The Measure of All Things

by Ken Alder

  The irony: For the latitude of Paris then and now, see Delambre, Grandeur, 222; Bigourdan, Système métrique, 154.

  “specious” adjustment: Delambre’s comments in AOP E2-9. See also KM, Delambre, Base, 1:484; AOP MS1033b, Anon. [Tranchot?], “Pour Delambre seul,” [c. 1807–9]. Méchain published an abbreviated version of his results for Barcelona; see CT pour l’an XII (Paris, X [1801–2]), 242–43.

  “it is a fact worthy”: Delambre, Base, 2:619; Delambre, “Auszug aus einem Briefe,” 1 February 1808, MC 18 (May 1806): 45–49. For his promise to publish all the data, see Delambre, “Base du système métrique,” CT pour l’an 1808 (1807), 463–66.

  Delambre’s solution: For the deposit of the papers, see Burckhardt, Biot, and Bouvard, “Dépôt des manuscrits à l’Observatoire impérial,” 12 August 1807; and Bouvard, Burckhardt, and Arago, “Dépôt,” 19 September 1810, in Base, 3:698–704. Delambre made the deposit in two lots because he wanted to hold on to some of the material while writing Volume 3 of the Base. However, unlike the published accounts of the second deposit in 1810, the manuscript version notes that Méchain’s letters had been placed under seal. See the original at AOP D5–38, “Dépôt,” 26 September 1810.

  “I have carefully”: AOP E2-9, Delambre’s final comments in Méchain’s notebook.

  “prudent”: Delambre (c. 1810), marginal note to AOP E2-19, Méchain to Delambre, 7 brumaire VII [28 October 1798].

  “in case someone”: AOP E2-19, Méchain to Lalande, 11 ventôse IV [1 March 1796]. For the claim that the double star Mizar-Alcor may have ruined Méchain’s data, see Jean-Nicolas Nicollet, Mémoire sur un nouveau calcul des latitudes de Mont-Jouy . . . lu à l’Académie des sciences le 10 mars 1828 (Paris: Huzard-Courcier, [1828]); also published in CT pour 1831, 58–77. However, Méchain had publicly noted that Mizar was a double star; see Méchain, MC 8 (November 1803): 455. Moreover, the astronomer royal of England, George Airy, later examined Mizar-Alcor through the repeating circle that Méchain had sold to the Milanese, and he found that he was able to resolve the double star; see George Airy, “The Figure of the Earth,” Encyclopaedia Metropolitana (London: Fellowes et al., 1845), 5:230. On the issue of refraction, see Delambre, “Auszug aus einem Briefe,” 1 February 1808, MC 18 (1808): 45–49. Delambre thought that Méchain’s observations of Mizar proved that the Bradley tables were in error; see Delambre, Base, 2:595.

  Delambre now speculated: For Delambre’s speculations, see Delambre, Base, 2:618–19. Méchain himself worried that the Pyrénées would distort his readings; see AOP E2-19, Méchain to Lalande, 3 brumaire IV [25 October 1795]. Méchain’s friend, the German astronomer Baron von Zach, cited Méchain’s experience at Barcelona as evidence of the gravitational pull of mountains; see Franz-Xaver Zach, L’attraction des montagnes et ses effets sur les fils à plomb (Avignon: Seguin, 1814), 19. At the time, some geodesers noted that the tug of the local geography should have created a discrepancy in the opposite direction; see Joseph Rodriguez, “Observations on the Measurement of Three Degrees of the Meridian,” Philosophical Transactions 102 (1812): 344.

  It is of course possible: Some have suggested that Méchain sold his circle to the Milanese astronomers to get rid of the defective apparatus. This seems unlikely. Méchain gave the Milanese astronomers free choice of his his two circles, and they chose the 360-degree old-fashioned circle rather than the 400-degree decimal circle, which is the one Méchain himself had used almost exclusively; see Delambre, Base, 3:503–4. For his sale to the Milanese, see AOAB Cart. 88, Méchain to Oriani, 12 February 1795. For the Catalan conspiracy theory, see Moreu-Rey, Naixement del metre, 91–92.

