Alexis Clairault
Encyclopedia
Alexis Claude de Clairaut (or Clairault) (3 May 1713 – 17 May 1765) was a prominent French
mathematician
, astronomer
, geophysicist, and intellectual
.
. He was a prodigy
— at the age of twelve he wrote a memoir on four geometrical curves and under his father's tutelage he made such rapid progress in the subject that in his thirteenth year he read before the Académie française
an account of the properties of four curves which he had discovered. When only sixteen he finished a treatise on tortuous curves, Recherches sur les courbes a double courbure, which, on its publication in 1731, procured his admission into the French Academy of Sciences
, although he was below the legal age as he was only eighteen.
, he took part in the expedition to Lapland
, which was undertaken for the purpose of estimating a degree of the meridian arc
. After his return he published his treatise Théorie de la figure de la terre (1743). In this work he promulgated the theorem, known as Clairaut's theorem
, which connects the gravity at points on the surface of a rotating ellipsoid with the compression and the centrifugal force at the equator
. This hydrostatic model of the shape of the Earth was founded on a paper by Colin Maclaurin
, which had shown that a mass of homogeneous fluid set in rotation about a line through its centre of mass would, under the mutual attraction of its particles, take the form of an ellipsoid. Under the assumption that the Earth was composed of concentric ellipsoidal shells of uniform density, Clairaut's theorem could be applied to it, and allowed the ellipticity of the Earth to be calculated from surface measurements of gravity. In 1849 Stokes
showed that Clairaut's result was true whatever the interior constitution or density of the Earth, provided the surface was a spheroid of equilibrium of small ellipticity.
The Théorie de la lune is strictly Newtonian in character. This contains the explanation of the motion of the apsis
which had previously puzzled astronomers, and which Clairaut had at first deemed so inexplicable that he was on the point of publishing a new hypothesis as to the law of attraction when it occurred to him to carry the approximation to the third order, and he thereupon found that the result was in accordance with the observations. This was followed in 1754 by some lunar tables, which he computed using a form of the discrete Fourier transform
.
Clairaut subsequently wrote various papers on the orbit
of the Moon
, and on the motion of comet
s as affected by the perturbation of the planets, particularly on the path of Halley's comet
.
, "with dining and with evenings, coupled with a lively taste for women, and seeking to make his pleasures into his day to day work, he lost rest, health, and finally life at the age of fifty-two."
He was elected a Fellow of the Royal Society of London in November, 1737.
Clairaut died in Paris in 1765.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
, geophysicist, and intellectual
Intellectual
An intellectual is a person who uses intelligence and critical or analytical reasoning in either a professional or a personal capacity.- Terminology and endeavours :"Intellectual" can denote four types of persons:...
.
Childhood
Clairaut was born in Paris, France, where his father taught mathematicsMathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. He was a prodigy
Child prodigy
A child prodigy is someone who, at an early age, masters one or more skills far beyond his or her level of maturity. One criterion for classifying prodigies is: a prodigy is a child, typically younger than 18 years old, who is performing at the level of a highly trained adult in a very demanding...
— at the age of twelve he wrote a memoir on four geometrical curves and under his father's tutelage he made such rapid progress in the subject that in his thirteenth year he read before the Académie française
Académie française
L'Académie française , also called the French Academy, is the pre-eminent French learned body on matters pertaining to the French language. The Académie was officially established in 1635 by Cardinal Richelieu, the chief minister to King Louis XIII. Suppressed in 1793 during the French Revolution,...
an account of the properties of four curves which he had discovered. When only sixteen he finished a treatise on tortuous curves, Recherches sur les courbes a double courbure, which, on its publication in 1731, procured his admission into the French Academy of Sciences
French Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
, although he was below the legal age as he was only eighteen.
The shape of the Earth
In 1736, together with Pierre Louis MaupertuisPierre Louis Maupertuis
Pierre-Louis Moreau de Maupertuis was a French mathematician, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Berlin Academy of Science, at the invitation of Frederick the Great....
, he took part in the expedition to Lapland
Lapland (region)
Lapland is a region in northern Fennoscandia, largely within the Arctic Circle. It streches across Norway, Sweden, Finland and the Kola Peninsula . On the North it is bounded by the Barents Sea, on the West by the Norwegian Sea and on the East by the White Sea...
, which was undertaken for the purpose of estimating a degree of the meridian arc
Meridian arc
In geodesy, a meridian arc measurement is a highly accurate determination of the distance between two points with the same longitude. Two or more such determinations at different locations then specify the shape of the reference ellipsoid which best approximates the shape of the geoid. This...
