must extend to the limits of the physical universe, and every point in space must be traversed by lines from all the centers in the universe, as otherwise there would be points in which the law of gravitation would not apply. Whether these lines of force are of different kinds, so that gravitation depends upon one kind, electric phenomena upon another kind and magnetic phenomena upon a third kind, Faraday does not state, but this condition would seem to follow from the rest of his theory.
When Maxwell undertook to interpret Faraday to the mathematicians he was compelled to choose between the more or less contradictory views which Faraday had expressed at different times, and he naturally undertook to select the views which could be used as the most satisfactory basis for a mathematical theory of electricity and magnetism. In doing this, he does not adopt Faraday's extreme views of the identity of matter and force. The distinction between force and energy was much more clearly understood at the time of Maxwell's writing than it was when Faraday was carrying on his investigations. In fact, energy, as a concept distinct from force, was not known to Faraday, and Maxwell shows early in his treatise that what had been defined as electricity or electrical quantity could not be measured as energy. He does, however, adopt Faraday's concept of physical lines of force, but somewhat in the manner of Faraday's earlier views, in which the lines of force were regarded as chains of polarized material particles.
Maxwell first defines his lines of force in a purely mathematical sense. Thus he says (Elec. and Mag. I, 97):
If a line be drawn whose direction at every point of its course coincides with that of the resultant intensity at that point, the line is called a Line of Force.
In every part of the course of a line of force, it is proceeding from a place of higher potential to a place of lower potential.
Hence a line of force cannot return into itself, but must have a beginning and an end. The beginning of a line of force must, by Number 80, be in a positively charged surface, and the end of a line of force must be in a negatively charged surface.
It is easily seen that such a line of force does not pull the positively and negatively charged surfaces together. It is merely the path along which a positively or negatively electrified particle would move if set free on the line of force. It does not explain the motion of the particle, it merely describes it. When he undertakes to explain why an electrified particle would travel along a line of force, Maxwell says:
