The art of fortifying a town, or other place; or of putting them in such a posture of defence, that every one of its parts defends, and is defended by some other parts, by means of ramparts, parapets, moats, and other bulwarks; to the end that a small number of men within may be able to defend themselves for a considerable time against the assaults of a numerous army without, so that the enemy in attacking them must of necessity suffer great loss.

The origin and rise of fortification, is undoubtedly owing to the degeneracy of mankind. In the first ages of the world, men were dispersed up and down the countries in separate families, as we are told in the histories of the Jews and Scythians, who wandered from one place to another, for the sake of finding pasture for their cattle. These families became in time so numerous as to form large communities, which settled all together in a place; from whence villages and towns had their origin and rise: but they found it was necessary, for the common security, to surround those towns with walls and ditches, to prevent all violences from their neighbours, and sudden surprizes. This was sufficient for some time, till offensive weapons were invented, and conquering became a fashion. Then walls with loop-holes were made at proper distances, in order to screen the defenders against the arrows of the assailants: but finding that, as soon as the enemy got once close to the walls, they could from no part be discovered or repelled; for this reason they added square towers at proper distances from each other, so that every part of the wall might be defended by the adjacent sides of the towers. However, this manner of inclosing of towns was found to be imperfect, because there remained still one of the faces of the towers which fronted the field that could not be seen from any other part, and therefore could not be defended. To remedy this, they made the towers round instead of square, imagining this figure to be the strongest to resist the battering engines, as likewise to be better defended from the other parts of the wall.

Notwithstanding the superiority of this method above the former, there remained yet a part of these towers uneven and incapable of being defended; which made them change the figure of the towers again; that is, they made them square as before; but, instead of presenting a face to the field as formerly, they presented an angle; by this means they effectually found out such a disposition of their works, that no part could be attacked without being seen or defended by some other part.

This last method was in use a long while; and would in all probability have continued to this day, if gunpowder had not been found out: but the violence of the guns and mortars soon convinced the world, that such towers and walls were but a weak defence against these thundering engines; and besides, as the nature of the attack was entirely changed, it was also necessary to change that of fortifying likewise.

From that time, ramparts were added to the walls, the towers enlarged into bastions, and all sorts of outworks have been added, such as ravelins, counterguards, horn and crown works, and others of the like nature, in order to render the defence in some measure equivalent to the attack.

Notwithstanding all the improvements which have been made in the art of fortifying since the invention of gun-powder, that of attacking is still superior to it: engineers have tried in vain to render the advantages of a fortification equal to those of the attack; the superiority of the besiegers fire, together with the greater number of men, obliges generally, sooner or latter, the besieged to submit.

The greatest improvement made in the art of attacking happened in the year 1697, when M. Vauban made first use of ricochet-firing at the siege of Ath, whereby the besieged placed behind the parapets were as much exposed to the fire of the besiegers as if there had been none; whereas, before, they had been secure as long as the parapet was not demolished: and the worst is, that there can be no remedy found to prevent this enfilading, without falling into inconveniences almost as bad as those which we endeavour to avoid.

Fortification is either regular or irregular. Regular fortification, is that built in a regular polygon, the sides and angles of which are all equal, being commonly about a musket-shot from each other. Irregular fortification, on the contrary, is that where the sides and angles are not uniform, equidistant, or equal; which is owing to the irregularity of the ground, valleys, rivers, hills, and the like.

SECTION I. Of Regular Fortification.

Although authors agree as to the general form in the present manner of fortifying, yet they mostly differ in particular constructions of the parts. As it would be both needless and superfluous to treat of all the different methods hitherto proposed, we shall content ourselves with explaining those only, which are most esteemed by the best judges, and have been mostly put in practice.

Construction of M. Vauban's Method.

This method is divided into little, mean, and great; the little is chiefly used in the construction of citadels, the mean in that of all forts of towns, and the great in particular cases only.

We shall give the construction of the mean, as being most useful; and refer the reader to the table hereafter, for those dimensions which are different in the several fortifications.

Inscribe in a circle a polygon of as many sides as the Plate CXB. fortification is designed to have fronts; let AB be one fig. 1. of the sides of half an hexagon, which bifect by the perpendicular CD; divide half AC of it into nine equal parts, and one of these into ten others; then these divisions will serve as a scale to construct all the parts of the fortification, and each of them is supposed to be a toise or fathom, that is, six French feet; and therefore. fore the whole side AB is supposed to be 180 toises.

