﻿Experiment 
  relating 
  to 
  the 
  Drift 
  of 
  the 
  JEther. 
  17 
  

  

  reflected 
  and 
  incident 
  waves 
  respectively, 
  

  

  X' 
  sin 
  6 
  ' 
  

  

  X 
  sin 
  </> 
  " 
  •••••• 
  \ 
  ) 
  

  

  This 
  result 
  is 
  true 
  whatever 
  be 
  the 
  law 
  of 
  reflexion. 
  

   Applying 
  the 
  actual 
  law 
  of 
  reflexion 
  above, 
  it 
  follows 
  that 
  

  

  X 
  " 
  V 
  2 
  -m; 
  2 
  + 
  2Vvcos<£ 
  

  

  (3) 
  

  

  Modification 
  produced 
  on 
  the 
  Light 
  at 
  any 
  point 
  by 
  motion 
  

   of 
  the 
  source. 
  — 
  Owing 
  to 
  motion 
  of 
  the 
  source 
  the 
  light 
  

   reaching 
  a 
  point 
  P 
  will 
  not 
  come 
  from 
  the 
  instantaneous 
  

   position 
  of 
  the 
  source 
  but 
  from 
  the 
  position 
  occupied 
  by 
  it 
  at 
  

   some 
  time 
  previously. 
  Consequently 
  if 
  S 
  denote 
  the 
  source, 
  

   P 
  this 
  position, 
  and 
  v 
  the 
  velocity 
  of 
  S 
  perpendicular 
  to 
  SP, 
  

   the 
  light 
  at 
  P 
  makes 
  an 
  angle 
  with 
  SP 
  where 
  

  

  Vsintf: 
  

  

  v. 
  

  

  Again, 
  if 
  X 
  denote 
  the 
  wave-length 
  at 
  P 
  (or 
  V/X 
  the 
  

   frequency), 
  and 
  if 
  A 
  denote 
  the 
  wave-length 
  if 
  the 
  source 
  is 
  

   at 
  rest, 
  and 
  u 
  denote 
  the 
  velocity 
  of 
  the 
  source 
  towards 
  P, 
  

  

  . 
  Vcos0 
  — 
  u 
  a 
  ... 
  

  

  X= 
  -= 
  Acostf 
  (4) 
  

  

  6. 
  Specification 
  of 
  the 
  Configuration. 
  — 
  We 
  shall 
  call 
  the 
  

   mirror 
  which 
  receives 
  the 
  light 
  after 
  reflexion 
  at 
  the 
  plate, 
  

   the 
  first 
  mirror 
  ; 
  that 
  which 
  receives 
  it 
  after 
  transmission 
  

   through 
  the 
  plate 
  the 
  second 
  mirror, 
  and 
  we 
  shall 
  refer 
  all 
  

   directions 
  to 
  the 
  line 
  through 
  the 
  source 
  parallel 
  to 
  the 
  first 
  

   mirror. 
  

  

  The 
  normal 
  to 
  the 
  plate 
  makes 
  an 
  angle 
  <j> 
  (fig. 
  5) 
  with 
  this 
  

   datum 
  line, 
  and 
  the 
  normal 
  to 
  the 
  second 
  plate 
  an 
  angle 
  x 
  

   (positive 
  as 
  in 
  fig.). 
  Let 
  6 
  be 
  the 
  inclination 
  of 
  the 
  incident 
  

   light 
  to 
  this 
  datum 
  line. 
  The 
  angles 
  of 
  incidence 
  on 
  the 
  

   plate 
  and 
  the 
  second 
  mirror 
  are 
  <j> 
  + 
  6 
  and 
  % 
  -f 
  6. 
  

  

  Let 
  the 
  angles 
  of 
  reflexion 
  be 
  <j>' 
  and 
  rf. 
  Let 
  the 
  angles 
  

   of 
  incidence 
  and 
  reflexion 
  on 
  the 
  first 
  mirror 
  be 
  fa, 
  </>/, 
  and 
  

   on 
  the 
  plate 
  after 
  reflexion 
  at 
  the 
  second 
  mirror 
  be 
  <j) 
  2 
  and 
  <£ 
  2 
  '. 
  

   Also 
  let 
  A, 
  B 
  denote 
  the 
  angles 
  the 
  final 
  wave-fronts 
  make 
  

   with 
  the 
  first 
  mirror 
  (or 
  the 
  datum 
  line). 
  This 
  specifies 
  the 
  

   light. 
  Let 
  the 
  apparatus 
  drift 
  with 
  velocity 
  U 
  in 
  a 
  direction 
  

   making 
  a 
  with 
  the 
  datum, 
  its 
  velocities 
  along 
  and 
  perpen- 
  

   dicular 
  thereto 
  being 
  denoted 
  by 
  u, 
  v. 
  

  

  The 
  velocity 
  of 
  the 
  plate 
  perpendicular 
  to 
  itself, 
  and 
  towards 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  3. 
  No. 
  13. 
  Jan. 
  1902. 
  C 
  

  

  