Nicolas Fatio presented the first formulation of his thoughts on gravitation in a letter to Christiaan Huygens in the spring of 1690. Two days later Fatio read the content of the letter before the Royal Society in London. In the following years Fatio composed several draft manuscripts of his major work De la Cause de la Pesanteur, but none of this material was published in his lifetime. In 1731 Fatio also sent his theory as a Latin poem, in the style of Lucretius, to the Paris Academy of Science, but it was dismissed. Some fragments of these manuscripts and copies of the poem were later acquired by Le Sage who failed to find a publisher for Fatio's papers. So it lasted until 1929, when the only complete copy of Fatio's manuscript was published by Bopp, and in 1949 Gagnebin used the collected fragments in possession of Le Sage to reconstruct the paper. The Gagnebin edition includes revisions made by Fatio as late as 1743, forty years after he composed the draft on which the Bopp edition was based. However, the second half of the Bopp edition contains the mathematically most advanced parts of Fatio's theory, and were not included by Gagnebin in his edition. For a detailed analysis of Fatio's work, and a comparison between the Bopp and the Gagnebin editions, see Zehe The following description is mainly based on the Bopp edition.
These passages are the most incomprehensible parts of Fatio's theory, because he never clearly decided, which sort of collision he actually preferred. However, in the last version of his theory in 1742 he shortened the related passages and ascribed "perfect elasticity or spring force" to the particles and on the other hand "imperfect elasticity" to gross matter, therefore the particles would be reflected with diminished velocities. Additionally, Fatio faced another problem: What is happening if the particles collide with each other? Inelastic collisions would lead to a steady decrease of the particle speed and therefore a decrease of the gravitational force. To avoid this problem, Fatio supposed that the diameter of the particles is very small compared to their mutual distance, so their interactions are very rare.Condensation
Fatio thought for a long time that, since corpuscles approach material bodies at a higher speed than they recede from them (after reflection), there would be a progressive accumulation of corpuscles near material bodies (an effect which he called "condensation). However, he later realized that although the incoming corpuscles are quicker, they are spaced fruther apart than are the reflected corpuscles, so the inward and outward flow rates are the same. Hence there is no secular accumulation of corpuscles, i.e., the density of the reflected corpuscles remains constant. Fatio also noted that, by increasing both the velocity and the elasticity of the corpuscles, the difference between the speeds of the incoming and reflected corpuscles (and hence the difference in densities) can be made arbitrarily small while still maintaining the same effective gravitational force.
Porosity of gross matter
In order to ensure mass proportionality, Fatio assumed that gross matter is extremely permeable to the flux of corpuscles. He sketched 3 models to justify this assumption:
Already in 1690 Fatio assumed, that the "push force" exerted by the particles on a plain surface is the sixth part of the force, which would be produced if all particles are lined up normal to the surface. Fatio now gave a proof of this proposal by determination of the force, which is exerted by the particles on a certain point zz. He derived the formula p=ρv²zz/6. This solution is very similar to the formula known in the kinetic theory of gases p=ρv²/3, which was found by Daniel Bernoulli in 1738. This was the first time that a solution analogous to the similar result in kinetic theory was pointed out - long before the basic concept of the latter theory was developed. However, Bernoulli's value is twice as large as Fatio's one, because according to Zehe, Fatio only calculated the value mv for the change of impulse after the collision, but not 2mv and therefore got the wrong result. (His result is only correct in the case of totally inelastic collisions.) Fatio tried to use his solution not only for explaining gravitation, but for explaining the behaviour of gases as well. He tried to construct a thermometer, which should indicate the "state of motion" of the air molecules and therefore estimate the temperature. But Fatio (unlike Bernoulli) didn't identify heat and the movements of the air particles - he used another fluid, which should be responsible for this effect. It is also unknown, whether Bernoulli was influenced by Fatio or not.Infinity (Problem III) In this chapter Fatio examines the connections between the term infinity and its relations to his theory. Fatio often justified his considerations with the fact that different phenomena are "infinitely smaller or larger" than others and so many problems can be reduced to an undetectable value. For example the diameter of the bars is infinitely smaller than their distance to each other; or the speed of the particles is infinitely larger than those of gross matter; or the speed difference between reflected and non-reflected particles is infinitely small.Resistance of the medium (Problem IV) This is the mathematically most complex part of Fatio's theory. There he tried to estimate the resistance of the particle streams for moving bodies. Supposing u is the velocity of gross matter, v is the velocity of the gravific particles and ρ the density of the medium. In the case v << u and ρ = const. Fatio stated that the resistance is ρu². In the case v >> u and ρ = const. the resistance is 4/3ρuv. Now, Newton stated that the lack of resistance to the orbital motion requires an extreme sparseness of any medium in space. So Fatio decreased the density of the medium and stated, that to maintain sufficient gravitational force this reduction must be compensated by changing v "inverse proportional to the square root of the density". This follows from Fatio's particle pressure, which is proportional to ρv². According to Zehe, Fatio's attempt to increase v to a very high value would actually leave the resistance very small compared with gravity, because the resistance in Fatio's model is proportional to ρuv but gravity (i.e. the particle pressure) is proportional to ρv².
