﻿180 
  ANNUAL 
  EEPORT 
  SMITHSONIAN 
  INSTITUTION, 
  1929 
  

  

  regions 
  outside 
  the 
  stars. 
  As 
  a 
  collection 
  of 
  oppositely 
  charged 
  

   particles 
  could 
  not 
  remain 
  uncombined 
  for 
  long, 
  he 
  postulates 
  a 
  

   continual 
  creation 
  of 
  protons 
  and 
  electrons 
  out 
  of 
  the 
  stray 
  radiation 
  

   of 
  the 
  stars; 
  matter 
  is 
  continually 
  being 
  annihilated 
  in 
  the 
  interior 
  

   of 
  the 
  stars, 
  and 
  re-created 
  outside 
  them. 
  This 
  gives 
  a 
  cyclic 
  universe 
  

   which 
  might 
  go 
  on 
  for 
  ever. 
  

  

  Like 
  all 
  other 
  cyclic 
  universes, 
  however, 
  it 
  clashes 
  with 
  the 
  second 
  

   law 
  of 
  thermodynamics. 
  A 
  universe 
  which 
  is 
  not 
  in 
  a 
  state 
  of 
  

   maximum 
  entropy 
  moves 
  irreversibly 
  along 
  the 
  path 
  of 
  increasing 
  

   entropy 
  and 
  so 
  can 
  not 
  be 
  cyclic; 
  one 
  which 
  is 
  already 
  in 
  such 
  a 
  

   state 
  must 
  be 
  macroscopically 
  dead, 
  and 
  so 
  can 
  not 
  be 
  cyclic 
  in 
  any 
  

   sense 
  perceptible 
  to 
  us. 
  Indeed, 
  it 
  is 
  easy 
  to 
  find 
  the 
  exact 
  spot 
  at 
  

   which 
  Millikan's 
  concept 
  comes 
  into 
  conflict 
  with 
  the 
  second 
  law 
  of 
  

   thermodynamics; 
  it 
  is 
  that 
  we 
  can 
  not 
  have 
  protons 
  and 
  electrons 
  

   transformed 
  into 
  radiation 
  at 
  a 
  high 
  temperature 
  and 
  then 
  have 
  the 
  

   process 
  reversed 
  at 
  a 
  lower 
  temperature. 
  

  

  Some 
  may 
  not 
  regard 
  this 
  as 
  a 
  fatal 
  objection 
  to 
  the 
  scheme 
  in 
  

   question. 
  All 
  our 
  discussion 
  has 
  been 
  based 
  on 
  the 
  supposition 
  

   that 
  the 
  laws 
  of 
  physics 
  remain 
  valid 
  at 
  enormously 
  high 
  tempera- 
  

   tures 
  and 
  under 
  conditions 
  entirely 
  outside 
  our 
  experience. 
  Conse- 
  

   quently, 
  all 
  our 
  conclusions 
  can 
  be 
  avoided, 
  and 
  everything 
  can 
  be 
  

   put 
  back 
  in 
  the 
  melting 
  pot, 
  by 
  the 
  single 
  hypothesis 
  that 
  the 
  laws 
  

   which 
  govern 
  matter 
  out 
  in 
  space 
  differ 
  from 
  those 
  which 
  govern 
  

   matter 
  on 
  earth. 
  Yet 
  we 
  have 
  only 
  found 
  it 
  necessary 
  to 
  assume 
  the 
  

   simplest 
  and 
  most 
  fundamental 
  of 
  physical 
  laws, 
  namely, 
  the 
  second 
  

   law 
  of 
  thermodynamics 
  and 
  the 
  broad 
  general 
  principles 
  of 
  the 
  

   quantum 
  theory; 
  and 
  it 
  is 
  hard 
  to 
  imagine 
  that 
  such 
  wide 
  laws 
  fail 
  

   outside 
  our 
  laboratories. 
  The 
  obvious 
  path 
  of 
  scientific 
  progress 
  

   would 
  seem 
  to 
  lie 
  in 
  the 
  direction 
  of 
  inquiring 
  what 
  consequences 
  are 
  

   involved 
  in 
  supposing 
  these 
  laws 
  to 
  be 
  of 
  universal 
  scope, 
  and 
  then 
  

   testing 
  these 
  consequences 
  against 
  the 
  ascertained 
  facts 
  of 
  observa- 
  

   tional 
  astronomy. 
  So 
  far 
  as 
  present 
  indications 
  go, 
  astronomy, 
  so 
  far 
  

   from 
  challenging 
  these 
  consequences, 
  goes 
  half-way 
  out 
  to 
  meet 
  them. 
  

   ^ 
  Apart 
  from 
  transitory 
  rearrangements 
  of 
  atomic 
  electrons, 
  the 
  

   fundamental 
  changes 
  in 
  atoms 
  consist 
  in 
  transitions 
  to 
  states 
  of 
  lower 
  

   energy. 
  Under 
  the 
  classical 
  electrodynamics, 
  an 
  electron 
  describing 
  

   a 
  circular 
  orbit 
  of 
  radius 
  r 
  about 
  a 
  charge 
  E 
  lost 
  energy 
  at 
  a 
  rate 
  

   y^EH^CIr^ 
  (Larmor's 
  formula), 
  and 
  this 
  caused 
  the 
  radius 
  r 
  to 
  decrease 
  

   at 
  a 
  calculable 
  rate; 
  the 
  charges 
  inevitably 
  and 
  spontaneously 
  fell 
  

   towards 
  one 
  another. 
  The 
  quantum 
  mechanics 
  replaced 
  this 
  steady 
  

   fall 
  by 
  a 
  sequence 
  of 
  sudden 
  drops, 
  but 
  according 
  to 
  Bohr's 
  corres- 
  

   pondence 
  principle 
  the 
  rate 
  of 
  fall 
  remains 
  statistically 
  the 
  same, 
  at 
  

   any 
  rate 
  so 
  long 
  as 
  the 
  orbits 
  are 
  large, 
  as 
  on 
  the 
  classical 
  electro- 
  

   dynamics'; 
  that 
  is 
  to 
  say, 
  the 
  sum 
  of 
  the 
  radii 
  of 
  the 
  orbits 
  of 
  a 
  whole 
  

   crowd 
  of 
  atoms 
  decreases 
  through 
  spontaneous 
  jumps 
  at 
  just 
  the 
  same 
  

  

  