﻿f 
  V 
  2 
  + 
  w 
  2 
  + 
  2ieV 
  cos 
  (0 
  + 
  (9)} 
  «j 
  

  

  Experiment 
  relating 
  to 
  the 
  Drift 
  of 
  the 
  /Ether. 
  19 
  

  

  Whence 
  by 
  (3) 
  

  

  \ 
  x 
  _ 
  (V 
  2 
  -te 
  2 
  )(V 
  2 
  -e 
  2 
  ) 
  -j 
  

  

  \" 
  ~ 
  { 
  V 
  2 
  + 
  ie 
  2 
  + 
  %wV 
  cos 
  (A 
  + 
  0) 
  } 
  { 
  V 
  5 
  + 
  v 
  2 
  - 
  2r 
  V 
  cos 
  fa 
  \ 
  \" 
  

  

  X, 
  (V»-ttg)(V»-ig«) 
  I 
  

  

  X 
  = 
  ~ 
  {V 
  2 
  + 
  «? 
  2 
  -2w?Vcos0 
  2 
  }{V 
  2 
  + 
  «j' 
  2 
  4-2wjTcos(x 
  + 
  ^)}J 
  

  

  It 
  will 
  be 
  convenient 
  to 
  denote 
  these 
  denominators 
  b} 
  r 
  D 
  2 
  2 
  

   and 
  D 
  2 
  2 
  . 
  

  

  Now 
  4> 
  l 
  = 
  (f> 
  + 
  <l> 
  t 
  — 
  ^7T. 
  

  

  Hence 
  

  

  D 
  1 
  2 
  = 
  (V 
  2 
  + 
  r 
  2 
  ){V 
  2 
  + 
  ^ 
  + 
  2^Vcos(<^ 
  + 
  (9)} 
  

  

  -2Vesin 
  (^ 
  + 
  ^){V 
  2 
  + 
  i» 
  2 
  + 
  2m?Vcos(£+0) 
  }. 
  

  

  <£' 
  is 
  the 
  reflected 
  angle 
  for 
  incident 
  angle 
  (<j> 
  + 
  0) 
  and 
  for 
  

   vel. 
  = 
  ie. 
  Therefore 
  

  

  sin<£'=(V 
  2 
  -w 
  2 
  )sin(# 
  + 
  0), 
  

  

  COS 
  0' 
  = 
  ( 
  V 
  2 
  + 
  !y2) 
  COS 
  (</> 
  + 
  6) 
  + 
  2 
  Vte. 
  

  

  Substituting 
  it 
  can 
  be 
  easily 
  shown, 
  remembering 
  the 
  values 
  

   of 
  to, 
  iv 
  f 
  given 
  by 
  (5, 
  6), 
  that 
  

  

  D 
  1 
  2 
  = 
  V 
  4 
  -2V 
  :5 
  cos^{!/cos(0 
  + 
  0)+^sin(0 
  + 
  <9)} 
  

  

  + 
  V 
  2 
  (e 
  2 
  -f 
  w 
  2 
  — 
  4 
  we 
  sin 
  <f>) 
  + 
  2eteV 
  cos 
  0(t? 
  cos 
  6 
  — 
  u 
  sin 
  0) 
  -J- 
  eV. 
  

  

  Similarly 
  it 
  may 
  be 
  shown 
  that 
  

  

  D 
  2 
  2 
  = 
  V 
  4 
  + 
  2Y 
  3 
  sin(^- 
  X 
  ){^sin((94-x-^)-ecos(0 
  + 
  )(: 
  -(/))} 
  

   + 
  V 
  2 
  {mj2+mj 
  /2 
  — 
  4«)?e 
  / 
  cos 
  (<£— 
  #)} 
  

  

  — 
  2ww'Y 
  sin 
  {(/>— 
  x) 
  (u 
  sin 
  0— 
  v 
  cos 
  (9) 
  + 
  z<; 
  2 
  ?y 
  /2 
  . 
  

  

  The 
  difference 
  of 
  wave-lengths 
  is 
  given 
  by 
  d\ 
  = 
  \ 
  ] 
  —\ 
  2} 
  

   where 
  

  

  *± 
  _ 
  rV 
  2 
  _ 
  , 
  A 
  (V 
  2 
  - 
  r) 
  D 
  2 
  2 
  - 
  [^-^Di 
  2 
  

   X 
  ~~ 
  l 
  ' 
  IVD? 
  * 
  

  

  Aft-r 
  some 
  reduction 
  this 
  becomes 
  

  

  <a 
  = 
  U(V 
  2 
  -u^PQ 
  

  

  x 
  D.'-iy 
  ' 
  (*v 
  

  

  C 
  2 
  

  

  