﻿Elliptic 
  Polarization. 
  205 
  

  

  hence 
  as 
  the 
  analyser 
  is 
  turned, 
  the 
  bands 
  traverse 
  the 
  spec- 
  

   trum, 
  retaining 
  the 
  same 
  intensity. 
  

  

  When 
  the 
  plate 
  is 
  parallel 
  to 
  the 
  optic 
  axis, 
  /3 
  = 
  or 
  is 
  at 
  

   any 
  rate 
  very 
  small, 
  and 
  

  

  I 
  = 
  ^c^{ 
  1 
  + 
  cos 
  2ot, 
  cos 
  2(^ 
  + 
  sin 
  2o(, 
  sin 
  2<f) 
  cos 
  8} 
  ; 
  

  

  wheii 
  </> 
  = 
  or 
  7r/2, 
  there 
  are 
  no 
  bands, 
  and 
  in 
  other 
  cases 
  

   the 
  bands 
  occur 
  where 
  S= 
  (2?z-f-l)7r 
  or 
  2/i7r, 
  according 
  to 
  

   the 
  sign 
  of 
  sin 
  2a 
  sin 
  2(/). 
  Thus 
  when 
  0<a<7r/2, 
  the 
  bands 
  

   occur 
  at 
  the 
  points 
  for 
  which 
  S= 
  (2;i 
  + 
  l)7r 
  so 
  long 
  as 
  

   0<(^<7r/2, 
  their 
  intensity 
  being 
  zero, 
  when 
  <^=7r/2 
  — 
  a; 
  

   and 
  as 
  4> 
  increases 
  through 
  7r/2, 
  they 
  change 
  their 
  position 
  

   to 
  that 
  of 
  the 
  former 
  maxima 
  of 
  intensity, 
  becoming 
  per- 
  

   fectly 
  black 
  when 
  ^ 
  = 
  7r/2H-a 
  *. 
  

  

  7. 
  Let 
  us 
  now 
  suppose 
  that 
  the 
  light 
  emergent 
  from 
  the 
  

   plate 
  is 
  examined 
  with 
  a 
  Savart's 
  analyser. 
  

  

  On 
  leaving 
  the 
  quartz, 
  the 
  stream 
  may 
  be 
  represented 
  by 
  

   the 
  components 
  

  

  (it, 
  u) 
  = 
  c(cos 
  7, 
  — 
  tsin^) 
  Exp 
  {i(?i^ 
  + 
  e)} 
  

  

  polarized 
  in 
  planes 
  making 
  angles 
  6 
  and 
  6 
  + 
  7r/2 
  with 
  the 
  

   principal 
  section 
  of 
  the 
  plate. 
  Hence 
  if 
  /a 
  be 
  the 
  angle 
  that 
  

   the 
  principal 
  section 
  of 
  the 
  quartz 
  makes 
  with 
  that 
  of 
  the 
  

   first 
  plate 
  of 
  the 
  analyser, 
  the 
  stream 
  emerging 
  from 
  the 
  

   Savart's 
  plate 
  will 
  have 
  components 
  

  

  I 
  = 
  {cosycos(^ 
  + 
  /x) 
  + 
  tsin7sin((9+/x)}Exp{i(?i^ 
  + 
  €' 
  + 
  D/2)} 
  

   77 
  = 
  {cos7sin(l9 
  + 
  /x) 
  — 
  fcsin7C0s(^ 
  + 
  ya)}Exp{i(wf 
  + 
  6'— 
  D/2)} 
  

  

  polarized 
  in 
  the 
  principal 
  sections 
  of 
  the 
  first 
  and 
  second 
  

   plate, 
  where 
  D 
  = 
  D2 
  — 
  Di, 
  Dj, 
  Dg 
  being 
  the 
  relative 
  retard- 
  

   ations 
  of 
  phase 
  introduced 
  by 
  the 
  two 
  plates. 
  

  

  On 
  analysation 
  in 
  an 
  azimuth 
  <^, 
  these 
  give 
  a 
  stream 
  

  

  H 
  = 
  f 
  cos 
  ^ 
  + 
  77 
  sin 
  (^ 
  

  

  = 
  [{cos 
  7 
  cos 
  {6 
  + 
  fi)-\-i 
  sin 
  7 
  sin 
  (O 
  + 
  fi)} 
  cos 
  (f> 
  Exp 
  (tD/2) 
  

   + 
  {cos 
  7 
  sin 
  (^ 
  + 
  yu) 
  — 
  tsin 
  7 
  cos 
  (^ 
  + 
  yu,)}sin 
  <^Exp 
  ( 
  — 
  fcD/2)] 
  

  

  X 
  Exp 
  {<w« 
  + 
  €')}, 
  

  

  * 
  The 
  above 
  results 
  agree 
  with 
  Beaulard's 
  description 
  of 
  the 
  pheno- 
  

   mena 
  {J. 
  de 
  Phys. 
  (3) 
  ii. 
  p. 
  399 
  (1893)). 
  Croullebois, 
  however, 
  gives 
  a 
  

   different 
  account 
  of 
  the 
  phenomena 
  in 
  the 
  lirst 
  and 
  last 
  cases 
  (loc. 
  cit. 
  

   p. 
  391). 
  

  

  