Nicolas Fatio and the Cause of Gravity

Early in the seventeenth century Rene Descartes proposed a mechanistic approach to physics, asserting that all causal influence is transmitted by direct contact between material entities. Like Aristotle, he rejected the idea of vacuum, believing that there can be no space (extension) without substance. In accord with his philosophy, Descartes denied the intelligibility of weight as a primitive quality of matter, and argued that material bodies are impelled toward the Earth by the impulse of particles of a “second species of matter” continually arriving at the Earth from all directions. Galileo, in his Dialogue Concerning Two New Sciences (1638), chose not to commit himself to any particular cause of gravity, indicating that he thought such speculations were premature at the (then) present state of science. He wrote

The present does not seem to be the proper time to investigate the cause of the acceleration of natural motion [i.e., gravity], concering which various opinions have been expressed by various phiolosophers, some explaining it by attraction to the center, others to repulsion between the very small parts of the body, while still others attribute it to a certain stress in the surrounding medium which closes in behind the falling body and drives it from one of its positions to another.

The first of these opinions is essentially the assertion of inate attraction (to the “center”), and the third is a variation of Aristotle’s proposal, which attribute the motive force of object in natural motion to a propagating interaction with a posited medium. (Aristotle’s model has sometimes been ridiculed as being akin to a perpetual motion machine, but it is in essence just a crude description of a propagating wave.) The second opinion mentioned by Galileo is much less clear, but it seems to be alluding to an explanation of gravitation attraction based on repulsion and involving the (posited) very small parts of the body. Unfortunately Galileo didn’t elaborate on this brief allusion, nor did he cite the philosophers who held that opinion, apparently because he considered these “opinions” to be common knowledge. But his comment suggests that people had speculated about the possibility of attributing the effects of gravity to repulsion acting on the microscopic parts of bodies. It’s possible that he had in mind the bombardment of Descartes’ “second species of matter”.

In the second half of the century, Isaac Newton deduced from a combination of terrestrial and celestial phenomena that every two particles of matter are compelled toward each other with a force directly proportional to their masses and inversely as the square of the distance between them. This “universal gravitation” provided a unified account of a wide range of phenomena that had previously seemed inexplicable and unrelated, but it was apparently contrary to the mechanistic precepts of Descartes, because it implied that widely separated bodies exert forces on each other directly, without explicit reference to any intervening substance. In private correspondence, Newton (on at least one occasion) disavowed the notion of direct action at a distance, but at the same time he allowed for the possibility that the means by which the action of gravity is transmitted may not be material – in which case the Cartesians would still regard it as unintelligible action at a distance. Indeed, Newton’s overall approach was much more consistent with the view of the ancient atomists, i.e., that nature consists of atoms moving according to abstract mathematical laws in an empty void, and he frequently stated that gravity might be a primary attribute of matter, with no material intervening mechanism.

Acknowledging the success and utility of Newton’s concept of universal gravitation, many continental scientists - such as Huygens, Leibniz, and the Bernoullis - sought some way of reconciling it with the mechanical philosophy of Descartes. In other words, they sought an explanation of universal gravitation in terms of direct contact between material entities. Now, any tendency for bodies to be drawn together is inherently problematic in the context of Cartesian physics, because contact forces are, by definition, directed outward from the surfaces of bodies. Even if we hypothesize bodies with hooks or other interconnecting shapes, we must still rely on a force of cohesion to maintain the shapes of the bodies, so we haven’t avoided the need for a primitive force of attraction. This shows that purely material mechanisms, in the sense of Descartes, are inherently inadequate to fully account for the phenomena of experience. Nevertheless, there were many attempts to give a mechanistic account of gravity in terms of contact interactions between material bodies, even though these attempts tacitly rely on unexplained primitive attractive forces to maintain the shapes and configurations of those bodies. (Oddly enough, these attempts usually took inertia for granted as a primitive attribute of matter, while the same people in other contexts sought to account for inertia in purely relational terms by invoking primitive interactions between material objects.)

