﻿Experiment 
  relating 
  to 
  the 
  Drift 
  of 
  tlie 
  jEther. 
  41 
  

  

  If 
  any 
  fringes 
  are 
  to 
  be 
  seen 
  at 
  all, 
  B 
  — 
  A 
  must 
  be 
  exceedingly 
  

   small. 
  Hence 
  in 
  the 
  small 
  term 
  multiplied 
  by 
  f 
  2 
  we 
  may 
  put 
  

   B 
  = 
  A, 
  C 
  = 
  2A, 
  Then 
  it 
  can 
  be 
  shown 
  that 
  

  

  S(B-A) 
  = 
  -£f 
  (1-cos 
  C) 
  sin 
  (C-2a) 
  = 
  -k^R 
  ; 
  

   and, 
  since 
  cos 
  (B— 
  A) 
  = 
  l, 
  

  

  b 
  

  

  x 
  = 
  

  

  sin(B-A)-(£ 
  + 
  i)Rf 
  

  

  Fig. 
  8. 
  

  

  21. 
  In 
  Michelson 
  and 
  Morley's 
  experiment 
  C=90°, 
  

  

  k 
  = 
  COS 
  2a, 
  

  

  b 
  

  

  x— 
  

  

  sin(B— 
  A) 
  — 
  (& 
  + 
  i)? 
  2 
  cos2a* 
  

  

  Hence 
  to 
  annul 
  the 
  effect 
  k 
  should 
  be 
  —J, 
  and 
  consequently 
  

   an 
  expansion 
  instead 
  of 
  a 
  contraction 
  is 
  necessary. 
  

  

  If 
  now 
  X 
  denote 
  the 
  true 
  coefficient 
  of 
  contraction 
  due 
  to 
  

   drift 
  k 
  = 
  \/cos 
  I, 
  and 
  if 
  the 
  vertical 
  component 
  of 
  drift 
  pro- 
  

   duce 
  (owing 
  to 
  motion 
  of 
  source) 
  no 
  direct 
  effect 
  in 
  displacing 
  

  

  the 
  fringe 
  

  

  x= 
  

  

  sin 
  (B 
  - 
  A) 
  — 
  ( 
  A/ 
  cos 
  I 
  + 
  £) 
  f 
  2 
  cos 
  2a. 
  

  

  Observations 
  at 
  noon 
  and 
  at 
  6 
  p.m. 
  give 
  the 
  direction 
  of 
  

   the 
  projection 
  of 
  the 
  total 
  drift 
  on 
  the 
  plane 
  of 
  the 
  apparatus 
  

   — 
  that 
  is, 
  we 
  have 
  the 
  projections 
  of 
  the 
  same 
  direction 
  on 
  

  

  