Page:Proceedings of the Royal Society of London Vol 69.djvu/444

426 XII. The linear dispersion of mass, and of momentum and energy of relative motion by convection.

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 a", A.", tr, and G- which define the state of the medium by the results of experience; (2) the general integration of the equation.

1. In this paper it is shown that there is one, and only one, con- ceivable purely mechanical system capable of accounting for all the physical evidence, as we know it, in the universe.

The system is neither more nor less than an arrangement of indefinite extent of uniform spherical grains, generally in normal piling, so close that the grains cannot change their neighbours, although continually in relative motion with each other, the grains being of changeless shape and size, thus constituting, to a first approximation, an elastic medium, with six axes of elasticity symmetrically placed.

The diameter of a grain, in C.G.S. units, is

5-534 xlO- ls = o-. The mean relative velocities of the grains are

6-777x10 = a". The mean path of the grains

These three quantities completely define the state of the medium in spaces where the piling is normal ; they also define the mean density of the medium as compared with the density of water as

10 4 = 22-Q.

The mean pressure in the medium equal in all directions is M72x 10 14 = p.

The coefficient of the transverse elasticity resulting from the gearing of the grains where the piling is normal is

9-030 x 10 SO = n. The rate of propagation of the transverse wave is

3-000 x 10 10 = r. (n/p). The rate of propagation of the normal wave is

7-161 x!0 10 = 2-387 XT.