Essay review

References

• For more details of this history see my (a) Mathematical physics in France, 1800–1835 Epistemological and social problems of the sciences in the early nineteenth century Jahnke H.N. Otte M. Dordrecht 1981 349 370 and (b) ‘Mathematical physics in France, 1800–1840: knowledge, activity and historiography’, in J. W. Dauben (ed.), Mathematical perspectives: essays on mathematics and its historical development (1981, New York), 95–138.
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• Brush , S.G. 1968 . “ Review of C. Truesdell ” . In Essays in the history of mechanics Berlin Isis., vol. 61, (1970), 115–118, 115. Our story does not much trouble the pages of R. Fox and G. Weisz (eds.), The organisation of science and technology in France 1808–1914 (1980, Cambridge). As for D. Outram's ‘Politics and vocation: French science, 1793–1830’, Brit. j. hist. sci., 13 (1980), 27–43, such a peculiar view is put forward that, for example, her list of ‘individuals … holding two or more posts within the scientific orbit’ (pp. 39–40) in the period 1800–1830 manages to exclude 28 of the 32 figures listed in my Table 1! I cannot deal here with the late-18th-century background, but a brief introduction is supplied by H. J. M. Bos's article ‘Mathematics and rational mechanics’, in G. S. Rousseau and R. Porter (eds.), The ferment of knowledge … (1980, Cambridge), 327–355. T. S. Kuhn's emphasis on the dichotomy between mathematized and non-mathematized sciences in his ‘Mathematical vs. experimental traditions in the development of physical sciences’, J. interdisc. hist., 7 (1976–1977), 1–31 (also in his The essential tension … (1977, Chicago and London), 31–65) is valuable, precisely because the dichotomy changed in the early 19th century into a variety of tensions between theoretical and practical aspects of the mathematized sciences, especially those such as mechanics where mathematics had long played a role. C. C. Gillispie's splendid Science and polity in France at the end of the old regime (1980, Princeton) is rather slight on mathematics and mechanics, although valuable on engineering; and, despite its title, it deals only with Paris.
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• 1795–1835 . PV, Procès-verbaux des séances de l'Académie … 1910 – 1922 . Paris 10 vols. general index volume 1979, Paris In the Revolutionary period the Académic des Sciences became one of the classes of the Institut de France. I refer to ‘Académie’ or ‘class’ as appropriate.
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• Among other recent studies of the early years of the EP, see Bradley M. Ecole Polytechnique Ann. sci. 1975 32 415 449 Scientific education versus military training: the influence of Napoleon Bonaparte on the her ‘The facilities for practical instruction in science during the early years of the Ecole Polytechnique’, Ann. sci., 33 (1976), 425–446; and J. Langins, ‘Sur la première organisation de l'Ecole Polytechnique. Texte de l'arrêté du 6 frimaire an III’, Rev. hist. sci., 33 (1980), 289–313 (drawing on his 1979 Toronto Ph.D. thesis, ‘The Ecole Polytechnique (1794–1804): from encyclopaedic school to military institution’, which I have not seen). Paul deals in ch. 1 with general educational philosophy at the end of the 18th century.
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• Olivier , T. 1851 . De l'Ecole Polytechnique’ to his Mémoires de géométrie descriptive, théorique et appliquée Vol. v , xi – xii . Paris 1847 preface (where he claimed that Laplace and Poisson later ‘sincerely deplored their error’ and hoped that Cauchy would too). See also his ‘Monge et l'Ecole Polytechnique’, Rev. sci. ind., no. 128 (September 1850), 64–68. In the late 1820s he was one of the founders of the Ecole Centrale des Arts et Manufactures, a school for industrial engineers modelled on Monge's hopes for the public service engineering school Ecole Centrale des Travaux Publics (as the EP was first called).
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• The main collections of documents are kept in boxes classified by year; but the materials often relate to other years, so that retrieving information is exceedingly difficult. Other records include the minute books of the Conseil d'Instruction and the Conseil de Perfectionnement; the printed annual Rapport sur la situation de l'Ecole Polytechnique and Programme générale of syllabi; and various decrees, especially in the early years (Langins has reprinted one in his Sur la première organisation de l'Ecole Polytechnique. Texte de l'arrêté du 6 frimaire an III Rev. hist. sci. 1980 33 289 313
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• Monge , G. 1811 . Géométrie descriptive 119 – 124 . Paris and Figure 41 (just the job for a rainy day).
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• Hachette , J.N.P. 1811 . ‘Supplément’ to Monge Géométrie descriptive iv – vii . Paris A useful history of descriptive geometry, surprisingly omitted from Paul's excellent bibliography, is G. Loria, Storia della geometria descrittiva dalle origini sino ai giorni nostri (1921, Milan).
