﻿491 
  Dr. 
  N. 
  Bohr 
  on 
  the 
  Constitution 
  

  

  Daring 
  the 
  displacements 
  of 
  the 
  rings 
  the 
  angular 
  momentum 
  

   of 
  the 
  electrons 
  round 
  the 
  axis 
  or! 
  the 
  system 
  will 
  remain 
  

   constant, 
  and 
  the 
  diameter 
  of 
  the 
  inner 
  ring 
  will 
  increase 
  

   while 
  that 
  of 
  the 
  outer 
  will 
  diminish. 
  At 
  the 
  beginning 
  of 
  

   the 
  displacement 
  the 
  magnitude 
  ot: 
  the 
  extraneous 
  forces 
  to 
  

   be 
  applied 
  to 
  the 
  original 
  inner 
  ring 
  will 
  increase 
  but 
  there- 
  

   after 
  decrease, 
  and 
  at 
  a 
  certain 
  distance 
  between 
  the 
  plane 
  

   of 
  the 
  rings 
  the 
  system 
  will 
  be 
  in 
  a 
  configuration 
  of 
  equili- 
  

   brium. 
  This 
  equilibrium, 
  however, 
  will 
  not 
  ha 
  stable. 
  If 
  

   we 
  let 
  the 
  rings 
  slowly 
  return 
  they 
  will 
  either 
  reach 
  their 
  

   original 
  position, 
  or 
  they 
  will 
  arrive 
  at 
  a 
  position 
  in 
  which 
  

   the 
  ring, 
  which 
  originally 
  was 
  the 
  outer, 
  is 
  now 
  the 
  inner,, 
  

   and 
  vice 
  versa. 
  

  

  If 
  the 
  charge 
  of 
  the 
  electrons 
  were 
  uniformly 
  distributed 
  

   along 
  the 
  circumference 
  of 
  the 
  rings, 
  we 
  could 
  by 
  the 
  

   process 
  considered 
  at 
  most 
  obtain 
  an 
  interchange 
  of 
  the 
  

   rings, 
  but 
  obviously 
  not 
  a 
  junction 
  of 
  them. 
  Taking, 
  how- 
  

   ever, 
  the 
  discrete 
  distribution 
  of 
  the 
  electrons 
  into 
  account, 
  

   it 
  can 
  be 
  shown 
  that, 
  in 
  the 
  special 
  case 
  when 
  the 
  number 
  

   of 
  electrons 
  on 
  the 
  two 
  rings 
  are 
  equal, 
  and 
  when 
  the 
  rings 
  

   rotate 
  in 
  the 
  same 
  direction, 
  the 
  rings 
  will 
  unite 
  by 
  the 
  

   process, 
  provided 
  that 
  the 
  final 
  configuration 
  is 
  stable. 
  In 
  

   this 
  case 
  the 
  radii 
  and 
  the 
  frequencies 
  of 
  the 
  rings 
  will 
  be 
  

   equal 
  in 
  the 
  unstable 
  configuration 
  of 
  equilibrium 
  mentioned 
  

   above. 
  In 
  reaching 
  this 
  configuration 
  the 
  electrons 
  in 
  the 
  

   one 
  ring 
  will 
  further 
  be 
  situated 
  just 
  opposite 
  the 
  intervals 
  

   between 
  the 
  electrons 
  in 
  the 
  other, 
  since 
  such 
  an 
  arrange- 
  

   ment 
  will 
  correspond 
  to 
  the 
  smallest 
  total 
  energy. 
  If 
  now 
  

   we 
  let 
  the 
  rings 
  return 
  to 
  their 
  original 
  plane, 
  the 
  electrons 
  

   in 
  the 
  one 
  ring 
  will 
  pass 
  into 
  the 
  intervals 
  between 
  the 
  

   electrons 
  in 
  the 
  other, 
  and 
  form 
  a 
  single 
  ring. 
  Obviously 
  

   the 
  ring 
  thus 
  formed 
  will 
  satisfy 
  the 
  same 
  condition 
  of 
  the' 
  

   angular 
  momentum 
  of 
  the 
  electrons 
  as 
  the 
  original 
  rings. 
  

  

  If 
  the 
  two 
  rings 
  contain 
  unequal 
  numbers 
  of 
  electrons 
  the 
  

   system 
  will 
  during 
  a 
  process 
  such 
  as 
  that 
  considered 
  behave 
  

   very 
  differently, 
  and, 
  contrary 
  to 
  the 
  former 
  case, 
  we 
  cannot 
  

   expect 
  that 
  the 
  rings 
  will 
  flow 
  together, 
  if 
  by 
  help 
  of 
  extraneous^ 
  

   forces 
  acting 
  parallel 
  to 
  the 
  axis 
  of 
  the 
  system 
  they 
  are 
  

   displaced 
  slowly 
  from 
  their 
  original 
  plane. 
  It 
  may 
  in 
  this 
  

   connexion 
  be 
  noticed 
  that 
  the 
  characteristic 
  for 
  the 
  dis- 
  

   placements 
  considered 
  is 
  not 
  the 
  special 
  assumption 
  about 
  

   the 
  extraneous 
  forces, 
  but 
  only 
  the 
  invariance 
  cf 
  the 
  angular 
  

   momentum 
  of 
  the 
  electrons 
  round 
  the 
  centre 
  of 
  the 
  rings 
  ; 
  

   displacements 
  of 
  this 
  kind 
  take 
  in 
  the 
  present 
  theory 
  a 
  

   similar 
  position 
  to 
  arbitrary 
  displacements 
  in 
  the 
  ordinary 
  

   mechanics. 
  

  

  