Energy in the Electromagnetic Field. 289 



where is the total current defined in terms of the magnetic 

 force by Ampere's relation, 



4 ^C = curlH; 

 c 



it thus consists of the part 



i 



2c 

 due to the electronic motions, and the part 



t e s (v s A) 



6ttc \ dt ) 



L(7 A *5 



7TCJ \ dt 



due to the ssthereal current. Since 

 we have 



Now in an equilibrium theory the first integral on the 

 right vanishes, and the second transforms by integration by 

 parts to 



7r — I -^.div A do 

 8ttcJ dt 



= -^J l 



(div h) 2 dv, 



as above. 



An exactly similar criticism also applies to the assumption 

 of the general validity of the form 



e*e B > 



for the mutual potential energy of two charges. The only 

 really consistent value for the potential energy in the field 

 in the most general case is 



and this can easily be shown by a similar argument to 

 contain the part 



~»y ( E i) 



dv 



due to the sethereal conditions. 



Phil Mag. S. 6. Vol. 33. No. 195. March 1917. U 



