﻿A. 
  A. 
  Michelson 
  — 
  Motion 
  of 
  the 
  Earth 
  and 
  the 
  Ether. 
  477 
  

  

  little 
  in 
  the 
  definition 
  of 
  each, 
  the 
  measurements 
  maybe 
  made 
  

   with 
  very 
  considerable 
  precision.* 
  

  

  The 
  observations 
  were 
  taken 
  in 
  the 
  morning, 
  at 
  noon, 
  even- 
  

   ing 
  and 
  night 
  ; 
  no 
  special 
  care 
  being 
  taken 
  as 
  to 
  the 
  exact 
  hour. 
  

   The 
  results 
  are 
  summed 
  up 
  in 
  the 
  table 
  containing 
  the 
  observa- 
  

   tions 
  taken 
  and 
  reduced 
  by 
  Mr. 
  Mann, 
  as 
  follows: 
  — 
  

  

  The 
  micrometer 
  was 
  set 
  on 
  one 
  spot, 
  then 
  on 
  the 
  central 
  

   fringe, 
  then 
  on 
  the 
  other 
  spot, 
  giving 
  three 
  readings 
  of 
  the 
  

   micrometer. 
  The 
  first 
  reading 
  was 
  subtracted 
  from 
  the 
  third, 
  

   giving 
  the 
  distance 
  between 
  the 
  spots 
  in 
  divisions 
  of 
  the 
  mi- 
  

   crometer 
  head. 
  The 
  second 
  reading 
  was 
  subtracted 
  from 
  the 
  

   third, 
  giving 
  the 
  distance 
  of 
  the 
  central 
  fringe 
  from 
  the 
  lower 
  

   in 
  divisions 
  of 
  the 
  micrometer 
  head. 
  This 
  last 
  remainder 
  was 
  

   divided 
  by 
  the 
  first, 
  giving 
  the 
  distance 
  n 
  of 
  the 
  central 
  fringe 
  

   from 
  the 
  lower 
  spot 
  in 
  fractions 
  of 
  the 
  distance 
  between 
  the 
  

   spots 
  regarded 
  as 
  unity. 
  

  

  Each 
  reading 
  was 
  reduced 
  this 
  way 
  and 
  the 
  mean 
  of 
  ten 
  taken 
  

   as 
  the 
  result 
  for 
  any 
  given 
  time. 
  The 
  weights 
  p 
  we're 
  calcu- 
  

   lated 
  as 
  usual 
  from 
  the 
  formula 
  : 
  p 
  = 
  c/e\ 
  

  

  Date. 
  

  

  

  6 
  A. 
  41 
  

  

  

  

  12 
  Noon. 
  

  

  

  6 
  P. 
  M 
  

  

  

  

  11 
  P. 
  M 
  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  n 
  

  

  P 
  

  

  pn 
  

  

  n 
  

  

  P 
  

  

  pn 
  

  

  n 
  

  

  P 
  

  

  pn 
  

  

  n 
  

  

  P 
  

  

  pn 
  

  

  March 
  11 
  

  

  •500 
  

  

  67 
  

  

  33-50 
  

  

  •515 
  

  

  40 
  

  

  20-60 
  

  

  •503 
  

  

  12 
  

  

  6-03 
  

  

  •480 
  

  

  20 
  

  

  9-60 
  

  

  

  •513 
  

  

  38 
  

  

  19-49 
  

  

  

  

  

  •506 
  

  

  10 
  

  

  506 
  

  

  •490 
  

  

  32 
  

  

  15-68 
  

  

  March 
  13 
  

  

  •495 
  

  

  11 
  

  

  5-44 
  

  

  •530 
  

  

  33 
  

  

  17-49 
  

  

  

  

  

  

  

  

  March 
  16 
  

  

  •507 
  

  

  55 
  

  

  27-88-499 
  

  

  50 
  

  

  24-95 
  

  

  •492 
  

  

  13 
  

  

  6-40 
  

  

  •479 
  

  

  60 
  

  

  28-74 
  

  

  

  •509 
  

  

  120 
  

  

  61-08I-491 
  

  

  45 
  

  

  22-09J-488 
  

  

  40 
  

  

  19-52 
  -487 
  

  

  22 
  

  

  1071 
  

  

  March 
  L7 
  

  

  •490 
  

  

  40 
  

  

  19-60-504 
  

  

  80 
  

  

  40-32 
  

  

  •500 
  

  

  35 
  

  

  17-50-488 
  

  

  105 
  

  

  51*24 
  

  

  

  •488 
  

  

  50 
  

  

  24-40 
  

  

  •502 
  

  

  60 
  

  

  30-12 
  

  

  •498 
  

  

  30 
  

  

  14-94 
  -496 
  

  

  100 
  

  

  49-60 
  

  

  March 
  18 
  

  

  •501 
  

  

  80 
  

  

  40-08 
  

  

  •492 
  

  

  80 
  

  

  39-36 
  

  

  •493 
  

  

  40 
  

  

  19-72-498 
  

  

  25 
  

  

  12-45 
  

  

  

  

  

  

  •507 
  

  

  50 
  

  

  25-35 
  

  

  •488 
  

  

  25 
  

  

  12-20-498 
  

  

  35 
  

  

  17-43 
  

  

  Sums. 
  

  

  

  461 
  

  

  231-47 
  

  

  

  438 
  

  

  220-28 
  

  

  

  205 
  

  

  101-37 
  

  

  399 
  

  

  195-45 
  

  

  Means. 
  

  

  

  •502 
  

  

  ± 
  -002 
  

  

  

  •503 
  

  

  ± 
  -003| 
  

  

  •494 
  

  

  ± 
  -002 
  

  

  •490 
  

  

  ± 
  -002 
  

  

  12 
  Noon 
  -11 
  P. 
  M. 
  =-013 
  

   1 
  fringe 
  = 
  -250 
  

  

  13 
  1 
  

   maximum 
  displacement 
  7^77 
  = 
  ttt; 
  fringe. 
  

  

  The 
  conclusion 
  from 
  these 
  results 
  is 
  that 
  if 
  there 
  is 
  any 
  dis- 
  

   placement 
  of 
  the 
  fringes 
  it 
  is 
  less 
  than 
  one-twentieth 
  of 
  a 
  

   fringe. 
  

  

  If 
  w 
  T 
  e 
  consider 
  the 
  times 
  occupied 
  by 
  the 
  two 
  pencils 
  in 
  com- 
  

  

  * 
  On 
  account 
  of 
  the 
  inequality 
  of 
  the 
  angles 
  of 
  incidence 
  and 
  reflection 
  there 
  

   will 
  be 
  a 
  slight 
  difference 
  between 
  the 
  real 
  and 
  apparent 
  positions 
  of 
  the 
  double 
  

   image. 
  This 
  difference 
  will 
  be 
  altogether 
  too 
  minute 
  to 
  produce 
  any 
  appreciable 
  

   error. 
  Again, 
  this 
  difference 
  in 
  direction 
  produces 
  a 
  difference 
  in 
  the 
  length 
  of 
  

   the 
  two 
  paths 
  — 
  which 
  is 
  however 
  of 
  the 
  second 
  order 
  and 
  can 
  also 
  be 
  neglected. 
  

  

  Am. 
  Jour. 
  Sci. 
  — 
  Fourth 
  Series, 
  Yol. 
  Ill, 
  No. 
  18. 
  

   33 
  

  

  -June, 
  1897. 
  

  

  