308 MR. S. H. BURBURY ON THE INDUCTION OP ELECTRIC 



at every point on each of the surfaces S ; that is 



d /do,, dn\ _ 



dv\dt dt)~ 



at every point on each of the surfaces S. 

 But also 



*(+)=,. ',.. 



at each point within S. 



It follows that 



df! da _ 



~dT + Ht' 



or constant, at all points on or within S. 



But dfl /dt being given, there is one, and only one, determinate system of closed electric 

 currents on S which has this effect, namely, the particular system determined by the 

 method of (8) and which we called the magnetic screen. This, then, is the system of 

 currents which will be formed from instant to instant on the surfaces S in response to 

 the continuous variation of the external magnetic system. This result is stated by 

 MAXWELL, 654, 655. 



Case of a Solid Conductor. 



. 17. I have assumed the conductors S to be hollow conducting shells. But if there 

 be within any of them any solid conductor, the proof shows that no closed electric 

 currents will, as the immediate effect of induction, be formed upon or within it, 

 because, as the immediate effect of induction, the magnetic force undergoes no change 

 within S. The outer shell S, with the induced currents upon it, acting for the instant 

 as a complete magnetic screen, completely shelters the enclosed solid from the direct 

 magnetic influence of the external system. As the superficial currents decay by 

 resistance, they cease to be a complete screen, and the interior solid becomes exposed, 

 in general very rapidly, to the influence of the external system. This effect we shall 

 have to consider later. But the immediate effect of induction is to produce only 

 superficial currents in the outer shell. And as this is true whatever be the form of the 

 enclosed solid, it is true if S consists of a solid conductor, instead of a hollow shell. 



It may be said that we cannot conceive an electric current otherwise than as existing 

 in a conducting stratum of some finite thickness, nor as independent of resistance, 

 which our expressions hitherto obtained are. And questions may be raised concerning 

 the thickness of the solid actually occupied by the currents at any time during the 

 induction, that is the rate at which the currents penetrate the solid. We shall see 

 reasons later, see (31) post, for determining the rate of penetration in certain cases as 

 a function of the resistance of the material. In the meantime we may treat of the 



