Page:Great Neapolitan Earthquake of 1857.djvu/126

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

$\Sigma =\mathrm {W} \times (r\pm r')t\cos i,$

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

$\mathrm {W} =\phi \times lbt\times \delta$

$\phi$ 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

$\Sigma =\phi (r\pm r')\cos i\times lbt^{2}\times \delta .$

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

$\mathrm {F} +\phi (r\pm r')\cos i\times lbt^{2}\times \delta$

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

$\mathrm {V} \times \delta \times lbt\times \delta .$

For similar forms of the fractured and separated masses,