pointing upwards, the hand represents the units
of each of those classes. Held horizontally,
with the palm outwards, it represents the tens
of each of those classes. Horizontally, with the
palm inwards, it represents the hundreds of
those same classes. Held vertically, with the
tips of the fingers downwards, it represents the
classes themselves.

The fingers represent: first, the quantity of
units, of tens, of hundreds contained in the
different classes; secondly, the classes themselves.

Thus, according to the position of the hand:
one finger represents one, ten, a hundred, or the
class of units properly so called; two fingers
represent two, twenty, two hundred, or the
class of thousands; three fingers represent
three, thirty, three hundred, or the class of
millions; four fingers represent four, forty, four
hundred, or the class of billions. The thumb
alone represents five, fifty, five hundred, or the
class of trillions; the thumb and one finger
represent six, sixty, six hundred, or the class of
quatrillions; the thumb and two fingers represent
seven, seventy, seven hundred, or the class
of quintillions; the thumb and four fingers
represent nine, ninety, nine hundred, or the
class of septillions.

For fractions, the numerator is represented in
the same manner as a whole number. The
denominator is also represented like a whole
number, but with the forefinger of one hand
placed across the fingers of the other, as a sign
of division. To represent a denominator which
requires two positions of the hand—for instance,
ten–thousandth's, one–hundred–millionth's—the
forefinger, the sign of division, will remain
applied to the fingers of the other hand during
its passage from the position which represents
the tens or the hundreds to the position which
represents the thousands or the millions. The
cipher or nought—the figure whose only use
in written numeration is to occupy the place
of the orders or classes which are absent in a
number—is represented by the little finger. The
little finger, therefore, indicates the missing
classes or orders of a number, which, moreover,
are clearly enough denoted to be wanting by
the omission of the positions of the hand which
designate those classes or those orders.

The fundamental operations of arithmetic may
be indicated as follows: the two hands held
vertically one beside the other, denote that the
numbers represented by the fingers of the two
hands are to be added together. The two hands
placed vertically one above the other, denote
that the number represented by the fingers of
the lower hand is to be subtracted from the
number represented by the fingers of the upper
hand. The two hands, crosswise, indicate the
multiplication of the two respective numbers.
The two hands placed one above the other, the
upper one vertically, the lower one horizontally,
indicate that the upper number is to be divided
by the lower one.

In these different exercises, the fingers, whatever
be the position of the hands, only indicate
simple units. The results of the operation
proposed to the pupils ought to be announced by
them by voice and gesture, or by gesture alone,
if the teacher desires the exercise to be
performed in silence. When the number which is
the answer to the question is composed of tens
and units, the right hand denotes the tens,
whilst the left hand denotes the units. These
exercises allow deaf–dumbs and hearing–speakers
to be simultaneously taught to reckon.

With all this, moral education is combined,
by making use of the innate emulation which
urges us day by day to behave better towards
those who form part of the family circle, small
or great, to which we belong. The directress
of an infant school in Paris has tried the experiment
with success. She selects from amongst
her pupils those who have most distinguished
themselves during the past month, by their
good conduct, their docility, their kindness to
their schoolfellows, and their efforts to prevent
them from doing wrong. Of these picked
pupils, under the title of Elder Brothers, she
makes the chiefs of little groups or bands, each
of which, as far as possible, is composed of
children belonging to the same neighbourhood.
She makes all the members of the same group
or family solidaire; that is, the good or bad
marks given to each individual are set down
to the account of the whole. At the end of
every month, a Tablet of Honour is drawn up,
on which the families are inscribed according to
their order of merit. Beneath the name of
each family are inscribed the names of the
children composing it, with their contingent of
good or bad marks.

To remind the children of the respect and
gratitude which they owe to persons devoted to
their education and welfare, the directress
names her families after the names of their
friends and benefactors: Saint Vincent de Paul,
the founder of Foundling Hospitals; Obeirln,
Madame Mallet, and other founders of the first
Infant Schools; Frœbel, the founder of
Children's Gardens; Péreire, the first teacher of
Deaf–Dumbs in France; and so on.

CAIROLA.

STANZAS BY A VENETIAN EXILE TO A PICTURE OF HIS
BIRTHPLACE, SENT HIM IN APRIL, 1866.

I.

I SEE the Brenta and its level shore,
The budding elms, the grey old sycamore;
The house, with all its windows opened wide,
Looks down with laughing eyes upon the tide,
The slow calm tide, which lapses smooth along,
And murmurs soft its low perpetual song
                                                            To Cairolà.

II.

O song, that came and came to heart and brain,
Through all those exiled years of dreary pain;
How oft amid the battle's charge I heard
Its echoes as an old familiar word,
And through the clarion's voice its whisper broke,
And 'mid the dying and the dead it spoke
                                                          Of Cairolà!