Page:Great Neapolitan Earthquake of 1857 Vol 2.djvu/384

coefficient, probably, somewhat too high for Apennine limestone.

Adopting that coefficient, the compression due to the pressure, of the mean focal depth, and of the maximum depth would be, respectively—

Mean f.d.=
Max. f.d.=

Pressure.
0·998
4·580

tons
⁠„

Compression in feet = $l$.
= 0·000445
= 0·00204

nearly.

The mean depth $o\ d$, (Diagrams Nos. 1 and 2 emergences) is 35,000 feet in round numbers, and the radius of the sphere of initial compression $o\ t$, due to the pressure of maximum depth = 71·25 feet. This is for statical pressure, and as the extension or compression of any elastic body, to which a given force is suddenly and at once applied, is double that due to the same gradually and slowly laid on—so here, the range of compression, for the suddenly-applied steam pressure, is double, or $o\ d$ = 142·5 feet, and the volume of the sphere of compression, = 0·5236 × 285³, and equal to the volume of the wave, or to the spherical shell, whose outer radius is 35,000 feet, and its thickness $d\ c$, which is also equal to the amplitude of the wave.

The actual thickness of the spherical shell, calculated on these data, and on the assumption that the compressing force, emanated from a physical point, at $o$ at the moment that the wave reached the surface at $d$; is very small, being only = 0·000787, of a foot.

If, however, upon the same data, we calculate the amplitude, on the assumption, that the impulse was conveyed, (Fig. 353) in directions from the plane of the fissure $f\ f'$, perpendicular to it, compressing both surfaces in the di-