﻿892 
  Mr. 
  H. 
  Bateman 
  on 
  the 
  Reflexion 
  of 
  

  

  It 
  will 
  be 
  noticed 
  that 
  the 
  laws 
  of 
  reflexion 
  depend 
  only 
  

   on 
  the 
  normal 
  component 
  of 
  the 
  mirror's 
  velocity. 
  

  

  What 
  I 
  wish 
  to 
  point 
  out 
  is 
  that 
  these 
  laws 
  of 
  re- 
  

   flexion 
  can 
  be 
  obtained 
  in 
  a 
  very 
  simple 
  way 
  by 
  supposing- 
  

   that 
  the 
  image 
  of 
  an 
  object 
  is 
  derived 
  by 
  means 
  of 
  the 
  space 
  

   time 
  transformation', 
  

  

  This 
  transformation 
  reduces 
  to 
  the 
  -one 
  considered 
  by 
  

   Voigt 
  *, 
  Lorentz 
  f, 
  and 
  Einstein 
  J, 
  if 
  we 
  change 
  the 
  sign 
  of 
  

   x' 
  and 
  put 
  

  

  jj_ 
  2c^v 
  

   ^-c^ 
  + 
  v^' 
  

   Since 
  

  

  it 
  is 
  clear 
  that 
  at 
  any 
  time 
  every 
  point 
  of 
  the 
  moving 
  mirror 
  

   (sc=vt) 
  is 
  transformed 
  into 
  itself. 
  The 
  image 
  of 
  a 
  point 
  

   moving 
  with 
  the 
  same 
  velocity 
  as 
  the 
  mirror 
  is 
  another 
  

   point 
  moving 
  with 
  the 
  same 
  velocity, 
  for 
  if 
  dots 
  denote 
  

   differentiations 
  with 
  regard 
  to 
  t 
  

  

  (.r— 
  1;) 
  = 
  ^', 
  

  

  c'-^v^ 
  

  

  y'=y, 
  ^'=2, 
  

  

  dx' 
  _ 
  . 
  dy 
  _ 
  . 
  dz' 
  . 
  

  

  The 
  image 
  of 
  a 
  stationary 
  point, 
  on 
  the 
  other 
  hand, 
  is 
  a 
  

   point 
  moving 
  with 
  the 
  uniform 
  velocity 
  

  

  U 
  = 
  -^-- 
  

  

  * 
  Gbitinger 
  NacJirichten, 
  1887, 
  p. 
  41. 
  

   t 
  AmsterdHin 
  Proceedings, 
  1904. 
  

   j: 
  Ann. 
  d. 
  Phys. 
  xvii. 
  (1905). 
  

  

  