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focus, but far more eccentric, and having their aphelions, or greatest distances from the sun, far remote in the regions of space.

The idea thus thrown out by Newton, was taken up by Dr. Halley, who collated the observations which had been made of all the twenty-four comets, of which notice had been taken previous to 1680. The results were abundantly curious ; with but few exceptions they had passed within less than the earth's shortest distance from the sun ; some of them within less than one third of it; and the average about one half. Out of the number, too, nearly two thirds had had their notions retrograde – or moved in the opposite way to the planets.

While Halley was engaged on these comparisons and deductions, the comet of 1682 made its appearance, and he set about observing it with great care, in order to deterining the elements of its orbit. Having done so, he found that there was a wonderful resemblance between it and three other cornets that he found recorded, — the comets of 1456, of 1531, and of 1607. The times of the appearance of these comets had been at very nearly regular intervals, – at least the differences had been only fractional parts of a year—the average period being between seventy-five and seventysix years. Their distances from the sun, when in perihelion, or nearest to that luminary, had been also nearly the same - being nearly six-tenths of that of the earth, and not varying more than one-sixtieth from each other. The inclination of their orbits to that of the earth had also been nearly the same, between 17o and 18°; and their motions had all been retrograde. Putting them together, Dr. Halley concluded, that the comets of 1456, 1531, 1607, and 1682, were re-appearances of one and the same comet, which revolved in an elliptic orbit round the sun, performing its circuit in a period varying from a little more than 76 years, to a little less than 75,– or having, as far as the observation had been carried, a variation of about fifteen months in the absolute duration of its year, as measured in turns of that of the earth. For this variation in the time of its revolution Dr. Halley accounted upon the supposition that the form of its orbit had been altered by the attraction of the remote planets, Jupiter and Saturn, as it passed near to them; and thence he concluded, that the period of its next appear. ance would be lengthened, but that it would certainly re-appear in 1757, or 1758. Its doing so was, of course, the fact that was to be decisive of the orbits of comets, and that they were regular and permanent bodies, obeying the general laws of matter.

Halley did not live to see the verification of his prediction ; he died in the year 1742, at the advanced age of eighty-four. Soon after his death, Clairault, D'Alembert, and Euler, three of the most eminent mathematicians of Europe, set obout the solution of what is called the problem of the three bodies, that is, to determine the paths described by three bodies, projected from three given points, in given directions, and with given velocities, their gravitating forces being directly as their quantities of matter, and inversely as the squares of their distances. The object of this problem is to find the disturbing effects that the bodies composing the solar system have upon each other; and it applies to comels, when within the limits of planetary action, as well as to the planets themselves. After some errors into which all the three had been led, and which gave a result that seemed to overturn the whole doctrine of gravitation, Clairault succeeded in obtaining an approximate solution, which agreed with and confirmed that theory. Having done so, he applied it to the calculation of the disturbing influence of Jupiter and Saturn, which Halley had predicted would retard the comet of 1682, in its re-appearance about 1753. The results of Clairault's calculations were, that the comet would be retarded' 100 days by the attraction of Saturn, and 518 days by that of Jupiter, so that it would not come to the perihelion, or point of its orbit nearest the sun, till the 13th of April, 1759. Clairault, however, fixed certain limits, within which his calculations might probably be erroneous. It was eventually found that the difference between calculation and observation was less than that which he assigned.

Clairault read his investigations to the Academy of Sciences in November, 1758; and, in little more than a month afterwards, the comet made its appearance; and it reached its perihelion on the 13th of March, in the fol. lowing year, being thirty days earlier than he had calculated. Subsequent calculations enabled him to reduce the error to nineteen days; and, though the calculations of the disturbing forces were only approximations, enough had been done to prove the return, and determine the orbit of one comet, and give every reason for concluding that all comets, being bodies of the same class, are subject to the same general laws as the planets, and only vary from each other in the proportion and magnitude of their orbits. There was one further confirmation; Clairault had calculated that the node of the comet's orbit, or the point in which it cut the plane of the orbit of the earth, would advance 2° 33' in absolute space, or 1° 29' more than the equinoctial points, the precession of which, in the time of the comet's revolution, was 1° 4'; and observation gave exacily the same result, --so that the only difficulty that remained in the doctrine of comets was in the

estimation of the disturbances to which they are exposed from the other - bodies of the system, more especially in the parts of their orbits most remote from the sun, where their motions are comparatively slow.

