Christiaan huygens discovered
Christiaan Huygens
Dutch mathematician and physicist (–)
For the ocean liner, see MS Christiaan Huygens.
Christiaan Huygens, Lord of Zeelhem, FRS (HY-gənz,[2]HOY-gənz;[3]Dutch:[ˈkrɪstijaːnˈɦœyɣə(n)s]ⓘ; also spelled Huyghens; Latin: Hugenius; 14 April – 8 July ) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution.[4][5] In physics, Huygens made seminal contributions to optics and mechanics, while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan.
As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, the most accurate timekeeper for almost years. A talented mathematician and physicist, his works contain the first idealization of a physical problem by a set of mathematicalparameters, and the first mathematical and mechanistic explanation of an unobservable physical phenomenon.[6][7]
Huygens first identified the correct laws of elastic collision in his work De Motu Corporum ex Percussione, completed in but published posthumously in [8] In , Huygens derived geometrically the formula in classical mechanics for the centrifugal force in his work De vi Centrifuga, a decade before Isaac Newton.[9] In optics, he is best known for his wave theory of light, which he described in his Traité de la Lumière ().
His theory of light was initially rejected in favour of Newton's corpuscular theory of light, until Augustin-Jean Fresnel adapted Huygens's principle to give a complete explanation of the rectilinear propagation and diffraction effects of light in Today this principle is known as the Huygens–Fresnel principle.
Huygens invented the pendulum clock in , which he patented the same year.
Christiaan huygens biography template word Andriesse 25 August To cite this article click here for a list of acceptable citing formats. In October there is the suspension bridge and the demonstration that a hanging chain is not a parabola , as Galileo thought. History of Science.His horological research resulted in an extensive analysis of the pendulum in Horologium Oscillatorium (), regarded as one of the most important 17th century works on mechanics.[6] While it contains descriptions of clock designs, most of the book is an analysis of pendular motion and a theory of curves.
In , Huygens began grinding lenses with his brother Constantijn to build refracting telescopes. He discovered Saturn's biggest moon, Titan, and was the first to explain Saturn's strange appearance as due to "a thin, flat ring, nowhere touching, and inclined to the ecliptic."[10] In Huygens developed what is now called the Huygenian eyepiece, a telescope with two lenses to diminish the amount of dispersion.[11]
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 ().[12] The use of expected values by Huygens and others would later inspire Jacob Bernoulli's work on probability theory.[13][14]
Biography
Christiaan Huygens was born into a rich and influential Dutch family in The Hague on 14 April , the second son of Constantijn Huygens.[15][16] Christiaan was named after his paternal grandfather.[17][18] His mother, Suzanna van Baerle, died shortly after giving birth to Huygens's sister.[19] The couple had five children: Constantijn (), Christiaan (), Lodewijk (), Philips () and Suzanna ().[20]
Constantijn Huygens was a diplomat and advisor to the House of Orange, in addition to being a poet and a musician.
He corresponded widely with intellectuals across Europe, including Galileo Galilei, Marin Mersenne, and René Descartes.[21] Christiaan was educated at home until the age of sixteen, and from a young age liked to play with miniatures of mills and other machines. He received a liberal education from his father, studying languages, music, history, geography, mathematics, logic, and rhetoric, alongside dancing, fencing and horse riding.[17][20]
In , Huygens had as his mathematical tutor Jan Jansz Stampioen, who assigned the year-old a demanding reading list on contemporary science.[22] Descartes was later impressed by his skills in geometry, as was Mersenne, who christened him the "new Archimedes."[23][16][24]
Student years
At sixteen years of age, Constantijn sent Huygens to study law and mathematics at Leiden University, where he enrolled from May to March [17]Frans van Schooten Jr., professor at Leiden's Engineering School, became private tutor to Huygens and his elder brother, Constantijn Jr., replacing Stampioen on the advice of Descartes.[25][26] Van Schooten brought Huygens's mathematical education up to date, introducing him to the work of Viète, Descartes, and Fermat.[27]
After two years, starting in March , Huygens continued his studies at the newly founded Orange College, in Breda, where his father was a curator.
Constantijn Huygens was closely involved in the new College, which lasted only to ; the rector was André Rivet.[28] Christiaan Huygens lived at the home of the jurist Johann Henryk Dauber while attending college, and had mathematics classes with the English lecturer John Pell. His time in Breda ended around the time when his brother Lodewijk, who was enrolled at the school, duelled with another student.[5][29] Huygens left Breda after completing his studies in August and had a stint as a diplomat on a mission with Henry, Duke of Nassau.[17] After stays at Bentheim and Flensburg in Germany, he visited Copenhagen and Helsingør in Denmark.
