﻿4£2 
  Prof. 
  A. 
  S. 
  Ed 
  din 
  e 
  ton 
  on 
  Electrical 
  Theories 
  

  

  » 
  i 
  

  

  and 
  by 
  finding 
  out 
  what 
  is 
  wrong, 
  we 
  may 
  perhaps 
  discover 
  

   something 
  instructive"*. 
  We 
  may 
  therefore 
  start 
  from 
  this 
  

   point 
  of 
  general 
  agreement. 
  

  

  The 
  foregoing 
  law 
  of 
  inertia 
  corresponds 
  to 
  the 
  Lorentz 
  

   electron 
  in 
  steady 
  motion, 
  but 
  the 
  method 
  applies 
  equally 
  

   to 
  any 
  other 
  law 
  of 
  variation 
  of 
  inertia 
  with 
  velocity 
  ; 
  the 
  

   only 
  difference 
  is 
  a 
  numerical 
  factor 
  which 
  is 
  of 
  no 
  con- 
  

   sequence 
  to 
  the 
  argument. 
  A 
  fundamental 
  revision 
  of 
  the 
  

   theory 
  is 
  therefore 
  necessary. 
  Walker 
  has 
  stepped 
  in 
  with 
  

   the 
  suggestion 
  that 
  a 
  trial 
  should 
  be 
  made 
  with 
  the 
  more 
  

   general 
  (and, 
  I 
  consider, 
  more 
  plausible) 
  assumption 
  that 
  

   the 
  inertia 
  involves 
  the 
  acceleration 
  as 
  well 
  as 
  the 
  velocity. 
  

   I 
  cannot 
  predict 
  whether 
  his 
  mode 
  of 
  developing 
  this 
  view 
  

   will 
  lead 
  to 
  an 
  accordance 
  with 
  observation 
  ; 
  but 
  I 
  certainly 
  

   do 
  not 
  undertake 
  to 
  prove 
  a 
  general 
  negative. 
  

  

  Walker's 
  thesis 
  that 
  the 
  Lagrangian 
  function 
  depends 
  on 
  

   the 
  acceleration 
  as 
  well 
  as 
  on 
  the 
  velocity 
  cannot 
  be 
  a 
  point 
  

   of 
  cleavage 
  between 
  relativity 
  dynamics 
  and 
  non-relativity 
  

   d}mamics 
  — 
  if 
  I 
  have 
  rightly 
  grasped 
  the 
  meaning 
  of 
  the 
  

   statement. 
  In 
  Newtonian 
  particle 
  dynamics, 
  and 
  also 
  in 
  the 
  

   quasi-stationary 
  treatment 
  of 
  these 
  problems, 
  the 
  Lagrangian 
  

   function 
  is 
  supposed 
  to 
  consist 
  of 
  two 
  parts, 
  (1) 
  the 
  kinetic 
  

   energy, 
  involving 
  the 
  velocity 
  only, 
  and 
  (2) 
  the 
  force- 
  

   function 
  involving 
  position 
  in 
  the 
  field 
  of 
  force. 
  The 
  con- 
  

   tention 
  is 
  that 
  this 
  separation 
  is 
  inadmissible, 
  and 
  that 
  there 
  

   is 
  a 
  cross-term 
  involving 
  both 
  the 
  velocity 
  and 
  the 
  force 
  (or 
  

   acceleration). 
  Walker's 
  standpoint 
  tends 
  to 
  associate 
  this 
  

   cross-term 
  with 
  the 
  kinetic 
  energy, 
  so 
  that 
  the 
  kinetic 
  

   energy 
  differs 
  from 
  the 
  value 
  calculated 
  without 
  regard 
  to 
  

   the 
  acceleration. 
  Sir 
  Oliver 
  Lodgef 
  and 
  the 
  writer 
  find 
  it 
  

   more 
  natural 
  to 
  group 
  the 
  term 
  with 
  the 
  force-function, 
  and 
  

   say 
  that 
  the 
  force 
  of 
  gravitation 
  involves 
  a 
  term 
  depending 
  

   on 
  the 
  velocity. 
  The 
  distinction 
  appears 
  to 
  be 
  purely 
  verbal. 
  

  

  It 
  is 
  essential 
  to 
  an 
  out-and-out 
  relativity 
  theory 
  that 
  this 
  

   cross-term 
  should 
  exist, 
  and 
  it 
  is 
  surprising 
  to 
  find 
  relativists 
  

   represented 
  as 
  opposed 
  to 
  it. 
  

  

  Nor 
  can 
  the 
  quasi-stationary 
  assumption 
  be 
  regarded 
  as 
  a 
  

   fundamental 
  point 
  of 
  difference. 
  It 
  would, 
  I 
  think, 
  be 
  

   absurd 
  either 
  to 
  affirm 
  or 
  deny 
  the 
  quasi-stationary 
  principle 
  

   irrespective 
  of 
  the 
  particular 
  application 
  proposed. 
  The 
  

   question 
  is 
  whether 
  it 
  is 
  a 
  legitimate 
  approximation 
  in 
  a 
  

   definite 
  problem. 
  I 
  sympathize 
  with 
  Walker 
  in 
  demanding 
  

   a 
  justification 
  of 
  this 
  approximation 
  in 
  the 
  cases 
  where 
  it 
  has 
  

   been 
  used 
  — 
  whether 
  by 
  relativists 
  or 
  others. 
  The 
  problem 
  of 
  

  

  * 
  Phil. 
  Mag. 
  February 
  1918, 
  p. 
  143. 
  

   f 
  Loc. 
  cit. 
  pp. 
  155-156. 
  

  

  