﻿Gravitational 
  Matter 
  in 
  any 
  part 
  of 
  the 
  Universe. 
  3 
  

  

  Ether 
  we 
  relegate, 
  not 
  to 
  a 
  limbo 
  of 
  imponderables, 
  but 
  to 
  

   distinct 
  species 
  of 
  matter 
  which 
  have 
  inertia, 
  rigidity, 
  elasticity, 
  

   compressibility, 
  but 
  not 
  heaviness. 
  In 
  a 
  paper 
  I 
  have 
  

   already 
  published 
  I 
  gave 
  strong 
  reasons 
  for 
  limiting 
  to 
  a 
  

   definite 
  amount 
  the 
  quantity 
  of 
  matter 
  in 
  space 
  known 
  to 
  

   astronomers. 
  I 
  can 
  scarcely 
  avoid 
  using 
  the 
  word 
  ' 
  universe/ 
  

   but 
  I 
  mean 
  our 
  universe, 
  which 
  may 
  be 
  a 
  very 
  small 
  affair 
  

   after 
  all, 
  occupying 
  a 
  very 
  small 
  portion 
  of 
  all 
  the 
  space 
  in 
  

   which 
  there 
  is 
  ponderable 
  matter. 
  

  

  Supposing 
  a 
  sphere 
  of 
  radius 
  3*09. 
  10 
  16 
  kilometres 
  (being 
  

   the 
  distance 
  at 
  which 
  a 
  star 
  must 
  be 
  to 
  have 
  parallax 
  ;/, 
  001) 
  

   to 
  have 
  within 
  it, 
  uniformly 
  distributed 
  through 
  it, 
  a 
  quantity 
  

   of 
  matter 
  equal 
  to 
  one 
  thousand 
  million 
  times 
  the 
  sun's 
  mass, 
  

   the 
  velocity 
  acquired 
  by 
  a 
  body 
  placed 
  originally 
  at 
  rest 
  at 
  

   the 
  surface 
  would, 
  in 
  five 
  million 
  years, 
  be 
  about 
  20 
  kilo- 
  

   metres 
  per 
  second, 
  and 
  in 
  twenty-five 
  million 
  years 
  would 
  be 
  

   108 
  kilometres 
  per 
  second 
  (if 
  the 
  acceleration 
  remained 
  

   sensibly 
  constant 
  for 
  so 
  long 
  a 
  time) 
  . 
  Hence, 
  if 
  the 
  thousand 
  

   million 
  suns 
  had 
  been 
  given 
  at 
  rest 
  twenty-five 
  million 
  years 
  

   ago, 
  uniformly 
  distributed 
  throughout 
  the 
  supposed 
  sphere, 
  

   many 
  of 
  them 
  would 
  now 
  have 
  velocities 
  of 
  20^ 
  or 
  30 
  kilo- 
  

   metres 
  per 
  second, 
  while 
  some 
  would 
  have 
  less 
  and 
  some 
  

   probably 
  greater 
  velocities 
  than 
  108 
  kilometres 
  per 
  second 
  ; 
  

   or, 
  if 
  they 
  had 
  been 
  given 
  thousands 
  of 
  million 
  years 
  ago 
  at 
  

   rest 
  so 
  distributed 
  that 
  now 
  r 
  they 
  were 
  equally 
  spaced 
  

   throughout 
  the 
  supposed 
  sphere, 
  their 
  mean 
  velocity 
  would 
  

   now 
  be 
  about 
  50 
  kilometres 
  per 
  second 
  *, 
  This 
  is 
  not. 
  

   unlike 
  the 
  measured 
  velocities 
  of 
  stars, 
  and 
  hence 
  it 
  seems 
  

   probable 
  that 
  there 
  might 
  be 
  as 
  much 
  matter 
  as 
  one 
  thousand 
  

   million 
  suns 
  within 
  the 
  distance 
  3*09. 
  10 
  16 
  kilometres. 
  The 
  

   same 
  reasoning 
  shows 
  that 
  ten 
  thousand 
  million 
  suns 
  in 
  

   the 
  same 
  sphere 
  would 
  produce 
  velocities 
  far 
  greater 
  than 
  the 
  

   known 
  star 
  velocities, 
  and 
  hence 
  there 
  is 
  probably 
  much 
  less 
  

   than 
  ten 
  thousand 
  million 
  times 
  the 
  sun's 
  mass 
  in 
  the 
  sphere 
  

   considered. 
  A 
  general 
  theorem 
  discovered 
  by 
  Green 
  seventy- 
  

   three 
  years 
  ago 
  regarding 
  force 
  at 
  a 
  surface 
  of 
  any 
  shape, 
  

   due 
  to 
  matter 
  (gravitational, 
  or 
  ideal 
  electric, 
  or 
  ideal 
  

   magnetic) 
  acting 
  according 
  to 
  the 
  Newtonian 
  law 
  of 
  the 
  

   inverse 
  square 
  of 
  the 
  distance," 
  shows 
  that 
  a 
  non-uniform 
  

   distribution 
  of 
  the 
  same 
  total 
  quantity 
  of 
  matter 
  would 
  give 
  

   greater 
  velocities 
  than 
  would 
  the 
  uniform 
  distribution. 
  

   Hence 
  we 
  cannot, 
  by 
  any 
  non-uniform 
  distribution 
  of 
  matter 
  

   within 
  the 
  supposed 
  sphere 
  of 
  3'09. 
  10 
  16 
  kilometres 
  radius, 
  

  

  * 
  PMl.'Mag. 
  August 
  1901, 
  pp. 
  169, 
  170. 
  

   B2 
  

  

  