﻿Experiment 
  relating 
  to 
  the 
  Drift 
  of 
  the 
  JEtlier. 
  2£ 
  

  

  If 
  b 
  be 
  measured 
  in 
  wave-lengths 
  =n\ 
  say, 
  

  

  x 
  = 
  _ 
  — 
  '- 
  . 
  = 
  2np 
  : 
  

  

  sin(B-A) 
  l 
  

  

  or 
  there 
  are 
  twice 
  as 
  many 
  bands 
  from 
  Ox 
  to 
  the 
  central 
  

   band 
  as 
  there 
  are 
  wave-lengths 
  in 
  C^L. 
  

  

  When 
  there 
  is 
  motion 
  Q 
  has 
  the 
  same 
  value 
  as 
  if 
  the 
  

   apparatus 
  were 
  at 
  rest 
  when 
  the 
  direction 
  of 
  drift 
  is 
  given 
  by 
  

  

  sin 
  (B— 
  A) 
  +sin 
  (2a— 
  2A) 
  cos 
  C 
  + 
  sin 
  (C 
  — 
  2«) 
  =0, 
  . 
  (19) 
  

  

  which 
  gives 
  two 
  real 
  values 
  for 
  tan 
  a. 
  In 
  the 
  actual 
  case 
  C 
  is 
  

  

  nearly 
  90° 
  and 
  B 
  nearly 
  =A 
  ; 
  whence 
  a. 
  is 
  nearly 
  j 
  or 
  7T+ 
  j, 
  

  

  i. 
  e. 
  the 
  drift 
  produces 
  no 
  effect 
  -when 
  it 
  is 
  nearly 
  'parallel 
  to 
  the 
  

   plane 
  of 
  the 
  plate. 
  

  

  The 
  interfering 
  waves 
  have 
  the 
  same 
  frequencies 
  when 
  

   either 
  

  

  (1) 
  U 
  =0, 
  

  

  (2) 
  w=±Y, 
  

  

  (3) 
  Q 
  =0, 
  

  

  (4) 
  P 
  =0. 
  

  

  (1) 
  is 
  the 
  case 
  of 
  no 
  motion. 
  

  

  (2) 
  makes 
  the 
  velocity 
  of 
  the 
  plate 
  perpendicular 
  to 
  itself 
  

   equal 
  to 
  that 
  of 
  light 
  — 
  a 
  case 
  which 
  may 
  be 
  put 
  aside. 
  

  

  (3) 
  is 
  the 
  case 
  which 
  will 
  have 
  to 
  be 
  discussed 
  immediately. 
  

  

  (4) 
  gives 
  the 
  direction 
  of 
  drift 
  to 
  be 
  that 
  of 
  the 
  maximal 
  

   lines. 
  It 
  is 
  the 
  case, 
  indeed, 
  already 
  discovered 
  by 
  general 
  

   reasoning 
  in 
  § 
  3. 
  To 
  prove 
  the 
  statement 
  it 
  is 
  necessary 
  to 
  

   show 
  that 
  when 
  a 
  — 
  it 
  — 
  ^, 
  P 
  = 
  0. 
  It 
  may 
  be 
  sufficient 
  to 
  

   do 
  this 
  for 
  the 
  case 
  of 
  a 
  fixed 
  source. 
  The 
  equations 
  are 
  : 
  — 
  

  

  2uv 
  

   — 
  cot 
  a 
  = 
  cot 
  C 
  + 
  y 
  2 
  _ 
  2 
  , 
  

  

  P= 
  (V 
  cos 
  6 
  — 
  u) 
  {V 
  2 
  sin 
  (C 
  + 
  a) 
  + 
  v 
  2 
  sin 
  (C-a) 
  } 
  

   = 
  (V 
  cos 
  6— 
  u){ 
  (V 
  2 
  -f- 
  v 
  2 
  ) 
  sin 
  C 
  cos 
  a+ 
  (V 
  2 
  — 
  v 
  2 
  ) 
  cos 
  C 
  sin 
  a}. 
  

   Now 
  the 
  first 
  equation 
  gives 
  at 
  once 
  

   (V 
  2 
  — 
  v 
  2 
  ) 
  cos 
  C 
  sin 
  a 
  + 
  cos 
  a 
  sin 
  C(V 
  2 
  — 
  v 
  2 
  ) 
  + 
  2uv 
  sin 
  C 
  sin 
  a 
  = 
  0, 
  

   and 
  usina 
  = 
  v 
  cos 
  a, 
  

  

  which 
  makes 
  the 
  second 
  factor 
  of 
  P 
  vanish. 
  

  

  14. 
  The 
  preceding 
  formula? 
  hold 
  whatever 
  the 
  velocity 
  of 
  

   drift 
  may 
  be. 
  It 
  is, 
  however, 
  extremely 
  unlikely 
  that 
  this 
  

  

  