﻿40 
  

  

  Dr. 
  W. 
  M. 
  Hicks 
  on 
  the 
  Michelson-Morley 
  

  

  These 
  formulae 
  hold 
  only 
  when 
  k% 
  2 
  is 
  small. 
  Hence 
  the 
  

   following 
  results 
  are 
  not 
  applicable 
  to 
  cases 
  where 
  the 
  velocity 
  

  

  Fig. 
  7, 
  

  

  of 
  drift 
  is 
  comparable 
  with 
  that 
  of 
  light. 
  Further, 
  we 
  shall 
  

   suppose 
  f 
  2 
  so 
  small 
  that 
  it 
  may 
  be 
  neglected 
  in 
  comparison 
  

   with 
  unity. 
  In 
  this 
  case 
  we 
  write 
  V 
  2 
  for 
  V 
  2 
  — 
  wr 
  and 
  

  

  cV 
  = 
  

  

  2b 
  sin 
  C 
  

  

  Q 
  

  

  b 
  sin 
  C 
  

  

  sin(B-A)-if.R' 
  

  

  where 
  

  

  R= 
  (1— 
  cos 
  C) 
  sin 
  (C 
  — 
  2a) 
  

   = 
  cos2« 
  when 
  C 
  = 
  90°. 
  

  

  The 
  change 
  in 
  b 
  sin 
  C 
  will 
  be 
  of 
  order 
  £ 
  2 
  and 
  may 
  be 
  

   neglected 
  in 
  comparison 
  with 
  it. 
  So, 
  too, 
  the 
  change 
  in 
  f 
  2 
  R 
  

   will 
  be 
  of 
  order 
  £ 
  4 
  and 
  may 
  be 
  neglected. 
  There 
  remains 
  

   only 
  the 
  change 
  in 
  B— 
  A. 
  

  

  In 
  fig. 
  8, 
  OjX, 
  2 
  Z 
  denote 
  the 
  directions 
  of 
  the 
  planes 
  of 
  

   the 
  mirrors 
  and 
  0,Y 
  that 
  of 
  the 
  plate. 
  XYZ 
  is 
  any, 
  line 
  

   perpendicular 
  to 
  the 
  direction 
  of 
  drift. 
  Then 
  to 
  compute 
  

   the 
  deformation 
  we 
  have 
  

  

  A=X0 
  1 
  Y=X0 
  1 
  L-Y0 
  1 
  L, 
  

   5A=S.X0 
  1 
  L-5.Y0 
  1 
  L 
  

  

  = 
  Pf 
  {sin 
  2«-sin 
  2(a-A)}. 
  

   So 
  also 
  

  

  8B=*Pf 
  {sin 
  2(«-A)+sin 
  2(C-«)}; 
  

  

  .-. 
  S(B-A) 
  =Pf 
  {sin 
  2(C-«) 
  +2 
  sin 
  2(« 
  - 
  A) 
  -sin 
  2a\. 
  

  

  