Another problematic aspect of Descartes’ physics vis a vis Newton’s universal gravitation is the Cartesian identification of volume with mass, which is unavoidable given Descartes’ identification of spatial extent with material substance. He cannot contemplate variations in density, because the very concept of density entails a distinction between space and matter. If matter is less dense in some regions of space than in others, we can hardly claim that the idea of a region of space with arbitrarily low density – or even zero density – is unintelligible. Thus his rejection of the vacuum and insistence on continuous substance obliged Descartes to make the mechanical properties of bodies, including both their inertial resistance to acceleration and the force of gravity propelling them toward the Earth, strictly dependent on their volumes. This was recognized as a shortcoming of Descartes’ physics, even among his followers. When they began to seek a mechanistic explanation for Newtonian gravity, this was among the first problems they needed to resolve. To do this, there was little choice but to reject the identification of matter with extent, so most mechanical philosophers departed from Descartes by adopting the ancient belief in particles (atoms) moving in a void.

The earliest proponents (that we know about) of the atomistic view were the ancient Greek philosophers Leucippus and Democritus, followed by Epicurus. Most of our knowledge of the teachings of these men comes to us second-hand through the Roman poet Lucretius, who wrote an account of the atomistic philosophy in the form of a monumental poem entitled De Rerum Natura (“On the Nature of Things”). We know almost nothing about Lucretius himself, except that he supposedly went mad as a result of drinking a love potion, and killed himself at the age of forty-four. By adopting the atomistic view, it was possible to rehabilitate Descartes’ mechanical model of gravity, and make it at least nominally consistent with the quantitative dynamical aspects of Newton’s universal gravitation.

The first to explicitly describe this model was a young Swiss mathematician named Nicolas Fatio de Duillier (1664-1753). Fatio had made a reputation for himself at an early age. When just seventeen he wrote an account of the rings of Saturn and sent it to the famous French astronomer Jean Dominique Cassini, who was favorably impressed and responded with encouragement. Fatio moved to Paris and worked closely with Cassini for a time. Cassini and others tried to get Fatio admitted to the French Academy in the early 1680s, but were unsuccessful because of Fatio’s Protestant religion. These were the years leading up to the revocation of the Edict of Nantes in 1685, at which time Fatio moved to Holland, and made the acquaintance of Christiaan Huygens and Jacques Bernoulli. In 1686 (two years after Leibniz published his first – admittedly cryptic – exposition of the calculus), Fatio wrote a paper on the “problem of inverse tangents” (which we would call the solution of first-order differential equations). This paper was sent by Huygens to Leibniz, who replied with some polite words, but who also rejected Fatio’s claim to have discovered his own version of calculus. This and other slights (such as Leibniz’s later omission of Fatio’s name from a list of mathematicians he considered capable of solving certain challenge problems) may have contributed to Fatio’s anti-Leibniz fervor in the calculus priority dispute. Indeed it was Fatio who, in 1699, first publicly charged Leibniz with having plagiarized the calculus from Newton.

In early 1687 Fatio somehow learned of a plot to assassinate the Prince of Orange, and passed along this information to Gilbert Burnet, who informed the authorities in time to foil the plot. Perhaps fearing that he had made dangerous enemies, Fatio then moved to England in May of that year, where he immediately began attending meetings of the Royal Society. At this time the secretary of the Society, Edmund Halley, was just completing the printing of Newton’s Principia (which was officially published in July of that year). In June, Fatio wrote to Huygens

I already was three times at the Society Royale, where I saw proposed rather good things sometimes, and sometimes rather poor.  Some of these gentlemen who make it up are extremely pronounced in favour of a book of Monsr. Newton, which is being printed at present and which will be out in three weeks time. They reproached me that I am too Cartesien, and made me hear that, since the meditations of their author, all will be changed for Physics. He treats in general the Mechanique of the Skies; the way in which circular movements which are done in a liquid medium are communicated in all the medium; gravity and of a force by which he supposes in all planets to attract one another... This treatise, that I have seen partly, assuredly is very beautiful, and is filled with a great number of beautiful propositions…”

Already he was falling under the Newtonian spell. He made a study of the Principia as soon as it was published, and immediately embraced its conclusions, declaring that the Cartesian system was finished. At the same time he began to conceive of a mechanism by which Newton’s universal gravity might operate. He took as his starting point the bombardment of “second nature” particles from all directions that Descartes had proposed, but applied it in the Lucretian universe of atoms in a void. In this context he pointed out that, not only is the resulting force between two bodies inversely proportional to the square of the distance between them, but it can also be made essentially proportional to the masses of ordinary macroscopic bodies by postulating that those bodies are almost entirely transparent to the shower of “second nature” particles. This was possible because Fatio, unlike Descartes, was not committed to the identity of space and substance, so he could imagine that material bodies consist mostly of empty space.

