Some Areas for Further Newtonian Studies

Mornet Daniel , Les sciences de la nature en France au XVIIIe siècle (Paris, 1911); Smith Preserved , A history of modern culture, ii (New York, 1934), esp. chs. 2–4.

Metzger Hélène , Attraction universelle et religion naturelle chez quelques commentateurs anglais de Newton (Paris, 1938).

The distinction between ‘internal’ and ‘external’ influences upon science is older than the present-day methodologists of the history of science may realise. The distinction—obvious enough in itself—and even the precise terminology appeared as early as 1948 in a paper presented by Jean Pelseneer to the Comité Belge d'Histoire des Sciences, and published as “Les influences dans l'histoire des sciences”, in the Archives internationales d'histoire des sciences, i (1947–48), 347–53.

Jacob Margaret C. , The Newtonians and the English Revolution, 1689–1720 (Ithaca, New York, 1976).

Brunet Pierre , L'Introduction des théories de Newton en France au XVIIIe siècle (Paris, 1931). This one volume carrying the story to 1738 was all that was published.

Philosophical transactions, vi (1671–72), 3075–87. Newton's “Accompt of a new catadioptrical telescope” was published later in the same volume, 4004–10. These optical papers may be conveniently consulted in Cohen I. Bernard (ed.), Isaac Newton's papers and letters on natural philosophy (Cambridge, Mass., 1958), 47–67.

Oldenburg first informed Huygens of Newton's new kind of telescope by letters of 1 and 15 January 1671/2 (O.S.). See Oeuvres complètes de Christiaan Huygens (La Haye, 1888–1950), vii, 124–5 and 128; also The correspondence of Isaac Newton (7 vols, Cambridge, 1959–77), i, 72–76 and 81–82; and The correspondence of Henry Oldenburg, ed. and tr. by Hall A. Rupert Hall Marie Boas (Madison and London, 1965-), viii, 443–5 and 468–73. Greatly impressed, Huygens sent a description of Newton's telescope, with a letter giving his opinion of it, to Jean Gallois, editor of the Journal des sçavans. Gallois published both in the issue of 29 February 1672. Other French savants, among them Adrien Auzout, Jean-Baptiste Denis, and of course Cassegrain, were interested in Newton's invention.

In March 1672 Oldenburg sent Huygens the number of the Transactions containing Newton's pioneer paper on light and colour, asking for his opinion of the new theory. See Oeuvres de Huygens, vii, 156; Newton correspondence, i, 117; and Oldenburg correspondence, viii, 584–85. Huygens contented himself with replying: “Pour ce qui est de sa nouvelle Théorie des couleurs, elle me paroit fort ingenieuse, mais il faudra veoir si elle est compatible avec toutes les expériences” (Oeuvres de Huygens, vii, 165). With slight variations this passage was quoted in a letter of Oldenburg to Newton (19 April 1672), in Newton correspondence, i, 135.

Pardies's Discours du mouvement local (Paris, 1670), published anonymously, had been translated by Oldenburg and published in London that same year. Pardies's first formal communication was a flattering letter to Oldenburg, dated 18 July 1671, remarking that he had just been shown parts of the Philosophical transactions and learned that Oldenburg had translated his Discours into English (Oldenburg correspondence, viii (1971), 143–5).

The Academy of the Abbé Bourdelot has been described in Brown Harcourt , Scientific organisations in seventeenth century France (Baltimore, 1934), ch. xi.

Huygens made an early reference to the Bourdelot group in a letter written from Paris on 26 April 1664 to his brother Lodewijk. See Brown , op cit. (ref. 10), 233.

Pardies did not live to complete his book on optics; but material from his draft was used, with full acknowledgment, by Father Pierre Ango, a fellow Jesuit, in his L'Optique divisée en trois livres (Paris 1682), un-paginated dedicatory preface and p. 14. If Pardies had accepted Newton's theory of colour, there is no trace of it in Father Ango's book, where all the colours are explained according to the old theory of a mixing of black and white.

