SECTION NINTH.

OF THE MOON'S PHASES.

By looking at the Moon with an ordinary telescope, [see plate 4th, fig. 2d,] we perceive that her surface is diversified with long tracts of prodigious high mountains and dark cavities. This ruggedness of the Moon's surface, is of great use to us, by reflecting the Sun's light to all sides; for if the Moon were smooth and polished, she could never distribute the Sun's light all around. In some positions she would show us his image no larger than a point, but with such lustre as would be hurtful to our eyes.

The Moon's surface being so uneven, many have wondered why her edge does not appear jagged, as well as the curve, bounding the light and the dark places. But if we consider, that what we call the edge of the Moon's disk is not a single line, set round with mountains, in which case it would appear irregularly indented, but a large zone, having many mountains lying behind each other from the observer's eye, we shall find that the mountains in some rows will be opposite to the vales in others, and so fill up the inequalities as to make her appear quite round.

The Moon being an opaque spherical body, (for her bills take off no more of her roundness than the inequalties on the surface of an orange take off from its roundness,) we can only see that part of her enlightened half which is towards the earth. Therefore, when she is in conjunction with the Sun, her dark half is towards the earth, and she disappears; there being no light on that part to render it visible. When she comes to her first octant, or has gone over one eighth part of her orbit from

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her conjunction, a quarter of her enlightened side is seen towards the earth, and she appears horned. When she has gone a quarter of her orbit from between the earth and Sun, she shows us one half of her enlightened side, and then she is said to be a quarter old. When she has gone another octant, she shows us more of her enlightened side, and then she appears gibbous; and when she has gone over half her orbit her whole enlightened side is towards the earth, and therefore she appears round: we then say it is full Moon, or the Moon is in opposition with the Sun. In her third octant, part of her dark side being towards the earth, she again appears gibbous, and is on the decrease. In her third quarter, she appears half decreased. When in her fourth octant, she again appears horned. And after having completed her course from the Sun to the Sun again, she disappears, and we say it is new Moon. [See plate 4th, fig. 1st.) But when she is seen from the Sun, she appears always full. Let S be the Sun, [plate 5th, fig. 3d,] E the earth, ABCDEFGH the Moon's orbit, the small circle at these letters the Moon in different parts of a lunation. The varied appearances of the Moon at the earth are represented in the external circle at abcdefgh. To understand these requires but a slight inspection.

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-diameter 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 find that the Moon's absolute motion is slower than the earth's 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 places 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 quantity 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 near the earth, and both of them so far from the Sun, that the attractive power of the Sun may be considered as equal on 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 astrono

mers.

In this instance of the Harvest Moon, as in many others discoverable by Astronomy, the wisdom and beneficence of the Deity are 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 sunset for several evenings together. At the polar circles, where the mild season is of very short duration, the autumnal full Moon rises at sunset 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 equable, 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 seen by elevating the pole of a common globe to any considerable latitude, and then turning it round on its own axis in the horizon. Consequently, when the Moon is in those signs which rise or set with the smallest angles, she rises or sets with the least difference of time, and with the greatest difference in those signs which rise or set with the greatest angles. On the parallel of London as much of the ecliptic rises about Pisces and Aries in two hours as the Moon goes through in six days, and therefore, when the Moon is in these signs, she differs but two hours in rising for six days together, that is about 20 minutes later every day or night than on the preceding, at a mean rate. But in 14 days afterwards the Moon comes to Virgo and Libra, which are the opposite signs to Pisces and Aries, and then she differs almost four times as much in rising-namely: one hour and about 15 minutes 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 on the parallel of London for 28 days, in which time the Moon finishes her period round the ecliptic, and gets 9 degrees into the same sign from the beginning of which she set out. It appears by the table, that when the Moon is in Virgo and Libra, she rises one hour and a quarter later