﻿Postulate 
  of 
  the 
  llieory 
  of 
  Relativity. 
  173 
  

  

  We 
  have, 
  therefore, 
  

  

  2kirdg 
  cos 
  a 
  cos 
  0\ 
  

  

  n'=nl 
  

  

  1 
  + 
  

  

  and, 
  by 
  the 
  hypothesis 
  of 
  the 
  invariability 
  of 
  c, 
  

  

  2kirdq 
  cos 
  u 
  cos 
  0\ 
  

  

  \'=\( 
  

  

  If 
  I 
  is 
  the 
  difference 
  of 
  path 
  of 
  two 
  interfering 
  rays 
  in 
  

   Michelson's 
  apparatus, 
  the 
  number 
  of 
  fringes 
  which 
  are 
  seen 
  

   to 
  cross 
  the 
  micrometer 
  thread 
  of 
  the 
  telescope 
  when 
  A. 
  

   becomes 
  \' 
  (that 
  is 
  to 
  say 
  when 
  the 
  velocity 
  of 
  rotation 
  

   varies 
  between 
  zero 
  and 
  g 
  turns 
  per 
  second) 
  is 
  

  

  - 
  I 
  2kirdg 
  cos 
  a 
  cos 
  6 
  

   *~X 
  c 
  ' 
  

  

  If 
  the 
  observation 
  is 
  made 
  by 
  noting 
  the 
  position 
  of 
  the 
  

   fringes 
  when 
  the 
  wheel 
  turns 
  in 
  one 
  sense 
  with 
  the 
  velocity 
  

   g, 
  and 
  that 
  corresponding 
  to 
  an 
  equal 
  and 
  contrary 
  velocity, 
  

   the 
  number 
  of 
  fringes 
  crossing 
  the 
  micrometer 
  thread 
  will 
  

   be 
  2f. 
  

  

  Now, 
  in 
  my 
  apparatus 
  d 
  = 
  38 
  cm., 
  a 
  = 
  29°, 
  = 
  27°, 
  & 
  = 
  4 
  

   (as 
  in 
  the 
  figure); 
  if 
  Xis 
  put 
  equal 
  to 
  0'546/x 
  (green 
  mercury 
  

   line), 
  Z 
  = 
  13 
  cm., 
  c 
  = 
  3 
  . 
  10 
  10 
  cm., 
  and 
  # 
  = 
  60 
  (turns 
  of 
  R 
  per 
  

   second 
  in 
  one 
  sense 
  and 
  afterwards 
  in 
  the 
  other), 
  we 
  may 
  

   expect, 
  according 
  to 
  the 
  preceding 
  formula, 
  a 
  fringe 
  dis- 
  

   placement 
  2/= 
  0*71. 
  

  

  Experiment 
  gives, 
  for 
  the 
  case 
  mentioned, 
  a 
  displacement 
  

   of 
  between 
  07 
  and 
  0*8 
  fringes 
  ; 
  and 
  it 
  is 
  not 
  possible, 
  for 
  

   reasons 
  of 
  visibility, 
  to 
  carry 
  the 
  precision 
  of 
  the 
  observa- 
  

   tions 
  further. 
  But, 
  as 
  is 
  seen, 
  the 
  agreement 
  between 
  the 
  

   predicted 
  result 
  and 
  observation 
  is 
  sufficient 
  ; 
  this 
  agreement 
  

   is 
  confirmed 
  by 
  observations 
  made 
  by 
  choosing 
  other 
  con- 
  

   venient 
  values 
  of 
  I 
  and 
  g, 
  of 
  which 
  for 
  brevity's 
  sake 
  I 
  shall 
  

   not 
  speak 
  here. 
  

  

  Experiment, 
  therefore, 
  authorizes 
  the 
  conclusion 
  that 
  

   reflexion 
  of 
  light 
  by 
  a 
  moving 
  metallic 
  mirror 
  does 
  not 
  alter 
  

   the 
  velocity 
  of 
  propagation 
  of 
  the 
  light 
  itself 
  in 
  air, 
  and 
  con- 
  

   sequently, 
  with 
  great 
  probability, 
  also 
  in 
  vacuo 
  ; 
  at 
  least, 
  in 
  

   the 
  conditions 
  of 
  the 
  experiment 
  above 
  described. 
  This 
  

   experimental 
  result, 
  as 
  to 
  which 
  no 
  doubt 
  can 
  be 
  entertained, 
  

   is 
  contrary 
  to 
  the 
  hypothesis 
  of 
  some 
  physicists 
  who, 
  like 
  

   Stewart 
  *, 
  basing 
  themselves 
  upon 
  the 
  electromagnetic 
  

   emission 
  theory 
  of 
  Thomson, 
  maintain 
  the 
  possibility 
  that 
  

  

  * 
  Phys. 
  Rev. 
  xxxii. 
  p. 
  418 
  (1911). 
  

   Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  35. 
  No. 
  206. 
  Feb. 
  1918. 
  

  

  