﻿22 
  Dr. 
  N. 
  Bohr' 
  07i 
  the 
  Conslituti 
  

  

  on 
  

  

  formation 
  'o£ 
  the 
  system 
  the 
  electrons 
  at 
  any 
  moment 
  are 
  

   situated 
  at 
  equal 
  angular 
  intervals 
  on 
  the 
  circumference 
  of 
  a 
  

   circle 
  with 
  the 
  nucleus 
  in 
  the 
  centre, 
  from 
  analogy 
  with 
  

   the 
  considerations 
  on 
  p. 
  5 
  we 
  are 
  here 
  led 
  to 
  assume 
  the 
  

   existence 
  of 
  a 
  series 
  of 
  stationary 
  configurations 
  in 
  which 
  

  

  O) 
  

  

  the 
  kinetic 
  energy 
  per 
  electron 
  is 
  equal 
  to 
  tIi 
  — 
  , 
  where 
  r 
  is 
  

  

  J* 
  

  

  an 
  entire 
  number, 
  It 
  Planck's 
  constant, 
  and 
  &> 
  the 
  frequency 
  

  

  of 
  revolution. 
  The 
  configuration 
  in 
  which 
  the 
  greatest 
  

  

  amount 
  of 
  energy 
  is 
  emitted 
  is, 
  as 
  before, 
  the 
  one 
  in 
  which 
  

  

  t 
  = 
  1. 
  This 
  configuration 
  we 
  shall 
  assume 
  to 
  be 
  the 
  permanent 
  

  

  state 
  of 
  the 
  system 
  if 
  the 
  electrons 
  in 
  this 
  state 
  are 
  arranged 
  

  

  in 
  a 
  single 
  ring. 
  As 
  for 
  the 
  case 
  of 
  a 
  single 
  electron 
  we 
  get 
  

  

  that 
  the 
  angular 
  momentum 
  of 
  each 
  of 
  the 
  electrons 
  is 
  equal 
  

  

  to 
  y— 
  It 
  may 
  be 
  remarked 
  that 
  instead 
  of 
  considering 
  the 
  

  

  single 
  electrons 
  we 
  might 
  have 
  considered 
  the 
  ring 
  as 
  an 
  

   entity. 
  This 
  would, 
  however, 
  lead 
  to 
  the 
  same 
  result, 
  for 
  in 
  

   this 
  case 
  the 
  frequency 
  of 
  revolution 
  co 
  will 
  be 
  replaced 
  by 
  

   the 
  frequency 
  na> 
  of 
  the 
  radiation 
  from 
  the 
  whole 
  ring 
  calcu- 
  

   lated 
  from 
  the 
  ordinary 
  electrodynamics, 
  and 
  T 
  by 
  the 
  total 
  

   kinetic 
  energy 
  ?iT. 
  

  

  There 
  may 
  be 
  many 
  other 
  stationary 
  states 
  corresponding 
  

   to 
  other 
  ways 
  of 
  forming 
  the 
  system. 
  The 
  assumption 
  of 
  the 
  

   existence 
  of 
  such 
  states 
  seems 
  necessary 
  in 
  order 
  to 
  account 
  

   for 
  the 
  line-spectra 
  of 
  systems 
  containing 
  more 
  than 
  one 
  

   electron 
  (p. 
  11) 
  ; 
  it 
  is 
  also 
  suggested 
  by 
  the 
  theory 
  of 
  

   Nicholson 
  mentioned 
  on 
  p. 
  6, 
  to 
  which 
  we 
  shall 
  return 
  in 
  

   a 
  moment. 
  The 
  consideration 
  of 
  the 
  spectra, 
  however, 
  gives, 
  

   as 
  far 
  as 
  I 
  can 
  see, 
  no 
  indication 
  of 
  the 
  existence 
  of 
  stationary 
  

   states 
  in 
  which 
  all 
  the 
  electrons 
  are 
  arranged 
  in 
  a 
  ring 
  and 
  

   which 
  correspond 
  to 
  greater 
  values 
  for 
  the 
  total 
  energy 
  

   emitted 
  than 
  the 
  one 
  we 
  above 
  have 
  assumed 
  to 
  be 
  the 
  

   permanent 
  state. 
  

  

  Further, 
  there 
  may 
  be 
  stationary 
  configurations 
  of 
  a 
  

   system 
  of 
  n 
  electrons 
  and 
  a 
  nucleus 
  of 
  charge 
  E 
  in 
  which 
  all 
  

   the 
  electrons 
  are 
  not 
  arranged 
  in 
  a 
  single 
  ring. 
  The 
  question, 
  

   however, 
  of 
  the 
  existence 
  of 
  such 
  stationary 
  configurations 
  is 
  

   not 
  essential 
  for 
  our 
  determination 
  of 
  the 
  permanent 
  state, 
  as 
  

   long 
  as 
  we 
  assume 
  that 
  the 
  electrons 
  in 
  this 
  state 
  of 
  the 
  

   system 
  are 
  arranged 
  in 
  a 
  single 
  ring. 
  Systems 
  corresponding 
  

   to 
  more 
  complicated 
  configurations 
  will 
  be 
  discussed 
  on 
  

   p. 
  24. 
  

  

  Using 
  the 
  relation 
  T 
  = 
  h~ 
  we 
  get, 
  by 
  help 
  of 
  the 
  above 
  

  

  expressions 
  for 
  T 
  and 
  o>, 
  values 
  for 
  a 
  and 
  co 
  corresponding 
  to 
  

  

  