, but small stones were
also used--hence the words "calculate" and "calculation," which are
derived from _calculus_, the Latin for a pebble-stone.

The Chinese counted for many years with notched sticks; and even in
England, in comparatively modern times, accounts were kept by tallies, in
which notches were cut alike in two parallel pieces of wood. Shakespeare
alludes to "the score and the tally" in his _Henry VI_; and this mode
of keeping accounts is still adopted by some of the bakers and dyers in
Warwickshire and Cheshire. And tallies are occasionally produced in the
small-debt courts, where they are admitted as authentic proofs of debt.
Hence the origin and name of the "tally court of the exchequer." The
Peruvians, at the time they were conquered by Pizarro, counted with
knotted strings.

After numerals, came picture-writing, hieroglyphics, and symbolic
characters, such are were used by the Egyptians, the Chinese, and the
Mexicans; which, however unconnected they may be with each other, are
of the same general character. Indeed, the Chinese have never advanced
beyond symbolic characters, of which it is said they have more than one
hundred thousand combinations or varieties.

Rude as these conditions of humanity may seem, they are matched in modern
England, even at a very recent date, if we may credit a well-known story:
A rustic shopkeeper in a remote district, being unable to read or write,
contrived to keep his accounts by picture-writing, and charged his
customer, the miller, with a cheese instead of a grindstone, from having
omitted to mark a hole in the centre.

After picture and symbolic writings would follow phonetic characters,
or marks for sounds; that is, the alphabet. Even the alphabet, which in
civilized countries has now existed for more than three thousand years,
was perfected by degrees; for it has been clearly ascertained that
the earliest known did not comprise more than one-half or, at most,
two-thirds of the letters which eventually formed its complement. Thus,
the Pelasgian alphabet, which is derived from the Phoenician, and is the
parent of the Greek and Roman, consisted originally of only twelve or
thirteen letters.

The invention of the alphabet, which, in a small number of elementary
characters, is capable of six hundred and twenty sextillions of
combinations, and of exhibiting to the sight the countless conceptions of
the mind which have no corporeal forms, is so wonderful that great me