As the dividing a line into so many equal parts, is troublesome and tedious; it is more convenient to have a scale of equal parts by which the works may be constructed.

If therefore, in this case, the radius is taken equal to 180 toises, and the circle described with that radius being divided into six equal parts, or the radius being carried five times round, you will have an hexagon inscribed; AB being bisected by the perpendicular CD as before, set off 30 toises from C to D, and draw the indefinite lines ADG, BDF; in which take the parts AE, BH, each equal to 50 toises; from the centre E describe an arc through the point H, meeting AD in G, and from the centre H describe an arc through the point E, meeting BD in F; or which is the same, make each of the lines EG, HF, equal to the distance EH; then the lines joining the points A, E, F, G, H, B, will be the principal or outline of the front.

If the same construction be performed on the other sides of the polygon, you will have the principal or outline of the whole fortification.

If, with a radius of 20 toises, there be described circular arcs, from the angular points B, A, M, T, and lines are drawn from the opposite angles E, H, &c. so as to touch these arcs their parts a b, b c, &c. together with these arcs, will represent the outline of the ditch.

Definitions.

1. The part FEALN, is called the bastion. 2. AE, AL, the faces of the bastion. 3. EF, LN, the flanks. 4. FG, the curtain. 5. FN, the gorge of the bastion. 6. AG, BF, the lines of defence. 7. AB, the exterior side of the polygon. 8. CD, the perpendicular. 9. Any line which divides a work into two equal parts, is called the capital of that work.

Table.

| Side of Polyg. | Forts. | Little Fortif. | Mean | Great | |---------------|--------|---------------|------|-------| | Perpendicular | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | 190 | 200 | 210 | 220 | 230 | 240 | 250 | 260 | | Faces baft. | 10 | 11 | 12½ | 14 | 15 | 16 | 20 | 23 | 25 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | | Cap. of ravel.| 22 | 25 | 28 | 30 | 33 | 35 | 40 | 42 | 45 | 47 | 50 | 53 | 55 | 56 | 58 | 60 | 62 | 64 | 66 | 68 |

In the first vertical column are the numbers expressing the lengths of the exterior sides from 80 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 become too narrow.

The little fortification is chiefly designed for citadels, and are commonly pentagons; the perpendiculars are made one seventh of the exterior side: the mean is used in all kinds of fortifications from an hexagon upwards to any number of sides: 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 7ths of the exterior sides, or nearly so, because the fractions are neglected.

It may be observed in general, that in all squares the perpendicular is 8th of the exterior side, and all pentagons 7th, and in all the rest upward 8th. 1. Construction of Orillons and retired Flanks.

Describe the front MPQRST as before, and divide the flank into three equal parts, of which suppose S r to be one; from the opposite flanked angle M draw a line M r, in which take the part m r of 5 toises; take likewise R n in the line of defence M R, produced, equal to 5 toises, and join n m, upon which as a base describe the equilateral triangle n p m, and from the angle p, opposite to the base as centre, is described the circular flank n m.

And if S r be bisected by the perpendicular 1, 2, and another be erected upon the face ST, at 3; 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.

2. Construction of Ravelins or Half-moons.

Fig. 2. Set off 55 toises, from the re-entering angle O of the countercarp, on the capital O L or on the perpendicular produced, and from the point L draw lines to the shoulders A B; whose parts L M, L N, terminated by the countercarp, will be the faces, and M O, O N, the semi-gorges of the ravelin required.

This is Mr Vauban's method of constructing ravelins, according to some authors; and others will have the faces of the ravelin to terminate on those of the bastions within 3 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 12 toises, its countercarp parallel to the faces of the ravelins; and is made in a circular arc, before the salient angle; as likewise all ditches are in general.

When the ravelins are made with flanks, as in fig. 3, the faces should terminate on those of the bastions, at least 5 toises from the shoulders.

The flanks are made by setting off 10 toises from the extremities of the faces, from f to h, and from m to l; and from the points h, l, the flanks h k, l p, are drawn parallel to the capital L O of the ravelin.

There are sometimes redoubts made in the ravelin, such as in fig. 2, which is done by setting off 16 toises from the extremities of the faces on the semi-gorges from N to b, 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 redoubt is 6 toises, and its countercarp parallel to the faces.

