Fatio, Lesage, and the Camisards

Soon after the appearance of Isaac Newton’s Principia, describing the law of universal gravitation, Newton’s young friend Nicolas Fatio (1664-1753) conceived the idea that the apparent force of gravitational attraction between material objects might be due to an imbalance of repulsive forces arising from the impacts of tiny rapidly moving corpuscles from the nether regions of space. Objects would tend to shield each other from this shower of gravific corpuscles, so they would be driven together, and it’s easy to see that the strength of this effect would be inversely proportional (at least approximately) to the square of the distance between the objects, in accord with Newton’s law.

Since the force of gravity depends strictly on the mass of an object (not on its apparent size), Fatio postulated that material objects are almost entirely transparent to the gravific corpuscles. At the time, this was a radical suggestion, but Fatio argued for its plausibility by noting that corpuscles of light can pass through solid glass, even though glass is as seemingly dense and impermeable as other solids. Fatio also noted that the lack of appreciable drag on moving objects could be explained by postulating a sufficiently high speed for the corpuscles. He also explained that the gravific corpuscles must be slowed by their interactions with ordinary matter in order to transfer the necessary momentum. Fatio continued to refine and promote his theory throughout the rest of his life, even after enlisting with the exiled Camisards, a insurrectionist sect of Huguenots from the south of France.

After the revocation of the edict of Nantes, the Camisards started an armed revolt, incited largely by the prophetic visions of young children. At one time, over 300 children were imprisoned for blasphemy and inciting revolt. In the early 1700’s the leaders of the movement, notably Durand Fage, Jean Cavailier, and Elie Marion, fled to England and formed a prophetic sect, speaking in tongues, preaching the immanent end of the world, and claiming the ability to raise the dead. Fatio, who was himself a Protestant exile of sorts, had always been sympathetic to the Camisards, and joined with the exiled prophets when they arrived in London in 1706. By 1707 Fatio had become the secretary of these prophets, recording and interpreting their inspired utterances. In November of that year, Fatio and Marion were arrested and convicted of blasphemy and “spreading terror among the Queen’s people”, and sentenced to the pillory.

Another of the Huguenot’s who fled southern France for England to escape persecution was an eight year old boy named Georges-Louis Le Sage (1676-1759). The Le Sages were said to have been a prominent Huguenot family, and in 1684 they emigrated to England, spurred like so many other Huguenots by the impending revocation of the Edict of Nantes. Did the young Le Sage know of Nicolas Fatio? It is not unlikely that the exiled boy and his family would have been aware of Fatio, if only because of the highly publicized trial of the Camisard leader Elie Marion and his associates, which would have been a focus of interest for fellow Protestant exiles. To Le Sage, Nicolas Fatio would have been a celebrity and prominent sympathizer with his family’s persecuted cause. In addition, it was well-known that Fatio was a mathematician and physicist, and a close friend of the world-famous Isaac Newton, so it’s easy to imagine that Le Sage would have heard of Fatio’s theory of gravity. He (Le Sage) certainly had an interest in such things, since he eventually became a teacher of mathematics and physics, which were Fatio’s avocation. As one last tantalizing fact, when Le Sage eventually left England in 1711, he emigrated to Geneva, which was Fatio’s original home.

In Geneva, Le Sage had a son, also named Georges Louis-Lesage (1724-1803). We are told that the elder Le Sage instructed his young son in the classics (certainly including Lucretius’ De Rerum Natura) as well as in mathematics and physics, before sending him off to the college in Geneva to study under the physicist Calandrani and mathematician Cramer.

