No doubt there is some reason for this feeling. Many of us have
already overcome the initial difficulties of mathematical training.
When we now go on with our study, we feel that it requires exertion
and involves fatigue, but we are confident that if we only work hard
our progress will be certain.

Some of us, on the other hand, may have had some experience of the
routine of experimental work. As soon as we can read scales, observe
times, focus telescopes, and so on, this kind of work ceases to
require any great mental effort. We may perhaps tire our eyes and
weary our backs, but we do not greatly fatigue our minds.

It is not till we attempt to bring the theoretical part of our
training into contact with the practical that we begin to experience
the full effect of what Faraday has called "mental inertia"--not only
the difficulty of recognising, among the concrete objects before us,
the abstract relation which we have learned from books, but the
distracting pain of wrenching the mind away from the symbols to the
objects, and from the objects back to the symbols. This however is
the price we have to pay for new ideas.

But when we have overcome these difficulties, and successfully bridged
over the gulph between the abstract and the concrete, it is not a mere
piece of knowledge that we have obtained: we have acquired the
rudiment of a permanent mental endowment. When, by a repetition of
efforts of this kind, we have more fully developed the scientific
faculty, the exercise of this faculty in detecting scientific
principles in nature, and in directing practice by theory, is no
longer irksome, but becomes an unfailing source of enjoyment, to which