SOURCE: "Newton on the Continent: The Early Reception of His Physical Thought," in Newton on the Continent, Cornell University Press, 1981, pp. 41-73.

[In the following essay, Guerlac investigates the nature of Newton's reputation in France prior to 1699 and reassesses the view held by some critics that, prior to 1738, there was great opposition between individuals who advocated Newton's physical theories and those who propounded the theories of René Descartes.]

Besides the technical study of Newton's achievements in mathematics, optics, and dynamics, there is a phase of Newtonian scholarship which has attracted renewed interest and which we may call the "influence," the "reception," or the "legacy" of Newton. This is ambiguous, of course, for there are at least two ways in which the subject can be viewed: we can consider Newton's reception by his learned contemporaries or his influence upon his scientific successors (by any definition of what the history of science is about, surely this is of major importance); or, on the other hand, we can deal with the influence he exerted through his natural philosophy and his advocacy of the experimental approach—that is, those aspects of his achievement comprehensible to the intelligent layman—upon the Weltanschauung of his age or later times. Clearly, this is a legitimate part of cultural or intellectual history, as scholars like Daniel Mornet and Preserved Smith (to name only two) long ago perceived.' And within our ranks of historians of science, Helene Metzger, with her book on what she called the Newtonian "commentators," was surely an outstanding pioneer.²

I hasten to add that this second aspect of Newton's "legacy" has little or nothing to do with the so-called "externalist" approach to the history of science. It projects outwardly from science, or a branch of science, to observe its reception by society, instead of pointing inwardly to seek social, economic, and intellectual influences upon a scientist's work, influences which I happen to believe we cannot, in many cases, safely ignore. The current externalist—internalist debate—like many "either-or" disputes—seems utterly contrived and fatuous.³

Mme Metzger's book is a classic; yet she did not seriously raise, or try to answer, the question why the Boyle lecturers, the popularizers like John Keill and Henry Pemberton, or mavericks like John Toland, felt it important to interpret Newton's new system of the world for their contemporaries. The problem has recently been tackled by Margaret Jacob in various articles and in her rather audacious book, where she has argued that the popular exposition of Newton's world view by these "commentators" served ideological, religious, and sociopolitical ends.⁴

As to the reception of Newton in France, we are left—despite the books of Pierre Brunet, Ira Wade, and others—with considerable murkiness and oversimplification; and for the early period, say from 1672 to 1699, we have only tantalizing allusions, and scattered nuggets, in books written with other purposes in mind. In this paper I should like to single out two areas, two aspects of Newton's reception in France, that seem to call for more systematic investigation, and in the second area, for some reassessment.

The first has to do with Newton's reputation on the Continent before 1699, the year in which he was made a foreign associate of the Royal Academy of Sciences in Paris. The second, which I shall treat in some detail, is the reassessment of the conventional picture—of Cartesians arrayed against Newtonians—which Pierre Brunet sets forth in his study of the introduction of Newton's physical theories in France before 1738, that is, before Maupertuis, Clairaut, and Voltaire hoisted the banner of Newtonian physics in France.⁵

When did scientists on the Continent first hear of Newton? By what stages did his reputation grow until, for his recognized accomplishments, he was honored by the Academy of Sciences in 1699? We can, I think, pass over the flattering reference to him by name, as early as 1669, in the preface of Isaac Barrow's lectures on optics, or the appearance of the edition of Varenius's Geographia generalis Newton published in Cambridge in 1672. Neither could have aroused much interest abroad in this obscure, if obviously very gifted, young Englishman.

The chief events that brought Newton's name before the European scientific public were doubtless: (1) the publication in February 1672 of his now-famous first letter on light and color;⁶ (2) his invention of the reflecting telescope, which brought about his election as F.R.S. in January 1672; and (3) Henry Oldenburg's orchestrated propaganda on Newton's behalf.

It was Newton's stubby little telescope, which promised to eliminate the chromatic aberration—the colored fringes—invariably encountered in the refracting telescopes of that day, that excited Christiaan Huygens (and others) when Oldenburg wrote him about Newton's discoveries.⁷ In the new theory of the origin of color, Huygens evinced little interest, although Oldenburg repeatedly importuned him for his opinion.⁸

The first French savant to give serious attention to Newton's early paper on light and color was the Jesuit scientist, Father Ignace Gaston Pardies (1636-1673). This has always struck me as curious. Pardies was not a member of the Academy of Sciences, nor had he any longstanding contact with the Royal Society.⁹ But he was a friend of Huygens, and a frequent participant at the meetings of the so-called Academy of the Abbe Bourdelot, an informal society, antedating the creation of the Academy.¹⁰ After 1666, the membership of Bourdelot's group consisted chiefly of persons whom the Academy, for one reason or another (such as being, like Pardies, a Jesuit) did not admit; but members of the Academy, Huygens among them, were sometimes seen chez Boudelot." Huygens, in any case, was aware that Pardies had a keen interest in optics, indeed was at work on a treatise that made use of a wave or pulse theory of the nature of light.¹² Perhaps Huygens, preoccupied with other matters (he had not begun to work out the theory he developed in his Traité de la lumière of 1690) brought Newton's paper to the attention of Pardies, with the suggestion that he evaluate it. All this, of course, is conjectural, but it may explain why Pardies's unsolicited paper, a letter to Oldenburg dated 9 April 1672, was the first response any French scientist made to Newton's new theory of color.¹³

Except for one element of confusion, the story of the cool reception of Newton's challenging new theory is all too familiar, and need not be repeated here. This element deserves at least a passing mention, otherwise it would be hard to understand the lack of interest in Newton's theory of color during these early years. Pardies never claimed to have repeated successfully Newton's famous two-prism experiment, the so-called experimentum crucis. Yet English or American readers could readily believe that this is so, if they confine their attention to the English version of the concessive phrases of Pardies's letter of 9 July 1672. The mistranslation of these important sentences appeared in the Philosophical Transactions Abridged (1809), which I. Bernard Cohen chose to use in his Isaac Newton's Papers and Letters on Natural Philosophy.¹⁴ This English version reads, with reference to the experimentum crucis, "When the experiment was performed after this manner, everything succeeded, and I have nothing further to desire."¹⁵ Pardies, in fact, having finally understood the experiment, with the help of a sketch supplied by Newton, had simply written: "L'experience ayant este faite de cette façon je n'ay rien A dire." There is no reference to an experiment "succeeding."

At all events it was Newton's optical work, together with the reflecting telescope, that first made his name familiar in French scientific circles.¹⁶ The experimental results he claimed, and the ingenuity of his theory, made it impossible to neglect his results for long. About 1679 France's leading experimental scientist, Edme Mariotte, determined to confirm or refute the Newtonian doctrine of color. He successfully repeated a number of Newton's experiments, but when he tried the experimentum crucis he concluded that the rays separated by the first prism did not appear to be monochromatic; on the contrary, they seemed to be further modified by the action of the second prism, yielding fringes of different colors.¹⁷ Newton's theory, he concluded, could not be accepted. For more than a generation, this was gospel in France, and Newton's theory of color remained in disfavor.¹⁸

It is generally agreed, although the supporting evidence has not been fully marshalled, that Newton's reputation in these years as a meteoric mathematical genius outshone his work on light and color or even the invention of his reflecting telescope. Although he had published none of his mathematical discoveries before the appearance of his Principia, his repute as a mathematician of extraordinary ability was clearly established.

As historians of ideas we are happiest when we can navigate from the firm ground of one document to the next, and we are prone to forget how great a part travel, gossip, and word-of-mouth have played in the diffusion of scientific knowledge, indeed of knowledge of all sorts. We are truly fortunate when surviving letters or memoranda give us some hint of these informal exchanges.