3. Construction of Tenailles.

A tenaille is a work made in the ditch before the curtains, the parapet of which is only 2 or 3 feet higher than the level ground of the ravelin. There are three different forts: the first are those as in fig. 4, which are made in the direction of the lines of defence, leaving a passage of 3 toises between their extremities and the flanks of the bastions, as likewise another of 2 in the middle for a bridge of communication to the ravelin.

The second fort are those as in fig. 5. Their faces are in the lines of defence, and 16 toises long, besides the passage of 3 toises between them and the flanks of the bastions; their flanks are found by describing arcs from one shoulder of the tenaille as centre through the other, on which are set off 10 toises for the flanks desired.

And the third fort are those as in fig. 6. Their faces are 16 toises, as in the second fort, and the flanks are parallel to those of the bastions.

The use in general of tenailles, 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 nowhere else so well as from them.

The first fort 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 has generally preferred them in the fortifying of places, as may be seen in the citadel of Lille, at Landau, New Brisac, and in a great many other places.

The second fort 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 fort, 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 it is not without reason. For when the ditch is dry, the part behind the tenailles serves as a place of arms, from which the troops may fall, destroy the works of the enemy in 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 make 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.

4. Construction of Lunettes.

Fig. 7. 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 L N; on which is set off 30 toises from the countercarp of the ditch, for one of its faces; the other face, P N, is found by making the semi-gorge T P of 25 toises; the ditch before the lunettes is 12 toises, the parapet 3, and the rampart 8, as in the ravelin.

There is sometimes another work made to cover the salient angle of the ravelin, such as A, called bonnet, whose faces are parallel to those of the ravelin, and when produced bisect those of the lunettes; the ditch before it is 10 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 20 toises.

These kind of works may make a good defence, and cost no very great expense; 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.

5. Construction of Tenailles.

Fig. 9. Produce the faces of the ravelin beyond the counterescarp of the ditch, at a distance MN of 30 toises, and take on the counterescarp of the great ditch 15 toises from the re-entering angle p to q, and draw Nq; then qNMP will be the tenailles required; its ditch is 12 toises, that is, the same as that of the ravelin. Sometimes there is made a retired battery in the front of the tenailles, as in B; this battery is 10 toises from the front to which it is parallel, and 15 toises long.

There are commonly retrenchments made in the tenailles, such as O; their parapets are parallel to the fronts MN, and bisect the side qN; the ditch before this retrenchment is 3 toises; and there is a banquette before the parapet next to the ditch of about 8 feet, called herm; which serves to prevent the earth of the parapet (which seldom has any revetment) from falling into the ditch.

It is to be observed, that the ravelin, before which tenailles are constructed, must have its saliant angle much greater than the former construction makes them; otherwise the saliant angles of the tenailles become too acute; for which reason we made the capital of this ravelin 45 toises, and the faces terminate within 3 toises of the shoulders.

6. Construction of Counterguards.

Fig. 10. 11. When the counterguard is placed before the ravelin, set off 40 toises on the capital of the ravelin from the saliant angle A, to the saliant angle B, of the counterguard; and 10 from C to D, on the counterescarp of the ditch.

When the counterguard is before the bastion, such as in fig. 2, its saliant angle F is 50 toises from the saliant angle E of the bastion, and the breadth near the ditch of the ravelin 10 toises as before.

The ditch before the counterguards is 12 toises, and its counterescarp 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 Cochon, will have them much narrower than they are here.

7. Construction of Hornworks.

Fig. 12. Produce the capital of the ravelin beyond the saliant angle A, at a distance AB of about 80 toises; draw DBE at right angles to AB; in which take BD, BE, each equal to 55 toises; and on the exterior side DE, trace a front of a polygon in the same manner as that of the body of the place, making the perpendicular BF 10 toises, and the faces 30.

The branches Da, Eb, of the hornwork, when produced, terminate on the faces of the bastions, within 5 toises of the shoulders. The ditch of the hornwork is 12 toises, and its counterescarp 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 hornwork is 35 toises, and the faces terminate on the shoulders, or rather 2 or 3 toises beyond them; and the ditch before the ravelin is 8 toises.

There are sometimes retrenchments made within the hornwork, such as S, S; which are constructed by erecting perpendiculars to the faces of the ravelins, within 25 toises of their extremities. This retrenchment, like all others, has a parapet turfed only with a berm of 8 feet before it; as likewise, a ditch from 3 to 5 toises broad.

