BIBLIOGRAPHICAL AFTERWORD

By Robin E. Rider

The intent of this afterword is to suggest some sources and directions that might prove helpful in further investigation of what we call the quantifying spirit. To keep the task within bounds, the emphasis is on publications of the 1980s. The essays in or into historiography in The ferment of knowledge. Studies in the historiography of eighteenth-century science afford a convenient point of departure. Its editors hoped that a historiographical approach would gather together the "detailed and discrete publications" that chronicle the complexity of 18th-century science—complexity that bedevils attempts to craft synthetic accounts of 18th-century knowledge about nature. To that end, they assembled a dozen detailed, not always discrete responses to the historiographic challenge, a challenge individual contributors defined in quite different ways.^[1]

Several essays in The ferment of knowledge speak directly to themes of the present volume. Henk Bos, for example, underscores the "direct and intense interaction" of mathematics with its applications in the 18th century.^[2] Simon Schaffer discusses, among other topics, Buffon's view of "natural philosophy as the discourse of order," drawing our attention to Foucault's distinction between a "general science of order" and mathematization.^[3] In making frequent reference to a study of the méthode numérique in 18th-century medicine, W. Bynum alerts us to quantification of medical experience

[1] G.S. Rousseau and Roy Porter, eds., The ferment of knowledge. Studies in the historiography of eighteenth-century science (Cambridge: Cambridge University Press, 1980), quotation on 5.

[2] H.J.M. Bos, "Mathematics and rational mechanics," in ibid., 327–56, on 353.

[3] Simon Schaffer, "Natural philosophy," in ibid., 55–92, on 85, footnote 89 on 89 for Foucault.

from the 1760s on.^[4] D.S.L. Cardwell highlights the significance of the "quantification of power" in 18th-century technology; for Cardwell, the roots of the Smeatonian method—"rational, systematic and comprehensive," aimed at "testable and preferably quantitative" answers—likely lie in Newtonianism.^[5] Roy Porter contends that quantification proved of dubious value "for explicating the environment" of the terraqueous globe, but he sets considerable store by the 18th-century view of nature as economical, "uniform, organized and integrative." He also underscores the challenge posed by "the growth of knowledge"—"the sheer quantity of newly available information" to be managed, lest chaos reign.^[6] In Rom Harré's discussion of scientific epistemology, the model of mathematical thought makes several appearances: Locke's views on certainty, seen as grounded in geometry; d'Alembert's adherence to the Cartesian doctrine of "mathematical abstractionism"; Adam Smith's "philosophical economics," aimed at optimizing the quantity of happiness.^[7] Maurice Crosland, in his stress on Lavoisier and the chemical revolution, plays familiar themes of classification and measurement.^[8]

J.L. Heilbron's essay offers the clearest invocation of the quantifying spirit. Heilbron reasons from the development of 18th-century electricity to a periodization of experimental natural philosophy in which quantification plays a crucial role. In the emphasis on experimental physics in the latter part of the century, in the preference for an instrumentalist approach stripping away metaphysical niceties, we hear tunes sounded in several chapters of the present volume.^[9]

The editors of The ferment of knowledge also asked their contributors to mark out fruitful directions for further research. From the desiderata listed by the contributors emerge several common concerns relevant to the influence of mathematics and the uses of quantifica-

[4] W.F. Bynum, "Health, disease and medical care," in ibid., 211–55, on 230.

[5] D.S.L. Cardwell, "Science, technology and industry," in ibid., 449–84, on 466, 470.

[6] Roy Porter, "The terraqueous globe," in ibid., 282–324, on 320, 314, 305, 309.

[7] Rom Harré, "Knowlege," in ibid., 11–54, on 21, 46, 34.

[8] Maurice Crosland, "Chemistry and the chemical revolution," in ibid., 389–416.

[9] J.L. Heilbron, "Experimental natural philosophy," in ibid., 357–88.

tion. Many of the authors urge that the disciplinary map be redrawn along lines more faithful to 18th-century categories of knowledge; most request greater attention to social, political, or economic context. Several recommend listening carefully to language, to the forms of discourse. All find plenty for historians to do.

