Page:Great Neapolitan Earthquake of 1857.djvu/190

cylinder, whose height above the horizontal plane of fracture is ${\displaystyle a}$, then ${\displaystyle f={\frac {a}{2}}}$. If ${\displaystyle \mathrm {L} }$ 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

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

(XXI.)

or

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

(XXII.)

Here

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

(XXIII.)

therefore

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

(XXIII.)

Here

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

(XXIII.)

therefore

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

(XXIV.)