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• See especially de Prony's Mécanique philosophique… JEP 1799–1800 3 1 iii vii cah. 8 bis 1–479; also published separately as a book under this title. This work, which is incomplete (see footnote 80 below), contains no diagrams at all. But he included some elsewhere; for example, in two pedagogical papers on Euler's equations (‘Théorie du mouvement, autour d'un axe libre de rotation …’, JEP, (1) 2, cah. 6 (1799), 297–342; and ‘Analyse détaillée des différentes questions …’, JEP, (1) 4, cah. 11 (1802–1803), 87–142).
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• For example, no reviews are listed in the critical bibliographies Isis even the Revue d'histoire des sciences passed it over.
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• Poinsot's Nachlass is in BI, mss. 948–965 (Documents 3 änd 4 come from it) and 4738 (one of the versions used by Bailhache of the 1806 paper, which is Théorie générale de l'équilibre et du mouvement des systèmes JEP 1806 6 1 206 241 cah. 13 Bailhache devotes his ch. 6 to a contemporary proof by Ampère, ‘Démonstration générale du principe des vitesses virtuelles’, ibid., 247–269, and on p. 185 rightly calls for study of relevant manuscripts (AS, Ampère, chs. 113–118).
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• Another valuable history, which unfortunately Bailhache missed, is Lindt R. Das Prinzip der virtuellen Geschwindigkeiten … Abh. Gesch. Math. 1904 18 145 195
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• See respectively Poinsot L. Elémens de statique , 1st ed. Paris 1803 and ‘Sur la composition des momens et la composition des aires’, JEP, (1) 6, cah. 13 (1806), 182–205. This paper was published immediately before his (footnote 11) in the JEP, and both papers were included in editions of the Statique between 1834 and 1861. Thus, as Bailhache sensibly warns on pp. 40–41, the papers can be confused. de Prony was the reporter for the class of the Institut on Poinsot's paper cited here (PV, vol. 3, 317–320).
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• Two months later the government purchased Lagrange's Nachlass, which is not held at BI, mss. 901–916. A commission composed of Lacroix, Legendre, Poisson and de Prony was set up to evaluate them for publication (PV, vol. 5, 513). On 3 November 1817 Lacroix read their report to the class PV 6 233 234 (also in Mag. enc., (1818), 2, 318–320); Hist. AS, 2 (1817: publ. 1819), lvii–lx; Lagrange, Mécanique analytique (3rd ed., ed. J. Bertrand), vol. 2 (1855, Paris), 389–390; Lagrange, Oeuvres, vol. 12, 387–388)). The commission's file is kept in AS, dossier personnel for Lagrange. BI, ms. 2737 contains manuscripts on the preparation of Lagrange's Oeuvres, while EP has two boxes of Lagrangiana.
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• See PV 5 217 218 Poinsot gained 30 votes to the 23 of the economist Duvillard de Durand, a (surprisingly popular?) candidate, who had been second to Biot's election in 1803 (vol. 2, 642), but never gained membership of the class although he was a correspondant of the classe d'histoire et de littéraire ancienne (vol. 2, 624).
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• Duchayla . 1804 . Demonstration du parallèlogramme des forces . BSP , 4 : 242 – 243 . (also in Corr. EP, 1 (1804-1808), 83–84). This brief paper seems to have been his only scientific publication; but it has given him some durability, for several classical textbooks in mechanics reproduce, with attribution, his proof. According to Bailhache (p. 37), Duchayla was Charles Dominique Marie Blanquet(-Duchayla), who entered the founding year of the EP rather late in April 1796 (see Corr. EP, 1 (1804–1808), 106). He became an inspecteur général in the Université (see A. L. Fourcy, Histoire de l'Ecole Polytechnique (1828, Paris), 399; compare Bailhache, p. 37). In 1809 a ‘M. Duchaila’ is reported to have helped Arago with some optical experiments (PV, vol. 4, 245).
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• On Fresnel's work, see Frankel E. Corpuscular optics and the wave theory of light … Soc. stud. sci. 1976 6 141 184 R. H. Silliman, ‘Augustin Fresnel (1768–1827) and the establishment of the wave theory of light’ (1967, Princeton Ph. D.); and his ‘Fresnel and the emergence of physics as a discipline’, Hist. stud. phys. sci., 4 (1975), 137–162.
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• 1978 . Ann. sci. , 35 : 434 – 436 . The principal collection of Malus manuscripts is held at BI, mass. 1692–1694; Chappert gives a valuable list of these and other items on pp. 221–224.
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• See Fox R. The rise and fall of Laplacian physics Hist. stud. phys. sci. 1974 4 81 136 On the place of Malus, see also E. Frankel, ‘The search for a corpuscular theory of double refraction …’, Centaurus, 18 (1974), 223–245.
