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210 about the sun, by a body revolving under the dominion of the law of gravitation, applied his theory to the great Comet of 1680 with the most complete success. He ascertained that this Comet described about the sun as its focus an elliptic orbit of such exceeding eccentricity as to degenerate into a parabola, and that in this orbit the areas described about the sun were, as in the planetary ellipses, proportional to the times. Two years after, in the year 1682, Halley applied the principles of the Newtonian theory to cometary bodies, and calculated thereby the orbits of several ancient comets, which led him to the discovery of a remarkable coincidence in the elements of the orbits of certain comets which had been observed at nearly equal intervals of time in 1531, 1607, and 1682. After mature consideration, he concluded that these comets must be identical, returning at certain fixed periods, and ventured to predict another return about the year 1759. Clairaut, an eminent mathematician of the period, undertook to calculate the delay which the return of this comet would experience from the disturbing influence exercised upon its orbit by the larger planets, and fixed the return for spring, 1759. True to the appointment, the Comet made its reappearance on the 12th of March of that year, and once more 76 years after—in October, 1835—as had been calculated by several eminent mathematicians.

The great Comet which appeared in 1680 is supposed to have a period of 575 years, and to be