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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 calcu. lated 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 bril.

liant 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 supersti. tious 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 suc. cessive 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 sin. gular 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 evi. dently the effect which would be produced by a resist. ance 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 the last apparition having taken place according to the prediction in 1832, the next will be in 1838. It is a small insignificant comet, without a tail, or any appearance of a solid nucleus whatever. Its orbit, by a remarkable coincidence, very nearly intersects that of the earth ; and had the latter, at the time of its passage in 1832, been a month in advance of its actual place, it would have passed through the comet, — a singular rencontre, perhaps not unattended with danger.*

(485.) Comets in passing among and near the planets are materially drawn aside from their courses, and in some cases have their orbits entirely changed. This is remarkably the case with Jupiter, which seems by some strange fatality to be constantly in their way, and to serve as a perpetual stumbling block to them. In the case of the remarkable comet of 1770, which was found by Lexell to revolve in a moderate ellipse in the period of about 5 years, and whose return was predicted by him accordingly, the prediction was disappointed by the comet actually getting entangled among the satellites of Jupiter, and being completely thrown out of its orbit by the attraction of that planet, and forced into a much larger ellipse. By this extraordinary rencontre, the motions of the satellites suffered not the least perceptible derangement, –a sufficient proof of the smallness of the comet's mass.

(486.) It remains to say a few words on the actual dimensions of comets. The calculation of the diameters of their heads, and the lengths and breadths of their tails, offers not the slightest difficulty when once the elements of their orbits are known, for by these we know their real distances from the earth at any time, and the true direction of the tail, which we see only foreshortened. Now calculations instituted on these principles lead to the surprising fact, that the comets are by far the most voluminous bodies in our system. The following are the dimensions of some of those which have been made the subjects of such enquiry.

* Should calculation establish the fact of a resistance experienced also by this comet, the subject of periodical comets will assume an extraordinary degree of interest. It cannot be doubted that many more will be discovered, and by their resistance questions will come to be decided, such as the following: What is the law of density of the resisting medium which surrounds the sun ? Is it at rest or in motion? If the latter, in what di. rection does it move? Circularly round the sun, or traversing space ? If circularly, in what plane? It is obvious that a circular or vorticose motion of the ether would accelerate some comets and retard others, according as their revolution was, relative to such motion, direct or retrograde. Supposing the neighbourhood of the sun to be filled with a material fluid, it is not conceivable that the circulation of the planets in it for ages should not have impressed upon it some degree of rotation in their own direction. And this may preserve them from the extreme effects of accumulated resistance - Author.

(487.) The tail of the great comet of 1680, imme. diately after its perihelion passage, was found by Newton to have been no less than 20000000 of leagues in length, and to have occupied only two days in its emission from the comet's body! a decisive proof this of its being darted forth by some active force, the origin of which, to judge from the direction of the tail, must be sought in the sun itself. Its greatest length amounted to 41000000 leagues, a length much exceeding the whole interval between the sun and earth. The tail of the comet of 1769 extended 16000000 leagues, and that of the great comet of 1811, 36000000. The portion of the head of this last comprised within the transparent atmospheric envelope which separated it from the tail was 180000 leagues in diameter. It is hardly conceivable that matter once projected to such enormous distances should ever be collected again by the feeble attraction of such a body as a comet — a consideration which accounts for the rapid progressive diminution of the tails of such as have been frequently observed.

(488.) A singular circumstance has been remarked respecting the change of dimensions of the comet of Encke in its progress to and retreat from the sun : viz. · that the real diameter of the visible nebulosity undergoes a rapid contraction as it approaches, and an equally rapid dilatation as it recedes from the sun. M. Valz, who, among others, had noticed this fact, has accounted for it by supposing a real compression or condensation of volume, owing to the pressure of an ethereal medium

growing more dense in the sun's neighbourhood. It is very possible, however, that the change may consist in no real expansion or condensation of volume (further than is due to the convergence or divergence of the different parabolas described by each of its molecules to or from a common vertex), but may rather indicate the alternate conversion of evaporable materials in the upper regions of a transparent atmosphere, into the states of visible cloud and invisible gas, by the mere effects of heat and cold. But it is time to quit a subject so. mysterious, and open to such endless speculation.

- CHAP. XI.

OF PERTURBATIONS.

SUBJECT PROPOUNDED, SUPERPOSITION OF SMALL MOTIONS.

PROBLEM OF THREE BODIES. — ESTIMATION OF DISTURBING FORCES. -MOTION OF NODES. CHANGES OF INCLINATION. — COMPENSATION OPERATED IN A WHOLE REVOLUTION OF THE NODE. — LAGRANGE'S THEOREX OF THE STABILITY OF THE INCLINATIONS. CHANGE OF OBLIQUITY OF THE ECLIPTIC. — PRECESSION OF THE EQUINOXES. — NUTATION. THEOREM RESPECTING FORCED VIBRATIONS OF THE TIDES. -VARIATION OF ELEMENTS OF THE PLANET'S ORBITS — PERIODIC AND SECULAR. — DISTURBING FORCES CONSIDERED AS TANGENTIAL AND RADIAL. EFFECTS OF TANGENTIAL FORCE. — IST, IN CIRCULAR ORBITS; 2DLY, IN ELLIPTIC. — COMPENSATIONS EFFECTED. — CASE OF NEAR COMMENSURABILITY OF MEAN MOTIONS. THE GREAT INEQUALITY OF JUPITER AND SATURN EXPLAINED. —THE LONG INEQUALITY OF VENUS AND THE EARTH. — LUNAR VARJATION, EFFECTS OF THE RADIAL FORCE. - MEAN EFFECT ON THE PERIOD AND DIMENSIONS OF THE DISTURBED ORBIT. — VARIABLE PART OF ITS EFFECT. — LUNAR EVECTION. SECULAR ACCELERATION OF THE MOON'S MOTION. — INVARIABILITY OF THE AXES AND PERIODS. THEORY OF THE SECULAR VARIATIONS OF THE EXCENTRICITIES AND PERIHELIA. - MOTION OF THE LUNAR APSIDES. -LAGRANGE'S THEOREM OF THE STABILITY OF THE EXCENTRICITIES, NUTATION OF THE LUNAR ORBIT. — PERTURBATIONS OF JUPITER'S SATELLITES.

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