Page:Great Neapolitan Earthquake of 1857.djvu/197

From Wikisource
Jump to: navigation, search
This page has been validated.


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

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.}