The sheer quantity of scholarship on 18th-century science published in the past decade or so speaks to needs and opportunities in this field, and tempts quantification of the art of bibliography. Beginning with the Isis Critical bibliography for 1981, the 18th century broke free, as a chronological classification, from the 17th. Though the total number of entries in the CB s has varied considerably for the 1980s (and though the numbers are softened by individual decisions regarding compilations of articles), the market share for the 18th century has held fairly steady at 9 to 10 percent of all CB entries, with a peak of 397 entries; annual figures for the 17th century have shown more variation. If we take into account all the entries in the Cumulative bibliography for the years 1976–85, we find that entries for 18th-century topics outnumber those for thee 17th century by about one-third (2,008 versus 1,572). Anniversaries of late 18th-century events have helped to swell the totals. Just as the 250th anniversary of Newton's death proved the occasion for another round of scholarly attention to his work and influence, the 200th anniversaries of scientific or political events or of the deaths of other 18th-century scientific figures have recently triggered reassessments, new editions of classic works, and bibliographies deserving of attention.^[10] In what follows, the stress is put on other manifestations of the quantifying spirit and the ways in which the message of quantification was spread.

[10] See, for example, Dix-huitième siècle, 16 (1984), about d'Alembert; A.T. Grigorian, A.P. Yushkevich, and B.D. Kovalev, "In memoriam Daniel Bernoulli," NTM, 19:2 (1982), 1-13; Ashot T. Grigorian and Boris D. Kovalev, Daniil Bernulli, 1700–1782 (Moscow: Nauka, 1981); Leonhard Euler, 1707–1783: Beiträge zu Leben und Werk (Basel: Birkhäuser, 1983); Arthur Donovan, ed., The Chemical Revolution: Essays in reinterpretation , in Osiris, 4 (1988); Ambix, 36:1 (March 1989), primarily about Lavoisier and the chemical revolution. Cf. note 36.

Other Expressions of the Spirit

The opinions of Fontenelle are frequently trotted out in characterizations of the Englightenment. Fontenelle commended the esprit géométrique for its promise of certainty and rationality, which might improve polity, morality, literature, and oratory as it had enriched astronomy and mechanics.^[11] By the end of the 18th century, a wealth of treatises and textbooks had praised the merits of mathematics and the solidity of reasoning in Euclidean geometry, often in terms borrowed from the previous century. Recent scholarship has pointed to John Arbuthnot's arguments in favor of the utility of mathematics,^[12] the appeal of the axiomatic approach and the persistence of Cartesian methods as mixed with mathematics,^[13] and the wide-ranging

[11] Thomas Hankins, Science and the Enlightenment (Cambridge: Cambridge University Press, 1985), 2. Cf. Charles B. Paul, Science and immortality: The éloges of the Paris Academy of Sciences (1699–1791) (Berkeley: University of California Press, 1980); Alain Niderst, "Fontenelle et la science de son temps," Studies on Voltaire and the eighteenth century, 216 (1983), 323–4; Birgit Fenner, "Vernünftige Skepsis—skeptische Vernunft: Fontenelle und die Anfänge der Aufklärung," Germanisch-Romanische Monatsschrift, 32 (1982), 156–73.

[12] Eddie Shoesmith, "The continental controversy over Arbuthnot's argument for divine providence," Historia mathematica, 14 (1987), 133–46; Richard Olson, "Tory–High Church opposition to science and scientism in the 18th century: The works of John Arbuthnot, Jonathan Swift, and Samuel Johnson," in John G. Burke, ed., The uses of science in the age of Newton (Berkeley: University of California Press, 1983), 171–204.

