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two together forming what is called the head of the comet. From the head, a stream or streams of light shoot out in a direction opposite to the sun, growing broader and more diffused as the distance from the head increases. This is called the tail of the comet.

The tail sometimes attains an immense length. That of the comet of 1680, one of the most celebrated of modern times, extended through an arc of more than 70°, or, according to some, more than 90°; which would make the real length to be more than 100 millions of miles. And there are records of others, in which the extent of this singular appendage was still greater.

A tail is not, however, by any means an invariable appendage of a comet. In some of the brighest, no tail has been perceptible; and in many it has been quite short. The smaller comets very frequently do not exhibit the least appearance of a tail. They appear only as round or somewhat oval masses of vaporous matter, increasing in density towards the centre; but without any distinct nucleus, or any thing that would indicate a central, solid mass. Stars, even of small magnitude, have been seen through what appeared to be the densest portion of their substance.

338. Small quantity of matter in a comet. Comets have been known to pass near to some of the planets and to have had their own motions much affected by the consequent attractions, without producing any sensible influence on the motions of these bodies. In one instance a comet passed among the satellites of Jupiter and was thrown by the attraction of the planet entirely out of the orbit it had been describing, and forced into another, quite different in extent; yet, not the least perceptible derangement of the motions of the satellites was produced. It is hence concluded that the quantity of matter in a comet must be very small.

339. Orbit of a Comet and its Elements. Investigations, founded on the law of gravitation, prove, that a body revol

ving about the sun and not influenced by the attraction of any other body, must move either in a circle or in some one of the three curves called Conic Sections. Comets are found generally to move in elliptical orbits of extremely great eccentricity; so great, that the part of the orbit described during the comet's visibility does not sensibly differ from a parabola. Some few have, however, been ascertained to have moved in hyperbolic orbits. These, after having passed their perihelions must, move off indefinitely and cannot again return.

The elements of a comet's orbit are, the perihelion distance, the longitude of the perihelion, the longitude of the node, the inclination of the orbit, and the time that the comet is at the perihelion. The determination of these elements from observed, geocentric places of a comet, is a problem of much difficulty and the requisite computations are laborious. Various methods of making them, have, however, been obtained, in some of which the labour is considerably lessened.* The computation is usually made, at least in the first place, on the assumption that the orbit is a parabola; which is equivalent to the assumption that it is an ellipse of great eccentricity. Three complete observed right ascensions and declinations of the comet, made at suitable intervals, with the times of observation, are sufficient; but a larger number is commonly employed in order that the results may be more independent of the unavoidable errors of observation.

When the elements of the orbits of a number of comets have been computed and arranged, if on comparing them, the same or nearly the same set of elements is met with at intervals of the same length, or nearly so, the presumption is that they appertain to the same comet returning at these times. If the intervals are long, a difference in them

* Dr. Bowditch, in an appendix to the third volume of his translation of Laplace's Mécanique Céleste has introduced several of the best methods in addition to that of the author, and has added tables which facilitate the computatoins. A more recent one by Airy, the present Astronomer Royal of England, is given in vol. XI of the Memoirs of the Royal Astron. Society.

of a year or more, may be the result of perturbations in the comet's motion, produced by the attractions of the planets.

340. Halley's Comet. In the early part of the last century, Halley, an eminent English astronomer, computed from recorded observations, the elements of a number of comets. On comparing them, he found that the elements of a comet, which had appeared in 1680, and which he had himself observed, corresponded very nearly with those of two others, which had previously appeared at intervals, proceeding backwards, of about 75 and 76 years. This led him to suppose, that instead of three different comets, it might be the same comet, which had appeared at these times. Making further researches, he became satisfied of the correctness of the supposition he had made, and concluded that the variation in period, must have been produced by the attractions of the other heavenly bodies. Having, therefore, made a rough calculation of the effect which the attraction of Jupiter would produce on the revolution the comet was then performing, he ventured to predict its return, in the latter part of 1758, or early part of 1759. Subsequently, Clairaut, an eminent French mathematician, calculated the effects of the attractions of both Jupiter and Saturn, and determined the time of the return to the perihelion, to be in the middle of April, 1759. It arrived there about a month prior to that time. In consequence of its return, nearly according to Halley's prediction, it has received his name.

