Joseph Fourier, the ‘greenhouse effect’, and the quest for a universal theory of terrestrial temperatures

James R. Fleming

The central role that the theory of terrestrial temperatures played in Fourier’s mathematical physics has not received the attention it deserves from historians, although his cryptic allusions to the heating of a greenhouse, taken out of context, have been widely cited by subsequent authors.

Jean Baptiste Joseph Fourier (1768-1830) ogies in Fourier’s writings, they are not found in the works which I have already was known by his contemporaries as a central to his theory of terrestrial tempera- published’; he called this work a ‘resume’ friend of Napoleon, administrator, tures, nor are they unambiguous precursors that included results from several earlier Egyptologist, mathematician and scientist of today’s theory of the greenhouse effect. memoirs. According to John Herivel, one whose fortunes rose and fell with the politi- Of greater significance, I will clarify what of Fourier’s biographers, this essay was cal tides. He was a mathematics teacher, a Fourier actually wrote on the subject of ‘largely expository in character and added secret policeman, a political prisoner terrestrial temperatures and locate this topic nothing essentially new’ on the subject of (twice), governor of Egypt, prefect of Is&e within the context of his analytical theory of terrestrial temperatures3. and Rhone, baron, outcast, and perpetual heat. In the article, Fourier discussed the heat- member and secretary of the French Most people writing on the history of the ing of the Earth by three distinct sources: Academy of Sciencesr. His reputation is greenhouse effect merely cite in passing (1) solar radiation, which is unequally dis- largely based on his ‘Fourier series’, a Fourier’s descriptive memoir of 1827 as the tributed over the year and which produces widely used mathematical technique in ‘first’ to compare the heating of the Earth’s the diversity of climates; (2) the tempera- which complex functions can be represented atmosphere to the action of glass in a green- ture communicated by interplanetary space by a series of sines and cosines. Among house. There is usually no evidence that irradiated by the light from innumerable physicists and historians of physics, he is they have read Fourier’s original papers or stars; and (3) heat from the interior of the also known for his book Thiorie analytique manuscripts (in French) or have searched Earth remaining from its formation (Figure 1). de la chaleur (1822), an elegant work that beyond the obvious secondary sources. He examined in turn each of these sources Lord Kelvin described as ‘a great math- Many authors, perhaps relying on secondary and the phenomena they produce. ematical poem’. sources, mistakenly cite Fourier’s paper of The article contains an extended discus- Recently, Fourier’s article of 1827, 1827 as his first on the subject of terrestrial sion of the distribution of solar heating over ‘Memoire sur les temperatures du globe temperatures; some claim that it is only the globe caused by the periodic and lati- terrestre et des espaces planemires’, pub- available in French. In fact Fourier pre- tude-dependent nature of the sun’s irradi- lished in the Memoirs of the French sented his paper on terrestrial temperatures ante. This section of the paper, based on Academy, has been mentioned repeatedly as to the Acadtmie Royale des Sciences in results established much earlier by Fourier, being the first reference in the literature to 1824 and published it that same year in the was a classic application of Fourier’s ana- the atmospheric ‘greenhouse effect’. Here I Annales de Chimie et de Physique; it was lytic techniques. Fourier also discussed will review the origins of this practice and reprinted in 1827 and translated into another factor controlling terrestrial tempera- demonstrate that most of these citations are English in the American Journal of Science tures: the internal heat of the globe and its unreliable, misdirected and anachronistic. in 1837 (Ref. 2). Secondary sources typi- secular cooling, but he determined this to be While there are indeed greenhouse anal- cally do not acknowledge references by a trivial amount: no more than three- Fourier to greenhouses in his magnum opus hundredths of a degree during the course of of 1822 or in his earlier papers. Moreover, recorded