﻿MODERN 
  ASTRONOMY 
  ABBOT 
  

  

  151 
  

  

  Thus 
  the 
  total 
  numbers 
  of 
  stars 
  brighter 
  than 
  a 
  given 
  magnitude 
  

   increase 
  nearly 
  by 
  ratios 
  of 
  3.0-fold 
  as 
  we 
  pass 
  from 
  step 
  to 
  step, 
  

   until 
  we 
  come 
  down 
  to 
  stars 
  of 
  magnitude 
  9, 
  which 
  are 
  some 
  fifty 
  

   times 
  fainter 
  than 
  the 
  naked 
  eye 
  can 
  see. 
  Then 
  the 
  ratio 
  of 
  increase 
  

   grows 
  steadily 
  smaller 
  until 
  at 
  the 
  nineteenth 
  magnitude 
  the 
  ratio 
  

   has 
  diminished 
  to 
  1.9. 
  The 
  relation 
  of 
  this 
  ratio 
  of 
  increase 
  to 
  the 
  

   magnitude 
  number 
  may 
  be 
  expressed 
  by 
  a 
  suitable 
  formula. 
  

  

  With 
  this 
  mathematical 
  expression 
  it 
  is 
  easily 
  possible 
  to 
  proceed 
  

   beyond 
  the 
  twentieth 
  magnitude 
  to 
  integrate 
  the 
  probable 
  numbers 
  

   of 
  stars, 
  on 
  the 
  assumption 
  that 
  this 
  formula, 
  which 
  holds 
  so 
  well 
  

   down 
  to 
  the 
  faintest 
  telescopic 
  magnitudes, 
  still 
  continues 
  to 
  retain 
  

   its 
  validity 
  beyond. 
  In 
  this 
  loay 
  Scares 
  has 
  comfuted 
  tJiat 
  our 
  galaxy 
  

   of 
  stars 
  prohaJjly 
  contains 
  about 
  SOpoOpoOpOO 
  stars^ 
  or 
  some 
  twenty 
  

   times 
  as 
  many 
  stars 
  as 
  t/iere 
  are 
  living 
  human 
  inhahifants 
  of 
  the 
  

   earth. 
  

  

  Looking 
  in 
  the 
  direction 
  of 
  the 
  constellations 
  of 
  Cassiopeia, 
  

   Aquila, 
  Sagittarius, 
  and 
  Crux, 
  we 
  see 
  the 
  hazy 
  brightness 
  of 
  the 
  

   milky 
  way, 
  which, 
  when 
  examined 
  with 
  a 
  telescope, 
  resolves 
  itself 
  

   into 
  a 
  multitude 
  of 
  stars. 
  The 
  milky 
  way 
  is 
  easily 
  seen 
  to 
  be 
  a 
  

   nearly 
  flat 
  ring, 
  extending 
  completely 
  around 
  the 
  heavens, 
  and 
  is 
  

   frequently 
  taken 
  as 
  the 
  datum 
  plane 
  from 
  which 
  to 
  chart 
  star 
  posi- 
  

   tions. 
  Thus 
  astronomers 
  speak 
  of 
  galactic 
  latitude 
  and 
  longitude. 
  

  

  If 
  the 
  average 
  number 
  of 
  stars 
  per 
  square 
  degree 
  brighter 
  than 
  

   a 
  given 
  magnitude 
  are 
  classified 
  with 
  reference 
  to 
  their 
  galactic 
  lati- 
  

   tudes, 
  it 
  is 
  immediately 
  seen 
  that 
  toward 
  the 
  galactic 
  poles 
  they 
  are 
  

   few 
  compared 
  to 
  the 
  numbers 
  near 
  or 
  in 
  the 
  galaxy 
  itself. 
  In 
  the 
  

   following 
  table 
  (after 
  Seares 
  and 
  van 
  Rliijn) 
  this 
  information 
  is 
  

   collected 
  : 
  

  

  Table 
  2. 
  — 
  Galactic 
  concentration 
  of 
  the 
  stars 
  

  

  NUMBERS 
  OF 
  STARS 
  PER 
  SQUARE 
  DEGREE 
  BRIGHTER 
  THAN 
  A 
  GIVEN 
  PnOTO- 
  

  

  GRAPHIC 
  MAGNITUDE 
  

  

  Naked-eye 
  stars 
  are 
  three 
  times 
  as 
  concentrated 
  in 
  the 
  milky 
  way 
  

   as 
  at 
  its 
  poles. 
  But 
  for 
  very 
  faint 
  stars 
  the 
  ratio 
  of 
  concentration 
  is 
  

   thirtyfold. 
  

  

  How 
  shall 
  we 
  explain 
  this 
  inequality 
  of 
  distribution 
  of 
  the 
  stars 
  

   and 
  more 
  especially 
  of 
  faint 
  ones? 
  Either 
  their 
  ranks 
  extend 
  much 
  

  

  