Jean-Baptiste Joseph Fourier was a French mathematician and physicist born in Auxerre
and 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.
Biography Fourier was born at Auxerre, the son of a
tailor. He was orphaned at age nine. Fourier was recommended to the Bishop of Auxerre,
and through this introduction, he was educated by the Benedictine Order 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, serving
on the local Revolutionary Committee. He was imprisoned briefly during the Terror but in
1795 was appointed to the École Normale Supérieure, and subsequently succeeded Joseph-Louis Lagrange
at the École Polytechnique. Fourier accompanied Napoleon Bonaparte on
his Egyptian expedition in 1798, as scientific adviser, and was appointed 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 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.
In 1801, Napoleon appointed Fourier Prefect of the Department of Isère in Grenoble, where
he oversaw road construction and other projects. However, Fourier had previously returned home
from the Napoleon expedition to Egypt to resume his academic post as professor at École Polytechnique
when Napoleon decided otherwise in his remark ... the Prefect of the Department of Isère
having recently died, I would like to express my confidence in citizen Fourier by appointing
him to this place. Hence being faithful to Napoleon, he took
the office of Prefect. It was while at Grenoble that he began to experiment on the propagation
of heat. He presented his paper On the Propagation of Heat in Solid Bodies to the Paris Institute
on December 21, 1807. He also contributed to the monumental Description de l'Égypte.
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 1830, his diminished health began to take its toll:
Fourier had already experienced, in Egypt and Grenoble, some attacks of aneurism of
the heart. At Paris, it was impossible to be mistaken with respect to the primary cause
of the frequent suffocations which he experienced. A fall, however, which he sustained on the
4th of May 1830, while descending a flight of stairs, aggravated the malady to an extent
beyond what could have been ever feared.
Shortly after this event, he died in his bed on 16 May 1830.
Fourier was buried in the Père 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 Description de l'Égypte. His name is one of the 72 names inscribed on the Eiffel Tower.
The Analytic Theory of Heat In 1822 Fourier published his work on heat
flow in Théorie analytique de la chaleur, 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. This book was translated, with
editorial 'corrections', into English 56 years later by Freeman. The book was also edited,
with many editorial corrections, by Darboux and republished in French in 1888.
There were three important contributions in this work, one purely mathematical, two essentially
physical. In mathematics, Fourier claimed 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 theorem, and had implied that the method was general, but he
had not pursued the subject. Peter Gustav Lejeune Dirichlet was the first to give a
satisfactory demonstration of it with some restrictive conditions.
One physical contribution in the book was the concept of dimensional homogeneity in
equations; i.e. an equation can be formally correct only if the dimensions match on either
side of the equality; Fourier made important contributions to dimensional analysis. The
other physical contribution was Fourier's proposal of his partial differential equation
for conductive diffusion of heat. This equation is now taught to every student of mathematical
physics. 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.
Discovery of the greenhouse effect In the 1820s Fourier calculated that an object
the size of the Earth, and at its distance from the Sun, should be considerably colder
than the planet actually is if warmed by only the effects of incoming solar radiation. He
examined various possible sources of the additional observed heat in articles published in 1824
and 1827. While he ultimately suggested that interstellar radiation might be responsible
for a large portion of the additional warmth, Fourier's consideration of the possibility
that the Earth's atmosphere might act as an insulator of some kind is widely recognized
as the first proposal of what is now known as the greenhouse effect.
In his articles, Fourier referred to an experiment by de Saussure, who lined a vase with blackened
cork. Into the cork, he inserted several panes of transparent glass, separated by intervals
of air. Midday sunlight was allowed to enter at the top of the vase through the glass panes.
The temperature became more elevated in the more interior compartments of this device.
Fourier concluded that gases in the atmosphere could form a stable barrier like the glass
panes. This conclusion may have contributed to the later use of the metaphor of the 'greenhouse
effect' to refer to the processes that determine atmospheric temperatures. Fourier noted that
the actual mechanisms that determine the temperatures of the atmosphere included convection, which
was not present in de Saussure's experimental device.
Works Fourier, Joseph. Théorie analytique de la
chaleur. Paris: Firmin Didot Père et Fils. Fourier, Joseph. Annales de chimie et de physique
27. Paris: Annals of Chemistry and Physics. pp. 236–281.
Fourier, Joseph. Mémoire sur la température du globe terrestre et des espaces planétaires
7. Memoirs of the Royal Academy of Sciences of the Institut de France. pp. 569–604.
Fourier, Joseph. Mémoire sur la distinction des racines imaginaires, et sur l'application
des théorèmes d'analyse algébrique aux équations transcendantes qui dépendent de
la théorie de la chaleur 7. Memoirs of the Royal Academy of Sciences of the Institut
de France. pp. 605–624. Fourier, Joseph. Analyse des équations déterminées
10. Firmin Didot frères. pp. 119–146. Fourier, Joseph. Remarques générales sur
l'application du principe de l'analyse algébrique aux équations transcendantes 10. Paris: Memoirs
of the Royal Academy of Sciences of the Institut de France. pp. 119–146.
Fourier, Joseph. Mémoire d'analyse sur le mouvement de la chaleur dans les fluides 12.
Paris: Memoirs of the Royal Academy of Sciences of the Institut de France. pp. 507–530.
Fourier, Joseph. Rapport sur les tontines 5. Paris: Memoirs of the Royal Academy of
Sciences of the Institut de France. pp. 26–43. See also
Fourier analysis Fourier number
Fourier–Deligne transform Fourier's Law
Heat equation References
Further reading Initial text from the public domain Rouse
History of Mathematics Fourier, Joseph.. Theorie Analytique de la
Chaleur. Firmin Didot Fourier, Joseph.. The Analytical Theory of
Heat. Cambridge University Press Fourier, J.-B.-J.. Mémoires de l'Académie
Royale des Sciences de l'Institut de France VII. 570–604
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 . 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.
Fourier 1827: MEMOIRE sur les températures du globe terrestre et des espaces planétaires
Université Joseph Fourier, Grenoble, France Joseph Fourier and the Vuvuzela on MathsBank.co.uk
Joseph Fourier at the Mathematics Genealogy Project
Joseph Fourier – Œuvres complètes, tome 2 Gallica-Math
Joseph Fourier, Théorie analytique de la chaleur Google books