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  XXXVI. 
  Relativity 
  and 
  Electrodynamics. 
  By 
  G. 
  W. 
  

   Walkek, 
  M.A., 
  F.R.S., 
  A.R.C.Sc, 
  formerly 
  Fellow 
  of 
  

   Trinity 
  College, 
  Cambridge* 
  '. 
  

  

  [Plate 
  X.] 
  

  

  SIR 
  OLIVER 
  LODGE'S 
  recent 
  papers 
  in 
  the 
  Philoso- 
  

   phical 
  Magazine 
  have 
  brought 
  into 
  prominence 
  once 
  

   more 
  the 
  difference 
  of 
  attitude 
  o£ 
  the 
  protagonists 
  in 
  " 
  Rela- 
  

   tivity 
  Doctrine 
  " 
  and 
  "Newtonian 
  Dynamics." 
  That 
  Sir 
  

   Oliver's 
  equation 
  of 
  motion 
  for 
  a 
  moving 
  planet 
  requires 
  

   some 
  amplification 
  in 
  order 
  to 
  take 
  full 
  account 
  of 
  the 
  

   special 
  features 
  of 
  electrical 
  inertia, 
  will 
  be 
  recognized, 
  

   and 
  Prof. 
  Eddington 
  has 
  suggested 
  a 
  method 
  of 
  dealing 
  

   with 
  the 
  problem. 
  Unfortunately, 
  Eddington's 
  method 
  

   introduces 
  an 
  assumption 
  which 
  is 
  frequently 
  made 
  by 
  

   relativists 
  in 
  dealing 
  with 
  electrical 
  inertia, 
  and 
  which 
  in 
  

   my 
  opinion 
  is 
  inconsistent 
  with 
  the 
  fundamental 
  equations 
  

   of 
  electrodynamics. 
  In 
  former 
  papers 
  I 
  have 
  drawn 
  atten- 
  

   tion 
  to 
  this 
  assumption, 
  which 
  is 
  closely 
  linked 
  with 
  the 
  

   " 
  quasi-stationary 
  principle," 
  and 
  I 
  had 
  not 
  intended 
  to 
  raise 
  

   the 
  point 
  again. 
  But 
  Sir 
  Oliver 
  has 
  suggested 
  to 
  me 
  that 
  

   an 
  exposition 
  of 
  my 
  views 
  as 
  to 
  the 
  parting 
  of 
  the 
  ways 
  

   between 
  the 
  logical 
  development 
  of 
  electrodynamics 
  and 
  the 
  

   doctrine 
  of 
  relativity 
  would 
  be 
  of 
  value, 
  and 
  I 
  have 
  agreed 
  

   to 
  his 
  request. 
  My 
  remarks 
  must, 
  however, 
  be 
  confined 
  to 
  

   electric 
  inertia, 
  and 
  I 
  do 
  not 
  propose 
  to 
  enter 
  on 
  the 
  gravi- 
  

   tational 
  and 
  astronomical 
  developments 
  of 
  Einstein's 
  hypo- 
  

   thesis. 
  

  

  The 
  main 
  point 
  at 
  issue 
  may, 
  I 
  think, 
  be 
  put 
  very 
  concisely. 
  

   Relativists 
  assume 
  that 
  " 
  the 
  kinetic 
  energy 
  of 
  a 
  moving 
  

   electrical 
  system 
  is 
  a 
  function 
  of 
  the 
  resultant 
  speed 
  only 
  

   and 
  is 
  independent 
  of 
  the 
  direction 
  of 
  motion."" 
  

  

  My 
  thesis 
  is 
  that 
  this 
  assumption 
  is 
  not 
  consistent 
  with 
  

   the 
  fundamental 
  electromagnetic 
  equations 
  for 
  the 
  aether 
  

   (supposed 
  immobile), 
  and 
  that 
  "the 
  energy, 
  or 
  preferably 
  

   the 
  modified 
  Lagrangean 
  function, 
  depends 
  on 
  the 
  accele- 
  

   ration 
  as 
  well 
  as 
  on 
  the 
  speed 
  of 
  the 
  system 
  and 
  involves 
  

   also 
  the 
  relative 
  direction 
  of 
  these." 
  

  

  While 
  the 
  above 
  appears 
  to 
  me 
  to 
  be 
  the 
  main 
  point, 
  there 
  

   is 
  no 
  doubt 
  that 
  subsidiary 
  considerations 
  arise. 
  Theory 
  and 
  

   experiment 
  have 
  interacted 
  in 
  a 
  curious 
  way, 
  and 
  I 
  think 
  

   the 
  discussion 
  should 
  proceed 
  by 
  taking 
  notice 
  of 
  the 
  his- 
  

   torical 
  development. 
  Sir 
  Joseph 
  Thomson 
  was 
  the 
  first 
  to 
  

  

  * 
  Communicated 
  by 
  Sir 
  Oliver 
  Lodge. 
  

   2 
  A2 
  

  

  