Inculcating the Spirit

Academies

It is a commonplace to see organized science as "entirely recast under the dominion" of the scientific academies and societies of the 18th century.^[19] Scientific academies and societies played a significant role in establishing the importance and extending the application of mathematical or quantitative methods. Much recent literature addresses questions of the founding and organization of academies and societies, and may thus enlighten us about the 18th-century disciplinary map. It may also contain clues about the place of mathematics and the mathematically adept in these institutions and about the ways in which academic prestige or authority could encourage the use of mathematics. Recent studies look at academies and societies in general^[20] and in particular.^[21] Studies of the use of mathematical

[19] James E. McClellan III, Science reorganized: Scientific societies in the 18th century (New York: Columbia University Press, 1985), xix.

[20] Ibid.; Daniel Roche, Le siècle des lumières en province: Académies et académiciens provinciaux, 1680–1789 , 2 vols. (Paris: Ecole des hautes etudes en sciences sociales, Mouton, 1978); Henry E. Lowood, Patriotism, profit, and the promotion of science in the German enlightenment: The economic and scientific societies, 1760–1815 (Ph.D. dissertation, University of California, Berkeley, 1987; DAI 49/06A, 1563).

[21] David M. Griffiths, "The early years of the Petersburg Academy of sciences as reflected in recent Soviet literature," Canadian-American Slavic studies, 14 (1980), 436–45; Elizabeth R. Kindleberger, The Société Royal des Sciences de Montpellier, 1706–1793 (Ph.D. dissertation, Johns Hopkins University, 1979; DAI 40/05A, 2816); Roy S. Porter, "Science, provincial culture, and public opinion in Enlightenment England," British journal for eighteenth-century studies, 3 (1980), 2–46; Roger L. Emerson, "The Philosophical Society of Edinburgh, 1748–1768," British journal of history of science, 14 (1981), 133–76; Rhoda Rappaport, "The liberties of the Paris Academy of Sciences, 1716–1785," in Harry Woolf, ed., The analytic spirit: Essays in the history of science in honor of Henry Guerlac (Ithaca, NY: Cornell University Press, 1981), 225–53; James R. Hansen, Scientific fellowship in a Swiss community enlightenment: A history of Zurich's Physical Society, 1746–1798 (Ph.D. dissertation, Ohio State University, 1981; DAI 42/05A, 2269); Ludwig Hammermayer, Geschichte der Bayerischen Akademie der Wissenschaften, 1759–1807 , 2 vols. (Munich: Beck, 1983); Vincenzo Ferrone, "Tecnocrati militari e scienziati nel Piemonte dell'Antico Regime: Alle origini della Reale Accademia delle Scienze di Torino," Rivista di storia italiana, 96 (1984), 414–509; James E. McClellan III, "The Académie Royale des Sciences, 1699–1793: A statistical portrait," Isis, 72 (1981), 541–76; Ugo Baldini, "L'attività scientifica nelle accademie lombarde del Settecento," in Economia, istituzioni, cultura in Lombardia nell'età di Maria Teresa , 3 vols. (Bologna: Il Mulino, 1982), 2, 503–32; Valeria Molla Losito, "La Società Patriottica di Milano (1776–1796)," in ibid., 3, 1039–56; Andreas Kleinert, "Mathematik und anorganische Naturwissenschaften," in Rudolf Vierhaus, ed., Wissenschaften im Zeitalter der Aufklärung (Göttingen: Vendenhoeck & Ruprecht, 1985), 218–48, esp. section IV; Michel Taillefer, Une académie interprète des Lumières: L'Académie des Sciences, Inscriptions, et Belles-Lettres de Toulouse au XVIIIe siècle (Paris: CNRS, 1984).

methods in the 18th century might follow the lead of works that discuss the place of particular sciences in specific academic contexts.^[22]

Studies that examine the role of individuals in academies and hence in the life of science, especially in conjunction with archival or edited correspondence, promise useful information. Historians have begun, for example, to trace the powerful academic influence of Leonhard Euler.^[23] Analysis of the éloges of the Paris Academy of Sciences yields insights both about its perpetual secretaries, including Fontenelle and Condorcet, and about the scientific ideologies and standards they promoted.^[24] The publications and prizes of academies and societies served to spread the quantifying spirit, and deserve more attention.

