﻿24 
  

  

  Mr. 
  W. 
  Sutherland 
  on 
  the 
  Relative 
  

  

  iiitely 
  that 
  the 
  earth's 
  surface 
  and 
  the 
  adjacent 
  aether 
  have 
  no 
  

   relative 
  motion. 
  I 
  propose 
  now 
  to 
  show 
  how 
  a 
  slight 
  altera- 
  

   tion 
  in 
  the 
  point 
  of 
  view 
  of 
  the 
  theory 
  of 
  that 
  experiment 
  will 
  

   make 
  it 
  appear 
  that, 
  until 
  a 
  special 
  adjustment 
  for 
  sensitive- 
  

   ness 
  of 
  the 
  optical 
  apparatus 
  has 
  heen 
  made, 
  it 
  is 
  not 
  com- 
  

   petent 
  to 
  decide 
  as 
  to 
  the 
  relative 
  rest 
  or 
  motion 
  of 
  earth 
  and 
  

   aath 
  er. 
  

  

  For 
  the 
  sake 
  of 
  clearness 
  let 
  us 
  briefly 
  repeat 
  the 
  authors' 
  

   account 
  of 
  the 
  theory 
  of 
  their 
  experiment 
  along 
  with 
  their 
  

   diagram, 
  b 
  and 
  c 
  are 
  two 
  mirrors 
  at 
  right 
  angles 
  to 
  one 
  

   another 
  (fig. 
  1), 
  and 
  at 
  equal 
  distances 
  D 
  from 
  a 
  a 
  piece 
  of 
  

  

  Fie:. 
  1. 
  

  

  glass 
  inclined 
  at 
  7r/4 
  to 
  them, 
  and 
  intended 
  to 
  divide 
  a 
  beam 
  

   of 
  light 
  sa 
  into 
  reflected 
  and 
  transmitted 
  parts 
  going 
  to 
  b 
  and 
  

   c 
  respectively. 
  Suppose 
  the 
  whole 
  apparatus 
  to 
  be 
  moving 
  

   in 
  the 
  direction 
  sc 
  with 
  velocity 
  v 
  relative 
  to 
  the 
  aether 
  in 
  

   which 
  the 
  beam 
  of 
  light 
  is 
  moving 
  with 
  velocity 
  Y; 
  then 
  

   while 
  the 
  reflected 
  beam 
  is 
  going 
  to 
  b 
  and 
  back 
  a 
  is 
  moving 
  

   to 
  «i, 
  so 
  that 
  the 
  path 
  of 
  the 
  reflected 
  part 
  is 
  aba 
  L 
  , 
  while 
  that 
  

   of 
  the 
  transmitted 
  part 
  is 
  aca 
  x 
  : 
  at 
  % 
  the 
  former 
  is 
  partly 
  

   transmitted 
  and 
  the 
  latter 
  partly 
  reflected 
  to 
  the 
  telescope 
  

   under 
  conditions 
  favourable 
  to 
  the 
  occurrence 
  of 
  interference. 
  

   Along 
  ac 
  the 
  beam 
  moves 
  with 
  velocity 
  V—v 
  relative 
  to 
  c, 
  

   so 
  that 
  the 
  time 
  of 
  traversing 
  ac 
  is 
  J) 
  /(V 
  — 
  v) 
  ; 
  similarly 
  the 
  

   time 
  for 
  ca 
  1 
  is 
  D/(Y 
  + 
  t'), 
  and 
  hence 
  

  

  ac 
  + 
  cay 
  

  

  \V 
  — 
  v 
  V 
  + 
  vj 
  

  

  2D 
  

  

  l-t^/V' 
  

  

  The 
  path 
  of 
  the 
  other 
  beam 
  is 
  taken 
  to 
  be 
  aba 
  1} 
  whose 
  length 
  

  

  