then
put the brass figure 9 on the tablet beneath, and they will see how
the amount is marked: then take eight balls and three, when they will
see that eight and three are eleven. Explain to them that they cannot
put underneath two figure ones which mean 11, but they must put 1
under the 8, and carry 1 to the 4, when you must place one ball under
the four, and, asking them what that makes, they will say, Five.
Proceed by saying, How much are five and nine? put out the proper
number of balls, and they will say, Five and nine are fourteen. Put
a four underneath, and tell them, as there is no figure to put the 1
under, it must be placed next to it: hence they see that 937 added to
482, make a total of 1419.

_Subtraction_ may be taught in as many ways by this instrument. Thus:
take 1 from 1, nothing remains; moving the first ball at the same time
to the other end of the frame. Then remove one from the second wire,
and say, take one from 2, the children will instantly perceive that
only 1 remains; then 1 from 3, and 2 remain; 1 from 4, 3 remain; 1
from 5, 4 remain; 1 from 6, 5 remain; 1 from 7, 6 remain; 1 from 8, 7
remain; 1 from 9, 8 remain; 1 from 10, 9 remain; 1 from 11, 10 remain;
1 from 12, 11 remain.

Then the balls may be worked backwards, beginning at the wire
containing 12 balls, saying, take 2 from 12, 10 remain; 2 from 11, 9
remain; 2 from 10, 8 remain; 2 from 9, 7 remain; 2 from 8, 6 remain; 2
from 7, 5 remain; 2 from 6, 4 remain; 2 from 5, 3 remain; 2 from 4, 2
remain; 2 from 3, 1 remains.

The brass figure should be used for the remainder in each case. Say,
then, can you take 8 from 3 as you point to the figures, and they will
say "Yes;" but skew them 3 balls on a wire and ask them to deduct 8
from them, when they will perceive their error. Explain that in such a
case they must _borrow_ one; then say take 8 from 13, placing 12 balls
on the top wire, borrow one from the second, and take away eight and
they will see the remainder is five; and so on through the sum, and
others of the same kind.

In _Multiplication_, the lessons are performed as follows. The teacher
moves the first ball, and immediately after the two balls on the
second wire, placing them underneath the first, saying at the same
time, twice one are two, which the children will readily perceive. We
next remove the two balls on the second wire for a multiplier, and
then remove two balls from the third wire, placing them exactly under
the fir