The most obvious bases presented by nature for this purpose are, in reference to time, the periodic returns of the sun and moon, or the day and the month; in reference to space, the length of the human foot, which is more easily applied in measuring than the arm; in reference to gravity, the burden which a man is able to poise (-librare-) on his hand while he holds his arm stretched out, or the "weight" (-libra-). As a basis for the notion of a whole made up of equal parts, nothing so readily suggests itself as the hand with its five, or the hands with their ten, fingers; upon this rests the decimal system. We have already observed that these elements of all numeration and measuring reach back not merely beyond the separation of the Greek and Latin stocks, but even to the most remote primeval times. The antiquity in particular of the measurement of time by the moon is demonstrated by language;(1) even the mode of reckoning the days that elapse between the several phases of the moon, not forward from the phase on which it had entered last, but backward from that which was next to be expected, is at least older than the separation of the Greeks and Latins.

Decimal System

The most definite evidence of the antiquity and original exclusive use of the decimal system among the Indo-Germans is furnished by the well-known agreement of all Indo-Germanic languages in respect to the numerals as far as a hundred inclusive.(2) In the case of Italy the decimal system pervaded all the earliest arrangements: it may be sufficient to recall the number ten so usual in the case of witnesses, securities, envoys, and magistrates, the legal equivalence of one ox and ten sheep, the partition of the canton into ten curies and the pervading application generally of the decurial system, the -limitatio-, the tenth in offerings and in agriculture, 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 double hand of ten fingers did the solar cycle of nearly twelve lunar periods first suggest to man the profound conception of an unit composed of equal units, and thereby originate the idea of a system of numbers, the first step towards mathematical thought. The consistent duodecimal development of this idea appears to have belonged to the Italian nation, and to have preceded the first contact with the Greeks.

Hellenic Measures In Italy

But when at length the Hellenic trader had opened up the route to the west coast of Italy, the measures of surface remained unaffected, but the measures of length, of weight, and above all of capacity--in other words those definite standards without which barter and traffic are impossible--experienced the effects of the new international intercourse. The oldest Roman foot has disappeared; that which we know, and which was in use at a very early period among the Romans, was borrowed from Greece, and was, in addition to its new Roman subdivision into twelfths, divided after the Greek fashion into four hand-breadths (-palmus-) and sixteen finger-breadths (-digitus-). Further, the Roman weights were brought into a fixed proportional relation to the Attic system, which prevailed throughout Sicily but not in Cumae--another significant proof that the Latin traffic was chiefly directed to the island; four Roman pounds were assumed as equal to three Attic -minae-, or rather the Roman pound was assumed as equal to one and a half of the Sicilian -litrae- or half-minae.(7) But the most singular and chequered aspect is presented by the Roman measures of capacity, as regards both their names and their proportions. Their names have come from the Greek terms either by corruption (-amphora-, -modius- after --medimnos--, -congius- from --choeus--, -hemina-, -cyathus-) or by translation (-acetabulum-from --ozubaphon--); while conversely --zesteis-- is a corruption of -sextarius-.