character as regards the formation of their banks. This is the "hygre," or "bore," and is due to the fact that a wide estuary at the mouth of the river suddenly contracts like a funnel. The result is, that the estual spring tide rushes up with an overpowering force, carrying all before it. This further peculiarity

likewise subsists: namely, that there is no "slack-water," as is ordinarily the case in other rivers, between the ebb and flow of the tide. The approach of the bore on the Severn may be heard at a considerable distance roaring, as it were, in its upward progress. The head is about 3ft high, and it frequently does

a good deal of mischief to property. The maximum effect is at the 4th tide after the Full Moon.

Fig. 174, represents the tidal phenomenon known as the "Mascaret" on certain French rivers, especially the Garonne and the Seine, which corresponds with the "Bore" of the Severn.

An inspection of the engraving coupled with the remarks made above will sufficiently indicate the general character of the phenomenon.

The evident connexion between the periods of the tides and those of the phases of the Moon led to the tides being attributed to the Moon's action long before their true theory was understood. Aristotle and Pytheas of Marseilles m are both said to have pointed out the connexion. Julius Cæsar adverts to the connexion existing between the Moon and spring tides ".

Pliny says: "Estus maris accedere et reciprocare, maxime mirum: pluribus quidem modis: verum causa in sole lunáque." Kepler clearly indicated that the principle of gravitation is concerned an opinion from which Galileo strongly dissented. Wallis, in 1666, also published a tidal theory". Before Sir Isaac Newton turned his attention to this subject, the explanations given were at best but vague surmises. "To him was reserved the glory of discovering the true theory of these most remarkable phenomena, and of tracing, in all its details, the operation of the cause which produces them."

CHAPTER III

PHYSICAL PHENOMENA.

Secular Variation in the Obliquity of the Ecliptic.-Precession.—Its value.—Its physical cause.-Correction for Precession.-History of its discovery.— Nutation. -Herschel's definition of it.-Connexion between Precession and Nutation.

ECULAR Tariation in the Obliquity of the Ecliptic.—Although

SECULA

it is sufficiently near for most purposes to consider the inclination of the plane of the ecliptic to that of the equator as invariable, yet this is not strictly the case, inasmuch as it is subject to a small but appreciable change of 46·45′′ (C. A. F. Peters) per century. This phenomenon has long been known to astronomers, on account of the increase it causes in the latitude of all stars in some situations, accompanied by a corresponding decrease in the opposite regions. Its effect at the present time is to diminish the inclination of the planes of the equator and the ecliptic to each other; but this diminution will not go on" beyond certain very moderate limits, after which it will again increase, and thus oscillate backwards and forwards through an arc of 1° 21', the time occupied in one oscillation being about 10,000 years. One effect of this variation of the plane of the ecliptic-that which causes its nodes on a fixed plane to change is associated with the phenomena of the precession of the equinoxes, and cannot be distinguished from it, except in theory b.

Precession. The precession of the equinoxes is a slow but Compare Genesis viii. 22. the epoch of January 1, 1890, is 23° 27' 12*79".

The inclination of the ecliptic for

continual shifting of the equinoctial points from East to West. Celestial longitudes and right ascensions are reckoned from the vernal equinox, and if this were a fixed point, the longitude of a star would never vary, but would remain the same from age to age as does its latitude (sensibly). Such, however, is not the case; as it has been found that apparently all the stars have changed their places since the first observations were made by the astronomers of antiquity. Two explanations only can be given to account for this phenomenon: we must either suppose that the whole firmament has advanced, or that the equinoctial points have receded. And as these points depend on the Earth's motion, it is far more reasonable to suppose that the phenomenon is owing to some perturbation of our globe rather than that the starry heavens should have a real motion relative to these points. The latter explanation is accordingly adopted, namely, that the equinoxes have a periodical retrograde motion from East to West, thereby causing the Sun to arrive at them sooner than it otherwise would had these points remained stationary. The annual amount of this motion is, however, exceedingly small, being only equal to 50-2′′; and since the circle of the ecliptic is divided into 360°, it follows that the time occupied by the equinoctial

It may be well to mention that the equinoxes are the two points where the ecliptic cuts the equator; and are so called because when the Sun in its annual course arrives at either of them, day and night are equal throughout the world. The point where the Sun crosses the equator, going north, is known as the vernal equinox; and the opposite point, through which the Sun passes going south, as the autumnal equinox. These intersecting points are also termed nodes, and an imaginary line joining the two, the line of nodes. The ascending node (8) answers to the vernal equinox, and the descending (8) to the autumnal.

d By "change of place" is here meant change of position of the Sphere as a whole to certain fixed co-ordinates, not change of place of the stars inter se, so as to alter the figures of the Constellations; although many individual stars-as we

shall see hereafter-have very considerable proper motions.

Bessel, by a careful discussion of the most reliable observations, fixed the value of general precession for the epoch of 1750 at 50 21129", and the value of lunisolar precession at 5037572". For the epoch of 1800 he gave for the value of the latter 50 36354". The lunar precession is about 2 times the solar precession, just as the lunar tide is 24 times the solar tide, and for much the same reason, namely, the difference of the attractions. Dreyer's value for 1800 for the general precession is 50 2365", and for the luni-solar precession 50*3752" (Copernicus, vol. ii. p. 155. 1882). And see a paper by L. Struve, Mém. de l'Acad. de St. Pétersbourg, 7th Ser., vol. xxxv. p. 3, cited Observatory, vol. xi. p. 200, April 1888.

points in making a complete revolution of the heavens is 25,817 years. It is owing to precession that the Pole-star varies from age to age, and also that whilst the sidereal year, or actual revolution of the Earth round the Sun, is 365d 6h 9m 110, the equinoctial, solar, or tropical year is only 365d 5h 48m 46-05o (Airy). The successive returns of the Sun to the same equinoctial points must therefore precede its return to the same point on the ecliptic by 20m 24.95 of time, which corresponds to about 50.27" of arc. It is also on account of the precession of the equinoxes that the signs of the ecliptic do not now correspond with the constellations of the same name, but lie about 28° Westward of them. Thus, that division of the ecliptic known as the sign of Taurus lies in the constellation Aries, the sign of Aries having passed into Pisces. It should be remarked, however, that the signs and constellations coincided with one another about 100 B. C. In recent times, the attempts that have been made to establish the motion of the solar system through space have rendered an accurate knowledge of precession indispensable; and the elaborate labours of C. A. F. Peters and O. Struve have led to a slight modification in the value of the constants of precession adopted by Bessel'. Their new value for the general precession is, for 1800, 50.2411′′ +0.0002268′′ t.

g

"The cause of precession is to be found in the combined action of the Sun and Moon upon the protuberant mass of matter accumulated at the Earth's equator, the attraction of the planets being scarcely sensible 1. The attracting force of the Sun and Moon upon this shell of matter is of a two-fold character; one parallel to the equator, and the other perpendicular to it. The tendency of the latter force is to diminish the angle which the plane of the equator makes with the ecliptic; and were it not for the rotatory motion of the Earth, the planes would soon coincide; but, by this motion, the planes remain nearly constant to each other. The effect produced by the action of the force in question

Tabula Regiomontanæ.

Called hence, luni-solar precession.

h When the value of the constant of

precession, given at any time, includes the variation caused by the planets, it is called the constant of general precession.