Page:Great Neapolitan Earthquake of 1857.djvu/188

140 the continuous beds of the masonry, or through homogeneous bodies, such as stone shafts of columns, &c.—to none of which the same uncertainty of coefficient applies—

If any prismatic or cylindrical (Fig. 103) solid structure be broken off, by an horizontal fracture at its base, from its own material below that base, and by a normal wave, neither turning over, nor being displaced, but tending to overturn, upon the axis of $$\mathrm{A}$$, by the first semiphase, and upon that of $$\mathrm{B}$$, by the second semiphase of the wave.

The condition for its fracture thus, without overthrow, is that the overturning moment, shall be equal to the moment of cohesion of the fractured surface of the base.

The fracturing force may be considered as applied at the centre of gravity of the mass detached; and the moment of cohesion at half the radius of oscillation of the plane of fracture, at the base, viewed as surface about to vibrate round the axis $$\mathrm{A}$$ or $$\mathrm{B}$$, as a compound pendulum.