By M. L. BARRE.
THE natural unities for the measurement of time are three, and are afforded by the rotation of the earth upon its axis, the revolution of the moon around the earth, and the revolution of the earth around the sun; of which the mean values respectively are 24 hours; 29 days, 12 hours, 44 minutes, 2*9 seconds; and 365·2422 days. These numbers are incommensurable and wholly independent of one another. But men have tried to connect them from the most remote ages, and have devised the lunar-solar year, the duration of which is related to the movements of the sun and the moon. Although this system may appear complicated, it is in reality quite simple, for the sun and moon spare man the trouble of calculating the days, while the years and months write themselves in large characters in the appearance of the sky and of vegetation.
The lunar-solar year thus having its origin in Nature, is found in the most ancient form of the Jewish calendar. The Israelite year was so regulated that the feast of the Passover was celebrated on the fourteenth day of the first month, when the barley to be offered in sacrifice was ripe at the full moon. This marked the first month of the year, named Nisan, and served as the point of departure for the twelve usual months. But, if the ripening of the barley did not occur during the fortnight following the end of the year, another month was intercalated, and the new year began with the next new moon. If we desire an exact and rigorous measure, this form of year is simply confusing. The Jews have years of twelve lunar months, of twenty-nine or thirty days, to which is added a thirteenth month, when the year is embolismic; and they might contain 353, 354, 355, 383, 384, or 385 days. The Jewish calendar also included a period of nineteen solar years, or a lunar cycle of 235 months. The years date from the creation of the world, which is fixed by the Jews at October 7th, b. c. 3761.
The Chinese month begins with the new moon; the first month when the sun enters Pisces, the second when it enters Aries, etc. But if the sun does not enter a new sign of the zodiac with the new month, an additional month is introduced, which is given the same name as the preceding one, with a distinctive sign. The months are of twenty-nine and thirty days, but there is no absolute rule for their succession, nor for the place of the supplementary month, nor for the intercalation of complementary years; and, as the beginnings of the months and the years are calculated from the movements of the celestial bodies, the whole year is uncertain and changeable. In the difficulty of ascertaining from what tables the ancient Chinese calculated their astronomical elements, there would be great uncertainty in com-