Christiaan Huygens

Christiaan Huygens FRS (/ˈhɡənz/ HY-gənz,[4] also US: /ˈhɔɪɡənz/ HOY-gənz,[5][6] Dutch: [ˈkrɪstijaːn ˈɦœyɣə(n)s] (About this soundlisten); Latin: Hugenius; 14 April 1629 – 8 July 1695), also spelled Huyghens, was a Dutch mathematician, physicist, astronomer and inventor, who is widely regarded as one of the greatest scientists of all time and a major figure in the scientific revolution. In physics, Huygens made groundbreaking contributions in optics and mechanics, while as an astronomer he is chiefly known for his studies of the rings of Saturn and the discovery of its moon Titan. As an inventor, he improved the design of telescopes and invented the pendulum clock, a breakthrough in timekeeping and the most accurate timekeeper for almost 300 years. An exceptionally talented mathematician and physicist, Huygens was the first to idealize a physical problem by a set of parameters then analyze it mathematically (Horologium Oscillatorium),[7] and the first to fully mathematize a mechanistic explanation of unobservable physical phenomena (Traité de la Lumière).[8] For these reasons, he has been called the first theoretical physicist and one of the founders of modern mathematical physics.[9][10]

Christiaan Huygens
Christiaan Huygens-painting.jpeg
Born(1629-04-14)14 April 1629
Died8 July 1695(1695-07-08) (aged 66)
The Hague, Dutch Republic
Alma materUniversity of Leiden
University of Angers
Known for
Scientific career
FieldsNatural Philosophy
InstitutionsRoyal Society of London
French Academy of Sciences
InfluencesGalileo Galilei
René Descartes
Frans van Schooten
InfluencedGottfried Wilhelm Leibniz
Isaac Newton[2][3]

In 1659, Huygens derived geometrically the now standard formulae in classical mechanics for the centripetal force and centrifugal force in his work De vi centrifuga.[11] Huygens also identified the correct laws of elastic collision for the first time in his work De motu corporum ex percussione, published posthumously in 1703. In the field of optics, he is best known for his wave theory of light, which he proposed in 1678 and described in his Traité de la Lumière (1690). His mathematical theory of light was initially rejected in favor of Newton's corpuscular theory of light, until Augustin-Jean Fresnel adopted Huygens's principle in 1818 to explain the rectilinear propagation and diffraction effects of light. Today this principle is known as the Huygens–Fresnel principle.

Huygens invented the pendulum clock in 1657, which he patented the same year. His research in horology resulted in an extensive analysis of the pendulum in Horologium Oscillatorium (1673), regarded as one of the most important 17th century works in mechanics. While the first part contains descriptions of clock designs, most of the book is an analysis of pendulum motion and a theory of curves. In 1655, Huygens began grinding lenses with his brother Constantijn to build telescopes for astronomical research. He was the first to identify the rings of Saturn as "a thin, flat ring, nowhere touching, and inclined to the ecliptic," and discovered the first of Saturn's moons, Titan, using a refracting telescope.[12][13] In 1662 Huygens developed what is now called the Huygenian eyepiece, a telescope with two lenses, which diminished the amount of dispersion.

As a mathematician, Huygens developed the theory of evolutes and wrote on games of chance and the problem of points in Van Rekeningh in Spelen van Gluck, which Frans van Schooten translated and published as De ratiociniis in ludo aleae (1657).[14] The use of expectation values by Huygens and others would later inspire Jacob Bernoulli's work on probability theory.[15][16]

Early lifeEdit

Portrait of Huygens's father (centre) and his five children (Christiaan at right). Mauritshuis, The Hague.

