﻿Principle 
  of 
  Relativity 
  and 
  Non-Neiotonian 
  Mechanics. 
  515 
  

  

  agree. 
  Otherwise 
  the 
  condition 
  o£ 
  symmetry 
  required 
  by 
  

   the 
  principle 
  o£ 
  relativity 
  would 
  not 
  be 
  fulfilled. 
  

  

  But 
  let 
  us 
  now 
  consider 
  distances 
  j>(2raZ/eZ 
  to 
  the 
  line, 
  of 
  

   relative 
  motion. 
  

  

  Fig. 
  2. 
  

  

  1 
  1 
  ^ 
  H 
  \ 
  

  

  m 
  m' 
  H5S— 
  > 
  n 
  1/ 
  

  

  A 
  system 
  (fig. 
  2) 
  has 
  a 
  source 
  of 
  light 
  at 
  m 
  and 
  a 
  reflecting 
  

   mirror 
  at 
  n. 
  If 
  we 
  consider 
  the 
  whole 
  system 
  to 
  be 
  at 
  abso- 
  

   lute 
  rest, 
  it 
  is 
  evident 
  that 
  a 
  light-signal 
  sent 
  from 
  m 
  to 
  the 
  

   mirror, 
  and 
  reflected 
  back, 
  passes 
  over 
  the 
  path 
  mnm. 
  If, 
  

   however, 
  the 
  entire 
  system 
  is 
  considered 
  to 
  be 
  in 
  absolute 
  

   motion 
  with 
  a 
  velocity 
  v, 
  the 
  light 
  must 
  pass 
  over 
  a 
  different 
  

   path 
  mn'm' 
  where 
  nn 
  is 
  the 
  distance 
  through 
  which 
  the 
  

   mirror 
  moves 
  before 
  the 
  light 
  reaches 
  it, 
  and 
  mm' 
  is 
  the 
  

   distance 
  traversed 
  by 
  the 
  source 
  before 
  the 
  light 
  returns 
  to 
  it. 
  

  

  Obviously 
  then, 
  

  

  

  

  nn 
  

   mn' 
  

  

  V 
  

  

  and 
  

  

  

  

  mm' 
  

  

  _ 
  V 
  

  

  ~ 
  c 
  ' 
  

  

  

  

  mn'm' 
  

  

  

  Also 
  from 
  

  

  the 
  fig 
  

  

  ure. 
  

  

  

  

  

  

  w.n' 
  := 
  

  

  mn 
  + 
  

  

  nn', 
  

  

  mn'm' 
  = 
  mnm 
  -^ 
  2nn 
  '— 
  mm' 
  , 
  

  

  Combining 
  we 
  have, 
  

  

  mnm 
  v^ 
  1-/3^* 
  

  

  Hence 
  if 
  we 
  call 
  the 
  system 
  in 
  motion, 
  instead 
  of 
  at 
  rest, 
  the 
  

  

  calculated 
  path 
  of 
  the 
  light 
  is 
  greater 
  in 
  the 
  ratio 
  ^^ 
  • 
  

  

  Xovv 
  the 
  velocity 
  of 
  light 
  must 
  seem 
  the 
  same 
  to 
  the 
  

   observer, 
  whether 
  he 
  is 
  at 
  rest 
  or 
  in 
  motion. 
  His 
  measure- 
  

   ments 
  of 
  velocity 
  depend 
  upon 
  his 
  units 
  of 
  length 
  and 
  time. 
  

   We 
  have 
  already 
  seen 
  that 
  a 
  second 
  on 
  a 
  moving 
  clock 
  is 
  

  

  lengthened 
  in 
  the 
  ratio 
  —- 
  -, 
  and 
  therefore 
  if 
  the 
  path 
  

  

  of 
  the 
  beam 
  of 
  light 
  were 
  also 
  greater 
  in 
  this 
  same 
  ratio, 
  we 
  

   should 
  expect 
  that 
  the 
  moving 
  observer 
  would 
  find 
  no 
  dis- 
  

   crepancy 
  in 
  his 
  determination 
  of 
  the 
  velocity 
  of 
  light. 
  From 
  

  

  