Fig. 13. When a hornwork is made before the bastion, the distance DL 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 5 toises from their extremities; all the rest is the same as before.

8. Construction of Crownworks.

From the saliant angle, A, 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 a polygon of the same dimensions as in the hornwork; that is, the perpendicular should be 18 toises, the faces 30, and the branches terminate on the faces of the bastions within 25 toises of the shoulders.

The ditch is 12 toises, the capital of the ravelin 35, and its ditch 8; that is, the same as in the hornwork.

Sometimes the crownwork is made before the bastion, 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 25 toises of their extremities; the rest of the dimensions and constructions are the same as before.

Hornworks, as well as crownworks, 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.

9. Construction of Covert-ways and Glacis.

Although we have not hitherto mentioned the covert-way, nevertheless all fortifications whatsoever have one; for they are deemed to be one of the most essential parts of a modern fortification; and it is certain, the taking the covert-way, when it is in a 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 outmost counterescarp of the ditches, at 6 toises distant from it; and the space mn, mn, included between that line and the counterescarp, will be the covert-way required. Fig. 3. There is in every re-entering angle of the counter-scarp a place of arms, m; which is found by setting off 20 toises from the re-entering angle a, on both sides from a to b, and from a to c; and from the points b, c, as centres, arcs are described with a radius of 25 toises, so as to intersect each other in d; then the lines drawn from this intersection to the points 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, at 20 toises distant from them, the spaces s, x, x, between these lines and those which terminate the covert way, will be the glacis.

At the extremities of the place of arms, are traverses made, such as v, v, which serve to inclose them; these traverses are 3 toises thick, and as long as the covert way is broad; and a passage is cut in the glacis round them, of about 6 or 8 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 salient angle of the bastion and outworks, 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 6 to 8 feet wide.

In each place of arms are two Sally ports z, z, which are 10 or 12 feet wide, for the troops to fall out; in time of a siege they are shut up, with barriers or gates.

10. Construction of Arrows and Detached Redoubts.

An arrow is a work made before the salient angles of the glacis, such as A, fig. 3. It is composed of a parapet of 3 toises thick, and 40 long; and the ditch before it 5 toises, terminating in a slope at both ends. The communication from the covert way into these arrows is 4 or 5 toises wide; and there is a traverse, r, at the entrance, of 3 toises thick, with a passage of 6 or 8 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 in order 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.

Their 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 40 toises; the flanks a c, b f, which are perpendicular to the gorge, 10; and the faces c d, f d, 30: the ditch before it is 6 toises, ending in slopes at both ends; the covert way 4; the branches of the covert way are 42 toises long, or thereabouts; the faces of the places of arms y, y, which are perpendicular to the branches, 10; and the other, which is parallel to them, 14.

The communication from the covert way into the redoubt, is 5 or 6 toises wide; and there is a traverse 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 50 toises distant from the covert way, the besiegers carry their trenches round, and enter through the gorge; by which 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.

11. Construction of Second Ditches and Covert ways.

Fig. 4. When the ground is low, and water to be found, there is often a ditch about 10 or 12 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 counter-scarp of the ditch is 10 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 8 to 10 toises wide.

The second covert way is 4 toises, the semi-gorges of the places of arms, m, about 15, and the faces perpendicular to the counter-scarp; the second glacis is from 15 to 18 toises broad.

This second covert way has traverses everywhere, in the same manner as the first.

12. Construction of Profiles.

A profile is the representation of a vertical section Pl. CXIII. of a work; it serves to show those dimensions which fig. 1 cannot be represented in plans, and is necessary in the building of a fortification. Profiles are generally constructed upon a scale of 30 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 6 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 approaches. Notwithstanding this specious pretence, there are several authors who 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 the same height, those within cannot be destroyed, 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.

But when works are low, they are easily enfiladed by the ricochet batteries, which is a kind of firing with a small quantity of powder, by giving the gun an elevation of 10 or 12 degrees: this might however be partly prevented, by making the parapets near the salient angles, for the space of 8 toises on each side, 5 or 6 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, 3 feet towards the field; or the inside, where the banquetttes should be, 3 feet higher than the outside.

7. When the revetment of a rampart goes quite up to the top, 4 feet of the upper-part is a vertical wall of 3 feet thick, with a square stone at the top of it, projecting 6 inches; and a circular one below, or where the slope begins, of 8 or 10 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 5 feet thick; and the counterforts or buttresses reach no higher than that place.

