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  890 
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  XCV. 
  The 
  Heflexion 
  of 
  Light 
  at 
  an 
  Ideal 
  Plane 
  Mirror 
  

   moving 
  with 
  a 
  Uniform 
  Velocity 
  of 
  Translation. 
  By 
  H. 
  

   Bateman*. 
  

  

  THE 
  question 
  whether 
  the 
  motion 
  of 
  a 
  mirror 
  has 
  any 
  

   effect 
  on 
  the 
  laws 
  of 
  reflexion 
  and 
  refraction 
  was 
  

   considered 
  by 
  Fresnelf, 
  who 
  came 
  to 
  the 
  conclusion 
  that 
  no 
  

   discrepancy 
  need 
  be 
  expected. 
  Stokes 
  J, 
  examining 
  the 
  

   question 
  in 
  a 
  more 
  general 
  manner, 
  showed 
  that 
  the 
  laws 
  of 
  

   reflexion 
  and 
  refraction 
  are 
  satisfied 
  provided 
  the 
  directions 
  

   of 
  the 
  rays 
  are 
  measured 
  relative 
  to 
  the 
  mirror 
  and 
  quantities 
  

   of 
  an 
  order 
  higher 
  than 
  the 
  first, 
  in 
  the 
  ratio 
  of 
  the 
  velocity 
  of 
  

   the 
  mirror 
  to 
  that 
  of 
  light, 
  are 
  neglected. 
  

  

  The 
  question 
  was 
  brought 
  into 
  prominence 
  in 
  the 
  discus- 
  

   sions 
  of 
  the 
  Michelson-Morley 
  experiment, 
  and 
  is 
  of 
  funda- 
  

   mental 
  importance 
  in 
  the 
  theory 
  of 
  radiation 
  §, 
  where 
  we 
  

   have 
  to 
  consider 
  the 
  case 
  in 
  which 
  the 
  mirror 
  is 
  moving 
  

   relatively 
  to 
  the 
  observer. 
  

  

  An 
  exact 
  theory 
  of 
  reflexion 
  is 
  required 
  for 
  a 
  rigorous 
  

   discussion 
  of 
  the 
  Michelson-Morley 
  experiment, 
  Wien's 
  law, 
  

   the 
  pressure 
  of 
  radiation 
  on 
  a 
  moving 
  mirror, 
  and 
  the 
  effect 
  

   of 
  motion 
  on 
  the 
  temperature 
  of 
  radiation. 
  The 
  precise 
  laws 
  

   of 
  reflexion 
  have 
  accordingly 
  been 
  discussed 
  by 
  Voigt||, 
  

   Lodge 
  IF, 
  Hicks**, 
  Abrahamff, 
  Einstein 
  J 
  J, 
  Planck 
  §§, 
  von 
  

   Mosengeil 
  ||||, 
  and 
  Kohllflf. 
  

  

  The 
  object 
  of 
  this 
  paper 
  is 
  to 
  make 
  a 
  small 
  addition 
  to 
  the 
  

   results 
  obtained 
  by 
  these 
  writers. 
  It 
  will 
  be 
  convenient 
  to 
  

   use 
  them 
  in 
  the 
  form 
  obtained 
  by 
  Hicks, 
  Abraham, 
  and 
  

   Einstein. 
  

  

  Let 
  c 
  be 
  the 
  velocity 
  of 
  light 
  in 
  free 
  aether, 
  w 
  the 
  velocity 
  

   of 
  the 
  mirror 
  referred 
  to 
  a 
  set 
  of 
  axes 
  which 
  are 
  at 
  rest 
  

   relatively 
  to 
  the 
  observer. 
  Let 
  v 
  be 
  the 
  component 
  of 
  w 
  along 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  t 
  A7inales 
  de 
  Chimie, 
  t. 
  ix. 
  (1818) 
  p. 
  57. 
  

  

  X 
  Phil. 
  Mag. 
  Tol. 
  xxvii. 
  (1846) 
  pi 
  76. 
  

  

  § 
  Larmor, 
  British 
  Association 
  Reports, 
  1900, 
  p. 
  657. 
  Encyclo'pcedia 
  

   Britannica^ 
  article 
  * 
  Radiation/ 
  in 
  vol. 
  xxxii. 
  (1903). 
  Boltzmann, 
  Fest- 
  

   schrift, 
  p. 
  590 
  (1904). 
  

  

  II 
  Gottinger 
  Nachrichten, 
  1887, 
  p. 
  215. 
  

  

  1" 
  Phil. 
  Trans. 
  A. 
  (1893) 
  p. 
  793. 
  

  

  ** 
  Phil. 
  Mag. 
  [6] 
  iii. 
  (1902) 
  p. 
  9. 
  

  

  tt 
  Boltzmann, 
  Festschrift, 
  p. 
  85 
  (1904) 
  ; 
  Ann. 
  d, 
  Phys. 
  [4] 
  xiv. 
  p. 
  236 
  

   (1904) 
  ; 
  Theone 
  der 
  Elektricitdt, 
  vol. 
  ii. 
  p. 
  343. 
  

  

  XX 
  Ann. 
  d. 
  Phys. 
  [4] 
  xvii. 
  (1905). 
  

  

  §§ 
  Theorie 
  der 
  Wnrmestrahlung, 
  p. 
  71. 
  

  

  Hi 
  Ann. 
  d. 
  Phys. 
  [4] 
  xxii. 
  (1907). 
  

  

  nil 
  Ibid. 
  xxTiii. 
  p. 
  28 
  (1909). 
  

  

  