And now, with a quite wonderful sagacity and intellectual precision, Faraday performed in his brain the work of a great mathematician without using a single mathematical formula. He saw with his mind’s eye that magnetised and dielectric bodies ought to have a tendency to contract in the direction of the lines of force, and to dilate in all directions perpendicular to the former, and that by these systems of tensions and pressures in the space which surrounds electrified bodies, magnets, or wires conducting electric currents, all the phenomena of electrostatic, magnetic, electromagnetic attraction, repulsion, and induction could be explained, without recurring at all to forces acting directly at a distance. This was the part of his path where so few could follow him; perhaps a Clerk Maxwell, a second man of the same power and independence of intellect, was needed to reconstruct in the normal methods of science the great building the plan of which Faraday had conceived in his mind, and attempted to make visible to his contemporaries. Nobody can deny that this new theory of electricity and magnetism, originated by Faraday and developed by Maxwell, is in itself well consistent, in perfect and exact harmony with all the known facts of experience, and does not contradict any one of the general axioms of dynamics, which have been hitherto considered as the fundamental truths of all natural science, because they have been found valid, without any exception, in all known processes of nature. And, after dealing with the phenomena discussed by Faraday, Von Helmholtz adds these pregnant words:-- Nevertheless, the fundamental conceptions by which Faraday was led to these much-admired discoveries have not received an equal amount of consideration. They were very divergent from the trodden path of scientific theory, and appeared rather startling to his contemporaries. His principal aim was to express in his new conceptions only facts, with the least possible use of hypothetical substances and forces. This was really an advance in general scientific method, destined to purify science from the last remnants of metaphysics. Faraday was not the first, and not the only man, who had worked in this direction, but perhaps nobody else at his time did it so radically. Clerk Maxwell said of him: The way in which Faraday made use of his lines of force in co-ordinating the phenomena of electric induction shows him to have been a mathematician of high order, and one from whom the mathematicians of the future may derive valuable and fertile methods. It is fitting to include in this review of Faraday’s place in relation to the mathematical side of physics some words of Lord Kelvin, taken from his preface to the English edition of Hertz’s “Electric Waves”:--