TRANSACTIONS OF SECTION A. 897 
In a complete treatment of the problem, friction must be closely considered ; 
but in the experiment shown it is not of consequence, the result being independent. 
The above statements will be true of any continuous mass of granules if we hold 
the boundaries. 
This principle of the dilatancy of such granular media explains many pheno- 
mena of common occurrence. For example, take a sack of corn, if set on end, it 
remains perfectly flexible ; but if placed on its side it becomes hard, and its shape 
will not alter. Now take an indiarubber sack, fill it with shot—it remains per- 
fectly flexible in all positions. The reason for this difference of behaviour is that 
in the former case the boundary of the granular mass is inextensible, while in the 
latter it allows increase of internal volume. So if it be possible with an extensible 
envelope to impose a limit to the volume of the contents, effects similar to 
those obtained with the inextensible boundary may be expected: and this can be 
done. If we place some shot (No. 6 was used in the experiment) in a thin india- 
rubber bag, and add a certain amount of water, we obtain the result wished. For 
if the amount of water added be such that the spaces between the granules when 
in close arrangement are all filled by it, while with a wide arrangement the amount 
is not enough, a point will be reached in passing from the first to the second 
arrangement such that any further change of volume, and consequently of shape, 
would produce a vacuum. When this stage is reached the whole mass becomes 
perfectly hard. Professor Reynolds illustrated this by means of a ball of shot to 
which a glass tube open at the end was fitted. With a close arrangement of the 
shot, the water, which was coloured, stood high in the tube; but when pressure 
was applied to the bag, the level was lowered. This was shown also with a ball con- 
taining sand instead of shot. The water level sank till the whole was at maximum 
density, and, still more pressure being applied, the level again rose, the maximum 
having been passed. In these experiments about 6 per cent. of the water was free 
at the top of the ball with the close arrangement of granules. When another ball 
containing 20 per cent. of free water was used, the hard condition could only be 
approximated to by pressure, and then passed. So long as the maximum is not 
passed in this case the ball springs back to its original state when the pressure is 
released. But if the maximum be passed, it will not spring back. Ifsome of the 
water be now let out, the maximum cannot be passed, except by shaking, and, if 
the flattened ball be then turned on edge, it will bear a pressure of a hundred 
weight without change of shape. 
When the dilatant material, such as shot or sand, is bounded by smooth sur- 
faces, the layer of grains adjacent to the surface is in a condition differing from 
that of the grains within the mass. This layer can slide between the one suc- 
ceeding it and the surface, causing much less dilatation than would be caused by 
the sliding of a layer within the mass. Hence, if two parts of the mass are con- 
_ nected by such a surface, certain conditions of strain may be accommodated by a 
streaming motion of the grains next the surface. Thus, if into a glass funnel par- 
tially filled with shot and held in a vertical position more shot be forced from 
below, the particles will flow up all around the sides—not rising in the centre as 
might have been thought. 
As the foot presses upon the sand when the falling tide leaves it firm, that 
portion of it immediately surrounding the foot becomes momentarily dry. When 
this happens the sand is filled, completely up to its surface, with water raised by 
capillary attraction. The pressure of the foot causes dilatation of the sand, and so 
more water is required. This has to be obtained either by depressing its level 
against the attraction or by drawing it through the interstices of the surronnding 
sand. As this latter requires time, for the moment the capillary forces are over- 
come, and the surface of the water is lowered below that of the sand, leaving it 
dry until a sufficient supply has been obtained from below, when it again becomes 
wet. On raising the foot we generally see that the sand under and around it be- 
comes wet for a little time. This is because the sand contracts when the distorting 
forces are removed, and the excess of water escapes at the surface. 
In referring to the results which might be expected to follow from a recognition 
of the property of dilatancy, the author said that it places a hitherto unknown 
1885, 3M 
