﻿22 
  Dr. 
  W. 
  M. 
  Hicks 
  on 
  the 
  Miclielson-Morlei/ 
  

  

  Therefore 
  

  

  D 
  1 
  D 
  2 
  sm 
  — 
  ~ 
  

  

  -V 
  4 
  cos 
  (20-%) 
  + 
  Y 
  3 
  { 
  -2w 
  sin 
  <f> 
  sin 
  ( 
  % 
  4- 
  0) 
  

  

  + 
  v 
  sin 
  (x 
  + 
  0) 
  - 
  iy 
  ' 
  cos 
  (2</> 
  + 
  (9) 
  } 
  

   4- 
  Y 
  2 
  ic 
  { 
  w? 
  cos 
  ^ 
  — 
  2 
  y 
  sin 
  ((/)—%) 
  } 
  

   4- 
  Yw{ 
  - 
  2tV 
  sin 
  (0 
  4- 
  0) 
  4- 
  r«- 
  sin 
  (% 
  + 
  0) 
  4- 
  iW 
  cos 
  \ 
  . 
  

  

  After 
  reduction 
  this 
  is 
  found 
  to 
  give 
  

  

  sin_ 
  T~^~2 
  Dil> 
  2 
  

  

  where 
  Q 
  has 
  the 
  value 
  given 
  above. 
  

  

  When 
  the 
  source 
  is 
  fixed 
  to 
  the 
  apparatus 
  (V 
  sin 
  6 
  = 
  v) 
  

  

  y{Y_Ucos(^-«)}=Y 
  2 
  -Vwcos^-v 
  2 
  = 
  V 
  2 
  cos 
  2 
  ^-V? 
  f 
  cos^ 
  

  

  =Vcos£(Vcos0-w), 
  

  

  and 
  then 
  

  

  . 
  A-B 
  lVcosfl(Vco 
  sfl-tt)Q 
  

  

  >2 
  

  

  A-B 
  1 
  V{V-Ucos(0-_«)jQ 
  (u) 
  

  

  sm 
  ~~Y~ 
  = 
  ~ 
  2 
  ~ 
  DA 
  

  

  This 
  gives 
  the 
  angle 
  between 
  the 
  wave-fronts. 
  

   9. 
  The 
  distance 
  heticeeii 
  the 
  maximal 
  lines 
  is 
  

  

  XjAg 
  

  

  V 
  v^V 
  + 
  V— 
  ^1^2 
  cos 
  (A-B)} 
  

  

  ^1^2 
  

  

  *J 
  I 
  Oi 
  ~^ 
  2 
  ) 
  2 
  + 
  4X 
  X 
  X 
  2 
  sin 
  2 
  A 
  ~ 
  B 
  | 
  

  

  (V 
  2 
  - 
  w 
  2 
  ) 
  V 
  { 
  U 
  2 
  P 
  2 
  Q* 
  + 
  ( 
  V 
  2 
  - 
  i> 
  2 
  ) 
  (V 
  2 
  - 
  itf' 
  2 
  ) 
  Y 
  2 
  (V 
  - 
  U 
  cos 
  6 
  -a) 
  2 
  Q 
  2 
  } 
  

   _X 
  (V»- 
  r 
  tg)(V 
  8 
  -«/ 
  8 
  j(V 
  2 
  --ig 
  a 
  J 
  - 
  

  

  "QVj 
  U 
  2 
  P 
  2 
  + 
  \■^Y^v^)\^ 
  J2 
  -w 
  ,2 
  ) 
  (Y-u 
  cos 
  e-af 
  \ 
  ; 
  

  

  for 
  source 
  fixed 
  to 
  apparatus 
  

   X 
  (V 
  8 
  -^ 
  (Y 
  2 
  - 
  w 
  2 
  ) 
  (Y 
  2 
  -w 
  2 
  ) 
  

  

  (15) 
  

  

  Q 
  (V 
  cos 
  fl-a) 
  V 
  { 
  (V 
  9 
  cos 
  x 
  -« 
  + 
  »* 
  cos 
  x 
  4- 
  «; 
  2 
  U 
  2 
  + 
  (V 
  2 
  -r*) 
  2 
  (V«- 
  a/ 
  2 
  ) 
  } 
  

  

  Acos# 
  (V 
  2 
  -t; 
  2 
  )(V 
  2 
  -«/ 
  2 
  )(V 
  2 
  -ze 
  2 
  ) 
  

  

  YQ 
  " 
  • 
  • 
  { 
  (Y2 
  cos 
  =, 
  + 
  ,2 
  C0S 
  £^)2XJ2 
  + 
  (V 
  2 
  -v 
  2 
  ) 
  2 
  tY 
  2 
  -^ 
  2 
  ) 
  F 
  

  

  where 
  A 
  is 
  actual 
  wave-length 
  of 
  light 
  emitted 
  by 
  the 
  source. 
  

  

  