﻿26 
  Dr. 
  W. 
  M. 
  Hicks 
  on 
  the 
  Michehon-Morley 
  

  

  (fig. 
  5) 
  cut 
  the 
  plane 
  of 
  the 
  first 
  mirror 
  in 
  W, 
  and 
  denote 
  

   0,W 
  by 
  x. 
  Draw 
  through 
  O 
  x 
  lines 
  parallel 
  to 
  the 
  respective 
  

   wave-fronts. 
  

  

  The 
  phase 
  of 
  that 
  belonging 
  to 
  the 
  first 
  set 
  at 
  1 
  is 
  the 
  same 
  

   as 
  that 
  of 
  the 
  incident 
  at 
  Oi, 
  say 
  II. 
  

  

  The 
  phase 
  of 
  wave-front 
  through 
  W 
  

  

  — 
  TT 
  — 
  x 
  S 
  * 
  n 
  ^ 
  

  

  The 
  phase 
  of 
  the 
  wave-front 
  through 
  2 
  of 
  the 
  second 
  set 
  

   is 
  the 
  same 
  as 
  that 
  of 
  the 
  incident 
  at 
  2? 
  that 
  is 
  of 
  the 
  

  

  incident 
  at 
  1 
  + 
  Q 
  i 
  Q 
  » 
  Bin 
  (£±JU 
  n 
  + 
  " 
  sin 
  (* 
  + 
  0) 
  , 
  

   A 
  A 
  

  

  since 
  the 
  incident 
  ray 
  makes 
  \tt 
  — 
  § 
  — 
  § 
  with 
  § 
  X 
  Q). 
  2 
  . 
  

  

  The 
  wave-front 
  through 
  O 
  x 
  belonging 
  to 
  this 
  set 
  has 
  phase 
  

  

  n 
  a 
  sin 
  (0 
  + 
  0) 
  aM_ 
  /sin 
  (0 
  + 
  0) 
  , 
  cos(0 
  + 
  B)"> 
  

  

  a 
  v- 
  ll+ 
  n 
  x 
  + 
  ^ 
  /> 
  

  

  and 
  phase 
  of 
  that 
  through 
  W 
  

  

  = 
  n 
  + 
  a 
  /?!l!_(* 
  + 
  W. 
  + 
  cosJ^ 
  + 
  B) 
  | 
  _ 
  £sin_B 
  

   1 
  X 
  X 
  2 
  " 
  / 
  " 
  X 
  2 
  " 
  * 
  

  

  Since 
  W 
  is 
  on 
  the 
  central 
  maximal 
  these 
  phases 
  are 
  equal. 
  

   Therefore 
  

  

  fsinB_sinA) 
  f 
  cos(0 
  + 
  B 
  ) 
  sin 
  (0 
  + 
  61)1 
  

  

  \ 
  \ 
  \ 
  ) 
  \ 
  ~\ 
  2 
  + 
  X~ 
  J' 
  

  

  Now 
  Xj 
  : 
  X 
  2 
  = 
  V+ 
  U 
  sin 
  («- 
  A) 
  : 
  V 
  + 
  U 
  sin 
  (a- 
  B). 
  

   Hence 
  

  

  4{V 
  + 
  Usin(a-A)}sinB-{Y 
  + 
  Vsin(a-B)}sinA] 
  « 
  

  

  = 
  a{V4-Usin(«-A)}jcos(0 
  + 
  B;+ 
  ( 
  -^^ 
  

  

  . 
  . 
  B-A 
  [, 
  r 
  A 
  + 
  B 
  A-B] 
  

  

  2# 
  sm 
  — 
  — 
  j 
  Y 
  cos 
  — 
  j~ 
  + 
  v 
  cos 
  — 
  --- 
  I 
  

  

  = 
  - 
  j^J 
  £>2 
  ir-^MV-Ucos(0---a)}{D 
  2 
  2 
  cos(0 
  + 
  B) 
  

  

  + 
  (V 
  a 
  -io")(V»-w 
  B 
  ) 
  sin 
  (0 
  + 
  0)}. 
  

   Substituting 
  the 
  values 
  for 
  the 
  factors 
  on 
  the 
  left 
  already 
  

  

  