Fatio was in communication with some of the most famous scientists of his time.
There was a strong personal relationship between Isaac Newton and Fatio in the years 1690 to 1693. Newton's statements on Fatio's theory differed widely. For example, after describing the necessary conditions for a mechanical explanation of gravity, he wrote in an (unpublished) note in his own printed copy of the Principia in 1692:The unique hypothesis by which gravity can be explained is however of this kind, and was first devised by the most ingenious geometer Mr. N. Fatio. On the other hand, Fatio himself stated that although Newton had commented privately that Fatio's theory was the best possible mechanical explanation of gravity, he also acknowledged that Newton tended to believe that the true explanation of gravitation was not mechanical. Also, Gregory noted in his "Memoranda": "Mr. Newton and Mr. Halley laugh at Mr. Fatio’s manner of explaining gravity." This was allegedly noted by him in December 28, 1691. However, the real date is unknown, because both ink and feather which were used, differ from the rest of the page. After 1694, the relationship between the two men cooled down.
Christiaan Huygens was the first person informed by Fatio of his theory, but never accepted it. Fatio believed he had convinced Huygens of the consistency of his theory, but Huygens denied this in a letter to Gottfried Leibniz. There was also a short correspondence between Fatio and Leibniz on the theory. Leibniz criticized Fatio's theory for demanding empty space between the particles, which was rejected by him (Leibniz) on philosophical grounds. Jakob Bernoulli expressed an interest in Fatio's Theory, and urged Fatio to write his thoughts on gravitation in a complete manuscript, which was actually done by Fatio. Bernoulli then copied the manuscript, which now resides in the university library of Basel, and was the base of the Bopp edition.
Nevertheless, Fatio's theory remained largely unknown with a few exceptions like Cramer and Le Sage, because he never was able to formally publish his works and he fell under the influence of a group of religious fanatics called the "French prophets" (which belonged to the camisards) and therefore his public reputation was ruined.
In 1731 the Swiss mathematician Gabriel Cramer published a dissertation, at the end of which appeared a sketch of a theory very similar to Fatio's - including net structure of matter, analogy to light, shading - but without mentioning Fatio's name. It was known to Fatio that Cramer had access to a copy of his main paper, so he accused Cramer of only repeating his theory without understanding it. It was also Cramer who informed Le Sage about Fatio's theory in 1749. In 1736 the German physician Franz Albert Redeker also published a similar theory. Any connection between Redeker and Fatio is unknown.
The first exposition of his theory, Essai sur l'origine des forces mortes, was sent by Le Sage to the Academy of Sciences at Paris in 1748, but it was never published. According to Le Sage, after creating and sending his essay he was informed on the theories of Fatio, Cramer and Redeker. In 1756 for the first time one of his expositions of the theory was published, and in 1758 he sent a more detailed exposition, Essai de Chymie Méchanique, to a competition to the Academy of Sciences in Rouen. In this paper he tried to explain both the nature of gravitation and chemical affinities. The exposition of the theory which became accessible to a broader public, Lucrèce Newtonien (1784), in which the correspondence with Lucretius’ concepts was fully developed. Another exposition of the theory was published from Le Sage's notes posthumously by Pierre Prévost in 1818.
Le Sage discussed the theory in great detail and he proposed quantitative estimates for some of the theory's parameters.
