Page:Great Neapolitan Earthquake of 1857 Vol 2.djvu/403

338 partly due to elasticity, and partly to small mutual displacements, of the separate blocks of stone; while in the case of an entire isolated steep hill, such as that of Saponara, the irregular form of the vibrating solid, which approaches nearest to that of a cone fixed at its base, as well as the imperfect homogeneity of its materials, and our ignorance of their precise nature, or of whether any or what intestine movements occur at the instant of shock in the interior, defy our obtaining by calculation, the proper velocity of oscillation of the summit, due to the velocity impressed at the centre of gravity, as distinct from that of the shock by any other method than experiment. It will be evident to the mechanician, however, that the elevation, of such an oscillating body, as well as the other conditions upon which L depends, will much affect the combined result, of the proper wave velocity, and that of the oscillation. When L is very great, as it must be, when so great as that of a lofty "colline" of limestone, some hundreds of feet in height, or where it is even that of a mere tower of moderate height, but whose modulus of elasticity, for the whole material, (i.e., the masonry, mortar, and stone, or brick, taken together), is small, then the time of oscillation being long, and the velocity of the summit small therefore, in relation to the time of the wave; the former may add but little to the total velocity deduced from the conjoint effect of both; and, in fact, with a given seismic wave velocity, and given modulus of elasticity of the oscillating mass, a determinate height, and that a very small one in reality, will produce the maximum total velocity.

If we took the true velocity of the seismic wave alone, at