﻿206 
  On 
  Elliptic 
  Polarization. 
  

  

  and 
  the 
  intensity, 
  obtained 
  by 
  multiplying 
  this 
  by 
  the 
  con- 
  

   jugate 
  expression, 
  is 
  

  

  I 
  = 
  {cos^ 
  7 
  cos^ 
  {6 
  4- 
  /a) 
  + 
  sin^ 
  7 
  sin^ 
  (d 
  + 
  fi)} 
  cos^ 
  

   + 
  {cos^ 
  7 
  sin^ 
  {d-\-fj)-t 
  sin^ 
  7 
  cos^ 
  (6-\- 
  jx)] 
  sin^ 
  <^ 
  

   + 
  (cos 
  27 
  sin 
  2(6 
  + 
  ix) 
  cos 
  D 
  — 
  sin 
  27 
  sin 
  D 
  } 
  sin 
  cos 
  ^ 
  

   = 
  i[H-cos 
  27 
  cos 
  2((9+ya) 
  C0S2(/) 
  

  

  + 
  sin2</>{cos27sin2(^+/i) 
  cos 
  D 
  — 
  sin 
  27 
  sin 
  D}], 
  

  

  and 
  when, 
  as 
  is 
  ordinarily 
  the 
  case, 
  (^ 
  = 
  7r/4 
  

  

  I 
  = 
  ■!{ 
  1 
  + 
  cos 
  27 
  sin 
  2(^+//,) 
  cos 
  D- 
  sin 
  27 
  sin 
  D 
  }. 
  

  

  In 
  order, 
  then, 
  that 
  the 
  bands 
  may 
  disappear, 
  we 
  must 
  

   have 
  

  

  sin 
  27 
  = 
  and 
  sin 
  2(l9 
  + 
  At) 
  = 
  ; 
  

  

  that 
  is, 
  the 
  light 
  emergent 
  from 
  the 
  quartz 
  must 
  be 
  plane 
  

   polarized 
  in 
  the 
  principal 
  section 
  of 
  one 
  of 
  the 
  plates 
  of 
  the 
  

   8avart''s 
  analyser 
  — 
  a 
  result 
  that 
  is 
  obvious 
  from 
  elementary 
  

   considerations. 
  

  

  Now 
  the 
  light 
  on 
  leaving 
  the 
  quartz 
  is 
  plane 
  polarized 
  (1) 
  

   when 
  5 
  = 
  27i7r, 
  the 
  plane 
  of 
  polarization 
  being 
  then 
  the 
  same 
  

   as 
  it 
  was 
  initially 
  ; 
  (2) 
  when 
  tanS/2= 
  —tan 
  2 
  (a—//,) 
  /sin 
  2/9,, 
  

   a 
  being 
  now 
  the 
  azimuth 
  of 
  the 
  initial 
  plane 
  of 
  polarization 
  

   with 
  respect 
  to 
  the 
  principal 
  section 
  of 
  the 
  first 
  plate 
  of 
  the 
  

   analyser, 
  and 
  in 
  this 
  case 
  tan 
  2(^ 
  + 
  yLt— 
  a) 
  = 
  —tan 
  4(a—/x). 
  

   Hence 
  in 
  the 
  first 
  case, 
  in 
  order 
  that 
  the 
  bands 
  may 
  dis~ 
  

   appear, 
  the 
  light 
  must 
  be 
  initially 
  polarized 
  in 
  one 
  of 
  the 
  

   principal 
  sections 
  of 
  the 
  Savart's 
  plate 
  ; 
  and 
  in 
  the 
  second 
  

   case 
  the 
  principal 
  section 
  of 
  the 
  quartz 
  must 
  be 
  in 
  the 
  

   azimuth 
  /x 
  = 
  ^7r/4 
  + 
  a/2. 
  

  

  It 
  follows, 
  then, 
  that 
  if 
  the 
  initial 
  polarization 
  be 
  such 
  

   that 
  there 
  are 
  no 
  bands 
  before 
  the 
  introduction 
  of 
  the 
  quartz 
  

   plate, 
  there 
  will 
  be 
  a 
  disappearance 
  of 
  the 
  bands 
  whenever 
  the 
  

   relative 
  retardation 
  of 
  phase 
  due 
  to 
  the 
  quartz 
  plate 
  is 
  5 
  = 
  2/i7r, 
  

   and 
  if 
  the 
  principal 
  section 
  of 
  the 
  quartz 
  bisect 
  the 
  angle 
  

   between 
  the 
  principal 
  sections 
  of 
  the 
  Savart's 
  plate 
  *, 
  there 
  

   will 
  be 
  a 
  further 
  disappearance 
  whenever 
  h 
  = 
  (2n 
  + 
  l)7r. 
  

   These 
  results 
  afford 
  a 
  method 
  of 
  setting 
  the 
  principal 
  section 
  

   of 
  a 
  quartz 
  plate 
  perpendicular 
  to 
  the 
  axis 
  of 
  a 
  spectrometer 
  

   and 
  of 
  determining 
  the 
  error 
  in 
  the 
  cutting 
  of 
  a 
  plate 
  that 
  is 
  

   supposed 
  to 
  be 
  normal 
  to 
  the 
  optic 
  axis. 
  

  

  The 
  collimator 
  is 
  furnished 
  with 
  a 
  web, 
  placed 
  by 
  the 
  

  

  * 
  The 
  second 
  of 
  the 
  above 
  cases 
  becomes 
  identical 
  with 
  first 
  when 
  

   a=0, 
  if 
  ^ 
  be 
  even, 
  and 
  "uhen 
  a 
  = 
  7r/2, 
  if 
  k 
  be 
  odd, 
  since 
  the 
  value 
  ol 
  d 
  

   then 
  becomes 
  2«7r. 
  

  

  