For Pardies's first letter see Newton correspondence, i, 130–3.

Philosophical transactions abridged (London, 1809), vii, 743 and Cohen , Newton's papers and letters (ref. 6), 109. The three-volume abridgement of the early Transactions by Lowthorpe John (London, 1705), gives Pardies's statement of concession only in Latin (i, 144).

The italics in the quotation are my own.

For the French original of this passage see Newton correspondence, i, 205–6. The error is not attributable to Oldenburg's translating the French into Latin, the language in which it appears in the original Transactions for what we read is a good rendering of the French: “Experimentum peractum cum fuerit isto modo, nil habeo in eo desiderem amplius” (Philosophical transactions, vii (1672–73), 5018, reproduced in Cohen , Papers and letters (ref. 6), 103).

Mariotte Edme , De la nature des couleurs (Paris, 1681), 211. This study was reprinted in the Oeuvres de Mariotte (2 vols, Leiden, 1717), i, 227–8, and in a later edition of the Oeuvres (2 vols-in-1. The Hague, 1740) consecutively paginated. The supposed refutation of Newton's experiment appears on pp. 227–8 of this edition.

For new material on the later stages of the penetration of Newtonian optics into France see Hall A. Rupert , “Newton in France: A new view”, History of science, xiii (1975), 233–50.

Whiteside Derek T. , The mathematical works of Isaac Newton (New York and London, 1964), p. xii. Whiteside reprints in facsimile John Stewart's 1745 English translation of the De analysi. For the original Latin version, a new translation, and illuminating notes see The mathematical papers of Isaac Newton, ed. Whiteside D. T. (Cambridge, 1967–), ii (1968), 206–47.

Newton correspondence, i, 155–6. For Newton's work on the Kinckhuysen Algebra see Whiteside , Mathematical papers, ii, 277–91.

Brugmans Henri L. , Le séjour de Christiaan Huygens à Paris (Paris, 1935), 72–3. In August 1676 Leibniz wrote to Oldenburg: “Inventa Neutoni ejus ingenio digna sunt, quod ex Optices experimentis et Tubo Catadioptrico abunde eluxit” (Newton correspondence, ii, 57). Oldenburg had earlier drawn Huygens's attention to Leibniz, mentioning in a letter of late March 1671 Leibniz's Hypothesis physica nova, his earliest study of motion, dedicated to the Royal Society. See Oldenberg correspondence, vii, 573–9. For this work see the article “Leibniz: Physics, logic, metaphysics” by Jürgen Mittelstrassand Aiton Eric J. in Dictionary of scientific biography, via (New York, 1973), 150–60.

For Leibniz's participation in the meeting of 22 January 1672/3 see Birch , History of the Royal Society of London (4 vols, London, 1756–57), iii, 73. Leibniz demonstrated an early version of his calculating machine. He was elected FRS on 9 April 1673.

For these Latin letters to Leibniz, with English translations, see Newton correspondence, ii, 20–47, and 110–61.

Newton correspondence, iii, 3–5.

Oeuvres de Huygens, ix, 167. Cf. Cohen I. Bernard , Introduction to Newton's “Principia” (Cambridge, 1971), 138, n. 9. For Fatio's aspirations as editor of a second edition of the Principia see Cohen , Introduction, 177–87.

“Je souhaitte de voir le livre de Newton. Je veux bien qu'il ne soit pas Cartesien pourveu qu'il ne nous fasse pas de suppositions comme celle de l'attraction” (Huygens to Fatio (11 July 1687), Oeuvres de Huygens, ix, 190). Cf. Westfall Richard S. , Force in Newton's physics (London and New York, 1971), 184.

