# Le Sage's Theory of Gravitation - Later Assessments

Later Assessments

Darwin

In 1905, George Darwin subsequently calculated the gravitational force between two bodies at extremely close range to determine if geometrical effects would lead to a deviation from Newton’s law. Here Darwin replaced Le Sage's cage-like units of ordinary matter with microscopic hard spheres of uniform size. He concluded that only in the instance of perfectly inelastic collisions (zero reflection) would Newton’s law stand up, thus reinforcing the thermodynamic problem of Le Sage's theory. Also, such a theory is only valid if the normal and the tangential components of impact are totally inelastic (contrary to Le Sage's scattering mechanism), and the elementary particles are exactly of the same size. He went on to say that the emission of light is the exact converse of the absorption of Le Sage's particles. A body with different surface temperatures will move in the direction of the colder part. In a later review of gravitational theories, Darwin briefly described Le Sage's theory and said he gave the theory serious consideration, but then wrote:

 “ 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 an 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, that 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 the 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.