﻿Liglit 
  at 
  an 
  Ideal 
  Plane 
  Mirror. 
  893 
  

  

  Further, 
  since 
  

  

  we 
  have 
  for 
  a 
  oiven 
  value 
  of 
  t' 
  

  

  

  -1-2-2— 
  Zi 
  — 
  ,0 
  . 
  

  

  The 
  image 
  of 
  a 
  stationary 
  object, 
  therefore, 
  sufEers 
  a 
  

   contraction 
  proportional 
  to 
  

  

  

  times 
  its 
  length 
  in 
  a 
  direction 
  parallel 
  to 
  the 
  axis 
  of 
  ,i\ 
  This 
  

   is 
  the 
  proper 
  contraction 
  for 
  velocity 
  U 
  according 
  to 
  the 
  

   hypothesis 
  put 
  forward 
  by 
  FitzGerald* 
  and 
  Lorentzf 
  to 
  

   explain 
  the 
  negative 
  result 
  of 
  the 
  famous 
  experiment 
  made 
  

   by 
  Michelson 
  and 
  Morley. 
  

  

  To 
  show 
  that 
  this 
  transformation 
  gives 
  the 
  correct 
  laws 
  of 
  

   reflexion 
  of 
  a 
  plane 
  wave 
  w^e 
  introduce 
  dashed 
  letters 
  into 
  

   the 
  argument 
  of 
  the 
  periodic 
  function 
  of 
  the 
  reflected 
  wave 
  

   and 
  make 
  the 
  necessary 
  substitutions. 
  The 
  argument 
  

  

  , 
  r 
  , 
  .r' 
  cos 
  (f)' 
  — 
  y' 
  sin 
  0^"1 
  

  

  is 
  then 
  transformed 
  into 
  

  

  L 
  c 
  — 
  V 
  c^-v^ 
  c 
  c 
  ^ 
  J 
  

  

  and 
  if 
  we 
  compare 
  this 
  with 
  

  

  r 
  ./■ 
  cos 
  (/)+// 
  sin 
  (/>"! 
  

  

  we 
  obtain 
  the 
  relations 
  (I). 
  

  

  The 
  transformation 
  can 
  evidently 
  be 
  applied 
  to 
  waves 
  of 
  

   any 
  form. 
  

  

  The 
  formulae 
  connecting 
  the 
  components 
  of 
  the 
  electric 
  

  

  * 
  Public 
  Lectures 
  in 
  Trinity 
  College, 
  Dublin. 
  

  

  t 
  'Versuch 
  einer 
  Theorie 
  der 
  Elektrischen 
  Kcirpern 
  ' 
  (1895). 
  See 
  

   also 
  Larmor's 
  ' 
  ^tber 
  and 
  Matter.' 
  

  

  