﻿(2) 
  

  

  Elliptic 
  Polarization. 
  197 
  

  

  whence 
  

  

  cos 
  7 
  cos 
  ( 
  0— 
  ^j 
  + 
  ismysinf 
  ^— 
  ^ 
  j 
  

  

  cos 
  7 
  sin 
  ( 
  ^ 
  — 
  — 
  j 
  — 
  6 
  sin 
  7 
  cos| 
  6— 
  ^\ 
  

  

  = 
  ecu 
  a 
  + 
  9 
  )(cos 
  A 
  + 
  1 
  sin 
  A) 
  ,. 
  

   which 
  gives 
  

  

  cos 
  27 
  sin 
  (2^ 
  -E) 
  ,/ 
  E\ 
  

  

  1 
  o 
  /oz} 
  — 
  1^\ 
  =C0t 
  a+ 
  ^ 
  I 
  cos 
  A 
  

  

  1— 
  COS 
  27 
  cos 
  (2^ 
  — 
  K) 
  \ 
  2/ 
  

  

  sin 
  27 
  ^/ 
  E\ 
  . 
  ^ 
  

  

  1 
  — 
  COS 
  27 
  cos 
  (2^ 
  — 
  K) 
  \ 
  2 
  / 
  

  

  From 
  these 
  we 
  obtain 
  the 
  equations 
  

  

  tan 
  (2(9-R)=tan 
  (2a 
  + 
  R) 
  cos 
  A, 
  -j 
  

  

  sin27 
  = 
  sin 
  (2a4-E)sinA, 
  J- 
  ... 
  (3) 
  

  

  ian27 
  = 
  tan 
  (a 
  + 
  (9) 
  tan 
  (a 
  + 
  R 
  ~ 
  6*) 
  -/ 
  

  

  that 
  determine 
  the 
  character 
  o£ 
  the 
  stream 
  emerging 
  from 
  

   the 
  quartz, 
  ^ 
  and 
  S 
  and 
  consequently 
  E 
  and 
  A 
  being 
  

   supposed 
  to 
  be 
  known. 
  

  

  2. 
  For 
  the 
  discussion 
  of 
  the 
  elliptic 
  polarization 
  it 
  is 
  more 
  

   convenient 
  to 
  express 
  tan 
  2 
  (^ 
  — 
  a) 
  and 
  sin 
  27 
  in 
  terms 
  of 
  

   tan 
  R. 
  SoMng 
  for 
  tan 
  2(^ 
  — 
  a) 
  we 
  obtain 
  

  

  tan 
  m-cA 
  ^^ 
  -^^^ 
  (2^ 
  4-E) 
  cos 
  A 
  -tan 
  (2a 
  - 
  E) 
  

   1 
  + 
  tan 
  (2a 
  + 
  E) 
  tan 
  (2a 
  — 
  E) 
  cos 
  A 
  

  

  ^ 
  sin2Ecos^ 
  A/2-sin4asin^A/2 
  

   cos 
  2E 
  cos^ 
  A/2 
  -h 
  cos 
  4a 
  sin^ 
  A/2' 
  

   sin 
  2R-sin 
  4a 
  cot^ 
  2B 
  sin^ 
  E 
  

  

  "■ 
  cos 
  2\i 
  + 
  cos 
  4a 
  cut^ 
  2^ 
  sin^ 
  E 
  

  

  _ 
  2 
  tan 
  E-2 
  sin 
  2a 
  cos 
  2a 
  cot^ 
  213 
  tan^ 
  E 
  

  

  "" 
  l+(cos4acot2 
  2/3— 
  l)tan2E 
  

   Also 
  

  

  sin 
  27= 
  sin 
  2a 
  cos 
  E 
  sin 
  A 
  + 
  cos 
  2a 
  sin 
  E 
  sin 
  A 
  

  

  _ 
  2 
  sin 
  2a 
  cot 
  2/3 
  tan 
  R 
  + 
  2 
  cos 
  2a 
  cot 
  23 
  tan^ 
  E 
  

   l-h(cot2 
  2y3 
  + 
  l)tanUi 
  

   since 
  

  

  . 
  2 
  tan 
  A/ 
  2 
  2cot2y3sinE 
  

  

  ^^" 
  1 
  + 
  tan^ 
  A:^ 
  - 
  1 
  + 
  cot^ 
  2^ 
  sin^E 
  ' 
  

  

  These 
  expressions 
  have 
  the 
  form 
  

  

  y 
  = 
  2{ax-^hx^)l(l 
  + 
  cx''). 
  

  

  