In an unpublished treatise called “On the Cause of Gravity”, which Fatio composed around 1690, he wrote that, despite the apparent heaviness of gold, it is entirely possible that a quantity of gold contains a trillion (10¹²) times more void than substance. In support of this, he notes that water and glass are dense materials, and yet they are almost totally transparent to the passage of light. By the same token, he argued, it is conceivable that all solid objects, even those that are opaque to light, could allow almost free passage to sufficiently small particles.

The most solid Bodies are only one extremely rare Fabric, which can exclude rays of Light, while it lets cross the ethereal matter with an extreme facility… If the Earth, instead of having a perfect Solidity, has many Pores, and gives through all our terrestrial Bodies, and even through the whole Earth and Planets, an extremely free Passage to the aforesaid ethereal matter moving in all directions, and which causes Gravity, the preceding Reasoning will take place for the ethereal Particles which are reflected on Parts external of the Earth…. but in addition to these Particles, there will be an Infinity of others…  some, which will make the greatest number incomparably, will have crossed it directly, without anything to meet.  Others will have run up, in their Way, against interior Parts…

Thus the total number of collisions on the body is essentially proportional to the quantity of matter, regardless of the shape or density of the body. This aspect of Fatio’s theory was not novel. Indeed it is an obvious necessity for any such theory. For example, Huygens’ wrote with regard to his own theory on the cause of gravity (published as an appendix to his famous treatise on light in 1691)

The extreme smallness of the parts of our fluid matter is again absolutely necessary to explain an observed property of weight, namely, that massive bodies, enclosed on all sides in a vessel of glass, metal, or whatever other material it may be, are found to always have the same weight. Thus the matter, which we have said to be the cause of weight, passes very freely through all the bodies deemed the most solid, and with the same facility as it goes through the air.

The difference between the theories of Huygens and Fatio is that Huygens was still strongly under the influence of Descartes, and persisted in thinking of vortices circling the earth at orbital speeds, tending to compell ordinary static bodies downward due to a gradient in their density, similar to a fluid pressure. In contrast, Fatio had seen the Newtonian light, and rejected Cartesian vortices as “an empty fiction”. His model assumed a purely isotropic omni-directional flux of particles. To account for the net force of attraction between two “coarse bodies” immersed in this bath of ethereal particles, Fatio assumed that the flux particles are entirely reflected, but with some diminished speed. In other words, the incident particles strike the body at a very high speed, but rebound with a slightly lower speed.

Gravity is produced, in my view, by Exceedence of the Speed of the Particles of this [ethereal] Matter which impinges on the Earth (for example, or some coarse Atom of which it is composed) over their Speed when they are reflected...

This is actually a more sophisticated model than simply assuming total absorption, because it recognizes that perfect reflection would result in no anisotropy at all in the surrounding flux, and therefore no net force of gravity, but it allows for a combination of reflection and absorption of momentum (which is the most efficient possible model), and it avoids mass accumulation. Fatio also stresses the fact that, to produce a given amount of gravity, we can suppose the bombarding particles are arbitrarily small by assuming the speeds of those particles is arbitrarily great, which automatically diminishes the drag induced by the movement of coarse bodies to a negligible amount. He also argued that by supposing the speed of the ethereal particles to be extremely great, the amount by which the reflected particles are slowed can be made as small as we wish, so there need be no appreciable dimunition of the agitation of those particles over time.

For the elementary constituents of coarse material bodies, Fatio imagined a fabric or lattice structure.

One reproached some modern Philosophers [Kepler?] for imagining the small Particles of Matter to be geometrical and extremely regular Figures, such as those of a Sphere, a Cube etc… Nevertheless if we reflect on how much Nature is an excellent Geometrician in his regular Productions, for example in the Spherical Figures of Water droplets, and Water Bubbles, and in the Figures so geometrical and so made up of Salts of several kinds, Crystals, Snow etc, it will appear extremely probable that they are geometrical Figures in the smallest Particles of the Bodies, and in the largest Particles that they compose… And this Reflexion, with the extreme Porosity of the terrestrial Bodies, and the Proportionality which is observed between their Mass and their Weight, can be used to gain insight into the structure of these Particles. 

