The analogy between Lesage’s theory of gravitation and the repulsion of light

I am not aware that anyone has taken the trouble to work out Lesage's theory, except in the case where the particles of gross matter, subjected to the bombardment of ultramundane corpuscles, are at a distance apart which is a large multiple of the linear dimensions of either of them. Some years ago I had the curiosity to investigate the case where the particles are near together, and having been reminded of my work by reading Professor Poynting’s paper on the pressure of radiation, I have thought it might be worth while to publish my solution, together with some recent additions thereto. If a corpuscle of massm moving with velocityv impinges on a plane surface, so that the inclination of its direction of motion before impact to the normal to the surface isϧ , it communicates to the surface normal momentumkmv cosϧ , and tangential momentumk'mv sinϧ ; wherek is 1 for complete inelasticity, and 2 for perfect elasticity, andk' is 0 for perfect smoothness and 1 for Perfect roughness.