194 Mr. 0. Heaviside on the 



ceases to have a definite value when the current is varying, if 

 C be taken to be the coil-current, on account of the external 

 generation of heat. But in the S.H. case, as before, the mean 

 value is necessarily a definite quantity (at a given frequency), 

 making -JR'^ 2 the heat per second, where R/ is the effective 

 resistance. That E/ is always greater than R is certain, and 

 obvious without mathematics ; for the coil-heat is ^-RC 2 , and 

 there is the external heat as well. It is suggested that, in a 

 similar manner, a non -mathematical and equally clear demon- 

 stration of the reduction of L is possible. The magnetic 

 energy of the coil-current alone is iLC 2 , and we have to 

 show non-mathematically, but quite as clearly as in the 

 argument relating to the heat, that the existence of induced 

 external current reduces the energy without any reference to 

 a particular kind of coil or kind of distribution of the external 

 conductivity. Perhaps Lord Rayleigh's dynamical generali- 

 zation* might be made to furnish what is required. 



When the matter is treated in an inverse manner, not 

 regarding electric current as causing magnetic force, but as 

 caused by or being an affection of the magnetic force, there is 

 some advantage gained, inasmuch as we come closer to the facts 

 as a whole, apart from the details relating to the reaction on the 

 coil-current. Magnetic force, and with it electric current, a 

 certain function of the former, are propagated with such 

 immense rapidity through air that we may, for present pur- 

 poses, regard it as an instantaneous action. On the other 

 hand, they are diffused through conductors in quite another 

 manner, quite slowly in comparison, according to the same 

 laws as the diffusion of heat, allowing for their being vector 

 magnitudes, and that the current must be closed, thus pro- 

 ducing lateral propagation. The greater the conductivity and 

 the inductivity, the slower the diffusion. Hence a conductor 

 brought with sufficient rapidity into a magnetic field is, at the 

 first moment, only superficially penetrated by the magnetic dis- 

 turbance to an appreciable extent ; and a certain time — which 

 is considerable in the case of a large mass of metal, especially 

 copper, by reason of high conductivity, and more especially 

 iron, by reason of high inductivity more than counteracting 

 the effect of its lower conductivity — is required before the 

 steady state is reached, in which the magnetic field is calcul- 

 able from the coil-current and the distribution of inductivity. 

 And hence a sufficiently rapidly oscillatory impressed force 

 in the coil-circuit induces only superficial currents in a piece 

 of metal in the field of the coil, the interior being com- 

 paratively free from the magnetic induction. 

 * Phil. Mag. May 1886. 