history. James Rodger Fleming existing accounts assume far too much con- The balance of the article is devoted to an tinuity in scientific understanding of the examination of a third factor: the tempera- Is Professor of Science, Technology and Society at greenhouse effect from Fourier to today. ture of space and its effect on the tempera- Colby College, Maine. He has published exten- sively on the history of meteorology and geo- Even his biographers fail to emphasize the ture of the Earth. Here reside most of physics, including social and military aspects and quest for a universal theory of terrestrial Fourier’s comments on the heating of the climatic change. He serves as a consultant for the temperatures as a key motivating factor in atmosphere. According to Fourier, ‘the American Meteorological Society and is chair of its all of Fourier’s theoretical and experimental influence of the stars, is equivalent to the history committee. His books include Meteorology in America, 1800-1870 (Johns Hopkins University work on heat. presence of an immense hollow sphere, with Press, 1990) Science, Technology, and the the earth in the center, the constant tempera- Environmenf (Akron University Press, 1994), Fourier’s article of 1824 ture of which should be a little below what lntemafional Bibliography of Mefeoro/ogy (Diane In an article published in 1824, Joseph would be observed in polar regionsi. In his Publishing, 1994) Historical Essays on Meteorology (American Meteorological Society, Fourier presented some ‘general remarks’ most memorable analogy, Fourier compared 1996) and Historical Perspectives on Climate on the temperature of the Earth and inter- the heating of the atmosphere to the action Change (Oxford University Press, 1998). He lives in planetary space. Fourier provided no of an instrument called a heliothennometer. China, Maine (not mainland China!) with his wife equations, and he told his readers that ‘the This instrument, designed and used in Miyoko and two sons, Jamitto and Jason. e-mail: jrfleminOcolby.edu analytic details which are omitted here are scientific mountaineering in the 1760s by

72 Endeavour Vol. 23(2) 1999 0160-9327/99/$-see front matter 0 1999 Elsevier Science, All rights reserved. PII: SO160-9327(99)01210-7 heat. He employed basic physical principles and formulated mathematical laws to explain and predict universal phenomena, such as ‘the progressive extinction of heat rays in the atmosphere’9. In his Thkorie analytique de la chaleur (1822), Fourier used these results to intro- duce the elements of a comprehensive mathematical theory of heat: the differential equations describing the movement of heat in solids and fluids, the variations intro- duced by external periodic heat sources, and the transmission of heat by diaphanous sub- stances. While these topics were all contri- butions to basic physical theory and have been read as such by generations of physi- cists and historians of physics, they were also the elements of Fourier’s theory of terrestrial temperatures, with the Earth as the cooling body, the Sun as the periodic heat source, and the atmosphere as the diaphanous intermediatyl0. Figure 1 Heat sources affecting terrestrial temperatures according to Fourier. ‘The earth receives the rays of the sun, which penetrate its mass, and are converted into non-luminous It is clear that Fourier considered himself heat; it likewise possessed an internal heat with which it was created, and which is the Newton of heat: ‘The principle of heat continually dissipated at the surface; and lastly, the earth receives rays of light and heat from penetrates, like gravity, all objects and all of innumerable stars, in the midst of which is placed the solar system. These are the three space, and it is subject to simple and con- general causes which determine the temperature of the earth’. Joseph Fourier, 1824 (Ref. 2). stant laws’. As an example of these laws, he cited the distribution of solar heat over the globe: the daily, yearly and longer periodic Horace Benedict de Saussure, consisted of a Fourier concluded by claiming that he had variations that heat both the surface and the small wooden box lined with a layer of ‘united in this article all the principal el- interior of the Earth, which cause variations black cork. Sunlight entered the box ements of the analysis of terrestrial tempera- beneath the surface and control the grand