Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/252

 Rh To determine the value of E, let us differentiate the quantity under the integral sign with respect to t, remembering that if the secondary circuit is in motion, x, y and z are functions of the time. We obtain

Now consider the second term of the integral, and substitute from equations (A), Art. 591, the values of $$\frac{dG}{dx}$$ and $$\frac{dH}{dx}$$. This term then then becomes, which we may write

Treating the third and fourth terms in the same way, and collecting the terms in $$\frac{dx}{ds}$$, $$\frac{dy}{ds}$$, and $$\frac{dz}{ds}$$, remembering that

and therefore that the integral, when taken round the closed curve, vanishes,