page_title: Le Sage's theory of gravitation
section_title: Features of Fatio's theory
hierarchical_section_title: Le Sage's theory of gravitation / Fatio / Features of Fatio's theory
caption_attribution_description: Fatio's Pyramide
context_page_description: 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 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.
context_section_description: 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 p
caption: P6: Fatio's pyramid
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