Christiaan Huygens was born on 14 April 1629 in The Hague, into a rich and influential Dutch family,[17][18] the second son of Constantijn Huygens. Christiaan was named after his paternal grandfather.[19][20] His mother was Suzanna van Baerle. She died in 1637, shortly after the birth of Huygens's sister.[21] The couple had five children: Constantijn (1628), Christiaan (1629), Lodewijk (1631), Philips (1632) and Suzanna (1637).[22] Constantijn Huygens was a diplomat and advisor to the House of Orange, and also a poet and musician. His friends included Galileo Galilei, Marin Mersenne, and René Descartes.[23] Christiaan was educated at home until turning sixteen years old. He liked to play with miniatures of mills and other machines. His father gave him a liberal education: he studied languages and music, history and geography, mathematics, logic and rhetoric, but also dancing, fencing and horse riding.[19][22][24]

In 1644 Huygens had as his mathematical tutor Jan Jansz Stampioen, who assigned the 15-year-old a demanding reading list on contemporary science.[25] Descartes was later impressed by his skills in geometry, as did Mersenne, who christened him "the new Archimedes."[8][18][26]

Student yearsEdit

His father sent Huygens to study law and mathematics at the University of Leiden, where he studied from May 1645 to March 1647.[19] Frans van Schooten was an academic at Leiden from 1646, and also a private tutor to Huygens and his elder brother, replacing Stampioen on the advice of Descartes.[27][28] Van Schooten brought his mathematical education up to date, in particular introducing him to the work of Viète, Descartes, and Fermat.[29]

After two years, from March 1647, Huygens continued his studies at the newly founded Orange College, in Breda, where his father was a curator: the change occurred because of a duel between his brother Lodewijk and another student.[30] Constantijn Huygens was closely involved in the new College, which lasted only to 1669; the rector was André Rivet.[31] Christiaan Huygens lived at the home of the jurist Johann Henryk Dauber, and had mathematics classes with the English lecturer John Pell. He completed his studies in August 1649.[19] He then had a stint as a diplomat on a mission with Henry, Duke of Nassau. It took him to Bentheim, then Flensburg. He took off for Denmark, visited Copenhagen and Helsingør, and hoped to cross the Øresund to visit Descartes in Stockholm. It was not to be.[32]

Although his father Constantijn had wished his son Christiaan to be a diplomat, circumstances kept him from becoming so. The First Stadtholderless Period that began in 1650 meant that the House of Orange was not in power, removing Constantijn's influence. Further, he realized that his son had no interest in such a career.[33]

Early correspondenceEdit

Christiaan Huygens. Cut from the engraving following the painting of Caspar Netscher by G. Edelinck, between 1684 and 1687.

Huygens generally wrote in French or Latin.[34] While still a college student at Leiden he began a correspondence with the intelligencer Mersenne, who died quite soon afterwards in 1648.[19] Mersenne wrote to Constantijn on his son's talent for mathematics, and flatteringly compared him to Archimedes (3 January 1647). The letters show the early interests of Huygens in mathematics. In October 1646 there is the suspension bridge, and the demonstration that a catenary is not a parabola.[35] In 1647/8 they cover the claim of Grégoire de Saint-Vincent to squaring the circle; rectification of the ellipse; projectiles, and the vibrating string.[36] Some of Mersenne's concerns at the time, such as the cycloid (he sent Evangelista Torricelli's treatise on the curve), the centre of oscillation, and the gravitational constant, were matters Huygens only took seriously towards the end of the 17th century.[37] Mersenne had also written on musical theory. Huygens preferred meantone temperament; he innovated in 31 equal temperament, which was not itself a new idea but known to Francisco de Salinas, using logarithms to investigate it further and show its close relation to the meantone system.[38]

In 1654, Huygens returned to his father's house in The Hague, and was able to devote himself entirely to research.[19] The family had another house, not far away at Hofwijck, and he spent time there during the summer. His scholarly life did not allow him to escape bouts of depression.[39]

Subsequently, Huygens developed a broad range of correspondents, though picking up the threads after 1648 was hampered by the five-year Fronde in France. Visiting Paris in 1655, Huygens called on Ismael Boulliau to introduce himself. Then Boulliau took him to see Claude Mylon.[40] The Parisian group of savants that had gathered around Mersenne held together into the 1650s, and Mylon, who had assumed the secretarial role, took some trouble from then on to keep Huygens in touch.[41] Through Pierre de Carcavi Huygens corresponded in 1656 with Pierre de Fermat, whom he admired greatly, though this side of idolatry. The experience was bittersweet and even puzzling, since it became clear that Fermat had dropped out of the research mainstream, and his priority claims could probably not be made good in some cases. Besides, Huygens was looking by then to apply mathematics, while Fermat's concerns ran to purer topics.[42]

Scientific debutEdit

The catenary in a manuscript of Huygens.

