Nicolas Fatio
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Nicolas Fatio de Duillier (also spelled Faccio or Facio; 16 February 1664 – 10 May 1753) was a mathematician,
natural philosopher Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics, that is, nature and the physical universe, while ignoring any supernatural influence. It was dominant before the developme ...
, 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 Giovanni Domenico Cassini (8 June 1625 – 14 September 1712) was an Italian-French mathematician, astronomer, astrologer and engineer. Cassini was born in Perinaldo, near Imperia, at that time in the County of Nice, part of the Savoyard sta ...
on the correct explanation of the astronomical phenomenon of
zodiacal light The zodiacal light (also called false dawn when seen before sunrise) is a faint glow of diffuse sunlight scattered by interplanetary dust. Brighter around the Sun, it appears in a particularly dark night sky to extend from the Sun's direct ...
, for inventing the "push" or "shadow" theory of gravitation, for his close association with both
Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...
and
Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
, and for his role in the
Leibniz–Newton calculus controversy In the history of calculus, the calculus controversy () was an argument between mathematicians Isaac Newton and Gottfried Wilhelm Leibniz over who had first discovered calculus. The question was a major intellectual controversy, beginning in 16 ...
. He also invented and developed the first method for fabricating
jewel bearing A jewel bearing is a plain bearing in which a metal spindle (tool), spindle turns in a gemstone, jewel-lined pivot hole. The hole is typically shaped like a torus and is slightly larger than the shaft diameter. The jewels are typically made ...
s for
mechanical watch A mechanical watch is a watch that uses a Movement (clockwork), clockwork mechanism to measure the passage of time, as opposed to quartz watches which function using the vibration modes of a piezoelectric quartz tuning fork, or radio clock, radio ...
es and clocks. Elected a
Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...
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 Millenarianism or millenarism () is the belief by a religious organization, religious, social, or political party, political group or Social movement, movement in a coming fundamental Social transformation, transformation of society, after which ...
religious sect, known in London as the " French prophets", and the following year he was sentenced to the
pillory The pillory is a device made of a wooden or metal framework erected on a post, with holes for securing the head and hands, used during the medieval and renaissance periods for punishment by public humiliation and often further physical abuse. ...
for
sedition Sedition is overt conduct, such as speech or organization, that tends toward rebellion against the established order. Sedition often includes subversion of a constitution and incitement of discontent toward, or insurrection against, establ ...
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 Smyrna ( ; , or ) was an Ancient Greece, Ancient Greek city located at a strategic point on the Aegean Sea, Aegean coast of Anatolia, Turkey. Due to its advantageous port conditions, its ease of defence, and its good inland connections, 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 Basel ( ; ), also known as Basle ( ), ; ; ; . is a city in northwestern Switzerland on the river Rhine (at the transition from the High Rhine, High to the Upper Rhine). Basel is Switzerland's List of cities in Switzerland, third-most-populo ...
, Switzerland, in 1664, into a family that originated in Italy and settled in Switzerland following the Protestant
Reformation The Reformation, also known as the Protestant Reformation or the European Reformation, was a time of major Theology, theological movement in Western Christianity in 16th-century Europe that posed a religious and political challenge to the p ...
. One of his cousins was the ill-fated
Geneva Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the ca ...
n political reformer
Pierre Fatio Pierre Fatio (7 November 1662 – 6 September 1707) was a lawyer and politician from the Republic of Geneva. His struggle against the dominance of the aristocracy in the Genevan government led to his execution on charges of conspiring against ...
. 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 Duillier () is a municipality in the district of Nyon in the canton of Vaud in Switzerland. History Duillier is first mentioned in 1145 as ''Duelliei''. Geography Duillier has an area, , of . Of this area, or 75.2% is used for agricultural pu ...
, 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. Nicolas's elder brother, Jean Christophe Fatio, was elected a Fellow of the Royal Society on 3 April 1706. Jean Christophe published in the ''Philosophical Transactions'' a description of the solar eclipse that he had observed in Geneva on 12 May of that year. He died at Geneva on 18 October 1720. Jean Christophe was married in 1709 to Catherine, daughter of Jean Gassand of
Forcalquier Forcalquier (; ) is a commune in the Alpes-de-Haute-Provence department in southeastern France. Forcalquier is located between the Lure Mountain( fr) and Luberon mountain ranges, about south of Sisteron and west of the Durance river. Dur ...
, in Provence. Catherine's will was proved at London in March 1752. Nicolas himself was never married.