Lesage later recalled that by the age of 13 he had conceived of a theory of gravity, based on and “correcting” (he said) the system of Lucretius. According to this theory, gravity was the result of the impacts of tiny rapidly moving particles, which Lesage later termed “ultra-mundane” (other-worldly or super-natural) corpuscles. By shadowing each other from the barrage of particles, objects of ordinary matter were pushed together. However, according to a letter he wrote to his father at the age of 23, it wasn’t until he was 19 that Lesage understood that the force of gravity could be made proportional to mass by positing that ordinary matter is virtually transparent to the ultra-mundane corpuscles, and it wasn’t until he was 23 that he understood the force in such a theory would vary as the inverse-square of the distance. The latter discovery is what prompted him to write to his father, beginning exuberantly with Archimedes’ exclamation, “EUREKA!”  From this letter we can infer that father and son shared an interest in the theory of gravity, although it’s not clear why it took them so many years to understand the most basic features of the theory (which Fatio had described long before).

Interestingly, Nicolas Fatio died when Lesage was 19, and we are told by Bernard Gagnebin (who wrote a historical introduction to Fatio’s paper on gravity when it was finally published in the Notes of the Royal Society in 1948) that “a few years after Fatio’s death” Lesage set about to acquire Fatio’s papers. Taken literally, this implies that Lesage came into possession of Fatio’s papers when he was 22 or 23 years old, the same age as when he wrote to his father about finally understanding the inverse-square relation. However, other evidence suggests that Lesage acquired Fatio’s papers somewhat later.

According to Gagnebin, Lesage  had undertaken to write “A History of the Theories of Universal Gravitation”, the implication being that this is what led to his interest in Fatio’s work – but no indication is given of how Lesage became aware of Fatio and his theory of gravity. I think the circumstances involving the family history outlined above make it at least plausible that Lesage first learned about Fatio from his father. In fact, it would be rather surprising if he didn’t. We know the elder Le Sage was aware of the Cartesian preference for impulse (contact forces) as the means of conveying every causal effect, and the apparent difficulty of accounting for attraction in these terms. In a pamphlet comparing scientific and religious thinking, written by the elder Le Sage in 1728 (when the younger Lesage was just four years old), and subsequently published as Essay’s on Various Subjects in 1743, he wrote

Truth is not always probable.  In physics, the principle of impulse is most probable; but that of attraction is established fact… [One is mistaken if] one believes Nature capable only of phenomena which can be explained by the assumptions that one has formed. 

In geometry, all that is possible is true. A geometrician admits indifferently several possible systems of astronomy. But in any other context, if a thing is possible, it by no means follows that it is fact. The majority of physicists act against this rule when they convince themselves that things are done in the way in which it seems to them they could be done.

Sometimes people base their reasoning on an imperfect enumeration [of the possibilities]…  There are physicists who claim to show the impossibility of Void philosophically, by saying that this Void is neither a substance nor an accident, without thinking that there can be a third category, to know the places of bodies.

What is true in some connection is not always true… Some physicists, having seen that one can explain well enough why certain bodies remain attached together due to pressure of the matter which surrounds them, believed themselves able by the same principle to return reason to the hardness of bodies.

Le Sage’s use of the phrase “return reason” is intriguing, because Fatio often referred to “returning reason” to the phenomena of gravity. It’s also interesting that Le Sage mentioned this immediately after remarking on a discredited miracle worker, considering that Fatio was a proponent of the miracle-working Cevenol Prophets (who claimed they could raise the dead, etc). Le Sage’s essays were primarily about spiritual and religious issues, but the above quotes show that he was familiar with, and interested in, the efforts of physicists to explain natural phenomena in general, and in particular the phenomena of attraction resulting from the pressure exerted by outside matter. His writing also shows that he was well-read, referring (for example) to the ideas of Gassendi (one of the first modern atomists). Given the parallel paths followed by Fatio and the elder Le Sage, both Protestant exiles in England, both residing in Geneva, and their common interests in mathematics, physics, and Protestant theology, it is at least plausible (if not highly probable) that the elder Le Sage was acquainted with Fatio’s model of gravitation. In addition, Cramer (the younger Lesage’s first outside teacher after being tutored by his father) is known to also have had a theory very much like Fatio’s, and in fact the younger Lesage later accused his teacher Cramer of having copied the idea from Fatio.