  This conclusion was not: For Delambre’s defense of the Fontana de Oro data, see Delambre, Base, 2:620. Méchain’s data for Mont-Jouy appear accurate by modern standards. In 1931, a Catalan astronomer measured the latitude of the exact same location on the Mont-Jouy tower, and using eighteenth-century methods of data reduction, found the latitude to be 41°21'44.62", which differs by only 0.44 seconds from the latitude found by Méchain. But without comparable measurements at the Fontana de Oro, which is no longer in business today, this information tells us little about the discrepancy between the two results. See Isadore Polit, cited in A. Ten, “Les expéditions de Méchain et Biot-Arago,” in Figure de la terre du XVIIIe siècle à l’ère spatiale, Henri Lacombe and Pierre Costabel, eds. (Paris: Gauthier-Villars, 1988), 245–65, especially 263.

  Nicollet reanalyzed: For Nicollet’s critique, see Nicollet, Mémoire. See the appreciation of this work in Airy, “Figure.” See the misguided critique of this work in Anon., “Réflexions sur un Mémoire de M. T. [sic] N. Nicollet,” Philosophical Magazine, new series, 5 (1829): 180–88. For eighteenth-century methods of calculating latitude, see Charles Cotter, A History of Nautical Astronomy (New York: Elsevier, 1968), 123–79; also F. Marguet, Histoire générale de la navigation du XVe au XXe siècle (Paris: Société d’Editions Géographiques, Maritimes et Coloniales, 1931).

  He emigrated to America: On arriving in the United States, Nicollet got in touch with Ferdinand Rudolph Hassler, described his geodetic instruments, books, and skills to him, and asked to become part of the U.S. Geodetic Survey; see NYPL Ford Collection, Nicollet to Hassler, 25 July 1832.

  By contrast, Delambre: As Delambre did not measure any stars that passed south of the zenith, it is not possible to verify the accuracy of his results. Interestingly, Delambre was aware that one might balance “north” and “south” stars in this way, but he did not measure any southern stars, nor did he manipulate Méchain’s data in this way, in part because he would have needed to know the declinations with much greater accuracy than was available in contemporary tables, and in part because the two stars he picked were much easier to locate than the stars Méchain selected; see Delambre, Base, 2:186.

  “to all intents”: Delambre, “Lui-même.” Delambre, Tables écliptiques des satellites de Jupiter (Paris: Courcier, 1817). On the savant who discovered an error in those tables, see Anon., “Nécrologie de M. le chevalier Delambre,” Nouvelles annales des voyages 15 (1822): 425–28.

  As to whether: For Delambre’s attitude toward perfection in nature, see UBL MS1872, Delambre to Moll, 21 July 1820. An obituary in Ami de la religion 33 (1822): 111–12, called Delambre an atheist who respected faith, principally because he did not use geodesy or astronomy to challenge publicly the age of earth as stated in the Bible.

  “a precision”: Delambre, Base, 3:103.

  He concluded: For Delambre’s revised meter, see Delambre, Base, 3:135.

  And he noted that the revision: For Delambre’s mnemonics, see Delambre, Base, 3:299.

  “Say what you like”: WL 65667, Delambre to Lindeman, 1 May 1811.

  Legendre’s answer: For Legendre’s discovery, see A.-M. Legendre, Nouvelles méthodes pour la détermination des orbites des comètes avec un supplément, 6 March 1805 (Paris: Courcier, 1806), especially 72–80. Stephen M. Stigler calls the least-squares method the Ford Model-T of statistics; see “Gauss and the Invention of Least Squares” [1981], in Statistics on the Table: The History of Statistical Concepts and Methods (Cambridge: Harvard University Press, 1999), 320. See also V. Parisot, “Adrien-Marie Legendre,” Biographie universelle, Michaud, ed., new ed. (Paris: Desplaces, n.d.), 23:610–15; Elie de Beaumont, “Eloge historique de Adrien-Marie Legendre,” MA 32 (1864): xxxvii-xciv.

