Page:Great Neapolitan Earthquake of 1857.djvu/104

$a$ and $b$ being equal or proportionate to the widths of $n$ and $w$, therefore—

$a:b::1:\tan \theta ',$

or

$b=a,\tan \theta '$

hence

$\tan \theta '={\frac {b}{a}};$

from which either the angle $\theta '$ or its sine can be had from the tables.

As the path of the wave divides the angle made by the two walls (whether the building be square or not) in the ratio of

$\sin \theta :\cos \theta ,{\mbox{ or of }}\sin \theta :\sin \theta ',$

its direction may be easily got geometrically, by an observer not accustomed to trigonometry.

It sometimes happens that eight main fissures may be observed, alternately wide and narrow, in a rectangular building exposed to an abnormal wave. This only happens when the building approaches a square in plan, the abnormal angle being not far from 45°, and the walls very uniform in structure and mass, and built of small material, such as brick.

There are then two fissures, one wider than the other, near each quoin, as in Fig. 39; four are primary and due to the direct action of the wave, the other four seem to arise from the shearing strains in the plane of the respective walls. The case is unusual, but when met with is best rejected for seismometry, as likely to lead to error.

The walls are sometimes, though rarely, found as in Fig. 42, the middle portions of $c$ and $d$ first reached by the wave, being overthrown inwards, and those $a$ and $b$ leaning