While the vicissitudes of the career of ‘la docte Emilie’ have often been chronicled, much remains to be said about the scientific and philosophical significance of her writings. Mangeot and, more recently, Mauzi have discussed the Discours sur le bonheur;¹ Wade has summarised and traced some of the history of the Examen de la genèse;² Cohen and Taton have commented on the translation of Newton's Principia mathematica;³ Barber and Iltis have dealt with some aspects of the writing and content of the Insititutions de physique;⁴ but these do no more than touch on a few of the many puzzles of mme Du Châtelet's career, and explicate a few among many of the theories which she takes up and develops in the surviving body of writings which we now possess. I propose here to add something to the exiguous body of commentary by looking more closely than has yet been done at the philosophical position adopted by mme Du Châtelet in the Institutions de physique. Although some general remarks have been made on the content and significance of this text, most notably by Wade⁵ and more recently in Vaillot's biography,⁶ and Barber's invaluable article on the composition of the text has helped to fill in many gaps in our knowledge of mme Du Châtelet's activities during the period in question, a great deal remains to be clarified with regard both to the inception and writing of the Institutions and to the book's philosophical and scientific import. Given that it represents the major extant work written independently by mme Du Châtelet (as distinct from translations and commentaries), an accurate understanding of its subject-matter and purpose is crucial for any attempt at assessing her intellectual ability and the relation of her thought to that of Voltaire—both still debatable topics more than two hundred years later.

Although the fragmentary state of several of her writings makes it difficult to date their composition with great accuracy, it is clear that the years 1736-1740 were the period of most concentrated metaphysical and scientific reading, thinking, corresponding, experimenting and writing for mme Du Châtelet. From that time date certainly her initial work on the translation and commenting of Mandeville's Fable of the bees,⁷ her laboratory experimentation, done jointly with Voltaire, which led to the writing (in her case, secretly and hurriedly at the last minute, in April 1738) of their respective essays on the nature and propagation of fire,⁸ her unpublished defence of Voltaire against Desfontaines,⁹ her review of Voltaire's Eléments de la philosophie de Newton (1738), published in the Journal des savants (septembre 1738, pp.534-41), her then unpublished Essay de l'optique,¹⁰ and, most importantly, the Institutions de physique (1740). The same period most probably saw the sketching out of the fragmentary Grammaire raisonné,¹¹ and possibly the beginning of the clandestine Examen de la genèse whose composition may well have lasted over five or six years.¹² At the same time, it was the period of Voltaire's work on the Eléments, to which, on his own account, mme Du Châtelet contributed a great deal (Best.D1255, c.15 January 1737), and on the Traité de métaphysique, about which I shall have more to say below. In short, a time of feverish and eclectic intellectual activity of which we now possess only partial and mostly fragmentary results, conjoined with an astonishing assortment of crises, contretemps and domestic upheavals of all sorts which we can pursue through the reading of Voltaire's and mme Du Châtelet's correspondence for the period in question.¹³

In order to assess the role of a series of influences which shaped the eventual form of the Institutions as they appeared in print in 1740, we have to follow the sequence of events in mme Du Châtelet's life from the mid-1730s onward; and even though many of the relevant details have to be reconstructed from hints, passing references or contemporary gossip, so that some of what follows here is inevitably circumstantial or conjectural, I believe that the account which I reconstruct makes the greatest sense of this episode in mme Du Châtelet's career. (As the reader familiar with Barber's version of the same story will recognise, I am not substantially in disagreement with him, but I do take issue with him on several particular points, and this in turn leads me to a somewhat different evaluation of the overall purpose and philosophical importance of the Institutions.)

Some years prior to this period of intense creativity, mme Du Châtelet had already developed an interest in philosophy (at least as early as August of 1733, according to Voltaire: Best.D649, 29 August 1733), had learned English with some degree of proficiency (Best.D672, 3 November 1733), and had tried in the face of many practical obstacles to study mathematics with Maupertuis (Best.D696-701, D703-705, D707,?January 1734). By 1734 she had become one of a circle of scientific acquaintances (including Fontenelle, Algarotti and Clairaut as well as Voltaire and Maupertuis), several of whom shared her combination of mathematical and metaphysical interests. And by the time she settled down at Cirey with Voltaire, in mid-1735, she had read Pope and Locke (apparently in English) and was embarking on Newton (most probably the Opticks) and the Leibniz-Clarke correspondence (Best.D764, 27 June 1734; D911, 11 September 1735; D978, 3 January 1736; D985, c.10 January 1763). Voltaire meanwhile had also become intrigued by metaphysical problems, as a result of his visit to England, his own reading of Locke, Pope and Clarke, his correspondence on the problem of ‘thinking matter’ with the Jesuit Tournemine in June-December 1735, and presumably the reading and discussion of works by members of their common circle of acquaintances in Paris during 1733-1735. As early as January 1734 he mentions a vague plan for writing out his ‘songes métaphysiques’ (Best.D697), and two years later this in fact turned into ‘quelques chapitres d'une métaphysique que j'ay composée pour me rendre compte de mes idées’ (Best.D951, 30 November 1735). This piece, the ancestor of the Traité de métaphysique, was reworked over the next year or two,¹⁴ and it seems safe to say that its composition must have accompanied philosophical discussions between Voltaire, mme Du Châtelet, and the series of visitors to Cirey which included the abbé Nollet (some time prior to April 1736) and Algarotti (in October-December 1735 and again in October 1736), both then concerned with projects for popularising current scientific knowledge. In most respects, it appears, Voltaire and mme Du Châtelet had had a common ‘training’ in philosophy and science up until 1736: both had carefully studied Locke, Pope's Essay on man, Mandeville's Fable of the bees, the Leibniz-Clarke correspondence and other works by Clarke, Descartes's philosophical and scientific works, and Plato's dialogues, among other major sources; they were also familiar with the writings of some prominent Cartesians, such as Malebranche, Fontenelle and Mairan, as well as, of course, works by close friends such as Algarotti and Maupertuis. In addition, mme Du Châtelet continued her study of the technicalities of physics and mathematics, through available ‘textbooks’ like L'Hospital's Traité analytique des sections coniques and Musschembroek's Essai de physique (cf. Best.D1885, 16?February 1739), to a much greater depth than Voltaire; he, on the other hand, had been reading more widely in moral philosophy (in addition to his continuing literary and historical interests which she only partially shared), and was also reading, by September 1736, a manuscript ‘Métaphysique’ sent him by prince Frederick of Prussia, which was in fact a partial translation of Christian Wolff's Vernünftige Gedanken von Gott, der Welt, und der Seele des Menschens, auch allen Dingen überhaupt. In view of mme Du Châtelet's later indebtedness to this same work, it is ironic that she (perhaps taking Voltaire's word for it that the book contained only nonsense) did not look at it until March 1737. Until that point at least, she, like Voltaire, identified herself with the embattled French Newtonians against the entrenched Cartesianism of the Académie des sciences. It is true that we in retrospect can recognise a greater degree of knowledge and sympathy for Newtonian theories among French scientists at the time, and tend to find Voltaire's diatribes against the obscurantists excessive or even anachronistic;¹⁵ but the fact remains that both Voltaire and mme Du Châtelet perceived themselves as members of a band of crusaders for scientific truth, progress and objectivity against the intellectual conservatism and provincialism which they encountered among some of their Paris acquaintances and in many of the scientific writings they studied during this period. A typical comment comes from mme Du Châtelet in a letter to Maupertuis in 1734: ‘On me mande de Paris qu'il y a vn père de la doctrine chrétienne qui fait vn liure qui paroîtra cet hiuer qui sape et réduit en poudre le sistème de mr Neuton. Il ne sait pas cet home là que vs le foudroyerés’ (Best.D797, 23 October 1734).

It was in July 1736 that Voltaire, urged on as we may conjecture by his fellow Newtonians Algarotti, Maupertuis and mme Du Châtelet, conceived the idea of writing an introduction to the new physics, the Eléments de la philosophie de Newton, as another contribution to the anti-Cartesian campaign which he had already helped to set going in the Lettres philosophiques some years earlier, but which was still far from victory in his view (cf. Best.D1113, [July] 1763). After completing it, he told prince Frederick that ‘madame Du Chastelet avoit sa part à l'ouvrage. Minerve dictoit et j'écrivois’ (Best.D1255, c.15 January 1737). What he seems to have meant by this typical hyperbole was not that literally mme Du Châtelet was the sole author; rather, since his own scientific expertise was inadequate to the task, or at any rate inferior to hers, he drew on her extensively for content, while contributing the organisation and ‘Voltairean’ tone of the finished product. (That he did not entirely trust her mathematical competence, nonetheless, is shown by his request to the mathematician Pitot that he check the figures and other details of the manuscript: Best.D1327, 17 May 1737.) The subsequent course of events indicates that the experience of collaborating with Voltaire, and indeed of contributing the essential factual basis of the Eléments, made mme Du Châtelet realise that there was nothing to stop her from writing and publishing something in the same field independently of Voltaire. She conceived the Eléments as strictly scientific in scope,¹⁶ and made Voltaire (much against his will) eliminate a chapter on metaphysics from the first edition, claiming, rightly as it turned out, that the implications for ethics and religion which he saw in the new physics were too dangerous to print with impunity (Best.D1273, 28 January 1737). She seems to have envisaged the possibility of a more general, philosophically relevant but not politically provocative, treatment of Newtonian science. It is hard to say precisely when she came to formulate this plan; but we do know that the first draft of the Eléments was completed by the end of October 1736 (Best.D1181, 24 October 1736), and that less than a year later the Institutions de physique were well under way.

My argument for this terminus a quo rests on the identification of the fragmentary ‘Chapitre 5. de la liberté’, published by Wade in his Studies on Voltaire (pp.92-108) and said by him to be Voltaire's work, as having been written in fact by mme Du Châtelet. Apart from Voltaire's own notes on the manuscript, identifying it as hers (and he should have known, after all), there are distinct stylistic similarities between the fragment and the early manuscript drafts of the Institutions; moreover, it was filed among her papers in the Leningrad collection of Voltaire's books and manuscripts and even has emendations in her own hand. The section numbering (comprising 84-87 on the fragment) and internal references show that it would have fitted neatly in as chapter five of the original draft of the Institutions. Firstly, the same section numbers still occur in the (substituted) fifth chapter of the published text; secondly, there are two references to a previous ‘15 n. 6’, that is, subheading number six of section fifteen, which note that the section dealt with divine freedom.¹⁷ Now, the actual section fifteen still occurs in the chapter on the nature of God, though it does not discuss freedom; however, section 25 of the published text does deal with just that topic, and God's freedom is in fact the sixth of a list of his attributes (eternity, immutability, simplicity, oneness, intelligence, freedom, and rationality) discussed in sections 20-26. Inspection of the manuscript shows that repeated section re-numberings were carried out before publication; it is thus entirely probable that the original numbering for the first draft submitted to the printer telescoped sections later divided up (even when the content remained largely unchanged), thus explaining the slight discrepancy in section numbering. A further proof is that the arguments for liberty set out in the fragment are echoed in passages in chapter 21 of the manuscript which were omitted from the published version.¹⁸ (Dr Charles Porset, in a forthcoming discussion of the authorship of the fragment, and hence of the largely identical ‘Extrait’ sent by Voltaire to Frederick in October 1737, which he has kindly communicated to me, adds some further arguments which, combined with those I have just set out, show conclusively that the fragment must be attributed to mme Du Châtelet and identified as part of the original fifth chapter of her Institutions.) Since chapter five refers back to previous and on to subsequent chapters, I conclude that the overall plan and some of the writing had already been completed by October 1737.

