Page:Great Neapolitan Earthquake of 1857.djvu/190

cylinder, whose height above the horizontal plane of fracture is $a$, then $f={\frac {a}{2}}$. If $\mathrm {L}$ be the modulus of dynamic cohesion—a coefficient representing the length of a prism of the same material, whose weight is equal to the force upon the unit of surface, if suddenly applied, which is sufficient to tear it directly asunder,—then

$V=g\times {\frac {\mathrm {L} }{a}}\times {\frac {K^{2}}{f\beta }}$

(XXI.)

or

$V=2g\times {\frac {\mathrm {L} k^{2}}{a^{2}\beta }}$

(XXII.)

1st. In the case of a solid cube, fractured from its horizontal base.

Here

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

(XXIII.)

therefore

${\begin{cases}V={\frac {2}{3}}g\times {\frac {\mathrm {L} }{\alpha }}\\or\\V=21.46{\frac {\mathrm {L} }{\alpha }}\end{cases}}$

(XXIII.)

2nd. In the case of a solid parallelopiped, fractured from its horizontal base.

Here

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

(XXIII.)

therefore

${\begin{cases}V={\frac {2g}{3}}\times {\frac {\mathrm {L} \beta }{\alpha ^{2}}}\\or\\V=21.46{\frac {\mathrm {L} \beta }{\alpha ^{2}}}\end{cases}}$

(XXIV.)