  Laplace had introduced: For Laplace’s Ancien Régime methods, see Laplace, “Mémoire sur la figure de la terre” (1783, pub. 1786), in Oeuvres, 11:5–9.

  And in Volume 3: For Delambre’s use of Legendre’s analysis, see Delambre, Base, 3:92.

  Four years after: For Gauss’ interpretation of least squares, see Ch.-Fr. Gauss, Méthodes des moindres carrés, J. Bertrand, trans. (Paris: Mallet-Bachelier, 1855). For evidence of his priority, Gauss claimed to have discussed it with several colleagues—although none of them seem to have understood him. Gauss clearly did have some kind of similar method at an early date because he was able to catch a typ
ographical error in Delambre and Méchain’s geodetic data, published in the Allgemeine Geographische Ephemeriden of 1799–1800. Delambre, in his role as Permanent Secretary of the Academy of Sciences, offered a fair-minded adjudication of this dispute, granting Legendre priority for the publication and the clarity of his presentation, while conceding Gauss’s undeniable contributions; see Delambre, “Analyse des travaux,” MA (1811, pub. 1814): iii-xiii. See Churchill Eisenhart, “The Meaning of Least Squares,” Journal of the Washington Academy of Sciences 54 (1964): 24–33; R. L. Plackett, “The Discovery of the Method of Least Squares,” [1972], in Studies in the History of Statistics and Probability, Maurice Kendall and R. L. Plackett, eds. (London: Griffin, 1977), 2:239–51; Stigler, “Gauss and the Invention of Least Squares,” 320–31. For Gauss’s work on least squares and geodesy, see O. B. Sheynin, “C. F. Gauss and the Theory of Errors,” and “C. F. Gauss and Geodetic Observations,” Archive for History of the Exact Sciences 20 (1979): 21–72; 46 (1994): 253–82. See also Laura Tilling, “The Interpretation of Observational Errors in the Eighteenth and Early Nineteenth Centuries” (Ph.D. diss., Imperial College of Science and Technology, University of London, 1973); Bernard Bru, “Laplace et la critique probabilistique des mesures géodesiques,” in Figure de la terre, Lacombe and Costabel, eds., 223–44; M. Armatte, “Théorie des erreurs, moyenne et loi normale,” in Moyenne, milieu, centre: Histoires et usages, Jacqueline Feldman, Gérard Lagneau and Benjamin Matalon, eds. (Paris: Editions de l’Ecole des Hautes Etudes en Sciences Sociales, 1991), 63–84; Eberhard Knobloch, “Historical Aspects of the Foundations of Error Theory,” in The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations, Javier Echeverria, Andoni Ibarra, and Thomas Mormann, eds. (Berlin: Gruyter, 1992), 253–79.

  Astronomers began to calibrate themselves: For the first French discussion of what later became known as the personal equation, see Delambre and Laplace, “Rapport sur la théorie de Mars, par Lefrançois-Lalande,” ASPV 2 (21 brumaire X [12 November 1801]): 426–29. The first cited instance of the personal equation was the discrepancy between Maskelyne and his assistant in England in 1796, though this was not “explained” for another twenty years. See Stephen M. Stigler, History of Statistics: The Measurement of Uncertainty before 1900 (Cambridge: Harvard University Press, 1986), 240–42. I am indebted for my analysis of the transformation of the astronomical discipline to Simon Schaffer, “Astronomers Mark Time: Discipline and the Personal Equation,” Science in Context 2 (1988): 115–45. See also Lorraine Daston, “Enlightenment Calculators,” Critical Inquiry 21 (1994): 182–202; Giora Hon, “Towards a Typology of Experimental Errors: An Epistemological View,” Studies in the History and Philosophy of Science 20 (1989): 469–504.

