400 Structure of the Universe 



a sort of gap or cracK in the granular medium, which forms a sur- 

 face of weakness, and it is shown that the pressure of the medium 

 is less between these "negative inequalities" or surfaces of weakness 

 than it is on the outside. There is a strain set up in the granular 

 medium in normal piling between them, which produces a curvature 

 in the normal piling. This produces space variations or dilatations 

 between the grains in the curved normal piling. These spaces vary 

 recording to the degree of the curve, and the total of the enlarged 

 spaces or dilatations so produced by the curvature is exactly equal 

 to the total of the spaces from which the grains are absent in the 

 negative inequalities which produce the curve. Owing to this, as 

 has been said, the pressure of the medium is less between the nega- 

 tive inequalities or masses of matter than it is in the medium out- 

 side, with the result that the extra outside pressure drives the nega- 

 tive insqualities together. The old physics calls this "space variation 

 of the potential." As the bodies approach the curvature is annihilated 

 and the medium is restored to the regular normal piling. 



It is somewhat difficult at first for one to understand this process; 

 but the dynamical reasoning upon which it is based is thoroughly 

 sound. Reynolds says: "This law of atti action, which satisfies all 

 the conditions of gravitation, is now shown by definite analysis to re- 

 sult from negative local inequalities in an otherwise uniform granular 

 medium under a mean pressure equal in all directions, as a conse- 

 quence of the property of dilatancy in such media when the grains 

 are so close that there is no diffusion and infinite relative motion and 

 further it is shown to be the only attraction which satisfies the con- 

 ditions of gravitation in a purely mechanical system." 



"Gravitation is not the result of that dilatation which results 

 from uniform parallel strains in the medium in normal piling, but re- 

 sults solely from those components of the dilatations caused by the 

 space variation of the inward strains. 



"Thus, as long as the dilatation strains are parallel there is no 

 attraction; but if there is curvature in the strains there will be 

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

 the negative inequalities to approach from a finite distance. 



"Thus gravitation is the rsult of those components of the dilata- 

 tions (taken to a first approximation) which are caused by the varia- 

 tions of the components of the inward strains, caused by curvature 

 in the normal piling of the medium. 



"The other components of the strains, being parallel distortions, 

 which satisfy the conditions of geometrical similarity, do not affect 

 the efforts. 



"Then, since if the grains were indefinitely small, while the curva- 

 ture in the normal piling was finite, there would be no effort. And 

 multiplying this parameter by the curvature of the medium, and again 

 by the mean pressure of the medium, the product measures the in- 

 tensity of the eft'orts to approach. 



"The dilatation diminishes as the centres of the negative inequali- 

 ties approach, and work is done by the pressure outside the singular 



