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.