Education and patronage

Nicolas Fatio received his elementary schooling at the ''
Collège de Genève In France, secondary education is in two stages: * ''Collèges'' () cater for the first four years of secondary education from the ages of 11 to 14. * ''Lycées'' () provide a three-year course of further secondary education for students between ...
'', proceeding in 1678 to the ''Académie de Genève'' (now the
University of Geneva The University of Geneva (French: ''Université de Genève'') is a public university, public research university located in Geneva, Switzerland. It was founded in 1559 by French theologian John Calvin as a Theology, theological seminary. It rema ...
), where he remained until 1680. At the Academy he came under the influence of the rector, Jean-Robert Chouet, a prominent Cartesian. Before he was eighteen, Fatio wrote to the director of the
Paris Observatory The Paris Observatory (, ), a research institution of the Paris Sciences et Lettres University, is the foremost astronomical observatory of France, and one of the largest astronomical centres in the world. Its historic building is on the Left Ban ...
, the astronomer
Giovanni Domenico Cassini Giovanni Domenico Cassini (8 June 1625 – 14 September 1712) was an Italian-French mathematician, astronomer, astrologer and engineer. Cassini was born in Perinaldo, near Imperia, at that time in the County of Nice, part of the Savoyard sta ...
, 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 Saturn has the most extensive and complex ring system of any planet in the Solar System. The rings consist of particles in orbit around the planet made almost entirely of water ice, with a trace component of Rock (geology), rocky material. Parti ...
. 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 The zodiacal light (also called false dawn when seen before sunrise) is a faint glow of diffuse sunlight scattered by interplanetary dust. Brighter around the Sun, it appears in a particularly dark night sky to extend from the Sun's direct ...
. 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 Nouvelles (; ) is a sub-municipality of the city of Mons located in the province of Hainaut, Wallonia, Belgium. It was a separate municipality until 1977. On 1 January 1977, it was merged Mergers and acquisitions (M&A) are business transacti ...
''. 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 Amsterdam ( , ; ; ) is the capital of the Netherlands, capital and Municipalities of the Netherlands, largest city of the Kingdom of the Netherlands. It has a population of 933,680 in June 2024 within the city proper, 1,457,018 in the City Re ...
in 1686. There Fatio correctly explained the zodiacal light as sunlight scattered by an
interplanetary dust cloud The interplanetary dust cloud, or zodiacal cloud (as the source of the zodiacal light), consists of cosmic dust (small particles floating in outer space) that pervades the space between planets within planetary systems, such as the Solar Sys ...
(the "zodiacal cloud") that straddles the
ecliptic plane The ecliptic or ecliptic plane is the orbital plane of Earth around the Sun. It was a central concept in a number of ancient sciences, providing the framework for key measurements in astronomy, astrology and calendar-making. From the perspec ...
. Fatio then studied the dilatation and contraction of the eye's
pupil The pupil is a hole located in the center of the iris of the eye that allows light to strike the retina.Cassin, B. and Solomon, S. (1990) ''Dictionary of Eye Terminology''. Gainesville, Florida: Triad Publishing Company. It appears black becau ...
. He described the fibres of the anterior
uvea The uvea (; derived from meaning "grape"), also called the uveal layer, uveal coat, uveal tract, vascular tunic or vascular layer, is the pigmented middle layer of the three concentric layers that make up an eye, precisely between the inne ...
and the
choroid The choroid, also known as the choroidea or choroid coat, is a part of the uvea, the vascular layer of the eye. It contains connective tissues, and lies between the retina and the sclera. The human choroid is thickest at the far extreme rear o ...
in a letter to
Edme Mariotte Edme Mariotte (; ; c. 162012 May 1684) was a French physicist and priest (abbé). He is particularly well known for formulating Boyle's law independently of Robert Boyle. Mariotte is also credited with designing the first Newton's cradle. Biog ...
, dated 13 April 1684. That same year he published an article in the ''
Journal des sçavans The (later renamed and then , ), established by Denis de Sallo, is the earliest academic journal published in Europe. It is thought to be the earliest published scientific journal. It currently focuses on European history and premodern literatu ...
'' on how to improve the fabrication of lenses for the objectives of
telescope A telescope is a device used to observe distant objects by their emission, Absorption (electromagnetic radiation), absorption, or Reflection (physics), reflection of electromagnetic radiation. Originally, it was an optical instrument using len ...
s. Also in 1684, Fatio met the
Piedmont Piedmont ( ; ; ) is one of the 20 regions of Italy, located in the northwest Italy, Northwest of the country. It borders the Liguria region to the south, the Lombardy and Emilia-Romagna regions to the east, and the Aosta Valley region to the ...
ese Count Fenil, who, having offended the
Duke of Savoy The titles of the count of Savoy, and then duke of Savoy, are titles of nobility attached to the historical territory of Savoy. Since its creation, in the 11th century, the House of Savoy held the county. Several of these rulers ruled as kings at ...
and the
King of France France was ruled by monarchs from the establishment of the kingdom of West Francia in 843 until the end of the Second French Empire in 1870, with several interruptions. Classical French historiography usually regards Clovis I, king of the Fra ...
, had taken refuge in the house of Fatio's maternal grandfather in
Alsace Alsace (, ; ) is a cultural region and a territorial collectivity in the Grand Est administrative region of northeastern France, on the west bank of the upper Rhine, next to Germany and Switzerland. In January 2021, it had a population of 1,9 ...
and then at Duillier. Fenil confided to Fatio his plan to stage a raid on the beach at
Scheveningen Scheveningen () is one of the eight districts of The Hague, Netherlands, as well as a subdistrict () of that city. Scheveningen is a modern seaside resort with a long, sandy beach, an esplanade, a pier, and a lighthouse. The beach is popular ...
to kidnap the Dutch Prince William of Orange. Fenil showed Fatio a letter from the
Marquis de Louvois A marquess (; ) is a nobleman of high hereditary rank in various European peerages and in those of some of their former colonies. The German-language equivalent is Markgraf (margrave). A woman with the rank of a marquess or the wife (or widow) ...
, the French Secretary of State, approving of the kidnapping, offering the king's pardon as recompense for the successful completion of the operation, and enclosing an order for money. Fatio betrayed Fenil's plot to
Gilbert Burnet Gilbert Burnet (18 September 1643 – 17 March 1715) was a Scottish people, Scottish philosopher and historian, and Bishop of Salisbury. He was fluent in Dutch language, Dutch, French language, French, Latin language, Latin, Greek language, Gree ...
, whom he then accompanied to Holland in 1686 to warn Prince William.