In 1669, the self-educated London mathematician, John Collins, that "clearing house for mathematical gossip," as D. T. Whiteside has called him, learned from Isaac Barrow of Newton's Deanalysi, the earliest of Newton's mathematical papers to be circulated.⁹ It contained an outline of his discoveries concerning infinite series and various applications of series expansion, but only a hint of the fluxional calculus. Collins, with his extensive contacts on the Continent, communicated Newton's results, but apparently not the precise methods used, to Slusius in Holland, to Jean Bertet and Francis Vernon in Paris, and to the venerable Giovanni Borelli in Italy. In May 1672, soon after he had learned about Newton's optical investigations, Christiaan Huygens heard from Henry Oldenburg that Newton had in hand an enlargement and corrected version of Mercator's Latin translation of Kinckhuysen's Algebra, a work for which Newton, it turned out, never found a publisher.²⁰

It was not long before Leibniz—diplomat, philosopher, and polyhistor, and soon to emerge as Europe's most brilliant mathematician—learned about Newton. We are so accustomed to thinking of these two great men in terms of their later dispute over the invention of the calculus or of their philosophical differences set forth in the letters of the Clarke-Leibniz correspondence, that we overlook their earlier relations, or at least the occasions on which Leibniz spoke of Newton with admiration.

In 1672 Leibniz came to Paris on a diplomatic mission, chiefly designed to dangle before Louis XIV the proposal that he embark on the conquest of Egypt to satisfy the French monarch's martial ambitions and to wean him away from invading the Low Countries and Germany. The plan was offered too late—although, long after, it appealed to Napoleon Bonaparte—for the troops of the Sun King were already on the march. During this visit, however, Leibniz formed a close tie with Christian Huygens, met other members of the Academy of Sciences, and must have learned something about Newton's reflecting telescope and the new theory of color.²¹

Early the following year Leibniz was in London where he surely heard echoes of Newton's mathematical prowess, for he came to know various English scientists (among them Oldenburg, Robert Boyle, and the mathematician John Pell) and attended a meeting of the Royal Society.²² Perhaps he met John Collins who, despite a lack of university training, had been made F.R.S. in 1667; but he certainly did not see Newton, comfortably immured in Trinity College, Cambridge. Leibniz's second English visit, in 1676, was in many respects more rewarding. At Collins's urging, Newton wrote for Leibniz his Epistola prior (13 June) describing his generalized binomial theorem. When Leibniz asked for more information, Newton replied with his Epistolaposterior (24 October) expounding in more detail his binomial theorem, but also giving the key to his calculus—to the general method of drawing tangents, solving problems of maxima and minima, and so on—but only by means of his famous cipher, a seemingly meaningless jumble of letters and numbers.²³ Leibniz was suitably impressed; and referring to Newton's work on series he wrote: "That remarkable man is one of the few who have advanced the frontiers of the sciences."²⁴

Whatever else it may have done—and it did not produce a crop of instant Newtonians across the Channel—the publication of the Principia greatly enhanced Newton's stature as a mathematician. As early as 1686, European scientists heard rumors about a forthcoming book by Newton. The source was, not surprisingly, Edmond Halley, who had not only cajoled Newton into writing and publishing it, and advanced the sum for printing it, but announced it in the Philosophical Transactions in 1686 and by personal letter. Huygens, for his part, learned of it in June 1687 through his young friend, Fatio de Duillier,²⁵ and wrote that he was eager to see the book.²⁶ His copy seems to have arrived sometime in 1688 and he read it carefully enough to comment on it that year, in what Westfall calls "a cryptic note": "Vortices destroyed by Newton. Vortices of spherical motion in their place."²⁷ Huygens's reference is to a theory he had defended as early as 1669 in a debate at the Academy in which Frenicle, Roberval, and others took part. While unhappy with the Cartesian vortex theory, he could not suffer Roberval's willingness to invoke an attractive power as the cause of gravity.²⁸ For an explanation to be intelligible Huygens argued, like the mechanical philosopher he essentially was, nothing should be invoked but matter in motion. He proposed a radical departure from the Cartesian tourbillons, suggesting that the circulatory motion of an aether or subtle matter took place in all planes about the earth; its tendency is everywhere centrifugal, thrusting heavy bodies toward the center.²⁹

Only the advent of Newton's Principia, with its references, albeit cautiously phrased, to an attractive force, caused Huygens to resurrect his early theory. Evidently he talked the matter over with Fatio de Duillier, for in July of 1688 Fatio was in England and described to the Royal Society the theory that Huygens had advanced to explain gravity. He promised "with Mr. Huygens's leave" to provide the Society with a copy "thereof in writing."³⁰ Whether this was done I do not know. In any case Huygens published his "Discours de la cause de la pesanteur" in 1690 as an appendage to his Traité de la lumière. Since the body of this little treatise, the "Discourse," had been written before the appearance of Newton's Principia, Huygens concluded with an "Addition" making mention of some of its contributions. It was impossible, he wrote, to withhold assent from the mathematical demonstration of Kepler's laws. Newton must be correct that gravity acts throughout the solar system and that it decreases in strength in proportion to the square of the distance. But the idea of an attractive force was unacceptable; gravity must be explained in some manner by motion.³¹

In 1688 reviews in European journals began to appear: in the Bibliothl'que universelle et historique, in the Leipzig Acta eruditorumn, and a well-known one in the Journal des s, avans.32 All attempted a summary of this complex book. But the reviewer in the Journal des scavans judged the Principia to be the work of a mathematician (un geometre) rather than that of a natural philosopher (un physicien). Its abstract, mathematical character was that of a work in mechanics (in the seventeenth century a recognized branch of the so-called mixed mathematics) rather than of a work of physics. To create a physics as perfect as his mechanics, so said the reviewer, the author must substitute real motions for those he has imagined.³³

Leibniz first read a summary of the Principia during a diplomatic mission to Italy in 1688, when a friend gave him some recent monthly issues of the Acta eruditoruin. In the June issue he read "eagerly and with much enjoyment" (avide et magna cum delectatione legi) an account of the celebrated Isaac Newton's Mathematical Principles of Nature.³⁴ The book itself, which had been given Fatio de Duillier to be sent to Leibniz, reached him in Rome, where he arrived on 14 April 1689.³⁵

After reading the summary of the Principia in the Acta, Leibniz—like Huygens—was inspired to put down his own views. His treatise attempting to explain the motions of the heavenly bodies (the Tentamen de motuum coelestium causis) was dispatched to the Acta from Vienna and published in the issue for February 1689.³⁶

The Principia was not as ignored on the European continent as is sometimes believed, yet Huygens and Leibniz were the only competent, sophisticated, and persistent critics of Newton's theory of celestial motions. They studied each other's attempts to devise a theory more compatible with their adherence to the mechanical philosophy, yet not at odds with Newton's manifest discoveries. From 1690 until Huygens's death in 1695 their points of agreement and disagreement, with each other and with Newton, frequently arose in their correspondence.³⁷ Both men were convinced that the tourbillons of Descartes had to be abandoned if Kepler's empirical laws were to be explained by a "deferent matter" carrying the planets around.³⁸ Neither accepted Newton's use of attractive forces, or was at all certain what Newton meant by his use of the word "attraction." On certain fundamental matters the two men differed. In April of 1692 Leibniz wrote: "In rereading your explanation of gravity recently, I noticed that you are in favor of a vacuum and of atoms.… I do not see the necessity which compels you to return to such extraordinary entities."³⁹

It should be noted that neither man attacked Newton in print, despite their differences with him. Both held him in high regard. Leibniz's position was not greatly different from the views set forth in the addition Huygens made to his "Discourse." It is true, Leibniz wrote Huygens in September 1689, that according to Newton's explanation planets "move as if there were only one motion of trajection or of proper direction, combined with gravity," yet they also move "as if they were carried along smoothly by a matter whose circulation is harmonious."⁴⁰ And he adds that he cannot abandon his deferent matter because he can find no other explanation for the fact (true as far as astronomical knowledge went in the seventeenth century) "that all the planets move somewhat in the same direction and in a single region." In a letter to Newton, written in March 1693, Leibniz is generous, and I think sincere, in his praise, yet candid as to the nature of his disagreement:

How great I think the debt owed to you, by our knowledge of mathematics and of all nature, I have acknowledged in public also when occasion offered.… You have made the astonishing discovery that Kepler's ellipses result simply from the conception of attraction or gravitation and passage [trajectio] in a planet. And yet I would incline to believe that all these are caused or regulated by the motion of a fluid medium, on the analogy of gravity and magnetism as we know it here. Yet this solution would not detract from the value and truth of your discovery.⁴⁸

Leibniz's last sentence is especially interesting, for it echoes the widely held position that Newton's brilliant explanation is a mathematical "hypothesis" that saves the phenomena, but does not provide a valid "physical" account.

