Page:L. Silberstein - The Theory of Relativity.djvu/38

22 magnetic view of all natural phenomena. Nor does it force upon us a purely mechanistic view, which till recently held the field, before the pan-electric tendencies arose. Modern Relativity is broader than this: it subordinates mechanical, electromagnetic and other images to a much wider Principle which is colourless, as it were.

Thus, the reason of returning here to Maxwell is, in the first place, of an historical (and partly didactic) character. But we have yet another reason for dwelling in the present chapter upon the great inheritance left to Science by Clerk Maxwell. It is widely known that but a few things of the old system of physics have remained untouched by the modern principle of relativity, though the changes required are generally but very slight. In fact, almost nothing of the old structure has been spared by the new theory of relativity; but Maxwell's fundamental equations, namely those known as his equations for 'stationary' media, have been spared. More than this: not only have they been preserved entirely in their original form, without the slightest modification of any order of magnitude whatever, but they form one and the best secured of the actual possessions of the new theory, the largest and brightest patch of colour, as it were, on the vast and as yet mostly colourless canvas contained within the frame of the new Principle. Moreover, a peculiar union or combination of the electric and magnetic vectors which appear in Maxwell's equations of the electromagnetic field became the standard and prototype (not as regards physical meaning, but mathematical transformational properties) of a very important class of entities admitted by the new theory (the so-called 'world-six-vectors' or 'physical bivectors').

So much to justify the insertion of the following topics of the present chapter.

Maxwell's fundamental laws of the electromagnetic field in a 'fixed' or 'stationary' non-conducting dielectric medium may be expressed in integral form as follows:


 * I. Electric displacement-current through any surface σ bounded by the circuit s = c × line integral of magnetic force M round s.
 * II. Magnetic current through σ = – c × line integral of electric force E round s,