Page:Great Neapolitan Earthquake of 1857.djvu/196

148 but not overthrown, the velocity impressed was sensibly no more than sufficient for fracture; if it be overthrown also, it was sufficient for both. Hence, if $$v_{f}$$ = the velocity determined by the Eq. XXI. to XXXV. for fracture only, and $$v_{t}$$ = that for overturning only, by the Eq. I. to XX., the total velocity of the wave will be found It may occur, that a structure shall be fractured from its base, but not overturned, (merely caused to oscillate within narrow limits), by the first semiphase of the wave; and being so broken, may be overturned in the direction of wave-transit, by the second semiphase; in such an example (which is of rare occurrence) the change of sign, in the second members of the equation, must be attended to, and also whether the proper velocity of the mass, viewed as a pendulum, in returning back upon its base, may have conspired with the velocity of the wave itself, in its second semiphase, to overturn the body. In such an example, if the wave be subnormal, with a pretty large angle ($$e$$), the impressed velocity will generally be found sufficient, to have projected the structure (if falling entire) to some distance from its base, as well as to have overturned it.