In 1759 Lalande, who was then the Director of the Paris Observatory, engaged Mme. Lepaute and the celebrated mathematician, Clairaut, to determine the amount of the attraction of Jupiter and Saturn on Halley's comet, whose return was expected in that year. So difficult was this problem, and so numerous were the complications involved, that Lalande frankly confesses that he would not have dared to undertake its solution without Mme. Lepaute's assistance. For it necessitated calculating for every degree, and for one hundred and fifty years the distances and forces of each of the planets with reference to the comet. "It would be difficult," declares Lalande, "to realize the courage which this enterprise required, if one did not know that for more than six months we calculated from morning until night, sometimes even at meals, and that at the end of this enforced labor I was stricken by a malady which affected me during the rest of my life." Clairaut was so impressed by Mme. Lepaute's energy and skill during this time that he declared "her ardor was surprising," and he did not hesitate to call her _La savante calculatrice_--the learned computer.[143] The eclipse of 1762 also engaged Mme. Lepaute's attention, as did also the annular eclipse of 1764. The latter was a curious phenomenon for France, as it had never before been observed. Mme. Lepaute calculated it for the whole of Europe and published a chart showing its path for every quarter of an hour. She also published another chart for Paris, in which were exhibited the different phases of the eclipse. On the occasion of the different eclipses which she had calculated, Mme. Lepaute recognized the advantage of having a table of parallactic angles. She accordingly prepared a very extended table of this kind which was published by the French government. Besides this table, she was the author of numerous memoirs on astronomical subjects. Among them was one embracing calculations based on all the observations which had been made on the transit of Venus in 1761. "In 1759," again writes Lalande, "I was given charge of the _Connaissance des Temps_, a work which the Academy of Sciences published every year for the use of astronomers and navigators, the calculations for which gave occupation to several persons. I had the good fortune to find in Mme. Lepaute a co-worker without whom I should not have been able to undertake the labor required. She continued in this occupation until 1774, when another Academician assumed this laborious task. But she thereupon began work on the _Ephemeris_, of which the seventh volume in quarto, which appeared in 1774, goes to 1784, and of which the eighth, published in 1783, extends to the year 1792. In this latter volume she made, unaided, all the computations for the sun, the moon and all the planets. "This long series of calculations finally enfeebled her eyesight, which had been excellent, and she was in the last years of her life obliged to discontinue them."[144]