of throwing projectiles with small charges, it is possible to use
shorter pieces for this purpose--such as howitzers for curved shots and
mortars for vertical ones. The curved shot finds one application in the
opening of breaches in scarp walls, despite the existence of a covering
of great thickness. If, from a point, a (Fig. 3), we wish to strike the
point, b, of a scarp, over the crest, c, of the covert-way, it will
suffice to pass a parabolic curve through these three points--the
unknown data of the problem, and the charge necessary, being
ascertained, for any given piece, from the artillery tables. In such
cases it is necessary to ascertain the velocity at the impact, since the
force of penetration depends upon the live force (mv²) of the
projectile, and the latter will not penetrate masonry unless it have
sufficient remanent velocity. Live force, however, is not the sole
factor that intervenes, for it is indispensable to consider the angle at
which the projectile strikes the wall. Modern guns, such as the Krupp 6
inch and De Bange 6 and 8 inch, make a breach, the two former at a
falling angle of 22°, and the latter at one of 30°. It is not easy to
lower the scarps enough to protect them from these blows, even by
narrowing the ditch in order to bring them near the covering mass of the
glacis.

The same guns are employed for dismounting the defender's pieces, which
he covers as much as possible behind the parapet. Heavy howitzers
destroy the _materiel_, while shrapnel, falling nearly vertically, and
bursting among the men, render all operations impossible upon an open
terre-plein.

[Illustration: FIG. 6.--STATE OF A CHILLED IRON CUPOLA BROKEN BY A 12
INCH BALL.]