Page:Great Neapolitan Earthquake of 1857.djvu/90

48 is impressed upon it in the return from $$\mathrm{C}$$ through $$q$$ to $$\mathrm{A}$$, and it comes to rest, with the fissure somewhat closer than it was, at an intermediate moment just after its formation, unless fragments have fallen between and prevented this, and always assuming that its parts hold coherent. Proceeding now to follow the train of action upon the end wall $$b$$, the wave affecting almost simultaneously the whole building, the two side walls and the end wall $$b$$ are forced forward together, the movement as before, commencing at the instant the initial movement of the wave $$\mathrm{D}$$ reaches them. They both (side and end walls) pass through the point $$r$$ of maximum velocity nearly together, and so to $$\mathrm{E}$$, when the motion of the wave itself is zero, and the motion of its second semi-vibration commences, which is retrograde as before.

Fracture cannot occur at the end $$b$$ during the first semi-vibration $$\mathrm{D}r\mathrm{E}$$, because the side and end walls are alike urged forward together and at equal velocities: there is therefore nothing to produce separation. If fracture, therefore, take place at the end $$b$$, it must occur at the point of maximum velocity $$s$$, in the second semi-vibration, from which to $$\mathrm{D}$$, the motion of the wave continues to promote separation; but the momentum impressed at $$s$$ is = $$\mathrm{M}(\mathrm{V}-v)$$, whereas at the former end at $$p$$ it was $$\mathrm{MV}$$. The force necessary to produce fracture of the materials being the same at both ends (which is, however, only strictly true for absolutely equal velocities), the amount of movement impressed upon the mass at the end $$a$$, will be greater than that at the end $$b$$, by the momentum due to $$\mathrm{M}v$$, (neglecting any small restoration of position of $$a$$, at the return semiphase of the wave), and so if