Page:Great Neapolitan Earthquake of 1857 Vol 2.djvu/356

that occurring at the same time up and down; then $\mathrm {T} =$ the time of rending sound will be

$\mathrm {T} =t+{\frac {\sqrt {d^{2}+x^{2}}}{v}}$

when it shall reach the ear from $x$. Therefore, the whole noise of rending, from $o$ to $x$, will reach the ear in the time,

$\mathrm {T} '=t+{\frac {{\sqrt {d^{2}+x^{2}}}-d}{v}}$

but $x$ and $t$ remaining the same for every station, and $d$ being variable, this function diminishes rapidly as $d$ increases, and at an infinite distance is equal to $t$. Hence the nearer the station of the hearer is to the middle of the length of the fissure, (as the above is true from 0 to $x$, in both directions of rending, from the centre or main focus,) in a line perpendicular to its plane, and the further he is off, provided he hear it at all, the more short, abrupt, and explosive like, will the sound appear to him: while, on the contrary, the more oblique, or nearly in the line of the fissure, he is situated, the more he will hear it, as a long rushing sound.

But as the fissure has considerable vertical dimensions, as well as horizontal ones, this is pro tanto true, for a vertical plane, as well as for the horizontal one; and hence, even were the fissure instantaneously opened, to its whole extent, as if by a single effort, no hearer could be so situated upon the earth's surface, as to hear the noise, however short and abrupt, as a single explosion, but must hear it as a prolonged sound.

In fact, it is quite analogous to standing a good way off, at the centre, of the front or rear, of a long line of troops,

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