Nicolas Fatio de Duillier (also spelled Faccio or Facio; 16 February 1664 – 10 May 1753) was a mathematician, natural philosopher, astronomer, inventor, and religious campaigner. Born in Basel, Switzerland, Fatio mostly grew up in the then-independent Republic of Geneva, of which he was a citizen, before spending much of his adult life in England and Holland. Fatio is known for his collaboration with Giovanni Domenico Cassini on the correct explanation of the astronomical phenomenon of zodiacal light, for his "push" or "shadow" theory of gravitation, for inventing the integrating factor as a method for solving ordinary differential equations, for his close association with both Christiaan Huygens and Isaac Newton, and for his role in the Leibniz–Newton calculus controversy. He also invented and developed the first method for fabricating jewel bearings for mechanical watches and clocks.

Elected a Fellow of the Royal Society of London at the age of 24, Fatio never achieved the position and reputation that his early achievements and connections had promised. In 1706 he became involved with a millenarian religious sect, known in London as the "French prophets", and the following year he was sentenced to the pillory for sedition over his role in the publication of the prophecies of Élie Marion, the leader of that sect. Fatio travelled with the French prophets as a missionary, going as far as Smyrna before returning to Holland in 1713, and finally settling in England. His extreme religious views harmed his intellectual reputation, but Fatio continued to pursue technological, scientific, and theological researches until his death at the age of 89.

Early life

Family background

Nicolas Fatio was born in Basel, Switzerland, in 1664, into a family that originated in Italy and settled in Switzerland following the Protestant Reformation. One of his cousins was the ill-fated Genevan political reformer Pierre Fatio. Nicolas was the seventh of fourteen children (six brothers and eight sisters) of Jean-Baptiste and Cathérine Fatio, née Barbaud. Jean-Baptiste had inherited a significant fortune, derived from his father in law'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. Nicolas himself was never married. At the Academy he came under the influence of the rector, Jean-Robert Chouet, a prominent Cartesian.

Also in 1684, Fatio met 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. Fatio hoped to procure Boyle's patronage, In the winter of 1687 Fatio went to the University of 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. 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 successful explanation of zodiacal light as sunlight scattered by a cloud of fine dust surrounding the Sun. Fatio was able to change Newton's mind with the aid of an experiment, and he shared Newton's amended proposition with Huygens.

Fatio then turned down Newton's offer to reside in Cambridge as his assistant, seeking instead academic preferment in the Netherlands.

In February of 1691, Fatio exchanged several letters with Huygens in which Fatio revealed his invention of the method of the integrating factor to solve certain ordinary differential equation. Huygens, in turn, communicated Fatio's method to Leibniz. Fatio later communicated that method to Newton, who included it in his treatise De quadratura curvarum ("On the quadrature of curves"), published years later as an appendix to the Opticks (1704). There, Newton credited Fatio with the method, which consists of multiplying an equation of the form

: <math> f_1(x,y) \dot x + f_2 (x,y) \dot y = 0</math>

by a factor of <math>x^a y^b</math> to give a new equation

: <math> M(x,y) \dot x + N(x,y) \dot y = 0</math>.

If the exponents <math>a</math> and <math>b</math> can be chosen so that <math> \partial M / \partial y = \partial N / \partial x </math>, then the solution to the equation can be expressed as

: <math> \int M(x,y) \, d x = \hbox{const.}</math>

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 mathematical discoveries superfluous. He reported as much to Huygens in 1692.

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.

Alchemy

thumb|300px|Detail from a letter by Fatio to Newton, dated June 24, 1693. Here Fatio describes "the skin which is upon mercury", after preparing an alloy or [[Mercury (element)|mercury and antimony.]]

Modern historian of alchemy William R. Newman regards Fatio as Newton's principal alchemical collaborator during Newton's long career in that field. Newton and Fatio corresponded extensively on this subject between 1689 and 1694. Both men were primarily interested in chrysopoeia and the deciphering of recipes for the preparation of the philosopher's stone that circulated privately within circles of alchemical adepts. They were also interested in the preparation of medical remedies.

