sion a Lyræ, denotes the star a in the constellation Lyra, a harp; and so of others. Some of the stars have particular names, as Sirius, Aldebaran, Arcturus, &c. 123. Definition. A Catalogue of fixed stars is a table containing a list of stars with their right ascensions and declinations, or their longitudes and latitudes. The first catalogue was formed by Hipparchus, about 130 years prior to the Christian era; and contained the positions of nearly 1000 stars. Various catalogues have since been formed; some of them containing the situations of many thousands of stars, most of which are only visible by the aid of a telescope. CHAPTER IX. PRECESSION OF THE EQUINOXES-ABERRATION-NUTATION. 124. Position of the ecliptic and motion of the equinoxes. From comparisons of catalogues of the stars, formed at different times, it is found that the latitudes of the stars continue always nearly the same. Hence the position of the ecliptic among the stars must be fixed, or nearly so. But it is found, from these comparisons, tnat the longitudes of the stars are continually increasing at the rate of about 50" in a year. This increase of longitude is common to all the stars, and, except for a few, is the same for each star. It cannot therefore be reasonably imputed to motions in the stars themselves. Hence it follows that the vernal equinox, the point from which longitude is reckoned, must have a backward or retrograde motion along the ecliptic, equal to the increase in the longitudes of the stars. Let ECFD, Fig. 20, be the ecliptic, p and p', its poles, E, the place of the vernal equinox at any time, and E', its place at some subsequent time, it having, during the intermediate time, retrograded along the ecliptic through the arc EE'. Then must the longitude of any star S, be changed during this interval of time from EH to E'H; being increased by the quantity EE'. As the autumnal equinox is always directly opposite to the vernal equinox, it must have the same motion. 125. Definition. The Precession of the Equinoxes is the retrograde motion which they have along the ecliptic. It is 50".2 in a year. 126. The poles of the equator revolve with retrograde motions in small circles around the poles of the ecliptic, at distances equal to the obliquity of the ecliptic. As the ecliptic remains in a fixed position or nearly so (124), it is evident the equator must change its position, otherwise there could be no motion in the equinoctial points; and a motion of the equator must necessarily produce motions of its poles. Let ECFD, Fig. 20, be the ecliptic, p and p', its poles, and Pab, a small circle about the pole p, at a distance equal to the obliquity of the ecliptic. Then, since the distance between the poles of two great circles is equal to the angle they make with each other, if we suppose the obliquity of the ecliptic to continue the same, as it does nearly, the north pole of the equator must always be in the circle Pab. Let EQFB be the position of the equator at any time. Then will the great circle pCp'D, having for its poles the equinoctial points E and F, be the position of the solstitial colure at that time (113), and P must therefore be the place of the north pole of the equator. Let E'Q'F'B' be the position of the equator at some subsequent time. Then will the great circle pC'p'D', having for its poles the equinoctial points E' and F', be the position of the solstitial colure, and P', the position of the north pole of the equator. Hence, while the vernal equinox has retrograded from E to E', the pole has retrograded from P to P' in the small circle Pab. The south pole of the equator must evidently have a corresponding motion. Cor. Since E and E' are the poles of pPp' and pP'p', the arc EE' is the measure of the angle PpP'. Hence the angular motion of the pole of the equator round the pole of the ecliptic is equal to the precession of the equinoxes: that is, it is 50.2 a year. It must therefore require nearly 26,000 years to make a complete revolution. 127. Precession in Right Ascension. If Em be perpendicular to E'G', then will E'm be the retrograde motion of the equinox in right ascension, sometimes called the precession in right ascension. Taking EE' = 50.2, we find E'm = 46", the annual precession in right ascension. 128. Annual Variations in right ascension and declination. As the longitudes of the stars are continually changing, their right ascensions and declinations must also change. These changes are, however, very different for different stars, depending on their positions. The change in the right ascension or declination of a star during a year, is called its annual variation in right ascension or declination. If we suppose E and E' to be two positions of the vernal equinox at an interval of a year, and PsG and P'sG' to be arcs of declination circles through a star at s, the annual variation of the star in right ascension will be the difference between EG and E'G'; and its annual variation in declination, the difference between SG and sG'. Formulæ are easily investigated for computing the annual variations in right ascension and declination.