Oeuvres de Huygens, xxi, 437. See Westfall , op. cit. (ref. 26), 186. Turnbull in Newton correspondence (iii, 2, n. 1) avers that Huygens “had recently” received his copy of the Principia from his brother Constantyn. Turnbull's reference is to a letter of Christiaan to Constantyn dated 30 December 1688 (Oeuvres de Huygens, ix, 304–5) which merely tells us that Huygens had read the book before that date. But a letter of Constantyn to Christiaan, dated from Loo in Western Flanders on 13 October 1687, includes the sentence: “Dr. Stanley est allé en Angleterre et me portera encore des livres curieux. Il ne revient que vers le temps que nous irons a la Haye c'est a dire dans un mois d'icy” (Oeuvres de Huygens, ix, 234). This supports the notion that Constantyn was the intermediary, but suggests that Christiaan may have received his copy of the Principia either late in 1687 or early in 1688. Stanley William (1647–1731), Dean of St Asaph, was chaplain to the future Queen Mary and after the accession of William in was made clerk of the closet.

For Roberval's gravitational theory, similar to that advanced by Copernicus Galileo , see “Un débat à l'Académie des sciences sur la pesanteur”, in Auger Léon , Gilles Personne de Roberval (1602–1675) (Paris, 1962), esp. p. 179. See also Westfall , op. cit. (ref. 26), 184–6.

Westfall , op. cit. (ref. 26), 187.

Royal Society Journal Book for 18 January 1687/8 and 4 July 1688. Fatio had been elected FRS in 1687. In May 1688 he described at a meeting of the Society the pendulum clock that Huygens had devised, and which had been “sent to the Cape of Good Hope by a person skilled in Astronomy, with design to trie what might be done in the matter of Longitude by that method of clocks” (Journal Book, 9 May 1688). When Huygens met Newton for the first time in 1689 it was on a trip to England in the company of Fatio. For the meeting at Gresham College on 12 June 1689, where Huygens “gave an account” of his forthcoming “Treatise concerning the Cause of Gravity” and had an exchange with Newton about the double refraction of Iceland spar, see Royal Society Journal Book, 12 June 1689, cited by Turnbull , Newton correspondence, iii, 31, n. 1.

Traité de la lumière … par C.H.D.Z. Avec un discours de la cause de la pesanteur (Leiden, 1690). The Traité, the Discours, and the Newtonian “Addition” are consecutively paginated. The Discours is reprinted separately in Oeuvres de Huygens, xxi, 451–99.

Edmond Halley's laudatory review, an unabashed and rhetorical bit of promotional material, can hardly have persuaded any Continental critic of Newton. See Philosophical transactions, vol. xvi, no. 186 (1687), 291–7.

Journal des sçavans, 2 August 1688 (Amsterdam, 1689), 237–8. A similar view was set forth by Malebranche who wrote in 1707: “Quoique Mr. Newton ne soit point physicien, son livre [the Optice] est tres curieux et tres utile a ceux qui ont de bons principes de physique, il est d'ailleurs excellent geometre …” (Oeuvres complètes de Malebranche (Bibliothèque des textes philosophiques: Directeur, Henri Gouhier), xix (1961), 771–2). This edition will be the one cited henceforth, except in ref. 47.

Mencke Leibniz to , Newton correspondence, iii (1961), 3–4.

In October 1690 Leibniz wrote to Huygens remarking on the “quantité de belles choses” the book contained (Newton correspondence, iii, 80). Leibniz's own copy of the first edition of the Principia was discovered in 1969 by Dr E. A. Fellmann of Basel. Leibniz's marginal annotations have been reproduced in facsimile, together with transcriptions of the marginalia and a commentary, in Marginalia in Newtoni Principia Mathematica, ed. Fellmann E. A. (Paris, 1973).

Aiton E. J. , The vortex theory of planetary motion (London and New York, 1972), 127.

Early in 1690 Leibniz received a copy of Huygens's Traité de la lumière, containing the Dutch scientist's Discours de la cause de la pesanteur. In an accompanying letter, Huygens asked Leibniz if he had modified his planetary theory after reading Newton's Principia, proof incidentally that Huygens had already digested the “Tentamen”.

