(477.) We come now to speak of the motions of comets. These are apparently most irregular and capricious. Sometimes they remain in sight for only a few days, at others for many months; some move with extreme slowness, others with extraordinary velocity; while not unfrequently, the two extremes of apparent speed are exhibited by the same comet in different parts of its course. The comet of 1472 described an arc of the heavens of 120° in extent in a single day. Some pursue a direct, some a retrograde, and others a tortuous and very irregular course; nor do they confine themselves, like the planets, within any certain region of the heavens, but traverse indifferently every part. Their variations in apparent size, during the time they continue visible, are no less remarkable than those of their velocity: sometimes they make their first appearance as faint and slow moving objects, with little or no tail; but by degrees accelerate, enlarge, and throw out from them this appendage, which increases in length and brightness till (as always happens in such cases) they approach the sun, and are lost in his beams. After a time they again emerge, on the other side, receding from the sun with a velocity at first rapid, but gradually decaying. It is after thus passing the sun, and not till then, that they shine forth in all their splendour, and that their tails acquire their greatest length and developement; thus indicating plainly the action of the sun's rays as the exciting cause of that extraordinary emanation. As they continue to recede from the sun, their motion diminishes and the tail dies away, or is absorbed into the head, which itself grows continually feebler, and is at length altogether lost sight of, in by far the greater number of cases never to be seen more.

(478.) Without the clue furnished by the theory of gravitation, the enigma of these seemingly irregular and capricious movements might have remained for ever unresolved. But Newton, having demonstrated the possibility of any conic section whatever being described about the sun, by a body revolving under the dominion

of that law, immediately perceived the applicability of the general proposition to the case of cometary orbits: and the great comet of 1680, one of the most remarkable on record, both for the immense length of its tail and for the excessive closeness of its approach to the sun (within one sixth of the diameter of that luminary), afforded him an excellent opportunity for the trial of his theory. The success of the attempt was complete. He ascertained that this comet described about the sun as its focus an elliptic orbit of so great an excentricity as to be undistinguishable from a parabola, (which is the extreme, or limiting form of the ellipse when the axis becomes infinite,) and that in this orbit the areas described about the sun were, as in the planetary ellipses, proportional to the times. The representation of the apparent motions of this comet by such an orbit, throughout its whole observed course, was found to be as complete as those of the motions of the planets in their nearly circular paths. From that time it became a received truth, that the motions of comets are regulated by the same general laws as those of the planets, the difference of the cases consisting only in the extravagant elongation of their ellipses, and in the absence of any limit to the inclinations of their planes to that of the ecliptic, or any general coincidence in the direction of their motions from west to east, rather than from east to west, like what is observed among the planets.

(479.) It is a problem of pure geometry, from the general laws of elliptic or parabolic motion, to find the situation and dimensions of the ellipse or parabola which shall represent the motion of any given comet. In general, three complete observations of its right ascension and declination, with the times at which they were made, suffice for the solution of this problem, (which is, however, a very difficult one,) and for the determination of the elements of the orbit. These consist, mutatis mutandis, of the same data as are required for the computation of the motion of a planet; and, once deter

mined, it becomes very easy to compare them with the whole observed course of the comet, by a process exactly similar to that of art. 426., and thus at once to ascertain their correctness, and to put to the severest trial the truth of those general laws on which all such calculations are founded.

(480.) For the most part, it is found that the motions of comets may be sufficiently well represented by parabolic orbits, that is to say, ellipses whose axes are of infinite length, or, at least, so very long that no appreciable error in the calculation of their motions, during all the time they continue visible, would be incurred by supposing them actually infinite. The parabola is that conic section which is the limit between the ellipse on the one hand, which returns into itself, and the hyperbola on the other, which runs out to infinity. A comet, therefore, which should describe an elliptic path, however long its axis, must have visited the sun before, and must again return (unless disturbed) in some determinate period, - but should its orbit be of the hyperbolic character, when once it had passed its perihelion, it could never more return within the sphere of our observation, but must run off to visit other systems, or be lost in the immensity of space. A very few comets have been ascertained to move in hyperbolas, but many more in ellipses. These then, in so far as their orbits can remain unaltered by the attractions of the planets, must be regarded as permanent members of our system.

