Page:Scientific Monthly, volume 14.djvu/560

 apparatus. Discharge is the return of these particles to their natural state of tension, whenever the two electric forces are allowed to be disposed of in some other direction.

The question as to the cause of this state of polarization is left entirely unanswered by Faraday, and this question is fundamental. The fact that electrical induction could take place in the best air pump vacuum seemed to require that all space must be filled with a medium made of polarizable particles, and this assumption was not readily accepted, especially at a time when the notion of force acting at a distance had become the common heritage of physicists. For this and other reasons Faraday's electrical theory did not meet with general acceptance at the time when it was proposed.

In 1873 Maxwell published the first edition of his Electricity and Magnetism which brought the fundamental ideas of Faraday into a position of prominence in English speaking countries which they have largely maintained up to very recent times.

Maxwell undertook to show in his treatise that the quantitative laws of electricity and magnetism which had been put into mathematical form on the assumption of forces acting at a distance could also be put into mathematical form on the basis of Faraday's notion of induction.

Thus Maxwell says:

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 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 centers of force attracting at a 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 electrical fluids.

When I had translated what I conceived to be Faraday's ideas into a mathematical form, I found that in general the two methods coincided, so that the same phenomena were accounted for, and the same laws of action deduced by both methods, but that Faraday's methods resembled those in which we begin with the whole and arrive at the parts by analysis, while the ordinary mathematical methods were founded on the principle of beginning with the parts and building up the whole by synthesis.

I also found that several of the most fertile methods of research discov-