228

OF PROJECTILES.

represents unity: on the contrary, if the shell at thepoint F meet a horizontal plane, a~o\ in this cafe,there will be no shock, and the shell will roll upon theplane.

3. If the shell strike the point B in the plane Z yinclined to the horizon with a direct struck, its forcewill be to the force of a shock on the horizontal planeB Q_, as the whole sine is to the right sine —« of theangle of incidence H B Q_: wherefore, if the shell in-stead of striking the horizontal plane B Q_, strikethe inclined plane I O, the force of the shock will beless; and will be in the proportion of the right sine of theangle of incidence IIBI to the sine of the angleHBQ.

4. If two (hells be projected from two mortars ofdifferent calibres, but of similar proportions, fired withthe largest quantity of powder, and with the fame de-gree of elevation ; the largest shell will have the mostforce in the corresponding points of the curves, owingto its superior weight, and greater compound velocity(229); since it describes a larger curve.

5. If two shells of different diameters, fired as above,in corresponding points of their curves strike two ob-jects in differently inclined planes, the shock of the leastshell may exceed that of the largest ; because the angle ofincidence of the latter may be most acute.

237. To strike with a direct shock, and with great force,a superficies whose position is given (234); it is necessary :

1. To place the mortar so that the axis producedmay cut the vertical plane of the object ; and that thecurve described by the shell, be at right angles to it atthe point of impact.

2. To use the largest quantity of powder that thechamber of the mortar can contain.

3. To observe the relative position and figure of thegiven superficies, whether flat, or convex like the roofof a casemate; whether horizontal or inclined.

4. Thence to determine the distance that the mortarshould be placed from the object and its proper elevation.

238. It is observed, that the curve described by shellsdoes not always cut the vertical plane of the object, in thedirection of the axis of the mortar, but deflects from it so asto describe a double curve. The solid sphere of bronze

projected