﻿Relativity 
  and 
  Electrodynamics. 
  329 
  

  

  Kaufmann 
  deflected 
  the 
  particles 
  by 
  crossed 
  electric 
  and 
  

   magnetic 
  fields, 
  by 
  which 
  the 
  particles 
  are 
  sifted 
  out 
  accord- 
  

   ing 
  to 
  their 
  speed, 
  so 
  that 
  the 
  ends 
  of 
  their 
  trajectories 
  form 
  

   a 
  curve 
  on 
  a 
  photographic 
  plate. 
  

  

  Kaufmann 
  considered 
  that 
  his 
  measurements 
  proved 
  that 
  

   Abraham's 
  expression 
  for 
  transverse 
  inertia 
  was 
  correct, 
  and 
  

   that 
  the 
  inertia 
  of 
  the 
  particles 
  was 
  purely 
  electromagnetic 
  

   in 
  origin. 
  

  

  We 
  must 
  now 
  retrace 
  our 
  steps 
  to 
  consider 
  the 
  important 
  

   contributions 
  to 
  the 
  theory 
  of 
  moving 
  systems 
  made 
  by 
  

   Prof. 
  H. 
  A. 
  Lorentz 
  and 
  Sir 
  Joseph 
  Larmor. 
  They 
  proved 
  

   that 
  a 
  mathematical 
  correlation 
  held 
  between 
  an 
  electrical 
  

   system 
  at 
  rest 
  and 
  a 
  certain 
  system 
  maintained 
  in 
  uniform 
  

   translation. 
  " 
  If 
  the 
  moving 
  system 
  has 
  a 
  uniform 
  speed 
  

   kc 
  (where 
  c 
  is 
  the 
  velocity 
  of 
  light) 
  in 
  the 
  direction 
  x, 
  and 
  

   the 
  x 
  linear 
  extent 
  of 
  the 
  moving 
  system 
  is 
  (1 
  — 
  k 
  2 
  )* 
  of 
  the 
  

   linear 
  extent 
  of 
  the 
  fixed 
  system, 
  and 
  the 
  variables 
  time 
  t 
  

   and 
  distance 
  x 
  in 
  the 
  fixed 
  system 
  are 
  transformed 
  to 
  t' 
  and 
  

   #'in 
  the 
  moving 
  system 
  by 
  a 
  certain 
  linear 
  transformation 
  in- 
  

   volving 
  k, 
  then 
  the 
  state 
  of 
  the 
  fixed 
  system 
  in 
  terms 
  of 
  t 
  and 
  x 
  

   is 
  the 
  same 
  as 
  that 
  of 
  the 
  moving 
  system 
  in 
  terms 
  of 
  t' 
  and 
  x'." 
  

   It 
  is 
  reasonable 
  to 
  inquire 
  if 
  the 
  contraction 
  in 
  the 
  pro- 
  

   portion 
  (1 
  — 
  k 
  2 
  )* 
  actually 
  takes 
  place 
  when 
  a 
  system 
  at 
  rest 
  

   is 
  put 
  into 
  uniform 
  translation, 
  for 
  if 
  so 
  it 
  provides 
  an 
  

   explanation 
  of 
  the 
  Michel 
  son-Mori 
  ey 
  experiment. 
  

  

  Now 
  it 
  is 
  quite 
  certain 
  that 
  the 
  mathematical 
  transforma- 
  

   tion 
  is 
  not 
  true 
  when 
  k 
  is 
  variable, 
  and 
  therefore 
  not 
  true 
  

   at 
  any 
  intermediate 
  stage 
  by 
  which 
  the 
  system 
  at 
  rest 
  might 
  

   conceivably 
  pass 
  to 
  the 
  correlated 
  system 
  in 
  uniform 
  motion, 
  

   if 
  it 
  ever 
  does 
  so 
  at 
  all. 
  But 
  relativists 
  have 
  assumed 
  that 
  

   the 
  correlation 
  proved 
  by 
  Lorentz 
  and 
  Larmor 
  for 
  a 
  uniform 
  

   translation 
  only 
  is 
  true, 
  and 
  that 
  the 
  change 
  actually 
  takes 
  

   place, 
  when 
  the 
  speed 
  is 
  variable. 
  It 
  appears 
  to 
  me 
  that 
  if 
  

   the 
  primary 
  equations 
  are 
  correct, 
  the 
  assumption 
  is 
  not 
  

   merely 
  not 
  permissible, 
  but 
  is 
  not 
  true 
  ; 
  and, 
  on 
  the 
  con- 
  

   trary, 
  if 
  the 
  assumption 
  does 
  represent 
  actual 
  truth, 
  then 
  the 
  

   primary 
  equations 
  are 
  wrong 
  and 
  must 
  go. 
  We 
  await 
  

   proof, 
  whicli 
  so 
  far 
  has 
  not 
  been 
  offered. 
  

  

  The 
  longitudinal 
  and 
  transverse 
  inertia 
  of 
  a 
  " 
  contracted 
  w 
  

   electron 
  have 
  been 
  calculated 
  by 
  the 
  quasi-stationary 
  method, 
  

   so 
  that 
  there 
  is 
  a 
  double 
  source 
  of 
  error 
  in 
  the 
  result. 
  

  

  Experiments 
  by 
  Kaufmann, 
  Bestelmeyer, 
  and 
  others 
  have 
  

   been 
  offered 
  as 
  experimental 
  proof 
  that 
  the 
  formula 
  for 
  

   transverse 
  inertia 
  of 
  a 
  contracted 
  electron 
  on 
  relativity 
  

   doctrine 
  is 
  correct. 
  My 
  contention 
  is 
  that 
  while 
  the 
  expe- 
  

   riments 
  do 
  not 
  conflict 
  with 
  the 
  relativity 
  formula, 
  the 
  

  

  