Huygens hoped to cross the Øresund to see Descartes in Stockholm but was prevented due to Descartes' death in the interim.[5][30]
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 meant that the House of Orange was no longer in power, removing Constantijn's influence.
Further, he realized that his son had no interest in such a career.[31]
Early correspondence
Huygens generally wrote in French or Latin.[32] In , while still a college student at Leiden, he began a correspondence with his father's friend, Marin Mersenne, who died soon afterwards in [17] Mersenne wrote to Constantijn on his son's talent for mathematics, and flatteringly compared him to Archimedes on 3 January [33]
The letters show Huygens's early interest in mathematics.
In October there is the suspension bridge and the demonstration that a hanging chain is not a parabola, as Galileo thought.[34] Huygens would later label that curve the catenaria (catenary) in while corresponding with Gottfried Leibniz.[35]
In the next two years (–48), Huygens's letters to Mersenne covered various topics, including a mathematical proof of the law of free fall, the claim by Grégoire de Saint-Vincent of circle quadrature, which Huygens showed to be wrong, the rectification of the ellipse, projectiles, and the vibrating string.[36] Some of Mersenne's concerns at the time, such as the cycloid (he sent Huygens Torricelli's treatise on the curve), the centre of oscillation, and the gravitational constant, were matters Huygens only took seriously later in the 17th century.[6] 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.[37]
In , Huygens returned to his father's house in The Hague and was able to devote himself entirely to research.[17] The family had another house, not far away at Hofwijck, and he spent time there during the summer.
Despite being very active, his scholarly life did not allow him to escape bouts of depression.[38]
Subsequently, Huygens developed a broad range of correspondents, though with some difficulty after due to the five-year Fronde in France. Visiting Paris in , Huygens called on Ismael Boulliau to introduce himself, who took him to see Claude Mylon.[39] The Parisian group of savants that had gathered around Mersenne held together into the s, and Mylon, who had assumed the secretarial role, took some trouble to keep Huygens in touch.[40] Through Pierre de Carcavi Huygens corresponded in with Pierre de Fermat, whom he admired greatly.
Christiaan huygens biography template These were later given to the Royal Society in London where they remain to date. Retrieved 12 May A number of monuments to Christiaan Huygens can be found across important cities in the Netherlands, including Rotterdam , Delft , and Leiden. The application of continued fractions in Christiaan Huygens planetarium.The experience was bittersweet and somewhat 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 to physics, while Fermat's concerns ran to purer topics.[41]
Scientific debut
Like some of his contemporaries, Huygens was often slow to commit his results and discoveries to print, preferring to disseminate his work through letters instead.[42] In his early days, his mentor Frans van Schooten provided technical feedback and was cautious for the sake of his reputation.[43]
Between and , Huygens published a number of works that showed his talent for mathematics and his mastery of classical and analytical geometry, increasing his reach and reputation among mathematicians.[33] Around the same time, Huygens began to question Descartes's laws of collision, which were largely wrong, deriving the correct laws algebraically and later by way of geometry.[44] He showed that, for any system of bodies, the centre of gravity of the system remains the same in velocity and direction, which Huygens called the conservation of "quantity of movement".
While others at the time were studying impact, Huygens's theory of collisions was more general.[5] These results became the main reference point and the focus for further debates through correspondence and in a short article in Journal des Sçavans but would remain unknown to a larger audience until the publication of De Motu Corporum ex Percussione (Concerning the motion of colliding bodies) in [45][44]
In addition to his mathematical and mechanical works, Huygens made important scientific discoveries: he was the first to identify Titan as one of Saturn's moons in , invented the pendulum clock in , and explained Saturn's strange appearance as due to a ring in ; all these discoveries brought him fame across Europe.[17] On 3 May , Huygens, together with astronomer Thomas Streete and Richard Reeve, observed the planet Mercury transit over the Sun using Reeve's telescope in London.[46] Streete then debated the published record of Hevelius, a controversy mediated by Henry Oldenburg.[47] Huygens passed to Hevelius a manuscript of Jeremiah Horrocks on the transit of Venus in , printed for the first time in [48]
In that same year, Sir Robert Moray sent Huygens John Graunt's life table, and shortly after Huygens and his brother Lodewijk dabbled on life expectancy.[42][49] Huygens eventually created the first graph of a continuous distribution function under the assumption of a uniform death rate, and used it to solve problems in joint annuities.[50] Contemporaneously, Huygens, who played the harpsichord, took an interest in Simon Stevin's theories on music; however, he showed very little concern to publish his theories on consonance, some of which were lost for centuries.[51][52] For his contributions to science, the Royal Society of London elected Huygens a Fellow in , making him its first foreign member when he was just 34 years old.[53][54]
France
The Montmor Academy, started in the mids, was the form the old Mersenne circle took after his death.[55] Huygens took part in its debates and supported those favouring experimental demonstration as a check on amateurish attitudes.[56] He visited Paris a third time in ; when the Montmor Academy closed down the next year, Huygens advocated for a more Baconian program in science.
