It is thus we have our bissextile year, from the fact that the inequality amounts to nearly a quarter of a day, so that in four years we have a whole day’s gain; but not exactly, because a fraction still remains to be accounted for. Now, if we should suppress the one day of leap-year once at the end of each three out of four centuries, the civil would be within a very small fraction equal to the solar year, as given by observation; this small fraction would be almost entirely eliminated, provided we suppressed the bissextile at the end of every four thousand years. Were this fraction neglected, the beginning of the new civil year would precede the tropical by just that much, so that in the course of 1507 years the whole day’s difference would obtain. The Egyptian year was dated from the heliacal rising of the star Sirius; it contained only 365 days. By easy computation it can be shown that in every 1461 years a whole year was lost; this cycle was called the Sothaic period, in which the heliacal rising of Sirius passed through the whole year and took place again on the same day. The commencement of that cycle took place 1322 years before Christ. The year by the Roman calendar was dated by Julius Cæsar the 1st of January, that being the day of the new moon immediately following the winter solstice in the 707th year of Rome. Christ’s nativity is dated on the 25th of December, in Cæsar’s 45th year, and the 46th year of the Julian calendar is assumed to be the 1st year of our era. The preceding year is designated by chronologists the 1st year before Christ, the dates thence running backward the same as they run forward subsequent to that period. Astronomically, that year is registered 0; the astronomical year begins at noon on the 31st of December, and the date of any observation expresses the number of days and hours which have actually elapsed since that time, the 31st of December--Year 0. The year is divided into months by old and almost universal consent, but the period of seven days is by far the most permanent division of a rotation of the earth around the sun. It was the division long before the historic period. The Brahmins in India used it with the same denominations as at the present day the Jews, Arabs, Egyptians, and Assyrians. “It has survived the fall of empires, and has existed among all successive generations, a proof of their common origin.” Nothing can be more interesting in the study of astronomy than its chronological value. La Place says: “Whole nations have been swept from the earth, with their languages, arts, and sciences, leaving but confused masses of ruins to mark the place where mighty cities stood; their history, with but the exception of a few doubtful traditions, has perished; but the perfection of their astronomical observations marks their high antiquity, fixes the periods of their existence, and proves that even at that early time they must have made considerable progress in science.”