Structure of the Universe 393 



52.381 and the empty space 47.619, or about 11 to 10. The other 

 four methods of piling lie between these two extremes. I append to 

 this lecture the figures of the proportions of full space to empty space 

 in the six arrangements. 



One of Reynolds' most inportant steps toward the discovery of 

 the cause of gravitation was the ^iscovery of the dilatancy of gran- 

 ular media under pressure. For instance, when shot or sand or 

 other spherical grains are put into a bag or other closed surface and 

 shaken, they settle into a very close position, and when in this posi- 

 tion the spaces or interstices which exist between the grains are 

 about the smallest possible. They may then be said to be in what 

 Reynolds calls "normal piling" and when in this position the shape of 

 the bag containing the shot or grains cannot be changed without at 

 the same time changing its bulk or volume; because if you endeavor 

 to change the shape of the containing vessel under such conditions, 

 you are at the same time disturbing the grains from their closest 

 possible positions into another arrangement less close, whereby the 

 spaces or interstices between the grains are enlarged, thereby pro- 

 ducing a vacuum, or working against atmospheric pressure. I have 

 here two hollow rubber balls, one filled with small shot and com- 

 pletely closed, except for a small opening which does not allow the 

 shot to escape, and into which a glass tube is inserted to measure the 

 dilatation. Colored water is poured into the bag through the tube to 

 fill the interstices between the shot, and if the bag is then subjected 

 to distortional squeezing, as it now is, the water, as you see, sinks 

 in the tube. It is drawn into the bag to fill the expanded spaces be- 

 tween the grains caused by the distortion. This is an experimental 

 model universe. I have here another similar bag filled only with 

 water, but, as you see, when it is similarly squeezed the water rises 

 in the tube. I have here also one of these thin rubber balloons which 

 children play with, filled with sand and just enough water to fill the 

 interstices between the sand when lying flat as you see it now. It is 

 closed tightly so as not to admit any air. It is now placed on its 

 edge, and, as you see, sustains a weight of 200 pounds without flinch- 

 ing. This appears to be nothing short of magical, but when the 

 phenomena of dilatation of granular media under pressure is under- 

 stood it is perfectly simple. (Experiment.) 



This remarkable property of dilatancy of all granular media was 

 discovered by Reynolds. It also furnished him the clue to the 

 cause of gravitation. In order to get granular media under pressure 

 it must be bounded by a closed surface. Reynolds says: "If, as in 

 the universe, the grains in normal piling extend indefinitely, there 

 can be no mean motion of the boundaries, whatever the pressure 

 may be; and thus the grains are virtually within a closed surface." 



Here is a model made out of small rubber balls of the way the 

 cosmic grains are arranged in space according to Reynolds. This 

 arrangement is what he calls "normal piling," and is such that the 

 grains are placed in a set of squarely formed layers horizontally, each 

 sphere resting on four in the layer below, and in its turn supporting 

 four in the layer above, these last four being vertically over the first 

 four. Besides touching these eight in adjoining layers it touches 



