﻿of 
  Atoms 
  and 
  Molecules. 
  487 
  

  

  Exceptions 
  to 
  this 
  rule 
  will 
  be 
  supposed 
  to 
  occur 
  only 
  at 
  

   such 
  places 
  in 
  the 
  series 
  where 
  deviation 
  from 
  the 
  periodic 
  

   law 
  of 
  the 
  chemical 
  properties 
  of 
  the 
  elements 
  are 
  observed. 
  

   In 
  order 
  to 
  show 
  clearly 
  the 
  principles 
  used 
  we 
  shall 
  first 
  

   consider 
  with 
  some 
  detail 
  those 
  atoms 
  containing 
  very 
  few 
  

   electrons. 
  

  

  For 
  sake 
  of 
  brevity 
  we 
  shall, 
  by 
  the 
  symbol 
  N(w 
  1? 
  n 
  2 
  . 
  . 
  . 
  .), 
  

   refer 
  to 
  a 
  plane 
  system 
  of 
  rings 
  of 
  electrons 
  rotating 
  round 
  

   a 
  nucleus 
  of 
  charge 
  N<?, 
  satisfying 
  the 
  condition 
  of 
  the 
  

   angular 
  momentum 
  of 
  the 
  electrons 
  with 
  the 
  approximation 
  

   used 
  in 
  § 
  2. 
  w 
  l5 
  n 
  2 
  , 
  . 
  . 
  . 
  are 
  the 
  numbers 
  of 
  electrons 
  in 
  the 
  

   rings, 
  starting 
  from 
  inside. 
  By 
  a 
  ly 
  a 
  2 
  , 
  . 
  . 
  . 
  and 
  © 
  1 
  , 
  <w 
  2 
  , 
  . 
  . 
  . 
  

   we 
  shall 
  denote 
  the 
  radii 
  and 
  frequency 
  of 
  the 
  rings 
  taken 
  

   in 
  the 
  same 
  order. 
  The 
  total 
  amount 
  of 
  energy 
  W 
  emitted 
  

   by 
  the 
  formation 
  of 
  the 
  svstem 
  shall 
  simply 
  be 
  denoted 
  by 
  

   W[N(n 
  l5 
  w 
  2 
  ,...)]. 
  

  

  N 
  = 
  1 
  . 
  Hydrogen 
  . 
  

  

  In 
  Part 
  I. 
  we 
  have 
  considered 
  the 
  binding 
  of 
  an 
  electron 
  

   by 
  a 
  positive 
  nucleus 
  of 
  charge 
  e, 
  and 
  have 
  shown 
  that 
  it 
  is 
  

   possible 
  to 
  account 
  for 
  the 
  Balmer 
  spectrum 
  of 
  hydrogen 
  

   on 
  the 
  assumption 
  of 
  the 
  existence 
  of 
  a 
  series 
  of 
  stationary 
  

   states 
  in 
  which 
  the 
  angular 
  momentum 
  of 
  the 
  electron 
  round 
  

  

  the 
  nucleus 
  is 
  equal 
  to 
  entire 
  multiples 
  of 
  the 
  value 
  ~— 
  , 
  where 
  

  

  h 
  is 
  Planck's 
  constant. 
  The 
  formula 
  found 
  for 
  the 
  frequencies 
  

   of 
  the 
  spectrum 
  was 
  

  

  27r 
  2 
  e 
  i 
  m 
  

  

  (£-£)• 
  

  

  where 
  r 
  x 
  and 
  r 
  2 
  are 
  entire 
  numbers. 
  Introducing 
  the 
  values 
  

   for 
  e, 
  m, 
  and 
  h 
  used 
  on 
  p. 
  479, 
  we 
  get 
  for 
  the 
  factor 
  before 
  

   the 
  bracket 
  3*1 
  . 
  10 
  15 
  *; 
  the 
  value 
  observed 
  for 
  the 
  constant 
  

   in 
  the 
  Balmer 
  spectrum 
  is 
  3*290 
  . 
  10 
  15 
  . 
  

  

  * 
  This 
  value 
  is 
  that 
  calculated 
  in 
  the 
  first 
  part 
  of 
  the 
  paper. 
  Using 
  the 
  

   values 
  e=4-78 
  . 
  10 
  -10 
  (see 
  R. 
  A. 
  Millikan, 
  Brit. 
  Assoc. 
  Hep. 
  1912, 
  p. 
  410), 
  

  

  -=5-31 
  . 
  10 
  17 
  (see 
  P. 
  Gmelin, 
  Ann. 
  d. 
  Phys. 
  xxviii. 
  p. 
  1086 
  (1909) 
  and 
  

  

  A. 
  H. 
  Bucherer, 
  Ann. 
  d, 
  Phys. 
  xxxvii. 
  p. 
  597 
  (1912)), 
  and 
  | 
  = 
  7*27 
  . 
  10 
  16 
  

  

  (calculated 
  by 
  Planck's 
  theory 
  from 
  the 
  experiments 
  of 
  E. 
  Warburg, 
  

   G. 
  Leithauser, 
  E. 
  Hupka, 
  and 
  C. 
  Miiller, 
  Ann. 
  d.Phys. 
  xl. 
  p. 
  611 
  (1913)) 
  

  

  we 
  get 
  -p 
  — 
  =3-26 
  . 
  10 
  15 
  in 
  very 
  close 
  agreement 
  with 
  observations. 
  

  

  