For Huygens's “spherical vortex” see Westfall , Force in Newton's physics (ref. 26), 187. Leibniz's “harmonic circulation” of a deferent aether is described by Aiton , Vortex theory (ref. 36), 125–51, and by Westfall . op. cit. (ref. 26), 303–10.

Leibniz , Philosophical papers and letters, ed. Loemker L. E. (2 vols, Chicago, 1956), ii, 679. Huygens saw no incompatibility between his aether and the concepts of atoms and the void. He conceived of his aether as rare because each particle is porous, its component subparticles being separated by many empty spaces.

Leibniz , Philosophical papers and letters, ii, 681.

Newton correspondence, iii, 257–8. “Trajection” or “projection” would be preferable translations of trajectio.

For this correspondence see Huygens , Oeuvres, ix, letters nos 2777, 2785, 2815, 2839, 2854, 2866, 2873, 2876. On 4 October 1694 the Marquis de l'Hospital remarked in a letter to Huygens (op. cit., letter no. 2879): “Je n'ai plus de curiosité de voir ce qu'il y a de Mr. Neuton dans le livre de Vallis apres ce que vous me mandez.”.

The extent to which Malebranche departed from Descartes in his fundamental doctrines has been much debated. Compare, for example, M. Geroult's article “Métaphysique et physique de la force chez Descartes et chez Malebranche”, in the Revue de métaphysique et de morale, lix (1954), 113–34, with the account of Malebranche by Willis Doney in the Encyclopedia of philosophy, v (New York, 1967), 140–4. In physics Malebranche differed from Descartes on the cause of the solidity of bodies, on the laws of impact, the nature of light and many other points. He emphasized that Descartes's Principes de la philosophie must be read with caution, “sans rien recevoir de ce qu'il dit, que lorsque la force et l'evidence de ses raisons ne nous permettront point d'en douter”. Cited by Mouy Paul , Le développement de la physique cartésienne (Paris, 1934), 279.

See Alquié Ferdinand , Le Cartésianisme de Malebranche (Paris, 1974), 25 and n. 9.

The originator of the doctrine of occasionalism is often said to be Geulincx of Antwerp (1625–69), but other followers of Descartes adopted a similar position. Malebranche, in any case, greatly extended Geulincx's doctrine, giving it a central rôle in his epistemology and his religious philosophy.

Gouhier Henri , La vocation de Malebranche (Paris, 1926) is a fine study of this aspect of Malebranche's career. Gouhier (56–62) pointed out that it was not merely the Traité de l'homme alone that introduced Malebranche to Descartes. The edition of 1664 that Malebranche purchased was that of Clerselier, and included Descartes's Description du corps humain, with its unfinished preface stressing the dualistic doctrine of mind and body, as well as writings of Clerselier and other Cartesians which gave Malebranche a conspectus of Descartes's philosophy in all its breadth. Cf. Alquié , op. cit. (ref. 44), 25.

For a compact view of Malebranche as mathematician and savant see the article by Pierre Costabel in the Dictionary of scientific biography, ix (New York, 1974), 47–53. A good introduction to Malebranche's interest in the progress of the life sciences is the single volume of the abortive Oeuvres complètes de Malebranche, ed. Roustan Désiré with the collaboration of Paul Schrecker, of which only the one volume (Paris, 1938) appeared before the outbreak of World War II and Schrecker's emigration to the United States. See especially the “Notes des éditeurs”, 399–447. Of interest too is Schrecker's “Malebranche et le preformisme biologique”, Revue internationale de philosophie, i (1938), 77–97.

Oeuvres de Malebranche , xx (“Malebranche vivant”, ed. Robinet André , 1967), ch. 6, “La bibliothèque de Malebranche”.

Ibid. .

Oeuvres de Malebranche, xx, ch. 3, “Le groupe malebranchiste de l'Oratoire”, 137–70; Robinet André , “Le groupe malebranchiste introducteur du calcul infinitésimal en France”, Revue d'histoire des sciences, xiii (1960), 287–308; Robinet André , Malebranche de l'Académie des sciences (Paris, 1970).

