# Joseph Fourier

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**Jean Baptiste Joseph Fourier** (21 March 1768 – 16 May 1830) was a French mathematician and physicist best known for initiating the investigation of Fourier series and their application to problems of heat transfer. The Fourier transform and Fourier's Law are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect.^{[1]}

## Contents

[show]## Life Edit

Fourier was born at Auxerre (now in the Yonne département of France), the son of a tailor. He was orphaned at age ten. Fourier was recommended to the Bishop of Auxerre, and through this introduction, he was educated by the Benvenistes of the Convent of St. Mark. The commissions in the scientific corps of the army were reserved for those of good birth, and being thus ineligible, he accepted a military lectureship on mathematics. He took a prominent part in his own district in promoting the French Revolution, and was rewarded by an appointment in 1795 in the *École Normale Supérieure*, and subsequently by a chair at the *École Polytechnique*.

Fourier went with Napoleon Bonaparte on his Egyptian expedition in 1798, and was made governor of Lower Egypt and secretary of the Institut d'Égypte. Cut off from France by the English fleet, he organized the workshops on which the French army had to rely for their munitions of war. He also contributed several mathematical papers to the Egyptian Institute (also called the Cairo Institute) which Napoleon founded at Cairo, with a view of weakening English influence in the East. After the British victories and the capitulation of the French under General Menou in 1801, Fourier returned to France, and was made prefect of Isère]], and it was while there that he made his experiments on the propagation of heat.

Fourier moved to England in 1816. Later he returned to France, and in 1822 succeeded Jean Baptiste Joseph Delambre as Permanent Secretary of the French Academy of Sciences. In 1830, he was elected a foreign member of the Royal Swedish Academy of Sciences.

In 1822 he published his *Théorie analytique de la chaleur*, in which he bases his reasoning on Newton's law of cooling, namely, that the flow of heat between two adjacent molecules is proportional to the extremely small difference of their temperatures. In this work he claims that any function of a variable, whether continuous or discontinuous, can be expanded in a series of sines of multiples of the variable. Though this result is not correct, Fourier's observation that some discontinuous functions are the sum of infinite series was a breakthrough. The question of determining when a Fourier series converges has been fundamental for centuries. Joseph Louis Lagrange had given particular cases of this (false) theorem, and had implied that the method was general, but he had not pursued the subject. Johann Dirichlet was the first to give a satisfactory demonstration of it with some restrictive conditions. A more subtle, but equally fundamental, contribution is the concept of dimensional homogeneity in equations; i.e. an equation can only be formally correct if the dimensions match on either side of the equality. Fourier also developed dimensional analysis, the method of representing physical units, such as velocity and acceleration, by their fundamental dimensions of mass, time, and length, to obtain relations between them.^{[2]}

Fourier left an unfinished work on determinate equations which was edited by Claude-Louis Navier and published in 1831. This work contains much original matter — in particular, there is a demonstration of Fourier's theorem on the position of the roots of an algebraic equation. Joseph Louis Lagrange had shown how the roots of an algebraic equation might be separated by means of another equation whose roots were the squares of the differences of the roots of the original equation. François Budan, in 1807 and 1811, had enunciated the theorem generally known by the name of Fourier, but the demonstration was not altogether satisfactory. Fourier's proof is the same as that usually given in textbooks on the theory of equations. The final solution of the problem was given in 1829 by Jacques Charles François Sturm.

Fourier believed that keeping the body wrapped up in blankets was beneficial to the health. He died in 1830 when he tripped and fell down the stairs at his home.^{[3]}

Fourier was buried in the Pere Lachaise Cemetery in Paris, a tomb decorated with an Egyptian motif to reflect his position as secretary of the Cairo Institute, and his collation of the landmark Description de l'Égypte.

## Discovery of greenhouse effect Edit

Fourier is also credited with the discovery in 1824 that gases in the atmosphere might increase the surface temperature of the Earth.^{[4]} This was the effect that would later be called the greenhouse effect. He described the phenomenon in 1824^{[5]} and then again in a very similar paper in 1827^{[6]} whereby an atmosphere serves to warm a planet.^{[7]} This established the concept of planetary energy balance — that planets obtain energy from a number of sources that cause temperature increase. Planets also lose energy by infrared radiation (which Fourier called *"chaleur obscure"* or "dark heat") with the rate increasing with temperature. A balance is reached between heat gain and heat loss; the atmosphere shifts the balance toward the higher temperatures by slowing the heat loss. Although Fourier understood that the rate of infrared radiation increased with temperature, the Stefan–Boltzmann law which gives the exact form of this dependency (a fourth-power law) was not discovered until fifty years later, while Planck's law, which refines this dependency to include wavelength, took a further twenty years.

Fourier recognized that Earth primarily gets energy from Solar radiation, to which the atmosphere is largely transparent, and that geothermal heat does not contribute much to the energy balance. However, he mistakenly believed that there is a significant contribution of radiation from interplanetary space.

Fourier referred to an experiment by M de Saussure, who exposed a wooden box lined with black cork to sunlight. Three panes of glass were inserted into the cork an inch and a half apart. The temperature became more elevated in the more interior compartments of this device.^{[8]}[1].

Infrared radiation had been discovered by William Herschel in 1800. Fourier was familiar with Herschel's work, as indicated by the fact that he delivered a lecture in praise of Herschel in 1824. [2]

## See also Edit

## Notes Edit

- ↑ Cowie, J. (2007).
*Climate Change: Biological and Human Aspects*, Cambridge University Press. - ↑ Mason, Stephen F.: A History of the Sciences (Simon & Schuster, 1962), p. 169.
- ↑ Fourier, Joseph (1768-1830). Science World Wolfram. URL accessed on 2009-05-06.
- ↑ Weart, S. (2008).
*The Carbon Dioxide Greenhouse Effect*. Retrieved on 27 May 2008 - ↑ Fourier J (1824). Remarques Générales Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires.
*Annales de Chimie et de Physique***27**: 136–67. - ↑ Fourier J (1827). Mémoire Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires.
*Mémoires de l'Académie Royale des Sciences***7**: 569–604. - ↑ The papers almost did not get written as Fourier was nearly guillotined during the French Revolution and only escaped when those who condemned him were ultimately guillotined themselves (Cowie 2007, p. 3)
- ↑ fr:Horace-Bénédict de Saussure

## References Edit

*Initial text from the public domain Rouse History of Mathematics*- Fourier, Joseph. (1822).
*Theorie Analytique de la Chaleur*. Firmin Didot (reissued by Cambridge University Press, 2009; ISBN 978-1-108-00180-9) - Fourier, Joseph. (1878).
*The Analytical Theory of Heat*. Cambridge University Press (reissued by Cambridge University Press, 2009; ISBN 978-1-108-00178-6) - Fourier, J.-B.-J.
*Mémoires de l'Académie Royale des Sciences de l'Institut de France*570–604 (1827) (**VII**.*greenhouse effect essay*) - The Project Gutenberg EBook of
*Biographies of Distinguished Scientific Men*by François Arago - Fourier, J. Éloge historique de Sir William Herschel, prononcé dans la séance publique de l'Académie royale des sciences le 7 Juin, 1824. Historie de l'Académie Royale des Sciences de l'Institut de France, tome vi., année 1823, p. lxi.[Pg 227]

## External links Edit

- Fourier 1827: MEMOIRE sur les températures du globe terrestre et des espaces planétaires
- Université Joseph Fourier, Grenoble, France
- Joseph Fourier at the Mathematics Genealogy Project

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