426 Prof. 0. Keynolds. 



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. 