Two years later, in , he moved to Paris on an invitation to fill a leadership position at King Louis XIV's new French Académie des sciences.[57]
While at the Académie in Paris, Huygens had an important patron and correspondent in Jean-Baptiste Colbert, First Minister to Louis XIV.[58] His relationship with the French Académie was not always easy, and in Huygens, seriously ill, chose Francis Vernon to carry out a donation of his papers to the Royal Society in London should he die.[59] However, the aftermath of the Franco-Dutch War (–78), and particularly England's role in it, may have damaged his later relationship with the Royal Society.[60]Robert Hooke, as a Royal Society representative, lacked the finesse to handle the situation in [61]
The physicist and inventor Denis Papin was an assistant to Huygens from [62] One of their projects, which did not bear fruit directly, was the gunpowder engine.[63][64] Huygens made further astronomical observations at the Académie using the observatory recently completed in He introduced Nicolaas Hartsoeker to French scientists such as Nicolas Malebranche and Giovanni Cassini in [5][65]
The young diplomat Leibniz met Huygens while visiting Paris in on a vain mission to meet the French Foreign Minister Arnauld de Pomponne.
Leibniz was working on a calculating machine at the time and, after a short visit to London in early , he was tutored in mathematics by Huygens until [66] An extensive correspondence ensued over the years, in which Huygens showed at first reluctance to accept the advantages of Leibniz's infinitesimal calculus.[67]
Final years
Huygens moved back to The Hague in after suffering another bout of serious depressive illness.
In , he published Astroscopia Compendiaria on his new tubeless aerial telescope. He attempted to return to France in but the revocation of the Edict of Nantes precluded this move.
Christiaan huygens biography template pdf On his third visit to England, Huygens met Newton in person on 12 June Pure Applied Engineering. This figure is only a few minutes off of the actual length of the Martian day of 24 hours, 37 minutes. University of Leiden University of Angers.His father died in , and he inherited Hofwijck, which he made his home the following year.[31]
On his third visit to England, Huygens met Newton in person on 12 June They spoke about Iceland spar, and subsequently corresponded about resisted motion.[68]
Huygens returned to mathematical topics in his last years and observed the acoustical phenomenon now known as flanging in [69] Two years later, on 8 July , Huygens died in The Hague and was buried, like his father before him, in an unmarked grave at the Grote Kerk.[70]
Huygens never married.[71]
Mathematics
Huygens first became internationally known for his work in mathematics, publishing a number of important results that drew the attention of many European geometers.[72] Huygens's preferred method in his published works was that of Archimedes, though he made use of Descartes's analytic geometry and Fermat's infinitesimal techniques more extensively in his private notebooks.[17][27]
Published works
Theoremata de Quadratura
Huygens's first publication was Theoremata de Quadratura Hyperboles, Ellipsis et Circuli (Theorems on the quadrature of the hyperbola, ellipse, and circle), published by the Elzeviers in Leiden in [42] The first part of the work contained theorems for computing the areas of hyperbolas, ellipses, and circles that paralleled Archimedes's work on conic sections, particularly his Quadrature of the Parabola.[33] The second part included a refutation to Grégoire de Saint-Vincent's claims on circle quadrature, which he had discussed with Mersenne earlier.
Huygens demonstrated that the centre of gravity of a segment of any hyperbola, ellipse, or circle was directly related to the area of that segment. He was then able to show the relationships between triangles inscribed in conic sections and the centre of gravity for those sections. By generalizing these theorems to cover all conic sections, Huygens extended classical methods to generate new results.[17]
Quadrature and rectification were live issues in the s and, through Mylon, Huygens participated in the controversy surrounding Thomas Hobbes.
