Five of Maxwells Papers | Page 5

recognized as the primary features to be observed in scientific inquiry.
As science has been developed, the domain of quantity has everywhere
encroached on that of quality, till the process of scientific inquiry
seems to have become simply the measurement and registration of
quantities, combined with a mathematical discussion of the numbers
thus obtained. It is this scientific method of directing our attention to
those features of phenomena which may be regarded as quantities
which brings physical research under the influence of mathematical
reasoning. In the work of the Section we shall have abundant examples
of the successful application of this method to the most recent
conquests of science; but I wish at present to direct your attention to
some of the reciprocal effects of the progress of science on those
elementary conceptions which are sometimes thought to be beyond the
reach of change.
If the skill of the mathematician has enabled the experimentalist to see
that the quantities which he has measured are connected by necessary
relations, the discoveries of physics have revealed to the mathematician
new forms of quantities which he could never have imagined for
himself.
Of the methods by which the mathematician may make his labours
most useful to the student of nature, that which I think is at present
most important is the systematic classification of quantities.
The quantities which we study in mathematics and physics may be
classified in two different ways.
The student who wishes to master any particular science must make

himself familiar with the various kinds of quantities which belong to
that science. When he understands all the relations between these
quantities, he regards them as forming a connected system, and he
classes the whole system of quantities together as belonging to that
particular science. This classification is the most natural from a
physical point of view, and it is generally the first in order of time.
But when the student has become acquainted with several different
sciences, he finds that the mathematical processes and trains of
reasoning in one science resemble those in another so much that his
knowledge of the one science may be made a most useful help in the
study of the other.
When he examines into the reason of this, he finds that in the two
sciences he has been dealing with systems of quantities, in which the
mathematical forms of the relations of the quantities are the same in
both systems, though the physical nature of the quantities may be
utterly different.
He is thus led to recognize a classification of quantities on a new
principle, according to which the physical nature of the quantity is
subordinated to its mathematical form. This is the point of view which
is characteristic of the mathematician; but it stands second to the
physical aspect in order of time, because the human mind, in order to
conceive of different kinds of quantities, must have them presented to it
by nature.
I do not here refer to the fact that all quantities, as such, are subject to
the rules of arithmetic and algebra, and are therefore capable of being
submitted to those dry calculations which represent, to so many minds,
their only idea of mathematics.
The human mind is seldom satisfied, and is certainly never exercising
its highest functions, when it is doing the work of a calculating
machine. What the man of science, whether he is a mathematician or a
physical inquirer, aims at is, to acquire and develope clear ideas of the
things he deals with. For this purpose he is willing to enter on long
calculations, and to be for a season a calculating machine, if he can

only at last make his ideas clearer.
But if he finds that clear ideas are not to be obtained by means of
processes the steps of which he is sure to forget before he has reached
the conclusion, it is much better that he should turn to another method,
and try to understand the subject by means of well-chosen illustrations
derived from subjects with which he is more familiar.
We all know how much more popular the illustrative method of
exposition is found, than that in which bare processes of reasoning and
calculation form the principal subject of discourse.
Now a truly scientific illustration is a method to enable the mind to
grasp some conception or law in one branch of science, by placing
before it a conception or a law in a different branch of science, and
directing the mind to lay hold of that mathematical form which is
common to the corresponding ideas in the two sciences, leaving out of
account for the present the difference between the physical nature of
the real phenomena.
The correctness of such an illustration depends on whether the two
systems of ideas which