of the earth at an angle of about 5° 9'. To illustrate this, let ABC (Fig. 13.) represent a portion of the earth's orbit, and the surface of the paper the plane of that orbit. Then, if another circle, as DEFG, be drawn to represent the moon's orbit, that circle, being in the same plane or surface with the larger circle, will not correctly show the position of the moon's orbit. But if it be supposed to be cut out of the paper, and placed in an inclined position, hinging, as it were, upon the line DF, so that one half, namely, DGF, may rise above the level of the paper, and the other half, DEF, may sink below it, making with the surface of the paper an angle of 5° 9′, as shown by the intersecting lines at H, it will then furnish a just representation of the position of the moon's orbit with respect to the earth's. The points D and F, where the plane of the moon's orbit intersects that of the earth's, are called the Nodes; and they are distin.-guished from one another by the epithets ascending and descending. The ascending node, F, is the point where the moon, moving from west to east, begins to ascend above the level of the earth's orbit: the descending node, D, is the point where she begins to descend below that level. The line DF, which joins them, is called the line of the nodes; and this line, be it observed, is not always pointed in the same direction; for the nodes shift backward or westward, at the rate of about 19 degrees every year, so that in the course of about five years the line DF will lie in the direction EG at right angles to its former position.

The moon, like the earth, revolves upon her axis, but with a much slower motion, her rotation being performed in 29d. 12h. 44′ 3′′, which is exactly the length of the lunation or synodical month. Hence it is that the same side of the moon is always presented towards the earth. This, however, is subject to a small variation called the moon's libration, which is of two kinds.

The moon's libration in longitude arises from the circumstance that the periods of her rotation upon her axis, and of her revolution in her orbit round the earth, though completed in exactly the same time, do not correspond in all their parts; her motion on her axis being always uniform, while that in her orbit is variable; the effect of which is, that we see sometimes a little more of her western side, sometimes a little more of her eastern, according as her motion in her orbit is accelerated or retarded.

The libration in latitude arises from the moon's axis being inclined to the plane of her orbit; on which account sometimes one of her poles, sometimes the other, is inclined towards the earth, and we see more or less of the polar regions.

The moon's distance from the earth is estimated at about 237,000 miles. This distance is so small, compared with the earth's distance from the sun, the latter being about 400 times the former, that the moon's path in space, resulting from her combined motion round the earth and round the sun, is not a series of looped curves, as might at first be supposed, but a

H

waving line always concave to the sun. To make this curious fact intelligible to the learner, let a circle be described upon a floor, by means of a string 40 inches long, attached at one end to a nail or pin stuck in the floor, and having a pencil at the other end for tracing the circle. Let this large circle represent the earth's orbit round the sun then, to represent the moon's orbit round the earth in the same proportion, a circle must be drawn with a radius of not more than 1-10th of an inch, this being the 400th part of 40 inches. Let the large circle be divided into 12 equal parts, to represent the portions of its orbit which the earth traverses in a month,* and conceive that, while the earth (represented by a little globe no larger than a grain of sand) moves through one of these portions, the moon (represented by a still smaller globe) performs one revolution round it at the distance of 1-10th of an inch. It will then be understood that the moon's absolute track, if marked upon the floor, would be a waving line crossing the earth's track 12 times, but never coming within it, or going out of it, further than 1-10th of an inch; and if lines be drawn, joining the points of intersection with one another, it will be seen that the moon's track, even when it comes within the earth's orbit, does not reach those lines, and is therefore always concave

*This is not strictly accurate, for, as 12 lunations are completed in 354 days, a 12th part of the earth's orbit exceeds the space traversed in a month in the ratio of 365 to 354. It is, however, sufficiently accurate for the purpose of this illustration.

towards the sun. This fact is well worthy of notice, as serving to convey a just idea of the comparative dimensions of the orbits of the earth and moon, and to correct the misapprehensions which are apt to arise from the false proportions of the diagrams usually employed in explanation of the moon's motions.

The diameter of the moon is estimated at 2180 miles, and her solid bulk is hence found to be about 1-48th part of that of the earth.

The surface of the moon is greatly diversified with inequalities, and when viewed through a telescope presents a most rugged appearance of cavities and mountains. The reality of these is proved more decisively by viewing her at any other time than when she is full; for then the edge or border, which separates the illumined from the darkened portion of her surface, presents a singularly broken and jagged appearance; and even in the dark part, near the borders of the lucid surface, some small detached spots of light may be found, which are evidently the tops of mountains catching the sun's rays, while the lower parts around are involved in shade. In all situations of the moon, moreover, the bright spots are constantly accompanied by a triangular shadow on the side opposite to the sun, while the dark spots have an edge of light on the same side-a circumstance which clearly proves that the former are mountains, and the latter cavities. Astronomers have endeavoured to calculate the height of these mountains, but differ widely in the results they have obtained, some having

CHAPTER XVI.

PROBLEMS RELATING TO THE MOON.

PROBLEM I.

To find the Moon's Place in the Heavens for any given Day and Hour.

IN White's Ephemeris will be found a column in which the moon's longitude, or place in the ecliptic, is stated for every day in the year; and another adjoining column which shows her latitude, or distance north or south of the ecliptic; for the moon's orbit, as already observed, being inclined to the plane of the earth's orbit at an angle of about 5° 9′, her motions in the heavens will range within that limit on each side of the ecliptic.* The point thus determined is the moon's place in the heavens for the noon of the given day. But as, by her rapid motion in her orbit, her longitude increases every hour of the day, at the mean rate of 13° 10′ in 24 hours, it is necessary, when the given hour is intermediate between two noons, to calculate how much farther she has advanced. For this purpose, take the difference between her longitude on the given day, and her longitude on the ensuing day :

*The angle varies from 50 to 5o 18'. The latter is, therefore, sometimes the amount of her latitude.