Page:Great Neapolitan Earthquake of 1857.djvu/399

perforations in the front, ends, and back, and was neither overthrown nor shoved out from the wall at back.

Referring to the Equation V., Part I.,

$V^{2}={\tfrac {4}{3}}g{\sqrt {a^{2}+b^{2}}}\times ({\frac {1-\cos {\theta }}{\cos ^{2}{\theta }}})$

we have here $\theta =33^{\circ }{\text{, }}\alpha ={\text{ 4.75 feet, and }}b=2.80{\text{ feet, }}$ as the mass must have fallen over, by rotating upon the most advanced angle at the base. Solving for $V$, therefore, we find the horizontal velocity necessary to have produced overthrow to be

$V=7.378{\text{ per second}}$

but $e$, the angle of emergence here, we have found to be 55° 49' from the "camine," and ${\text{V}}$, the velocity in the path of the wave, is

${\text{V}}=V\sec {e},$

whence

${\text{V}}=13.1328{\text{ feet per second.}}$

The velocity, ${\text{V}}$, given by the "camine," which was overthrown, is 12.863 feet per second by our first calculation; that necessary to overthrow this cabinet, which was not overthrown, we find is 13.133. We have therefore obtained the true value for ${\text{V}}$, within limit of the difference, or within 0.270 feet per second of the total velocity—a possible error of less than 21/2 inches per second.

The maximum velocity of the wave vibration at Polla may therefore be concluded with confidence to have been in round numbers 13 feet per second. The mean velocity obtained from both calculations, 13.176 feet per second, is a little more (0.043 feet per second) than sufficient to have overturned this cabinet; but the slightest inequality in its loading, or in its parts, by altering the height of the