﻿376 
  Lord 
  Ray 
  lei 
  oh 
  on 
  the 
  Scattering 
  of 
  Light 
  by 
  a 
  

  

  The 
  first 
  set 
  of 
  factors 
  remains 
  as 
  before. 
  Taking 
  both 
  sets 
  

   into 
  account, 
  we 
  get 
  for 
  tbe 
  vibration 
  parallel 
  to 
  X 
  

  

  —A 
  sin 
  cos 
  6 
  cos 
  <fi 
  + 
  C 
  cos 
  sin 
  6 
  cos 
  <f>, 
  

  

  the 
  square 
  of 
  which 
  is 
  

  

  (C-A) 
  2 
  sin 
  2 
  0cos 
  2 
  0eos 
  2 
  (3) 
  

  

  The 
  mean 
  value 
  of 
  cos 
  2 
  <f> 
  is 
  \. 
  That 
  of 
  cos 
  2 
  6 
  is 
  J 
  and 
  that 
  

   of 
  cos 
  4 
  is 
  J, 
  as 
  above, 
  so 
  that 
  corresponding 
  to 
  (2) 
  we 
  have 
  

   for 
  the 
  mean 
  intensity 
  of 
  the 
  vibrations 
  parallel 
  to 
  X 
  

  

  i 
  ( 
  C-A)'(J-i)=J 
  5 
  (C-A)s. 
  ... 
  (4) 
  

  

  The 
  ratio 
  of 
  intensities 
  of 
  the 
  two 
  components 
  is 
  thus 
  

  

  (C-A) 
  2 
  

  

  8A 
  2 
  + 
  3C 
  2 
  + 
  4AC 
  

  

  (5) 
  

  

  Two 
  particular 
  cases 
  are 
  worthy 
  of 
  notice. 
  If 
  A 
  can 
  be 
  

   neglected 
  in 
  comparison 
  with 
  0, 
  (5) 
  becomes 
  simply 
  one- 
  

   third. 
  On 
  the 
  other 
  hand, 
  if 
  A 
  is 
  predominant, 
  (5) 
  reduces 
  

   to 
  one-eighth. 
  

  

  The 
  above 
  expressions 
  apply 
  when 
  the 
  primary 
  light, 
  pro- 
  

   pagated 
  parallel 
  to 
  X, 
  is 
  completely 
  polarized 
  with 
  vibrations 
  

   parallel 
  to 
  Z, 
  the 
  direction 
  of 
  the 
  secondary 
  ray 
  being 
  along 
  

   OY. 
  If 
  the 
  primary 
  light 
  be 
  unpolarized, 
  we 
  have 
  further 
  

   to 
  include 
  the 
  effect 
  of 
  the 
  primary 
  vibrations 
  parallel 
  to 
  Y. 
  

   The 
  two 
  polarized 
  components 
  scattered 
  along 
  OY, 
  resulting 
  

   therefrom, 
  both 
  vibrate 
  in 
  directions 
  perpendicular 
  to 
  OY, 
  

   and 
  accordingly 
  are 
  both 
  represented 
  by 
  (4). 
  In 
  the 
  case 
  of 
  

   unpolarized 
  primary 
  light 
  we 
  have 
  therefore 
  to 
  double 
  (4) 
  

   for 
  the 
  secondary 
  vibrations 
  parallel 
  to 
  X, 
  and 
  to 
  add 
  to- 
  

   gether 
  (2) 
  and 
  (4) 
  for 
  the 
  vibrations 
  parallel 
  to 
  Z. 
  The 
  

   latter 
  becomes 
  

  

  J-(9A 
  2 
  + 
  4C 
  2 
  + 
  2AC), 
  

   and 
  for 
  the 
  ratio 
  of 
  intensities 
  of 
  the 
  two 
  components 
  

  

  2(C-A) 
  2 
  

  

  9A 
  2 
  + 
  4e 
  2 
  -r2A(J 
  

   When 
  A 
  = 
  0, 
  this 
  ratio 
  is 
  one-half. 
  

  

  (6) 
  

  

  For 
  a 
  more 
  general 
  treatment, 
  which 
  shall 
  include 
  all 
  

   forms 
  of 
  particle, 
  we 
  must 
  introduce 
  another 
  angle 
  t/t 
  to 
  

  

  