﻿Motion 
  of 
  the 
  Earth 
  and 
  JEthev. 
  25 
  

  

  is 
  evidently 
  2D(1 
  -f?; 
  2 
  /V 
  2 
  )^, 
  so 
  that 
  with 
  omission 
  of 
  the 
  third 
  

   and 
  higher 
  powers 
  of 
  v/V 
  the 
  difference 
  between 
  aca 
  l 
  and 
  aba-i 
  

   can 
  be 
  set 
  down 
  as 
  Di> 
  2 
  /V 
  2 
  . 
  If 
  v 
  is 
  the 
  velocity 
  of 
  the 
  earth 
  

   in 
  its 
  orbit, 
  then 
  if 
  the 
  whole 
  apparatus 
  is 
  turned 
  through 
  tt/2 
  

   the 
  longer 
  path 
  becomes 
  the 
  shorter, 
  and 
  vice 
  versa 
  : 
  so 
  that 
  

   the 
  difference 
  of 
  path 
  which 
  occasioned 
  the 
  interference-fringes 
  

   in 
  the 
  first 
  position 
  is 
  altered 
  in 
  the 
  second 
  by 
  2Dv 
  2 
  /V 
  2 
  , 
  which 
  

   ought 
  to 
  produce 
  a 
  difference 
  in 
  the 
  position 
  of 
  the 
  fringes 
  in 
  

   the 
  telescope. 
  And 
  this 
  motion 
  of 
  the 
  fringes 
  is 
  what 
  Michel- 
  

   son 
  and 
  Morley 
  found 
  not 
  to 
  occur, 
  even 
  after 
  they 
  had 
  given 
  

   the 
  apparatus 
  a 
  sensitiveness 
  which 
  they 
  supposed 
  to 
  be 
  quite 
  

   adequate 
  to 
  its 
  accurate 
  measurement, 
  minute 
  as 
  is 
  v 
  2 
  /'V 
  2 
  , 
  

   namely 
  about 
  10 
  -8 
  . 
  Hence 
  the 
  startling 
  conclusion 
  that 
  the 
  

   relative 
  motion 
  of 
  earth 
  and 
  aether 
  must 
  be 
  small 
  compared 
  to 
  

   the 
  earth's 
  orbital 
  velocity, 
  in 
  short 
  that 
  the 
  earth 
  drags 
  the 
  

   aether 
  with 
  it. 
  

  

  In 
  the 
  supplement 
  to 
  their 
  paper 
  Michelson 
  and 
  Morley 
  

   (p. 
  460) 
  show 
  that 
  the 
  angle 
  which 
  ah 
  makes 
  with 
  the 
  mirror 
  

   at 
  b 
  is 
  more 
  strictly 
  v/V 
  + 
  v 
  2 
  /2 
  V 
  2 
  , 
  while 
  ca 
  i 
  after 
  reflexion 
  

   makes 
  an 
  angle 
  with 
  the 
  normal 
  to 
  b 
  which 
  is 
  more 
  strictly 
  

   v/V 
  — 
  ?' 
  2 
  /2V 
  2 
  , 
  so 
  that 
  the 
  two 
  rays 
  which 
  are 
  to 
  interfere 
  after 
  

   passing 
  % 
  are 
  inclined 
  at 
  an 
  angle 
  v 
  2 
  /V 
  2 
  to 
  one 
  another. 
  This 
  

   is 
  of 
  no 
  importance 
  in 
  the 
  actual 
  experiments, 
  because 
  to 
  get 
  

   interference-bands 
  of 
  a 
  convenient 
  width 
  it 
  is 
  necessary 
  to 
  

   have 
  the 
  rays 
  inclined 
  at 
  a 
  much 
  larger 
  angle 
  than 
  this, 
  

   though 
  still 
  at 
  a 
  very 
  small 
  angle, 
  which 
  is 
  obtained 
  by 
  slight 
  

   derangements 
  of 
  the 
  mirrors 
  and 
  plate 
  from 
  the 
  ideal 
  ma- 
  

   thematical 
  positions 
  assigned 
  to 
  them 
  in 
  the 
  theory 
  of 
  the 
  

   experiment. 
  

  

  To 
  ascertain 
  what 
  really 
  happens 
  with 
  the 
  two 
  interfering 
  

   rays, 
  let 
  us 
  take 
  a 
  small 
  area 
  of 
  plane 
  wave 
  equal 
  to 
  the 
  area 
  

   of 
  the 
  pupil 
  of 
  the 
  observer's 
  eye, 
  and 
  take 
  its 
  image 
  in 
  b 
  as 
  

   it 
  appears 
  immediately 
  after 
  reflexion 
  at 
  a, 
  and 
  let 
  us 
  take 
  the 
  

   image 
  of 
  its 
  transmitted 
  part 
  after 
  reflexion 
  at 
  c 
  and 
  a 
  1 
  ; 
  then 
  

   if 
  the 
  whole 
  apparatus 
  and 
  aether 
  were 
  at 
  rest, 
  and 
  the 
  angles 
  

   were 
  all 
  exactly 
  as 
  supposed, 
  we 
  should 
  have 
  the 
  two 
  images 
  

   coincident 
  as 
  represented 
  in 
  section 
  at 
  AB 
  (fig. 
  2) 
  . 
  

  

  Now 
  suppose 
  that 
  by 
  slight 
  derangement 
  the 
  images 
  are 
  

   separated 
  as 
  in 
  CD 
  and 
  EF. 
  Fringes 
  now 
  appear 
  whose 
  

   width 
  depends 
  on 
  the 
  angle 
  COE. 
  When 
  the 
  images 
  coin- 
  

   cided 
  they 
  represented 
  coincident 
  trains 
  of 
  waves 
  with 
  double 
  

   illumination 
  along 
  their 
  path. 
  If 
  the 
  derangement, 
  which 
  

   separated 
  the 
  image 
  AB 
  into 
  two, 
  left 
  them 
  still 
  parallel, 
  

   there 
  would 
  be 
  only 
  circular 
  fringes 
  visible 
  in 
  any 
  plane 
  

   parallel 
  to 
  them, 
  and 
  only 
  a 
  uniform 
  resultant 
  central 
  illumi- 
  

   nation 
  to 
  an 
  infinitely 
  small 
  eye 
  moving 
  along 
  a 
  normal, 
  

  

  