  The field of statistics: For the role of nineteenth-century statistics in the various sciences, see Theodore M. Porter, The Rise of Statistical Thinking, 1820–1900 (Princeton: Princeton University Press, 1986).

  scientifiques: Jean-Paul Marat, Les Pamphlets—1792, C. Vellay, ed. (Paris: Fasquelle, 1911), 295. This is, however, a precocious use of the term. The term “scientist” was introduced into English in the 1840s by William Whewell. The equivalent term in French, “scientifique,” used as a noun, did not come into general use in France until the early twentieth century, and the term “savant” continued to be used there throughout the nineteenth century. Nevertheless, many of the elements of the new scientific “professionalism” (and the new political world that sustained it) emerged in the early nineteenth century.

  “To divide one’s night”: Napoleon to Lalande, 15 frimaire V [5 December 1796], in Napoleon, Correspondance, 2:175–76.

  “Lalande is still”: BVCS MS99, Lalande, “Journal,” 23 November 1805: also Jérôme Lalande, Histoire céleste française (Paris: Imprimerie de la République, IX [1801]). A few years later, his grandson Isaac, named after Isaac Newton, was hard at work in the family astronomical workshop; see Lalande, “History of Astronomy for the Year 1805,” Philosophical Magazine 26 (1806–7): 362.

  “Observe the dwarf”: BNR MS Fr 12273 fol. 73 Anon. “Air des fraises: Voyez du nain des savans / La fierté peu commune / Il voulait savoir des vents / Si l’on parle de lui dans / La lune, la lune, la lune.” On Mademoiselle Henry, see Aulard, Thermidorienne 4 (22 messidor VI [10 July 1798]): 533.

  “insects of distinction”: Gazette de France, 4 ventôse XIII [23 February 1805], cited in François-Alphonse Aulard, Paris sous le premier Empire (Paris: Cerf, 1912–23), 1:620.

  “Buonaparte”: Lalande in BN R43050, Sylvain M[aréchal], [with Jérôme Lalande], Dictionnaire des athées anciens et modernes (Paris: Grabit, VIII [1799]), 57.

  “Look at his”: BN Ln27 11115, Anon., Grand conseil tenu par les sylphes (Paris: Sourds-Muets, n.d.). For attacks on Lalande’s atheism in the press, see Aulard, Consulat 1 (12 December 1799, 18 March 1800): 48, 221–22.

  “That men are witless”: NL FRC18618, Lalande, Notice sur Sylvain Maréchal (n.p., n.d.), 48–49. “Les hommes fous, méchans ou bêtes / Prouvent que tout est mal dans cet indigne lieu. / Un scélérat suffit pour renverser les têtes; / L’homme ne serait plus s’il existait un Dieu.”

  “I do renounce”: Delambre, “Lui-même.”

  “It is up to the”: Jérôme Lalande, Second supplément au Dictionnaire des Athées (N.p., 1805), 76. The publisher only printed the dictionary after being told by the Ministry of Police that he might do so for Lalande’s private use. Lalande then “accidentally” left some copies in the antechamber of the French Senate, where they were discovered. For a full discussion of this episode, see Aulard, “Napoléon et l’athée Lalande,” Révolution française, 4th series, 9 (1904): 303–16. For Lalande’s views on the function of religion, see NL FC18618, Lalande, Notice sur Sylvain Maréchal (N.p., n.d.), 36–37, and his conversation with the Pope, p. 88. See also his cheeky attack on Napoleon as a warmonger in Journal de l’Empire, 13 fructidor XIII [31 August 1805], in Aulard, Empire, 2:147.

  From the battlefield: For Napoleon’s accusation against Lalande, see Napoleon (at Schönbrunn) to Min. Int. Champagny, 23 frimaire XIV [13 December 1805], in Napoleon, Correspondance, 11:574–76. For Lalande’s acceptance of the conditions, see AN AF IV 1050, Delambre to Min. Int., 5 nivôse XIV [26 December 1805]; and CUS, Président de l’Institut, “Certifie que ce qui suit . . . ,” 5 nivôse XIV [26 December 1805]. Delambre gave a detailed account of this episode and his attempt to make Lalande conform, while preserving academic freedom; see BI MS2041 v. 2, fol. 610, Delambre, “Lalande,” [1805]. For the re-edition of the Dictionary, see BN 8°R13719, Jérôme Lalande, Second supplément au Dictionnaire des Athées (N.p., 1806).

