﻿380 
  Lord 
  Rayleigh 
  on 
  the 
  Scattering 
  of 
  Light 
  by 
  a 
  

  

  the 
  component 
  vibrating 
  parallel 
  to 
  Z 
  is 
  thus 
  

  

  tV{3(A» 
  + 
  B 
  2 
  + 
  C 
  2 
  ) 
  + 
  2(AB 
  + 
  BO 
  + 
  CA) 
  } 
  

  

  + 
  T 
  1 
  5 
  {A 
  2 
  + 
  B 
  2 
  + 
  C 
  2 
  -AB--BC--CA} 
  

  

  = 
  T 
  i 
  5 
  {4(A 
  2 
  + 
  B 
  2 
  + 
  C 
  2 
  ) 
  + 
  AB 
  + 
  BC 
  + 
  CA} 
  ; 
  . 
  (21) 
  

  

  while 
  that 
  of 
  the 
  component 
  vibrating 
  parallel 
  to 
  X 
  is 
  

   simply 
  

  

  1 
  %{A 
  2 
  + 
  B 
  2 
  + 
  C 
  2 
  -AB-BC-OA). 
  . 
  . 
  (22) 
  

  

  The 
  ratio 
  o£ 
  the 
  two 
  intensities 
  is 
  

  

  2(^ 
  + 
  B 
  > 
  + 
  C 
  s 
  -AB-BC-CA) 
  

  

  4(A 
  2 
  4-B 
  3 
  + 
  C 
  2 
  ) 
  + 
  AB 
  + 
  BC 
  + 
  CA' 
  • 
  • 
  K™) 
  

  

  reducing 
  to 
  (6) 
  when 
  B 
  = 
  A. 
  

  

  It 
  may 
  be 
  observed 
  that, 
  since 
  (21) 
  = 
  (14) 
  + 
  (19), 
  we 
  

   obtain 
  the 
  same 
  intensity 
  whether 
  we 
  use 
  a 
  polarizer 
  trans- 
  

   mitting 
  vibrations 
  parallel 
  to 
  Z 
  and 
  no 
  analyser, 
  or 
  whether 
  

   we 
  use 
  an 
  analyser 
  transmitting 
  vibrations 
  parallel 
  to 
  Z 
  and 
  

   no 
  polarizer. 
  

  

  It* 
  neither 
  polarizing 
  nor 
  analysing 
  apparatus 
  is 
  employed, 
  

   we 
  may 
  add 
  (21) 
  and 
  (22), 
  thus 
  obtaining 
  

  

  ^[6(A 
  2 
  + 
  B 
  2 
  + 
  C 
  2 
  )-AB-BC-CA]. 
  . 
  . 
  (24) 
  

  

  When 
  the 
  particles 
  are 
  supposed 
  to 
  be 
  of 
  uniform 
  quality, 
  

   with 
  a 
  specific 
  inductive 
  capacity 
  K/ 
  as 
  compared 
  with 
  K 
  for 
  

   the 
  undisturbed 
  medium, 
  and 
  to 
  be 
  of 
  ellipsoidal 
  form 
  with 
  

   semi-axes 
  a, 
  b, 
  c, 
  we 
  have 
  

  

  where 
  • 
  • 
  • 
  (25) 
  

  

  L 
  = 
  2 
  7 
  ra^j 
  o(a2 
  + 
  x)S/2(J2+ 
  X 
  x)]/2(cJ 
  + 
  x)1/2 
  , 
  . 
  (26) 
  

  

  with 
  similar 
  expressions 
  for 
  M 
  and 
  N. 
  

  

  If 
  the 
  ellipsoid 
  be 
  of 
  revolution 
  the 
  case 
  is 
  simplified 
  *. 
  

   For 
  example, 
  if 
  it 
  be 
  of 
  the 
  elongated 
  or 
  ovary 
  form 
  with 
  

   eccentricity 
  e, 
  

  

  a 
  = 
  b 
  = 
  c*/{l-e-) 
  ; 
  (27) 
  

  

  L=M=2.{l- 
  1 
  -/logi±f}, 
  . 
  . 
  (28) 
  

  

  * 
  See 
  the 
  paper 
  of 
  1897. 
  

  

  