James Clerk Maxwell (1831-1879)

334

                    Proceedings of the Royal Society

to those who possess peculiarly ready mastery over symbols, whether
they try to understand the significance of each step or no, Maxwell
was not, and certainly never attempted to be, in the foremost rank
of mathematicians. He was slow in “writing out,” and avoided as
far as he could the intricacies of analysis. He preferred always to
have before him a geometrical or physical representation of the pro-
blem in which he was engaged, and to take all his steps with the
aid of this: afterwards, when necessary, translating them into
symbols. In the comparative paucity of symbols in many of his
great papers, and in the way in which, when wanted, they seem to
grow full-blown from pages of ordinary text, his writings resemble
much those of Sir William Thomson, which in early life he had with
great wisdom chosen as a model.

There can be no doubt that in this habit, of constructing a mental
representation of every problem, lay one of the chief secrets of his
wonderful success as an investigator. To this were added an extra-
ordinary power of penetration, and an altogether unusual amount of
patient determination. The clearness of his mental vision was quite
on a par with that of Faraday; and in this (the true) sense of the
word he was a mathematician of the highest order.

But the rapidity of his thinking, which he could not control, was
such as to destroy, except for the very highest class of students, the
value of his lectures. His books and his written addresses (always
gone over twice in MS.) are models of clear and precise exposition;
but his extempore lectures exhibited, in a manner most aggravating
to the listener, the extraordinary fertility of his imagination.

During his undergraduateship in Cambridge he developed the
germs of his future great work on “Electricity and Magnetism”
(1873) in the form of a paper “On Faraday's Lines of Force,” which
was ultimately printed in 1856 in the “Trans, of the Cam. Phil.
Soc.” He showed me the MS. of the greater part of it in 1853. It
is a paper of great interest in itself, but extremely important as
indicating the first steps to such a splendid result. His idea of a
fluid, incompressible and without mass, but subject to a species of
friction in space, was confessedly adopted from the analogy pointed
out by Thomson in 1843 between the steady flow of heat and the
phenomena of statical electricity.

In recent years he came to the conclusion that all such analogies,