Before going on to reconstruct in more detail the process of writing the Institutions, it is worthwhile recalling that the development of mme Du Châtelet's philosophical position—which we can trace through the successive drafts of her book and through contemporaneous letters, especially those to Maupertuis (from Best.D1448, c.10 February 1738, on)—did not proceed in ideal academic seclusion uninterrupted by the demands of the external world. Firstly, in spite of her disdain for the supposed constraints of her social position, she could not simply forget the obligations of her status. The renovation of Cirey, the Du Châtelet estate which had fallen virtually into ruin, occupied much of her time between early 1735 and the end of 1736 (cf. Best.D1179, 21 October 1736). A much greater and less pleasant distraction was a complicated lawsuit involving some large estates in Belgium claimed by two branches of the Du Châtelet family: to ensure the success of her own branch, mme Du Châtelet was forced to take charge of the suit herself, and hence to leave Cirey for Brussels in May 1739. Over the next five or six years, a large proportion of her time was spent there, overseeing the efforts of her lawyers. Even before this disruption of her preferred activities, she admitted to Maupertuis during the writing of the Institutions that she had too little time to keep abreast of new publications (Best.D1636, 24 October 1738):

la vie est si courte et si remplie de deuoirs et de détails inu[ti]les, quand on a vne famille et vne maison, que ie ne sors guère de mon petit plan d'étude pr lire les liures nouueaux. Ie suis au désespoir de mon ignorance et de toutes les choses qui m'empêchent d'en sortir. Si i'étois home ie serois au mont Valerien avec vs.

And as the lawsuit dragged on, she expressed her increasing frustration at the waste of time it meant for her. Indeed, one additional reason for dating the start of her work on the Institutions in 1737 is that that year was one of the few in which no time-consuming obligations interrupted her studies at Cirey.

Secondly, her association with Voltaire turned out to have some distinct disadvantages for her own work: she in effect functioned as his secretary, writing his letters during periods of illness, or passing on his voluminous correspondence in the times of crisis in which he had to go into hiding to escape the threat of imprisonment (for example, Best.D1224, 14 [December 1736] and others in the following weeks). She spent perhaps even more time going over Voltaire's writings, both as a critic (which Voltaire valued) and in order to pick out any potentially dangerous material that might get him into hot water with the censor (which Voltaire seemingly resented, especially when she abstracted particularly fiery pieces like the Pucelle and locked them away out of his reach). In short, any crisis in Voltaire's life meant the interruption of her own research, as she admits, for example, to their mutual friend d'Argental in a letter of April 1739, full of fears for Voltaire's safety from his enemies' persecution, and ending: ‘Mon cher ami, ne m'abandonnés pas, dites-moi ce qu'il faut que ie fasse, i'ay besoin de vos conseils et de votre amitié car depuis quelques mois, ma vie est bien trauersée’ (Best.D1987, 20 [April 1739]). Both Voltaire and her family obligations perforce took precedence over the vocation she preferred, and, moreover, often circumscribed the possibilities of consulting or studying with the leading thinkers of the time, whom she could only contact by letter, if at all.¹⁹ Constant interruptions and restrictions, then, accompanied the writing of the Institutions, as they did the whole of mme Du Châtelet's intellectual career, which she could pursue at all, it seems, only because of her exceptional energy and stamina (cf., for example, Best.D2034, 21 June 1739).

This situation helps to explain her tendency to take up projects of translation and commentary, which can both be carried on intermittently and concurrently with other activities, rather than large-scale systematic treatises or serious pieces of scientific research which would have demanded the long uninterrupted periods of time unavailable to her. In the case of the Institutions in particular, it explains why she confined herself, in 1739, to grasping as quickly as possible the gist of Leibniz's and Wolff's ideas, once she had come to believe in their philosophical value, and to extracting what seemed to her their most salient points, rather than attempting an exhaustive study and full-scale analysis of either one. Ironically, the constraints she was subject to turned out in one sense to be of positive value, since they forced her to focus her attention on a few key points within the systems of Leibniz and Wolff, and on their implications for the programme of empirical science with which she had gradually become familiar during 1733-1738. This in turn made her relatively brief and non-technical exposition of a combination of Leibniz's and Wolff's theories in the opening chapters of the Institutions far more accessible and widely-read than the other ‘introductions’ to Leibniz or Wolff (such as those produced by Deschamps, Vattel, and Formey and Chambrier) published soon after. Even those who, like Voltaire, had no patience with the metaphysical elaborations of the two Germans, were ready to admit that she had, if not convinced, at least enlightened her readers (for example, Best.D2496, 6 June 1741, from de Crousaz; Best.D2522, 8 August [1741], to Maupertuis).

An assortment of indirect and circumstantial evidence is all we have to go on in reconstructing the moment of inception of the Institutions. Nevertheless, a coherent picture does emerge from the mass of relevant data. In the first place, although it is true that Voltaire's own writing on philosophy and science mostly precedes mme Du Châtelet's, and that, as I suggested above, it may have prompted her to similar work, it was not mere emulation of her famous companion which led mme Du Châtelet to conceive the project of a new introduction to Newtonian physics. Rather, during the whole period from 1733 to 1737 and especially during the time of discussion arising from Voltaire's composition of the Traité de métaphysique and from her collaboration with him on the Eléments, she was gradually coming to disagree with him on a series of philosophical questions. She continued to share his enthusiasm for the Newtonian method and for mechanistic explanation of observable phenomena, as practised with such evident success by Newton and his followers, and she shared his rejection of the Cartesians both in science and philosophy. (Though even here she demonstrates more respect for Descartes and remains open to the possibility that he may have been right on some points, as passages in her Dissertation sur la nature et propagation du feu and the ‘Avant-propos’ in the first manuscript draft of the Institutions both indicate.) But (as Barber has already pointed out²⁰) she distrusted the anti-metaphysical stance which Voltaire took over from Locke and which made him reject any search for a deeper, rational explanation of the mechanistic workings of the universe. As he says in a much-quoted remark (here in a letter to Frederick): ‘Toute la métaphysique à mon gré contient deux choses, la première ce que tous les hommes de bon sens savent, la seconde ce qu'ils ne sauront jamais’ (Best.D1320, c.25 April 1737). Mme Du Châtelet, revealingly, transforms this expression in the published version of the Institutions (p.14): ‘La métaphysique contient deux espèces de choses: la première, ce que tous les gens qui font un bon usage de leur esprit, peuvent savoir; et la seconde, qui est la plus étendue, ce qu'ils ne sauront jamais.’ In spite of the apparent note of caution, the context makes it clear that the knowable ‘espèce de choses’ includes rationally demonstrable truths in mathematics and metaphysics. In a letter to Maupertuis, which sounds suspiciously like an echo of arguments with mme Du Châtelet, Voltaire insists: ‘Le grand principe de Leibniz, que rien n'existe sans une cause suffisante, est très vrai; mais il est tout aussi vrai que les premiers ressorts de la nature n'ont pour cause suffisante que la volonté infiniment libre de l'être infiniment puissant’ (Best.D1622, c.1 October 1738). But, as I want to show later, it is just this distortion of Leibniz's principle into a rejection of rational explanations of nature (and the accompanying conflation of cause and reason which Voltaire performs here) that mme Du Châtelet seeks to avoid; thus a primary claim of the Institutions is that the universe is open to rational explanation through ‘bon usage de l'esprit’.

To take refuge in the inscrutable will of God or the limitations of the human understanding did not seem to her an adequate response to questions like ‘What are the basic constituents of the universe?’, ‘Why does the law of gravitation hold?’, or ‘How is human freedom possible in a mechanistic universe?’ None of her extant references to Locke displays the effusive admiration for his metaphysical caution which Voltaire expresses, and whereas Voltaire is altogether on Clarke's side in his debate with Leibniz, she is readier, even from her earliest acquaintance with Leibniz, to adopt some of his ideas—notably the anti-Newtonian doctrine of force vive invoked in the first draft of the Institutions and perhaps the principles of sufficient reason and of contradiction, also alluded to though not elaborated upon in the first draft chapters. Early in 1738, she writes to Maupertuis (Best.D1448, c.10 February 1738):

Le docteur Clarke […] traite mr de Leibnits auec autant de mépris sur la force des corps, que sur le plein, et les monades, mais il [a] grand tort à mon gré, car vn home peut être dans l'erreur sur plusieurs chefs, et auoir raison dans le reste. Mr de Leibnitz à la vérité n'auoit guères raison que sur les forces viues, mais enfin il les a découuertes, et c'est auoir deuiné vn des secrets du créateur.

By 1740 this qualified respect (‘guères’, at least, rather than ‘point’), had grown into much more thoroughgoing admiration, as the first half of the Institutions shows. Another significant document pointing to the divergence of mme Du Châtelet's opinions from Voltaire's is the copy of Plato's dialogues which belonged to Voltaire's library: the margins of the book contain frequent annotations in the hands of both Voltaire and mme Du Châtelet, and there is a marked contrast between the mixture of criticism and assent in her comments and the outright irritation, not to say contempt, in Voltaire's.²¹ Although it is unfortunately impossible to say precisely when these marginalia were produced, they do serve to underline the difference between Voltaire's resolute ‘pre-positivism’ and mme Du Châtelet's more pronounced inclination towards metaphysics in general.

