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at the time of the winter solstice is represented P is the north pole, a b the ecliptic, 0 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 G 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 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 H fg, and instead of crossing the ecliptic at E it will cross at g a Uttle sooner than it otherwise would. The s'ame influence, though in a less degree, obtains on the opposite side of the earth. The mountain passes around the earth in a curve nearer

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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 0 P must move with the equator, it slowly revolves, keeping its inclination unchanged, around C Q, 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 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 C P nearer to 0 Q, but that in consequence of this rotation the effect really produced is that OP, the earth's axis,

[graphic]

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 C Q the vertical line. The direct tendency of the earth's attraction is to bring C P further, from C Q (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 C P slowly revolves around C Q 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 vi5,Tsrfif,jrsif 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 cfrbit 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 ^ ^

[graphic]

PATH OP THE NORTH POLE

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 ra THB Heavens.
and is represented by the dotted circle.

Periodical change in the obliquity of tJie 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

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