He had thought at first of suppressing the south flanks of the two extreme bastions, but in that case the exteriors of the east and west faces of these bastions would have been too slanting to sweep the crests of the plateau effectively, while the two curtains answered this object. Besides, the enemy could not then, without risk, commence his trenches on the slopes of the plateau and rapidly approach fronts insufficiently flanked. Vauban therefore set out the plan of the great outwork according to the following method ([Fig. 68]):—To the outside he gave a length of 180 toises, or 1,156 feet. To the western side, a c, 1,120 feet; to the eastern side, b d, 1,054 feet—that is, he placed the points c and d according with the edge of the plateau; the two angles a and b being equal to one another. On the centre of the side a b of the polygon he erected the perpendicular, e f, having a length equal to one-sixth of a b. From this extreme point, f, were drawn the lines of defence, a g, b h, on which the lengths of the faces of the bastion, a k, b i, were set off equal to two-sevenths of the outer side, a b. To find the flanks of the bastion, according to the method usually adopted in these defences, points k and i, he described arcs of a circle, k l, taking i k as the radius. The point of intersection of this arc with the line b h gave the length and the direction of the flank of the bastion; but, not having been able to trace a regular half-hexagon, and the angles a and b being less obtuse than those of a regular hexagon, by proceeding in this manner, the gorges of the bastion would have been too contracted. Therefore, to determine the flank of the bastion, from the points i and k, he let fall perpendiculars to the lines of defence, a g, b h, and the point h gave the re-entering angle in the curtain, h g, parallel to the side a b. This exposed the flanks a little too much, but enabled them to sweep the outsides more effectively, and in this particular case that was the principal consideration.
Fig. 68.
The width of the ditch of the main work was fixed at 112 ft. 7 in., to the rounding of the counterscarp; and this was determined by a tangent to this rounding, drawn from the angle of the epaule of the opposite bastion.
The ditches being dry, Vauban sunk cunettes in the middle, 23 ft. 4 in. wide and 6 ft. 8 in. deep. Double caponnières connected the tenailles with the demi-lunes. The demi-lune was set out as follows:—Taking g k as radius, the arc k m was drawn. Its meeting with the perpendicular, e f, prolonged, gave the point of intersection m, the salient of the demi-lune. From m, the face m n was directed upon a point, o, taken on the face of the bastion at 31 ft. 3 in. from the angle of the epaule, i. The width of the covered way was fixed at 31 ft. 3 in., and that of the glacis at 124 ft. 4 in. The internal places d'armes were 100 ft. across the demi-gorge and 133 ft. 4 in. along the faces. These places d'armes were closed by traverses. The ditch of the demi-lune was 89 ft. 7 in. in width. The tenailles, g, constructed in the direction of the lines of defence, were 43 ft. 9 in. wide at the base.
Cavaliers were made on the bastions to obtain convenient views over the slopes of the plateau. Their faces and sides, parallel to those of the bastions, had to be placed at a considerable distance from the epaulements, in order that the un-cased external foot of the talus might leave the necessary room for the easy working of the pieces of artillery.[22]
The same method was followed for the sides a c and b d. The width of the ditch was increased to 100 ft., and the great demi-lune, t, was so formed that its faces had a length of 332 ft. and its narrow sides 66 ft. The old bastions restored and enlarged, u v, were armed with cavaliers, and the escarp of these bastions was 6 ft. 6½ in. higher than that of the bastions of the outwork,[23] which difference, for that matter, was favoured by the conformation of the ground.
All the escarps and counterscarps were cased with strong masonry, with counterforts in the terre-plein; as shown in the sections of [Fig. 67] and [Fig. 69].
