SECTION THIRTEENTH. SHOWING THE PRINCIPLES ON WHICH THE FOLLOWING THE TIMES OF NEW & FULL MOONS & ECLIPSES BY THEM. THE nearer that any object is to the eye of an obser ver, the greater is the angle under which it appears.— The farther from the eye, the less it appears. The diameters of the Sun and Moon subtend different angles at different times. And at equal intervals of time, these angles are once at the greatest, and once at the least, in somewhat more than a complete revolution of the luminary through the ecliptic from any given fixed star, to the same star again. This proves that the Sun and Moon are constantly changing their distances from the earth and that they are once at their greatest distance, and once at their least, in a little more than a complete revolution. The gradual differences of these angles are not what they would be,if the luminaries moved in circular orbits, the earth beiug supposed to be placed at some distanco from the centre. But they agree perfectly with elliptical orbits, supposing the lunar focus of each orbit to be at the centre of the earth. The farthest point of each orbit from the earth's centre, is called the apogee; & the nearest point the perigee. These points are directly opposite each other. Astronomers divide each orbit into 12 equal parts, called signs; and each sign into 30 equal parts called degrees; each degree into sixty equal parts, called minutes,and each minute into 60 equal parts, called seconds. The distance, therefore, of the Sun or Moon from any point of its orbit, is reckoned in Signs, Degrees, Minutes and Seconds. The distance here meant, is that through which the luminary has moved from any given point, (not the space it falls short thereof,) in coming round again,be it ever so little. The distance of the Sun or Moon from its apogee at any given time, is called its mean anomaly, so that in the apogee, the anomaly is nothing, in the perigee, it is six signs, The motions of the Sun and Moon are observed to be continually accelerated from the apogee to the perigee; and as gradually retarded from the perigee to the apogee; being slowest of all when the mean anomaly is nothing, and swiftest when it is six signs. When the luminary is in its apogee or perigec, its place is the same as it would be if its motions were cquable in all parts of its orbit. The supposed equable motions are called mean, the unequable are justly called the true. The mean place of the Sun or Moon is always forwarder than the true, whilst the luminary is moving from its apogee to its perigee; and the true place is always forwarder than the mean, whilst the luminary is moving from its perigee to its apogee. In the former case, the anomaly is always less than six signs, in the latter more. It has been discovered by a long series of observations, that the Sun goes through the ecliptic, from the vernal equinox to the same again, in 365 days, 5 hours, 48m. and 54s. And from the first star of Aries, to the same star again, in 365 days, 6 hours, 9 minutes, and 24 seconds. And from his apogee to the same again in 365 days, 6 hours, and 14 minutes. The first of these, is called the Solar year; the second the sydereal, and the third the anamolistic year. The solar year is 20 minutes and 29 seconds shorter than the sydereal; and the sydereal year is 4 minutes and 36 seconds shorter than the anamolistic. Hence it appears, that the equinoxial point, or intersection of the ecliptic and equator at the beginning of Aries, goes backward, with respect to the fixed stars, and that the Sun's apogee goes forward. The yearly motion of the earth's or Sun's apogee, is found to be one minute and six seconds, which being subtracted from the Sun's yearly motion, in longitude, the remainder is the Sun's mean anomaly. It is also observed, that the Moon goes through her orbit from any given fixed star to the same again, in 27 days, 7 hours, 43 minutes, and 4 seconds, at a mean rate; from her apcgee to her apogee again in 27 days, 13 hours, 18 minutes, and 43 secords: and from the Sun to the Sun again in 29 days, 12 hours, 44 minutes, T 20 and 3 and seconds. This confirms the idea that the Moon's apogee moves forward in the ecliptic, and that at a much greater rate than the Sun's apogee; since the Moon is 5 hours, 55 minutes, and 39 seconds longer in revolving from her apogee to her apogee again, than from any star to the same again. The Moon's orbit crosses the ecliptic in two opposite points, which are called her nodes, and it is observed that she revolves sooner from any node to the same node again, than from any star to the same star again, by 2 hours, 33 minutes and 27 seconds; which shows that her nodes move backward, or contrary to the order of signs in the ecliptic. To find the Moon's mean motion in a common year of 365 days, the proportion is As the Moon's period, Is to her whole orbit, or So is a common year of D H M S 27 7 43 43 5 360 degrees, 365 days, To 13 revolutions and 4s.--9d.-23 minutės, .5 seconds. The thirteen revolutions are rejected, and the remainder is taken for the Moon's motion in 365 days. To calculate the Moon's mean anomaly : The Moon's apogee moves once round her whole orbit in 8 years, 309 days, 8 hours, and 20 minutes, or, (adding two days for leap years,) in 3231 days, eight hours and 20 minutes. Then, As Is to the whole circle, or So is a common year of 3231d.-Sh.-20 360 degrees, 365 days, To the motion of the Moon's apogee in one year= 40 degrees, 39 minutes, and 50 seconds. From the Moon's mean motion in longitude. during To find the mean motion of the Moon's node: The Moon's node moves backward round her whole orbit in 18 years, 224 days, 5 hours, therefore for its motion in 365 days, As 18 years, 224 days, 5 hours Is to the whole circle or 360 degrees, So is the year of 365 days To the motion of the Moon's node in 365 days=19 degrees, 19 minutes and 43 seconds. To find the mean motion of the Moon from the Sun. The Moon's mean motion in a common year of 365 days, is 4 signs, 9 degrees, 23 minutes and 5 seconds over and above 13 revolutions, and the Sun's apparent mean motion in the same time is 11 signs, 29 degrees, 45 minutes and 40 seconds. Then from the Moon's mean motion for one year, subtract the mean motion of the Sun for the same time, and the remainder will be the mean motion of the Moon from the Sun in one year 4 signs, 9 degrees, 37 minutes and 25 seconds. |
