﻿Asymmetry 
  of 
  the 
  Zeeman 
  Effect. 
  24D 
  

  

  As 
  first 
  integrals 
  of 
  the 
  equations 
  we 
  get 
  

  

  m^ 
  l 
  + 
  m 
  2 
  a;., 
  = 
  (m 
  l 
  + 
  m 
  2 
  )u 
  + 
  eR(y 
  l 
  — 
  y 
  2 
  ), 
  

   m 
  l 
  y 
  l 
  + 
  m 
  2 
  y. 
  z 
  = 
  (m 
  1 
  + 
  m 
  a 
  ) 
  v 
  — 
  eR 
  (a?, 
  — 
  # 
  2 
  ), 
  

   m 
  1 
  2r 
  l 
  + 
  m 
  2 
  z 
  2 
  = 
  (m 
  x 
  + 
  #0 
  w, 
  

  

  where 
  w, 
  v, 
  w> 
  are 
  constants 
  o£ 
  integration. 
  

   Using 
  these 
  equations 
  and 
  putting 
  

  

  p 
  " 
  = 
  a 
  2 
  ( 
  1 
  •), 
  

  

  rv 
  \m 
  x 
  mj 
  

  

  *!—*%=& 
  yi—y 
  z 
  =v, 
  ^-^a=£ 
  

  

  we 
  get 
  

  

  •• 
  <? 
  2 
  H 
  2 
  ,. 
  eHf^-ra,) 
  • 
  cHfm.+m,.) 
  

  

  J 
  ° 
  m^ 
  m^j 
  m 
  x 
  m 
  2 
  

  

  t+iHrt: 
  =o. 
  

  

  The 
  terms 
  in 
  u 
  and 
  v 
  have 
  no 
  influence 
  on 
  the 
  periodic 
  

   parts 
  of 
  £ 
  and 
  77. 
  Hence 
  putting 
  f 
  , 
  ??, 
  f 
  proportional 
  to 
  e 
  £ 
  

   we 
  get 
  for 
  the 
  f 
  vibration 
  

  

  and 
  for 
  the 
  f 
  and 
  7; 
  vibrations 
  the 
  roots 
  of 
  7? 
  given 
  by 
  

  

  e 
  2 
  H 
  2 
  eK(m—m,) 
  

   P'—Pa 
  = 
  + 
  , 
  P 
  » 
  

  

  ,2 
  ^2 
  

  

  and 
  hence 
  

  

  ?»,»»., 
  — 
  m 
  x 
  m 
  2 
  

  

  *~ 
  ± 
  2 
  m^ 
  +P 
  » 
  V 
  i+ 
  4^ 
  2 
  m> 
  2 
  2 
  

   Neglecting 
  squares 
  of 
  

  

  e 
  2 
  H 
  2 
  (m, 
  + 
  m.,)2 
  

  

  4:p 
  2 
  m 
  x 
  2 
  m 
  2 
  2 
  

  

  we 
  get 
  

  

  p 
  Q 
  m 
  l 
  2 
  m 
  2 
  2 
  

  

  1 
  eH( 
  w, 
  — 
  m,) 
  1 
  e 
  2 
  H 
  2 
  (m 
  1 
  + 
  m 
  2 
  )< 
  

  

  Putting: 
  

  

  1 
  1_ 
  

  

  we 
  set 
  

  

  'G 
  

  

  ?==t» 
  ^0=57, 
  5 
  = 
  ^—^0, 
  

  

  * 
  1 
  eH 
  (»/.,-»/*,) 
  2 
  1 
  e»H*(»i, 
  4- 
  iw 
  s 
  )« 
  3 
  

  

  6_± 
  2 
  m 
  ]W2 
  ^° 
  ~8 
  ~7ttT 
  

  

  1 
  '"2 
  

  

  