Let s be a
dateram buried in x; and T the string to which it is tied. Now, on
considering fig. 2, where a series of balls are drawn on a larger scale
and on a plane surface, it is clear that the ball A cannot move in any
degree to the right or the left without disturbing the entire layer of
balls on the same plane as itself: its only possible movement is
vertically upwards. In this case, it disturbs B1 and B2. These, for the
same reason as A, can only move vertically upwards, and, in doing so,
they must disturb the three balls above them, and so on. Consequently,
the uplifting of a single ball in fig. 2, necessitates the uplifting of
the triangle of balls of which it forms the apex; and it obviously
follows from the same principle, that the uplifting of S, in the depth of
X, in fig. 1, necessitates the uplifting of a cone of balls whose apex is
at S. But the weight of a cone is as the cube of its height and,
therefore, the resistance to the uplifting of the dateram, is as the cube
of the depth at which it has been buried. In practice, the grains of sand
are capable of a small but variable amount of lateral displacement, which
gives relief to the movement of sand caused by the dateram, for we may
observe the surface of the ground to work very irregularly, although
extensively, when the dateram begins to stir. On the other hand, the
friction of the grains of sand tends to increase the difficulty of
movement.
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