Page:Great Neapolitan Earthquake of 1857.djvu/205

Rh If $$b$$ denote the height through which the centre of gravity has descended, to reach the ground, or the horizontal plane pessing through the centre of gravity, when so deposited, and $$a$$ the horizontal distance, traversed by the same centre, on striking the ground, then from which the following expressions are easily deduced for the angle of emergence (which is alternate and equal, to the angle of projection) and for the velocity:   In the second semiphase of the wave (or return shock) the displaced body is thrown, not downwards, but more or less upwards, if projected by the inertia of motion, acquired from a subnormal wave. If the wave were perfectly normal, the projection of course would be horizontal, and $$e = 0$$ for both semiphases.

In the case of projection by subnormal wave, observing that the axis of $$y$$ is measured vertically upwards, and that of $$x$$ horizontally, from the origin, in the centre of gravity of the body as before, we have for the trajectory (Fig. 106) and substituting in this as before