simple effort in the earlier rules of arithmetic. He may place, beneath each other, any number of balls which his fancy may suggest, which he may assist the children to add together; or he may vary the rule, by a different position of the balls.

I may be permitted here to mention some of the other uses, not immediately connected with the subject now before us, to which this instrument may be put: as, in order to excite the failing attention of the little pupils, it is always desirable to have the power of introducing a change from one subject to another in the course of the instruction.

It is proposed, then, that the several rows of balls should be painted, so as to afford an opportunity for introducing the older children to some incipient knowledge of the combinations of colours. The three higher rows may be red, yellow, and blue. The fourth may be purple, and the fifth again red; because a mixture of red and blue makes purple. The sixth and seventh may be light brown and yellow, because red and yellow form a light brown. The eighth and ninth may be green and blue; as green is a mixture of yellow and blue. The last three rows may, on the same principle, be white, grey, and black.

It will farther commend itself to the reader,

that it is possible, by varying the position of balls, to represent to the children any of the rectilinear geometrical figures; the forms and names of which may offer occasionally a useful lesson. The ingenuity of the teacher will suggest to him many other uses of the Numeral Frame, besides those which have been mentioned.

To assist him in the farther progress of his school in the arithmetical art, another frame, of a very simple construction, may be made, the representation of which is offered to the reader on the other side.

This frame consists of a large board, divided into a sufficient number of compartments (a). The divisions of these compartments are so formed as to receive within themselves and retain small squares of wood (b), of which the numbers should be equal to the number of compartments: (cc) is a movable line of wood painted black. On the squares are painted the following figures,-1, 2, 3, 4, 5, 6, 7, 8, 9, 0, separately, and as many times repeated as the number of the squares may allow. The divisions should be so formed, that the squares may be placed and removed without the slightest difficulty. On this frame, it will be

evident to the reader, that the teacher may form any combinations of figures which may be necessary. His first attempt in the use of it must be, to instruct his little pupils in the forms of the figures. The names they have already attained, in the acquirement of number. He may lead them from simple number to its various combinations, and proceed to an accurate numeration of any number of figures which he is able to place in one line on the frame. The progress, from this point through the first rules of arithmetic, will be simple; and, with the previous acquirement of number, which the pupils have made, most easy and rapid. When it is proposed to do a sum, the little class is placed in either one or two lines, as convenience may suggest, before the frame. The teacher then fits slowly the several figures in their places, each of which the class must name both singly and in its combination. When the whole is formed, the class unitedly proceed through the sum. They thus correct each other's errors; and whilst comparative ignorance is not discouraged, the more advanced have less opportunity for the display of their superior attainments.

TABLES.-I may here add, that. the various useful arithmetical tables are taught from the rostrum, in the same manner as the foregoing