days instead of five every four years; and only to make this addition the eighth time every fifth year. The years thus aug mented were called sextile, to distinguish them from the others, called common. According to this mode of intercalation, in thirty-three years, eight are sextile and twenty-five are common, This supposes the length of the 365 days greater by * 0.000202 of a day than the tropical year determined by observations; but a great number of centuries must elapse before the origin of the year would be so far removed from the equinox as to be sensible to the agriculturist. It is much to be wished that all nations would adopt one common æra, not depending on moral revolutions, but determined We by astronomical phenomena alone. might fix its origin in the year in which the apogee of the solar orbit coincided with the summer solstice, which happened about the year 1250; we should take for this origin the moment of the mean vernal equinox, which in that year answered to the 15th March,* 5h 3676 at Paris. The universal meridian, from which terrestrial longitudes should be reckoned, should he that of the place at which it was midnight at that instant, and which is to the east of Paris 185°2960. If after a long succession of ages, the origin of the æra should become uncertain, it would be difficult to recover it exactly by the motion of the apogee, considering the slowness and the irregularity of this motion; but we should have no uncertainty as to this origin, or as to the position of the universal meridian, upon calling to mind that at the moment of the mean equinox the mean longitude of the moon was 143°7714. Thus whatever is arbitrary in the origin of time, and of terrestrial longitudes might be made * 12h 52′ 56" 0. +166° 51′ 59′′ 0. 129° 23′ 39′ 3. to disappear. By afterwards adopting the preceding intercalation and division of the year, month, and day, we should obtain the most natural and simple calendar that can be suited to the inhabitants of this side of the equator. One hundred years form a century, which is the longest period hitherto employed in the division of time. CHAP. IV. Of the Motion of the Moon, its Phases and Eclipses. AFTER the Sun, the Moon of all the heavenly bodies is that which interests us the most; its phases afford us a measure of time so remarkable that it has been primitively in use among all people. The Moon, like the Sun, has a proper motion from west to east, the length of its siderial revolution was * 27°32166118036, at the commencement of 1700; it is not the same for every century. The comparison of modern with ancient observations shews incontestably an acceleration in the mean motion of the Moon. This acceleration, though but little sensible since the most ancient recorded eclipse, will be developed in progress of time. But will it for ever continue *27 7 43' 11" 5. to increase, or will it stop and be changed into a retardation? this cannot be determined by observations, except after an immense number of ages; fortunately the discovery of its cause has anticipated them and shewn that it is periodical. The Moon moves in an elliptic orbit, of which the Earth occupies one of the foci. Its radius vector describes about this point equal areas in equal times. The mean distance. of the Moon from the Earth being taken as unity, the excentricity of its ellipse is 0.0550368, which gives for the greatest equation of its centre *7°0099. The lunar perigee has a direct motion, that is, in the same direction as the motion of the Sun, and the length of its sidereal revolution is + 3232,46643 days. These laws, analogous to those of the solar motion, are very far from being sufficient to represent the observations; the lunar motion is subject to a great many other irregularities, which are evidently con * 6° 18' 32". + 9 312d 11h 11′ 29′′ 5. |