Le Sage said that he was the first one, who drew all consequences from the theory and also Prévost said that Le Sage's theory was more developed than Fatio's theory. However, by comparing the two theories and after a detailed analysis of Fatio's papers (which also were in possession of Le Sage) Zehe judged that Le Sage contributed nothing essentially new and he often didn't reach Fatio's level.
Le Sage’s ideas were not well-received during his day, except for some of his friends and associates like Pierre Prévost, Charles Bonnet, Jean-André Deluc and Simon Lhuilier. They mentioned and described Le Sage's theory in their books and papers, which were used by their contemporaries as a secondary source for Le Sage's theory (because of the lack of published papers by Le Sage himself) .Euler, Bernoulli, and Boscovich Leonhard Euler once remarked that Le Sage's model was "infinitely better" than that of all other authors, and that all objections are balanced out in this model, but later he said the analogy to light had no weight for him, because he believed in the wave nature of light. After further consideration, Euler came to disapprove of the model, and he wrote to Le Sage:
You must excuse me Sir, if I have a great repugnance for your ultramundane corpuscles, and I shall always prefer to confess my ignorance of the cause of gravity than to have recourse to such strange hypotheses.
Daniel Bernoulli was pleased by the similarity of Le Sage's model and his own thoughts on the nature of gases. However, Bernoulli himself was the opinion that his own kinetic theory of gases was only a speculation, and likewise he regarded Le Sage's theory as highly speculative.
Roger Joseph Boscovich pointed out, that Le Sage's theory is the first one, which actually can explain gravity by mechanical means. However, he rejected the model because of the enormous and unused quantity of ultramundane matter. John Playfair described Boscovich's arguments by saying:
An immense multitude of atoms, thus destined to pursue their never ending journey through the infinity of space, without changing their direction, or returning to the place from which they came, is a supposition very little countenanced by the usual economy of nature. Whence is the supply of these innumerable torrents; must it not involve a perpetual exertion of creative power, infinite both in extent and in duration?
A very similar argument was later given by Maxwell (see the sections below). Additionally, Boscovich denied the existence of all contact and immediate impulse at all, but proposed repulsive and attractive actions at a distance. Lichtenberg, Kant, and Schelling Georg Christoph Lichtenberg's knowledge of Le Sage's theory was based on "Lucrece Newtonien" and a summary by Prévost. Lichtenberg originally believed (like Descartes) that every explanation of natural phenomena must be based on rectilinear motion and impulsion, and Le Sage's theory fulfilled these conditions. In 1790 he expressed in one of his papers his enthusiasm for the theory, believing that Le Sage's theory embraces all of our knowledge and makes any further dreaming on that topic useless. He went on by saying: "If it is a dream, it is the greatest and the most magnificent which was ever dreamed..." and that we can fill with it a gap in our books, which can only be filled by a dream.
He often referred to Le Sage's theory in his lectures on physics at the University of Göttingen. However, around 1796 Lichtenberg changed his views after being persuaded by the arguments of Immanuel Kant, who criticized any kind of theory that attempted to replace attraction with impulsion. Kant pointed out that the very existence of spatially extended configurations of matter, such as particles of non-zero radius, implies the existence of some sort of binding force to hold the extended parts of the particle together. Now, that force cannot be explained by the push from the gravitational particles, because those particles too must hold together in the same way. To avoid this circular reasoning, Kant asserted that there must exist a fundamental attractive force. This was precisely the same objection that had always been raised against the impulse doctrine of Descartes in the previous century, and had led even the followers of Descartes to abandon that aspect of his philosophy.
Another German philosopher, Friedrich Wilhelm Joseph Schelling, rejected Le Sage's model because its mechanistic materialism was incompatible with Schelling's very idealistic and anti-materialistic philosophy.Laplace Partly in consideration of Le Sage's theory, Pierre-Simon Laplace undertook to determine the necessary speed of gravity in order to be consistent with astronomical observations. He calculated that the speed must be “at least a hundred millions of times greater than that of light”, in order to avoid unacceptably large inequalities due to aberration effects in the lunar motion. This was taken by most researchers, including Laplace, as support for the Newtonian concept of instantaneous action at a distance, and to indicate the implausibility of any model such as Le Sage's. Laplace also argued that to maintain mass-proportionality the upper limit for earth's molecular surface area is at the most the ten-millionth of earth surface. To Le Sage's disappointment, Laplace never directly mentioned Le Sage's theory in his works.
