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likewise the saliant angles G, H, of the tower

bastions.

If EF be drawn parallel to G H, and at nine toises distant from it, the intersections E, F, with the capitals of the counterguards, will be the centres of the towers; from which set off seven toises from E to a for the semi-gorges, and draw the flanks bc through the extremities of these semi-gorges perpendicular to the line EF; these flanks are four toises inwards from a to c, and five outwards from a to b; the faces b G are drawn from the point b to the point G, and the lines joining the inside of the flanks at the end of four toises will complete the towers.

The ditch is six toises before the saliant angle of the towers, and its counterscarp meets the line GH, within ten toises of the extremities M, N, of the flanks of the counterguards.

If from the point n, where the line EF intersects the perpendicular CD produced, you set off five toises to the point r, and the lines of defence are drawn from the extremities of the semigorges a of the towers through this point r then the flanks of the counterguards produced will determine the little flanks p, q, of the inside rampart, and the extremities of these little flanks, being joined, will give the curtain between them. The great ditch before the counterguards is fifteen toises, and its counterscarp parallel to the faces; the capital of the ravelin is five toises, and that of the redoubt within it twenty-three; the faces of the ravelin are drawn to the faces of the counterguards within fifteen toises from the shoulders, and those of the redoubt parallel to these twelve toises are cut off from the faces of the ravelin, and six from those of the redoubt, by the flanks which are parallel to the capital; the ditch before the ravelin is twelve toises, and that before the redoubt six; the covert-way and glacis are the same as in the second method. It must be observed, that the parapets of the counterguards, on both sides of the saliant angles, are raised four feet higher, for the space of twenty feet, above the rest, to prevent the enfilades of the ricochet batteries.

SECT. III. OF THE SYSTEMS OF M. MINNO,

BARON OF COEHORN.

This officer, a contemporary with Vauban, was a lieutenant general in the Dutch service, and director general of all the fortified places belonging to the united provinces and along the Scheldt. He was the inventor of three systems of fortification, in which he chiefly attended to the means of flanking and covering the works as effectually as possible, whilst those parts of the fortifications which are advantageously situated for the besieger's batteries, would not afford sufficient space for them. He also had for his object to facilitate an active and obstinate defence to the garrison; for which purpose he contrived such dispositions as would, in his opinion, enable the besieged troops to oppose the besieged, within the fortifications, with forces superior to his, and upon a larger front; besides securing the retreat of these troops, and exposing those of the besieger to the fire of the casemated batteries, covered caponiers, crenelled galleries, and coffers, which are employed in the systems. Coehorn

likewise disposed the covert-ways and dry ditches in such a manner that the besieger, not being able to dig the ground deeper than about one foot without finding water, may be obliged to convey to the spot the requisite materials for his lodgments and the passage of the ditches in question. But this disposition, as well as the combined use that Coehorn makes of wet and dry ditches, and which forms an essential part of his systems, evidently requires that the fortifications should be erected in aquatic ground, as he supposes them to be. We shall therefore only advert to their principal and more general features.

In his first system, Coehorn supposes the polygon to be a regular hexagon, and that the surface of the water is but four feet lower than the ground.

Let therefore the interior side, AB plate IV. fig. 1, of an hexagon be 150 toises, take AC, BD, each equal to thirty-nine, and the capitals A E, BF, each of eighty; and AG, BH, of forty; from the points E, F, draw the lines of defence through the points D, C; and through the points G, H, lines parallel to ED, FC; in which take G I, HK, each equal to forty toises, for the length of the higher faces of the bastions.

To determine the lower faces EM, FN, draw IO perpendicular to IG, equal to four toises; or parallel to IG, likewise equal to four; then r M perpendicular to EM will determine the lower face EM.

In order to determine the tower 3, see fig. 2, in r M, take rS of five toises; draw Sm parallel to E M, and equal to fourteen; in Or produced take likewise rn equal to four, and in EM, MV, to eight; then if the points n, m, are joined by a right line, and m, V, by an arc of sixty degrees you will have the outline of the tower.

The lines I O, and Or, express two walls, the first has two embrasures, and the second three; by which the author intended to defend the dry ditch, and the approach to the tower.

If from the points C, D, fig. 1, there be set off on the lines of defence fourteen toises to the points Y, W, and upon each of the bases YI, W K, be described an equilateral triangle, the angles opposite to these bases, will be the centres of the higher flanks Y I, W K.

And if R be the intersection of the two lines of defence, R M bisected at S, and RC at Q; by drawing SQ, v SQ R will be half the tenaille; and drawing from the point C, a line parallel to I Y, so as to meet the tower upon which the mean flank is described in the same manner as the former.

The parapets o. the three flanks, and those of the parts m V, V M, of the towers, are twentyfour feet thick; the other parts Mr,rnm, but sixteen; and all the other parapets in general are twenty feet.

There is a wet ditch before the mean flank of six toises broal, and another ≈ behind the towers of the same breadth, over which are made two draw-bridges, parallel to the higher faces.

