suppose
that three hundred pupils, all ignorant of the method of reducing
fractions to a common denominator, and yet all old enough to learn, are
collected in one room. Suppose they are all attentive and desirous of
learning, it is very plain that the process may be explained to the
whole at once, so that half an hour spent in that exercise, would enable
a very large proportion of them to understand the subject. So, if a
teacher is explaining to a class in Grammar, the difference between a
noun and verb, the explanation would do as well for several hundred, as
for the dozen who constitute the class, if arrangements could only be
made to have the hundreds hear it. But there are, perhaps, only a
hundred in the school, and of these a large part understand already the
point to be explained, and another large part are too young to attend to
it. I wish the object of these remarks not to be misunderstood. I do not
recommend the attempt to teach on so extensive a scale; I admit that it
is impracticable; I only mean to show in what the impracticability
consists, namely, in the difficulty of making such arrangements as to
derive the full benefit from the instructions rendered. They are, in the
nature of things, available to the extent I have represented, but, in
actual practice, the full benefit cannot be derived. Now, so far as we
thus fall short of this full benefit, so far there is, of course, waste;
and it is difficult or impossible to make such arrangements as will
avoid the waste, in this manner, of a large portion of every effort,
which the teacher makes.

A very small class instructed by an able teacher, is like a factory of a
hundred spindles, with a water-wheel of power sufficient for a thousand.
In such a case, even if the owner, from want of capital, or any other
cause, cannot add the other nine hundred, he ought to know how much of
his power is in fact unemployed, and make arrangements to bring it into
useful exercise, as soon as he can. The teacher in the same manner,
should understand what is the full beneficial effect, which it is
possible, _in theory_, to derive from his instructions. He should
understand, too, that just so far as he falls short of this full effect,
there is waste. It may be unavoidable; part of it unquestionably is,
like the friction of machinery, unavoidable. Still, it is waste; and it
ought to be so understood, that by the gradual perfection of the
machinery, it may be more and more fully pre