ly, when properly and sympathetically addressed to the
understanding, formed a most attractive study for youth. But it was
my habitual practice to withdraw the boys from the routine of the
book, and to appeal to their self-power in the treatment of questions
not comprehended in that routine. At first, the change from the
beaten track usually excited aversion: the youth felt like a child
amid strangers; but in no single instance did this feeling continue.
When utterly disheartened, I have encouraged the boy by the anecdote
of Newton, where he attributes the difference between him and other
men, mainly to his own patience; or of Mirabeau, when he ordered his
servant, who had stated something to be impossible, never again to use
that blockhead of a word. Thus cheered, the boy has returned to his
task with a smile, which perhaps had something of doubt in it, but
which, nevertheless, evinced a resolution to try again. I have seen
his eye brighten, and, at length, with a pleasure of which the ecstasy
of Archimedes was but a simple expansion, heard him exclaim, 'I have
it, sir.' The consciousness of self-power, thus awakened, was of
immense value; and, animated by it, the progress of the class was
astonishing. It was often my custom to give the boys the choice of
pursuing their propositions in the book, or of trying their strength
at others not to be found there. Never in a single instance was the
book chosen. I was ever ready to assist when help was needful, but my
offers of assistance were habitually declined. The boys had tasted
the sweets of intellectual conquest and demanded victories of their
own. Their diagrams were scratched on the walls, cut into the beams
upon the playground, and numberless other illustrations were afforded
of the living interest they took in the subject. For my own part, as
far as experience in teaching goes, I was a mere fledgling--knowing
nothing of the rules of pedagogics, as the Germans name it; but
adhering to the spirit indicated at the commencement of this
discourse, and endeavouring to make geometry a means rather than a
branch of education. The experiment was successful, and some of the
most delightful hours of my existence have been spent in marking the
vigorous and cheerful expansion of mental power, when appealed to in
the manner here described.

Our pleasure was enhanced when we applied our mathematical knowledge
to the solution of physical problems. Many objects of hourly c