﻿330 
  Mr. 
  G. 
  W. 
  Walker 
  on 
  

  

  formula 
  is 
  inconsistent 
  with 
  the 
  electrodynamic 
  equations, 
  

   and 
  that 
  several 
  other 
  formulae 
  correctly 
  deduced 
  from 
  the 
  

   primary 
  equations 
  agree 
  with 
  the 
  experiments 
  equally 
  well. 
  

  

  I 
  doubt 
  if 
  many 
  people 
  in 
  this 
  country 
  realize 
  the 
  very 
  

   meagre 
  character 
  of 
  the 
  experimental 
  results, 
  and 
  I 
  therefore 
  

   give 
  a 
  fall-sized 
  reproduction 
  (PL 
  X.) 
  of 
  the 
  photographic 
  

   plate 
  from 
  which 
  Kaufmann 
  made 
  his 
  measurements. 
  The 
  

   electric 
  deflexion 
  is 
  across 
  the 
  paper 
  and 
  the 
  magnetic 
  

   deflexion 
  up 
  the 
  paper, 
  and 
  it 
  may 
  be 
  pointed 
  out 
  that 
  if 
  the 
  

   inertia 
  of 
  the 
  particles 
  were 
  quite 
  independent 
  of 
  speed, 
  the 
  

   small 
  curved 
  arcs 
  would 
  be 
  parabolas, 
  and 
  that 
  it 
  is 
  only 
  in 
  

   so 
  far 
  as 
  these 
  arcs 
  differ 
  from 
  parabolas 
  that 
  any 
  depen- 
  

   dence 
  of 
  inertia 
  on 
  speed 
  can 
  be 
  made 
  out 
  at 
  all. 
  Further, 
  

   the 
  highest 
  speed 
  particles 
  are 
  those 
  for 
  which 
  the 
  deflexion 
  

   is 
  least. 
  

  

  I 
  now 
  return 
  to 
  the 
  theoretical 
  treatment 
  of 
  electric 
  

   inertia. 
  In 
  order 
  to 
  avoid 
  the 
  error 
  of 
  the 
  quasi-stationary 
  

   principle, 
  I 
  developed 
  some 
  time 
  ago 
  a 
  method 
  of 
  obtaining 
  

   the 
  longitudinal 
  and 
  transversal 
  inertia 
  directly 
  from 
  the 
  

   primary 
  equations 
  by 
  Newtonian 
  methods. 
  The 
  method 
  is 
  

   rather 
  tedious, 
  but 
  its 
  correctness 
  has 
  not 
  been 
  called 
  in 
  

   question. 
  Its 
  application 
  is 
  general, 
  but 
  to 
  get 
  definite 
  

   results 
  the 
  character 
  of 
  the 
  nucleus 
  must 
  be 
  specified. 
  

   Various 
  systems 
  may 
  be 
  examined 
  provided 
  they 
  do 
  not 
  

   violate 
  any 
  fundamental 
  restriction 
  imposed 
  by 
  electro- 
  

   dynamic 
  conditions. 
  In 
  this 
  way 
  I 
  examined 
  the 
  nucleus 
  

   assumed 
  by 
  Sir 
  Joseph 
  Thomson 
  and 
  was 
  able 
  to 
  confirm 
  his 
  

   result 
  for 
  transverse 
  inertia, 
  but 
  obtained 
  a 
  different 
  result 
  

   for 
  longitudinal 
  inertia. 
  On 
  the 
  other 
  hand, 
  with 
  the 
  

   nucleus 
  assumed 
  by 
  Abraham 
  I 
  was 
  able 
  to 
  confirm 
  his 
  

   result 
  for 
  longitudinal 
  inertia, 
  but 
  not 
  that 
  for 
  transverse 
  

   inertia. 
  

  

  Again, 
  recently 
  I 
  examined 
  the 
  case 
  of 
  a 
  contracted 
  con- 
  

   ducting 
  spheroid 
  which 
  agreed 
  in 
  form 
  with 
  Lorentz's 
  con- 
  

   tracted 
  electron 
  for 
  the 
  uniform 
  speed, 
  but 
  did 
  not 
  alter 
  its 
  

   form 
  when 
  acceleration 
  was 
  imposed 
  *. 
  The 
  results 
  for 
  both 
  

   longitudinal 
  and 
  transverse 
  inertia 
  differ 
  from 
  those 
  adopted 
  

   by 
  relativists. 
  

  

  The 
  differences 
  that 
  arise 
  in 
  these 
  examples 
  only 
  become 
  

   important 
  when 
  squares 
  and 
  higher 
  terms 
  in 
  the 
  speed 
  are 
  

   retained, 
  and 
  they 
  arise 
  from 
  the 
  fact 
  that 
  when 
  acceleration 
  

   is 
  imposed, 
  additional 
  electric 
  forces 
  are 
  set 
  up 
  which 
  have 
  

   to 
  be 
  allowed 
  for 
  in 
  utilizing 
  the 
  boundary 
  conditions 
  at 
  

  

  * 
  The 
  restriction 
  is 
  unnecessary, 
  as 
  I 
  now 
  find 
  that 
  my 
  results 
  are 
  

   not 
  altered 
  when 
  the 
  surface 
  deforms 
  under 
  acceleration 
  as 
  Lorentz 
  

   assumes. 
  

  

  