through a window covered with three panes ture’ and had summarized the results of his movements of the oceans and the atmos- of glass separated by air spaces. This earlier researches, ‘long since given to the phere. For Fourier the analytical theory of arrangement served to magnify the heating public’. While raising the possibility that heat constituted a ‘rational law of atmos- effect of the Sun’s rays (measured by a ther- new properties of radiating heat or causes pheric motion, ocean motion, change of sea- mometer enclosed in the box) while elimi- modifying the temperature of the globe sons, and so on - a grand geophysical law nating the cooling effect of wind currents. might yet be discovered, he was positive confirmed in the laboratory and expressed In 1774, simultaneous heliothermometric that ‘all the principal laws of the motion of by calculus’l’. observations taken at different locations by heat are known’6. In his mind, this essay of Saussure and an assistant demonstrated an 1824 on terrestrial temperatures, although Citation patterns appreciable increase in solar heat with providing no equations, had rendered more In 1836 the physicist C.S.M. Pouillet, altitudes. complete his magnum opus of 1822 on the following in Fourier’s tradition, wrote a For Fourier, the atmosphere was like analytical theory of heat. memoir on solar heat, the radiative effects a giant heliothermometer, sandwiched of the atmosphere, and the temperature of between the surface of the Earth and the Earlier comments by Fourier on space. Tenth on his list of 16 related objec- imaginary cap provided by the finite terrestrial temperatures and tives was to determine the ‘general condi- temperature of interstellar space. The inte- greenhouses tions of equilibrium of temperature of a rior of this heliothermometer, especially the The question of terrestrial temperatures was body protected by a diathermanous cover- fluid and aerial components, possessed on Fourier’s mind as early as 1807, when he ing analogous to the atmosphere’. Pouillet radiative properties of its own: ‘The trans- wrote on the unequal heating of the globe. argued that the equilibrium temperature of parency of the waters appears to concur By 1816, he had composed a manuscript of the atmosphere must be higher than the tem- with that of the air in augmenting the degree 650 pages on the subject’. His magnum perature of outer space and lower than the of heat already acquired, because luminous opus of 1822 discusses the problem of temperature of the Earth’s surface. This was heat flowing in, penetrates, with little diffi- terrestrial temperatures and the principles mainly because the atmosphere exerts culty, the interior of the mass, and non-lumi- governing the temperature of a greenhouse ‘unequal absorbing actions’ on ‘rays of heat nous heat has more difficulty in finding its (‘serre’). In his writings, Fourier acknowl- derived from space’ as well as those emitted way out in a contrary direction’. Fourier edged earlier works on heat by John Leslie, from the Earth’s surface. He credited admitted, however, that it is ‘difficult to Count Rumford, and others. One of the Fourier with this insight, which was based know how far the atmosphere influences the earliest such references was to the work of on earlier experimental work by Saussure: mean temperature of the globe; and in this Edme Mariotte who wrote in 1681 that examination we are no longer guided by a although the Sun’s light and heat easily M. Fourier is, I think, the first who has regular mathematical theory’. Fourier’s passed through glass and other transparent had the idea of regarding the unequal statement most suggestive of the green- materials, heat from other sources (‘chaleur absorption of the atmosphere as exercis- house effect, and most cited out of context, de feu’) did nots. ing an influence on the temperatures of was the following: ‘the temperature [of the Fourier made observations on the heating the soil. He had been led to this by the Earth] can be augmented by the interpos- power of the Sun and on night-time refrig- beautiful experiments made by De ition of the atmosphere, because heat in the eration. He conducted experiments on the Saussure, in 1774, on some elevated state of light finds less resistance in pen- heating and cooling of objects of different summits of the Alps and in the adjacent etrating the air, than in repassing into the air composition and shape, and on the trans- plains, with a view to compare the rela- when converted into non-luminous heat’. mission, absorption and reflection of radiant tive intensities of solar heat. On that

