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See Waff (1986) for a discussion of the public awareness of the comet's return in England during the 1750s. There was considerable controversy in astronomical circles regarding the accuracy of Clairaut's calculation, with d'Alembert pointing out that the error of 33 days was quite large when compared with the differences between successive periods of the comets. Clairaut later refined his calculations and eventually produced a figure he claimed was in error by just 19 days. Comparison with a modern analysis, due to Kiang (1971), shows that six of these days can be accounted for by Clairaut's neglect of the four innermost planets, and a further six due to the effects of the as yet undiscovered planets beyond Saturn (Broughton

Quoted from Gingerich (1992), pp. 150-1. The Astronomical Tables were first printed in 1719, but not published until 1749, 7 years after Halley's death. Newton Principia, Book III, Proposition 13. 36 Wilson (1980), p. 91

attraction of the other planets was by Euler, who thereby won the prize from the Paris Academy in 1756. However, the first solar tables based on perturbation theory that were used widely - those of Lacaille (1758) - were based on Clairaut's calculations. Clairaut's method, which was based on the same principles that he had brought to bear on the lunar problem, was easier to apply than Euler's. Lacaille's tables were not free from either theoretical or observational errors, but represented a marked improvement over the contemporary tables of Halley and Jacques Cassini. As well as including perturbations due to the Moon, Venus, and Jupiter, they also took account of the effects of two new astronomical

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