Page:Great Neapolitan Earthquake of 1857 Vol 2.djvu/409

enabled to deduce from their movements, a measure of the amplitude of the wave at Naples. In this aspect, however, the problem (exactly stated) leads to a differential equation, which cannot be integrated, but in the investigation, the difference of velocity in the two semiphases was evolved.

The velocity of the horizontal component, of the wave of shock, (which may be viewed as practically identical with the velocity of the wave, at Naples,) being known, the arc φ through which a pendulum will be swung by a single undulation of shock, is given by the following expression, or φ being given, $\mathrm {V}$ can be obtained.

$V^{2}=2gl(1-\cos \phi )$

And if the time between the like points, in the two semiphases, or time of the wave, be very small, compared with the time of vibration due to $l$, the length of the swinging pendulum, then this velocity will express the loss of velocity of the second semiphase as compared with the first one.

Applying this to the Naples chandeliers, we had one 4 feet 5 inches long, and having a certain time of oscillation by trial, (Part II.) from which,

$l=g\times {\frac {T^{2}}{\pi ^{2}}}=3.25$ feet;

then$\sin \phi ={\frac {105}{1060}}$,

and$\mathrm {V} =1.02$ feet per second.

In the other pendulum (Lardner's chandelier), 8 feet 9 in. long, &c., we have, in the same way,

$l=6.987$ feet,

$sin\phi ={\frac {11}{105}}$,

and$\mathrm {V} =1.57$ feet per second.