[13] Michael Heyd, Between orthodoxy and the Enlightenment: Jean-Robert Chouet and the introduction of Cartesian science in the Academy of Geneva, International archives of the history of ideas, 96 (The Hague: Nijhoff; Jerusalem: Magnes Press, 1982); Gereon Wolters, Basis und Deduktion: Studien zur Entstehung und Bedeutung der Theorie der axiomatischen Methode bei J.H. Lambert (1728–1777), Quellen und Studien zur Philosophie, 15 (Berlin: de Gruyter, 1980); C. Hakfoort, "Christian Wolff tussen Cartesianen en Newtonianen," Tijdschrift voor de geschiedenis der geneeskunde, natuurwetenschappen, wiskunde en techniek, 5 (1982), 27–38; Jean Dhombres, "Un style axiomatique dans l'écriture de la physique mathématique au 18ème siècle: Daniel Bernoulli et la composition des forces," Sciences et techniques en perspective, 11 (1986–7), 1–-68; Daniel Klein, "Deductive economic methodology in the French Enlightenment: Condillac and Destutt de Tracy," History of political economy, 17 (1985), 51–71; Wolfgang Röd, "Descartes dans la philosophie universitaire allemande du XVIIIe siècle," Etudes philosophiques , 1985, 161–73; Pierre Costabel, "Euler lecteur de Descartes," Dix–huitième siècle, 18 (1986), 281–8; Mariafranca Spallanzani, "Descartes dans l'Encyclopédie: La méthode," Recherches sur le XVIIème siècle, 8 (1986), 1037–25; cf. Spallanzani, "Notes sur le cartésianisme dans l'Encyclopédie," Studies on Voltaire and the eighteenth century, 216 (1983), 326–7.

influence of what one author calls the mathematical method-model.^[14]

What was reasonable or certain in the 17th and 18th centuries was intimately bound up with questions of probability and risk, in contexts ranging from law to morality, economics to public health. The richness of the analysis and examples in recent studies on probability will warrant careful attention in subsequent exploration of the esprit géométrique and the quantifying spirit.^[15] As the 18th-century controversy over inoculation against smallpox makes clear, the stakes could be high in disputes over the validity of quantitative arguments.^[16]

[14] Hans-Jürgen Engfer, Philosophie als Analysis: Studien zur Entwicklung philosophischer Analysiskonzeptionen unter dem Einfluss mathematischer Methodenmodelle im 17. um frühen 18. Jahrhundert (Stuttgart-Bad Cannstatt: Frommann-Holzboog, 1982). For Wolff's influence and the ways in which he built on 17th-century systèmes , see Sonia Carboncini, "L'Encyclopédie et Christian Wolff: A propos de quelques articles anonymes," Etudes philosophiques , 1987, 489–504; Hakfoort, "Christian Wolff tussen Cartesianen en Newtonianen" (note 13); Werner Schneiders, ed., Christian Wolff, 1679–1754: Interpretation zu seiner Philosophie und deren Wirkung. Mit einer Bibliographie der Wolff-Literatur, (Hamburg: Meiner, 1983); Röd, "Descartes dans la philosophie universitaire allemande"; and Fabio Todesco, "Dal 'calcolo logico' alla 'riforma della metafisica': Johann Heinrich Lambert tra Wolff e Locke," Rivista di storia della filosofia, 77 (1986), 337–58.

[15] Lorraine J. Daston, "Probabilistic expectation and rationality in classical probability theory," Historia mathematica, 7 (1980), 234–60, "Mathematical probability and the reasonable man of the 18th century," in History and philosophy of science: Selected papers , ed. Joseph W. Dauben and Virginia Staudt Sexton (New York: New York Academy of Sciences, 1983), 57–62, and Classical probability in the Enlightenment (Princeton: Princeton University Press, 1988); Lorenz Krüger, Lorraine J. Daston, and Michael Heidelberger, eds., The probabilistic revolution , 2 vols. (Cambridge: MIT Press, 1987), esp. 1: Ideas in history ; Luigi Cataldi Madonna, "Wahrscheinlichkeit und wahrscheinliches Wissen in der Philosophie Christian Wolffs," Studia Leibnitiana, 19 (1987), 2–40; Douglas Lane Patey, Probability and literary form: Philosophic theory and literary practice in the Augustan age (Cambridge: Cambridge University Press, 1984).

