﻿Theory 
  of 
  Gravity. 
  

  

  661 
  

  

  The 
  electromagnetic 
  energy 
  and 
  momentum 
  per 
  unit 
  

   volume 
  I 
  denote 
  by 
  W 
  e 
  and 
  M 
  e 
  respectively. 
  

  

  W 
  e 
  =—-(W+K 
  2 
  ) 
  

  

  OTT 
  

  

  (70) 
  

  

  e 
  Aire 
  l 
  j 
  

  

  It 
  is 
  well 
  known 
  that 
  

   d 
  

  

  dt 
  

  

  IF 
  + 
  c 
  2 
  DivM 
  e 
  =-c7uE; 
  

  

  where 
  as 
  before 
  cr 
  denotes 
  the 
  density 
  of 
  electric 
  charge. 
  

   If 
  cr 
  is 
  zero 
  it 
  follows 
  that 
  

  

  dt 
  

  

  IF+Div(c 
  2 
  M 
  e 
  ) 
  = 
  0, 
  

  

  (71) 
  

  

  so 
  that 
  the 
  momentum 
  is 
  proportional 
  to 
  the 
  flux 
  of 
  the 
  

   energy. 
  These 
  results 
  are 
  of 
  course 
  well 
  known. 
  

  

  The 
  gravitational 
  energy 
  and 
  momentum 
  are 
  W 
  n 
  and 
  M„, 
  

  

  OTT 
  ' 
  blTC 
  2 
  

  

  1_ 
  (dJV 
  

   iTcAdt) 
  

  

  mJ 
  

  

  And 
  

  

  dW 
  n 
  

  

  dt 
  

  

  + 
  c 
  3 
  DivM„=0. 
  

  

  (72) 
  

  

  (73) 
  

  

  The 
  total 
  energy 
  W 
  is 
  equal 
  to 
  W 
  e 
  + 
  W 
  n} 
  the 
  total 
  momentum 
  

   M 
  to 
  M, 
  + 
  M„. 
  

  

  Formulae 
  equivalent 
  to 
  (72) 
  and 
  (73) 
  have 
  already 
  been 
  

   published 
  by 
  Abraham. 
  

  

  (71) 
  and 
  (73) 
  determine 
  the 
  flux 
  of 
  energy; 
  it 
  is 
  also 
  

   desirable 
  to 
  follow 
  the 
  flux 
  of 
  momentum. 
  Let 
  M 
  the 
  

   momentum 
  have 
  components 
  M 
  x 
  , 
  M 
  y 
  , 
  Mz. 
  

  

  M.={M 
  xi 
  M 
  lh 
  M 
  z 
  ) 
  

  

  ^■ 
  + 
  DivP*=0 
  

  

  dt 
  

  

  dM 
  

  

  dt 
  

   dM 
  

  

  y 
  +DivP 
  y 
  = 
  

   + 
  DivP 
  2 
  =0 
  

  

  (74) 
  

  

  dt 
  

   P*=(P, 
  U,T) 
  

  

  F 
  g 
  =(T,S,R) 
  

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

  

  (75) 
  

  

  2 
  Y 
  

  

  