Energy in the Electrodynamie Field. 397 



potential of the field is constant in both space and time, 

 so that the electric force is determined solely by its dynamic 

 component 



1 dA x _ in 



c dt c 



The current density is now 



where e, a- are the usual dielectric and conductivity constants 

 of the medium of the field. The condition for the propa- 

 gation is 



— en 2 + i . 4:7rncr = c 2 [a -f ib) 2 j 



so that ~ / ine + 4z7r(T\ 



A,. 



4tt 



c 2 (a + ib) 2 



4776' 



The density of the magnetic energy on the generalized 

 form of the new theory is thus equal to 



1 i /V< <^M -. A^i 2(int—a 



—a+ibz + ie m ) 



Sir 



and the same result is obtained on Macdonald's own form of 

 the theory. Thus the distribution of kinetic energy in the 

 new theory is identical in both cases with that deduced on 

 Poyn ting's theory, although it is of opposite sign. 



The result that the kinetic energy on the new theory is 

 of negative amount is not confined to the simple type of 

 radiation field here examined, and in the present case it 

 leads to the rather remarkable conclusion that the total 

 energy in the field, consisting of the kinetic and potential 

 energies, is negative in amount and equal to the energy 

 dissipated in the field with its sign changed. 



Equally remarkable results are obtained from a discussion 

 of the transfer of energy in these fields. We have seen 

 already that the scalar potential in radiation fields must be 

 taken to be constant, and if this constant were zero there 

 would, on the general form of the present theory, be no 

 transfer of energy at all in the field, for the vector 



S = £C 



