﻿and 
  the 
  Constitution 
  of 
  the 
  Atom, 
  307 
  

  

  q 
  f 
  electrons. 
  Let 
  the 
  effective 
  charge 
  of 
  the 
  ^'-ring 
  be 
  

  

  In 
  order 
  to 
  find 
  expressions 
  for 
  the 
  energy, 
  we 
  suppose 
  

   that 
  the 
  removal 
  of 
  an 
  electron 
  from 
  one 
  ring 
  does 
  not 
  

   change 
  the 
  energy 
  of 
  any 
  of 
  the 
  other 
  systems 
  which 
  keep 
  

   their 
  electron 
  number 
  unaltered. 
  This 
  will 
  mean 
  that 
  the 
  

   removal 
  of 
  an 
  electron 
  will 
  change 
  the 
  radius 
  of 
  the 
  external 
  

   rings 
  if 
  we 
  suppose 
  the 
  angular 
  momenta 
  to 
  be 
  kept 
  

   unaltered. 
  

  

  Let 
  the 
  energy 
  of 
  the 
  normal 
  and 
  broken 
  

  

  ^-ring 
  be 
  W 
  q 
  and 
  W 
  ? 
  _j. 
  

  

  ^-ringbeW^andW 
  tf 
  _i. 
  

  

  vA 
  = 
  W,+W,._i-(W 
  9 
  - 
  + 
  W,. 
  1 
  ). 
  

   From 
  equation 
  (7) 
  we 
  get 
  : 
  

  

  B 
  = 
  ^?(N,-S,) 
  2 
  -(2-l)(N 
  5 
  -8 
  M 
  )^ 
  

  

  C^i 
  

  

  ^2'(N 
  s 
  .-S 
  4 
  .) 
  2 
  -( 
  ? 
  '-l)(N 
  s 
  .-S 
  s 
  ,_ 
  1 
  ) 
  2 
  }, 
  

  

  !>.(16) 
  

  

  n 
  and 
  r^ 
  being 
  the 
  quant 
  numbers 
  corresponding 
  to 
  the 
  two 
  

   circles 
  q 
  and 
  q'. 
  The 
  formula 
  may 
  also 
  take 
  the 
  form 
  : 
  

  

  ., 
  4>*(pq) 
  _ 
  <I»W) 
  

  

  where 
  n 
  2 
  n 
  ± 
  2 
  ' 
  

  

  <pi(pq) 
  = 
  q(S 
  q 
  -S 
  q 
  -i) 
  + 
  S 
  g 
  -i+p, 
  

   MP!) 
  = 
  ^(2p+S 
  g 
  + 
  S 
  ? 
  _ 
  1 
  )(S 
  2 
  -S 
  ? 
  _ 
  1 
  )+(p 
  + 
  S 
  g 
  _ 
  1 
  ) 
  s 
  

  

  Comparing 
  the 
  equations 
  (15) 
  and 
  (16) 
  we 
  see 
  that, 
  if 
  we 
  

   assume 
  the 
  normal 
  atom 
  to 
  have 
  rings 
  with 
  increasing 
  number 
  

   of 
  n 
  as 
  we 
  pass 
  from 
  the 
  centre, 
  the 
  assumption 
  that 
  the 
  

   recombining 
  electron 
  comes 
  from 
  one 
  other 
  ring 
  with 
  a 
  

   higher 
  quant 
  number 
  leads 
  to 
  an 
  equation 
  of 
  the 
  right 
  type. 
  

   Whether 
  we 
  shall 
  assume 
  that 
  the 
  X-ray 
  spectra 
  are 
  pro- 
  

   duced 
  by 
  recombination 
  from 
  a 
  secondary 
  or 
  a 
  primary 
  circle 
  

   is 
  a 
  question 
  to 
  be 
  decided 
  by 
  the 
  ability 
  of 
  the 
  assumption 
  

   to 
  give 
  a 
  satisfactory 
  agreement 
  with 
  observational 
  data. 
  

  

  To 
  test 
  whether 
  the 
  second 
  hypothesis 
  (eq. 
  16) 
  may 
  be 
  

   possible, 
  let 
  us 
  try 
  if 
  the 
  K-line 
  can 
  be 
  explained 
  by 
  a 
  

   recombination 
  from 
  an 
  L-ring. 
  

  

  