long with the period of this comet, and its perihelion distance, the mag. nitude and forin of its path were known. Estimating the mean distance of the earth from the sun at 95,000,000 miles, the mean distance of the comet is 1,705,250,000 miles, its greatest distance fiom the sun, 3,355,400,000 ; its least distance, 55,100,000; and the transverse, or largest diameter of its orbit, 3,410,500,000. Therefore, though its aphelion distance be great, its mean distance is less than that of Herschel; and, great as is the aphelion distance, it is but a very trifling fraction less than one five-thousandth part of that distance from the sun, nearer than which the very nearest of the fised stars cannot be situated; and, as the determination of their distance is negative and not positive, - a distance within which they cannot be, and not one at which they actually are, the nearest of them may be at twice or ten times that distance.

The comet of 1750 is, therefore, a body belonging to the solar system, and quite without the attraction of any body which does not belong to that system; and, as this is determined of one comet, analogy points it out as being the case with them all. Their appearances and disappearances have, therefore, no connexion with the affairs of men; but, like the planets, form part of the proper province of astronomical observation, the chief difference being that the study of them is more recent and difficult, and the knowledge, consequently, more imperfect.

Besides the comet of 1759, of which there have been four authenticated returns, and which may be expected again about 1833, there are two others, of which something like a return has been traced at long intervals. One of these passed its perihelion at about eight on the morning of the 6th of July, 1264, reckoning mean time at Greenwich; and again, at a little past eight on the evening of the 21st of April, 1556. Thus its period is about 292 years, and it may be expected in 1848. The perihelion distance, however, of this comet, which was more than half that of the earth, in 1264, had diminished an eighth part by 1556; and, as this must have caused a great elongation of its orbit, and as, from the length of its period, it must go far into the regions of space, there is no knowing how both the time of its revolution, and the form and position of its orbit, may have been altered.

The other comet, in the elements of whose orbit there is a similarity, from which its identity might be with probability inferred, appeared in 1532, and again in 1661, having thus a period of about 129 years. The return of that comet should, therefore, have been about 1790. In that year, three comets made their appearance; but neither of them resembled the one of 1661. Two of them moved in the opposite direction; and the remaining one was more than twice the distance from the sun in its perihelion, and its orbit at nearly double the angle with ihat of the earth.

The comet, denominated Encke's comet, which has engrossed the public mind generally, and the scientific world in particular, has justly claimed and received the careful attention of astronomers, since its appearance in 1818 engaged Professor Encke to consider the elements of its orbit. He was enabled to identify it with a comet described by Messrs. Mechain and Messier in 1786, in the constellation Aquarius ; also with a comet discovered in 1795 by Miss Herschel in the constellation Cygnus; and with the comet in 1805. The investigation of the diligent professor enabled him to foretell its re-appearance in 1322, and to state the probability of its not being observable in our climate. This anticipation was realized by the fortunate circumstance of the attachment to astronomical pursuits of Sir Thomas Brisbane, who was then governor of New South Wales, and had fitted up an observatory there, and provided himself with the able assistance of Mr. Rumker. The latter gentleman appears to have discovered the comet on June 2, 1822; and his accurate observations afforded Encke the means of reconsidering the true elements of its orbit, and with ad. ditional confidence to compute its return for 1825. This occurred as was expected; the fresh data afforded by that return were carefully collated by the professor, to enable him still more satisfactorily to define the orbit, and with increased confidence to predict its return this year. It was observed by Mr. South first on October 30, 1828. This comet affords particular interest to the mind of the astronomer, though it does not offer a splendid object to his eye. Its orbit is an ellipse of comparatively small dimensions, wholly within the orbit of Jupiter ; its period is about three years and threetenths,- a much shorter period than has hitherto appeared to comprise the revolution of any other comet, with the exception of one seen in 1770, which did nut satisfy as far observation has been able to show, the predic. tion of the period of five years and a hali which was attributed to it. In the opinion of Encke and other astronomers, this comet may afford an opportunity of proving that the heavens oppose a resisting medium to the motion of bodies. The subject has been discussed in the Transactions of the Astronomical Society of London, by the able mathematician, Massotti; and that gentleman offers reasons for considering coine : capable of affording a demonstration of a resisting medium in the heavens, though planets may give no indication of it. Another comet which encourages the anticipation of much astronomical gratification, is one which Biela discovered, February 27, 1826, and which was afterwards seen by Gambart and others. It seems to possess similar claims to the attention of astronomers as that of Encke, it being conceived to revolve about the sun in about six years seven-tenths, and to be the same as the comet which appeared in 1772, and that which appeared in 1806. Encke's comet was in its perihelion, by computation, on 10th January, 1829.

