﻿154 
  ANNUAL 
  REPORT 
  SMITHSONIAN 
  INSTITUTION, 
  1927 
  

  

  orbits. 
  However, 
  it 
  is 
  not 
  of 
  such 
  close 
  double 
  stars 
  as 
  the 
  eclipsinu; 
  

   iind 
  the 
  spectroscopic 
  binaries 
  that 
  distances 
  are 
  determined, 
  but 
  of 
  

   the 
  numerous 
  pairs 
  of 
  stars 
  seen 
  telescopically 
  separate, 
  and 
  ob- 
  

   served 
  sufficiently 
  long 
  to 
  trace 
  a 
  considerable 
  part 
  of 
  their 
  apparent 
  

   orbits 
  in 
  the 
  heavens. 
  

  

  In 
  such 
  cases 
  the 
  law 
  of 
  Kepler, 
  which 
  is 
  a 
  consequence 
  of 
  New- 
  

   ton's 
  law, 
  informs 
  us: 
  Mi+M2=AVP- 
  where 
  Mi 
  and 
  Mj 
  are 
  the 
  

   masses 
  of 
  the 
  two 
  stars 
  compared 
  to 
  the 
  earth 
  plus 
  the 
  sun. 
  A, 
  the 
  

   semiaxis 
  of 
  their 
  orbit 
  in 
  terms 
  of 
  the 
  semiaxis 
  of 
  the 
  earth's 
  orbit, 
  

   and 
  P 
  the 
  period 
  of 
  rotation 
  measured 
  in 
  years. 
  If 
  M^ 
  + 
  Mo 
  were 
  

   known, 
  A 
  could 
  be 
  computed. 
  Fortunately 
  the 
  study 
  of 
  eclipsing 
  

   and 
  spectroscopic 
  binaries 
  has 
  proved 
  that 
  for 
  most 
  double 
  stars 
  

   (he 
  combined 
  masses 
  differ 
  little 
  from 
  double 
  the 
  mass 
  of 
  the 
  earth 
  

   and 
  sun. 
  Hence 
  it 
  is 
  assumed 
  in 
  this 
  method 
  of 
  obtaining 
  star 
  

   distances 
  that 
  Mi+M2=2. 
  

  

  If 
  so 
  A 
  = 
  v/2P 
  

  

  Inasmuch 
  as 
  the 
  factor 
  of 
  the 
  combined 
  mass 
  enters 
  in 
  the 
  cube 
  

   root, 
  the 
  result 
  w^ould 
  be 
  only 
  100 
  per 
  cent 
  in 
  error 
  if 
  M^ 
  + 
  Mo 
  were 
  

   really 
  16 
  instead 
  of 
  2, 
  so 
  that 
  measurements 
  of 
  A, 
  made 
  in 
  this 
  

   manner, 
  are 
  generally 
  of 
  comparatively 
  high 
  accuracy. 
  Since 
  the 
  

   angular 
  measure 
  of 
  A 
  is 
  readily 
  observed 
  with 
  the 
  telescope, 
  the 
  

   star's 
  distance 
  from 
  the 
  earth 
  corresponding 
  to 
  the 
  linear 
  measure 
  

   found 
  by 
  the 
  application 
  of 
  Kepler's 
  law 
  follows 
  immediately. 
  

   Nearly 
  1,000 
  stellar 
  distances 
  have 
  been 
  determined 
  by 
  this, 
  the 
  

   so-called 
  " 
  dynamical 
  " 
  method. 
  

  

  A 
  still 
  more 
  fruitful 
  means 
  of 
  measuring 
  star 
  distances 
  depends 
  

   on 
  a 
  close 
  scrutiny 
  of 
  certain 
  absorption 
  lines 
  in 
  their 
  photographic 
  

   spectra. 
  In 
  the 
  latter 
  years 
  of 
  the 
  nineteenth 
  century 
  the 
  spectra 
  of 
  

   the 
  stars 
  were 
  arranged 
  at 
  the 
  Harvard 
  College 
  Observatory 
  in 
  cer- 
  

   tain 
  great 
  classes 
  called 
  B, 
  A, 
  F, 
  G, 
  K, 
  M, 
  ranging 
  from 
  the 
  blue 
  stars 
  

   of 
  type 
  B, 
  through 
  the 
  solar 
  stars 
  of 
  type 
  G, 
  to 
  the 
  red, 
  or 
  Antarian 
  

   stars 
  of 
  type 
  M. 
  Certain 
  gradations 
  of 
  these 
  great 
  classes 
  are 
  recog- 
  

   nized, 
  such 
  as 
  B5, 
  meaning 
  a 
  type 
  half 
  way 
  between 
  the 
  most 
  extreme, 
  

   or 
  BO 
  stars, 
  and 
  the 
  most 
  extreme 
  varieties 
  of 
  type 
  A, 
  called 
  AO. 
  

  

  It 
  is 
  found, 
  however, 
  that 
  two 
  stars 
  both 
  of 
  the 
  type 
  G5, 
  for 
  in- 
  

   stance, 
  though 
  generally 
  identical 
  in 
  spectrum, 
  may 
  show 
  a 
  few 
  of 
  

   their 
  characteristic 
  spectral 
  lines 
  in 
  very 
  different 
  intensities. 
  These 
  

   minute 
  spectral 
  differences 
  have 
  been 
  shown, 
  from 
  both 
  observational 
  

   and 
  theoretical 
  standpoints, 
  to 
  be 
  due 
  to 
  differences 
  in 
  size 
  of 
  the 
  

   stars. 
  If 
  two 
  such 
  stars 
  were 
  at 
  equal 
  distances, 
  so 
  as 
  to 
  display 
  their 
  

   absolute 
  magnitudes, 
  or 
  true 
  luminosities, 
  the 
  one 
  of 
  larger 
  diameter 
  

   would, 
  of 
  course, 
  be 
  the 
  brighter. 
  The 
  distances 
  of 
  a 
  great 
  many 
  

   stars 
  have 
  been 
  so 
  well 
  determined 
  by 
  the 
  trigonometric 
  and 
  dy- 
  

   namical 
  methods 
  that 
  it 
  has 
  become 
  possible 
  to 
  fix 
  a 
  scale 
  of 
  appear- 
  

  

  