﻿548 
  On 
  MacCullagli 
  and 
  Stokes's 
  Elliptic 
  Analyser. 
  

   But 
  according 
  to 
  Gouy's 
  hypothesis, 
  

  

  a/cos 
  p=—/3/smp 
  = 
  e~ 
  lK 
  l 
  l 
  i, 
  y/sin 
  p 
  = 
  S/cos 
  p 
  = 
  e~ 
  lK 
  ^, 
  

   whence 
  

  

  and 
  

  

  p'+p'^fH 
  + 
  fh* 
  

  

  6. 
  As 
  a 
  final 
  example, 
  let 
  lis 
  consider 
  the 
  passage 
  of 
  

   a 
  'stream 
  of 
  polarized 
  light 
  through 
  a 
  closed 
  symmetrical 
  

   packet 
  of 
  plates, 
  the 
  case 
  considered 
  qualitatively 
  by 
  Poincare. 
  

  

  The 
  effect 
  of 
  the 
  packet 
  on 
  the 
  polarization 
  of 
  the 
  stream 
  

   is 
  given 
  by 
  the 
  resultant 
  of 
  successive 
  rotations 
  about 
  axes 
  

   CAj, 
  CA 
  2 
  in 
  the 
  plane 
  of 
  the 
  equator 
  through 
  an 
  angle 
  S, 
  

   where 
  C 
  is 
  the 
  centre 
  of 
  the 
  sphere, 
  S 
  the 
  relative 
  retardation 
  

   of 
  phase 
  introduced 
  by 
  each 
  plate, 
  and 
  A 
  1 
  A 
  2 
  = 
  A 
  2 
  A 
  3 
  = 
  . 
  . 
  . 
  

   = 
  27r/p, 
  p 
  being 
  the 
  number 
  of 
  plates 
  in 
  the 
  packet. 
  

  

  If 
  then 
  A 
  n 
  denote 
  a 
  rotation 
  B 
  about 
  the 
  axis 
  CA 
  n 
  , 
  and 
  

   S 
  p 
  a 
  rotation 
  27rjp 
  round 
  the 
  polar 
  axis 
  CP, 
  the 
  combined 
  

   rotation 
  is 
  

  

  Aj 
  . 
  A 
  2 
  . 
  A 
  3 
  . 
  . 
  . 
  Ap 
  = 
  A 
  1 
  . 
  S-pAiSp 
  . 
  S_2 
  P 
  A 
  1 
  S 
  2p 
  .... 
  S-^-DpAjS^-i^, 
  

  

  but 
  

  

  S(p-l)p» 
  fep=b 
  p 
  . 
  p 
  = 
  $27r— 
  1 
  0r 
  b(p_i) 
  p 
  =b_ 
  2 
  „ 
  

  

  whence 
  

  

  A 
  1 
  .A 
  2 
  .A 
  3 
  ...Ap 
  = 
  (A 
  1 
  S_p>>; 
  

  

  or 
  the 
  effect 
  of 
  the 
  p 
  successive 
  rotations 
  is 
  the 
  same 
  as 
  

   p 
  times 
  the 
  resultant 
  of 
  the 
  rotations 
  A 
  x 
  and 
  S_ 
  P 
  . 
  

  

  Fig. 
  5. 
  

  

  To 
  determine 
  this 
  resultant, 
  we 
  must 
  draw 
  through 
  A 
  l 
  a 
  

   great 
  circle 
  making 
  °an 
  angle 
  8/2 
  with 
  A 
  X 
  P 
  in 
  a 
  direction 
  

   opposite 
  to 
  the 
  rotation 
  round 
  CA 
  l5 
  and 
  through 
  P 
  a 
  great 
  

   circle 
  making 
  with 
  PA 
  X 
  an 
  angle 
  irjp 
  in 
  the 
  same 
  direction 
  as 
  

  

  