﻿190 
  ANNUAL 
  REPORT 
  SMITHSONIAN 
  INSTITUTION, 
  1929 
  

  

  is 
  less 
  than 
  fourfold 
  when 
  the 
  counts 
  are 
  extended 
  by 
  a 
  magnitude, 
  

   the 
  stars 
  must 
  thin 
  out 
  with 
  increasing 
  distance 
  from 
  the 
  point 
  of 
  

   observation; 
  further, 
  the 
  more 
  the 
  factor 
  drops 
  below 
  4, 
  the 
  faster 
  

   does 
  the 
  thinning 
  out 
  take 
  place. 
  

  

  Consider 
  now 
  more 
  in 
  detail 
  the 
  ratios 
  in 
  Table 
  II, 
  and 
  first, 
  those 
  

   in 
  the 
  second 
  column, 
  corresponding 
  to 
  directions 
  toward 
  the 
  Milky- 
  

   Way. 
  From 
  what 
  has 
  been 
  said 
  it 
  follows 
  that 
  the 
  brightest 
  of 
  

   these 
  stars 
  thin 
  out 
  with 
  increasing 
  distance, 
  while 
  the 
  faint 
  stars, 
  

   which, 
  as 
  a 
  whole, 
  are 
  at 
  much 
  greater 
  distances, 
  thin 
  out 
  even 
  more 
  

   rapidly. 
  Consider 
  now 
  the 
  last 
  column, 
  referring 
  to 
  the 
  direction 
  

   perpendicular 
  to 
  the 
  plane 
  of 
  the 
  Milky 
  Way. 
  Here 
  the 
  ratios 
  are 
  

   generally 
  smaller 
  than 
  those 
  standing 
  opposite 
  them 
  in 
  the 
  second 
  

   column, 
  which 
  leads 
  to 
  the 
  important 
  conclusion 
  that 
  the 
  stars 
  in 
  

   this 
  direction 
  not 
  only 
  thin 
  out, 
  but 
  thin 
  out 
  very 
  much 
  faster 
  than 
  

   they 
  do 
  toward 
  the 
  Milky 
  Way. 
  

  

  The 
  statement 
  that 
  the 
  stars 
  thin 
  out 
  with 
  increasing 
  distance 
  often 
  

   rouses 
  the 
  feehng 
  of 
  an 
  implied 
  contradiction 
  with 
  the 
  rapidly 
  in- 
  

   creasing 
  numbers 
  of 
  Table 
  I. 
  Discrimination 
  as 
  to 
  what 
  is 
  meant 
  

   sets 
  the 
  matter 
  straight, 
  however. 
  The 
  conclusion 
  that 
  the 
  stars 
  thin 
  

   out 
  means 
  only 
  that 
  the 
  number 
  of 
  stars 
  per 
  unit 
  volume 
  decreases 
  

   with 
  increasing 
  distance; 
  while 
  the 
  total 
  number 
  of 
  stars 
  counted 
  

   depends 
  on 
  the 
  density, 
  it 
  also 
  depends 
  on 
  how 
  many 
  units 
  of 
  volume 
  

   are 
  included. 
  Thus 
  in 
  the 
  case 
  of 
  the 
  candles, 
  the 
  extension 
  of 
  the 
  

   counts 
  by 
  one 
  magnitude 
  gives 
  a 
  total 
  which 
  includes 
  all 
  the 
  candles 
  

   in 
  a 
  volume 
  four 
  times 
  that 
  which 
  the 
  eye 
  alone 
  can 
  survey. 
  The 
  

   additional 
  volume 
  made 
  accessible 
  by 
  the 
  extension 
  is 
  therefore 
  three 
  

   times 
  that 
  already 
  known 
  to 
  the 
  unaided 
  eye; 
  the 
  density 
  of 
  candles 
  

   in 
  the 
  added 
  volume 
  might 
  therefore 
  drop 
  to 
  one-third 
  that 
  near 
  the 
  

   center 
  of 
  the 
  collection 
  and 
  the 
  total 
  number 
  visible 
  would 
  still 
  be 
  

   doubled 
  by 
  extending 
  the 
  counts. 
  

  

  In 
  brief, 
  therefore, 
  Table 
  II 
  indicates 
  that 
  the 
  stars 
  of 
  our 
  system 
  

   are 
  not 
  equally 
  scattered 
  in 
  space, 
  but 
  thin 
  out 
  in 
  all 
  directions 
  with 
  

   increasing 
  distance 
  from 
  the 
  point 
  at 
  which 
  we 
  make 
  our 
  observations, 
  

   least 
  rapidly 
  in 
  directions 
  toward 
  the 
  Milky 
  Way 
  and 
  fastest 
  in 
  a 
  

   direction 
  perpendicular 
  to 
  its 
  plane. 
  

  

  The 
  table 
  also 
  suggests 
  another 
  inference 
  with 
  respect 
  to 
  the 
  stellar 
  

   system 
  in 
  that 
  the 
  ratios 
  steadily 
  decrease 
  as 
  the 
  magnitude 
  hmit 
  is 
  

   extended 
  downward. 
  If 
  this 
  decrease 
  continues 
  for 
  stars 
  beyond 
  the 
  

   reach 
  of 
  existing 
  telescopes, 
  the 
  ratios 
  themselves 
  must 
  eventually 
  

   become 
  zero. 
  Hence 
  for 
  some 
  low 
  limit 
  of 
  brightness 
  no 
  more 
  stars 
  

   will 
  be 
  added 
  when 
  we 
  attempt 
  to 
  extend 
  the 
  counts 
  to 
  a 
  still 
  lower 
  

   limit; 
  the 
  total 
  number 
  of 
  stars 
  in 
  the 
  system 
  is 
  therefore 
  limited. 
  

  

  The 
  evidence 
  afforded 
  by 
  star 
  counts 
  alone 
  does 
  not 
  fully 
  estabhsh 
  

   this 
  inference 
  as 
  a 
  fact, 
  for 
  the 
  counts 
  do 
  not 
  indicate 
  with 
  certainty 
  

   the 
  relations 
  among 
  fainter 
  and 
  still 
  undiscovered 
  stars; 
  the 
  extra- 
  

  

  