Huygens was often slow to publish his results and discoveries. In the early days his mentor Frans van Schooten was cautious for the sake of his reputation.[43] His preferred methods were those of Archimedes and Fermat.[29]

The first work Huygens put in print was Theoremata de quadratura (1651) in the field of quadrature. It included material discussed with Mersenne some years before, such as the fallacious nature of the squaring of the circle by Grégoire de Saint-Vincent. In De circuli magnitudine inventa (1654), Huygens approximated the center of gravity of a segment of a circle by the center of the gravity of a segment of a parabola, and thus found an approximation of the quadrature; with this he was able to refine the inequalities between the area of the circle and those of the inscribed and circumscribed polygons used in the calculations of π. The same approximation with segments of the parabola, in the case of the hyperbola, yields a quick and simple method to calculate logarithms.[44] Quadrature was a live issue in the 1650s, and through Mylon, Huygens intervened in the discussion of the mathematics of Thomas Hobbes. Persisting in trying to explain the errors Hobbes had fallen into, he made an international reputation.[45]

Huygens studied spherical lenses from a theoretical point of view in 1652–3, obtaining results that remained unpublished until the work of Isaac Barrow (1669). His aim was to understand telescopes.[46] He began grinding his own lenses in 1655, collaborating with his brother Constantijn.[47] He designed in 1662 what is now called the Huygenian eyepiece, with two lenses, as a telescope ocular.[48][49] Lenses were also a common interest through which Huygens could meet socially in the 1660s with Baruch Spinoza, who ground them professionally. They had rather different outlooks on science, Spinoza being the more committed Cartesian, and some of their discussion survives in correspondence.[50] He encountered the work of Antoni van Leeuwenhoek, another lens grinder, in the field of microscopy which interested his father.[51]

Huygens gave the most coherent presentation of a mathematical approach to games of chance in De ratiociniis in ludo aleae (On Reasoning in Games of Chance).[16][52] He had been told of recent work in the field by Fermat, Blaise Pascal and Girard Desargues two years earlier, in Paris.[53] Frans van Schooten translated the original Dutch manuscript into Latin and published it in his Exercitationum mathematicarum (1657). It contains early game-theoretic ideas and deals in particular with the problem of points.[14] Huygens took as intuitive his appeals to concepts of a "fair game" and equitable contract, and used them to set up a theory of expected values.[54] In 1662 Sir Robert Moray sent Huygens John Graunt's life table, and in time Huygens and his brother Lodewijk worked on life expectancy.[55]

On 3 May 1661, Huygens observed the planet Mercury transit over the Sun, using the telescope of instrument maker Richard Reeve in London, together with astronomer Thomas Streete and Reeve.[56] Streete then debated the published record of the transit of Hevelius, a controversy mediated by Henry Oldenburg.[57] Huygens passed to Hevelius a manuscript of Jeremiah Horrocks on the transit of Venus, 1639, which thereby was printed for the first time in 1662.[58] In that year Huygens, who played the harpsichord, took an interest in music and Simon Stevin's theories on it; he showed very little concern to publish his theories on consonance, some of which were lost for centuries.[59][60] The Royal Society of London elected him a Fellow in 1663.[61]

In FranceEdit

Christiaan Huygens, relief by Jean-Jacques Clérion, around 1670?

