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106 exercise some disturbing influence on the motions of comets. The discrepancies already pointed out in the orbits of the 3 comets just mentioned made Halley hesitate for some time as to their identity, and in his memoir on comets published in 1705 he only, as it were, hinted his suspicions. Eventually, however, he became much more confident. This appears to have been the result of his investigations as to the probable influence of the Planet Jupiter. He found that between 1607 and 1682 the comet had passed so near Jupiter that its velocity in its orbit must have been considerably augmented, and its period, consequently, shortened; he was therefore induced to predict its return about the end of 1758 or the beginning of 1759. Finally, when he had matured his labours, he thus plaintively wrote on the subject:—"Wherefore if it should return according to our prediction about the year 1758 impartial posterity will not refuse to acknowledge that this was first discovered by an Englishman." On this Hind judiciously remarked as follows:— "Nor has posterity at- tempted to deprive him of the honours which were his due; his discovery forms an epoch, and an important one, in the history of Astronomy. His calculations must have been laborious in the extreme. He assures us himself they were 'prodigiously' long and troublesome; but the zeal which induced such an amount of exertion was well rewarded by the final result."

Halley 's first formal announcement of his expectations concerning his comet appears to have been in the paper presented to the Royal Society, in which the following passage (in Latin) occurs:—"Now many things lead me to believe that the Comet of the year 1531, observed by Apian, is the same as that which, in the year 1607, was described by Kepler and Longomontanus, and which I saw and observed