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.