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• This is the group of scientists patronized by Laplace and the chemist Berthollet; see Crosland M.P. The Society of Arcueil London 1967
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• Arago , D.F.J. 1811 . Mémoire sur une modification qu'éprouvent les rayons lumineux … . MCI , 12 : 93 – 134 . pt. 1 publ. 1812 (also in Oeuvres, vol. 10, 36–74); J. B. Biot, ‘Mémoire sur les nouveaux rapports qui existent entre la réflexion et la polarisation’, ibid., 135–280 (also in his Recherches expérimentales et mathématiques sur les mouvemens des molécules … (1814, Paris), 8–152).
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• See PV 5 224 225 and Crosland (footnote 20), 332–335.
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• Biot , J.B. and Arago , D.F.J. Mémoire sur les affinités des corps … . MCI , 7 1806 – 1806 . and (in the end) 301–385 The 1813 affair had a curtain-raiser in March and April 1812, when Arago vindicated a claim made against Biot having by his records at the Bureau des Longitudes checked by members of the class (see PV, vol. 5, 41, 43; and Arago, Oeuvres, vol. 10, 75–84). This event seems to have become transformed into the story that one day Arago explained some optical phenomenon to Biot by drawing it on a church column. Two days later Biot presented a paper on the matter to the Académie, whereupon Arago demanded that a commission examine the church column. His drawing was found still to be there; and Biot absented himself for six months from the Académie (see L. A. Sédillot, ‘Les professeurs de mathématiques et de physique générale au Collège de France’, Bull. bibl. stor. sci. mat. fis., 3 (1870), 107–170 (p. 161)). The ‘six months’ element comes from the 1813 affair itself. Biot was away from Paris (on scientific work) for most of the latter half of 1812 (see PV, vol. 4, 576–577), and mentioned his absence in his footnote against Arago (Document 2); indeed, Duchayla reported it as a six months' absence in Document 4. Biot left his Nachlass to his son-in-law F. Lefort; I do not know what happened to it after that. Two boxes of letters are held at BI, mss. 4895–4896, and interesting early letters to Lacroix are among the Smith Collection, Columbia University, New York (see E. Frankel, ‘Career-making in post-revolutionary France: the case of Jean-Baptiste Biot’, Brit. j. hist. sci., 11 (1978), 36–48). Manuscripts pertaining to his many pendulum experiments are kept at the Paris Observatoire.
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• See PV 7 384 384 (Arago appointed to the selection committee), 386 (Arago, Biot and Fourier proposed, but Arago ‘too busy’ to accept nomination) and 394 (Fourier elected by 38 votes to Biot's 10). A story circulated that Laplace chose his vote by putting the two names in a hat, finding ‘Fourier’ on the sheet which he withdrew, and discarding the other without opening it—and thus revealing, in the opinion of the Académie, that ‘Fourier’ was written on it also (see Sédillot (footnote 23), 162). Biot ignored the election in his recollections of secrétaires ([Review of C.r.AS, 1–14 (1836–1842)], J. sav., (1842), 641–661 (pp. 647–649)). His absences from Académie meetings in the 1820s can be traced from the attendance registers in PV, vols. 7–9. On the election of secrétaires, see Lacroix's remarks of 1832 in PV, vol. 10, 81–82.
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• See Silliman Frankel Corpuscular optics and the wave theory of light … Soc. stud. sci. 1976 6 141 184
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• Poisson secured 30 votes to the 24 of the engineer Girard PV 5 40 40
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• I note the book only briefly, as a review is being prepared for this journal by a colleague. The lack of a bibliography, and the provision of cross-references only by the useless ‘op. cit.’, make the references difficult to use. I would also have welcomed a listing of Germain's rather scattered Nachlass, which Bucciarelli and Dworsky have used. The main collections are held at BN, mss. f.f.n.a. 4073, 5166, 9114–9118, 9544; and BI, ms. 2381. The British Library copy of the published version of her prize paper, Recherches sur la théorie des surfaces élastiques (1821, Paris), contains the manuscript of her letter to Wheatsone, published in her posthumous essay ‘Mémoire sur l'emploi de l'épaisseur dans la théorie des surfaces élastiques’ J. math. pures appl. 1880 6 3 60 64 ‘supplément’, 64 pp. EN PC has some manuscript notes in de Prony's copy of this book, but has lost from ms. 715 the manuscript of the posthumous essay. The editor of this essay, G. de Courcel, attributes to de Prony the patronizing notice of Germain in Biographie nouvelle des contemporains, vol. 8 (1827, Paris), 115.
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• See my and Ravetz's Joseph Fourier 1768–1830 … Cambridge, Mass. 1972 which contains on pp. 496–498 a list of Fourier's manuscripts, held principally at BN, mss. f.f.n.a. 22501–22529. For details of Fourier's 1811 prize paper, see footnote 61 below.
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• Herivel , J. 1976 . Joseph Fourier. The man and the physicist Oxford I have not seen the doctoral thesis of L. Charbonneau, ‘L'oeuvre mathématique de Joseph Fourier’ (1976, Paris).
