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The radiation of the sun in which the planet is incessantly plunged, penetrates the air, the earth, and the waters; its elements are divided, change direction in every way, and, penetrating the mass of the globe, would raise its temperature more and more, if the heat acquired were not exactly balanced by that which escapes in rays from all points of the surface and expands through the sky.” __The Analytical Theory of Heat, Joseph Fourier
Few works in the mathematical or physical sciences have had such a profound and varied influence as Joseph Fourier’s Analytical Theory of Heat. It changed the way scientists think about functions and successfully stated the equations governing heat transfer in solids.
Joseph Fourier lived a remarkable life. A son of a tailor in the village of Auxerre, Fourier was born on March 21, 1768, and from an early age, he showed interest in mathematics. At the age of 14 he had completed a study of the six volumes of Bézout's Cours de mathématiques1 and a year later, in 1783, he received the first prize for his study of Bossut's Mécanique en général. Around that time, Fourier decided to be trained for the priesthood and entered the Benedictine abbey of St Benoit-sur-Loire. But his interest in mathematics prevailed, and he never took the religious vows. Instead, he became a teacher at the Benedictine college, École Royale Militaire of Auxerre, the school he had studied when he was younger.
Drawn by ideas of the French Revolution, Fourier joined the local Revolutionary Committee, and by Messidor Year II, he was elected president of the Revolutionary Committee in Auxerre.2 The revolution, with its many fractions, was a complicated affair and, as Fourier soon discovered, a dangerous one. On 4 July 1794, following an event where Fourier defended members of one faction while in Orléans, he was arrested and imprisoned. Thanks to the intervention of his friends in Auxerre, he was released only to be arrested again a few days later, on 17 July, after the testimony of a certain commissioner, Demaillot, who claimed that Fourier was a Hébertist, that is, an extremist, and therefore unfit for public office. 3
In a letter written from prison, in justification of his part in the Auxerre, Fourier describes the growth of his political views:
“The first events of the Revolution did not change my way of life. Because of my age I was still unable to speak in public; and impaired by night studies my health scarcely suffices for the work my position required of me.
From another point of view, I will admit frankly that I regarded these events as the customary disturbances of a state in which a new usurper tends to pluck the sceptre from his predecessor. History will say to what extent this opinion was justified. Republican principles still belonged to an abstract theory. It was not always possible to profess them openly. As the natural ideas of equality developed it was possible to conceive the sublime hope of establishing among us a free government, exempt from kings and priests, and to free from this double yoke the long-usurped soil of Europe. I readily became enamoured of this cause, in my opinion the greatest and the most beautiful which any nation has ever undertaken.” 4(Herivel, 1975, p. 27)
Fourier was finally released when Robespierre was beheaded after Thermidor 9 (1794). His biographer, John Herivel, suggests that his release was due to the intervention of Laplace, Lagrange, or Monge, who were well aware of Fourier’s talents as a mathematician. More probably, his release may simply have been due to the changing political climate. In any case, after his release, Fourier was nominated to study at the École Normale Supérieure, a teacher-training school that was founded to help rebuild France, as many would-be teachers have lost their heads due in part to the excess of the Terror. By September 1795, Fourier was teaching at the prestigious École Polytechnique. (Then École Centrale.)
On March 1798, Fourier received a letter from the Directory to the Ministry of Interior that instructed him to put himself “at the disposition of General Bonaparte” for an expedition to an unknown destination. Not being able to refuse Napoleon’s orders, Fourier found himself, a few months later, in the company of Bonaparte and “his fellow generals and officers, and members of the scientific and literary commission together with 30,000 soldiers and sailors all stowed into some 180 ships…” sailing towards Egypt. In Egypt, Fourier was appointed to several administrative positions and was entrusted with delicate diplomatic negotiations with Murad Bey, the formidable leader of the Mamelukes, who had evaded capture by both Bonaparte and Desaix. 5 (Herivel, 1975, p. 69)
In the preface of The Description de L’Egypte, where it was recorded everything, the French said, seen, and studied during their mission in Egypt, Fourier conscious of his European audience, he writes:
One remembers the impression made on the whole of Europe by the astounding news that the French were in the Orient. … This great project was meditated in silence, and was prepared with such activity and secrecy that the worried vigilance of our enemies was deceived; only at the moment that it happened did they learn that it had been conceived, undertaken, and carried out successfully …
After the French capitulation of Alexandria in Egypt and the preliminary Anglo-French Treaty of Peace in October 1801, Fourier returned to France and resumed his post as Professor of Analysis at the École Polytechnique. But it didn’t last for long. Bonaparte had other plans for him. When the Prefect of the Department of Isère died, Bonaparte appointed Fourier to this position. We’ll never know if Fourier was happy at the prospect of leaving the academic world in Paris, but he couldn’t ignore the Bonaparte’s request and soon he left Paris to assume his duties in Grenoble. His tasks as prefect were varied. As a representative of the executive power in the department, Fourier was to see to the enforcement of the various laws and directives coming from Paris, especially those concerned with taxation and recruitment for the consular and imperial armies. He was also expected to keep the central government constantly informed about the state of the department, especially as regards the morale of its citizens and the prevention of law and order. Among the many useful things that Fourier did for the region were the draining of the marshes in Bourgoin and the construction of a new road from Grenoble to Turin. It was also during his time in Grenoble that he did his most important mathematical work on the analytical theory of heat.
