in the first vertical column are the numbers expressing the lengths of the exterior sides from eighty to 260. In the second, the perpendiculars answering to these sides. In the third, the lengths of the faces of bastions; and in the fourth, the lengths of the capitals of the ravelins. The forts are mostly, if not always, squares : for which reason, the perpendiculars are made one-eighth of the exterior sides; because, if they were more, the gorges of the bastions would be come too narrow. In the little fortification or citadels, chiefly pentagons, the perpendiculars are made oneseventh of the exterior side. In mean fortification, from any number of sides to an hexagon upwards is used; and the great is seldom used but in an irregular fortification, where there are some sides that cannot be made less without much expense; or in a town which lies near a great river, where the side next the river is made from 200 to 260 toises; and, as that side is less exposed to be attacked than any other, the perpendicular is made shorter, which saves much expense. The faces of the bastions are all two-sevenths of the exterior sides, or nearly so, because the fractions are neglected. In general, in all squares, the perpendicular is one-eighth of the exterior side, and all pentagons one-seventh, and in all the rest upwards of one-sixth. Of the Construction of Orillons and retired Flanks.-Describe the front MPQRST as before, and divide the flank into three equal parts, of which suppose Sr to be one; from the opposite flanked angle M draw a line Mr, in which take the part mr of five toises; take likewise Rn in the line of defence MR, produced equal to five toises, and join nm, upon which as a base describe the equilateral triangle npm, and from the angle p, opposite to the base as centre, is described the circular flank nm. And if Sr be bisected by the perpendicular 1, 2, and another be erected upon the face ST, at S, the intersection 2 of these two perpendiculars will be the centre of the arc which forms the orillon. The orillons are very useful in covering the retired flanks, which cannot be seen but directly in the front; and, as these orillons are round, they cannot be so easily destroyed as they would be if they were of any other figure. Of the Construction of Ravelins or Half-moons.— Fig. 2. Set off fifty-five toises, from the re-enter ing angle O of the counterscarp, on the capital OL, or on the perpendicular produced; and from the point L draw lines to the shoulder A B; whose parts L M, LN, terminated by the counterscarp, will be the faces, and MO, ON, the semi-gorges of the ravelin required. This is Mr. Vauban's method of constructing ravelins, according to some authors: others say the faces of the ravelin should terminate on those of the bastions within three toises of the shoulders; which seems to be the best way, for these ravelins cover the flanks much better than the others. The ditch before the ravelin is twelve toises, its counterscarp parallel to the faces of the ravelins, and is made in a circular arc, before the saliant angle; as likewise all ditches are in general. When the ravelins are made with flanks, as in plate I. fig. 3, the faces should terminate on those of the bastions, at least five toises from the shoulders. The flanks are made by setting off ten toises from the extremities of the faces, from fto h, and from m to ; and from the points h, l, the flanks h k, p, are drawn parallel to the capital LO of the ravelin. There are sometimes redoubts made in the ravelin, such as in fig. 2, which is done by setting off sixteen toises from the extremities of the faces on the semi-gorges from N to h, and from M to a; and from the points b, a, the faces are drawn parallel to those of the ravelin; the ditch before the redoubts is six toises, and its counterscarp parallel to the faces. Of Tenailles.-A tenaille is a work made in the ditch before the curtains; the parapet is only two or three feet higher than the level ground of the ravelin. There are three different sorts; the first are those, as in fig. 4, which are made in the direction of the lines of defence, leaving a passage of five toises between their extremities and the flanks of the bastions, as likewise another of two in the middle for a bridge of communication to the ravelin. The second sort are as those in fig. 5. Their faces are in the lines of defence, and sixteen toises long, besides the passage of three toises between them and the flanks of the bastion; their flanks are found by describing arcs from one shoulder of the tenaille as centre through the other, or on which are set ten toises for the flanks desired. The third sort are those as in fig. 6. Their faces are sixteen toises, as in the second sort, and the flanks are parallel to those of the bastions. The use of tenailles, in general, is to defend the bottom of the ditch by a grazing fire, as likewise the level ground of the ravelin, and especially the ditch before the redoubt within the ravelin, which can be defended from no where else so well as from them. The first sort do not defend the ditch so well as the others, as being too oblique a defence; but, as they are not subject to be enfiladed, M. Vauban generally preferred them in the fortifying of places, as in the citadel of Lille, at Landau, New Brisac, and in many other places. The second sort defend the ditch much better than the first, and add a low flank to those of the bastions; but, as these flanks are liable to be enfiladed, they have not been much put in practice. This defect might however be remedied, by making them so as to be covered by the extremities of the parapets of the opposite ravelins, or by some other work. As to the third sort, they have the same advantage as the second, and are likewise liable to the same objections; for which reason, they may be used with the same precautions which have been mentioned in the second. Tenailles are esteemed so necessary, that there is hardly any place fortified without them; and with reason: for, when the ditch is dry, the part behind the tenailles serves as a place of arms from which the troops may sally, and destroy the works of the enemy and the ditch, oppose their descent, and retire with safety; and the communication from the body of the place to the ravelin becomes easy and secure, which is a great advantage; for by that means the ravelin may be a much better defence, as it can be supplied with troops and necessaries at any time. And, if the ditch is wet, they serve as harbours for boats, which may carry out armed men to oppose the passage over the ditch whenever they please; and the communication from the tenailles to the ravelin becomes likewise much easier than it would be without them. Of Lunettes.