The Montmor Academy was the form the old Mersenne circle took after the mid-1650s.[62] Huygens took part in its debates, and supported its "dissident" faction who favoured experimental demonstration to curtail fruitless discussion, and opposed amateurish attitudes.[63] During 1663 he made what was his third visit to Paris; the Montmor Academy closed down, and Huygens took the chance to advocate a more Baconian programme in science. In 1666 he moved to Paris and earned a position at King Louis XIV's new French Academy of Sciences.[64]

In Paris Huygens had an important patron and correspondent in Jean-Baptiste Colbert, First Minister to Louis XIV.[65] However, his relationship with the Academy was not always easy, and in 1670 Huygens, seriously ill, chose Francis Vernon to carry out a donation of his papers to the Royal Society in London, should he die.[66] Then the Franco-Dutch War took place (1672–8). England's part in it (1672–4) is thought to have damaged his relationship with the Royal Society.[67] Robert Hooke for the Royal Society lacked the urbanity to handle the situation, in 1673.[68]

Denis Papin was assistant to Huygens from 1671.[69] One of their projects, which did not bear fruit directly, was the gunpowder engine.[70] Papin moved to England in 1678, and continued to work in this area.[71] Using the Paris Observatory (completed in 1672), Huygens made further astronomical observations. In 1678 he introduced Nicolaas Hartsoeker to French scientists such as Nicolas Malebranche and Giovanni Cassini.

It was in Paris, also, that Huygens met the young diplomat Gottfried Leibniz, there in 1672 on a vain mission to meet Arnauld de Pomponne, the French Foreign Minister. At this time Leibniz was working on a calculating machine, and he moved on to London in early 1673 with diplomats from Mainz; but from March 1673 Leibniz was tutored in mathematics by Huygens.[72] Huygens taught him analytical geometry; an extensive correspondence ensued, in which Huygens showed at first reluctance to accept the advantages of infinitesimal calculus.[73]

Later lifeEdit

Hofwijck, home to Christiaan Huygens from 1688

Huygens moved back to The Hague in 1681 after suffering serious depressive illness. In 1684, he published Astroscopia Compendiaria on his new tubeless aerial telescope. He attempted to return to France in 1685 but the revocation of the Edict of Nantes precluded this move. His father died in 1687, and he inherited Hofwijck, which he made his home the following year.[33]

On his third visit to England, in 1689, Huygens met Isaac Newton on 12 June. They spoke about Iceland spar, and subsequently corresponded about resisted motion.[74]

Huygens observed the acoustical phenomenon now known as flanging in 1693.[75] He died in The Hague on 8 July 1695, and was buried in an unmarked grave in the Grote Kerk there, as was his father before him.[76]

Huygens never married.[77]

Work in natural philosophyEdit

Huygens was the leading European natural philosopher between Descartes and Newton.[19][78] However, unlike many of his contemporaries, Huygens had no taste for grand theoretical or philosophical systems, and generally avoided dealing with metaphysical issues (if pressed, he adhered to the Cartesian and mechanical philosophy of his time).[9][79] Instead, Huygens excelled in extending the work of his predecessors, such as Galileo, to derive solutions to unsolved physical problems that were amenable to mathematical analysis. In particular, he sought explanations that relied on contact between bodies and avoided action at a distance.[19][80]

In common with Robert Boyle and Jacques Rohault, Huygens advocated an experimentally oriented, corpuscular-mechanical natural philosophy during his Paris years. In the analysis of the Scientific Revolution, this approach was sometimes labeled "Baconian," without being inductivist or identifying with the views of Francis Bacon in a simple-minded way.[81] After his first visit to England in 1661 and attending a meeting at Gresham College where he learned directly about Boyle's air pump experiments, Huygens spent time in late 1661 and early 1662 replicating the work. It proved a long process, brought to the surface an experimental issue ("anomalous suspension") and the theoretical issue of horror vacui, and ended in July 1663 as Huygens became a Fellow of the Royal Society. It has been said that Huygens finally accepted Boyle's view of the void, as against the Cartesian denial of it;[82] and also (in Leviathan and the Air Pump) that the replication of results trailed off messily.[83]

Newton's influence on John Locke was mediated by Huygens, who assured Locke that Newton's mathematics was sound, leading to Locke's acceptance of a corpuscular-mechanical physics.[84]

Laws of motion, impact, and gravitationEdit

Depiction from Huygens, Oeuvres Complètes: a boating metaphor underlay the way of thinking about relative motion, and so simplifying the theory of colliding bodies

