a follow the law of the inverse squares of the distances. Hence will arise a series of perturbations, extremely small in amount, but still perceptible, in the lunar motions; by which the node and the apogee will be affected. A more remarkable consequence of this cause, however, is a small nutation of the lunar orbit, exactly analogous to that which the moon causes in the plane of the earth's equator, by its action on the same elliptic protuberance. And, in general, it may be observed, that in the systems of planets which have satellites, the elliptic figure of the primary has a tendency to bring the orbits of the satellites to coincide with its equator, tendency which, though small in the case of the earth, yet in that of Jupiter, whose ellipticity is very considerable, and of Saturn especially, where the ellipticity of the body is reinforced by the attraction of the rings, becomes predominant over every external and internal cause of disturbance, and produces and maintains an almost exact coincidence of the planes in question. Such, at least, is the case with the nearer satellites. The more distant are comparatively less affected by this cause, the difference of attractions between a sphere and spheroid diminishing with great rapidity as the distance increases. Thus, while the orbits of all the six interior satellites of Saturn lie almost exactly in the plane of the ring and equator of the planet, that of the external satellite, whose distance from Saturn is between sixty and seventy diameters of the planet, is inclined to that plane considerably. On the other hand, this considerable distance, while it permits the satellite to retain its actual inclination, prevents (by parity of reasoning) the ring and equator of the planet from being perceptibly disturbed by its attraction, or being subjected to any appreciable movements analogous to our nutation and precession. If such exist, they must be much slower than those of the earth; the mass of this satellite (though the largest of its system) being, as far as can be judged by its apparent size, a much smaller fraction of that of Saturn than the moon is of the earth; while the solar precession, by reason of the immense distance of the sun, must be quite inappreciable. In the (579.) It is by means of the perturbations of the planets, as ascertained by observation, and compared with theory, that we arrive at a knowledge of the masses of those planets, which, having no satellites, offer no other hold upon them for this purpose. Every planet produces an amount of perturbation in the motions of every other, proportioned to its mass, and to the degree of advantage or purchase which its situation in the system gives it over their movements. The latter is a subject of exact calculation; the former is unknown, otherwise than by observation of its effects. determination, however, of the masses of the planets by this means, theory lends the greatest assistance to observation, by pointing out the combinations most favourable for eliciting this knowledge from the confused mass of superposed inequalities which affect every observed place of a planet; by pointing out the laws of each inequality in its periodical rise and decay; and by showing how every particular inequality depends for its magnitude on the mass producing it. It is thus that the mass of Jupiter itself (employed by Laplace in his investigations, and interwoven with all the planetary tables) has of late been ascertained, by observations of the derangements produced by it in the motions of the ultra-zodiacal planets, to have been insufficiently determined, or rather considerably mistaken, by relying too much on observations of its satellites, made long ago by Pound and others, with inadequate instrumental means. The same conclusion has been arrived at, and nearly the same mass obtained, by means of the perturbations produced by Jupiter on Encke's comet. The error was one of great importance; the mass of Jupiter being by far the most influential element in the planetary system, after that of the sun. It is satisfactory, then, to have ascertained, -as by his observations Professor Airy is understood to have recently done, — the cause of the error; to have traced it up to its source, in insufficient micrometric measurements of the greatest elongations of the satellites; and to have found it disappear when measures taken with more care, and with infinitely superior instruments, are substituted for those before employed. (580.) In the same way that the perturbations of the planets lead us to a knowledge of their masses, as compared with that of the sun, so the perturbations of the satellites of Jupiter have led, and those of Saturn's attendants will, no doubt, hereafter lead, to a knowledge of the proportion their masses bear to their respective primaries. The system of Jupiter's satellites has been elaborately treated by Laplace; and it is from his theory, compared with innumerable observations of their eclipses, that the masses assigned to them in art. 463. have been fixed. Few results of theory are more surprising, than to see these minute atoms weighed in the same balance which we have applied to the ponderous mass of the sun, which exceeds the least of them in the enormous proportion of 65000000 to 1. CHAP. XII. OF SIDEREAL ASTRONOMY. OF THE STARS GENERALLY. THEIR DISTRIBUTION INTO CLASSES (581.) BESIDES the bodies we have described in the foregoing chapters, the heavens present us with an in numerable multitude of other objects, which are called generally by the name of stars. Though comprehending individuals differing from each other, not merely in brightness, but in many other essential points, they all agree in one attribute, -a high degree of permanence as to apparent relative situation. This has procured them the title of "fixed stars ;" an expression which is to be understood in a comparative and not an absolute sense, it being certain that many, and probable that all are in a state of motion, although too slow to be perceptible unless by means of very delicate observations, continued during a long series of years. (582.) Astronomers are in the habit of distinguishing the stars into classes, according to their apparent brightness. These are termed magnitudes. The brightest stars are said to be of the first magnitude; those which fall so far short of the first degree of brightness as to make a marked distinction are classed in the second, and so on down to the sixth or seventh, which comprise the smallest stars visible to the naked eye, in the clearest and darkest night. Beyond these, however, telescopes continue the range of visibility, and magnitudes from the 8th down to the 16th are familiar to those who are in the practice of using powerful instruments; nor does there seem the least reason to assign a limit to this progression; every increase in the dimensions and power of instruments, which successive improvements in optical science have attained, having brought into view multitudes innumerable of objects invisible before; so that, for any thing experience has hitherto taught us, the number of the stars may be really infinite, in the only sense in which we can assign a meaning to the word. (583.) This classification into magnitudes, however, it must be observed, is entirely arbitrary. Of a multitude of bright objects, differing probably, intrinsically, both in size and in splendour, and arranged at unequal distances from us, one must of necessity appear the brightest, one next below it, and so on. An order of succession (relative, of course, to our local situation among them) must exist, and it is a matter of absolute indifference, where, in that infinite progression downwards, from the one brightest to the invisible, we choose to draw our lines of demarcation. All this is a matter of pure convention. Usage, however, has established such a convention; and though it is impossible to determine exactly, or à priori, where one magnitude ends and the next begins, and although different observers have differed in their magnitudes, yet, on the whole, astronomers have restricted their first magnitude to about 15 or 20 principal stars; their second to 50 or 60 next inferior; their third to about 200 yet smaller, and so on; the numbers increasing very rapidly as we descend in the scale of brightness, the whole number of stars already registered down to the seventh magnitude, inclusive, amounting to 15000 or 20000. (584.) As we do not see the actual disc of a star, but judge only of its brightness by the total impression made upon the eye, the apparent "magnitude" of any star will, it is evident, depend, 1st, on the star's distance from us; 2d, oh the absolute magnitude of its illuminated surface; 3d, on the intrinsic brightness of that surface. Now, as we know nothing, or next to nothing, of any of these data, and have every reason for believing that each of them may differ in different individuals, in the proportion of many millions to one, it is clear that we are not to expect much satisfaction in any conclusions we may draw from numerical statements of the number of individuals arranged in our artificial classes. In fact, astronomers have not yet agreed upon any principle by which the magnitudes may be photometrically arranged, though a leaning towards a geometrical progression, of which each term is the half of the preceding, may be discerned.* Nevertheless, it were much to be wished, that, setting aside all such arbitrary subdivisions, a numerical estimate should be formed, * Struve, Dorpat Catal. of Double Stars, p. xxxv. |