﻿196 
  Mr. 
  James 
  Walker 
  on 
  

  

  with 
  its 
  plane 
  of 
  maximum 
  polarization 
  (/8 
  being 
  numerically 
  

   less 
  than 
  wjA. 
  and 
  positive 
  or 
  negative 
  according 
  as 
  the 
  

   quartz 
  is 
  left- 
  or 
  right-hand) 
  in 
  the 
  principal 
  section, 
  together 
  

   with 
  the 
  oppositely 
  polarized 
  stream 
  defined 
  by 
  the 
  vector 
  

  

  (fsj 
  Vi) 
  =<^2(— 
  sin 
  l3, 
  —i 
  cos 
  /3) 
  Exp 
  ]i(w^ 
  -feg) 
  }, 
  

   where 
  

  

  Ci 
  Exp 
  (tei) 
  = 
  cos 
  a 
  cos 
  /3 
  + 
  ^ 
  sin 
  a 
  sin 
  yS, 
  

  

  C2 
  Exp 
  (^62) 
  = 
  —cos 
  a 
  sin 
  /3 
  + 
  4 
  sin 
  a 
  cos 
  /3. 
  

  

  These 
  oppositely 
  polarized 
  streams 
  traverse 
  the 
  plate 
  with 
  

   different 
  speeds, 
  and 
  on 
  emergence 
  the 
  second 
  is 
  retarded 
  in 
  

   phase 
  relatively 
  to 
  the 
  first 
  by 
  an 
  amount 
  3, 
  so 
  that 
  the 
  emer- 
  

   gent 
  light 
  will 
  be 
  in 
  general 
  elliptically 
  polarized 
  and 
  may 
  be 
  

   denoted 
  by 
  

  

  (if, 
  v) 
  = 
  c(cos 
  7, 
  — 
  i 
  sin 
  7) 
  Exp 
  { 
  l 
  [nt 
  4- 
  e) 
  } 
  , 
  

   where 
  

  

  c(cos 
  7 
  cos 
  ^ 
  -j- 
  fc 
  sin 
  7 
  sin 
  6) 
  Exp 
  { 
  /■ 
  (e 
  4- 
  3/2) 
  

  

  = 
  CiCos/5Exp{t(ei 
  + 
  3/2)}— 
  C2sin/3Exp{6(€2— 
  S/2)}, 
  

  

  c(cos7sin^— 
  fcsin 
  7 
  cos 
  6) 
  Exp{t(6-{-S/2)} 
  

  

  = 
  — 
  iCi 
  sin 
  /3 
  Exp{f 
  (e^ 
  -f- 
  S/2)} 
  — 
  LC2 
  cos 
  ^ 
  Exp{fc(e2 
  — 
  S/2)}, 
  

  

  d 
  being 
  the 
  angle 
  between 
  the 
  principal 
  section 
  of 
  the 
  plate 
  

   and 
  the 
  plane 
  of 
  maximum 
  or 
  minimum 
  polarization 
  of 
  the 
  

   resultant 
  stream, 
  according 
  as 
  7 
  is 
  numerically 
  less 
  or 
  greater 
  

   than 
  7r/4. 
  

  

  Substituting 
  for 
  CiExp(fc6i) 
  and 
  C2 
  Exp 
  (462) 
  and 
  writing 
  

  

  tan 
  11= 
  sin 
  2/3 
  tan 
  8/2, 
  tan 
  A/ 
  2 
  = 
  cot 
  2/3 
  sin 
  R, 
  . 
  (1) 
  

   we 
  obtain 
  

  

  ^(cos 
  7 
  cos 
  ^ 
  + 
  i 
  sin 
  7 
  sin 
  6) 
  Exp{t(6 
  + 
  8/2)} 
  

  

  ~ 
  cos 
  {a 
  + 
  R) 
  cos 
  A/2 
  + 
  1 
  cos 
  a. 
  sin 
  A/25 
  

   c(cos 
  7 
  sin 
  ^ 
  — 
  i 
  sin 
  7 
  cos 
  6) 
  Exp 
  { 
  ^(e 
  + 
  8/2) 
  J- 
  

  

  = 
  sin 
  (a 
  + 
  R) 
  cos 
  A/2 
  — 
  i 
  sin 
  a 
  sin 
  A/2, 
  

   or 
  

  

  c\ 
  cos7COs(^— 
  ^j 
  + 
  tsin7sin( 
  ^— 
  ^j 
  r^^p-! 
  ^^+9) 
  ( 
  

   c\ 
  cosysin(0— 
  ^j 
  — 
  tsinycosl^— 
  X-) 
  |-Exp//e+ 
  ^^ 
  I 
  

  

  