This object could only be attained by inventing a board to slide in and hide the greater number from their view, and so far we succeeded in gaining their undivided attention to the balls we thought necessary to move out.

Time and experience only could shew that there was another thing wanting, and that was a tablet, as represented in the second woodcut, which had a tendency to teach the children the difference between real numbers and representative characters, therefore the necessity of brass figures, as represented on the tablet; hence the children would call figure seven No.

1, it being but one object, and each figure they would only count as one, thus making 937, which are the representative characters, only three, which is the real fact, there being only three objects.

It was therefore found necessary to teach the children that the figure seven would represent 7 ones, 7 tens, 7 hundreds, 7 thousands, or 7 millions, according to where it might be placed in connection with the other figures; and as this has already been described, I feel it unnecessary to enlarge upon the subject.
[Illustration] THE ARITHMETICON.
It will be seen that on the twelve parallel wires there are 144 balls, alternately black and white.

By these the elements of arithmetic may be taught as follows:-- _Numeration_ .-- Take one ball from the lowest wire, and say units, _one_, two from the next, and say tens, _two_; three from the third, and say hundreds, _three_; four from the fourth, and say thousands, _four_; five from the fifth, and say tens of thousands, _five_; six from the sixth, and say hundreds of thousands, _six_; seven from the seventh, and say millions, _seven_; eight from the eighth, and say tens of millions, _eight_; nine from the ninth, and say hundreds of millions, _nine_; ten from the tenth, and say thousands of millions, _ten_; eleven from the eleventh, and say tens of thousands of millions, _eleven_; twelve from the twelfth, and say hundreds of thousands of millions, _twelve_.
The tablet beneath the balls has six spaces for the insertion of brass letters and figures, a box of which accompanies the frame.