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appear to move through the equinoctial. He would rise and set every day at the same points on the horizon, and pass through the same circle in the heavens, while the days and nights would be equal the year round. There would be near the equator a fierce torrid heat, while north and south the climate would melt away into temperate spring, and, lastly, into the rigors of a perpetual winter.
XX. Besults, if the equator of the earth were perpendicular to the ecliptic.—Were this the case, to a spectator at the equator, as the earth leaves the vernal equinox, the sun would each day pass through a smaller circle, until at the summer solstice he would reach the north pole, when he would halt for a time and then slowly return in an inverse manner.
In our own latitude, the sun would make his diurnal revolutions in the way we have just described, his rays shining past the north pole further and further, until we were included in the region of perpetual day, when he would seem to wind in a spiral course up to the north pole, and then return in a descending curve to the equator. v^precession Of The Equinoxes.—We have spoken of the equinoxes as if they were stationary in the orbit of the earth. Over two thousand years ago, Hipparchus found that they were falling back along the ecliptic. Modern astronomers fix the rate at about 50" of space annually. If we mark either point in the ecliptic at which the days and nights are equal over the earth, which is where the plane of the earth's equator passes exactly through the centre of the sun, we shall find the earth the next year comes back to that position 50" (20 m. 20 s. of time) earlier. This remarkable effect is called the Precession of the Equinoxes, because the position of the equinoxes in any year precedes that which they occupied the year before. Since the circle of the ecliptic is divided into 360°, it follows that the time occupied by the equinoctial points in making a complete revolution at the rate of 50.2" per year is 25,816 years.
Besults of the Precession of the Equinoxes.—In Fig. 31, we see that the line of the equinoxes is not at right angles to the ecliptic. In order that the plane of the terrestrial equator should pass through the sun's centre 50" earlier, it is necessary that the plane itself should slightly change its place. The axis of the earth is always perpendicular to this plane, hence it follows that the axis is not rigorously parallel to itself. It varies in direction, so that the north pole describes a small circle in the starry vault twice 23° 28' in diameter. To illustrate this, in the cut we suppose that after a series of years the position of the earth's equator has changed from e/h to g K I. The inclination of the axis of the earth, 0 P, to C Q, the pole of the ecliptic, remains unchanged; but as it must turn with the equator, its position is moved %gm CP to CP', and it passes slowly around through a portion of a circle whose centre is C Q. The direction of this motion is the same as that of the hands of a watch, or just the reverse of that of the revolution
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: 4,500 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 E. 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
greater the nearer a body is to it 3. The attraction f 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, C Q 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 C P toward C Q, 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 0 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 H fg, and instead of crossing the^ecliptic at E it will cross at g a little sooner tharr^etherwise would. The same influence, though in a less degree, obtains on the opposite side of the earth. The mountain passes around the earth in a curve nearer