Career in Holland and England

In Holland, Fatio met
Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...
in 1682-1683, with whom he began to collaborate on mathematical problems concerning the new infinitesimal
calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...
. Encouraged by Huygens, Fatio compiled a list of corrections to the published works on differentiation by
Ehrenfried Walther von Tschirnhaus Ehrenfried Walther von Tschirnhaus or Tschirnhauß (; 10 April 1651 – 11 October 1708) was a German mathematician, physicist, physician, and philosopher. He introduced the Tschirnhaus transformation and is considered by some to have been the ...
. 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. Fatio arrived in England in June 1687, carrying with him the conviction that the two greatest living natural philosophers were
Robert Boyle Robert Boyle (; 25 January 1627 – 31 December 1691) was an Anglo-Irish natural philosopher, chemist, physicist, Alchemy, alchemist and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the foun ...
, "for the details of his experiments concerning earthly bodies", and Christiaan Huygens "for physics in general, above all in those areas in which it is involved with mathematics." Fatio hoped to procure Boyle's patronage, and in London he soon made the acquaintance of
John Wallis John Wallis (; ; ) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 Wallis served as chief cryptographer for Parliament and, later, the royal court. ...
,
John Locke John Locke (; 29 August 1632 (Old Style and New Style dates, O.S.) – 28 October 1704 (Old Style and New Style dates, O.S.)) was an English philosopher and physician, widely regarded as one of the most influential of the Enlightenment thi ...
,
Richard Hampden Richard Hampden (baptized 13 October 1631 – 15 December 1695) was an English Whig politician and son of Ship money tax protester John Hampden. He was sworn a Privy Counsellor in 1689 and was Chancellor of the Exchequer from 18 March 1690 un ...
, and his son
John Hampden John Hampden (24 June 1643) was an English politician from Oxfordshire, who was killed fighting for Roundhead, Parliament in the First English Civil War. An ally of Parliamentarian leader John Pym, and a cousin of Oliver Cromwell, he was one of ...
, among other important figures connected with the Whig party. Fatio worked out new solutions of the "inverse tangent problem" (i.e., the solution of
ordinary differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable (mathematics), variable. As with any other DE, its unknown(s) consists of one (or more) Function (mathematic ...
s) and was introduced to the
Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
by
Henri Justel Henri Justel (1619–1693) was a French scholar and royal administrator, and also a bibliophile and librarian. He is known also as Henry Justel and Henricus Justellus. He was son of the scholar Christophe Justel. He acted as a secretary to Lou ...
. He began to attend Society's meetings in June of that year, thus learning of the upcoming publication of Newton's ''
Principia Principia may refer to: * ''Philosophiæ Naturalis Principia Mathematica'', Isaac Newton's three-volume work about his laws of motion and universal gravitation * Principia ( "primary buildings"), the headquarters at the center of Roman forts () * ...
''. In the winter of 1687 Fatio went to the
University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...
, where he collaborated with
Edward Bernard Edward Bernard (1638 – 12 January 1697) was an English scholar and Savilian professor of astronomy at the University of Oxford, from 1673 to 1691. Life He was born at Paulerspury, Northamptonshire. He was educated at Merchant Taylors' Scho ...
, the
Savilian Professor of Astronomy The position of Savilian Professor of Astronomy was established at the University of Oxford in 1619. It was founded (at the same time as the Savilian Professorship of Geometry) by Sir Henry Savile, a mathematician and classical scholar who was ...
, in an investigation into the units of measurement used in the ancient world.


Participation in the Royal Society

Aged only 24, Fatio was elected
fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...
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
Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
's work on universal gravitation. Fatio's personal prospects seemed to brighten even further as a result of the
Glorious Revolution The Glorious Revolution, also known as the Revolution of 1688, was the deposition of James II and VII, James II and VII in November 1688. He was replaced by his daughter Mary II, Mary II and her Dutch husband, William III of Orange ...
of 1688–9, which marked the ascendancy of the Whigs and culminated with
Parliament In modern politics and history, a parliament is a legislative body of government. Generally, a modern parliament has three functions: Representation (politics), representing the Election#Suffrage, electorate, making laws, and overseeing ...
deposing the Catholic King James II and giving the English throne jointly to James's Protestant daughter
Mary Mary may refer to: People * Mary (name), a female given name (includes a list of people with the name) Religion * New Testament people named Mary, overview article linking to many of those below * Mary, mother of Jesus, also called the Blesse ...
and to her husband, the Dutch
Prince William of Orange William III (William Henry; ; 4 November 1650 – 8 March 1702), also known as William of Orange, was the sovereign Prince of Orange from birth, Stadtholder of Holland, Zeeland, Utrecht, Guelders, and Overijssel in the Dutch Republic from 167 ...
. Fatio also had an opportunity to enhance his intellectual reputation during Huygens' visit to London in the summer of 1689. Fatio met Newton, probably for the first time, at a meeting of the Royal Society on 12 June 1689. Newton and Fatio soon became 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 The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...
. In 1690, Fatio wrote to Huygens outlining his own understanding of the physical cause of gravity, which would later become 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 successful explanation of zodiacal light as sunlight scattered by a cloud of fine dust surrounding the Sun. Fatio turned down Newton's offer to reside in Cambridge as his assistant, seeking instead academic preferment in the Netherlands. In the spring of 1690 he traveled to
The Hague The Hague ( ) is the capital city of the South Holland province of the Netherlands. With a population of over half a million, it is the third-largest city in the Netherlands. Situated on the west coast facing the North Sea, The Hague is the c ...
as tutor to two of John Hampden's nephews. There, 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 Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, Sir Isaac Newton, with the creation of calculus in ad ...
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 Integration may refer to: Biology *Multisensory integration *Path integration * Pre-integration complex, viral genetic material used to insert a viral genome into a host genome *DNA integration, by means of site-specific recombinase technology, ...
, ''De quadratura curvarum''. Initially, he also expected to collaborate with Newton on a new edition of the ''Principia'' that 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."