[22] E.g., E.P. Ozhigova, Matematika v Peterburgskoy Akademii Nauk v kontse XVIII–pervoy polovine XIX veka (Leningrad: Nauka, 1980); Jacqueline Giroux, "Genèse de la météorologie scientifique dans les milieux de l'Académie de Dijon au XVIIIe siècle," Académie des sciences, arts, et belles-lettres (Dijon), Mémoires, 125 (1981–2), 135–55; Dhombres, "Mathématisation" (note 18). Cf. Theodore S. Feldman, The history of meteorology, 1750–1800: A study in the quantification of experimental physics (Ph.D. dissertation, University of California, Berkeley, 1983, DAI 43/05A, 922); and Karl Hufbauer, The formation of the German chemical community, 1720–1795 (Berkeley: University of California Press, 1982).

[23] Wolfgang Knobloch, ed., Leonhard Eulers Wirken an der Berliner Akademie der Wissenschaften, 1741–1766: Specialinventar Regesten der Euler-Documente aus dem Zentralen Archiv der Akademie der Wissenschaften der DDR (Berlin: Akademie-Verlag, 1974); Leonhard Euler, 1707–1783: Beiträge zu Leben und Werk (Basel: Birkhäuser, 1983), including Judith Kh. Kopelevic, "L. Euler und die Petersburger Akademie," 373–84; Rüdiger Thiele, Leonhard Euler (Leipzig: BSB B.G. Teubner Verlagsgesellschaft, 1982).

[24] Paul, Science and immortality (note 11).

Education

Educational institutions and strategies also played a role. The significance of science, especially mathematics, in the technical training establishment in France was sketched in older works that remain useful.^[25] Such works have recently been supplemented by studies of the royal engineering corps and military school in France;^[26] a comparative perspective is afforded by analysis of military and engineering training in old and New Spain.^[27] All need to be read against the evidence assembled in the work of Charles Gillispie,^[28] in biographical dictionaries of 18th-century engineers,^[29] in documentary histories of engineering,^[30] and in general histories of education.^[31] The roles played by academicians in beefing up the technical curricula bear more scrutiny.^[32] Data and studies of the teaching of mathematics and

[25] E.g., René Taton, ed., Enseignement et diffusion des sciences en France au XVIIIe siècle , recently republished in six parts (Paris: Hermann, 1986); the studies by François de Dainville collected in L'éducation des jésuites, 16e–18e siècles (Paris: Minuit, 1978). For England, cf. Geoffrey Howson, A history of mathematics education in England (Cambridge: Cambridge University Press, 1982).

[26] Anne Blanchard, Les ingénieurs du "Roy" de Louis XIV à Louis XVI: Etude du Corps des Fortifications , Collection du Centre d'histoire militaire et d'etudes de defense nationale de Montepellier, 9 (Montpellier, 1979); Jean-Claude David, "Grimm, Lalande et le quart de cercle de l'Ecole Royale Militaire," Dix-huitième siècle, 14 (1982), 277–87; J.-F. Pernot, "Une important contribution à la connaissance des ingénieurs d'Ancien Régime," Revue d'histoire des sciences, 35 (1982), 275–80.

[27] José Omar Moncada Maya, "Una aproximación al estudio del Cuerpo de Ingenieros Militares en la Nueva España," Quipu, 3 (1986), 55–66; Antonio Lafuente and José Luis Peset, "Las academias militares y la inversión en ciencia en la España ilustrada (1750–1760)," Dynamis , 2 (1982), 193–209.

[28] C.C. Gillispie, Science and polity in France at the end of the Old Regime (Princeton: Princeton University Press, 1980).

[29] Anne Blanchard's massive Dictionnaire des ingénieurs militaires, 1691–1791 (Montpellier: CNRS, 1981); Los ingenieros militares en España siglo XVIII: Repertorio biográfico e inventario de su labor cientifica y espacial (Barcelona: University Barcelona, 1983).

[30] Paul K. Walker, Engineers of independence: A documentary history of the Army Engineers in the American Revolution, 1775–1783 (Washington: Historical Division, Office of the Chief of Engineers, 1981).

