PRECESSION AND NUTATION, the abbreviated way of ex pressing the precession of the equinoxes and the nutation of the earth's axis.
These phenomena should always be considered in connection wit the rotation of the earth, of which they really fonn a part ; that is to sae, diurnal rotation, precession, and notation are the motions of the earth about its centre, independently of the motion of that centre along its orbit retina the sun. It. will amidst our comprehension of the subject to auppose the earth's centre a fixed point, the relative motions of the heavenly bodies being adjusted accordingly. [Mo. vox.] The rotation of the earth round its axis is visiblo from hour to hour by the change of place in the stars: the precession and notation are motion,' of too slow a nature to be rendered visible, and indeed could hardly be made so unless the ecliptic and equator were visible eirrles If such were the case, and if the motions were large enough, the equinoxes, or intersections of the equator and ecliptic, would appear to change place, the equator moving slowly round the ecliptic with a retrograde .motion, that is, contrary to the annual course of the inn. The equinoxes would appear to move with a variable motion, sometimes a little faster and sometimes a little slower than the mean motion. At the name time the equator would appear to swing backward, and forwards to and from the ecliptic, turning upon the equinoxes as pivots. Of these motions the average motion of the equinoxea upon the ecliptic is the precession ; the alternate sentient tion and retardation is one part of the nutation ; and the alternate increase and diminution of the angle contained between the two is the other part.. It is however common to call the acceleration and re tardation of the motion of the equinoxes by the name of the equation of the equinoxes, and to reserve the name of notation for the motion of the pole which corresponds to it.
Let c be the centre of the earth, c r half its axis, r the north polo, and half of the equator. Let et x be part of the plane of the ecliptic, and Cg a line perpendicular to it, pointing therefore to the pole of the ecliptic in the heavens : and lot the direction of the diurnal rotation be that of the arrow marked on the equator. If then r were
carried uniformly round a circle perpendicular to c q, so that c P should describe a conical surface, the equinoxes B and e would be carried round in a direction contrary to that of the diurnal motion, and with them the equator n 8 A, till) angle which the equator makes with the ecliptic remaining unaltered This motion of © and A is the precession. But suppose that instead of r being placed on the circle, it is placed on the circumference of a small oval, which has its centre on the eirolo. While the centre of the oval moves forward on the circle with the motion of precession, let the pole r move round the oval with a motion much slower than that of the precession. It will then trace out in apace an undulating curve, as shown in the principal diagram, and the effect will be an alternate retardation and accelera tion of the motion of the equinoxes aloug the plane of the ecliptic, together with a vibration of the plane of the equator to and from the ecliptic ; which are the motions described as constituting the na tation.
'131e preceding is a description of time effect of any one of the heavenly bodies, theoretically speaking, upon the axis of the earth. The whole procession and notation is tho united effect of the sun, mom, and planets. The effect of the planets however is insensible, except in a slight annual alteration of the plane of the ecliptic, which is mixed up with the precession, and makes it appear a very little smaller than it would be if the system of the sun, moon, and earth were undieturbed by the plauotary attraction. The general reader need only attend to the main phenomenon, namely, that the equinox (the point of the heavens at which the sun is at the commencement of spring) moves slowly • backwards along the ecliptic, at the rate of .,01 seconds per annum, or about 14' in one thousand years. This rate of motion is subject to a very slow increase, which is not perhaps sufficiently well determined to make it worth while to compute ex actly the time in which the equinox describes the whole heavens, a period of between twenty.five and twenty-six thousand years.