  “I have sometimes amused”: Lalande, “Testament moral,” [21 October 1804], in Amiable, Lalande, 53, emphasis added.

  “I don’t need”: Delambre, “Lalande,” Biographie universelle, 613; Salm-Reifferscheid-Dyck, La Lande, 34. For rumors about Lalande’s will, see Gazette de France, 8 April 1807, and Journal de Paris, 11 April 1807, in Aulard, Empire, 3:115, 117. For Delambre’s increasingly harsh assessment of Lalande after his death, see Delambre, “Eloge historique de M. de Lalande,” 4 January 1808, MA (1807): 30–57; Delambre, “Lalande,” Biographie universelle, 603–13; Delambre, “Lalande,” Astronomie au dix-huitième, 547–621.

  “I have all my life”: BMA Arch. Rev. 2K10, Delambre to [Louis-François] Janvier, 12 August 1806.

  Delambre’s face had thickened: On Delambre’s debilitating illness of 1803, see CUS, Delambre to Cagnoli, 6 August 1810.

  For several years: For Delambre’s loans to Madame de Pommard at favorable interest in 1800–1801, see BI MS1041, fol. 29. Her property was located in Courcelles-sur-Viosne; see AN M.C. Etude II 797, “Donation entrevis par Madame Delambre,” 5 vendémiaire XIII [27 September 1804]. For his housing, see CUS, Delambre to Delambre (his cousin, a notary), 7 floréal [c. 1800]. For a description of Madame Delambre, see Charles Dupin, “Notice nécrologique sur M. Delambre,” Revue encyclopédique 48 (December 1822): 22–23. For
their mutual friendship with Humboldt, who may have introduced them, see Delambre to Humboldt, 22 January 1801, in Alexander von Humboldt, Briefe aus Amerika, 1799–1804 (Berlin: Akademie, 1993), 121.

  “Ah! Love”: BI MS2041, in Delambre’s hand: “An Athenian Air, Translation from the Roman.” Charles de Pommard’s examiner for the Ecole Polytechnique was Biot, one of Delambre’s scientific protégés, who ranked him near the middle of the incoming class; see BEP II/1, Ecole Impériale Polytechnique, “Liste des élèves admis à l’Ecole Polytechnique en l’an 9,” [1801]. Delambre to Humboldt, 22 January 1801, in Humboldt, Briefe aus Amerika, 120; WL 7080/7, Humboldt to Delambre, 27 August 1807.

  “Official positions”: BMA Arch. Rev. 2K10, Delambre to [Louis-François] Janvier, 12 August 1806. On Delambre’s move, see Delambre, Grandeur, 192. See his addresses in Almanach national.

  According to Gauss: For the view of Gauss, see Gauss to Bessel, 13 November 1814, in Briefwechsel C. F. Gauss–F. W. Bessel (Hildesheim: Olms, 1975), 1:202. For a more generous view, see Wilson, “Perturbations,” 283–96. Delambre’s tables were plagiarized while still in manuscript form by the German astronomer Baron von Zach, who took advantage of Lalande’s generosity in conveying scientific results. This infuriated Delambre, though he restrained himself publicly; see Delambre, “Lui-même.”

  Delambre made himself useful: For Delambre’s military research, see AN AF IV 1205, Delambre to Gen. Duroc, 23 vendémiaire XII [16 October 1803]; see also Fernand Beaucour, “Un problème d’optique posé par Napoléon à l’Institut, en 1803, résolu par Delambre,” Bulletin historique de la Société de Sauvegarde du Château Impérial de Pont-de-Briques (1972): 196–206. For the background of the threatened invasion, see Edouard Desbrière, Projets et tentatives de débarquement aux îles Britanniques (Paris: Chapelot, 1902), vol. 3.