The general approach of the mechanical philosophers was to postulate theories of the kind now called "contact action." Huygens adopted this method, but not without seeing its difficulties and failures.[85] Leibniz, his student in Paris, abandoned the theory.[86] Seeing the universe this way made the theory of collisions central to physics. The requirements of the mechanical philosophy, in the view of Huygens, were stringent. Matter in motion made up the universe, and only explanations in those terms could be truly intelligible. While he was influenced by the Cartesian approach, he was less doctrinaire.[87] He studied elastic collisions in the 1650s but delayed publication for over a decade.[29]

Huygens concluded quite early that Descartes's laws for the elastic collision of two bodies must be wrong, and he formulated the correct laws.[88] An important step was his recognition of the Galilean invariance of the problems.[89] His views then took many years to be circulated. He passed them on in person to William Brouncker and Christopher Wren in London, in 1661.[90] What Spinoza wrote to Henry Oldenburg about them, in 1666 which was during the Second Anglo-Dutch War, was guarded.[91] Huygens had actually worked them out in a manuscript De motu corporum ex percussione in the period 1652–6. The war ended in 1667, and Huygens announced his results to the Royal Society in 1668. He published them in the Journal des sçavans in 1669.[29]

Huygens stated what is now known as the second of Newton's laws of motion in a quadratic form.[92] In 1659 he derived the now standard formula for the centripetal force, exerted on an object describing a circular motion, for instance by the string to which it is attached. In modern notation:


with m the mass of the object, v the velocity and r the radius. The publication of the general formula for this force in 1673 was a significant step in studying orbits in astronomy. It enabled the transition from Kepler's third law of planetary motion, to the inverse square law of gravitation.[93] The interpretation of Newton's work on gravitation by Huygens differed, however, from that of Newtonians such as Roger Cotes; he did not insist on the a priori attitude of Descartes, but neither would he accept aspects of gravitational attractions that were not attributable in principle to contact of particles.[94]

The approach used by Huygens also missed some central notions of mathematical physics, which were not lost on others. His work on pendulums came very close to the theory of simple harmonic motion; but the topic was covered fully for the first time by Newton, in Book II of his Principia Mathematica (1687).[95] In 1678 Leibniz picked out of Huygens's work on collisions the idea of conservation law that Huygens had left implicit.[96]


Refraction of a plane wave, explained using Huygens's principle as shown in Traité de la Lumière (1690).

Huygens is remembered especially for his wave theory of light, which he first communicated in 1678 to the Paris Académie des sciences. It was published in 1690 in his Traité de la Lumière[97] (Treatise on light[98]), making it the first mathematical theory of light. He refers to Ignace-Gaston Pardies, whose manuscript on optics helped him on his wave theory.[99]

Huygens assumes that the speed of light is finite, as had been shown in an experiment by Ole Christensen Rømer in 1679, but which Huygens is presumed to have already believed.[100] The challenge for the wave theory of light at that time was to explain geometrical optics, as most physical optics phenomena (such as diffraction) had not been observed or appreciated as issues. It posits light radiating wavefronts with the common notion of light rays depicting propagation normal to those wavefronts. Propagation of the wavefronts is then explained as the result of spherical waves being emitted at every point along the wave front (the Huygens–Fresnel principle).[101] It assumed an omnipresent ether, with transmission through perfectly elastic particles, a revision of the view of Descartes. The nature of light was therefore a longitudinal wave.[100]

Huygens had experimented in 1672 with double refraction (birefringence) in Icelandic spar (calcite), a phenomenon discovered in 1669 by Rasmus Bartholin. At first he could not elucidate what he found.[49] He later explained it[98] with his wave front theory and concept of evolutes. He also developed ideas on caustics.[102] Newton in his Opticks of 1704 proposed instead a corpuscular theory of light. The theory of Huygens was not widely accepted, one strong objection being that longitudinal waves have only a single polarization which cannot explain the observed birefringence. However the 1801 interference experiments of Thomas Young and François Arago's 1819 detection of the Poisson spot could not be explained through any particle theory, reviving the ideas of Huygens and wave models. In 1821 Fresnel was able to explain birefringence as a result of light being not a longitudinal (as had been assumed) but actually a transverse wave.[103] The thus-named Huygens–Fresnel principle was the basis for the advancement of physical optics, explaining all aspects of light propagation. It was only understanding the detailed interaction of light with atoms that awaited quantum mechanics and the discovery of the photon.

