﻿32 
  Dr. 
  W. 
  M. 
  Hicks 
  on 
  the 
  Michelson-Morley 
  

  

  and 
  D'^f^ 
  2 
  bands 
  = 
  D 
  / 
  £ 
  cos* 
  cm. 
  

   A1A2 
  

  

  Hence 
  the 
  distance 
  of 
  the 
  observed 
  central 
  fringe 
  is 
  

  

  D£ 
  2 
  

   x=T)+ 
  -j 
  c 
  cos2« 
  + 
  D 
  / 
  £ 
  cos 
  a. 
  . 
  . 
  . 
  (20) 
  

  

  In 
  the 
  actual 
  experiment 
  D 
  was 
  about 
  11 
  metres, 
  and, 
  so 
  

   far 
  as 
  can 
  be 
  estimated 
  from 
  the 
  description, 
  D' 
  nearly 
  

   3 
  metres. 
  

  

  The 
  relative 
  importance 
  of 
  these 
  terms 
  depends 
  for 
  given 
  £ 
  

   on 
  the 
  value 
  chosen 
  for 
  the 
  breadth 
  of 
  the 
  band. 
  No 
  indi- 
  

   cation 
  is 
  given 
  of 
  this, 
  but 
  it 
  must 
  probably 
  have 
  been 
  

   adjusted 
  to 
  something 
  between 
  ^ 
  mm. 
  and 
  10 
  mm. 
  The 
  

   following 
  are 
  a 
  few 
  cases, 
  taking 
  A 
  = 
  5 
  . 
  10" 
  5 
  cm. 
  and 
  writing 
  

   x=a-\-b 
  cos 
  2a 
  + 
  c 
  cos 
  a, 
  and 
  measuring 
  in 
  millims., 
  

  

  Band 
  

  

  •1 
  

  

  1 
  

  

  10 
  

  

  b 
  

  

  •2 
  

  

  2 
  

  

  20 
  

  

  c 
  

  

  •3 
  

  

  •3 
  

  

  •3 
  

  

  b 
  

  

  •002 
  

  

  •02 
  

  

  •2 
  

  

  c 
  

  

  •03 
  

  

  •03 
  

  

  •0, 
  

  

  f=io-* 
  r 
  

  

  Earth's 
  orbital 
  velocity. 
  \ 
  

  

  j 
  = 
  10-». 
  { 
  

  

  For 
  f=10 
  -4 
  a 
  breadth 
  of 
  *1 
  mm. 
  would 
  therefore 
  make 
  

   both 
  terms 
  equally 
  sensible 
  ; 
  whilst 
  for 
  £=10 
  -5 
  , 
  the 
  second 
  

   would 
  overpower 
  the 
  first, 
  but 
  would 
  be 
  of 
  equal 
  weight 
  for 
  a 
  

   breadth 
  of 
  1 
  mm. 
  If 
  D' 
  = 
  D, 
  i. 
  e. 
  if 
  the 
  instrument 
  was 
  

   focussed 
  on 
  the 
  actual 
  first 
  mirror, 
  then 
  for 
  f 
  =10~ 
  5 
  a 
  breadth 
  

   of 
  band 
  of 
  1 
  cm. 
  would 
  make 
  both 
  terms 
  about 
  equally 
  

   sensible. 
  

  

  Finally, 
  aberration 
  would 
  displace 
  the 
  apparent 
  position 
  to 
  

   the 
  right. 
  Hence 
  

  

  ,27 
  = 
  « 
  + 
  5cos2a 
  + 
  CCOSa 
  — 
  d 
  sill 
  a, 
  

  

  where 
  d 
  involves 
  the 
  first 
  power 
  of 
  f 
  . 
  

  

  16. 
  From 
  conversation 
  with 
  Professor 
  Morley 
  I 
  learn 
  that 
  

   in 
  the 
  actual 
  experiment 
  no 
  slit 
  was 
  used, 
  and 
  that 
  the 
  

   reading-telescope 
  was 
  focussed 
  on 
  the 
  first 
  mirror. 
  To 
  com- 
  

   plete 
  the 
  theory 
  therefore 
  it 
  is 
  necessary 
  to 
  take 
  account 
  of 
  

   the 
  finite 
  breadth 
  of 
  the 
  flame. 
  The 
  flame 
  may 
  be 
  regarded 
  

   as 
  built 
  up 
  of 
  vertical 
  narrow 
  strips 
  of 
  light, 
  from 
  each 
  of 
  

   which, 
  as 
  has 
  been 
  seen, 
  there 
  results 
  a 
  system 
  of 
  fringes 
  on 
  

   whatever 
  point 
  the 
  reading-telescope 
  is 
  focussed. 
  It 
  is 
  

   necessary 
  then 
  to 
  see 
  whether 
  these 
  fringes 
  overlap, 
  or 
  

   whether 
  there 
  are 
  places 
  where 
  the 
  superposed 
  fringes 
  exactly 
  

   fit. 
  Now 
  the 
  fringes 
  are 
  given 
  by 
  the 
  maximals; 
  and 
  the 
  

  

  