probably adopted from the Greeks of Southern Italy[5], that odd numbers were of good omen, even numbers of ill omen. This principle, as we shall see, holds good throughout the Roman calendar. But this reckoning of the year, if it ever existed at all, could not have lasted long as it stood. As we know it in historical times, it has become modified by applying to it the principle of the solar year. The reason for this should be noted carefully. A lunar year, being about 11 days short of the solar year, would in a very short time become out of harmony with the seasons. Now if there is one thing certain about the Roman religious calendar, it is that many at least of its oldest festivals mark those operations of husbandry on which the population depended for its subsistence, and for the prosperous result of which divine agencies must be propitiated. These festivals, when fixed in the calendar, must of course occur at the right seasons, which could not be the case if the calendar were that of a purely lunar year. It was therefore necessary to work in the solar principle; and this was done[6] by a somewhat rude expedient, not unlike that of the Athenian Octaeteris, and probably derived from it[7]. A cycle of 4 years was devised, of which the first had the 355 days of the lunar year, the second 355 + 22, the third 355 again, and the fourth 355 + 23. The extra periods of 22 and 23 days were inserted in February, not at the end, but after the 23rd (_Terminalia_)[8]. The total number of days in the cycle was 1465, or about 1 day too much in each year; and in course of time even this system got out of harmony with the seasons and had to be rectified from time to time by the Pontifices, who had charge of the calendar. Owing to ignorance on their part, misuse or neglect of intercalation had put the whole system out of gear before the last century of the Republic. All relation to sun and moon was lost; the calendar, as Mommsen says, ‘went on its own way tolerably unconcerned about moon and sun.’ When Caesar took the reform of the calendar in hand the discrepancy between it and the seasons was very serious; the former being in advance of the latter probably by some weeks. Caesar, aided by the mathematician Sosigenes, put an end to this confusion by extending the year 46 B.C. to 445 days, and starting afresh on Jan. 1, 45 B.C.[9]—a day henceforward to be that of the new year—with a cycle of 4 years of 365 days[10]; in the last of which a single day was added, after the _Terminalia_. This cycle produced a true solar year with a slight adjustment at short intervals; and after a few preliminary blunders on the part of the Pontifices, lasted without change until A.D. 1582, when Pope Gregory XIII set right a slight discrepancy by a fresh regulation. This regulation was only adopted in England in 1752, and is still rejected in Russia and by the Greek Church generally. II. Order of Months in the Year.