# Page:Great Neapolitan Earthquake of 1857.djvu/197

CHAPTER XVII.

VALUES OF THE COEFFICIENT ${\displaystyle \scriptstyle {\mathrm {L} }}$.

Before concluding this section, it remains to assign the values of the coefficient ${\displaystyle \mathrm {L} }$ for practical use.

It consists of two factors: the tenacity or resistance to rupture, by a force suddenly applied; and the specific gravity of the mass fractured off, by direct pull from an unit of section.

When a direct force, producing fracture by extension, is gradually applied to any prism, whose length and section are both unity, the work necessary to produce the rupture is

 ${\displaystyle \mathrm {W} ={\frac {1}{2}}\mathrm {P} l}$ ${\displaystyle {\mathfrak {A.}}}$

${\displaystyle \mathrm {P} }$ being the static load gradually applied, and ${\displaystyle l}$ the amount of extension of the body on the unit of length at the limit of rupture. But if ${\displaystyle \mathrm {P} }$ be applied at once (suddenly), then ${\displaystyle 2\mathrm {W} =\mathrm {P} l}$, the accumulated work, is twice that necessary for fracture, or ${\displaystyle {\frac {\mathrm {P} }{2}}=}$ the force, whose tension suddenly applied, as by an earthquake shock, shall rupture the prism.

This force we suppose applied by the weight of a prism of the material fractured, whose base is the unit of section fractured; or being the specific gravity

 ${\displaystyle \mathrm {L} =L\delta ={\frac {\mathrm {P} }{2}}}$ ${\displaystyle {\mathfrak {B.}}}$