of the earth itself. The position of the north pole in the heavens is therefore gradually but almost insensibly changing. It is now distant from the north polar star about 1°. It will continue to approach

it until they are not more than half a degree apart. In 12,000 years Lyra will be our polar star: 4,50C years ago the polar star was the bright star in the constellation Draco. As the right ascension of the stars is reckoned eastward from the vernal equinox along the equinoctial, the precession of the equinoxes increases the R. A. of the stars 50" per year. On this account, star maps must be accompanied by the date of their calculations, that they may be corrected to correspond with this annual variation. The constellations are fixed in the heavens, while the signs of

the zodiac are not; they are simply abstract divisions of the ecliptic which move with the equinox. When named, the sun was in both the sign and constellation Aries, at the time of the vernal equinox; but since then the equinoxes have retrograded nearly a whole sign, so that now while the sun is in the sign Aries on the ecliptic, it corresponds to the constellation Pisces in the heavens. Pisces is therefore the first constellation in the zodiac. (See Fig. 72.)

Causes of the Precession of the Equinoxes.-Before commencing the explanation of this phenomenon, it is necessary to impress upon the mind a few facts. 1. The earth is not a perfect sphere, but is swollen at the equator. It is like a perfect sphere covered with padding, which increases constantly in thickness from the poles to the equator; this gives it a turnip-like shape. 2. The attraction of the sun is

Fig. 33.

I

INFLUENCE OF THE SUN ON A MOUNTAIN NEAR THE EQUATOR.

greater the nearer a body is to it. 3. The attraction is not for the earth as a mass, but for each particle separately. In the figure, the position of the earth

at the time of the winter solstice is represented. P is the north pole, a b the ecliptic, C the centre of the earth, CQ a line perpendicular to the ecliptic, so that the angle QCP equals the obliquity of the ecliptic. In this position the equatorial padding we have spoken of the ring of matter about the equator—is turned, not exactly toward the sun, but is elevated above it. Now the attraction of the sun pulls the part D more strongly than the centre; the tendency of this is to bring D down to a. In the same way the attraction for C is greater than for I, so it tends to draw C away from I, and as at the same time D tends toward a, to pull I up toward b. The tendency of this, one would think, would be to change the inclination of the axis CP toward CQ, and make it more nearly perpendicular to the ecliptic. This would be the result if the earth were not revolving upon its axis. Let us consider the case of a mountain near the equator. This, if the sun did not act upon it, would pass through the curve HDE in the course of a semi-revolution of the earth. It is nearer the sun than the centre C is; the attraction therefore tends to pull the mountain downward and tilt the earth over, as we have just described; so the mountain will pass through the curve Hfg, and instead of crossing the ecliptic at E it will cross at g a little sooner than it otherwise would. The same influence, though in a less degree, obtains on the opposite side of the earth. mountain passes around the earth in a curve nearer

The

to b, and crosses the ecliptic a little earlier. The same reasoning will apply to each mountain and to all the protuberant mass near the equatorial regions. The final effect is to turn slightly the earth's equator so that it intersects the ecliptic sooner than it would were it not for this attraction. At the summer sol stice the same tilting motion is produced. At the equinoxes the earth's equator passes directly through the centre of the sun, and therefore there is no tendency to change of position. As the axis CP must move with the equator, it slowly revolves, keeping its inclination unchanged, around CQ, the pole of the ecliptic, describing, in about 26,000 years, a small circle twice 23° 28' in diameter.

Fig. 34.
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Precession illustrated in the spinning of a top.-This motion of the earth's axis is most singularly illus trated in the spinning of a top, and the more remarkably because there the forces are of an opposite character to those which act on the earth, and so produce an opposite effect. We have seen that if the earth had no rotation, the sun's attraction on the "padding" at the equator would bring CP nearer to CQ, but that in consequence of this rotation the effect really produced is that CP, the earth's axis,

SPINNING OF A TOP.

slowly revolves around C Q, the pole of the heavens, in a direction opposite to that of rotation.

In Fig. 34, let CP be the axis of a spinning top, and CQ the vertical line. The direct tendency of the earth's attraction is to bring CP further from CQ (or to make the top fall), and if the top were not spinning this would be the result; but in consequence of the rotary motion the inclination does not sensibly alter (until the spinning is retarded by friction), and so CP slowly revolves around CQ in the same direction as that of rotation.

NUTATION (nutatio, a nodding).-We have noticed the sun as producing precession; the moon has, however, treble its influence; for although her mass is not 20.000.000 part that of the sun, yet she is 400 times nearer and her effect correspondingly greater. (See p. 168.) The moon's orbit does not lie parallel to the ecliptic, but is inclined to it. Now the sun attracts the moon, and disturbs it as he would the path of the mountain we have just supposed, and the effect is the same-viz., the intersections of the moon's orbit with the ecliptic travel backward, completing a revolution in about 18 years. During half of this time the moon's orbit is inclined to the ecliptic in the same way as the earth's equator; during the other half it is inclined in the opposite way. In the former state, the moon's attractive tendency to tilt the earth is very small, and the precession is slow; in the latter, the tendency is great, and precession goes on rapidly.