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• See my On Joseph Fourier: the man, the mathematician and the physicist Ann. sci. 1975 32 503 514
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• BI mss. , 2396 – 2403 .
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• Laplace published his work in Sur le mouvement de la lumière dans les milieux diaphanes Mém. Soc. Arcueil 1809 2 300 342 and again, with an additional ‘Note’, in MCI, 10 (1809; publ. 1810), 300–342 (also in Oeuvres complètes, vol. 12, 265–298). Herivel reproduces the relevant part of the paper on his pp. 78–80. Laplace's Nachlass was destroyed long ago; a body of materials, of no special importance, is held at BI, ms. 2242.
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• Biot , J.B. 1809 . Mercure de France , 38 : 327 – 338 . [Review of P. Prévost, Du calorique rayonnant … (1809, Paris and Geneva)] Herivel reproduces the relevant part of the paper on his p. 81. Biot's review seems to have excited Lagrange to make a contribution to heat diffusion in analysing Prevost's two-body heat exchange model. Lagrange did not publish this work; but manuscripts survive in his Nachlass (footnote 14) at BI, ms. 903, fols. 150–171 passim, and Lacroix summarized the analysis on a sheet surviving with Documents 8 and 9 (ms. 2400).
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• Biot , J.B. 1804 . Mémoire sur la propagation de la chaleur . Bibl. brit. , 27 : 310 – 329 . (also in J. mines, 17 (1804), 203-224). Herivel reprints a not particularly crucial passage on his pp. 76–77. On the bearing of Biot's work Fourier, see my and Ravetz's (footnote 28), ch. 4.
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• Poisson, of course, used Laplacian models to study heat diffusion. He presented his work first to the class in May 1815 PV 5 513 514 and published extracts then, principally ‘Mémoire sur la distribution de la chaleur dans les corps solides’, BSP, (1815), 85–91, (1816), 11–13; and ‘Extrait d'un mémoire …’, J. phys., 80 (1815), 434–441 (of which Herivel reprints parts on his pp. 82–84). However, Poisson withdrew the main paper(s) for seven years while he wrote additional sections. The whole appeared mainly as a sequence of papers constituting most of JEP, (1) 12, cah. 19 (1823). He had found out the extent of Fourier's progress, perhaps with the aid of Fourier's own first publication, ‘Théorie de la chaleur’, Ann. chim. phys., (1) 3 (1816), 350–375 (omitted by Darboux from Fourier's Oeuvres as being only of historical interest …). On Poisson's treatment of Fourier's 1807 paper, see footnote 62 below.
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• Ampère , A.M. 1806 . Recherches sur quelques points de la théorie des fonctions dérivées … . JEP , 6 ( 1 ) : 148 – 181 . cah. 16
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• 1811–1812 . EP, Rapport sur la situation de l'Ecole Polytechnique , 5. Laplace's advocacy of this move is recorded in, of all places, R. de Prony, ‘Brunacci’, in Biographie universelle ancienne et moderne, vol. 6 (1843, Paris), 10–12. Laplace, normally inclined to theory, presumably felt that the theory of limits was too theoretical.
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• Ampère , A.M. 1824 ? . Précis de calcul différentiel et de calcul intégral Paris The date is suggested by the request in 1822 of the EP graduation examiners, de Prony and Poisson, for the professors to print their lecture notes (EP, box 1822: compare Documents 11, 13 and 14), and also by some of the manuscripts on the calculus in AS, Ampère, chs. 74–77. Taton gives the date 1824 in his ‘Repères pour une biographie intellectuelle d'Ampère’, Rev. hist. sci., 31 (1978), 233–248 (p. 237). Ampère also published in the mid 1820s ‘Démonstration du théorème de Taylor …’, Ann. math. pures appl., 17 (1826–1827), 317–330; and especially ‘Essai sur un nouveau mode d'exposition des principes du calcul différentiel …’, ibid., 16 (1825–1826), 329–349, an algebraic treatment of the difference quotient which Cauchy extended in ‘Sur les fonctions interpolaires’, C.r.AS, 11 (1840), 775–789 (also in Oeuvres, ser. 1, vol. 5, 409–424), and on which manuscripts by both Ampère and Cauchy survive in AS, Ampére, box 322.
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• Ampère , A.M. 1815 . Considérations générales sur les intégrales des équations aux différentielles partielles . JEP , 10 ( 1 ) : 549 – 611 . cah. 17 with a continuation in JEP, (1) 11, cah. 18 (1820), 1–188; compare proofs and manuscripts in AS, Ampère, chs. 75, 87 and 325, and box 321. Ampère's lecture notes are entitled Résumé des leçons sur l'intégration des équations aux différentielles partielles; copy in Sorbonne library. Compare the manuscripts in ch. 83, and especially the partial set of proofs in ch. 392, where Ampère's handwritten note beginning ‘J'irai aujourd'hui lundi 27 Janv[ie]r' strongly suggests the year 1823 (rather than the other possible years 1806, 1817, 1828 and 1834). Gilain reprints from the EP Programme (footnote 6) some of the analysis syllabi of this period (pp. 142–146).
