Nicolas Fatio de Duillier

Early life

Nicolas Fatio was born in Basel, Switzerland, in 1664, into a family that originated in Italy and settled in Switzerland following the Protestant Reformation. Nicolas was the seventh of nine children (two brothers and seven sisters) of Jean-Baptiste and Cathérine Fatio, née Barbaud. Jean-Baptiste had inherited a significant fortune, derived from his father's interests in iron and silver mining, and in 1672 he moved the family to an estate that he had purchased in Duillier, some twenty kilometres from the town of Geneva.

Jean-Baptiste, a devout Calvinist, wished Nicolas to become a pastor, whereas Cathérine, a Lutheran, wanted him to find a place in the court of a Protestant German prince. Instead, the young Nicolas pursued a scientific career. He attended the Académie de Genève (now the University of Geneva) from 1678 to 1680 becoming a protégé of the rector, Jean-Robert Chouet, a prominent Cartesian. Before he was eighteen, Fatio wrote to the astronomer Giovanni Domenico Cassini, director of the Paris Observatory, suggesting a new method of determining the distances to the Sun and Moon from the Earth, as well as an explanation of the form of the rings of Saturn. With Chouet's support, Fatio travelled to Paris in the spring of 1682 and was warmly received by Cassini.

That same year, Cassini presented his findings on the astronomical phenomenon of zodiacal light. Fatio repeated Cassini's observations in Geneva in 1684, and in 1685 he offered an important development of Cassini's theory, which was communicated by Chouet in the March 1685 number of Nouvelles de la république des lettres. Fatio's own Lettre à M. Cassini ... touchant une lumière extraordinaire qui paroît dans le Ciel depuis quelques années ("Letter to Mr. Cassini ... concerning the extraordinary light that has appeared in the Heavens for some years") was published in Amsterdam in 1686.

In 1684, Fatio became acquainted with the Piedmontese Count Fenil, who, having offended the Duke of Savoy and the King of France, had taken refuge in the house of Fatio's maternal grandfather in Alsace, and then at Duillier. Fenil confided to Fatio his plan to stage a raid on the beach at Scheveningen to kidnap the Dutch Prince William of Orange. Fenil showed Fatio a letter from the Marquis de Louvois, the French Secretary of State, approving of the kidnapping, offering the king's pardon, and enclosing an order for money. Fatio betrayed Fenil's plot to Gilbert Burnet, whom he then accompanied to Holland in 1686 to warn Prince William.

In Holland, Fatio met Christiaan Huygens, with whom he began to collaborate on mathematical problems concerning the new infinitesimal calculus. Encouraged by Huygens, Fatio compiled a list of corrections to the published works on differentiation by Ehrenfried Walther von Tschirnhaus. The Dutch authorities wished to reward Fatio, whose mathematical abilities Huygens vouched for, with a professorship. While those plans were delayed, Fatio received permission to visit England in the spring of 1687. In England, Fatio hoped to procure the patronage of Robert Boyle.

Move to England

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.

Role in Newton's quarrel with Leibniz

As a result of reading Newton's De quadratura curvarum, Fatio became convinced that Newton had for some time had a complete understanding of the differential and integral calculus, rendering Fatio's own discoveries superfluous. He reported as much to Huygens in 1692. In 1696, Johann Bernoulli, a close ally of Leibniz, posed the brachistochrone problem as a challenge to the mathematicians who claimed to understand the new calculus. The problem was solved by Leibniz, Tschirnhaus, L'Hôpital, Jacob Bernoulli, and Newton. In 1699, Fatio published Lineæ brevissimæ descensus investigatio geometrica duplex, cui addita est investigatio geometrica solidi rotundi in quo minima fiat resistentia ("A two-fold geometrical investigation of the line of briefest descent, to which is added a geometric investigation of the solid of revolution that produces the minimum resistance") in which he discussed the brachistochrone as well as another problem, treated by Newton in book II of the Principia, also relating to what is modernly called the "calculus of variations".

In his book, Fatio drew attention to his own original work on the calculus from 1687, while stressing Newton's absolute priority and questioning the claims of Leibniz and his followers.

I recognize that Newton was the first and by many years the most senior inventor of this calculus: whether Leibniz, the second inventor, borrowed anything from him, I prefer that the judgment be not mine, but theirs who have seen Newton's letters and his other manuscripts. Nor will the silence of the more modest Newton, or the active exertions of Leibniz in everywhere ascribing the invention of the calculus to himself, impose upon any person who examines these papers as I have done.

— Fatio, Lineæ brevissimæ (1699), p. 18

This provoked angry responses from Johann Bernoulli and Leibniz in the Acta Eruditorum. Leibniz stressed that Newton himself had admitted in his Principia to Leibniz's independent discovery of the calculus. Fatio's reply to his critics was finally published, in abbreviated form, in 1701. Fatio also corresponded on the history of calculus and on his own theory of gravity with Jacob Bernoulli, who was by then estranged from his brother Johann. Fatio's writings on the history of the calculus are often cited as precursors to the bitter priority dispute that would erupt between Newton and Leibniz in the 1710s, after John Keill effectively accused Leibniz of plagiarism.

