“Aplatisseur DU MONDE ET DE CASSINI”: Maupertuis,Precision Measurement,and the Shape of the Earth in the 1730s

Young A. , Journal entry for 16 October 1787; in Maxwell C. (ed.), Travels in France (Cambridge, 1950), 82–83.

A good recent account of the Lapland expedition is Taton R. , “L'Expédition géodésique de Laponie (avril 1736–août 1737)”, in Lacombe H. and Costabel P. (eds), La figure de la Terre du XVIII^e siècle à l'ère spatiale (Paris, 1988), 115–37. See also Martin J.-P. , La figure de la Terre: Reçit de l'expédition française en laponie suedoise (1736–37; Cherbourg, 1987); Brown H. , “French scientists on Tornionjoki”, in Amelinckx F. C. and Megny J. N. (eds), Travel, quest and pilgrimage as a literary theme (Ann Arbor, 1978), 153–60. The Swedish-Finnish perspective (Finland seceded from Swedish control in 1801) is well covered in Tobé E. , Fransyk visit i Tornedalen 1736–37 (Luleå, 1986); Nordenmark N. V. E. , Anders Celsius: Professor i Uppsala 1701–44 (Uppsala, 1936); and Widmalm S. , “Maupertuis' expedition to the Arctic Circle: The Swedish context” (unpubl. typescript, 1987). For the Peruvian experience, see Lafuente A. and Delgado A. J. , La geometrización de la Tierra (1735–44) (Madrid, 1984), and Lafuente and Estrella E. , “Scientific enterprise, academic adventure and drawing room culture in the geodesic mission to Quito (1735–1755)”, XVII International Congress of History of Science, v (Berkeley, 1985).

For later critiques of the Lapland undertaking, see Maire Ch. and Boskovič R. J. , De litteraria expeditione per Pontificiam ditionem ad dimitiendos duos meridiani gradus et corrigendam mappam geographicam jussu … (Rome, 1755); Svanberg J. (ed.), Exposition des opérations, faites en Laponie pour la détermination d'un arc de méridien en 1801–1803 (Stockholm, 1805); Delambre J.-B. J. , Grandeur et figure de la Terre , ed. by Bigourdan B. (Paris, 1912); Todhunter I. , “On the arc of meridian measured in Lapland”, Transactions of the Cambridge Philosophical Society, xii (1873), 1–26; and Leinberg Y. , “Über die Ergebnisse der Maupertuisischen Gradmessung in Lappland”, in Comptes rendus de la quatrième séance de la Commission Géodesique Baltique (Berlin, 1928).

Earman J. and Glymour C. , “Relativity and eclipses: The British expeditions of 1919 and their predecessors”, Historical studies in the physical sciences (hereafter: HSPS), xi (1981), 49–85, pp. 84–85.

Konvitz J. , Cartography in France, 1660–1848: Science, engineering and statecraft (Chicago, 1987), 4–7; Gallois L. , “L'Académie des Sciences et les origines de la carte de Cassini”, Annales de géographie, xviii (1909), 194–204 and 289–310; Histoire de l'Académie Royale des Sciences (hereafter: HARS) (1701, publ. 1703), 96–97. For a fine account of the history of attempts to ‘map’, ‘know’ and hence produce the territory of France, see Revel J. , “Knowing the territory”, Science in context, iv (1991), 133–62, pp. 155–7.

Newton was a foreign member of the Académie, elected after its reorganization in 1699. For the relationship between Newton and France, see Cohen I. B. , “Isaac Newton, Hans Sloane, and the Académie Royale des Sciences”, in Cohen and Taton R. (eds), Mélanges Alexandre Koyré, i: L'aventure de la science (Paris, 1964), 61–116; Guerlac H. , Newton on the Continent (Ithaca, N. Y., 1981), 41–163; Brunet P. , L'introduction des théories de Newton en France au XVIII^e siècle, i: Avant 1738 (Paris 1931); Jacquot J. , “Sir Hans Sloane and French men of science”, Notes and records of the Royal Society of London, x (1953), 85–98; and de La Harpe J. , “Le Journal des savants et l'Angleterre, 1702–1789”, University of California publications in modern philology , xxii (1937–41), 289–520. For Newton's problems with Bernoulli see The correspondence of Isaac Newton , ed. by Turnbull G. H. Tilling L. and Hall A. R. (7 vols, Cambridge, 1959–81), vi, 387 and iv, 296, and Aiton E. , The vortex theory of planetary motions (London, 1972), 219.

