﻿of 
  Atoms 
  and 
  Molecule*. 
  13 
  

  

  energy 
  emitted 
  and 
  the 
  frequency 
  of 
  revolution 
  of 
  the 
  

   electron 
  for 
  the 
  different 
  stationary 
  states 
  is 
  given 
  by 
  

   the 
  equation 
  W 
  = 
  /(t) 
  . 
  hco, 
  instead 
  of 
  by 
  the 
  equation 
  (2). 
  

   Proceeding 
  in 
  the 
  same 
  way 
  as 
  above, 
  we 
  get 
  in 
  this 
  case 
  

   instead 
  of(3) 
  

  

  Assuming 
  as 
  above 
  that 
  the 
  amount 
  of 
  energy 
  emitted 
  

   during 
  the 
  passing 
  of 
  the 
  system 
  from 
  a 
  state 
  corresponding 
  

   to 
  t 
  = 
  t, 
  to 
  one 
  for 
  which 
  t 
  = 
  t., 
  is 
  equal 
  to 
  hv, 
  we 
  get 
  instead 
  

   of 
  (4) 
  

  

  _ 
  Tr-»)e 
  2 
  Ei 
  2 
  / 
  1 
  1 
  \ 
  

  

  AVe 
  see 
  that 
  in 
  order 
  to 
  get 
  an 
  expression 
  of 
  the 
  same 
  form 
  

   as 
  the 
  Balmer 
  series 
  we 
  must 
  put/(V) 
  = 
  cT. 
  

  

  In 
  order 
  to 
  determine 
  c 
  let 
  us 
  now 
  consider 
  the 
  passing 
  of 
  

   the 
  system 
  between 
  two 
  successive 
  stationary 
  states 
  corre- 
  

   sponding 
  to 
  t 
  = 
  X 
  and 
  r 
  = 
  X 
  — 
  1 
  ; 
  introducing 
  f{r) 
  — 
  CT, 
  we 
  

   get 
  for 
  the 
  frequency 
  of 
  the 
  radiation 
  emitted 
  

  

  _ 
  7rWE 
  2 
  2N-1 
  

   ' 
  2c 
  2 
  /t 
  3 
  # 
  N 
  2 
  (N-1) 
  2 
  " 
  

  

  For 
  the 
  frequency 
  of 
  revolution 
  of 
  the 
  electron 
  before 
  and 
  

   after 
  the 
  emission 
  we 
  have 
  

  

  irhn^W 
  , 
  ttWE 
  2 
  

  

  »bt= 
  o^isMa 
  and 
  w 
  sr 
  _i= 
  

  

  If 
  X 
  is 
  great 
  the 
  ratio 
  between 
  the 
  frequency 
  before 
  and 
  

   after 
  the 
  emission 
  will 
  be 
  very 
  near 
  equal 
  to 
  1 
  ; 
  and 
  according 
  

   to 
  the 
  ordinary 
  electrodynamics 
  we 
  should 
  therefore 
  expect 
  

   that 
  the 
  ratio 
  between 
  the 
  frequency 
  of 
  radiation 
  and 
  the 
  

   frequency 
  of 
  revolution 
  also 
  is 
  very 
  nearly 
  equal 
  to 
  1. 
  This 
  

  

  condition 
  will 
  only 
  be 
  satisfied 
  if 
  c=J. 
  Putting 
  /(r) 
  = 
  -, 
  we, 
  

  

  however, 
  again 
  arrive 
  at 
  the 
  equation 
  (2) 
  and 
  consequently 
  

   at 
  the 
  expression 
  (3) 
  for 
  the 
  stationary 
  states. 
  

  

  If 
  we 
  consider 
  the 
  passing 
  of 
  the 
  system 
  between 
  two 
  states 
  

   corresponding 
  to 
  t 
  = 
  X 
  and 
  r 
  = 
  X 
  — 
  ?z, 
  where 
  n 
  is 
  small 
  

   compared 
  with 
  X, 
  we 
  get 
  with 
  the 
  same 
  approximation 
  as 
  

  

  T 
  

  

  above, 
  putting/(*r)= 
  — 
  

  

  V=11Q). 
  

  

  