428 Prof. 0. Eeynolds. 



and in whatever new direct/ion the singular surface is propagated, the 

 motion of the medium outside is such as represents equal and opposite 

 momentum, as when a bubble is rising in a glass of water. 



In exactly the same way, for inequalities resulting from an excess 

 of grains, the momentum resulting from the displacement of the 

 medium would be positive. 



The principal stresses in the medium outside the singular surface of 

 a negative inequality are to a first approximation two equal tangential 

 pressures equal in all directions : 



and a normal pressure : 



the mean of these pressures being everywhere the mean pressure of 

 the medium equal in all directions. 



Efforts, proportional to the inverse square of the distance, to cause 

 two negative inequalities to approach from a finite distance, are the 

 result of those components of the dilatation (taken to a first approxi- 

 mation) which are caused by the variation of those components of the 

 inward strains which cause curvature in the normal piling of the 

 medium. 



The other components of the strain, being parallel distortions, which 

 satisfy the condition of geometrical similarity, do not affect the efforts. 

 If the grains were indefinitely small there would be no effort ; thus the 

 diameter of a grain is the parameter of the effort, and, multiplying 

 this diameter by the curvature of the medium and again by the mean 

 pressure of the medium, the product measures the intensity of the 

 effort. 



The dilatation diminishes as the centres of the negative inequalities 

 approach, and work is done by the pressure in the medium outside the 

 singular surfaces to bring the negative inequalities together. 



The efforts to cause the negative inequalities to approach correspond 

 exactly to the gravitation, if matter represents negative mass. 



Taking the mean density of the earth as - 5*67 as compared with 

 water (-1), 



The reciprocal of the density of the medium being 0'10~ 4 , 



The mean pressure of the medium .................. 1 -172 x 10 14 , 



<r the diameter of a grain .............................. 5 '534 x 10~ 18 , 



The mean radius of the earth .......................... 6-3709 x 10 s , 



the effort to cause approach between the earth and a unit of matter 

 on the earth's surface ( - 1) is the product of these quantities multi- 

 plied by 4:r/3, or : 



- pa- x 10~ 4 x f TT x 5-67 x 6-3709 x 10 s = 9-81 x 10 2 . 



O 