[16] The many studies of smallpox and its prevention in the 18th century include Andrea Rusnock, "When counting counts: The reception of quantitative arguments in eighteenth-century England and France" (unpublished paper, History of Science Society meeting, 1989); Jean-Claude David, "À la querelle de l'inoculation en 1763: Trois lettres inédites de Suard et du Chevalier d'Eon," Dix–huitième siècle, 17 (1985), 271–84; Maxine Van de Wetering, "A reconsideration of the inoculation controversy," New England quarterly, 58 (1985), 46–67; Jean-François de Raymond, Querelle de l'inoculation, ou, Préhistoire de la vaccination (Paris: Vrin, 1982); Antoinette S. Emch-Dériaz, "L'inoculation justifiée—or was it?" Eighteenth century life, 7:2 (1982), 65–72. Patricia Cline Cohen, A calculating people: The spread of numeracy in early America (Chicago: University of Chicago Press, 1982) also addresses the issue of smallpox statistics and risks.

Such arguments could still carry weight even when the numbers were soft or when measurement was out of the question, as in discussions of moral arithmetic, meandering rivers, or thermometers for female emotional response, as calibrated from modesty through impudence. Here it is necessary to attend to what quantification promised: useful comparisons whatever the scale, informative models without measurement, precision (clarity, distinctness, intelligibility) rather than a close fit with the real world.^[17]

Although moral barometers scarcely belong to the realm of exact science, comparisons of soft and hard quantification may prove instructive. In particular, it is worthwhile measuring the play of the quantifying spirit in the 18th century against conspicuous accomplishments in the mathematization of science in the 17th century and the successes of mathematical physics in the late 18th and early 19th centuries. The articles in Nature mathematized explore examples of 17th-century exact science that enlightened thinkers subsequently found so persuasive. A recent issue of Revue d'histoire des sciences investigates the "conquest of new territories" by mathematical science between 1780 and 1830. And Jean Dhombres links the achievements of mathématisation with the nature of the French scientific community in the half-century between 1775 and 1825 in another recent article.^[18]

[17] Daston, "The quantification of probability" (unpublished paper, History of Science Society meeting, 1989) and Classical probability in the Enlightenment (note 15); Garland P. Brooks and Sergei K. Aalto, "The rise and fall of moral algebra: Francis Hutcheson and the mathematization of psychology," Journal of the history of the behavioral sciences, 17 (1981), 343–56; Robin E. Rider, Mathematics in the Enlightenment: A study of algebra, 1685–1800 (Ph.D. dissertation, University of California, Berkeley, 1980; DAI 42/01A, 351), esp. chap. 9; Marguerite Carozzi, "From the concept of salient and reentrant angles by Louis Bourguet to Nicolas Desmarest's description of meandering rivers," Archives des sciences (Geneva), 39 (1986), 25–51; Terry Castle, "The female thermometer," Representations, 17 (1987), 1–27. Cf. Mark H. Waymack, Moral philosophy and Newtonianism in the Scottish Enlightenment: A study of the moral philosophies of Gershom Carmichael, Francis Hutcheson, David Hume, and Adam Smith (Ph.D. dissertation, Johns Hopkins, 1986; DAI 48/02A, 413), and a late 17th-century example in Paul McReynolds and Klaus Ludwig, "Christian Thomasius and the origin of psychological rating scales," Isis, 75 (1984), 546–53.

[18] William R. Shea, ed., Nature mathematized: Historical and philosophical case studies in classical modern natural philosophy (Dordrecht: D. Reidel, 1983); Revue d'histoire des sciences, 42:1 (1989), special issue "La mathématisation 1780–1830," quotation on 3; Jean Dhombres, "Mathématisation et communauté scientifique française (1775–1825)," Archives internationales d'histoire des sciences, 36 (1986), 249–93. The papers delivered at the international workshop, "The quantification of scientific concepts in their social context" (Tel Aviv, 1986) also speak to issues of quantification from the 17th century through the late 20th century.

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]

Other Directions

It is in the nature of bibliographical essays to point to topics or directions of research worth pursuing. Out of the diversity of the chapters in this volume on The quantifying spirit , as well as from a

[36] For bibliography, see Ronald J. Caldwell, The era of the French Revolution: A bibliography of the history of western civilization, 1789–1799 , 2 vols. (New York: Garland Pub., 1985) and Aux livres citoyens! (Livry Gargan: Sciences Sociales Export, 1989), reprinted from a special issue of Préfaces , 1989; cf. Samuel F. Scott and Barry Rothaus, eds., Historical dictionary of the French Revolution 1789–1799 (Westport, Conn.: Greenwood Press, 1985). On a pre-revolutionary reform proposal, see Arnold de Lesseux, "L'éducation publique d'après Guyton de Morveau," Académie des sciences, arts, et belles-lettres (Dijon), Mémoires, 123 (1976–8; published 1979), 207–39.

