﻿and 
  tlie 
  Constitution 
  of 
  the 
  Atom. 
  297 
  

  

  outer 
  electronic 
  system 
  is 
  responsible 
  for 
  the 
  light 
  emission, 
  

   for 
  the 
  homogeneous 
  X-rays, 
  and 
  for 
  the 
  chemical 
  properties 
  

   of 
  the 
  atom. 
  

  

  Bohr* 
  was 
  able 
  to 
  show 
  that 
  the 
  K- 
  spectrum 
  could 
  be 
  

   approximately 
  explained 
  by 
  assuming 
  it 
  to 
  be 
  produced 
  

   by 
  the 
  removal 
  and 
  recombination 
  of 
  .an 
  electron 
  next 
  to 
  

   the 
  nucleus. 
  

  

  Moseley 
  f 
  found 
  a 
  better 
  agreement 
  by 
  assuming 
  four 
  

   electrons 
  in 
  the 
  system 
  next 
  to 
  the 
  nucleus 
  ; 
  but 
  the 
  way 
  

   in 
  which 
  he 
  deduced 
  his 
  formula 
  was 
  open 
  to 
  criticism. 
  

   His 
  formula 
  may 
  therefore 
  be 
  regarded 
  as 
  empirical, 
  

   although 
  ^Nicholson 
  J 
  points 
  out 
  that 
  it 
  can 
  be 
  deduced 
  by 
  

   a 
  proper 
  modification 
  of 
  Bohr's 
  frequency 
  law 
  to 
  systems 
  

   of 
  electrons. 
  

  

  Kossel 
  § 
  was 
  the 
  first 
  to 
  point 
  out 
  some 
  very 
  interesting 
  

   relations 
  between 
  the 
  lines 
  of 
  the 
  K- 
  and 
  L-series. 
  Denoting 
  

   the 
  frequency 
  by 
  v, 
  the 
  following 
  relation 
  very 
  nearly 
  

   holds 
  true 
  : 
  

  

  v 
  H~ 
  VK 
  a= 
  v 
  \ 
  ( 
  6 
  ) 
  

  

  According 
  to 
  Bohr's 
  frequency 
  law 
  (III.) 
  the 
  frequency 
  

   is 
  proportional 
  to 
  the 
  differences 
  of 
  energy 
  of 
  the 
  electron 
  in 
  

   the 
  initial 
  and 
  final 
  state, 
  and, 
  as 
  pointed 
  out 
  by 
  Bohr 
  || 
  , 
  the 
  

   above 
  relations 
  would 
  naturally 
  convey 
  the 
  following 
  con- 
  

   ception 
  with 
  regard 
  to 
  the 
  formation 
  of 
  the 
  high-frequency 
  

   spectra. 
  

  

  The 
  electrons 
  may 
  be 
  supposed 
  to 
  be 
  arranged 
  in 
  rings 
  

   round 
  the 
  nucleus. 
  When 
  an 
  electron 
  is 
  removed 
  from 
  the 
  

   ring 
  nearest 
  the 
  nucleus, 
  an 
  electron 
  from 
  the 
  next 
  ring 
  may 
  

   replace 
  it 
  and 
  give 
  rise 
  to 
  the 
  emission 
  of 
  K 
  a 
  . 
  If 
  the 
  electron 
  

   is 
  taken 
  from 
  the 
  third 
  ring, 
  we 
  get 
  Kp. 
  When 
  an 
  electron 
  

   of 
  the 
  second 
  ring 
  is 
  removed 
  and 
  replaced 
  by 
  one 
  from 
  the 
  

   third, 
  we 
  might 
  get 
  L 
  a 
  , 
  and 
  in 
  this 
  way 
  Kossel's 
  frequency 
  

   relations 
  should 
  be 
  explained. 
  

  

  Sommerfeld^f, 
  following 
  up 
  this 
  line 
  of 
  thought, 
  has 
  

   been 
  able 
  to 
  express 
  a 
  number 
  of 
  lines 
  of 
  the 
  X-ray 
  

   spectra 
  by 
  introducing 
  a 
  number 
  of 
  " 
  terms 
  " 
  peculiar 
  to 
  the 
  

   various 
  X-ray 
  series. 
  Thus, 
  e.g., 
  he 
  introduces 
  a 
  K-term 
  

  

  ^ 
  (N-l-6) 
  2 
  , 
  T 
  . 
  T 
  (E-3'5) 
  2 
  , 
  . 
  , 
  

   K= 
  i 
  — 
  — 
  -and 
  a 
  L-term 
  L= 
  v 
  n9 
  J 
  and 
  finds 
  

  

  l 
  2 
  2 
  2 
  

  

  *k=K-L. 
  

  

  * 
  N. 
  Bohr, 
  Phil. 
  Mag. 
  (6) 
  xxvi. 
  p. 
  408 
  (1913). 
  

  

  t 
  Loc. 
  cit. 
  

  

  % 
  J. 
  W. 
  Nicholson, 
  Phil. 
  Mag. 
  (6) 
  xxviii. 
  p. 
  562 
  (1914), 
  

  

  § 
  W. 
  Kossel, 
  Verh. 
  d. 
  D. 
  Phys. 
  Ges. 
  1914. 
  

  

  || 
  N. 
  Bohr, 
  Phil. 
  Mag. 
  xxx. 
  p. 
  394 
  (1915). 
  

  

  <j[ 
  A. 
  Sommerfeld, 
  Ann. 
  d. 
  Phys. 
  li. 
  p. 
  125 
  (1916). 
  

  

  