“It appears, therefore, that certain phenomena in electricity and magnetism lead to the same conclusion as those of optics, namely, that there is an ætherial medium pervading all bodies, and modified only in degree by their presence; that the parts of this medium are capable of being set in motion by electric currents and magnets; that this motion is communicated from one part of the medium to another by forces arising from the connection of those parts; that under the action of these forces there is a certain yielding depending on the elasticity of these connections; and that, therefore, energy in two different forms may exist in the medium, the one form being the actual energy of motion of its parts, and the other being the potential energy stored up in the connections in virtue of their elasticity. “Thus, then, we are led to the conception of a complicated mechanism capable of a vast variety of motion, but at the same time so connected that the motion of one part depends, according to definite relations, on the motion of other parts, these motions being communicated by forces arising from the relative displacement of the connected parts, in virtue of their elasticity. Such a mechanism must be subject to the general laws of dynamics, and we ought to be able to work out all the consequences of its motion, provided we know the form of the relation between the motions of the parts.” These general laws of dynamics, applicable to the motion of any connected system, had been developed by Lagrange, and are expressed in his generalised equations of motion. It is one of Maxwell’s chief claims to fame that he saw in the electric field a connected system to which Lagrange’s equations could be applied, and that he was able to deduce the mechanical and electrical actions which take place by means of fundamental propositions of dynamics. The methods of the paper now under discussion were developed further in the “Treatise on Electricity and Magnetism,” published in 1873; in endeavouring to give some slight account of Maxwell’s work, we shall describe it in the form it ultimately took. The task which Maxwell set himself was a double one; he had first to express in symbols, in as general a form as possible, the fundamental laws of electro-magnetism as deduced from experiments, chiefly the experiments of Faraday, and the relations between the various quantities involved; when this was done he had to show how these laws could be deduced from the general dynamical laws applicable to any system of moving bodies.