Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/864

result of this is that the obliquity of the ecliptic is chang ing, for the mean inclination of the earth s axis to the invariable plane does not change, so that the mean inclina tion of this axis to the ecliptic must necessarily change. Change of At present the obliquity of the ecliptic that is, the inclina- obliquityof tion of the equator to the ecliptic is diminishing; and a " 11 " tl p this process, which has been going on for many centuries, will continue for a long time yet to come, after which the obliquity will increase, the total range on either side of the mean value amounting to about 3 3 . The various observa tions and traditions by which the progressive diminution of the obliquity is confirmed have been collected by Bailly. The following table contains those which appear to be the best authenticated, as well as the results of some more recent observations, from which the present value

of the obliquity and the rate of its diminution may be deduced:—

I recession of the equinoxes. Year. 1 Name of Obsenrer Obliquity. Before Christ. 1100 Tcheou-KonT 23 54 3 200 j Eratosthenes, confirmed by Hip- parchus and Ptolemy | 23 51 15 160 The Chinese 23 45 52 After Christ. 827 Arabians at Baghdad 23 33 52 880 Albate^ni ... 23 35 40 1150 Almansor 23 33 30 1278 The Chinese 23 32 12 1437 Ulugh Be<*h 23 31 58 1490 Walther. 23 29 47 1590 Tycho 23 29 52 1646 Riccioli. ... ... 23 30 20 1660 Hevelius .... 23 29 10 1672 Cassini 23 29 00 1690 Flamsteed 23 28 48 1703 Bianchini ^. 22 28 35 1736 Condamine 23 28 24 1743 Cassini de Thury 23 28 26 1750 Lacaille 23 28 19 1755 Bradley 23 28 15 1756 T. Mayer 23 28 16 1769 Maskelyne 23 28 10 1780 Cassini . ... 23 27 54 1800 Maskelyne 23 27 56 6 Piazzi ., 23 27 56-3 Delambre . 23 27 57 1813 Pond 23 27 48-66 1815 Bessel 23 27 47-46 1816 Brinkley 23 27 49-21 1825 Pearson 23 27 44-01

Although the comparison of these observations with one another gives very discordant results relatively to the law according to which the obliquity varies, their totality places the fact of its progressive diminution be yond all manner of doubt. It amounts to about 45J" per century at present, and may be regarded as uniform for many centuries to come.

The longitudes of the stars, as has already been mentioned, are measured on the ecliptic from the vernal equinox ; and therefore, if the line of the equinoxes, which is the same as the line of the nodes, is invariable, the longitude of any star will always be the same, whatever interval of time may elapse between two observations of that longitude. But on com paring the actual state of the heavens with the observations recorded by ancient astronomers, it is perceived that the longitudes of all the stars are considerably increased. The phenomenon is to be explained by attributing to the equi noctial points a retrograde motion from east to west, in con sequence of which the sun, whose motion is direct, p-rrivps at them sooner than if they remained at rest ; and therefore the equinoxes, and spring, autumn, and the other season?, happen before the sun has completed an entire circuit. Oil this account the motion has been denominated the Precession of the Equinoxes. As this motion is extremely slow, its exact amount can be discovered only by a comparison of observations separated from each other by long intervals of time. The comparison of modern observations with those of Hipparchus gives as its annual amount 50". The mean result of the observations of Tycho, compared with those of Lacaille, gives 50". On comparing modern observations with one another, we find 50" 06. Delambre, in his solar tables, supposes the annual precession to be equal to 50" l. According to this estimate the equinoctial points go backwards at the rate of 1 in 71 6 years nearly, and therefore will make a complete revolution of the heavens in about 25,868 years.

The diminution of the obliquity of the ecliptic arises from the displacement of the ecliptic itself ; the precessiou of the equinoxes is, on the contrary, occasioned by the con tinual displacement of the plane of the terrestrial equator. This displacement results from the combined action of the sun and moon (for the influence of the planets amounts only to a fraction of a second, and is consequently scarcely sensible) on the mass of protuberant matter accumulated about the earth s equator, or the matter which forms the excess of the terrestrial spheroid above its inscribed sphere. The attracting force of the sun and moon on this shell of matter may be resolved into two ; one parallel to the plane of the equator, the other perpendicular to it. The tendency of this last force is to diminish the angle which the plane of the equator makes with that of the ecliptic ; and if the earth had no motion of rotation, it would soon cause the two planes to coincide. In consequence, however, of the rotatory motion of the earth, the inclination of the two planes remains constant ; but the effect produced by the action of the force in question is, that the plane of the equator is constantly shifting its place, in such a manner that the line of the equinoxes advances in the direction of the diurnal motion, or contrary to the order of the signs, its pole having a slow angular motion about the pole of the ecliptic.

If the sun and moon moved in the plane of the equator,

there would evidently be no precession; and the effect of their action in producing it varies with their distance from that plane. Twice a year, therefore, the effect of the sun in causing precession is nothing ; and twice a year, namely, at the solstices, it is a maximum. On this account the obliquity of the ecliptic is subject to a semi-annual variation ; for the sun s force, which tends to produce a change in the obliquity, is variable, while the diurnal motion of the earth, which prevents the change from taking place, is constant. Hence the plane of the equator is subject to an irregular motion, which is technically called the Solar Nutation. The existence of the solar nutation Nuta is, however, only a deduction from theory, for its amount is too small to be perceptible by observation ; but a simi lar effect of the moon s action is sufficiently appreciable, and was, in fact, discovered by Bradley before theory had indicated its existence. Its period, however, is different, and depends on the time of the revolution of the moon s nodes, which is performed in 18 years and about 7 months. During this time the intersection of the lunar orbit with the ecliptic has receded through a complete circumference ; and the inequality of the moon s action will consequently, in the same time, have passed through all its different degrees. Bradley observed that the declinations of the stars continued to augment during nine years, that they diminished during the nine years following, and that the greatest change of declination amounted to 18". He

remarked further, that this motion was connected with an