With more ample means for correct computations, furnished by the observations during its appearance in 1759, and by the improvements in analysis, the recent return of Halley's comet in 1835, was much more accurately predicted. It arrived at the perihelion of its orbit, within less than two days of the time assigned for its return, by Pontécoulant, a distinguished French astronomer.

341. Encke's Comet. The periodical character of this small comet, was discovered in 1819, by Professor Encke

of Berlin. He found its period to be only about 1207 days or nearly 3 years; and he predicted its return in 1822, which was verified by observation. Its subsequent returns have been predicted and observed.

From observations that have been made on the successive returns of this comet, it has been found that its period is subject to a small, but continued diminution. It also appears, that this diminution is not produced by the actions of the planets. Encke, therefore assumes, that instead of a perfect vacuum in space, there must exist an exceedingly rare medium, which, opposing no perceptible obstruction to the motions of dense bodies, sensibly resists the motion of a mere mass of vapour like that of the comet. The obvious effect of such a resistance would be a diminution of the comet's velocity, in consequence of which, it would move nearer the earth, and perform its revolution in less time.*

342. Biela's Comet. This is a very small comet without the least appearance of a nucleus. Biela, of Josephstadt, discovered its periodic character on its appearance in 1825. It moves in a moderately eccentric ellipse, performing its revolution in about 63 years.

343. Number of Comets. The number of comets that have been visible to the naked eye amounts to some hundreds; but it is probable that many of these, were only reappearances of the same comet. The actual number of comets is not known; but including those that become

Encke infers from the observations made on the comet. that the resistance is only sensible in a portion of space round the sun, not extending beyond the orbit of Venus. He thus accounts for the fact, that the motions of Halley's comet, and another periodi cal one, noticed in the next article, have not indicated any resistance; for, but a very small part of the orbit of the former, and none of that of the latter, are within that distance of the sun.

The positions of Encke's comet at its recent return in the present year (1842), as observed on several evenings, by Professor Kendall at the observatory of the Central High School in Philadelphia, were found to be within 30" of space of its positions as given in Encke's Ephemeris, previously computed. This affords a striking evidence of the accuracy of the investigations and computations of its orbit and motion.

visible by the aid of the telescope, it is believed to amount to some thousands.

CHAPTER XVIII.

CLASSIFICATION OF THE FIXED STARS.-CLUSTERS AND NEBULE.-VARIABLE AND TEMPORARY STARS.-DOUBLE STARS. BINARY SYSTEMS.-PROPER MOTIONS OF SOME STARS AND MOTION OF THE SOLAR SYSTEM.-ANNUAL PARALLAX AND DISTANCE OF THE STARS.-CATALOGUES

OF THE STARS.

344. Classification of the Stars. The stars are divided into classes, according to their apparent magnitudes or brightness. The most conspicuous stars form the first class, and are called stars of the first magnitude; those that are markedly less bright, form the second class, and are called stars of the second magnitude; and thus on, down to stars of about the 16th magnitude, which are the smallest, that are distinctly visible with the most powerful telescopes. The stars that are visible to the naked eye, are included in the first six or seven magnitudes; principally, however, in the first six.

The magnitudes are denoted by the numbers 1, 2, 3, &c. A star that is regarded as intermediate in brightness between those of two consecutive classes, so as to render it doubtful in which it would be more appropriately placed, is frequently distinguished by two numbers with a point between them. Thus, 1.2, denotes a star intermediate between those of the first and second magnitudes.

The

345. Number of stars in some of the classes. distribution of the stars into magnitudes, is arbitrary, and it has not been made on any definite principles. There is, therefore, some diversity in the distribution; different astronomers having differed in the magnitude

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