﻿294 
  Dr. 
  L. 
  Vegard 
  on 
  the 
  X-Ray 
  Spectra 
  

  

  II. 
  To 
  produce 
  the 
  line 
  of 
  a 
  series 
  it 
  is 
  necessary 
  that 
  an 
  

   electron 
  should 
  be 
  removed 
  in 
  some 
  way 
  or 
  other 
  from 
  one 
  

   of 
  the 
  rings. 
  The 
  recombination 
  of 
  an 
  electron 
  towards 
  the 
  

   broken 
  ring 
  may 
  take 
  place 
  in 
  steps 
  between 
  stability 
  orbits 
  

   determined 
  by 
  the 
  condition 
  : 
  

  

  m(oa 
  2 
  = 
  Ty- 
  (lb) 
  

  

  III. 
  To 
  each 
  stability 
  circle 
  of 
  the 
  recombining 
  electron 
  

   corresponds 
  a 
  certain 
  energy 
  of 
  the 
  atomic 
  system. 
  When 
  

   the 
  electron 
  in 
  one 
  step 
  passes 
  from 
  a 
  stability 
  circle 
  t 
  2 
  to 
  

   one 
  t 
  2 
  the 
  energy 
  must 
  be 
  removed 
  from 
  the 
  system, 
  and 
  

   Bohr 
  assumes 
  it 
  to 
  be 
  radiated 
  out 
  in 
  one 
  quantum 
  homo- 
  

   geneous 
  radiation, 
  or 
  

  

  hv=W 
  2 
  -W 
  1} 
  (2) 
  

  

  where 
  v 
  is 
  the 
  frequency 
  and 
  W 
  the 
  total 
  energy. 
  The 
  

   latter 
  relation 
  we 
  may 
  call 
  Bohr's 
  frequency 
  law. 
  The 
  orbits 
  

   corresponding 
  to 
  the 
  normal 
  state 
  of 
  the 
  atom 
  we 
  shall 
  call 
  

   primary 
  orbits, 
  and 
  the 
  stability 
  orbits 
  which 
  the 
  electron 
  

   may 
  take 
  up 
  during 
  its 
  recombination 
  we 
  denote 
  as 
  secondary 
  

   orbits. 
  

  

  By 
  means 
  of 
  these 
  assumptions 
  Bohr 
  was 
  able 
  to 
  deduce 
  

   the 
  complete 
  series 
  spectrum 
  of 
  hydrogen 
  and 
  a 
  spectrum 
  of 
  

   helium 
  which 
  was 
  emitted 
  when 
  a 
  single 
  electron 
  recombined 
  

   to 
  the 
  isolated 
  nucleus. 
  He 
  was 
  also 
  able 
  to 
  give 
  an 
  ex- 
  

   planation 
  of 
  the 
  appearance 
  in 
  the 
  series 
  formula 
  of 
  the 
  

   universal 
  frequency 
  constant 
  (R) 
  of 
  Rydberg, 
  and 
  his 
  fre- 
  

   quency 
  law 
  explained 
  in 
  a 
  simple 
  manner 
  the 
  combination 
  

   principle 
  of 
  Ritz. 
  But 
  up 
  to 
  the 
  present 
  the 
  atomic 
  model 
  

   based 
  on 
  the 
  assumption 
  I. 
  has 
  not 
  been 
  able 
  to 
  yield 
  any 
  

   theoretical 
  deduction 
  of 
  the 
  series 
  spectra 
  in 
  general. 
  

  

  In 
  the 
  case 
  of 
  hydrogen 
  and 
  those 
  spectra 
  similar 
  to 
  that 
  

   of 
  hydrogen, 
  the 
  theory 
  of 
  Bohr 
  has 
  proved 
  to 
  be 
  very 
  

   successful 
  indeed. 
  Through 
  the 
  introduction 
  of 
  noncircular 
  

   orbits 
  already 
  Bohr 
  * 
  was 
  able 
  to 
  deduce 
  a 
  formula 
  for 
  the 
  

   Stark-effect 
  which 
  gave 
  the 
  right 
  order 
  of 
  magnitude 
  and 
  

   the 
  right 
  type 
  of 
  variation. 
  Later 
  on 
  the 
  question 
  of 
  non- 
  

   circular 
  orbits 
  has 
  been 
  much 
  more 
  completely 
  treated 
  by 
  

   Sommerfeld 
  t, 
  Schwarzschild 
  J, 
  and 
  Epstein 
  §. 
  

  

  Sommerfeld 
  gave 
  a 
  generalization 
  of 
  the 
  quant-conditions 
  

  

  * 
  N. 
  Bohr, 
  Phil. 
  Mag. 
  xxviii. 
  p. 
  506 
  (1914). 
  

  

  t 
  A. 
  Sommerfeld, 
  Sitz. 
  Ber. 
  d. 
  Miinchener 
  Akad. 
  d. 
  Wiss. 
  1915; 
  

   Ann. 
  d. 
  Phys. 
  li. 
  pp. 
  1 
  & 
  125 
  (1916). 
  

  

  % 
  K. 
  Schwarzschild, 
  Berliner 
  Akad. 
  d. 
  Wiss. 
  p. 
  548 
  (1916). 
  

   § 
  P. 
  Epstein, 
  Ann. 
  d. 
  Phys. 
  1. 
  p. 
  489 
  (1916). 
  

  

  