Cohen I. B. , Introduction to Newton's ‘Principia’ (Cambridge, 1971), 247. For a brief account of Huygens's and Newton's calculations regarding the shape of the Earth, see Costabel P. , “Science positive et forme de la Terre au début du XVIII^e siècle”, in Lacombe and Costabel (eds), op. cit. (ref. 2), 97–113; see also Newton Isaac , Principia mathematica (London, 1687), Bk 3, Props 18 and 19. The Newtonian flattening is 1/230 compared with the Huygenian value of 1/578.

Cf. Cassini G.-D. , “De la grandeur de la Terre et de sa figure”, in Mémoires de l'Académie Royale des Sciences (hereafter: MARS), 1718 (publ. 1720), 245–6, and idem, Traité de la grandeur et la figure de la Terre (Paris, 1720). A detailed explanation of the link between increasing northward lengths of degrees and the oblate Earth (and the converse), is in Mignard F. , “La théorie des figures”, in Lacombe and Costabel (eds), op. cit. (ref. 2), 281–319; see also Chapin S. , “The size and shape of the World”, in The size and shape of the World: A catalog of an exhibition of books from the collection of Robert B. Honeyman Jr (UCLA Library Occasional Papers, no. 6; Los Angeles, 1957), 1–16.

de Mairan J. J. d'O. , “Recherches géométriques sur la diminution des degrés terrestres, en allant de l'équateur vers les Pôles”, MARS , 1720 (publ. 1722), 231–77, pp. 275–6; Greenberg J. , “Geodesy in Paris in the 1730s and the Paduan Connection”, HSPS, xiii (1983), 239–60, pp. 245–53; idem, “Degrees of longitude and the Earth's shape: The diffusion of a scientific idea in Paris in the 1730s”, Annals of science, xli (1984), 151–8; idem, “Mathematical physics in eighteenth century France”, Isis, lxxvii (1986), 59–78; Schaffer S. , “Halley, Delisle, and the making of the Comet”, in Thrower N. J. W. (ed.), Standing on the shoulders of giants: A longer view of Newton and Halley (Oxford, 1990), 254–98, pp. 267–70.

Greenberg , “Degrees of longitude” (ref. 9), 152–6; idem, “Geodesy in Paris” (ref. 9), 246–53; Desaguliers J. T. , “A dissertation concerning the figure of the Earth”, Philosophical transactions, xxxiii (1725), 201–2, 239–55 and 277–305.

de Maupertuis P. L. M. , “Sur la figure de la Terre, et sur les moyens que l'astronomie et la géographie fournissent pour la déterminer”, Académie des Sciences, Registres des Procès-Verbaux (hereafter: ASRP-V), 1733, fols 111^r, 115^v and 116^r–118^v; publ. in MARS, 1733 (publ. 1735), 153–64; Greenberg , “Degrees of longitude” (ref. 9), 155.

The best account of Maupertuis's life and work is Pierre Brunet's Maupertuis, 1: Étude biographique; 2: L'œuvre et sa place dans la pensée scientifique et philosophique du XVIII^e siècle (Paris, 1931). See also Brown Harold , “From London to Lapland and Berlin”, in his Science and the human comedy: Natural philosophy in French literature from Rabelais to Maupertuis (Toronto and Buffalo, 1976), 167–206, esp. pp. 167–8 and 172. For Maupertuis and the promotion of mathematics in 1720s and 1730s France, see Greenberg , “Mathematical physics” (ref. 9), 67 and 70.

Cf. “De figura quas fluida rotata induere possunt problemata duo …”, Philosophical transactions, xxxvii (1732), 240–56; Brown , op. cit. (ref. 12), 173. A translation of the letter to Sloane is in the Royal Society Letter Book Copy (hereafter: R. S. LBC), which reveals that Maupertuis was also attempting to correspond with Halley. Maupertuis matriculated at the University of Basel to work with Bernoulli; cf. Greenberg , “Mathematical physics” (ref. 9), 67. All dates are New Style unless otherwise stated.