In 1761 the younger Lesage (at the age of 27) learned that a large box containing many of Fatio’s papers was in possession of Fatio’s last landlord (in England), a Mr. John Ingram. The listed contents included three copies of Fatio’s famous paper in which he gives a full account of the theory, and which was signed by Newton, Halley, and Huygens, attesting that they had seen it. After negotiating with Ingram, Lesage was able to purchase the box for 8 pounds sterling, but, alas, when he examined the contents, the three copies of the crucial paper were missing. Only the cover sheets were present. What became of these crucial papers is a mystery, even to the point of encouraging conspiracy theories. For example, it’s been suggested that individuals wishing to protect the reputation of Isaac Newton wanted to expunge all potentially embarrassing correspondences and connections between the disgraced Fatio and the national hero Newton. Since Newton had signed the crucial papers, they would have been candidates for redaction. Perhaps a more likely explanation is that anything with Newton’s and/or Huygens’s writing on it was considered valuable, so someone simply appropriated those papers.

Whatever the reason for their disappearance, the absence of Fatio’s main papers had significant consequences for Lesage. Had those papers been contained in the collection (as the inventory had stated), Lesage would have been confronted with the fact that what he regarded as his great achievement (his Eureka!) and claim to immortality had actually been fully described in detail by Fatio half a century earlier. Never having seen Fatio’s main paper on the theory, but only fragmentary comments in various letters, Lesage was able to conclude that Fatio had put forward the idea only in a “vague and ill-assured fashion”. Thereafter, Lesage often referred to his predecessors (sometimes without naming them) in similar terms, disparaging their anticipations of what he clearly regarded as his theory, which he spent over sixty years promoting and defending. Had he ever laid eyes on Fatio’s paper, attested by Halley, Newton, and Huygens, it seems hard to imagine Lesage devoting his life to this activity, and claiming the theory as his own.

Ironically, when William Thomson (later Lord Kelvin) wrote about this theory in the 1870’s, his only knowledge of Fatio (and Lesage’s other predecessors) came from the writings of either Lesage himself or Lesage’s friend Pierre Prevost, so Thomson repeated Prevost’s praise of Lesage for being scrupulous about crediting his predecessors.

Nicolas Fatio is quoted by Le Sage and Prevost as a friend of Newton, who in 1689 or 1690 had invented a theory of gravity perfectly similar to that of Le Sage, except certain essential points; had described it in a Latin poem not yet printed; and had written, on the 30th March 1694, a letter regarding it, which is to be found in the third volume of the works of Leibniz, having been communicated for publication to the editor of those works by Le Sage… Fatio supposed the corpuscles to be elastic, and seems to have shown no reason why their return velocities after collision with mundane matter should be less than their previous velocities, and therefore not to have explained gravity at all… Redeker, we are told by Prevost, had very limited ideas of the permeabilities of great bodies, and therefore failed to explain the law of the proportionality of gravity to mass: "He enunciated this law very correctly… but the manner in which he explains it shows that he had but little reflected upon it. Notwithstanding these imperfections… Le Sage has never failed on any occasion to call attention to the system of Redeker, as also to that of Fatio."

The last sentences are Kelvin quoting Prevost praising his friend Lesage for acknowledging his predecessors, but of course in the preceding sentences Lesage and Prevost inform us that “Fatio supposed the corpuscles to be elastic” [which Fatio explicitly did not] and therefore did not explain gravity at all, and Redeker “failed to explain the law of proportionality to mass”, although he “enunciated this law very correctly… but “shows that he had but little reflected upon it”. Far from crediting his predecessors, these remarks are actually disparaging, evidently intended to explain why Lesage rather than any of his predecessors deserves to be called the originator of the theory. Compare this with the comments about his predecessors contained in the most famous and polished of Lesage’s expositions of the theory, and one of only two that were actually published, written in 1782 (when he was 58), and consider whether Prevost was accurate in claiming that Lesage “never failed on any occasion to call attention to the system of Redeker, as also to that of Fatio”:

