- Hence several works pertinent to Fourier's life and/or physics are not mentioned. For brevity I use the references in the bibliography of secondary sources in Fourier, 498–502 (itself not mentioned by Herivel): Bellone 1967a, Burkhardt 1908a, Duché 1871a, de Feletz 1830a, Girard [and others] 1830a (there may be an oblique citation of this work on p. 76 at footnote 33), Parisot 1856a, Ravetz 1960a, Unsigned 1849a and Vielh de Boisjolin 1830a. Since Fourier was published there has appeared E. Bellone, ‘Per una rilittura de Fourier’ and L. Besana, ‘Alcune riflessioni sui rapporti intercorrenti tra la Theorie … e modelli esplicativi del calori …’, together in Physis 1972 14 113 119
- In an undated letter to an unknown correspondent Fourier mentioned the manuscript that was actually read at the Institut in December 1807 in lieu of the 1807 paper itself. In annotation to, and on the apparently sole strength of, this remark Herivel identifies on p. 320 that manuscript with the one which we called ‘Extrait’ and conjecturally dated in 1809. We felt unwilling to make this possibly true claim even after reading the undated letter because the title page of the manuscript mentions only a meeting of December 1808, and a covering note has the date 29 October 1809. Secretary Delambre's appendicial remarks to the 1807 paper Fourier 24 24 imply a greater number of supplementary papers than now survive, and Fourier's 1807 summary could be lost.
- The Poisson-Fourier contest began with Poisson's 1808 published review of Fourier's 1807 paper. Herivel finds that the review ‘if not enthusiastic, was perfectly fair and correct in manner’ (p. 153; see also p. 100), and in a footnote he ‘can find no reasons’ for my view (expressed in a paper) that it represented ‘the ultimate in denigration’ of the paper (p. 160 at footnote 42). It is useless to fight over opinions, but our description Fourier 441 443 of Poisson's studied omission of almost all of Fourier's mathematics and his readiness to challenge any aspect of the fragments that are in themselves correctly described, is an elaboration of mine.
- The reader will not grasp the range of physical problems which receive discussion in Fourier's published writings and especially in his main Nachlass in the Bibliothèque Nationale in Paris; in fact surprisingly few manuscripts are cited at all. A brief summary of the Nachlass is given in Fourier 496 497 and manuscripts on specific topics are cited in many footnotes.
- On these points see Fourier 169 173 and 470–474, and references there cited. Among the most significant of the later influences of Fourier series was its role as inspirant of Cantor's theory of sets (pace Herivel's p. 218 again); see J. W. Dauben, ‘The trigonometric background to Georg Cantor's theory of sets’, Arch. hist. exact sci., 7 (1971), 181–216.
- I shall not consider here the prehistory to this idea. The correction to K may well have motivated Fourier's later interest in units and dimensions Fourier 476 476 a striking feature of Fourier's physics which Herivel ignores.
- Fourier is sometimes a little sloppy in his use of ‘molécule prismatique’, for on occasion he seems to use it synonymously with ‘molécule’ instead of referring the latter to the appropriate corner (see, for example, Fourier 122 122 and 125).
- The reader of our article on Fourier in the Dictionary of scientific biography New York 1972 5 93 99 will be puzzled by our description at the bottom of p. 95, col. 2 of a similar difficulty in Biot's analysis of the bar; for after we passed proofs someone corrected our deliberately inaccurate statement of the diffusion equation and thus rendered unintelligible our framing interpretation.
- I shall not proceed to a detailed analysis of the consequences of this situation, but as an example I mention briefly Herivel's remarks on Fourier's derivation in the 1807 paper of the surface diffusion condition for the sphere of radius X. ‘x’ denoted the radius variable and ‘z’ the temperature. Fourier partitioned the sphere ‘into an infinity of concentric layers [couches] of an equal thickness dx’ Fourier 119) 119) and in commenting on his internal diffusion term he used the phrase ‘… the function dz/dx taking the value which applies [convient] to it when x = X’ (Fourier, 293). Herivel describes Fourier here as considering ‘the flow of heat up to, but just beneath, the surface’ and studying ‘heat flux immediately within the surface’ (pp. 170, 215). The italics are mine, and apply to words which hardly describe the processes behind Fourier's ratio ‘dz/dx … when x = X’ with historical adequacy.
