Faraday's own words,[1] that "whether the wire moves directly or obliquely across the lines of force, in one direction or another, it sums up the amount of the forces represented by the lines it has crossed," so that "the quantity of electricity thrown into a current is directly as the number of curves intersected."[2] The induced electromotive force is, in fact, simply proportional to the number of the unit lines of magnetic force intersected by the wire per second.
This is the fundamental principle of the induction of currents. Faraday is undoubtedly entitled to the full honour of its discovery; but for a right understanding of the progress of electrical theory at this period, it is necessary to remember that many years elapsed before all the conceptions involved in Faraday's principle became clear and familiar to his contemporaries; and that in the meantime the problem of formulating the laws of induced currents was approached with success from other points of view. There were indeed many obstacles to the direct appropriation of Faraday's work by the mathematical physicists of his own generation; not being himself a mathematician, he was unable to address them in their own language; and his favourite mode of representation by moving lines of force repelled analysts who had been trained in the school of Laplace and Poisson. Moreover, the idea of electromotive force itself, which had been applied to currents a few years previously in Ohm's memoir, was, as we have seen, still involved in obscurity and misapprehension.
A curious question which arose out of Faraday's theory was whether a bar-magnet which is rotated on its own axis carries its lines of magnetic force in rotation with it. Faraday himself believed that the lines of force do not rotate[3]: on this view a revolving magnet like the earth is to be regarded as moving through its own lines of force, so that it must become charged at the equator and poles with electricity of opposite signs, and if a wire not partaking in the earth's rotation were to have sliding contact with the earth at a pole and at the
