﻿COUNTING 
  THE 
  STARS 
  SEAEES 
  191 
  

  

  polation 
  is 
  too 
  great. 
  The 
  conclusion 
  itself, 
  however, 
  is 
  well 
  founded, 
  

   but 
  the 
  proof 
  comes 
  from 
  evidence 
  other 
  than 
  star 
  counts. 
  This 
  

   being 
  the 
  case, 
  we 
  may 
  accept 
  the 
  conclusion 
  and 
  thus 
  arrive 
  at 
  the 
  

   certain 
  result 
  that 
  the 
  numbers 
  in 
  Table 
  II 
  would 
  eventually 
  become 
  

   zero 
  were 
  the 
  table 
  sufficiently 
  extended. 
  

  

  If 
  the 
  limiting 
  magnitude 
  for 
  which 
  this 
  occurs 
  were 
  accurately 
  

   known, 
  we 
  should 
  be 
  able 
  to 
  estimate 
  with 
  fair 
  approximation 
  the 
  

   total 
  number 
  of 
  stars 
  in 
  the 
  system. 
  As 
  it 
  is, 
  we 
  know 
  that 
  such 
  

   a 
  limit 
  exists, 
  but 
  the 
  only 
  guide 
  to 
  its 
  value 
  is 
  the 
  rate 
  of 
  decrease 
  

   in 
  the 
  ratios 
  of 
  Table 
  II. 
  This 
  rate 
  is 
  slow, 
  and 
  as 
  the 
  ratios 
  for 
  the 
  

   faintest 
  stars 
  known 
  are 
  still 
  rather 
  large, 
  the 
  magnitudes 
  for 
  which 
  

   they 
  become 
  zero, 
  in 
  different 
  directions 
  in 
  the 
  sky, 
  are 
  very 
  uncertain. 
  

  

  Any 
  attempt 
  to 
  learn 
  the 
  total 
  number 
  of 
  stars 
  in 
  the 
  system 
  by 
  

   extrapolating 
  Table 
  II 
  can 
  therefore 
  lead 
  only 
  to 
  the 
  roughest 
  sort 
  

   of 
  an 
  estimate. 
  About 
  a 
  thousand 
  million 
  stars 
  are 
  within 
  reach 
  of 
  

   the 
  100-inch 
  reflector. 
  If 
  the 
  invisible 
  stars 
  behave 
  as 
  those 
  acces- 
  

   sible 
  to 
  observation 
  would 
  lead 
  us 
  to 
  expect, 
  the 
  total 
  number 
  in 
  

   the 
  system 
  must 
  be 
  some 
  thirty 
  times 
  greater, 
  or 
  of 
  the 
  order 
  of 
  

   30,000,000,000. 
  The 
  uncertainty 
  of 
  this 
  result 
  is 
  illustrated 
  by 
  the 
  

   fact 
  that 
  the 
  estimated 
  total 
  in 
  the 
  direction 
  of 
  the 
  Milky 
  Way 
  is 
  

   about 
  seventy 
  times 
  the 
  number 
  of 
  stars 
  actually 
  counted. 
  

  

  The 
  stellar 
  system 
  thus 
  appears 
  to 
  be 
  a 
  limited 
  collection 
  includ- 
  

   ing 
  many 
  thousand 
  million 
  stars; 
  as 
  a 
  first 
  approximation 
  it 
  may 
  

   be 
  thought 
  of 
  as 
  having 
  the 
  form 
  of 
  a 
  much-flattened 
  swarm 
  of 
  bees, 
  

   with 
  the 
  densest 
  part 
  of 
  the 
  swarm 
  at 
  the 
  center. 
  The 
  rate 
  at 
  which 
  

   the 
  stars 
  thin 
  out 
  in 
  different 
  directions 
  shows 
  that 
  the 
  greatest 
  

   extent 
  of 
  the 
  system 
  is 
  in 
  the 
  direction 
  of 
  the 
  Milky 
  Way 
  and 
  equal 
  

   to 
  some 
  six 
  or 
  seven 
  times 
  its 
  thickness. 
  The 
  actual 
  linear 
  dimen- 
  

   sions 
  are 
  very 
  uncertain. 
  Indeed 
  they 
  lie 
  outside 
  the 
  conclusions 
  

   that 
  may 
  be 
  derived 
  from 
  star 
  counts 
  alone; 
  but 
  for 
  completeness 
  it 
  

   may 
  be 
  added 
  that 
  two 
  or 
  three 
  lines 
  of 
  evidence 
  suggest 
  values 
  of 
  two 
  

   to 
  three 
  hundred 
  thousand 
  light 
  years 
  for 
  the 
  diameter 
  in 
  the 
  plane 
  

   of 
  the 
  Milky 
  Way, 
  although 
  even 
  larger 
  values 
  are 
  by 
  no 
  means 
  

   excluded. 
  The 
  gradual 
  thinning 
  out 
  of 
  the 
  stars 
  probably 
  means 
  

   that 
  no 
  sharply 
  marked 
  boundary 
  exists, 
  just 
  as 
  none 
  exists 
  for 
  the 
  

   upper 
  hmit 
  of 
  the 
  earth's 
  atmosphere. 
  Star 
  counts, 
  supplemented 
  

   by 
  other 
  information, 
  do 
  tell 
  us, 
  however, 
  something 
  about 
  the 
  

   distance 
  at 
  which 
  the 
  number 
  of 
  stars 
  per 
  unit 
  of 
  volume 
  drops 
  to 
  

   a 
  given 
  value, 
  say 
  to 
  1 
  per 
  cent 
  of 
  what 
  it 
  is 
  in 
  our 
  own 
  neighborhood. 
  

   Thus 
  we 
  should 
  probably 
  have 
  to 
  travel 
  out 
  in 
  the 
  direction 
  of 
  the 
  

   Milky 
  Way 
  at 
  least 
  30,000 
  light 
  years, 
  on 
  the 
  average, 
  before 
  we 
  

   reached 
  the 
  point 
  at 
  which 
  the 
  stars 
  had 
  thinned 
  out 
  to 
  this 
  extent. 
  

   In 
  the 
  direction 
  perpendicular 
  to 
  the 
  Milky 
  Way 
  the 
  distance 
  would 
  

   be 
  much 
  less 
  — 
  perhaps 
  4,000 
  or 
  5,000 
  light 
  years. 
  

  

  