Page:Great Neapolitan Earthquake of 1857.djvu/126

84 transit of the wave; $$i$$, the slope of the joint, if any, to the horizon; $$r$$, the fraction of $$t$$, that measures the distance of the point where the line of resistance cuts it, from the mid-length; $$r'$$, the distance from the bisecting point of $$t$$, to where it is intersected by the vertical through the centre of gravity of the mass, $$\mathrm{W}$$ its weight, and $$\Sigma$$ its moment of stability; then

according as the line of resistance and the vertical through the centre of gravity, are at the same or at opposite sides of the bisection of $$t$$.

The weight of the mass (whatever be its form, assumed approaching regular), may be expressed

$$\phi$$ being a factor, determined by the angles that its three dimensions $$l$$, $$b$$, and $$t$$ make with each other, and on its form, and $$\delta$$ the specific gravity of the masonry. Therefore

If $$\mathrm{F}$$ be the force necessary to fracture the mortar at the joint $$t$$, acting in the direction of the wave transit,

is equal the total resistance of the mass to being overturned by the force of the shock, acting at the centre of gravity in the same line, but opposite direction

For similar forms of the fractured and separated masses,