Huygens was the leading European natural philosopher between Descartes and Newton. 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). 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. In common with
Robert Boyle and
Jacques Rohault, Huygens advocated an experimentally oriented, mechanical natural philosophy during his Paris years. Already in his first visit to England in 1661, 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. 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. 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. 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.
Laws of motion, impact, and gravitation Elastic collisions , simplifying the theory of colliding bodies, from Huygens's
Oeuvres Complètes 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, while Leibniz, his student in Paris, later abandoned it. 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. He studied
elastic collisions in the 1650s 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 1652 to 1656 in a manuscript entitled
De Motu Corporum ex Percussione, though his results took many years to be circulated. In 1661, he passed them on in person to
William Brouncker and
Christopher Wren in London. What Spinoza wrote to
Henry Oldenburg about them in 1666, during the
Second Anglo-Dutch War, was guarded. The war ended in 1667, and Huygens announced his results to the Royal Society in 1668. He later published them in the
Journal des Sçavans in 1669. 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: :F_{c}={m\ \omega^2}{r} with
m the
mass of the object,
ω the
angular velocity, and
r the
radius.
Gravitation The general idea for the centrifugal force, however, was published in 1673 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 (1687). In 1678 Leibniz picked out of Huygens's work on collisions the idea of
conservation law that Huygens had left implicit.
Horology Pendulum clock (1657), with a copy of the
Horologium Oscillatorium (1673), at
Museum Boerhaave, Leiden In 1657, 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 300 years until the 1930s. 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 1658. The oldest known Huygens-style pendulum clock is dated 1657 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 1660, 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 1662, and Huygens called in Sir Robert Moray and the Royal Society to mediate and preserve some of his rights.
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 1686 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 1673, 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. 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. 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. 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: :T = 2 \pi \sqrt{\frac{l}{g}} 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.
Balance spring watch In 1675, while investigating the oscillating properties of the cycloid, Huygens was able to transform a cycloidal pendulum into a vibrating spring through a combination of geometry and higher mathematics. In the same year, Huygens designed a spiral
balance spring and patented a
pocket watch. These watches are notable for lacking a
fusee for equalizing the mainspring torque. The implication is that Huygens thought his spiral spring would isochronize the balance in the same way that cycloid-shaped suspension curbs on his clocks would isochronize the pendulum. Huygens's design came around the same time as, though independently of, Robert Hooke's. Controversy over the priority of the balance spring persisted for centuries. 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, presumably tipping the evidence in Hooke's favour.
Optics Dioptrics from
Astroscopia Compendiaria (1684) Huygens had a long-term interest in the study of
light refraction and lenses or
dioptrics. From 1652 date the first drafts of a Latin treatise on the theory of dioptrics, known as the
Tractatus, which contained a comprehensive and rigorous theory of the telescope. Huygens was one of the few to raise theoretical questions regarding the properties and working of the telescope, and almost the only one to direct his mathematical proficiency towards the actual instruments used in astronomy. Huygens repeatedly announced its publication to his colleagues but ultimately postponed it in favor of a much more comprehensive treatment, now under the name of the
Dioptrica. Huygens also worked out practical ways to minimize the effects of spherical and chromatic aberration, such as long focal distances for the objective of a telescope, internal stops to reduce the aperture, and a new kind of ocular known as the
Huygenian eyepiece. He designed in 1662 what is now called the Huygenian eyepiece, a set of two planoconvex lenses used as a telescope ocular. Huygens's lenses were known to be of superb quality and polished consistently according to his specifications; however, his telescopes did not produce very sharp images, leading some to speculate that he might have suffered from
near-sightedness. Lenses were also a common interest through which Huygens could meet socially in the 1660s with
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. He encountered the work of
Antoni van Leeuwenhoek, another lens grinder, in the field of
microscopy which interested his father. There are others to whom such a lantern device has been attributed, such as
Giambattista della Porta and
Cornelis Drebbel, though Huygens's design used lens for better projection (
Athanasius Kircher has also been credited for that).
Traité de la Lumière '' (1690) Huygens is especially remembered in optics for his
wave theory of light, which he first communicated in 1678 to the Académie des sciences in Paris. Originally a preliminary chapter of his
Dioptrica, Huygens's theory was published in 1690 under the title
Traité de la Lumière (
Treatise on light), and contains the first fully mathematized, mechanistic explanation of an unobservable physical phenomenon (i.e., light propagation). Huygens refers to
Ignace-Gaston Pardies, whose manuscript on optics helped him on his wave theory. The challenge at the time was to explain
geometrical optics, as most
physical optics phenomena (such as
diffraction) had not been observed or appreciated as issues. Huygens had experimented in 1672 with double refraction (
birefringence) in the Iceland spar (a
calcite), a phenomenon discovered in 1669 by
Rasmus Bartholin. At first, he could not elucidate what he found but was later able to explain it using his wavefront theory and concept of evolutes. Huygens's theory posits light as 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 (known today as the
Huygens–Fresnel principle). 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. The thus-named Huygens–Fresnel principle was the basis for the advancement of physical optics, explaining all aspects of light propagation until
Maxwell's electromagnetic theory culminated in the development of
quantum mechanics and the discovery of the
photon.
Astronomy Systema Saturnium In 1655, Huygens discovered the first of Saturn's moons,
Titan, and observed and sketched the
Orion Nebula using a
refracting telescope with a 43x magnification of his own design. He was also the first to propose that the
appearance of Saturn, which had baffled astronomers, was due to "a thin, flat ring, nowhere touching, and inclined to the ecliptic”. More than three years later, in 1659, Huygens published his theory and findings in
Systema Saturnium. It is considered the most important work on telescopic astronomy since Galileo's
Sidereus Nuncius fifty years earlier. Much more than a report on Saturn, Huygens provided measurements for the relative distances of the planets from the Sun, introduced the concept of the
micrometer, and showed a method to measure angular diameters of planets, which finally allowed the telescope to be used as an instrument to measure (rather than just sighting) astronomical objects. He was also the first to question the authority of Galileo in telescopic matters, a sentiment that was to be common in the years following its publication. In the same year, Huygens was able to observe
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.
Planetarium 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 died in the interim and Huygens never got to deliver his planetarium to the
French Academy of Sciences as the new minister,
François-Michel le Tellier, decided not to renew Huygens's contract. 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). In this work, Huygens speculated on the existence of
extraterrestrial life, which he imagined 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, though without acknowledging Newton's laws of gravitation or the fact that planetary atmospheres are composed of different gases.
Cosmotheoros, translated into English as
The celestial worlds discover’d, is fundamentally a
utopian work that owes some inspiration to the work of
Peter Heylin, and it was likely seen by contemporary readers as a piece of fiction in the tradition of
Francis Godwin,
John Wilkins, and
Cyrano de Bergerac. 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. 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. It was also in this book that Huygens published his estimates for the relative sizes of the
Solar System and his method for calculating
stellar distances. == Legacy ==