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• In his adulation of a biography Valson C.A. La vie et les travaux du Baron Cauchy Paris 1868 refers to these manuscripts 2 vols. repr. in 1 vol., 1970, Paris), vol. 2, viii–x). On this and other problems in Cauchy studies, see my ‘On the publication of the last volume of the works of Augustin Cauchy’, Janus, 62 (1975), 179–191.
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• Cauchy , A.L. 1809 . Mémoire sur les moyens de perfectionner la navigation des rivières en général et celle de la Marne en particulier . ENPC , ms. 1982); compare it with ‘Théorie de la propagation des ondes …’, Mem. prés. AS div. sav., (2) 1 (1827), 3–312 (also in Oeuvres, ser. 1, vol. 1, 4–318), which won a prize in 1815. The other two 1809 manuscripts in ENPC, ‘Mémoire sur les ponts en pierre’ and ‘Second mémoire …’ (32 and 52 pp. respectively), seem, to my perusal, to be of less interest.
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• Cauchy , A.L. Mémoire sur le calcul différentiel et le calcul des variations, présentant le résumé de ces deux calculs . AS, dossier personnel for Cauchy , 36 – 36 . I think that Cauchy sent in this paper to the Académie from Geneva in June or July 1831 (PV, vol. 9, 656). AS contains various other manuscripts by Cauchy in certain pochettes of its weekly meetings; some may be significant.
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• Cauchy , A.L. 1827 . Notes sur quelques parties de la mécanique Paris 35 pp. (comprising one ‘Note’): copy in EP library.
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• 1812 . fr|Notice sur la vie et l'ouvrage de M. Lagrange . Hist. AS , : xxvii – lxxx . Delambre' éloge is publ. 1814 (also in Lagrange, Oeuvres, vol. 1, ix-li; manuscript in BI, ms. 2041). Delambre's éloges of Lagrange and Malus appeared together in Mag. enc., (1814), 1, 317–393, and it was extracts of these that appeared in Mon. univ., (1814), 63, 67–68, 69–71, 73–74. ‘L.B.M.D.G.'s letter is on pp. 226–228; for my identification of the author as Guyton de Morveau, see my introduction to Document 5.
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• See Précis de calcul différentiel et de calcul intégral Paris 1824 this one is from AS, Ampère, ch. 75 (holograph).
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• Lhuilier , S. 1786 . Exposition élémentaire des principes des calculs supérieurs … Berlin
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• Biot . 1811 . Mémoire sur les nouveaux rapports qui existent entre la réflexion et la polarisation . MCI , 12 : 135 – 280 . pt. 1 publ. 1812 The unaltered copy of the Mémoires is held in the University Library in Aarhus (see Frankel (footnote 17), 82); I am grateful to K. Andersen for furnishing me with a copy of the page.
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• Arago , D.F.J. 1810–1811 . fr|Extrait d'un mémoire …’ . BSP , 2 : 358 – 360 . 371–375, 387–389 (the numbers of the Bulletin are for October-December 1811); ‘Mémoire …’, Mon. univ., (1811), 932–933.
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• BI , ms. 953, fols. 162–163 (both holograph).
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• Duchayla's remark is too vague to lead to precise identification. Presumably Poisson attacked Poinsot's Nachlass is in BI, mss. 948 965 although none of his writings on mechanics around 1813 seems to deal with Poinsot; but the two had several disagreements in the 1820s and 1830s, often sarcastically phrased, on Euler's torque theorem and its consequences (footnote 85 below), the precession of the equinoxes, the attraction of ellipsoids, osculating surfaces, probability and power-series expansions. Their relations were not helped by Poisson's preferment over Poinsot in 1822 for Delambre's place on the Conseil Royale d'Instruction Publique. There is a story that Poinsot also had a row with Biot; he found his theory of couples in a book by Biot, who had to replace a few pages after publication (Sédillot (footnote 23), 161). The book involved must be Biot's Notions élémentaires de statique … (1829, Paris), perusal of which lends credence to the story. For example, there is a seemingly unnecessary erratum on p. vii, asking that the phrase ‘M. Poinsot, who first remarked upon the usage’ of couples (p. 42), be changed to ‘M. Poinsot, who first discovered the principle and the usage’ of couples. Further, the only explicit acknowledgement in the ‘Avant-propos’ is an uncharacteristic gush to ‘the theory of couples, invented a long time ago by M. Poinsot, and applied by him in such an illuminating way in his works’.
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• On Poisson's papers on heat diffusion see PV 5 513 514
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• L.B.M.D.G. 1814 . fr|Lettre à M. le Redacteur … . Mon. univ. , : 226 – 228 .
