Belidor’s method is divided also into little, mean, and great: and in all three the exterior side is 200 toises; the perpendicular of the little is 50, that of the mean 55, and the great 40: the faces of the first 70, the second 70, and the third 55 toises.
Scheiter’s method is divided into the great, mean, and small sort. The exterior side of the polygon for the great sort is 200 toises, the mean sort 180, and the small 160. The line of defence in the first is 140 toises, the second 130, and the third 120. This line is always rasant. All the other lines are fixed at the same length for all polygons, whose structure chiefly depends upon the knowlege of the exterior side, of the capital, or of the flanked angle, the rest being easily finished.—See the [Table].
Table of capitals and flanked Angles.
| Polygons. | IV | V | VI | VII | VIII | IX | X | XI | XII | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| The flanked angles in the 3 sorts of fortification. | deg. | |||||||||||||||||
| 64 | 76 | 84 | 90 | 95 | 97 | 99 | 101 | 103 | ||||||||||
| Capital for the great sort. | toises | |||||||||||||||||
| 46 | 49 | 51 | 52 | 53 | 54 | ¹⁄₂ | 56 | ¹⁄₂ | 58 | 59 | ||||||||
| Capital for the mean sort. | 42 | 44 | ¹⁄₂ | 46 | ¹⁄₂ | 48 | ¹⁄₂ | 50 | 51 | 52 | ¹⁄₂ | 54 | 54 | |||||
| Capital for the small sort. | 39 | 41 | ¹⁄₂ | 42 | ¹⁄₂ | 45 | 46 | 47 | ¹⁄₂ | 48 | ¹⁄₂ | 50 | 50 | ¹⁄₂ | ||||
Errard, of Bois le-Duc, who was employed by Henry IV. and was the first that laid down rules in France respecting the best method of fortifying a place so as to cover its flank, constructs that flank perpendicular to the face of the bastion; but by endeavoring to cover it effectually, he makes the gorges too exiguous, the embrasures too oblique, and leaves the ditch almost defenceless.
The Chevalier de Ville, who succeeded Errard, draws the flank line perpendicular to the curtain; but here again the embrasures are too oblique, especially in the polygons, and the ditch is necessarily ill guarded. This engineer’s method of fortifying is stiled by most authors, the French method. His favorite maxim is to make the flank angle straight, and the flank equal to the demigorge.
Count Pagan makes the flank perpendicular to the line of defence, which method seems to agree perfectly with this maxim, because by that means the flank so raised covers as much as possible the face of the opposite bastion; but notwithstanding this apparent advantage the flank becomes too small and is too much exposed to the enemy’s batteries. This engineer acquired great reputation during the several sieges which he assisted in conducting under Louis XIII. His system has been improved upon by Alain Marrison Mallet, and his construction in fortification is to this day esteemed the most perfect. It differs very little from Marshal Vauban’s first system. Count Pagan has pointed out the method of building casemates in a manner peculiar to himself.
Marshal Vauban has judiciously steered between these different methods. He has drawn his flank in such a manner, that it does not stand too much exposed, nor does its collateral line of defence extend too far from the direct line of defence. He has effected this by lengthening out his flank and giving it a circular form.
It cannot be disputed but that large and extensive flanks and demi-gorges are superior to narrow and confined ones. The more capacious the flank is, the better calculated will it prove for the disposition of a formidable train of artillery. From this conviction many writers in their proposed systems of fortification, have added a second flank, in order to augment the line of defence; but they did not foresee, that this second flank is not only incapable of covering the face of the opposed bastion, except in a very oblique and insecure direction, but that the right flank, or the flank of the bastion, is thereby more exposed to the enemy’s batteries, which, it must be acknowleged, is a great fault.
The prevailing system of the present day is to make the flanks of the bastion as wide as possible, without having recourse to a second flank, unless it be absolutely necessary. Those gorges are likewise best which are most capacious, because they afford space and ground in the bastion for the construction of intrenchments within, should the enemy have effected a practicable breach.