But during the next interval of 76 years the theory of planetary perturbations had been more perfectly developed. The masses of Jupiter and Saturn had been determined with greater accuracy, and Uranus had been added to the known members of the planetary system. A nearer approximation to the exact time of the comet's perihelion passage in 1835 was therefore to be expected. Prizes were offered by two of the learned societies of Europe--the Academy of Sciences at Turin, and the French Institute--for the most perfect discussion of its motions. That of the former was awarded to Damoiseau,--that of the latter to Pontecoulant. The times assigned by these distinguished mathematicians for the comet's perihelion passage were very nearly the same, and differed but a few days from the true time. Had the present received mass of Jupiter been used in the calculations, Pontecoulant, it is believed, would not have been in error as much as 24 hours. It may be proper to remark that, during the entire period from 1759 to 1835, the position of Neptune was such that it could produce no considerable effect on the motion of the comet. This interesting object will again return about 1911. The visit of 1531 was the earliest that Halley succeeded in determining with any degree of certainty. Peter Apian, by whom it was at that time observed, was the first European to ascertain the fact that, as a general thing, the tails of comets are turned from the sun.[3] To confirm this discovery, he carefully followed the body in its progress through the constellations. By means of his recorded observations Halley was enabled to identify this comet with that of 1607 and 1682. The great comet of 1456 he _conjectured_ to be the same, from the date of its appearance. Pingré subsequently confirmed this suspicion by a careful examination of the few trustworthy records that could be collected from the writers of that period. [3] The Chinese, however, as appears from Biot's researches, had observed the same fact 700 years earlier. See Humboldt's Cosmos, vol. iv. (Bohn's ed.), p. 544. From the earlier descriptions of this comet we infer that its brilliancy is gradually diminishing. In 1456 its tail, which was slightly curved like a sword or sabre, extended two-thirds of the distance from the horizon to the zenith. The appearance of such an object, in a grossly superstitious age, excited throughout Europe the utmost consternation. The Moslems had just taken Constantinople, and were threatening to advance westward into Europe. Pope Calixtus III., regarding the comet as confederate with the Turk, ordered prayers to be offered three times a day for deliverance from both. The alarm, however, was of short duration. Within ten days of its appearance the comet reached its perihelion. Receding from the sun, the sword-like form began to diminish in brilliancy and extent; and finally, to the great relief of Europe, it entirely disappeared.