With regard to the teaching of geometry by this frame, it may be necessary to add, that the balls can be variously arranged so as to form different figures in general use. The teacher will perceive, the balls, as they appear in the figure, represent an acute scalene triangle.

To do anything like justice to the instrument, would form a volume of itself; suffice it to say, that it is one of the best instruments that was ever introduced into an infant school, and I do sincerely hope that no nursery will be without it. I shall next proceed to speak of

TEACHING NUMBER BY MEANS OF INCH
CUBES OF WOOD.

This plan, is either adapted for teaching children in classes, in the class-room, or in the gallery altogether. The children are formed into a square in the class-room, in the centre of which is placed a table; on this table the cubes are placed, one, two, or three at a time, according to the age and capacity of the children. For example, the master puts down three, and enquires of the children how many there are? The children, seeing three on the table, naturally call out three; the master puts down two more, and enquires as before, how many are three and two, they answer five; he puts five more and asks how many they make. Perhaps some of the children will answer right, and others wrong; he then calls those that answer wrong to the table, and lets them count the cubes, one at a time, until they are correct. He then adds more to those on the table, as far as he thinks proper; say, for example, as far as eighty. The teacher may ask his little pupils

how many tens there are in eighty, taking care to place the cubes ten in a row; the children, seeing eight rows will most likely say eight. Then he can ask them how many are eight times ten; the children will answer eighty. They may be cross-examined in this way with good effect, until they begin to be tired, which as soon as the teacher perceives, he must proceed to substract, saying, take 2 from 80, how many remain ? Answer, 78. Q. Take 8 from 78, how many remain? A. 70. The teacher may vary his questions in this way as much as he pleases, which will exercise the children's judgment, and also please them. But in order that the children may thoroughly understand what they are about, it is necessary to call a child, and cause him to count them himself, by placing them singly on the table. It must be observed, that it requires much patience, attention, and trouble, to give the children an insight into this part of the system; but the teacher will be amply recompensed for his pains. There are many little children in the different schools, who will readily answer almost any question in the multiplication, pence, addition, and substraction tables. We have 100 of those cubes, and they may be placed in tens, fives, or in any way that the teacher may think will be most advantageous to the scholar; keeping in view that these things present to the children so many facts relating to number, which alone can create correct ideas in their minds upon the subject. The next thing is to make the children acquainted with the signs of number, which can be most effectually done by means of the brass figures.

To assist the understanding, and exercise the judgment, in teaching numeration, slide a figure

S

in the frame, say figure 8. Question. What is this? Answer. 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. 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 hand 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 well practised in this way they will soon learn numeration. Addition is taught with the brass figures by placing one figure over the other; for example, put figure 5 in the frame: the teacher will then enquire what figure it is; some of the children will answer five; if none of them know it, (which will be the case at first,) they must of course be told. Then place the figure 3 over the 5, and ask what the last figure is, and if the children answer correctly, then ask them how many are 3 and 5. Their having answered this question, place another figure over the 3, the figure 6 for example: enquire as before, what figure it is, and then, how many are

eight and six when added together; and so on progressively as the teacher may think proper. This may be taught the children when they are in the gallery, or in the class-room. When a sufficient number of figures are up, begin to take away the bottom figures, saying if I take away this figure, how many are left, and so on until they are all taken out of the frame. This will both please, amuse, and edify the little ones. The only remaining branch of numerical knowledge, which consists in an ability to comprehend the powers of numbers, without either visible objects or signs-is imparted as follows:

Addition.

One of the children ascends the rostrum or small pulpit, and repeats aloud, in a kind of chaunt, the whole of the school repeating after him; One and one are two; two and one are three; three and one are four; &c. up to twelve. Two and two are four; four and two are six; six and two are eight, &c. to twenty-four.

Three and three are six; six and three are nine; nine and three are twelve, &c. to thirtysix.

Substraction.

One from twelve leaves eleven; one from eleven leaves ten, &c.

Two from twenty-four leaves twenty-two; two from twenty-two leaves twenty, &c.

Multiplication.

Twice one are two; twice two are four; &c. &c.

Three times three are nine, three times four are twelve, &c. &c.

Twelve times two are twenty-four; eleven times two are twenty-two, &c. &c.

Twelve times three are thirty-six; eleven times three are thirty-three, &c. &c. until the whole of the multiplication table is gone through.

Division.

There are twelve twos in twenty-four.-There are eleven twos in twenty-two, &c. &c. There are twelve threes in thirty-six, &c. There are twelve fours in forty-eight, &c. &c.

Fractions.

Two is the half () of four.

third () of six.

fourth (4) of eight.

fifth (3) of ten.

sixth () of twelve.

seventh () of fourteen.

twelfth () of twenty-four; two is

the eleventh (+) of twenty-two, &c. &c. Three is the half (7) of six.

third (3) of nine.

fourth () of twelve.

twelfth (2) of thirty-six; three is

the eleventh (1) of thirty-three, &c. &c. Four is the half (1) of eight, &c.

In twenty-three are four times five, and threefifths (3) of five; in thirty-five are four times eight, and three-eighths (3) of eight.

In twenty-two are seven times three, and onethird (4) of three.