CUPOLA AFTER THE ACTION OF
THIRTY-SEVEN 6 IN. PROJECTILES.]

In order to protect the masonry of the scarp, engineers first lowered
the cordon to the level of the covert-way. Under these circumstances,
the enemy, although he could no longer see it, reached it by a curved or
"plunging" shot. When, in fact, for a given distance we load a gun with
the heaviest charge that it will stand, the trajectory, AMB (Fig. 2), is
as depressed as possible, and the angles, a and a', at the start and
arrival are small, and we have a direct shot. If we raise the chase of
the piece, the projectile will describe a curve in space which would be
a perfect parabola were it not for the resistance of the air, and the
summit of such curve will rise in proportion as the angle so increases.
So long as the falling angle, a, remains less than 45 deg., we shall have a
curved shot. When the angle exceeds this, the shot is called "vertical."
If we preserve the same charge, the parabolic curve in rising will meet
the horizontal plane at a greater distance off. This is, as well known,
the process employed for reaching more and more distant objects.

[Illustration: Fig. 5.--STATE OF A CAST-IRON CUPOLA AFTER THE BREAKAGE
OF A VOUSSOIR.]

The length of a gun depends upon the maximum charge burned in it, since
the combustion must be complete when the projectile reaches the open
air. It results from this that although guns of great length are capable
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 (mv squared) 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