﻿204 
  Mr. 
  James 
  Walker 
  on 
  

  

  Hence 
  

  

  cos 
  2y 
  cos 
  26 
  = 
  cos 
  2u(cos^ 
  2/3 
  + 
  sin^ 
  2/3 
  cos 
  S) 
  — 
  sin 
  2a 
  sin 
  2y3 
  sin 
  8 
  

  

  = 
  cos 
  2« 
  cos2 
  2^ 
  + 
  sin 
  2/3 
  ^sin^ 
  2a 
  -h 
  cos^ 
  2a 
  sin2"2^' 
  

  

  cos 
  (S 
  + 
  -yjr) 
  

   cos 
  27 
  sin 
  20 
  = 
  cos 
  2a 
  sin 
  2j3 
  sin 
  8 
  + 
  sin 
  2u 
  cos 
  5 
  

  

  = 
  \/sin2 
  2a 
  + 
  cos2 
  2asin2 
  2yS 
  sin 
  (5 
  + 
  -f 
  ), 
  

   where 
  tan 
  i/r^tan 
  2a/sin 
  2^, 
  

   and 
  

  

  I 
  = 
  lc2 
  [1 
  + 
  COS 
  2a 
  C0S2 
  2y8 
  COS 
  2<^ 
  

  

  + 
  Vsin^ 
  2a 
  -h 
  cos^ 
  2oi 
  sin^ 
  2y8{sin 
  2^ 
  cos 
  2^ 
  cos(S 
  4- 
  i/r) 
  

  

  + 
  sin2(/)sin(S 
  + 
  '\/r)}] 
  

   =ic2[l 
  + 
  cos2acos2 
  2/3cos2(^ 
  

  

  + 
  \/sin^2a 
  + 
  cos'2asin2 
  2y8 
  V'sii?2^+cos22^sii?2^ 
  

  

  cos(S 
  + 
  t~V^O]> 
  

   where 
  tan 
  sjr' 
  = 
  tan 
  2(f)/sin 
  2/3. 
  

  

  This 
  formula 
  contains 
  the 
  theory 
  of 
  the 
  interference 
  

   phenomena 
  that 
  are 
  obtained 
  when 
  a 
  conical 
  pencil 
  of 
  polarized 
  

   light 
  traverses 
  the 
  plate 
  and 
  is 
  subsequently 
  analysed. 
  

  

  It 
  may 
  also 
  be 
  employed 
  for 
  the 
  case 
  in 
  which 
  the 
  stream 
  

   that 
  passes 
  through 
  the 
  polarizer, 
  quartz 
  plate 
  and 
  analyser 
  

   is 
  a 
  parallel 
  pencil 
  of 
  white 
  light 
  that 
  is 
  investigated 
  with 
  a 
  

   spectroscope. 
  With 
  a 
  su^ciently 
  thick 
  plate, 
  /3 
  may 
  be 
  

   regarded 
  as 
  constant 
  over 
  a 
  region 
  of 
  the 
  spectrum 
  corre- 
  

   spending 
  to 
  a 
  variation 
  of 
  B 
  by 
  several 
  multiples 
  of 
  tt, 
  and 
  

   we 
  see 
  that 
  the 
  minima 
  of 
  intensity 
  occur 
  for 
  the 
  radiations 
  

   for 
  which 
  B 
  = 
  (2n 
  + 
  l)7r 
  + 
  '^, 
  where 
  

  

  \Tr 
  _ 
  ^^^ 
  ^/^ 
  (^^^ 
  2(l> 
  — 
  tan 
  2a) 
  

   sin2 
  2/i^ 
  + 
  tan2(/)tan2a' 
  

  

  the 
  intensity 
  then 
  being 
  

  

  I 
  = 
  ic2{l 
  + 
  cos 
  2ot 
  cos2 
  20 
  cos 
  2<^ 
  

  

  ~ 
  v^l 
  — 
  cos'^ 
  2a 
  cos^ 
  2/3 
  Vl-cos2 
  2/3cos2 
  2(^}. 
  

  

  Thus 
  as 
  the 
  analyser 
  is 
  turn 
  3d, 
  the 
  dark 
  bands 
  travel 
  along 
  

   the 
  spectrum, 
  changing 
  their 
  intensity 
  as 
  they 
  progress 
  : 
  

   they 
  are 
  perfectly 
  black 
  when 
  (f) 
  = 
  7r/2 
  + 
  a, 
  and 
  are 
  least, 
  

   marked 
  when 
  </) 
  = 
  and 
  7r/2. 
  

  

  With 
  a 
  plate 
  perpendicular 
  to 
  the 
  optic 
  axis, 
  yS=7r/4, 
  and 
  

  

  i 
  = 
  c^ 
  COS" 
  — 
  ^ 
  = 
  c^ 
  cos^ 
  I- 
  — 
  ' 
  ; 
  

  

  