ability to comprehend the powers of numbers, without either visible
objects or signs--is imparted as follows:

_Addition_.

One of the children is placed before the gallery, and repeats aloud,
in a kind of chaunt, the whole of the school repeating after him; One
and one are two; two and one are three; three and one are four, &c. up
to twelve.

Two and two are four; four and two are six; six and two are eight, &c.
to twenty-four.

Three and three are six; six and three are nine; nine and three are
twelve, &c. to thirty-six.

_Subtraction_.

One from twelve leaves eleven; one from eleven leaves ten, &c.

Two from twenty-four leave twenty-two; two from twenty-two leave
twenty, &c.

_Multiplication_.

Twice one are two; twice two are four, &c. &c. Three times three are
nine, three times four are twelve, &c. &c.

Twelve times two are twenty-four; eleven times two are twenty-two, &c.
&c.

Twelve times three are thirty-six; eleven times three are
thirty-three, &c. &c. until the whole of the multiplication table is
gone through.

_Division_.

There are twelve twos in twenty-four.--There are
eleven twos in twenty-two, &c. &c.
There are twelve threes in thirty-six, &c.
There are twelve fours in forty-eight, &c. &c.

_Fractions_.

Two are the half (1/2) of four.
" " " third (1/3) of six.
" " " fourth (1/2) of eight.
" " " fifth (1/5) of ten.
" " " sixth (1/6) of twelve.
" " " seventh (1/7) of fourteen.
" " " twelfth (1/12) of twenty-four; two are the
eleventh (1/11) of twenty-two, &c. &c.

Three are the half (1/2) of six.
" " " third (1/3) of nine.
" " " fourth (1/4) of twelve.

Three are the twelfth (1/12) of thirty-six; three are
the eleventh (1/11) of thirty-three, &c. &c.

Four are the half (1/2) of eight, &c.

In twenty-three are four times five, and three-fifths
(3/5) of five; in thirty-five are four times eight, and three-eighths
(3/8) of eight.

In twenty-two are seven times three, and one-third
(1/3) of three.

In thirty-four are four times eight, and one-fourth
(1/4) of eight.

The tables subjoined are repeated by the same method, each section
being a distinct lesson. To give an idea to the reader, the boy in the
rostrum says ten shillings the half (1/2) of a pound; six shillings
and eightpence one-third (1/3) of a pound, &c.

Sixpence the half (1/2) of a shilling, &c. Always reme