﻿328 
  Mr. 
  G. 
  W. 
  Walker 
  on 
  

  

  prove 
  theoretically 
  that 
  a 
  moving 
  electrified 
  system 
  would 
  

   possess 
  inertia, 
  which 
  Heaviside 
  showed 
  would 
  depend 
  on 
  the 
  

   speed 
  with 
  which 
  the 
  system 
  moves. 
  A 
  later 
  calculation 
  b} 
  r 
  

   Thomson 
  referred 
  to 
  a 
  particular 
  form 
  of 
  nucleus 
  and 
  to 
  the 
  

   momentum 
  which 
  it 
  would 
  carry 
  with 
  it 
  in 
  virtue 
  of 
  a 
  

   uniform 
  translation. 
  It 
  is 
  extremely 
  important 
  to 
  realize 
  that 
  

   the 
  character 
  of 
  the 
  nucleus 
  determines 
  the 
  manner 
  in 
  which 
  

   the 
  speed 
  enters 
  in 
  the 
  expression 
  for 
  the 
  momentum 
  or 
  for 
  the 
  

   energy. 
  It 
  is 
  also 
  vital 
  to 
  realize 
  that 
  while 
  the 
  momentum 
  

   or 
  the 
  energy 
  can 
  be 
  calculated 
  for 
  a 
  particular 
  form 
  of 
  

   nucleus 
  moving 
  with 
  a 
  uniform 
  speed, 
  it 
  has 
  not 
  so 
  far 
  been 
  

   found 
  possible 
  to 
  give 
  a 
  complete 
  solution 
  when 
  the 
  speed 
  is 
  

   variable. 
  

  

  M. 
  Abraham 
  extended 
  Thomson's 
  calculations, 
  and 
  he 
  

   assumed 
  that 
  while 
  the 
  nucleus 
  was 
  still 
  a 
  sphere 
  it 
  was 
  a 
  

   perfect 
  conductor, 
  and 
  he 
  consequently 
  obtained 
  a 
  value 
  for 
  

   the 
  momentum 
  in 
  a 
  state 
  of 
  uniform 
  translation 
  which 
  differed 
  

   from 
  that 
  found 
  by 
  Thomson 
  when 
  squares 
  of 
  the 
  speed 
  were 
  

   retained. 
  He 
  emphasized 
  the 
  distinction 
  between 
  the 
  effec- 
  

   tive 
  inertia 
  for 
  acceleration 
  along 
  and 
  perpendicular 
  to 
  the 
  

   direction 
  of 
  motion. 
  

  

  But 
  finding 
  that 
  he 
  could 
  not 
  obtain 
  the 
  exact 
  solution 
  for 
  

   a 
  variable 
  speed, 
  Abraham 
  made 
  use 
  of 
  what 
  is 
  called 
  the 
  

   " 
  quasi-stationary 
  principle/' 
  which 
  amounts 
  to 
  saying 
  that 
  

   if 
  we 
  can 
  calculate 
  the 
  momentum, 
  or 
  if 
  we 
  prefer 
  it 
  the 
  

   Lagrangean 
  function, 
  for 
  a 
  uniform 
  motion 
  we 
  can 
  infer 
  the 
  

   equations 
  of 
  motion 
  for 
  a 
  small 
  departure 
  from 
  this 
  state 
  in 
  

   the 
  ordinary 
  way. 
  My 
  contention 
  is 
  that 
  we 
  can 
  no 
  more 
  

   do 
  this 
  logically 
  for 
  electromagnetic 
  systems 
  than 
  we 
  can 
  

   for 
  ordinary 
  dynamical 
  systems. 
  We 
  know 
  quite 
  well 
  that 
  

   we 
  do 
  not 
  get 
  the 
  correct 
  equations 
  for 
  small 
  departures 
  

   from 
  a 
  steady 
  state, 
  when 
  the 
  steady 
  motion 
  values 
  are 
  

   inserted 
  in 
  the 
  Lagrangean 
  function 
  before 
  the 
  differential 
  

   equations 
  of 
  motion 
  are 
  formed. 
  The 
  steady 
  motion 
  values 
  

   may 
  be 
  inserted 
  after 
  the 
  equations 
  have 
  been 
  formed 
  from 
  

   the 
  general 
  Lagrangean 
  function. 
  

  

  Abraham 
  calculated 
  expressions 
  for 
  longitudinal 
  and 
  trans- 
  

   versal 
  electric 
  inertia 
  by 
  means 
  of 
  the 
  quasi-stationary 
  

   principle. 
  Experiments 
  on 
  transverse 
  inertia 
  became 
  possible 
  

   with 
  the 
  discovery 
  of 
  the 
  Becquerel 
  rays, 
  and 
  of 
  the 
  minute 
  

   negatively 
  charged 
  particles 
  projected 
  from 
  radium 
  with 
  

   speeds 
  only 
  little 
  short 
  of 
  that 
  of 
  light. 
  

  

  The 
  matter 
  was 
  taken 
  up 
  first 
  by 
  W. 
  Kaufmann, 
  and 
  I 
  

   have 
  a 
  special 
  personal 
  interest 
  in 
  this 
  since 
  I 
  was 
  working 
  

   side 
  by 
  side 
  with 
  him 
  in 
  the 
  laboratory 
  at 
  Gottingen 
  while 
  

   his 
  experiments 
  were 
  in 
  progress. 
  

  

  