In the margin of the sheet that contains these words, Fatio sketched an icosahedral frame, with an indication of how the triangular faces of this framework might be further triangularized (in the pattern of the so-called “geodesic dome” framework popularized by Buckminster Fuller in the 20^th century). A reproduction of his drawing is shown below.

Fatio valued very highly his theory of the true cause of gravity, and managed to get Halley, Huygens, and Newton to affix their signatures to a copy of his treatise in 1690 and 1691, attesting that they had examined it on those dates. He also corresponded with these and other prominent scientists about his theory, and carefully preserved their replies as proof that these great men took his idea seriously. He was especially proud of what he regarded as an endorsement from Newton himself:

Sir Isaac Newton's Testimony is of the greatest weight of any. It is contained in some Additions written by himself at the End of his own printed Copy of the first Edition of his Principles, while he was preparing it for a second Edition, And he gave me leave to transcribe that Testimony. There he did not scruple to say That there is but one possible Mechanical cause of Gravity, to wit that which I had found out: Tho he would often seem to incline to think that Gravity had its Foundation only in the arbitrary Will of God ...

Of course, it’s unclear how much “weight” should be given to an unpublished note written in the margin of some proof sheets. It may actually be that Newton and the others were just being kind to Fatio, or humoring him, especially judging from David Gregory’s statement that “Mr. Halley and Mr. Newton laugh at Mr. Fatio’s manner of explaining gravity”. (Interestingly, on another occasion Gregory remarked that “Mr. C. Wren smiles at Mr. Newton’s belief that gravity does not occur by mechanical means, but was introduced originally by the Creator”. Apparently Gregory was an acute judge of what amused people.)

During the years from 1689 to 1693 Fatio enjoyed an extremely close personal relationship with Isaac Newton, and for some time they planned to produce a second edition of the Principia together. Fatio evidently first met Newton on the occasion of Huygens’s visit to the Royal Society, when Huygens read his treatise on light along with an appendix on “the cause of gravity”. This was another mechanistic model for universal gravitation, based on fluidic action, quite distinct from Fatio’s model. In private correspondence Huygens critiqued Fatio’s model on the grounds that the rebounding flux particles, being slower, would necessarily be closer together, so (Huygens suggested) the density of the flux would increase in the vicinity of a massive body, and hence produce a repulsive rather than an attractive force. Fatio says he himself was “detained” by this objection for three years, but eventually convinced himself that the momentum flux of the rebounding particles would be lower than of the incident flux, because of the lower speed, despite the increased spatial density. Huygens conceded the point. (More than once in Fatio’s treatise he reports that “I had fully satisfied him of that objection”, and “I answered all objections that were made to me”, and so on.)

The relationships that Fatio had with both Newton and Huygens – more or less simultaneously – are fascinating. During the years 1691 and 1692 Fatio shuttled back and forth between lodgings in London and the Hague, dividing his time between Newton and Huygens. Upon his return to England in February of 1692 he wrote to Huygens in a state of alarm:

Since coming back to England I can not find the Theory of Gravity which You saw while I was in the Hague, and that I had already communicated to Messrs Newton and Halley.  If there is still some hope to find it, Sir, it is necessary that I left it on your premise or with the Academy; which I ask You very humbly to investigate.

Huygens replied a few days later, saying it would be a great misfortune if Fatio’s Theory of Gravity had been lost, and telling him that he well remembered returning it to Fatio, and that he had inquired of others (Monsr Dierquens and Monsr Fabre) but none could find it. Also, he had not kept a copy or extract. Fatio answered

I send you a thousand graces for the trouble you were given to find my Treatise on Gravity.  I hope any more to never re-examine it nor to even compose new because of a dislike and of an invincible loathing that I feel for seeking a second time the same things as I already have.

Oddly enough, the document turned out to be still in Fatio’s possession, and indeed the copy in question, bearing the signatures of Halley, Newton, and Huygens, was later sent to Jacques Bernoulli in 1701 and George Cheyne in 1735.  The document was found among Fatio’s possessions after his death, and still survives.

