﻿On 
  Magneto- 
  Optical 
  Rotativity. 
  363 
  

  

  of 
  frequency 
  n, 
  the 
  first 
  two 
  of 
  the 
  above 
  equations 
  reduce 
  

   to 
  

  

  px 
  — 
  iqy 
  = 
  e 
  (E 
  z 
  + 
  aP 
  x 
  ), 
  

  

  py 
  + 
  iqx 
  = 
  e(& 
  y 
  + 
  aP 
  y 
  ), 
  

  

  where 
  9 
  , 
  . 
  7 
  7 
  e^.H 
  

  

  » 
  = 
  — 
  miv 
  -j- 
  inn 
  -f 
  A:, 
  <7 
  = 
  — 
  — 
  ? 
  

  

  G 
  

  

  whence 
  we 
  have 
  

  

  (p+q)(x±iy) 
  = 
  e(E 
  x 
  ±iEy)+ae(P 
  x 
  ±iPy), 
  

  

  whence 
  also 
  since 
  

  

  2a&=P 
  x 
  , 
  2^-=P 
  y 
  , 
  

   we 
  have 
  

  

  P,±iP,=(2^)(B,±iB 
  y 
  ) 
  + 
  (2^)(P,±;P 
  y 
  ), 
  

  

  where 
  the 
  sums 
  2 
  are 
  taken 
  per 
  unit 
  volume 
  over 
  all 
  the 
  

   optically 
  excitable 
  electrons. 
  From 
  this 
  relation 
  we 
  deduce 
  

   in 
  the 
  usual 
  manner 
  that 
  right- 
  and 
  left-handed 
  circularly 
  

   polarized 
  beams 
  are 
  propagated 
  with 
  different 
  velocities. 
  The 
  

   indices 
  of 
  refraction 
  for 
  the 
  two 
  beams 
  are 
  /j, 
  + 
  and 
  /!_, 
  where 
  

  

  ,4=1+ 
  _ 
  p+i 
  

  

  y^ 
  ' 
  ae 
  2 
  

  

  p 
  + 
  q 
  

  

  The 
  rate 
  of 
  rotation 
  of 
  the 
  plane 
  of 
  polarization 
  which 
  

   arises 
  from 
  the 
  interaction 
  of 
  these 
  two 
  circularly 
  polarized 
  

   beams 
  is 
  then 
  determined 
  by 
  

  

  PL— 
  A. 
  

  

  — 
  \n 
  

  

  /*-+/*+' 
  

  

  and 
  on 
  account 
  of 
  the 
  always 
  small 
  difference 
  between 
  yu_ 
  

   and 
  /ub 
  + 
  this 
  is 
  practically 
  

  

  0,= 
  ^ 
  01-/4), 
  

  

  where 
  /m 
  is 
  the 
  ordinary 
  index 
  of 
  refraction 
  of 
  the 
  substance. 
  

   If 
  now 
  we 
  use 
  this 
  result 
  for 
  a 
  region 
  of 
  the 
  spectrum 
  where 
  

   there 
  is 
  no 
  absorption, 
  the 
  terms 
  in 
  h 
  can 
  be 
  neglected,, 
  and 
  

  

  2 
  B 
  2 
  

  

  