﻿28 
  Dr. 
  W. 
  M. 
  Hicks 
  on 
  the 
  Mkhelson-Morley 
  

  

  It 
  will 
  be 
  convenient 
  to 
  collect 
  the 
  formulae 
  expressed 
  in 
  

   these 
  new 
  quantities 
  : 
  — 
  

  

  Ai-A 
  2 
  _ 
  U(V 
  2 
  --^ 
  2 
  )PQ 
  

   A 
  D^ 
  2 
  ' 
  

  

  P 
  Q* 
  ^{U 
  2 
  P 
  2 
  + 
  V 
  2 
  (V 
  2 
  -r 
  2 
  )(V 
  2 
  -it; 
  /2 
  )(V-Ucos^^} 
  

  

  tan 
  (V 
  2 
  -v 
  2 
  ){{VcosO-u) 
  sinC-(Vsm0-tf) 
  cosC} 
  

  

  ~ 
  (V 
  cos 
  — 
  u) 
  { 
  V 
  2 
  — 
  v 
  2 
  ) 
  cos 
  C 
  + 
  2uv 
  sin 
  C 
  } 
  

  

  + 
  (Vsin0-iO(V 
  2 
  -^)sinC 
  

  

  where 
  

  

  F 
  = 
  V{V2sm(C 
  + 
  a-0)-VUsinC 
  + 
  U 
  2 
  smasin 
  (a-0) 
  sin 
  (C-«)} 
  

   = 
  (V 
  cos 
  - 
  u) 
  { 
  V 
  2 
  . 
  sin 
  (C 
  + 
  a) 
  + 
  v 
  2 
  sin 
  (C 
  - 
  a) 
  } 
  

  

  -(V 
  sin 
  0-r){ 
  V 
  2 
  cos 
  (C 
  + 
  a) 
  + 
  uv 
  sin 
  (C-a)}, 
  

   Q 
  = 
  2V 
  2 
  sin(B-A)-U 
  2 
  {sin(B-A) 
  + 
  sin(2a-2A)cosC 
  + 
  sin(C-2 
  fi 
  

   For 
  the 
  case 
  of 
  V 
  sin 
  Q 
  = 
  v, 
  source 
  fixed 
  to 
  apparatus, 
  

  

  V- 
  

  

  '2 
  

  

  A 
  cos 
  (V 
  2 
  -v 
  2 
  ) 
  (\ 
  2 
  -w 
  2 
  ) 
  (Y 
  2 
  -w 
  /2 
  ) 
  

  

  V 
  2 
  Q 
  s/ 
  [ 
  (V 
  2 
  -v 
  2 
  )2 
  sin 
  2 
  C+ 
  { 
  (V 
  2 
  - 
  u 
  2 
  ) 
  cos 
  C 
  + 
  2uv 
  sin 
  C} 
  2 
  ] 
  

  

  U 
  2 
  . 
  : 
  

  

  cot 
  -^r 
  = 
  cot 
  C 
  + 
  yg__ 
  2 
  sin 
  2a, 
  

  

  P= 
  (Vcos 
  0-m) 
  {V 
  2 
  sin 
  (C 
  + 
  «) 
  + 
  v 
  2 
  sin 
  (C-«) 
  } 
  

   When 
  there 
  is 
  no 
  motion, 
  

   Aj 
  =^ 
  A,2 
  — 
  \ 
  f 
  

  

  sin±(B-A)=sin(B-A), 
  

  

  = 
  A 
  

  

  P 
  2 
  sin 
  (B- 
  A)' 
  

  

  sin(B-A)* 
  

  

  