Maxwell shows how to obtain a mathematical expression for Faraday’s electro-tonic state. In his “Electricity and Magnetism,” this electro-tonic state receives a new name. It is known as the Vector Potential,[61] and the paper under consideration contains, though in an incomplete form, his first statement of those equations of the electric field which are so indissolubly bound up with Maxwell’s name. The great advance in theory made in the paper is the distinct recognition of certain mathematical functions as representing Faraday’s electrotonic-state, and their use in solving electro-magnetic problems. The paper contains no new physical theory of electricity, but in a few years one appeared. In his later writings Maxwell adopted a more general view of the electro-magnetic field than that contained in his early papers on “Physical Lines of Force.” It must, therefore, not be supposed that the somewhat gross conception of cog-wheels and pulleys, which we are about to describe, were anything more to their author than a model, which enabled him to realise how the changes, which occur when a current of electricity passes through a wire, might be represented by the motion of actual material particles. The problem before him was to devise a physical theory of electricity, which would explain the forces exerted on electrified bodies by means of action between the contiguous parts of the medium in the space surrounding these bodies, rather than by direct action across the distance which separates them. A similar question, still unanswered, had arisen in the case of gravitation. Astronomers have determined the forces between attracting bodies; they do not know how those forces arise. Maxwell’s fondness for models has already been alluded to; it had led him to construct his top to illustrate the dynamics of a rigid body rotating about a fixed point, and his model of Saturn’s rings (now in the Cavendish Laboratory) to illustrate the motion of the satellites in the rings. He had explained many of the gaseous laws by means of the impact of molecules, and now his fertile ingenuity was to imagine a mechanical model of the state of the electro-magnetic field near a system of conductors carrying currents.