It is well known in mechanics that the rotation of a body is in no way affected, if we suppose its centre of gravity to be fixed instead of moveable, provided the same forces act In both cases. Thus if a stick be tossed into the air (or rather into vacuum) by an impulse commu nicated to a similar stick which revolves on its centre of gravity, the first in its combined rotation and translation, and the second in ha rotation only, will always remain parallel to each other, if they were so at first: Let its now suppose a needle placed on a point, and mag netic, round which a ball of iron revolves frotn a. If the needle be Lending to destroy its fonner effect, pulling the end e towards it. It may thus be seen that if the needle were heavy enough, the ball would by its motion cause an oscillation, working to pnxhioe rotation In one direction during half its revolution, or rather more, and the opposite effect during rather more than another half revolution, in alternate quarters. But if the needle were light enough, it is easily seen that the rotation In the first direction might be produced so rapidly, that the second mode of action should never be exerted, or the revolving ball should never so far outstrip the needle that le o c should become a right angle. In this case the action would go on in one direction until the needle would acquire a rotation equal to and even exceeding that of the bill. But In the latter case, when the needle overtakes and passes the ball, the opposite action would be Immediately exerted, and the acceleration of rotation would be checked. The end would be, that the needle would acquire a rotation equal to that of the ball, on the average, and would revolve so an always to present its point either to the ball, or alternately a little on one side and on the other. The same effect would be produced if the needle, at the com mencement, had a rotation nearly equal to that of the irdl ; the con sequence would be, that the action in :one direction would continue long enough to establish permanent equality of the average rotations.
Without supposing the moon a long needle, with one end turned towards the earth, it Is found by calculation, that it is sufficient to suppose it slightly spheroidal, with the longer axis towards the earth.
The same mathematical considerations which have so completely re solved the orbital motions, show that the figure of the moon must be an ellipsoid [Sone/ices Or THE SECOND DEORr.E) revolving round the
shorter axis, and presenting the extremity of the longer axis to the earth. But the proportions of these axes have not been well deter mined, from want of observations. theory has outrun practice on this point. It is but comparatively lately that even the inclination of the moon's equator to the ecliptic has been determined at I° 30' 10"•8; that of the equator to the orbit being 5° 8' 49" as already noticed.
One more very curious phenomenon has been shown to be of the same kind as the preceding; namely, of the sort which must be made absolutely true by the earth's attraction, if it were nearly true at the beginning. The moon's equator cuts her orbit In a line which is always parallel, or very nearly so, to the mean position, for the time being, of the line of nodes of the moon's orbit. If the axis of the moon's rotation were perpendicular to the ecliptic, this must be the case, [or the moon's equator and the ecliptic would then be parallel planes. And the inoou's axis being nearly perpendicular to the ecliptic, it may be shown from spherical trigonometry that the two lines in question could not snake an angle of many degrees. But the fact observed (by Dominic Cassini, before the theory of gravitation was thought of) is either actual parallelism, or something differing from it by very trivial oscillations. It is difficult to represent this phenomenon to a person unacquainted with geometry. It may be thus stated : the moon's orbit, the ecliptic, and the moon's equator, are three planes which folio a triangular prism when produced. Or thus : if the moon were made to revolve rapidly round its axis, and If the earth were made a source of light and heat giving seasons to the moon, as the sun does to the earth, then the nodes of the moon's orbit on the ecliptic would coincide with the equinoxea, and the moon's orbit would be divided into summer and winter paths by the same lino as that in which the sun's path cuts the orbit.
A groat many miscellaneous phenomena connected with the moon might be collected, for which wo have not space. For the light thrown on her surface when eclipsed see Reettacitos; for a remarkable appear ance sometimes observed when she lasses over A star Bee OCCULTATION; for her use in finding LONOITUDE see that word.