﻿MODERN" 
  ASTEONOMY 
  ABBOT 
  155 
  

  

  ance 
  of 
  these 
  telltale 
  spectral 
  lines, 
  such 
  that, 
  knowing 
  their 
  

   appearance 
  in 
  a 
  given 
  star, 
  its 
  absolute 
  brightness 
  is 
  immediately 
  

   assigned. 
  Knowing, 
  also, 
  its 
  apparent 
  brightness 
  from 
  photometric 
  

   observations, 
  the 
  distance 
  follows 
  at 
  once. 
  In 
  this 
  way 
  the 
  distances 
  

   of 
  nearly 
  3,000 
  individual 
  stars 
  have 
  been 
  measured 
  spectroscopically. 
  

  

  Omitting 
  in 
  this 
  hasty 
  sketch 
  distances 
  determined 
  by 
  several 
  spe- 
  

   cial 
  methods 
  of 
  limited 
  application, 
  we 
  come 
  finally 
  to 
  the 
  wholesale 
  

   methods 
  depending 
  on 
  apparent 
  brightness 
  and 
  on 
  apparent 
  angular 
  

   motion. 
  It 
  is 
  sufficiently 
  obvious 
  that 
  if 
  all 
  stars 
  were 
  of 
  identical 
  

   spectrum 
  and 
  luminosity, 
  their 
  brightness 
  would 
  vary 
  inversely 
  as 
  

   the 
  square 
  of 
  their 
  distance. 
  By 
  making 
  allowance 
  for 
  spectrum, 
  

   and 
  assuming 
  that 
  large 
  and 
  small 
  stars 
  are 
  mixed 
  in 
  the 
  same 
  pro- 
  

   portions 
  in 
  the 
  distant 
  parts 
  of 
  the 
  universe 
  that 
  they 
  are 
  in 
  those 
  

   relatively 
  near, 
  formulae 
  have 
  been 
  devised 
  which 
  give 
  the 
  average 
  

   relative 
  distances 
  of 
  stars 
  of 
  the 
  successive 
  stellar 
  magnitudes. 
  It 
  is 
  

   also 
  obvious 
  that 
  on 
  the 
  average 
  of 
  great 
  numbers 
  the 
  apparent 
  

   angular 
  motion 
  of 
  stars, 
  or 
  so-called 
  "proper 
  motion," 
  must 
  be 
  in- 
  

   versely 
  as 
  their 
  distances. 
  This 
  wholesale 
  method 
  of 
  estimating 
  

   stellar 
  distances 
  in 
  terms 
  of 
  proper 
  motions 
  has 
  been 
  extensively 
  

   applied, 
  and 
  appropriate 
  formulae 
  have 
  been 
  devised 
  to 
  express 
  it. 
  

  

  These 
  wholesale 
  formulae 
  are 
  checked 
  by 
  the 
  known 
  individual 
  

   distances 
  of 
  several 
  thousand 
  stars. 
  They 
  enable 
  us 
  to 
  treat 
  statis- 
  

   tically 
  such 
  majestic 
  'problems 
  as 
  the 
  absolute 
  size 
  of 
  our 
  stellar 
  

   system,, 
  which 
  tve 
  call 
  our 
  gal<txy. 
  It 
  is 
  estimated 
  to 
  he 
  approxi- 
  

   mately 
  100,000 
  light 
  years 
  in 
  its 
  maxiiwum 
  and 
  WpOO 
  light 
  years 
  in 
  

   its 
  minimuiih 
  diameter. 
  Its 
  20 
  nearest 
  stars 
  are 
  froin 
  Jf. 
  to 
  16 
  light 
  

   years 
  diMant 
  from 
  us. 
  

  

  Knowing 
  the 
  distances 
  of 
  several 
  thousand 
  stars 
  individually, 
  it 
  

   has 
  been 
  found 
  that 
  our 
  sun 
  is 
  near 
  the 
  middle 
  rank 
  in 
  absolute 
  

   brightness, 
  although, 
  to 
  us, 
  it 
  seems 
  brighter 
  than 
  Sirius. 
  Yet, 
  in 
  

   fact, 
  Rigel 
  is 
  about 
  ten 
  thousand 
  times 
  brighter 
  than 
  the 
  sun, 
  and 
  the 
  

   sun 
  about 
  ten 
  thousand 
  times 
  brighter 
  than 
  the 
  faintest 
  stars 
  yet 
  

   known. 
  

  

  As 
  for 
  the 
  sun, 
  its 
  diameter 
  has 
  long 
  been 
  known 
  to 
  be 
  860,000 
  

   miles. 
  Only 
  recently 
  have 
  the 
  diameters 
  of 
  some 
  other 
  stars 
  been 
  

   determined. 
  This 
  has 
  been 
  done 
  in 
  some 
  cases 
  by 
  direct 
  measure- 
  

   ments 
  with 
  the 
  interferometer 
  according 
  to 
  the 
  method 
  of 
  Michel- 
  

   son, 
  but 
  only 
  for 
  a 
  few 
  stars, 
  including 
  Betelgeuse, 
  Antares, 
  Arcturus, 
  

   Aldebaran, 
  and 
  some 
  others. 
  The 
  gigantic 
  red 
  stars 
  first 
  named 
  are 
  

   found 
  to 
  be 
  from 
  200,000,000 
  to 
  1^00,000,000 
  miles 
  in 
  diameter, 
  or 
  

   several 
  himdred 
  times 
  that 
  of 
  the 
  sun. 
  On 
  the 
  other 
  extreme, 
  several 
  

   bright 
  stars, 
  including 
  Sirius, 
  are 
  found 
  less 
  than 
  twice 
  the 
  diameter 
  

   of 
  the 
  sun. 
  If 
  it 
  were 
  possible 
  to 
  carry 
  the 
  measurements 
  to 
  very 
  

   faint 
  stars, 
  doubtless 
  some 
  would 
  be 
  found 
  much 
  smaller 
  than 
  the 
  

  

  