Endeavour Vol. 23(2) 1999 73 occasion [1824] M. Fourier states in a Ramanathan repeated the claim that perhaps Mark Handel and James Risbey have precise manner one of the principles Fourier’s 1827 article was a famous first: improved the situation somewhat by noting which have served me to establish the that Fourier’s essay was in fact published in equations of equilibrium’z. Fourier’s (1827) paper is basically a dis- 1824 and reprinted in 1827. The following course on the processes governing the annotation appears in their very helpful Pouillet compared the atmosphere to heat balance of the atmosphere, the sur- bibliography: experiments he had done on solid and liquid face, and the interior of the Earth. diathermanous screens, for example, panes Fourier pointed out that the atmosphere This was the first paper to qualitatively of glass and layers of water, concluding that behaves like the transparent glass cover describe the greenhouse effect. ‘the atmospheric stratum acts in the manner of a box (exposed to the sun) by allow- Compares the effect of the atmosphere of screens of this kind, and . . . exercises a ing sunlight to penetrate to the Earth’s of the earth to that of a pane of glass greater absorption upon the terrestrial than surface and retaining the longwave radi- covering a bowl. (It is easier to find the on the solar rays’. He called this the ‘effect ation (or ‘obscure radiation’ according 1827 version than the nearly identical of diathermanous envelopes’. Pouillet, how- to Fourier) from the Earth’s surface. 1824 version. In French. No known ever, had not arrived at a final theory of This inference is perhaps one of the published translation, though unpub- terrestrial temperatures. Like Fourier, earliest suggestions of the now well- lished ones exist.)23 Pouillet was also quite interested in what known greenhouse effect of the atmos- was called ‘the temperature of space’ and pherel6. Several corrections are in order here. Both the quantities of heat the Earth received the Annales de Chimie et de Physique and from the Sun, from space, and from other M.D.H. Jones and A. Henderson-Sellers the M&moires de I’Acaddmie Royale des ‘celestial bodies’, factors that we have cited Ramanathan rather than Fourier in Sciences de l’lnstitut de France are easy to shown were more central to the theory of their 1990 article, ‘History of the find in most major libraries. The 1827 arti- terrestrial temperatures than was the green- Greenhouse Effect’, asserting the following: cle also appeared in the Oeuvres de Fourier, house effect. a readily available source24. As mentioned John Tyndall referred to Fourier’s work in The French physicist, Fourier, was earlier, an English translation of Fourier’s his 1861 essay ‘On the Absorption and probably the first person, in 1827, to 1824 essay, by Ebeneser Burgess, was pub- Radiation of Heat by Gases and Vapours’. allude to the greenhouse effect when he lished in the American Journal of Science Tyndall credited Fourier and others with the compared the influence of the atmos- for 1837. notion that ‘the interception of terrestrial phere to the heating of a closed space As I have demonstrated, Fourier’s article rays [by the atmosphere exercises] the most beneath a pane of glass”. of 1824 was not the first in which he men- important influence on climate’. By now, tioned the behavior of greenhouses. Nor however, Tyndall had identified a mecha- In Dead Heat, Michael Oppenheimer and was this article in essence about the green- nism. His laboratory experiments showed Robert Boyle also cited Fourier’s 1827 house effect. According to Jones and that water vapor, although transparent to article but severely garbled the citatio@. In Henderson-Sellers, ‘the history of the light rays, was the best absorber of ‘calorific their notes the authors quoted an English greenhouse effect is not well known outside rays’ and that ‘every variation of this con- translation of a section of Fourier’s article the atmospheric sciences’25. We may also stituent must produce a change of climate’. that, although relevant, does not mention safely say that it is not well known inside He thought similar effects could be caused