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  XXV, 
  On 
  Magneto- 
  Optical 
  Rotativity. 
  By 
  Gr. 
  H. 
  Livens, 
  

   B. 
  A., 
  Fellow 
  of 
  Jesus 
  College, 
  Cambridge*. 
  

  

  IN 
  several 
  recent 
  communications 
  to 
  this 
  Journal 
  i 
  have 
  

   discussed 
  and 
  developed 
  a 
  modification 
  of 
  Drude's 
  

   analysis 
  of 
  the 
  electromagnetic 
  theory 
  o£ 
  optics, 
  which 
  pro- 
  

   vides 
  a 
  good 
  account 
  of 
  many 
  hitherto 
  unexplained 
  pheno- 
  

   mena, 
  chiefly 
  concerned 
  with 
  the 
  effect 
  of 
  the 
  nature 
  of 
  a 
  

   substance 
  on 
  its 
  optical 
  behaviour. 
  The 
  subject 
  discussed 
  in 
  

   the 
  present 
  paper 
  provides 
  further 
  evidence 
  in 
  support 
  of 
  

   the 
  theory 
  there 
  discussed. 
  

  

  It 
  is 
  a 
  well-established 
  fact 
  that 
  the 
  magneto-optical 
  

   behaviour 
  of 
  simple 
  liquid 
  mixtures 
  is 
  not 
  simply 
  additive, 
  as 
  

   the 
  elementary 
  form 
  of 
  Drude's 
  theory 
  would 
  lead 
  one 
  to 
  

   expect. 
  The 
  present 
  theory 
  leads 
  to 
  a 
  much 
  more 
  compli- 
  

   cated 
  relation, 
  which 
  appears 
  to 
  be 
  supported 
  by 
  the 
  ex- 
  

   perimental 
  evidence, 
  at 
  least 
  as 
  far 
  as 
  I 
  can 
  judge 
  from 
  the 
  

   rather 
  limited 
  amount 
  of 
  information 
  I 
  have 
  access 
  to 
  at 
  the 
  

   present 
  moment. 
  No 
  new 
  hypothesis 
  is 
  required 
  to 
  be 
  added 
  

   to 
  the 
  previous 
  assumptions 
  to 
  obtain 
  these 
  new 
  results, 
  

   which 
  follow 
  directly 
  from 
  equations 
  already 
  deduced. 
  

  

  In 
  the 
  first 
  paper 
  of 
  the 
  series 
  the 
  general 
  equations 
  of 
  

   motion 
  of 
  the 
  typical 
  electron 
  oscillating 
  in 
  an 
  external 
  

   magnetic 
  field 
  were 
  shown 
  to 
  be 
  of 
  a 
  type 
  

  

  m,c 
  

  

  eR 
  

  

  + 
  lix 
  + 
  he 
  y 
  = 
  e 
  (E 
  x 
  + 
  aPi) 
  , 
  

  

  eR 
  ■ 
  

   my 
  +hy 
  + 
  ky+— 
  7 
  x=: 
  e(Ej/ 
  + 
  a? 
  y 
  ) 
  , 
  

  

  o 
  

  

  m'z 
  +hz 
  + 
  kz 
  = 
  e(E 
  z 
  + 
  a~P 
  z 
  ), 
  

  

  where 
  the 
  notation 
  needs 
  no 
  explaining. 
  We 
  see 
  at 
  once 
  

   that 
  the 
  vibration 
  component 
  parallel 
  to 
  the 
  magnetic 
  field 
  

   is 
  unaltered 
  by 
  the 
  field, 
  and 
  is 
  therefore 
  merely 
  modified 
  in 
  

   the 
  manner 
  previously 
  described. 
  It 
  is, 
  however, 
  otherwise 
  

   with 
  the 
  two 
  components 
  perpendicular 
  to 
  the 
  magnetic 
  

   field. 
  In 
  the 
  previous 
  paper 
  the 
  results 
  of 
  the 
  analysis 
  of 
  

   these 
  vibrations 
  were 
  given 
  as 
  far 
  as 
  they 
  refer 
  to 
  the 
  actual 
  

   modification 
  in 
  the 
  appearance 
  of 
  the 
  spectrum 
  lines. 
  In 
  

   the 
  present 
  paper 
  it 
  is 
  proposed 
  to 
  investigate 
  the 
  rotation 
  

   of 
  the 
  plane 
  of 
  polarization 
  of 
  a 
  plane 
  polarized 
  beam 
  of 
  

   homogeneous 
  light 
  of 
  frequency 
  n 
  propagated 
  parallel 
  to 
  the 
  

   lines 
  of 
  the 
  applied 
  magnetic 
  field. 
  In 
  dealing 
  with 
  light 
  

  

  * 
  Communicated 
  "bv 
  the 
  Author. 
  

  

  