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108 Lalande and a lady, Madame Lepaute, the immense mass of calculations requisite for the complete attainment of his object. It was necessary to compute the distances of the comet from the disturbing planets, Jupiter and Saturn, not only from 1682, when it was last observed, but for the previous revolution, or for a space of more than 150 years. This of itself was a most laborious business; but the succeeding part of the work, where the disturbing force of each planet was required for this long period, involved much greater and more intricate calculations. Lalande minutely describes the plan adopted: for 6 months they computed from morning to night, with but little intermission, even, as he states, at meals; and he mentions, as one result of this assiduous attention to the

PLAN OF THE ORBIT OF HALLEY'S COMET COMPARED WITH THE ORBITS OF CERTAIN PLANETS.

work, that he contracted an illness which remained upon him during the rest of his life. Madame Lepaute's assistance is said to have been so important, that without it they would hardly have completed the investigation before the comet reappeared. However, by dint of these extraordinary exertions, the calculations were brought to a close."

On Nov. 14, 1758, Clairaut announced in a paper addressed to the Academy of Sciences at Paris, that by the influence of Jupiter the comet would be retarded 518 days, and that to this must be added 100 days due to Saturn, so that the total retardation would be 618 days, or about 20 months. On this basis he predicted April 13, 1759, as the date of the coming