Voltaire to Maupertuis, 3 November 1732, 15 November 1732, 29 April 1734 and c. October 1734: Besterman T. (eds), Les Oeuvres complètes de Voltaire (135 vols, Oxford, 1968–), lxxxvi, 246, 251 and 468–9; lxxxvii, 73.

Greenberg , “Degrees of longitude” (ref. 9), 157. Godin's and La Condamine's papers were published as “Méthode pratique de tracer sur terre un parallèle par un degré de latitude donné; et du rapport du même parallèle dans le sphéroïde oblong, et dans le sphéroïde applati”, MARS, 1733 (publ. 1735), 223–32, and “Description d'un instrument qui peut servir à déterminer, sur la surface de la terre, tous les points, d'un cercle parallèle à l'équateur”, ibid., 294–301. La Condamine formally proposed the equatorial jaunt on 23 December 1733; see ARSP-V, 1733, fol. 233^v.

For Clairaut's work in the 1730s, see Taton R. , “Sur la diffusion des théories Newtoniennes en France: Clairaut et le problème de la figure de la Terre”, Vistas in astronomy, xxii (1979), 485–509. Clairaut delivered a paper on Cassini's work on 5 and 9 December 1733; cf. MARS, 1733 (publ. 1735), 406–16. For Orry's interest in reactivating the project, see Konvitz, op. cit. (ref. 5), 9ff, and for the work of the Cassinis in the 1730s, see idem, “Redating and rethinking the Cassini geodetic surveys of France, 1730–1750”, Cartographica, xviii (1982), 1–15. Cf. Cassini J. , “Réponse aux remarques qui ont été faites dans le Journal historique de la république des lettres sur le traité De la grandeur et de la figure de la Terre” (inserted by Fontenelle in the Mémoires for 1732), MARS, 1732 (publ. 1735)), 497–513; and “De la perpendiculaire à la méridienne de Paris prolongée vers l'Orient”, MARS , 1734 (publ. 1736), 622.

Maupertuis to Bernoulli , 17 February 1734, and Bernouli to Maupertuis, 8 May 1734; quoted in Brown, op. cit. (ref. 12), 174. Celsius already had practical experience in geodesy and cartography from his stay in Italy; he soon showed renewed interest in the problem of geodesy when he arrived in Paris, where he made the acquaintance of Godin. Cf. Widmalm, op. cit. (ref. 2), 4.

For Celsius , see Nordenmark , op. cit. (ref. 2). Algarotti did not travel with the team to Lapland: See Mme du Châtelet to Algarotti, 1 October 1735, 7 January and 20 April 1736, and 27 August 1738; idem to Maupertuis, 18 July 1736, in Besterman , op. cit. (ref. 14), lxxxvii, 216–17, 307–8 and 435; lxxxix, 277; lxxxviii, 21. Algarotti's Il Neutonianismo per le dame, ovvero dialoghi sopra la luce i colori (Naples, 1737) was translated into English by Elisabeth Carter and into French by Du Perron de Castera the following year.

Brunet , Étude biographique (ref. 12), 31; Taton , op. cit. (ref. 16), 488–9.

Cassini , “Réponse aux remarques …” (ref. 16), 499 and 511; Greenberg , “Degrees of longitude …” (ref. 9), 157. Bernoulli was a personal friend of the Cassinis, as he told Maupertuis when Maupertuis was staying at Thury: Brown, op. cit. (ref. 12), 177, letter of 13 October 1735. In 1734, he had called the agreement between his theory of the shape of the Earth, and the work of the Cassinis — “entreprise et exécuté … avec une exactitude inconcevable” — “[une] heureuse conformité”; cf. Bernoulli , Opera omnia (4 vols, Lausanne and Geneva, 1742), iii, 354–5.