[37] In general, Robert R. Palmer, The improvement of humanity: Education and the French Revolution (Princeton: Princeton University Press, 1985); John Lough, The philosophes and post-revolutionary France (Oxford: Clarendon Press, 1982); Jean Dhombres, "Formation des cadres scientifiques et techniques: La marque des débuts de la Révolution," Institut des recherches marxistes, Cahiers d'histoire, 32 (1988), 189–200; and Janis Langins, La République avait besoin de savants: Les débuts de L'Ecole Polytechnique—L'Ecole Centrale des Travaux Publics et les cours révolutionnaires de l'an III (Paris: Belin, 1987). On the Ecole polytechnique, Terry Shinn, L'Ecole polytechnique: 1794–1914 (Paris: Presses de la Fondation nationale des sciences politiques, 1980); Ambroise Fourcy, Histoire de l'Ecole polytechnique , new ed. (Paris: Belin, 1987); Jean-Pierre Callot with Philippe Journau, Histoire de l'Ecole polytechnique (Paris: Charles Lavauzelle, 1982); Janis Langins, The Ecole Polytechnique (1794–1804): From encyclopaedic school to military institution (Ph.D. dissertation, University of Toronto, 1979; DAI 40/12A, 6396); Ivor Grattan-Guinness, "Euler's mathematics in French science, 1795–1815," in Leonhard Euler, 1707–1783: Beiträge zu Leben und Werk (note 23), 395–408, esp. section 6. On the role of mathematicians in educational reform, Langins, "Sur l'enseignement et les examens à l'Ecole Polytechnique sous la Directoire: À propos d'une lettre inédite de Laplace," Revue d'histoire des sciences, 40 (1987), 145–177; Catherine Kintzler, Condorcet: L'instruction publique et la naissance du citoyen (Paris: Le Sycomore, 1984); Langins, "Une lettre inédite de Fourier sur l'enseignement destiné aux ingénieurs en 1797," Revue d'histoire des sciences, 34 (1981), 193–207; Robin E. Rider, "Poisson and algebra: Against an 18th-century background," Michael Métivier, Pierre Costabel, and Pierre Dugac, eds., Siméon Denis Poisson et la science de son temps (Paris: Ecole polytechnique, 1981), 167–76; Eduard Glas, "On the dynamics of mathematical change in the case of Monge and the French Revolution," Studies in history and philosophy of science, 17 (1986), 249–68.

survey of recent literature on the 18th century, emerge a number of possibilities, which may be collected under headings of economics and polity, discourse, and evidence of opposition.

Economics and Polity

In the discussions (in the "Introductory essay" and chapters 5, 6, 10, 11, and 12) of political arithmetic, economic development and policy, and meteorology, as well as in the work of Keith Baker and Charles Gillispie, we see signposts pointing to economics and polity as loci for the operation of the quantifying spirit. Vital statistics had economic value to tax collectors, conscription agents, and actuaries, and government bureaus and functionaries sought to police health as they managed princely coffers, coal, bread, and trees. The expanding literature on vital statistics and on public medicine in the 18th century thus promises a reasonable return on scholarly investment.^[38]

