﻿SO 
  Relative 
  Motion 
  of 
  the 
  Earth 
  and 
  JEther. 
  

  

  detection, 
  because 
  while 
  « 
  was 
  adjusted 
  for 
  by 
  reason 
  of 
  the 
  

   necessity 
  of 
  making 
  the 
  fringes 
  of 
  convenient 
  width, 
  there 
  

   was 
  no 
  adjustment 
  for 
  making 
  c 
  zero, 
  beyond 
  the 
  comparatively 
  

   rough 
  one 
  of 
  causing 
  images 
  of 
  an 
  object 
  to 
  coincide 
  apparently, 
  

   and 
  therefore 
  on 
  the 
  average 
  c 
  may 
  be 
  assumed 
  to 
  be 
  large 
  

   compared 
  to 
  2pa. 
  The 
  case 
  in 
  which 
  c 
  becomes 
  not 
  very 
  

   different 
  from 
  2pa 
  has 
  already 
  been 
  partly 
  discussed 
  in 
  the 
  

   extreme 
  form 
  when 
  c 
  — 
  2pa, 
  a 
  relation 
  wdiich 
  we 
  saw 
  makes 
  

   x 
  indeterminate. 
  When 
  c 
  — 
  2pa 
  is 
  small 
  but 
  not 
  zero, 
  since 
  

   x=—c/2 
  + 
  qc/(c 
  — 
  2pa) 
  we 
  can, 
  by 
  keeping 
  q 
  small, 
  also 
  keep 
  

   x 
  as 
  near 
  —e/2 
  as 
  we 
  please, 
  so 
  that 
  the 
  central 
  region 
  of 
  the 
  

   fringes 
  is 
  still 
  peculiar 
  and 
  characteristic. 
  In 
  this 
  case 
  the 
  

   approximation 
  given 
  for 
  x' 
  — 
  x 
  in 
  (5) 
  is 
  no 
  longer 
  of 
  use 
  ; 
  

   and 
  we 
  must 
  reason 
  in 
  the 
  following 
  way, 
  that 
  before 
  the 
  

   shift 
  (fig. 
  3), 
  the 
  central 
  region 
  will 
  lie 
  along 
  OZ, 
  and 
  after 
  

   the 
  shift 
  along 
  a 
  parallel 
  to 
  OZ 
  through 
  L, 
  so 
  that 
  the 
  system 
  

   of 
  fringes 
  shifts 
  as 
  expected 
  by 
  Michelson 
  and 
  Morley 
  ; 
  in 
  

   short, 
  when 
  q 
  is 
  small 
  we 
  are 
  observing 
  near 
  the 
  central 
  fringe 
  

   which 
  moves 
  the 
  full 
  s/2oi. 
  Thus 
  we 
  see 
  that 
  while 
  an 
  im- 
  

   proper 
  use 
  of 
  the 
  formula 
  (6) 
  might 
  make 
  it 
  seem 
  as 
  if 
  we 
  

   could 
  get 
  infinite 
  magnification 
  of 
  the 
  effect 
  looked 
  for 
  in 
  the 
  

   experiment, 
  in 
  reality 
  the 
  shift 
  s/2a 
  of 
  the 
  fringes 
  is 
  the 
  largest 
  

   practically 
  obtainable, 
  and 
  can 
  be 
  secured 
  only 
  by 
  making 
  

   either 
  g 
  nearly 
  equal 
  to 
  0, 
  or 
  as 
  we 
  saw 
  before 
  (fig. 
  2) 
  c 
  = 
  ; 
  

   while 
  if 
  c 
  is 
  allowed 
  to 
  be 
  larger 
  than 
  2pa 
  the 
  shift 
  may 
  be 
  

   any 
  fraction 
  of 
  this 
  maximum. 
  In 
  other 
  words, 
  the 
  shift 
  

   expected 
  by 
  the 
  experimenters 
  can 
  be 
  obtained 
  in 
  only 
  two 
  

   cases: 
  first 
  when 
  the 
  intersection 
  of 
  the 
  two 
  images 
  corresponds 
  

   to 
  itself, 
  in 
  which 
  case 
  the 
  eye 
  may 
  observe 
  anywhere; 
  and 
  

   second, 
  when 
  there 
  is 
  a 
  lateral 
  shift 
  of 
  one 
  image 
  relative 
  to 
  

   the 
  other, 
  and 
  the 
  eye 
  is 
  in 
  the 
  axis 
  of 
  quasi-symmetry 
  OZ. 
  

   If 
  the 
  contention 
  here 
  advanced 
  is 
  sound, 
  it 
  appears 
  that 
  the 
  

   failure 
  of 
  Michelson 
  and 
  Morley 
  to 
  get 
  evidence 
  of 
  the 
  

   relative 
  motion 
  of 
  earth 
  and 
  asther 
  is 
  due 
  to 
  the 
  absence 
  of 
  a 
  

   certain 
  adjustment 
  required 
  to 
  give 
  their 
  method 
  the 
  sensitive- 
  

   ness 
  aimed 
  at, 
  and 
  not 
  to 
  any 
  real 
  defect 
  in 
  the 
  theory 
  of 
  the 
  

   experiment. 
  Their 
  method 
  has 
  been 
  since 
  applied 
  to 
  other 
  

   attempts 
  to 
  measure 
  motion 
  of 
  the 
  aether, 
  as 
  in 
  Lodge's 
  

   experiment 
  with 
  the 
  whirling 
  steel 
  disks 
  (Phil. 
  Trans, 
  clxxxiv. 
  

   1893), 
  Threlfall 
  and 
  Pollock's 
  on 
  the 
  Effect 
  of 
  Rontgen 
  Rays 
  

   (Phil. 
  Mag. 
  [5] 
  xlii.), 
  and 
  Henderson 
  and 
  Henry's 
  (Phil. 
  

   Mag. 
  [5] 
  xliv.) 
  on 
  the 
  Motion 
  of 
  iEther 
  in 
  an 
  Electromagnetic 
  

   Field 
  ; 
  in 
  all 
  these 
  experiments 
  only 
  negative 
  results 
  have 
  

   been 
  obtained. 
  But 
  it 
  is 
  to 
  be 
  remembered 
  that 
  in 
  the 
  last 
  

   three 
  the 
  two 
  parts 
  of 
  the 
  divided 
  beam 
  are 
  sent 
  in 
  opposite 
  

   directions 
  round 
  the 
  same 
  path, 
  whereas 
  in 
  Michelson 
  and 
  

   Morley 
  J 
  s 
  experiment 
  the 
  two 
  beams 
  travel 
  in 
  independent 
  

  

  