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• EP, box 1821, in a file of manuscripts on the matter (including also Document 7); both manuscripts are copyist. The Governor of the EP then was one Baron Bouchu. The incident is noted in Callot J.P. Histoire de l'Ecole Polytechnique Paris 1958 65 65
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• The ‘second division’ comprised the first-year students; the year later they became the ‘first division’. This confusing terminology was introduced in 1806 EP, Rapport sur la situation de l'Ecole Polytechnique 1806 16 16 until then years and divisions had shared the same ordinals
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• The Directeur d'Etudes , of the school repared monthly reports on the teaching progress. Many of them survive in the EP archives, one in the file containing this document.
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• BI , ms. 2400, file entitled ‘Astronomie’, containing Documents 8 and 9 (both holograph).
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• Lacroix forgot that Monge was also an examiner PV 3 632 632 Doubtless Monge will have been in favour; but apparently he was not an influential member of the commission.
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• Biot . 1809 . Mercure de France , 38 : 327 – 338 . [Review of P. Prévost Du calorique rayonnant … (1809, Paris and Geneva)]
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• The prize was announced on 16 December 1811 PV 4 562 562 and awarded on 6 January 1812. But Fourier could not get his paper published until the 1820s (‘Théorie du mouvement de la chaleur dans les corps solides’, MAS, 4 (1819–1820: publ. 1824), 185–555; 5 (1821–1822: publ. 1826), 153–246 (the second part also in Oeuvres, vol. 2, 1–94)).
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• Lacroix added in the margin Nouveau bulletin etc. T.1 112 112 (mars 1808) He was citing Poisson's report (also published in Fourier's Oeuvres, vol. 2, 213–221); but he was naive in regarding it as assuring Fourier his rights, for in it Poisson belittled Fourier's achievements in the 1807 paper to a remarkable degree (see my and Ravetz's (footnote 28), 442–443).
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• Laplace . 1809 . Sur le mouvement de la lumière dans les milieux diaphanes . Mém. Soc. Arcueil , 2 : 300 – 342 .
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• Lacroix was referring to the Laplace/Legendre competition during the late 18th century over attraction theory and ‘Legendre polynomials’ (or ‘Laplace's functions’, as Laplace's endeavours succeeded in having them called for much of the 19th century). For recent information on this matter, see Gillispie C.C. fr|Mémoires inédits ou anonymes de Laplace Rev. hist. sci. 1979 32 223 280 (pp. 257–264). For another example of Lacroix's disapproval of Laplace's conduct, see R. Taton, ‘Laplace et Sylvestre-François Lacroix’, Rev. hist. sci., 6 (1953), 350–360.
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• The word ‘established’ is not historically defensible, given the chaotic state of thermometric calibration at Newton's time (see Ruffner J.A. Reinterpretation of the genesis of Newton's “Law of cooling” Arch. hist. exact. sci. 1962–1966 2 138 152 In the analysis which now follows, Lacroix's dy/dx is a ratio of partial differentials.
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• Lacroix is following Poisson PV 5 10 13 here. ф(s) is an inter-molecular heat conductivity function which, after Poisson's excruciating derivation of the diffusion equation for the rod, ends up in integrands of functions which define for him the internal and external conductivity coefficients (as Lacroix notes below). Above Lacroix used Fourier's ‘K’ for the internal coefficient.
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• See my and Ravetz's Joseph Fourier 1768–1830… Cambridge, Mass. 1972 50 52 ch. 5; or Herivel
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• Lacroix's references in this passage are to Laplace Sur le mouvement de la lumière dans les milieux diaphanes Mém. Soc. Arcueil 1809 2 300 342 and Poisson (footnote 35); his remarks on the integrals relate to Poisson's definitions of internal and external conductivity noted in footnote 66.
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• See my and Ravetz's Joseph Fourier 1768–1830… Cambridge, Mass. 1972 293 293
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• On this committee, see Fourcy Histoire de l'Ecole Polytechnique Paris 1828 364 365 Evidence of de Prony's diligence as a graduation examiner is seen in, for example, the mounds of pertinent files for various years between 1819 and 1828 in ENPC, ms. 2806. de Prony's Nachlass is held among the ENPC archives. There is also a volume of letters for the family at BI, ms. f.f.n.a. 15778; and sets of the cadastral survey tables at BI, mss. 1496–1514 and at the Paris Observatoire.
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• 1826 . EP , box draft in EN PC, ms. 2806. Both manuscripts are holograph.
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• de Prony's concern for this topic is manifest, for example, in his Note sur l'application de la théorie des solutions particulières des équations différentielles … JEP 1810 4 1 49 58 cah. 10 Some years after this report he reprinted the article in Ann. EN PC, (1) 8 (1834), 97–108.
