﻿Stokes's 
  Elliptic 
  Analyser. 
  547 
  

  

  zation-vectors 
  is 
  given 
  by 
  

  

  tan 
  2/3 
  = 
  2p/ 
  \ 
  k(hi 
  — 
  fju 
  2 
  ) 
  } 
  . 
  

  

  In 
  the 
  case 
  of 
  quartz 
  and 
  other 
  positive 
  crystals, 
  /t 
  2 
  > 
  p,i, 
  and 
  

   the 
  stream 
  with 
  its 
  plane 
  o£ 
  maximum 
  polarization 
  in 
  the 
  

   principal 
  section 
  o£ 
  the 
  plate, 
  is 
  left- 
  or 
  right-handed, 
  

   according 
  as 
  p 
  is 
  positive 
  or 
  negative, 
  that 
  is 
  according 
  as 
  

   the 
  crystal 
  is 
  left- 
  or 
  right-handed. 
  

  

  In 
  traversing 
  unit 
  thickness 
  the 
  phase 
  of 
  the 
  vibrations 
  in 
  

   the 
  right-handed 
  stream 
  is 
  retarded 
  relatively 
  to 
  that 
  of 
  the 
  

   left-handed 
  vibrations 
  by 
  an 
  amount 
  

  

  the 
  upper 
  or 
  lower 
  sign 
  being 
  taken, 
  according 
  as] 
  p 
  is 
  

   positive 
  or 
  negative 
  ; 
  and 
  in 
  order 
  to 
  obtain 
  the 
  actual 
  re- 
  

   tardations 
  of 
  phase 
  kjj/ 
  and 
  k/j, 
  11 
  of 
  the 
  streams^ 
  we 
  require 
  to 
  

   know 
  the 
  value 
  of 
  #(// 
  + 
  p>") 
  . 
  

  

  In 
  order 
  to 
  determine 
  this 
  *, 
  let 
  a 
  stream 
  of 
  permanent 
  type 
  

   be 
  replaced 
  by 
  its 
  components 
  polarized 
  in 
  planes 
  parallel 
  

   and 
  perpendicular 
  to 
  the 
  principal 
  section 
  with 
  the 
  J 
  polari- 
  

   zation-vectors 
  

  

  g=Ae" 
  lt 
  , 
  r) 
  — 
  Be 
  int 
  , 
  

  

  and 
  suppose 
  that 
  after 
  traversing 
  unit 
  thickness 
  these 
  become 
  

  

  then 
  we 
  have 
  

  

  A'=*A 
  + 
  #B, 
  °B'= 
  7 
  A 
  + 
  SB, 
  

  

  where 
  a, 
  /3, 
  7, 
  3 
  are 
  constants 
  depending 
  upon 
  the 
  nature 
  of 
  

   the 
  plate. 
  

  

  But 
  the 
  stream 
  being 
  of 
  permanent 
  type, 
  we 
  have 
  

  

  A'/A=B'/B 
  =«-•«, 
  

  

  where 
  kx 
  is 
  the 
  retardation 
  of 
  phase 
  ; 
  hence 
  

  

  ( 
  a 
  _e-^)A-f/3B==0, 
  yA 
  + 
  (8-e- 
  lKX 
  )B 
  = 
  0, 
  

  

  and 
  

  

  

  

  7, 
  S—e- 
  

  

  ■ 
  OCX 
  

  

  =0. 
  

  

  The 
  roots 
  of 
  this 
  equation 
  give 
  the 
  values 
  of 
  e~~ 
  lK 
  F 
  9 
  e-W^ 
  

   and 
  their 
  product 
  is 
  

  

  cch-/3y 
  = 
  e- 
  lK 
  ^+i 
  J 
  -"\ 
  

   * 
  Poincare, 
  loc. 
  cit. 
  p. 
  299. 
  

  

  