124 Mr. 0. Heaviside on the 



of this, rather unmanageable, although they are not really 

 general, for impressed forces are omitted, and the intrinsic 

 magnetization must be zero, and the medium isotropic. Again, 

 and this is an objection of some magnitude, the two potentials 

 A and P, if given everywhere, are not sufficient to specify the 

 state of the electromagnetic field. Try it ; and fail. 



Even without using these complex general equations referred 

 to, but those on which they are based, (1) and (2), the very 

 artificial nature of A and P greatly obscures and complicates 

 many investigations. Not being able to work practically in 

 terms of A and P in a general manner, and yet knowing 

 there was nothing absolutely wrong, I went to the root of the 

 evil, and cured it, thus: — 



As a companion to equation (1) use this, 



-curlE i = 47rG; (3) 



where Gr is the magnetic current, or B/47T. That this may 

 be derived at once from (2) is obvious. But what is of greater 

 importance in view of the difficult establishment of (2), is that 

 (3) can be got immediately independently, and that (2) is its 

 consequence. Equation (3) is in fact the mathematical ex- 

 pression of the Faraday law of induction, that the electromotive 

 force of induction in any closed circuit is to be measured by 

 the rate of decrease of the induction through it. 



Now make (1) and (3) the fundamental equations of motion, 

 and ignore (2) altogether, except for special purposes. There 

 are several great advantages in the use of (3). First, the 

 abolition of the two potentials. Next, we are brought into 

 immediate contact with E x and Hj, which have physical sig- 

 nificance in really defining the state of the medium anywhere 

 (k, fju, and c of course to be known), which A and P do not, 

 and cannot, even if given over all space. Thirdly, by reason 

 of the close parallelism between (1) and (3), electric force 

 related to magnetic current, as magnetic force to electric cur- 

 rent, we are enabled to easily perceive many important relations 

 which are not at all obvious when the potentials A and P are 

 used, and (3) ignored. Fourthly, we are enabled with con- 

 siderable ease, if we have obtained solutions relating to variable 

 states in which the lines of Ej and B. x are related in one way, 

 to at once get the solutions of problems of quite different 

 physical meaning, in which E x and H 1? or quantities directly 

 related to them, change places. For example, the variation 

 of magnetic force in a core in a coil, and of electric current 

 in a round wire ; and many others. 



That the advantages attending the use of (3) as a funda- 

 mental equation are not imaginary, I have repeatedly verified. 