2. When the rampart is partly walled, and partly turred, then one fifth of the height which is turred must be added to 5 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 30 feet high from the bottom of the ditch, and that 10 of which are to be turred; then the fifth part of 10, which is 2, added to 5, gives 7 for the wall above; and as this wall is 20 feet high, the fifth of which is 4, and 4 added to the thickness 7 above, gives 11 for the thickness near the foundation.

Plate CXIII. fig. 1. Represents, in military perspective, the profiles of the body of a place, the ravelin and covert-way: which gives a clear idea of what is meant by a profile, and from which those of all other works may be easily conceived.

Sect. II. Of Irregular Fortification.

The most essential principle in fortification, consists in making all the fronts of a place equally strong, so that the enemy may find no advantage in attacking either of the sides. This can happen no otherwise in a regular fortification situated in a plain or even ground: but as there are but few places which are not irregular, either in their works or situations, and the nature of the ground may be such as makes it impracticable to build them regular, without too great expense; it is so much the more necessary to show in what consists the strength or weakness of a town irregularly fortified, so that the weakest part may be made stronger by additional outworks; as likewise, if such a place is to be attacked, to know which is the strongest or weakest part.

1. Construction of an irregular place situated in an open country.

If the place to be fortified is an old town inclosed by a wall or rampart, as it most frequently happens, the engineer is to consider well all the different circumstances of the figure, situation, and nature of the ground; and to regulate his plan accordingly, so as to avoid the disadvantages, and gain all the advantages possible: he should examine, whether by cutting off some parts of the old wall or rampart, and taking in some ground, the place can be reduced into a regular figure, or nearly so; for, if that can be done without increasing the expense considerably, it should by no means be omitted. Old towns have often towers placed from distance to distance, as Douay, Tournay, and many other places, which are generally made use of, and mended when it may be done. If there is a rampart without bastions or towers, it must be well considered, whether bastions may not be added, or if it is not better to make only some outworks: if the ditch about this rampart is not too wide and deep, it would be advantageous to make detached bastions; otherwise ravelins and counterguards must be constructed. Special care must be taken, to make all the sides of the polygon as nearly equal as possible, and that the length of the lines of defence do not exceed the reach of musket-shot; but if that cannot be done, those sides which are on the narrowest part should be made the longest.

If it should happen, that some of the sides are inaccessible, or of very difficult approach, either on account of some precipice, marshy ground, or inundation, they may be made much longer than the others, which are of easy access, and the flanks need not be so large as the rest; by doing so, there will be some expenses saved, which may be used in making the other sides stronger by adding more outworks.

There are few situations, but what are more advantageous in some parts than in others; it is therefore the business of an engineer to distinguish them, and to render those sides strong by art, which are not so by nature.

If the situation is low and watery, lunettes or terrains, and such other small outworks, should be constructed; because they are not of any great expense, and may make a very good defence. But if one side of the place only is low, and running water is to be had, a second ditch and covert-way with lunettes may be made, by observing, that if the first glacis is made to slope, so as to become even with the level of the water in the second ditch; or if the water can be swelled by means of dykes or sluices, so as to overflow the best part of the first glacis, it should be done: for, by so doing, these works will be able to make a very good defence; since the besiegers will find it a difficult matter to lodge themselves upon this glacis; which cannot be done but within a few toises of the first covert-way, where the besieged are ready to receive them, and to destroy their works with great advantage; whereas the enemy cannot support their workmen but from the second covert-way, which is too far off to be of any great service to them.

But if the situation is of a dry nature, without any water about it, caponiers should be made in the great ditch, from the curtains to the ravelin, and batteries raised. raised in the entrance of the ditch before the ravelin, whose parapet must slope off into a glacis so as to afford no cover for the enemy behind them. Arrows and detached redoubts are likewise very proper to be used in such a case; and sometimes horn or crown-works, if it should be thought convenient: but these works should never be constructed, without an absolute necessity, either to occupy a spot of ground which might be advantageous to the enemy, or to cover some gate or entrance into the town; for they are of great expense, and their defence seems not to be answerable to it.

Most of the places in Flanders are fortified with horn-works, such as Ipres, Tournay, Lille, and others.

