ousand. We do not use the word ten as the French do _une
dizaine_; ten does not, therefore, present the idea of an integer till
we learn arithmetic. This is a defect in our language, which has
arisen from the use of duodecimal numeration; the analogies existing
between the names of other numbers in progression, is broken by the
terms eleven and twelve. _Thirteen_, _fourteen_, &c. are so obviously
compounded of three and ten, and four and ten, as to strike the ears
of children immediately, and when they advance as far as twenty, they
readily perceive that a new series of units begins, and proceeds to
thirty, and that thirty, forty, &c. mean three tens, four tens, &c. In
pointing out these analogies to children, they become interested and
attentive, they show that species of pleasure which arises from the
perception of _aptitude_, or of truth. It can scarcely be denied that
such a pleasure exists independently of every view of utility and
fame; and when we can once excite this feeling in the minds of our
young pupils at any period of their education, we may be certain of
success.

As soon as distinct notions have been acquired of the manner in which
a collection of ten units becomes a new unit of a higher order, our
pupil may be led to observe the utility of this invention by various
examples, before he applies it to the rules of arithmetic. Let him
count as far as ten with black pebbles,[17] for instance; let him lay
aside a white pebble to represent the collection of ten; he may count
another series of ten black pebbles, and lay aside another white one;
and so on, till he has collected ten white pebbles: as _each_ of the
ten white pebbles represents ten black pebbles, he will have counted
one hundred; and the ten white pebbles may now be represented by a
single red one, which will stand for one hundred. This large number,
which it takes up so much time to count, and which could not be
comprehended at one view, is represented by a single sign. Here the
difference of colour forms the distinction: difference in shape, or
size, would answer the same purpose, as in the Roman notation X for
ten, L for fifty, C for one hundred, &c. All this is fully within the
comprehension of a child of six years old, and will lead him to the
value of written figures by the _place_ which they hold when compared
with one another. Indeed he may be led to invent this arrangement, a
circumstance which would encourage him in every part of his educ