Maupertuis , “Sur la figure de la Terre” (25 and 27 May) and “Sur la figure de la Terre et de quelle utilité peuvent être les voyages pour la déterminer” (8 June), ARSP-V (1735), fols. 124ff.; Brunet , Maupertuis: L'œuvre (ref. 12), 132–40. Clairaut's paper was finally published in 1739 as “Sur la mesure de la Terre par plusieurs arcs de méridien pris à différentes latitudes”, MARS, 1736 (publ. 1739), 111–20. The letters between Maupertuis and Bernoulli are partially printed in Brown, op. cit. (ref. 12), 175–7. The following information about the diplomatic background to the Lap trip is based on the excellent paper by Nordmann Claude J. , “L'Expédition de Maupertuis et Celsius en Laponie”, Cahiers d'histoire mondiale, x (1966), 74–97; for a general background to Swedish politics in this period, see Roberts M. , The Age of Liberty: Sweden, 1719–1782 (Cambridge, 1986), 111ff.

Nordenmark , Celsius (ref. 2), 244 and 58; Widmalm , op. cit. (ref. 2), 3ff.; Nordmann , op. cit. (ref. 21), 80–82, p. 82, n. 33. A Swedish prohibition on map-making (dating from 1725) had only been repealed in 1735, and in the winter of 1736–37 the Director of the Swedish Surveying Office, Nordencreutz, corresponded with Celsius about techniques for determining latitudes. Nevertheless, no maps were produced; cf. Widmalm, op. cit. (ref. 2), 6.

Nordmann , op. cit. (ref. 21), 80–81.

Celsius had also viewed an eclipse of the Moon with Graham on 21 September 1735 — see Acta literia Sveciae, 1737, 243–5, and “Observations on the lunar eclipse of March 15, 1735–6 …”, Philosophical transactions , xl (1737–38), 15; Nordmann , op. cit. (ref. 21), 81–82, p. 82, n. 31, citing Celsius to Delisle, 16 May 1736. Delisle lauded the merits of this sector in a paper read before the Academy of Sciences of St Petersburg on 21 January 1737; cf. Philosophical transactions , xl (1737–38), 27–49, pp. 44–47. Delisle was already aware from his correspondence with Celsius that the early pendulum work performed in Lapland supported the Newtonian value for the shape of the Earth; ibid., 38.

Nordmann , op. cit. (ref. 21), 82–88; the total cost of the voyage was 4068 livres, which included 340 bottles of wine and 4 tonnes of beer, as well as the cost of the talented naval cook which the Naval Commisary at Dunkirk thoughtfully added at the last moment “in case they died of hunger”: ibid., 86, n. 47.

Cf. Nordmann , op. cit. (ref. 21), 85, n. 47. For Clairaut's work on the pendulum, cf. Clairaut to Bernoulli, 27 March 1736, mentioned in Taton, op. cit. (ref. 2), 120–1. Maupertuis's letter of the same date is in Brown, op. cit. (ref. 12), 178, and his paper, “Sur le voyage qu'on fait à l'équateur et celui qu'on va faire au Nord”, is extant in ASRP-V, 1736, fol. 72^r. This was reread in the Académie after Maupertuis's departure on 28 April; cf. Nordenmark , op. cit. (ref. 2), 243.

Nordmann , op. cit. (ref. 21), 85–87; Nordenmark , op. cit. (ref. 2), 246 and 60. Currency could present a major problem at this time, and La Condamine was accused in early 1737 of bringing illegal merchandise into Peru (in the form of letters of credit for 12000 pesos brought from Paris) when their supplies were exhausted. The expedition had by now split irreconcilably into two camps, with La Condamine and Pierre Bouguer in one, and Godin in the other. As early as February 1736, Jussieu was told that Godin and La Condamine were eating “comme chien et chat”, and that each side was trying to ruin the other's observations. Maurepas had finally to rule on whether they should measure along an arc or a parallel and decided upon the former; see Lafuente A. and Peset J. L. , “La Question de la figure de la Terre: L'agonie d'un débat scientifique au XVIII^e siècle”, Revue d'histoire des sciences, xxxvii (1984), 235–54, pp. 243 and 244, n. 24.

The basis for accounts of the Lap expedition are the works by Maupertuis, La figure de la Terre déterminée par les observations de M.M. de Maupertuis, Clairaut, Camus, Le Monnier, Outhier, Celsius au cercle polaire (Paris, 1738), and Outhier R. , Journal d'un voyage au nord en 1736 and 1737 (Paris, 1744). Maupertuis's text was translated into English as The figure of the Earth, determined from observations made by order of the French King, at the Polar Circle (London, 1738).

Outhier , op. cit. (ref. 28), 33; Brunet , op. cit. (ref. 19), 39ff.

