composed of Rigid Particles in Contact, 477 



able to look into it, seems to promise great things, besides 

 possessing the inherent advantage of extreme simplicity. 



Hitherto no medium has ever been suggested which would 

 cause a statical force of attraction between two bodies at a 

 distance. Such attraction would be caused by granular media 

 in virtue of this dilatancy and stress. More than this, when 

 two bodies in a granular medium under stress are near 

 together, the effect of dilatancy is to cause forces between the 

 bodies in very striking accordance with those necessary to 

 explain coherence of matter. 



Suppose an outer envelope of sufficiently large extent, at 

 first not absolutely rigid, rilled with granular media, at its 

 maximum density. Suppose one of the grains of the media 

 commences to grow into a larger sphere ; as it grows, the 

 surrounding medium will be pushed outwards radially from 

 the centre of the expanding sphere, Considering spherical 

 envelopes following the grains of the medium, these will ex- 

 pand as the grains move outwards. This fixes the distortion 

 of the medium, which must be contraction along the radii, 

 and expansion along all tangents. 



The consequent amount of dilation depends on the relation 

 of distortion and dilation, and on the arrangement of the 

 grains in the medium. At first the entire medium will un- 

 dergo dilation, which will diminish as the distance from the 

 centre increases. As the expansion goes on, the medium 

 immediately adjacent to the sphere will first arrive at a con- 

 dition of minimum density ; and for further expansion this 

 will be returning to a maximum density, while that a little 

 further away will have reached a minimum. The effect of 

 continued growth will therefore be to institute concentric 

 undulations of density from maximum to minimum density, 

 which will move outwards ; so that after considerable growth 

 the sphere will be surrounded with a series of envelopes of 

 alternately maximum and minimum density, the medium at 

 a great distance being at maximum density. At a definite 

 distance from the centre of the sphere not more than 



1.4R, 



where R is the radius of the sphere, the density will be a 

 minimum, and between this and the sphere there may be a 

 number of alternations depending on the relative diameters of 

 the grains and the spheres. 



The distance between these alternations will diminish rapidly 

 as the sphere is approached. The distance of the next maxi- 

 mum is 1 . 2 R, the next minimum is given by 1.09 R, and 

 the next maximum 1 . 06 R. 