Whatever their reluctance to follow Newton into the mysterious realm of an attractionist dynamics, the readers of the Principia were provided with the best illustration of his mathematical brilliance, with tantalizing glimpses of his new calculus, veiled though it was by a geometrical, rather than an analytical, presentation. What both Huygens and Leibniz saw in the Principia aroused their curiosity and their interest in the rumor that the expected Latin version of John Wallis's Algebra was to contain something by Newton himself about his new methods. Both Leibniz and the Marquis de l'Hospital (of whom more shortly) asked Huygens, as soon as a copy should reach him, to transcribe the Newtonian passages for them. When Leibniz finally received his copy of the extract, he thanked Huygens, but expressed his disappointment; much that he found there, he wrote, was already familiar to him.⁴²

I should like to turn my attention to the second area of this proto-investigation: the need for a reassessment of the so-called Cartesian-Newtonian debates in France before 1738. 1 doubt that we can accept, without modification, the highly polarized—indeed oversimplified—image that Pierre Brunet has handed on to us. To this end I wish first to discuss briefly the central figure of this reinterpretation: the French philosopher, Father Nicolas Malebranche (1638-1715). Malebranche has aroused a mild amount of interest on the part of English and American historians of philosophy for the influence he exerted upon the thought of John Norris and Bishop Berkeley, on Hume's dismemberment of the notion of causation, and at one remove upon the American Samuel Johnson (1696-1772). For most modern writers, however, Malebranche simply appears as a relic of a religious age, a metaphysician whose goal, unlike that of Descartes to whom he owed so much, was to put the master's New Philosophy at the service of religion, not for ensuring man's dominance over nature. While it is not difficult to describe Malebranche's philosophical position—it has been done many times—it is less easy to categorize him and determine at what points, and how far, he departed from Descartes.⁴³ His Christian metaphysics can be described as more voluntarist than (in the theological sense) rationalist, and his epistemology is often summed up in the phrase that "we see all things in God." The influence of Saint Augustine was acknowledged by Malebranche himself,⁴⁴ but his Platonism is also evident: ideas are not innate in the human mind (in the Cartesian sense); they are imperfect reflections of ideas in God. Indeed, it is not too much to say that Malebranche anchored Plato's archetypal ideas in the divine mind. His doctrine of occasionalism, by no means original with Malebranche, is always stressed when his philosophy is summarized: events in the physical world are not caused, but provide the occasion for God, constantly conserving his creation,⁴⁵ to set in motion laws of nature which we perceive as rapports, or relations, between the objects of our experience.

Malebranche came to philosophy, to Descartes, and to mathematics, fairly late in his career. Frail as a child—indeed appearing so all his long life—he was educated at home until 1754-1756 when he studied at the College de la Marche under a Peripatetic master. After three years of theological study at the Sorbonne, he began his novitiate in 1660 in the Congregation of the Oratory, a priestly order founded by Pierre Berulle during the Catholic religious revival in early seventeenth-century France, and which soon was famed as a liberal teaching order. He was ordained in 1664, having devoted himself to Church history, biblical scholarship, and the study of Hebrew. From that time on until his death he lived in the Paris house of the Oratorians on the rue St. Honore, across the street from the Louvre where the Academy of Sciences, to which he was admitted in his later years, held its biweekly meetings.

As is well known, Malebranche's intellectual inspiration—what has been called his conversion—came from his reading of Descartes's posthumously published Traité de l'homme (1664), which aroused his interest not only in physiology and psychology, but in other branches of science and the great scheme of Cartesian philosophy.⁴⁶ He cast aside his historical and linguistic inquiries and set out to master all the writings of Descartes. From these, notably the Géométrie, stemmed his preoccupation with mathematics, and his urge to keep abreast of developments in the sciences. These interests are clearly evident in the first edition (1675) of his most important work: the Recherche de la verite. This work shows his familiarity with discoveries in embryology, microscopy, and the psychology and physiology of perception.⁴⁷ He admired Mariotte's work, as exemplifying the role of experiment, and cited Von Guericke's famous experiments. The books in his library tell us still more: on hhs shelves were the writings of Steno, Bartholinus, Malpighi, Pecquet, Redi, and Swammerdam among other physiciaos and naturalists. Chemistry, where we note the books of Beguin, Robert Boyle, and Christopher Glaser, played only a small part. But he owned, among physical and astronomical works, Kepler's Epitome astronomiae Copernicanae, Huygen's Horologium, and La Hire's Traité de mécanique."

Of the scientific disciplines, the centrally important one for Malebranche was mathematics. His library was rich in mathematical works: besides the classical authors (Euclid, Apollonius, and the rest) and of course, the Géométrie of Descartes, he owned the books of Herigone and Slusius, Oughtred's famous Clavis, Franz van Schooten's Exercitationes (the chief work that made Descartes's analytical geometry comprehensible) and Isaac Barrow's Mathematical Lectures.49 And Malebranche once described mathematics as "the foremost and fundamental discipline of all the human sciences," excluding, that is, theology, which is a divine, not a human, subject.

At the Oratory, always the teacher, Malebranche brought together a group of mathematicians and physicists who are fairly credited with introducing the Leibnizian calculus into France,⁵⁰ and this in turn opened the way to the fuller understanding of Newton's accomplishments. With one of his early disciples, Jean Prestet (1648-1690), Malebranche supervised, or at least collaborated in the writing of, an Elemens des mathématiques (1675) that was published under Prestet's name. Malebranche was later to disavow this conservative treatise, for it supported the Cartesian position that mathematics has no business dealing with the infinite, whether large or small. Later this group came to include a fellow Oratorian, Father Charles-René Reyneau (1656-1728), Louis Carré (1663-1711), Pierre Rémond de Montmort (1678-1720), and the man whom Andre Robinet has called the leader, the "chef de file," of the Malebranchistes: the Marquis de l'Hospital (1661-1704). These men not only introduced the Leibnizian calculus into France, but defended it against its conservative detractors, like Pierre Rolle (1652-1749). On the fringes of this group, all of whom sooner or later became members of the Academy of Sciences, stood the figure of Pierre Varignon (1654-1722), something of a late convert to the new mathematics.

The steps by which the calculus came to France have often been retraced, and a brief summary here should suffice. Leibniz's first publication of 1684 on the calculus was a compressed memoir of six pages published in the Acta eruditorum. Cryptic, tightly constructed, and further obscured by numerous misprints, it made no immediate impact upon the scientific world. Nevertheless, without instruction or elucidations from Leibniz, Jacob (James) Bemoulli, a professor of mathematics at Basel, fought his way through it, and taught it to his younger brother Johann (John or Jean I). Johann, on a visit to Paris in 1691-1692, came into contact with Malebranche and his circle and lectured on the Leibnizian calculus. His lessons, as well as notes taken by Malebranche, have survived.⁵¹ Here Johann met the Marquis de l'Hospital, who became his most assiduous convert, studying with him in Paris and engaging him to continue his teaching at l'Hospital's country seat at Oucques, a village in the Orleanais. In 1696 appeared the first French textbook of the calculus, I'Hospital's Analyse des infiniment petits pour l'intelligence des lignes courbes.52

Before going further, we should perhaps stop to ask what made the Malebranche circle, and Malebranche himself, so receptive to the Leibnizian "infinitesimal calculus," as it soon came to be called. How, to paraphrase Andre Robinet, can one explain the transformation of Malebranche-Prestet, opposed to infinitudes, into Malebranche-l'Hospital, so readily persuaded to adopt this radical new posture?

