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Nicolas Fatio de Duillier FRS (also spelled Faccio or Facio; 16 February 1664 – 12 May 1753) was a Swiss-born mathematician, natural philosopher, and inventor. He spent much of his adult life in England and Holland. Fatio is known for his work on the zodiacal light problem in astronomy, for originating the "push" or "shadow" theory of gravitation, for his close association with both Christiaan Huygens and Isaac Newton, and for his role in the Newton v. Leibniz calculus controversy. He also invented and developed the first method for fabricating jewel bearings for mechanical watches and clocks.
In London in 1687, Fatio made the acquaintance of John Wallis, John Locke, Richard Hampden, and his son John Hampden, among other important figures connected with the Whig party. Fatio worked out new solutions of the "inverse tangent problem" (i.e., of ordinary differential equations) and was introduced to the Royal Society by Henri Justel. He began to attend Society's meetings in June of that year, thus learning of the upcoming publication of Newton's Principia. In the winter of 1687 Fatio went to Oxford, where he collaborated with Edward Bernard, the Savilian Professor of Astronomy, in an investigation into the units of measurement used in the ancient world.
Fatio was elected fellow of the Royal Society on 2 May 1688. That year, Fatio gave an account of Huygens's mechanical explanation of gravitation before the Royal Society, in which he tried to connect Huygens' theory with that of Isaac Newton. Fatio's personal prospects seemed to brighten even further as a result of the Glorious Revolution of 1688–9, which marked the ascendancy of the Whigs and culminated with Parliament deposing the Catholic King James II and giving the English throne jointly to James's Protestant daughter Mary and to her husband, the Dutch Prince William of Orange. Fatio also had an opportunity to enhance his intellectual reputation during Huygen's visit to London in the summer of 1698.
Fatio encountered Newton, probably for the first time, at a meeting of the Royal Society on 12 June 1689. Newton and Fatio soon became close friends and Newton even suggested that the two share rooms in London while Newton attended the post-Revolutionary session of Parliament, to which he had been elected as member for the University of Cambridge. In 1690, Fatio wrote to Huygens outlining his own understanding of the physical cause of gravity, which later became known as "Le Sage's theory of gravitation". Soon after that, he read his letter to Huygens before the Royal Society. Fatio's theory, on which he continued to work until his death, is based on minute particles streaming through space and pushing upon gross bodies, an idea that Fatio probably derived in part from his explanation of zodiacal light as sunlight scattered by a cloud of fine dust surrounding the Sun.
Fatio went to the Netherlands in the spring of 1690 as tutor to two of John Hampden's nephews. In The Hague, Fatio shared with Huygens a list that he had compiled of errata to Newton's Principia. Fatio and Huygens collaborated on problems relating to differential equations, gravity, and optics. At this time, Huygens shared with Gottfried Leibniz some of Fatio's work on differential equations. Fatio returned to London in September 1691, following the death of one of his pupils. He vied unsuccessfully for the Savilian Professorship of Astronomy at Oxford, a post that had been left vacant by the death of his friend Edward Bernard.
Fatio convinced Newton to write a new treatise on a general method of integration, De quadratura curvarum. Initially, he also expected to collaborate with Newton on an entirely new edition of the Principia, which would include Fatio's mechanical explanation of gravity. By the end of 1691, Fatio realised that Newton would not proceed with that project, but he still hoped to collaborate with Newton on corrections to the text of the Principia. In a letter to Huygens, Fatio wrote, concerning those corrections, "I may possibly undertake it myself, as I know no one who so well and thoroughly understands a good part of this book as I do."
Fatio refused Newton's offer to reside in Cambridge as his assistant, seeking instead academic preferment in the Netherlands. By the summer of 1694 he was employed as a tutor to Wriothesley Russell, the heir of the Duke of Bedford, a position for which he had been recommended by Locke. Fatio accompanied his pupil to Oxford and, during 1697–8, to Holland. Fatio was in Switzerland in 1699, 1700, and 1701.
The 1700s, Fatio began to associate with the radical Protestant Camisards in London, known there as the "French prophets". The government suspected this group of contriving a political scheme, and in 1707 Fatio, Élie Marion, and Jean Daudé were tried before the Queen's Bench on charges brought against them by the mainstream French Protestant churches in England. The three were found guilty of sedition and sentenced to the pillory. On 2 December, Fatio stood on a scaffold at Charing Cross with an inscription on his hat describing him as an accomplice in spreading "wicked and counterfeit prophecies". By the influence of the Duke of Ormonde, to whose brother, Lord Arran, Fatio had been tutor, he was protected from the violence of the mob.
Fatio was among those who believed in the prophecy that Thomas Emes would be raised from the dead, attracting ridicule and condemnation even from his own brother. In 1711 Fatio travelled to Berlin, Halle, and Vienna as a missionary of the French prophets. A second mission in 1712–13 took him to Stockholm, Prussia, Halle, Constantinople, Smyrna, and Rome. After his return to England, Fatio retired to Worcester, where he formed some congenial friendships and busied himself with scientific pursuits, alchemy, and study of the cabbala.
In 1732, through the influence of John Conduitt, Newton's nephew-in-law, Fatio endeavoured unsuccessfully to obtain a reward for having saved the Prince of Orange from Count Fenil's kidnapping plot. He also assisted Conduitt in designing Newton's funerary monument in Westminster Abbey and in writing the inscription for it. Fatio died, on 28 April or 12 May 1753, in Madresfield and was buried at the church of St. Nicholas, Worcester. His Swiss compatriot Georges-Louis Le Sage later purchased many of his scientific papers which, together with those of Le Sage, are now in the university library in Geneva.
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