﻿COUNTING 
  THE 
  STARS 
  — 
  SEARES 
  201 
  

  

  that 
  the 
  local 
  system 
  is 
  symmetrical 
  about 
  a 
  central 
  point, 
  or 
  at 
  

   least 
  that 
  it 
  is 
  not 
  highly 
  asymmetrical. 
  Stated 
  in 
  another 
  way^ 
  

   though 
  rather 
  crudely, 
  we 
  suppose 
  that 
  the 
  point 
  within 
  the 
  local 
  

   system 
  where 
  the 
  stars 
  are 
  thickest 
  is 
  not 
  far 
  from 
  its 
  geometrical 
  

   center. 
  Such 
  an 
  assumption 
  is 
  not 
  without 
  inherent 
  probability, 
  for 
  

   most 
  aggregations 
  of 
  stars 
  seen 
  in 
  the 
  sky 
  possess 
  a 
  rough 
  symmetry 
  

   of 
  this 
  kind; 
  and 
  within 
  the 
  local 
  cluster 
  itself, 
  in 
  the 
  nucleus 
  of 
  

   hehum 
  stars, 
  we 
  find 
  evidence 
  of 
  its 
  presence. 
  

  

  The 
  operations 
  involved 
  in 
  separating 
  the 
  local 
  and 
  larger 
  systems 
  

   are 
  illustrated 
  by 
  Figure 
  3, 
  where, 
  as 
  already 
  explained, 
  the 
  upper- 
  

   most 
  curve 
  represents 
  the 
  variation 
  in 
  the 
  number 
  of 
  stars 
  per 
  unit 
  

   volume 
  in 
  the 
  direction 
  of 
  the 
  center 
  and 
  of 
  the 
  point 
  diametrically 
  

   opposite. 
  From 
  the 
  densities 
  corresponding 
  to 
  this 
  curve 
  we 
  must 
  

   subtract 
  those 
  contributed 
  by 
  the 
  local 
  system. 
  By 
  the 
  assumption 
  

   just 
  made, 
  these 
  will 
  be 
  represented 
  by 
  a 
  curve, 
  nearly 
  symmetrical, 
  

   having 
  a 
  maximum 
  coinciding 
  closely 
  with 
  the 
  sun. 
  The 
  size 
  and 
  

   shape 
  of 
  the 
  curve 
  are 
  not 
  otherwise 
  specified, 
  and 
  the 
  choice 
  of 
  a 
  

   definite 
  form 
  is 
  beset 
  with 
  uncertainty. 
  Nevertheless, 
  certain 
  

   guiding 
  principles 
  may 
  be 
  laid 
  down: 
  Thus, 
  the 
  central 
  density 
  of 
  

   the 
  local 
  system, 
  represented 
  by 
  the 
  height 
  of 
  the 
  maximum 
  of 
  the 
  

   symmetrical 
  curve, 
  must 
  be 
  greater 
  than 
  some 
  minimum 
  value; 
  

   otherwise, 
  after 
  the 
  local 
  system 
  has 
  been 
  removed, 
  the 
  region 
  of 
  

   maximum 
  density 
  in 
  the 
  larger 
  system 
  will 
  remain 
  near 
  the 
  sun, 
  

   which 
  is 
  at 
  variance 
  with 
  all 
  our 
  ideas 
  as 
  to 
  the 
  structure 
  of 
  the 
  

   system. 
  On 
  the 
  other 
  hand, 
  the 
  central 
  density 
  of 
  the 
  local 
  system 
  

   can 
  not 
  exceed 
  a 
  certain 
  amount 
  without 
  leaving 
  in 
  the 
  larger 
  system, 
  

   close 
  to 
  the, 
  sun, 
  a 
  region 
  of 
  abnormally 
  low 
  density. 
  Finally, 
  the 
  

   relation 
  between 
  density 
  and 
  size 
  in 
  the 
  local 
  system 
  must 
  be 
  such 
  

   that 
  the 
  change 
  in 
  density 
  in 
  the 
  larger 
  system 
  revealed 
  by 
  removing 
  

   the 
  adopted 
  local 
  system 
  is 
  everywhere 
  smooth. 
  

  

  The 
  result 
  of 
  the 
  analysis 
  is 
  shown 
  by 
  the 
  two 
  component 
  curves 
  

   in 
  Figure 
  3. 
  Under 
  the 
  circumstances 
  described 
  we 
  should 
  scarcely 
  

   expect 
  more 
  than 
  a 
  qualitative 
  indication 
  of 
  relations; 
  nevertheless, 
  

   the 
  central 
  density 
  and 
  the 
  diameter 
  thus 
  found 
  for 
  the 
  local 
  system 
  

   are 
  in 
  general 
  numerical 
  agreement 
  with 
  the 
  results 
  derived 
  from 
  

   Figure 
  2, 
  namely, 
  a 
  density 
  of 
  three-fourths 
  the 
  total 
  near 
  the 
  sun 
  

   and 
  a 
  diameter 
  of 
  six 
  or 
  eight 
  thousand 
  parsecs. 
  Further, 
  the 
  curve 
  

   for 
  the 
  larger 
  system 
  shows 
  an 
  increase 
  in 
  the 
  density 
  in 
  the 
  direction 
  

   of 
  the 
  center, 
  as 
  we 
  should 
  expect, 
  but, 
  surprisingly 
  enough, 
  the 
  stars 
  

   seem 
  to 
  reach 
  their 
  highest 
  concentration 
  at 
  a 
  distance 
  of 
  only 
  3,000 
  

   to 
  6,000 
  light 
  years, 
  according 
  to 
  the 
  degree 
  of 
  asymmetry 
  admitted 
  

   in 
  the 
  local 
  system. 
  

  

  The 
  position 
  of 
  this 
  maximum 
  must 
  be 
  far 
  short 
  of 
  the 
  geometrical 
  

   center 
  of 
  the 
  system; 
  and 
  even 
  where 
  thickest, 
  the 
  concentration 
  

   of 
  stars 
  is 
  only 
  about 
  one-half 
  that 
  at 
  the 
  center 
  of 
  the 
  local 
  system. 
  

  

  