﻿30 
  Dr. 
  W. 
  M. 
  Hicks 
  on 
  the 
  Michelson- 
  Movie 
  y 
  

  

  velocity 
  amounts 
  to 
  anything 
  approximating 
  to 
  100 
  times 
  the 
  

   velocity 
  of 
  the 
  earth 
  in 
  its 
  orbit, 
  which 
  latter 
  is 
  roughly 
  

   10 
  -4 
  times 
  that 
  of 
  light. 
  Even 
  in 
  this 
  extreme 
  case 
  the 
  

   square 
  of 
  the 
  ratio 
  of 
  the 
  velocities 
  may 
  be 
  neglected 
  in 
  all 
  

   terms 
  except 
  those 
  which 
  are 
  divided 
  by 
  a 
  small 
  quantity. 
  

   In 
  the 
  discussion 
  which 
  follows 
  we 
  shall 
  suppose 
  the 
  con- 
  

   ditions 
  to 
  be 
  those 
  o£ 
  the 
  actual 
  apparatus 
  of 
  Michelson 
  and 
  

   Morley, 
  and 
  that 
  the 
  square 
  of 
  the 
  velocity 
  ratios 
  may 
  be 
  

   neglected 
  except 
  under 
  the 
  circumstances 
  mentioned 
  above. 
  

   The 
  ratio 
  U/V 
  will 
  be 
  denoted 
  by 
  f 
  . 
  

   The 
  breadth 
  of 
  a 
  band 
  is 
  then 
  given 
  by 
  

  

  _A 
  

  

  P 
  2sin(B-A)-| 
  2 
  {sin(B-A)4-sin(2«-2A)cosC+sin(C-2«)} 
  

  

  hi 
  the 
  particular 
  apparatus 
  A, 
  B 
  were 
  nearly 
  45° 
  and 
  C 
  

   nearly 
  90°. 
  Hence 
  in 
  terms 
  which 
  multiply 
  £ 
  2 
  we 
  may 
  put 
  

   A 
  = 
  B 
  = 
  45°, 
  C 
  = 
  90° 
  exactly. 
  Then 
  

  

  V 
  

  

  2sin(B-A)-f 
  2 
  cos2a 
  

  

  If 
  B 
  — 
  A 
  is 
  <if 
  2 
  , 
  the 
  breadths 
  of 
  the 
  bands 
  of 
  a 
  fringe 
  will 
  

   change 
  from 
  the 
  breadth 
  they 
  would 
  have 
  without 
  drift 
  to 
  

   infinity, 
  as 
  the 
  direction 
  of 
  the 
  drift 
  alters. 
  

  

  In 
  the 
  case 
  of 
  f=10- 
  4 
  , 
  A 
  = 
  5 
  . 
  10~ 
  5 
  cm., 
  and 
  B-A 
  = 
  ^ 
  2 
  , 
  

   the 
  breadth 
  of 
  a 
  band 
  when 
  the 
  drift 
  is 
  parallel 
  to 
  the 
  plate 
  is 
  

   50 
  metres 
  ; 
  so 
  that 
  such 
  a 
  disposition 
  would 
  be 
  impossible 
  to 
  

   observe. 
  If 
  the 
  velocity 
  of 
  drift 
  were 
  100 
  times 
  that 
  of 
  the 
  

   earth's 
  orbit, 
  this 
  minimum 
  breadto 
  would 
  be 
  5 
  mm., 
  and 
  

   under 
  these 
  circumstances 
  the 
  observations 
  would 
  have 
  shown 
  

   enormous 
  variations 
  in 
  the 
  breadth 
  of 
  the 
  bands. 
  

  

  It 
  maybe 
  taken 
  ascertain 
  then 
  that 
  B 
  — 
  A 
  was 
  considerably 
  

   larger 
  than 
  | 
  2 
  , 
  although 
  in 
  itself 
  exceedingly 
  small. 
  If 
  c 
  

   denote 
  the 
  breadth 
  of 
  band 
  when 
  there 
  is 
  no 
  drift 
  or 
  when 
  

  

  «= 
  -r, 
  then 
  in 
  general 
  

   4" 
  

  

  c 
  

   P 
  = 
  

  

  1 
  — 
  > 
  • 
  ,t 
  ; 
  — 
  r\ 
  cos 
  2a 
  

  

  2 
  sin 
  (B 
  — 
  A) 
  

  

  It 
  has 
  been 
  seen 
  that 
  for 
  all 
  probable 
  values 
  of 
  0, 
  sin 
  (B 
  — 
  A) 
  

   will 
  be 
  considerably 
  greater 
  than 
  J 
  J 
  2 
  , 
  so 
  that 
  f&j2 
  sin 
  (B 
  — 
  A) 
  

   will 
  be 
  a 
  small 
  quantity 
  ; 
  whence 
  

  

  p=cll+i 
  

  

  P 
  cos 
  2a 
  

  

  sin 
  (B-A) 
  

  

  