Period of Revolution. 805 This pletely away from the earth, and the moon is invisible to us. is at new moon, A. In the course of two days a thin curved line of light is apparent, B; in three days and a half she reaches the octant, C, and appears "horned," as it is termed. In the second octant, she is in quadrature, D, and is then half enlightened. In the third octant, she is three-quarters enlightened, or "gibbous," E. The next octant is full moon, G; she is then in opposition to the sun. The second half of her course is a gradual decline in the inverted order, till by coming again into conjunction, she disappears. Now the period of accomplishing this course is (in mean duration) 29 days, 12 hours, 44 minutes, and is our recognized month, technically called the moon's synodic revolution. The reason for its being more than two days longer than the sidereal month is that the sun likewise has advanced among the stars, so that the moon has to perform more than a complete sidereal revolution in order to be up with him. The sun performs almost one-twelfth of his annual course among the stars in thirty days; so that from one conjunction tc another, the moon must go round the whole heavens once, and perform nearly a twelfth of a second circuit between one new moon, or one full moon, and another. 1040. If the moon's path through the stars were exactly the sun's path (as it appears to be), then at every conjunction the moon would overlie the sun, and cause an eclipse of the sun. Less obviously, but with equal certainty, at every opposition, the earth would lie in an exact line between the sun and the moon, and the earth, intercepting the sun's light, would make an eclipse of the moon. Now such eclipses do happen, but not every month. The track of the moon is not exactly coincident with the sun's apparent track, termed the ecliptic. The moon's track or orbit is slightly inclined to the ecliptic, the angle being a little more than five degrees (mean, 5° 8' ; extremes, 5° 3' to 5° 13'). It is thus possible for the moon to pass the sun without causing an eclipse. The sun in his annual course through the stars will approach and pass the places where the moon's orbit intersects or cuts the ecliptic, called the nodes. If the moon comes up when the sun is in one of the nodes, or within a little distance of the node, she will pass over the face of the sun, either wholly or partially, according to the sun's position. Of course, if the sun be exactly in the node when the moon comes up, there must be a perfect coincidence of the two. This is a comparatively rare occurrence. But an eclipse of the sun takes place, provided, at the time of the conjunction, the sun is within 131° of the 806 Eclipses of the Sun and Moon. node, which gives a wide chance, although the farther from the node, the smaller is the eclipse. A lunar eclipse will happen if, at the time of opposition, the moon and sun are within 7° of the node. In figure 319, let s be the sun, E, the earth, M, the moon given in two positions; one beyond the earth, and lying in the earth's shadow; the other, within the earth, and making its own shadow fall upon a small part of the earth's surface. In any part of the carth's shadow, the moon will be eclipsed totally, as often happens ; if only partially within its shadow, there will be a partial eclipse. The sun is totally eclipsed only in a limited spot of the earth, and very rarely. Sometimes the cone of the shadow falls short of the earth, and then the eclipse is annular. To the spectators outside the umbra, or shadow, the eclipse is only partial. Every year there are two eclipse seasons, and, at least, one eclipse in each. Most commonly there are, each year, two solar eclipses and one lunar. Many centuries before Christ, the discovery was made that, in a period of nearly nineteen years, the series of eclipses occurred exactly in the same order, so that they could be predicted beforehand. 1041. Unlike the earth, the moon spins very nearly upright as compared with the plane of her orbit. The deviation is only a degree and a half. The period of rotation of the moon is found to be precisely the period of her revolution round the earth. From this fact it happens that the same side is always turned to he earth, and consequently one half of the surface is permanently hidden from our view. There are various circumstances that extend the visible portion, so that, at one time or another, nearly six-tenths of the surface may be seen. The extension of view thus caused was first observed by Galileo, and has been designated the Moon's Libration or swinging. These circumstances are easily explained. For one thing, the rotation of the moon is constant and equable, while the pace of revolution varies; whence the two motions do not exactly coincide. If we suppose the angular motion of revolution somewhat slower than the average, then the rotation gets ahead, and brings round into view a small portion that would be hidden if the two motions were coincident. When the revolution is above the average, the rotation seems to lag, and so exposes to view an extra portion on the other limb. In this way an extension of visible surface is gained, amounting in all to 7° 45', which is called the Libration in Longitude. Again, as the axis of rotation is not perfectly upright, the two poles are alternately visible from the earth, whence the circumpolar surface is visible all round for a little way. This is Libration in Latitude, and amounts to 6° 44'. A small additional extension of visible surface is gained through the variation of the observer's position by virtue of the rotation of the earth. The greatest amount of this corresponds to the moon's parallax, which is almost one degree. It is called Diurnal Librationi. By the aid of the telescope the moon's visible surface has been mapped out in minute detail. The blotched and variegated appearance is resolved into an alternation of plains and mountains; the darker patches are plains, of greater or less extent, surrounded by mountains, whose shadows are seen when the sun shines obliquely on them as at new moon. These enclosed plains, or hollows, are of very various sizes, but