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