Page:Great Neapolitan Earthquake of 1857 Vol 2.djvu/77

sider so much of it as affected the front block, as equivalent to 12 inches of material added to its height.

Applying the equation

$V^{2}={\frac {4}{3}}g{\sqrt {a^{2}+b^{2}}}\times \left({\frac {1-\cos \theta }{\cos ^{2}\theta }}\right)$

we have $a=3$ feet. $b=6+1$ foot, $\theta =23^{o}\ 20'$

therefore,

$V^{2}=31.71$ and $V=5.63$ feet per second,

which is the horizontal velocity that would have upset this block edgeways.

The actual velocity of the shock (i.e., of the wave itself in the direction of its path) was found to be almost 13 feet per second, at Polla, and from the very short distance (under five geogr. miles) between, was, in all probability, the same here. Therefore, the direction of emergence of the wave here, must have been at such an angle with the horizon, that its horizontal component, was less than 5·63 feet per second, or otherwise this front block must have been upset; that is, $e$ being the angle of emergence.

⁠5.63 feet $\times \sec e$ must be = less than 13 feet,

or,⁠ $\sec e$ = greater than 2·30;

therefore,⁠$e$ greater than 64°15'.

This is therefore the maximum angle of emergence, derived from the block of greatest stability, in the structure; but it is not the greatest possible maximum; for with the same path as before, the wave affected either of the two side blocks, $s\ s$, in the line of their least horizontal dimensions, or direction of least stability. We may consider each of these side blocks $s\ s'\ -s''\ s'''\ s''''$, as one mass, the superimposed pieces, having the same effect upon the overthrow, as