Fatio also acted as an intermediary between Newton and a French-speaking alchemist living in London whom he identified as "Monsieur de Tegny", a Huguenot captain in the infantry regiment led by Colonel François Dupuy de Cambon, which fought with William III in Flanders during the Nine Years' War. Fatio wrote to Newton that this M. de Tegny owned an estate in Poitou, close to a place "where they dig some excellent Antimony". Back in London, Fatio partnered with the Huguenot brothers Peter and Jacob Debaufre (or "de Beaufré"), who kept a successful watchmaking shop in Church Street, Soho. In 1704, Fatio and the Debaufres obtained a fourteen-year patent (no. 371) for the sole use in England of Fatio's invention relating to rubies.

In March 1705, Fatio exhibited specimens of watches thus jewelled to the Royal Society. 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 mechanical watches.

Later life

By the summer of 1694, Fatio 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. In Duillier he was reconciled to his father and collaborated with his brother Jean-Christophe in surveying the mountains around Lac Léman. At this time Fatio began a deep study of the prophetic books in the Bible. 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.Fatio then moved to Holland, where he wrote accounts of his missions and of the prophecies delivered during them. Some of these accounts, in French and Latin, were published in 1714.

In 1732, Fatio collaborated with Newton's nephew-in-law and executor, John Conduitt, in the design of the funerary monument to Newton in Westminster Abbey, and in composing the inscription for it. in Madresfield, at the age of 89. He was buried at the church of St Nicholas, Worcester, now deconsecrated. His compatriot Georges-Louis Le Sage later purchased many of his scientific papers which, together with those of Le Sage, are now in the Geneva Library.

Legacy

Inventions

thumb|450px|Engraving for a work published by Nicolas Fatio de Duillier in 1699, describing his invention of sloping fruit walls, intended to collect heat from sunlight and thus to promote plant growth.

Throughout his long life Fatio proposed and developed various technological innovations. Undoubtedly the most significant of these was the jewel bearing, still used today in the manufacture of luxury mechanical watches. But Fatio's efforts as an inventor extended into many areas beyond watchmaking.

To optimise the capture of solar energy and thereby increase agricultural yields, Fatio suggested building sloping fruit walls, precisely angled to maximize the collection of heat from sunlight. Having supervised the building of such walls in Belvoir Castle, in 1699 he published an illustrated treatise that described his invention and included theoretical considerations about solar radiation. Fatio also proposed a tracking mechanism that could pivot to follow the Sun. Such ideas were superseded by the development of modern greenhouses.

One must add to the catalogue of Fatio's inventions his early work on improving the grinding of lenses for the objectives of telescopes, as well as his later proposals for taking advantage of a ship's motion 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 detailed map of Lac Léman.

Push-shadow gravity

thumb|180px|Diagram from Fatio's account of his theory of push-shadow gravity, as reproduced for publication by Karl Bopp.

Fatio considered that his greatest work was his explanation of Newtonian gravity in terms of collisions between ordinary matter and aetherial corpuscles moving rapidly in all directions. and perhaps also by the success of his explanation of zodiacal light as sunlight scattered by an interplanetary cloud of fine particles. Huygens may also have found Fatio's theory uncongenial because it assumed an empty space in which the aetherial corpuscles moved, a view contrary to the plenism of Huygens and Leibniz, who conceived of the aether as a fluid pervading all of space. Another leading physicist who took this theory seriously was Nobel laureate J. J. Thomson.

Fatio's account of his gravitational theory finally published in 1929, in an edition prepared by the German historian of mathematics Karl Bopp, A. M. Ignatov showed in 1996 that a similar process produces an attraction between dust grains in a dusty plasma.

