Page:Great Neapolitan Earthquake of 1857.djvu/197



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 $$\mathrm{P}$$ 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