Newton’s law of universal gravitation describes all the phenomena that were explained in the three preceding chapters. However, what is gravity? Gravity is the universal force of attraction between all matter, depending on the mass of each object and the distance between the objects. And what is attraction? According to the Newtonians attraction is (InstPhy, § 385):

une propriété donnée de Dieu à la matière, par laquelle toutes ses parties tendent l’une vers l’autre en raison directe de leur masse, & en raison inverse du quarré de leurs distances. (Amsterdam 1742)

a property given by God to all matter, by which all parts of matter tend towards one another in direct proportion to their mass and in inverse proportion to the squares of their distances. (Copyright © 2018 KB)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

One finds the root of this idea in Kepler’s Astronomia nova seu physica coelestis, tradita commentariis de motibus stellae Martis (1609, VIII):

Si duo lapides in aliquo loco mundi collocarentur propinqui invicem, extra orbem virtutis tertii cognati corporis, illi lapides ad similitudinem duorum Magnetum coïrent loco intermedio, quolibet accedens ad alterum tanto intervallo, quanta est alterius moles in comparatione. Si terra & luna non retinerentur vi animali, aut aliâ aliquâ equipoltenti qualibet, in suo circuitu, terra ascenderet ad lunam quinquagesimâ quartâ parte intervalli, luna descenderet ad terram quinquaginta tribus circiter partibus intervalli, ibique jungerentur. Posito tamen quod substantia utriusque sit unius & eiusdem densitatis.

In his introductory discussion of a moving earth, Kepler stated that the traditional Aristotelian doctrine that heavy things strive toward the center of the world was completely erroneous. He proposed an attractive force as tendency between material bodies toward contact, so the earth draws a stone much more than the stone draws the earth. Heavy bodies are attracted by the earth not because it is the center of the universe, but simply because it contains a lot of material, all of which attracts the heavy body. Du Châtelet, quoting the above passage, offers a French translation in a footnote, where she translates “vi animali,” or “animare force,” as “acting soul”  (“âme agissante”).

In a paper delivered at the Academy’s session of 14 August 1669, Bernard Frenicle de Bessy defended the view of gravity as a kind af attraction. Gilles Personne de Roberval, leaving aside any considerations of the cause of gravity, defined it: “Vim quamdam corporibus insitam qua partes illius in unum coïre affectent” (qtd. Jean-Baptiste Du Hamel: Regiae Scientiarum Academiae Historia 1700, 80). To quote from Du Châtelet (InstPhy, § 387):

Képler n’est pas le seul qui ait parlé de l’attraction. Frénicle, un des prémiers, Académiciens des Sciences la concevoit comme une force mise par le Créateur dans son Ouvrage pour le conserver; & Roberval la définissoit: Vim quamdam corporibus insitam quâ partes illius in unum coire affectant. (Amsterdam 1742)

Kepler is not alone in having spoken about attraction. Frenicle, one of the first Academicians of the Sciences, conceived of it as a force put by the Creator into his Work to conserve it; and Roberval defined it: Vim quamdam corporibus insitam qua partes illius in unum coïre affectent. (Copyright © 2018 KB)

[ This passage is missing in the Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

Newton’s law of universal gravitation expresses a mathematical relationship, where the attractive force is proportional to the product of their masses and inversely proportional to the square of the distance between them (InstPhy, § 388):

L’attraction […] elle est toujours supposée reciproque: ainsi, la terre en gravitant vers le Soleil, fait graviter le Soleil vers elle, & le Soleil la terre s’attirent réciproquement l’un l’autre en raison inverse de ces mêmes masses, & le chemin que la terre fait vers le Soleil, est au chemin que le Soleil, fait vers la terre dans le même tems, par cette feule attraction comme la masse du Soleil eft à la masse de la terre. (Amsterdam 1742)

Attraction […] is always assumed to be reciprocal: thus, the earth in gravitating towards the Sun makes the Sun gravitate towards it, and the Sun and the earth attract one another reciprocally in direct proportion to their masses. But they move towards one another in inverse proportion to these same masses, and the path that the earth makes toward the Sun is to the path that the Sun makes toward the earth, in the same time by this attraction alone, as the mass of the Sun is to the mass of the earth. (Copyright © 2018 KB)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

There is no doubt about the high explanatory power of the law of gravity (InstPhy, § 388):

Il est certain, que si on accorde aux Newtoniens cette supposition d’une attraction répandue dans toutes les parties de la matiére, ils expliquent merveilleusement par cette attraction les Phénoménes astronomiques, a chute des corps, le flux & le reflux de la mer, & qu’ils l’appliquent même avec affez de succès, aux effets de la lumière, à la cohéfion, aux opérations chimiques, & qu’en fin presque tous les effets naturels deviennent une suite de cette force, lorsqu’on la une fois admise. (Amsterdam 1742)

