COMETS are bodies which arc only occasionally seen in the heavens. They have no visible disc, and shine with a faint and nebulous light, accompanied with a train, or tail, turned from the sun. They appear in every re gion of the heavens, and move in every possible direc tion.
In order to find the figure of Saturn's ring, add 13° 43 30" to his geocentric longitude, and with this as an argument enter the Table, with the signs at the head or foot, and the degrees at the side ; and the corresponding numbers in the Table will express the conjugate or small er axis of the ring, the transverse or greater axis being 1000. This result, however, requires a correction de pending upon the latitude of Saturn. Reduce his lati In the ages of ignorance and superstition, comets were regarded as the infallible harbingers of great political and physical convulsions ; and wars, pestilence, and fa mine, were among the dreadful evils which they fore told. While some of the ancients sagaciously conjec tured, that the comets were a distinct species of celestial bodies, situated beyond the region of the moon, it was generally believed that they were simple meteors, ge nerated by inflammable vapours in the earth's atmos phere. This opinion prevailed for a long time ; and even Vien astronomy had made great advances, the true theo ry of comets was completely unknown. Tycho, who of) served the comet of 1577, concluded, from his observa tions, that it had no diurnal parallax, and was therefore situated at a much greater distance than the moon. Kep ler at first supposed that they moved in rectilineal paths ; but he afterwards showed, that they described parabolic orbits concave towards the sun. From the numerous observations made on the comet of 1680, combined with his theory of the planetary motions, sir Isaac Newton concluded that comets revolved round the sun like pla nets, but that they moved in ellipses extremely eccen tric, stretching far beyond the limits of the planetary system, as is shown in Fig. 1. Plate XXXIII. where the path of a comet is represented. The aphelion part of its orbit is not drawn in the figure, on account of its great distance from the sun.
Following out the Newtonian theory of comets, Dr Halley collected all the observations which had been made upon these bodies, and calculated the elements of 24 of them. The resemblance between the elements of the comets of 1456, 1531, 1607, and 1682, induced this astro nomer to believe that the same comet had returned at these different periods, and performed its revolution in about 75 or 76 years. He therefore predicted the re
turn of the same comet in the end of the year 1758, or in the beginning of the year 1759. The period of the comet from 1531 to 1607 was 76 years and 66 days, while the period from 1607 to 1682 was only 74 years and 323 days. By adopting the first of these periods, the comet ought to have reappeared in November 1758, and by employing the second, in August 1757. This great difference, of no less than 15 months, in the pe riod of the same cornet, was ascribed by Halley to the attraction of Jupiter and Saturn, which altered the form of its orbit; and he concluded that its next period would be longer than any of the preceding.
The solution of the problem of the three bodies ena bled astronomers to calculate with more certainty the changes produced upon the orbits of the comets by the action of the planetary bodies. Clairaut applied his so lution of that problem to the motion of the comet of 1682 ; and after computing the separate effects of Jupi ter and Saturn in accelerating and retarding its motions, he concluded that its period ought to be lengthened 100 days by the action of Saturn, and 518 days by the action of Jupiter, and that, instead of being 74 years 323 days, it ought to be 76 years and 211 days. Since the comet therefore passed its perihelion on the 14th September 1682, it ought to reach the same point of its orbit on the 13th of April 1759. These calculations were read before the Academy of Sciences on the 14th Novem ber 1758. The cornet appeared about the end of De cember 1758, and reached its perihelion on the 13th of March 1759, 30 days before the time mentioned by Clai rant. By revising his calculations, however, the French astronomer reduced this error to 22 days; and, in a pa per which shared the prize of the Academy of St Pe tersburg with Albert Euler, in 1762, he reduced the error to 19 days. During the period of the comet be tween 1682 and 1759, the node of its orbit had advanced 2° 33', or rather 1° 29', 10 4' being the precession of the equinoctial points ; and it is a very singular circumstance, that the calculations of Clairaut gave the very same re sult. This comet may be expected to return in the year 1835. By employing the third law of Kepler, and sup posing the mean distance of the earth 1, it will be found that the mean distance of the comet is 17.95, and its greater axis 35.9 ; Its perihelion distance being, accord ing to observation, 0.58, its aphelion distance will be 35.9-0.58=35.32, or 35 times greater than the mean distance of the earth from the sun.