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- But when the rate of change of aethereal strain - that is, of (f,g,h) specified as Maxwell's electric displacement in free aether - is added to it, an analytically convenient vector (u,v,w) is obtained which possesses the characteristic property of being
**circuital**like the flow of an incompressible fluid, and has therefore been made fundamental in the theory by Maxwell under the name of the total electric current. - The current of aethereal displacement d/dt(f,g,h) is what adds on to the true electric current to produce the total
**circuital**current of Maxwell. - We have now to substitute these data in the universally valid
**circuital**relations - namely, (i) line integral of magnetic force round a circuit is equal to Orr times the current through its aperture, which may be regarded as a definition of the constitution of the aether and its relation to the electrons involved in it; and (ii) line integral of the electric force belonging to any material circuit (i.e. - These
**circuital**relations, when expressed analytically, are then for a dielectric medium of types = (dt + x) (f',g',h')+dt(f,g,h), dR dQ = da dy dz dt' ' I See H. - For the simplest case of polarized waves travelling parallel to the axis of x, with the magnetic oscillation y along z and the electric oscillation Q along y, all the quantities are functions of x and t alone; the total current is along y and given with respect to our moving axes by __ (d_ d Q+vy d K-1 Q, dt dx) 47rc 2 + dt (4?rc 2) ' also the
**circuital**relations here reduce to _ dydQ _dy _ dx 47rv ' _ dt ' d 2 Q dv dx 2 -417t giving, on substitution for v, d 2 Q d 2 Q d2Q (c2-v2)(7372 = K dt 2 2u dxdt ' For a simple wave-train, Q varies as sin m(x-Vt), leading on substitution to the velocity of propagation V relative to the moving material, by means of the equation KV 2 + 2 uV = c 2 v2; this gives, to the first order of v/c, V = c/K i - v/K, which is in accordance with Fresnel's law.

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