-Fig. 7, plate I. Lunettes are placed on both sides of the ravelin, such as B, to increase the strength of a place: they are constructed by bisecting the faces of the ravelin with the perpendicular LN; on which is set off thirty toises from the counterscarp of the ditch, for one of its faces; the other face, PN, is found by making the semi-gorge, TP, of twenty-five toises; the ditch before the lunettes is twelve toises, the parapet three, and the rampart eight, as in the ravelin. There is sometimes anotner work made to cover the saliant angle of the ravelin, such as A, called the bonnet, whose faces are parallel to those of the ravelin, and when produced bisect those of the lunettes; the ditch before is ten toises. There are likewise lunettes, such as D in fig. 8, whose faces are drawn perpendicular to those of the ravelin, within a third part from the saliant angle; and their semi-gorges are only twenty toises. These kinds of works may make a good defence, at no very great cost; for, as they are so near the ravelin, the communication with it is very easy, and one cannot well be maintained till they are all three taken. Of Tenaillons.-Fig. 9, plate I. Produce the faces of the ravelin beyond the counterscarp of the ditch, at a distance M N of thirty toises, and take on the counterscarp of the great ditch fifteen toises from the re-entering angle p'to 9, and draw Nq; then q N Mp will be the tenailles required; its ditch is twelve toises, that is, the same as that of the ravelin. Sometimes a retired battery is made in the front of the tenaillons, as in B; this battery is ten toises from the front to which it is parallel, and fifteen toises long. Retrenchments are commonly made in the tenaillons, such as O; their parapets are parallel to the fronts M N, and bisect the side qN; the ditch before the retrenchment is three toises; and there is a banquette before the parapet next to the ditch of about eight feet, called berm; which serves to prevent the earth of the parapet which seldom has any revetment from falling into the ditch. The ravelin, before which tenaillons are constructed, must have its saliant angle much greater than the former construction makes them; otherwise the saliant angles of the tenaillons become too acute; for which reason we made the capital of this ravelin forty-five toises, and the faces terminate within three toises of the shoulders. Of Counterguards.-Fig. 10, 11. When the counterguard is placed before the ravelin, set off forty toises on the capital of the ravelin from the saliant angle A to the saliant angle B, of the counterguard; and ten from C to D, on the counterscarp of the ditch. When the counterguard is before the bastion, such as in fig. 2, its saliant angle F is fifty toises from the saliant angle E of the bastion, and the breadth near the ditch of the ravelin ten toises as before. The ditch before the counterguards is twelve toises, and its counterscarp parallel to the faces. Counterguards are made before the ravelin on some particular occasions only; but are frequently constructed before the bastions, as covering the flanks wonderfully well. Some authors, as Mr. Blondel and Mr. Coehorn, will have them much narrower than they are here. Of Horn-works.—Fig. 12, plate I. Produce the capital of the ravelin beyond the saliant angle A, at a distance A B of about eighty toises draw DBE at right angles to A B; in which take BD, BE, each equal to fifty-five toises; and on the exterior side, D E, trace a front of a polygon in the same manner as that of the body of the place, making the perpendicular B F ten toises, and the faces thirty. The branches Da, Eb, of the horn-work, when produced, terminate on the faces of the bastions, within five toises of the shoulders. The ditch of the horn-work is twelve toises, and its counterscarp parallel to the branches; and in the front, terminates at the shoulders, in the same manner as the great ditch before the bastions. The capital of the ravelin before the front of the horn-work is thirty-five toises, and the faces terminate on the shoulders, or rather two or three toises beyond them: and the ditch before the ravelin is eight toises. Retrenchments are sometimes made within the horn-works, such as S, S; which are constructed by erecting perpendiculars to the faces of the ravelins, within twenty-five toises of their extremities. This retrenchment, like all others, has a parapet turfed only with a berm of eight feet before it; as likewise a ditch from three to five toises broad. Fig. 13. When a horn-work is made before the bastion, the distance D L of the front from the saliant angle of the bastion is 100 toises, and the branches terminate on the faces of the adjacent ravelins within five toises from their extremities; all the rest is the same as before. Of Crown-works. From the saliant angle, A, fig. 1, plate II. of the ravelin, as a centre, describe an arc of a circle with a radius of about 120 toises, cutting the capital of the ravelin produced at C; from the point C, set off the cords CB, CF, each of them equal to 110 toises; and on each of which, as an exterior side, construct a front of polygon of the same dimensions as in the horn-work; that is, the perpendicular should be eighteen toises, the faces thirty, and the branches terminate on the faces of the bastions within twenty-five toises of the shoulders. The ditch is twelve toises, the capital of the ravelins thirty-five, and its ditch eight; that is, the same as in the horn-work. Sometimes the crown-work is made before the bastions, as in fig. 2. The arc is described from the saliant angle A of the bastion, with a radius of 120 toises as before; and the branches terminate on the faces of the adjacent ravelins within twenty-five toises of their extremities: the rest of the dimensions and constructions are the same as before. Horn-works, as well as crown-works, are never made but when a large spot of ground falls beyond the fortification, which might be advantageous to an enemy in a siege, or to cover some gate or entrance into a town. Of Covert-ways and Glacis.