MOON'S LIBRATION.

303

3. Although our atmosphere must, at least, give our planet a belted appearance, and more or less obscure the outlines of our continents and seas, the mapping of our globe's surface is probably evident enough from the moon to be a means of exactly marking our daily rotation. But, since the moon's revolution about us is in the same direction as our rotation, and she thus partly accompanies our surface eastward ::

c The time of our rotation, as noted by inhabitants of the moon, will not appear to be 23h. 56m. 4sec., but nearly 25 hours; just as the sun's rotation, marked by his spots, appears, when viewed from the earth, to take place in 27 days instead of 25 days, because we are moving around him in the same direction (see 4 of p. 241; and, also def. 88).

W It has been stated (a p. 302) that in consequence of the correspondence in period of the moon's rotation and orbitual revolution, one-half of her surface has never been viewed by the earth's inhabitants :-This would have been strictly true if her orbit had been circular, and her velocity of revolution, therefore, such as it is on an average: but the only equable motion of the moon is that about her own axis; for her path being an ellipse of considerable excentricity, her orbitual motion is accelerated when she is near her perigee, and retarded when she is near her apogee. Hence, whilst she is equably rotating,

d We see a little around her right, or west limb, when her orbitual motion is faster, and a little around her left, or east limb, when her motion is slower than her average rate; the average rate alone according with her rate of rotation. This occasional appearance of a few degrees around her east or west limb, is called her "libration in longitude."

[*** Her axis, also, not being perpendicular to the plane of her orbit, we alternately see a little over her north pole, and a little under her south pole; and this is termed her "libration in latitude."]

Hence, too, there are certain parts of the moon besides one hemisphere, to which the earth sometimes appears.

*See "Earth," p. 263.

MOTION OF THE MOON'S NODes, and otheR DISTURBANCES OF HER ORBITUAL MOTION.

The pupil will recognize the table as representing the plane of the earth's orbit; and the button of the te-to-tum as shewing the inclined plane of her equator. We have marked out (as before, on page 108), the ecliptic line on parts of the wall in the same plane with the table; but the equinoctial is not inserted, for fear of its being confounded with the plane of the moon's orbit, the inclination of which is necessarily very extravagant.

We must bear in mind that the moon's path (represented with exaggerated inclination by the little beaded ellipse above and below the table) is four hundred times as near to us as the sun (S); and hence, as delineated on the distant wall (or sky), the moon's disk and the sun's disk would be nearly equal (Q, p. 138). The lines joining the te-to-tum (or earth) to the little circles, or beadings, are extended to the wall, and point to those phases, or appearances of the moon in the sky, which result from her several daily positions with respect to the sun and earth.

X

We have to refer particularly to the moon's nodes—that point in her orbit at which she comes above the ecliptic plane (or table), as A N or mn; and that at which, after performing half her course, she descends below that plane, as M, &c.

When at A N, and therefore ascending northward, the moon, as seen from the earth (our te-to-tum), is crossing the ecliptic (on the wall) at a point diametrical to DN, and therefore behind us as we view the diagram. It is evident

MOTION OF NODES.

305

that, at such an instant, the principal disturbing effect of an attraction exerted from S (the sun), must be that of an acceleration of her progress. But as she proceeds, in consequence of her inertia and the attraction of the nearer earth, to fulfil her course above, the effect of S's attraction is also to drag her downward towards him and the table plane, thus rendering the angle or inclination of the plane of her path less than that of the continuous line which represents what her path would otherwise be; and she proceeds towards m, along the dotted line, into the situations marked by the little disks.

Having arrived at m, and begun to pass that point, one of the disturbing effects of S is evidently that of retarding her; but this is not all, for his attraction also bends her course into one of greater inclination, and compels her so to anticipate her crossing the plane that she goes below it at a point somewhat to the west, or right of that diametrical to A N (at which she came above it); and thus, instead of being seen to cross the ecliptic at D N, she appears at d n to form her node. She is similarly accelerated, retarded, and perverted, during the fortnight of her being south of our plane (or below the table); and thus comes up again, not at A N as before, nor even at the point diametrical to d n, but at a point opposite to one a little farther still to the right or west of it.

