﻿COUNTING 
  THE 
  STARS 
  SEARES 
  185 
  

  

  compared 
  with 
  the 
  eleventh, 
  is 
  100X100 
  or 
  10,000 
  times 
  as 
  intense; 
  

   if 
  we 
  extend 
  the 
  scale 
  downward 
  another 
  10 
  magnitudes, 
  which 
  brings 
  

   us 
  to 
  the 
  practicable 
  working 
  limit 
  of 
  large 
  modern 
  telescopes, 
  the 
  

   intensity 
  ratio 
  takes 
  on 
  another 
  factor 
  of 
  10,000, 
  and 
  we 
  have 
  for 
  the 
  

   interval 
  of 
  20 
  magnitudes 
  a 
  ratio 
  of 
  100,000,000 
  to 
  1. 
  The 
  light 
  of 
  

   a 
  first-magnitude 
  star 
  is 
  thus 
  1 
  00,000,000 
  times 
  as 
  intense 
  as 
  that 
  of 
  a 
  

   star 
  of 
  the 
  twenty-first 
  magnitude. 
  The 
  numbers 
  involved 
  are 
  to 
  

   each 
  other 
  about 
  as 
  the 
  distance 
  separating 
  California 
  from 
  New 
  

   York 
  is 
  to 
  a 
  length 
  of 
  two 
  inches. 
  

  

  The 
  construction 
  of 
  the 
  magnitude 
  scale 
  therefore 
  requires 
  the 
  

   ultimate 
  comparison 
  of 
  sources 
  of 
  light 
  differing 
  by 
  an 
  enormous 
  

   ratio; 
  in 
  part, 
  the 
  undertaking 
  is 
  analogous 
  to 
  finding 
  how 
  many 
  

   times 
  a 
  length 
  of 
  two 
  inches 
  is 
  contained 
  in 
  a 
  distance 
  of 
  about 
  3,000 
  

   miles, 
  without 
  having 
  even 
  a 
  foot 
  rule 
  or 
  an 
  engineer's 
  chain 
  to 
  start 
  

   the 
  measurement. 
  Actually 
  the 
  photometric 
  probleni 
  is 
  far 
  the 
  more 
  

   troublesome, 
  for 
  the 
  unavoidable 
  error 
  in 
  measuring 
  the 
  intensity 
  of 
  

   a 
  light 
  is 
  much 
  greater, 
  proportionally, 
  than 
  that 
  involved 
  in 
  measur- 
  

   ing 
  a 
  length. 
  Indeed 
  it 
  is 
  so 
  much 
  the 
  more 
  difficult 
  that, 
  although 
  

   the 
  concept 
  and 
  definition 
  of 
  the 
  magnitude 
  scale 
  have 
  been 
  clear 
  

   enough 
  for 
  many 
  years, 
  it 
  is 
  only 
  recently 
  that 
  some 
  approach 
  to 
  

   practical 
  realization 
  has 
  been 
  made 
  in 
  the 
  attempt 
  to 
  fix 
  standard 
  

   limits 
  of 
  brightness 
  within 
  which 
  the 
  stars 
  may 
  be 
  counted. 
  

  

  Before 
  turning 
  to 
  the 
  results 
  of 
  counting, 
  the 
  impossibility 
  of 
  

   counting 
  all 
  the 
  stars 
  must 
  be 
  noted. 
  The 
  whole 
  sky 
  over, 
  about 
  

   6,000 
  stars 
  may 
  be 
  seen 
  without 
  a 
  telescope; 
  but 
  among 
  the 
  fainter 
  

   stars 
  the 
  numbers 
  run 
  into 
  millions 
  and 
  hundreds 
  of 
  millions. 
  For 
  

   these 
  even 
  the 
  simplest 
  enumeration 
  would 
  be 
  impossible, 
  whereas 
  

   much 
  more 
  than 
  simple 
  enumeration 
  is 
  required. 
  In 
  order 
  to 
  specify 
  

   the 
  group 
  with 
  which 
  any 
  star 
  is 
  to 
  be 
  counted, 
  the 
  scale 
  of 
  magni- 
  

   tudes 
  must 
  be 
  applied 
  to 
  the 
  star 
  to 
  measure 
  its 
  brightness, 
  much 
  as 
  a 
  

   yardstick 
  might 
  be 
  applied 
  to 
  a 
  man 
  to 
  determine 
  his 
  height. 
  Only 
  

   when 
  this 
  has 
  been 
  done 
  can 
  it 
  be 
  said 
  that 
  the 
  star 
  belongs 
  with 
  those 
  

   whose 
  magnitudes 
  are 
  between, 
  say, 
  10.0 
  and 
  10.5. 
  But 
  measure- 
  

   ments 
  of 
  brightness 
  take 
  time. 
  At 
  Potsdam 
  Miiller 
  and 
  Kempf 
  

   spent 
  19 
  years 
  in 
  deriving 
  the 
  magnitudes 
  of 
  14,000 
  stars. 
  At 
  Mount 
  

   Wilson 
  we 
  have 
  measured 
  some 
  70,000 
  stars; 
  but 
  even 
  with 
  modern 
  

   photographic 
  methods, 
  the 
  labor 
  involved 
  represents 
  the 
  continuous 
  

   occupation 
  of 
  several 
  people 
  for 
  a 
  number 
  of 
  years. 
  

  

  To 
  avoid 
  a 
  task 
  that 
  could 
  never 
  be 
  ended, 
  we 
  follow 
  the 
  plan 
  first 
  

   used 
  for 
  the 
  star 
  gauges 
  of 
  the 
  Herschels 
  and 
  count 
  only 
  stars 
  in 
  

   representative 
  regions 
  of 
  the 
  sky. 
  We 
  deal 
  with 
  samples 
  of 
  stars, 
  

   just 
  as 
  the 
  census 
  taker, 
  if 
  pressed 
  for 
  time, 
  might 
  count 
  the 
  inhabit- 
  

   ants 
  of 
  only 
  every 
  other 
  block, 
  or 
  perhaps 
  of 
  every 
  fifth 
  block, 
  of 
  a 
  

   great 
  city 
  like 
  New 
  York, 
  and 
  still 
  arrive 
  at 
  useful 
  conclusions 
  about 
  

   the 
  population 
  of 
  the 
  city 
  as 
  a 
  whole. 
  In 
  any 
  such 
  restriction 
  of 
  

  

  