﻿24 
  Dr. 
  W. 
  M. 
  Hicks 
  on 
  the 
  Michelson-Morley 
  

  

  Hence 
  when 
  the 
  source 
  is 
  fixed 
  to 
  the 
  apparatus, 
  or 
  

   v 
  = 
  V 
  sin 
  0, 
  

  

  V— 
  U 
  cos 
  (0-a) 
  = 
  (Vcos0-tt) 
  cos 
  6; 
  

  

  and 
  the 
  apparent 
  frequency 
  becomes 
  

  

  (Vcosfl— 
  tt)cosfl 
  __V. 
  

   X 
  A' 
  

  

  or 
  the 
  apparent 
  frequency 
  is 
  the 
  same 
  as 
  if 
  the 
  whole 
  apparatus 
  

   were 
  at 
  rest. 
  Whatever, 
  therefore, 
  be 
  the 
  velocity 
  of 
  drift, 
  

   the 
  apparent 
  frequency 
  remains 
  the 
  same. 
  

  

  11. 
  Direction 
  of 
  Maximal 
  Lines. 
  — 
  Let 
  the 
  common 
  direction 
  

   of 
  the 
  maximal 
  lines 
  make 
  an 
  angle 
  yjr 
  with 
  the 
  first 
  mirror. 
  

   Then, 
  considering 
  a 
  mesh 
  of 
  the 
  network 
  formed 
  by 
  the 
  two 
  

   trains 
  of 
  waves, 
  the 
  sides 
  are 
  inclined 
  to 
  the 
  diagonal 
  at 
  

   angles 
  180 
  — 
  (ty 
  + 
  A) 
  and 
  yjr 
  + 
  B, 
  supposing 
  A 
  > 
  B. 
  The 
  sides 
  

   are 
  proportional 
  to 
  the 
  sines 
  of 
  these 
  angles 
  and 
  also 
  to 
  the 
  

   wave-lengths. 
  Consequently, 
  

  

  sin 
  (yfr 
  + 
  A) 
  _ 
  \ 
  x 
  

   sin 
  Ojr 
  + 
  B) 
  ~X 
  2 
  

  

  _V 
  + 
  Usin(*-A). 
  

   V 
  + 
  UsinO-B)' 
  

   whence 
  

  

  T7 
  A 
  + 
  B 
  A-B 
  

  

  V 
  COS 
  g 
  1- 
  V 
  COS 
  — 
  ~ 
  

  

  tan 
  <dr 
  = 
  z 
  L_ 
  . 
  

  

  T7 
  . 
  A 
  + 
  B 
  A-B 
  

  

  V 
  sin 
  — 
  - 
  — 
  — 
  u 
  cos 
  — 
  - 
  — 
  

  

  A-B 
  

   From 
  the 
  value 
  of 
  e 
  2 
  above, 
  

  

  D^cos 
  ^y? 
  =V 
  4 
  sin 
  (2c/>-x) 
  + 
  V 
  3 
  {-2zo 
  cos 
  </> 
  sin 
  ( 
  % 
  + 
  <9) 
  

  

  — 
  v 
  cos 
  (x 
  + 
  6) 
  + 
  to' 
  sin 
  ( 
  2<£ 
  + 
  0) 
  } 
  

  

  4- 
  V 
  2 
  ( 
  — 
  to't? 
  — 
  w* 
  sin 
  x) 
  4- 
  V 
  {to'to 
  2 
  sin 
  + 
  wio* 
  cos 
  (x 
  4- 
  0) 
  } 
  4- 
  vwho'. 
  

   Also 
  

  

  A+B, 
  

  

  D 
  x 
  D 
  2 
  2 
  

   = 
  V 
  4 
  [x+^]+V 
  3 
  |^^[-* 
  + 
  x]-^~%]-^[|-2^ 
  + 
  X 
  ] 
  +to'[0]| 
  

  

  4-V 
  2 
  jtno|J-(£-x-0] 
  -w«7 
  fJ-^ 
  + 
  x 
  +0j 
  + 
  u™[-£-01 
  

  

  -ivw[<f> 
  + 
  6]-vic'^- 
  i 
  2<l>-0}-w 
  2 
  [-x--0]\ 
  

   + 
  V 
  -j 
  wtc 
  2 
  j~J 
  — 
  x~| 
  —iv'w 
  2 
  [0] 
  1 
  + 
  wgV 
  f^ 
  + 
  6~\ 
  . 
  

  

  