I surmise, then, that the writing of both the Traité de métaphysique (which Voltaire was still retouching at the end of 1736) and the Eléments, as well as the reading in philosophy which they did in common, engendered disputes between them which helped mme Du Châtelet to formulate her own independent philosophical opinion. It is especially noteworthy that the Traité's discussions of the social virtues show clear dependence on Mandeville's Fable of the bees, which mme Du Châtelet was translating and commenting on at the same time, and moreover that the other topics discussed in the Traité reappear in the early draft of the Institutions (and to some extent in the published version as well) including the nature of God, the reality of the external world, and the arguments for human freedom. There are even a few direct borrowings from the Traité, notably in the ‘Avant-propos’. Here the split between Voltaire and mme Du Châtelet is strikingly evident: Voltaire asserts, in the context of an attack on metaphysical speculation in Descartes:

Cette manière de philosopher est encore plus dangereuse que le jargon méprisable de l'école. Car ce jargon étant absolument vide de sens, il ne faut qu'un peu d'attention à un esprit droit pour en apercevoir tout d'un coup le ridicule, et pour chercher ailleurs la vérité; mais une hypothèse ingénieuse et hardie, qui a d'abord quelque lueur de vraisem-blance, intéresse l'orgueil humain à la croire; l'esprit s'applaudit de ces principes subtils, et se sert de toute sa sagacité pour les défendre. Il est clair qu'il ne faut jamais faire d'hypothèse; il ne faut point dire: Commençons par inventer des principes avec lesquels nous tâcherons de tout expliquer. Mais il faut dire: Faisons exactement l'analyse des choses.²²

But mme Du Châtelet takes the very same phrases in another context to derive just the opposite conclusion:

un des torts des neutoniens est encor de vouloir bannir les hipothèses de la phisique, elles y sont aussi nécessaire que les échafaus dans un bâtiment il est vray que lorsque le bâtiment est achevé on n'a plus besoin de l'échafaut mais on n'auroit pu le lever sans son secours, toute l'astronomie p.e. n'est fondée que sur des hipothèses, et si on les eut bannis de la phisique il y a aparence qu'on n'i auroit pas fait grand progrès, rien n'est d'ailleurs plus capable de retarder le progrés des sciences que cette idée confuse d'attraction sur laquelle quelques neutoniens se reposent, car on ne cherche point ce que l'on croit connoître ainsi l'aplication des principes de la méchanique aux effets phisiques qui est tres difficile et cependant si nécessaire reste imparfaitte, et cette présomption ou l'on est que l'on a trouvé le grand ressort qui fait agir toute la nature ns prive peutêtre des travaux et des recherches de plusieurs beaux génies capables de découvrir la véritable cause, il est vray que les hipothèses deviennent la poison de la philosophie quand on les veut faire passer pr la vérité, et peutêtre même alors sont-elles plus dangereuses que ne l'étoit le jargon inintelligible de l'école car ce jargon étant absolumt vide de sens il ne falloit qu'un peu d'attention à un esprit droit pr en apercevoir tout d'un coup le ridicule, mais une hipothèse ingénieuse et hardie qui a d'abord quelque vraisemblance intéresse l'orgueil humain à la croire, l'esprit s'aplaudit d'avoir trouvé ces principes subtils et se sert ensuite de toute sa sagacité pr les deffendre, la plupart des grands hommes qui ont fait des sistèmes ns en fournissent des exemples ce sont de grans vaisseaux emportés par des courants, ils font les plus belles manœuvres du monde, mais le courant les entraine.²³

In a sense, it could be said that she conceived her book as a synthesis of the subject-matter of the Traité and the Eléments—a synthesis which Voltaire would never carry out. Studying the Institutions makes it clear that one of her basic convictions, from the beginning of its composition, was that science, whether Newtonian or otherwise, was dangerously incomplete without some kind of metaphysical foundation. The scientific theories of Descartes (and, indeed, of his predecessors) had all possessed such a foundation. These theories had, of course, largely been overthrown by Newton; but what neither Newton himself nor his philosophical disciples, including Voltaire, had been able or willing to do was to supply their own rational explanation of why, rather than simply how, the universe worked as it did. Insistence on not feigning hypotheses, appeals to the will of God, or the mysticism which Newton himself was subject to, were no substitute in mme Du Châtelet's eyes for the necessary metaphysical account of why the universe functioned—as it undoubtedly did—according to Newton's eternal laws.²⁴ In a letter written from Cirey in the midst of its rebuilding, she told Maupertuis: ‘Ie partage mon tems entre les maçons et m. Lock, car ie cherche le fons des choses tout come une autre’ (Best.D797, 23 October 1734). She continued to look for ‘le fons des choses’, but as she no doubt soon realised, Locke was hardly the place to dig. The ‘bon sens’ praised by Voltaire failed to provide answers to the questions which grew more and more to occupy her.

She thus developed a plan for a different kind of introduction to the new physics, to consist of an enquiry into the fundamental properties of matter, the role of hypotheses, the nature of explanation, the function of God in the universe, the possibility of free will in a mechanistic world, and other such metaphysical problems. The structure of the Institutions, in which these metaphysical chapters precede the exposition of physical theory, indicates that by 1738 she had already come to hold that only in the context of such an enquiry could the significance of Newton's discoveries, and the value and limitations of his method, be properly expounded. It is tempting though unverifiable to argue that her reading of the translated ‘Métaphysique’ of Wolff in March 1737 (Best.D1307, c.30 March 1737) was the catalyst which prompted her to a more positive evaluation of rationalistic speculation, and suggested the possibility of grounding Newtonian physics in some kind of philosophical theory. Later on, when the Institutions were closer to completion, the research and writing which went into the production of her entry for the Académie des sciences essay contest on the nature of fire, in April 1738, may have brought mme Du Châtelet to think further about the limits of scientific explanation and its overlap with metaphysical problems. In those pre-phlogiston days, the less advanced state of chemistry compared with physics meant that mechanical explanation of phenomena relating to heat and combustion was much more problematic, so that mme Du Châtelet (like the other contestants) was drawn to speculate as well as experiment—to consider, for instance, whether fire is a material substance or a unique kind of being with its own laws unrelated to those of physics.²⁵

Whatever the reasons for her decision to undertake such an ambitious project as the explanation and philosophical justification of Newtonian science, she worked intensively, in spite of many interruptions, from some time in early or mid-1737 until September of 1738, when the still incomplete manuscript was submitted anonymously to Pitot, the official censor, for the required ‘approbation’. By November the work was about to be printed (Best.D1645, 1 November 1738). However, during the course of printing, over the next few months, mme Du Châtelet began to overwhelm Prault, her long-suffering printer, with proof corrections of increasing magnitude (Best.D1885, 16?February 1739),²⁶ until finally the publication came to a complete halt. The fact was that by mid-1739 she had changed her views both on Newton and on the role of metaphysics in science so radically that a complete rewriting had to be done.

The first step in this radical reappraisal was occasioned by a visit to Cirey from Maupertuis, still mme Du Châtelet's scientific and mathematical mentor, in January 1739 (that is, during the period of the first printing of the Institutions). Up to that moment mme Du Châtelet had kept her authorship a secret from all but a close friend, mme de Chambonin; even Voltaire, it seems, was unaware of the project, and mme de Chambonin dealt directly with the printer so as to preserve the author's anonymity. When mme Du Châtelet began to work on the book, Maupertuis himself had been absent from France, taking part in the famous Arctic expedition organised by the Académie des sciences to make the observations in extreme northern latitudes needed to settle the vexed question of the exact shape of the earth. He had returned to Paris in August 1737; by the end of that year Emilie Du Châtelet had come to realise that she needed the expertise which, she felt, only Maupertuis of all her friends could provide. Throughout 1738 she sent him letter after letter on various scientific topics, especially that of force vive, begging for information, enlightenment, and especially his personal presence at Cirey (Best.D1400, 11 December [1737]; D1422, 10 January 1738). In September 1738 she sent him a ‘petit extrait de Newton’, that is, her review of Voltaire's Eléments, for his approval, without telling him where it came from but enjoining him to keep her authorship secret (Best.D1620, 29 September 1738). Although she did not tell him during the January visit that she planned to publish the Institutions too, she must certainly have shown him some of the manuscript. He would thus have been the first person to see the work who was competent to detect any errors or oversights in the exposition.

Why did mme Du Châtelet insist on such anonymity and deliberate isolation? A possible explanation is that she felt the need to defer to the social convention which would have made the public avowal of such a dubious occupation as scientific or philosophical study an absurd if not positively shameful act; but (as the ‘Préface du traducteur’ of her version of the Fable of the bees makes clear) she strongly resented the intellectual restrictions placed on women by society and refused to abide by them.²⁷ Later, she herself explained that this was not the consideration holding her back from communicating her plan to friends or colleagues (Best.D2254, 30 June 1740). Rather, she was well aware that if her authorship was revealed before publication, the book would inevitably be greeted by flattery from her friends and ridicule from her enemies, in accordance with the ‘etiquette’ of the time. This being the case, it would be impossible to get an objective evaluation of the book's content and importance. But by remaining anonymous it would be possible to find out what people really thought of it; and no doubt, if the reception were favourable, she could reveal herself as the author at a suitable moment. Conversely, if it were a failure, she would not have to submit to the inevitable reflections on the ‘singularité’ and impropriety of such an undertaking for a woman in her position. Naturally, however, this secrecy, maintained over the whole period of composition, could only be kept up at the price of abandoning any chance of valuable criticism before publication. At the last moment, I conjecture, mme Du Châtelet decided to risk exposure and showed Maupertuis her manuscript, hoping he would not suspect it was intended for publication. It would hardly have been surprising if Maupertuis had found some serious flaws in her exposition, and recommended extensive changes; this at least is strongly indicated by the subsequent course of events.

My suspicion is that Maupertuis sharply criticised some of the mathematics of the later chapters, which discuss, for instance, the properties of cycloids and their application to pendulum motion, and other such technical topics. On the surviving manuscript of some of these chapters, which have already been fair-copied by a secretary, lengthy sections, sometimes several pages at a stretch, have been crossed out.²⁸ A careful comparison of the section numbers on the manuscript shows that two chapters originally placed as nineteen and twenty are missing altogether from manuscript and published text. These would have comprised sections 585-667 in the original numbering sequence; a single reference, to section 661, in the manuscript of chapter 21, shows that one topic discussed in the missing material was ‘ressort’, that is, elasticity. (The manuscript numbering goes as high as 720, but telescoping of section numbers in the published text results in the latter's only containing 590 sections; this discrepancy helps to make possible a reconstruction of the order of the book as it was envisaged in 1738, and to distinguish stages in the addition or deletion of material.)

A letter written to Maupertuis soon after his departure from Cirey confirms the hypothesis that he insisted then on mme Du Châtelet's need to study more mathematics, in a more organised and thorough way than she had previously done (Best.D1804, 20 [January] 1739):

Vs m'aués donné vn désir Extrême de m'apliquer à la géométrie et au calcul. Si vs pouués déterminer vn de mrs Bernoüilli à aporter la lumière dans mes ténèbres j'espère qu'il sera content de la docilité, de l'aplication, et de la reconnoissance de son Ecolière. Ie ne puis répondre que de cela, ie sens auec douleur que ie me donne autant de peine que si j'aprenois le calcul, et que je n'auance point, parce que ie manque de guide.

