PRECESSION. If the earth were truly spherical and homogeneous; or if it were com posed of spherical layers each, of uniform denSity; or, more generally, if it were such that the resultant of the attractions exerted on all its parts by any other body should always pass through a definite point in its mass, its diurnal rotation would not be affected by the attraction of any other bodies. If originally rotating about a principal axis of inertia (q.v.), it would forever revolve about it, and the direction of the axis would remain fixed in space. To put this in more popular language, the pole-star (q. v.) would always be the same star. But, although the earth rotates about an axis almost exactly coinciding with its axis of figure, the attraction of various bodies, especially the sun and moon, on the oblate portion at the equator, tends to give it a rotation about an axis in the plane of the equator; and the combination of these two rotations gives rise to a shifting of the instantaneous axis of rotation in the earth and also in space. As already mentioned (see NUTATION), the earth's axis of revolution describes a waved curve (very nearly circular) about the pole of the ecliptic, and in a direction contrary to that of the order of the signs of the zodiac (q.v.). This waved curve may be conceived to be "described as follows: The pole of the earth, P, revolves in about 19 years in a little ellipse, whose center, 0, travels uniformly in a small circle of the sphere, AO; the center, E, of the latter is tht pole of the ecliptic. The precession is the portion AO of tins circle measured from any assumed point, A; and the small arc, OP, by which the true place of the earth's pole differs from its mean place, is the nutation. The notation is generally resolved along, and perpen dicular to, E0; and the components so found are the notation in ecliptical latitude and longitude. This rough sketch is intended merely to show nature of the phenomenon, for the curve described by P about 0 is only approximately elliptic. Its greatest radius-vector, however, is exceed ingly small, amounting only to about eighteen_ seconds of arc. AO, also, is not exactly circular, but very nearly so, as its radius, EO, is the obliquity of the ecliptic (q.v.), which we know varies very little from the angle 23° 28'. The equinoxes, being 90° distant from E, and also from 0, which may be taken as the mean place of P, are at and r in the diagram. And as 0 moves round E in the reverse order of the signs, so do the equinoxes, and in the same period—viz., 25,868 years. The effect is, of course, that while the earth's pole describes the small circle, AO, in the heavens, about the pole of the ecliptic, the equinoxes make one complete revolution in the ecliptic against the order of the signs. Thus, in turn, all stars lying near the circle AO become, each for a time, the pole-star (q.v.). It may seem strange that the term precession should be applied to a retrograde motion; but, from the point of view of the observer, it is evident that the equinox, if on one day it arrive at the meridian of a place simultaneously with a fixed star, will next day arrive at the meridian sooner than the star, or will precede it in time of transit; and this is the origin of the term.
The physical explanation of the cause of precession is almost identical with that of the conical motion of the axis of a top about the vertical; the difference between the two being that, in the case of the top, the conical rotaticn of the axis takes place in the same direction as the rotation of the top about the axis, while in the case of the earth, the pole of the axis turns about the pose of the ecliptic in the opposite direction to that in which the earth revolves about its axis. But the circumstances of the earth's motion are easily procured by a modification of the spinning-top, such as that of Troughton (used for the deterMination of latitudes at sea), if the center of gravity of the whole mass be depressed &doze the point of suspension. If the axis of a top be vertical, there is no precession; similarly, when the sun or moon is in the piffle of the equator, no effect is produced by them on the position of the earth's axis. When the axis of the common top is inclined, rravity tends to make it fall over; in similar circumstances, it tends to restore the axis of Troughton's top to the vertical; in either case tending to give the top a rotation about a horizontal axis perpendicular to that about which it is at the instant rotating; and the .effect on the top is to cause it slow conical motion of its axis about the vertical. The sun or moon, in like manner, when not in time plane of the equator, tend to make, by their attraction, the earth turn about an axis perpendicular to that about which it is actually rotating. It is the composition of these rotations which gives rise to precession; 'out. though it would not be difficult to give a satisfactory investigation of the' question without using formidable mathematical methods, the length of such an investigation prevents our giving it here. The simplest approximation we can give to the physical that originally given by :Newton, must therefore suffice. We have seen (see PEIITUIMATIONS) that the node of a satellite's orbit tends always to regrede on the 'plane of relative motion of the primary and the disturbing body. Suppose, for an instant, the protuberant parts of the earth at the equator to be satellites, revolving about et spherical earth. The effect of the sun's or moon's disturbing force upon these satel lites would be to make the nodes of their orbits regrede. And exactly the same result will follow if they be attached to the earth, only that the rate of regression will now be much slower, as the whole mass of the earth will share in the motion. This is one of the most ingenious of the wonderful series of explanations of celestial phenomena which were given in the Pi-id/a:pia.