demi-lunes are untenable, and the ditches partly filled up; disorder and confusion prevail on all sides. No breach is practicable, certainly; but all the works are seriously injured on three or four fronts, and at one thousand yards distance, a breach may be made, and that a wide one. The garrison may sustain the assault to the last, and sell the possession of the _débris_ of its work dearly; but in this case the final result is not doubtful. [Illustration: FIG. 80.] In proportion to the length of the trajectory, therefore, the defence must remove its defensive arrangement from the centre of the place. [Illustration: FIG. 81.] If each front of Vauban's defence was about four hundred yards in length, it ought to be from thirteen to fourteen thousand yards now (Fig. 81). That is to say, the side of the hexagon which was four hundred yards--_i.e._, from one salient of a bastion to another--should be fourteen hundred yards. Let A be the main body of the fortress--on a plain suppose; forts will be erected at B and C, the zone of action of each of these works being eight thousand yards, they will protect each other and cross their fires without the possibility of their projectiles falling into the fortress if any of them should be in the power of the enemy. [Illustration: FIG. 82.] Fig. 82 presents the block plan of each of those forts B and C, to whose interior arrangements we shall return. But by this excessive lengthening of the _capitals_, the forts B (Fig. 81), may be swept along the whole extent of the arc of a circle _a b_ (more than the third of the circumference); they occupy the points of a triangle, and if one of them were taken the enemy would be able to batter two of the forts C. It is therefore necessary, with an extended radius, to multiply the defences, and to enable them to protect each other in a more effective manner. This is the method indicated in Fig. 83. Here we have a dodecagon. The forts of the outer zone are seven thousand yards apart, and the works, A, flank each other; a second zone of forts B commands the latter, if required, and the zone of action of these second works extends beyond the outer line of forts. Railways are required to connect the forts of each zone, and to put them in communication with the body of the place. This extension of the fields of defence may, according to the nature of the ground, be divided into two zones with a central nucleus. [Illustration: FIG. 83.] The interior zone would consist of permanent works, forming an _enceinte de préservation_; a line of forts at intervals sufficiently strengthened, in case of war, by field works. The exterior zone would be fixed by occupying strategic points well chosen and considered beforehand, forming small camps protected by temporary works, and affording security to a numerous army, whose manoeuvres the enemy could not espy.