Maupertuis , Figure of the Earth (ref. 28), 42–47. On 1 July, Celsius informed Mortimer that they were experiencing a continual day and that they were finding the gnats “somewhat troublesome”. He urged him to speak to Graham to expedite the sector. See also Du Fay to Mortimer (the official request for the sector), 29 January 1736, Lbc R. S. and Nordenmark , op. cit. (ref. 2), 71.

Hellant later recorded (in 1758) that a number of mishaps had occurred in handling the instruments because the French were “weak-sighted and clumsy”; see Widmalm , op. cit. (ref. 2), 19, n. 16.

Maupertuis , Figure of the Earth (ref. 28), 55–56; Outhier , op. cit. (ref. 28), 203–4.

Maupertuis , Figure of the Earth (ref. 28), 65–66, 123–5; his description of the way the instrument was used is at pages 125–8 and 152–3. See Le Monnier to de Charost M. , 11 November 1736, in Mercure de France, Dec. 1736, 2730; days were spent hunting and sleeping — nights were taken up observing the heavens.

Maupertuis , Figure of the Earth (ref. 28), 65–67, 73–75. Cf. Celsius to Sloane, 4 December 1736, R. S. LBC; I use the transcription in Nordenmark, op. cit. (ref. 2), 70–71, n. 5 and 72, although this differs slightly from the ms. copy.

On 7 January, Le Monnier recorded that his Réaumur mercury thermometer (hand built by Nollet) had dropped to −37°. Maupertuis attempted to keep the toise length at a temperature of approximately 15° Réaumur as well as a constant temperature “in his Chamber” for the Graham pendulum, though there could sometimes be a fluctuation in temperature of 20° within a single day. Cf. Brown , op. cit. (ref. 12), 179, n. 7; Maupertuis, op. cit. (ref. 28), 163, 191−2, and Nordenmark, op. cit. (ref. 2), 74; English holograph translation of Celsius to Sloane, 9 April 1737 in R. S. LBC. At this time, the two major institutions in Paris and London were exchanging instruments for measuring and calibrating temperature, as well as other phenomena; see Nollet to Mortimer , 11 December 1737; R. S. LBC; and the following reference.

Maupertuis , Figure of the Earth (ref. 28), 76–77 and 80–83; Outhier , op. cit. (ref. 28), 138–43. The “toise du Nord”, as it came to be called, was calibrated with the famous du Châtelet toise in Paris, although it was later pointed out that this toise differed significantly from the unit used to calibrate the measurements of Picard. For this, see Outhier, op. cit. (ref. 28), 210–12; Strasser G. , “The toise, the yard, and the metre — the struggle for a universal unit of length”, Surveying and mapping, xxxv (1975), 25–46, and Du Fay to Mortimer, 29 January 1736; R. S. LBC. Du Fay sent a brass length for which Graham had asked (from Maupertuis) on behalf of the Royal Society; in turn, the Académie requested a British 3-ft rule. Du Fay acknowledged its receipt in a letter to Graham of 7 March 1738 in which he proposed for an international standard the length of a pendulum that beat seconds at the equator: R. S. LBC.

Maupertuis , Figure of the Earth (ref. 28), 84, 90–97; Maupertuis stressed that they had always measured from all three angles of their triangles, a precaution that was obviously strictly unnecessary. Cf. Celsius to Mortimer, 19 February 1737, R. S. LBC; Clairaut , “Investigationes aliquot, ex quibus probatur Terrae figuram secundum Leges attractionis in ratione inversa quadrati distantiarum maxime ad Ellipsin accedere debere”, Philosophical transactions, xl (1738), 19–25.

Maupertuis , Figure of the Earth (ref. 28), 100. See Nordenmark , op. cit. (ref. 2), 68–69 and esp. 74, n. 2; Celsius to Mortimer, 9 April 1737, R. S. LBC. For Delisle's plans see Delisle to Celsius , 8 October 1737 and idem to Camus, 28 December 1737, cited in Nordmann, op. cit. (ref. 21), 93, n. 82. In August 1737 the Gazette d'Utrecht scooped the news that the team “ont trouvé que le globe de la Terre est parfaitement rond, suivant le système du célèbre chevalier Newton”.