(481.) The most remarkable of these is the comet of Halley, so called from the celebrated Edmund Halley, who, on calculating its elements from its perihelion passage in 1682, when it appeared in great splendour, with a tail 30° in length, was led to conclude its identity with the great comets of 1531 and 1607, whose elements he had also ascertained. The intervals of these successive apparitions being 75 and 76 years, Halley was encouraged to predict its re-appearance about the year 1759. So remarkable a prediction could not fail to attract the attention of all astronomers, and, as the time approached,

it became extremely interesting to know whether the attractions of the larger planets might not materially interfere with its orbitual motion. The computation of their influence from the Newtonian law of gravity, a most difficult and intricate piece of calculation, was undertaken and accomplished by Clairaut, who found that the action of Saturn would retard its return by 100 days, and that of Jupiter by no less than 518, making in all 618 days, by which the expected return would happen later than on the supposition of its retaining an unaltered period,—and that, in short, the time of the expected perihelion passage would take place within a month, one way or other, of the middle of April, 1759. -It actually happened on the 12th of March in that year. Its next return to the perihelion has been calculated by Messrs. Damoiseau and Pontecoulant, and fixed by the former on the fourth, and by the latter on the seventh of November, 1835, about a month or six weeks before which time it may be expected to become visible in our hemisphere; and, as it will approach pretty near the earth, will very probably exhibit a brilliant appearance, though, to judge from the successive degradations of its apparent size and the length of its tail in its several returns since its first appearances on record, (in 1305, 1456, &c.) we are not now to expect any of those vast and awful phænomena which threw our remote ancestors of the middle ages into agonies of superstitious terror, and caused public prayers to be put up in the churches against the comet and its malignant agencies.

(482.) More recently, two comets have been especially identified as having performed several revolutions about the sun, and as having been not only observed and recorded in preceding revolutions, without knowledge of this remarkable peculiarity, but have had already several times their returns predicted, and have scrupulously kept to their appointments. The first of these is the comet of Encke, so called from Professor Encke, of Berlin, who first ascertained its periodical return. It revolves in an ellipse of great excentricity, inclined at an

angle of about 13° 22′ to the plane of the ecliptic, and in the short period of 1207 days, or about 3 years. This remarkable discovery was made on the occasion of its fourth recorded appearance, in 1819. From the ellipse then calculated by Encke, its return in 1822 was predicted by him, and observed at Paramatta, in New South Wales, by M. Rümker, being invisible in Europe: since which it has been re-predicted, and re-observed in all the principal observatories, both in the northern and southern hemispheres, in 1825, 1828, and 1832. Its next return will be in 1835.

(483.) On comparing the intervals between the successive perihelion passages of this comet, after allowing in the most careful and exact manner for all the disturbances due to the actions of the planets, a very singular fact has come to light, viz. that the periods are continually diminishing, or, in other words, the mean distance from the sun, or the major axis of the ellipse, dwindling by slow but regular degrees. This is evidently the effect which would be produced by a resistance experienced by the comet from a very rare ethereal medium pervading the regions in which it moves; for such resistance, by diminishing its actual velocity, would diminish also its centrifugal force, and thus give the sun more power over it to draw it nearer. Accordingly (no other mode of accounting for the phænomenon in question appearing), this is the solution proposed by Encke, and generally received. It will, therefore, probably fall ultimately into the sun, should it not first be dissipated altogether, a thing no way improbable, when the lightness of its materials is considered, and which seems authorised by the observed fact of its having been less and less conspicuous at each re-appearance.

(484.) The other comet of short period which has lately been discovered is that of Biela, so called from M. Biela, of Josephstadt, who first arrived at this interesting conclusion. It is identical with comets which appeared in 1789, 1795, &c., and describes its moderately excentric ellipse about the sun in 63 years; and