tinuous in space. But it is doubtful whether the significance of this continuity has been realized.
We have defined the pressure in such media as being enormous, and it now becomes necessary to realize that, in order to get granular material under pressure, one or other of two conditions must be satisfied.
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.
But if the number of grains is limited—and we can only experiment on a finite number of grains—it is necessary, in order to realize the dilatation, that the grains should be in a closed envelope of some kind which constrains them; and it may be mentioned here that the reason why dilatancy had not been discovered previously was undoubtedly the general absence of any constraining surface.
Without such a surface, in order to illustrate the dilatation, we may join the horizontal layers of grains in normal piling together, as in model (1), then subjecting these layers of grains in normal piling to transverse strain, the dilata-
