﻿1032 
  Mr. 
  H. 
  G. 
  J. 
  Moseley 
  on 
  the 
  

  

  We 
  will 
  now 
  examine 
  the 
  relation 
  

  

  V 
  %V 
  

  

  more 
  closely. 
  So 
  far 
  the 
  argument 
  has 
  relied 
  on 
  the 
  fact 
  

   that 
  Q 
  is 
  a 
  quantity 
  which 
  increases 
  from 
  atom 
  to 
  atom 
  by 
  

   equal 
  steps. 
  Now 
  Q 
  has 
  been 
  obtained 
  by 
  multiplying 
  v' 
  z 
  

   by 
  a 
  constant 
  factor 
  so 
  chosen 
  as 
  to 
  make 
  the 
  steps 
  equal 
  to 
  

   unity. 
  We 
  have, 
  therefore, 
  

  

  where 
  k 
  is 
  a 
  constant. 
  Hence 
  the 
  frequency 
  v 
  varies 
  as 
  

   (N-£) 
  2 
  . 
  If 
  N 
  for 
  calcium 
  is 
  really 
  20 
  then 
  k= 
  1. 
  

  

  There 
  is 
  good 
  reason 
  to 
  believe 
  that 
  the 
  X~ray 
  spectra 
  

   with 
  which 
  we 
  are 
  now 
  dealing 
  come 
  from 
  the 
  innermost 
  

   ring 
  of 
  electrons 
  *. 
  If 
  these 
  electrons 
  are 
  held 
  in 
  equi- 
  

   librium 
  by 
  mechanical 
  forces, 
  the 
  angular 
  velocity 
  co 
  with 
  

   which 
  they 
  are 
  rotating 
  and 
  the 
  radius 
  r 
  of 
  their 
  orbit 
  are 
  

   connected 
  by 
  

  

  e 
  2 
  

   moo 
  2 
  r 
  z=~(N 
  — 
  a 
  n 
  ), 
  

  

  where 
  <r 
  n 
  is 
  a 
  small 
  term 
  arising 
  from 
  the 
  influence 
  of 
  the 
  

   n 
  electrons 
  in 
  the 
  ring 
  on 
  each 
  other, 
  and 
  cr 
  2 
  = 
  0'25, 
  o- 
  4 
  = 
  0"96, 
  

   o- 
  6 
  = 
  l*83, 
  cr 
  8 
  = 
  2*81. 
  In 
  obtaining 
  this 
  simple 
  expression 
  the 
  

   very 
  small 
  effect 
  of 
  other 
  outside 
  rings 
  has 
  been 
  neglected. 
  

   If 
  then, 
  as 
  we 
  pass 
  from 
  atom 
  to 
  atom, 
  the 
  number 
  of 
  

   electrons 
  in 
  the 
  central 
  ring 
  remains 
  unaltered, 
  

  

  (&)V) 
  N 
  1 
  — 
  (cwV 
  3 
  )-^ 
  remains 
  constant 
  ; 
  

   but 
  these 
  experiments 
  have 
  shown 
  that 
  

  

  v 
  n+i 
  ~ 
  v 
  n 
  * 
  ti 
  a 
  ^ 
  S0 
  cons 
  kmt, 
  

  

  and 
  therefore 
  

  

  ft) 
  2 
  r 
  3 
  . 
  . 
  . 
  . 
  

  

  ~x- 
  is 
  constant. 
  

   v 
  2 
  

  

  For 
  the 
  types 
  of 
  radiation 
  considered 
  by 
  Bohr, 
  provided 
  

   the 
  ring 
  moves 
  from 
  one 
  stationary 
  state 
  to 
  another 
  as 
  

   a 
  whole, 
  and 
  for 
  the 
  ordinary 
  transverse 
  vibrations 
  of 
  the 
  

   ring, 
  provided 
  the 
  influence 
  of 
  outer 
  rings 
  can 
  be 
  neglected, 
  

   v 
  is 
  proportional 
  to 
  w. 
  

  

  This 
  gives 
  &>^> 
  3 
  and 
  therefore 
  moor 
  2 
  , 
  the 
  angular 
  momentum 
  

   of 
  an 
  electron, 
  the 
  same 
  for 
  all 
  the 
  different 
  atoms. 
  Thus 
  we 
  

  

  * 
  J. 
  J. 
  Thomson, 
  Phil. 
  Mag-, 
  xxiii. 
  p. 
  45G 
  (1912). 
  

  

  