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28th or 29th day of the month.

The Athenians in the days of Solon, five hundred years later than this, adopted months alternately twenty-nine and thirty days in length, which gives a result very nearly correct.

The Jews after the Dispersion adopted the system of thus alternating the lengths of their months, and with some slight modifications it holds good to the present day. As will be shown in the following chapter, the ordinary years are of twelve months, but seven years in every nineteen are "embolismic," having an extra month. The names employed are those learned during the Babylonian captivity, and the year begins with the month Tishri, corresponding to September-October of our calendar. The lengths of most of the months are fixed as given in the following table, but any adjustment necessary can be effected either by adding one day to Heshvan, which has usually twenty-nine days, or taking away one day from Kislev, which has usually thirty—

  Ordinary Year Embolismic Year   Days Days Tishri 30   30   Heshvan 29 + 29 + Kislev 30 - 30 - Tebeth 29   29   Shebat 30   30   Adar 29   30   Ve-adar ... 29   Nisan 30   30   Yiar 29   29   Sivan 30   30   Tamuz 29   29   Ab 30   30   Elul 29   29  

The Jewish month, therefore, continues to be essentially a true lunar one, though the exact definition of each month is, to some extent, conventional, and the words of the Son of Sirach still apply to the Hebrew calendar—

"The moon also is in all things for her season,
For a declaration of times, and a sign of the world.
From the moon is the sign of the feast day;
A light that waneth when she is come to the full."

For so God—

"Appointed the moon for seasons."

CHAPTER IV THE YEAR

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.

The sidereal year is the time occupied by the sun in apparently completing the circuit of the heavens from a given star to the same star again. The length of the sidereal year is 365 days, 6 hours, 9 minutes. In some cases the ancients took the sidereal year from the "heliacal" risings or settings of stars, that is from the interval between the time when a bright star was first seen in the morning just before the sun rose, until it was first so seen again; or last seen just after the sun set in the evening, until it was last so seen again.

But to connect the spring new moon with the day when the sun has returned to the equinox is a more difficult and complicated matter. The early Hebrews would seem to have solved the problem practically, by simply watching the progress of the growing grain. If at one new moon in spring time it appeared clear that some of the barley would be ready in a fortnight for the offering of the green ears at the feast of unleavened bread, then that was taken as beginning the new year. If it appeared doubtful if it would be ready, or certain that it would not be, then the next new moon was waited for. This method was sufficient in primitive times, and so long as the nation of Israel remained in its own land. In the long run, it gave an accurate value for the mean tropical year, and avoided all the astronomical difficulties of the question. It shows the early Hebrews as practical men, for the solution adopted was easy, simple and efficient. This practical method of determining the beginning of the year amongst the early Hebrews, does not appear to have been the one in use amongst the Babylonians either early or late in their history. The early Babylonians used a sidereal year, as will be shown shortly. The later Babylonians used a tropical year dependent on the actual observation of the spring equinox.

To those who have no clocks, no telescopes, no sundials, no instruments of any kind, there are two natural epochs at which the day might begin; at sunrise, the beginning of daylight; and at sunset, the beginning of darkness. Similarly, to all nations which use the tropical year, whether their calendar is dependent on the sun alone, or on both sun and moon, there are two natural epochs at which the year may begin; at the spring equinox, the beginning of the bright half of the year, when the sun is high in the heavens, and all nature is reviving under its heat and light; and at the autumn equinox, the beginning of the dark half of the year, when the sun is low in the heavens, and all nature seems dying. As a nation becomes more highly equipped, both in the means of observing, and in knowledge, it may not retain either of these epochs as the actual beginning of its year, but the determination of the year still rests directly or indirectly upon the observation of the equinoxes.

At the exodus from Egypt, in the month Abib, the children of Israel were commanded in these words—

"This month shall be unto you the beginning of months: it shall be the first month of the year to you."

This command may have abolished and reversed the previously existing calendar, or it may have related solely to the ecclesiastical calendar, and the civil calendar may have been still retained with a different epoch of commencement.

An inquiry into the question as to whether there is evidence in Scripture of the use of a double calendar, shows that in every case that the Passover is mentioned it is as being kept in the first month, except when Hezekiah availed himself of the regulation which permitted its being kept in the second month. Since the Passover was a spring feast, this links the beginning of the year to the spring time. Similarly the feast of Tabernacles, which is an autumn festival, is always mentioned as being held in the seventh month.

These feasts would naturally be referred to the ecclesiastical calendar. But the slight evidences given in the civil history point the same way. Thus some men joined David at Ziklag during the time of his persecution by Saul, "in the first month." This was spring time, for it is added that Jordan had overflowed all its banks. Similarly, the ninth month fell in the winter: for it was as he "sat in the winter-house in the ninth month, and there was a fire on the hearth burning before him" that king Jehoiakim took the prophecy of Jeremiah and "cut it with the penknife, and cast it into the fire that was on the hearth." The same ninth month is also mentioned in the Book of Ezra as a winter month, a time of great rain.

The same result is given by the instances in which a Babylonian month name is interpreted by its corresponding Jewish month number. In each case the Jewish year is reckoned as beginning with Nisan, the month of the spring equinox.

In one case, however, two Babylonian month names do present a difficulty.

In the Book of Nehemiah, in the first chapter, the writer says—

"It came to pass in the month Chisleu, in the twentieth year, as I was in Shushan the palace, that Hanani, one of my brethren, came"—

and told him concerning the sad state of Jerusalem. In consequence of this he subsequently approached the king on the subject "in the month Nisan, in the twentieth year of Artaxerxes the king."

If the twentieth year of king Artaxerxes began in the spring, Nisan, which is a spring month, could not follow Chisleu, which is a month of late autumn. But Artaxerxes may have dated his accession, and therefore his regnal years, from some month between Nisan and Chisleu; or the civil year may have been reckoned at the court of Shushan as beginning with Tishri. It may be noted that Nehemiah does not define either of these months in terms of the Jewish. Elsewhere, when referring to the Jewish Feast of Tabernacles, he attributes it to the seventh month, in accord with its place in the Mosaic calendar. An alteration of the beginning of the year from the spring to the autumn was brought about amongst the Jews at a later date, and was systematized in the Religious Calendar by the Rabbis of about the fourth century a.d. Tishri begins the Jewish year at the present day; the first day of Tishri being taken as the anniversary of the creation of the world.

The Mishna, "The Law of the Lip," was first committed to writing in 191 a.d., and the compilation of the Babylonian Talmud, based on the Mishna, was completed about 500 a.d. In

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