Various scholars have pointed out the fact that Malebranche's metaphysical principles dovetailed admirably with his mathematical interests. In particular, it has been suggested that the philosophy of mathematics Malebranche evolved in his later years—which tied in closely with his epistemology, and which can be traced as it evolved in later editions of the Recherche de la verite—was a powerful force leading him to depart from the strictly Cartesian mathematics with which he had begun.⁵³

Malebranche's theory of mathematics is intimately tied to his metaphysical postulate that the only truth open to man's finite intellect is the perception of the relations, the rapports, between things; knowledge can only be knowledge of such relations. Furthermore, the clearest and most distinct relations we can determine are those of equality and inequality: relations of magnitude. Consequently, since mathematics is precisely the science of these relations, it is the most exact and unimpeachable form of knowledge we can attain. The emphasis here, as in Malebranche's epistemology, must be placed on formal relations, relations of relations, and so on, instead of on conceivability. These basic assumptions led to important consequences: (1) doubts were set aside as to the logical foundations of the calculus, widely recognized as dubious, so the way was opened to accept infinitesimals, the inconceivable "infinitely small"; and (2) a premium was placed upon enriching and developing the mathematically expressed laws increasingly used to describe the observed relations of the natural world; (3) finally those, or at least some of those, who accepted these assumptions, were disposed to look with a degree of understanding upon Newton's mathematical world picture.

It would be interesting to know with some exactitude when Malebranche, or members of his group, first came to know Newton's Principia. What Paul Mouy calls the "diatribe" against the idea of attraction in the first edition of the Recherche de la verite (1675) could not, from the date alone, have been directed against Newton who, in any case, was invoking the aether in his "Hypothesis explaining the properties of light," and was not (as Mouy has claimed) already an attractionist. We are told that Malebranche first came into direct contact with Newton's writings sometime between 1700 (when the fifth edition of the Recherche appeared) and the year 1712, when the sixth edition of that work was published.⁵⁴ This may be so, for Malebranche read Newton's Opticks soon after its appearance and became at least a partial convert to Newton's discoveries about color. Yet he certainly knew about the Principia, and heard it discussed, at a much earlier date. A letter from Malebranche's friend Jacquemet to Charles-René Reyneau, written on 9 April 1690, contains the remark—if indeed it was not a boast—that he, Jacquemet, had completed his reading of Newton's book earlier that year.⁵⁵ Yet, although there is no mention of the Principia in Malebranche's Recherche, there is a passage in the sixth edition of that work (the edition where his approval of Newton's optical experiments is announced) which suggests that he had grasped Newton's essential discovery concerning planetary motion. For what the evidence is worth, we know that a copy of the first edition of the Principia is listed as having had a place on Malebranche's bookshelves.

It was soon evident to the men of Malebranche's circle that Newton's celestial dynamics—his mathematical approach to physical nature—had to be taken seriously, despite his attack on Descartes's vortex theory of planetary motion, from which they could not free themselves completely. There was much in the Principia with which they were intellectually attuned: newly discovered relations or rapports, laws of the physical world, the mathematical approach to nature. It struck a number of them that this Newtonian mathematization of nature could be clarified and enriched if it could be translated into Leibnizian analytical methods and symbolism.

Both Johann Bernoulli and the Marquis de l'Hospital began cautiously to treat central forces analytically. But it was Varignon, Professor of Mathematics at the newly founded College Mazarin (a post he later combined with a chair at the College Royal), who took up these questions as matters of real importance. Earlier he had remained faithful to Descartes and had difficulty in moving beyond a mathematics of finitude to an acceptance of the Leibnizian calculus. But at last, reassured by Malebranche's position on mathematical intelligibility (as distinguished from conceivability), he became a convert to the new mathematics and turned to applying the calculus of Leibniz to Newtonian dynamics.⁵⁶ In a series of papers contributed to the Memoires of the Academy of Sciences during the early years of the eighteenth century he treated such problems as: (1) given the law of force, to find the path of a moving body; or (2) conversely, given the path, to find the implied law of force. He was able to show, for example, that a logarithmic or hyperbolic spiral path implied a central force proportional to the cube of the distance.

Earlier in this paper I questioned the sharp polarity between Cartesians and Newtonians that Voltaire taught us and which, in our century, Pierre Brunet set forth in his book on the acceptance of the Newtonian physics in France. I shall now suggest that the followers of Malebranche—indeed the aging philosopher himself—occupied a midway position, and conceded enough to Newton to pave the way for the full-fledged Newtonianism of the later eighteenth century. These men, far from merely tinkering with Descartes's tourbillon model (which they continued to do as had Huygens and Leibniz), abandoned at least the outworks of the Cartesian fortress. These Malebranchistes in the Royal Academy of Sciences brought into the Age of Enlightenment not only Malebranche's doctrine that knowledge of nature is a knowledge of mathematical relationships, but carried too the Master's respect for evidence, his willingness to recast, or depart from, the specific doctrines of Descartes. In so doing they weakened the opposition to Newton and prepared the way for the more militant Newtonianism of Maupertuis, Clairaut, and Voltaire in the late 1730s. Let me offer the following general propositions to be examined a fond by others:

1. These Malebranchistes (and in this they were not alone) recognized Newton as a major figure to reckon with, not only in mathematics, but in the mathematizing of nature.
2. On the basis of what they regarded as Newton's experimental brilliance, they were the first in France to deem Newton's optical experiments a model of proper procedure to follow, and an essential part of his doctrine of the origin of color, albeit with certain theoretical deviations.
3. They were won over to Newton's laws, the inverse square principle of "universal" gravitation, and the successful application of his mathematical rules of nature to Kepler's empirical description of planetary motion.

All this they accepted without being obliged to adopt the notion of a void, and the apparently absurd notion of bodies attracting one another through the emptiness of space. Although all adhered to some sort of doctrine of an aetherial vortex, the concessions, the departures from Descartes, paved the way for an overt acceptance of Newtonian doctrine, root and branch.

The first steps were taken by Malebranche himself when in several respects he departed from Cartesian physical thought. Most thoroughly studied are the changes he made in the Cartesian laws of impact—probably influenced by the experiments of John Wallis and of Mariotte—but he further denied that cohesion and solidity were simply caused by matter at rest. Indeed, in suggesting that rest is a mere privation of motion, he came close to the Newtonian position that rest and motion are merely "states" of matter. More fundamental, perhaps, was his modification of Descartes's theory of matter.⁵⁷ Descartes constructed his universe of three elements: his first element is composed of exceedingly fine particles that make up the luminous matter of the sun and fixed stars, and are so fine, and of such varied shapes, that they can fill all the spaces between the other elements. The second element is the key to Descartes's physical model; it consists of rounded, hard, and inflexible particles through which the light of the sun is instantaneously transmitted to illumine the larger masses of the terrestrial bodies: the earth, moon, the planets and their satellites, that make up the third element.

Malebranche, even before encountering Newton, had fundamentally revised this picture of the second element. Instead of being hard spheres, the particles are compressed fluid matter, tiny vortices. Nor did he precisely follow the Cartesian theory of the nature of light. For example, Olaus Roemer's discovery convinced him that light was not transmitted instantaneously, but required time for its passage through the second element.

Soon after his election to the Academy of Sciences in 1699, Malebranche communicated a theory of light and color that departed from Descartes. Here he attempted to supply a mechanical model, a plausible hypothesis, to account for the origin of color. Light, to Malebranche as to Pardies, Huygens, and others, is a pulse or vibratory motion of the aether or second element. But for Malebranche, colors result from the different frequencies of these pulses. Not all the hues of the spectrum are produced by this mechanism, but only the primaries (red, yellow, and blue). The sensation of white is produced when the original vibrations from a luminous source are unaltered in their transmission.⁵⁸ This is a version of what historians call a modification theory of prismatic color.

