﻿26 
  

  

  Mr. 
  W. 
  Sutherland 
  on 
  the 
  Relative 
  

  

  which 
  will 
  have 
  the 
  special 
  value 
  zero 
  when 
  the 
  distance 
  

   between 
  the 
  separated 
  images 
  is 
  equal 
  to 
  half 
  a 
  wave-length 
  

  

  Fig-. 
  2. 
  

  

  of 
  the 
  light 
  employed. 
  Thus, 
  then, 
  while 
  the 
  images 
  are 
  

   parallel 
  no 
  straight 
  fringes 
  can 
  be 
  seen, 
  and 
  the 
  effect 
  of 
  

   varying 
  the 
  distance 
  between 
  the 
  images 
  is 
  to 
  cause 
  motion 
  

   among 
  the 
  circular 
  fringes. 
  Returning 
  now 
  to 
  the 
  case 
  of 
  

   a 
  symmetrical 
  angular 
  separation 
  of 
  the 
  images 
  as 
  at 
  CD 
  and 
  

   EF, 
  we 
  see 
  that 
  the 
  central 
  bright 
  fringe 
  (really 
  dark 
  in 
  the 
  

   actual 
  experiments 
  because 
  of 
  the 
  opposite 
  conditions 
  of 
  re- 
  

   flexion 
  of 
  the 
  two 
  beams) 
  will 
  be 
  seen 
  anywhere 
  along 
  OP; 
  

   and 
  the 
  next 
  may 
  be 
  said 
  to 
  be 
  approximately 
  along 
  the 
  line 
  

   GH 
  (and 
  only 
  approximately 
  straight), 
  at 
  such 
  a 
  distance 
  

   from 
  that 
  GrH 
  is 
  equal 
  to 
  X, 
  the 
  wave-length. 
  Thus 
  the 
  

   interval 
  between 
  the 
  fringes 
  PQ 
  is 
  approximately 
  given 
  by 
  the 
  

   equation 
  

  

  PQ=X/2tanCOA. 
  

  

  For 
  brevity 
  we 
  will 
  confine 
  the 
  discussion 
  to 
  two-dimensioned 
  

   space, 
  that 
  is, 
  to 
  straight-line 
  waves 
  travelling 
  in 
  a 
  plane. 
  

  

  Next 
  let 
  the 
  relative 
  motion 
  of 
  the 
  aether 
  and 
  the 
  apparatus 
  

   cause 
  the 
  separation 
  of 
  the 
  images 
  contemplated 
  by 
  Michelson 
  

   and 
  Morley, 
  namely 
  by 
  a 
  distance 
  s=Dy 
  2 
  /V 
  2 
  , 
  which 
  is 
  also 
  

   accompanied 
  by 
  the 
  angular 
  rotation 
  of 
  the 
  two 
  images 
  through 
  

   i? 
  2 
  /2V 
  2 
  in 
  opposite 
  directions 
  ; 
  but 
  when 
  COA 
  is 
  large 
  com- 
  

   pared 
  to 
  v 
  2 
  /V 
  2 
  this 
  last 
  effect 
  can 
  be 
  neglected. 
  Suppose, 
  

   then, 
  that 
  CD 
  is 
  moved 
  to 
  CD' 
  so 
  that 
  00 
  / 
  = 
  s, 
  and 
  let 
  C/D' 
  

   cut 
  EF 
  in 
  L. 
  It 
  seems 
  to 
  be 
  assumed 
  by 
  Michelson 
  and 
  

   Morley 
  that 
  the 
  locus 
  of 
  the 
  central 
  fringe 
  moves 
  along 
  to 
  

   LR, 
  so 
  that 
  

  

  OM 
  = 
  PR=LM/tan 
  COA 
  = 
  s/2 
  tan 
  COA, 
  and 
  .-. 
  PR 
  = 
  PQ*/\; 
  

  

  and 
  therefore 
  that 
  the 
  whole 
  system 
  of 
  fringes 
  is 
  moved 
  late- 
  

   rally 
  by 
  the 
  same 
  fraction 
  of 
  the 
  width 
  of 
  a 
  fringe 
  as 
  s 
  is 
  of 
  X. 
  

  

  