Page:Great Neapolitan Earthquake of 1857 Vol 2.djvu/159

but may be judged by "tact" to have been very near 45° E. of north, or between that and 55° E. of north, the plane of the wall being 110° E. of north. It gives a tolerable measure of velocity. The wall was 26 feet in height, 4 feet in thickness at the base, and the velocity was obviously not quite, but very nearly sufficient, to overturn its unsupported extremity; the angle θ is here = 8^o 30'; $a=26;\ b=4$.

The horizontal velocity necessary for overthrow is therefore first to be calculated without reference to the dislocation of the masonry, which was of inferior quality, and not above one-fourth the strength of the best limestone rubble work, and then the fracturing velocity for the latter, and both added, and resolved from the horizontal direction, and perpendicular to the plane of the wall, into the direction of the wave-path.

The horizontal velocity of overthrow is

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

$V^{2}=42.93\times 26.3\times 0.0112=12.64$;

$V=v_{t}=3.555$ feet per second.

The horizontal velocity for fracture is

$v={\frac {2}{3}}g\times {\frac {L\beta }{a^{2}}}$

$\mathrm {L}$ here 52/4, one-fourth the coefficient for the best rubble masonry, and,

$V=v_{f}=42.93\times 0.153=6.568$ feet per second.

$v_{t}+v_{f}=3.555+6.568=10.123$ feet per second,

therefore, would have been a velocity, which if applied