394 Mr. G. H. Livens on the Flux of 



of the field is not equal to the available energy. In other 

 words, we shall have to assume something of the nature of 

 a hysteretic quality for the free aether, so that the magnetic 

 energy in any field will be a function of the history of the 

 generation of the field and may not vanish when the field 

 is again reduced to zero. We shall see presently what this 

 means. 



Considering the difficulties which any assumption of this 

 kind would naturally entail, it might seem desirable to throw 

 over any attempt to reduce the theory to a physical basis on 

 the strength of our preconceived notions on such matters, and 

 to accept Macdonald's theory as determining all that we can 

 know about such things. In such a theory the irreversible 

 part of the energy distribution is withdrawn from the kinetic 

 energy and attributed to the radiation, so that the energy 

 density would appear in it as determined by the mean 

 of the expressions just used for the intrinsic and available 

 energies in the aether, which contain the irreversible part 

 with opposite signs. But even this procedure is not without 

 difficulty, as may be exemplified by the discussion of a 

 particular case. Let us examine the circumstances in 

 a part of the field occupied by conducting and dielectric 

 substances, and assume that throughout it the scalar 

 potential is constant in time and space, as would for 

 instance be the case if the field were of the pure radiation 

 type determined in the ordinary way. In this case the 

 electric force is determined simply by its dynamic part, 



so that the expression for the current density is 

 e d 2 A_a dA 

 4ttc dt 2 ~c d,V 



€, a being the dielectric and conductivity constants at the 

 typical field point. 



Thus on the generalized theory the kinetic energy 

 density is given by 



1 j'Ve d 2 A dA dA\ u 



e /dAV a CldAV 

 -~S^?'\df)~'c 2 J\dt) dt 



8 



E 2 C 