The space X between the higher and lower faces of the bastions is a dry ditch, whose bottom is but six inches above the surface of the water in the wet ditch.

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Behind the lower parapet there is a banquette of three feet, and a rampart of five; and under this rampart a stone gallery, which runs from one end to the other, and is divided into several apartments, which are shut with doors; as likewise another, going from the saliant angle of the lower faces, to that of the higher, with loop-holes from distance to distance facing the dry ditch; there is likewise a row of palisades placed parallel to the higher faces, and at four toises distant from them.

2

There are three embrasures in Or, as has been said, to flank the ditch a behind the towers; and two in J() to flank the dry ditch near the higher faces.

The great ditch is twenty-four toises broad; and its counterscarp parallel to the lower faces of the bastions; the semi-gorges O L of the ravelin are twenty-nine toises, and the faces LP, forty-five; the dry ditch Y is sixteen toises, the rampart twenty-eight feet, and the lower faces a Tare parallel to the higher ones; the parapet of which is twenty and the banquette three.

The level ground of the rampart in the ravelin near the saliant angle is twenty feet broad, for the length of twenty toises from that angle, and the rest but fifteen.

In the gorge of the ravelin is a small redoubt a, of about five feet high, and underneath a lodgment of stones, the walls being eighteen inches thick at the sides; the roof is made of planks, with three feet of earth over them.

There is a dry ditch going from the extremities of the faces to the redoubt, and round its angle, having a row of palisades before it, to secure the retreat from the ravelin into this redoubt; there is likewise another row going from the extremities of the faces, in a round form, turning towards the gorge of the ravelin.

In the dry ditch of the ravelin, within six toises from the great ditch, is a coffer, and a ditch p of six toises before it: this coffer has a wall on both sides, and the roof is planked and covered with a foot and a half of earth; above this is a stone parapet of five feet high, with a banquette behind it.

There runs a covered gallery under the rampart of the lower faces, and another joining the two saliant angles, together with a row of palisades, in the same manner as in the dry ditch before the bastions.

The wet ditch before the ravelin is eighteen toises; the counterguards r, which the author calls cover-faces, are twenty-five feet broad, and the ditch before them fourteen toises; the covertway is twelve toises broad, and the glacis twenty; the semi-gorges fg, gh, of the places of arms, are twenty-two toises, and are taken from the point g, where the branches of the covert-way meet, and the faces fk, hk, are twenty-eight; within these places of arms are traverses of twenty feet thick and eighteen toises long, within ten or twelve feet from, and parallel to the faces.

The stone lodgments b, within the places of arms, are found by setting off twelve toises from the point g, for the semi-gorges, and the faces are drawn parallel to those of the places

of arms

At six toises froin the places of arms are

coffers q of eight feet broad, made with planks at the sides, and above with a foot of earth over and before them.

There are two banquettes all round the covert way, and before the traverses; as also two rows of palisades before the traverses, one of which joins them, and the other goes round the covertway.

Lastly, the re-entering angles of the counterscarp next to the covert-way are made a little round as likewise that in the ravelin: but the contrary way, that is, they are made hollow.

His Second System he adapts to a heptagon whose interior side is 126 toises, and the level of the ground to be three feet above the surface of the water.

Let, therefore, the interior side, A B plate IV. fig. 3, of an heptagon be 126 toises; take in the capitals, AC, BD, each of seventy-two toises; at the extremities C, D, make the angles ACE, BDF, each of forty degrees; and set off sixtysix toises for the faces CE, DF, of the bastions; on the interior side, take AG, BH, each of thirty toises, and from the point D, as centre, describe an arc through the point G, on which set off a chord of thirty; and on this chord describe the mean flank GI, which is an arc of sixty degrees.

Draw a line from the saliant angle D through the extremity I of this flank, on which take I a of ten toises; join a E, on which describe the orillon as usual.

The outline of the higher flank is thirteen toises distant from that of the outline of the mean; this flank is an arc described from the the same centre as that of the former, the chord of which is forty toises.

From the points G, H, draw the broken parts of the curtain, perpendicular to the capital of the bastion, and make it nine toises long; the extremity of the higher flank is terminated by the inside line of the parapet of the curtain produced.

The tenaille is found by producing the faces of the bastions ten toises; through the extremity of which an arc is described from the opposite saliant angle of the bastion, as centre; on this arc is set off a chord of twenty toises; and this chord serves to describe the flank, upon which is an arc of sixty degrees; the curtain is a right line.

There is a wet ditch before the tenailles of en toises broad, with two bridges at each end, near the orillons; the one directly over it, and the other along the faces of the bastion.

The dry ditch round the body of the place is twenty toises broad, before the faces of the bastion to which it is parallel, and the lower rampart, K L, twenty-nine feet; the semi-gorges ML are fifteen toises, and the flanks LN eigh ten, and are described from the saliant angles K of the lower faces as centres.

