. To bisect a line, to erect a perpendicular,
to describe a square, to bisect an angle, to draw a line parallel to a
given line, to describe a hexagon, are problems which a little patience
will enable him to find out. And from these he may be led on step by
step to more complex questions: all of which, under judicious
management, he will puzzle through unhelped. Doubtless, many of those
brought up under the old regime, will look upon this assertion
sceptically. We speak from facts, however; and those neither few nor
special. We have seen a class of boys become so interested in making out
solutions to such problems, as to look forward to their geometry-lesson
as a chief event of the week. Within the last month, we have heard of
one girl's school, in which some of the young ladies voluntarily occupy
themselves with geometrical questions out of school-hours; and of
another, where they not only do this, but where one of them is begging
for problems to find out during the holidays: both which facts we state
on the authority of the teacher. Strong proofs, these, of the
practicability and the immense advantage of self-development! A branch
of knowledge which, as commonly taught, is dry and even repulsive, is
thus, by following the method of Nature, made extremely interesting and
profoundly beneficial. We say profoundly beneficial, because the effects
are not confined to the gaining of geometrical facts, but often
revolutionise the whole state of mind. It has repeatedly occurred that
those who have been stupefied by the ordinary school-drill--by its
abstract formulas, its wearisome tasks, its cramming--have suddenly had
their intellects roused by thus ceasing to make them passive recipients,
and inducing them to become active discoverers. The discouragement
caused by bad teaching having been diminished by a little sympathy, and
sufficient perseverance excited to achieve a first success, there arises
a revulsion of feeling affecting the whole nature. They no longer find
themselves incompetent; they, too, can do something. And gradually as
success follows success, the incubus of despair disappears, and they
attack the difficulties of their other studies with a courage insuring
conquest.

A few weeks after the foregoing remarks were originally published,
Professor Tyndall in a lecture at the Royal Institution "On the
Importance of the Study of Physics as a Branch of Education," gave some
conclusive evidence to the same effect. His