It is certain, that if we grant the Newtonians this assumption of an attraction distributed in all the parts of matter, they explain marvelously by this attraction the Astronomical Phenomena, the fall of bodies, the ebb and flow of the sea, the effects of light, the cohesion of bodies, and the chemical processes; and it is certain that almost all natural effects become a consequence of this force that one assumes is distributed in all matter, when one has once admitted it. (Copyright © 2018 KB)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

Noteworthy, Du Châtelet mentions the Royal Astronomer John Flamsteed, who gathered observational data about a massive comet that passed Earth in 1680 (InstPhy, § 388). Based on his observations, Flamsteed hypothesized that there was only one comet, not a pair of comets. Moreover, he thought that the comet did not move in a circular pattern, but rather, in an ellipse. He contacted his colleague, Isaac Newton, at the time Lucasian Professor of Mathematics at Cambridge University, an provided him his data. Flamsteed’s data allowed Newton to prove Kepler’s law of parabolic orbits, and to prove that the comet went around the sun in an elliptical orbit.

For Du Châtelet, the validity of the law of gravity is indisputable, as are the phenomena resulting from attraction. Nevertheless, she warns against a premature transfer of the universal validity to phenomena other than astronomical ones, criticizing John Keill’s hypothesis in his Introductio adveram Astronomiam (1718) that not only are cohesion and chemical effects the consequences of attraction, but the elasticity of bodies and the Phenomena of electricity are also subject to it (InstPhy, § 391). Even more suspect was Mr. Keill’s brother’s hypothesis (James Keill in Essays on Several Parts of the Animal Oeconomy 1717)  that animal secretion could be also explained by attraction.

Not to forget to mention: It was Pierre Louis Moreau de Maupertuis who maintained that Newton’s law of universal gravitation is a strong candidate for a theory of everything. In 1732 Maupertuis published the first French text to accurately explain Newton’s theory of gravitation, “Sur les lois de l’attraction,” in the Mémoires de l’Académie royale des sciences. Du Châtelet, discussing this essay, criticized Maupertuis’ speculations regarding God’s possible reasons for choosing the inverse square law (over all the other possible variants). Du Châtelet, facing the problem whether attraction is metaphysically impossible, aims to show that attraction cannot be an inherent and essential property or matter, nor given to matter by God (InstPhy, § 369). She uses the principle of sufficient reason in order to undermine these metaphysical suppositions and their theological implications. Du Châtelet argues as follows (InstPhys, § 395):

Car soit le corps A. qui soit attiré par le corps B. selon une certaine loi a travers le vuide BA. le corps A, s’approchera de corps B. dan la direction AB. avec une vitesse à tout moment accelerée, l’état du corps A lorsqu’il se meut avec cette vitesse accélerée, & dans une certaine direction, et assurement differént de son état précédent, c’est à- dire, de l’état de repos, dans lequel il étoit avant d’être dans la Sphére d’activité du corps B. car le corps mû ne peut être substitué, sauf toutes les déterminations, à la place du corps en repos; il est donc arrivé un chanement dans le corps A. ce changement a eu sa raison: ainsi, il faut chercher cette raison, ou dans ce corps A, ou hors de lui, & dans les Etres extérieurs qui agissent sur lui. (Amsterdam 1742)

For, let body A be attracted by body B according to a certain law, through the void BA; body A will approach body B in the direction AB with a speed at every moment accelerated, and the state of body A, when it moves with this accelerated speed and in a determined direction, is assuredly different from the preceding state, that is to say, from the state of rest in which it was before being transported into the Sphere of activity of body B, for the moved body cannot be substituted, without all its determinations, into the place of the body at rest, and therefore a change occurs in body A. This change had its reason: thus we must seek this reason, either in the moved body, or outside of it and in the exterior Beings that act on it. (Copyright © 2018 KB)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

According to Du Châtelet, the dilemma that we cannot find the cause of Newtonian attraction, neither in the body nor outside of it, means that whe should presuppose attraction as a phenomenon, and as nothing more (InstPhy, § 397). All experiments that have been carried out so far in order to find the mechanical cause of the attraction have been unsuccessful. This is even true for the experiments conducted by Pierre Bouguer confirming Newtonian gravitational attraction and estimating the mean density of the Earth. The possible existence of an electric aether is not excluded, although the search for the mechanical cause that brings about the phenomena that we attribute to attraction remains an open one.

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