﻿306 
  Dr. 
  L. 
  Vegard 
  on 
  the 
  X-Ray 
  Spectra 
  

  

  arbitrary 
  whole 
  number 
  to 
  be 
  determined 
  so 
  as 
  to 
  fit 
  in 
  

   with 
  observations, 
  because 
  there 
  seems 
  a 
  priori 
  no 
  necessity 
  

   for 
  putting 
  n 
  = 
  l 
  for 
  all 
  systems 
  in 
  the 
  normal 
  state 
  of 
  the 
  

   atom. 
  

  

  Under 
  these 
  generalized 
  conditions 
  we 
  shall 
  calculate 
  

   the 
  frequencies 
  which 
  are 
  produced 
  when 
  an 
  electron 
  is 
  

   recombining 
  to 
  a 
  normal 
  system 
  with 
  q 
  electrons 
  which 
  

   have 
  lost 
  one 
  electron. 
  

  

  Let 
  the 
  number 
  of 
  electrons 
  between 
  the 
  ^-ring 
  and 
  the 
  

   nucleus 
  be 
  p\ 
  then 
  the 
  effective 
  nucleus 
  charge 
  is 
  

  

  X 
  t 
  = 
  K-p; 
  

  

  and 
  forming 
  the 
  energies 
  from 
  equation 
  (7) 
  in 
  the 
  same 
  way 
  

   as 
  before, 
  we 
  get: 
  — 
  

  

  Energy 
  of 
  unbroken 
  g-ring: 
  W 
  x 
  = 
  — 
  2 
  (N 
  ? 
  ' 
  — 
  S 
  2 
  ) 
  2 
  AR 
  ; 
  

  

  broken 
  „ 
  : 
  W 
  2 
  '= 
  ^ 
  (N.-S^AR 
  ; 
  

   and 
  energy 
  of 
  recombining 
  electron 
  in 
  the 
  secondary 
  circle 
  : 
  

   W 
  2 
  ''= 
  t 
  *(N 
  9 
  -?+1) 
  2 
  /iR. 
  

  

  If 
  we 
  still 
  stick 
  to 
  Bohr's 
  frequency 
  law, 
  we 
  get 
  

  

  ^ 
  = 
  W 
  1 
  -(W, 
  , 
  +W 
  S 
  "). 
  

   Hence 
  

  

  E 
  = 
  Q-Qw+Mr, 
  q, 
  n, 
  t)N 
  +/,<>, 
  q, 
  n, 
  r), 
  

  

  / 
  1 
  ( 
  W 
  nT)=J(p 
  + 
  5-l)-J(.p 
  + 
  S,. 
  1 
  )-?f(S 
  9 
  -S 
  8 
  . 
  1 
  ), 
  

  

  Mpqnr) 
  = 
  ^(2^+s,+s,. 
  1 
  )(S,-s 
  9 
  . 
  1 
  ) 
  + 
  (£=^- 
  1 
  ) 
  2 
  

  

  On 
  the 
  more 
  general 
  assumption 
  (14) 
  we 
  might 
  now 
  also 
  

   possibly 
  explain 
  the 
  formation 
  of 
  lines 
  by 
  assuming 
  that 
  an 
  

   electron 
  removed 
  from 
  a 
  ring 
  is 
  replaced 
  by 
  an 
  electron 
  

   coming 
  from 
  one 
  of 
  the 
  other 
  normal 
  ring-systems. 
  

  

  Let, 
  as 
  before, 
  an 
  electron 
  be 
  removed 
  from 
  the 
  g-ring, 
  

   and 
  let 
  it 
  be 
  replaced 
  by 
  an 
  electron 
  from 
  another 
  ring 
  with 
  

  

  (15) 
  

  

  