The Jewish, Christian, and Mohammedan religions all regulate their sacred anniversaries more or less by the moon. Various nations have constructed their years on the lunar revolution, though most of them have accommodated their years to the solar year by intercalated months. Now, the time between two new moons (that is, the average time) is days, or about 294 days. If, then, months were made alternately of 29 and 30 days, 12 months would contain 354 days, and 111 days would be necessary to complete the Julian year of 3651 days. This would amount to more than a month in three years. Taking the most exact values both of the lunation and the solar year, and applying the method in Fiteerioxs, CONTINUED, it will be seen that the year contains, over and above 12 lunations, something leas than 3 lunationa in 8 years ; more exactly, something more than 4 lunations in 11 years; more exactly, something less than 7 lunations in 19 years; more exactly still, something more than 123 lunations in 334 years, less than 130 in 353, more than 253 in 687, less than 1395 in 37S8. Taking the Julian year, the above figures should be changed into less than 3 out of 3, more than 7 out of 19, less than 171 out of 464. This excess of 7 lunations in 19 years, which varies very little from the truth, whether as to the real, Julian, or even Gregorian year, is the foundation of tho celebrated Metunie cycle [METON, in Bloa. Div.], which, among the Greeks and all who have derived knowledge from them, has always been the foundation of the lunieolear calendar. It is now well under stood that the Metonic moon, amid not that of the heavens, is the referee in the settlement of religious festivals; that is to say, a moon moving uniformly at such a rate as to make 235 lunationa in 19 calendar years.
Owing to the alternate acceleration and retardation of the son's motion in its orbit, the lengths of the four astronomical seasons are different, as follows :— d. b.
From vernal equinox to summer solstice . . 92 From summer sol,tiee to autumnal equinox . . 93 131 From autumnal equinox to winter solstice . . 89 From 'winter solstice to vernal equinox . . . 89 11 We shall now state the principal facts connected with the years of the nations who are most connected with history.
The Jews, from the time of their departure from Egypt, began their year with the vernal equinox in all religious reckoning, retaining the old beginning, which was at the autumnal equinox, in all civil affairs. In both cases they reckoned from the new moon near the equinox. By making twelve months in the year, each of 29 or 30 days, with an intercalary month once in three years, they secured themselves from the necessity of any but an occasional alteration. They might have gradually allowed the beginning of the year to slide away from the vernal equinox, but this their rites prevented them from doing, since the sacrifices required the offering of various specimens of agri cultural produce, dependent upon season, at specified times of the year.
The necessity of being provided with young lambs, for instance, at the Passover, obliged them to keep this feast at one time of the solar year, and fixed it at the full moon following the vernal equinox. How they managed their calendar in the first instance, does not appear ; but as we know they once depended upon catching sight of the new moon to settle the beginning of the month, and only used 29 or 30 days when they missed their object, we must infer that they were in the habit of making corrections frequently, and at short notice ; which could be done, as remarked by the editor of the Art de v6rifier les Dates,' while they were in possession of Palestine, and within reasonable distance of each other. There is not any trace of astronomy in the old Jewish writings, nor reason to infer that they brought any knowledge of it from Egypt. But during the Captivity they acquired from the nations among whom they were thrown, either a period of 84 years or know ledge to construct one. Several of the Fathers mention this Jewish period, and state that it had long been used by them. It has the ap pearance of a CArarrns PERIOD of 76 years all but a day, with the period of eight years added, on the supposition that the making of three intercalary months in the additional eight years would have an error of a contrary kind from this contained in the Calippic period. But this is not the case; and 84 years is really not so near to an exact number of lunation as 76 years all but a day. Some of the early Christians used this period, and thereby contributed to the confusion on the subject of Easter.
The modern Jewish calendar is regulated by the cycle of 19 years, and its lunar years contain various adjustments which refer to the religious ceremonies. Their present usages date from A.D. 338, ac cording to their own account. They have also a value of the length of a lunation 29" 44". 3', which is within a tenth of a second of the truth. This has been stated as of extraordinary correctness by thoao who forget that the average month is much more easily found than the year. Hipperchns and Ptolemy had 29" 44'3A. ; reject the frac tion, as was so often done, and we have the Jewish value ; and as it happens that Ptolemy and Hipparehus had got just a little more than the fraction too much, this saving of trouble is an accidental correction.
There is no accompanying value of the sun's motion more correct than that implied in the Julian year. On the Jewish calendar, see the Art de v6rifier les Dates,' vol. ii., p. 113, the ' Jewish Calendar for 64 Years,' by E. 11. Lindo, 1838, 8vo, which goes up to A.D. 1901, and also the Hebrew work, published with a Latin translation by Sebastian Munster,' Kalendarium Hebraicurn; Basel, 1527.