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 Ng; 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 0; 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 [. 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, mn, 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, r, 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, 2, 2, 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, fd, thirty: the ditch before it is six toises, ending in slopes at both ends; the covert-way four; the branches of the coverway 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 semi gorges 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 OF M. VAUBAN. the same height, those within cannot be destroyed SECT II.-OF THE SECOND AND THIRD SYSTEMS till such time as those before them are taken : guns might be placed in the covert-way and outworks to obstruct the enemy's approach; and, when they come near the place, they might be transported into the inner works; and, as the body of the place would be much lower, the expense would be considerably diminished. It should not, however, be forgotten that, when works are low, they are easily enfiladed by the ricochet batteries, though this might be partly prevented by making the parapets near the saliant angles, for the space of eight toises on each side, five or six feet higher than the rest of the works. 2. The covert-way should be lower than the level ground, otherwise the body of the place must be raised very high, especially where there are several outworks: this is to be understood only when the works exceed each other in height, otherwise it need not be below the level. 3. The bases of all inward slopes of earth should be at least equal to the height, if not more. 4. The bases of all outward slopes of earth, two-thirds of their heights. 5. The slopes of all walls or revetments should be one-fifth of their height; or one-sixth might, perhaps, be sufficient; the height of a wall is estimated from the bottom of the ditch, and not from the beginning of its foundation. 6. The slopes of all parapets and traverses are one-sixth of their breadth; that is, three feet towards the field, or the inside, where the banquettes should be three feet higher than the outside. 7. When the revetment of a rampart goes quite up to the top, four feet of the upper part is a vertical wall of three feet thick, with a square stone at the top of it projecting six inches; and a circular one below, or where the slope begins, of eight or ten inches diameter; they go quite round the rampart, and the circular projection is called the cordon. Where the straight part of the wall ends, and the slope begins, the wall is always made five feet thick; and the counterforts or buttresses reach no higher than that place. 8. When the rampart is partly walled and partly turfed, then one-fifth of the height which is turfed must be added to five feet, to get the thickness of the wall above. And, having the thickness of any wall above, by adding one-fifth of its height from the bottom of the ditch, the sum will be the thickness of the wall at the bottom; but, if a sixth part is only taken for the slope, then a sixth part must be added. For instance, suppose a rampart of thirty feet high from the bottom of the ditch, and that ten of these are to be turfed, then the fifth part of ten, which is two, added to five, gives seven for the wall above; and as this wall is twenty feet high, the fifth of which is added four, and four to the thickness seven above, gives eleven for the thick ness near the foundation. Plate III. fig. 1, represents, in military perspective, the profiles of the body of a place, the ravelin and covertway: which gives a clear idea of what is meant by a profile, and from which those of all other works may be easily conceived. M. Vauban's Second and Third Systems were chiefly designed, as we have stated, to protect the besieged from the ricochet fire of his own invention, and to improve the near defence. To accomplish these and some minor purposes, he composed the body of the plan of works which resemble small bastions, and are called towerbastions. His second method is thus exemplified. He begins his construction inwards, and fortifies outwards, which is found a very convenient plan for improving a place. Let A B, Plate III. fig. 2, be the interior side of an hexagon of 120 toises, some authors will have it 130, and say that they are so at Landau, draw AC, BD, from the centre through the extremities of the sides; set off six toises from A to b, and from B to c; through the points b and c, draw lines at right angles to AB, from the point b set off six toises to foutwards, and four from b to d inwards; and from the points f,d, draw perpendiculars fr, d n, to the capital AC; then, if r E is made equal to rf, the point E will be the saliant angle of the tower bastion; and E fd n half that tower. If in the capitals there be taken from the saliant angles of the tower-bastions, the distances EC, FD, each of forty toises, the points C and D will be the saliant angles of the counterguards before the towers; from the points C and D draw the lines of defence Cc, Db, to the points where the flanks of the towers cut the cur tain; and which set off fifty-six toises for the faces of the counterguards; the flanks are found as in the first method, and likewise the tenailles. The ditch before the saliant angles of the towers is six toises, and its counterscarp drawn to the extremities of the flanks of the counterguards; the right line which joins the ends of these flanks will determine the inside of the tenailles. The ditch before the counterguards is twelve toises at the saliant angles, and the counterscarp is drawn to the opposite shoulders in the same manner as in the first method. The capital of the ravelin is forty-five toises; its faces, when produced, terminate on those of the counterguards, within ten toises of the shoulders; ten toises are cut off from the faces by the flanks which are parallel to the capital as usual. The ditch before the ravelin is ten toises, the covert-way five, the semi-gorges of the places of arms twelve, the faces seventeen, and the glacis twenty. The following is the construction of M. Vauban's third method, according to his plan of New-Brisach. This method is applied to an octagon, whose exterior side, A B fig. 3, is 180 toises, the perpendicular CD thirty; the faces AK, BL, of the counterguards sixty; the flanks LN, K M, are found by setting off twenty-two toises, as chords to the arcs described from the opposite shoulders as centres; from the extremities of the flanks a line is drawn, which will be parallel to the exterior side A B, meeting the capitals AE, BF, of the counterguards at G and H; this line terminates the inside of the tenaille, as |