﻿34 
  Dr. 
  W. 
  M. 
  Hicks 
  on 
  the 
  Michelson-Morley 
  

  

  The 
  maximals 
  for 
  different 
  small 
  strips 
  of 
  the 
  flame 
  are 
  

   therefore 
  differently 
  inclined. 
  It 
  has 
  been 
  seen 
  that 
  these 
  

   intersections 
  with 
  the 
  plane 
  of 
  the 
  first 
  mirror 
  coincide. 
  

   Hence 
  they 
  coincide 
  nowhere 
  else. 
  Consequently 
  a 
  fringe 
  

   will 
  be 
  seen 
  if 
  the 
  telescope 
  is 
  focussed 
  on 
  the 
  first 
  mirror, 
  

   which 
  will 
  gradually 
  become 
  more 
  and 
  more 
  indistinct 
  as 
  

   the 
  plane 
  on 
  which 
  it 
  is 
  focussed 
  recedes 
  more 
  and 
  more 
  

   from 
  it. 
  

  

  If 
  7 
  denote 
  the 
  angular 
  breadth 
  of 
  the 
  flame 
  as 
  seen 
  from 
  

   the 
  point 
  on 
  the 
  plate 
  where 
  the 
  datum 
  line 
  meets 
  it, 
  the 
  

   maximals 
  for 
  the 
  various 
  points 
  of 
  the 
  flame 
  will 
  form 
  a 
  

   system 
  of 
  pencils 
  of 
  angular 
  breadth 
  7, 
  whose 
  vertices 
  pass 
  

   through 
  the 
  maximal 
  points 
  on 
  the 
  first 
  mirror 
  which 
  have 
  

   just 
  been 
  shown 
  to 
  be 
  the 
  same 
  for 
  every 
  point 
  on 
  the 
  flame. 
  

   The 
  fringe 
  on 
  a 
  screen 
  parallel 
  to 
  the 
  first 
  mirror 
  will 
  then 
  

   completely 
  fade 
  into 
  white 
  light 
  when 
  its 
  distance 
  from 
  the 
  

   first 
  mirror 
  is 
  such 
  that 
  the 
  pencils 
  intersect, 
  each, 
  the 
  suc- 
  

   ceeding 
  one. 
  This 
  takes 
  place 
  at 
  a 
  distance 
  y 
  such 
  that 
  

   yy 
  = 
  breadth 
  of 
  a 
  band. 
  At 
  distances 
  greater 
  than 
  y 
  no 
  fringes 
  

   can 
  be 
  seen 
  at 
  all. 
  At 
  distances 
  nearly 
  as 
  great 
  as 
  y 
  we 
  should 
  

   expect 
  dark 
  lines 
  on 
  a 
  more 
  or 
  less 
  uniformly 
  bright 
  back- 
  

   ground. 
  

  

  Discussion 
  of 
  the 
  Displacement 
  of 
  Fringe. 
  

   17. 
  The 
  position 
  of 
  the 
  central 
  band 
  is 
  given 
  by 
  

  

  b 
  

   X 
  ~ 
  sin 
  (B— 
  A) 
  — 
  £P 
  cos 
  2a' 
  

  

  If 
  then 
  B>A, 
  b 
  must 
  be 
  positive, 
  that 
  is 
  the 
  plane 
  of 
  the 
  

   second 
  mirror 
  must 
  lie 
  to 
  the 
  right 
  of 
  the 
  intersection 
  of 
  

   the 
  first 
  mirror 
  and 
  the 
  plate. 
  If 
  on 
  the 
  other 
  hand 
  A>B, 
  

   b 
  must 
  be 
  negative, 
  or 
  the 
  second 
  plane 
  must 
  lie 
  to 
  the 
  left 
  

   of 
  the 
  same 
  intersection. 
  It 
  will 
  be 
  convenient 
  to 
  distinguish 
  

   these 
  two 
  cases 
  as 
  the 
  B 
  and 
  the 
  A 
  type 
  respectively. 
  

  

  Suppose 
  an 
  experiment 
  to 
  start 
  with 
  the 
  drift 
  in 
  the 
  same 
  

   direction 
  as 
  the 
  incident 
  light. 
  Then 
  as 
  the 
  drift 
  alters 
  from 
  

   this 
  position 
  in 
  either 
  direction, 
  the 
  central 
  band 
  is 
  displaced 
  

   to 
  the 
  right 
  in 
  the 
  B 
  type 
  and 
  to 
  the 
  left 
  in 
  the 
  A 
  type. 
  As 
  

   A 
  — 
  B 
  is 
  exceedingly 
  small 
  — 
  of 
  order 
  10~ 
  5 
  (or 
  2 
  sec.) 
  at 
  

   most 
  — 
  the 
  adjustment 
  of 
  the 
  mirrors 
  can 
  easily 
  change 
  from 
  

   one 
  type 
  to 
  the 
  other 
  on 
  consecutive 
  days. 
  It 
  follows 
  that 
  

   averaging 
  the 
  results 
  of 
  different 
  days 
  in 
  the 
  usual 
  manner 
  is 
  

   not 
  allowable 
  unless 
  the 
  types 
  are 
  all 
  the 
  same. 
  If 
  this 
  

   is 
  not 
  attended 
  to 
  the 
  average 
  displacement 
  may 
  be 
  expected 
  

   to 
  come 
  out 
  zero 
  — 
  at 
  least 
  if 
  a 
  large 
  number 
  are 
  averaged. 
  

  

  