We have already seen, that the earth is swelled out at the equator, and that the equator is inclined about 23° 28' to the ecliptic. The orbit of the moon is inclined about 5.1° to the ecliptic, and therefore it is sometimes inclined 29° to the earth's equator. Thus if NS (Plate XXXIX. Fig. 8.) be the earth, EE its equator, C one of the equinoctial points, abd the redundant matter ac cumulated at the equator in consequence of its spheroi dal form, EE the ecliptic, and M the moon in the ecliptic. Now if the moon's action upon the redundant matter abd be represented by ME, it may be resolved into two forces EN or PM, and EP, one of which PM or EN draws the earth in the plane of the ecliptic, while the other EP draws down the redundant matter to the eclip tic. The equinoctial point will therefore recede in the ecliptic from C to c about 35".2. The sun will evidently produce a similar effect, which amounts, however, only to 15".1, the whole precession produced by the action of the sun and moon being 50".3 in a year. In conse quence of this recession of the equinoctial points, the longitudes of all the stars will increase 50" every year, since their place on the ecliptic is reckoned from one of.the equinoxes C, (see p. 570, col. 2.) A star, for example, placed in the ecliptic at M, will have its lon gitude equal to MC, but in consequence of the reces sion of C to c at the end of a year, its longitude will now be Mc, increased by the precession of the equinoxes Cc. Since the equinoctial point therefore retreats at the rate of 50".3 in a year, it will make a complete re volution round the ecliptic in about 26,000 years, and the stars will appear to perform a complete revolution in the heavens in the same time.
If the sun were to set out from the equinoctial point C on his way round the ecliptic, he would evidently arrive at the equinoctial point again some time sooner than he performs a complete revolution in the heavens ; for the equinox C has in tbe.course of a year retreated to c, to meet as it were the sun. The revotution of the sun from one equinox to the same again, is Gallon the Tropical ycar, which is 365 days 5h 48' 48". Before tne suit, however,
has performed a complete revolution in absolute space, he must pass over the space cC of 50".3, which he does in 20' 24". By adding this therefore to the tropical year, we obtain 365 clays 6h 9' 12", for the time in whicn the sun performs a revolution front C to the same point in absolute space. This is called the Sider,at year, because from the stars being absolutely fixed, n is the time in which the sun will revolve front any star to the same star again. In like manner all the other planets will have a tropical and sidereal revolution, which may be found in the same way.
As the inclination of the moon's orbit to the earth's equator, and the position of her nodes, are perpetually changing, there is an inequality in the part of the pre session produced by her action; and also a lioration or deviation of the earth's axis, called its Natation, by which it describes a small ellipse in the heavens, whose dia meters are 19".1, and 14".2, and its period 18 years, the time of the revolution of the moon's macs. This nuta tion will manifestly produce a change in tlic deelivations, of the fixed stars. It was hinted at by Flamstead, and also by Roemer, but the honour of the discovery was reser ved for Dr Bradley, who employed it to account for the changes in the declinations of some of these distant bodies.
As the orbits of all the other planets of the system are also inclined to the earth's equator, their action upon the redundant matter must have a tendency to diminish the obliquity of the ecliptic, and produce a small reces sion in the equinoctial points. The diminution of the obliquity of the ecliptic, arising from the action of all the planets, amounts to 50" in a century, and the corres ponding precession to 18".5. The effects produced by the different planets are, By comparing about 150 observations on the obliqui ty of the ecliptic, with that made by Mayer in 1756, the writer of this article has found that the secular diminu tion is 51". See the references at the end of Physical