ered by the mathematicians could be expressed much better in terms of ideas derived from Faraday than in their original form.
Maxwell takes pains to emphasize this statement of the purpose of his treatise. Thus in Vol. II, p. 176, 3d Ed., he says:
It was perhaps for the advantage of science that Faraday, though thoroughly conscious of the fundamental forms of space, time and force, was not a professed mathematician. He was not tempted to enter into the many interesting researches in pure mathematics which his discoveries would have suggested if they had been exhibited in a mathematical form, and he did not feel called upon either to force his results into a shape acceptable to the mathematical taste of the time, or to express them in a form which mathematicians might attack. He was thus left at leisure to do his proper work, to coordinate his ideas with his facts, and to express them in natural, untechnical language.
It is mainly with the hope of making these ideas the basis of a mathematical method that I have undertaken this treatise.
Maxwell accordingly undertook to specify the conditions in a dielectric medium by means of which the induction effects discussed by Faraday could be explained from the known laws of mechanics. In doing this he used as much as possible the fundamental concepts of Faraday in so far as these could be determined.
Faraday's researches were carried on through a term of years and were presented as they were finished. Naturally, one who departed so fundamentally in his electrical concepts from all who had preceded him, and who discovered so many new phenomena in electricity and magnetism, was obliged to modify his views as he proceeded. In his Experimental Researches Faraday gives us, not his mature opinion at the conclusion of his work, but the evolution of his theory as it took shape in his mind. It is accordingly possible to get different notions of Faraday's theory from different parts of his Researches.
Thus, in the discussion of induction which has been in part quoted Faraday speaks of the phenomena as being entirely due to a condition in the dielectric medium, and he discusses the direction of the lines of force of the inductive stress in this medium. In the early stages of his work he uses the term "lines of force" in a purely mathematical sense, that is, as giving throughout their length the direction of the inductive force. Later he came to think of the dielectric medium as consisting wholly of physical lines of force. In one of his latest papers (Proc. Roy. Inst., June 11, 1852) he discusses the characteristics which must distinguish physical lines of force from abstract, or mathematical, lines of force, and decides that both electrical and magnetic phenomena are dependent upon physical lines of force; that is, the lines of force are no longer used to describe phenomena, but to explain them.