Y To avoid complexity, the earth's motion during the lunation has been disregarded, and that relative position of the sun alone considered which is at right angles to the moon's node. The moon's nodes, as exhibited thus (on our left), are said to be in quadrature; that is, she is crossing our plane when a half-moon: under these circumstances she is so disturbed as to have her node rapidly regressing, or falling back in an order contrary to that of the signs of the zodiac. But it is evident that, as the earth revolves accompanied by the moon, the sun will be, relatively, in very different positions. It will, for instance, happen (as on the right) that the line of the moon's nodes pass through the sun, or coincide with what is called the line of syzygy: whilst this is the case the node is undergoing no change. In other parts of our yearly revolution, as her nodes are variously presented towards the sun, she

is variously affected in different portions of her monthly path; but the average result of each month's disturbing attraction of the sun is a retreat of these nodal points of about one degree and a half.

10

100

Z" 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 years, the ascending node is carried round in a direction contrary to the moon's motion in its orbit, 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 in the beginning. Its apparent path, then, will be among totally different stars and constellations at different parts of this period; and this kind of spiral revolution being constantly kept up, it will, at one time or other, cover with its disk every point of the heavens within that limit of latitude or distance from the ecliptic which its inclination permits (p. 299); that is to say, a belt or zone of the heavens of 10° 18' in breadth, having the ecliptic for its middle line.”—Sir J. Herschel, p. 217.

B We must keep in mind that it is the inequality + of the attractions of the earth and sun upon the moon, that is the cause of her perturbations. The moon is differently affected when in conjunction (as at m) than when, a fortnight afterward, she is in opposition, or on the other side of the earth; for not only, in the former case, is she nearer to the sun than the earth is by 240,000 miles, and in the latter case, more distant than the earth by the same quantity; but the earth's attraction thus alternately combines with the sun's and opposes it. The moon's monthly orbit itself having an excentricity of rather more than, she is, from

* When the moon's node is given (as it is in the Ephemeris on our page 51, for every sixth day), it must be understood to be the ascending node of her instantaneous ellipse; that is, such a degree and minute of the ecliptic line as would be cut by an ellipse which corresponds to the tendency of that portion of her disturbed path which she is then pursuing.

+ See the first lines of p. 257.

OCCASIONS OF ECLIPSE.

307

this circumstance too, alternately more and less affected by the earth's influence.

But the excentricity of the earth's orbit also affects the orbit of the moon. When we are nearer to him, or approach our perihelion, her orbit is enlarged by the sun's increased attraction, and she moves the slower :- whilst we recede towards our aphelion, her orbit contracts, because the earth's control over her is less disputed, and she moves the faster, as a counterbalance to her increased gravity towards us. (D, p. 233, and G, p. 234.)

The irregularities, or inequalities, arising from such circumstances as the foregoing, are all estimated by astronomers: they are all compensated in short times, and are therefore called periodical* (W, p. 258). But there is a secular inequality of the moon, which is of great chronological interest:

Eclipses can take place only when the new or full moon is at, or very near to, her node. There would, for instance, be a solar eclipse, that is, the moon's dark body would be seen partly or wholly upon the sun, if she were crossing our plane, or nearly crossing it, as at M (see the diagram, p. 304), whilst the earth and the node were in the relative positions represented by the te-to-tum, &c. on the right. Or if, whilst the earth and the moon's node were so circumstanced, the moon were coming across our plane (as at m n), or nearly so, she would receive our shadow, and be herself eclipsed. The times of such occurrences, the pupil is aware, are predicted with remarkable exactness; and it is easy to conceive that laborious calculation, extended backward, might verify the dates of the eclipses which have taken place in past ages. But, in calculating backward, with every advantage derived from the precision of modern discovery and observation, it was aṣcertained that the precise hour given for the eclipse of ear

*The same positions of the moon with regard to the sun, her apogee, and her node, are all repeated, or nearly so, at the end of a period of 223 lunations, or 18 years and 11 days. This is what is meant by the cycle of the moon's nodes. It was known to the ancients as the Chaldean Saros. The inequalities of the moon's motions which result during these several relative positions must, therefore, also be repeated with the positions from which they so result, however numerous and complex they may be.