Page:Great Neapolitan Earthquake of 1857.djvu/206

158 we find whence the angle of emergence or of projection is  and the velocity of projection  As the velocity of projection by earthquake-shock has been proved, by the examination of this shock of December, 1857, to be small, and therefore $$\mathrm{H}$$, the height due to it, also small; we can find either $$\mathrm{V}$$ or $$e$$, geometrically, by the application of Prof. Galbraith's very beautiful problem, for determining graphically, either of these quantities for a projectile; and as this method may be applied by any unmathematical observer, who measures on the ground, the vertical and horizontal heights of a body thrown, and can use a pair of compasses, it will be well to transcribe it.

Let $$\mathrm{A}$$ (Fig. 107) be the top of any tower or other elevation from which a body has been projected. From $$\mathrm{A}$$ draw $$\mathrm{AB}$$ vertical and $$= 4\mathrm{H} $$ ($$\mathrm{H}$$ being the height due to the velocity, supposed given). Through $$\mathrm{A}$$ draw $$\mathrm{AX}$$ horizontal. Bisect $$\mathrm{CB}$$ in $$\mathrm{Y}$$, and on $$\mathrm{BC}$$ describe the semicircle $$\mathrm{BXC}$$. Bisect $$\mathrm{BA}$$ in $$\mathrm{O}$$, and with $$\mathrm{O}$$ as centre and $$\mathrm{OX}$$ as radius