﻿36 
  Dr. 
  W, 
  M. 
  Hicks 
  on 
  the 
  Michelson-Morley 
  

  

  four 
  cases 
  of 
  k='5, 
  1, 
  1*5, 
  and 
  2. 
  When 
  k<l, 
  these 
  curves 
  

   have 
  an 
  asymptote 
  which 
  as 
  k 
  increases 
  from 
  to 
  1 
  moves 
  

   up 
  to 
  the 
  origin. 
  The 
  negative 
  infinity 
  branch 
  becomes 
  

   narrower 
  and 
  at 
  the 
  same 
  time 
  moves 
  off 
  to 
  infinity. 
  When 
  

   # 
  = 
  1 
  there 
  is 
  no 
  negative 
  branch, 
  but 
  a 
  series 
  of 
  curves 
  with 
  

   positive 
  infinite 
  peaks. 
  As 
  k 
  increases 
  beyond 
  1, 
  these 
  peaks 
  

   shorten 
  until 
  when 
  k 
  is 
  large 
  the 
  curves 
  become 
  the 
  ordinary 
  

   harmonic 
  curve 
  y=.k 
  cos 
  2a. 
  In 
  Michelson 
  and 
  Morley's 
  

   experiment 
  k 
  was 
  apparently 
  always 
  large. 
  

  

  Discussion 
  of 
  Michelson 
  and 
  Morley's 
  Observations. 
  

  

  18. 
  The 
  result 
  of 
  §17, 
  that 
  it 
  is 
  not 
  allowable 
  to 
  average 
  

   the 
  results 
  of 
  different 
  sets 
  of 
  observations 
  until 
  the 
  type 
  of 
  

   each 
  has 
  been 
  determined, 
  naturally 
  leads 
  us 
  to 
  a 
  recon- 
  

   sideration 
  of 
  the 
  numerical 
  data 
  obtained 
  by 
  Michelson 
  and 
  

   Morley, 
  who 
  did 
  lump 
  together 
  the 
  observations 
  taken 
  on 
  

   different 
  days. 
  I 
  propose 
  to 
  show 
  that, 
  instead 
  of 
  giving 
  a 
  

   null 
  result, 
  the 
  numerical 
  data 
  published 
  in 
  their 
  paper 
  show 
  

   distinct 
  evidence 
  of 
  an 
  effect 
  of 
  the 
  kind 
  to 
  be 
  expected. 
  

  

  It 
  may 
  here 
  be 
  recalled 
  that 
  in 
  taking 
  an 
  observation, 
  the 
  

   apparatus 
  was 
  rotated 
  in 
  its 
  mercury 
  bath 
  and 
  readings 
  taken 
  

   at 
  16 
  equidistant 
  points 
  as 
  the 
  reading-telescope 
  passed 
  them. 
  

   On 
  each 
  occasion 
  this 
  was 
  repeated 
  six 
  times, 
  and 
  the 
  means 
  

   of 
  the 
  six 
  readings 
  in 
  each 
  position 
  taken. 
  These 
  means 
  are 
  

   the 
  numbers 
  printed 
  in 
  their 
  paper. 
  They 
  are 
  given 
  for 
  noon 
  

   on 
  July 
  8, 
  9, 
  and 
  11, 
  and 
  for 
  6 
  p.m. 
  on 
  July 
  8, 
  9, 
  and 
  12. 
  

   The 
  means 
  of 
  these 
  three 
  days 
  are 
  taken 
  and 
  then 
  the 
  means 
  

   of 
  the 
  first 
  eight 
  and 
  of 
  the 
  second 
  eight, 
  thus 
  eliminating 
  

   any 
  effect 
  depending 
  on 
  cos 
  a 
  alone. 
  The 
  result 
  is 
  that 
  there 
  

   is 
  no 
  apparent 
  displacement 
  of 
  the 
  fringe. 
  

  

  In 
  looking 
  at 
  the 
  sets 
  of 
  readings, 
  one 
  is 
  struck 
  at 
  once 
  

   with 
  the 
  fact 
  that 
  all 
  the 
  readings 
  continuously 
  increase 
  or 
  

   decrease. 
  This 
  is 
  evidently 
  the 
  effect 
  of 
  temperature 
  changes. 
  

   For 
  short 
  intervals, 
  it 
  is 
  extremely 
  likely 
  that 
  the 
  tempera- 
  

   ture 
  disturbances 
  will 
  be 
  a 
  linear 
  function 
  of 
  the 
  time. 
  If 
  

   this 
  is 
  exactly 
  so, 
  and 
  if 
  the 
  readings 
  were 
  taken 
  at 
  equal 
  

   intervals 
  of 
  time, 
  it 
  is 
  possible 
  to 
  eliminate 
  the 
  disturbances 
  

   due 
  to 
  this. 
  For 
  the 
  readings 
  at 
  the 
  beginning 
  and 
  at 
  the 
  

   end 
  of 
  a 
  complete 
  revolution 
  ought 
  (in 
  absence 
  of 
  tempera- 
  

   ture 
  effects) 
  to 
  be 
  the 
  same, 
  whilst 
  on 
  the 
  supposition 
  made 
  

   above 
  there 
  would 
  be 
  a 
  temperature 
  error 
  altering 
  by 
  equal 
  

   steps 
  for 
  each 
  successive 
  reading 
  — 
  in 
  a 
  way 
  to 
  be 
  indicated 
  

   immediately. 
  The 
  readings 
  for 
  each 
  set 
  of 
  complete 
  revolu- 
  

   tions 
  should 
  first 
  be 
  corrected 
  in 
  this 
  way 
  and 
  then 
  the 
  

   average 
  of 
  the 
  six 
  taken 
  to 
  eliminate 
  accidental 
  and 
  personal 
  

  

  