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of the motions of these two planets adapted themselves naturally to the theory; they before had seemed to form an exception to the law of universal gravitation; they are now become one of the most striking examples of its truth. Such has been the fate of this brilliant discovery, that every difficulty that has arisen has only furnished a new subject of triumph for it, which is the most indubitable characteristic of the true system of nature.

I cannot in this place refrain from making a comparison of the real effects of this relation between the mean motion of Jupiter and Saturn, with those which astrology had attributed to it. In consequence of this relation, if the conjunction of the two planets arrives in the first point of Aries, it will in twenty years afterwards take place in Sagittarius, and in twenty years afterwards in Leo, it will continue to take place in these three signs for nearly two hundred years. In the same manner in the next two hundred years, it will go through the signs Taurus, Capricornus, and Virgo. In the

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next two hundred years it will proceed through the signs Gemini, Aquarius, and Libra; and finally, in the last two hundred years it will describe the remaining signs Cancer, Pisces, and Scorpio; after which it will again begin with the sign Aries as before. From hence arises a great year, each season of which is equal to two cen turies. They attributed different tempe ratures to the different seasons of this year, as likewise to the signs which belonged to them. The assemblage of these three signs was called a trigon. The first trigon was that of Fire, the second of Earth, the third of Air, and the fourth of Water.We may easily imagine that astrology made great use of these trigons, which even Kepler himself describes with great exactness, in several of his works: but it is very remarkable that sound astronomy in dissipating the imaginary influence that was supposed to attend this relation in the motion of the two planets, should have recognised in the harmony of this relation, the

source of the greatest perturbations of the planetary system.

The planet Uranus, though lately discovered, offers already incontestable indications of the perturbations which it experiences from the action of Jupiter and Saturn. The laws of elliptic motion do not exactly satisfy its observed positions, and to represent them its perturbations must be considered. Their theory, by a very remarkable coincidence, places it in the years 1769, 1756, and 1690, in the same points of the heavens, where Monnier, Mayor, and Flamstead, had determined the position of three stars, which cannot be found at present this leaves no doubt of the identity of these stars with the new planet.

CHAP. IV.

Of the Perturbations in the Elliptic Motion of Comets.

THE action of the planets produces, in the motion of comets, inequalities which are principally sensible in the intervals of their returns to the perihelion. Halley having remarked that the elements of the orbits of the comets observed in 1531, 1607, and 1682, were nearly the same, concluded that they belonged to the same comet which in the space of 151 years had made two revolutions. It is true that the period of the first revolution is thirteen months longer than the second. But this great astronomer thought, and with reason, that the attraction of the planets, particularly of Jupiter and Saturn, might have occasioned this difference, and after a vague estimation

of this action for the course of the follow

ing period, he judged that it should retard the return of the comet, and he fixed it for the end of 1758, or the commencement of 1759. This prediction was too important in itself, and too intimately connected with the theory of universal gravitation, not to excite the curiosity of all those who were interested in the progress of the sciences; for about this time geometricians were very much engaged in extending the application of this theory. During the whole year of 1757, astronomers looked for this comet; and Clairaut, who had been one of the first to solve the problem of the three bodies, applied his solution to the determination of the inequalities which the comet had sustained by the action of Jupiter and Saturn. The 14th November, 1758, he announced in the academy of sciences, that the interval of the return of the comet to its perihelion, would be 618 days longer in the present actual period than in the former one, and that consequently the comet would pass its peribelion about the middle of April

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