If the place to be fortified is new, and the situation will not admit of a regular construction; particular care must be taken in choosing such a spot of ground as is most advantageous, and least liable to any disadvantages either in the building or in the maintaining of it. All hills or rising grounds should be avoided, which might command any part of the works; marshy grounds, because such situations are unwholesome; or lakes and standing waters, for the same reason, excepting a lake is or may be made navigable: good water should be had either within the place or near it, for it is absolutely necessary for men and cattle; the air should be wholesome, otherwise the continual sicknesses that may reign in such a place might prevent people to come and live in it, and the garrison would not be in a condition to defend themselves as they ought to do: in short, all the different circumstances attending such an undertaking should be maturely considered, before a resolution is taken to fortify any place.

When a situation is fixed upon, the next thing to be considered is, the bigness of the town and the number of its outworks; which must absolutely depend upon the consequence such a place is of to a nation. If it is only to guard a pass, or entrance into a country, it need not be so large; but if it is to be a place either to promote or to protect trade, it should be large and commodious; the streets should be wide, and the buildings regular and convenient. As to what regards the fortification, its construction should depend on the nature of the situation; and the number of works, on the funds or expense a prince or a nation will be at; which, however, ought to be according to the benefit arising from such a place: for, as such undertakings are of very great expense, an engineer cannot be too sparing in his works; on the contrary, the greatest economy should be used, both in regard to the number of works, and to their construction. The body of the place may have (a) revetments quite up to the top, or only in part, and the rest turfed: but as to the outworks, they should have half revetments, or they may be made with turf only; as being not so necessary to prevent the place from being surprised, which may nevertheless make a good defence.

On Plate CXIII. fig. 2. is the plan of an octagon, one half of which is similar and equal to the other half; it being supposed, that the situation would not admit of fortification quite regular; the exterior sides are each 180 toises, and the works are constructed according to our method: but because the sides AB, EF, are weaker than the rest, as has been proved before, we have added tenailles, redoubts in the ravelins, and lunettes, to render them nearly equal in strength with the others; and if counter-guards were made before the bastions A and B, it would effectually secure that front. Instead of lunettes, any other works may be made, as may be thought convenient and according to the nature of the ground. If it should be judged necessary to add other outworks to the ravelins all round the place, care must be taken to add likewise more to the fronts AB, EF, in order to render the advantages and disadvantages of attacking on either side equal.

2. Construction of an irregular place, situated on a hill or rock.

In the construction of such places, care must be taken that no neighbouring hill commands any part of the works; the town should always be built on the highest part; but if it should be thought more convenient to place it lower, then the upper part must be fortified with a fort; the situation should be made level as near as possible, by removing the earth from some places to fill up others; and if it cannot well be levelled without extraordinary expense, works must be made on the highest part, so as to command and protect the lower. The works ought to occupy all the upper part of the hill; but if it should be too extensive to be all inclosed, or so irregular as not to be fortified without great inconvenience, the parts which fall without should be fortified with some detached works, and a communication with the place must be made either above or under ground. There should be no cavity or hollow roads, within cannon-shot, round about the place, where the enemy might be able to approach under cover. If there should happen to be a spring near the top of the hill, it should be inclosed in the fortification; or if that cannot be done, by some work or other: for there is nothing more necessary, and at the same time scarcer, in such situations, than water; for which reason there cannot be too much care in providing it: several cisterns are to be made to receive the rain-water, and to preserve it; wells should be dug likewise, though ever so deep, the water of which will serve for common use.

Places built on hills or rocks, should never be large; for their use is generally to guard passes or inlets into a country, and are seldom useful in traffic, and it is a difficult matter to provide for a large garrison in such situations, neither should any such place be built without some very material reasons: but when it is absolutely necessary, great care and precaution should be taken to render the works as perfect as the situation will admit of, and at the same time to be as frugal in the expense as possible.

3. Construction of irregular fortifications situated near rivers, lakes, or the sea.

As the intent of building these kind of places is chiefly to facilitate and protect trade, they are of more importance than any other kind, especially in maritime countries, where the principal strength and power depends on them: for which reason, we shall treat of:

(a) Revetments are chiefly made to prevent a place from being surprised: outworks do not want to be made so; the taking them by surprise is of no great consequence, except in a siege, when other cautions are used to prevent it. of this construction more largely than of any other.