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…

In this paper he mentions neither Redeker nor Fatio by name, and, although he does acknowledge that the idea “has come to many writers” before, he immediately goes on to say they all “presented it in a vague and ill-assured fashion…”. In view of this and other examples of Lesage’s “acknowledgements”, what Prevost ought to have said is that Lesage never failed on any occasion to assert his own priority of discovery by denigrating the accomplishments of his (in this case un-named) predecessors. As Kelvin’s review shows, it’s clear that Lesage was largely successful, and of course the very fact that Fatio’s theory is now always referred to as Lesage’s theory is evidence of how successful Lesage was (with the help of his friend Prevost) in establishing himself as the prime originator of the theory.

One possible explanation for why Lesage spoke so disparagingly about Fatio is that he (Lesage) never actually saw Fatio’s main paper on his theory. If so, his erroneous appraisals of what Fatio had actually accomplished would be somewhat understandable. Indeed, as mentioned above, Fatio’s most important paper, “Of the Cause of Gravity”, was apparently not contained in the collection of papers which Lesage acquired in 1761. The only known copy of the paper was discovered among the papers of Jacob Bernoulli, and published in 1929 by Carl Bopp. However, this explanation began to unravel in 1943 when the contents of the 55 boxes of Lesage’s papers residing in the library in Geneva were finally catalogued, and among them were discovered scattered sheets of Fatio’s writings thought to have been absent from the collection of Fatio’s work acquired by Lesage. First to be uncovered was a copy of the first 22 sections of Fatio’s paper. The cover sheet bears the hand-written words

Mr. Jallabert communicated to me this Book, this 17th Oct 1770. Lesage.

Soon thereafter another set of Fatio’s papers were discovered in the Geneva collection, extending from the middle of section 16 to the middle of section 35. To these sections were added the sections 36 to 41, at the end of which appear the signatures of Halley, Newton, and Huygens. Following this, sections 42 to 52 were recovered from an archive in Cambridge, allowing for the complete reconstruction of Fatio’s paper. It was published for the first time in the Transactions of the Royal Society in 1948. (Fatio’s papers had been read at meetings of the Royal Society in the early 1690’s but not formally published.)  Gagnebin concludes his account with

The most famous text of Fatio de Duillier, already lost during the life of its author, fortunately found by him, missing since his death, and sought by Lesage, is thus reconstituted thanks to the three fragments preserved in Geneva and which were joined together for the first time in 1948. 

(Evidently Gagnebin was unaware of the Bopp edition.) Since key portions of the paper were found among Lesage’s papers, one wonders whether Lesage really was totally ignorant of Fatio’s complete theory, especially after 1770. We know he continued to belittle Fatio’s accomplishment, even as late as 1782 with the above-quoted appraisal in Newtonian Lucretius. After describing how he (Lesage) first conceived of the theory in his childhood, he writes

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. But we may say, how is it that none of these physicists have pushed these consequences to their conclusions and communicated the research?

This is quite strange, first because he seems to be speaking conjecturally about being “well convinced” that “the thought will have occurred to many [unnamed] physicists”, contradicting Prevost’s claim that Lesage “never failed on any occasion” to call attention to Fatio’s work. Second, Lesage implies that “none of these physicists have pushed these consequences to their conclusions”, whereas by 1782 he had long been in possession of the knowledge that Fatio had fully developed the theory, in some ways surpassing Lesage’s own considerations. Third, Lesage says none of these physicists “communicated the research”, whereas he surely knew that Fatio’s works had been presented to the Royal Society, and that Fatio had gone to the trouble of having his paper signed by Halley, Newton, and Huygens, attesting that they had seen it, and he also corresponded with others (including Leibniz), attempting to promote his theory. Lesage also knew that Fatio had composed a long poem, in the fashion of Lucretius, describing the theory, and submitted it as an entry in a prize paper competition (just as Lesage’s first account of the theory, Essai de Chymie Mechanique, was written as a contest entry). It hardly seems justified to accuse Fatio of never communicating his research. What could Lesage have been thinking when he wrote those words? But this is not all… he goes on to write regarding his predecessors