At the time his paper was presented, Malebranche seems to have been wholly ignorant of, or indifferent to, Newton's famous early paper of 1672.⁵⁹ In 1706, it seems, the Latin edition of Newton's Opticks came into his hands, and he was soon converted. Thus when he prepared the last edition of his Recherche de la verite, the sixth (1712), he profoundly altered that appendix or "eclaircissement" he had added in 1700 and which was, in effect, his 1699 paper. In his revision he accepted Newton's notion that there existed in white light an infinite range of properties producing the different colors. The colors corresponded to various frequencies which the prism sorted out. Each color, he wrote, citing the "excellent work of M. Newton," has its characteristic refrangibility. He even adopts Newton's terminology, at least up to a point. The "primitive colours" of his earlier paper he now refers to, as Newton does, as "simple" or "homogeneous." White solar light ("the most composite of all") is described according to his own adaptation of Newton as "composed of an assemblage of different vibrations." Owing in part to Malebranche's great influence, Newton's Opticks was accepted, early in the eighteenth century in France, as a model of scientific inquiry.⁶⁰ One of Malebranche's disciples, Pierre Varignon, was a key figure in seeing through the press the Paris edition (1722) of Pierre Coste's French translation of the Opticks.⁶¹ But it should be emphasized that there is no evidence that Malebranche, an elderly cleric, repeated any of Newton's optical experiments. He seems simply to have been persuaded by Newton's testimony as presented in the Optice. This last edition of the Recherche shows that Malebranche was led on to the Principia, for he added a sort of appendix to his theory of little vortices to alter the Cartesian explanation of gravity and adjust his thought so far as possible to Newton's findings.

To illustrate my point that we can no longer justly speak of an academic world divided between Cartesians and Newtonians (or, if you will, dominated by strict Cartesians struggling to fend off a Newtonian invasion) I should like to say something about three of Malebranche's disciples and admirers: the Oratorian father, Charles René Reyneau, Jean-Baptiste Dortous de Mairan (1678-1771), and Joseph Privat de Molieres (1676-1742).

In 1708 Father Reyneau, a professor of mathematics at Angers, published his Analyse demontrée which continued and brought up to date Descartes's work on the theory of equations and introduced the reader to the calculus. Modern analysis, he wrote, had its beginnings in Descartes's Géométrie. But Descartes lacked a mathematics that could precisely represent nature; for nature produces curves by continuous motion, and nature's curves are made up of "parties insensibles," parts smaller than we can determine, and of instants of time swifter than we can imagine. What was needed was a new form of mathematical expression, and this was devised "at the same time in Germany by M. Leibniz and in England by M. Newton." Further on the mentions the "savant ouvrage" (the learned work) of Newton, the Principia.⁶²

Dortous de Mairan, a young provincial of the country gentry, was born in Beziers. He was sent to Paris to attend a sort of finishing school, where horsemanship, fencing, dancing, and other proper accomplishments were taught to young noblemen. In Paris, he came under the spell of Malebranche who taught him to understand the Marquis de l'Hospital's Analyse des infinment petits, and gave him other lessons in mathematics and physics.⁶³

Mairan returned to his native Languedoc. Uncertain of his future course, he toyed with the philosophical and theological difficulties encountered in reading Spinoza, and wrote his old teacher, the aging Malebranche, for guidance.

In their correspondence, Malebranche not only rescued Dortous from the pitfall of Spinozistic pantheism, but incidentally informed his young friend that he had abandoned his earlier views about light and color after reading Newton's Opticks. He went on to tell Mairan (in August 1714) that his version of Newton's theory could be found in the last edition of his Recherche. Mairan promptly acquired Malebranche's book, and probably soon afterward the Latin Optice as well, for Pierre Coste, the translator of the Opticks into French (1720 and 1722), tells us that Mairan in 1716-1717 was the first in France to repeat successfully Newton's optical experiments. The influence of Newton's work soon became apparent in Mairan's memoirs. In his earliest scientific contribution, his Dissertation sur les variations du barometre (Bordeaux, 1715), he mentioned Richer's discovery that a pendulum, whose period of oscillation in Paris is a second, has to be shortened near the equator. And he remarked that "certain celebrated mathematicians" had concluded that the earth was a globe flattened at the poles. A note cites Huygens's Discours de la cause de la pesanteur and Newton's Principia.64 The following year (1716) in his Dissertation sur la glace Mairan showed himself quite at home with the Optice, for he wrote about the relation of color to refrangibility, the transparency of bodies, and other matters discussed by Newton.

The most explicit of Mairan's early references to Newton's work on light and color appears in a short essay on phosphorescence published in 1717.⁶⁵ Here he summarized Newton's discovery that each colored ray has its characteristic refrangibility, and recounted the "ingenious experiments" which had led Newton to this discovery "in order to acquaint those who have not seen the Opticks of Mr. Newton with what I shall have to say on this matter."

Not so long after, we find Mairan in Paris, for in 1718 he became associé gèométre in the Academy of Sciences, taking the place of Guisnée, a member of Malebranche's circle who died in that year. His earliest contributions as an academician show the profound influence the Opticks had on him. In one, he draws upon Newton's analogy between the colors of the spectrum and the intervals of the octave and suggests that, just as Malebranche believed colors to be caused by differently vibrating globules of the matière subtile, so air must transmit sound by means of distinct particles having different rates of vibration.⁶⁶ In another paper he argued against Descartes's theory that colors are derived from the differential rotation of kinds of globules, by showing that spheres rotating differently and striking a surface obliquely would reflect at different angles. Thus, contrary to the established law of equiangular reflection, rays of different colors would then have characteristic reflectivities.⁶⁷ Mairan, more explicitly than Newton, held an emission theory in which light rays consist of trains of corpuscles, of corps lumineux. Moreover, he believed that reflection does not occur at the point of actual contact of rays of light with a solid surface, but when the corpuscles encounter a "fluide subtile répandu dans leurs pores," a view he recognized as similar to that held by Newton in the Opticks.⁶⁸

There can be little doubt that Mairan was reluctant to abandon the mechanism of subtle fluids, nor that he felt increasingly allured by Newton's views and by his own respect for experimental evidence. Often he was troubled by contradictions in empirical data and he tried to reconcile them. For example he found Jacques Cassini's geodetic measurements, leading to the inference of an elongated earth, in conflict with Huygens's and Newton's inference from Richer's pendulum observations at Cayenne that the earth should have the shape of an oblate spheroid. He attempted to show that both observations led to a sphéroïde oblong, if one denied the primitive sphericity of the earth which Huygens had assumed as a postulate.⁶⁹

Mairan's reluctance to give up the vortex theory led him to some extraordinary mental gymnastics. A much-cited argument against Descartes's tourbillons was the existence of retrograde comets, comets whose motion is opposite to that of the planets. Mairan pointed out that planets at portions of their orbits appear to stop and reverse their "direct" motion from west to east, but he pointed out that this is merely an optical effect produced by a combination of the earth's revolution and the direct planetary path. Could not retrograde comets be planets that are only visible during the retrograde portion of their path?

