Page:Great Neapolitan Earthquake of 1857.djvu/197

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Before concluding this section, it remains to assign the values of the coefficient 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

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

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 P be applied at once (suddenly), then 2 W = P l, the accumulated work, is twice that necessary for fracture, or \frac{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

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