﻿512 
  Messrs. 
  G. 
  N. 
  Lewis 
  and 
  E. 
  C. 
  Tolman 
  on 
  the 
  

  

  Bucherer 
  * 
  on 
  the 
  mass 
  o£ 
  a 
  /3 
  particle, 
  to 
  which 
  we 
  shall 
  

   refer 
  later. 
  

  

  Therefore, 
  in 
  as 
  far 
  as 
  present 
  knowledge 
  goes, 
  we 
  may 
  

   consider 
  the 
  principle 
  of 
  relativity 
  established 
  on 
  a 
  pretty 
  

   firm 
  basis 
  of 
  experimental 
  fact. 
  Accepting 
  this 
  principle, 
  

   we 
  shall 
  accept 
  the 
  consequences 
  to 
  which 
  it 
  leads, 
  however 
  

   extraordinary 
  they 
  may 
  be, 
  provided 
  that 
  they 
  are 
  not 
  incon- 
  

   sistent 
  with 
  one 
  another, 
  nor 
  with 
  known 
  experimental 
  facts. 
  

  

  The 
  consequences 
  which 
  one 
  of 
  us 
  has 
  obtained 
  from 
  a 
  

   simple 
  assumption 
  as 
  to 
  the 
  mass 
  of 
  a 
  beam 
  of 
  light, 
  and 
  the 
  

   fundamental 
  conservation 
  laws 
  of 
  mass, 
  energy, 
  and 
  momen- 
  

   tum, 
  Einstein 
  has 
  derived 
  from 
  the 
  principle 
  of 
  relativity 
  and 
  

   the 
  electromagnetic 
  theory. 
  We 
  propose 
  in 
  this 
  paper 
  to 
  show 
  

   that 
  these 
  consequences 
  may 
  also 
  be 
  obtained 
  merely 
  from 
  the 
  

   conservation 
  laivs 
  and 
  the 
  principle 
  of 
  relativity, 
  without 
  any 
  

   reference 
  to 
  electromagnetics. 
  

  

  In 
  dealing 
  with 
  such 
  fundamental 
  questions 
  as 
  we 
  meet 
  

   here 
  it 
  seems 
  especially 
  desirable 
  to 
  avoid 
  as 
  far 
  as 
  possible 
  

   all 
  technicalities. 
  We 
  have 
  endeavoured 
  to 
  find 
  for 
  each 
  of 
  

   the 
  following 
  theorems 
  the 
  simplest 
  and 
  most 
  obvious 
  proof, 
  

   and 
  have 
  used 
  no 
  mathematics 
  beyond 
  the 
  elements 
  of 
  algebra 
  

   and 
  geometry. 
  

  

  The 
  Units 
  of 
  Sjjace 
  and 
  Tiyne. 
  

  

  The 
  following 
  development 
  will 
  be 
  based 
  solely 
  upon 
  the 
  

   conservation 
  laws, 
  and 
  the 
  two 
  postulates 
  of 
  the 
  principle 
  of 
  

   relativity. 
  

  

  The 
  first 
  of 
  these 
  postulates 
  is 
  that 
  there 
  can 
  be 
  no 
  method 
  

   of 
  detecting 
  absolute 
  translatory 
  motion 
  through 
  space, 
  or 
  

   through 
  any 
  kind 
  of 
  aether 
  which 
  may 
  be 
  assumed 
  to 
  pervade 
  

   space. 
  The 
  only 
  motion 
  which 
  has 
  physical 
  significance 
  is 
  

   the 
  motion 
  of 
  one 
  system 
  relative 
  to 
  another. 
  Hence 
  two 
  

   similar 
  bodies 
  having 
  relative 
  motion 
  in 
  parallel 
  paths 
  form 
  a 
  

   perfectly 
  symmetrical 
  arrangement. 
  If 
  w^e 
  are 
  justified 
  in 
  

   considering 
  the 
  first 
  at 
  rest 
  and 
  the 
  second 
  in 
  motion, 
  we 
  are 
  

   equally 
  justified 
  in 
  considering 
  the 
  second 
  at 
  rest 
  and 
  the 
  first 
  

   in 
  motion. 
  

  

  The 
  second 
  postulate 
  is 
  that 
  the 
  velocity 
  of 
  light 
  as 
  

   measured 
  by 
  any 
  observer 
  is 
  independent 
  of 
  relative 
  motion 
  

   between 
  the 
  observer 
  and 
  the 
  source 
  of 
  light 
  f. 
  This 
  idea, 
  

   that 
  the 
  velocity 
  of 
  light 
  will 
  seem 
  the 
  same 
  to 
  two 
  different 
  

   observers, 
  even 
  though 
  one 
  may 
  be 
  moving 
  towards 
  and 
  the 
  

  

  * 
  Ber. 
  Phys. 
  Ges. 
  vi. 
  p. 
  688 
  (1908) 
  ; 
  Ann. 
  Fhysik, 
  xxviii. 
  p. 
  513 
  (1909). 
  

  

  t 
  We 
  will 
  imagine 
  that 
  the 
  observer 
  measures 
  the 
  velocity 
  of 
  light 
  by 
  

   means 
  of 
  two 
  clocks 
  placed 
  at 
  the 
  ends 
  of 
  a 
  metre 
  stick 
  which 
  is 
  situated 
  

   lengthwise 
  in 
  the 
  path 
  of 
  the 
  light. 
  

  

  