﻿28 
  Mr. 
  W. 
  Sutherland 
  on 
  the 
  Relative 
  

  

  either 
  p 
  = 
  or 
  « 
  = 
  0. 
  The 
  case 
  of 
  p=-§ 
  is 
  of 
  no 
  interest, 
  and 
  

   with 
  c 
  = 
  0, 
  a 
  = 
  we 
  have 
  the 
  case 
  of 
  absolutely 
  coincident 
  

   images 
  with 
  no 
  fringes 
  at 
  all. 
  Thus 
  the 
  case 
  with 
  c 
  — 
  2pa 
  = 
  

   and 
  c 
  = 
  can 
  be 
  dismissed, 
  and 
  we 
  have 
  to 
  consider 
  next 
  

   c 
  — 
  2pa 
  = 
  and 
  q 
  = 
  0, 
  which 
  amounts 
  to 
  this, 
  that 
  at 
  the 
  par- 
  

   ticular 
  position 
  of 
  P 
  given 
  by 
  ]j 
  — 
  c/2ot 
  and 
  q 
  = 
  Q, 
  both 
  of 
  each 
  

   pair 
  of 
  corresponding 
  points 
  are 
  nearly 
  equidistant 
  from 
  P, 
  so 
  

   that 
  both 
  of 
  each 
  pair 
  of 
  corresponding 
  disturbances 
  reach 
  

   this 
  position 
  of 
  P 
  in 
  the 
  same 
  phase. 
  In 
  this 
  case 
  there 
  is 
  

   one 
  point 
  p 
  = 
  c/2a 
  and 
  q 
  = 
  which 
  stands 
  nearly 
  in 
  the 
  same 
  

   sort 
  of 
  symmetry 
  with 
  respect 
  to 
  the 
  two 
  images 
  as 
  does 
  

   when 
  0' 
  and 
  are 
  identical. 
  We 
  will 
  return 
  to 
  this 
  as 
  a 
  

   special 
  case 
  after 
  we 
  have 
  studied 
  the 
  general 
  case 
  in 
  which 
  

   c 
  — 
  2pa 
  is 
  not 
  equal 
  to 
  zero. 
  Here 
  we 
  have 
  

  

  x= 
  c{q-(c-2pa)/2} 
  ^ 
  ... 
  (3) 
  

  

  C—2pa 
  

  

  Let 
  the 
  state 
  of 
  affairs 
  we 
  have 
  been 
  discussing 
  so 
  far 
  be 
  that 
  

   in 
  which 
  there 
  is 
  no 
  relative 
  motion 
  of 
  the 
  apparatus 
  and 
  the 
  

   aether, 
  so 
  that 
  the 
  want 
  of 
  coincidence 
  of 
  the 
  two 
  images 
  is 
  

   due 
  entirely 
  to 
  experimental 
  imperfection 
  ; 
  and 
  now 
  suppose 
  

   the 
  apparatus 
  to 
  acquire 
  its 
  velocity 
  v 
  relative 
  to 
  the 
  aether, 
  

   the 
  effect 
  of 
  which 
  is 
  to 
  shift 
  CD' 
  relatively 
  to 
  EF 
  in 
  the 
  

   manner 
  contemplated 
  by 
  Michelson 
  and 
  Morley. 
  Let 
  us 
  

   suppose 
  the 
  shift 
  to 
  be 
  the 
  simplest 
  possible, 
  namely, 
  that 
  of 
  

   C 
  / 
  D 
  / 
  parallel 
  to 
  itself 
  to 
  GH 
  through 
  a 
  distance 
  OK 
  = 
  s 
  = 
  Bv 
  2 
  /V 
  2 
  

   along 
  the 
  normal 
  to 
  AB, 
  and 
  let 
  GH 
  intersect 
  E 
  If 
  in 
  L, 
  which 
  

   is 
  now 
  to 
  be 
  regarded 
  as 
  a 
  new 
  origin. 
  c 
  has 
  not 
  been 
  

   altered 
  by 
  the 
  shift, 
  p 
  has 
  been 
  increased 
  by 
  0Y 
  = 
  s/2, 
  and 
  q 
  

   has 
  been 
  diminished 
  by 
  YL 
  = 
  a/ 
  2 
  tan 
  a=^s/2at 
  nearly; 
  thus 
  then 
  

   for 
  the 
  distance 
  x 
  defining 
  the 
  distance 
  of 
  a 
  point 
  along 
  LF 
  

   from 
  L 
  which 
  is 
  at 
  the 
  same 
  distance 
  from 
  P 
  as 
  its 
  corre- 
  

   sponding 
  point 
  in 
  LH, 
  we 
  get 
  by 
  making 
  in 
  (3) 
  the 
  changes 
  

   indicated 
  

  

  j 
  _ 
  c{q 
  — 
  sl2a— 
  {c^-2pa 
  — 
  sa)!2\ 
  

   X 
  — 
  o 
  .... 
  y±) 
  

  

  c— 
  ■ 
  Zpa 
  — 
  s<z 
  

  

  so 
  that 
  approximately 
  as 
  s 
  and 
  a 
  are 
  small 
  

  

  it 
  j 
  & 
  s 
  , 
  

  

  C 
  — 
  Zpoc 
  La. 
  

  

  But 
  x 
  is 
  measured 
  from 
  L, 
  so 
  that 
  the 
  actual 
  shift 
  of 
  the 
  

   corresponding 
  points 
  is 
  x 
  — 
  x' 
  — 
  0Ij 
  = 
  x-^-x' 
  — 
  s/2<x 
  

  

  = 
  ±J!p^_ 
  (6) 
  

  

  2<XC 
  — 
  2pOL 
  ' 
  

  

  