Cultural references

The Genevan naturalist Jean Senebier, writing thirty years after Fatio's death, declared that

Two scholarly biographies of Isaac Newton published in the 20th century, Frank E. Manuel's A Portrait of Isaac Newton (1968) and Richard S. Westfall's Never at Rest (1980) considered at length the personal relationship between Fatio and Newton. Manuel and Westfall both suggested that there might have been a sentimental or sexual element to the attachment between both men, and that Newton's nervous breakdown in 1693 might have been connected with a rupture in that relationship. A similar interpretation appears in Michael White's popular biography Isaac Newton: The Last Sorcerer (1997). Alternatively, historian Scott Mandelbrote writes:

Mandelbrote's judgment has found support in later work by professional historians specializing on Newton, including Robert Iliffe

Fatio's connection with Newton has been treated in several works of historical fiction. He appears as a supporting character in Michael White's novel Equinox (2006), in Neal Stephenson's trilogy The Baroque Cycle (2003–04), and in Gregory Keyes's novel series The Age of Unreason (1998–2001).

Works

Books

Fatio was the author of the following works, published in book form during his lifetime:

  • Epistola de mari æneo Salomonis ("Letter on Solomon's Brazen Sea"), in Edward Bernard's De Mensuris et Ponderibus antiquis Libri tres ("On Ancient Measures and Weights, in three books"), 8vo<!--sic-->, Oxford, 1688
  • 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"), 4to<!--sic-->, London, 1699
  • Fruit-walls improved by inclining them to the horizon, by a member of the Royal Society (signed N. F. D.), 4to<!--sic-->, London, 1699
  • N. Facii Duillerii Neutonus. Ecloga. ("N. Fatio de Duillier's Newton. Eclogue."), 8vo<!--sic-->, Oxford, 1728
  • Navigation improved: being chiefly the method for finding the latitude at sea as well as by land, by taking any proper altitudes, with the time between the observations, fol., London, 1728

With Jean Allut, Elie Marion, and other of the "French prophets", Fatio 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<!--sic-->, 1714, of which a Latin version appeared during the same year.

Periodicals

In periodicals Fatio published the following works:

  • Lettre sur la manière de faire des Bassins pour travailler les verres objectifs des Telescopes ("Letter on the manner of making basins for grinding the objective glasses of telescopes"), Journal des sçavans, Paris, 1684
  • 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"), in Jean Leclerc's Bibliothèque Universelle et Historique, vol. III, Amsterdam, 1686
  • Réflexions sur une méthode de trouver les tangentes de certaines lignes courbes, qui vient d'être publiée dans un livre intitulé: Medicina Mentis ("Reflections on a method for finding the tangents of certain curves, recently published in a book titled Medicina Mentis"), Bibliothèque Universelle et Historique, vol. V, 1687
  • Excerpta ex suâ responsione ad excerpta ex litteris J. Bernouilli ("Excerpts from his response to excerpts from a letter by Johann Bernoulli"), Acta Eruditorum, Leipzig, 1700
  • "Epistola ad fratrem Joh. Christoph. Facium, qua vindicat Solutionem suam Problematis de inveniendo solido rotundo seu tereti in quo minima fiat resistentia" ("Letter to his brother Jean Christophe Fatio, vindicating his solution to the problem of the solid of revolution that produces the minimum resistance"), Philosophical Transactions, vol. XXVIII, pp.&nbsp;172–6, 1713
  • "Four theorems, with their demonstration, for determining accurately the sun's parallax", Miscellanea curiosa mathematica, vol. II, no. 1 (London, 1745)

Fatio also contributed articles on astronomy and ancient Hebrew units of measurement to nearly every number of the Gentleman's Magazine for 1737–38.

Manuscripts

Upon his death, Fatio left a number of manuscripts, some of which passed into the hands of Dr. James Johnstone of Kidderminster. Others were acquired by Prof. Georges-Louis Le Sage of Geneva, who amassed a large collection of Fatio's letters, now at the Bibliothèque de Genève.