XIII. The exchanges between the mean and relative systems.
XIV. The conservation of inequalities in the mean mass and their motions about local centres.
XV. The determination (1) of the relative quantities α″, λ″, σ, and G which define the state of the medium by the results of experience;
(2) the general integration of the equation.
From the research it appears that the motion of the medium must be such as admits of analytical separation into two systems:
(1) A system of mean varying motion, displacing momentum:
(2) A system of relative motion without mean momentum, within a certain space.
It also appears:
(3) that it is only media consisting of absolutely rigid parts that can satisfy the condition of being mean and relative systems of motion.
(4) that the rigid parts must be uniform spheres.
The actions between such spheres is outside all experience. But it follows, since there is no elasticity, that for the conservation of energy, when these spheres, or grains, as they will now be called, come into collision, they will exchange