The subject of heat had become one of pressing concern to Fourier, probably because of his extreme need for heat. He never went out, even in the hottest weather, without his overcoat. It is said that the excessive warmth of his rooms when he returned to Paris might have hastened his death. Whether this personal interest in heat had anything to do with his theoretical work on the subject remains a matter of conjecture. What is certain is that by the end of 1807, his early work on the subject of the propagation of heat had become a memoir titled “On the Propagation of Heat in Solid Bodies”. The memoir contained essentially the whole of Fourier’s Théorie analytique de la chaleur (Analytical Theory of Heat) as published in 1822, apart from the treatment of the diffusion of heat in infinite solids. In his memoir, Fourier introduced the mathematical laws governing heat diffusion and proposed that an infinite mathematical series may be used to analyse the conduction of heat in solids; this is now known as the ‘Fourier Series’.
In 1824 Joseph Fourier presented a paper titled “Mémoire sur la température du globe terrestre et des espaces planétaires” (On the Temperatures of the Terrestrial Sphere and Interplanetary Space) on the L’Academie Royale des Sciences. It was published that same year in the Annales de Chimie and de Physique and translated into English in the American Journal of Science in 1837. In this paper, Fourier presented some ‘general remarks' on the temperature of the Earth, and as such, it is often referred to as the first reference in the literature to the atmospheric ‘greenhouse effect’. Fourier’s main contribution to this article is the introduction of planetary temperature. He begins his paper:
“The question of the Earth’s temperature distribution, one of the most important and most difficult of all Natural Philosophy, is made up of rather diverse elements that must be considered from a general point of view. It has occurred to me that it would be useful to unite in a single work the principle consequences of this theory; the analytical details that have been omitted here can for the most part be found in the Works which I have already published.” 6 (Fourier J.-B. J.)
The Earth, writes Fourier, derives its heat from three sources.
1. solar radiation, the unequal distribution of which produces the diversity of climates.
2. temperature which is radiated by the light from the innumerable stars in the solar system.
3. primordial heat from the interior of the Earth remaining from its formation.
“The Earth receives the rays of the Sun, which penetrate its mass and are converted there into dark heat; the Earth also possesses heat of its own which it retains from its origin, and which dissipates continually at the surface; finally, this planet receives rays of light and heat from the countless stars among which the solar system is located. These are the three general causes which determine terrestrial temperatures.”
Engraved portrait of French mathematician Jean Baptiste Joseph Fourier (1768 - 1830), early 19th century. Credit: Wikipedia:Louis-Léopold Boilly / Public domain https://commons.wikimedia.org/wiki/File:Fourier2.jpg
Fourier compared the heating of the atmosphere to the action of a heliothermometer, an instrument that was designed and used in scientific mountaineering in the 1760s by Horace Benedict de Saussure. James R. Fleming describes the instrument in his book Historical Perspectives on Climate Change.
“It consisted of a small wooden box lined with a layer of black cork. Sunlight entered the box of glass separated by air spaces. This arrangement served to magnify the heating effect of the Sun’s rays (measured by a thermometer enclosed in the box) while eliminating the cooling effect of wind currents.”
For Fourier, the atmosphere was like a giant heliothermometer, “sandwiched between the surface of the Earth and an imaginary cap provided by the finite temperature of interstellar space”. Fourier didn’t use the term greenhouse, but a different metaphor: “diaphanous envelope.” 7(Fleming, Joseph Fourier, the ‘greenhouse effect’ and the quest for a universal theory of terrestrial temperatures, 1999, p. 73)
Fourier’s article of 1824 was mentioned by John Tyndall, Svante Arrhenius, and many others. Today, many scientific review articles also cite Fourier’s article, but most of them contain brief historical references typically drawn from secondary rather than original sources. “Those seeking to understand Fourier’s scientific contributions to climate change need to look well beyond the secondary literature”, says James Fleming. It is in his Analytic Theory of Heat (Théorie analytique de la chaleur) (Fourier J. , 1978, pp. 3–4) that Fourier discusses the problem of terrestrial temperatures and the principles governing the temperature of a greenhouse (serre in French). He argues that the mean temperature of the earth would be on the rise if the heat acquired from the radiation of the sun were not balanced by that which escapes in rays from all points of the earth’s surface.
Étienne Bézout was a French mathematician known for his theorem on the number of solutions of polynomial equations.
Messidor was the tenth month in the French Republican Calendar. The month was named after the Latin word messis, which means harvest. Messidor was the first month of the summer quarter (mois d'été). It started on 19 or 20 June. It ended on 18 or 19 July. It follows the Prairial and precedes the Thermidor.
Hébertist, also called Exagéré (“Exaggerator”), was any one that belong to a group of extremists of the French Revolution, followers of Jacques-René Hébert, who demanded a Revolutionary government that was anti-Christian and dedicated to the eradication of Girondists and other moderates.
Herivel, J. (1975). Joseph Fourier: The Man and the Physicist. Oxford: Cladendon Press.
Louis de Veygoux Desaix fought under Jourdan and Moreau and He allied with Bonaparte in Italy. He followed him in Egypt where he led the operations against Murad Bay in Upper Egypt.
Fourier, .I. (1824) Remarques generales sur les temperatures du globe terrestre et des espaces planataires, Ann. Chim. Phys. (Paris) 2nd ser., 27, 136167. This essay was reprinted, with slight changes, as Fourier, J. (1827) Memoire sur les temperatures du globe terrestre et des espaces planetaires, M&r. Acud. Sci. 2nd ser., 7, 569-604. The English translation of Fourier’s 1824 article, by Ebeneser Burgess, was published in 1837 in the American Journal of Science 32, l-20