Page:Great Neapolitan Earthquake of 1857.djvu/181

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Let $$\mathrm{O'O}$$ be the wave-path passing through any building whatever, as Fig. 99.

Let $$\mathrm{OX}$$ be perpendicular to the lines $$\mathrm{OZ}$$ and $$\mathrm{OY}$$, and let $$\alpha$$, $$\beta$$, and $$\gamma$$ be the angles made by $$\mathrm{O'O}$$, with $$\mathrm{OX..OY..OZ}$$.

If $$\mathrm{V}$$ = the total velocity, or that in the path of the wave, and $$v_{x} v_{y} v_{z}$$ the components along $$\mathrm{X}$$, $$\mathrm{Y}$$and $$Z$$, then   The effect of $$v_{x}$$ in overturning the structure has been already considered. The component $$v_{y}$$ produces no direct effect in overturning, although its action parallel to $$\mathrm{Y}$$ may fracture and disintegrate the building.

If the structure is capable of being overturned in the plane of $$\mathrm{YZ}$$, and also in the plane of $$\mathrm{XZ}$$, the components $$v_{x}$$ and $$v_{y}$$ must act together, and compel it to turn round upon one of the extreme points in the line $$\mathrm{OY}$$. In that case, the motion ceases to be comparable with that of a compound pendulum, and is reduced to the movement of