﻿300 
  Dr. 
  L. 
  Vegard 
  on 
  the 
  X-Ray 
  Spectra 
  

  

  these 
  conditions 
  can 
  be 
  derived 
  from 
  the 
  ordinary 
  equations 
  

   simply 
  by 
  putting 
  

  

  m 
  = 
  m 
  j 
  - 
  , 
  (9) 
  

  

  In 
  this 
  case 
  a 
  fairly 
  simple 
  calculation 
  gives 
  for 
  the 
  total 
  

   energy 
  

  

  w=2eJ5{i- 
  v 
  /i-£(N-s,)'}, 
  . 
  (io) 
  

  

  where 
  

  

  »=S 
  =5 
  ' 
  30 
  - 
  10 
  - 
  5 
  (11) 
  

  

  Forming 
  from 
  equation 
  (10) 
  the 
  expressions 
  for 
  the 
  

   energies 
  of 
  the 
  broken 
  and 
  unbroken 
  system, 
  the 
  equation 
  

   (8) 
  gives 
  the 
  frequency 
  of 
  the 
  radiation. 
  

  

  Letting 
  the 
  electron 
  recombine 
  from 
  a 
  state 
  corresponding 
  

   to 
  t=3, 
  Debye 
  finds 
  frequencies 
  which 
  are 
  fairly 
  near 
  to 
  

   those 
  of 
  Kp. 
  

  

  Ambiguities 
  with 
  regard 
  to 
  the 
  Determination 
  of 
  

   the 
  K-System. 
  

  

  § 
  3. 
  The 
  question 
  as 
  to 
  the 
  system 
  of 
  electrons 
  which 
  

   produces 
  the 
  K-series 
  is 
  a 
  most 
  important 
  one, 
  being 
  the 
  

   first 
  step 
  towards 
  a 
  determination 
  of 
  the 
  outer 
  system 
  of 
  

   electrons 
  in 
  the 
  atom, 
  and 
  it 
  should 
  not 
  be 
  out 
  of 
  place 
  

   to 
  see 
  how 
  far 
  the 
  most 
  promising 
  solution 
  found 
  by 
  Debye 
  

   is 
  the 
  only 
  one 
  which 
  may 
  give 
  a 
  satisfactory 
  agreement 
  

   with 
  observations. 
  

  

  When 
  we 
  stick 
  to 
  the 
  assumptions 
  of 
  Debye 
  (a, 
  b, 
  c, 
  d) 
  

   and 
  suppose 
  the 
  K-lines 
  to 
  be 
  produced 
  by 
  the 
  removal 
  of 
  

   one 
  single 
  electron, 
  his 
  result 
  that 
  there 
  are 
  three 
  electrons 
  

   in 
  the 
  inner 
  ring 
  is 
  the 
  only 
  one 
  possible. 
  

  

  We 
  might, 
  however, 
  more 
  generally 
  assume 
  that 
  a 
  group 
  

   of 
  q 
  electrons 
  were 
  removed 
  from 
  the 
  inner 
  circuit 
  of 
  

   p 
  electrons, 
  and 
  we 
  could 
  assume 
  that 
  the 
  lines 
  were 
  formed 
  

   when 
  the 
  system 
  of 
  q 
  electrons 
  reproduced 
  the 
  original 
  

   system 
  under 
  the 
  emission 
  of 
  q 
  energy 
  quanta. 
  

  

  From 
  equation 
  (7) 
  we 
  get 
  for 
  the 
  energies 
  : 
  — 
  

  

  For 
  the 
  normal 
  ring, 
  

  

  W^phRCN-Sp)*. 
  

   For 
  the 
  broken 
  system, 
  

  

  W 
  2 
  =(jt>- 
  ? 
  )MJ(N-S,_,)2 
  + 
  s 
  ^(N- 
  j 
  p 
  + 
  , 
  ? 
  -S 
  ? 
  )s. 
  

  

  