Nordenmark , op. cit. (ref. 2), 76; Brown , op. cit. (ref. 12), 184–5 (letter of 11 August). For a more detailed account of the advantages of the Graham sector, see Maupertuis, Degré du méridien entre Paris et Amiens déterminée par la mesure de M. Picard, et par les observations de Mrs de Maupertuis … et al. … d'où l'on déduit la figure de la Terre (Paris, 1740).

Cf. Taton , op. cit. (ref. 2), 130; Brown , op. cit. (ref. 12), 186–7; Konvitz , op. cit. (ref. 5), 12–13; Le Sueur A. , Maupertuis et ses correspondants (Paris, 1890), 108–9.

Nordenmark , op. cit. (ref. 2), 78. From Maurepas, Maupertuis procured the expedition's quadrant for Celsius, while he also kept in touch with Casteja and Gedda. Finding it difficult to readjust to Parisian life, he told Celsius that he felt “ensuedoisé, ou même embothnisé de telle façon”.

Clairaut to Mortimer, 15 September 1737, in Taton , op. cit. (ref. 2), 130; Voltaire to Fromont, 23 December 1737, idem to Maupertuis, c. 10 January 1737, and Mme. du Châtelet to Algarotti, 10 January 1737, in Besterman et al. (ref. 14), lxxxviii, 431, 456–8 and 453–4. Voltaire was being persecuted on account of a rumour (which he believed originated with Rousseau) that he had discussed Spinozism with 'sGravesande in Holland. The only change in the Élements (then being printed in Holland) which owed anything to the expedition is in the verse dedication to Mme du Châtelet, where Maupertuis suggested adding the lines: “Change de forme o terre! et que la pesanteur/Augmentant sous le pôle Elève l'Équateur.” This was translated with some license into English in 1738 as: “Earth, change thy Form; let the great Law of Matter, The Pole depressing, elevate th'Equator!” Cf. Mme du Châtelet to Maupertuis, 11 December 1737, in Besterman , op. cit. (ref. 14), lxxxviii, 417, and The elements of Sir Isaac Newton's philosophy (London, 1738), vi, lines 79–80. See also Maupertuis , “La figure de la Terre déterminée par Messieurs de l'Académie des Sciences qui ont mesuré le degré du méridien au Cercle Polaire”, MARS, 1737 (publ. 1739), 389–466 (delivered on 13, 16, 20 and 23 November).

The Mercure de France reported the results of the voyage in September (p. 2032) and in greater detail in November 1737 (pp. 2460–24, esp. p. 2461); the Journal des savants for October 1739 (pp. 588–601) and the Mémoires de Trévoux of June 1738 (pp. 1282–1307) both reported on the team's initial surprise at the result (described in Maupertuis's La figure de la Terre of 1738) and their subsequent resolution to perform the most rigorous verifications. See Chouillet A.-M. , “Rôle de la presse périodique de langue française dans la diffusion des informations concernant les missions en Laponie ou sous l'Équateur”, in Lacombe and Taton , op. cit. (ref. 2), 171–89, pp. 176–81. The Journal historique was apparently hostile to the enterprise; cf. Nordmann , op. cit. (ref. 21), 94, n. 85. Maupertuis's short note on the expedition after the results from the equator were known makes the nationalist implications of the result clear; cf. Oeuvres (4 vols, Lyon, 1756), iv, 262–6.

Maupertuis to Celsius, 31 January 1738, in Nordenmark , op. cit. (ref. 2), 80–82. Celsius completed his De observationibus pro figura telluris determinanda in Gallia habitis, Disquisitio (Uppsala, 1738) on 10 February; a brief account was printed in Philosophical transactions, xli (1739–40), 371–82. See also Celsius to Mortimer , 14 March 1738, R. S. LBC. For Maupertuis and the salons, see Brunet , op. cit. (ref. 19), 60.

Nordenmark , op. cit. (ref. 2), 81.

Ibid.

Cf. Cassini J. , Réponse à la dissertation de M. Celsius, Professeur Royal d'Astronomie à Upsal, sur les observations que Von a faites en France pour determiner la figure de la Terre (Paris, 1738 (repr. in Nordenmark, op. cit. (ref. 2)), 224–33, pp. 224–6.

