XVI. Summer longer than winter.-As the sun is not in the centre of the earth's orbit, but at one of its foci, that portion of the orbit which the earth passes through in going from the vernal to the autumnal equinox comprises more than one-half the entire ecliptic. On this account the summer is longer than the winter. The difference is still fürther enhanced by the variation in the earth's velocity at aphelion and perihelion. The annexed table gives the mean duration of the seasons:

The difference of time in the earth's stay in the two portions of the ecliptic, as will be seen from the above, is 7.8 days.

XVII. Varying velocity of the earth.—We can see, by looking at the plate, that the velocity of the earth must vary in different portions of its orbit. When passing from the vernal equinox to aphelion, the attraction of the sun tends to check its speed; from that point to the autumnal equinox, the attraction is partly in the direction of its motion, and so increases its velocity. The same principle applies when going to and from perihelion.

XVIII. Curious appearance of the sun at the north pole.-"To a person standing at the north pole, the sun appears to sweep horizontally around the sky every twenty-four hours, without any perceptible

variation in its distance from the horizon. It is,' however, slowly rising, until, on the 21st of June, it is twenty-three degrees and twenty-eight minutes above the horizon, a little more than one-fourth of the distance to the zenith. This is the highest point it ever reaches. From this altitude it slowly descends, its track being represented by a spiral or screw with a very fine thread; and in the course of three months it worms its way down to the horizon, which it reaches on the 22d of September. On this day it slowly sweeps around the sky, with its face half hidden below the icy sea. It still continues to descend, and after it has entirely disappeared it is still so near the horizon that it carries a bright twilight around the heavens in its daily circuit. As the sun sinks lower and lower, this twilight grows gradually fainter, till it fades away. December 21st, the sun is 23° 28' below the horizon, and this is the midnight of the dark polar winter. From this date the sun begins to ascend, and after a time it is heralded by a faint dawn, which circles slowly around the horizon, completing its circuit every twenty-four hours. This dawn grows gradually brighter, and on the 22d of March the peaks of ice are gilded with the first level rays of the six months day. The bringer of this long day continues to wind his spiral way upward, till he reaches his highest place on the 21st of June, and his annual course is completed."

XIX. Results, if the axis of the earth were perpendicular to the ecliptic.-The sun would then always

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. Results, 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.

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. 20s. 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.

Results 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 efh to g Kl. The inclination of the axis of the earth, CP, to CQ, the pole of the ecliptic, remains unchanged; but as it must turn with the equator, its position is moved from CP to CP', and it passes slowly around through a portion of a circle whose centre is CQ. 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 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