[38] Studies of medicine and public welfare include, but should scarcely be limited to, Theodore M. Brown, "J.P. Frank's 'Medical police' and its implications for medicalization in America," in Marten de Vries et al., eds., The use and abuse of medicine (New York: Praeger, 1982), 208–18; Othmar Keel, "The politics of health and the institutionalisation of clinical practices in Europe in the second half of the 18th century," in W.F. Bynum and Roy Porter, eds., William Hunter and the 18th-century medical world (Cambridge: Cambridge University Press, 1985); Mary E. Lindemann, Producing policed man: Poor relief, population policies, and medical care in Hamburg, 1750–1806 (Ph.D. dissertation, University of Cincinnati, 1980; DAI 41/10A, 4474); Harvey Mitchell, "Politics in the service of knowledge: The debate over the administration of medicine and welfare in late 18th-century France," Social history, 6 (1981), 185–207; Jean-Pierre Goubert, "The medicalization of French society at the end of the Ancien Régime," in Lloyd G. Stevenson, ed., A celebration of medical history (Baltimore: Johns Hopkins University Press, 1982), 157–79. On vital statistics and demography, see J. Hoock, "Sciences camérales et statistique démographique en Allemagne aux XVIIe et XVIIIe siècles," Annales de démographie historique (1979), 145–55; Jacqueline Hecht, "Johann Peter Süssmilch. Point alpha ou omega de la science démographique naive," ibid. (1979), 101–34; Peter Buck, "People who counted: Political arithmetic in the 18th century," Isis, 73 (1982), 28–45; Thomas R. Forbes, "Births and deaths in a London parish: The record from the registers, 1654–1693 and 1729–1743," Bulletin of the history of medicine, 55 (1981), 371–91; Patricia Cline Cohen, "Death and taxes: The domain of numbers in 18th century popular culture," in Stephen H. Cutcliffe, ed., Science and technology in the 18th century: Essays of the Lawrence Henry Gipson Institute for 18th Century Studies (Bethlehem, Penn.: Gipson Institute, 1984) and her A calculating people (note 16); Pehr Wargentin, den svenska statisikens fader: En minnesskriff me sju originaluppsatser ur Kungl. Svenska Vetenskapsakademiens Handlingar för åren 1754, 1755 samt 1766 (Stockholm: Statistika Centralbyrån, 1983); J. Lecuir, "Deux siècles après: Montyon, véritable auteur des 'Recherches et considérations sur la population de la France' de Moheau," Annales de démographie historique (1979), 195–249; William Coleman, "Inventing demography: Montyon on hygiene and the state," in Everett Mendelsohn, ed., Transformation and tradition in the sciences: Essays in honor of I. Bernard Cohen (Cambridge: Cambridge University Press, 1984), 215–33. On J.S. Mill's skepticism in the face of vital statistics, see Spencer Davis, "Scottish philosophy and political economy," in Donald C. Mell, Jr., et al., eds., Man, God, and nature in the Enlightenment (East Lansing, Mich.: Colleagues Press, 1988).

Cameralism and political economy, as they developed in theory and practice and in local and national settings, should not be ignored,^[39] nor studies of Adam Smith, influences on him, and impact of his ideas.^[40] The economic writings and policies of Physiocrats and Idéologues, especially as they relate to the philosophes and to intellectual movements in the Enlightenment, merit another look with the quantifying spirit in mind.^[41] The economic and political import of

[39] On political economy, Keith Tribe, "University teaching on cameralism in 18th-century Germany," Studi settecenteschi, 7–8 (1985–6), 55–69, and his Governing economy: The reformation of German economic discourse, 1750–1840 (Cambridge and New York: Cambridge University Press, 1988); Terence Hutchison, Before Adam Smith: The emergence of political economy, 1662–1776 (Oxford: Blackwell, 1988); Sergio Cremaschi, Il sistema della ricchezza: Economia politica e problema del metodo in Adam Smith (Milan: Angeli, 1984); Girolamo Imbruglia, "Economia e politica nel De l'esprit di Helvétius," Naples, University, Facoltà di Lettere, Filosofia e Magistero, Annali, 20 (1977–8), 237–81; Hans Erich Bödeker, "Der staatswissenschaftliche Fächersystem im 18. Jahrhundert," in Wissenschaften im Zeitalter der Aufklärung, 143–62; F. Etner, "L'Ancien Régime et le calcul économique," Enconomy and society, 18:3 (1984), special issue on "Aspects de l'économie politique en France au XVIIIe siècle," and his book on "calcul économique" in France. On 18th-century appeals to quantification and classification in social analysis, P.J. Corfield, "Class by name and number in 18th-century Britain," History, 72 (1987), 38–61; Gianni Vaggi, "Social classes and income distribution in 18th-century economics," History of European ideas, 9 (1988), 171–82.

