﻿316 
  Dr. 
  L. 
  Vegard 
  on 
  the 
  X-Ray 
  Spectra 
  

  

  The 
  line 
  M 
  a 
  , 
  say, 
  can 
  be 
  approximately 
  expressed 
  by 
  the 
  

   empirical 
  formula 
  : 
  

  

  4 
  = 
  T 
  ^N 
  2 
  -2-37N 
  + 
  40. 
  . 
  . 
  . 
  (24 
  a) 
  

   it 
  144 
  v 
  y 
  

  

  If 
  in 
  equation 
  (15) 
  we 
  would 
  try 
  to 
  give 
  p 
  and 
  q 
  such 
  

   values 
  as 
  to 
  agree 
  with 
  this 
  empirical 
  equation, 
  we 
  should 
  

   find 
  the 
  best 
  possible 
  agreement 
  by 
  putting 
  

  

  p=lS 
  and 
  q 
  = 
  9 
  or 
  10. 
  

  

  Thus 
  in 
  order 
  to 
  explain 
  the 
  M-series 
  we 
  should 
  have 
  to 
  

   assume 
  a 
  number 
  of 
  electrons 
  inside 
  the 
  M-ring 
  just 
  equal 
  

   to 
  that 
  found 
  for 
  the 
  K- 
  and 
  L-rings. 
  Thus 
  the 
  assumption 
  

   of 
  an 
  outer 
  Z-ring 
  of 
  8 
  electrons 
  is 
  also 
  necessary 
  to 
  explain 
  

   the 
  M-radiation. 
  9 
  electrons 
  in 
  the 
  M-ring 
  give 
  

  

  . 
  . 
  (24 
  6) 
  

  

  

  V 
  

  

  7 
  

   — 
  N 
  2 
  - 
  

   144 
  

  

  -2-45N 
  + 
  28 
  ; 
  

  

  electrons 
  

  

  give 
  

  

  

  

  

  V 
  

  

  7 
  

  

  — 
  -N 
  2 
  - 
  

   144 
  

  

  -2-55N 
  + 
  31. 
  

  

  . 
  . 
  (24 
  c) 
  

  

  Although 
  the 
  agreement 
  between 
  observed 
  and 
  calculated 
  

   values 
  is 
  not 
  so 
  good 
  as 
  in 
  the 
  case 
  of 
  L 
  a 
  , 
  the 
  empirical 
  and 
  

   theoretical 
  equations 
  are 
  of 
  essentially 
  the 
  same 
  type, 
  and 
  

   even 
  the 
  numerical 
  agreement 
  is 
  surprisingly 
  good. 
  

   The 
  radius 
  of 
  the 
  rings 
  is 
  given 
  by 
  the 
  expression 
  

  

  e 
  2 
  n 
  2 
  

   a 
  = 
  2KR(N-p--S 
  g 
  y 
  (25) 
  

  

  where 
  p 
  and 
  q 
  have 
  the 
  same 
  meaning 
  as 
  in 
  equation 
  (15). 
  

   To 
  correct 
  for 
  variation 
  of 
  mass 
  we 
  should 
  have 
  to 
  multiply 
  

  

  with 
  y^l-f 
  (N-^-8,)'. 
  

  

  The 
  expression 
  for 
  the 
  velocity 
  is 
  

  

  v 
  = 
  /m 
  N-p-B, 
  = 
  2 
  _ 
  1Q8 
  N-p-S 
  _ 
  

  

  V 
  m 
  n 
  n 
  y 
  

  

  and 
  is 
  not 
  changed 
  when 
  the 
  variation 
  of 
  the 
  mass 
  is 
  taken 
  

   into 
  account. 
  

  

  The 
  values 
  of 
  a 
  for 
  the 
  K-, 
  L-, 
  Z-, 
  and 
  M-rings 
  for 
  a 
  

   couple 
  of 
  elements 
  are 
  given 
  in 
  Table 
  VII. 
  and 
  in 
  fig. 
  1. 
  

  

  