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• Difference calculus was a principal concern of de Prony's own teaching at the school from the start (see his Suite des leçons d'analyse JEP 1796 1 1 1 23 cah. 2 cah. 3, 209–273; cah. 4, 459–569 (also in his Méthode directe et inverse des différences … (1796, Paris), 31–53, 107–282)). The rest of the reprint (pp. 54–106) was taken up with a second showing of his ‘Essai expérimental et analytique sur les lois de la dilatabilité des fluides élastiques …’, JEP, (1) 1 (1796), cah. 2, 24–76, where he applied difference calculus to a physical theory.
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• I suppose that de Prony was concerned here to derive the expression for (ds)2 in polar coordinates by applying differentials directly to the coordinate transformation rather than by using the complex variable form of the transformation and bringing in limits. Cauchy did give a real-variable argument in his lectures (although it is not clear whether he is using the differential in a traditional form or in his own, limit-oriented, sense); and he also offered the complex-variable version as a shorter proof (see lecture 12 of his Leçons sur les applications du calcul infinitésimal à la géométrie Paris 1826 1 (with vol. 2 (1828), also in Oeuvres, ser. 2, vol. 5)).
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• I presume that de Prony had in mind Euler's theory of the translation and rotation of a rigid body, handled in Poinsotian terms of forces and couples (see Poinsot's Elémens de statique , 1st ed. Paris 1803 ch. 1
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• 1827 . EP , box (holograph). Two days later a proposal was accepted from the Conseil d'Instruction to stop verbal interrogations of the students in the presence of a graduation examiner, as the students did not like it (ibid.).
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• Cauchy . 1826 . Leçons sur les applications du calcul infinitésimal à la géométrie Vol. 1 , Paris vol. 1
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• As far as I know, Cauchy never published a proof of the principle of virtual velocities; but his lecture notes on mechanics Mémoire sur le calcul différentiel et le calcul des variations, présentant le résumé de ces deux calculs AS, dossier personnel for Cauchy 36 36 which deal with linear moments and the resolution of forces), could lead to an intuitive proof along the lines that if force Fr makes an angle ur with a given direction, which is displaced by an amount dp when the equilibrate system {Fr } of forces is disturbed, then from the equilibrium condition the principle follows, in the form de Prony would have liked a proof like that, for he argued in such a way in his own lectures at the EP (see, for example, (footnote 9), 35–39).
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• See EP, Rapport sur la situation de l'Ecole Polytechnique and text
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• de Prony's ‘Mécanique philosophique’ seems to have been designated as cahiers 7–10 of JEP. Eventually only the first three parts appeared, as cahier 8 bis (see Mécanique philosophique … JEP 1799–1800 1 iii vii cah. 8 bis 1–479, and the original cahiers were assigned to other material. Soon afterwards he published a complete, though abridged, version of his mechanics teaching, under the modest title Plan raisonné de la partie de l'ensignment de l'Ecole Polytechnique, qui a pour objet l'équilibre et le mouvement des corps (1800–1801, Paris). He also published various later sets of notes; one is cited in footnote 89.
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• I recall that de Prony was the Director of the EN PC
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• EN PC , ms. 2806 (holograph)
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• 1789 . Nova acta Acad. Sci. Petrop. , 7 : 191 – 204 . publ. 1793 (also in Opera omnia, ser. 2, vol. 9, pp. 387–398). If P, Q and R are the torques of a system of forces with respect to the axes of a rectangular coordinate system, then the torque M with respect to an axis through the origin with direction cosines (p, q, r) is given by the linear combination. de Prony praised this theorem highly in his (footnote 9), 110, and gave a trigonometrical proof in a rare pamphlet Démonstration d'un théorème sur la composition des moments des forces (1804, Paris), published by his EN PC. I use the word ‘torque’ to avoid the confusing use of ‘moment’ of that time to cover both moment and torque.
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• Laplace , P.S. 1798 . Sur la détermination d'un plan … . JEP , 2 ( 1 ) : 155 – 159 . cah. 5 (also in Oeuvres complètes, vol. 14, 3–7). In terms of the notation of the preceding footnote, the plane has (P, Q, R) as direction ratios, when M is maximal.
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• Poinsot . 1803 . Elémens de statique , 1st ed. Paris At the time of de Prony's note, Poinsot and Poisson held a badtempered exchange in Ferrusac's Bulletin on Euler's theorem, Laplace's version and its originality, and the phrase ‘composition of moments’ used to describe such theory (S. D. Poisson, ‘Note sur la composition des moments’, Bull. univ. sci. ind., sci. math. phys., 7 (1827), 357–358, 8 (1828), 338–339; L. Poinsot, ‘Note de M. Poinsot …’, 9 (1828), 74–77 (see also his ‘Mémoire sur la composition des moments en mécanique’, Mém. AS, 7 (1827), 556–568)).