Persisting in highlighting his mathematical contributions, he made an international reputation.[73]
De Circuli Magnitudine Inventa
Huygens's next publication was De Circuli Magnitudine Inventa (New findings on the magnitude of the circle), published in In this work, Huygens was able to narrow the gap between the circumscribed and inscribed polygons found in Archimedes's Measurement of the Circle, showing that the ratio of the circumference to its diameter or pi (π) must lie in the first third of that interval.[42]
Using a technique equivalent to Richardson extrapolation,[74] Huygens was able to shorten the inequalities used in Archimedes's method; in this case, by using the centre of the gravity of a segment of a parabola, he was able to approximate the centre of gravity of a segment of a circle, resulting in a faster and accurate approximation of the circle quadrature.[75] From these theorems, Huygens obtained two set of values for π: the first between and , and the second between and [76]
Huygens also showed that, in the case of the hyperbola, the same approximation with parabolic segments produces a quick and simple method to calculate logarithms.[77] He appended a collection of solutions to classical problems at the end of the work under the title Illustrium Quorundam Problematum Constructiones (Construction of some illustrious problems).[42]
De Ratiociniis in Ludo Aleae
Huygens became interested in games of chance after he visited Paris in and encountered the work of Fermat, Blaise Pascal and Girard Desargues years earlier.[78] He eventually published what was, at the time, the most coherent presentation of a mathematical approach to games of chance in De Ratiociniis in Ludo Aleae (On reasoning in games of chance).[79][80] Frans van Schooten translated the original Dutch manuscript into Latin and published it in his Exercitationum Mathematicarum ().[81][12]
The work contains early game-theoretic ideas and deals in particular with the problem of points.[14][12] Huygens took from Pascal the concepts of a "fair game" and equitable contract (i.e., equal division when the chances are equal), and extended the argument to set up a non-standard theory of expected values.[82] His success in applying algebra to the realm of chance, which hitherto seemed inaccessible to mathematicians, demonstrated the power of combining Euclidean synthetic proofs with the symbolic reasoning found in the works of Viète and Descartes.[83]
Huygens included five challenging problems at the end of the book that became the standard test for anyone wishing to display their mathematical skill in games of chance for the next sixty years.[84] People who worked on these problems included Abraham de Moivre, Jacob Bernoulli, Johannes Hudde, Baruch Spinoza, and Leibniz.
Unpublished work
Huygens had earlier completed a manuscript in the manner of Archimedes's On Floating Bodies entitled De Iis quae Liquido Supernatant (About parts floating above liquids). It was written around and was made up of three books. Although he sent the completed work to Frans van Schooten for feedback, in the end Huygens chose not to publish it, and at one point suggested it be burned.[33][85] Some of the results found here were not rediscovered until the eighteenth and nineteenth centuries.[8]
Huygens first re-derives Archimedes's solutions for the stability of the sphere and the paraboloid by a clever application of Torricelli's principle (i.e., that bodies in a system move only if their centre of gravity descends).[86] He then proves the general theorem that, for a floating body in equilibrium, the distance between its centre of gravity and its submerged portion is at a minimum.[8] Huygens uses this theorem to arrive at original solutions for the stability of floating cones, parallelepipeds, and cylinders, in some cases through a full cycle of rotation.[87] His approach was thus equivalent to the principle of virtual work.
Biography template for professionals: The Curious Life of Robert Hooke. Devices known as escapements regulate the rate of a watch or clock, and the anchor escapement represented a major step in the development of accurate watches. It appears that his departure from Paris, in , was at least partly due to the loss of tolerance for Protestantism by the French monarchy. In the year , Huygens moved to Paris , where he held a position at the French Academy of Sciences.
Huygens was also the first to recognize that, for these homogeneous solids, their specific weight and their aspect ratio are the essentials parameters of hydrostatic stability.[88][89]
Natural philosophy
Huygens was the leading European natural philosopher between Descartes and Newton.[17][90] 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 philosophy of his time).[7][33] 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.[17][91]
In common with Robert Boyle and Jacques Rohault, Huygens advocated an experimentally oriented, mechanical natural philosophy during his Paris years.[92] Already in his first visit to England in , Huygens had learnt about Boyle's air pump experiments during a meeting at Gresham College.
Shortly afterwards, he reevaluated Boyle's experimental design and developed a series of experiments meant to test a new hypothesis.[93] It proved a yearslong process that brought to the surface a number of experimental and theoretical issues, and which ended around the time he became a Fellow of the Royal Society.[94] Despite the replication of results of Boyle's experiments trailing off messily, Huygens came to accept Boyle's view of the void against the Cartesian denial of it.[95]
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.[96]
Laws of motion, impact, and gravitation
Elastic collisions
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 limitations,[97] while Leibniz, his student in Paris, later abandoned it.[98] Understanding the universe this way made the theory of collisions central to physics, as only explanations that involved matter in motion could be truly intelligible.
