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.
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