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• In addition to Cauchy's lecture notes (footnote 43) on mechanics, four papers in Exercices de mathématiques 1826 1 (also in Oeuvres, ser. 2, vol. 6) deal explicitly with linear moments. Cauchy attributed one of his results to Coriolis; but Poinsot pointed out its presence in his own 1806 paper (footnote 13), and commented sarcastically on Cauchy's terminology (‘Note de M. Poinsot …’, Bull. univ. sci. ind., sci. math. phys., 7 (1827), 224–226). Cauchy responded by discussing an edition of Poinsot's Statique in which the paper was not reproduced (see footnote 13) and claiming his own theory to be different, a remark which surprised the editor of the Bulletin (Sturm, I believe) in one of his critical footnotes to Cauchy's response (‘Note de M. Cauchy’, ibid., 333–337 (also in Oeuvres, ser. 2, vol. 15, pp. 138–140)). This dispute interlocks with the one described in footnote 85.
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• 1828 . EP , box (copyist); draft in EN PC, ms. 2806 (holograph), where the file also contains Cauchy's syllabus for the year written in his own hand (it is, of course, printed in the EP Programme (footnote 6) for 1827–1828).
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• ‘Those students who are destined for a career in teaching and science must devote their late nights to the study of the Mécanique analytique and the Mécanique céleste’ de Prony R. Sommaire des leçons sur le mouvement des corps solides … Paris 1809 9 9 lectures 31–33
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• A. M. Legendre to Treuttel and Wurtz, seemingly concerning a proposed new edition of his Eléments de géométrie: le goût des études mathématiques sérieuses se refroidit de plus en plus dans notre pays, et s'échauffe au contraire dans les pays étrangers, en telle sorte que la supériorité passera de leur côté si elle n'y est déjà Smith Collection Columbia University New York
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• Especially Ben-David J. The rise and decline of France as a scientific centre Minerva 1970 8 160 179 (who says nothing about the engineering component of French science, and who on p. 166 lays more emphasis on the Collège de France than the EP!).
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• See my Mathematical physics in France, 1800–1840: knowledge, activity and historiography Mathematical perspectives: essays on mathematics and its historical development Dauben J.W. New York 1981 120 125 these developments are badly in need of research. On an aspect of the situation at the EP after 1830, see also footnote 99 below. The bottom third of Table 1 lists the principal members of a distinguished new generation. The 1830s and early 1840s saw the emergence of further figures, of both types indicated in Table 1: Bertrand, Brassine, Bravais, Catalan, Chasles, Delauney, Leverrier, Pontécoulant; and Combes, Didion, Morin, Pambour, Piobert, Saint-Venant.
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• 1829 . EP , box (copyist); draft in EN PC, ms. 2806 (holograph).
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• Cauchy , A.L. 1829 . Leçons sur le calcul différentiel Paris (also in Oeuvres, ser. 2, vol. 4, 263–609).
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• Lacroix , S.F. 1810–1819 . Traité du calcul différentiel et du calcul intégral , 2nd ed. Paris 3 vols. his Traité élémentaire on the calculus appeared in its fourth edition in 1828. S. D. Poisson, Traité de mécanique (1st ed. 2 vols., 1811, Paris); the second edition did not appear until 1833. Lacroix's calculus tends to favour Lagrange's approach, with some role for differentials. Poisson uses differentials extensively in both editions of his Traité (to the protest of J. J. V. Guilloud, Examen critique de la doctrine des infiniment petits, exposée par M. Poisson … (1836, Paris)). de Prony's recommendation here may thus be interpreted as an insult to Cauchy. In view of de Prony's insistence on printed lecture notes for the EP, it is rather strange that he omitted to mention here Poisson's 500-page Cours de mécanique, published in 1810 (or so it appears from documents in EP, boxes 1809 (2) and 1810 (1): copy in EP library, and part also in AS, Ampère, ch. 129). de Prony's oversight has proved to be prophetic, for this work, which was revised into the first edition of the Traité, has been entirely overlooked by Poisson scholars.
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• The status of the graduate examiners had been reduced after the Restoration in 1816, in that three positions had been given to peers of the realm; even the Governorship was among the Jobs for the Boys (compare footnote 55). On such matters see D. F. J. Arago (who was Governor after the July 1830 revolution until the November reform) Réponse de M. Arago à M. Aimé-Martin … J. gén. civ. 1831 10 98 109 (compare Oeuvres, vol. 12, pp. 634–692).
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• See, for example Pinkney D. The French Revolution of 1830 Princeton 1972 Cauchy never taught again at the EP after his return to Paris in the late 1830s.
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• The syllabi printed in the EP Programme (footnote 6) in the 1830s show no essential changes from Cauchy's. This is rather surprising, as his teaching was taken over by Coriolis and his chair assigned to Navier, both of whom were engineering savants (see Table 1), and exemplifies well the uncertainty over policy. The continuing disagreements over the nature and role of the EP are well illustrated in the controversy between de Chambray G. De l'Ecole Polytechnique Paris 1836 (reprinted in his Oeuvres (5 vols., 1839, Paris)) and Y. D. E. Bugnot, De l'Ecole Polytechnique (1837, Paris).
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