﻿184 
  ANNUAL 
  REPORT 
  SMITHSONIAN 
  INSTITUTION, 
  19 
  2 
  9 
  

  

  The 
  sky 
  has 
  no 
  naturally 
  marked 
  boundaries 
  within 
  which 
  the 
  stars 
  

   may 
  be 
  counted 
  and 
  intercompared; 
  but 
  as 
  far 
  as 
  direction 
  is 
  con- 
  

   cerned, 
  it 
  is 
  easy 
  to 
  find 
  how 
  many 
  stars 
  there 
  are, 
  say 
  per 
  square 
  

   degree 
  of 
  the 
  sky, 
  in 
  different 
  parts 
  of 
  the 
  heavens. 
  The 
  counting 
  

   of 
  stars 
  according 
  to 
  brightness, 
  however, 
  is 
  another 
  matter. 
  

  

  The 
  practical 
  difficulty, 
  as 
  already 
  stated, 
  hes 
  in 
  recognizing 
  the 
  

   limits 
  of 
  brightness 
  within 
  which 
  the 
  stars 
  are 
  to 
  be 
  counted. 
  To 
  

   overcome 
  this, 
  a 
  scale 
  of 
  brightness 
  is 
  required, 
  with 
  which 
  individual 
  

   stars 
  may 
  be 
  matched 
  to 
  determine 
  their 
  light; 
  for 
  example, 
  a 
  sequence 
  

   of 
  stars, 
  progressing 
  by 
  known 
  steps, 
  from 
  the 
  most 
  brilliant 
  in 
  the 
  sky 
  

   to 
  the 
  faintest 
  seen 
  in 
  our 
  telescopes. 
  Whatever 
  the 
  procedure 
  

   adopted, 
  it 
  is 
  essential 
  that 
  the 
  unit 
  of 
  measurement 
  be 
  known 
  in 
  terms 
  

   of 
  the 
  intensity 
  of 
  star 
  light, 
  because 
  the 
  intensity 
  of 
  the 
  light 
  re- 
  

   ceived 
  by 
  the 
  eye 
  depends 
  partly 
  on 
  the 
  distances 
  of 
  the 
  stars, 
  and 
  

   distances 
  we 
  wish 
  very 
  much 
  to 
  know. 
  Initially, 
  no 
  such 
  scale 
  

   existed, 
  and 
  one 
  had 
  to 
  be 
  constructed. 
  

  

  The 
  earliest 
  records 
  of 
  the 
  brightness 
  of 
  stars, 
  which 
  go 
  back 
  1,800 
  

   years 
  to 
  the 
  Alexandrian 
  astronomer 
  Ptolemy, 
  represent 
  rough 
  eye 
  

   estimates, 
  expressed 
  in 
  a 
  unit 
  called 
  a 
  magnitude. 
  To 
  the 
  brightest 
  

   stars 
  Ptolemy 
  assigned 
  the 
  first 
  magnitude; 
  to 
  those 
  just 
  visible 
  to 
  the 
  

   unaided 
  eye, 
  the 
  sixth 
  magnitude; 
  and 
  to 
  stars 
  of 
  intermediate 
  bright- 
  

   ness, 
  magnitudes 
  2, 
  3, 
  4, 
  and 
  5. 
  When 
  the 
  invention 
  of 
  the 
  telescope 
  

   brought 
  fainter 
  stars 
  into 
  view, 
  Ptolemy's 
  scale 
  was 
  extended, 
  still 
  by 
  

   simple 
  eye 
  estimates. 
  At 
  length, 
  about 
  a 
  century 
  ago, 
  instruments 
  for 
  

   measuring 
  the 
  intensity 
  of 
  a 
  star's 
  light 
  were 
  devised, 
  and 
  then 
  for 
  

   the 
  first 
  time 
  the 
  physical 
  equivalent 
  of 
  the 
  unit 
  of 
  magnitude 
  became 
  

   clear. 
  At 
  this 
  point 
  it 
  must 
  be 
  noted 
  that 
  magnitude 
  is 
  a 
  measure 
  

   of 
  visual 
  sensation 
  — 
  a 
  very 
  different 
  thing 
  from 
  the 
  intensity 
  of 
  the 
  

   light 
  which 
  produces 
  the 
  sensation. 
  On 
  measurement 
  it 
  turned 
  out 
  

   that 
  the 
  intensity 
  of 
  Ptolemy's 
  first-magnitude 
  stars 
  was 
  about 
  one 
  

   hundred 
  times 
  that 
  of 
  stars 
  of 
  the 
  sixth 
  magnitude, 
  and 
  for 
  conven- 
  

   ience 
  the 
  simple 
  relation 
  thus 
  approximately 
  satisfied 
  by 
  Ptolemy's 
  

   magnitudes 
  was 
  adopted 
  as 
  a 
  precise 
  definition 
  of 
  the 
  unit 
  of 
  magni- 
  

   tude. 
  As 
  now 
  used, 
  therefore, 
  the 
  unit 
  is 
  such 
  that 
  a 
  difference 
  of 
  five 
  

   magnitudes 
  corresponds 
  exactly 
  to 
  a 
  ratio 
  of 
  100 
  to 
  1 
  in 
  the 
  intensities, 
  

   whence 
  a 
  difference 
  in 
  brightness 
  of 
  one 
  magnitude 
  is 
  equivalent 
  to 
  an 
  

   intensity 
  ratio 
  of 
  2.512. 
  A 
  further 
  detail 
  is 
  the 
  beginning, 
  or 
  zero 
  

   point 
  of 
  the 
  scale 
  of 
  magnitudes, 
  which 
  must 
  be 
  the 
  same 
  everywhere 
  

   in 
  the 
  sky, 
  if 
  the 
  measures 
  of 
  brightness 
  in 
  different 
  parts 
  of 
  the 
  heav- 
  

   ens 
  are 
  to 
  be 
  comparable. 
  Again 
  for 
  convenience, 
  the 
  zero 
  point 
  

   adopted 
  was 
  such 
  that 
  the 
  precisely 
  defined 
  magnitudes 
  agree 
  as 
  

   closely 
  as 
  possible 
  with 
  the 
  old 
  values 
  obtained 
  by 
  eye 
  estimates. 
  

  

  Note 
  now 
  how 
  this 
  definition 
  appUes 
  to 
  faint 
  stars. 
  It 
  means 
  that 
  

   a 
  sixth-magnitude 
  star 
  is 
  one 
  hundred 
  times 
  as 
  intense 
  as 
  one 
  of 
  the 
  

   eleventh 
  magnitude, 
  and 
  hence, 
  that 
  the 
  first-magnitude 
  star, 
  as 
  

  

  