is, however, that the plane of the equator is constantly, though slowly, shifting its place in the manner we have endeavoured to describe." In the reduction of astronomical observations the correction to be applied for precession in right ascension is almost always additive; increasing in the regions round the poles of the heavens, but becoming very small near the poles of the ecliptic. It is in the space included between these poles in each hemisphere that the correction becomes subtractive; in the northern hemisphere, this small space comprehends the constellations lying near the XVIIIth hour of R.A., that being the R.A. of the North ecliptic pole; and in the southern hemisphere, the constellations lying near the VIth hour, that being the R.A. of the South ecliptic pole. The remarks I 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 only, 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 i. 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. 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 A useful table of precessions will be given in a later volume of this work. Almagest, lib. vii. 1 Nutatio, nodding. 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 is uneven, and the obliquity of the ecliptic is 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 even its existence had been inferred from theory m. : The nature of nutation cannot be better explained 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 it); 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 m Phil. Trans., vol. xlv. p. 1. 1748. n Other values are: Busch's 9*2320", Lundahl's 92361", C. A. F. Peters's 9'2164". A mean of these, namely 92231", is the value finally adopted by Peters. (Numerus constans Nutationis, 4to. Petropoli, 1842: see p. 5 of W. Struve's Rapport on Peters's Memoir.) 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 as a solid shell around 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 "." 。 Treatise on Ast., p. 172. 1833. In his Outlines of Astronomy Sir John altered this statement of nutation, but the original version strikes me as being the better of the two, and therefore I retain it here. CHAPTER IV. ABERRATION AND PARALLAX. 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. A1 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 186,660a 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 precise. A simple illustration will shew this: if we take the mean distance of our globe from the Sun at 92,890,000 miles, and consider that light travels at the rate of 186,150 miles per second, we may ascertain by a simple arithmetical process that the time occupied by a ray of light in reaching us from the Sun is 8m 198, 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 was 8m 198 previously. If the Earth were at rest, this would be a a A. Cornu (Proceedings of the Roy. Inst., vol. vii. p. 472, May 1875) makes it 186,660 miles, but it is probably somewhat less. Other values obtained experimentally are: Helmert, 299,990 kilometres; Michelson, 299,910 kilometres; Young and Forbes, 301,382 kilometres. For a comprehensive review, historical and practical, of the whole subject of the velocity of light, see a Memoir by Newcomb in Astron. Papers prepared for American Naut. Alm., vol. ii. part III. trivial matter; but as the Earth is in motion, it follows that 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 19 the Earth will have advanced in its orbit 20.492"; this quantity is called the Constant of Aberration b. Aberration may be defined to be a phenomenon resulting from the combined effect of the motion of Fig. 175. --- B ABERRATION. light and of the motion of the Earth in its orbit. 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 forwards 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 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 in the tube; and a spectator b Baily's value is 20-419"; W. Struve's is 20-445"; C. A. F. Peters's, 20.425", 20.503", and 20.481"; Lindenau's, 20.448"; Lundahl's, 20.550"; Maclear's, 20-53′′; Main's, 20-335′′; Nyrén's, 20.492′′. Struve's was long considered the best, but • See a paper by Challis in Phil. Mag., 4th ser., vol. ix. p. 430. June 1855. |