The first thing to be considered is their situation, which ought to be such as to afford a good harbour for shipping, or a safe and easy entrance in stormy weather; but as it is hardly possible to find any, where ships may go in and lie secure with all winds, care should be taken to make them safe to enter with those woods which are most dangerous: but it is not sufficient that the harbour is safe against stormy weather, they should likewise be so against an enemy, both by land and water; for it often happens, that ships are destroyed where it was imagined they were secure, which is of too great consequence not to be provided against; for which reason, forts or batteries must be built in the most convenient places, to prevent the enemy's ships from coming too near, so as to be able to cannonade those in the harbour, or fling shells amongst them; and if there is any danger of an enemy's approach by land, high ramparts and edifices must be built, so as to cover them.

When a river is pretty large, and it is not convenient for making a harbour without great expense, the ships may ride along the shore; which, for that reason, must be made accessible for ships of burden: this may be done by advancing the quay into the river, if the water is too shallow, or by digging the river sufficiently deep for that purpose.

And to prevent an enemy from coming up the river, forts must be built on both sides, especially when there are any turnings or windings. Antwerp is such a place: for the Scheldt is sufficiently deep to carry ships of great burden, which may come quite near the town-wall; and several forts are built below it on both sides, so that it would not be an easy matter for an enemy to come up the river.

When the river is but small, so that no ships of burden can come thro' it; it is sufficient to make it run thro' some of the works, where proper landing places are contrived, from whence the goods may be carried in to the place; as at Sarrelouis, where a hornwork is built beyond the Sarre, in the gorge of which the goods are landed.

If the breadth of the river does not exceed 200 yards, it commonly passes through the middle of the town, and proper quays are made on each side; in such a case, the fortification is so contrived, as that the river passes through the curtain, in order to have a bastion on each side to defend the coming in and going out.

When M. Vauban fortified near rivers, he made always the exterior side near the water much longer than any of the others; such as Hunningen on the Rhine, and Sarrelouis on the Sarre; but for what reason he fortified these places in that manner, has not been told by any author.

But it is plain that the sides which terminate at the river, are the weakest; because the besiegers trenches being secured by the river, they may draw most of their troops off, and act therefore with more vigour and strength on the other side: besides, as the strength of a side increases in proportion as the angle of the polygon is greater, by making the side next the river longer, the angles at its extremities become wider, and consequently the adjacent sides stronger.

There are other advantages, besides those mentioned already, which arise from the lengthening that side; for if the river is pretty deep so as not to be fordable, that side is not liable to be attacked; and by increasing its length, the capacity of the place increases much more in proportion to the expense, than if more sides were made; the centre of the place will be likewise nearer the river, which makes it more convenient for transporting the goods from the water-side to any part of the town.

To illustrate this method of M. Vauban's, we shall give the plan of Hunningen: this place was built for the sake of having a bridge over the Rhine, for which reason he made it only a pentagon; the side AB next to the river is 200 toises, and each of the others but 180.

About the space a b c, which lies before the front AB, is a stone wall; and the passages x, x, are shut up with sluices, to retain the water in the ditches in dry seasons; and to prevent an enemy from destroying the sluice near the point c, whereby the water would run out and leave the ditches dry, the redoubt y was built in the little island hard by, in order to cover that sluice; without which precaution the place might be insulted from the river side, where the water is shallow in dry season.

The hornwork K beyond the Rhine was built to cover the bridge; but as this work cannot be well defended across the river, the hornwork H was made to support the other.

Before finishing the description of this plan, we shall show how to find the long side AB.

After having inscribed the two sides GE, GF, in a circle, draw the diameter CD, so as to be equally distant from the line joining the points E, F, that is parallel to it; on this diameter set off 100 toises on each side of the centre; from these points draw two indefinite perpendiculars to the diameter; then if from the points E, F, as centres, two arcs are described with a radius of 180 toises, their intersections A and B, with the said perpendiculars, will determine the long side AB, as likewise the other two FB and EA. In like manner may be found the long or short side of any polygon whatsoever.

When a place near a river is to be fortified, for the safety of commerce, particular care should be taken in leaving a good space between the houses and the water-side, to have a key, or landing place for goods brought by water; it should also be contrived to have proper places for ships and boats to lie secure in stormy weather, and in time of a siege; and as water-carriage is very advantageous for transporting goods from one place to another, as likewise for bringing the necessary materials, not only for building the fortification, but also the place itself, the expenses will be lessened considerably when this convenience can be had; for which reason, places should never be built anywhere else but near rivers, lakes, or the sea; excepting in extraordinary cases, where it cannot be avoided.