Contributions to watchmaking

In the 1690s, Fatio discovered a method for piercing a small and well-rounded hole in a ruby, using a diamond drill. Such pierced rubies can serve as jewel bearings in mechanical watches, reducing the friction and corrosion of the watch's internal mechanism, and thereby improving both accuracy and working life. Fatio sought unsuccessfully to interest Parisian watchmakers in his invention. Back in London, Fatio partnered with the Huguenot brothers Peter and Jacob Debaufre (or "de Beaufre"), who kept a successful watchmaking shop in Church Street, Soho. In 1704, Facio and the Debaufres obtained a fourteen-year patent for the sole use in England of Facio's invention relating to rubies. They later attempted unsuccessfully to have the patent extended to "the sole applying [of] precious and more common stones in Clocks and Watches".

In March 1705, Fatio exhibited specimens of watches thus jewelled to the Royal Society. The correspondence of Isaac Newton shows that in 1717 Fatio agreed to make a watch for Richard Bentley in exchange for a payment of £15, and that in 1724 he sought permission from Newton to use Newton's name in advertising his jewelled watches. Fatio's method for piercing rubies remained a speciality of English watchmaking until it was adopted in the Continent in 1768 by Ferdinand Berthoud. Jewel bearings are still used today in luxury mechanical watches.

Later life and death

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.

Fatio left a number of manuscripts, some of which passed into the hands of Dr. Johnstone of Kidderminster; others were acquired by Professor Le Sage of Geneva, who also possessed a large collection of his letters. A few of his papers and letters are in the British Museum. Among them is a Latin poem entitled "N. Facii Duellerii Auriacus Throno-servatus" (Addit. MS. 4163), containing a curious narrative of Fenil's plot and a description of the jewelled watches. A series of letters to Sir Hans Sloane (ib. 4044) extend from 1714 to 1736. Other letters of his are in fasciculus 2 of C. Hugenii aliorumque seculi xvii. virorum celebrium Exercitationes Mathematicæ et Philosophicæ, 4to, the Hague, 1833. To vol. v. of Le Clerc's 'Bibliothèque Universelle,' 1687, Fatio contributed Réflexions sur une méthode de trouver les tangentes de certaines lignes courbes, qui vient d'être publiée dans un livre intitulé: Medicina Mentis. The Acta Lipsiensia for 1700 contains Excerpta ex suâ responsione ad excerpta ex litteris J. Bernouilly. Besides a paper in the Philosophical Transactions, xxviii. 172–6, entitled "Epistola ad fratrem Joh. Christoph. Facium, qua vindicat Solutionem suam Problematis de inveniendo solido rotundo seu tereti in quo minima fiat resistentia", Fatio contributed articles on astronomy and Hebrew metres in nearly every number of the Gentleman's Magazine for 1737 and 1738. In addition to the works already mentioned he was author of:

• "Epistola … de mari æneo Salomonis ad E. Bernardum" in the latter's De Mensuris et Ponderibus antiquis Libri tres, 8vo, Oxford, 1688.
• Fruit-walls improved by inclining them to the horizon, by a member of the Royal Society (signed N. F. D., i.e. N. Faccio de Duillier), 4to, London, 1699.
• N. Facii Duillerii Neutonus. Ecloga, 8vo (Ghent?), 1728.
• Navigation improv'd: being chiefly the method for finding the latitude at sea as well as by land, fol., London, 1728).

With Jean Allut, Elie Marion, and other of the "French prophets", he issued a prophecy with the title Plan de la Justice de Dieu sur la terre dans ces derniers jours et du relévement de la chûte de l'homme par son péché ("Plan of God's Justice upon the earth in these last days, and of the release of man's fall by his sin") 2 parts, 8vo, 1714, of which a Latin version appeared during the same year.

Fatio's most important invention was the jewel bearing, which is still used today in mechanical watches. To optimise the capture of solar energy, and thereby plant productivity, Fatio suggested in 1699 using a tracking mechanism which could pivot to follow the Sun. He also studied the dilatation and contraction of the pupil of the eye, and described the fibres of the anterior uvea and the choroid in a letter to Mariotte, dated 13 April 1684. He introduced improvements in the fabrication of lenses for telescope. He showed how to take advantage of a ship's motion through the water to grind corn, saw, raise anchors, and hoist rigging. He also contrived a ship's observatory and measured the height of the mountains surrounding Geneva, planning, but never completing, a map of Lac Léman.

An elder brother, Jean-Christophe Fatio, was elected a Fellow of the Royal Society on 3 April 1706. He published in the Philosophical Transactions a description of an eclipse of the sun which he had observed at Geneva on 12 May of that year. He died at Geneva on 18 October 1720. By his wife Catherine, daughter of Jean Gassand of Forealquiere in Provence, whom he married in 1709, he left no issue. Her will was proved at London in March 1752,

Fatio appears as a supporting character in Michael White's novel Equinox (2006), Neal Stephenson's novel series, The Baroque Cycle (2003–04), and in Gregory Keyes's novel series, The Age of Unreason (1998–2001).