﻿Motion 
  of 
  the 
  Earth 
  and 
  JEthev. 
  29 
  

  

  Therefore 
  if 
  c 
  is 
  large 
  compared 
  to 
  2pa 
  the 
  shift 
  of 
  corre- 
  

   sponding 
  points 
  is 
  only 
  a 
  small 
  fraction 
  of 
  that 
  (s/2a) 
  con- 
  

   templated 
  by 
  Michelson 
  and 
  Morley 
  for 
  the 
  fringes. 
  Now 
  to 
  

   see 
  how 
  the 
  consideration 
  of 
  corresponding 
  points 
  bears 
  upon 
  

   the 
  problem 
  we 
  have 
  only 
  to 
  remember 
  that 
  each 
  wave-front 
  

   propagates 
  itself 
  normal 
  to 
  itself, 
  and 
  that 
  therefore 
  the 
  best 
  

   interference 
  effects 
  are 
  to 
  be 
  sought 
  along 
  the 
  normal 
  to 
  AB 
  

   which 
  is 
  equally 
  inclined 
  to 
  the 
  normals 
  to 
  the 
  two 
  image 
  

   waves 
  ; 
  if 
  we 
  fix 
  our 
  attention 
  on 
  two 
  small 
  elements 
  of 
  the 
  

   image 
  waves 
  around 
  two 
  corresponding 
  points, 
  we 
  see 
  that 
  

   their 
  most 
  vivid 
  interference 
  effects 
  will 
  be 
  along 
  the 
  normal 
  

   to 
  AB 
  which 
  is 
  at 
  distance 
  (x 
  + 
  c/2) 
  cos 
  a, 
  or 
  nearly 
  x 
  + 
  c/2 
  

   along 
  AB 
  from 
  0. 
  In 
  order 
  that 
  g, 
  which 
  is 
  cc(c 
  — 
  2pa)/c 
  

   + 
  (c 
  — 
  2pa)/2, 
  should 
  be 
  nearly 
  this 
  x 
  + 
  c/2, 
  the 
  fraction 
  2pa/c 
  

   is 
  to 
  be 
  small, 
  or 
  c 
  is 
  to 
  be 
  large 
  compared 
  to 
  2pcc, 
  which 
  is 
  

   the 
  condition 
  just 
  found 
  in 
  order 
  that 
  the 
  shift 
  of 
  corresponding 
  

   points 
  should 
  be 
  small 
  compared 
  to 
  that 
  of 
  the 
  fringes 
  sought 
  

   by 
  Michelson 
  and 
  Morley. 
  If 
  the 
  eye 
  of 
  the 
  observer 
  is 
  

   placed 
  in 
  OZ 
  (fig. 
  3), 
  that 
  is 
  if 
  ^ 
  = 
  0,*then 
  x= 
  -c/2, 
  and 
  in 
  

   the 
  whole 
  system 
  of 
  possible 
  fringes 
  there 
  is 
  along 
  OZ 
  a 
  

   peculiar 
  central 
  region 
  characterized 
  by 
  a 
  certain 
  symmetry; 
  

   but 
  at 
  the 
  same 
  time 
  to 
  an 
  eye 
  placed 
  anywhere 
  the 
  central 
  

   band 
  in 
  its 
  field 
  may 
  be 
  characterized 
  by 
  maximum 
  clearness, 
  

   yet 
  it 
  will 
  have 
  none 
  of 
  the 
  peculiar 
  character 
  of 
  the 
  one 
  abso- 
  

   lute 
  symmetrical 
  central 
  one. 
  To 
  an 
  eye 
  placed 
  anywhere 
  the 
  

   central 
  band 
  in 
  its 
  field 
  is 
  at 
  such 
  a 
  point 
  that 
  the 
  mean 
  dis- 
  

   tance 
  from 
  equal 
  corresponding 
  areas 
  of 
  the 
  two 
  images 
  is 
  the 
  

   same 
  ; 
  and 
  according 
  to 
  what 
  we 
  have 
  just 
  seen 
  if 
  the 
  one 
  

   image 
  is 
  shifted 
  through 
  a 
  distance 
  s 
  along 
  the 
  normal 
  to 
  the 
  

   mean 
  position 
  of 
  the 
  two 
  images, 
  then 
  the 
  position 
  of 
  corre- 
  

   sponding 
  points 
  is 
  only 
  changed 
  by 
  the 
  small 
  fraction 
  

   2pa/(c—2pa) 
  or 
  2pa/c 
  of 
  s/2ct, 
  and 
  therefore 
  the 
  fringes 
  will 
  

   be 
  seen 
  in 
  the 
  eye 
  to 
  move 
  approximately 
  only 
  the 
  small 
  

   fraction 
  2pa.jc 
  of 
  the 
  expected 
  $/2a. 
  If 
  things 
  were 
  adjusted 
  

   so 
  that 
  the 
  absolutely 
  central 
  region 
  of 
  the 
  fringes 
  appeared 
  

   in 
  the 
  eye, 
  then 
  just 
  as 
  in 
  fig. 
  '6 
  moves 
  to 
  L, 
  the 
  complete 
  

   shift 
  s/2a 
  of 
  the 
  central 
  region 
  would 
  be 
  observed 
  ; 
  but 
  this 
  

   adjustment 
  would 
  be 
  a 
  tedious 
  business. 
  

  

  In 
  the 
  final 
  experimental 
  arrangements 
  the 
  simplicity 
  of 
  the 
  

   scheme 
  given 
  in 
  fig. 
  1 
  was 
  somewhat 
  departed 
  from, 
  because 
  

   each 
  half 
  of 
  the 
  divided 
  beam 
  was 
  reflected 
  backwards 
  and 
  

   forwards 
  four 
  times 
  along 
  its 
  initial 
  path 
  in 
  order 
  to 
  increase 
  

   the 
  effective 
  value 
  of 
  1) 
  : 
  the 
  images 
  were 
  brought 
  into 
  

   apparent 
  coincidence 
  and 
  so 
  adjusted 
  that 
  2a 
  was 
  such 
  as 
  

   gave 
  fringes 
  of 
  convenient 
  width 
  ; 
  but 
  c 
  was 
  quite 
  unknown 
  

   and 
  might 
  be 
  large 
  compared 
  to 
  2pa, 
  or 
  say 
  2Da, 
  without 
  

  

  