CHAPTER VII.

OF THE MOON. ITS SIDEREAL PERIOD. ITS APPARENT DIAMETER. ITS PARALLAX, DISTANCE, AND REAL DIAMETER. FIRST APPROXIMATION TO ITS ORBIT. ·AN ELLIPSE ABOUT THE EARTH IN THE FOCUS. ITS EXCENTRICITY AND INCLINATION. MOTION OF ITS NODES AND APSIDES.- -OF OCCULTATIONS AND SOLAR ECLIPSES GENERALLY. -LIMITS WITHIN WHICH THEY ARE POSSIBLE. THEY PROVE THE MOON TO BE AN OPAKE SOLID. -ITS LIGHT DERIVED FROM THE SUN. --- - ITS PHASES. SYNODIC REVOLUTION OR LUNAR MONTH. OF ECLIPSES MORE PARTICULARLY. THEIR PHENOMENA.

THEIR PERIODICAL RECURRENCE. PHYSICAL CONSTITUTION OF THE MOON. ITS MOUNTAINS AND OTHER SUPERFICIAL FEATURES. -INDICATIONS OF FORMER VOLCANIC ACTIVITY.—ITS ATMOSPHERE. CLIMATE. RADIATION OF HEAT FROM ITS SURFACE. ROTATION ON ITS OWN AXIS. LIBRATION. APPEARANCE OF THE EARTH FROM IT.

(401.) THE moon, like the sun, appears to advance among the stars with a movement contrary to the general diurnal motion of the heavens, but much more rapid, so as to be very readily perceived (as we have before observed) by a few hours' cursory attention on any moonlight night. By this continual advance, which, though sometimes quicker, sometimes slower, is never intermitted or reversed, it makes the tour of the heavens in a mean or average period of 27 7h 43m 11s-5, returning, in that time, to a position among the stars nearly coincident with that it had before, and which would be exactly so, but for reasons presently to be stated.

(402.) The moon, then, like the sun, apparently describes an orbit round the earth, and this orbit cannot be very different from a circle, because the apparent angular diameter of the full moon is not liable to any great extent of variation.

(403.) The distance of the moon from the earth is concluded from its horizontal parallax, which may be found either directly, by observations at remote geographical stations, exactly similar to those described in art. 355, in the case of the sun, or by means of the phænomena called occui

tations, from which also its apparent diameter is most readily and correctly found. From such observations it results that the mean or average distance of the centre of the moon from that of the earth is 59.9643 of the earth's equatorial radii, or about 237,000 miles. This distance, great as it is, is little more than one-fourth of the diameter of the sun's body, so that the globe of the sun would nearly twice include the whole orbit of the moon; a consideration wonderfully calculated to raise our ideas of that stupendous luminary!

(404.) The distance of the moon's centre from an observer at any station on the earth's surface, compared with its apparent angular diameter as measured from that station, will give its real or linear diameter. Now, the former distance is easily calculated when the distance from the earth's centre is known, and the apparent zenith distance of the moon also determined by observation; for if we turn to the figure of art. 339, and suppose S the moon, A the station, and C the earth's centre, the distance S C, and the earth's radius C A, two sides of the triangle A CS are given, and the angle C A S, which is the supplement of Z A S, the observed zenith distance, whence it is easy to find AS, the moon's distance from A. From such observations and calculations it results, that the real diameter of the moon is 2160 miles, or about 0-2729 of that of the earth, whence it follows that, the bulk of the latter being considered as 1, that of the former will be 0.0204, or about. The difference of the apparent diameter of the moon, as seen from the earth's centre and from any point of its surface, is technically called the augmentation of the apparent diameter, and its maximum occurs when the moon is in the zenith of the spectator. Her mean angular diameter, as seen from the centre, is 31' 7", and is always =0.545 × her horizontal parallax.

(405.) By a series of observations, such as described in art. 403, if continued during one or more revolutions of the moon, its real distance may be ascertained at every point of its orbit; and if at the same time its apparent places in the heavens be observed, and reduced by means of its parallax to the earth's centre, their angular intervals will become known, so that the path of the moon may then be laid down on a chart supposed to represent the plane in which its orbit lies, just as was explained in the case of the solar ellipse (art. 349.) Now, when this is done, it is found that, neglecting certain small (though very perceptible) deviations (of which a satisfactory account will hereafter be rendered), the form of the apparent orbit, like that of the sun, is elliptic, but considerably more eccentric, the eccentricity amounting to 0·05484 of the mean distance, or the major semi-axis of the ellipse, and the earth's centre being situated in its focus.

(406.) The plane in which this orbit lies is not the ecliptic, however, but is inclined to it at an angle of 5° 8′ 48′′, which is called the inclination of the lunar orbit, and intersects it in two opposite points, which are called its nodes - the ascending node being that in which the moon passes from the southern side of the ecliptic to the northern, and the descending the reverse. The points of the orbit at which the moon is nearest to, and farthest from, the earth, are called respectively its perigee and apogee, and the line joining them and the earth of the line of apsides.

