When resuming the research in December, Faraday investigated the point whether it was essential or not that the moving wire should, in “cutting” the magnetic curves, pass into positions of greater or lesser magnetic force; or whether, always intersecting curves of equal magnetic intensity, the mere motion sufficed for the production of the current. He found the latter to be true. This notion of _cutting_ the invisible magnetic lines as the essential act necessary and sufficient for induction was entirely original with Faraday. For long it proved a stumbling-block to the abstract mathematicians, since there was, in most cases, no direct or easy way in which to express the number of magnetic lines that were cut. Neither had any convention been adopted up to that time as to how to reckon numerically the number of magnetic lines in any given space near a magnet. Later, in 1851, Faraday himself gave greater precision to these ideas. He found that the current was proportional to the velocity, when the conductor was moving in a uniform magnetic field with a uniform motion. Also, that the quantity of electricity thrown by induction into the circuit was directly proportional to the “amount of curves intersected.” The following passage, from Clerk Maxwell’s article on Faraday in the “Encyclopædia Britannica,” admirably sums up the matter:-- The magnitude and originality of Faraday’s achievement may be estimated by tracing the subsequent history of his discovery. As might be expected, it was at once made the subject of investigation by the whole scientific world, but some of the most experienced physicists were unable to avoid mistakes in stating, in what they conceived to be more scientific language than Faraday’s, the phenomena before them. Up to the present time the mathematicians who have rejected Faraday’s method of stating his law as unworthy of the precision of their science, have never succeeded in devising any essentially different formula which shall fully express the phenomena without introducing hypotheses about the mutual action of things which have no physical existence, such as elements of currents which flow out of nothing, then along a wire, and finally sink into nothing again. After nearly half a century of labour of this kind, we may say that, though the practical applications of Faraday’s discovery have increased and are increasing in number and value every year, no exception to the statement of these laws as given by Faraday has been discovered, no new law has been added to them, and Faraday’s original statement remains to this day the only one which asserts no more than can be verified by experiment, and the only one by which the theory of the phenomena can be expressed in a manner which is exactly and numerically accurate, and at the same time within the range of elementary methods of exposition.