hour of R.A., that being the R.A. of the north ecliptic pole; and in the southern hemisphere, the constellation lying near the VIth hour, that being the R.A. of the south ecliptic pole. The remarks we have just made apply only to those stars whose declination north or south exceeds 67°. The annual precession in declination, however, depends on the star's right ascension, both as to amount and direction. At VI and XVIII hours it is at zero; at XII hours it reaches the northern maximum of 20′′; and at XXIV it reaches a similar southern maximum. From XVIII to XXIV hours, and from XXIV to VI hours, the precession is N., consequently additive to stars of north declination, but subtractive from those of south declination: but from VI to XVIII, the precession being S., it is additive to southern, and subtractive from northern stars.

The discovery of precession dates from about 125 B. C., when it was detected by Hipparchus, by means of a comparison of his own observations with those of Timocharis and Aristyllus, made about 178 years previously its existence was afterwards confirmed by Ptolemy 1. It was Copernicus, however, who first gave the true explanation of the phenomenon, and Newton who discovered its physical cause.

Nutation-It must be borne in mind that the effect of precession varies according to the time of year, on account of the ever-varying distance of the Earth from the Sun. Twice a year, at the equinoxes, the influence of the Sun is at zero; and twice a year also, at the solstices, it is at its maximum. On no two successive days is it of exactly the same value, and consequently the precession of the equinoctial points must be uneven, and the obliquity of the ecliptic subject to a half-yearly variation; since the Sun's force which changes the obliquity is constantly varying, while the rotation of the Earth is continuous. This then gives rise to a small oscillating motion of the Earth's axis, termed the solar nutation: of a far more considerable amount, however, is the value of the nutation arising from the agency of the Moon; so much so that it was detected by Bradley before its existence had been inferred from theory *.

h Almagest, lib. vii.

i Nutatio, nodding.

* Phil. Trans., vol. xlv. p. 1 et seq. 1748.

it);

I cannot better explain the nature of precession than in nearly the words of Sir J. Herschel, who says:-"The nutation of the Earth's axis is a small and slow gyratory movement, by which, if subsisting alone, the pole would describe among the stars, in a period of 18 years, a minute ellipse having its longer axis equal to 18.5′′, and its shorter to 13.74" (the longer being directed towards the pole of the ecliptic, and the shorter of course at right angles to the semi-axis major is, therefore, equal to 9.25′′, which quantity is called the coefficient of nutation. The consequence of this real motion of the pole is an apparent advance and recess of all the stars in the heavens to the pole in the same period. Since, also, the place of the equinox on the ecliptic is determined by the place of the pole in the heavens, the same agency will cause a small alternating motion to and fro of the equinoctial points, by which, in the same periods, both the longitudes and the right ascensions of the stars will be alternately increased and diminished.

"Precession and nutation, although for convenience here considered separately, in reality exist together; they are, in fact, constituent parts of the same general phenomenon: and since, while in virtue of this nutation, the pole is describing its little ellipse of 18.5" in diameter, it is carried on by the greater and regularly progressive motion of precession over so much of its circle round the pole of the ecliptic as corresponds to 18 years—that is to say, over an angle 18 times 50.1" round the centre (which, in a small circle of 23° 28' in diameter, corresponds to 6' 20", as seen from the centre of the sphere); the path which it will pursue in virtue of the joint influence of the 2 motions will be neither an ellipse nor an exact circle, but a slightly undulating ring.

"These movements of precession and nutation are common to all the celestial bodies, both fixed and erratic; and this circumstance makes it impossible to attribute them to any other cause than the real motion of the Earth's axis, as we have described. Did they only affect the stars, they might, with equal plausibility, be considered as arising from a real rotation of the starry heavens

Other values are: Busch's 9.2320", Lundahl's 92164", C. A. Peters 9 2361". A mean of these, namely 9:2231", is the

R

value finally adopted by Peters. (Numerus Constans Nutationis.)

as a solid shell round our axis, passing through the poles of the ecliptic in 25,868 years, and a real elliptic gyration of that axis in rather more than 18 years: but since they also affect the Sun, Moon, and planets, which, having motions independent of the general body of the stars, cannot without extravagance be supposed to be attached to the celestial conclave, this idea falls to the ground; and there only remains, then, a real motion of the Earth by which they can be accounted for m❞

m Treatise on Ast., p. 172. 1833. In his Outlines of Astronomy Sir John has altered this statement of nutation, but

the original version strikes me as being the better one of the two, and therefore I retain it here.

CHAPTER IV.

OPTICAL-ILLUSION PHENOMENA.

Aberration.-The constant of Aberration.-Familiar illustration.-History of the circumstances which led to its discovery by Bradley.-Parallax-Explanation of its nature.-Parallax of the heavenly bodies.-Parallax of the Moon.—Importance of a correct determination of the Parallax of an object.—Leonard Digges on the distance of the Planets from the Earth.

ABE

BERRATION.-The aberration of light is another important phenomenon which requires to be taken into consideration in the reduction of astronomical observations. Although light travels with the enormous velocity of (about) 184,000 miles per second-a speed so great, that for all practical terrestrial purposes we may consider it to be propagated instantaneously; yet the astronomer, who has to deal with distances of millions of miles is obliged to be more particular. A simple illustration will shew this: the mean distance of our globe from the Sun is 91,400,000 miles, and since light travels at the rate of 184,000 miles per second, we ascertain by a mere arithmetical process that the time occupied by a ray of light in reaching us from the Sun is 8m 17.2", so that in point of fact, in looking at the Sun at a given moment, we do not see it shining as it is, but as it did 8m 17.2° previously. If the Earth were at rest, this would be all very well; but since the Earth is in motion, when the solar ray enters the eye of a person on its surface, he will be some way removed from the point in space at which he was situated when the ray left the Sun; he will consequently see that luminary behind the true place it actually occupies when the ray enters his eye. In the course of

8m 17.2 the Earth will have advanced in its orbit 20.4192"; this quantity is called the constant of aberration". Aberration may be summed up as a phenomenon resulting from the combined effect of the motion of light and the Earth's motion in its orbit b. Suppose a ball let fall from a point P above the horizontal line AB, and a tube, of which A is the lower extremity, placed to receive it; if the tube were fixed the ball would strike it on the lower side, but if the tube were carried forward in the direction AB, with a velocity properly adjusted at every instant to that of the ball, while preserving its inclination to the horizon, so that when the

Fig. 81.

B

ABERRATION.

ball in its natural descent reached B, the tube would have been carried into the position BQ, it is evident that the ball throughout its whole descent would be found in the tube; and a spectator referring to the tube the motion of the ball, and carried along with the former, unconscious of its motion, would fancy that the ball had been moving in an inclined direction and had come from Q. The following similes are frequently made use of to exemplify aberration: a shower of rain descending perpendicularly will appear to fall in its true direction to a person at rest, but if

This is Baily's value. W. Struve's is 204451"; C. A. Peters's, 20 ̊4255", 20'503", and 20.481"; Lindenau's,

204486"; and Lundahl's, 205508". Struve's is considered the best.

See a paper by Challis in Phil. Mag., 1855.