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HISTORY OF PHYSICAL ASTRONOMY.

We shall now proceed to give some account of the researches of astro-nomers on the motions of comets. These bodies were generally consideredto be meteoric substances, generated in the upper regions of the atmo-sphere, until Tycho Brahe demonstrated that they were situated beyondthe moon’s orbit. That astronomer erred, however, in supposing them torevolve in circular orbits, nor did Kepler approach nearer the truth whenhe affirmed that they moved in straight lines. IJevelius first remarkedthat the paths of comets are curved near the perihelion, the concave sidebeing turned towards the sun*. He even threw out the suggestion thatthe form of the curve might be a parabola; but he did not assert that thesun would occupy the focus. Borelli also about the same time hintedthat the orbits of comets might be either parabolic or elliptic. Dorfel,a native of Upper Saxony, was the first person who proved that cometsmove in parabolas, having the sun in the focus. This he did, in 1681, bymeans of a careful discussion of the observations on the great comet whichappeared in the preceding year. It is right, however, to state that hearrived at this conclusion merely by a graphic process, and that he makesno mention of any fixed law regulatiug the motions of comets.

Newton , having been already assured by the researches of astrono-mers that comets traverse the regions of the planets, was led, by hisdiscovery of the principle of gravitation, to suppose that they move inconic sections round the sun in the focus. He was of opinion that theorbits are really elliptic, like those of the planets; hut he remarked thaton account of their great eccentricity they might be assumed, without anyappreciable error, to be parabolas near the perihelia. He demonstrated,by a comparison of his theory with the observations of astronomers, thatthe comet of 1680, and several other bodies of the same class, revolved inorbits which were sensibly parabolic, and that the radii vectores drawn tothem from the sun, supposed in the focus, described in each case equalareas in equal times. ITe also invented a method for determining theelements of a comet's orbit by means of three distinct observations. Thismethod, being founded oil the supposition of the body moving in a parabola,did not extend to the determination of the major axis when the comet re-volved in an elliptic orbit. Newton , how r ever, remarked that this elementand the time of revolution might he derived from a comparison of thosecomets which returned in the same orbits after very long periods f.

The researches of Newton were soon enriched by a brilliant corollary.Halley , having collected all the recorded observations on comets whichcould be entitled to any credit for accuracy, proceeded to calculate theelements of their orbits, in hopes of thereby detecting the reappearance ofsome of the bodies. This illustrious astronomer, having devised an arith-metical calculus for Newton 's method of investigation, succeeded, after in-credible labour, in computing the elements of twenty-four comets. Amongthese there were three which, on account of the close resemblance of theirorbits and the uniformity of their appearances, afforded strong grounds forsuspicion that they were the same comet. The first was observed by Ap-pian in 1531; the second by Kepler in 1607; and the third by Halley himself in 1682. His suspicion of their identity was further confirmedby historical records of the appearance of a comet in 1305, of another in1380, and of a third in 1450. In all these cases the periods seemed tovary alternately from 75 to 70 years, every two successive revolutions oc-

* Cometographia, fob Gedani. 1668.

+ Principia, lib. iii. prop. i.