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 solstice 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.

Precession illustrated in the spinning of a top.-This motion of the earth's axis is most singularly illustrated in the spinning

Fig. 34.

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,

t

SPINNING OF A TOP.

slowly revolves around CQ, 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.

The consequence of this is, that the pole of the

earth is irregularly shifted, so

that it travels in a slightly
curved line, giving it a kind of
"wabbling" or "nodding" mo-
tion, as shown-though greatly
exaggerated-in Fig. 35. The
obliquity of the ecliptic, which
we consider 23° 28', is the mean
of the irregularly curved line
and is represented by the dotted circle.

Fig. 35.

PATH OF THE NORTH POLE
IN THE HEAVENS.

Periodical change in the obliquity of the ecliptic.Although it is sufficiently near for all general purposes to consider the obliquity of the ecliptic invariable, yet this is not strictly the case. It is subject to a small but appreciable variation of about 46′′ per century. This is caused by a slow change of the position of the earth's orbit, due to the attraction of the planets. The effect of this movement is to gradually diminish the inclination of the earth's equator to the ecliptic (the obliquity of the ecliptic). This will continue for a time, when the angle will as gradually increase; the extreme limit of change being only 1° 21'. The orbit of the earth thus vibrates backward and forward, each oscillation requiring a period of 10,000 years. This change is so intimately blended, in its effect upon the obliquity of the ecliptic, with that caused by precession and nutation, that they are only separable in theory; in point of fact, they all combine to

produce the waving motion we have already described. As a consequence of this variation in the obliquity of the ecliptic, the sun does not come as far north nor decline as far south as at the Creation, while the position of all the terrestrial circles— Tropic of Cancer, Capricorn, Arctic, etc.-is constantly but slowly changing. Besides this, it tends to vary slightly the comparative length of the days and nights, and, as the obliquity is now diminishing, to equalize them. As the result of this variation in the position of the orbit, some stars which were formerly just south of the ecliptic are now north of it, and others that were just north are now a little further north; thus the latitude of these stars is gradually changing.

Change in the major axis (line of apsides) of the earth's orbit. Besides all the changes in the position of the earth in its orbit due to precession, the line connecting the aphelion and perihelion points of the orbit itself is slowly moving. The consequence of this is a variation in the length of the seasons at different periods of time. In the year 4089 B. C., about the supposed epoch of the creation, the earth was in perihelion at the autumnal equinox, so that the summer and autumn seasons were of equal length, but shorter than the winter and spring seasons, which were also equal.* In the

* There is much discrepancy in the views held concerning the Great Year of the astronomers, as it is often called. (See 14 Weeks in Geology, pp. 272-3, note.) The statement given in the text is that held by Lockyer, Hind and others. The terms, it

year 1250 A. D., the earth was in perihelion when it was at the winter solstice, December 21, instead of January 1st, as now; the spring quarter was therefore equal to the summer one, and the autumn quarter to the winter one, the former being the longer. In the year 6589 A. D., the earth will be in perihelion when it is at the vernal equinox; summer will then be equal to autumn and winter to spring, the former seasons being the longer. In the year 11928 A. D., the earth will be in perihelion when it is at the summer solstice: finally, in 17267 A. D., the cycle will be completed, and for the first time since the creation of man the autumnal equinox will coincide with the earth's perihelion.

PERMANENCE IN THE MIDST OF CHANGE.-We thus see that the ecliptic is constantly modifying its elliptical shape; that the orbit of the earth slowly oscillates upward and downward; that the north pole steadily turns its long index-finger over a dial that marks 26,000 years; that the earth, accurately poised in space, yet gently nods and bows to the attraction of sun and moon. Thus changes are continually taking place that would ultimately entirely reverse the order of nature. But each of these has its bounds, beyond which it cannot pass. The promise made to man after the Deluge, is that "while the earth remaineth, seed-time and harvest, and cold and heat, and summer and winter, and

should be noticed, are applied to the real position of the earth and not the apparent position of the sun. The dates are those given by Chambers in his Descriptive Astronomy.