[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 as the Krupp 6 inch and De Bange 6 and 8 inch, make a breach, the two former at a falling angle of 22 deg., and the latter at one of 30 deg..  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.]

The effect of 6 and 8 inch rifled mortars is remarkable.  The Germans have a 9 inch one that weighs 3,850 pounds, and the projectile of which weighs 300.  But French mortars in nowise cede to those of their neighbors; Col.  De Bange, for example, has constructed a 101/2 inch one of wonderful power and accuracy.

Seeing the destructive power of these modern engines of war, it may well be asked how many pieces the defense will be able to preserve intact for the last period of a siege—­for the very moment at which it has most need of a few guns to hold the assailants in check and destroy the assaulting columns.  Engineers have proposed two methods of protecting these few indispensable pieces.  The first of these consists in placing each gun under a masonry vault, which is covered with earth on all sides except the one that contains the embrasure, this side being covered with armor plate.