the greenhouse effect directly and that stops the atmospheric sciences. by carbon dioxide and by ‘an almost inap- just short of Fourier’s important statement preciable admixture of any of the hydro- that ‘the effect of solar heat upon air con- Conclusion carbon vapours’. Without venturing quanti- fined within transparent covers has long Understanding of Fourier’s scientific world- tative estimates, he suggested that changes since been observed’l9. Ian Rowlands view has steadily eroded over the years and in the amount of radiatively active gases in repeated this error in his otherwise excellent is just now being recovered. His article of the atmosphere could have produced ‘all the book, The Politics of Global Atmospheric 1827, cited by Arrhenius and by many mutations of climate which the researches Change (1995); he briefly cited the 1827 others since as containing the ‘first’ allusion of geologists reveal’l3. In his 1896 essay article and cited it wrongly in his notes in a to the greenhouse effect, was merely a ‘On the Influence of Carbonic Acid in the way very similar to Oppenheimer and reprint of a descriptive memoir published Air upon the Temperature of the Ground’, Boyle. History was not his focus, however; three years earlier. Moreover, Fourier did Svante Arrhenius began the practice of he covered the 130 years from Fourier to not actually use the term ‘serre’ (green- citing Fourier’s 1827 reprint as the first Roger Revelle in one pagezO. house) in his essay of 1824 in which he dis- mention of the greenhouse effect: ‘Fourier Revelle himself alluded broadly to cussed the behavior of the heliothermom- maintained that the atmosphere acts like the Fourier’s pioneering work on the green- eter. For Fourier the ‘temperature of space’, glass of a hot-house, because it lets through house effect but did not give references; more than the ‘greenhouse effect’, was a the light rays of the Sun but retains the dark William Kellogg cited Revelle. Wilfrid primary factor controlling terrestrial tem- rays from the groundl4. Arrhenius’s famous Bach said Fourier (1827) ‘[w]as probably peratures. Those seeking to understand essay, more than any other, seems to be the the first to discuss the CO, [sic]/ greenhouse Fourier’s scientific contributions must be proximate source of the misquotations and effect and compare it with the warming of willing to look well beyond the secondary the tendency to conflate current and histori- air isolated under a glass plate’. Never literature and well before 1827 to place his cal understandings. mind that the radiative properties of CO, quest for a universal theory of terrestrial Today many scientific review articles and were not investigated until the mid-19th temperatures in the context of his work on textbooks contain brief historical allusions, century21. the analytic theory of heat. typically drawn from secondary rather than Spencer Weart, a historian of physics, original sources. This trend can be identified cited Fourier (1827) and claimed that the Notes and references in recent citations of Fourier’s work. In a greenhouse effect was ‘discovered’ in 1896 1 Grattan-Guinness, I., with .I. Ravitz (1972) 1988 review essay, V. Ramanathan, an by Arrhenius. His article, a stimulating Joseph Fouriel; 1768-1830: A survey of his authority on atmospheric radiation, cited comparison of nuclear issues and global life and work, based on a critical edition of his monograph on the propagation heat Fourier’s 1827 article, claiming, ‘The green- warming, followed the established pattern of presented to the Institute of France in house effect of the atmosphere was pointed of citing Fourier: ‘In 1827 [sic], French 1807, MIT Press out, perhaps for the first time, by Fourier, physicist Jean-Baptiste Fourier had suggested 2 Fourier, .I. (1824) Remarques gknkrales sur who also suggested that human activity can that the Earth is kept warm because air traps les temperatures du globe terrestre et des modify climate’ls. Again in 1988, heat, as if under a pane of glass’22. espaces planhtaires, Ann. Chim. Phys.

