availed himself of the Greek alphabet, when it reached him, to form ciphers for 50 and 1000, perhaps also for 100, out of the signs for the three aspirated letters which he had no use for.  In Etruria the sign for 100 at least appears to have been obtained in a similar way.  Afterwards, as usually happens, the systems of notation among the two neighbouring nations became assimilated by the adoption in substance of the Roman system in Etruria.

The Italian Calendar before the Period of Greek Influence in Italy

In like manner the Roman calendar—­and probably that of the Italians generally—­began with an independent development of its own, but subsequently came under the influence of the Greeks.  In the division of time the returns of sunrise and sunset, and of the new and full moon, most directly arrest the attention of man; and accordingly the day and the month, determined not by cyclic calculation but by direct observation, were long the exclusive measures of time.  Down to a late age sunrise and sunset were proclaimed in the Roman market-place by the public crier, and in like manner it may be presumed that in earlier times, at each of the four phases of the moon, the number of days that would elapse from that phase until the next was proclaimed by the priests.  The mode of reckoning therefore in Latium—­and the like mode, it may be presumed, was in use not merely among the Sabellians, but also among the Etruscans—­was by days, which, as already mentioned, were counted not forward from the phase that had last occurred, but backward from that which was next expected; by lunar weeks, which varied in length between 7 and 8 days, the average length being 7 3/8; and by lunar months which in like manner were sometimes of 29, sometimes of 30 days, the average duration of the synodical month being 29 days 12 hours 44 minutes.  For some time the day continued to be among the Italians the smallest, and the month the largest, division of time.  It was not until afterwards that they began to distribute day and night respectively into four portions, and it was much later still when they began to employ the division into hours; which explains why even stocks otherwise closely related differed in their mode of fixing the commencement of day, the Romans placing it at midnight, the Sabellians and the Etruscans at noon.  No calendar of the year had, at least when the Greeks separated from the Italians, as yet been organized, for the names for the year and its divisions in the two languages have been formed quite independently of each other.  Nevertheless the Italians appear to have already in the pre-Hellenic period advanced, if not to the arrangement of a fixed calendar, at any rate to the institution of two larger units of time.  The simplifying of the reckoning according to lunar months by the application of the decimal system, which was usual among the Romans, and the designation of a term of ten months as a “ring”