Very nearly the same face of the moon is always turned towards the earth, it be ing subject to only a small change within certain limits, those spots which lie near the edge appea. i appearing and disappearing by turns; thus is called its libration. The moon turns about its axis in the same direction in .which it revolves in its orbit. Now the angular velocity about its axis is uniform, and it turns about its axis in the same time in which it makes a complete revolution in its or bit ; if therefore the angular motion about the earth were also uniform, the same face of the moon would always be turned towards the earth. For if the moon had no rotation on her axis, when she is on op posite sides of the earth, she would chew different faces ; but if, after she has made half a revolution in her orbit, she has al so turned half round her axis, then the face, which would otherwise have been shewn, will be turned behind, and the same face will appear. And thus, if the moon's angular velocity about her axis were always equal to her angular veloci ty in her orbit about the earth, the same side of the moon would be always to wards the earth. But as the moon's an gular velocity about her axis is uniform, and her angular velocity in her orbit is not uniform, their angular velocities can not continue always equal, and therefore the moon will sometimes show a little more of her eastern parts, and sometimes a little more of her western parts ; this is called a libration in longitude. Also, the moon's axis is not perpendicular to the plane of' her orbit, and therefore, at opposite points of her orbit, her opposite poles arc turn ed towards the earth ; therefore her poles appear, and disappear, by turns ; this is called a libration in latitude. Hence, nearly one half of the moon is never visi ble at the earth, and therefore nearly one half of its inhabitants (if it have any) ne ver saw the earth, and nearly the other half never lose sight of it. Also the time of its rotation about its axis being a month, the length of the lunar days and nights will be about a fortnight each. It Is a very extraordinary circumstance, that the time of the moon's revolution about her axis should be equal to that in her orbit.
Sir I. Newton, from the altitude of the tides upon the earth, has computed the altitude of the tides on the moon's sur face to be ninety-three feet, and there fore the diameter of the moon, perpendi cular to a line joining the earth and moon, is less than the diatheter directed to the earth, by one hundred and eighty. six feet. Hence, says he, the same face must always be towards the earth, except a small oscillation ; for if the longest dia meter should get a little out of that di rection, it would be brought in it again by the earth's attraction. The supposi tion of D. de Mairan is, that the hemi sphere of the moon next the earth is more dense than the opposite one ; and hence the same face would be kept to wards the earth, upon the same principle as before.
When the moon is in conjunction with the sun, she is then said to be new, and her dark side being next to the earth, she is then invisible. As she recedes from the sun, we first discover some of her bright part, and she appears horned till she gets 90° from the sun, when she appears half enlightened, or dichotomis ed; from thence, till she comes into op position, she appears above half enlight ened, or gibbous; and at opposition she appears full orbecl, the same face being then turned towards the earth which is towards the sun, and she is then said to be at her full. And from opposition to
conjunction, her apparent bright part de creases as it before increased. When the moon is about three days from the new, the dark part is very visible, by the light reflected from the earth, which is moonlight to the lunatics, considering our earth as a moon to them ; and in the most unfavourable state some of the spots may be then seen. But when the moon gets into quadratures, its great light prevents the dark part from being seen. According to Dr. Smith, the strength of moonlight, at the full moon, is ninety thousand times less than the light of the sun ; but from experiments made by M. Bouguer, he concluded it to be three hundred thousand times less. The light of the moon, condensed by the best mirrors, produces no sensible effect upon the Our earth, in the course of a month, shewa the same phases to the lunaries, as the moon does to us; the earth is at the full at the time of the new moon, and new at the time of the full moon. The surface of the earth being about thirteen times greater than that of the moon, it affords thirteen times more light to the moon than the moon does to us.
Dr. Herschel has measured the height of a great many of the lunar mountains, and finds, that, a few excepted, they ge nerally do not much exceed half a mile. Before he measured them, they were reckoned much higher, being generally over-rated. He observes, that it should be examined whether the mountain stands on level ground, which is neces aary,that the measurement may be exact. As the spectator is carried by the earth's rotation, his horizon will continually change its situation, and therefore it will continually cut the moon's orbit, at differ ent points, till it has gone through the whole orbit ; and the inclination of the orbit to the horizon will be continually chansred. Now clifropenrok Ma? non the times of the rising of the moon on two successive nights will depend upon the angle which the moon's orbit makes with the horizon; the less the angle is, the less the moon will have descended by lo% the horizon, at the time when the horizon is brought into the same situation it was twenty-four hours before; therefore, when the angle which the moon's orbit makes with the horizon is the least, there will be the least difference of the times of her ris ing. Now, that angle is the least when the first point of Aries rises, at which time, in the latitude of London, there is only about seventeen minutes difference of the moon's rising on two successive nights. Now, about the 22d of Septem ber, the first point of Aries rises at the time the moon rises, if the moon be then at the full, because it will then be at the beginning of Aries. In this case, there fore, the moon will rise about the full for several nights, with but a small difference of the times .of her rising. This hap pening in the time of harvest, it is called the harvest moon. As the full moon may not happen on the 22d of September, that which happens nearest to it is called the harvest moon. The same small dif ference of the times of rising of the moon happens every month, but it not happening at the full moon, and at that time of the year, it is not taken notice of. The greatest difference of the times of the moon's rising at London on two suc cessive nights, is about one hour and se. venteen minutes; and this happens when the moon is in the first point of Libra, and therefore it happens at the vernal full moons.