The method of tracing out a fortification as described above, has undergone many changes, and received consi derable improvements since the time of Errard. Of the engineers who immediately succeeded him, Pagan occu pies the first place. That writer having witnessed all the wars of Louis XI IL soon perceived that the method of de fending a place, hacl by no means kept pace with the art of attacking, and was, in consequence, led to introduce con siderable changes into the position and arrangement of the different works. Ile fortified on the exterior polygon, the side of which lie determined to be from 900 to 1150 feet. From the middle point of the side, he erected a perpendi cular towards the centre of the place, from 120 to 170 feet. Lines drawn through the extremity of the pet pendicular to the angles of the polygon determined the faces, which he made from 170 to 340 feet. The ditch was parallel to the faces, and 90 feet wide, and the faces of the ravelin were directed to the angles of the shoulders. The ditch before the ravelin was 55 feet, the covered way 30, and the faces of the places of arms 48 to 60. He also laid down as a rule, that the line of defence should not exceed 750 feet, terminating at the extremity of the curtain, and at right angles to the flank.
Vauban, who may be regarded as the father of the pre sent system of attack, also made considerable improve ments in the method of defence. In his trace, the perpen dicular is determined by the length and number of the sides in the polygon. If the enceinte be a square, the perpen dicular is one eighth of the side; if a pentagon, one se venth ; and if a hexagon or upwards, one sixth. The fa ces are determined as in Pagan's method, and are made equal to two-sevenths of the side. The flanks are at right angles to the line of defence, and the orillons, which arc curved outwards, one third of the flanks. The most ad vantageous length for the side of the polygon is fixed at 1250 feet, and 1000 for the line of defence. This construc tion possesses considerable advantages over the method adopted by Pagan. It can be more easily adapted to local circumstances, as all the parts diminish with the side and angle of the polygon. The flanks have an advantageous position, and the bastions are more spacious.
Vauban also introduced a change in the construction of cavaliers or mounds of earth raised above the rest of the fortification, for the purpose of commanding a distant part of the field. Formerly these had been placed in the cur tain and various other parts of the fortification, and were sometimes used for defending the ditch. In these posi tions, however, they were found to embarrass the manoeu vres of the slaldiers. Vauban, therefore, enlarged their size, and placed them in the bastions, whence they could more effectually defend the cultain. They are traced thus :
A parallel, 36 feet from the interior of the parapet, de notes the exterior side of the talud or slope of the escarpe, and 18 or 20 feet farther back, is drawn the fire-line or in terior side of the cavalier. In small bastions, the talud is almost perpendicular, and the earth is prevented from fall ing down by a revetement. This revetement, however, ought in no case to be higher than the parapet of the bas tion, that it may not be seen by the enemy, and that the garrison may not be injured by the splinters. It is also a disadvantage attending cavaliers of this kind, that they prevent the bastion from being intrenched farther back. Nor is this defect remedied by carrying a parapet, as some engineers have done, from the cavalier to the bastion, and constructing a ditch before it, as such a parapet is destroy ed as soon as a breach is made. A more advantageous method of constructing cavaliers will be given in a subse quent part of this article.
The improvements which Vauban introduced, were not confined to the enceinte alone. He also made several ad antageous alterations in the construction of outworks, though, it must be admitted, that lie left not a little to be done in this way by his successor Carmontaigne. The first outwork used by Vauban, is the tenaille a C t, Plate CCLVII. Fig. S. It is placed before the curtain, and se parated by a ditch sufficiently large to receive the earth that may fall from the curtain, and which might otherwise Jill the terre-plein. Of course it, in a great measure, su persedes the use of the fausse brave. In his first tenailles, Vauban used flanks, as b e, g f, though they were after wards omitted. In constructing tenailles or this kind, h r f are parallel to the curtain, the first at 16, and the last at 60 feet distance ; a k, t I, 30 feet from the flanks of the bastion ; a b, t g, equal to one•half of a C or t C ; and the flanks b e,f, parallel to those of the bastion. Having determined a b e, and t ,g f, there are drawn parallel to these, and at the distance of 54 feet, a k h and t /i for the interior side of the terre-plein. Thus the terre-plein of the faces and flanks of the tenaille is 30 feet, but that of the curtain only 18.
In constructing tenailles without flanks, which are found •ri be most advantageous, the flanks being easily destroy cd, the faces a b and t g are continued till they meet oppo site the centre of the curtain. By this form, the tenaille is not enfiladed, and the besieged may retain it even after the fosse is taken. The form would be still farther im proved, if, instead of forming an angle a C t, it were paral lel to the curtain. It would thus afford a direct fire on the terre-plein of the ravelin, and allow the ditch to be made larger.