﻿478 
  A. 
  A. 
  Michelson 
  — 
  Motion 
  of 
  the 
  Earth 
  and 
  the 
  Ether. 
  

  

  pleting 
  their 
  paths 
  at 
  noon 
  and 
  at 
  midnight 
  (when 
  the 
  horizon- 
  

   tal 
  parts 
  of 
  the 
  path 
  are 
  parallel 
  with 
  the 
  earth's 
  motion 
  in 
  its 
  

  

  v 
  

   orbit), 
  we 
  find 
  the 
  difference 
  is 
  4s-- 
  where 
  s 
  is 
  the 
  length 
  of 
  

  

  the 
  horizontal 
  part 
  of 
  the 
  path, 
  ?;, 
  the 
  difference 
  of 
  relative 
  

   velocities 
  above 
  and 
  below, 
  and 
  V 
  the 
  velocity 
  of 
  light. 
  This 
  

  

  corresponds 
  to 
  a 
  displacement 
  A 
  = 
  4- 
  - 
  fringes. 
  

  

  If 
  the 
  relative 
  motion 
  be 
  assumed 
  to 
  follow 
  an 
  exponential 
  

   law 
  it 
  may 
  be 
  represented 
  by 
  

  

  v=v 
  (l-e~ 
  M 
  ) 
  

   where 
  v 
  is 
  the 
  velocity 
  of 
  the 
  earth 
  and 
  A, 
  the 
  height 
  above 
  

   the 
  surface. 
  

  

  Suppose 
  — 
  falls 
  to 
  — 
  of 
  its 
  surface 
  value 
  in 
  one 
  hundred 
  

  

  . 
  v 
  e 
  

  

  kilometers. 
  Then 
  in 
  fifteen 
  meters, 
  which 
  is 
  the 
  difference 
  of 
  

  

  level 
  of 
  the 
  two 
  horizontal 
  pipes 
  

  

  Substituting 
  this 
  for 
  v 
  in 
  the 
  equation 
  for 
  A 
  we 
  have 
  

  

  A 
  = 
  -0006-f 
  ^;. 
  

  

  A 
  V 
  

  

  Putting 
  y 
  = 
  12xl0i 
  and 
  ^=10~ 
  4 
  we 
  find 
  A 
  = 
  7'2 
  fringes. 
  

  

  As 
  the 
  actual 
  displacement 
  was 
  certainly 
  less 
  than 
  a 
  twen- 
  

   tieth 
  of 
  a 
  fringe, 
  it 
  would 
  follow 
  that 
  the 
  earth's 
  influence 
  upon 
  

   the 
  ether 
  extended 
  to 
  distances 
  of 
  the 
  order 
  of 
  the 
  earth's 
  

   diameter.* 
  

  

  Such 
  a 
  conclusion 
  seems 
  so 
  improbable 
  that 
  one 
  is 
  inclined 
  

   to 
  return 
  to 
  the 
  hypothesis 
  of 
  Fresnel 
  and 
  to 
  try 
  to 
  reconcile 
  

   in 
  some 
  other 
  way 
  the 
  negative 
  results 
  obtained 
  in 
  the 
  experi- 
  

   ment 
  cited 
  in 
  the 
  first 
  paragraph. 
  

  

  The 
  only 
  attempt 
  of 
  this 
  character 
  is 
  due 
  to 
  H. 
  A. 
  Lorentz.f 
  

   It 
  involves 
  the 
  hypothesis 
  that 
  the 
  length 
  of 
  bodies 
  is 
  altered 
  

   by 
  their 
  motion 
  through 
  the 
  ether. 
  

  

  In 
  any 
  case 
  we 
  are 
  driven 
  to 
  extraordinary 
  conclusions, 
  and 
  

   the 
  choice 
  lies 
  between 
  these 
  three 
  : 
  — 
  

  

  1. 
  The 
  earth 
  passes 
  through 
  the 
  ether 
  (or 
  rather 
  allows 
  the 
  

   ether 
  to 
  pass 
  through 
  its 
  entire 
  mass) 
  without 
  appreciable 
  in- 
  

   fluence. 
  

  

  2. 
  The 
  length 
  of 
  all 
  bodies 
  is 
  altered 
  (equally 
  ?) 
  by 
  their 
  

   motion 
  through 
  the 
  ether. 
  

  

  3. 
  The 
  earth 
  in 
  its 
  motion 
  drags 
  with 
  it 
  the 
  ether 
  even 
  at 
  

   distances 
  of 
  many 
  thousand 
  kilometers 
  from 
  its 
  surface. 
  

  

  * 
  Of 
  course 
  this 
  will 
  depend 
  on 
  the 
  law 
  assumed 
  for 
  the 
  rate 
  of 
  diminution 
  of 
  

   relative 
  velocity 
  with 
  distance 
  from 
  the 
  earth's 
  surface 
  ; 
  and 
  possibly 
  an 
  exponen- 
  

   tial 
  law 
  is 
  far 
  from 
  the 
  truth. 
  It 
  may 
  be 
  desirable 
  to 
  repeat 
  the 
  experiment 
  with 
  

   a 
  much 
  greater 
  difference 
  of 
  level, 
  and 
  perhaps 
  to 
  bury 
  the 
  lower 
  tube 
  some 
  dis- 
  

   tance 
  underground. 
  

  

  f 
  " 
  Yersueh 
  einer 
  Theorie 
  der 
  El. 
  u. 
  Op. 
  Erscheinungen 
  in 
  bewegten 
  Korpern," 
  

   H. 
  A. 
  Lorentz. 
  

  

  