74 Endeavour Vol. 23(2) 1999 (Paris) 2nd ser., 27, 136167. This essay 7, Ouvrages sur la chaleur, MS, Collection 18 Oppenheimer, M. and Boyle, R.H. (1990) was reprinted, with slight changes, as des papiers du mathematicien Fourier 29 Dead Heat: The Race Against the Fourier, J. (1827) Memoire sur les tem- (MSS francais 22529), 79, Bibliotheque Greenhouse Effect, p. 34, Basic Books. peratures du globe terrestre et des espaces nationale, Paris (hereafter Fourier Papers). They provide the following citation on planetaires, M&r. Acud. Sci. 2nd ser., 7, My translation. The five laws of radiant p. 222, Fourier, J. (1824) [sic] Les tempcra- 569-604. The English translation of heat are enumerated in Fourier, 5. (nd.), tures [sic] du globe terrestre et des espaces Fourier’s 1824 article, by Ebeneser Precis historique sur la thtorie de la planetaires, Memoires [sic] de L’Academe Burgess, was published in 1837 in the chaleur, ThCorie de la chaleur 3. Histoire de [sic] Royal des Sciences de L’lnstitut de Amer: J. Sci. 32, l-20 la Theorie, Fourier Papers 25 (MSS France 7, 569-604. The correct citation is Herivel, J. (1975) Joseph Fourier; The francais 22525), 168 given in Ref. 2 Man und the Physicist, p. 197, Clarendon 12 Pouillet, C.S.M. (1836) Memoir on the 19 Fourier, J. (1824) Remarques &en&ales sur Press Solar Heat, on the Radiating and Absorbing les temperatures du globe terrestre et des Fourier, J. (1824)Remarques generales sur Powers of the Atmospheric Air, and on the espaces planetaires, Ref. 2, 153, p. 12 les temperatures du globe terrestre et des Temperature of Space’. trans. Richard 20 Rowlands, I.A. (1995) The Politics of espaces planttaires, Ref. 2, pp. 163-164; Taylor (I 846) Scientific Memoirs 4,6869. Global Atmospheric Change, p. 66, Burgess translation, pp. 17-18 In 1833 Macedonio Melloni had defined Manchester Univ. Press Saussure. H.B. de (1874) [letter dated the term ‘diathermic’ as ‘diaphanous for 21 Revelle, R. (1985) Introduction: The March 30, 17841, Journal de Paris no. 108, heat’, from ‘dia’ (across) and ‘thermo’ (to Scientific History of Carbon Dioxide, in 475-478; Saussure (1779-1796) Voyages warm) The Carbon Cycle and Atmospheric CO?: duns les Alpes, Neuchatel-Geneva, vol. 4, 13 Tyndall, J. (1861) On the Absorption and Natural Variations Archean to Present section 932, pp. 136-139 Radiation of Heat by Gases and Vapours, (Sundquist. E.T. and Broecker, W.S., eds), 6 Fourier, J. (1824) Remarques get&ales sur and on the Physical Connection of Geophysical Monographs, Vol. 32, les temperatures du globe terrestre et des Radiation, Absorption. and Conduction, American Geophysical Union. l-4. espaces planetaires, Ref. 2, pp. 151-155 Phil. Mag. ser. 4, 22. 169-194 and Kellogg, W.W. (1987) Mankind’s Impact and 165-167; Burgess translation, pp. l&l3 273-285 on Climate: The Evolution of an and 19 14 Arrhenius, S. (1896) On the Influence of Awareness, Climatic Change IO. I 13-l 36. Fourier, J. (1807) Sur la propagation de la Carbonic Acid in the Air upon the Bach, W. ( 1984) Our Threatened Climate: chaleur, presentt a l’lnstitut le 21 decembre Temperature of the Ground, Phil. Mug. ser. Ways ofAverting the CO, Problem Through 1807, avec notes presenttes en 1808 et 5,4 I, 237-276 Rational Energ! Use. p. 320. trans. Jill 1809, reproduced in Ref. 1 15 Ramanathan, V. (1988) The Greenhouse Jager, D. Reidel Mariotte. E. (1681) Traite de la nature des Theory of Climate Change: A Test by 22 Weart, S. (1992) From the Nuclear Frying couleurs, in Oeuvres de M. Mariotte 2nd Inadvertent Global Experiment, Science Pan into the Global Fire, Bull. Atom. Sk, edn. 2 vols in 1, The Hague, p. 288 240, 293-299, quote from p. 293 June. pp. 19-27; Weart, S. (1997) The Fourier, J. (1817) Questions sur la 16 Ramanathan, V. (1988) The Radiative and Discovery of the Risk of Global Warming, theorie physique de la chaleur rayonnante, Climatic Consequences of the Changing Physics Today, January, p. 36 Ann. Chim. Phys. (Paris) 2nd ser., 6, Atmospheric Composition of Trace Gases, 23 Handel. M.D. and Risbey. J.S. (1992) An 259-303 in The Changing Atmosphere (Rowland, Annotated Bibliography on the Greenhouse 10 Fourier, J. (1822) Theorie analytique de la F.S. and Isaksen, I.S.A., eds), Wiley, Effect and Climate Change, Climatic chaleur, Paris 159-186, quote from p. 160 Change 21. no. 2, pp. 97-255 11 Fourier, J. (n.d.) Extrait d’une memoire sur I7 Jones, M.D.H. and Henderson-Sellers, A. 24 Fourier, J. (1890) Oeuvres de Fourier, l’etat actual de la theorie physique et math- (1990) History of the Greenhouse Effect, (Gaston Darboux, ed.). Paris. 2, 97ff ematique de chaleur, Theotie de la chaleur Prog. Phys. Geog. 14, no. 1, p. 5 25 Ref. 17, p. 5

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