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. In 1696,
Johann Bernoulli Johann Bernoulli (also known as Jean in French or John in English; – 1 January 1748) was a Swiss people, Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infin ...
, a close ally of Leibniz, posed the
brachistochrone problem In physics and mathematics, a brachistochrone curve (), or curve of fastest descent, is the one lying on the plane between a point ''A'' and a lower point ''B'', where ''B'' is not directly below ''A'', on which a bead slides frictionlessly under ...
as a challenge to the mathematicians who claimed to understand the new calculus. The problem was solved by Leibniz, Tschirnhaus, L'Hôpital,
Jacob Bernoulli Jacob Bernoulli (also known as James in English or Jacques in French; – 16 August 1705) was a Swiss mathematician. He sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy and was an early proponent of Leibniz ...
, 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 In geometry, a solid of revolution is a Solid geometry, solid figure obtained by rotating a plane figure around some straight line (the ''axis of revolution''), which may not Intersection (geometry), intersect the generatrix (except at its bound ...
that produces the minimum resistance"), a pamphlet containing his own solutions to the brachistochrone and to another problem, treated by Newton in book II of the ''Principia'' (see
Newton's minimal resistance problem Newton's minimal resistance problem is a problem of finding a solid of revolution which experiences a minimum resistance when it moves through a homogeneous fluid with constant velocity in the direction of the axis of revolution, named after Isaac N ...
), in what is now called the "
calculus of variations The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...
". 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. This provoked angry responses from Johann Bernoulli and Leibniz in the ''
Acta Eruditorum (from Latin: ''Acts of the Erudite'') was the first scientific journal of the German-speaking lands of Europe, published from 1682 to 1782. History ''Acta Eruditorum'' was founded in 1682 in Leipzig by Otto Mencke, who became its first edit ...
''. 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, 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 In science, priority is the credit given to the individual or group of individuals who first made the discovery or proposed the theory. Fame and honours usually go to the first person or group to publish a new finding, even if several researchers a ...
that would erupt between Newton and Leibniz in the 1710s, after the Scottish mathematician
John Keill John Keill FRS (1 December 1671 – 31 August 1721) was a Scottish mathematician, natural philosopher, and cryptographer who was an important defender of Isaac Newton. Biography Keill was born in Edinburgh, Scotland on 1 December 1671. His fa ...
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 Ruby is a pinkish-red-to-blood-red-colored gemstone, a variety of the mineral corundum ( aluminium oxide). Ruby is one of the most popular traditional jewelry gems and is very durable. Other varieties of gem-quality corundum are called sapph ...
, using a diamond drill. Such pierced rubies can serve as
jewel bearing A jewel bearing is a plain bearing in which a metal spindle (tool), spindle turns in a gemstone, jewel-lined pivot hole. The hole is typically shaped like a torus and is slightly larger than the shaft diameter. The jewels are typically made ...
s in
mechanical watch A mechanical watch is a watch that uses a Movement (clockwork), clockwork mechanism to measure the passage of time, as opposed to quartz watches which function using the vibration modes of a piezoelectric quartz tuning fork, or radio clock, radio ...
es, 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 The Huguenots ( , ; ) are a Religious denomination, religious group of French people, French Protestants who held to the Reformed (Calvinist) tradition of Protestantism. The term, which may be derived from the name of a Swiss political leader, ...
brothers Peter and Jacob Debaufre (or "de Beaufré"), who kept a successful watchmaking shop in Church Street,
Soho SoHo, short for "South of Houston Street, Houston Street", is a neighborhood in Lower Manhattan, New York City. Since the 1970s, the neighborhood has been the location of many artists' lofts and art galleries, art installations such as The Wall ...
. 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. They later attempted unsuccessfully to have the patent extended to "the sole applying fprecious 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 Richard Bentley FRS (; 27 January 1662 – 14 July 1742) was an English classical scholar, critic, and theologian. Considered the "founder of historical philology", Bentley is widely credited with establishing the English school of Hellenis ...
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 Ferdinand Berthoud (; born 18 March 1727, in Couvet, Plancemont-sur-Couvet, Principality of Neuchâtel; died 20 June 1807, in Groslay, Val d'Oise), was a scientist and watchmaker. He became master watchmaker in Paris in 1753. Berthoud, who held ...
. Jewel bearings are still used today in luxury mechanical watches.


Alchemical work

Modern historian of
alchemy Alchemy (from the Arabic word , ) is an ancient branch of natural philosophy, a philosophical and protoscientific tradition that was historically practised in China, India, the Muslim world, and Europe. In its Western form, alchemy is first ...
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
alchemy Alchemy (from the Arabic word , ) is an ancient branch of natural philosophy, a philosophical and protoscientific tradition that was historically practised in China, India, the Muslim world, and Europe. In its Western form, alchemy is first ...
between 1689 and 1694. Both men were primarily interested in
chrysopoeia In alchemy, the term chrysopoeia () refers to the artificial production of gold, most commonly by the alleged transmutation of base metals such as lead. A related term is argyropoeia (), referring to the artificial production of silver, often ...
and the deciphering of recipes for the preparation of the
philosopher's stone The philosopher's stone is a mythic alchemical substance capable of turning base metals such as mercury into gold or silver; it was also known as "the tincture" and "the powder". Alchemists additionally believed that it could be used to mak ...
that circulated privately within circles of alchemical adepts. They were also interested in the preparation of medical remedies. Fatio acted as an intermediary between Newton and a French-speaking alchemist living in London. Modern scholars have tentatively identified this Huguenot alchemist as M. de Tegny, a captain in the infantry regiment led by Colonel François Dupuy de Cambon, which fought with William III in Flanders during the
Nine Years' War The Nine Years' War was a European great power conflict from 1688 to 1697 between Kingdom of France, France and the Grand Alliance (League of Augsburg), Grand Alliance. Although largely concentrated in Europe, fighting spread to colonial poss ...
.


