Page:Great Neapolitan Earthquake of 1857.djvu/177

Rh substituting in (Eq. II.) and since

$$V^2 = \frac{15 \beta^2 + 16 \alpha^2}{12 \alpha^2} \times g \sqrt{\alpha^2 + \beta^2} \left ( 1 - \cos \phi \right )$$ (VII.)



4th. In the case of a hollow rectangular parallelopiped overturned (Fig. 96).

Let the edges of the parallelopiped be $$\alpha, \beta, \gamma$$ the thickness of its walls being small in relation to their lengths, and suppose it overturned round the edge or axis $$\gamma$$.

It is easily demonstrable that

and

and therefore

from which, substituting the value of $$l$$ in Eq. II., and remembering that $$\tan \phi = \frac{\beta}{\alpha}$$ we obtain $$V$$, the horizontal velocity.