Page:Great Neapolitan Earthquake of 1857.djvu/194

8th. In the case of a solid parallelopiped, fractured from its horizontal base, by subnormal wave.

Here

$k^{2}={\frac {\beta ^{2}}{3}}$

$a={\frac {1}{2}}\alpha \sec {\phi }$

and substituting in Eq. XXIX., we find

${\begin{cases}\mathrm {V} ={\frac {2}{3}}g\times {\frac {\mathrm {L} \beta }{\alpha ^{2}}}\times {\frac {\cos {\phi }}{\cos {(\phi \pm e)}}}\\or\\\mathrm {V} =21.46{\frac {\mathrm {L} \beta }{\alpha ^{2}}}\times {\frac {\cos {\phi }}{\cos {(\phi \pm e)}}}\end{cases}}$

(XXXI.)

9th. In the case of a right circular solid cylinder, fractured from its horizontal base, by subnormal wave.

Here

$k^{2}={\frac {5}{16}}\beta ^{2}$

$a={\frac {1}{2}}\alpha \sec {\phi }$

therefore

${\begin{cases}\mathrm {V} ={\frac {5}{8}}g\times {\frac {\mathrm {L} \beta }{\alpha ^{2}}}\times {\frac {\cos {\phi }}{\cos {(\phi \pm e)}}}\\or\\\mathrm {V} =20.12{\frac {\mathrm {L} \beta }{\alpha ^{2}}}\times {\frac {\cos {\phi }}{\cos {(\phi \pm e)}}}\end{cases}}$

(XXXII.)

10th. In the case of a hollow parallelopiped, fractured from its horizontal base, by subnormal wave.

Substituting for $k^{2}$ and $a$ their values

$k^{2}={\frac {\beta ^{2}(\beta +2\gamma )}{4(\beta +\gamma )}}$

$a={\frac {1}{2}}\alpha \sec {\phi }$