lin, redoubts, and tenaille, are 6 feet, and that of the enceinte 12 feet. The breadth of the terreplein is 24 feet, and base of interior slope 14; the breadth of the terreplein of the ravelin is 18 feet, and the base of its interior slope 10 feet. The relief of the principal works in this system is as follows:-The crest, that is, the uppermost edge, of the principal parapet is 22 feet above the plane of site; that of the ravelin 16 feet, and of its redoubt 18 feet; of the tenaille 4 feet; of the redoubt in the re-entering place of arms 16 feet, and of the glacis there 11 feet; and of the glacis at the salient place of arms 9 feet. The salient place of arms is the space left by rounding off the counterscarpe of the ditch at the salient angles, as at A and E. The depth of the main ditch below the plane of site is 24 feet; of that of the ravelin 18 feet; of its redoubt 6 feet; and of the redoubt of the place of arms 8 feet. There are ramps, that is, oblique sloping passages cut in the interior talus or slope of the rampart, or at S', to facilitate the ascent and descent of troops and artillery. Their breadth is 10 or 12 feet; and their base, or horizontal length, is at least 6 times the height of the rampart. A barbette battery is represented within the flanked angle of the bastion A'. When guns fire over a parapet without embrasures, they are said to fire en barbette. Embrasures are openings cut down from the top of the parapet to within 3 feet of the level of the terreplein, and are 2 feet wide at the bottom on the inside, and nearly 4 feet broad at the top. The lower side or sole is parallel to the superior slope of the parapet, and its horizontal width. at the exterior slope of the parapet is about 9 feet. The embrasures are placed at intervals of about 18 feet. A parapet, when constructed without a banquette for musketry or embrasures for guns, is called an epaulement. This method is allowed to possess considerable superiority over Vauban's first system; but it is admitted by the best judges that the important problem still remains unsolvedto construct a system of fortification to which no wellfounded objections can be made. 272. In determining the slope of a glacis, it must be observed that its plane when produced ought not to pass above any of the lower or artillery lines of fire; and the slope, or plonge, of the parapets should be so regulated, that the guns of the garrison may be enabled to bear upon the enemy's works when near; but it ought not to be so great as to weaken the upper part or crest of the parapet. As a musket ball is not effective at a greater distance than 160 fathoms, the length of the lines of defence of any part of the works ought not to exceed this distance. 273. Of two batteries having equal fronts, that whose fire is directly across the front is the more advantageous. Let DE be an object to be fired at from the oblique battery, BC. E MAXIMS. D B A Divide BC into an equal number of parts, and let one of its divisions be the space required for one gun; then it is evident that there is space for no more guns in the oblique battery, BC, than in the direct one, AB, and the oblique battery is not so convenient for firing from. When ED is a counter-battery, the oblique one, BC, will not sustain its fire any better than the battery AB. For, if BC and AB are erected at the same expense, BC must be narrower than AB, in the proportion of AB to BC. Now, the oblique impact of a ball in the line DC upon BC is weaker than its direct impact on AB, in the proportion of DL to DC, or of AB to BC; and therefore the strengths of the two batteries are exactly proportional to the force of the impact against them. 274. If the fire from a battery is to be directed towards a point, as P, the battery ought to be of a circular form, its centre being the above point, as ABC. The sloping lines across the parapet ABC represent embrasures. If the fire of a battery is to be directed to a line DE, it ought also to be of the form of a circular arc P ABC, such that the radius through its extremities AD, CE, may make equal angles with the line DE. E A F 275. The larger the inclination of two faces of a work, that is, the greater any salient angle of it is, the better will it be defended. B G E C D B H A For, since the men fire generally in a direction perpendicular to the line, if ABC is a greater angle than BCD, the undefended space EBF will be less than the corresponding space GCH. The greater the number of sides of a fortress, the better is it defended. For the undefended angular spaces are less than when the polygon has fewer sides. They also contain more space within the same boundary, and can therefore contain a larger garrison, and afford a greater number of men for defending the outworks, and they require fewer outworks to give them the same degree of strength. A dodecagon will contain upwards of 5000 men, and requires an army of 50,000 to invest it. Polygons of fewer sides can contain fewer men, and can be invested by a smaller force. FIELD FORTIFICATIONS. 276. As field fortifications are only temporary works, they are generally constructed in a less substantial and complete form than a regular fortress. As field works are attacked on many points at once, in the direction of the capitals, the dispositions for defence require to be somewhat different. Some of the more important maxims for constructing them are the following: A salient angle should not be less than 60°, at least when it has no flank defence. The length of the lines of defence ought not to exceed 80 fathoms. Protect the salient angles by some other works, unless there happen to be natural obstacles in front of them sufficient to prevent the assailants from attacking them in the direction of their capitals. There ought to be as many flank defences as possible. Any part of the works that affords a flank defence to another part, ought to be inclined to it at an angle not less than 90°, and exceeding 90° as little as possible. There ought not to be any cover near the works that would allow the enemy to approach unperceived. The following are the principal parts of which field works are composed : : Redans, or Flêches. 277. A redan consists of two faces, inclined at a considerable angle like those of a bastion. These works are frequently used in the field when an obstinate defence is not required, and when they can be easily defended in the rear, where they are otherwise unsupported. They are sometimes placed before other works to strengthen them. No rule can be given for their construction, as B they vary in dimensions with the nature of the ground and other circumstances. Têtes-de-Pont. 278. Têtes-de-pont, or bridge heads, are works similar to redans, intended to defend the passage of a bridge or other communication across a river. When the communication is of much importance, other works are erected without the simpler one, of the redan form, of greater extent, and encompassing it. Redoubts. с 279. Redoubts are works enclosed on all sides, sometimes triangular, and sometimes square. A redoubt is sometimes of a square form, without any bastions, or any means of flank defence. They are sometimes triangular, with half bastions, as ABC. Triangular redoubts sometimes have no bastions at the corners; but, instead of them, they have complete bastions placed in the middle of the sides. Redoubts are isolated works intended to cover an advanced post or a retreat, to defend a height, a defile, or a communication, or the passage of a bridge or river. Various practical rules are given for determining the dimensions of a redoubt, according to the number of the garrison. Field Forts. Field forts are commonly of a regular figure, and are named according to the number of the salient angles. Thus, according as it has four, five, or six salient angles, it is called a square, pentagonal, or hexagonal fort. Forts that have alternate, salient, and re-entering angles, are called star forts. The sides ought not to be less than 50 nor greater than 100 feet. Star forts have seldom fewer than five salient angles. Bastion forts are forts with bastions. Forts of this kind, with redans for bastions, are inferior to the star forts; but when the bastion is complete, this kind of fort is advantageous. In such a fort the sides ought not to be less than |