Five of Maxwells Papers | Page 6

are compared together are really analogous in
form, or whether, in other words, the corresponding physical quantities
really belong to the same mathematical class. When this condition is
fulfilled, the illustration is not only convenient for teaching science in a
pleasant and easy manner, but the recognition of the formal analogy
between the two systems of ideas leads to a knowledge of both, more
profound than could be obtained by studying each system separately.
There are men who, when any relation or law, however complex, is put
before them in a symbolical form, can grasp its full meaning as a
relation among abstract quantities. Such men sometimes treat with
indifference the further statement that quantities actually exist in nature
which fulfil this relation. The mental image of the concrete reality
seems rather to disturb than to assist their contemplations. But the great
majority of mankind are utterly unable, without long training, to retain
in their minds the unembodied symbols of the pure mathematician, so
that, if science is ever to become popular, and yet remain scientific, it

must be by a profound study and a copious application of those
principles of the mathematical classification of quantities which, as we
have seen, lie at the root of every truly scientific illustration.
There are, as I have said, some minds which can go on contemplating
with satisfaction pure quantities presented to the eye by symbols, and to
the mind in a form which none but mathematicians can conceive.
There are others who feel more enjoyment in following geometrical
forms, which they draw on paper, or build up in the empty space before
them.
Others, again, are not content unless they can project their whole
physical energies into the scene which they conjure up. They learn at
what a rate the planets rush through space, and they experience a
delightful feeling of exhilaration. They calculate the forces with which
the heavenly bodies pull at one another, and they feel their own
muscles straining with the effort.
To such men momentum, energy, mass are not mere abstract
expressions of the results of scientific inquiry. They are words of power,
which stir their souls like the memories of childhood.
For the sake of persons of these different types, scientific truth should
be presented in different forms, and should be regarded as equally
scientific whether it appears in the robust form and the vivid colouring
of a physical illustration, or in the tenuity and paleness of a symbolical
expression.
Time would fail me if I were to attempt to illustrate by examples the
scientific value of the classification of quantities. I shall only mention
the name of that important class of magnitudes having direction in
space which Hamilton has called vectors, and which form the
subject-matter of the Calculus of Quaternions, a branch of mathematics
which, when it shall have been thoroughly understood by men of the
illustrative type, and clothed by them with physical imagery, will
become, perhaps under some new name, a most powerful method of
communicating truly scientific knowledge to persons apparently devoid

of the calculating spirit.
The mutual action and reaction between the different departments of
human thought is so interesting to the student of scientific progress,
that, at the risk of still further encroaching on the valuable time of the
Section, I shall say a few words on a branch of physics which not very
long ago would have been considered rather a branch of metaphysics. I
mean the atomic theory, or, as it is now called, the molecular theory of
the constitution of bodies.
Not many years ago if we had been asked in what regions of physical
science the advance of discovery was least apparent, we should have
pointed to the hopelessly distant fixed stars on the one hand, and to the
inscrutable delicacy of the texture of material bodies on the other.
Indeed, if we are to regard Comte as in any degree representing the
scientific opinion of his time, the research into what takes place beyond
our own solar system seemed then to be exceedingly unpromising, if
not altogether illusory.
The opinion that the bodies which we see and handle, which we can set
in motion or leave at rest, which we can break in pieces and destroy,
are composed of smaller bodies which we cannot see or handle, which
are always in motion, and which can neither be stopped nor broken in
pieces, nor in any way destroyed or deprived of the least of their
properties, was known by the name of the Atomic theory. It was
associated with the names of Democritus, Epicurus, and Lucretius, and
was commonly supposed to admit the existence only of atoms and void,
to the exclusion of any other basis of things from the universe.
In many physical reasonings and mathematical calculations