﻿864 
  Dr. 
  N. 
  Bohr 
  on 
  the 
  Constitution 
  

  

  method 
  employed 
  it 
  seems 
  difficult 
  to 
  estimate 
  the 
  accuracy 
  

   to 
  be 
  ascribed 
  to 
  the 
  latter 
  value. 
  In 
  order 
  to 
  bring 
  the 
  

   theoretical 
  value 
  in 
  agreement 
  with 
  Langmuir's 
  value, 
  the 
  

   magnitude 
  of 
  the 
  angular 
  momentum 
  of 
  the 
  electrons 
  should 
  

   be 
  only 
  2/3 
  of 
  that 
  adopted 
  ; 
  this 
  seems, 
  however, 
  difficult 
  to 
  

   reconcile 
  with 
  the 
  agreement 
  obtained 
  on 
  other 
  points. 
  

  

  From 
  (6) 
  we 
  get 
  G= 
  -^ 
  =0-325. 
  For 
  the 
  frequency 
  of 
  

  

  vibration 
  o£ 
  the 
  whole 
  ring 
  in 
  the 
  direction 
  parallel 
  to 
  the 
  

   axis 
  of 
  the 
  system 
  we 
  get 
  

  

  v=o) 
  a/o 
  ^ 
  =0-61o> 
  = 
  3-8 
  . 
  10 
  15 
  1/sec. 
  

  

  We 
  have 
  assumed 
  in 
  Part 
  I. 
  and 
  Part 
  II. 
  that 
  the 
  frequency 
  

   of 
  radiation 
  absorbed 
  by 
  the 
  system 
  and 
  corresponding 
  to 
  

   vibrations 
  of 
  the 
  electrons 
  in 
  the 
  plane 
  of 
  the 
  ring 
  cannot 
  be 
  

   calculated 
  from 
  the 
  ordinary 
  mechanics, 
  bat 
  is 
  determined 
  

   by 
  the 
  relation 
  7u' 
  = 
  E, 
  where 
  h 
  is 
  Planck's 
  constant, 
  and 
  E 
  

   the 
  difference 
  in 
  energy 
  between 
  two 
  different 
  stationary 
  

   states 
  of 
  the 
  system. 
  Since 
  we 
  have 
  seen 
  in 
  § 
  2 
  that 
  a 
  con- 
  

   figuration 
  consisting 
  of 
  two 
  nuclei 
  and 
  a 
  single 
  electron 
  

   rotating 
  round 
  the 
  line 
  between 
  them 
  is 
  unstable, 
  we 
  may 
  

   assume 
  that 
  the 
  removing 
  of 
  one 
  of 
  the 
  electrons 
  will 
  lead 
  to 
  

   the 
  breaking 
  up 
  of 
  the 
  molecule 
  into 
  a 
  single 
  nucleus 
  and 
  a 
  

   hydrogen 
  atom. 
  If 
  we 
  consider 
  the 
  latter 
  state 
  as 
  one 
  of 
  

   the 
  stationary 
  states 
  in 
  question 
  we 
  get 
  

  

  E=W-W 
  =l-20Wo, 
  and 
  v=l'2^ 
  =3"7 
  . 
  10 
  15 
  1/sec. 
  

  

  The 
  value 
  for 
  the 
  frequency 
  of 
  the 
  ultra-violet 
  absorption 
  

   line 
  in 
  hydrogen 
  calculated 
  from 
  experiments 
  on 
  dispersion 
  

   is 
  */ 
  = 
  3*5 
  . 
  10 
  15 
  1/sec* 
  Further, 
  a 
  calculation 
  from 
  such 
  expe- 
  

   riments 
  based 
  on 
  Drude's 
  theory 
  gives 
  a 
  value 
  near 
  two 
  for 
  

   the 
  number 
  of 
  electrons 
  in 
  a 
  hydrogen 
  molecule. 
  The 
  latter 
  

   result 
  might 
  have 
  connexion 
  with 
  the 
  fact 
  that 
  the 
  frequencies 
  

   calculated 
  above 
  for 
  the 
  radiation 
  absorbed 
  corresponding 
  to 
  

   vibrations 
  parallel 
  and 
  perpendicular 
  to 
  the 
  plane 
  of 
  the 
  ring 
  

   are 
  nearly 
  equal. 
  As 
  mentioned 
  in 
  Part 
  II., 
  the 
  number 
  of 
  

   electrons 
  in 
  a 
  helium 
  atom 
  calculated 
  from 
  experiments 
  on 
  

   dispersion 
  is 
  only 
  about 
  2/3 
  of 
  the 
  number 
  of 
  electrons 
  to 
  be 
  

   expected 
  in 
  the 
  atom, 
  viz. 
  two. 
  For 
  a 
  helium 
  atom, 
  as 
  for 
  a 
  

   hydrogen 
  molecule, 
  the 
  frequency 
  determined 
  by 
  the 
  relation 
  

   v./i 
  = 
  E 
  agrees 
  closely 
  with 
  the 
  frequency 
  observed 
  from 
  

   dispersion 
  ; 
  in 
  the 
  helium 
  system, 
  however, 
  the 
  frequency 
  

  

  * 
  C. 
  and 
  M. 
  Cuthbertson, 
  Proc. 
  Roy. 
  Soc. 
  lxxxiii. 
  p. 
  151 
  (1910). 
  

  

  