Page:Great Neapolitan Earthquake of 1857.djvu/111

and

but as ${\displaystyle {\text{L}}+{\text{M}}:{\text{L}}-{\text{M}}::\tan {\frac {1}{2}}\rho :\tan {\frac {1}{2}}(\sigma -\tau )}$

and ${\displaystyle \angle }$${\displaystyle \tau ={\frac {1}{2}}\rho }$, + arc corresponding to, ${\displaystyle \tan {\frac {1}{2}}(\sigma -\tau )}$
${\displaystyle \angle }$${\displaystyle \sigma ={\frac {1}{2}}\rho }$ – the same arc.

Again, ${\displaystyle \sin \tau :{\text{L}}::\sin \phi :2x}$

${\displaystyle 2x={\frac {{\text{L}}\sin \phi }{\sin \tau }}}$ = the distance from one fracture to the other diagonally opposite

which gives the angle of emergence, or that made by the polar ${\displaystyle a,~b,}$ of the subabnormal wave, with the horizon.

${\displaystyle 2\times {\frac {y}{\cos \theta ''}}}$ = R, the common resultant in the polar ${\displaystyle ab,}$ and, ${\displaystyle 2y\tan \theta ''=f''}$ the vertical component.

An extremely easy method may be practised of finding the path of a subabnormal wave by an observer in the field.

Referring to Fig. 44. Let a line be stretched across the top of the walls (or anywhere below that, but horizontally), from the exterior or interior angle of fracture,