e _it_ goes, there _it_ goes."

When they have repeated "There it goes" long enough to impress it on
their memory, stop the ball; the children will probably say, "Now _it_
stops, now _it_ stops." When that is the case, move another ball to
it, and then explain to the children the difference between singular
and plural, desiring them to call out, "There _they_ are, there _they_
are;" and when they have done that as long as may be proper, set both
balls moving, and it is likely they will call out, "There _they_ go,
there _they_ go." I do not particularize further, because I know that
good teachers will at once see the principle aimed at, and supply the
other requisite lessons: the object of this book being rather to shew
the principle of the thing, than to go into detail.

CHAPTER XII.

ARITHMETIC.

_The arithmeticon--How applied--Numeration--Addition--Subtraction--
Multiplication--Division--Fraction--Arithmetical tables--Arithmetical
Songs--Observations_.

* * * * *

"In arithmetic, as in every other branch of education, the principal
object should be to preserve the understanding from implicit belief,
to invigorate its powers, and to induce the laudable ambition of
progressive improvement."--_Edgeworth_

* * * * *

The advantage of a knowledge of arithmetic has never been disputed.
Its universal application to the business of life renders it an
important acquisition to all ranks and conditions of men. The
practicability of imparting the rudiments of arithmetic to very young
children has been satisfactorily shewn by the Infant-school System;
and it has been found, likewise, that it is the readiest and surest
way of developing the thinking faculties of the infant mind. Since the
most complicated and difficult questions of arithmetic, as well as
the most simple, are all solvable by the same rules, and on the same
principles, it is of the utmost importance to give children a clear
insight into the primary principles of number. For this purpose we
take care to shew them, by visible objects, that all numbers are
combinations of unity; and that all changes of number must arise
either from adding to or taking from a certain stated number. After
this, or rather, perhaps I should say, in conjunction with this
instruction, we exhibit to the children the _signs_ of number, and
make them acquainted with their various combinations; and lastly, we
bring the