(407.) There are, however, several remarkable circumstances which interrupt the closeness of the analogy, which cannot fail to strike the reader, between the motion of the moon around the earth, and of the earth around the sun. In the latter case, the ellipse described remains, during a great many revolutions, unaltered in its position and dimensions; or, at least, the changes which it undergoes are not perceptible but in a course of very nice observations, which have disclosed, it is true, the existence of "perturbations," but of so minute an order, that, in ordinary parlance, and for common purposes, we may leave them unconsidered. But this cannot be done in the case of the moon. Even in a single revolution, its deviation from a perfect ellipse is very sensible. It does not return to the same exact position among the stars from which it set out, thereby indicating a continual change in the plane of its orbit. And, in effect, if we trace by observation, from month to month, the point where it traverses the ecliptic, we shall find that the nodes of its orbit are in a continual state of retreat upon the ecliptic. Suppose O to be the earth, and A bad that portion of the plane of the ecliptic which is intersected by the moon, in its alternate passages through it, from south to north, and vice versâ; and let A B C D E F be a portion of the moon's orbit, em

bracing a complete sidereal revolution. Suppose it to set out from the ascending node, A; then, if the orbit lay all in one plane, passing through O, it would have a, the opposite point in the ecliptic, for its descending node; after passing which, it would again ascend at A. But, in fact, its real path carries it not to a, but along a certain curve, A B C, to C, a

point in the ecliptic less than 180° distant from A; so that the angle A O C, or the arc of longitude described between the ascending and the descending node, is somewhat less than 180°. It then pursues its course below the ecliptic, along the curve C D E, and rises again above it, not at the point c, diametrically opposite to C, but at a point E, less advanced in longitude. On the whole, then, the arc described in longitude between two consecutive passages from south to north, through the plane of the ecliptic, falls short of 360° by the angle A OE; or, in other words, the ascending node appears to have retreated in one lunation on the plane of the ecliptic by that amount. To complete a sidereal revolution, then, it must still go on to describe an arc, E F, on its orbit, which will no longer, however, bring it exactly back to A, but to a point somewhat above it, or having north latitude.

(408.) The actual amount of this retreat of the moon's node is about 3′ 10′′·64 per diem, on an average, and in a period of 6793.39 mean solar days, or about 18.6 years, the ascending node is carried round in a direction contrary to the moon's motion in its orbit (or from east to west) over a whole circumference of the ecliptic. Of course, in the middle of this period the position of the orbit must have been precisely reversed from what it was at the beginning. Its apparent path, then, will lie among totally different stars and constellations at different parts of this period; and this kind of spiral revolution being continually kept up, it will, at one time or other, cover with its disc every point of the heavens within that limit of latitude or distance from the ecliptic which its inclination permits; that is to say, a belt or zone of the heavens, of 10° 18′ in breadth, having the ecliptic for its middle line. Nevertheless, it still remains true that the actual place of the moon, in consequence of this motion, deviates in a single revolution very little from what it would be were the nodes at rest. Supposing the moon to set out from its node A, its latitude, when it comes to F, having completed a revolution in longitude, will not exceed 8'; which, though small in a single revolution, accumulates in its effect in a succession of many: it is to account for, and represent geometrically, this deviation, that the motion of the nodes is devised.

(409.) The moon's orbit, then, is not, strictly speaking, an ellipse returning into itself, by reason of the variation of the plane in which it lies, and the motion of its nodes. But even laying aside this consideration, the axis of the ellipse is itself constantly changing its direction in space, as has already been stated of the solar ellipse, but much more rapidly; making a complete revolution, in the same direction with the moon's own motion, in 3232.5753 mean solar days, or about nine years

being about 3° of angular motion in a whole revolution of the moon. This is a phenomenon known by the name of the revolution of the moon's apsides. Its cause will be hereafter explained. Its immediate effect is to produce a variation in the moon's distance from the earth, which is not included in the laws of exact elliptic motion. In a single revolution of the moon, this variation of distance is trifling; but in the course of many it becomes considerable, as is easily seen, if we consider that in four years and a half the position of the axis will be completely reversed, and the apogee of the moon will occur where the perigee occurred before.

(410.) The best way to form a distinct conception of the moon's motion is to regard it as describing an ellipse about the earth in the focus, and, at the same time, to regard this ellipse itself to be in a twofold state of revolution, 1st, in its own plane, by a continual advance of its axis in that plane; and 2dly, by a continual tilting motion of the plane itself, exactly similar to, but much more rapid than, that of the earth's equator produced by the conical motion of its axis described in art. 317.

(411.) As the moon is at a very moderate distance from us (astronomically speaking), and is in fact our nearest neighbour, while the sun and stars are in comparison immensely beyond it, it must of necessity happen, that at one time or other it must pass over and occult or eclipse every star and planet within the zone above described (and, as seen from the surface of the earth, even somewhat beyond it, by reason of parallax, which may throw it apparently nearly a degree either way from its place as seen from the centre, according to the observer's station). Nor is the sun itself exempt from being thus hidden, whenever any part of the moon's disc, in this her tortuous course, comes to overlap any part of the space occupied in the heavens by that luminary. On these occasions is exhibited the most striking and impressive of all the occasional phenomena of astronomy, an eclipse of the sun, in which a greater or less portion, or even in some rare conjunctures the whole, of its dise is obscured, and, as it were, obliterated, by the superposition of that of the moon, which appears upon it as a circularly-terminated black spot, producing a temporary diminution of daylight, or even nocturnal darkness, so that the stars appear as if at midnight. In other cases, when, at the moment that the moon is centrally superposed on the sun, it so happens that her distance from the earth is such as to render her angular diameter less than the sun's, the very singular phenomenon of an annular solar eclipse takes place, when the edge of the sun appears for a few minutes as a narrow ring of light, projecting on all sides beyond the dark circle occupied by the moon in its centre.

(412.) A solar eclipse can only happen when the sun and moon are in