Huygens investigated the use of lenses in projectors. He is credited as the inventor of the magic lantern, described in correspondence of 1659.[104] There are others to whom such a lantern device has been attributed, such as Giambattista della Porta, and Cornelis Drebbel: the point at issue is the use of a lens for better projection. Athanasius Kircher has also been credited for that.[105]


Huygens developed the oscillating timekeeping mechanisms that have been used ever since in mechanical watches and clocks, the balance spring and the pendulum, leading to a great increase in timekeeping accuracy. In 1656, inspired by earlier research into pendulums by Galileo Galilei, he invented the pendulum clock, which was a breakthrough in timekeeping and became the most accurate timekeeper for the next 275 years until the 1930s.[106] Huygens contracted the construction of his clock designs to Salomon Coster in The Hague, who built the clock. The pendulum clock was much more accurate than the existing verge and foliot clocks and was immediately popular, quickly spreading over Europe. However Huygens did not make much money from his invention. Pierre Séguier refused him any French rights, Simon Douw of Rotterdam copied the design in 1658, and Ahasuerus Fromanteel also, in London.[107] The oldest known Huygens-style pendulum clock is dated 1657 and can be seen at the Museum Boerhaave in Leiden.[108][109][110][111]

Huygens motivation for inventing the pendulum clock was to create an accurate marine chronometer that could be used to find longitude by celestial navigation during sea voyages. However the clock proved unsuccessful as a marine timekeeper because the rocking motion of the ship disturbed the motion of the pendulum. In 1660 Lodewijk Huygens made a trial on a voyage to Spain, and reported that heavy weather made the clock useless. Alexander Bruce elbowed into the field in 1662, and Huygens called in Sir Robert Moray and the Royal Society to mediate and preserve some of his rights.[112] Trials continued into the 1660s, the best news coming from a Royal Navy captain Robert Holmes operating against the Dutch possessions in 1664.[113] Lisa Jardine[114] doubts that Holmes reported the results of the trial accurately, and Samuel Pepys expressed his doubts at the time: The said master [i.e. the captain of Holmes' ship] affirmed, that the vulgar reckoning proved as near as that of the watches, which [the clocks], added he, had varied from one another unequally, sometimes backward, sometimes forward, to 4, 6, 7, 3, 5 minutes; as also that they had been corrected by the usual account. One for the French Academy on an expedition to Cayenne ended badly. Jean Richer suggested correction for the figure of the Earth. By the time of the Dutch East India Company expedition of 1686 to the Cape of Good Hope, Huygens was able to supply the correction retrospectively.[115]


Spring-driven pendulum clock, designed by Huygens, built by instrument maker Salomon Coster (1657),[116] and a copy of the Horologium Oscillatorium.[117] Museum Boerhaave, Leiden

In 1673 Huygens published Horologium Oscillatorium sive de motu pendulorum, his major work on pendulums and horology. It had been observed by Mersenne and others that pendulums are not quite isochronous: their period depends on their width of swing, with wide swings taking slightly longer than narrow swings.[118][119]

Huygens analyzed this problem by finding the curve down which a mass will slide under the influence of gravity in the same amount of time, regardless of its starting point; the so-called tautochrone problem. By geometrical methods which were an early use of calculus, he showed it to be a cycloid, rather than the circular arc of a pendulum's bob, and therefore that pendulums are not isochronous. He also solved a problem posed by Mersenne: how to calculate the period of a pendulum made of an arbitrarily-shaped swinging rigid body. This involved discovering the centre of oscillation and its reciprocal relationship with the pivot point. In the same work, he analysed the conical pendulum, consisting of a weight on a cord moving in a circle, using the concept of centrifugal force.

