Five of Maxwells Papers | Page 4

in contact)
to build up the Ideal Pyramid is a discourse on the Relation of the two
branches (Mathematics and Physics) to, their action and reaction upon,
one another, a magnificent theme, with which it is to be hoped that
some future President of Section A will crown the edifice and make the
Tetralogy (symbolizable by A+A', A, A', AA') complete."
The theme thus distinctly laid down for his successor by our late
President is indeed a magnificent one, far too magnificent for any
efforts of mine to realize. I have endeavoured to follow Mr
Spottiswoode, as with far-reaching vision he distinguishes the systems
of science into which phenomena, our knowledge of which is still in
the nebulous stage, are growing. I have been carried by the penetrating
insight and forcible expression of Dr Tyndall into that sanctuary of
minuteness and of power where molecules obey the laws of their
existence, clash together in fierce collision, or grapple in yet more
fierce embrace, building up in secret the forms of visible things. I have
been guided by Prof. Sylvester towards those serene heights
"Where never creeps a cloud, or moves a wind, Nor ever falls the least
white star of snow, Nor ever lowest roll of thunder moans, Nor sound
of human sorrow mounts to mar Their sacred everlasting calm."
But who will lead me into that still more hidden and dimmer region
where Thought weds Fact, where the mental operation of the
mathematician and the physical action of the molecules are seen in their
true relation? Does not the way to it pass through the very den of the
metaphysician, strewed with the remains of former explorers, and
abhorred by every man of science? It would indeed be a foolhardy
adventure for me to take up the valuable time of the Section by leading
you into those speculations which require, as we know, thousands of
years even to shape themselves intelligibly.
But we are met as cultivators of mathematics and physics. In our daily
work we are led up to questions the same in kind with those of

metaphysics; and we approach them, not trusting to the native
penetrating power of our own minds, but trained by a long-continued
adjustment of our modes of thought to the facts of external nature.
As mathematicians, we perform certain mental operations on the
symbols of number or of quantity, and, by proceeding step by step from
more simple to more complex operations, we are enabled to express the
same thing in many different forms. The equivalence of these different
forms, though a necessary consequence of self-evident axioms, is not
always, to our minds, self-evident; but the mathematician, who by long
practice has acquired a familiarity with many of these forms, and has
become expert in the processes which lead from one to another, can
often transform a perplexing expression into another which explains its
meaning in more intelligible language.
As students of Physics we observe phenomena under varied
circumstances, and endeavour to deduce the laws of their relations.
Every natural phenomenon is, to our minds, the result of an infinitely
complex system of conditions. What we set ourselves to do is to
unravel these conditions, and by viewing the phenomenon in a way
which is in itself partial and imperfect, to piece out its features one by
one, beginning with that which strikes us first, and thus gradually
learning how to look at the whole phenomenon so as to obtain a
continually greater degree of clearness and distinctness. In this process,
the feature which presents itself most forcibly to the untrained inquirer
may not be that which is considered most fundamental by the
experienced man of science; for the success of any physical
investigation depends on the judicious selection of what is to be
observed as of primary importance, combined with a voluntary
abstraction of the mind from those features which, however attractive
they appear, we are not yet sufficiently advanced in science to
investigate with profit.
Intellectual processes of this kind have been going on since the first
formation of language, and are going on still. No doubt the feature
which strikes us first and most forcibly in any phenomenon, is the
pleasure or the pain which accompanies it, and the agreeable or

disagreeable results which follow after it. A theory of nature from this
point of view is embodied in many of our words and phrases, and is by
no means extinct even in our deliberate opinions.
It was a great step in science when men became convinced that, in
order to understand the nature of things, they must begin by asking, not
whether a thing is good or bad, noxious or beneficial, but of what kind
is it? and how much is there of it? Quality and Quantity were then first