﻿200 
  

  

  Mr. 
  James 
  Walker 
  on 
  

  

  Tbe 
  following 
  tables 
  give 
  some 
  of 
  the 
  principal 
  cases; 
  

   of 
  the 
  changes 
  of 
  the 
  plane 
  of 
  maximum 
  polarization 
  and 
  of 
  

   sin 
  2y 
  as 
  E, 
  increases 
  from 
  to 
  tt, 
  ^ 
  being 
  taken 
  as 
  positive. 
  

  

  Table 
  I.— 
  cos^ 
  2a 
  > 
  tan^ 
  2/5. 
  

   0<a<7r/4. 
  

  

  

  tanE. 
  

  

  tan2(6>-a). 
  9. 
  

  

  sin 
  2y. 
  

  

  1. 
  

  

  2. 
  

   3. 
  

   4. 
  

  

  5. 
  

  

  6. 
  

  

  7. 
  

   8. 
  

   9. 
  

  

  

  

  tan(x-a) 
  

  

  tan^ 
  '2(5 
  

   sin 
  2a 
  cos 
  2a 
  

  

  sin 
  2/3 
  cot 
  J 
  

  

  2 
  

  

  cot 
  2a 
  

  

  -tan 
  (x 
  4- 
  2a) 
  

  

  -tan 
  2a 
  

  

  -sh\2j3tsin^ 
  

  

  

  

  

  

  tan 
  (x-2a) 
  

  

  

  

  -tan 
  2a 
  

  

  —tan 
  4 
  a 
  

   -tan(x+2a) 
  

  

  — 
  tan 
  4a 
  

  

  -tan 
  2a 
  

  

  

  

  a 
  

  

  U 
  

  

  

  

  — 
  a 
  

  

  _x 
  

  

  2 
  

  

  — 
  a 
  

   

  

  

   tan 
  2/3 
  

   cos 
  2a 
  

   sin2/tan-1^^^2/3\ 
  

   V 
  cos 
  2a 
  / 
  

  

  sin 
  2a 
  cos 
  2/3 
  cot 
  ^ 
  

  

  2 
  

  

  sin2ftan-it^"2^\ 
  

   \ 
  cos 
  2a 
  / 
  

  

  tan 
  2/3 
  

   cos 
  2a 
  

  

  

  

  — 
  sin 
  2a 
  cos 
  2/3 
  tan 
  ^ 
  

   2 
  

  

  

  

  7r/4<a<7r/2. 
  

  

  

  tanE. 
  

  

  tan 
  2(0-0). 
  

  

  ^. 
  

  

  sin 
  2y, 
  

  

  1. 
  

  

  

  

  

  

  a 
  

  

  

  

  2, 
  

  

  sin 
  2/3 
  cot 
  J 
  

  

  -tan 
  2a 
  

  

  IT 
  

   7) 
  

  

  sin 
  2a 
  cos 
  2/3 
  cot 
  

  

  3. 
  

  

  — 
  tan 
  2a 
  

  

  — 
  tan 
  4a 
  

  

  TT 
  — 
  a 
  

  

  

  

  4. 
  

  

  tan(x-2a) 
  

  

  lan(x-2a) 
  

  

  2 
  +2 
  

  

  tan 
  2/3 
  

   cos 
  2a 
  

  

  5. 
  

  

  cot 
  2a 
  

  

  — 
  tan 
  4a 
  

  

  TT 
  — 
  a 
  

  

  sm2/tan-l'™f\ 
  

   \ 
  cos 
  2a 
  / 
  

  

  6. 
  

  

  -sin 
  2/3 
  tan 
  ^^ 
  

  

  -tan 
  2a 
  

  

  TT 
  

  

  -sin2acos2/3tan^ 
  

  

  7. 
  

  

  tan2 
  2/3 
  

   sin 
  2a 
  cos 
  2a 
  

  

  

  

  a 
  

  

  sin2/tan-l^'-2m 
  

   \ 
  cos 
  2a/ 
  

  

  8. 
  

  

  -tan(x+2a) 
  

  

  -tan(x+2a) 
  

  

  2 
  ~ 
  2 
  

  

  tan 
  2/3 
  

   cos 
  2a 
  

  

  9. 
  

  

  

  

  

  

  a 
  

  

  

  

  