﻿166 
  ANNUAL 
  REPORT 
  SMITHSONIAN 
  INSTITUTION, 
  19 
  2 
  9 
  

  

  for 
  a 
  collection 
  of 
  massive 
  points, 
  having 
  the 
  masses 
  and 
  mean 
  dis- 
  

   tances 
  of 
  the 
  stars 
  and 
  attracting 
  according 
  to 
  the 
  law 
  of 
  gravitation. 
  

   It 
  proves 
  to 
  be 
  of 
  the 
  order 
  of 
  millions 
  of 
  millions 
  of 
  years. 
  After 
  inter- 
  

   acting 
  on 
  one 
  another 
  for 
  a 
  certain 
  number, 
  then, 
  of 
  millions 
  of 
  millions 
  

   of 
  years, 
  the 
  stars 
  must 
  attain 
  to 
  a 
  final 
  state 
  of 
  equipartition 
  of 
  energy 
  

   in 
  which 
  the 
  average 
  energy 
  of 
  all 
  types 
  of 
  stars 
  is 
  the 
  same, 
  regardless 
  

   of 
  their 
  mass. 
  

  

  So 
  far 
  back 
  as 
  1911, 
  Halm 
  had 
  suspected 
  an 
  approximation 
  to 
  equal- 
  

   ity 
  in 
  the 
  energies 
  of 
  massive 
  and 
  light 
  stars, 
  and 
  suggested 
  that 
  the 
  

   velocities 
  of 
  the 
  stars, 
  like 
  those 
  of 
  the 
  molecules 
  of 
  a 
  gas, 
  might 
  con- 
  

   form 
  to 
  the 
  law 
  of 
  equipartition 
  of 
  energy. 
  A 
  more 
  exhaustive 
  inves- 
  

   tigation 
  by 
  Seares 
  in 
  1922 
  showed 
  the 
  supposed 
  approximation 
  to 
  be 
  

   real. 
  Table 
  I 
  show^s 
  the 
  average 
  total 
  velocity 
  (C) 
  obtained 
  for 
  stars 
  

   of 
  different 
  types 
  having 
  different 
  mean 
  masses. 
  

  

  Everywhere, 
  except 
  in 
  its 
  first 
  two 
  lines, 
  the 
  table 
  reveals 
  a 
  marked 
  

   approximation 
  to 
  equality 
  of 
  energy 
  of 
  motion. 
  The 
  last 
  10 
  lines 
  

   show 
  a 
  range 
  of 
  10 
  to 
  1 
  in 
  mass, 
  but 
  the 
  average 
  deviation 
  of 
  energy 
  

   from 
  the 
  mean 
  is 
  only 
  9 
  per 
  cent. 
  This 
  equality 
  of 
  energy 
  can 
  only 
  be 
  

   attributed 
  to 
  the 
  gravitational 
  interaction 
  of 
  the 
  stars. 
  For 
  if 
  it 
  were 
  

   produced 
  by 
  any 
  physical 
  agencj, 
  such 
  as 
  pressure 
  of 
  radiation, 
  

   bombardment 
  by 
  molecules, 
  atoms 
  or 
  high-speed 
  electrons, 
  this 
  agency, 
  

   as 
  the 
  last 
  column 
  of 
  the 
  table 
  shows, 
  would 
  have 
  to 
  be 
  in 
  thermody- 
  

   namical 
  equilibrium 
  w^ith 
  matter 
  at 
  a 
  temperature 
  of 
  the 
  order 
  of 
  

   2X10^^ 
  degrees. 
  Since 
  no 
  such 
  temperatures 
  are 
  laiown 
  in 
  nature, 
  

   we 
  must 
  conclude 
  that 
  the 
  observed 
  equality 
  of 
  energy 
  is 
  the 
  result 
  of 
  

   gravitational 
  interactions 
  extending 
  over 
  millions 
  of 
  millions 
  of 
  years. 
  

   The 
  stars 
  must, 
  then, 
  have 
  an 
  age 
  of 
  this 
  order 
  of 
  magnitude. 
  

  

  Other 
  lines 
  of 
  astronomical 
  investigation 
  lead 
  to 
  the 
  same 
  conclusion 
  ; 
  

   I 
  will 
  limit 
  myself 
  to 
  one. 
  A 
  number 
  of 
  stars 
  are 
  "binary," 
  consisting 
  

   of 
  two 
  distinct 
  masses 
  which 
  travel 
  through 
  space 
  in 
  double 
  harness, 
  

   describing 
  closed 
  orbits 
  about 
  one 
  another 
  because 
  neither 
  can 
  escape 
  

   from 
  the 
  gravitational 
  hold 
  of 
  its 
  companion. 
  The 
  single 
  stars 
  we 
  

   have 
  just 
  discussed 
  may 
  appropriately 
  be 
  compared 
  to 
  monatomic 
  

   molecules, 
  but 
  these 
  binary 
  stars 
  must 
  be 
  compared 
  to 
  diatomic 
  

   molecules. 
  Energy 
  can 
  reside 
  in 
  their 
  orbital 
  motion 
  as 
  well 
  as 
  in 
  

   their 
  motion 
  through 
  space. 
  Again 
  we 
  find 
  that 
  endless 
  gravita- 
  

   tional 
  encounters 
  must 
  result 
  in 
  equipartition 
  of 
  energy, 
  both 
  from 
  

   star 
  to 
  star 
  and 
  also 
  between 
  the 
  different 
  motions 
  of 
  which 
  each 
  

   binary 
  system 
  is 
  capable. 
  Further, 
  when 
  this 
  final 
  state 
  is 
  reached, 
  

   the 
  eccentricities 
  of 
  the 
  elliptic 
  orbits 
  must 
  be 
  distributed 
  over 
  all 
  

   values 
  from 
  e=0 
  to 
  e=l 
  in 
  such 
  a 
  way 
  that 
  all 
  values 
  of 
  e^ 
  are 
  equally 
  

   probable. 
  

  

  