[31] L.W.B. Brockliss, French higher education in the 17th and 18th centuries: A cultural history (Oxford: Clarendon Press, 1987), esp. 337–443 on natural sciences.

[32] Cf. Ferrone, "Tecnocrati militari e scienziati" (note 21), and the works cited in note 38 below. Cf. Thérèse Charmasson, L'enseignement technique de la Revolution à nos jours. Textes officiels avec introduction, notes et annexes (Paris: Institut national de recherche pedagogique, 1987).

science in colleges and universities offer possibilities for comparison.^[33]

The mathematical content, rhetoric, and appeal of popular courses and self-help books also helped to secure a place for quantification in popular culture. Studies of public courses and of the marketing of science thus warrant further investigation.^[34] So too do mathematical periodicals, textbooks for the self-taught, and the corps of mathematical author/practitioners.^[35]

For the end of the century, consideration of education and of the French Revolution raises twin issues of continuity and reform, both

[33] Hanspeter Marti, Philosophische Dissertationen deutscher Universitäten, 1660–1750: Eine Auswahlbibliographie (Munich: Saur, 1982); Karl A.F. Fischer, "Jesuiten-Mathematiker in der französischen und italienischen Assistenz bis 1762 bzw. 1773," Archivum historicum Societatis Jesu , 52 (1983), 52–92; Marie-Madeleine Compère and Dominique Julia, eds., Les Collèges français, 16e–18e siècles (Paris: INRP and CNRS, 1984); Ugo Baldini, "L'insegnamento fisico-matematico a Pavia alle soglie dell'età teresiana," in Economia, istituzioni, cultura in Lombardia, 3 (note 21), 863–86; Luigi Belloni, "L'insegnamento delle scienze sperimentali a Milano," in ibid., 2, 441–9.

[34] John S. Reid, "Late 18th-century adult education in the sciences at Aberdeen: The natural philosophy classes of Professor Patrick Copland," in Jennifer J. Carter and Joan H. Pittock, eds., Aberdeen and the Englightenment (Aberdeen: Aberdeen University Press, 1987), 168–79; Gad Freudenthal, "Littérature et sciences de la nature en France au début du XVIIIe siècle: Pierre Polinière, l'introduction de l'enseignement de la physique expérimentale, l'Université de Paris, et l'Arrêt burlesque de Boileau," Revue de synthèse, 101 (1980), 267–95; John R. Millburn, "The London evening courses of Benjamin Martin and James Ferguson: 18th-century lectures on experimental philosophy," Annals of science, 40 (1983), 437–55, and Retailer of the sciences: Benjamin Martin's scientific instrument catalogues, 1756–1782 (London: Vade-Mecum, 1986); Simon Schaffer, "Natural philosophy and public spectacle in the 18th century," History of science, 21 (1983), 1–43; Alexander Rüger, "Populäre Naturwissenschaft in Nürnberg am Ende des 18. Jahrhunderts: Reisende Experimentatoren, öffentliche Vorlesungen und physikalisches Spielzeug," Berichte zur Wissenschaftsgeschichte, 5 (1982), 173–91. Cf. J.L. Heilbron, Physics at the Royal Society during Newton's presidency (Los Angeles: William Andrews Clark Memorial Library, 1983); and Robin E. Rider, The show of science (Berkeley: The Bancroft Library, 1983).

[35] Ruth Wallis and Peter Wallis, "Female philomaths," Historia mathematica , 7 (1980), 57–64; Robert R. Bataille, "Robert Heath, Thomas Cowper, and 18th-century mathematical journalism," Bibliographical Society of America, Papers, 81 (1987), 339–43; Dhombres, "Mathématisation" (note 18), and his account of scientific books in Robert Darnton and Daniel Roche, eds., Revolution in print: The press in France, 1775–1800 (Berkeley: University of California Press, 1989); R.V. Wallis and P.J. Wallis, Biobibliography of British mathematics and its applications , Part 2: 1701–1760 (Newcastle upon Tyne: Project for Historical Biobibliography, 1986).

pertinent to the place of mathematics in a revolutionary curriculum.^[36] Numerous studies unravel the organization and ideology of new institutions and trace their teachers, students, and lessons.^[37]