Le Sage's theory of gravitation is a kinetic theory of gravity originally proposed by Nicolas Fatio de Duillier in 1690 and later by Georges-Louis Le Sage in 1748. The theory proposed a mechanical explanation for Newton's gravitational force in terms of streams of tiny unseen particles (which Le Sage called ultra-mundane corpuscles) impacting all material objects from all directions. According to this model, any two material bodies partially shield each other from the impinging corpuscles, resulting in a net imbalance in the pressure exerted by the impact of corpuscles on the bodies, tending to drive the bodies together. This mechanical explanation for gravity never gained widespread acceptance.
Basic theory The theory posits that the force of gravity is the result of tiny particles (corpuscles) moving at high speed in all directions, throughout the universe. The intensity of the flux of particles is assumed to be the same in all directions, so an isolated object A is struck equally from all sides, resulting in only an inward-directed pressure but no net directional force (P1).
With a second object B present, however, a fraction of the particles that would otherwise have struck A from the direction of B is intercepted, so B works as a shield, i.e. from the direction of B, A will be struck by fewer particles than from the opposite direction. Likewise B will be struck by fewer particles from the direction of A than from the opposite direction. One can say that A and B are "shadowing" each other, and the two bodies are pushed toward each other by the resulting imbalance of forces (P2). Thus the apparent attraction between bodies is, according to this theory, actually a diminished push from the direction of other bodies, so the theory is sometimes called push gravity or shadow gravity, although it is more widely referred to as Lesage gravity.
Nature of collisions
If the collisions of body A and the gravific particles are fully elastic, the intensity of the reflected particles would be as strong as of the incoming ones, so no net directional force would arise. The same is true if a second body B is introduced, where B acts as a shield against gravific particles in the direction of A. The gravific particle C which ordinarily would strike on A is blocked by B, but another particle D which ordinarily would not have struck A, is re-directed by the reflection on B, and therefore replaces C. Thus if the collisions are fully elastic, the reflected particles between A and B would fully compensate any shadowing effect. In order to account for a net gravitational force, it must be assumed that the collisions are not fully elastic, or at least that the reflected particles are slowed, so that their momentum is reduced after the impact. This would result in streams with diminished momentum departing from A, and streams with undiminished momentum arriving at A, so a net directional momentum toward the center of A would arise (P3). Under this assumption, the reflected particles in the two-body case will not fully compensate the shadowing effect, because the reflected flux is weaker than the incident flux.
Inverse square law
Since it is assumed that some or all of the gravific particles converging on an object are either absorbed or slowed by the object, it follows that the intensity of the flux of gravific particles emanating from the direction of a massive object is less than the flux converging on the object. We can imagine this imbalance of momentum flow – and therefore of the force exerted on any other body in the vicinity – distributed over a spherical surface centered on the object (P4). The imbalance of momentum flow over an entire spherical surface enclosing the object is independent of the size of the enclosing sphere, whereas the surface area of the sphere increases in proportion to the square of the radius. Therefore, the momentum imbalance per unit area decreases inversely as the square of the distance.
Mass proportionality From the premises outlined so far, there arises only a force which is proportional to the surface of the bodies. But gravity is proportional to the masses. To satisfy the need for mass proportionality, the theory posits that a) the basic elements of matter are very small so that gross matter consists mostly of empty space, and b) that the particles are so small, that only a small fraction of them would be intercepted by gross matter. The result is, that the "shadow" of each body is proportional to the surface of every single element of matter. If it is then assumed that the elementary opaque elements of all matter are identical (i.e., having the same ratio of density to area), it will follow that the shadow effect is, at least approximately, proportional to the mass (P5).
Fatio
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.See secondary sources, Prévost (1805) So it lasted until 1929, when the only complete copy of Fatio's manuscript was published by Karl 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.Zehe (1980), secondary sources The following description is mainly based on the Bopp edition.
Features of Fatio's theory Fatio's pyramid (Problem I)
Fatio assumed that the universe is filled with minute particles, which are moving indiscriminately with very high speed and rectilinearly in all directions. To illustrate his thoughts he used the following example: Suppose an object C, on which an infinite small plane zz and a sphere centered about zz is drawn. Into this sphere Fatio placed the pyramid PzzQ, in which some particles are streaming in the direction of zz and also some particles, which were already reflected by C and therefore depart from zz. Fatio proposed that the mean velocity of the reflected particles is lower and therefore their momentum is weaker than that of the incident particles. The result is one stream, which pushes all bodies in the direction of zz. So on one hand the speed of the stream remains constant, but on the other hand at larger proximity to zz the density of the stream increases and therefore its intensity is proportional to 1/r2. And because one can draw an infinite number of such pyramids around C, the proportionality applies to the entire range around C.
Reduced speed In order to justify the assumption, that the particles are traveling after their reflection with diminished velocities, Fatio stated the following assumptions: Either ordinary matter, or the gravific particles, or both are inelastic, or the impacts are fully elastic, but the particles are not absolutely hard, and therefore are in a state of vibration after the impact, and/or due to friction the particles begin to rotate after their impacts. 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 further 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 (assuming that they are small enough that no noticeably greater rate of self-collision occurs near the massive body). More importantly, Fatio 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: He assumed that matter is an accumulation of small "balls" whereby their diameter compared with their distance among themselves is "infinitely" small. But he rejected this proposal, because under this condition the bodies would approach each other and therefore would not remain stable. Then he assumed that the balls could be connected through bars or lines and would form some kind of crystal lattice. However, he rejected this model too – if several atoms are together, the gravific fluid is not able to penetrate this structure equally in all direction, and therefore mass proportionality is impossible. At the end Fatio also removed the balls and only left the lines or the net. By making them "infinitely" smaller than their distance among themselves, thereby a maximum penetration capacity could be achieved.
Pressure force of the particles (Problem II)