cubes to which they were united before; the third and fifth pair, which, like the rest, formed rectangles, have been disunited, and no longer lie in the same line with the 6 remaining rectangles.

At another exercise the mother, placing 8 pair of cubes at equal distances, as before, desires the children to turn about, and then

makes the following changes,

ᄆ ᄆ ᄆ

Moth. Now look, and tell me what changes

the cubes have undergone.

Child. Oh! what confusion!

Moth. Examine them minutely pair by pair, and you will be able to state all the changes that have taken place:

How many times 2 were there before?

Child. The half of two has been taken away. Moth. That is what I do not wish to know at present; I want to hear how many times 2 there were before.

(It is important to be distinct and precise in proposing questions, and to require the children to return precise answers.)

Child. 8 times 2.

Moth. How many times 2 are yet here? Child. 7 times 2 and the half of 2. Moth. How many times 2 are wanting? Child. None; the half of two only is wanting.

Moth. From whence has the half of 2 been taken away?

Child. Here, (pointing to the vacant place above the single oblong.)

Moth. Describe minutely the place where the wanting cube was situated.

Child. The wanting cube was situated above that which is the fourth in the lower row from the right.

Moth. Exactly! We now know that one cube has been taken away, and the place from whence it has been taken away.-But mention all the other changes which have taken place. (As one child noticed first this, another that change, she said :) I have made so many alterations, that we must go step by step, and examine one pair after the other; and to do this the better, let us once more repeat whatever we noticed when we looked at them last.

Here the before-mentioned situation of the cubes is to be repeated.)

Moth. In their former position each pair of cubes formed a rectangle; is this the case still?

Child. No; the first pair on the right, which before formed a rectangle, is now disunited. Of the second pair, one cube has been moved a little to the right, and forms no longer a rectangle with the other. Of the third pair, one also has been placed to the right, and at some distance from its fellow. The fourth no longer forms a pair, for one is wanting. The cubes of the fifth and sixth pairs are still close together, but not parallel, and for that reason can no longer form rectangles. The seventh and eighth pair are so situated as to form a square.

Moth. In the former figure the rectangles were placed at equal distances; is this the case now?

Child. No! the seventh and eighth rectangle are moved close together; the remaining six no longer exist.

Moth. In the former figure the long sides of the rectangles were parallel; how are they

now?

Child. Now the long sides of the seventh and eighth rectangle only are parallel.

Moth. Right! Let us, before we proceed, recapitulate what we have hitherto noticed. (The mother now repeats with the children all the changes she has contrived, in the same order in which they have found them out.)

This occupation of the children may be considered as one of the most useful and developing in domestic education; but it cannot be too frequently pressed upon the attention of mothers, that whatever may be the exercise, it should be step by step, and hurry is to be avoided on their part, as well as carefully guarded against on the part of the child-and that one of the most important of the children's daily duties is to teach their young companions, with patience and cheerfulness, what they themselves have acquired : let them constantly keep in remembrance, by hourly practice, that they are learning, in order to communicate.

It is a principal character of Pestalozzi's method, not to admit of any, not even of the smallest omission; but to set out from the first point of knowledge, and to lead the pupil insensibly to the highest possible degree of proficiency.

If the mother be aware that the child can

not perform any exercise with accuracy and firmness, she should not proceed.

It is only the full conviction of the child's being perfect master of the preceding step, that should determine the teacher to lead him on to the next.

The same exercises which have been given with material objects, may afterwards be given without them. Thus, the mother seeing that the child, with the aid of real objects, has so far advanced as to know that 8 times 1 are 4 times 2, and 4 times 2, 8 times 1, may propose, without the aid of them, questions similar to those which follow:

Moth. 3 times 2 and the half of 2, how many times 1 ?

Child. 3 times 2 and the half of 2 are 7 times 1.

Moth. Why?

Child. 3 times 2 are 6 times 1-the half of 2 is 1, 6 times 1 and once 1 are 7 times 1.

Moth. 5 times 1, how many times 2?

. Child. 5 times 1 are twice 2 and the half of 2.

Moth. Why?