Not long after, another letter, this time to Frederick, informs him that she has been obliged to return to mathematics and has arranged to hire a Swiss protégé of Maupertuis and the Bernouilli family, Samuel Koenig, to tutor her for at least a year (Best.D1912, 27 February 1739). If my reconstruction is correct, his first task would have been the correction and revision of the mathematical sections of the Institutions, presented to him by mme Du Châtelet not as proposed chapters of a book but simply as her exercises. But what in fact transpired next was more complicated than mme Du Châtelet had foreseen. As well as being a mathematician, Koenig was an ardent disciple of Christian Wolff, and was closely associated with the Bernouilli family in Basel, a dynasty of mathematicians whose philosophical leanings were decidedly Leibnizian. (Maupertuis himself, partly under the influence of the Bernouillis, gradually became more attracted to Leibnizianism as time went on.) Wolf's synthesis of elements from both Leibnizian and neo-scholastic German metaphysics had by this time become the philosophical orthodoxy in many German universities, but was virtually unknown in France. The manuscript ‘Métaphysique’ which Frederick had sent to Cirey was one of the earliest renderings of any of Wolff's work into French.²⁹ It seems highly likely that mme Du Châtelet welcomed the unexpected opportunity to learn about Wolff's metaphysics from Koenig, since she had already been exposed to a brief—and, given her total lack of training in scholastic terminology and style of argumentation, very puzzling—extract from his works. Many years later Koenig claimed he had introduced his pupil to Wolff's ideas because she had ridiculed metaphysics,³⁰ but we know that in fact mme Du Châtelet had chosen herself to take the ‘Métaphysique’ with her to Brussels, on a journey made in Koenig's (and Voltaire's) company in May 1739, only two weeks after Koenig's arrival to take up his position at Cirey, and that she was already familiar with what she calls his ‘Physique’, presumably the Elementa matheseos (Best.D1620, 29 September 1738). It sounds, then, as if she sought to draw upon Koenig's expertise in metaphysics as well as mathematics from the beginning of their association, and expected him to fill a gap in her philosophical knowledge which none of her friends and mentors had thus far been able to do. (Voltaire, for example, had nothing good to say about Leibniz and Wolff, and later ‘replied’ to mme Du Châtelet's championing of their views in a ‘Parallèle’ of Newton and Leibniz added to the 1740 edition of the Eléments, in which he ridiculed as much as he could understand of Leibniz's ideas.)

A further interesting possibility is suggested by a letter from Jean Bernouilli the elder (who had already been corresponding with mme Du Châtelet) to Maupertuis, sent on 12 April 1739, just before Koenig's arrival at Cirey on the 27th. Bernouilli chides Maupertuis for giving mme Du Châtelet wrong ideas about force vive:

Je m'étonne, Monsieur, que depuis si longtemps que vous connoissez cette Dame philosophique, vous ne lui ayez pas donné de meilleures instructions sur cette importante matière. Je m'apperçois bien que Mr. de Voltaire croupit dans la même erreur, mais je le lui pardonne, car il a épousé les sentiments de Newton et des Anglois en général, il n'ose donc pas être plus clairvoyant qu'eux.³¹

The clear implication of this remark is that mme Du Châtelet, unlike Voltaire, had not ‘épousé les sentiments de Newton’ wholeheartedly and was a potential ‘convert’ to the Leibniz-Wolff camp. Since Koenig was associated with the Bernouillis (and in fact had made his first, brief, visit to Cirey in March with Maupertuis and Jean Bernouilli the younger), he may well have been urged to encourage any glimmering of interest shown by his new pupil in any aspect of Leibniz's or Wolff's philosophy.

If such an aim was indeed formulated, it certainly succeeded. Between May and August of 1739, Koenig—unwittingly, as he was unaware until September of the forthcoming book—induced mme Du Châtelet to carry out a massive rewriting of the earlier chapters of the Institutions, in order to bring her so far rather eclectic metaphysical views directly into line with some of the major doctrines of Wolff and Leibniz. Printing began again in September—which meant, incidentally, that mme Du Châtelet had had approximately four months, during the crucial and extremely busy period of the family lawsuit in Brussels, to rewrite entirely about a quarter of her text and substantially revise the mathematical and other details in the remaining chapters—with, unavoidably, Koenig at last admitted to the secret of the forthcoming publication.

This in turn brought about exactly the situation which she had hoped to avoid: Koenig, ‘dont la franchise helvétique alloit jusqu'à la rusticité’³² was dissatisfied with his position as tutor and with mme Du Châtelet's high-handed treatment of him and, apparently out of spite, revealed her authorship in November, on the eve of publication. Even worse, he put about the story that he himself was the real author, in the sense that mme Du Châtelet had simply copied out his notes and presented them as hers. (The conflicting accounts of Koening's accusations and mme Du Châtelet's response can be followed in a series of letters from the period of November 1739 to June 1740, written by mme Du Châtelet, Voltaire, Maupertuis and mme de Graffigny.)³³ Faced with this betrayal of her confidence, she contemplated stopping publication altogether, or alternatively revising the book once again to remove any trace of Koenig's influence. She did in fact write another new chapter, criticising the Newtonian conception of gravitational attraction, after Koenig's departure, probably some time in early 1740, and cut out the two others mentioned above, perhaps because the mathematical revision of them was incomplete and she now had no tutor to replace the departed Koenig.³⁴ But any putative plan for extensive revision was abandoned; after all, Koenig's public accusation of plagiarism and incompetence had already made her the laughing-stock of Paris (cf., for example, Best.D2227, 10 June 1740), and no doubt she realised that any longer delay would lend credence to Koenig's story precisely by implying that she was trying to rewrite ‘his’ material. And more importantly, from the final text and from comments made about Wolff and Leibniz right up to the end of her life, it is clear that their metaphysics did satisfy her intellectually,³⁵ and solved the problems outstanding in the 1738 version of the Institutions which I shall discuss in due course. She had no reason to turn her personal quarrel with Koenig into a philosophical about-face. In any case, the final version of the Institutions was submitted for the ‘privilège’ of publication to the second censor in September 1740, and the book finally appeared in December, to exactly the partisan, subjective response which mme Du Châtelet had feared. Two letters from Frederick, one addressed to her on receipt of a proof copy of chapters one to eight, and another addressed to his protégé Jordan a few months later, encapsulate the range of responses. To mme Du Châtelet Frederick enthuses (Best.D2208, 19 May 1740):

On ne saurait lire sans étonnement l'ouvrage d'un profond métaphysicien allemand, traduit & refondu par une aimable dame française […] Vos institutions physiques séduisent, & c'est beaucoup pour un livre de métaphysique […] On ne saurait assez vous encourager dans ce goût si rare que vous avez pour les sciences,

while to Jordan he comments acidly (Best.D2317, 24 September 1740):

La Minerve vient de faire sa physique. Il y a du bon, c'est Koenik qui lui a dicté son thème. Elle l'a ajusté & orné par-ci par-là de quelque mot échappé à Voltaire à ses soupers. Le chapitre sur l’étendue est pitoyable, l'ordre de l'ouvrage ne vaut rien […] Enfin c'est une femme qui écrit & qui se mêle d'écrire au moment où elle commence ses études.

The value of reconstructing this story is that through it we can follow the development of mme Du Châtelet's growing philosophical sophistication in considerable detail, as well as registering the accidental, external factors which played such a large role in her career. The Institutions went through three distinct stages, represented by the 1738 (partially printed) version, the radical rewriting of 1739 under Koenig's tutelage, and the final published version of late 1740. (Strictly speaking, there is a fourth stage, represented by the second edition published in Amsterdam in 1742, but I leave consideration of its mostly minor changes aside.) When she began writing in 1737, mme Du Châtelet combined an enthusiastic acceptance of Newton's physics with a pronounced but rather generalised conviction that empirical science needed a philosophical foundation to be intellectually respectable. The first of these attitudes reflects her identification with the Newtonian ‘crusaders’, Voltaire, Clairaut, Maupertuis, and Algarotti, in particular; the second attitude develops through her debates with Voltaire during the writing of the Traité de métaphysique and the Eléments. By 1740 she had progressed to a much more independent and critical assessment of the basic concepts of Newtonianism (including an outright attack on the reality of solid atoms and of a vacuum), particularly in the ‘pre-positivist’ interpretation given by Voltaire; this was combined with a conviction that the main doctrines of Wolffian and Leibnizian metaphysics (which she made no attempt to distinguish from one another) were not only compatible with, but indeed essential to, the justification and explanation of our knowledge of the world of physics. She continued to find this philosophical position congenial in spite of its unpopularity in France, and although more translations and introductory treatises on Wolff and Leibniz began to appear in the 1740s,³⁶ hers was the only one at that time to argue for the compatibility of the basic Wolffian doctrines with Newtonian physics. Indeed, a reading of the reviews and letters describing the Institutions makes it clear that her audience (including Voltaire) failed to recognise that this was her aim.³⁷ Many people seem to have read only the first ten chapters, in which the Leibniz-Wolff position is expounded, and the last chapter on the topical force-vive controversy, without realising that the version of Newtonian physics given in the intervening part was no mere ‘vulgarisation’ but in effect a reinterpretation of Newton on the basis of a thoroughly Wolffian ontology, relying heavily on the principle of sufficient reason to justify both Newton's empirical discoveries and their metaphysical necessity.

What led mme Du Châtelet to this radically new position, and how did she come to believe in the complementarity of Wolff and Leibniz with Newton? Comparing the 1738 version of the text with its 1740 revision allows us to answer this question in some detail. Although we do not possess all of the 1738 manuscript, enough has been preserved to enable us to form a coherent picture of mme Du Châtelet's original stance. What we still have are the ‘Avant-propos’, chapters two and four,³⁸ part of chapter five, the proof-sheets of what became chapter eleven, but was originally placed as chapter ten, and the (later heavily corrected but still legible) fair-copied chapters ten to eighteen and twenty-one, most of which were reordered in the 1740 text. What we lack altogether are 1738 chapters one and three, six to nine, nineteen and twenty. But from the surviving chapters and from internal references on the manuscript it is evident that chapters ten to twenty-one were on strictly scientific topics: they begin with Newton's laws of motion and go on to the behaviour of falling bodies, projectile motion, pendulums and other terrestrial phenomena whose laws were set out in the Principia. The only scientific question over which mme Du Châtelet took issue with Newton at this stage was that of force vive, on which the opinion of experts was divided. Here, as I mentioned above, in spite of Bernouilli's misgivings she followed Leibniz in upholding the real distinction of two kinds of force in the universe where Newton, like Descartes, had argued for only one. Leibniz had argued that without this distinction the concomitant one between quantity of motion and quantity of force was obscured. Against Descartes he had maintained that the quantity of force, not of motion, had to be constant in the universe if it was not to come eventually to a halt.³⁹ A similar objection held against Newton's own conception of force, as the Leibniz-Clarke correspondence made clear,⁴⁰ and mme Du Châtelet accepted this as a valid criticism of Newton.⁴¹ Already during the first writing of the Institutions, that is, she was prepared to be critical of Newton and to allow some modification (in this case a far-reaching one) in his account of the cosmos. In this respect (as Bernouilli recognised) she was quite unlike Voltaire, who was prepared on the authority of his friends to accept all Newton's theories almost without question, even before he had come to know much about them.

