480 Prof. Osborne Reynolds on the Dilatancy of Media. 



The assumed elasticity of the surrounding envelope, or of 

 the balls, has only been introduced to make the argument clear. 



The medium itself may be supposed to possess kinetic 

 elasticity arising from internal distortional motion, such as 

 would arise from the transmission of waves in which the 

 motion of the medium is in the plane of their fronts. 



The fitness of a dilatant medium to transmit such waves is 

 only less striking than its property of causing attraction, 

 because in the first respect it is not unique. 



But as far as I can see such transmission is not possible in 

 a medium composed of uniform grains. If, however, we have 

 comparatively large grains uniformly interspersed, then such 

 transmission becomes possible. If, notwithstanding the large 

 grains, the medium is at maximum density, the large grains 

 will not be free to move without causing further dilation; and 

 it seems that the medium would transmit distortional vibra- 

 tions in which the distortions of the two sets of grains are 

 opposite. 



Such waves, although the motion would be essentially in 

 the plane of the wave, would cause dilation, just as waves in a 

 chain cause contraction in the reach of the chain. They 

 would in fact impart elasticity to the medium, exactly as, 

 in the case of a slack chain having its ends fixed but other- 

 wise not subject to forces, any lateral motion imparted to the 

 chain will cause tension proportional to the energy of distur- 

 bance divided by the slackness or free length of chain. 



Distortional weaves therefore, travelling through dilatant 

 material which does not quite occupy the space in which it is 

 confined when at maximum density, would render the medium 

 uniformly elastic to distortion, but not in the same degree to 

 compression or extension. The tension caused by such waves 

 would depend on the gross energy of motion of the waves 

 divided by the total dilation from maximum density conse- 

 quent on the wave-motion. All such waves, whatever might 

 be their length, would therefore move with the same velocity. 



If, when rendered elastic by such waves, the medium were 

 thrown into a state of distortion by some external cause, this 

 would diminish the possible dilation caused by the waves. 

 Thus work would have to be done on the medium in producing 

 the external distortion which would be spent in increasing 

 the energy of the waves. For instance, the separation of two 

 bodies in such a medium, which, as already shown, would in- 

 crease the statical distortion, would increase the energy of 

 the waves and vice versa. 



As far as the integrations have been carried for this con- 

 dition of elasticity, it appears, with a certain arrangement of 



