Joseph Fourier

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 applications to problems of heat transfer and vibrations. 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]

Life

Fourier was born at Auxerre (now in the Yonne département of France), the son of a tailor. He was orphaned at age eight. 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.
1820 watercolor caricatures of French mathematicians Adrien-Marie Legendre (left) and Joseph Fourier (right) by French artist Julien-Leopold Boilly, watercolor portrait numbers 29 and 30 of Album de 73 Portraits-Charge Aquarelle’s des Membres de I’Institute.[2]

Circa 1820 sketching Fourier.

In 1806 he quit the post of full professor at the École Polytechnique because Napoleon sent him to Grenoble. He was replaced by Siméon Denis Poisson.

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.

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.

Théorie analytique de la chaleur

In 1822 Fourier presented his work on heat flow in Théorie analytique de la chaleur,[4] in which he based 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.[5]

Determinate equations

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.

Misattribution of the "greenhouse effect"

Fourier is also credited with the idea in 1824 that gases in the atmosphere might increase the surface temperature of the Earth [6]. However the assertion of Arrhenius (1896) that Fourier thought that the atmosphere acted like the glass of a greenhouse is factually incorrect. Fourier (1827)[7] did refer to the invisible rays that occasion heat as "chaleur obscure" or "dark heat" without attribution to Herschel. However, Fourier (1827, p. 586) makes it very clear that in order for the atmosphere to act like the glass of a greenhouse, it must become immobilised to stop convection.

In effect, if all the levels of the air of which the atmosphere is formed were to retain their density and transparency, and lose only their mobility, this mass of air thus becoming solid, being exposed to the rays of the sun, would produce an effect of the same type as that which one has just described.

As this "solid" air is an impossible proposition, Fourier (1827, p. 597) concludes that the earth's heating comes from penetration by solar heat, without reference to the insulative properties of air, but in addition to contributions from the earth's interior and from stars other than the sun. While this reinforced Fourier's concept of heat transfer, Fourier (1827, p. 598) suggests that we may yet discover an alternative mode of heat transfer in space. While planets only lose energy to space by infrared radiation, it was not until the discovery of electromagnetic radiation by Maxwell in 1864, that a separate mode of heat transfer was proven. Until then, the term "radiation" was used to describe the indirect propagation of light and heat through intermediary mediums such as liquids, gases and the luminiferous aether.
Bust of Fourier in Grenoble

According to Fourier (1827), his calculations yielded a sensible temperature for the surface of the earth provided the assumption that the luminiferous aether of space was roughly the same temperature as the poles. In his method of calculating heat transfer, Fourier did not differentiate molecule to molecule heat transfer from internal radiation processes, such as the loss of orbital potential by the emission of a photon subsequently absorbed by another molecule that is not in direct contact. Fourier's law only governed bulk heat transfer and so includes any amount of internal radiation and internal backradiation in addition to kinetic transfer mechanisms shared by bodies in thermal contact. The definitive quantification of purely radiative transfer is the Stefan–Boltzmann law which gives the exact form of this dependency (a fourth-power law), but was not discovered until five decades later, while Planck's law, which refines this dependency to include wavelength, took a further twenty years. Until then, only bulk heat transfer between bodies in thermal contact could be calculated, using Fourier's Law. As such, Fourier's calculations were independent of any purported "greenhouse" effects.
Fourier's grave, Pere Lachaise

Fourier (1827) referred to an experiment by G. B. 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. Against this, Fourier (1827, p. 587) contrasted the turbulent convecting atmosphere, to explain that the heat gain in the partitions of the box with proximity to the blackened cork core is due to the fact that the partitions trap the air and prevent its replenishment. In doing so, the partitions prevent the normal thermal gradient of the air from being steepened by convection. Svante Arrhenius later misunderstood Fourier's explanation and then misattributed his own misunderstanding of how greenhouses work to Fourier (Arrhenius, 1896). Uncritical acceptance of such claims (without checking the source texts) is how the misconception that Fourier discovered the "greenhouse effect" made it's way into modern literature. For historical details see James Rodger Fleming, Historical Perspectives on Climate Change (Oxford, 1998).

See also

* Fourier analysis
* Fourier number
* Fourier–Deligne transform
* Fourier's Law
* Heat equation

Notes and references

1. ^ Cowie, J. (2007). Climate Change: Biological and Human Aspects. Cambridge University Press. p. 3. ISBN 978-0521696197.
2. ^ Boilly, Julien-Leopold. (1820). Album de 73 Portraits-Charge Aquarelle’s des Membres de I’Institute (watercolor portrait #29). Biliotheque de l’Institut de France.
3. ^ "Fourier, Joseph (1768-1830)". Science World Wolfram. http://scienceworld.wolfram.com/biography/Fourier.html. Retrieved 2009-05-06.
4. ^ Jan Gullberg: Mathematics: from the birth of numbers, W.W. Norton, 1997, ISBN 039304002X
5. ^ Mason, Stephen F.: A History of the Sciences (Simon & Schuster, 1962), p. 169.
6. ^ Weart, S. (2008). The Carbon Dioxide Greenhouse Effect. Retrieved on 27 May 2008
7. ^ Fourier J (1827). "Mémoire Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires". Mémoires de l'Académie Royale des Sciences 7: 569–604.

* 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. (1824) [1]Remarques Générales Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires., in Annales de Chimie et de Physique, Vol. 27, pp. 136–167.
* Fourier, J.-B.-J. Mémoires de l'Académie Royale des Sciences de l'Institut de France VII. 570–604 (1827) (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

* O'Connor, John J.; Robertson, Edmund F., "Joseph Fourier", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Fourier.html .
* Fourier, J. B. J., 1824, Remarques Générales Sur Les Températures Du Globe Terrestre Et Des Espaces Planétaires., in Annales de Chimie et de Physique, Vol. 27, pp. 136–167 - translation by Burgess (1837).
* 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

Mathematician