﻿TOTAL 
  INTENSITY 
  OF 
  INTERFERING 
  LIGHT. 
  319 
  

  

  j^f 
  (*-x) 
  ^j- 
  (y'-y) 
  \ 
  dx 
  dy 
  dx' 
  dy' 
  dp 
  dq 
  

  

  = 
  limit 
  0l 
  ffff~-jpk=5y 
  ■ 
  ^^lf-ny 
  ■ 
  

  

  cos 
  -4 
  — 
  y— 
  - 
  (x' 
  2 
  — 
  x 
  2 
  +y 
  2 
  —y 
  2 
  ) 
  dx 
  dy 
  dx' 
  dy'. 
  

  

  Now, 
  when 
  a 
  vanishes, 
  the 
  whole 
  of 
  the 
  integral 
  

  

  2 
  a 
  dx' 
  

  

  / 
  2adx 
  

  

  a 
  + 
  (-Xb) 
  

  

  is 
  ultimately 
  comprised 
  between 
  limits 
  for 
  which 
  x' 
  is 
  infinitely 
  close 
  to 
  x, 
  and 
  

   similarly 
  with 
  respect 
  to 
  y' 
  ; 
  so 
  that 
  ultimately 
  

  

  cos 
  ?^±3 
  (x' 
  2 
  -x 
  2 
  +y' 
  2 
  -y 
  2 
  ) 
  = 
  l 
  

  

  within 
  the 
  limits 
  for 
  which 
  the 
  quantity 
  under 
  the 
  integral 
  sign 
  does 
  not 
  vanish. 
  

   Hence, 
  passing 
  to 
  the 
  limit, 
  we 
  get 
  

  

  D 
  2 
  I 
  = 
  A 
  2 
  b 
  2 
  CCdx 
  dy=X 
  2 
  b 
  2 
  A, 
  as 
  before. 
  

  

  Case 
  III. 
  Everything 
  the 
  same 
  as 
  in 
  Case 
  II., 
  except 
  that 
  the 
  phase 
  of 
  vibra- 
  

   tion 
  is 
  retarded 
  by 
  p, 
  where 
  p 
  is 
  some 
  function 
  of 
  x 
  and 
  y. 
  

  

  This 
  case 
  is 
  very 
  general. 
  It 
  includes, 
  as 
  particular 
  cases, 
  those 
  numbered 
  I. 
  

   and 
  II. 
  The 
  experiment 
  with 
  Feesnel's 
  mirrors 
  or 
  a 
  flat 
  prism 
  is 
  also 
  included 
  

   as 
  a 
  particular 
  case.* 
  

  

  From 
  what 
  precedes, 
  it 
  is 
  plain 
  that 
  we 
  should 
  have 
  in 
  this 
  case 
  

   D'T 
  _ 
  limit 
  offfff^^^y 
  . 
  ^ 
  +( 
  ^iy 
  

  

  COS 
  

  

  [^ 
  ^p 
  [x' 
  2 
  -x 
  2 
  +y' 
  2 
  -y 
  2 
  ]- 
  p' 
  + 
  p\ 
  dx 
  dy 
  dx! 
  dy', 
  

  

  where 
  p' 
  is 
  the 
  same 
  function 
  of 
  x' 
  and 
  y 
  that 
  p 
  is 
  of 
  x 
  and 
  y. 
  The 
  same 
  reason- 
  

   ing 
  as 
  before 
  leads 
  to 
  the 
  same 
  result. 
  

  

  I 
  do 
  not 
  regard 
  the 
  preceding 
  demonstration 
  of 
  a 
  result 
  which 
  you 
  were 
  the 
  

   first 
  to 
  announce, 
  as 
  of 
  any 
  physical 
  interest 
  after 
  what 
  you 
  have 
  yourself 
  done. 
  

   Still 
  it 
  may 
  not 
  seem 
  wholly 
  uninteresting, 
  in 
  an 
  analytical 
  point 
  of 
  view, 
  to 
  de- 
  

   monstrate 
  the 
  proposition 
  for 
  any 
  form 
  of 
  aperture. 
  

  

  * 
  Thus, 
  in 
  the 
  case 
  of 
  the 
  flat 
  prism, 
  if 
  P, 
  Q 
  he 
  the 
  virtual 
  images 
  corresponding 
  to 
  the 
  halves 
  

   A 
  B, 
  B 
  C, 
  if 
  we 
  produce 
  A 
  B 
  to 
  D, 
  we 
  may 
  suppose 
  the 
  light 
  ^ 
  

  

  which 
  falls 
  on 
  B 
  C, 
  instead 
  of 
  coming 
  from 
  Q, 
  to 
  come 
  from 
  P, 
  and 
  

   to 
  have 
  been 
  accelerated 
  by 
  the 
  passage 
  through 
  the 
  wedge 
  DBC 
  

   of 
  air 
  instead 
  of 
  the 
  same 
  wedge 
  of 
  glass. 
  

  

  