Later life

By the summer of 1694, Fatio was employed as a tutor to Wriothesley Russell, the heir of the
Duke of Bedford Duke of Bedford (named after Bedford, England) is a title that has been created six times (for five distinct people) in the Peerage of England. The first creation came in 1414 for Henry IV's third son, John, who later served as regent of Fran ...
, a position for which he had been recommended by Locke. Fatio accompanied his pupil to
Oxford Oxford () is a City status in the United Kingdom, cathedral city and non-metropolitan district in Oxfordshire, England, of which it is the county town. The city is home to the University of Oxford, the List of oldest universities in continuou ...
and, during 1697–8, to Holland. Fatio was in Switzerland in 1699, 1700, and 1701. In Duillier he was reconciled to his father and collaborated with his brother Jean-Christophe in surveying the mountains around
Lac Léman Lake Geneva is a deep lake on the north side of the Alps, shared between Switzerland and France. It is one of the largest lakes in Western Europe and the largest on the course of the Rhône. Sixty percent () of the lake belongs to Switzerl ...
. At this time Fatio began a deep study of the prophetic books in the Bible.


Involvement with the "French prophets"

Back in London, Fatio worked as a mathematical tutor in
Spitalfields Spitalfields () is an area in London, England and is located in the London Borough of Tower Hamlets. It is in East London and situated in the East End of London, East End. Spitalfields is formed around Commercial Street, London, Commercial Stre ...
. In 1706, he began to associate with the
Camisards Camisards were Huguenots (French Protestants) of the rugged and isolated Cévennes region and the neighbouring Vaunage in southern France. In the early 1700s, they raised a resistance against the persecutions which followed Louis XIV's Revocatio ...
, radical Protestant exiles ("Huguenots") who had fled from France during the
Wars of Religion A religious war or a war of religion, sometimes also known as a holy war (), is a war and conflict which is primarily caused or justified by differences in religion and beliefs. In the modern period, there are frequent debates over the extent ...
in that country. Fatio became attached to a
millenarian Millenarianism or millenarism () is the belief by a religious organization, religious, social, or political party, political group or Social movement, movement in a coming fundamental Social transformation, transformation of society, after which ...
group known as the "French prophets", who preached impending destruction and judgment. In 1707, Élie Marion, Jean Daudé, and Fatio were tried before the
Queen's Bench The King's Bench (), or, during the reign of a female monarch, the Queen's Bench ('), refers to several contemporary and historical courts in some Commonwealth jurisdictions. * Court of King's Bench (England), a historic court of common law in ...
on charges brought against them by the mainstream Huguenot churches in London. This prosecution for
sedition Sedition is overt conduct, such as speech or organization, that tends toward rebellion against the established order. Sedition often includes subversion of a constitution and incitement of discontent toward, or insurrection against, establ ...
was backed by the British government, which suspected the French prophets of contriving a political scheme. Marion, Daudé, and Fatio were convicted of sedition and sentenced to the
pillory The pillory is a device made of a wooden or metal framework erected on a post, with holes for securing the head and hands, used during the medieval and renaissance periods for punishment by public humiliation and often further physical abuse. ...
. On 2 December, Fatio stood on a scaffold at
Charing Cross Charing Cross ( ) is a junction in Westminster, London, England, where six routes meet. Since the early 19th century, Charing Cross has been the notional "centre of London" and became the point from which distances from London are measured. ...
with an inscription on his hat that read By the influence of the
Duke of Ormonde The peerage title Earl of Ormond and the related titles Duke of Ormonde and Marquess of Ormonde have a long and complex history. An earldom of Ormond has been created three times in the Peerage of Ireland. History of Ormonde titles The earldom ...
, 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 Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
, Halle, and
Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...
as a missionary of the French prophets. A second mission in 1712–13 took him to
Stockholm Stockholm (; ) is the Capital city, capital and List of urban areas in Sweden by population, most populous city of Sweden, as well as the List of urban areas in the Nordic countries, largest urban area in the Nordic countries. Approximately ...
,
Prussia Prussia (; ; Old Prussian: ''Prūsija'') was a Germans, German state centred on the North European Plain that originated from the 1525 secularization of the Prussia (region), Prussian part of the State of the Teutonic Order. For centuries, ...
, Halle,
Constantinople Constantinople (#Names of Constantinople, see other names) was a historical city located on the Bosporus that served as the capital of the Roman Empire, Roman, Byzantine Empire, Byzantine, Latin Empire, Latin, and Ottoman Empire, Ottoman empire ...
,
Smyrna Smyrna ( ; , or ) was an Ancient Greece, Ancient Greek city located at a strategic point on the Aegean Sea, Aegean coast of Anatolia, Turkey. Due to its advantageous port conditions, its ease of defence, and its good inland connections, 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.