Having alarmed Huygens over the possible loss of his paper in February, Fatio sent an even more alarming letter to Newton in November of the same year. He wrote (from London, to Newton, who was in Cambridge)

I have Sir almost no hopes of ever seeing you again. With coming from Cambridge I got a grevious cold, which is fallen upon my lungs… I thank God my soul has been extremely quiet, in which you have had the chief hand… Were I in a lesser feaver I should tell you Sir many things. If I am to depart this life I could wish my eldest brother, a man of extraordinary integrity, could succeed me in your friendship…

Newton was understandably distraught when he received this letter, writing back

I last night received your letter, with which how much I was affected I cannot express. Pray procure ye advice and assistance of Physicians before it be too late, and if you want any money I will supply you. I rely upon the character ye give of your elder brother, and if I find that my acquaintance may be to his advantage I intend he shall have it… Sir, with my prayers for your recovery, I rest, Your most affectionate and faithful friend, to serve you, Is Newton

As it happens, Fatio recovered from the cold and lived for another 61 years, but not long after this incident the close relationship between Newton and Fatio came to an abrupt end. At the same time Newton evidently suffered a severe nervous breakdown.

The Edict of Nantes had been revoked in 1685, and the Protestants in France were again denied many rights they had previously held, and were subject to a greater degree of persecution. In response to this, and prompted by a wave of prophetic visions, a group of radical Protestants known as the Camisards began a violent insurrection in the French countryside. During the first phase of the revolt, many of the visionaries were children, and at one time over 300 children were imprisoned for inciting sedition. After the movement was put down in France, some of the leaders, including Elie (Elias) Marion, immigrated to England in 1706, and tried to arouse support and win converts to their apocalyptic visions. These men, who became known as the French Prophets, went into animated visionary trances during their public sermons, claimed to perform miracles (including raising the dead), and made extravagant prophesies of the imminent end of the world. Fatio had been an ardent supporter of the Camisards, and became a disciple of Elie Marion when he arrived in England. (At this time Fatio was 42 and Marion was 28.)

Late in 1707 Marion, Fatio, and another of Marion’s followers were convicted of blasphemy and sedition, and in December the three of them were sentenced to be pilloried for two days. A sign was placed over Fatio’s head, reading

Nicolas Fatio convicted for abbeting and favouring Elias Marion, in the Wicked and counterfeit prophecies, and causing them to Be printed and published, to terrify the Queen’s people.

In 1710 the French Prophets (along with Fatio) left England for Holland, where Fatio was twice more sentenced to the pillory for publishing Marion’s blasphemous prophesies. Subsequently in the Hague Fatio was imprisoned for 6 weeks, reportedly at the request of some of his old friends, who wished to separate him from the influence of Marion and the other “Brothers of Christ”. However, these efforts failed, and Fatio then accompanied Marion on travels through Germany and other Eastern European countries, attempting to make converts. In Turkey Marion fell ill, and died in 1712 at the age of 35.

After this, Fatio returned to England, settling in Worcester, where he remained for the rest of his life, dividing his time between meditations on the prophesies and pursuing various scientific ideas. Interestingly, one of his projects was to cast his theory on the cause of gravity in the form of a long poem, apparently modeled after De Rerum Natura of Lucretius. In 1729 he entered this poem in a contest held by the Paris Academy of Science, but did not win a prize. He continued to elaborate on the theory over the years, and even seems to have entertained doubts, perhaps influenced by the views of Newton. In a late revision of his paper on the cause of gravitation, Fatio wrote

I am persuaded that what I have descrbed is the only possible Mechanical cause of universal gravity… one can find nothing simpler nor easier than my assumptions, as to matter and movement, that are necessary besides to return reason to the phenomena of nature… But I acknowledge that I am not held too assured that gravity is not an immediate effect of the will of God, and one of the first rules by which he controls the universe…it is not impossible nor even out of probability, that God, by a law, established that matter attracts itself mutually, with a force proportional to its mass and reciprocal with the square of the distance.

