Page:Great Neapolitan Earthquake of 1857 Vol 2.djvu/361

height of the barometric column, $\epsilon$the modulus of elasticity, and $\mathrm {D}$the density of the body torn; for this, the velocity of sound, or of force transmission, in the given solid, is the limit of the rate at which the rending force can be propagated, from particle to particle. Again, a force will produce rending by impulse, when its velocity

$V={\frac {\mu }{\phi }}$

$\mu$, being the modulus of force transmission, involved in the former equation, and $\phi$ that of final extension or compression at rupture; and in this case, the progress of the rent may merely follow on, at the velocity ${\frac {\mu }{\phi }}$^[1]

These are the limits of the rate, at which the focal cavity enlarges in any one dimension, by rending; and as the amplitude of the wave impulse, at the instant of its original transmission, depends upon the range of original disturbance, that is, upon the length of the rent, or enlargement of the focal cavity, which has already occurred at that instant, and upon the velocity together, (which, if it fall below the latter value of $\mathrm {V}$ ceases to generate a wave at all;) so, at the instant the rending or enlargement of the focal cavity commences with sufficient velocity, (tremulous,) waves of extremely small amplitude, begin to be transmitted; their amplitudes rapidly increase up to a maximum and then suddenly diminish to 0.

Such waves of very small amplitude, at the commencement and end, are those of the tremors, and most probably of the sounds; although it is as yet not quite certain, that

1. See 'Mallet on the Physical Conditions involved in the Construction of Artillery, Trans. Roy. Irish Acad.,' Vol. xxiii., Part I.