 
  our 
  

   supposed 
  universe 
  were 
  reduced 
  to 
  globules 
  of 
  density 
  1*4 
  

   (being 
  the 
  sun's 
  mean 
  density), 
  and 
  of 
  2 
  centimetres 
  diameter, 
  

   distributed 
  uniformly 
  through 
  a 
  sphere 
  of 
  3*09. 
  10 
  16 
  kilometres 
  

   radius, 
  an 
  eye 
  at 
  the 
  centre 
  of 
  this 
  sphere 
  would 
  lose 
  only 
  

   1/36*9 
  of 
  the 
  light 
  of 
  a 
  luminary 
  outside 
  it 
  ! 
  The 
  smallness 
  

   of 
  this 
  loss 
  is 
  easily 
  understood 
  when 
  we 
  consider 
  that 
  there 
  

   is 
  only 
  one 
  globule 
  of 
  2 
  centimetres 
  diameter 
  per 
  364,000,000 
  

   cubic 
  kilometres 
  of 
  space, 
  in 
  our 
  supposed 
  universe 
  reduced 
  

   to 
  globules 
  of 
  2 
  centimetres 
  diameter. 
  Contrast 
  with 
  the 
  

  

  * 
  Phil. 
  Mag. 
  August 
  1901, 
  p. 
  175. 
  

  

  