﻿4 
  Lord 
  Kelvin 
  on 
  the 
  Clustering 
  of 
  

  

  escape 
  from 
  the 
  conclusion 
  limiting 
  the 
  total 
  amount 
  of 
  the 
  

   matter 
  within 
  it 
  to 
  something 
  like 
  one 
  thousand 
  million 
  

   times 
  the 
  sun's 
  mass. 
  

  

  If 
  we 
  compare 
  the 
  sunlight 
  with 
  the 
  light 
  from 
  the 
  

   thousand 
  million 
  stars, 
  each 
  being 
  supposed 
  to 
  be 
  of 
  the 
  same 
  

   size 
  and 
  brightness 
  as 
  our 
  sun, 
  we 
  find 
  that 
  the 
  ratio 
  of 
  the 
  

   apparent 
  brightness 
  of 
  the 
  star-lit 
  sky 
  to 
  the 
  brightness 
  of 
  

   our 
  sun's 
  disc 
  would 
  be 
  3*87. 
  10 
  -13 
  . 
  This 
  ratio 
  * 
  varies 
  

   directly 
  with 
  the 
  radius 
  of 
  the 
  containing 
  sphere, 
  the 
  number 
  

   of 
  equal 
  globes 
  per 
  equal 
  volume 
  being 
  supposed 
  constant 
  ; 
  

   and 
  hence 
  to 
  make 
  the 
  sum 
  of 
  the 
  apparent 
  areas 
  of 
  discs 
  

   3*87 
  per 
  cent, 
  of 
  the 
  whole 
  sky, 
  the 
  radius 
  must 
  be 
  3*09. 
  10 
  27 
  

   kilometres. 
  With 
  this 
  radius 
  light 
  would 
  take 
  34.IO 
  14 
  years 
  

   to 
  travel 
  from 
  the 
  outlying 
  stars 
  to 
  the 
  centre. 
  Irrefragable 
  

   dynamics 
  proves 
  that 
  the 
  life 
  of 
  our 
  sun 
  as 
  a 
  luminary 
  is 
  

   probably 
  between 
  25 
  and 
  100 
  million 
  years 
  ; 
  but 
  to 
  be 
  

   liberal, 
  suppose 
  each 
  of 
  our 
  stars 
  to 
  have 
  a 
  life 
  of 
  1 
  00 
  million 
  

   years 
  as 
  a 
  luminary 
  : 
  and 
  it 
  is 
  found 
  that 
  the 
  time 
  taken 
  by 
  

   light 
  to 
  travel 
  from 
  the 
  outlying 
  stars 
  to 
  the 
  centre 
  of 
  the 
  

   sphere 
  is 
  three 
  and 
  a 
  quarter 
  million 
  times 
  the 
  life 
  of 
  a 
  star. 
  

   Hence 
  it 
  follows 
  that 
  to 
  make 
  the 
  whole 
  sky 
  aglow 
  with 
  

   the 
  light 
  of 
  all 
  the 
  stars 
  at 
  the 
  same 
  time 
  the 
  commencements 
  

   of 
  the 
  stars 
  must 
  be 
  timed 
  earlier 
  and 
  earlier 
  for 
  the 
  more 
  and 
  

   more 
  distant 
  ones, 
  so 
  that 
  the 
  time 
  of 
  the 
  arrival 
  of 
  the 
  light 
  

   of 
  every 
  one 
  of 
  them 
  at 
  the 
  earth 
  may 
  fall 
  within 
  the 
  

   durations 
  of 
  the 
  lights 
  of 
  all 
  the 
  others 
  at 
  the 
  earth. 
  My 
  

   supposition 
  as 
  to 
  uniform 
  density 
  is 
  quite 
  arbitrary 
  ; 
  but 
  

   nevertheless 
  I 
  think 
  it 
  highly 
  improbable 
  that 
  there 
  can 
  be 
  

   enough 
  of 
  stars 
  (bright 
  or 
  dark) 
  to 
  make 
  a 
  total 
  of 
  star-disc 
  

   area 
  more 
  than 
  10 
  -12 
  or 
  10~ 
  n 
  of 
  the 
  whole 
  sky. 
  

  

  To 
  help 
  to 
  understand 
  the 
  density 
  of 
  the 
  supposed 
  

   distribution 
  of 
  1000 
  million 
  suns 
  in 
  a 
  sphere 
  of 
  3'09,10 
  16 
  

   kilometres 
  radius, 
  imagine 
  them 
  arranged 
  exactly 
  in 
  cubic 
  

   order, 
  and 
  the 
  volume 
  per 
  sun 
  is 
  found 
  to 
  be 
  123*5. 
  10 
  39 
  cubic 
  

   kilometres, 
  and 
  the 
  distance 
  from 
  one 
  star 
  to 
  any 
  one 
  of 
  its 
  

   six 
  nearest 
  neighbours 
  would 
  be 
  4*98.10 
  13 
  kilometres 
  The 
  

   sun 
  seen 
  at 
  this 
  distance 
  would 
  probably 
  be 
  seen 
  as 
  a 
  star 
  of 
  

   between 
  the 
  first 
  and 
  second 
  magnitude 
  ; 
  but 
  supposing 
  our 
  

   1000 
  million 
  suns 
  to 
  be 
  ail 
  of 
  such 
  brightness 
  as 
  to 
  be 
  stars 
  

   of 
  the 
  first 
  magnitude 
  at 
  distance 
  corresponding 
  to 
  parallax 
  

   l^'O, 
  the 
  brightness 
  at 
  distance 
  3*09.10 
  16 
  kilometres 
  would 
  be 
  

   one 
  one-millionth 
  of 
  this 
  ; 
  and 
  the 
  most 
  distant 
  of 
  our 
  stars 
  

   would 
  be 
  seen 
  through 
  powerful 
  telescopes 
  as 
  stars 
  of 
  the 
  

  

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

  

  