﻿Experiment 
  relating 
  to 
  the 
  Drift 
  of 
  the 
  ^Efrher. 
  39 
  

  

  solid 
  through 
  the 
  aether 
  produces 
  a 
  small 
  extension 
  perpen- 
  

   dicular 
  to 
  the 
  direction 
  of 
  drift, 
  or 
  contraction 
  in 
  the 
  direction, 
  

   the 
  amount 
  being 
  proportional 
  to 
  £ 
  2 
  . 
  This 
  has 
  received 
  some 
  

   justification 
  from 
  the 
  fact 
  that 
  on 
  the 
  theories 
  of 
  Larmor 
  

   and 
  of 
  Lorentz 
  as 
  to 
  the 
  connexion 
  between 
  matter 
  and 
  

   aether, 
  a 
  contraction 
  such 
  as 
  is 
  indicated 
  should 
  be 
  expected. 
  

   At 
  first 
  sight 
  — 
  especially 
  in 
  the 
  theory 
  of 
  the 
  experiment 
  as 
  

   given 
  by 
  Michelson 
  and 
  Morley 
  — 
  an 
  effect 
  of 
  this 
  kind 
  of 
  the 
  

   proper 
  amount 
  might 
  seem 
  capable 
  of 
  annulling 
  any 
  observed 
  

   displacement. 
  If, 
  however, 
  the 
  effect 
  of 
  such 
  a 
  contraction 
  

   on 
  the 
  displacement 
  of 
  the 
  fringe 
  be 
  worked 
  out 
  on 
  the 
  lines 
  

   of 
  the 
  rigorous 
  theory 
  developed 
  in 
  the 
  present 
  paper, 
  it 
  will 
  

   be 
  found 
  that 
  not 
  only 
  is 
  it 
  incapable 
  of 
  explaining 
  the 
  null 
  

   result, 
  but 
  that 
  in 
  fact 
  it 
  should 
  increase 
  the 
  displacement 
  to 
  

   be 
  observed. 
  To 
  produce 
  annulment 
  an 
  extension 
  along 
  the 
  

   line 
  of 
  drift 
  is 
  required. 
  It 
  is 
  the 
  object 
  of 
  the 
  present 
  section 
  

   to 
  prove 
  this 
  and 
  to 
  show 
  how 
  by 
  a 
  suitable 
  modification 
  of 
  

   Michelson 
  and 
  Morley's 
  experiment 
  it 
  lies 
  at 
  our 
  disposal 
  to 
  

   test 
  the 
  truth 
  or 
  otherwise 
  of 
  Larmor 
  and 
  Lorentz's 
  result, 
  and, 
  

   if 
  such 
  contraction 
  exists, 
  to 
  measure 
  its 
  amount. 
  

  

  We 
  shall 
  assume 
  then 
  that 
  when 
  a 
  solid 
  moves 
  through 
  the 
  

   aether, 
  it 
  suffers 
  a 
  contraction 
  along 
  the 
  direction 
  of 
  the 
  drift 
  

   such 
  that 
  a 
  length 
  I 
  parallel 
  to 
  it 
  is 
  contracted 
  by 
  an 
  amount 
  kg 
  H. 
  

   The 
  effective 
  changes 
  in 
  the 
  apparatus 
  are 
  those 
  which 
  occur 
  in 
  

   the 
  horizontal 
  plane. 
  If 
  then 
  the 
  total 
  drift 
  makes 
  an 
  angle 
  I 
  

   with 
  the 
  plane 
  of 
  the 
  apparatus, 
  lines 
  in 
  the 
  plane 
  will 
  be 
  

   distorted 
  as 
  if 
  there 
  were 
  a 
  contraction 
  kg 
  2 
  cos 
  I 
  . 
  I 
  in 
  the 
  

   direction 
  of 
  the 
  component 
  of 
  the 
  drift 
  in 
  the 
  plane, 
  or 
  — 
  if 
  £ 
  

   represent 
  this 
  component 
  as 
  in 
  the 
  preceding 
  pages 
  — 
  a 
  con- 
  

   traction 
  A,f 
  2 
  Z/cosI. 
  In 
  what 
  immediately 
  follows 
  we 
  shall 
  

   replace 
  k\ 
  cos 
  I 
  by 
  k, 
  

  

  20. 
  Owing 
  to 
  the 
  distortion 
  produced 
  both 
  the 
  lengths 
  of 
  

   lines 
  and 
  the 
  magnitudes 
  of 
  angles 
  lying 
  in 
  the 
  plane 
  will 
  be 
  

   altered. 
  It 
  is 
  first 
  necessary 
  to 
  determine 
  this 
  alteration. 
  

  

  In 
  fig. 
  7 
  (p. 
  40) 
  AB 
  denotes 
  any 
  line, 
  LB 
  the 
  direction 
  of 
  

   drift. 
  Draw 
  AL 
  perpendicular 
  to 
  BL. 
  

  

  Through 
  the 
  contraction 
  B 
  comes 
  to 
  B' 
  where 
  

   BB' 
  = 
  £f 
  2 
  .BL 
  

   and 
  the 
  line 
  AB 
  is 
  displaced 
  to 
  AB'. 
  If 
  AB 
  =r, 
  ABL 
  = 
  0, 
  

   oY 
  = 
  Bn 
  = 
  kf 
  . 
  BL 
  cos 
  ABL 
  

  

  = 
  hfr 
  cos 
  2 
  9 
  = 
  \Wr 
  (1 
  + 
  cos 
  20) 
  , 
  

  

  ofl=BAB^ 
  B 
  '* 
  = 
  ** 
  2 
  - 
  BLsin 
  fl 
  

   r 
  r 
  

  

  = 
  Pfsin20. 
  

  

  