decimation,
and the praenomen -Decimus-. Among the applications of this most
ancient decimal system in the sphere of measuring and of writing,
the remarkable Italian ciphers claim a primary place. When the Greeks
and Italians separated, there were still evidently no conventional
signs of number. On the other hand we find the three oldest and
most indispensable numerals, one, five, and ten, represented by
three signs--I, V or /\, X, manifestly imitations of the outstretched
finger, and the open hand single and double--which were not derived
either from the Hellenes or the Phoenicians, but were common to
the Romans, Sabellians, and Etruscans. They were the first steps
towards the formation of a national Italian writing, and at the same
time evidences of the liveliness of that earlier inland intercourse
among the Italians which preceded their transmarine commerce.(3)
Which of the Italian stocks invented, and which of them borrowed,
these signs, can of course no longer be ascertained. Other traces
of the pure decimal system occur but sparingly in this field;
among them are the -versus-, the Sabellian measure of surface of
100 square feet,(4) and the Roman year of 10 months.

The Duodecimal System

Otherwise generally in the case of those Italian measures, which
were not connected with Greek standards and were probably developed
by the Italians before they came into contact with the Greeks, there
prevailed the partition of the "whole" (-as-) into twelve "units"
(-unciae-). The very earliest Latin priesthoods, the colleges of
the Salii and Arvales,(5) as well as the leagues of the Etruscan
cities, were organized on the basis of the number twelve. The
same number predominated in the Roman system of weights and in the
measures of length, where the pound (-libra-) and the foot (-pes-)
were usually subdivided into twelve parts; the unit of the Roman
measures of surface was the "driving" (-actus-) of 120 square feet,
a combination of the decimal and duodecimal systems.(6) Similar
arrangements as to the measures of capacity may have passed into
oblivion.

If we inquire into the basis of the duodecimal system and consider
how it can have happened that, in addition to ten, twelve should
have been so early and universally singled out from the equal series
of numbers, we shall probably be able to find no other source to
which it can be referred than a comparison of the solar and lunar
periods. Still more than the doub