﻿248 
  Mr. 
  G. 
  W. 
  Walker 
  on 
  

  

  the 
  red 
  end 
  o£ 
  the 
  spectrum. 
  Professor 
  Zeeman 
  has 
  verified 
  

   this 
  and 
  is 
  endeavouring 
  to 
  measure 
  the 
  amount, 
  which 
  is- 
  

   excessively 
  small. 
  

  

  Professor 
  Voigt 
  finds 
  that 
  

  

  where 
  t 
  and 
  r 
  are 
  the 
  undisturbed 
  and 
  disturbed 
  periods 
  

  

  d= 
  

  

  T 
  

  

  : 
  2^ 
  ' 
  

  

  3 
  - 
  T 
  ° 
  

  

  Z7T 
  

  

  8 
  = 
  § 
  — 
  d 
  , 
  

  

  ?= 
  

  

  s 
  «Aj 
  

  

  

  

  p= 
  

  

  = 
  strength 
  

  

  of 
  the 
  magnetic 
  field. 
  

  

  The 
  quantities 
  e 
  x 
  and 
  c 
  are 
  constants 
  depending 
  on 
  the 
  system 
  

   which 
  produces 
  the 
  fundamental 
  line. 
  f 
  is 
  supposed 
  very 
  

   small, 
  and 
  upon 
  it 
  the 
  asymmetry 
  depends 
  ; 
  for 
  if 
  £ 
  = 
  we 
  

   get 
  

  

  which 
  represents 
  the 
  ordinary 
  Zeeman 
  effect. 
  If 
  f 
  is 
  

   retained 
  we 
  see 
  that 
  the 
  asymmetry 
  will 
  be 
  most 
  marked 
  in 
  

   a 
  weak 
  magnetic 
  field. 
  

  

  I 
  find 
  that 
  asymmetry 
  may 
  be 
  accounted 
  for 
  as 
  a 
  second 
  

   order 
  term 
  arising 
  from, 
  the 
  magnetic 
  field, 
  and 
  will 
  now 
  

   obtain 
  the 
  result. 
  

  

  Let 
  us 
  take 
  as 
  our 
  representative 
  molecule 
  producing 
  

   radiation, 
  a 
  system 
  consisting 
  of 
  two 
  atoms 
  equally 
  and 
  

   oppositely 
  charged. 
  Let 
  the 
  charge 
  be 
  e 
  and 
  the 
  effective 
  

   masses 
  m 
  l 
  and 
  m 
  2 
  respectively. 
  In 
  order 
  to 
  avoid 
  difficulties 
  

   about 
  the 
  law 
  of 
  force 
  between 
  the 
  two 
  atoms 
  we 
  shall 
  

   consider 
  the 
  motion 
  as 
  a 
  disturbed 
  circular 
  orbit, 
  so 
  that 
  we 
  

   may 
  write 
  the 
  equations 
  of 
  motion 
  as 
  

  

  m 
  l 
  x 
  l 
  +a?{x 
  l 
  — 
  £'.,) 
  = 
  <?H2/ 
  i; 
  7n 
  2 
  x 
  2 
  — 
  a 
  2 
  (x 
  l 
  — 
  x 
  2 
  ) 
  = 
  — 
  #H?/ 
  a 
  , 
  

  

  ™> 
  x 
  y 
  x 
  + 
  a\y 
  x 
  -y^ 
  = 
  -<?Ha? 
  |5 
  - 
  m 
  2 
  y 
  2 
  -a 
  2 
  {y 
  } 
  -?/,)= 
  +eRx 
  2 
  , 
  

  

  m,z 
  l 
  + 
  a\z-z 
  2 
  ) 
  = 
  0, 
  m^-tf^-zj 
  =0, 
  

  

  where 
  &iy 
  1 
  z 
  1 
  , 
  w 
  2 
  y. 
  ) 
  z 
  2 
  are 
  the 
  coordinates 
  of 
  the 
  centres 
  of 
  the 
  

   two 
  atoms 
  and 
  H 
  is 
  the 
  strength 
  of 
  magnetic 
  field 
  supposed 
  

   uniform 
  and 
  parallel 
  to 
  the 
  z 
  axis. 
  

  

  In 
  general 
  a 
  in 
  these 
  equations 
  may 
  differ 
  slightly 
  from 
  

   the 
  undisturbed 
  value, 
  but 
  for 
  the 
  present 
  purpose 
  this 
  does 
  

   not 
  matter. 
  

  

  