[40] Among them, Andrew S. Skinner, "Adam Smith: Rhetoric and the communication of ideas," in A.W. Coats, ed., Methodological controversy in economics: Historical essays in honor of T.W. Hutchison (Greenwich, Conn.: JAI Press, 1983), 71–88; Donald Winch, "Science and the legislator: Adam Smith and after," Economics journal, 93 (1983), 501–20; M. Dey, Adam Smith and Adam Ferguson: Philosophy, economic change, and class limitations in 18th-century Scotland (Ph.D. dissertation, Aberdeen University, 1985); Cremaschi, Il sistema della ricchezza (note 39); Norriss S. Hetherington, "Isaac Newton's influence on Adam Smith's natural laws in economics," Journal of the history of ideas, 44 (1983), 497–505; Adam Smith, Essays on philosophical subjects, ed. W.P.D. Wightman and J.C. Bryce (Oxford: Clarendon Press, 1980), one in a set of recent scholarly editions of Adam Smith's writings; R.H. Campbell and A.S. Skinner, Adam Smith (London: Croom Helm, 1982); cf. Martha Bolar Lightwood, A selected bibliography of significant works about Adam Smith (Philadelphia: University of Pennsylvania Press, 1984).

[41] Gianni Vaggi, The economics of François Quesnay (Durham, N. Car.: Duke University Press, 1987); Christian Bordes and J. Morange, eds., Turgot, économiste et administrateur (Paris: PUF, [1981]); Marco Minerbi, "I presupposti dell'analisi economica del fisiocratici," in Lezioni sull'illuminismo (Milan: Feltrinelli, 1980); Daniel Klein, "Deductive economic methodology in the French Enlightenment: Condillac and Destutt de Tracy," History of political economy, 17 (1985), 51–71; Stephen F. Gudeman, "Physiocracy: A natural economics," American ethnologist, 7 (1980), 240–58; Leonora Cohen Rosenfield, "La Mettrie and Quesnay, physician-philosophes of the Enlightenment," in Alfred J. Bingham and Virgil W. Topazio, eds., Enlightenment studies in honour of Lester G. Crocker (Oxford: Voltaire Foundation, 1979); cf. Hutchison, Before Adam Smith (note 39).

scientism and the place of mathematics in scientism have relevance as well.^[42]

Discourse

Mathematical metaphors and images frequently found their way into discourse in the 18th century, whatever the topic, and hence illustrate both the cultural appeal of quantification and a means by which the quantification message was reinforced and spread. Studies of language for other scientific fields explore the malleability and power of metaphor, and suggest useful approaches for considering the language of quantification.^[43]

[42] A few titles are Keith Michael Baker, "Scientism at the end of the Old Regime: Reflections on a theme of Professor Charles Gillispie," Minerva, 25 (1987), 21–34; Paul Alkon, "Changing the calendar," Eighteenth-century life, 7:2 (1982), 1–18; Harvey Mitchell, "Politics in the service of knowledge: The debate over the administration of medicine and welfare in late 18th-century France," Social history, 6 (1981), 185–207.

[43] See, for example, Geoffrey Cantor, "Weighing light: The role of metaphor in 18th-century optical discourse," in Andrew E. Benjamin et al., eds., The figural and the literal: Problems of language in the history of science and philosophy, 1630–1800 (Manchester: Manchester University Press, 1986), 124–46; Wilda C. Anderson, Between the library and the laboratory: The language of chemistry in eighteenth-century France (Baltimore and London: Johns Hopkins University Press, 1984); Rhoda Rappaport, "Borrowed words: Problems of vocabulary in 18th-century geology," British journal for the history of science, 15 (1982), 27–44; Imbruglia, "Economia e politica nel De l'esprit di Helvétius" (note 39); Tribe, Governing economy (note 39); Martin Rudwick, "The emergence of a visual language of geology, 1760–1840," History of science, 14 (1976), 149–95; cf. Roger Lewinter, "La quadrature du cercle: Remarques sur Diderot et l'Encyclopédie," Revue de métaphysique et de morale, 89 (1984), 226–31. Cantor speaks of metaphors as "malleable" (142) and claims that they quietly direct research.