. After his return he published his treatise Théorie de la figure de la terre (1743). In this work he promulgated the theorem, known as Clairaut's theorem
Clairaut's theorem
Clairaut's theorem, published in 1743 by Alexis Claude Clairaut in his Théorie de la figure de la terre, tirée des principes de l'hydrostatique, synthesized physical and geodetic evidence that the Earth is an oblate rotational ellipsoid. It is a general mathematical law applying to spheroids of...
, which connects the gravity at points on the surface of a rotating ellipsoid with the compression and the centrifugal force at the equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....
. This hydrostatic model of the shape of the Earth was founded on a paper by Colin Maclaurin
Colin Maclaurin
Colin Maclaurin was a Scottish mathematician who made important contributions to geometry and algebra. The Maclaurin series, a special case of the Taylor series, are named after him....
, which had shown that a mass of homogeneous fluid set in rotation about a line through its centre of mass would, under the mutual attraction of its particles, take the form of an ellipsoid. Under the assumption that the Earth was composed of concentric ellipsoidal shells of uniform density, Clairaut's theorem could be applied to it, and allowed the ellipticity of the Earth to be calculated from surface measurements of gravity. In 1849 Stokes
George Gabriel Stokes
Sir George Gabriel Stokes, 1st Baronet FRS , was an Irish mathematician and physicist, who at Cambridge made important contributions to fluid dynamics , optics, and mathematical physics...
showed that Clairaut's result was true whatever the interior constitution or density of the Earth, provided the surface was a spheroid of equilibrium of small ellipticity.
Focus on astronomical motion
He obtained an ingenious approximate solution of the problem of the three bodies; in 1750 he gained the prize of the St Petersburg Academy for his essay Théorie de la lune; and in 1759 he calculated the perihelion of Halley's comet.The Théorie de la lune is strictly Newtonian in character. This contains the explanation of the motion of the apsis
Apsis
An apsis , plural apsides , is the point of greatest or least distance of a body from one of the foci of its elliptical orbit. In modern celestial mechanics this focus is also the center of attraction, which is usually the center of mass of the system...
which had previously puzzled astronomers, and which Clairaut had at first deemed so inexplicable that he was on the point of publishing a new hypothesis as to the law of attraction when it occurred to him to carry the approximation to the third order, and he thereupon found that the result was in accordance with the observations. This was followed in 1754 by some lunar tables, which he computed using a form of the discrete Fourier transform
Discrete Fourier transform
In mathematics, the discrete Fourier transform is a specific kind of discrete transform, used in Fourier analysis. It transforms one function into another, which is called the frequency domain representation, or simply the DFT, of the original function...
.
Clairaut subsequently wrote various papers on the orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
of the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
, and on the motion of comet
Comet
A comet is an icy small Solar System body that, when close enough to the Sun, displays a visible coma and sometimes also a tail. These phenomena are both due to the effects of solar radiation and the solar wind upon the nucleus of the comet...
s as affected by the perturbation of the planets, particularly on the path of Halley's comet
Comet Halley
Halley's Comet or Comet Halley is the best-known of the short-period comets, and is visible from Earth every 75 to 76 years. Halley is the only short-period comet that is clearly visible to the naked eye from Earth, and thus the only naked-eye comet that might appear twice in a human lifetime...
.
Personal life and death
His growing popularity in society hindered his scientific work: "He was focused," says BossutCharles Bossut
Charles Bossut was a French mathematician and confrère of the Encyclopaedists. He was born at Tartaras, Loire, and died in Paris.His works include...
, "with dining and with evenings, coupled with a lively taste for women, and seeking to make his pleasures into his day to day work, he lost rest, health, and finally life at the age of fifty-two."
He was elected a Fellow of the Royal Society of London in November, 1737.
Clairaut died in Paris in 1765.
See also
- Symmetry of second derivativesSymmetry of second derivativesIn mathematics, the symmetry of second derivatives refers to the possibility of interchanging the order of taking partial derivatives of a functionfof n variables...
- Clairaut's theoremClairaut's theoremClairaut's theorem, published in 1743 by Alexis Claude Clairaut in his Théorie de la figure de la terre, tirée des principes de l'hydrostatique, synthesized physical and geodetic evidence that the Earth is an oblate rotational ellipsoid. It is a general mathematical law applying to spheroids of...
- Clairaut's equation
- Clairaut's relation
- Human computerHuman computerThe term "computer", in use from the mid 17th century, meant "one who computes": a person performing mathematical calculations, before electronic computers became commercially available....