pears horned. And after having completed her course from the Sun, to the Sun again, she disappears, and we say it is new Moon. But when she is seen from the Sun, she appears always full. The Moon's absolute motion from her change to her first quarter is so much slower than the earth's that she falls 240 thousand miles (equal to the semi-diame ter of her orbit) behind the earth at her first quarter, that is, she falls back a space equal to her distance from the earth. From that time her motion is gradually accelerated to her opposition or full, and then she is come up as far as the earth, having regained what she lost in her first quarter, her motion continues accelerated so as to be just as far before the earth as she was behind it at her first quarter. But from her third quarter her motion is so retarded, that she loses as much with respect to the earth, as is equal to her distance from it, or to the semi-diameter of her orbit, and by that means the earth comes up with her, and she is again in conjunction with the sun as seen from the earth. Hence we we find that the moon's absolute motion is slower than the earths from her third quarter to her first, and swifter than the earth's from her first quarter to her third; her path being less curved than the earth's in the former case, and more in the latter. Yet it is still bent the same way towards the sun; for if we imagine the concavity of the earth's orbit to be measured by the length of a perpendicular line let down from the earth's place upon a straight line at the full of the moon, and connecting the pla ces of the earth at the end of the moon's first and third quarters; that length will be about 640,000 miles, and the moon when new only approaching nearer to the sun by 240,000 miles than the earth. The length of the perpendicular line let down from her place at that time upon the same straight line, and which shows the concavity of that part of her path will be about 400,000 miles. The moon's path being concave to the sun throughout, demonstrates that her gravity towards the sun at the time of her conjunction, exceeds her gravity towards the earth. And if we consider that the quan tity of matter in the sun, is nearly 230 thousand times as great as the quantity of matter in the earth, and that the attraction of each body diminishes as the squares of their distances from each other increase, we shall soon find that the point of equal attraction between the earth and the sun is about 70 thousand miles nearer the earth, than the moon is at her change. It may then appear surprising that the moon does not abandon the earth when she is between it and the sun, for she is considerably more attracted by the sun, than by the earth at that time. But this difficulty vanishes when we discover that a common impulse on any system of bodies affects not their relative motions; but that they will continue to attract, impel or circulate round one another in the same manner, as if there were no such impulse. The moon is so pear the earth, and both of them so far from the sun, that the attractive power of the sun may be considered as equal on M both. Therefore the moon will continue to circulate round the earth in the same manner, as if the sun did not attract them at all. OF THE PHENOMENA OF THE HARVEST MOON. It is generally believed that the Moon rises about 50 minutes later every day, than on the preceding; but this is true only to places on the equator. In places of considerable latitude, there is a remarkable difference, especially in the time of the autumnal harvest, with which farmers were formerly better acquainted than Astronomers. In this instance of the Harvest Moon, as in many others discoverable by Astronomy, the wisdom and beneficence of the Deity is conspicuous, who really ordered the course of the Moon, so as to bestow more or less light on all parts of the earth, as their several circumstances and seasons render it more or less serviceable. About the equator, where there is no variety of seasons, and the weather seldom changes, except at stated times; moonlight is not necessary for gathering the produce of the ground, and there the Moon rises about 50 minutes later every day or night, than on the former. In considerable distances from the equator, where the weather and seasons are more uncertain, the autumnal full Moons rise very soon after Sun-set, for several evenings together. At the polar circles, where the mild season is of very short duration, the autumnal full Moon rises at Sun-set from the first to the third quarter: and at the poles, where the Sun is during half the year absent, the winter full Moons shine constantly without setting from the first to the third quarter. It is evident that all these phenomena are owing to the different angles made by the horizon, and different parts of the Moon's orbit, and that the Moon can be full but once or twice in a year, in those parts of her orbit which rise with the least angles. The plane of the Equinox is perpendicular to the earth's axis, and therefore as the earth turns round in its diurnal revolution, all parts of the Equinox make equal parts with the horizon, both at rising and setting; so that equal portions of it always rise or set in equal times. Consequently if the Moon's motions were equible, and in the equinox at the rate of 12 degrees and 11 minutes from the Sun every day, as it is in her orbit; she would rise and set 50 minutes later every day than on the preceding; for 12 degrees, 11 minutes of the equator rise or set in 50 minutes of time in all latitudes. The different parts of the ecliptic, on account of its obliquity to the earth's axis, make very different angles with the horizon, as they rise or set. These parts or signs, which rise with the smallest angles, set with the greatest, and rise vice versa, In equal times, whenever this angle is least, a greater portion of the ecliptic rises, than when the angle is larger, as may be Consequently, 50 50 261 100 43 101 140 37 4 231 170 32 5 Virgo, 61 160 28i 191 150 24 21 150 20 151 150 18 ence in those signs which 7 Libra, 281 150 17 London, as much of the 10 Scorpio, 121 150 22 ecliptic rises about Pisces 11 251 140 30 and Aries in two hours, as 2 Sagitarius,81 130 39 the Moon goes through in 13 211 100 47 six days, & therefore, when 14 Capricorn, 41 the Moon is in these signs, 15 40 56 170 461 5 she differs but two hours in 16 Aquarius, 10 401 8 rising for six days together, 17 that is about 20 miuutes la-18 ter every day or night, than 19 Pisces, 140 351 12 270 301 15 100 251 16 230 201 17 70 171 16 200 171 15 30 201 15 160 241 15 290 301 14 130 401 13 260 561 7 one hour and about 15 min-28 Cancer, 91 001 58 utes later every day or night than the former, whilst she is in these signs. The annexed table shows the daily mean difference of the Moon's rising and setting |