It’s interesting to compare these sentiments with those expressed by Albert Einstein regarding the “unified field theory”, which he felt was “necessary to return reason to the phenomena of nature”, and on which he had meditated in isolation for the last half of his life:

In my opinion the theory presented here is the logically simplest relativistic field theory which is at all possible. But this does not mean that nature might not obey a more complex field theory… [furthermore] one can give good reasons why reality cannot be represented by a continuous field theory at all…

To the end of his life, Fatio remained proud of his membership in the Royal Society, and often submitted his thoughts on various subjects to that body. For example, in 1736 he wrote

Sir, I think I ought to inform the Royal Society that it has pleased God Almighty to permit that I should find the true and accurate Method of determining a priori in Feet, the distance of the Sun from the Earth…

He died on April 24, 1753, and was buried near the Church of St. Nicolas in Worcester.

About ten years after Fatio’s death, another young scientist from Geneva, named Georges Louis Lesage, was preparing to write a history of theories of gravity, and began trying to acquire Fatio’s papers. He contacted the landlord of Fatio’s last residence, and through him was able to track down and acquire some boxes containing Fatio’s papers. He was surprised to find that the great majority of the writings were on prophetic and religious issues (just as Lord Keynes found when he examined Newton’s papers), but among these papers he also found writings on Fatio’s gravitational theory. Oddly enough, Lesage never did write a history of gravitational theories, but in 1758 he published his “own” theory of the cause of gravity (along with a peculiar theory attempting to account for the cohesion of bodies)… which was nothing but a slightly less sophisticated version of Fatio’s theory. (See the note on Lesage’s Shadows.) Ironically, the most complete exposition of this theory that Lesage ever wrote was entitled “Newtonian Lucretius” (1782), in which Lesage presented the theory as a natural extension of the ideas of Lucretius, supposing the latter had had the benefit of knowing Newton’s laws. Lesage also mentions that he conceived the idea for his theory of gravity when he was just a boy, conceeding that the idea is fairly obvious.

Indeed, the extremely simple idea of trying to explain the principal natural phenomena by the aid of a subtle fluid vigorously agitated in every direction has come to many writers who have before presented it in a vague and ill-assured fashion, not to mention that there has been without doubt a still greater number who have not even deigned to communicate at all. I am well convinced that since the law governing the intensity of universal gravitation is similar to that for light, the thought will have occurred to many physicists that an ethereal substance moving in rectilinear paths may be the cause of gravitation, and that they may have applied to it whatever of skill in the mathematics they have possessed.

It’s odd that Lesage should write in this manner, as if he can only presume that this model of gravitation has been thought of previously by others, considering that he had been in possession of Fatio’s papers for almost twenty years. (See also the discussion in Fatio, Lesage, and the Camisards.) It’s possible that Lesage did not have access to all the material that has since been uncovered regarding Fatio’s work, but he surely had enough to understand Fatio’s theory. At yet Lesage does not once mention Fatio’s name in this paper (just as he had not mentioned Fatio in 1758), a fact which is especially surprising because – considering the poem submitted to the Paris Academy, and Fatio’s close association with Newton – one would have to say that Nicolas Fatio was literally the Newtonian Lucretius incarnate.

Today the model of gravity proposed by Fatio is known almost exclusively as “Lesage’s theory”, with Fatio relegated to a footnote, so Fatio was ultimately denied even his rightful recognition as the originator of this idea, which in any case has long since been discredited. (Already in the early 1800s Laplace had realized that the speed of the gravific corpuscles would need to be at least a million times greater than the speed of light in order to account for the absence of appreciable aberration and drag in the force of gravity.) He never gained the status of an equal among the men whose approval he most coveted. In retrospect, his life seems almost like a series of love affairs, as he was inexorably drawn to a sequence of famous individuals - and they to him – beginning with Cassini, then Huygens, then Newton, and finally the messianic prophet Marion. Considering how different were the personalities of these men, it’s not easy to account for the mutual attractions that drew each of them together with Fatio.

By proposing my Thoughts, I do not fear the objections that will be raised by little Persons. I address only the Savants, in time, those who are both excellent Mathematicians and good Philosophers, such as, for example, Monsr. Hugens, Monsr. Newton, and a small number of others.  Those who are only Mathematicians, but have never applied their reason to natural Philosophy, and especially those Philosophers who have no understanding of Mathematics, I do not regard them as my Judges.

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