﻿174 
  

  

  ANNUAL 
  EEPOET 
  SMITHSONIAN 
  INSTITUTION, 
  1927 
  

  

  withdrawn. 
  In 
  the 
  next 
  year 
  Kramers 
  (Phil. 
  Mag., 
  46, 
  p. 
  83G) 
  put 
  

   forward 
  the 
  theory 
  of 
  opacity 
  which 
  has 
  now 
  gained 
  general 
  ac- 
  

   ceptance. 
  Using 
  the 
  value 
  of 
  the 
  opacity 
  coefficient 
  given 
  by 
  this 
  

   theory, 
  it 
  is 
  possible 
  to 
  determine 
  the 
  complete 
  build 
  of 
  a 
  star 
  

   having 
  any 
  given 
  mass 
  and 
  an}^ 
  given 
  rate 
  of 
  generation 
  of 
  energy. 
  

   In 
  this 
  way 
  I 
  have 
  shown 
  (Mon. 
  Not. 
  K. 
  A. 
  S., 
  85, 
  pp. 
  196 
  and 
  394) 
  

   that 
  a 
  star 
  of 
  given 
  mass 
  can 
  rest 
  in 
  equilibrium 
  with 
  any 
  radius 
  

   from 
  zero 
  to 
  infinity, 
  different 
  radii 
  corresponding 
  to 
  different 
  rates 
  

   of 
  generation 
  of 
  energy 
  from 
  zero 
  to 
  infinity 
  by 
  the 
  star. 
  A 
  star 
  

   adjusts 
  its 
  radius 
  to 
  suit 
  its 
  rate 
  of 
  generation 
  of 
  energy, 
  and 
  in 
  

   so 
  doing 
  fixes 
  its 
  surface 
  temperature 
  and 
  spectral 
  type. 
  If 
  a 
  star's 
  

   rate 
  of 
  generation 
  of 
  energy 
  were 
  suddenly 
  to 
  change, 
  the 
  star 
  would 
  

   expand 
  or 
  contract 
  until 
  it 
  had 
  assumed 
  the 
  radius 
  and 
  tempera- 
  

   ture 
  suited 
  to 
  its 
  new 
  rate 
  of 
  generation 
  of 
  energy. 
  Contrary 
  to 
  

   common 
  belief, 
  an 
  increase 
  in 
  a 
  star's 
  rate 
  of 
  generation 
  of 
  energy 
  

   causes 
  it 
  to 
  contract 
  its 
  radius 
  and 
  increase 
  its 
  temperature, 
  while 
  

   a 
  slackening 
  in 
  its 
  generation 
  of 
  energy 
  is 
  found 
  to 
  result 
  in 
  ex- 
  

   pansion 
  and 
  cooling. 
  Thus 
  we 
  see 
  the 
  giant 
  red 
  stars 
  such 
  as 
  

   Betelgeuse 
  do 
  not 
  owe 
  their 
  immense 
  size 
  to 
  their 
  radiating 
  so 
  much 
  

   energy, 
  but 
  to 
  their 
  radiating 
  so 
  little; 
  indeed, 
  comparatively 
  com- 
  

   pact 
  stars 
  such 
  as 
  Plaskett's 
  star 
  and 
  V 
  Puppis 
  are 
  radiating 
  far 
  

   more 
  in 
  proportion 
  to 
  their 
  masses. 
  The 
  general 
  theoretical 
  prin- 
  

   ciple 
  can 
  be 
  verified 
  by 
  the 
  examination 
  of 
  pairs 
  of 
  stars 
  of 
  approxi- 
  

   mately 
  equal 
  mass, 
  as, 
  for 
  example, 
  the 
  two 
  pairs 
  in 
  the 
  following 
  

   table. 
  The 
  surface 
  temperatures 
  are 
  here 
  deduced 
  directly 
  from 
  the 
  

   observed 
  spectra, 
  the 
  radii 
  then 
  being 
  calculated 
  in 
  the 
  way 
  already 
  

   explained. 
  

  

  STELLAR 
  EVOLUTION 
  

  

  There 
  is 
  not 
  likely 
  to 
  be 
  any 
  abrupt 
  change 
  in 
  the 
  rate 
  of 
  genera- 
  

   tion 
  of 
  energy 
  of 
  an 
  actual 
  star. 
  There 
  will 
  be 
  a 
  slow 
  secular 
  

   decrease, 
  but 
  this 
  will 
  be 
  associated 
  with 
  a 
  slow 
  secular 
  decrease 
  of 
  

   the 
  star's 
  mass 
  resulting 
  from 
  its 
  continual 
  emission 
  of 
  radiation. 
  For 
  

   example, 
  the 
  560,000 
  calories 
  of 
  radiation 
  which 
  stream 
  out 
  every 
  

   minute 
  from 
  each 
  square 
  inch 
  of 
  the 
  sun's 
  surface 
  have 
  a 
  mass 
  of 
  

   2.5X10-^ 
  gm., 
  whence 
  it 
  is 
  readily 
  calculated 
  that 
  the 
  sun's 
  mass 
  

  

  