﻿££=*(*/' 
  +*»*/"), 
  

  

  Relativity 
  and 
  Electrodynamics. 
  331 
  

  

  the 
  surface 
  of 
  the 
  electron. 
  Thus, 
  for 
  instance, 
  with 
  a 
  

   conductor 
  there 
  is 
  a 
  redistribution 
  of 
  the 
  charge, 
  which 
  

   depends 
  on 
  the 
  acceleration, 
  the 
  speed, 
  and 
  the 
  direction 
  of 
  

   the 
  acceleration 
  relative 
  to 
  that 
  of 
  the 
  speed. 
  So 
  the 
  

   Lagrangean 
  function 
  must 
  involve 
  these 
  things, 
  and 
  I 
  am 
  

   doubtful 
  if 
  it 
  is 
  the 
  resultant 
  speed 
  that 
  alone 
  enters. 
  

  

  The 
  results 
  I 
  have 
  obtained 
  for 
  electric 
  inertia 
  by 
  my 
  

   direct, 
  if 
  pedestrian, 
  method, 
  can 
  be 
  shown 
  to 
  prove 
  that 
  the 
  

   energy 
  cannot 
  be 
  expressed 
  as 
  a 
  function 
  of 
  resultant 
  speed 
  

   only. 
  For 
  if 
  

  

  we 
  find 
  that 
  in 
  the 
  direction 
  of 
  motion, 
  say 
  along 
  a, 
  we 
  get 
  

  

  d^dT 
  

  

  dtdx 
  

  

  and 
  at 
  right 
  angles 
  to 
  this, 
  say 
  along 
  y, 
  we 
  get 
  

   d 
  dT 
  .. 
  OJ 
  , 
  

  

  therefore 
  longitudinal 
  inertia 
  =m 
  1 
  = 
  2/'-f 
  4v 
  2 
  /", 
  

   and 
  transversal 
  inertia 
  =m 
  2 
  = 
  2/'. 
  

  

  Hence, 
  since 
  

  

  dm 
  2 
  v 
  

  

  must 
  be 
  satisfied. 
  But 
  it 
  does 
  not 
  follow 
  that 
  T=f(v 
  2 
  ) 
  if 
  

  

  wii= 
  —^- 
  is 
  satisfied. 
  

   dv 
  

  

  My 
  results 
  for 
  the 
  cases 
  mentioned 
  do 
  not 
  satisfy 
  this 
  

   condition, 
  and 
  unless 
  it 
  can 
  be 
  shown 
  directly 
  from 
  the 
  

   primary 
  equations 
  that 
  arithmetical 
  error 
  has 
  entered 
  into 
  my 
  

   calculations, 
  it 
  follows 
  that 
  the 
  kinetic 
  energy 
  of 
  a 
  system 
  in 
  

   variable 
  motion 
  is 
  not 
  expressible 
  as 
  a 
  function 
  of 
  «the 
  

   resultant 
  speed 
  only. 
  

  

  The 
  conclusion 
  is 
  that 
  Eddington's 
  proposed 
  treatment 
  of 
  

   the 
  astronomical 
  problem 
  is 
  invalid, 
  and 
  I 
  see 
  no 
  help 
  for 
  it 
  

   but 
  to 
  start 
  with 
  the 
  equations 
  in 
  the 
  tangential 
  form, 
  

  

  m 
  > 
  v 
  dS 
  =T 
  > 
  

  

  m 
  2 
  v 
  2 
  /p 
  = 
  N, 
  

  

  where 
  7n 
  2 
  and 
  m 
  2 
  are 
  different 
  functions 
  of 
  v 
  2 
  , 
  which 
  can 
  be 
  

   calculated 
  when 
  the 
  electrical 
  system 
  is 
  fully 
  specified. 
  

  

  