Page:Great Neapolitan Earthquake of 1857.djvu/479

and from other observations yet to be referred to I conclude, that this arc was not more than 15° at either side the vertical, or with a horizontal chord at the centre of gravity of about 12 inches. We shall not make a sensible error, however, by assuming the arc described, as the largest possible.

Taking the time of oscillation from the equation

$T=\pi {\sqrt {\frac {l}{g}}}\times (1+{\frac {a}{8\,l}}+{\frac {9a^{2}}{256\times l^{2}}}+{\text{. . . . .}})$

where $a$ = ver sine of haft the arc of vibration; we have

$T=3.14{\sqrt {\frac {4.33}{32.2}}}\times (1+{\frac {.066}{8\times 4.33}}+{\frac {9\times 0.66^{2}}{256\times 4.33^{2}}}+{\text{. . . . .}})$

${\text{or }}=3.14\times .3668\times 1.0019{\text{ approximately,}}$

${\text{and }}T=1.5635{\text{ seconds;}}$

correction for latitude being needless.

From the moment of arrival of the first shock, up to the arrival of the second transverse to it, the chimney had made, one half and one complete, vibration, and possibly had just commenced another. At the moment that the chimney relapsed upon its base it lost vis vivâ, and therefore time, before it rose again, to complete the arc westward. This minute loss of time we can only estimate, because although we know the velocity at the moment the mass of the chimney struck its base, on resuming the perpendicular ($\mathrm {B}$, Fig. 237), we do not know its hardness, elasticity, &c., upon which at loss also depends.

Neither can we calculate precisely, how much of the commencing arc of the third oscillation had been performed (if any), before the second shock reached the chimney, because we do not know the precise point round which it rotated, &c.