Detail of illustration from Horologium Oscillatorium (1673), by Huygens
Huygens's clock, Rijksmuseum, Amsterdam

Huygens was the first to derive the formula for the period of an ideal mathematical pendulum (with massless rod or cord and length much longer than its swing), in modern notation:


with T the period, l the length of the pendulum and g the gravitational acceleration. By his study of the oscillation period of compound pendulums Huygens made pivotal contributions to the development of the concept of moment of inertia.[92]

Huygens also observed coupled oscillations: two of his pendulum clocks mounted next to each other on the same support often became synchronized, swinging in opposite directions. He reported the results by letter to the Royal Society, and it is referred to as "an odd kind of sympathy" in the Society's minutes.[120][121] This concept is now known as entrainment.

Experimental setup of Huygens's synchronization of two clocks

Balance spring watchEdit

Huygens developed a balance spring watch in the same period as, though independently of, Robert Hooke. Controversy over the priority persisted for centuries. A Huygens watch employed a spiral balance spring; but he used this form of spring initially only because the balance in his first watch rotated more than one and a half turns. He later used spiral springs in more conventional watches, made for him by Thuret in Paris from around 1675.

Huygens's explanation for the aspects of Saturn, Systema Saturnium, 1659.

Such springs were essential in modern watches with a detached lever escapement because they can be adjusted for isochronism. Watches in the time of Huygens and Hooke, however, employed the very undetached verge escapement. It interfered with the isochronal properties of any form of balance spring, spiral or otherwise.

In February 2006, a long-lost copy of Hooke's handwritten notes from several decades of Royal Society meetings was discovered in a cupboard in Hampshire, England. The balance-spring priority controversy appears, by the evidence contained in those notes, to be settled in favour of Hooke's claim.[122][123]

In 1675, Huygens patented a pocket watch. The watches which were made in Paris from c. 1675 and following the Huygens plan are notable for lacking a fusee for equalizing the mainspring torque. The implication is that Huygens thought that his spiral spring would isochronise the balance, in the same way that he thought that the cycloidally shaped suspension curbs on his clocks would isochronise the pendulum.


Huygens's telescope without tube. Picture from his 1684 Astroscopia Compendiaria tubi optici molimine liberata (compound telescopes without a tube)

Saturn's rings and TitanEdit

In 1655, Huygens was the first to propose that the rings of Saturn were "a thin, flat ring, nowhere touching, and inclined to the ecliptic”.[124] Using a refracting telescope with a 43x magnification that he designed himself,[12][13] Huygens also discovered the first of Saturn's moons, Titan.[125] In the same year he observed and sketched the Orion Nebula. His drawing, the first such known of the Orion nebula, was published in Systema Saturnium in 1659. Using his modern telescope he succeeded in subdividing the nebula into different stars. The brighter interior now bears the name of the Huygenian region in his honour.[126] He also discovered several interstellar nebulae and some double stars.

Mars and Syrtis MajorEdit

In 1659, Huygens was the first to observe a surface feature on another planet, Syrtis Major, a volcanic plain on Mars. He used repeated observations of the movement of this feature over the course of a number of days to estimate the length of day on Mars, which he did quite accurately to 24 1/2 hours. This figure is only a few minutes off of the actual length of the Martian day of 24 hours, 37 minutes.[127]


At the instigation of Jean-Baptiste Colbert, Huygens undertook the task of constructing a mechanical planetarium that could display all the planets and their moons then known circling around the Sun. Huygens completed his design in 1680 and had his clockmaker Johannes van Ceulen built it the following year. However, Colbert passed away in the interim and Huygens never got to deliver his planetarium to the French Academy of Sciences as the new minister, Fracois-Michel le Tellier, decided not to renew Huygens's contract.[128][129]

In his design, Huygens made an ingenious use of continued fractions to find the best rational approximations by which he could choose the gears with the correct number of teeth. The ratio between two gears determined the orbital periods of two planets. To move the planets around the Sun, Huygens used a clock-mechanism that could go forwards and backwards in time. Huygens claimed his planetarium was more accurate that a similar device constructed by Ole Rømer around the same time, but his planetarium design was not published until after his death in the Opuscula posthuma (1703).[128]