Further intellectual work

Back in London, Fatio once again communicated with the Royal Society, of which his old friend Sir Isaac Newton had been president since 1704. In 1717 Fatio presented a series of papers on the
precession of the equinoxes In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's Rotation around a fixed axis, rotational axis. In the absence of precession, the astronomical body's orbit would show ...
and
climate change Present-day climate change includes both global warming—the ongoing increase in Global surface temperature, global average temperature—and its wider effects on Earth's climate system. Climate variability and change, Climate change in ...
, subjects that he regarded from both a scientific and a millenarian perspective. In the spring of that same year he moved to
Worcester Worcester may refer to: Places United Kingdom * Worcester, England, a city and the county town of Worcestershire in England ** Worcester (UK Parliament constituency), an area represented by a Member of Parliament * Worcester Park, London, Engl ...
, where he formed some congenial friendships and busied himself with scientific pursuits,
alchemy Alchemy (from the Arabic word , ) is an ancient branch of natural philosophy, a philosophical and protoscientific tradition that was historically practised in China, India, the Muslim world, and Europe. In its Western form, alchemy is first ...
, and study of the cabbala. Fatio would spend the rest of his life in Worcester and nearby
Madresfield Madresfield is a village and civil parish in the administrative district of Malvern Hills in the county of Worcestershire, England. It is located about two miles east of Malvern town centre at the foot of the Malvern Hills and is less than two ...
. After the death of Isaac Newton in 1727, Fatio composed a poetic hymn (
eclogue An eclogue is a poem in a classical style on a pastoral subject. Poems in the genre are sometimes also called bucolics. The term is also used for a musical genre thought of as evoking a pastoral scene. Classical beginnings The form of the word ...
) on Newton's genius, written in Latin and published in 1728. According to modern Newton scholar Robert Iliffe, this is "the most interesting poetic response to Newton". In 1732, Fatio collaborated with Newton's nephew-in-law and executor,
John Conduitt John Conduitt (; c. 8 March 1688 – 23 May 1737), of Cranbury Park, Hampshire, was a British landowner and Whig politician. He sat in the House of Commons from 1721 to 1737. He was married to the half-niece of Sir Isaac Newton, whom Conduitt ...
, in the design of the funerary monument to Newton in
Westminster Abbey Westminster Abbey, formally titled the Collegiate Church of Saint Peter at Westminster, is an Anglican church in the City of Westminster, London, England. Since 1066, it has been the location of the coronations of 40 English and British m ...
, and in composing the inscription for it. At that time, Fatio also sought Conduitt's help in his effort (which was ultimately unsuccessful) to obtain a belated reward for having saved the Prince of Orange from Count Fenil's kidnapping plot. Fatio also unsuccessfully sought Conduitt's support for the publication of his "push-shadow" theory of gravity, on which he had been working for more than forty years.


Death

Fatio died on either 28 April or 12 May 1753 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 Georges-Louis Le Sage (; 13 June 1724 – 20 November 1803) was a Genevan physicist and is most known for his theory of gravitation, for his invention of an electric telegraph and his anticipation of the kinetic theory of gases. He was a cont ...
later purchased many of his scientific papers which, together with those of Le Sage, are now in the Geneva Library.


Legacy


Inventions

Throughout his long life Fatio proposed and developed various technological innovations. Undoubtedly the most significant of these was the
jewel bearing A jewel bearing is a plain bearing in which a metal spindle (tool), spindle turns in a gemstone, jewel-lined pivot hole. The hole is typically shaped like a torus and is slightly larger than the shaft diameter. The jewels are typically made ...
, 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 Solar energy is the radiant energy from the Sun's sunlight, light and heat, which can be harnessed using a range of technologies such as solar electricity, solar thermal energy (including solar water heating) and solar architecture. It is a ...
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 Belvoir Castle ( ) is a faux historic castle and stately home in Leicestershire, England, situated west of the town of Grantham and northeast of Melton Mowbray. A castle was first built on the site immediately after the Norman Conquest of 10 ...
, in 1699 he published an illustrated treatise that described his invention and included theoretical considerations about solar radiation. That work appeared with the imprimatur of the Royal Society. Fatio also proposed a tracking mechanism that could pivot to follow the Sun. Such ideas were superseded by the development of modern
greenhouse A greenhouse is a structure that is designed to regulate the temperature and humidity of the environment inside. There are different types of greenhouses, but they all have large areas covered with transparent materials that let sunlight pass an ...
s. 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

