Page:Great Neapolitan Earthquake of 1857.djvu/182

a body round a fixed point under the influence of gravity; one which, even in its simplest cases, would be too difficult of reduction for practical purposes, and which virtually never occurs in seismometric observation. If, therefore, the force of the wave be confined to the plane $\mathrm {XZ}$, and be emergent at an angle $e$ with the horizon, we have

$v_{x}=\mathrm {V} \cos e$

$v_{z}=\mathrm {V} \sin e$

(XII.)

It being remarked that when the wave is not strictly subnormal, we may always view it as such in the first instance, and resolve the value of $\mathrm {V}$ found, through the abnormal angle, the latter being less than sufficient for longitudinal disintegration of the wall or structure.

The general case of the subnormal wave must be distinguished into two. First, when the wave-path through the centre of gravity falls within the base, second, when it falls without the base of the structure.

Let $\mathrm {O'} o'\mathrm {C}$ (Fig. 100) be the wave-path emergent within the base. The structure is urged by inertia against the ground in the direction $\mathrm {CO'}$ (contrary to the wave in its first semiphase), and it cannot be overturned by that movement of the wave at any velocity, (that is, by the direct shock); but it may be overturned by the wave in its second semiphase (or by the return shock). The limit of this, is where the wavepath, passes through the centre of gravity and the arris of the base, round which the structure should turn, when it