Because the theories of Fatio, Cramer and Redeker were not widely known, Le Sage's exposition of the theory enjoyed a resurgence of interest in the latter half of the nineteenth century, coinciding with the development of the kinetic theory.Leray Since Le Sage's particles must lose speed when colliding with ordinary matter (in order to produce a net gravitational force), a huge amount of energy must be converted to internal energy modes. If those particles have no internal energy modes, the excess energy can only be absorbed by ordinary matter. Addressing this problem, P. Leray proposed a particle model (perfectly similar to Le Sage's) in which he asserted that the absorbed energy is used by the bodies to produce magnetism and heat. He suggested, that this might be an answer for the question of where the energy output of the stars comes from. Kelvin and Tait
Le Sage's own theory became a subject of re-newed interest in the latter part of the 19th century following a paper published by Kelvin in 1873. Unlike Leray, who treated the heat problem imprecisely, Kelvin stated that the absorbed energy represents a very high heat, sufficient to vaporize any object in a fraction of a second. So Kelvin re-iterated an idea that Fatio had originally proposed in the 1690s for attempting to deal with the thermodynamic problem inherent in Le Sage's theory. He proposed that the excess heat might be absorbed by internal energy modes of the particles themselves, based on his proposal of the vortex-nature of matter. In other words, the original translational kinetic energy of the particles is transferred to internal energy modes, chiefly vibrational or rotational, of the particles. Appealing to Clausius's proposition that the energy in any particular mode of a gas molecule tends toward a fixed ratio of the total energy, Kelvin went on to suggest that the energized but slower moving particles would subsequently be restored to their original condition due to collisions (on the cosmological scale) with other particles. Kelvin also asserted that it would be possible to extract limitless amounts of free energy from the ultramundane flux, and described a perpetual motion machine to accomplish this. (The flaw in Kelvin's reasoning was that Clausius's proposition would apply only if ordinary matter was in thermodynamic equilibrium with the ultramundane flux - in which case there would no net gravitational effect.)
Subsequently, Peter Guthrie Tait called the Le Sage theory the only plausible explanation of gravitation which has been propounded at that time. He went on by saying:
The most singular thing about it is that, if it be true, it will probably lead us to regard all kinds of energy as ultimately Kinetic.
Kelvin himself, however, was not optimistic that Le Sage's theory could ultimately give a satisfactory account of phenomena. After his brief paper in 1873 noted above, he never returned to the subject, except to make the following comment:
This kinetic theory of matter is a dream, and can be nothing else, until it can explain chemical affinity, electricity, magnetism, gravitation, and the inertia of masses (that is, crowds) of vortices. Le Sage s theory might give an explanation of gravity and of its relation to inertia of masses, on the vortex theory, were it not for the essential aeolotropy of crystals, and the seemingly perfect isotropy of gravity. No finger post pointing towards a way that can possibly lead to a surmounting of this difficulty, or a turning of its flank, has been discovered, or imagined as discoverable.Preston Samuel Tolver Preston illustrated that many of the postulates introduced by Le Sage concerning the gravitational particles, such as rectilinear motion, rare interactions, etc., could be collected under the single notion that they behaved (on the cosmological scale) as the particles of a gas with an extremely long mean free path. Preston also accepted Kelvin's proposal of internal energy modes of the particles. He illustrated Kelvin's model by comparing it with the collision of a steel ring and an anvil - the anvil wouldn't be shaken very much, but the steel ring would be in a state of vibration and therefore departs with diminished velocity. He also argued, that the mean free path of the particles is at least the distance between the planets - on longer distances the particles regain their translational energy due collisions with each other, so he concluded that on longer distances there would be no attraction between the bodies, independent of their size. Paul Drude suggested that this could possibly be a connection with some theories of Carl Gottfried Neumann and Hugo von Seeliger, who proposed some sort of absorption of gravity in open space.Maxwell
A review of the Kelvin-Le Sage theory was published by James Clerk Maxwell in the Ninth Edition of the Encyclopaedia Britannica under the title Atom in 1875. After describing the basic concept of the theory he wrote (with sarcasm according to Aronson):
Here, then, seems to be a path leading towards an explanation of the law of gravitation, which, if it can be shown to be in other respects consistent with facts, may turn out to be a royal road into the very arcana of science.