While Huygens was influenced by the Cartesian approach, he was less doctrinaire.[99] He studied elastic collisions in the s but delayed publication for over a decade.[]
Huygens concluded quite early that Descartes's laws for elastic collisions were largely wrong, and he formulated the correct laws, including the conservation of the product of mass times the square of the speed for hard bodies, and the conservation of quantity of motion in one direction for all bodies.[] An important step was his recognition of the Galilean invariance of the problems.[] Huygens had worked out the laws of collision from to in a manuscript entitled De Motu Corporum ex Percussione, though his results took many years to be circulated.
In , he passed them on in person to William Brouncker and Christopher Wren in London.[] What Spinoza wrote to Henry Oldenburg about them in , during the Second Anglo-Dutch War, was guarded.[] The war ended in , and Huygens announced his results to the Royal Society in He later published them in the Journal des Sçavans in []
Centrifugal force
In Huygens found the constant of gravitational acceleration and stated what is now known as the second of Newton's laws of motion in quadratic form.[] He derived geometrically the now standard formula for the centrifugal force, exerted on an object when viewed in a rotating frame of reference, for instance when driving around a curve.
In modern notation:
with m the mass of the object, ω the angular velocity, and r the radius.[8] Huygens collected his results in a treatise under the title De vi Centrifuga, unpublished until , where the kinematics of free fall were used to produce the first generalized conception of force prior to Newton.[]
Gravitation
The general idea for the centrifugal force, however, was published in and 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.[] Yet, the interpretation of Newton's work on gravitation by Huygens differed 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 between particles.[]
The approach used by Huygens also missed some central notions of mathematical physics, which were not lost on others.
In his work on pendulums Huygens came very close to the theory of simple harmonic motion; the topic, however, was covered fully for the first time by Newton in Book II of the Principia Mathematica ().[] In Leibniz picked out of Huygens's work on collisions the idea of conservation law that Huygens had left implicit.[]
Horology
Pendulum clock
In , inspired by earlier research into pendulums as regulating mechanisms, Huygens invented the pendulum clock, which was a breakthrough in timekeeping and became the most accurate timekeeper for almost years until the s.[] The pendulum clock was much more accurate than the existing verge and foliot clocks and was immediately popular, quickly spreading over Europe.
Clocks prior to this would lose about 15 minutes per day, whereas Huygens's clock would lose about 15 seconds per day.[] Although Huygens patented and contracted the construction of his clock designs to Salomon Coster in The Hague,[] he did not make much money from his invention. Pierre Séguier refused him any French rights, while Simon Douw in Rotterdam and Ahasuerus Fromanteel in London copied his design in [] The oldest known Huygens-style pendulum clock is dated and can be seen at the Museum Boerhaave in Leiden.[][][][]
Part of the incentive 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 , Lodewijk Huygens made a trial on a voyage to Spain, and reported that heavy weather made the clock useless. Alexander Bruce entered the field in , and Huygens called in Sir Robert Moray and the Royal Society to mediate and preserve some of his rights.[][] Trials continued into the s, the best news coming from a Royal Navy captain Robert Holmes operating against the Dutch possessions in []Lisa Jardine doubts that Holmes reported the results of the trial accurately, as Samuel Pepys expressed his doubts at the time.[]
A trial 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 to the Cape of Good Hope, Huygens was able to supply the correction retrospectively.[]
Horologium Oscillatorium
Sixteen years after the invention of the pendulum clock, in , Huygens published his major work on horology entitled Horologium Oscillatorium: Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae (The Pendulum Clock: or Geometrical demonstrations concerning the motion of pendula as applied to clocks).
It is the first modern work on mechanics where a physical problem is idealized by a set of parameters then analysed mathematically.[6]
Huygens's motivation came from the observation, made 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.[] He tackled 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 anticipated the calculus, Huygens showed it to be a cycloid, rather than the circular arc of a pendulum's bob, and therefore that pendulums needed to move on a cycloid path in order to be isochronous. The mathematics necessary to solve this problem led Huygens to develop his theory of evolutes, which he presented in Part III of his Horologium Oscillatorium.[6][]
He also solved a problem posed by Mersenne earlier: 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.[6][]
Huygens was the first to derive the formula for the period of an ideal mathematical pendulum (with mass-less 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.[]
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.[] This concept is now known as entrainment.[]