When in the late spring of 1689 Huygens paid his first visit to England, Fatio escorted his friend about the capital. He was also present at the Royal Society meeting where Huygens and Newton met for the first time. It probably also served as the occasion for Fatio's introduction to Newton. The encounter had a strong impact on both men. Before long Fatio openly expressed his veneration of Newton, 'the most honourable man I know, and the ablest mathematician who has ever lived'. Newton's letters to Fatio show that the affection was mutual and in Newton's case exceptionally strong. The scrutiny of Newton's Principia convinced Fatio of the failure of all theories based upon Cartesian vortices, including Huygens' theory of gravity.^

In March 1690 Fatio presented his own theory of gravity to the Royal Society. Two days later Newton came over to London and spent a month in the

f Westfall, Never at rest, 493-495

company of Fatio. Fatio took care to obtain Newton's signature at the bottom of the paper that he had presented, as well as that of Halley. Together Fatio and Newton studied Huygens' recently published Traité de la Lumière, which also contained Huygens' views of gravity as well as some brief comments on Newton's theory.

Later that spring, having accepted a position as a private tutor, Fatio accompanied his pupil on a trip to the Netherlands. Here he repeatedly visited Huygens, with whom he discussed his own theory of gravity as well as his mathematical innovations. After the death of the young man entrusted in his care Fatio returned to England in September 1691.* Upon his return, Fatio and Newton immediately resumed contact. Fatio ignored his brother's advice to compose a book on his theory of gravity and instead started work on a new edition of Newton's Principia in which he meant to include his own theory. By adding extensive comments to Newton's forbidding mathematics, he hoped to make the work more accessible. But the task proved to be more demanding than he had expected and in fact it never materialised.*

As the correspondence between Newton and Fatio makes clear, Fatio came to share Newton's interests in alchemy and biblical prophecies. It has been suggested that it was Newton who set Fatio on the course leading to his religious extravaganza.5 In early 1693 Newton invited Fatio to come over to Cambridge and take the chambers adjacent to his own. He even offered him an allowance. At the time Fatio was considering a voyage to Geneva to settle his affairs after the death of his mother. Although he was strongly tempted by Newton's offer, he did not move to Cambridge. Fatio and Newton met in London in the summer of 1693, but their relationship seems to have come to a sudden end later that year. In September of the following year Fatio admitted to Huygens that he had not heard of Newton for seven months. Whatever its cause, the rupture between both men was never fully healed.

Meanwhile Fatio had declined offers for professorships in Amsterdam and Wolfenbüttel, the latter coming from Leibniz. As he explained, he lacked the required 'knowledge, health, and diligence'.** Instead Fatio once again accepted a private tutorship in early 1694, spending most of the following years in Oxford. Only in January 1698, during a trip to Holland, did he part company with his young protégé. In June Fatio returned to London, where he spent the following year. Here he resumed his mathematical studies, solving a problem set by Johann Bernoulli four years earlier.** The problem in question was that of the brachistochrone, or the curve of quickest descent.

* Gagnebin, 'De la cause de la pesanteur', 115-116; Westfall, Never at rest, 496.

t Zehe, Die Gravitationstheorie, 25-27.

§ Domson, Nicolas Fatio de Duillier, 37, 42-43, 48-52, 55-66.

^ Domson, Nicolas Fatio de Duillier, 41; Zehe, Die Gravitationstheorie, 34. M Ibid., 35.

Within a few months following Bernoulli's public challenge, the problem had been solved by Europe's foremost mathematicians, being, apart from Johann himself and his brother Jakob, L'Hôpital, Leibniz and Newton. In response to the various solutions, Leibniz had remarked that he had correctly predicted the names of those capable of tackling the problem. Fatio, who had not bothered with mathematics for years, was deeply hurt by the implicit suggestion of impotence. In 1699 Fatio published a small mathematical tract, in which he expounded his own solution to the Bernoulli-problem as well as those to other mathematical questions. He boasted that the invention of his own version of the calculus had been independent of Leibniz' publications. He added that Newton's letters and manuscripts proved Newton to be the first inventor. He also insinuated that Leibniz, notwithstanding his own priority claims, had actually 'borrowed' some vital insights from Newton.

The accusation may have helped to at least partly restore the relationship with Newton. Three years later, again tutoring in London after a two-year stay in Geneva, Fatio was mentioned by Gregory as being among those to whom Newton had promised to publish his own mathematical methods as well as his work on optics. In 1704 Gregory noted that Newton was trying watches with jewel bearings made by Fatio, and in 1706 Gregory mentioned a manuscript by Fatio on comets that he had seen. Fatio repeatedly visited the meetings of the Royal Society, now under Newton's presidency. Apparently, he was still active in scientific circles.^

But in the course of 1706 Fatio sealed his scientific fate. That year he joined the Cévenol prophets, becoming a secretary to Elie Marion, one of the leaders of the movement. Fatio did not restrict himself to keeping records of miracles and divine messages. He even seems to have made a public attempt to raise a man from the dead. His punishment did not serve to sober him. In 1710 he left London to accompany Marion on a missionary tour through Europe, bringing them as far as Constantinople. By the time he returned to London his reputation as a mathematician and philosopher had been effectively ruined.*

Subsequent attempts to renew contacts with the Royal Society did not meet with success. In spite of some new papers on mathematics, astronomy and technological innovations, Fatio failed to regain scientific respectability. He died in May 1753, ninety years old, and little more than a curiosity.

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