These may be removed either by arranging the lines of the work with this object in view, as in the bastioned system, or by means of auxiliary works, termed capon-nieres, scarp galleries, counterscarp galleries, etc, as in the polygonal system.-Bastioned System. If, supposing the place enclosed by a bastioned system, we connect the salients of the bastions by straight lines, these will form a polygon of as many sides as there are bastions. If the curtains be produced, they will form a second polygon within the first. They are respectively called exterior and interior polygons. Either of these may be taken as a general outline to enclose the place to be fortified. The exterior polygon is generally used, and sometimes called the polygon of the fortification. It may be regular or irregular. We will suppose the site to be fortified to be level or approximately so, and the polygon to be regular. There is an intimate relation between the length of the side of the polygon and the lengths of the lines of the fortification, which will be referred to hereafter. Assume the length of a side, called the exterior side, to be 380 yards. To lay off the lines of the work, some one line must be selected as the directing one.

In permanent fortifications the line of intersection of the front face of the scarp wall with the top or upper surface of coping is taken, and receives the name of magistral. In giving the method for locating the lines on one side or front, all the information necessary for the entire work will be known. Bisect the side of the polygon by a perpendicular, and lay off on it inside the polygon a distance equal to -1/8, 1/7-, or 1/6 of the side, according as the polygon is a square, a pentagon, or a polygon of a greater number of sides. In this particular case lay off 1/6, or 63.33 yards; this will be the distance for the hexagon or any greater polygon. Lines drawn through this point and the extremities of the exterior side determine the directions of the faces and the lines of defence. We may assume the lengths of the faces and then deduce the flanks and curtain, or assume the curtain and deduce the others. If we take the first plan, we lay off from the salient a distance equal to 2/7 of the exterior side, which gives us the length of the face and the positions of the shoulder angles; then draw the flanks, making an angle of 110° with the lines of defence or 100° with the curtain. Lay off on each flank a distance of 50 yards and join their extremities by a straight line.

This will give the curtain, 140 yards in length. This length of curtain admits of the flanks having a relief of 44.50 ft., and at the same time thoroughly sweeping the ditch in front of the curtain by the fire from them. Let X X, fig. 2, be the exterior side; then, following the foregoing construction, we have X Y the magistral of the face, Y Z of the flank, and Z Z the curtain. The line X Y produced to Z, the opposite extremity of the curtain, is the line of defence. From their positions it is evident that an intimate relation exists between these lines; any change in one affects all the others. The angle at X is called the salient angle of the bastion; X Y Z, the shoulder angles; Y Z Z, the curtain angles; and X X Y, the diminished angle. From an examination of the figure, it is seen that we have now laid out the plan of the enceinte. The heavy line parallel to the one constructed is the interior crest. Although drawn parallel in the figure, it is not absolutely so in practice. To explain these details would extend this article to a degree that is not admissible.

The other lines are easily understood by looking at the profile (fig. 1) taken on m' m' n' n'. Communication from the interior to the exterior is made by a postern through the middle of the curtain that comes out 6 ft. above the bottom of the ditch. A wooden ramp is used to descend from the postern to the ditch. In front of the curtain is placed the tenaille O, its form being a curtain parallel to that of the enceinte with two wings the scarps of which are on the prolongations of the scarps of the faces. It is separated from the curtain by a ditch 13 yards wide, and from the flanks by ditches 11 yards wide. It is intended to mask the masonry of the curtain and flanks and cover the postern. It is arranged for defence having its fire to bear upon the ditches. The object of the double capon-niere P is to afford a secure communication across the ditch, and to be a defensive work for the main ditch. The object of the demilune G is to secure the gates of the place from a surprise, to mask the flanks and curtains of the enceinte from the enemy's batteries, and to give cross fires on the salients of the bastions. They favor sorties by the strong reenterings made in the front.

The cuts K K are made to isolate its extremities from the salient portion, and prevent the enemy from driving the defence from the redoubts of the reentering places of arms if he should gain possession of the demilune. The demilune redoubt J is for the purpose of sweeping at close range the terreplein of the demilune, and render its defence more obstinate by the support it receives from the redoubt. The covered way D D, bordering the ditches of the main work and demilune, forms a secure communication around the entire work. It is an indispensable outwork, and is of the highest importance where an active defence is to be made. Traverses, a, a, are placed at intervals to protect the troops in it from ricochet fire, and are arranged for defence. The covered way is broken forward in the reentering angles for the purpose of enlarging the covered way at these points, and producing a flanking arrangement by which the glacis can be swept and a cross fire brought to bear upon the ground in front of the salients. Within this enlarged space, or reentering place of arms, a redoubt M is placed. Its object is to strengthen the covered way and sweep with its fire the enemy's establishments on the glacis of the demilune. Sometimes a redoubt is placed in the salient place of arms.