The third great natural division of time is the year, and, like the day and the month, it is defined by the relative apparent movements of the heavenly bodies. As the Rabbi Aben Ezra pointed out, _shanah_, the ordinary Hebrew word used for year, expresses the idea of _annus_ or _annulus_, a closed ring, and therefore implies that the year is a complete solar one. A year, that is purely lunar, consists of twelve lunations, amounting to 354 days. Such is the year that the Mohammedans use; and since it falls short of a solar year of 365 days by 10 or 11 days, its beginning moves backwards rather rapidly through the seasons. The Jews used actual lunations for their months, but their year was one depending on the position of the sun, and their calendar was therefore a luni-solar one. But lunations cannot be made to fit in exactly into a solar year--12 lunations are some 11 days short of one year; 37 lunations are 2 or 3 days too long for three years--but an approximation can be made by giving an extra month to every third year; or more nearly still by taking 7 years in every 19 as years of 13 months each. This thirteenth month is called an intercalary month, and in the present Jewish calendar it is the month Adar which is reduplicated under the name of Ve-Adar. But, though from the necessity of the case, this intercalation, from time to time, of a thirteenth month must have been made regularly from the first institution of the feast of unleavened bread, we find no allusion, direct or indirect, in the Hebrew Scriptures to any such custom. Amongst the Babylonians a year and a month were termed "full" when they contained 13 months and 30 days respectively, and "normal" or "incomplete" when they contained but 12 months or 29 days. The succession of full and normal years recurred in the same order, at intervals of nineteen years. For 19 years contain 6939 days 14-1/2 hours; and 235 months, 6939 days 16-1/2 hours; the two therefore differing only by about a couple of hours. The discovery of this cycle is attributed to Meton, about 433 B.C., and it is therefore known as the Metonic cycle. It supplies the "Golden Numbers" of the introduction to the Book of Common Prayer. There are two kinds of solar years, with which we may have to do in a luni-solar calendar--the tropical or equinoctial year, and the sidereal year. The tropical year is the interval from one season till the return of that season again--spring to spring, summer to summer, autumn to autumn, or winter to winter. It is defined as the time included between two successive passages of the sun through the vernal equinox, hence it is also called the equinoctial year. Its length is found to be 365 days, 5 hours, 49 minutes, and some ancient astronomers derived its length as closely as 365 days, 6 hours, by observing the dates when the sun set at exactly the opposite part of the horizon to that where it rose.