The comet of 7770, to which allusion has been made, would lead us to conclude that we are still ignorant of many of the causes by which the form of the orbits of comets, and the times of their revolution and return, may be disturbed. That comet moved almost in the plane of the earth's orbit, having an inclination of only about a degree and a half; it had been observed with great care; and the result of the observations was, that it should return about every five years and a half. Instead of going out of the system, as may be presumed to be the case with those comets that have long periods and eccentric orbits, its greatest distance could not be much greater than that of Jupiter, while its mean distance from the sun was not much more than three times the perihelion distance of the earth. No comet, at all answering to that one, has, however, been again discovered ;

and therefore the conclusion is, that there are, within the system itself, causes which can completely alter the motions of these bodies; but what those ca ses are, other than the attraction of the planets, has not yet been ascertained.

One remarkable difference between the comets and the planets, is in the angles which their orbits make with that of the earth. Leaving out the small planets that have recently been discovered, all the others are contained within a zone extending only 70 on each side of the earth's orbit; and with the exception of Mercury (by far the smallest of the old planets), they are within half that space. But the orbits of the comets are at all possible angles; and the number increases with the angle, so that they approximate to an equal distribution, in all directions, round the sun as a centre. The numbers that have been observed are as follows: - Under 100 of inclination, 8; under 20°, 19; under 30°, 26 ; under 40°, 37; under 50°, 47; under 60°, 63; under 70°, 79; under 80°, 88; and under 90°, about 100. Thus, by far the greater number of the comets have their paths out of the direction of those of the planets; and hence, though they be bodies of such consistency as that their collision with the planets would produce serious consequences, there is but little chance that such collision can take place. The comets that have been observed have made their passages through very different parts of the solar system; 24 have passed within the orbit of Mercury; 47 within that of Venus ; 58 within that of the Earth; 73 within that of Mars; and the whole within that of Jupiter. of the hundred, or thereabouts, that have appeared, about one half have moved from west to east, in the same direction as the planets, and the other half in the opposite direction. The direct and retrograde ones do not appear to follow each other according to any law that has been discovered. From 1299 to 1532, all that are mentioned were retrograde; and five that were observed from 1771 to 1780 were all direct.

Being quite ignorant both of the size of the comets, and their quantities of matter, we can form no conclusion as to their effects, even upon the positions of the planets. Hitherto, their influence, if any thing, has been very small; for, within the limits that must be allowed for error, even in the best tables that are calculated upon an approximation, the whole of the irregularities are explainable upon the hypothesis of planetary disturbance alone ; and the system appears to have gone on just as if there had been no comets in it. That the comets are formed of matter of some sort or other we know, from the dense and opaque appearance of their nucleus, as well as from the action of the planets upon them; but, as their action upon the planets has not been great, or even almost perceptible, we are led to the conclusion that they are not bodies of the same density or magnitude as even the smallest and rarest of the planets. When a comet is viewed through a telescope of considerable power, there appears a dense nucleus in the centre of the luminous and apparently vaporous matter, of which the

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