composed of Rigid Particles in Contact. 479 



infinite. Thus, while the total separate dilations are infinite, 

 the compound dilations differ from the sum of the separate 

 by finite terms, and these are functions of the product of the 

 volumes and the reciprocal of the distance. 



Assuming stress in the medium, the difference in the value 

 of these finite terms for two relative positions of the bodies 

 multiplied by the stresses, represents an amount of work which 

 must be done by the bodies on the medium in moving from 

 one position to another. 



To get rid of the difficulty of infinite extent of medium, if 

 for the moment we assume the envelope sufficiently large and 

 imposing a normal pressure upon the medium, then, since the 

 work done will be proportional to the dilation, the force be- 

 tween the bodies will be proportional to the rate at which 

 this dilation varies with the distance between them. 



The force between the bodies would depend on the cha- 

 racter of the elasticity as well as on the dilation. 



It is not necessary to assume the outer envelope elastic; this 

 may be absolutely rigid and one or both the balls elastic. 



In such case the two balls are connected by a definite 

 kinematic relation. As they approach they must expand, 

 doing work which is spent in producing energy of motion ; 

 as they recede, the kinetic energy is spent in the work of com- 

 pressing the balls. 



As already stated, the momentum of the infinite medium 

 for a single ball in finite motion may be infinite, and propor- 

 tional to the product of the volume of the ball by the velocity ; 

 but with two balls moving in opposite directions, with velo- 

 cities inversely as the masses, the momentum of the system 

 is zero. Therefore such motion may be the only motion 

 possible in a medium of infinite extent. 



When the distance between the balls is of the same order 

 as their dimensions, the law of attraction changes with the 

 law of the compound dilations and becomes periodic, corre- 

 sponding to the undulations of density surrounding the balls. 

 Thus, before actual contact were reached, the balls would 

 suffer alternate repulsion and attraction, with positions of 

 equilibrium more or less stable between, as shown in figs. 4 

 and 5 (PI. X.). 



We have thus a possible explanation of the cohesion and 

 chemical combination of molecules, which I think is far more 

 in accordance with actual experience than anything hitherto 

 suggested. 



It was the observation of these envelopes of maximum and 

 minimum density which led me to look more fully into the 

 property of dilatancy. 