Maxwell commented on Kelvin’s suggestion of different energy modes of the particles that this implies the gravitational particles are not simple primitive entities, but rather systems, with their own internal energy modes, which must be held together by (unexplained) forces of attraction. He argues that the temperature of bodies must tend to approach that at which the average kinetic energy of a molecule of the body would be equal to the average kinetic energy of an ultra-mundane particle and he states that the latter quantity must be much greater than the former and concludes that ordinary matter should be incinerated within seconds under the Le Sage bombardment. He wrote:
We have devoted more space to this theory than it seems to deserve, because it is ingenious, and because it is the only theory of the cause of gravitation which has been so far developed as to be capable of being attacked and defended.
Maxwell also argued that the theory requires "an enormous expenditure of external power" and therefore violating the conservation of energy as the fundamental principle of nature. Preston responded to Maxwell's criticism by arguing that the kinetic energy of each individual simple particle could be made arbitrarily low by positing a sufficiently low mass (and higher number density) for the particles. But this issue later was discussed in a more detailed way by Poincaré, who showed that the thermodynamic problem within Le Sage models remained unresolved.Isenkrahe, Rysanik, du Bois-Reymond Caspar Isenkrahe presented his model in a variety of publications between 1879-1915. His basic assumptions were very similar to those of Le Sage and Preston, but he gave a more detailed application of the kinetic theory. However, by asserting that the velocity of the corpuscles after collision was reduced without any corresponding increase in the energy of any other object, his model violated the conservation of energy. He noted that there is a connection between the weight of a body and its density (because any decrease in the density of an object reduces the internal shielding) so he went on to assert that warm bodies should be heavier than colder ones (related to the effect of thermal expansion).
In another model A. Rysanek in 1887 also gave a careful analysis, including an application of Maxwell's law of the particle velocities in a gas. He distinguished between a gravitational and a luminiferous aether. This separation of those two mediums was necessary, because according to his calculations the absence of any drag effect in the orbit of Neptune implies a lower limit for the particle velocity of 5 · 1019 cm/sec. He (like Leray) argued that the absorbed energy is converted into heat, which might be transferred into the luminiferous aether and/or is used by the stars to maintain their energy output. However, these qualitative suggestions were unsupported by any quantitative evaluation of the amount of heat actually produced.
In 1888 Paul David Gustav du Bois-Reymond argued against Le Sage's model, partly because the predicted force of gravity in Le Sage's theory is not strictly proportional to mass. In order to achieve exact mass proportionality as in Newton's theory (which implies no shielding or saturation effects and an infinitely porous structure of matter), the ultramundane flux must be infinitely intense. Du Bois-Reymond rejected this as absurd. In addition, du Bois-Reymond like Kant observed that Le Sage's theory cannot meet its goal, because it invokes concepts like "elasticity" and "absolute hardness" etc., which (in his opinion) can only be explained by means of attractive forces. The same problem arises for the cohesive forces in molecules. As a result, the basic intent of such models, which is to dispense with elementary forces of attraction, is impossible.
After these attempts other authors substituted electromagnetic radiation for Le Sage’s particles early 1900s. This was in connection with the Lorentz ether theory and the electron theory of that time, in which the electrical constitution of matter was assumed.
In 1900 Hendrik Lorentz wrote, that Le Sage's particle model is not consistent with the electron theory of his time. But the detection that trains of electromagnetic waves could produce some pressure in combination with the penetrating power of Röntgen rays (now called x-rays), led him to the conclusion, that nothing is speaking against the possible existence of an even more penetrating radiation then x-rays, which could replace Le Sage's particles. Lorentz showed that an attractive force between charged particles (which might be taken to model the elementary subunits of matter) would indeed arise, but only if the incident energy were entirely absorbed. This was the same fundamental problem which had afflicted the particle models. So Lorentz wrote:
The circumstance however, that this attraction could only exist, if in some way or other electromagnetic energy were continually disappearing, is so serious a difficulty, that what has been said cannot be considered as furnishing an explanation of gravitation. Nor is this the only objection that can be raised. If the mechanism of gravitation consisted in vibrations which cross the aether with the velocity of light, the attraction ought to be modified by the motion of the celestial bodies to a much larger extend than astronomical observations make it possible to admit.
