﻿Theory 
  of 
  Gravity. 
  645 
  

  

  § 
  2. 
  Least 
  Action 
  in 
  Electrodynamics. 
  

  

  In 
  the 
  form 
  given 
  to 
  electromagnetic 
  theory 
  by 
  Lorentz 
  

   matter 
  and 
  electricity 
  are 
  identified. 
  iEther 
  is 
  merely 
  the 
  

   field 
  of 
  application 
  of: 
  Maxwell's 
  equations, 
  and 
  the 
  only 
  

   substance 
  is 
  electric 
  fluid. 
  I 
  now 
  assume 
  that 
  this 
  electric 
  

   fluid 
  is 
  of 
  the 
  type 
  considered 
  in 
  last 
  section. 
  Every 
  element 
  

   of 
  it 
  is 
  however 
  subject 
  not 
  only 
  to 
  its 
  own 
  pressure 
  but 
  

   also 
  to 
  electric 
  and 
  magnetic 
  forces. 
  None 
  the 
  less 
  a 
  vortex 
  

   theory 
  analogous 
  to 
  that 
  given 
  in 
  last 
  section 
  is 
  still 
  possible. 
  

  

  The 
  formula 
  for 
  L 
  the 
  Lagrangian 
  function 
  is 
  now 
  

  

  + 
  <r(6- 
  1 
  uF-4>)+i€<r 
  ! 
  (y-c 
  2 
  ), 
  . 
  (16) 
  

  

  <r 
  is 
  the 
  density 
  of 
  the 
  electric-fluid 
  and 
  satisfies 
  the 
  equation 
  

   of 
  continuity 
  

  

  J+DivM=0 
  (17) 
  

  

  The 
  electric 
  and 
  magnetic 
  intensities 
  E 
  and 
  H 
  are 
  given 
  by 
  

  

  E= 
  - 
  t^ 
  - 
  V<£, 
  H= 
  Curl 
  F. 
  

   c 
  at 
  T 
  

  

  I 
  find 
  that 
  (16), 
  omitting 
  the 
  last 
  term 
  on 
  the 
  right, 
  has 
  

   already 
  been 
  used 
  by 
  Schwarzschild 
  (see 
  fine, 
  der 
  Math. 
  Wiss. 
  

   Bd. 
  v. 
  Art. 
  14, 
  S. 
  170). 
  (16) 
  is 
  invariant 
  under 
  the 
  Lorentz- 
  

   Einstein 
  substitution. 
  

  

  Maxwell's 
  form 
  for 
  the 
  Electromagnetic 
  equations 
  is 
  

   reached 
  by 
  varying 
  F 
  and 
  <£ 
  in 
  (16), 
  

  

  ('•-?£) 
  F 
  -'( 
  D 
  »-'n 
  1 
  f)+'™-'<"'=».1 
  

  

  The 
  Hertz-Heaviside 
  formulae 
  are 
  deduced 
  from 
  (18), 
  

  

  ^+47r<m 
  = 
  cCurlH, 
  ^ 
  = 
  -cCurlE 
  I 
  

   dt 
  dt 
  y 
  . 
  (19) 
  

  

  DivE 
  = 
  47T(7, 
  DivH 
  = 
  0. 
  

   Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  No. 
  154. 
  Oct. 
  1913. 
  2 
  X 
  

  

  