It is related by Apollonius the Myndian, that the Chaldean astronomers held comets to be bodies which travel in extended orbits around the solar system. 'The Chaldeans spoke of comets,' he says, 'as of travellers, penetrating far into the upper celestial spaces.' He adds, that those ancient astronomers were even able to predict the return of comets. How far it may be safe to accept the statements of Apollonius is uncertain. He ascribed other powers to the Chaldeans, of which we may fairly doubt their possession-for instance, the power of predicting earthquakes and floods. In fact, there is so marked a disposition among ancient writers to exaggerate the acquisitions of Chaldean astronomers, that it becomes extremely difficult to distinguish truth from falsehood. Still, there is sufficient evidence of their skill and patience as observers, to render it fully possible that they may have discovered the periodicity of one or two comets.

But until the rise of modern astronomy, the opinion which was almost universally held respecting comets was that of Aristotle, that they are of the same nature as meteors or shooting-stars, existing either in the air not far above the clouds, or certainly far below the moon.

The discovery of the periodicity of Halley's comet following quickly on Newton's announcement of the law of gravitation, led astronomers to examine the orbits of all the comets which became visible, with the hope of finding that some of these bodies may be travelling in re-entering paths. But inasmuch as none of the brilliant comets of whose appearance records had been preserved seemed to have ever revisited the earth save Halley's alone, while even Halley's travelled in an orbit of enormous extent, an orbit which reached out in space more than three times as far as the orbit of the most distant known planet, astronomers held that the only kind of path which they might expect a comet to pursue was a long oval. They accordingly confined their calculations, and limited the invention of new mathematical processes, to the case of very eccentric orbits.

But in 1770 a comet appeared which led astronomers to form wholly new views. No orbit which could be devised (subject to the above-mentioned condition) could be reconciled with the motions of the new arrival. At length the astronomer Lexell discovered that the path of the comet was not an oval of extreme eccentricity, but an ellipse of such a figure that the comet's period of revolution was less than six years. But here a difficulty arose. The comet was sufficiently conspicuous; and it was asked, how could such an object have gone on circulating so rapidly around the sun, and yet have remained undiscovered ? A very singular result rewarded the inquiry into this question. It was found that the aphelion of the comet's path lay just outside the orbit of Jupiter; and, further, that when the comet was last in aphelion, Jupiter was quite close to it. Thus it became clear that the comet had been travelling in another, and doubtless much wider orbit, when its motions had brought it into the neighbourhood of the planet Jupiter-the giant of the solar system. The comet had actually approached the planet nearer than his fourth satellite. 'It had intruded,' says Sir J. Herschel, 'an uninvited member into his family circle.'

The result of this close appulse may be readily conceived. Just as Halley's comet, when close to the sun, sweeps rapidly round him - that is, in a sharply curved path - so the new comet's path was sharply bent around the temporary focus formed by the great planet. But just as Halley's comet, after perihelion passage, moves away from the sun, so Lexell's comet, after what may be termed perijovian passage, moved away from Jupiter, and passed again within the sun's attraction. From this time the comet began to follow a new orbit around the sun. This new orbit was an oval of moderate eccentricity, round which the comet travelled in about five and a half years.

At the next return of the comet to perihelion, it was not likely that astronomers would obtain a view of it; for, on account of the odd half-year in its period, it came to perihelion when the earth held a point in her orbit exactly opposite to that which she had occupied at the comet's former perihelion passage; therefore, the comet, which before was favourably, was now unfavourably situated for observation.

As the period for the comet's second return approached, astronomers looked out eagerly for its advent. Again and again the heavens were 'swept' for the faint speck of nebulous light which should have announced the return of the wanderer. But days, and weeks, and months passed, until it became certain that either the comet had been shorn of nearly all its former brilliancy, and had thus escaped unnoticed, or that something had happened to deflect it from its course.

The last alternative appeared so much the more probable one, that mathematicians began to examine the path of the comet, to see whether it had approached so near to any disturbing body as to have been driven from its recently adopted orbit. The examination was soon rewarded with success. If we consider the nature of orbital motion, we shall at once see that, so long as Lexell's comet was subjected to no new disturbing attractions, it was compelled, once in every revolution, to return to the scene of its former encounter with the planet Jupiter. This return was fraught with danger to the stability of the comet's motions. So long as Jupiter was not near that particular part of his orbit at which the encounter had taken place, the comet was free to pass the point of danger, and return towards the sun; but if ever it should happen that Jupiter was close at hand when the comet approached his orbit, then the comet would be as liable to have its motions disarranged as at the original encounter. It happened that the period of the comet's motion in its new orbit was almost exactly one-half of Jupiter's period. This was unfortunate; since it clearly follows that, when the comet had revolved twice, Jupiter had revolved once round the sun. Thus the comet again encountered the planet, with what exact result has never become known; but certainly with this general result, that the comet's movements were completely disarranged. It has never returned to the neighbourhood of the earth.