Page:Great Neapolitan Earthquake of 1857.djvu/197

CHAPTER XVII.

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

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Before concluding this section, it remains to assign the values of the coefficient $\mathrm {L}$ 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

$\mathrm {W} ={\frac {1}{2}}\mathrm {P} l$

${\mathfrak {A.}}$

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

$\mathrm {L} =L\delta ={\frac {\mathrm {P} }{2}}$

${\mathfrak {B.}}$