In 1922 Lorentz first examined Martin Knudsen's investigation on rarefied gases and in connection with that he discussed Le Sage's particle model, followed by a summary of his own electromagnetic Le Sage model - but he repeated his conclusion from 1900: Without absorption no gravitational effect.
In 1913 David Hilbert referred to Lorentz's theory and criticised it by arguing that no force in the form 1/r² can arise, if the mutual distance of the atoms is large enough when compared with their wavelength. J.J. Thomson In 1904 J. J. Thomson considered a Le Sage-type model in which the primary ultramundane flux consisted of a hypothetical form of radiation much more penetrating even than x-rays. He argued that Maxwell's heat problem might be avoided by assuming that the absorbed energy is not be converted into heat, but re-radiated in a still more penetrating form. He noted that this process possibly can explain where the energy of radioactive substances is coming from - however, he stated that an internal cause of radioactivity is more probable. In 1911 Thomson went back to this subject in his article "Matter" in the Encyclopædia Britannica Eleventh Edition. There he stated, that this form of secondary radiation is somewhat analogous to how the passage of electrified particles through matter causes the radiation of the even more penetrating x-rays. He remarked:
It is a very interesting result of recent discoveries that the machinery which Le Sage introduced for the purpose of his theory has a very close analogy with things for which we have now direct experimental evidence....Röntgen rays, however, when absorbed do not, as far as we know, give rise to more penetrating Rontgen rays as they should to explain attraction, but either to less penetrating rays or to rays of the same kind.Tommasina and Brush
Unlike Lorentz and Thomson, Thomas Tommasina between 1903 and 1928 suggested long wavelength radiation to explain gravity, and short wave-length radiation for explaining the cohesive forces of matter. Charles F. Brush in 1911 also proposed long wavelength radiation. But he later revised his view and changed to extremely short wavelengths.
I will not refer further to this conception, save to say that I believe that no man of science is disposed to accept it as affording the true road.Poincaré
Partially based on the calculations of Darwin, an important criticism was given by Henri Poincaré in 1908. He concluded that the attraction is proportional to , where S is earth's molecular surface area, v is the velocity of the particles, and ρ is the density of the medium. Following Laplace he argued that to maintain mass-proportionality the upper limit for S is at the most a ten-millionth of the earth's surface. Now, drag (i.e. the resistance of the medium) is proportional to Sρv and therefore the ratio of drag to attraction is inversely proportional to Sv. To reduce drag Poincaré calculated a lower limit for v = 24 · 1017 times the speed of light. So there are lower limits for Sv and v, and a upper limit for S and with those values one can calculate the produced heat, which is proportional to Sρv3. The calculation shows that earth's temperature would rise by 1026 degrees per second. Poincaré noticed, "that the earth could not long stand such a regime." Poincaré also analyzed some wave models (Tommasina and Lorentz), remarking that they suffered the same problems as the particle models. To reduce drag, superluminal wave velocities were necessary, and they would still be subject to the heating problem. After describing a similar re-radiation model like Thomson he concluded: "Such are the complicated hypotheses to which we are led when we seek to make Le Sage's theory tenable".
He also stated that if in Lorentz' model the absorbed energy is fully converted into heat, this would raise earth's temperature by 1013 degrees per second. Poincaré then went on to consider Le Sage's theory in the context of the "new dynamics" that had been developed at the end of the 19th and beginning of the 20th centuries, specifically recognizing the relativity principle. For a particle theory he remarked that "it is difficult to imagine a law of collision compatible with the principle of relativity", and the problems of drag and heating remain.
Although matter is postulated to be very sparse in the Fatio-Le Sage theory, it cannot be perfectly transparent, because in that case no gravitational force would exist. However, the lack of perfect transparency leads to problems: with sufficient mass the amount of shading produced by two pieces of matter becomes less than the sum of the shading that each of them would produce separately, due to the overlap of their shadows (P10, above). This hypothetical effect, called gravitational shielding, implies that addition of matter does not result in a direct proportional increase in the gravitational mass. Therefore, in order to be viable, Fatio and Le Sage postulated that the shielding effect is so small as to be undetectable, which requires that the interaction cross-section of matter must be extremely small (P10, below). This places an extremely high lower-bound on the intensity of the flux required to produce the observed force of gravity. According to standard physics any form of gravitational shielding is a violation of the equivalence principle and therefore is inconsistent with general relativity. For more historical information on the connection between gravitational shielding and Le Sage gravity, see Martins, and Borzeszkowski et al.
