, 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. Suppose
then the only figure inserted is the 7 in the second space from the
top: now were the children asked what it was, they would all say,
without instruction, "It is one." If, however, you tell them that an
object of such a form stands instead of seven ones, and place seven
balls together on a wire, they will at once see the use and power of
the number. Place a 3 next the seven, merely ask what it is, and they
will reply, "We don't know;" but if you put out three balls on a wire,
they will say instantly, "O it is three ones, or three;" and that they
may have the proper name they may be told that they have before
them _figure 7_ and _figure 3_. Put a 9 to these figures, and their
attention will be arrested: say, Do you think you can tell me what
this is? and, while you