﻿14 
  Dr. 
  W. 
  M. 
  Hicks 
  on 
  the 
  Michelson-Morley 
  

  

  moves 
  with 
  the 
  apparatus. 
  For 
  consider 
  a 
  point 
  P 
  fixed 
  

   relatively 
  to 
  it. 
  At 
  every 
  instant 
  the 
  phases 
  of 
  the 
  two 
  

   wave-fronts 
  at 
  P 
  (each 
  phase 
  measured 
  as 
  a 
  fraction 
  of 
  its 
  

   corresponding 
  period) 
  differ 
  by 
  the 
  same 
  amount. 
  Conse- 
  

   quently 
  as 
  P 
  moves 
  through 
  the 
  aether 
  the 
  two 
  waves 
  at 
  P 
  

   interfere. 
  The 
  apparent 
  frequency 
  to 
  an 
  observer 
  at 
  P 
  of 
  

   each 
  system 
  must 
  consequently 
  be 
  the 
  same. 
  A 
  formal 
  proof 
  

   of 
  this 
  is 
  given 
  below. 
  

  

  So 
  far 
  then 
  as 
  the 
  phenomena 
  at 
  points 
  moving 
  with 
  the 
  

   apparatus 
  are 
  considered, 
  we 
  may 
  consider 
  the 
  space 
  as 
  

   divided 
  up 
  into 
  a 
  network 
  of 
  parallelograms 
  (not 
  now 
  equal- 
  

   sided) 
  with 
  a 
  corresponding 
  set 
  of 
  maximal 
  lines. 
  These 
  

   maximal 
  lines 
  are 
  not 
  fixed 
  in 
  the 
  aether, 
  but 
  move 
  as 
  if 
  fixed 
  

   to 
  the 
  apparatus. 
  The 
  intersections 
  of 
  these 
  maximals 
  with 
  a 
  

   screen 
  moving 
  with 
  the 
  apparatus 
  give 
  the 
  fringes, 
  as 
  in 
  the 
  

   case 
  of 
  no 
  motion. 
  The 
  maximal 
  lines 
  will 
  not 
  now 
  be 
  

   equally 
  inclined 
  to 
  the 
  two 
  wave-fronts. 
  If 
  as 
  before 
  c 
  

   denote 
  the 
  distance 
  between 
  the 
  maximals, 
  it 
  can 
  easily 
  be 
  

   shown 
  that 
  

  

  A.1 
  A/9 
  

  

  " 
  V{ 
  (Ai-A. 
  2 
  ) 
  2 
  + 
  4X^2 
  sin 
  2 
  W 
  

  

  The 
  maximal 
  lines 
  move 
  as 
  a 
  rigid 
  system 
  attached 
  to 
  

   the 
  apparatus. 
  They 
  give 
  the 
  phenomena 
  taking 
  place 
  in 
  the 
  

   fixed 
  aether 
  as 
  w 
  r 
  ell. 
  If 
  a 
  screen 
  be 
  fixed 
  in 
  the 
  aether 
  the 
  

   intersections 
  with 
  the 
  maximals 
  move, 
  and 
  we 
  get 
  fringes 
  

   which 
  drift 
  along 
  it, 
  and 
  which 
  therefore 
  in 
  general 
  produce 
  

   the 
  effect 
  of 
  white 
  light 
  on 
  the 
  eye 
  owing 
  to 
  their 
  rapid 
  

   motion. 
  If, 
  however, 
  the 
  direction 
  of 
  drift 
  be 
  parallel 
  to 
  a 
  

   maximal 
  line, 
  there 
  is 
  no 
  drift 
  of 
  fringes 
  on 
  the 
  screen, 
  and 
  

   the 
  eye 
  will 
  see 
  a 
  fixed 
  fringe. 
  If 
  the 
  drift 
  slightly 
  alters, 
  

   the 
  fringe 
  will 
  begin 
  to 
  move 
  slowly 
  along 
  the 
  screen. 
  The 
  

   observation 
  naturally 
  cannot 
  be 
  made, 
  but 
  the 
  result 
  is 
  

   important, 
  because, 
  if 
  the 
  fringes 
  exist, 
  the 
  interfering 
  waves 
  

   must 
  have 
  equal 
  frequencies. 
  Hence 
  the 
  two 
  sets 
  of 
  wave- 
  

   lengths 
  will 
  be 
  equal 
  when 
  the 
  drift 
  is 
  parallel 
  to 
  a 
  maximal. 
  

   That 
  this 
  is 
  actually 
  the 
  case 
  the 
  formula 
  to 
  be 
  developed 
  

   later 
  will 
  show. 
  

  

  4. 
  If 
  a 
  photographic 
  plate 
  be 
  exposed 
  in 
  any 
  position, 
  an 
  

   image 
  of 
  the 
  fringe 
  there 
  situated 
  will 
  be 
  impressed. 
  If, 
  

   however, 
  the 
  eye 
  be 
  focussed 
  on 
  the 
  same 
  plane, 
  either 
  directly 
  

   or 
  by 
  any 
  optical 
  instrument, 
  the 
  fringe 
  observed 
  will 
  not 
  be 
  

   the 
  same 
  as 
  that 
  impressed 
  on 
  the 
  plate. 
  The 
  rays 
  through 
  

   any 
  point 
  of 
  the 
  object 
  fringe 
  all 
  pass 
  through 
  the 
  optical 
  

   image 
  on 
  the 
  retina, 
  and 
  all 
  traverse 
  the 
  same 
  optical 
  distance, 
  

  

  