470 Prof. Osborne Reynolds on the Dilatancy of Media 



collisions ; sucli motion being rendered necessary to account 

 for the property of diffusion. 



Without attempting anything like a complete dynamical 

 theory, which will require a large development of mathema- 

 tics, I would point out the existence of a singular fundamental 

 property of such granular media which is not possessed by 

 known fluids or solids. On perceiving something which 

 resembles nothing within the limits of one's knowledge, a 

 name is a matter of great difficulty. I have called this unique 

 property of granular masses " dilatancy/' because the property 

 consists in a definite change of bulk, consequent on a definite 

 change of shape or distortional strain, any disturbance what- 

 ever causing a change of volume and generally dilation. 



In the case of fluids, volume and shape are perfectly inde- 

 pendent ; and although in practice it is often difficult to alter 

 the shape of an elastic body without altering its volume, yet 

 the properties of dilation and distortion are essentially distinct, 

 and are so considered in the theory of elasticity. In fact 

 there are very few solid bodies which are to any extent dila- 

 table at all. 



With granular media, the grains being sensibly hard, the 

 case is, according to the results I have obtained, entirely dif- 

 ferent. So long as the grains are held in mutual equilibrium 

 by stresses transmitted through the mass, every change of 

 relative position of the grains is attended by a consequent 

 change of volume ; and if in any way the volume be fixed, 

 then all change of shape is prevented. 



In speaking of a granular medium, it is assumed to be in 

 such a condition that the position of any internal particle 

 becomes fixed when the positions of the surrounding particles 

 are fixed. 



This condition is very generally fulfilled, but not always 

 where there is friction ; without friction it would be always 

 fulfilled. 



From this assumption it at once follows that no grain in 

 the interior can change its position in the mass by passing 

 between the contiguous grains without disturbing these; 

 hence, whatever alterations the medium may undergo, the 

 same particle will always be in the same neighbourhood. 



If, then, the medium is subject to an internal strain, the 

 shapes of the internal groups of molecules will all be altered, 

 the shape of each elementary group being determined by the 

 shape of the surrounding particles. This will be rendered 

 most intelligible by considering instances ; that of equal 

 spheres is the most general, and presents least difficulty. 

 A group of such spheres being arranged in such a manner 