* In catalogues of the stars, the values of the annual variations for each star, computed for the time for which the catalogue is formed, are annexed to the right ascension and declination of the star at that time. From these, the right ascension and declination of any star, contained in the catalogue, may be found for any given time, provided it be not many years distant from the time for which the catalogue was formed. In consequence, however, of small changes which the annual variations themselves undergo, from the changes in the positions of the stars in reference to the equator, it is requisite that new catalogues should be occasionally formed. 128 a. Constellations of the zodiac and signs of the ecliptic. At the time of the first catalogue of the stars, 130 years prior to the Christian era, the signs of the ecliptic corresponded very nearly to the constellations of the zodiac bearing the same names. But, in the interval of nearly 2000 years since that period, the vernal equinox has retrograded about 28°; so that the sign Taurus now * See Appendix, art. 54. nearly corresponds with the constellation Aries, the sign Gemini with the constellation Taurus, and so for the others. 129. Visible effect of the precession of the equinoxes. The effect of the precession of the equinoxes becomes, in the course of ages, very conspicuous in the northern and southern parts of the heavens. The poles of the heavens, in their slow retrograde revolutions about the poles of the ecliptic (126), must approach near to different stars in succession. At the time the first catalogue of the stars was formed, the north pole was nearly 12° distant from the present pole star, and its distance from it is now only about 11°. The pole will continue to approach this star till the distance between them is about half a degree, and will then recede. In a period of 12,000 years from the present time, the pole will have arrived within about 5° of a very bright star, a Lyræ, from which it is now more than 50° distant, and consequently will then be more than 40° from the present pole star. This continual change in the position of the pole, must also make changes in the class of stars that are circumpolar at any given place. For a star cannot be circumpolar at any place, if its distance from the pole is greater than the altitude of the pole at the place, or (57) than the latitude of the place. In process of time our present pole star will cease to be a circumpolar star in the latitude of Philadelphia. The student will, however, observe that these changes must be periodical. At the termination of a period of 26,000 years (126), the position of the pole, with reference to the stars, and consequently the class of circumpolar stars at a place, will again become nearly the same as at the commencement of that period. 130. Cause of the precession of the equinoxes. Investigations in physical astronomy prove that the precession of the equinoxes is produced by the attractions of the sun and moon on that portion of the earth that is on the outer side of an imaginary sphere, conceived to be described about the earth's axis. The effect of these actions is a slow change in the direction of the earth's axis, and consequently corresponding changes in the positions of the equator and its poles. ABERRATION. 131. Dr. Bradley's Observations. In the early part of the last century, Dr. Bradley, a celebrated English astronomer, commenced a series of accurate observations on the positions of some of the fixed stars, which he continued for a number of years. In the course of these observations, he found the apparent places of the stars to be subject to periodical changes, amounting, in some, to about 40′′, and that the period of these changes was a year. After several unsuccessful attempts to account for these changes, it at length occurred to him that the annual motion of the earth, combined with the motion of light, must generally cause a star or other heavenly body to appear to be in a position different from its true position; and, on investigation, he found that the changes in the apparent positions of the stars which must thus be produced, corresponded with those he had observed. 132. Effect of the combined motions of the earth and of light on the apparent place of a body. From phenomena that will be hereafter noticed, it had been ascertained, prior to the time of Bradley, that the transmission of light, though inconceivably rapid, is not instantaneous. It occupies 8 m. 13 sec. in passing the distance from the sun to the earth, and consequently moves with a velocity of about 192,000 miles per second. The velocity of the earth in its annual motion is 19 miles per second (107). Disregarding the motion of an observer at the earth's surface, that is produced by the rotation on the axis, which is small in comparison with the annual motion, let BD, Fig. 21, be the path in which he is carried at any time by the annual motion of the earth, during an interval so short that the path may be regarded as straight. Let E be any point in BD, s, the position of a star, having the direction Es from the point E, AE, the distance through which the observer is carried during some small interval of time, and Ea, the distance through which light moves in the same time. Let A'a', A''a'', &c., and Es', be drawn parallel to Aa; and the former will divide EA and Ea proportionally. Then, if a particle of light in the ray sE be at a when the observer is at A, it will be at a' when he is at A', at a' when he is at A", &c. The particle therefore continues in the |