composed of Rigid Particles in Contact. 475 



reached, approximate restitution follows quite as nearly as 

 could be expected, considering that friction opposes restitution. 

 But when the squeezing has been carried past the point of 

 maximum volume, then restitution requires expansion ; and 

 this the elasticity of shape is not equal to accomplish, so that 

 the bag retains its flattened condition. This experiment has 

 been varied in a great variety of ways. 



The very finest quartz sand, or glass balls f inch in dia- 

 meter, all give the same results. Sand is, on the whole, the 

 most convenient material, and its extreme fineness reduces any 

 effect of the squeezing of the india-rubber between the inter- 

 stices of the balls at the boundaries ; which effect is very 

 apparent with ihe balloon bags, and shot as large as No. 6. 



A well-marked phenomenon receives its explanation at once 

 from the existence of dilatancy in sand. When the falling 

 tide leaves the sand firm, as the foot falls on it the sand 

 whitens, or appears momentarily to dry round the foot. 

 When this happens the sand is full of water, the surface 

 of which is kept up to that of the sand by capillary attrac- 

 tion ; the pressure of the foot causing dilation of the sand, 

 more water is required, which has to be obtained either 

 by depressing the level of the surface against the capillary 

 attraction, or by drawing water through the interstices of 

 the surrounding sand. This latter requires time to accom- 

 plish, so that for the moment the capillary forces are overcome ; 

 the surface of the water is lowered below that of the sand, 

 leaving the latter white or dryer until a sufficient supply has 

 been obtained from below, when the surface rises and wets 

 the sand again. On raising the foot it is generally seen that 

 the sand under the foot and around becomes momentarily 

 wet ; this is because, on the distorting forces being removed, 

 the sand again contracts, and the excess of water finds 

 momentary relief at the surface. 



Leaving out of account the effect of friction between the 

 balls and the envelope, the results obtained with actual balls, 

 as regards the relation between distortion and dilation, appear 

 to be the same as would follow if the balls were smooth. 



The friction at the boundaries is not important as long as 

 the strain over the boundaries is homogeneous, and particu- 

 larly if the balls indent themselves into the boundaries, as 

 they do in the case of india-rubber. But with a plane surface 

 the balls at the boundaries are in another condition from the 

 balls within. The layer of balls at the surface can only vary 

 its density from 2/^/3 to 1. This means that the layer of 

 balls at a surface can slide between that surface and the adja- 

 cent layer, causing much less dilaliun than would be caused 



