362 Professor Osborne Beynolds [Feb. 12, 



I have now shown as fully as time will allow, the exi:>eriments 

 which afford evidence of the existence of the property of dilatancy, and 

 how it exi)lains natural phenomena hitherto but little noticed. 



Beyond affording evidence of the existence of the property of 

 dilatancy, these experiments have no direct connection with gravi- 

 tation or the physical properties of matter. 



These properties cannot be deduced by direct experiment on 

 granular material, for the simple reason that the grains of the 

 medium which constitutes the aether must be free from friction, 

 while the grains with which we work are subject to friction. These 

 properties can only be deduced by mathematical reasoning, into 

 which I will not drag you to-night. I will merely show you one 

 or two or three facts which may serve to convey an idea of how 

 dilatancy should have such a bearing on the foundation of the 

 universe. 



If you look at this diagram, you see it represents a ball surrounded 

 by a continuous mass of grain, the density of the grains being indi- 

 cated by the depth of colour. If that ball were to grow in volume, 

 it would have to push out the medium on all sides, and in that way 

 it would distort the groups of grains or change their form, causing 

 the interstices to increase ; those nearer the ball would be dis- 

 torted more than those further away. Then the interstices of these 

 would grow the most rapidly, and those adjacent to the ball would 

 first come to their openest order for further growth ; these would 

 contract somewhat, those a little further away would reach the 

 openest order, and if the process of growth steadily continued, 

 we should have a series of undulations of density commencing 

 at the ball and moving outwards ; the first of these waves of open 

 order would not, however, get beyond half the diameter of the 

 ball away. The diagram represents the interstices that would 

 result if a single grain of the material had grown to the size of the 

 ball, pushing the medium out before it. It is not necessary that the 

 ball should have grown, to produce this result ; however the ball 

 were originally placed, if it were moved away from its original place 

 it would assume this arrangement, and with this arrangement it 

 would be free to move. Now, although I cannot attempt to enter 

 upon the relation between the density of the medium and the force 

 of attraction between two bodies in it, I may call your attention 

 to this fact, that the dilation as calculated varies exactly as the 

 force of gravitation, inversely as the square of the distance from an 

 infinite distance till close to the ball, and then goes through several 

 undulations, corresponding exactly to tlie variations in the attraction 

 of bodies necessary to explain the elasticity and cohesion of mole- 

 cules. As is shown in the other diagrams, these undulations in 

 density, which may be experimentally produced, not only appear to 

 afford a clear explanation of cohesion, but arc the only suggestion 

 of an explanation ever made. And further, similar undulations have 

 been found necessary to explain one of the phenomena of light. My 



