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net had become general among astronomers, as there seemed to he no other way of accounting for the apparent anomalies in the motion of Uranus.
Mr. Adams of Cambridge, England, was the first to attempt the discovery of this unknown body. He communicated to Professor Airy in November, 1845, as the result of his investigation, the mass and the elements of the orbit of the disturbing planet. These results were not made public until some months afterwards. In the mean time, Mr. Le Verrier of Paris had undertaken a thorough investigation of this subject, and presented the results of his labours to the Academy of Sciences in three papers. The last of these, announcing the mass and orbit of the required body, was read on the 31st of August, 1846. Le Verrier soon after wrote to Dr. Galle of Berlin, stating that the longitude of his planet for the end of September was 325°, and requesting him to look for it. And on the evening of the 23d of September, 1846, the day on which the letter reached him, Dr. Galle found the planet in longitude 325° 53′, or within less than a degree of the place assigned by Le Verrier. At the suggestion of Professor Airy, Professor Challis of Cambridge had commenced, on the 29th of July, a systematic search for the planet, and had actually observed it twice prior to the 23d of September, as he ascertained by a subsequent reduction of his observations.
The orbits predicted by Adams and Le Verrier agree remarkably well with each other, but differ widely from the true orbit which has been deduced from three years observations made since the discovery of Neptune, and two observations made in 1795 by Lalande, who mistook it for a fixed star. These two were discovered among some 50,000 observations of Lalande, by Mr. Walker, of Washington, who computed the elements given in Article 411.
338. General remarks. On the first of January, 1801, the planet Ceres was discovered at Palermo, by Piazzi, one of an association of astronomers, engaged in searching for a planet between the orbits of Mars and Jupiter (289); and on the 28th of March, 1802, Dr. Olbers, of Bremen, discovered the planet Pallas, which
was found to have nearly the same mean distance from the sun as Ceres; their orbits approach each other very closely at the intersection of their planes, and both planets are extremely small. These facts led Dr. Olbers to conceive the idea, that they might be fragments of a large planet, which formerly revolved round the sun in nearly the same part of space, but which had been destroyed by some internal convulsion, and that more of these fragments might be found. Within five years, two more small planets were discovered: Juno, by M. Harding, of Lilienthal, in 1804, and Vesta, by Dr. Olbers, in 1807. The search was continued several years longer, but with no further success, and was abandoned in 1816. The discovery of another asteroid, Astræa, by M. Hencke, of Driesen, on the 8th of December, 1845, stimulated a number of observers to renew the search for other fragments, and their labours have been rewarded by the discovery of twenty-seven asteroids in a period of nine years; Astræa and Hebe, by Hencke; Iris, Flora, Clio, Irene, Melpomene, Fortuna, Calliope, Thalia, Euterpe, and one other, by Hind, of London; Metis, by Graham, of Ireland; Hygeia, Parthenope, Egeria, Eunomia, Psyche and Themis, by De Gasparis, of Naples; Thetis, Proserpine and Bellona, by Luther, of Bilk; Massalia and Phocea, by Chacornac, of Paris; Lutetia, by Goldschmidt, of Paris; Amphitrite, by Marth, of London; and one recently, by Ferguson, of Washington.
These discoveries have been greatly facilitated by the publication of the Berlin charts, containing all the stars to the 8th or 9th magnitude within 15° of the equator. When a star is noticed in the heavens, which is not on the chart, the observer, presuming it to be a planet, carefully notes its position relative to the surrounding stars; if, after the lapse of an hour or two, he finds it has moved, his suspicion is confirmed. In this way most of these small planets have been discovered. They closely resemble small stars, even when viewed with good telescopes; hence, they are called Asteroids. Owing to their extreme smallness, very little is known of their physical peculiarities. In Vesta and Pallas only have sensible discs been detected. The diameter of Vesta has been conjectured at about 270 miles.
339. Periods and distances of the Asteroids. The following table contains the times of revolution in days, and the mean distances in millions of miles, of the twenty-nine asteroids whose orbits are known.
340. General remarks. Comets revolve about the sun, shine by reflecting his light, and are retained in their orbits by his attraction. But, in almost every thing else, they differ widely from the planets. They are not confined to the zodiac or adjacent regions, but traverse all parts of the heavens, and in all directions; the motions of some being direct, and others retrograde. They generally move in elliptical orbits of great eccentricity, alternately approaching comparatively near to the sun, and receding to immense distances; and some of them, moving off into the boundless regions of space, never return. They continue visible only for a few weeks or months, and some only for a few days; being only within the reach of observation while in those parts of their orbit that are adjacent to their perihelions. They are not solid bodies like the planets, but seem to consist mainly of masses of vaporous
Some comets have presented very splendid appearances; and others, though less brilliant, have still been conspicuous objects; but, by far the most numerous class are barely discernible by the naked eye, or can only be seen by the aid of the telescope.
341. Appearance of a comet. A comet of the more conspicuous class, usually consists of a small, bright, central part or nucleus, enveloped to a considerable extent by an ill-defined nebulous mass of light, called the coma; the 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 brightest, 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.
342. 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.
343. Orbit of a comet and its elements. Investigations, founded on the law of gravitation, prove, that a body revolving 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, and 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 of a year or more, may be the result of perturbations in the comet's motion, produced by the attractions of the planets.
344. 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
* 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 computations. 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.