﻿482 
  Dr. 
  N. 
  Bohr 
  on 
  the 
  Constitution 
  

  

  the 
  centre 
  of 
  its 
  orbit 
  will 
  obviously 
  be 
  equal 
  to 
  its 
  original 
  

   value 
  ; 
  the 
  increase 
  in 
  the 
  potential 
  energy 
  of 
  the 
  system 
  

   will 
  be 
  equal 
  to 
  the 
  work 
  done 
  by 
  the 
  extraneous 
  forces 
  

   during 
  the 
  displacements. 
  From 
  such 
  considerations 
  we 
  are 
  

   led 
  to 
  assume 
  that 
  the 
  ordinary 
  mechanics 
  can 
  be 
  used 
  in 
  

   calculating 
  the 
  vibrations 
  of 
  the 
  electrons 
  perpendicular 
  to 
  

   the 
  plane 
  of 
  the 
  ring 
  — 
  contrary 
  to 
  the 
  case 
  of 
  vibrations 
  in 
  

   the 
  plane 
  of 
  the 
  ring. 
  This 
  assumption 
  is 
  supported 
  by 
  the 
  

   apparent 
  agreement 
  with 
  observations 
  obtained 
  by 
  Nichol- 
  

   son 
  in 
  his 
  theory 
  of 
  the 
  origin 
  of 
  lines 
  in 
  the 
  spectra 
  of 
  the 
  

   solar 
  corona 
  and 
  stellar 
  nebulae 
  (see 
  Part 
  I. 
  pp. 
  6 
  & 
  23). 
  

   In 
  addition 
  it 
  will 
  be 
  shown 
  later 
  that 
  the 
  assumption 
  seems 
  

   to 
  be 
  in 
  agreement 
  with 
  experiments 
  on 
  dispersion. 
  

  

  The 
  following 
  table 
  gives 
  the 
  values 
  of 
  s 
  n 
  and 
  p 
  n 
  —p 
  n 
  m 
  

   from 
  n 
  = 
  l 
  to 
  n 
  = 
  16. 
  

  

  n, 
  s 
  . 
  p 
  — 
  v 
  ; 
  n. 
  s 
  , 
  p 
  — 
  p 
  

  

  ' 
  iv 
  L 
  n, 
  o 
  J- 
  n, 
  m 
  ' 
  TV 
  J- 
  no, 
  -*• 
  n, 
  m 
  

  

  1 
  9 
  3-328 
  13-14 
  

  

  2 
  025 
  0-25 
  ; 
  10 
  3-863 
  18-13 
  

  

  3 
  0-577 
  0-58 
  11 
  4-416 
  23-60 
  

  

  4 
  0-957 
  1-41 
  12 
  4-984 
  30"80 
  

  

  5 
  1-377 
  2-43 
  13 
  5-565 
  38-57 
  

  

  6 
  1-828 
  4-25 
  14 
  6-159 
  48-38 
  

  

  7 
  2-305 
  6-35 
  15 
  6764 
  58-83 
  

  

  8 
  2-805 
  9-56 
  16 
  7'379 
  71*65 
  

  

  We 
  see 
  from 
  the 
  table 
  that 
  the 
  number 
  of 
  electrons 
  which 
  

   can 
  rotate 
  in 
  a 
  single 
  ring 
  round 
  a 
  nucleus 
  of 
  charge 
  ~Ne 
  

   increases 
  only 
  very 
  slowly 
  for 
  increasing 
  N 
  ; 
  for 
  N 
  = 
  20 
  the 
  

   maximum 
  value 
  is 
  n 
  = 
  10 
  ; 
  for 
  N 
  = 
  40, 
  n 
  = 
  13 
  ; 
  for 
  IN" 
  = 
  60, 
  

   ?i 
  = 
  15. 
  We 
  see, 
  further, 
  that 
  a 
  ring 
  of 
  n 
  electrons 
  cannot 
  

   rotate 
  in 
  a 
  single 
  ring 
  round 
  a 
  nucleus 
  of 
  charge 
  ne 
  unless 
  

  

  7l<8. 
  

  

  In 
  the 
  above 
  we 
  have 
  supposed 
  that 
  the 
  electrons 
  

   move 
  under 
  the 
  influence 
  of 
  a 
  stationary 
  radial 
  force 
  and 
  

   that 
  their 
  orbits 
  are 
  exactly 
  circular. 
  The 
  first 
  condition 
  

   will 
  not 
  be 
  satisfied 
  if 
  we 
  consider 
  a 
  system 
  containing 
  

   several 
  rings 
  of 
  electrons 
  which 
  rotate 
  with 
  different 
  fre- 
  

   quencies. 
  If, 
  however, 
  the 
  distance 
  between 
  the 
  rings 
  is 
  not 
  

   small 
  in 
  comparison 
  with 
  their 
  radii, 
  and 
  if 
  the 
  ratio 
  between 
  

   their 
  frequencies 
  is 
  not 
  near 
  to 
  unity, 
  the 
  deviation 
  from 
  

   circular 
  orbits 
  may 
  be 
  very 
  small 
  and 
  the 
  motion 
  of 
  the 
  

   electrons 
  to 
  a 
  close 
  approximation 
  may 
  be 
  identical 
  with 
  

   that 
  obtained 
  on 
  the 
  assumption 
  that 
  the 
  charge 
  on 
  the 
  

   electrons 
  is 
  uniformly 
  distributed 
  along 
  the 
  circumference 
  of 
  

   the 
  rings. 
  If 
  the 
  ratio 
  between 
  the 
  radii 
  of 
  the 
  rings 
  is 
  not. 
  

  

  