are speaking, move the balls gently out, and,
as soon as they see them, they will immediately cry out "Nine;" and in
this way they may acquire a knowledge of all the figures separately.
Then you may proceed thus: Units 7, tens 3; place three balls on the
top wire and seven on the second, and say, Thirty-seven, as you point
to the figures, and thirty-seven as you point to the balls. Then go
on, units 7, tens, 3, hundreds 9, place nine balls on the top wire,
three on the second, and seven on the third, and say, pointing to
each, Nine hundred and thirty-seven. And so onwards.

To assist the understanding and exercise the judgment, slide a figure
in the frame, and say, Figure 8. Q. What is this? A. No. 8. Q. If No.
1 be put on the left side of the 8, what will it be? A. 81. Q. If the
1 be put on the right side, then what will it be? A. 18. Q. If the
figure 4 be put before the 1, then what will the number be? A. 418. Q.
Shift the figure 4, and put it on the left side of the 8, then ask the
children to tell the number, the answer is 184. The teacher can keep
adding and shifting as he pleases, according to the capacity of his
pupils, taking care to explain as he goes on, and to satisfy himself
that his little flock perfectly understand him. Suppose figures
5476953821 are in the frame; then let the children begin at the left
hand, saying, units, tens, hundreds, thousands, tens of thousands,
hundreds of thousands, millions, tens of millions, hundreds of
millions, thousands of millions. After which, begin at the right side,
and they will say, Five thousand four hundred and seventy-six million,
nine hundred and fifty-three thousand, eight hundred and twenty-one.
If the children are practised in this way, they will soon learn
numeration.

The frame was employed for this purpose long before its application to
others was perceived; but at length I found we might proceed to

_Addition_.--We proceed as follows:--1 and 2 are 3, and 3 are 6, and 4
are 10, and 5 are 15, and 6 are 21, and 7 are 28, and 8 are 36, and 9
are 45, and 10 are 55, and 11 are 66, and 12 are 78.

Then the master may exercise them backwards, saying, 12 and 11 are 23,
and 10 are 33, and 9 are 42, and 8 are 50, and 7 are 57, and 6 are 63,
and 5 are 68, and 4 are 72, and 3 are 75, and 2 are 77, and 1 is 78,
and so on in great variety.

Again: place seven balls on one wire, and two on the next, and ask
them how many 7 and 2 are; to this they will soon answer, Nine: