﻿186 
  AN-NUAL 
  REPORT 
  SMITHSONIAN" 
  INSTITUTION, 
  192 
  9 
  

  

  the 
  counting 
  the 
  samples 
  must 
  really 
  represent 
  the 
  whole, 
  a 
  condition 
  

   satisfied 
  in 
  practice 
  by 
  counting 
  regions 
  uniformly 
  distributed 
  over 
  

   the 
  sky, 
  and, 
  by 
  using 
  areas 
  that 
  are 
  not 
  too 
  small. 
  In 
  general, 
  

   much 
  smaller 
  areas 
  ma}^ 
  be 
  used 
  in 
  counting 
  faint 
  stars 
  than 
  for 
  stars 
  

   of 
  moderate 
  brightness. 
  Thus, 
  for 
  the 
  very 
  faint 
  stars 
  counted 
  at 
  

   Mount 
  Wilson 
  the 
  sample 
  regions 
  are 
  so 
  small 
  that 
  their 
  total 
  area 
  

   is 
  less 
  than 
  a 
  thousandth 
  part 
  of 
  the 
  sky. 
  Notwithstanding 
  the 
  gen- 
  

   eral 
  sufficiency 
  of 
  small 
  sample 
  regions, 
  it 
  must 
  not 
  be 
  supposed 
  that 
  

   the 
  resulting 
  counts 
  are 
  free 
  from 
  statistical 
  irregularities. 
  They 
  are 
  

   not; 
  but 
  those 
  present 
  are 
  chiefly 
  of 
  a 
  local 
  character, 
  and 
  may 
  be 
  

   smoothed 
  out 
  by 
  averaging 
  the 
  counts 
  in 
  several 
  neighboring 
  regions. 
  

  

  II 
  

  

  THE 
  GENERAL 
  FORM 
  OF 
  THE 
  STELLAR 
  SYSTEM 
  

  

  From 
  these 
  general 
  considerations, 
  we 
  turn 
  to 
  some 
  of 
  the 
  results 
  

   of 
  counting, 
  noting 
  at 
  once 
  an 
  important 
  conclusion 
  which 
  follows, 
  

   not 
  from 
  the 
  actual 
  numbers 
  of 
  stars 
  counted, 
  but 
  from 
  the 
  size 
  of 
  

   the 
  sample 
  regions 
  which 
  is 
  sufficient 
  for 
  the 
  counting. 
  If 
  counts 
  

   covering 
  a 
  total 
  area 
  of 
  only 
  a 
  thousandth 
  of 
  the 
  whole 
  sky 
  give 
  

   useful 
  information, 
  then 
  the 
  stellar 
  system 
  must 
  possess 
  much 
  struc- 
  

   tural 
  unity 
  and 
  regularity. 
  Otherwise, 
  small 
  sample 
  regions 
  chosen 
  

   at 
  random 
  could 
  not 
  reveal 
  as 
  they 
  do 
  the 
  underlying 
  structural 
  

   features 
  of 
  the 
  system. 
  

  

  The 
  first 
  peculiarity 
  to 
  be 
  noted 
  in 
  the 
  counts 
  themselves 
  is 
  the 
  

   extraordinary 
  rapidity 
  with 
  which 
  the 
  numbers 
  of 
  stars 
  increase 
  as 
  

   we 
  pass 
  to 
  fainter 
  and 
  fainter 
  limits 
  of 
  brightness. 
  Four 
  photographs 
  

   of 
  the 
  same 
  region 
  (pi. 
  1), 
  exposed 
  just 
  long 
  enough 
  to 
  show 
  stars 
  

   brighter 
  than 
  the 
  twelfth, 
  fifteenth, 
  eighteenth, 
  and 
  twentieth 
  magni- 
  

   tudes, 
  respectively, 
  are 
  perhaps 
  as 
  impressive 
  as 
  the 
  numbers 
  them- 
  

   selves. 
  

  

  Another 
  peculiarity 
  is 
  that 
  the 
  stars 
  are 
  most 
  numerous 
  in 
  the 
  

   Milky 
  Way 
  and 
  decrease 
  in 
  numbers 
  as 
  we 
  count 
  in 
  regions 
  more 
  and 
  

   more 
  distant, 
  in 
  either 
  direction, 
  from 
  this 
  cloud-like 
  band 
  which 
  

   encircles 
  the 
  sky. 
  This 
  also 
  is 
  well 
  shown 
  by 
  photographs 
  (pi. 
  2) 
  

   which 
  record 
  stars 
  to 
  the 
  same 
  limit 
  of 
  brightness 
  in 
  the 
  two 
  regions, 
  

   one 
  in 
  the 
  Milky 
  Way 
  itself, 
  the 
  other 
  far 
  distant 
  therefrom. 
  The 
  

   phenomenon 
  is 
  so 
  striking, 
  and 
  the 
  changes 
  in 
  the 
  numbers 
  on 
  the 
  

   two 
  sides 
  of 
  the 
  Milky 
  Way 
  are 
  so 
  similar, 
  that 
  it 
  suggests, 
  as 
  it 
  

   did 
  to 
  Sir 
  William 
  Herschel, 
  a 
  symmetrical 
  arrangement 
  of 
  the 
  stars 
  

   about 
  the 
  plane 
  passing 
  through 
  the 
  Milky 
  Way 
  clouds. 
  The 
  regu- 
  

   larity 
  of 
  the 
  system 
  already 
  inferred 
  from 
  the 
  sufficiency 
  of 
  small 
  

   sample 
  regions 
  as 
  an 
  indication 
  of 
  stellar 
  distribution 
  thus 
  becomes 
  

   the 
  regularity 
  of 
  a 
  symmetrical 
  arrangement 
  in 
  which 
  the 
  Milky 
  

   Way 
  stands 
  out 
  as 
  the 
  framework 
  of 
  the 
  system. 
  

  

  