Opposition

If there was a quantifying spirit or esprit géométrique in the 18th century, there was surely a critical spirit as well, and the voices raised in favor of rethinking the place and power of mathematics and quantification ought also to be heeded. Buffon's criticism of mathematics and Diderot's quotable doubts about the future of mathematics^[44] speak to the prevailing faith in mathematics and mathematicians.^[45] Even d'Alembert wrote with some skepticism about the "esprit de calcul," which he saw as the dominant "goût de philosophie" in the 18th century.^[46] Tracts that decried the "abuse of mathematics in natural science,"^[47] need to be set against 18th-century pæans in praise of mathematics.

The bibliographical burden can be made more enjoyable by seeing how mathematics and quantification fared in 18th-century scientific satires. Jonathan Swift's Gulliver watched savants labor to extract sunbeams from cucumbers; he heard their scheme for establishing a

[44] In On the interpretation of nature , quoted for example in Ernst Cassirer, The philosophy of the Enlightenment , transl. Fritz C.A. Koelln and James P. Pettegrove (Princeton: Princeton University Press, 1951), 74; cf. Hankins, Science and the Enlightenment (note 11), 169.

[45] On Diderot and mathematics, Jean Dhombres, "Quelques rencontres de Diderot avec les mathématiques," in Anne-Marie Chouillet, ed., Colloque international Diderot (1713–1784) (Paris: Aux Amateurs de Livres, 1985); Robert Morin, Diderot et l'imagination (Paris: Les Belles Lettres, 1987), esp. the chapter on mathematical imagination; Michael Kessler, "A puzzle concerning Diderot's presentation of Saunderson's Palpable arithmetic," Diderot studies, 20 (1981), 159–73; Merle L. Perkins, Diderot and the time-space continuum: His philosophy, aesthetics and politics, Studies on Voltaire and the 18th century, 211 (Oxford: Voltaire Foundation, 1982), esp. chaps. 3–4; Charles Dedeyan, Diderot et la pensée anglaise (Florence: Olschki, 1987), part III; Renate Wahsner, "Das Verhältnis von Mathematik und Physik aus der Sicht von Denis Diderot," NTM, 24 (1987), 13–20; Anne-Marie Chouillet, ed., 1984; L'année Diderot , supplement to Dix-huitième siècle, 17 (1985); and Frederick A. Spear, Bibliographie de Diderot: Repertoire analytique international , Historie des idées et critique littéraire, 187 (Geneva: Droz, 1980), and its supplements.

[46] Encyclopédie, 6 (1756), s.v. "Fluide," quoted in Costabel, "Euler lecteur de Descartes" (note 13), 287. Nonetheless, Costabel considers that it was confidence in mathematics that "profoundly united Euler and d'Alembert," whatever their differences (p. 286). Cf. d'Alembert, Essai d'une nouvelle théorie de la résistance des fluides (Paris: Chez David l'ainé, 1752).

[47] Giuseppe Mosca, Vita di Giovambattista Morgagni. . .con due lettere, l'una intorno all'abuso della matematica nella scienza naturale (Naples: V. Manfredi, 1764).

universal language by abolishing all words; and he talked with an innovative projector in speculative learning. This worthy had secured the services of forty pupils to crank the handles on a frame twenty feet square: it carried a grid of "all of the Words of their language," based on careful computation of the proportions obtaining among the various parts of speech. Commanded first to crank, then to read and record the results, the pupils might thereby generate automatically books on all arts and sciences.^[48] That is not the method by which this book or this essay was composed.

[48] Daryll M. Anderson, Satires of science in the 17th and 18th centuries (Ph.D. dissertation, University of Louisville, 1980; DAI 41/07A, 3114); Olson, "Tory-High Church opposition" (note 12); Brooks and Aalto, "The rise and fall of moral algebra" (note 17); Eric A. Weiss, "Jonathan Swift's computing invention," Annals of the history of computing, 7 (1985), 164–5, which reproduces a portion of chap. 5 of Gulliver's third voyage.