Since Isenkrahe's proposal on the connection between density, temperature and weight was based purely on the anticipated effects of changes in material density, and since temperature at a given density can be increased or decreased, Isenkrahe's comments do not imply any fundamental relation between temperature and gravitation. (There actually is a relation between temperature and gravitation, as well as between binding energy and gravitation, but these actual effects have nothing to do with Isenkrahe's proposal. See the section below on "Coupling to Energy".) Regarding the prediction of a relation between gravitation and density, all experimental evidence indicates that there is no such relation.
Suppose that, contrary to Maxwell's hypothesis, the molecules of gross matter actually possess more energy than the particles. In that case the particles would, on the average, gain energy in the collision and the particles intercepted by body B would be replaced by more energetic ones rebounding from body B. Thus the effect of gravity would be reversed: there would be a mutual repulsion between all bodies of mundane matter, contrary to observation. If, on the other hand, the average kinetic energies of the particles and of the molecules are the same, then no net transfer of energy would take place, and the collisions would be equivalent to elastic ones, which, as has been demonstrated, do not yield a gravitational force.Likewise Isenkrahe's violation of the energy conservation law is unacceptable, and Kelvin's application of Clausius' theorem leads (as noted by Kelvin himself) to some sort of perpetual motion mechanism. The suggestion of a secondary re-radiation mechanism for wave models attracted the interest of JJ Thomson, but was not taken very seriously by either Maxwell or Poincaré, because it entails a gross violation of the second law of thermodynamics (huge amounts of energy spontaneously being converted from a colder to a hotter form), which is one of the most solidly established of all physical laws.
The energy problem has also been considered in relation to the idea of mass accretion in connection with the Expanding Earth theory. Among the early theorists to link mass increase in some sort of push gravity model to Earth expansion were Yarkovsky and Hilgenberg. The idea of mass accretion and the expanding earth theory are not currently considered to be viable by mainstream scientists. This is because, among other reasons, according to the principle of mass-energy equivalence, if the Earth was absorbing the energy of the ultramundane flux at the rate necessary to produce the observed force of gravity (i.e. by using the values calculated by Poincaré), its mass would be doubling in each fraction of a second.Coupling to energy Based on observational evidence, it is now known that gravity interacts with all forms of energy, and not just with mass. The electrostatic binding energy of the nucleus, the energy of weak interactions in the nucleus, and the kinetic energy of electrons in atoms, all contribute to the gravitational mass of an atom, as has been confirmed to high precision in Eötvös type experiments. This means, for example, that when the atoms of a quantity of gas are moving more rapidly, the gravitation of that gas increases. Le Sage's theory does not predict any such effect, nor does any of the known variants of Le Sage's theory.
The re-examination of Le Sage's theory in the 19th century identified several closely interconnected problems with the theory. These relate to excessive heating, frictional drag, shielding, and gravitational aberration. The recognition of these problems, in conjunction with a general shift away from mechanical based theories, resulted in a progressive loss of interest in Le Sage’s theory. Ultimately in the twentieth century Le Sage’s theory was eclipsed by Einstein’s theory of general relativity.
In 1965 Richard Feynman examined the Fatio/Lesage mechanism, primarily as an example of an attempt to explain a "complicated" physical law (in this case, Newton's inverse-square law of gravity) in terms of simpler primitive operations without the use of complex mathematics, and also as an example of a failed theory. He notes that the mechanism of "bouncing particles" reproduces the inverse-square force law and that "the strangeness of the mathematical relation will be very much reduced", but then notes that the scheme "does not work", because of the drag it predicts would be experienced by moving bodies, "so that is the end of that theory".
Although it is not regarded as a viable theory within the mainstream scientific community, there are occasional attempts to re-habilitate the theory outside the mainstream, including those of Radzievskii and Kagalnikova (1960), Shneiderov (1961), Buonomano and Engels (1976), Adamut (1982), Jaakkola (1996), Tom Van Flandern (1999), and Edwards (2007). A variety of Le Sage models and related topics are discussed in Edwards, et al.