- The full historical record of the relationship between Euler's and Lagrange's views on the foundations of the calculus is more complicated than is indicated by this sentence, which is designed solely for the current concern with Fourier. Among an extensive secondary literature, see especially the following: Dickstein S. Zur Geschichte der Prinzipien der Infinitesimalrechnung … Abh. Gesch. Math. 1899 9 65 79 A. P. Youschkewitsch, ‘Euler und Lagrange über die Grundlagen der Analysis’, Sammelband der zu Ehren des 250. Geburtstages Leonhard Eulers (1959, Berlin), 224–244; and sect. 5 of H. J. M. Bos, ‘Differentials, higher-order differentials and the derivative in the Leibnizian calculus’, Arch. hist. exact sci., 14 (1974–75), 1–90.
- Molestation of the ‘d’s in the “letter” of 1809–10 occurs mainly in the top thirds of pp. 308 and 309. In fact, even when the ‘d’s are preserved they are printed as roman ‘d’ whereas Fourier usually printed an italic ‘d’. The point is not a quibble, because Fourier used ‘d’ as another of his alternatives to ‘d’ when working on problems with several independent variables (see Fourier 110 110 123–126 and elsewhere). Fourier physically wrote ‘∂’, but this was a foible of his handwriting. Some other comments have to be made about Herivel's rendering of the alleged letter. Firstly, ‘K’ has been rendered as ‘k’ throughout. The other principal features require precise location by page and line numbers; lineations from the top (excluding running-heads) are indicated by ‘d’ and from the bottom by ‘u’: (1) Fourier drew several diagrams of the configurations and graphs of temperatures in the margins. They are very useful though not vital to his argument. They occur at around 307, 9u; 308, 11u (presumably relating to 19u-17u); 310, 19d, 22d, 12u, 2u; and 311, 13d, 17u, 10u, 3u. (2) The following passages are marked ‘[ ]’, meaning ‘unreadable’: 310, 14d. Insert ‘each of the elements’ (‘chacun des élémens’). 310, 12u. Insert ‘at any instant’ (‘à tout instant’). 311, 13d. I think that ‘they will be sufficiently adjacent to exchange’ (‘elles seront assez[?] voisines pour se transmettre’), taking in Herivel's ‘transmit’, is to be inserted. 311, 13u. I think that something like ‘que l'ai veut’ occurs, but the rest of Fourier's villainous scrawl eludes me also. 313, 2d. The end of this line should read ‘solid. One has also’, using the unread ‘On aura’. 313, 16d. Insert ‘is confirmed’ (‘est confirmé’), and for ‘Rickmann’ read ‘Richmann’ (Fourier, 324). 314, 13d. Insert ‘which divide the solid in equal parts’ (‘qui partagent la solide en parties égales’). (3) The following are mathematical errors: 308, 12d. For ‘δ2 x’ read ‘dx 2’. 311, 16u. For ‘kS(a-b)e’ read ‘KS(a-b/e)’. 314, 18d. For ‘kSf'(x)’ read ‘-KSf'x’. (4) A ‘[sic]’ has been inserted at 314, 17d in the middle of Fourier's ‘second proposition’, deterring the reader from making the obvious back reference to the second proposition in the middle of p. 309. (5) The ellipsis dots at 310, 6d slide over an extremely heavily modified section of the manuscript. At the end of the translated part of the manuscript there are five further short propositions which Fourier crossed out. I would not wish these comments to be taken either as a complete correction to the text or as my acceptance of Herivel's translation. For example, even in my short quotation in section 9 I changed Herivel's translation a little and corrected his ‘x-x'’ in the line above equation (4). I also noticed some insertions of words, and omitted paragraphings, in the lines involved in the details of (2)–(4) above.
- There are still other neglected sides of Fourier. The treatment in Fourier of his life-long interest in the theory of equations was only intended to be introductory, while Fourier the statistician and linear programmer would well reward the attention of a specialist (see Fourier, 484–486’, and now also D. Kohler, ‘Translation of a report by Fourier on his work on linear inequalities Opsearch 1973 10 38 42 More than half of the main Nachlass (see footnote 5) relates to these areas.
Annals of Science
Volume 32, 1975 - Issue 5