(-annus-) or complete year, bear in them all the traces of a high antiquity.  Later, but still at a period very early and undoubtedly previous to the operation of Greek influences, the duodecimal system (as we have already stated) was developed in Italy, and, as it derived its very origin from the observation of the fact that the solar period was equal to twelve lunar periods, it was certainly applied in the first instance to the reckoning of time.  This view accords with the fact that the individual names of the months—­which can only have originated after the month was viewed as part of a solar year—­particularly those of March and of May, were similar among the different branches of the Italian stock, while there was no similarity between the Italian names and the Greek.  It is not improbable therefore that the problem of laying down a practical calendar which should correspond at once to the moon and the sun—­a problem which may be compared in some sense to the quadrature of the circle, and the solution of which was only recognized as impossible and abandoned after the lapse of many centuries—­had already employed the minds of men in Italy before the epoch at which their contact with the Greeks began; these purely national attempts to solve it, however, have passed into oblivion.

The Oldest Italo-Greek Calendar

What we know of the oldest calendar of Rome and of some other Latin cities—­as to the Sabellian and Etruscan measurement of time we have no traditional information—­is decidedly based on the oldest Greek arrangement of the year, which was intended to answer both to the phases of the moon and to the seasons of the solar year, constructed on the assumption of a lunar period of 29 1/2 days and a solar period of 12 1/2 lunar months or 368 3/4 days, and on the regular alternation of a full month or month of thirty days with a hollow month or month of twenty-nine days and of a year of twelve with a year of thirteen months, but at the same time maintained in some sort of harmony with the actual celestial phenomena by arbitrary curtailments and intercalations.  It is possible that this Greek arrangement of the year in the first instance came into use among the Latins without undergoing any alteration; but the oldest form of the Roman year which can be historically recognized varied from its model, not indeed in the cyclical result nor yet in the alternation of years of twelve with years of thirteen months, but materially in the designation and in the measuring off of the individual months.  The Roman year began with the beginning of spring; the first month in it and the only one which bears the name of a god, was named from Mars (-Martius-), the three following from sprouting (-aprilis-) growing (-maius-), and thriving (-iunius-), the fifth onward to the tenth from their ordinal numbers (-quinctilis-, -sextilis-, -september-, -october-, -november-, -december), the eleventh from commencing (-ianuarius-),(8) with