“All the views which Faraday has brought forward and illustrated, as demonstrated by experiment, lead to this method of establishing the mathematical theory, and, as far as the analysis is concerned, it would in most _general_ propositions be more simple, if possible, than that of Coulomb. Of course the analysis of _particular_ problems would be identical in the two methods. It is thus that Faraday arrives at a knowledge of some of the most important of the mathematical theorems which from their nature seemed destined never to be perceived except as mathematical truths.” Lord Kelvin’s papers on “The Mathematical Theory of Electricity,” published from 1848 to 1850, his “Propositions on the Theory of Attraction” (1842), his “Theory of Electrical Images” (1847), and his paper on “The Mathematical Theory of Magnetism” (1849), contain a statement of the most important results achieved in the mathematical sciences of Electrostatics and Magnetism up to the time of Maxwell’s first paper. The opening sentences of that paper have already been quoted. In the preface to the “Electricity and Magnetism” Maxwell writes thus:-- “Before I began the study of electricity I resolved to read no mathematics on the subject till I had first read through ‘Experimental Researches on Electricity.’ I was aware that there was supposed to be a difference between Faraday’s way of conceiving phenomena and that of the mathematicians, so that neither he nor they were satisfied with each other’s language. I had also the conviction that this discrepancy did not arise from either party being wrong. I was first convinced of this by Sir William Thomson, to whose advice and assistance, as well as to his published papers, I owe most of what I have learned on the subject. “As I proceeded with the study of Faraday, I perceived that his method of conceiving the phenomena was also a mathematical one, though not exhibited in the conventional form of mathematical symbols. I also found that these methods were capable of being expressed in the ordinary mathematical forms, and thus compared with those of the professed mathematicians. “For instance, Faraday, in his mind’s eye, saw lines of force traversing all space where the mathematicians saw centres of force attracting at a distance. Faraday saw a medium where they saw nothing but distance. Faraday sought the seat of the phenomena in real actions going on in the medium. They were satisfied that they had found it in a power of action at a distance impressed on the electric fluids.”