composed of Rigid Particles in Contact. 473 



relative dilation and distortion with different degrees of fric- 

 tion. If the dilation were in any sense a consequence of 

 friction, it would be greater when the coefficient of friction 

 between the spheres was greater. Where the granular mass 

 is bounded by solid surfaces, the friction of the grains against 

 these surfaces will considerably modify the results. 



The problem presented by frictionless balls is much simpler 

 than that presented in the case of friction. In the former 

 case the theoretical problem may be attacked with some hope 

 of success. With friction the property is most easily studied 

 by experiment. 



As a matter of fact, if we take means to measure the volume 

 of a mass of solid grains more or less approximately spheres, 

 the property of dilatancy is evident enough, and its effects 

 are very striking, affording an explanation of many well- 

 known phenomena. 



If we have in a canvas bag any hard grains or balls, so 

 long as ihe bag is not nearly full it will change its shape as it 

 is moved about ; but when the sack is approximately full a 

 small change of shape causes it to become perfectly hard. 

 There is perhaps nothing surprising in this, even apart from 

 familiarity ; because an inextensible sack has a rigid shape 

 when extended to the full, any deformation diminishing its 

 capacity, so that contents which did not fill the sack at its 

 greatest extension fill it when deformed. On careful conside- 

 ration, however, many curious questions present themselves. 



If, instead of a canvas bag, we have an extremely flexible 

 bag of india-rubber, this envelope, when filled with heavy 

 spheres (No. 6 shot), imposes no sensible restraint on their 

 distortion; standing on the table it takes nearly the form of a 

 heap of shot. This is apparently accounted for by the fact 

 that the capacity of the bag does not diminish as it is deformed. 

 In this condition it really shows us less of the qualities of its 

 granular contents than the canvas bag. But as it is imper- 

 vious to fluid, it will enable me to measure exactly the volume 

 of its contents. 



Filling up the interstices between the shot with water so 

 that the bag is quite full of water and shot, no bubble of air 

 in it, and carefully closing the mouth, I now find that the bag 

 has become absolutely rigid in whatever form it happened to 

 be when closed. 



It is clear that the envelope now imposes no distortional 

 constraint on the shot within it, nor does the water. What, 

 then, converts the heap of loose shot into an absolutely rigid 

 body ? Clearly the limit which is imposed on the volume by 

 the pressure of the atmosphere. 