Oeuvres de Malebranche, xvii-2 (Mathematica, ed. Costabel Pierre , 1968), 131–294.

Only in the fifth edition of the Recherche de la vérité does Malebranche mention the Marquis de l'Hospital and his book, and introduce the names of two new mathematical sciences, the differential calculus and the integral calculus. The former, he writes, has been carefully treated by l'Hospital; the letter still awaits a comparable book, although “plusieurs savants géomètres” are working on the subject. For the moment one must be content with the “petit ouvrage de M. Carré”, his Méthode pour la mesure des surfaces, etc. Cited by Mouy , op. cit. (ref. 43), 269.

See Schrecker Paul , “Malebranche et les mathématiques”, Travaux du IXe congrès international de philosophie—Congrès Descartes (Paris, 1937), 33–40, and his “Le parallélisme théologico-mathématique chez Malebranche”, Revue philosophique, lxiii (1938), 215–52. Also Robinet André , “La philosophie malebranchiste des mathématiques”, Revue d'histoire des sciences, xvi (1961), 205–54, p. 232.

See Mouy Paul , “Malebranche et Newton”, Revue de métaphysique et de morale, xlv (1938), 411–35.

Oeuvres de Malebranche, xvii-2 (Mathematica, ed. Costabel Pierre , 1968), 62. See also the later letter in which Jacquemet thanks Reyneau for information on Barrow's method, remarking that “dans le fond” it is the same as that of the Marquis de l'Hospital and Newton, except that the latter applied it to incommensurables “qu'on prétend être une des plus belles et des plus utiles inventions de ce siècle dont Messieurs Leibniz et Newton ont tout l'honneur” (ibid., 61).

For. Varignon see the article by Pierre Costabel in the Dictionary of scientific biography, xiii (New York, 1976), 584–7, and his Pierre Varignon et la diffusion en France du calcul différentiel et intégral (Paris, 1965). An important article is Fleckenstein J. O. , “Pierre Varignon und die mathematischen Wissenschaften im Zeitalter der Cartesianismus”, Archives internationales d'histoire des sciences, ii (1945), 76–138.

Mouy , Développement de la physique cartésienne (ref. 43), 282–90.

Duhem Pierre , “L'Optique de Malebranche”, Revue de métaphysique et de morale, xliii (1916), 37–91.

Ibid.

As, for example, Fontenelle's éloge of Newton. For the early English version (London, 1728) see Cohen , Newton's papers and letters (ref. 6), 444–74.

Hall , op. cit. (ref. 18), 244.

Mouy , “Malebranche et Newton” (ref. 54), 421.

See my “Newtonianism of Dortous de Mairan”, reprinted in my Essays and papers in the history of modern science (Baltimore and London, 1977), 479–90. Originally published in the Festschrift for Ira Wade, it suffered from some typographical legerdemain on the part of the printer. This has been corrected, and the article somewhat expanded.

Mairan had doubtless read Huygens's “Discours de la cause de la pesanteur” appended to his Traité de la lumière. Whether at this time he had seen Newton's Principia is less certain, although he refers to it, for he could have learned of Newton's views on the shape of the Earth from the remarks in Huygens's “Addition”. See above, ref. 31.

Dissertation sur la cause de la lumière des phosphores et des noctiluques (Bordeaux, 1717), 48.

Fontenelle , Histoire de l'Académie royale des Sciences, 1720 (1722), 11–12 (cited by Brunet , op. cit. (ref. 5), 84–85). See also the article on Mairan (by Sigalia Dostrovsky) in the Dictionary of scientific biography, xiii (New York, 1974), 33.

Mémoires de l'Académie royale des Sciences, 1722 (1724), 6–51.

Ibid., 50–51. Cited by Brunet , op. cit. (ref. 5), 115–16.

“Recherches géométriques sur la diminution des degrès terrestres, en allant de l'équateur vers les pôles”, Mémoires de l'Académie royale des Sciences, 1720 (1722), 231–77.