…the most of them having no clear view of this chaos (of which the first glance is, I admit, frightful) … have not known how to disentangle it and subject it to their calculations. Or not having firmly grasped the principles of the theory, they have allowed themselves to be seduced by specious sophisms, by which men have pretended to refute in advance all imaginable explanations of gravitation. Or they will have had the foible of bowing to the authority of great names, when it is alleged (whether justly or falsely) that they have pronounced upon the impossibility of this or upon the uselessness of that branch of knowledge. Or they have lacked sufficient love of truth or courage of their convictions to abandon easy pleasures and exterior advantages in order to devote themselves simply to researches at the time difficult and little welcome. Or, finally, they have failed to become impressed with the strength and fecundity of this beautiful system so distinctly as to lead them, in their enthusiasm, to sacrifice to it their other views and projects.

What could Prevost have been thinking when he commended his friend and colleague Lesage for scrupulously “calling attention to” his predecessors contributions on every occasion? Is the above text an example of what Prevost regarded as a scrupulous acknowledgement? Surely if Kelvin had actually been acquainted with Lesage’s writings, instead of basing his opinions entirely on the word of Prevost, he would have thought better of simply repeating Prevost’s assessment of Lesage’s generosity. Nothing could be more clear than the fact that Lesage represented himself as the sole true originator of this theory, and that he went out of his way to denigrate all those who had preceded him… and this was written many years after he had acquired Fatio’s papers, by which time he knew full well the extent to which Fatio had anticipated and described every significant feature of the theory.

Interestingly, Lesage’s unpublished papers include the beginnings of a draft “Note on the Life and the Writings of Nicolas Fatio”, but didn’t complete it. Such a note would have been of questionable fullness if it were written in ignorance of Fatio’s main scientific work, whereas if it had included an acknowledgement of that work it would have utterly undermined Lesage’s claim to priority. Perhaps it is not surprising that Lesage never finished this “note”. In any case, it would have been only a small part of the large “History of Theories of Gravity” on which he worked for many years, but which he also never completed.

One concept to which Lesage actually has a legitimate claim is the idea of a fractal structure. In a posthumously published work he gives a description of how ordinary matter could have arbitrarily low “measure” by having a hierarchy of structural levels. The construction is identical to what is now called Menger’s sponge (a three-dimensional analog of Sierpinski’s gasket), named after the Austrian mathematician Karl Menger, who is credited with having invented it in 1926. Of course, Lesage didn’t explicitly discuss the implications of having infinitely many levels, leading to a solid with precisely zero volume, but it is obvious from his description that the levels can be continued indefinitely.

Another concept sometimes credited to Lesage (or as a prediction of “push theories” of gravity) is the notion that ordinary solid matter is actually mostly empty space, as required for gravity to be proportional to mass in a Lesagean theory. Of course, this was already pointed out quite clearly by Fatio in relation to a theory of gravitation, so it surely cannot be credited to Lesage. We may also mention that in 1758 Roger Boscovich proposed a theory in which matter consists entirely of point-like particles surrounded by force fields (attractive at some distances, repulsive at others). This conception was highly influential, and entails the sparseness of material substances in a way that is even closer to the modern conception of matter than is the Fatio/Lesage theory. Furthermore, the atomistic concept of matter, according to which solid matter is mostly empty space, was not unique to Fatio/Lesage theories of gravity. It was always an explicit part of the atomistic doctrine of Democritus, explaining why it was possible to compress solid substances, even though the atoms themselves were incompressible.

Return to MathPages Main Menu