356 Professor Osborne Reynolds \^^^' 12, 



composed of grains of any possible shape possessed tliis property of dila- 

 tancy so long as one important condition was satisfied. 



This condition is that the medium should be continuous, infinite 

 in extent, or that the grains at the boundary should be so held as to 

 prevent a rearrangement commencing. All that is wanted is a mass 

 of hard smooth grains, each grain being held by the adjacent grains, 

 and the grains on the outside prevented from rearranging. 



Smooth hard spheres arranged as an ordinary pile of shot are in 

 their closest order, the interstices occupying a space about one-third 

 that occupied by the spheres themselves. By forcing the outside shot 

 so as to give the pile a different shape, the inside spheres are forced 

 by those on the outside, and the interstices increase. Thus by shaping 

 the outside of the pile, the interstices may be increased to any extent 

 until they occupy about nine-tenths the volume of the spheres : this is 

 the most open formation. A further change of shape in the same direc- 

 tion causes a contraction of the interstices until a minimum volume 

 is reached, and then again an expansion, and so on. The point to be 

 realised is that in any of these arrangements if the whole of the 

 spheres on the outside of the group are fixed, those inside will be 

 fixed also. {Shown by a model.) 



An interior portion of a mass of smooth hard spheres therefore 

 cannot have its shape changed by the surrounding spheres without 

 altering the room it occupies, and the same is true for any granular 

 mass, whatever be the shape of the grains. 



Considering the generality of this conclusion, the non-discovery of 

 this property as existing in tangible matter requires a word of 

 explanation. 



The physical properties of elasticity, adhesion, and friction so far 

 render the molecules of ordinary matter incapable of behaving as a 

 system of parts with the sole property of keeping their shape, and so 

 prevents evidence of dilatancy in solids and fluids. This is quite 

 consistent with dilatancy in the sether, for the properties of 

 elasticity, cohesion, and friction in tangible matter are due to the 

 presence of the sether, so that it would be illogical for the elementary 

 atoms of the aether to possess these properties. 



This although a sufficient reason why dilatancy has not been 

 recognised as a property of solid and fluid matter, does not explain 

 its non-existence in masses of solid, hard, free grains, as of corn, shot, 

 and sand. To understand why it has not been observed in these, it 

 must be remembered that to ordinary observation these present only 

 an outside ajipearance, and that the condition essential for dilatancy, 

 that the outside grains should not be free to rearrange, is seldom ful- 

 filled. Also these granular forms of matter, though commonplace, 

 have not been the subjects of physical research, and hence such 

 evidence as they do afford has escaped detection. 



Once, however, having recognised dilatancy as a universal pro- 

 perty of granular masses, it was obvious that if evidence of it was 

 to be sought from tangible matter, it must be sought in what have 