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. Fatio was motivated by Huygens's earlier work on a "mechanical" explanation of gravity in terms of contact interactions between ordinary matter and an aether, and perhaps also by the success of his explanation of
zodiacal light The zodiacal light (also called false dawn when seen before sunrise) is a faint glow of diffuse sunlight scattered by interplanetary dust. Brighter around the Sun, it appears in a particularly dark night sky to extend from the Sun's direct ...
as sunlight scattered by an interplanetary cloud of fine particles. The need to make the collisions between ordinary matter and the aetherial corpuscles inelastic implied that Fatio's aetherial corpuscles must also exert a drag resistance on the motion of celestial bodies. Fatio therefore failed to interest Huygens (who believed in the conservation of ''
vis viva ''Vis viva'' (from the Latin for "living force") is a historical term used to describe a quantity similar to kinetic energy in an early formulation of the principle of conservation of energy. Overview Proposed by Gottfried Leibniz over the period ...
'') in his proposal. 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 Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many ...
, who conceived of the aether as a fluid pervading all of space. Finding that the drag resistance was proportional to the product of the speed and the density of the aetherial corpuscles, while the gravitational attraction was proportional to the density and the ''square'' of the speed of the corpuscles, Fatio concluded that the drag could be made negligible by decreasing the density while increasing the speed. However, despite some initial enthusiasm on the part of Newton and Halley, Fatio's theory of gravity soon fell into oblivion and Newton abandoned all attempts to explain gravity in terms of contact interactions. Fatio corresponded about his theory with
Jacob Bernoulli Jacob Bernoulli (also known as James in English or Jacques in French; – 16 August 1705) was a Swiss mathematician. He sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy and was an early proponent of Leibniz ...
in 1700 and he continued to revise and promote his theory until the end of his life, but he never published that work. A copy of Fatio's manuscript came to the attention of the Genevan mathematician
Gabriel Cramer Gabriel Cramer (; 31 July 1704 – 4 January 1752) was a Genevan mathematician. Biography Cramer was born on 31 July 1704 in Geneva, Republic of Geneva to Jean-Isaac Cramer, a physician, and Anne Mallet. The progenitor of the Cramer family i ...
, who in 1731 published a dissertation containing a summary of Fatio's theory, without attribution. Another Genevan,
Georges-Louis Le Sage Georges-Louis Le Sage (; 13 June 1724 – 20 November 1803) was a Genevan physicist and is most known for his theory of gravitation, for his invention of an electric telegraph and his anticipation of the kinetic theory of gases. He was a cont ...
, independently re-discovered the same idea before Cramer introduced him to Fatio's work in 1749. Since then, the corresponding theory has been commonly known as " Le Sage's theory of gravitation". The success of the
kinetic theory of gases The kinetic theory of gases is a simple classical model of the thermodynamic behavior of gases. Its introduction allowed many principal concepts of thermodynamics to be established. It treats a gas as composed of numerous particles, too small ...
contributed to reviving interest in the Fatio-Le Sage theory during the second half of the 19th century. In 1878,
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism an ...
characterized it as "the only theory of the cause of gravitation which has been so far developed as to be capable of being attacked and defended." Another leading physicist who took this theory seriously was Nobel laureate
J. J. Thomson Sir Joseph John Thomson (18 December 1856 – 30 August 1940) was an English physicist who received the Nobel Prize in Physics in 1906 "in recognition of the great merits of his theoretical and experimental investigations on the conduction of ...
. Fatio's account of his gravitational theory finally published in 1929, in an edition prepared by the German historian of mathematics Karl Bopp, and then again independently in 1949 by Bernard Gagnebin, the conservator of manuscripts at the Geneva Library. Even though the modern scientific consensus is that the Fatio-Le Sage theory is inviable as an account of gravity, the process that he described does give rise to an attractive inverse-square force between particles immersed in a rare medium at a higher temperature.
George Gamow George Gamow (sometimes Gammoff; born Georgiy Antonovich Gamov; ; 4 March 1904 – 19 August 1968) was a Soviet and American polymath, theoretical physicist and cosmologist. He was an early advocate and developer of Georges Lemaître's Big Ba ...
proposed in 1949 that such a "mock gravity" could have played a role in
galaxy formation In cosmology, the study of galaxy formation and evolution is concerned with the processes that formed a Homogeneity and heterogeneity, heterogeneous universe from a Big Bang, homogeneous beginning, the formation of the first galaxies, the way ga ...
after the
Big Bang The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...
. A. M. Ignatov showed in 1996 that a similar process produces an attraction between dust grains in a
dusty plasma A dusty plasma is a Plasma (physics), plasma containing micrometer (10−6) to nanometer (10−9) sized particles suspended in it. Dust particles are charged and the plasma and particles behave as a plasma. Dust particles may form larger particles ...
.