Already in 1738 the first nine chapters were intended to form a philosophical foundation for the second half. After a general ‘Avant-propos’ in which mme Du Châtelet announces her intention to uphold Newton against Descartes, two chapters follow on the ‘principes de nos raisonnements’ and the ‘existence de Dieu’. Since the manuscript contains two drafts of each of these, the first set might be expected to represent mme Du Châtelet's ‘pre-Koenig’ position. This is certainly true of the ‘Avant-propos’. (Its first draft contains no reference to Voltaire's Eléments, while the second refers to the work as ‘paru cette année’, dating that draft as 1738 and the first as prior to that date.) But references later in the Institutions manuscript to a section ten⁴² indicate that the 1738 first chapter discussed Newton's rules of reasoning in science, drawn from the Principia; so what remain extant must be the second and third drafts of the first chapter, both Leibnizian in their advocacy of the principles of sufficient reason and contradiction, but the third being more explicitly Leibnizian (and the 1740 text more so yet). This third draft has queries to Koenig and even a note apparently in his hand in the margin,⁴³ thus it at least was composed under his supervision; the second draft, as a rougher sketch of the same material, must also date from about the same period in mid-1739. Chapter two, on the other hand, though altered between first and second drafts and again on the 1740 text, has no marginal queries and seems not to have been submitted to anyone; and as the fragmentary chapter five already refers to a chapter on God at about this stage of the manuscript, we may conclude that at least the first draft of chapter two pre-dated Koenig's appearance, and thus must express some of mme Du Châtelet's ideas from 1738.

Chapter three, ‘des essences, des attributs et des modes’, is heavily Wolffian in its combination of scholastic terminology and Leibnizian principles, and has no echo in any of mme Du Châtelet's pre-Koenig writings or letters now extant. Chapter four, however, ‘des hypothèses’, develops in more detail the point made briefly against Voltaire in the 1738 ‘Avant-propos’. Both chapters have several queries, addressed apparently to Koenig: for example, in chapter four a crossed-out marginal note, ‘definition du mot de phénomène et de celui d'hipothèse’⁴⁴ is ‘answered’ further down the page with the Leibnizian definition, ‘un phénomène est une aparence que nos sens ns représentent confusément’.⁴⁵ Given that not only chapters written under Koenig's instruction but previously composed chapters from the work (for example the proof-sheets of 1738 chapter ten) were also submitted to Koenig, I would argue simply on the basis of content that the manuscript of chapter three dates from 1739, while chapter four mostly predates Koenig and was not substantially reworked: the definition of hypothesis supplied and quoted above, for instance, does not appear after all in the 1740 text.

The fragment on liberty, as I have shown, formed part of the 1738 chapter five, which seems to have begun by discussing the topic of conservation of motion; it in turn refers to another previous chapter on the arguments for and against the existence of a material world, and to a ‘chapter eight’ on the difference between quantity of motion and quantity of force, and its implications for human freedom.⁴⁶ References to sections 98 and 124⁴⁷ which would have occurred in chapter six or seven, show that that chapter dealt with the nature of matter, and in particular with the question of whether ultimate particles are inelastic and indivisible, a topic also broached in letters to Maupertuis (for example, Best.D1606, 1 September 1738). Finally, the last page of 1738 chapter nine, on the back of the first proof-sheet retained in the manuscript, indicates that chapter nine discussed the concept of motion, seemingly on Lockean lines, asking whether it is a factitious idea derived indirectly from our experience of physical bodies, or a concept to which a real entity of some sort corresponds. (Problems of infinity and some features of the general laws of motion were also mentioned in the first chapters, though presumably not discussed to any great extent since a full treatment is included in the second half of the book.)⁴⁸

This partial reconstruction of chapters one to nine, then, shows that the 1738 version raised the same questions about methodology, including the use of hypotheses, in science; the existence and nature of God, the external world, and of human freedom; the properties of the ultimate constituents of the natural world; and the relation between our concepts (such as those of motion and force) and reality.⁴⁹ But under the influence of Koenig, in the philosophical half of the Institutions only the ‘Avant-propos’ and the chapters on God and hypotheses were retained in anything like their original form. All others were replaced by new chapters (1740 chapters one, three, and five to ten) which substitute a Wolffian account of reasoning, ontology, space, time, and the ultimate constituents of reality and their relation to matter. In other words, attention is still focused on the same kinds of question—in particular, the points of contact between physics and metaphysics, and the nature of human conceptualisation of experience—but the philosophical theories now invoked are, to say the least, radically different.

I have already indicated that mme Du Châtelet was, and was recognised to be, less purely Newtonian than Voltaire, well before the supposedly fateful encounter with Koenig. In fact, the traditional assumption that Voltaire was her primary philosophical influence up to 1739 (an assumption which we can trace to Voltaire himself) is not borne out by the evidence of her correspondence, which reveals that the most lasting and decisive influence on her thinking was that of Maupertuis, to whom she constantly turned for information, approval and advice of all kinds. The series of letters exchanged between them in 1738 and early 1739 (of which we possess only part, since she admits at one point to be writing to him by every post from Cirey, that is, three times a week: Best. D1821, 26 January 1739), though wide-ranging in the issues they raise, suggest that one or two questions intrigued her especially. In particular, she read and re-read Maupertuis's own 1732 Mémoire to the Académie des sciences, ‘Sur les loix d'attraction’.⁵⁰ The main thrust of that paper was the claim that the inverse-square law established by Newton was in fact the only law of attraction which could operate in a self-consistent universe, and that this was why God had chosen it. In other words, it raised precisely the issues—of the necessity and rationality of scientific truths, and of the relation of God to the universe—which are eventually taken up in the opening chapters of the 1740 text of the Institutions. By then, of course, the discussion is couched in the Leibnizian terminology of the principle of sufficient reason: but her previous interest in Maupertuis's Mémoire leads to the inference that mme Du Châtelet was already, in 1738, concerned not merely with general questions about the foundations of physics but with this one specific physico-theological problem. It was this which focused her attention on the more general issue of the extent to which physical laws and entities can be explained rationally, and the extent to which we have to bow to the inscrutable will of God.

In the 1738 draft of the last chapter several passages appear in which she, albeit unwillingly, is prepared to appeal to divine choice as the only available explanation of the ultimate laws of the universe:

d'ailleurs il me semble qu'il n'est pas plus aisé de concevoir la simple communication de mouvmt entre les corps suposés entièremt durs, que de savoir ce que leurs forces deviennent après le chocq, il faut, ie crois, demander l'un et l'autre à dieu.⁵¹

le cas de tous le plus simple est celui d'un corps qui frape un obstacle immobile et ce cas est sujet aux plus grandes difficultés […] j'ay bien peur qu'il ne faille encore recourir à dieu pr le chocq des corps.⁵²

These passages were excised from the final text; their overall tone indicates her dislike of such facile and unscientific solutions for fundamental scientific or philosophical questions. They contrast obviously with Voltaire's readiness to view our knowledge as strictly limited because of the degree to which unfathomable divine purposes govern events: she is, as it were, already the potential Leibniz to his Clarke. Letters to Maupertuis show that other phenomena worried her in the same way, particularly the supposed elasticity and indivisibility of physical bodies (Best.D1804, 20 January 1739, and D1620, 29 September 1738). But in 1738 she still had no alternative principle of explanation, no way of going beyond exposition of mechanistic laws to a general metaphysical account of their necessity and rationality.

The 1738 version of the Institutions was thus, on her own terms, deficient in a critical respect. That is, there was no indication of how any metaphysical doctrine could be invoked in practice, to form the ultimate level of explanation needed to transcend the mechanistic, causal, ‘Newtonian’ level and thus complete our knowledge of the cosmos, in the way that Maupertuis's Mémoire had sought to do for the inverse-square law. From the letters to Maupertuis it is unclear whether she thought this detailed correlation of physics and metaphysics could be made, or whether instead she was inclined to hold that all we can be sure of is that there is a rational justification for all phenomena, albeit one which is inaccessible to human beings. She explicitly praises his application of metaphysics to the study of the inverse-square law and the force vive controversy (Best.D1496, 9 May 1738):

Ie crois donc, s'il m'est permis d'auoir vn opinion sur cela, que la force de ces cors se consomeroit reëllement dans les efforts qu'ils feroient pr surmonter réciproquement leur impénétrabilité, et leur force d'inertie, et que cet effet qu'ils auroient produit l'un sur l'autre en surmontant la force que tout cors en mouvement a pr persévérer à se mouuoir, cet effet, dis je, représente métaphysiquement la force qui la produit et ce seroit bien alors que la métaphysique seroit contente. Ie vs croyois reconcilié auec elle depuis que vs aués décidé pr la loy d'attraction en raison inuerse du quarré des distances en faueur d'une raison métaphysique, mais ie vois bien que vs n'en voulés que lorsqu'elle justifie les loix Etablies par le créateur, et découuertes par Neuton. Vs ne voulés point Eclairer ses profondeurs, vs aués cependant bien tort.

In other words, she was clearly intrigued by the possibilities of a more metaphysical approach; but it seems that in 1738 she was still hesitant as to whether a whole new programme for scientists and philosophers—that of demonstrating the synthetic a priori character of physics, in effect—could be carried out, or whether she meant simply to provide reassurance of a vaguely theological sort to scientists worried about the anti-religious or merely empirical character of their profession.

It was this sense of dissatisfaction with a still amorphously conceived project that Koenig's explanation of Wolffian metaphysics resolved. Mme Du Châtelet's sudden and complete adoption of central doctrines of Leibniz and Wolff (including those she did not fully understand, like the identity of indiscernibles or the pre-established harmony) in the 1739 rewriting of the Institutions can be explained only on the supposition that she had recognised how imprecise and vague was the connection supposedly linking the methodological and philosophical topics discussed in the first half, and the specific theories of physics expounded in the second half, of her book. Indeed, in the 1738 version the last twelve chapters could be read as a self-contained summary of Newtonian physics: virtually no attempt was made, until the very end of the last chapter, to reintroduce the philosophical issues which in principle were meant to be so necessary to the understanding of science.

