Page:Great Neapolitan Earthquake of 1857.djvu/181

II. OBLIQUE FORCE (Subnormal, Abnormal, and Subabnormal Waves).

Let $\mathrm {O'O}$ be the wave-path passing through any building whatever, as Fig. 99.

Let $\mathrm {OX}$ be perpendicular to the lines $\mathrm {OZ}$ and $\mathrm {OY}$, and let $\alpha$, $\beta$, and $\gamma$ be the angles made by $\mathrm {O'O}$, with $\mathrm {OX..OY..OZ}$.

If $\mathrm {V}$ = the total velocity, or that in the path of the wave, and $v_{x}v_{y}v_{z}$ the components along $\mathrm {X}$, $\mathrm {Y}$and $Z$, then

$v_{x}=\mathrm {V} \cos {\alpha }$

$v_{y}=\mathrm {V} \cos {\beta }$

(XI.)

$v_{z}=\mathrm {V} \cos {\gamma }$

The effect of $v_{x}$ in overturning the structure has been already considered. The component $v_{y}$ produces no direct effect in overturning, although its action parallel to $\mathrm {Y}$ may fracture and disintegrate the building.

If the structure is capable of being overturned in the plane of $\mathrm {YZ}$, and also in the plane of $\mathrm {XZ}$, the components $v_{x}$ and $v_{y}$ must act together, and compel it to turn round upon one of the extreme points in the line $\mathrm {OY}$. In that case, the motion ceases to be comparable with that of a compound pendulum, and is reduced to the movement of