Unlike some of his contemporaries who favored the existence of a deferent subtle fluid, Mairan had—even more than Malebranche—a keen respect for observed fact. Certain Cartesians, like Villemont, argued that comets did not enter the solar system below Saturn. Mairan knew that in fact, on occasion, they did. But if they come close, yet do not penetrate our solar vortex, then our vortex, Mairan argued, cannot be spherical but must sometimes be depressed. Comets, he suggested, are planets of nearby vortices, moving about their own suns; their vortices can act upon others, including ours, engaging one another, as Fontenelle put it—like gears of a clock—but altering their shape. The flattening of our vortex allows comets to approach closely yet without penetrating it.⁷⁰

We can detect, I believe, a growing familiarity with, and acceptance of, much that we associate with Newton. In a memoir of 1724 he sought to explain short-range forces of attraction and repulsion, in particular the behavior of water and mercury in capillary tubes. Assuming that around all bodies—not only magnets—there is an atmosphere of matière subtile, he sought to explain why bodies attract or repel. Water wets glass because the atmospheres are in some manner compatible, whereas in the case of mercury its surrounding atmosphere is opposed by that of the glass, thus accounting for the convex meniscus. Here, as Fontenelle perceived, Mairan was toying dangerously with those attractive forces which a good Cartesian held in abhorrence.⁷¹

Another problem brought the Cartesian scheme into court, that of the diurnal rotation of the earth. The Newtonian world view simply took the spin of the earth for granted: once established, inertia would keep the planets rotating. But there was no way that the Newtonian attractionist system could start a planet spinning. A Cartesian vortex by itself was little help: indeed it would seem to demand a rotation opposite to that which actually takes place. Mairan believed the key was the assumption that the two hemispheres of a spherical planet must "weigh" differently towards the sun, according to the inverse square law of gravity, and respond oppositely to the deferent fluid of the vortex. Brunet found it ironic that a Cartesian should find it necessary to go to Newton for principles with which to defend Cartesianism.⁷²

There is clear evidence that Mairan was moved to study the Principia. From Newton's gravitational data, he estimated the relative weight of an identical mass on the surface of the sun and on the earth, noting that the numbers Newton cited differed in the three editions, because—he pointed out—Newton used different values for the solar parallax. By 1733 Mairan had not only made use of points here and there in the Principia but had gone a long way toward accepting Newton's celestial dynamics, and the Newtonian principle that central forces in the solar system operate according to the inverse square law. These laws of the solar system, he wrote, are well known and fit modern observations. And he continues:

We therefore admit these principles in conformity with what one finds about them in the Mathematical principles of Newton … without claiming to enter … into the discussion of causes.

The heavens better understood, the laws of motion better developed, gave to this great man [Newton] an advantage over Descartes and the early Cartesians which cannot deprive them of the glory they have justly gained…or forbid them the use of knowledge that time has brought forth, on the pretext that this knowledge did not emanate from their school.⁷³

My third specimen, Joseph Privat de Molières (1677-1742), was, like Dortous deMairan, a man from the Midi. Born in Provence of a distinguished family he was educated in various nearby Oratorian schools (at Aix-en-Provence, Arles, and Marseilles), eventually ending up at Angers, where he studied mathematics and natural philosophy with Charles René Reyneau in 1698-1699. This relationship influenced his future. Against the wishes of his family, he became a priest of the Congregation of the Oratory, and in 1704, determined to devote his life to science, he came to Paris to sit at the feet of Malebranche and absorb his wisdom.⁷⁴ To Malebranche's influence we can safely attribute his central concern: the elaboration of a modified Cartesian physics in which, while remaining faithful to the notion of a plenum and to strictly mechanical explanations, he attempted to account mathematically for the inverse square law of gravitation and Newton's demonstration of Kepler's laws, by means of a modified vortex model.

In 1721 Privat de Molières entered the Academy of Sciences as adjoint méanicien, and two years later he succeeded Varignon as professor of philosophy at the Collège Royal. In memoirs read to the Academy in 1728 and 1729, and at greater length in the four volumes of his Leçons de physique—lectures delivered at the Collège Royal and published between 1734 and 1739—he concentrated upon what Mme du Châtelet called the "curious business" of trying to reconcile Newton and Descartes. The result was what Robinet has called a "monument malebranchiste," in which—while opposing the doctrines of empty space and the hypothesis of attraction—he freed himself from the narrow Cartesians and took the position of the "cartésiens malebranchistes réformateurs."⁷⁵

In 1728, taking his cue from Varignon's work on central forces, he launched his effort to shore up the theory of tourbillons by a mathematical analysis of the centrifugal forces at work in a cylindrical vortex whose axis is equal to the diameter of its base. He found that if the various layers into which one imagines the cylindrical mass to be composed revolve in times proportional to the distance from the axis, no part or globule will approach or recede from the axis. On the other hand, in a spherical vortex the condition of equilibrium is different: there will be stability of all layers if the central forces are inversely as the square of the distance from the center.⁷⁶ Privat de Molières claimed to show, also, that in a spherical vortex the distances from the center of points moving in the concentric shells are as the cube roots of the squares of the periodic times. This, he pointed out, was "la fameuse règle de Képler."⁷⁷ Unfortunately, as he recognized, this held only for points moving in the plane of the equator, and his law lacked the generality it had with Kepler and Newton.

In 1729 he tackled the problem of deriving Kepler's First Law, i.e., the elliptical path of planets, from vortex theory.⁷⁸ It was clear that the problem was insoluble if the vortex was made up of the hard globules of Descartes. In consequence, he adapted Malebranche's theory of petits tourbillons, of small, elastic vortices, composed in their turn of still smaller vortices (tourbillons du second genre).79 In effect he assumed the infinite divisibility of matter, imagining as many levels as were necessary to account for particular phenomena, and applying to matter the infiniment petits so useful to the "mathematicians of our age." His model envisaged a planet moving in a vortex "distorted into an elliptical shape by the unequal pressures of the neighbouring vortices."⁸⁰

In the Leçons de physique his theory of mini-vortices was elaborated and applied not only to celestial mechanics, but also to chemistry and electricity. The successive volumes of the Leçons received the official approval of committees of the Academy of Sciences, on each of which sat his Malebranchiste colleague, Dortous de Mairan.⁸¹ From the first, Privat de Molières set out to demonstrate, as he put it, that "the chief doctrines of the two most celebrated philosophers of our time, Descartes and Newton," which appear so incompatible, can in fact be reconciled. In a series of closely articulated propositions, the reader, he predicted, will find "perhaps with surprise that, although the two men followed what seem to be completely opposing paths, these paths nevertheless led to the same goal." And Privat goes on confidently:

You will see emerging out of the plenist system that Descartes followed, even Newton's void, that non-resisting space of which this philosopher has irrefutably established the existence.

And from impulse or impact he will find derived that attraction of gravity

which increases and decreases inversely as the squares of the distances, from which Newton, without however being able to discover the mechanical cause, has drawn so many splendid consequences, based on a calculus … of which this great man is the first inventor.⁸²

Dortous de Mairan and Privat de Molières have both been described as leading eighteenth-century Cartesians. Pierre Brunet gives special treatment to both men in his chapter entitled "L'effort des grands cartesiens." Quite recently Martin Fichman wrote in his article in the Dictionary of Scientific Biography that Dortous de Mairan was a "major figure in the protracted struggle against the importation of Newtonian science in France," and "devoted his career to developing and improving Cartesian physics."

Yet both writers—Brunet and Fichman—have had to emphasize that the two men in question were by no means rigidly Cartesian. At one point, Brunet remarked that while Dortous remained attached to Cartesianism on most fundamental questions (whatever that may mean) he was nevertheless enticed—his word is seduit—by Newton's ideas, chiefly because of his admiration, like Fontenelle's, for Newton's experimental skill. And Martin Fichman conceded in another Dictionary article that Privat de Molières, while persuaded of the correctness of Descartes's ideal of a purely mechanical science (that is, of a mechanics of impact) was nevertheless "cognizant of the superiority of Newtonian precision in comparison with Cartesian vagueness in its explication of natural phenomena." Vagueness is hardly a word I should use in connection with Descartes. I was glad to discover that my friend John Heilbron of Berkeley, in his book on the early history of electricity, quite bluntly and accurately calls Privat de Molières "a devout Malebranchiste."

I can only repeat the main theme of this part of my paper: that Malebranche and his followers broke down the initial barriers of the Cartesian fortress, and made the way easier for radical Newtonians like Maupertuis, Clairaut, and Voltaire.⁸³ Paul Mouy did not exaggerate when he wrote that around 1730 an eclectic fusion of Malebranchiste and Newtonian ideas was very much a la mode in French science. As Voltaire's Minerva of France, his "immortelle Emilie," wrote of Cartesianism to Cistemay Dufay: "It is a house collapsing into ruins, propped up on every side…I think it would be prudent to leave."⁸⁴

Notes

From History of Science, 17 (1979). Originally entitled "Some Areas for Further Newtonian Studies," this paper was presented at a Colloquium held at Churchill Collège, Cambridge, in August 1977 and devoted to this subject. The problems raised here were first gone over in my graduate seminar at Cornell in 1962, and I am indebted to the stimulus of my students.

