﻿Experiment 
  relating 
  to 
  the 
  Drift 
  of 
  the 
  JEither. 
  13 
  

  

  distance 
  from 
  one 
  another 
  c 
  = 
  A/( 
  2 
  sin 
  ^- 
  ), 
  where 
  \ 
  is 
  the 
  

  

  common 
  wave-length 
  and 
  /3 
  the 
  angle 
  between 
  the 
  two 
  sets 
  of 
  

   wave-fronts. 
  For 
  convenience 
  we 
  shall 
  call 
  these 
  lines 
  maximal 
  

   lines. 
  If 
  a 
  screen 
  be 
  placed 
  perpendicularly 
  to 
  them 
  we 
  shall 
  

   get 
  a 
  fringe, 
  the 
  intersections 
  with 
  the 
  maximals 
  being 
  the 
  

   centres 
  of 
  the 
  bright 
  bands, 
  and 
  the 
  distance 
  between 
  the 
  

   bands 
  being 
  c. 
  If 
  the 
  screen 
  is 
  placed 
  at 
  an 
  angle 
  y 
  to 
  these 
  

   lines, 
  the 
  breadth 
  of 
  the 
  bands 
  is 
  c/sin 
  y. 
  

  

  All 
  the 
  waves 
  interfering 
  at 
  points 
  along 
  a 
  given 
  maximal 
  

   differ 
  in 
  phase 
  by 
  the 
  same 
  integral 
  number 
  of 
  wave-lengths. 
  

   We 
  can 
  therefore 
  designate 
  any 
  maximal 
  by 
  this 
  number. 
  

   It 
  is 
  important 
  to 
  be 
  able 
  to 
  determine 
  it. 
  

  

  If 
  the 
  plate 
  and 
  the 
  first 
  mirror 
  intersect 
  at 
  0! 
  (fig. 
  1), 
  the 
  

   phase 
  of 
  the 
  reflected 
  wave 
  of 
  the 
  first 
  train 
  at 
  O 
  l 
  is 
  the 
  same 
  

   as 
  that 
  of 
  the 
  incident. 
  Let 
  p 
  1 
  denote 
  the 
  perpendicular 
  dis- 
  

   tance 
  of 
  any 
  point 
  P 
  from 
  the 
  wave-front 
  through 
  O 
  x 
  . 
  Then 
  

   the 
  phase 
  of 
  the 
  first 
  train 
  at 
  T=p 
  1 
  /\-j- 
  phase 
  of 
  incident 
  

   light 
  at 
  Oi. 
  Similarly 
  if 
  the 
  plate 
  and 
  the 
  second 
  mirror 
  

   intersect 
  at 
  2 
  , 
  and 
  p> 
  2 
  denote 
  the 
  distance 
  of 
  P 
  from 
  the 
  wave- 
  

   front 
  of 
  the 
  second 
  train 
  through 
  2 
  , 
  the 
  phase 
  of 
  the 
  second 
  

   train 
  at 
  P 
  = 
  p 
  2 
  /\ 
  + 
  phase 
  of 
  incident 
  light 
  at 
  2 
  . 
  If 
  then 
  the 
  

   distance 
  Oi 
  2 
  resolved 
  perpendicularly 
  to 
  the 
  incident 
  sys- 
  

   tem 
  be 
  q, 
  the 
  interfering 
  waves 
  at 
  P 
  differ 
  in 
  phase 
  by 
  

   ilh 
  + 
  q—P])/^ 
  This 
  is 
  the 
  amount 
  by 
  which 
  the 
  second 
  

   train 
  is 
  ahead 
  of 
  the 
  first. 
  If 
  this 
  be 
  zero 
  we 
  have 
  the 
  central 
  

   maximal, 
  which 
  is 
  the 
  same 
  for 
  all 
  colours. 
  Consequently, 
  

   when 
  white 
  light 
  is 
  used 
  it 
  is 
  only 
  near 
  this 
  maximal 
  that 
  

   fringes 
  will 
  be 
  visible. 
  

  

  It 
  follows 
  from 
  this 
  that 
  if 
  the 
  planes 
  of 
  the 
  plate 
  and 
  the 
  

   mirrors 
  intersect 
  in 
  a 
  point 
  the 
  central 
  maximal 
  will 
  pass 
  

   through 
  that 
  point. 
  There 
  is 
  no 
  need 
  to 
  consider 
  specially 
  

   the 
  quantitative 
  theory 
  for 
  no 
  drift, 
  as 
  it 
  will 
  be 
  included 
  in 
  

   the 
  more 
  general 
  case 
  of 
  motion 
  to 
  follow. 
  

  

  3. 
  Taking 
  now 
  the 
  case 
  where 
  the 
  apparatus 
  moves 
  in 
  an 
  

   aether 
  at 
  rest, 
  the 
  wave-diagram 
  gives 
  as 
  before 
  an 
  instan- 
  

   taneous 
  state 
  of 
  the 
  aether. 
  But 
  now 
  the 
  conditions 
  are 
  very 
  

   different. 
  In 
  the 
  first 
  place, 
  as 
  will 
  be 
  shown 
  later, 
  when 
  the 
  

   two 
  reflected 
  systems 
  are 
  inclined 
  their 
  wave-lengths 
  will 
  in 
  

   general 
  be 
  different, 
  whilst 
  if 
  the 
  wave-lengths 
  are 
  equal 
  the 
  

   two 
  systems 
  must 
  be 
  parallel. 
  Thus 
  to 
  a 
  person 
  fixed 
  in 
  the 
  

   aether, 
  no 
  fringes 
  can 
  in 
  general 
  be 
  seen, 
  either 
  because 
  the 
  

   waves 
  which 
  ought 
  to 
  interfere 
  have 
  different 
  frequencies, 
  or 
  

   because 
  when 
  they 
  have 
  the 
  same, 
  the 
  interference 
  produces 
  

   a 
  uniform 
  change 
  of 
  illumination 
  and 
  not 
  bands 
  of 
  finite 
  

   breadth. 
  This 
  is 
  not 
  the 
  case, 
  however, 
  to 
  a 
  person 
  who 
  

  

  