The saliant angle of the ravelin is 125 toises distant from the curtain of the body of the place, and is seventy degrees; the faces are fifty toises long; the faces of the redoubt r are sixteen toises distant from those of the ravelin, and fourteen long.

The wet ditch round the lower faces of the ravelin is twenty-four toises broad: the work be

yond this ditch, which the author calls the second counterscarp, is twenty, parallel to the ditch.

To find the broken part of this work, join the two re-entering angles, m,r; on which take mr of thirty toises, and draw r t, rv, parallel to the outline of the counterscarp, each equal to twelve; set off twenty-two from t to s, and from v to q; and upon these lines as chords describe the round flanks, which are arcs of sixty degrees.

The traverses in this counterscarp are drawn at ten toises from the flanks perpendicular to the parapet.

The redoubt z, in the re-entering angles, are found by setting off sixteen toises from the points m to n, for their capitals, and the faces are parallel to the broken curtain before them; those marked y, which are in the saliant angles, are found by producing the counterscarps of the great ditch, and setting off twelve toises from the points of their intersections for their faces; and the flanks are drawn parallel to their capitals.

The ditch before this work is fourteen toises; as to the covert-way and glacis, they are the same as in the author's first method.

Coehorn applies his third system to an octagon, and supposes the level of the water to be five feet below the horizontal ground. The exterior works of this system, that is, the detached bastions and the counterguards, ravelins, covertways, &c., alone present the same arrangement as that of the whole first system; with the exception, however, that independently of the detached bastions being not joined together by any curtains, they only have double flanks instead of treble ones. Each of these bastions also has a redoubt at its gorge, with a dry ditch in front and a crenelled gallery adapted to the counterscarp of this ditch. There is likewise a dry ditch before the redoubt at the gorge of every capital ravelin, which ditch is connected with the faces of the ravelin, as the dotted lines show, by means of coupures made in the direction of the coffers between the capital and the lower ravelins, or nearly in that direction. Besides, in addition to the coffers in front of the re-entering places of arms, Coehorn constructs a crenelled gallery along the faces of these works, on which account the palisades in this part of the covert-way are to be two toises distant from the crest of the glacis.

Behind the exterior works above mentioned is the body of the place, consisting of bastions with common orillons, a revetment, and double flanks. The curtains which connect the lower flanks are broken as in the first system, and at each of their extremities, between them and the principal curtains, a kind of harbour is constructed, by means of which, as well as of vaulted passages made under the lower curtains, the garrison is able to keep up a communication with the exterior works. There is also a kind of circular harbour at the gorge of these works.

Some of Coehorn's dispositions in his third system are certainly not below the high reputation of such an eminent engineer; but, independently of the great labor and quantity of masonry which this system requires, the communications with the exterior works, across wet ditches, are

difficult; the arrangement of the system in question also has the inconvenience of occasioning several openings to be left, through which the besieger can see the exterior works and the body of the place from the crowning of the covert-way. Therefore, all engineers coincide in their opinion that it is inferior to the first system, and consequently to the second.

We shall not therefore detain the reader by a more particular description of it.

SECT. IV.-CORMONTAINGNE'S SYSTEM. This is, in fact, with some modifications, the modern bastion system of fortification. Upon Vauban's first or general system, this able engneer suggested the improvement, first of a much greater projection which he allowed to the ravelins, whereby he considerably augmented their action upon the attacks. Secondly, of constructing the ravelins without flanks, and directing their faces to a smaller distance from the flanked angles of the bastions, by which he covered the shoulders of these works still more effectually than Vauban had done, as well as the curtains, and the openings between the flanks of the bastions and the profiles of the tenailles. Thirdly, Cormontaingne's redoubts in the ravelins are better contrived than those of Vauban, and answer purposes much more important; whilst the larger size of his re-entering places of arms renders them also more beneficial to the defence, and particularly on account of their substantial redoubts, which, besides the other material advantages derived from them, have their faces so disposed as to secure them from enfilade, and allow their fire to have a direction close and nearly parallel to the prolongations of the capitals. This advantage, which none of Vauban's systems afford, is so much more important as the besieger generally advances in the direction of the capitals. Cormontaingne likewise concealed the masonry of all the revetments of the place from the view of the besieger previous to his gaining the glacis, and thereby secured it from the fire of his more distant batteries. Lastly, this engineer much improved the communications, although not to such a degree as would be requisite for attacking the besieger to advantage, in the works which he may have taken so as to drive him out of them.

Independently of the above improvements, which Cormontaingne has made in Vauban's First System, he also illustrated the superior properties that a fortification acquires, from the exterior sides of the fronts which compose it either forming very obtuse angles with each other, or being all in the same straight line.

To describe Cormontaingne's system, with such alterations as have been since suggested and are at present most generally adopted, proceed as follows::

The length of the exterior side being at least 130 toises, but not exceeding 180 toises, construct the bastions and curtains as in Vauban's First System: with the exception, however, that the length of the faces AC and BD (plate V.) of the bastions is to be one-third of the exterior side, and the direction of the flanks perpendicular to the lines of defence. It is here supposed

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