﻿310 
  Dr. 
  L. 
  Vegard 
  on 
  the 
  X-Ray 
  Spectra 
  

  

  agreement 
  with 
  observations 
  ; 
  and 
  we 
  shall 
  also 
  see 
  that 
  the 
  

   assumption 
  of 
  an 
  inner 
  ring 
  of! 
  three 
  electrons 
  very 
  well 
  

   fits 
  in 
  with 
  the 
  chemical 
  relations 
  of 
  the 
  elements 
  as 
  they 
  

   are 
  expressed 
  in 
  the 
  periodic 
  system. 
  It 
  may 
  also 
  in 
  this 
  

   connexion 
  be 
  mentioned 
  that 
  Sommerfeld 
  *, 
  from 
  his 
  

   expresssions 
  of 
  the 
  frequencies 
  by 
  means 
  of 
  his 
  " 
  terms/' 
  

   comes 
  to 
  the 
  conclusion 
  " 
  that 
  none 
  of 
  the 
  L-lines 
  can 
  be 
  

   derived 
  from 
  the 
  K-lines 
  by 
  means 
  of 
  the 
  principle 
  of 
  

   combination." 
  

  

  In 
  our 
  further 
  investigation 
  we 
  shall 
  then 
  build 
  on 
  the 
  

   assumption 
  that 
  the 
  electron 
  producing 
  the 
  X-radiation 
  

   recombines 
  from 
  secondary 
  systems 
  in 
  a 
  way 
  which 
  is 
  

   independent 
  of 
  the 
  systems 
  exterior 
  to 
  the 
  primary 
  ring 
  to 
  

   which 
  recombination 
  takes 
  place. 
  

  

  On 
  the 
  Explanation 
  of 
  the 
  La-Line. 
  

  

  § 
  5. 
  We 
  now 
  suppose 
  the 
  result 
  of 
  Debye 
  as 
  regards 
  the 
  

   K-radiation 
  to 
  be 
  true, 
  and 
  we 
  ask 
  whether 
  it 
  is 
  possible 
  

   in 
  equation 
  (15) 
  to 
  give 
  q, 
  n, 
  and 
  t 
  such 
  values 
  that 
  the 
  

   observations 
  are 
  satisfied. 
  

  

  We 
  put 
  p 
  = 
  3, 
  and 
  from 
  the 
  formula 
  of 
  Moseley 
  for 
  

   the 
  La-line, 
  

  

  = 
  (i-i)(N-7-4)>, 
  

  

  we 
  see 
  that 
  we 
  must 
  put 
  

  

  n=2, 
  t= 
  3. 
  

  

  If 
  in 
  (15) 
  we 
  further 
  put 
  

  

  q 
  = 
  i, 
  2, 
  3 
  , 
  

  

  we 
  find 
  that 
  q 
  — 
  1 
  gives 
  : 
  

  

  Mp, 
  q, 
  n, 
  t) 
  = 
  -2-0846, 
  

  

  Mp, 
  q, 
  n 
  , 
  T 
  ) 
  = 
  +5*3 
  ; 
  

   and 
  we 
  get 
  for 
  the 
  frequency 
  : 
  

  

  ^ 
  = 
  4n 
  2 
  -2-0846N4-5-3. 
  # 
  m 
  m 
  (19a 
  ) 
  

   si 
  do 
  

  

  The 
  formula 
  of 
  Moseley 
  put 
  into 
  the 
  same 
  form 
  gives 
  : 
  

  

  £= 
  ^N 
  2 
  -2-0556N 
  + 
  7-6. 
  . 
  . 
  . 
  (19 
  6) 
  

   * 
  A. 
  Sommerfeld, 
  Ann. 
  d. 
  Phys. 
  li. 
  p. 
  155 
  (1916). 
  

  

  v 
  

  

  