Cultural references

The Genevan naturalist
Jean Senebier Jean Senebier (25 May 1742 – 22 July 1809) was a Republic and Canton of Geneva#History, Genevan Calvinist pastor and naturalist. He was chief librarian of the Republic of Geneva. A pioneer in the field of photosynthesis research, he provided ...
, 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. Westfall (April 22, 1924 – August 21, 1996) was an American biographer and historian of science. He is best known for his biography of Isaac Newton, ''Never at Rest'', and his work on the Scientific Revolution of the 17th century. He ta ...
'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 and
William R. Newman William R. Newman (born March 13, 1955) is Distinguished Professor and Ruth N. Halls Professor in the Department of History and Philosophy of Science at Indiana University. Most of Newman’s work in the History of Science has been devoted to al ...
. According to Newman, 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 Neal Town Stephenson (born October 31, 1959) is an American writer known for his works of speculative fiction. His novels have been categorized as science fiction, historical fiction, cyberpunk, and baroque. Stephenson's work explores mathemati ...
's trilogy ''
The Baroque Cycle ''The Baroque Cycle'' is a series of novels by American writer Neal Stephenson. It was published in three volumes containing eight books in 2003 and 2004. The story follows the adventures of a sizable cast of characters living amidst some of th ...
'' (2003–04), and in
Gregory Keyes Gregory Keyes (born April 11, 1963) is an American writer of science fiction and fantasy who has written both original and media-related novels under both the names J. Gregory Keyes and Greg Keyes. Early life Keyes was born in Meridian, Mississ ...
's novel series ''
The Age of Unreason ''The Age of Unreason'' is a series of four novels written by Gregory Keyes: * '' Newton's Cannon'' (1998), * '' A Calculus of Angels'' (1999), * '' Empire of Unreason'' (2000), * '' The Shadows of God'' (2001), Its title is a reference to ...
'' (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 Edward Bernard (1638 – 12 January 1697) was an English scholar and Savilian professor of astronomy at the University of Oxford, from 1673 to 1691. Life He was born at Paulerspury, Northamptonshire. He was educated at Merchant Taylors' Scho ...
's ''De Mensuris et Ponderibus antiquis Libri tres'' ("On Ancient Measures and Weights, in three books"), 8vo, 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 In geometry, a solid of revolution is a Solid geometry, solid figure obtained by rotating a plane figure around some straight line (the ''axis of revolution''), which may not Intersection (geometry), intersect the generatrix (except at its bound ...
that produces the minimum resistance"), 4to, London, 1699 * ''Fruit-walls improved by inclining them to the horizon'', by a member of the Royal Society (signed N. F. D.), 4to, London, 1699 *
N. Facii Duillerii Neutonus. Ecloga.
' ("N. Fatio de Duillier's Newton.
Eclogue An eclogue is a poem in a classical style on a pastoral subject. Poems in the genre are sometimes also called bucolics. The term is also used for a musical genre thought of as evoking a pastoral scene. Classical beginnings The form of the word ...
."), 8vo, 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, 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 The (later renamed and then , ), established by Denis de Sallo, is the earliest academic journal published in Europe. It is thought to be the earliest published scientific journal. It currently focuses on European history and premodern literatu ...
'', 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
tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points o ...
s 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 Johann Bernoulli (also known as Jean in French or John in English; – 1 January 1748) was a Swiss people, Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infin ...
"), ''
Acta Eruditorum (from Latin: ''Acts of the Erudite'') was the first scientific journal of the German-speaking lands of Europe, published from 1682 to 1782. History ''Acta Eruditorum'' was founded in 1682 in Leipzig by Otto Mencke, who became its first edit ...
'', 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 ''Philosophical Transactions of the Royal Society'' is a scientific journal published by the Royal Society. In its earliest days, it was a private venture of the Royal Society's secretary. It was established in 1665, making it the second journ ...
'', vol. XXVIII, pp. 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 ''The Gentleman's Magazine'' was a monthly magazine founded in London, England, by Edward Cave in January 1731. It ran uninterrupted for almost 200 years, until 1907, ceasing publication altogether in 1922. It was the first to use the term '' ...
'' 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 Kidderminster is a market town and civil parish in Worcestershire, England, south-west of Birmingham and north of Worcester, England, Worcester. Located north of the River Stour, Worcestershire, River Stour and east of the River Severn, in th ...
. Others were acquired by Prof.
Georges-Louis Le Sage Georges-Louis Le Sage (; 13 June 1724 – 20 November 1803) was a Genevan physicist and is most known for his theory of gravitation, for his invention of an electric telegraph and his anticipation of the kinetic theory of gases. He was a cont ...
of Geneva, who amassed a large collection of Fatio's letters, now at the ''
Bibliothèque de Genève The Bibliothèque de Genève (BGE, English: Geneva Library, Library of Geneva), founded in 1559, was known as ''Bibliothèque publique et universitaire'' (BPU, English: Public and University Library) from 1907 to 2006. It occupies different buil ...
''. A few of Fatio's papers and letters are in the
British Library The British Library is the national library of the United Kingdom. Based in London, it is one of the largest libraries in the world, with an estimated collection of between 170 and 200 million items from multiple countries. As a legal deposit li ...
. Among them is a Latin poem entitled ''N. Facii Duellerii Auriacus Throno-servatus'' ("N. Fatio de Duillier's Orange Throne Preserved", Addit. MS. 4163), containing a narrative of Count Fenil's plot against Prince William of Orange, as well as a description of Fatio's jewelled watches. A series of letters to Sir
Hans Sloane Sir Hans Sloane, 1st Baronet, (16 April 1660 – 11 January 1753), was an Irish physician, naturalist, and collector. He had a collection of 71,000 items which he bequeathed to the British nation, thus providing the foundation of the British ...
(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.


Posthumous publications

Some of Fatio's letters were included in the correspondence volumes of the ''Oeuvres complètes'' ("Complete Works") of
Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...
(published between 1888 and 1950 by the Dutch Academy of Sciences) and in ''The Correspondence of Isaac Newton'' (published between 1959 and 1977 by the
Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
). Fatio's treatise describing his work on the push-shadow theory of gravity circulated during his lifetime only as a manuscript. That work was published, long after his death, in two independent scholarly editions: * * Even though it appeared twenty years earlier, Bopp's edition of Fatio's manuscript is the more complete of the two. The full Latin text of Fatio's 1728
eclogue An eclogue is a poem in a classical style on a pastoral subject. Poems in the genre are sometimes also called bucolics. The term is also used for a musical genre thought of as evoking a pastoral scene. Classical beginnings The form of the word ...
on Newton, along with an English translation and commentary, was published in: *


Notes


Other sources

* *


External links

* Fatio de Duillier, N.: De la cause de la Pesanteur, 1690–1701, Bopp edition. On pp. 19–22 is an introduction by Bopp (in German). Fatio's paper starts at the end of p. 22 (in French). * Fatio de Duillier, N.
De la Cause de la Pesanteur
1690–1743, Gagnebin edition. For an introduction by Gagnebin, se
Introduction
/small> * Fatio de Duillier, N.: "Letters no
2570
pp. 384–389 an
2582
pp. 407–412, 1690, Huygens Oeuvres, Vol. IX. These letters contain the first written expositions of his gravitational theory. Huygens gave an answer in letter no
2572


{{DEFAULTSORT:Fatio de Duillier, Nicolas 17th-century scientists from the Republic of Geneva 18th-century mathematicians from the Republic of Geneva Fellows of the Royal Society Swiss Protestants 1664 births 1753 deaths 17th-century Swiss astronomers 18th-century Swiss inventors Clockmakers from the Republic of Geneva Scientists from Basel-Stadt 17th-century Swiss mathematicians 18th-century Swiss astronomers