Shortly before his death in 1695, Huygens completed Cosmotheoros. At his direction, it was to be published only posthumously by his brother, which Constantijn did in 1698.[130] In it he speculated on the existence of extraterrestrial life, on other planets, which he imagined was similar to that on Earth. Such speculations were not uncommon at the time, justified by Copernicanism or the plenitude principle. But Huygens went into greater detail,[131] although without the benefit of understanding Newton's laws of gravitation, or the fact that the atmospheres on other planets are composed of different gases.[132] The work, translated into English in its year of publication and entitled The Celestial Worlds Discover’d, has been seen as being in the fanciful tradition of Francis Godwin, John Wilkins, and Cyrano de Bergerac, and fundamentally Utopian; and also to owe in its concept of planet to cosmography in the sense of Peter Heylin.[133][134]

Huygens wrote that availability of water in liquid form was essential for life and that the properties of water must vary from planet to planet to suit the temperature range. He took his observations of dark and bright spots on the surfaces of Mars and Jupiter to be evidence of water and ice on those planets.[135] He argued that extraterrestrial life is neither confirmed nor denied by the Bible, and questioned why God would create the other planets if they were not to serve a greater purpose than that of being admired from Earth. Huygens postulated that the great distance between the planets signified that God had not intended for beings on one to know about the beings on the others, and had not foreseen how much humans would advance in scientific knowledge.[136]

It was also in this book that Huygens published his method for estimating stellar distances. He made a series of smaller holes in a screen facing the Sun, until he estimated the light was of the same intensity as that of the star Sirius. He then calculated that the angle of this hole was  th the diameter of the Sun, and thus it was about 30,000 times as far away, on the (incorrect) assumption that Sirius is as luminous as the Sun. The subject of photometry remained in its infancy until the time of Pierre Bouguer and Johann Heinrich Lambert.[137]


Possible depiction of Huygens right of center, from L'établissement de l'Académie des Sciences et fondation de l'observatoire, 1666 by Henri Testelin, c. 1675.

During his lifetimeEdit


Named after HuygensEdit




Tome I: Correspondance 1638–1656 (1888).
Tome II: Correspondance 1657–1659 (1889).
Tome III: Correspondance 1660–1661 (1890).
Tome IV: Correspondance 1662–1663 (1891).
Tome V: Correspondance 1664–1665 (1893).
Tome VI: Correspondance 1666–1669 (1895).
Tome VII: Correspondance 1670–1675 (1897).
Tome VIII: Correspondance 1676–1684 (1899).
Tome IX: Correspondance 1685–1690 (1901).
Tome X: Correspondance 1691–1695 (1905).
Tome XI: Travaux mathématiques 1645–1651 (1908).
Tome XII: Travaux mathématiques pures 1652–1656 (1910).
Tome XIII, Fasc. I: Dioptrique 1653, 1666 (1916).
Tome XIII, Fasc. II: Dioptrique 1685–1692 (1916).
Tome XIV: Calcul des probabilités. Travaux de mathématiques pures 1655–1666 (1920).
Tome XV: Observations astronomiques. Système de Saturne. Travaux astronomiques 1658–1666 (1925).
Tome XVI: Mécanique jusqu’à 1666. Percussion. Question de l'existence et de la perceptibilité du mouvement absolu. Force centrifuge (1929).
Tome XVII: L’horloge à pendule de 1651 à 1666. Travaux divers de physique, de mécanique et de technique de 1650 à 1666. Traité des couronnes et des parhélies (1662 ou 1663) (1932).
Tome XVIII: L'horloge à pendule ou à balancier de 1666 à 1695. Anecdota (1934).
Tome XIX: Mécanique théorique et physique de 1666 à 1695. Huygens à l'Académie royale des sciences (1937).
Tome XX: Musique et mathématique. Musique. Mathématiques de 1666 à 1695 (1940).
Tome XXI: Cosmologie (1944).
Tome XXII: Supplément à la correspondance. Varia. Biographie de Chr. Huygens. Catalogue de la vente des livres de Chr. Huygens (1950).

See alsoEdit


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