﻿Principle 
  of 
  Relativity 
  and 
  Non-Xeictonian 
  Mechanics. 
  519 
  

  

  It 
  has, 
  howeA-er. 
  been 
  universally 
  considered 
  that 
  the 
  charge 
  

  

  e 
  is 
  constant. 
  In 
  other 
  wcrds, 
  that 
  the 
  force 
  acting 
  upon 
  the 
  

  

  electron 
  in 
  a 
  uniform 
  electrostatic 
  field 
  is 
  independent 
  of 
  its 
  

  

  velocity 
  relative 
  to 
  the 
  field. 
  Hence 
  the 
  observed 
  change 
  

  

  , 
  e 
  

  

  in 
  — 
  is 
  attributed 
  solely 
  to 
  the 
  chanoe 
  in 
  mass. 
  It 
  mio;ht 
  

  

  be 
  well 
  to 
  subject 
  this 
  view 
  to 
  a 
  more 
  careful 
  analysis 
  than 
  

   has 
  hitherto 
  been 
  done. 
  At 
  present, 
  however, 
  we 
  will 
  adopt 
  

   it 
  without 
  further 
  scrutiny. 
  

  

  The 
  original 
  experiments 
  of 
  Kaufmann"^ 
  showed 
  only 
  a 
  

   qualitative 
  agreement 
  with 
  equation 
  (1). 
  Recently, 
  however, 
  

   Bucherer 
  t 
  by 
  a 
  method 
  of 
  exceptional 
  ingenuity, 
  has 
  made 
  

   further 
  determinations 
  of 
  the 
  mass 
  of 
  electrons 
  moving 
  with 
  

   varying 
  velocities, 
  and 
  his 
  results 
  are 
  in 
  remarkable 
  accord 
  

   with 
  this 
  equation 
  obtained 
  from 
  the 
  principle 
  of 
  relativity. 
  

  

  This 
  very 
  satisfactory 
  corroboration 
  of 
  the 
  fundamental 
  

   equation 
  of 
  non-Newtonian 
  mechanics, 
  must 
  in 
  future 
  be 
  

   regarded 
  as 
  a 
  very 
  important 
  part 
  of 
  the 
  experimental 
  

   material 
  which 
  justifies 
  the 
  principle 
  of 
  relativity. 
  By 
  a 
  

   slight 
  extrapolation 
  we 
  may 
  find 
  with 
  accuracy 
  from 
  the 
  

   results 
  of 
  Bucherer 
  that 
  limiting 
  A'elocity 
  at 
  which 
  the 
  mass 
  

   becomes 
  infinite, 
  in 
  other 
  words, 
  a 
  numerical 
  value 
  of 
  c 
  which 
  

   in 
  no 
  way 
  depends 
  upon 
  the 
  properties 
  of 
  light. 
  Indeed 
  

   merely 
  from 
  the 
  first 
  postulate 
  of 
  relativity 
  and 
  these 
  experi- 
  

   ments 
  of 
  Bucherer 
  we 
  may 
  deduce 
  the 
  second 
  postulate 
  and 
  

   all 
  the 
  further 
  conclusions 
  obtained 
  in 
  this 
  paper. 
  This 
  fact 
  

   can 
  hardly 
  be 
  emphasized 
  too 
  strongly. 
  

  

  Leaving 
  now 
  the 
  subject 
  of 
  mass, 
  let 
  us 
  consider 
  whether 
  

   the 
  unit 
  of 
  force 
  depends 
  upon 
  our 
  choice 
  of 
  a 
  point 
  of 
  rest. 
  

   An 
  observer 
  in 
  a 
  given 
  system 
  allows 
  such 
  a 
  force 
  to 
  act 
  

  

  upon 
  unit 
  mass 
  as 
  to 
  give 
  it 
  an 
  acceleration 
  of 
  one 
  !,, 
  and 
  

  

  calls 
  this 
  force 
  the 
  dyne. 
  If 
  now 
  we 
  assume 
  that 
  the 
  system 
  

   is 
  in 
  motion, 
  with 
  a 
  velocity 
  v, 
  in 
  a 
  direction 
  perpendicular 
  

   to 
  the 
  line 
  of 
  application 
  of 
  the 
  force, 
  we 
  conclude 
  that 
  the 
  

   acceleration 
  is 
  really 
  less 
  than 
  unity, 
  since 
  in 
  a 
  moving 
  

  

  system 
  the 
  second 
  is 
  lono-er 
  in 
  the 
  ratio 
  — 
  j—^^- 
  — 
  and 
  the 
  

  

  centimetre 
  in 
  this 
  transverse 
  direction 
  is 
  the 
  same 
  as 
  at 
  rest. 
  

   On 
  the 
  other 
  hand, 
  the 
  mass 
  is 
  increased 
  owing 
  to 
  the 
  motion 
  

  

  of 
  the 
  system 
  by 
  the 
  factor 
  — 
  77^^ 
  q-^ 
  • 
  ^ii^ce 
  the 
  time 
  enters 
  

   to 
  the 
  second 
  power, 
  the 
  product 
  of 
  mass 
  and 
  acceleration 
  

   * 
  See 
  Lewis, 
  loc. 
  cit, 
  • 
  t 
  Bucherer, 
  ioc. 
  nit. 
  

  

  