﻿314 
  Dr. 
  L. 
  Vegard 
  on 
  the 
  X-Ray 
  Spectra 
  

  

  It 
  appears 
  that 
  the 
  calculated 
  frequencies 
  come 
  out 
  consi- 
  

   derably 
  greater 
  than 
  those 
  of 
  L 
  ; 
  at 
  any 
  rate, 
  for 
  lower 
  atomic 
  

   numbers 
  they 
  very 
  nearly 
  fall 
  into 
  the 
  7 
  region 
  of 
  Siegbahn, 
  

   being 
  quite 
  close 
  to 
  Sommerfeld's 
  lines 
  B 
  and 
  % 
  As 
  to 
  how 
  

   this 
  discrepancy 
  is 
  to 
  be 
  explained, 
  I 
  should 
  not 
  venture 
  

   to 
  express 
  any 
  definite 
  idea. 
  In 
  any 
  case 
  it 
  shows 
  that 
  

   equation 
  (15) 
  cannot 
  be 
  applied 
  for 
  values 
  of 
  r 
  higher 
  than 
  3 
  

   without 
  the 
  introduction 
  of 
  certain 
  correction 
  terms, 
  — 
  or 
  the 
  

   secondary 
  stability 
  circles 
  of 
  higher 
  quant 
  numbers 
  cannot 
  

   be 
  determined 
  as 
  if 
  the 
  electrons 
  outside 
  the 
  normal 
  L-ring 
  

   were 
  removed. 
  

  

  When 
  proceeding 
  to 
  interpret 
  the 
  L-spectrum 
  we 
  should 
  

   also 
  be 
  aware 
  of 
  the 
  possibility 
  that 
  an 
  L-radiation 
  can 
  be 
  

   produced 
  when 
  an 
  electron 
  is 
  recombining 
  towards 
  the 
  

   K-ring 
  — 
  to 
  a 
  secondary 
  corresponding 
  to 
  r 
  = 
  2. 
  A 
  re- 
  

   combination 
  from 
  a 
  cirele 
  corresponding 
  to 
  t 
  = 
  3 
  would 
  

   give 
  

  

  J--£(*-V{l 
  + 
  g£<N-S>'}- 
  . 
  . 
  (22) 
  

  

  This 
  formula, 
  which 
  takes 
  into 
  account 
  the 
  variation 
  of 
  

   mass, 
  would 
  give 
  frequencies 
  in 
  the 
  /3-region 
  of 
  Siegbahn. 
  

  

  Whether 
  lines 
  of 
  the 
  L-series 
  are 
  produced 
  by 
  a 
  recombina- 
  

   tion 
  towards 
  a 
  broken 
  K-ring, 
  can 
  be 
  tested 
  experimentally 
  

   by 
  exciting 
  the 
  L-radiation 
  with 
  cathode 
  rays 
  which 
  have 
  not 
  

   sufficient 
  energy 
  to 
  excite 
  the 
  K-radiation. 
  

  

  The 
  ISeries. 
  

  

  § 
  7. 
  The 
  softest 
  line 
  given 
  by 
  the 
  ring 
  of 
  7 
  electrons 
  

   should 
  be 
  the 
  L 
  a 
  -line 
  ; 
  but 
  now 
  we 
  have 
  in 
  the 
  L-series 
  

   the 
  /-line 
  discovered 
  by 
  Siegbahn, 
  with 
  a 
  wave-length 
  con- 
  

   siderably 
  greater 
  than 
  that 
  of 
  L 
  a 
  ; 
  and 
  to 
  this 
  line 
  the 
  

   lines 
  77, 
  f, 
  S 
  are 
  probably 
  closely 
  related. 
  These 
  lines 
  we 
  

   shall 
  call 
  the 
  /-series. 
  

  

  The 
  explanation 
  suggests 
  itself 
  that 
  the 
  /-series 
  is 
  due 
  to 
  a 
  

   second 
  ring 
  surrounding 
  the 
  L-ring 
  and 
  with 
  the 
  same 
  quant 
  

   number 
  n 
  = 
  2. 
  This 
  /-ring 
  would 
  have 
  a 
  radius 
  just 
  a 
  little 
  

   greater 
  than 
  that 
  of 
  the 
  L-ring, 
  and 
  the 
  calculation 
  of 
  the 
  

   frequencies 
  due 
  to 
  the 
  /-ring 
  would 
  be 
  very 
  complicated, 
  as 
  

   we 
  can 
  no 
  longer 
  suppose 
  the 
  effective 
  atomic 
  number 
  to 
  be 
  

   N— 
  p, 
  where 
  p 
  is 
  the 
  number 
  of 
  electrons 
  inside 
  the 
  ring. 
  

  

  If, 
  however, 
  we 
  take 
  N— 
  p 
  to 
  represent 
  the 
  effective 
  

   atomic 
  number, 
  and 
  assuming 
  8 
  electrons 
  in 
  the 
  /-ring, 
  

   we 
  get 
  : 
  

  

  ^= 
  1n 
  2 
  -4-37N 
  + 
  30'8 
  (23 
  a) 
  

  

  