But in the radical rewriting of 1739, eight entirely new chapters appear in the first half, and smaller-scale but equally radical alterations are made for consistency in the rest of the book. The new chapters, on the principles of sufficient reason and contradiction, essences, attributes and modes, space, time, the ‘elements of matter’ (that is, monads or ‘êtres simples’), and the nature and properties of physical bodies (‘êtres composées’ or ‘phenomena bene fundata’ in the Wolffian sense), all propound methodological and ontological doctrines quite at odds with those of the Newtonians, and, one may assume, with the contents of the 1738 draft. From the manuscripts of these chapters, it appears that, after all, Koenig's accusations of plagiarism contained a grain of truth: they are a patchwork of mme Du Châtelet's own exposition and of material copied or translated from some source provided by her tutor. She later explained to Jean Bernouilli the younger that she had worked from the ‘extraits’ of Wolff's Ontologia and Cosmologia generalis prepared for her by Koenig (Best.D2254, 30 June 1740). That she actually copied or translated parts of these directly is shown by the character of several of the marginal queries in her own hand on the manuscript: for instance, frequent annotations are ‘expliquer’ and ‘fiat lux’,⁵³ indicating that she is in the process of copying out material she does not fully comprehend. At one point she copies an abbreviation (‘par’ for ‘parcourt’), resulting in a meaningless sentence which is queried by her in turn.⁵⁴ Other queries are of the form ‘cela est-il bien’, ‘ceci n'est pas le mot’, ‘un autre mot’,⁵⁵ which suggest that she is translating from Wolff's or Koenig's Latin and is dissatisfied with the precision of her rendering. (The same technique occurs again in the manuscript of the Principia translation.) Chapters five to ten especially contain frequent annotations of these kinds, as well as others which we may read as ‘reminders’ to herself to add or clarify something.

Why mme Du Châtelet did not take the time to, at least, rework the material given her by Koenig into something more purely her own is hard to say, though, of course, given the rather loose conception of authorship and literary property at the time, there is no reason why she should have felt compelled to rewrite what was avowedly an exposition of Wolff and Leibniz and could thus be expected to contain a lot of direct quotation or close paraphrase. And she did credit Koenig for his assistance, though reducing the number of references to him, even after their quarrel and his attempt to ridicule her publicly. In any case, however these chapters came to be composed, we cannot attribute any original metaphysical doctrines to mme Du Châtelet; but we can still consider the version of Wolffianism introduced into the second version of the Institutions as an accurate representation of her new position on the relation of science and metaphysics.

The major ‘discovery’ which she made in Wolff was the principle of sufficient reason. In the light of her previously unsatisfied search for some principles of rational explanation or justification, it is easy to see why the principle of sufficient reason seemed so attractive. As I indicated above, she had no absolute objection against appealing to God as a source of explanation; what she distrusted was the Voltairean readiness to use ‘divine choice’ as a blanket pseudo-explanation of everything for which no other explanation was immediately forthcoming, and hence to equate the appeal to divine will with a confession of ignorance. She had of course already come across the principle of sufficient reason in her reading of the Leibniz-Clarke correspondence.⁵⁶ Voltaire, as I noted above, made no attempt to distinguish the principle from the claim that every event has a cause; but mme Du Châtelet immediately recognised the importance of distinguishing causal and rational explanation. She therefore interpreted the principle not as a causal one but as one which precedes and supplements any causal account of physical phenomena, assuring us that there is a rational explanation for the necessary occurrence of one specific set of contingent things or events rather than any other:

ns reconnoissons dans tous les cas que ns ne pouvons point forcer notre esprit à admettre quelque chose sans raison sufisante, c'est à dire, sans une raison qui fasse pleinement comprendre pourquoi la chose est plutost ainsi que tout autrement.⁵⁷

In the second draft of the chapter she amplified this:

Ainsi il faut qu'une cause contienne non-seulement le principe de l'actualité de la chose dont elle est cause; mais encore la raison sufisante de cette chose, c'est à dire, ce par où un Etre intelligent puisse comprendre pourquoi cette chose existe.⁵⁸

At the same time, she remained highly suspicious of arbitrary and imaginative use of the principle, and in particular of ad hoc appeals to it which block rather than advance the search for knowledge. The scholastics, she says, are especially guilty of this abuse (according to a comment made in the first draft and expanded in the second as follows):

les Scholastiques admettoient bien qu'il ne se fait rien sans cause, mais ils alléguoient pour causes des natures plastiques, des âmes végétatives, et d'autres mots vides de sens; mais quand on a une fois établi qu'une cause n'est bonne qu'autant qu'elle satisfait au principe de la raison suffisante, c'est à dire, qu'autant qu'elle contient quelque chose par où on puisse voir comment, et pourquoi un effet peut arriver, alors on ne peut plus se payer de ces grands mots qu'on mettoit à la place des idées […] cette âme végétative étant posée, je n'entens point de là pourquoi la Plante que je considère, a plutost une telle structure que toute autre, ni comment cette âme peut former une Machine telle que celle de cette Plante.⁵⁹

But for mme Du Châtelet the value of the principle, correctly used, is just that it eliminates arbitrary pseudo-explanation: ‘il est le bride de l'imagination qui fait des escarts sans nombre dès qu'on ne l'assujettit pas aux règles d'un raisonnemt sévère’.⁶⁰

The role of hypotheses as tools of scientific advance, which she had already argued for in the 1738 version of the book, now fits into the framework of the principle of sufficient reason. Hypotheses are simply the suppositions we formulate in the process of mechanistic-causal explanation of observable phenomena, essential to constructing the empirical scientific account of the physical world which in turn is to be explicable in terms of sufficient reason. Hypothesis too can degenerate into metaphysical fantasy, as it did in the atomism of Lucretius:

Si ceux qui ont voulu expliquer tant d'effets surprenants par le moyen des particules crochuës, branchuës, et cannelées, avoient fait attention à ce qui est requis pour faire un hypothèse véritablement philosophique, ils n'auroient pas retardé comme ils ont fait, les progrès des sciences, en créant des monstres qu'il falloit ensuite combattre comme des réalités.⁶¹

But straightforward rules can be introduced for avoiding these abuses (and she indicates some of these in chapter four);⁶² there is no reason to react as Newton is supposed to have done by banishing hypotheses altogether. In any case, to do so would be impossible; the task of science is to propose putative causes for observable events, and whenever these causes are not themselves directly observable, a hypothesis is by definition being formulated. In short, she claims that in a sense Newton's whole project was based on the formulation of hypotheses, and that the mistake of assuming Newton to have espoused some kind of pure Baconian observation has to be rectified by pointing out that the most important thing scientists can do is to learn to distinguish good from bad hypotheses by indicating the limits of hypothesis-construction, instead of consigning all equally to the realm of the imagination.

On the whole question of theorising in science, at whatever level, mme Du Châtelet rejected out of hand the Baconian ideology espoused by many New-tonians; as she says, anyone can observe phenomena, but to construct fruitful hypotheses is the mark of a great scientist:

mais en distinguant entre le bon et le mauvais usage des hipothèses, on évite ces deux extrémités, et sans se livrer aux fictions, on n'ôte point aux sciences une méthode trèsnécessaire à l'art d'inventer, et qui est la seule qu'on puisse employer dans les recherches difficiles qui demandent la correction de plusieurs siècles, et les travaux de plusieurs hommes, avant d'atteindre à une certaine perfection […] Les bonnes hipothèses seront donc toujours l'ouvrage des plus grands hommes. Copernic, Kepler, Huyghens, Descartes, Leibnits, M. Newton même, ont tous imaginé des hipothèses compliqués et difficiles; et les exemples de ces grands hommes et leurs succès doivent nous faire voir combien ceux qui veulent bannir les hipothèses de la Philosophie, entendent mal les intérests des sciences.⁶³

She refused to take seriously the sceptical attacks on human thinking which might be raised against her advocacy of hypotheses and the principle of sufficient reason. Not that she was by any means unaware of the standard sceptical arguments against the possibility of human knowledge; she simply held the thoroughgoing sceptical position to be self-refuting in practice and hence not worth serious consideration, as she notes in passing in the fragment on liberty. Responding to the argument that the sensation of acting freely does not prove we are really free, she points out:

mais si ie croyois être libre, et que je ne le fus point, il faudroit que Dieu m'eut créé exprès pour me tromper. car nos actions nous paroissent libres précisément de la même manière qu'elles nous le paroitroient si nous l'étions véritablement

(note 4).

The ‘note 4’ in question adds:

La réponse à cette seconde objection est presque la même que celle du 3e argument [du chapitre précédent] contre l'existence des corps mais cela ne peut être autrement puisque les personnes qui nient la liberté font contr'elle ‹à peu près› ‹les mêmes› une partie des objections que ceux qui nient l'existance des corps font contre cette existance.⁶⁴

She rejected any form of the ‘argument from illusion’ as illegitimate generalisation. That is to say, our recognition of false hypotheses and specious or vacuous sufficient reasons shows, in her view, not that all of these are probably false or unjustifiable, but that we do know how to correct our beliefs and hence make progress, in the sciences as elsewhere.

Having established a role for the principle of sufficient reason, mme Du Châtelet proceeds to explain its connection with Wolffian ontology (which she mistakenly equated with that of Leibniz). She sketches out Wolff's doctrine of ‘êtres simples’, a derivation from Leibniz's monadism which eliminated the purely metaphysical, dynamic, ‘windowless’ character of Leibniz's conception while retaining the features of non-spaciality and ontological primacy.⁶⁵ And she adopts the resulting distinction of real and phenomenal worlds as characterised in Wolff's Ontologia, a move which entails a series of concomitant doctrines. In particular, her previous belief in the Newtonian corpuscular theory as a true account of the ultimate constituents of the universe (the belief in absolutely inelastic and invisible extended atoms as the basic units whose behaviour mechanistic laws are to describe) has to be abandoned. Repeating the gist of Leibniz's arguments for the logical impossibility of such material particles' being ultimate, she relegates them to the phenomenal world. In consequence, she adopts the absolute distinction between non-extended ‘êtres simples’—unobservable but truly real substances—and material atoms—the convenient fictions (‘êtres composés’) which figure in mechanistic accounts of observable (and hence equally fictional) phenomena.⁶⁶ Consequently, she replaces the ‘two-tier’ world-picture of Newton, composed of atoms and their normally visible aggregates, with a ‘three-tier’ picture, in which atoms themselves are material, extended aggregates of ‘êtres simples’, and normally visible objects simply larger, more complex aggregates yet.

