Page:Great Neapolitan Earthquake of 1857.djvu/183

is still capable of being overturned by the first semiphase of the wave.

In either case, overthrow by the second semiphase, although mechanically possible, seldom occurs (for the same object), in parts of buildings, as some support or obstacle generally props it against the latter.

Let a body cylindrical or prismatic be overturned by a wave in the path $\mathrm {OC}$ (Fig. 101). Inertia of motion, due to

the first semiphase, acting in the contrary direction $\mathrm {CO}$, tends to make the structure turn round the axis $\mathrm {A}$.

The overturning couple is

${\frac {v_{x}\alpha -v_{z}\beta }{2}},$

where $\alpha$ and $\beta$ are double the co-ordinates of the centre of gravity, or, $\mathrm {M}$ being the mass,

${\frac {\mathrm {MV} (\alpha \cos e-\beta \sin e)}{2}},$

Dividing this by the moment of inertia, we obtain

$\omega ={\frac {\mathrm {V} (\alpha \cos e-\beta \sin e)}{2k^{2}}},$