pected, is at least older than the separation of the Greeks and Latins.
Decimal system. The most distinct 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 (P. 18). In the case of Italy the decimal system pervaded all the earliest arrangements: it may be sufficient to mention the occurrence of the number ten so commonly in the case of witnesses, securities, ambassadors, 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 prænomen 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 Λ, X, manifestly imitations of the outstretched finger, and the open hand single and double—which have not been derived either from the Hellenes or the Phœnicians, but are common to the Romans, Sabellians, and Etruscans. They are 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 (P. 203). 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 vorsus, the Sabellian measure of surface of 100 square feet (P. 22), and the Roman year of ten months.
The duodecimal system. In the case of other Italian measures, which were not connected with Greek standards and were probably developed by the Italians before they came in contact with the Greeks, there prevailed universally the partition of the "whole" (as) into twelve "units" (unciæ). The earliest Latin priesthoods, the colleges of the Salii and Arvales (P. 175), as well as the leagues of the Etruscan cities, were organized on the basis of the number twelve. The same