Page:Great Neapolitan Earthquake of 1857.djvu/110

70 that produced the fractures at $$n$$ and $$w$$; $$f''$$ the vertical component corresponding to these; $$u$$ the intersection of the polar (or direction of emergence of the wave), with the plane passing through $$n$$, $$w$$ and $$p$$.

The angles made by $$o p$$ and $$a b$$ = 90°.

R being the common resultant of $$f$$, $$f'$$, $$f''$$, in $$a b$$.

Then $$\mathrm{L} + \mathrm{M} : \mathrm{L} - \mathrm{M} :: \tan \frac{1}{2} \phi : \tan \frac{1}{2}(\theta - \theta')$$

$$\tan \frac{1}{2}(\theta - \theta') = \frac{\tan \frac{1}{2} \phi (\mathrm{L} - \mathrm{M})}{\mathrm{L} + \mathrm{M}}$$

But $$\sin \theta : \mathrm{L} :: \sin \rho : 2 \mathrm{Y}$$

as the diagonals $$s e$$ and $$w n$$ mutually bisect