﻿302 
  Dr. 
  L. 
  Vegard 
  on 
  the 
  X-Ray 
  Spectra 
  

  

  We 
  see 
  that 
  the 
  formula 
  (12 
  c) 
  satisfies 
  the 
  observations 
  

   with 
  the 
  same 
  accuracy 
  as 
  does 
  Debye's 
  formula. 
  In 
  fact 
  

   the 
  two 
  formulas 
  give 
  almost 
  identical 
  values. 
  If 
  we 
  assume 
  

   the 
  whole 
  ring 
  of 
  four 
  electrons 
  to 
  the 
  normal 
  state 
  from 
  a 
  

   three-quantical 
  secondary, 
  we 
  should 
  get 
  frequencies 
  nearly 
  

   equal 
  to 
  those 
  of 
  K. 
  The 
  accuracy 
  would 
  be 
  about 
  the 
  

   same 
  as 
  that 
  found 
  by 
  Debye. 
  

  

  If 
  we 
  adopt 
  the 
  frequency 
  law 
  in 
  this 
  more 
  general 
  sense 
  

   there 
  are 
  two 
  possible 
  solutions. 
  The 
  one 
  would 
  give 
  four, 
  

   the 
  other 
  three 
  electrons 
  in 
  the 
  K-ring. 
  Which 
  of 
  the 
  two 
  

   is 
  the 
  right 
  solution 
  cannot 
  be 
  determined 
  from 
  a 
  mere 
  

   numerical 
  comparison 
  with 
  the 
  observations, 
  but 
  we 
  must 
  

   have 
  regard 
  to 
  the 
  physical 
  consequences 
  to 
  which 
  they 
  lead, 
  

   and 
  in 
  this 
  respect 
  the 
  solution 
  of 
  Debye 
  has 
  the 
  advantage. 
  

  

  In 
  the 
  case 
  of 
  four 
  electrons 
  the 
  whole 
  ring 
  of 
  electrons 
  

   would 
  have 
  to 
  operate 
  intact. 
  We 
  should 
  have 
  to 
  assume 
  

   that 
  the 
  system 
  formed 
  a 
  kind 
  of 
  unity, 
  in 
  such 
  a 
  way 
  that 
  

   they 
  tried 
  to 
  keep 
  the 
  same 
  angular 
  momentum. 
  I 
  think 
  

   that 
  there 
  is 
  reason 
  to 
  believe 
  that 
  as 
  a 
  component 
  of 
  the 
  

   atomic 
  system 
  the 
  electrons 
  are 
  not 
  to 
  be 
  considered 
  as 
  

   independent 
  unities 
  ; 
  but 
  that 
  they 
  are 
  linked 
  together 
  by 
  

   forces 
  which 
  are 
  different 
  from 
  the 
  ordinary 
  central 
  attrac- 
  

   tion 
  and 
  repulsion 
  between 
  the 
  centres. 
  The 
  arrangement 
  

   of 
  electrons 
  in 
  conformity 
  with 
  certain 
  quant-conditions 
  is 
  

   one 
  aspect 
  of 
  these 
  as 
  yet 
  unknown 
  forces. 
  But 
  energy 
  

   considerations 
  seem 
  to 
  show 
  that 
  this 
  mutual 
  attachment 
  

   cannot 
  be 
  so 
  close 
  as 
  to 
  prevent 
  one 
  single 
  electron 
  from 
  

   leaving 
  the 
  system. 
  

  

  The 
  experiments 
  of 
  Barkla 
  and 
  Sadler 
  * 
  have 
  shown 
  that 
  

   in 
  order 
  to 
  excite 
  the 
  K-radiation 
  by 
  means 
  of 
  Rontgen 
  rays 
  

   the 
  hardness 
  of 
  the 
  incident 
  rays 
  must 
  just 
  surpass 
  that 
  of 
  

   the 
  excited 
  radiation. 
  The 
  frequency 
  Ka 
  of 
  those 
  rays 
  which 
  

   are 
  just 
  sufficient 
  to 
  produce 
  the 
  K-radiation 
  is 
  accurately 
  

   determined 
  by 
  Wagner 
  t 
  and 
  de 
  Broglie 
  ±, 
  and 
  they 
  also 
  

   find 
  Ka 
  just 
  a 
  little 
  greater 
  than 
  the 
  frequency 
  Kp. 
  

  

  This 
  fact 
  is 
  simply 
  explained 
  by 
  the 
  quantum 
  theory 
  and 
  

   Bohr's 
  conception 
  of 
  the 
  X-ray-and-light 
  emission. 
  An 
  

   electron 
  will 
  be 
  expelled 
  from 
  the 
  ring 
  when 
  the 
  energy 
  

   quantum 
  is 
  equal 
  to 
  or 
  greater 
  than 
  the 
  energy 
  required 
  to 
  

   remove 
  it 
  from 
  the 
  atom. 
  Debye's 
  formula 
  involves 
  the 
  

   assumption 
  that 
  one 
  quantum 
  is 
  sufficient 
  to 
  excite 
  radiation. 
  

   The 
  assumption 
  of 
  four 
  electrons 
  would 
  mean 
  that 
  four 
  

  

  * 
  C. 
  G. 
  Barkla 
  and 
  C. 
  A. 
  Sadler, 
  Phil. 
  Mag. 
  xvi. 
  p. 
  550 
  (1908). 
  

   t 
  E. 
  Wagner, 
  Ann. 
  d. 
  Phys. 
  xlvi. 
  p. 
  868 
  (1915) 
  ; 
  Phys. 
  Z.S. 
  p. 
  432 
  

   (1917). 
  

  

  X 
  M. 
  de 
  Broglie, 
  C. 
  R. 
  clxiii. 
  pp. 
  87, 
  354 
  (1916). 
  

  

  