¹ Daniel Mornet, Les sciences de la nature en France au XVIII' siècle (Paris, 1911); Preserved Smith, A History of Modern Culture, II (New York, 1934), esp. chaps. 2-4.

² Helene Metzger, Attraction universelle et religion naturelle chez quelques commentateurs anglais de Newton (Paris, 1938).

³ The distinction between "internal" and "external" influences upon science is older than the present-day methodologists of the history of science may realize. 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 Comite Belge d'Histoire des Sciences, and published as "Les influences dans l'histoire des sciences," in the Archives internationales d'histoire des sciences, 1 (1947-48), 347-353.

⁴ Margaret C. Jacob, The Newtonians and the English Revolution, 1689—1720 (Ithaca, N.Y., 1976).

⁵ Pierre Brunet, L 'introduction des théories de Newton en France au XVIIIe siéle, I: Avant 1738 (Paris, 1931). This one volume carrying the story to 1738 was all that was published.

⁶Phil. Trans., 6 (1671-72), No. 80, 3075-3087. Newton's "Accompt of a New Catadioptrical Telescope" was published later in the same volume, 4004-4010. These optical papers may be conveniently consulted in Newton's Papers, pp. 47-67.

⁷ Oldenburg first informed Huygens of Newton's new kind of telescope by letters of I and 15 January 1671/72. See Oeuvres de Huygens, VII (1897), 124-125, and 128; also Newton Correspondence, I (1959), 72-76, and 81-82; and Oldenburg Correspondence, VIII (1971), 443-445, and 468-473. 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.

⁸ In March 1672 Oldenburg sent Huygens the number of the Transactions containing Newton's pioneer paper on light and color, asking for his opinion of the new theory. See Oeuvres de Huygens, VII, 156; Newton Correspondence, I, 117; and Oldenburg Correspondence, VIII, 584-585. 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 expéiences" (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.

⁹ 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, 143-145).

¹⁰ The Academy of the Abbé Bourdelot has been described in Harcourt Brown, Scientific Organisations in Seventeenth Century France (1620-1680) (Baltimore, 1934), chap. 11.

¹¹ 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, p. 233.

¹² 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), unpaginated dedicatory preface and p. 14. If Pardies had accepted Newton's theory of color, there is no trace of it in Father Ango's book, where all the colors are explained according to the old theory of a mixing of black and white.

¹³ For Pardies's first letter see Newton Correspondence I, 130-133.

¹⁴Philosophical Transactions Abridged (London, 1809), VII, 743, and Newton's Papers, p. 109. The three-volume abridgement of the early Transactions by John Lowthorpe (London, 1705), gives Pardies's statement of concession only in Latin (I, 144).

¹⁵ The italics in the quotation are my own.

¹⁶ For the French original of this passage see Newton Correspondence, I, 205-206. 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 cúm fuerit isto modo, nil habeo quod in eo desiderem ampliùs (Phil. Trans., 7 [1672-75], 5018, reproduced in Newton's Papers, p. 103).

¹⁷ Edme Mariotte, De la nature des couleurs (Paris, 1681), p. 211. This paper was reprinted in the Oeuvres de Mariotte,2 vols. (Leiden, 1717), I, 227-228, and in a later edition of the Oeuvres, 2 vols-in-one (The Hague, 1740), consecutively paginated. The supposed refutation of Newton's experiment appears on pp. 227-228 of this edition.

¹⁸ For new material on the later stages of the penetration of Newtonian optics into France see A. Rupert Hall, "Newton in France: A New View," History of Science, 13 (1975), 233-250.

¹⁹ Derek T. Whiteside, 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 Whiteside, Newton's Mathematical Papers, II (1968), 206-247.

²⁰ Newton Correspondence, I, 155-156. For Newton's work on the Kinckhuysen Algebra, see Whiteside, Newton's Mathematical Papers, II, 277-291.

²¹ Henri L. Brugmans, Le séjour de Christian Huygens à Paris (Paris, 1935), pp. 72-73. 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 (1960), 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 Oldenburg Correspondence, VII (1977), 573-579. For this work see the article "Leibniz: Physics, Logic, Metaphysics" by Jürgen Mittelstrass and Eric J. Aiton in DSB, VIII (1973), 150-160.

²² For Leibniz's participation in the meeting of 22 January 1672/73, see Birch, History of the Royal Society, III, 73. Leibniz demonstrated an early version of his calculating machine. He was elected F.R.S. on 9 April 1673.

²³ For these Latin letters to Leibniz, with English translations, see Newton Correspondence, II, 20-47, and 110-161.

²⁴ Newton Correspondence, III (1961), 3-5.

²⁵Oeuvres de Huygens, IX (1901), 167. Cf. I. Bernard Cohen, Introduction to Newton's "Principia" (Cambridge, Mass., 1971), p. 138, n. 9. For Fatio's aspirations as editor of a second edition of the Principia, see ibid., pp. 177-187.

²⁶ "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. Richard S. Westfall, Force in Newton's Physics (London and New York, 1971), p. 184.

²⁷Oeuvres de Huygens, XXI, 437. See Westfall, 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, 304-305) 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 alle 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. William Stanley (1647-1731), Dean of St. Asaph, was chaplain to the future Queen Mary and after the accession of William III was made clerk of the closet.

²⁸ For Roberval's gravitational theory, similar to that advanced by Copernicus and Galileo, see "Un débat à l'Académie des sciences sur la pesanteur," in Léon Auger, Gilles Personne de Roberval (1602-1675) (Paris, 1962), esp. p. 179. See also Westfall, pp. 184-186.

²⁹ Westfall, p. 187.

³⁰ Royal Society Journal Book for 18 January 1687/88 and 4 July 1688. Fatio had been elected F.R.S. 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 Collège 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.

³¹Traité de la lumiere … 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, 451-499.

³² Edmond Halley's laudatory review, an unabashed and rhetorical bit of promotional material, can hardly have persuaded any Continental critic of Newton. See Phil. Trans., 16, No. 186 (1687), 291-297.

³³Journal des sçavans, 2 August 1688 (Amsterdam, 1689), 237-238. 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 completes de Malebranche [Bibliotheque des textes philosophiques: Directeur, Henri Gouhier], XIX [1961], 771-772). This edition will be the one cited henceforth, except in n. 47.

³⁴ Leibniz to Mencke, in Newton Correspondence, III, 3-4.

³⁵ 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 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. E. A. Fellmann (Paris, 1973).

³⁶ E. J. Aiton, The Vortex Theory of Planetary Motion (London and New York, 1972), p. 127.

³⁷ 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."

³⁸ For Huygens's "spherical vortex" see Westfall, p. 187. Leibniz's "harmonic circulation" of a deferent aether is described by Aiton, Vortex Theory, pp. 125-151, and by Westfall, Force, pp. 303-310.

³⁹ Leibniz, Philosophical Papers and Letters, ed. L. E. Loemker, 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.

⁴⁰ Leibniz, Philosophical Papers and Letters, II, 681.

⁴¹ Newton Correspondence, III, 257-258. "Trajection" or "projection" would be preferable translations of trajectio.

⁴² For this correspondence, see Oeuvres de Huygens, 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 (letter no. 2879): "Je n'ai plus de curiosite de voir ce qu'il y a de Mr. Neuton dans le livre de Vallis apres ce que vous me mandez."

⁴³ 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 metaphysique et de morale, 54 (1954), 113-134, with the account of Malebranche by Willis Doney in the Encyclopedia of Philosophy, V (New York, 1967), 140-144. 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 Paul Mouy, Le développement de la physique cartésienne (Paris, 1934), p. 279.