Once this ontological picture has been introduced (and its details spelled out in the new chapters seven to ten), the original vague project of an ultimate justification of truths of Newtonian science could be given real substance. One might reconstruct mme Du Châtelet's reasoning as follows: if one accepts Newtonian ontology in which everything real is in principle observable, because composed of extended atoms in motion, mechanistically related by discoverable laws, then the laws, once discovered, must so to speak exhaust the explanation-space. In a perfectly literal sense, nothing remains over as explanandum or explanans. It is easy enough to insist that there is still ‘something’ to be explained: why just these laws rather than any others? But as no left-over entities within the universe itself can be appealed to for an answer to that question, the only obvious recourse, as Newton and Voltaire—and, reluctantly, mme Du Châtelet herself up to 1739—recognised, is a theological one. That is, if one rejects a straightforwardly positivist position in which the continued accuracy of scientific regularities neither needs nor can have explanation, then the only alternative seems to be to appeal to some non-material entity to provide a more profound explanation of material entities and their mechanistic causal behaviour; and for the Newtonians God looked like the only available candidate. But in mme Du Châtelet's eyes, the result of accepting Leibniz's and Wolff's claim that the material world is not the only one, nor the most fundamental one, is that the distinction between mechanistic and rational explanation, between cause and sufficient reason, neatly matches that between material and immaterial, phenomenal and real, ‘êtres composés’ and ‘êtres simples’. And the conclusion implicit in the structure of the 1740 text of the Institutions is that a re-evaluation of the foundations of scientific knowledge needs to be worked out in the light of this new ontology.

The virtue of a thoroughgoing Wolffianism from mme Du Châtelet's point of view was, I believe, that she saw how it provided the essential link between science and its metaphysical underpinnings which she had previously only dimly perceived through her study of Maupertuis's ‘Sur les loix d'attraction’. According to her interpretation of the principle of sufficient reason, it was to be invoked to carry out Maupertuis's suggestion that descriptions of contingent mechanical regularities be, in principle, supportable by a theoretical account of why only those particular regularities could in fact occur in the combinations we observe. Maupertuis, she apparently realised, had tried to do this to some extent; but by refusing to delve into metaphysical issues he had doomed his project from the start. But by replacing generalised appeals to ‘divine will’ with an application of the principle of sufficient reason, and by admitting an immaterial level of reality, explanation could transcend the physical, phenomenal level and ultimately demonstrate the rational necessity of very general truths about the cosmos, truths lying on the borderline of science and metaphysics.

By appealing to this principle it would be possible to decide questions for which the physical data are permanently inadequate. And the attractiveness of this prospect for mme Du Châtelet, I think, lay precisely in the fact that many burning questions of this kind were occupying scientists and philosophers in the 1730s and 1740s. Examples discussed in the Institutions had in fact sparked some of the major debates of the early eighteenth century: what are the basic constituents of the universe? is there a vacuum? is gravity an essential property of matter? are the properties of organic beings different from those of inorganic matter? what is the nature of force? does God intervene in the workings of nature? What these questions have in common, as mme Du Châtelet points out in her discussion of force,⁶⁷ is that the relevant factual information is not in dispute; it is the interpretation of the facts which divides philosophers and scientists, and in her view this implied that a resolution could be reached only by going beyond the facts to their sufficient reasons.

Needless to say, however, the application of the principle of sufficient reason to particular questions presents its own difficulties, and indeed mme Du Châtelet is still inclined to be pessimistic in her estimation of just how far we can take such inquiries. The complete, rational explanation of everything is, of course, as Leibniz and Wolff both readily admitted, knowable only to God, and in many areas of science we cannot even reach knowledge about physical laws, let alone begin to construct our own rational explanations of them.⁶⁸ One example serves to demonstrate the way in which mme Du Châtelet conceived the domain of sufficient reason. After distinguishing between ‘force primitive’, which is an essential property of ‘êtres simples’, and ‘force dérivative’, the phenomenal force whose effects we observe and calculate mathematically, mme Du Châtelet cautions:

La force primitive étant indifférente à toutes sortes de vîtesses et de directions, on ne peut s'en servir pour rendre raison, pourquoi dans un cas donné, un corps a une vîtesse quelconque, et se meut dans une certaine direction, puisqu'il pourroit se mouvoir en toute autre direction, et avec une toute autre vîtesse. Ainsi, pour rendre raison des Phénomènes particuliers, on ne peut se servir de la force primitive: car il ne faut jamais alléguer des raisons éloignés, lorsque l'on en demande d'immédiates et de prochaines, puisque ce seroit retourner aux formes substantielles de l'Ecole: mais par les raisons générales, on ne peut expliquer que les phénomènes en général, et il faut en venir à des raisons immédiates, lorsqu'il s'agit des Phénomènes particuliers. C'est donc par la force dérivative qui naît du choq des Corps, qu'on peut rendre raison des Phénomènes qui naîssent du mouvement, par l'action des Corps les uns sur les autres, et par laquelle la force primitive est modifiée, et limitée, lorsqu'elle reçoit une certaine vîtesse et une certain direction; et comme le Corps ne peut point se donner par lui-meme cette vîtesse et cette direction, il faut qu'il la reçoive par le choq des Corps environnans, et par-là la force dérivative devient explicable distinctement, parce que l'on peut expliquer par les loix du mouvement pourquoi un Corps ayant été choqué, il se meut avec une vîtesse plutôt qu'avec toute autre, c'est-à-dire, pourquoi la force primitive a été modifiée de cette manière dans un cas donné.⁶⁹

The point of this involved passage, and of many others like it, is to make clear that the function of the principle of sufficient reason is not to supplant causal accounts of the physical world, but rather to determine the limits of the possible by specifying the most general features of the cosmos. It is impossible to jump directly from these latter to specific physical laws; but we can in principle draw on such general features to construct a chain of gradually more precise reasons, narrowing down the possibilities, until we eventually demonstrate why only one set of contingent observed events does take place. My surmise is that mme Du Châtelet still had Maupertuis's ‘Sur les loix d'attraction’ in mind and conceived her Wolffian account of the interconnection between science and philosophy as a ‘solution’ to Maupertuis's difficulties with the inverse-square law. (It is significant that she later returned to just the same problem, working out the implications of possible alternatives to the inverse-square law, in her commentary to the Principia mathematica.)⁷⁰

She recognised that we are unable at this point to complete the proposed chains of explanation; however, our ability to contribute something towards such a project pointed to a new programme for scientific enquiry which was yet to be undertaken, and which in fact could not have been undertaken before we possessed the body of discoveries at the phenomenal level made by Newton. Successful investigation of the phenomenal world, she insists, is an autonomous activity prerequisite to rational explanation; it can go on satisfactorily (as it has so far) on its own terms, and in any case it should not be mixed up with non-causal, non-empirical reasoning or interpretation:

les Philosophes qui veulent que l'on n'admette en Philosophie que des principes méchaniques, et qui prétendent que tous les effets naturels doivent être explicables méchaniquement, ont raison; car la possibilité d'un effet se doit prouver par la figure, la grandeur, et la situation du composé, et son actualité, par le mouvement.⁷¹

The philosophers in question are the Newtonians, and it is one of their major virtues to have stressed the autonomy of scientific method from metaphysical considerations. Rational explanations, in mme Du Châtelet's view, should neither interfere with nor replace a posteriori knowledge; but they complete that knowledge by eventually showing how it is grounded in non-phenomenal reality and hence why it is necessarily true.

In the final analysis, for mme Du Châtelet the justification of scientific knowledge via the principle of sufficient reason was a project to be undertaken with extreme caution and self-criticism, constantly subjected to correction, likely never to reach more than a tentative and elementary stage, and in practice irrelevant to the activity of most scientists. But: firstly, its feasibility in principle shows that our science is something more than an accidental assemblage of contingent regularities, and secondly, it is essential to the solving of a group of fundamental questions on the frontier of science and metaphysics which no amount of experiment at the phenomenal level will settle, including the nature of the basic constituents of the universe, the relation of God to the world, and the possibility of human freedom.

Mme Du Châtelet's aim in the Institutions was not to turn the battle of Cartesians and Newtonians, which still raged in the 1730s and 1740s, into a three-cornered fight by introducing Leibniz and Wolff onto the French intellectual scene. It was, rather, to demonstrate the complementarity of what to others appeared to be diametrically opposed systems and modes of thought. Further analysis would show how in the revised second half of the book mme Du Châtelet meant to demonstrate that Newtonian physics could be rewritten in Wolffian terms, without loss of content, in such a way as to be compatible with an ostensibly alien ontology (in a way that it could never have been made compatible with Cartesianism). Even though her grasp of the detail of Leibniz's and Wolff's theories was still elementary, she realised. I think, that by reconciling them with Newtonian science she could find the way out of a paradox which was soon to become apparent to other philosophers as well. That is, the very successes of Newtonian science, based supposedly on a Baconian model of investigation and justification, entailed inevitable metaphysical questions about the origin and necessity of scientific laws which respectable empiricists wanted to avoid. The available alternatives of ‘pre-positivism’, scepticism, deism and mysticism were all ways of doing just that. But these metaphysical questions, though awkward, were bound to become more pressing with the spreading acceptance of Newton's system throughout Europe. For anyone who wanted substantive answers to them, Wolffian ontology and the concomitant conception of rational explanation via the principle of sufficient reason were the single current alternative solution. Mme Du Châtelet seems to have been the first to recognise that fact and to seek a middle ground between, on the one hand, the facile empiricism of the Newtonians and, on the other, adherence to a metaphysical system for its own sake, regardless of its relation to empirical fact, which Cartesianism had already become and where Wolffianism threatened to follow it. And even though she failed to spell out explicitly many of the difficulties and advantages of such a synthesising project, the originality of that project itself can not be doubted.

Notes

1. G. Mangeot, ‘Les Réflexions sur le bonheur de la marquise Du Châtelet’, Mélanges Lanson (1922); R. Mauzi (ed.) Discours sur le bonheur (Paris 1961).

2. I. O. Wade, Voltaire and mme Du Châtelet (Princeton 1941).

3. I. B. Cohen, ‘The French translation of Newton's Principia’, Archives internationales d'histoire des sciences 21 (1968), pp.261-90; R. Taton, ‘Mme Du Châtelet, traductrice de Newton’, Archives internationales d'histoire des sciences 22 (1969), pp.185-210.

4. W. H. Barber, ‘Mme Du Châtelet and Leibnizianism: the genesis of the Institutions de physique’, The Age of the Enlightenment, ed. Barber and others (Edinburgh, London 1967), pp.200-22; C. Iltis, ‘Mme Du Châtelet's metaphysics and mechanics’, Studies in the history and philosophy of science 8 (1977), pp.29-48.

5. I. O. Wade, The Intellectual development of Voltaire (Princeton 1969), pp.276-91.

6. A. Vaillot, Mme Du Châtelet (Paris 1978), pp.185-91.

7. Published for the first time in I. O. Wade, Studies on Voltaire (Princeton 1947), pp.131-87.

8. Recueil des pièces qui ont concouru … (1739, repr. 1752), pp.87-170.

9. Voltaire, Correspondence and related documents, ed. Th. Besterman (Voltaire 85-135) (Genève, Banbury, Oxford 1968-1977), Best.D.app.51.