Brunet , op. cit. (ref. 5), 134–5.

Brunet writes: “Cette explication par la physique tourbillonnaire est d'autant plus caractéristique ici des preférences cartésiennes de Dortous de Mairan que, puisqu'il faisait appel à une sorte d'extension du magnétisme, il pouvait encore trouver là une occasion de se rallier, plus ou moins directement et explicitement, à la théorie de l'attraction” (op. cit. (ref. 5), 121).

Brunet , op. cit. (ref. 5), 170. For a detailed analysis of Mairan's theory of the éloge pronounced by his friend Dortous de Mairan in Histoire de (ref. 36), 182–7.

Traité physique et historique de l'aurore boréale (Paris, 1733), 88. In the expanded edition of his Dissertation sur la glace (Paris, 1749), Dortous de Mairan expressed his pleasure that Newton's letter to Boyle of 1678, recently published by Thomas Birch (in 1744), showed Newton an advocate of the sort of matière subtile that he, Mairan, used to explain various phenomena. See the “Preface”, xviii–xxii.

The primary source for biographical information on Privat de Molières is the éloge pronounced by his friend Dortous de Mairan in Histoire de l'Académie royale des Sciences, 1742 (1745), 195–205, reprinted in de Mairan Jean-Jacques Dortous , Eloges des académiciens de l'Académie royale des Sciences, morts dans les années 1741, 1742, 1743 (Paris, 1747), 201–34. There is a brief summary by Martin Fichman in his article on Privat de Molières in Dictionary of scientific biography, xi (New York, 1975), 157–8.

Oeuvres de Malebranche, xx, 170–1.

“Lois générales du mouvement dans le tourbillon sphérique”, in Mémoires de l'Académie royale des Sciences, 1728 (1730), 245–67.

Cited by Brunet , op. cit. (ref. 5), 159.

“Problème physico-mathématique, dont la solution tend à servir de réponse à une des objections de M. Newton contre la possibilité des tourbillons célestes”, in Mémoires de l'Académie royale des Sciences, 1729 (1731), 235–44.

Privat de Molières was not alone in being influenced by Malebranche's theory of petits tourbillons. In 1726 Pierre Mazière offered a mechanical explanation of elastic collision in terms of such tiny aetherial vortices. See Iltis Carolyn , “The decline of Cartesianism in mechanics: The Leibnizian-Cartesian debates”, Isis, lxiv (1973), 360–3. Cf. Brunet , op. cit. (ref. 5), 140–4.

Aiton , Vortex theory (ref. 36), 209.

For vol. i (1734) the committee was composed of Mairan and Louis Godin; for the subsequent three volumes of 1735, 1737, and 1739, the committee consisted of Mairan and the Abbé de Bragelongne, the latter also a disciple of Malebranche. See Robinet in Oeuvres de Malebranche, xx, 152–3, 170, 359.

de Molières Joseph Privat , Leçons de physique (4 vols, Paris, 1734–39), i, pp. vii–x. His vortices, he writes (i, 307), provide “une cause mécanique de la pesanteur, ou de la force centripete, telle que M. Newton la demande, qui croît & décroît en raison inverse des quarrés des distances au centre, & qu'il avouë n'avoir pu déduire de ses suppositions”. Newton, he adds (i, 308), was obliged to regard gravity as a universal principle “& un effet sans cause”.

For the persistent influence of Malebranche, especially his criticism of the concept of force, on these later Newtonians, notably Maupertuis, see the excellent article of Hankins Thomas L. , “The influence of Malebranche on the science of mechanics during the eighteenth century”. Journal of the history of ideas, xxviii (1967), 193–210.

Les lettres de la marquise du Châtelet, ed. Besterman T. (2 vols, Geneva, 1958), i, 261. Cited by Heilbron J. L. in his Electricity in the seventeenth and eighteenth centuries. A study of early modern physics (in press).