Page:Great Neapolitan Earthquake of 1857.djvu/127

Rh therefore, and like direction of emergence and velocity of wave, the resistance to fracture $$\mathrm{F}$$, depends upon the cohesion per unit of surface and total area of fracture, and the resistance to fall $$\Sigma$$, upon the density of the masonry, the height, the breadth, and the square of that one of the two horizontal dimensions, which lies in the direction of the shock, and may be called the thickness.

The mass being severed free, from all others, by fracture, it depends upon the value of $$(\tau \pm \tau')$$, and upon the emergent angle of the wave, whether it shall fall forward, in the direction of the wave transit, or in the reverse one. And from the nature of the applied force (being that of inertia), $$\delta$$ disappears.

Such are the general conditions as to equilibrium, upon which the fracture and fall of the separated masses, producing final dissolution of the building or structure, depends, and from which, equations for various architectural forms and conditions may be deduced.

The circumstances of fall of simple rectangular buildings have now been explained. Cruciform buildings, such as churches, are affected much in the same ways, the twelve sides of such a building being, in fact, capable of being viewed or arranged, as separable into those as three simple rectangular ones.

Polygonal buildings are rare, and when the number of sides are few, and the length of each considerable, do not present features materially different.

Cylindrical buildings, or conic frastra, however, which may be viewed as polygons of an infinite number of sides, have some peculiarities.

Whatever be the direction of shock, if horizontal, upon