10. Published in Wade, Studies, pp.188-208.

11. Wade, Studies, p.127, dates this as 1736, and publishes it, pp.209-41.

12. Wade, Voltaire and mme Du Châtelet, p.126.

13. Vaillot does so, to some extent, in Mme Du Châtelet, chapters 7-11.

14. He tells Frederick he plans to ‘revoir et transcrire’ the work, in Best.D1243, c.1 January 1737.

15. See, for example, R. Hall, ‘Newton in France’, History of science 13 (1975), pp.233-50, which modifies the traditional picture given by P. Brunet, L'Introduction des théories de Newton en France au dix-huitième siècle (Paris 1931).

16. The second version of the ‘Avant-propos’ on the manuscript of the Institutions de physique (Bn f. fr. 12266), remarks of Newtonian attraction, ‘vous pouvés tirer beaucoup d'instruction sur cette matière des Elémens de la philosophie de neuton, qui ont paru cette année, et ie suprimerois ce que j'ay à vs dire sur cela si leur illustre auteur avoit embrassé un plus grand terrain, mais il s'est renfermé dans des bornes si étroites que ie n'ay pas cru qu'il peut me dispenser de vs en parler’ (Institutions, ms. f.18).

17. Wade, Studies, pp.102, 107.

18. Wade's attribution of the fragment to Voltaire (Studies, pp.20-21) rests only on the supposition that Voltaire would never have passed off the ‘extrait’, which repeats the fragment almost verbatim, as his own work; but given the close collaboration of the two on the projects I have mentioned, the idea of ‘literary property’ seems out of place. Mme Du Châtelet, who disliked and distrusted Frederick, may even have derived ironic satisfation from seeing him praise a piece supposedly by his hero Voltaire. Voltaire's self-attribution of course explains why the chapter on liberty never appeared in the published Institutions, as mme Du Châtelet would have been obliged to withdraw it to ‘save face’ for Voltaire. Whether she came to reject the views expressed in it is harder to say.

19. A plan to visit England with Algarotti, for instance, came to nothing; cf. Best.D1421, 10 January 1738.

20. ‘Mme Du Châtelet’, p.220.

21. E. Philips, ‘Madame Du Châtelet, Voltaire and Plato’, Romanic review 23 (1942), pp.250-63; there seems to be no justification whatsoever for the claim made in this article that the comments in mme Du Châtelet's hand represent Voltaire's views.

22. Voltaire, Traité de métaphysique, Œuvres complètes, ed. L. Moland (Paris 1877-1885), xxii.203.

23. ‘Avant-propos’, first version, Institutions ms. fols 7-8r; the 1740 text leaves out the direct reference to the Newtonians but otherwise retains the passage almost verbatim, pp.9-10.

24. One of the comments on the substance of Newton's work in the margins of the manuscript translation of the Principia occurs against the passage of the Scholium generale in which Newton describes the universe as ‘God's sensorium’: mme Du Châtelet laconically notes ‘ridicule’ (Bn f. fr. 1266, f.455). The strength of her feeling on this point is underscored by the extreme scarcity of other substantive comment on the translation ms., where mme Du Châtelet is usually content to keep to the role of faithful translator.

25. ‘Dissertation sur la nature et propagation du feu’, Recueil des pièces, pp.98-99.

26. In Best.D1661, 19 November 1738, to Maupertuis, mme Du Châtelet already suggests despair over the state of the manuscript in her declaration that the recently published Dissertation may be all she will ever produce.

27. Wade, Studies, pp.135-36.

28. Institutions, ms., for example fols 233-34, from eventual chapter 20 on vector analysis; 256v-272, from eventual chapter 15 on attraction; 306v-309, from eventual chapter 18 on cycloids.

29. Barber, ‘Mme Du Châtelet’, p.205n, identifies the earliest published French translation of any of Wolff's works as the Logique (1736), a translation by Deschamps of the Vernünftige Gedanken von den Kräften des menschlichen Verstandes und ihrem richtigen Gebrauche (1712).

30. J. S. Formey, Souvenirs d'un citoyen (Paris 1789), i.174.

31. Harcourt Brown, ‘From London to Lapland: Maupertuis, Johann Bernouilli 1, and La Terre aplatie, 1728-38’, Literature and history in the age of ideas, ed. C. G. S. Williams (Columbia, Ohio 1975), p.90.

32. Formey, Souvenirs, i.173.

33. The letters collected by Besterman (especially Best.D2080n, 14 September 1739; D2125n, 28 December 1739; D2140, 12 January 1740; and D2254, 30 June 1740) must now be supplemented by the letters of mme de Graffigny published by E. Showalter, ‘Voltaire et ses amis d'après la correspondance de mme de Graffigny’, Studies on Voltaire 139 (1975), especially letter 187, 28 November 1739.

34. That chapter 16 on attraction was added later is shown by several considerations. Firstly, its stance is definitely pro-Leibniz to an extent found only after her instruction by Koenig began; secondly, it is the only one of the later chapters not to have been fair-copied by a secretary, and has no section numbering but has simply been inserted bodily between two existing chapters; thirdly, unlike the other surrounding chapters, it has no marginal queries at all. Moreover, very similar subject-matter is covered in chapters 13-15, so that if it had been written or revised during the same period as they were (that is, early 1738-September 1739), it could be expected to have been combined with chapters 13-15 or referred to in those chapters. As it is, however, chapter 16 is entirely self-contained.

35. As Barber also notes (‘Mme Du Châtelet’, p.221).

36. Jean Deschamps, Cours abrégé de la philosophie Wolfienne (1743); J. S. Formey and S. Chambrier, La Belle Wolfienne (1746); E. de Vattel, Défense du système leibnitien (1741).

37. Both reviews and letters about the Institutions indicate this: in addition to the review written by Voltaire for the Mercure de France (June 1741, pp.1274-1310), see Best. D2420, 1 February 1741, from A. M. Ramsay, and Best.D2429, 19 February 1741, from Cideville.

38. Barber, ‘Mme Du Châtelet’, fails to notice that the manuscript contains two versions of the ‘Avant-propos’ and chapters 1 and 2, fols 2-74.

39. G. W. F. Leibniz, ‘Brevis demonstratio erroris memorabilis Cartesii’, Acta eruditorum (1686).

40. H. G. Alexander (ed.), Leibniz-Clarke correspondence (Manchester 1956); Leibniz's fifth paper, paragraphs 93-103.

41. Institutions, sections 586, 588.

42. Institutions, ms. f.267.

43. Institutions, ms. f.48.

44. Institutions, ms. f.99.

45. Incidentally, Barber's assumption (‘Mme Du Châtelet’, p.219n) that the majority of marginal comments were addressed by Voltaire to mme Du Châtelet is unfounded: examination of the content of the queries and their relation to the main body of the text makes clear that mme Du Châtelet herself was adding them, simultaneously with the composition of the work (as the conformity of ink colour and pen-point sizes shows), at points where she felt dissatisfied with her own exposition's accuracy or clarity, sometimes to remind herself to rewrite or check a reference, sometimes to submit her difficulties to Koenig for guidance or correction. Exactly the same procedure occurs later on in the manuscript of the Principia translation, when Clairaut had become her adviser. It is highly unlikely that Voltaire had anything to do with any of the Institutions text, except perhaps the chapter on ‘force vive’, a topic he continued to take an interest in even after his Eléments were published; mme Du Châtelet could hardly have expected him to clarify points of Wolffian doctrine or mathematical exposition.

46. Wade, Studies, pp.97, 92.

47. Institutions, ms. fols 368, 247v.

48. Institutions, ms. fols 196v, 197.

49. Barber, who draws on much of the same data as I do, concludes, wrongly I believe, that the first half of the 1738 version was more scientific and closer to the topics of the second half (‘Mme Du Châtelet’, p.220). Apart from the evidence of the fragment on liberty, this interpretation would imply that the 1738 text as a whole would have had to be extremely—and improbably—repetitious: for instance, why talk at length about the laws of motion in sections 29-58 when, as the 1738 proof-sheets show, a thorough exposition was to be introduced later on in chapter 10? Barber's own opinion, with which I concur, that the opening chapters were conceived as a philosophical introduction, makes far more sense in the light of the reconstruction of their content advanced here.

50. L. M. de Maupertuis, ‘Sur les loix d'attraction’, Mémoires de l'Académie royale des sciences de 1732 (1735), pp.343-62.

51. Institutions, ms. f.359v.

52. Institutions, ms. f.360v.

53. Institutions, ms. fols 105v, 111, 112.

54. Institutions, ms. f.119.

55. Institutions, ms. fols 111, 127, 131, 140, and passim.

56. She was, naturally, also familiar with the principle of contradiction, which features in the 1739 draft of the Institutions but receives noticeably less attention in the 1740 text and evidently does not strike her as equally illuminating or relevant to her picture of the foundations of science.

57. Institutions, ms. f.28; cf. Institutions, p.22.

58. Institutions, ms. f.46; cf. Institutions, p.26.

59. Institutions, ms. f.45; cf. Institutions, pp.27-28.

60. Institutions, ms. f.30v; cf. Institutions, p.26.

61. Institutions, ms. f.100; cf. Institutions, p.88.

62. She insists, for instance, on thorough gathering of data and willingness to have new data overturn existing hypotheses, and also on constantly recalling that hypotheses are instruments for getting truth, becoming truths themselves only when all relevant observations confirm them: Institutions, sections 61-62. Conversely, she cautions that hypotheses may be a complicated mixture of truth and falsity, so that apparent wholesale falsification must be analysed to make sure that only the genuinely refuted parts of the hypothesis are rejected: Institutions, section 65. (Much of the detail of this chapter derives from Wolff: cf., for example, C. Wolff, Discursus praeliminaris de philosophia in genere (1728), sections 126-29.)

63. Institutions, ms. f.100; cf. Institutions, pp.88-89.

64. Wade, Studies, pp.96-97.

65. The clearest account of the differences between Wolff and Leibniz on this question is to be found in J. Ecole, ‘Cosmologie wolffienne et dynamique leibnitienne’, Les Etudes philosophiques 19 (1964), pp.3-9.

66. Institutions, ch.7.

67. Institutions, sections 568, 573.

68. Cf. Institutions, section 162.

69. Institutions, pp.172-73; cf. Wolff, Cosmologia generalis (1731), section 358.

70. Principes mathématiques de la philosophie naturelle (1759), ii, ‘Solution analytique’.

71. Institutions, pp.160-61; this is not in the ms. so presumably was added on the 1740 proof copy.