THE art of fortifying a town, or other place; or of putting it 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 surprize. 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. This manner of enclosing towns, however, 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 point, and therefore could not be defended. To remedy this, they made the towers round instead of square, imagining this figure to be 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 Vauban's towers unseen 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 long in use; 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 gunpowder, 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 later, 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.

SECT. 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 sorts 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 these several fortifications.

Inscribe in the circle a polygon of as many sides as the fortification is designed to have fronts; let AB (fig. 1.) be one of the sides of half an hexagon, which bisection 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, fix French feet; and therefore 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 fix equal parts, or the radius being carried fix times round, you will have a 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. 10. a b c, the counterface of the ditch. 11. A, M, the flanked angles. 12. H, E, L, the angles of the shoulder, or shoulder only. 13. G, F, N, the angles of the flank. 14. Any angle whose point turns from the place is called a salient angle, such as Δ, M; and any angle whose whose point turns towards the place, a re-entering angle, such as \( b \), F, N.

15. If there be drawn two lines parallel to the principal or outline, the one at 3 toises distance, and the other at 8 from it; then the space \( y z \) included between the principal one and that farther distant, is called the rampart.

And the space \( xx \), contained by the principal line, and that near to it, and which is generally stained black, is called the parapet.

16. There is a fine line drawn within four feet of the parapet, which expresses a step called banquette.

N. B. All works have a parapet of three toises thick, and a rampart of 8 to 10, besides their slopes. The rampart is elevated more or less above the level of the place from 10 to 20 feet, according to the nature of the ground and the particular constructions of engineers.

The parapet is a part of the rampart elevated from 6 to 7\( \frac{1}{2} \) feet above the rest, in order to cover the troops which are drawn up there from the fire of the enemy in a siege; and the banquette is two or three feet higher than the rampart, or about four feet lower than the parapet; so that when the troops stand upon it they may just be able to fire over the parapet.

17. The body of the place, is all that which is contained within this first rampart: for which reason it is often said to construct the body of the place; which means properly, the construction of the baillons and curtains.

18. All the works which are constructed beyond the ditch before the body of the place are called outworks.

<table> <tr> <th rowspan="2">Side of Polyg.</th> <th colspan="4">Forts.</th> <th colspan="4">Little Fort.</th> <th colspan="4">Mean.</th> </tr> <tr> <th>80</th><th>90</th><th>100</th><th>110</th><th>120</th><th>130</th><th>140</th><th>150</th><th>160</th><th>170</th><th>180</th><th>190</th><th>200</th><th>260</th> </tr> <tr> <td>Perpendicular.</td> <td>10</td><td>11</td><td>12\( \frac{1}{2} \)</td><td>14</td><td>15</td><td>16</td><td>20</td><td>21</td><td>23</td><td>25</td><td>30</td><td>31</td><td>25</td><td>22</td> </tr> <tr> <td>Faces baft.</td> <td>22</td><td>25</td><td>28</td><td>30</td><td>33</td><td>35</td><td>40</td><td>42</td><td>45</td><td>47</td><td>50</td><td>53</td><td>55</td><td>60</td> </tr> <tr> <td>Cape of ravel.</td> <td>25</td><td>28</td><td>30</td><td>35</td><td>38</td><td>40</td><td>54</td><td>50</td><td>50</td><td>52</td><td>55</td><td>55</td><td>60</td><td></td> </tr> </table>

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 baillons: 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 baillons 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 baillons are all \( \frac{3}{4} \)ths 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 \( \frac{4}{7} \)th of the exterior side, and all pentagons \( \frac{4}{7} \)th, and in all the rest upward \( \frac{4}{7} \)th.

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 MR, in which take the part m r of 5 toises; take likewise R n in the line of defence MR, 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 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.

2. Construction of Ravelins or Half-moons.

Fig. 2. Set off 55 toises, from the re-entering angle Fig. 4, O of the counterfarp, on the capital OL or on the perpendicular produced, and from the point L draw lines to the shoulders AB; whose parts LM, LN, terminated by the counterfarp, will be the faces, and MO, ON, the semi-gorges, of the ravelin required.

This is M. 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 baillons 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 counterfarp parallel to the faces of the ravelins; and it 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, fig. 3. the faces should terminate on those of the baillons, 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 LO 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 Brifac, 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 bastion : 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 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.

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 LN ; on which is set off 30 toises from the countercarp of the ditch, for one of its faces; the other face, PN, is found by making the semi-gorge TP 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-Fig. 8, whose faces are drawn perpendicular to those of the ravelin, within a third part from the salient angle ; and their semi-gorges are only 20 toises.

These kinds 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 Tenailons.

Fig. 9. Produce the faces of the ravelin beyond the countercarp of the ditch, at a distance MN of 30 toises, and take on the countercarp of the great ditch 15 toises from the re-entering angle p to q, and draw N q; then q NM p 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 tenailons, 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 tenailons, such as O; their parapets are parallel to the fronts MN, and bisect the side q N; the ditch before this retrenchment is 5 toises; and there is a banquet before the parapet next to the ditch of about 8 feet, called berme; 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 tenailons are constructed, must have its salient angles much greater than the former construction makes them; otherwise the salient angles of the tenailons 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 salient angle A to the salient angle B, of the counterguard; and 10 from C to D, on the countercarp of the ditch.

When the counterguard is before the bastion, such as