all of one type, corresponding to our volcanic mountains. There is always a cup, or crater, surrounded with mountain walls, and often a conical peak in the centre. According to the degree of deviation from a level surface, the depressions are denominated Walled Plains, Ring-mountains, Craters, and Holes. Among the craters the most remarkable is that named "Tycho," which is a circular enclosure forty-seven miles across. The inner side of the surrounding ridge is a steep mountain-wall, sixteen thousand feet high, while the height outside is only twelve thousand feet, showing a depression below the surface of four thousand feet. In the centre of the enclosed plain, or hollow, is a cone five thousand feet high. There are few of what we term mountain ranges. The most conspicuous is named the Apennines, a chain of four hundred and ifty miles in length, one of its peaks rising to eighteen thousand feet. Several mountains exceed twenty thousand feet. Although the structure of the moon's surface is apparently 808 The Moon follows the Laws of the Planets. volcanic, there are no traces of volcanoes in a state of activity. The whole surface is dead and fixed. There is no water, and nc atmosphere; consequently living beings do not exist. There may have been originally the same gaseous elements as make up our air and water, but being too small in quantity they have been all absorbed into the solid mineral compounds. . The illuminating power of the full moon has been estimated at about one six hundred thousandth part of the sun's light. While there is this amount of reflected light, the most delicate thermoscopes have failed to show the emission of heat. MECHANICAL LAWS OF THE MOON'S MOTIONS. 1042. In describing the mechanical principles of the earth's revolution round the sun, as determined by the two forces-central attraction and a tangential impulse-the case of the moon's revolution about the earth was included; the forces being exactly the same, with the difference in the central body, which is, in the one case, the sun, and, in the other case, the earth. If no extraneous power were at work, the calculation of the moon's place would be determined according to Kepler's laws, with the sole qualification, not known to Kepler, namely, that the centre of the moon's revolu tion is not the centre of the earth, but the common centre of gravity of the earth and the moon. This is known from the relative masses of the earth and moon; it is nearly three thousand miles from the earth's centre, or nearly one thousand miles beneath the surface. But the moon is not left solely to the attraction of the earth. According to the theory of Universal Gravitation, every body attracts every other body; yet, since the amount of attraction varies directly according to the mass of the attracting body, and inversely as the square of the distance, a body that is either very small or very distant from another, may be left out of account. The disturbance of the moon by the stars is practically nothing; the disturbance by the other planets is trifling; but the effect of the sun is so considerable that to neglect it would involve very large errors. The Lunar Theory consists in explaining the various modes of deviation from the elliptic path caused by the sun. 1043. In the first place, the effect upon the moon of the sun's attraction as a whole is to counteract or lessen the gravitating force of the earth. For, if the moon is on the same side of the earth as the sun (that is, in conjunction), the sun's attraction draws her away from the earth by a certain fixed amount; and when the moon is Perturbations of the Moon. 809 in opposition, or on the side of the earth away from the sun, the sun attracts the earth more than it does the moon, and still widens the interval between them. At the quarters or quadratures, the sun's tendency is to draw the moon towards the earth, or to add to the central attraction; this effect, however, being much less than the other, so that, on the whole, the sun's influence operates to counteract the earth's attraction. Now, if the earth's path around the sun were in a circle, the earth would be always at the same distance from the sun, and the reduction of the earth's gravitation, as far as the moon is concerned, would be a constant quantity, and would come to the same thing as if the mass of the earth were smaller than it is. As regards the computation of the moon's motions, it could be left out of account. But the elliptic orbit of the earth makes the influence more powerful at one time than at another, and the effect is to produce a yearly disturbance in the moon's rate of motion. Any diminution in the earth's attracting power makes the moon's motion slower; hence, when the sun is nearest the earth (which is in winter) the lunar month is slightly increased. The greatest amount of this displacement, as compared with the mean motion, is about one-fifth of a degree in angular motion (11′ 12′′), or in time about twenty-four minutes. This dis. turbance is called the yearly or Annual Equation. A second variation is due to the inequality of the sun's action in the course of the moon's revolution. As already stated, in conJunction and in opposition, the sun lessens the effect of the earth's attraction; in the quadratures it increases it. But, farther, we must look at the sun's action at right angles to the radius vector, which action is at its maximum in the quadratures. On that side of the orbit, when the moon is moving nearer the sun, its velocity will be increased until it reaches the line of conjunction; when it passes this line, and moves in the opposite direction, it will be steadily retarded until it reaches the point of opposition. The deviation of the moon from what would otherwise be her position may in this way amount to upwards of half a degree, or more than her own breadth. To this disturbance is given the title Variation. A third inequality is one due to the eccentricity of the moon's orbit; it would not exist if the moon moved in a circle. It is plain that the sun's attraction must vary according as the moon is at its nearest or its greatest distance from the earth-called respectively |