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
S Fig. 1.
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 Bl 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