⁴⁴ See Ferdinant Alquié, Le Cartésianisme de Malebranche (Paris, 1974), p. 25 and n. 9.

⁴⁵ The originator of the doctrine of occasionalism is often said to be Geulincx of Antwerp (1625-1669), but other followers of Descartes adopted a similar position. Malebranche, in any case, greatly extended Geulincx's doctrine, giving it a central role in his epistemology and his religious philosophy.

⁴⁶ Henri Gouhier, La vocation de Malebranche (Paris, 1926) is a fine study of this aspect of Malebranche's career. Gouhier (pp. 56-62) pointed out that it was not the Traité de 1'homme alone that introduced Malebranche to Descartes. The edition of 1664 which Malebranche purchased was that of Clerselier, and included Descartes's Description du corps human, 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, Cartésianisme, p. 25.

⁴⁷ For a compact view of Malebranche as mathematician and savant, see the article by Pierre Costabel in the DSB, IX (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 completes de Malebranche, ed. Desire Roustan with the collaboration of Paul Schrecker, of which only the one volume (Paris, 1938) appeared before the outbreak of World War 11 and Schrecker's emigration to the United States. See especially the "Notes des editeurs," pp. 399-447. Of interest too is Schrecker's "Malebranche et le preformisme biologique," Revue international de philosophie, 1 (1938), 77-97.

⁴⁸Oeuvres de Malebranche, XX ("Malebranche vivant," ed. Andre Robinet, 1967), chap. 6, "La bibliothèque de Malebranche."

⁴⁹ Ibid.

⁵⁰Oeuvres de Malebranche, XX, chap. 3, "Le groupe malebranchiste de l'Oratoire," 137-170; André Robinet, "Le groupe malebranchiste introducteur du calcul infinitesimal en France," Revue d'histoire des sciences, 13 (1960), 287-308; André Robinet, Malebranche de l'Académie des sciences (Paris, 1970).

⁵¹Oeuvres de Malebranche, XVII-2 (Mathematica, ed. Pierre Costabel, 1968), 131-294.

⁵² Only in the fifth edition of the Recherche de la verite does Malebranche mention the Marquis de l'Hospital and his book, and introduce the names of two new mathematical sciences, the differential 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, Developpement de la physique cartésienne, p. 269.

⁵³ See Paul Schrecker, "Malebranche et les mathématiques," Travaux du IX' congres international de philosophie—Congres Descartes (Paris, 1937), pp. 33-40, and his "Leparallelisme theologico-mathematique chez Malebranche," Revue philosophique, 63 (1938), 215-252. Also André Robinet, "La philosophie malebranchiste des mathématiques," Revue d'histoire des sciences, 14 (1961), 205-254.

⁵⁴ See Paul Mouy, "Malebranche et Newton," Revue de metaphysique et de morale, 45 (1938), 411-435.

⁵⁵Oeuvres de Malebranche, XVII-2 (Mathematica, ed. Pierre Costabel, 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 pretend etre une des plus belles et des plus utiles inventions de ce siècle dont Messieurs Leibniz et Newton ont tout l'honneur" (ibid., p. 61).

⁵⁶ For Varignon, see the article by Pierre Costabel in DSB, XIII (1976), 584-587, and his Pierre Varignon et la diffusion en France du calcul differentiel et integral (Paris, 1965). An important article is J. O. Fleckenstein, "Pierre Varignon und die mathematischen Wissenschaften im Zeitalter der Cartesianismus," Archives internationales d'histoire des sciences, 2 (1945), 76-138.

⁵⁷ Mouy, Développement de la physique cartésienne, pp. 282-290.

⁵⁸ Pierre Duhem, "L'optique de Malebranche," Revue de metaphysique et de morale, 43 (1916), 37-91.

⁵⁹ Ibid.

⁶⁰ As, for example, Fontenelle's éloge of Newton. For the early English version (London, 1728) see Newton's Papers, pp. 444-474.

⁶¹ Hall, "Newton in France," p. 244.

⁶² Mouy, "Malebranche et Newton," p. 421.

⁶³ See my "Newtonianism of Dortous de Mairan," reprinted in my Essays and Papers in the History of Modern Science (Baltimore and London, 1977), pp. 479-490. 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.

⁶⁴ 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, n. 31.

⁶⁵Dissertation sur la cause de la lumière des phosphores et des noctiluques (Bordeaux, 1717), p. 48.

⁶⁶ Fontenelle, His. Acad. Sci., 1720 (1722), pp. 11-12 (cited by Brunet, pp. 84-85). See also the article on Mairan (by Sigalia Dostrovsky) in DS B XIII, 33.

⁶⁷Mem. Acad. Sci., 1722 (1724), pp. 6-51.

⁶⁸ Ibid., pp. 50-51. Cited by Brunet, pp. 115-116.

⁶⁹ Recherches geometriques sur la diminution des degres terrestres, en allant de l'equateur vers les pôles," Mem. Acad. Sci., 1720 (1722), pp. 231-277.

⁷⁰ Brunet, pp. 134-135.

⁷¹ Brunet writes: "Cette explication par la physique tourbillonnaire est d'autant plus caracteristique ici des preferences cartésiennes de Dortous de Mairan que, puisqu'il faisait appel à une sorte d'extension du magnetisme, il pouvait encore trouver là une occasion de se rallier, plus ou moins directement et explicitement, a la theorie de l 'attraction" (ibid., p. 121).

⁷² Ibid., p. 170. For a detailed analysis of Mairan's theory of planetary notation, see Aiton, Vortex Theory, pp. 182-187.

⁷³Traité physique et historique de l'aurore boréale (Paris, 1733), p. 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 February 1678/79, recently published by Thomas Birch in his Life of the Honourable Robert Boyle (1744), showed Newton an advocate of the sort of matière subtile that he, Mairan, used to explain various phenomena. See the "Preface," pp. xviii-xxii.

⁷⁴ The primary source for biographical information on Privat de Molières is the éloge pronounced by his friend Dortous de Mairan in Hist. Acad. Sci., 1742 (1745), pp. 195-205, reprinted in Jean-Jacques Dortous de Mairan, Eloges des académiciens de I'Académie royale des Sciences, morts dans les années 1741, 1742, 1743 (Paris, 1747), pp. 201-234. There is a brief summary by Martin Fichman in his article on Privat de Molières in DSB, XI (1975), 157-158.

⁷⁵Oeuvres de Malebranche, XX, 170-171.

⁷⁶ "Lois generales du mouvement dans le tourbillon spherique," in Mem. Acad. Sci., 1728 (1730), 245-267.

⁷⁷ Cited by Brunet, p. 159.

⁷⁸ "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 Mém. Acad. Sci., 1729 (1731), pp. 235-244.

⁷⁹ 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 Carolyn Iltis, "The Decline of Cartesianism in Mechanics: The Leibnizian-Cartesian Debates," Isis, 64 (1973), 360-363. Cf. Brunet, L 'introduction, pp. 140-144.

⁸⁰ Aiton, Vortex Theory, p. 209.

⁸¹ 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 Abbe de Bragelongne, the latter also a disciple of Malebranche. See Robinet in Oeuvres de Malebranche, XX, 152-153, 170, 359.

⁸² Joseph Privat de Molières, Leçons de physique, 4 vols. (Paris, 1734-39), 1, 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 croit & decroit en raison inverse des quarres des distances au centre, & qu'il avoue n'avoir pfi deduire de ses suppositions." Newton, he adds (I, 308), was obliged to regard gravity as a universal principle "& un effet sans cause."

⁸³ 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 Thomas L. Hankins, "The Influence of Malebranche on the Science of Mechanics during the Eighteenth Century," Journal of the History of Ideas, 28 (1967), 193-210.

⁸⁴Les lettres de la marquise du Châtelet, ed. T. Besterman, 2 vols. (Geneva, 1958), I, 261. Cited by J. L. Heilbron in his Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics (Berkeley and Los Angeles, 1979), p. 278.