﻿and 
  the 
  Constitution 
  of 
  the 
  Atom. 
  305 
  

  

  The 
  energy 
  after 
  an 
  electron 
  from 
  the 
  q-ving 
  has 
  regenerated 
  

   the 
  p-ring 
  will 
  be 
  : 
  

  

  Applying 
  Bohr's 
  emission 
  law 
  

  

  lw 
  = 
  Wi-W 
  2 
  

  

  and 
  inserting 
  the 
  values 
  of 
  Wi 
  and 
  W 
  2 
  , 
  the 
  frequency 
  takes 
  

   the 
  form 
  : 
  

  

  P 
  = 
  Apg 
  r 
  JN 
  + 
  ijpqn 
  v.-*-^/ 
  

  

  where 
  A 
  pqr 
  and 
  B 
  pqr 
  are 
  functions 
  of 
  p, 
  q, 
  and 
  r. 
  We 
  see 
  

   that 
  the 
  factor 
  of 
  S" 
  2 
  vanishes 
  for 
  all 
  values 
  of 
  (p, 
  q 
  } 
  r) 
  ; 
  

   whence 
  we 
  conclude 
  that 
  the 
  above 
  equation 
  cannot 
  express 
  

   any 
  of 
  the 
  Rontgen-ray 
  spectra, 
  or 
  the 
  high-frequency 
  

   radiation 
  cannot 
  be 
  explained 
  by 
  interchange 
  of 
  electrons 
  

   between 
  rings 
  of 
  the 
  normal 
  atom, 
  when 
  each 
  electron 
  in 
  

  

  7 
  

  

  this 
  state 
  has 
  an 
  angular 
  momentum 
  -— 
  . 
  

  

  Z7T 
  

  

  It 
  can 
  also 
  be 
  shown 
  that 
  from 
  the 
  assumptions 
  of 
  Bohr 
  

   and 
  Debye 
  we 
  cannot 
  get 
  the 
  right 
  formula 
  for 
  L 
  a 
  by 
  any 
  

   recombination 
  to 
  a 
  system, 
  where 
  each 
  electron 
  has 
  an 
  

  

  angular 
  momentum 
  of 
  ^- 
  . 
  On 
  the 
  other 
  hand, 
  the 
  relation 
  

  

  between 
  the 
  absorption 
  and 
  emission 
  frequencies 
  leads 
  us 
  to 
  

   the 
  assumption 
  that 
  the 
  L-series 
  is 
  produced 
  by 
  a 
  recom- 
  

   bination 
  to 
  some 
  system 
  which 
  exists 
  in 
  the 
  atom 
  in 
  its 
  normal 
  

   state. 
  If 
  then 
  we 
  are 
  to 
  explain 
  the 
  L-radiation, 
  we 
  must 
  

   in 
  some 
  way 
  alter 
  at 
  least 
  one 
  of 
  the 
  assumptions 
  at 
  first 
  

   made 
  by 
  Bohr. 
  

  

  In 
  all 
  cases 
  where 
  Bohr's 
  principles 
  have 
  led 
  to 
  a 
  complete 
  

   or 
  satisfactory 
  determination 
  of 
  the 
  spectrum, 
  we 
  have 
  always 
  

   dealt 
  with 
  systems 
  next 
  to 
  the 
  nucleus. 
  It 
  might 
  then 
  be 
  

   natural 
  to 
  suppose 
  that 
  it 
  is 
  only 
  for 
  this 
  inner 
  ring 
  that 
  

   Bohr's 
  assumption 
  I. 
  is 
  fulfilled. 
  The 
  quant-condition 
  to 
  be 
  

   satisfied 
  by 
  circular 
  systems 
  in 
  the 
  normal 
  state 
  of 
  the 
  atom 
  

   might 
  more 
  generally 
  be 
  written 
  

  

  mcoa 
  2 
  = 
  n— 
  , 
  (14) 
  

  

  Z7T 
  v 
  7 
  

  

  where 
  n 
  is 
  an 
  integer. 
  

  

  This 
  would 
  indeed 
  seem 
  to 
  complicate 
  matters, 
  as 
  we 
  

   introduce 
  a 
  new 
  parameter 
  n 
  into 
  the 
  conditions 
  which 
  

   secure 
  the 
  stability 
  of 
  the 
  electronic 
  systems. 
  But 
  still 
  it 
  

   seems 
  the 
  right 
  procedure 
  to 
  begin 
  work 
  with 
  n 
  as 
  an 
  

  

  