-These are esteemed some of the most essential parts of a modern fortification; and it is certain the taking the covert-way, when it is in good condition and well defended, is generally the most bloody action of the siege. After having constructed the body of the place, and all the outworks which are thought necessary, lines are drawn parallel to the utmost counterscarp of the ditches, at six toises distant from it; and the space m n, m n, included between that line and the counterscarp, will be the covert-way required. Fig. 3. There is in every re-entering angle of the counterscarp a place of arms, m; which is found by setting off twenty toises from the reentering and angle a, on both sides from a to b, and from a to c: and from the points bc, as centres, arcs are described with a radius of twenty-five toises, so as to intersect each other in d; then the lines drawn from this intersection to the point b, c, will be the faces of the places of arms. If lines are drawn parallel to the lines which terminate the covert-way, and the places of arms, it twenty toises distant from them, the space r, ,, between these lines and those which terminate the covert-way, will be the glacis. At the extremities of the places of arms are traverses made, such as v, v, which serve to enclose them; these traverses are three toises thick, and as long as the covert-way is broad, and a passage is cut in the glacis round them, of about six or eight feet, in order to have a free communication with the rest of the covert-way. There are also traverses of the same dimensions before every saliant angle of the bastion and out works, and are in the same direction as the faces of those works produced; and the thickness lies at the same side as the parapets. The passages round these last traverses are likewise from six to eight feet wide. In each place of arms are two sally ports, z, z, which are ten or twelve feet wide, for the troops to sally out in time of a siege they are shut up, with barriers of gates. Of Arrows and Detached Redoubts.-An arrow is a work made before the saliant angles of the glacis, such as A, fig. 3. It is composed of a parapet of three toises thick, and forty long; and the ditch before it five toises, terminating in a slope at both ends. The communication from the covert-way into these arrows is four or five toises wide; and there is a traverse, r, at the entrance, of three toises thick, with a passage of six or eight feet round it. A detached redoubt is a kind of work much like a ravelin, with flanks placed beyond the glacis, such as B; they are made to occupy some spot of ground which might be advantageous to the besiegers; likewise to oblige the enemy to open their trenches farther off than they would do otherwise. The distance from the covert-way ought not to exceed 120 toises, that it may be defended by musket-shot from thence. The gorge, a b, is forty toises; the flanks, ac, bf, which are perpendicular to the gorge, ten; and the faces c d, f'd, thirty: the ditch before it is six toises, ending in slopes at both ends; the covert-way four; the branches of the covertway are forty-two toises long, or thereabouts; the faces of the places of arms y, y, which are perpendicular to the branches, ten; and the other, which is parallel to them, fourteen. The communication from the covert-way into the redoubt, is five or six toises wide: a traverse is made just at the entrance, and another in the middle when it is pretty long. The parapets of this communication terminate in a slope or glacis. If these redoubts are above fifty toises distant from the covert-way, the besiegers carry their trenches round, and enter through the gorge; by which means the troops that are in them are made prisoners of war, if they do not retire betimes; to prevent which some other outworks should be made to support them. Of Second Ditches and Covert-ways.—Plate II. fig. 4. When the ground is low, and water to be found, there is often a ditch about ten or twelve toises made round the glacis; and opposite to the places of arms are constructed lunettes, beyond the ditch: such as D, whose breadth on the counterscarp of the ditch is ten toises, from b to a, and from c to d; and the faces a L, d L, are parallel to those of the places of arms; the ditch before them is from eight to ten toises wide. The second covert-way is four toises, the semigorges of the places of arms, m, about fifteeen, and the faces perpendicular to the counterscrap; the second glacis is from fifteen to eighteen toises broad. This second covert-way has traverses every where in the same manner as the first. Of Profiles.-A profile is the representation of a vertical section of a work; it serves to show those dimensions which cannot be represented in plans, and is necessary in the building of a fortification. Profiles are generally constructed upon thirty feet to an inch. It would be endless to describe all their particular dimensions; we shall, therefore, lay down the principal rules only, given by M. Vauban, on this subject. 1. Every work ought to be at least six feet higher than that before it, so that it may command those before it; that is, that the garrison may fire from all the works at the same time, with great and small arms, at the besiegers in their aproaches. Several authors, however, object against it. For, say they, if you can discover the enemy from all the works, they can discover, by the same reason, all the works from their batteries; so that they may destroy them without being obliged to change their situation, and thereby dismount all the guns of the place before they come near it. But, if all the works were of |