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were the case, it should have been visible at intervals of about seventy-five years in the past.

So he subtracted this period from the several dates in order to determine whether any comets were recorded. Subtracting seventy-five from 1607 we have 1532. He found that a comet had actually appeared in 1531, which he had reason to believe was moving in the same orbit. Again subtracting seventy-five from this year we have the year 1456. A comet really did appear in 1456, which spread such horror throughout Christendom that Pope Calixtus III ordered prayers to be offered for protection against the comet as well as against the Turks, who were at war against Europe. It is probable that the myth of "the Pope's Bull against the comet" refers to this circumstance.

Other possible appearances of the comet were found in past history, but Halley was not able to identify the comet with exactness, owing to the absence of any precise description of the body. But the four well-observed dates, 1456, 1531, 1607, and 1682, afforded ample ground for predicting that the comet would again return to the sun about 1758. Clairaut, one of the most eminent mathematicians then in France, was able to calculate what effect would be produced by the action of Jupiter and Saturn on the period of the comet. He found that this action would so delay its return that it would not reach perihelion until the spring of 1759. It appeared according to the prediction, and actually passed perihelion on March twelfth of that year.

The next predicted return was in 1835. Several