Ibid ., 228–9. For Celsius's response to these attacks, cf. Celsius to Delisle, 17 April 1738, cited in Nordman, op. cit. (ref. 21), 94, n. 84.

ibid., 230–3; the letters from de Plantade were composed on 15 July and 14 November 1736.

Maupertuis , “L'Aberration apparente des étoiles causée par le mouvement progressif de la lumière”, MARS , 1737 (publ. 1739), 285ff.; Taton , op. cit. (ref. 16), 496; and Terrall M. , “Representing the Earth's shape: The polemics surrounding Maupertuis's expedition to Lapland”, Isis, lxxxiii (1992), 218–39. See also Maupertuis to Bradley , c. January 1738, R. S. LBC, and Delisle, op. cit. (ref. 24), 45 (on Bradley's use of the Graham sector and Delisle's wish to have a similar one in Russia). In the R. S. LBC translation of the 22 November 1735 letter from Maupertuis to Celsius (cf. this paper, ref. 22), the translator has added “N.B. In a former letter Mr Maupertuis had desired a model of Mr Bradley's Instrument for observing the transits of the fixt stars: But in this he desired to have the instrument itself …”.

Nordenmark , op. cit. (ref. 2), 94–95. Le Monnier made a brief mention of the forthcoming book in a letter to Graham of c. February 1738: R. S. LBC. The remark to Bernoulli is cited in D. Beeson's introduction to his edition of Lettre d'un horloger anglois à un astronome de Pékin, in Studies on Voltaire, ccxxx (1985), 189–222, p. 203.

The Journal Helvétique for September 1740 published a letter from de Mairan to Bernoulli which was complimentary of the work: Brunet , op. cit. (ref. 19), 95.

Maupertuis , op. cit. (ref. 39); Anon., Anecdotes physiques et morales (Paris, 1739), 3–4 and 8; though Beeson thinks the attribution of this work to Maupertuis is “dubious” — see idem (ref. 51), 205. Maupertuis's paper was “Sur la figure de la Terre”, read on 4 and 11 February 1736: MARS, 1736 (publ. 1739), 302–12; cf. Nordenmark , op. cit. (ref. 2), 243.

Lettre d'un horloger anglais à un astronome de Pékin (Paris, 1740), 4–6, 11–12 and 23–24; I quote from Brunet, op. cit. (ref. 19), 80–83. As a number of commentators have pointed out, only four copies of this book were printed.

Clairaut A.-C. , “An inquiry concerning the figure of such planets as revolve about an axis, supposing the density continually to vary, from the centre towards the surface”, Philosophical transactions, xl (1738), 277–306. His paper, “Sur les représentations cartésienne et newtonienne de la réfraction de la lumière”, was read on 24 July and 5 August 1739, and published in MARS, 1739 (publ. 1741), 259–79.

In fact, de Thury mentioned that his new results supported a flattened Earth as early as 1739; see Terrall, op. cit. (ref. 50), 25. In 1740, de Thury and LaCaille remeasured Picard's initial baseline five times, finding that the baseline (between Villejuif and Juvisy) was five toises shorter than the value given by Picard: Konvitz, op. cit. (ref. 5), 13.

For linkage, see Pinch T. , Confronting nature: The sociology of solar-neutrino detection (Dordrecht and Boston, 1986); for craft knowledge and calibration, see Collins H. , Changing order: Replication and induction in scientific practice (London, 1985), 55–106.

For similar views, see Latour B. , Science in action (Milton Keynes, 1986).

Nevertheless, throughout the expedition Le Monnier and Celsius made a number of verifications of their instruments including reversing them: Nordenmark, op. cit. (ref. 2), 70–71, n. 5.

Nollet to Jallabert , 9 June 1740, cited in Benguigui I. , Théories électriques du XVIII^e siècle (Geneva, 1984), 98. For another usage of ‘extra-scientific’ resources to close dispute, see Collins (ref. 57), 95.

Earman and Glymour , op. cit. (ref. 4), 57–58, 59, 73, 76, 79–80, 84–85.

Maupertuis , Figure of the Earth (ref. 28), 225; Mme du Châtelet to Maupertuis, c. 10 Feb 1738, in Besterman , op. cit. (ref. 14), lxxxix, 28.