them to sweep the outsides more effectively, and in this particular case that was the principal consideration. [Illustration: 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.[59] 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. 6-1/2 in. higher than that of the bastions of the outwork,[60] 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. [Illustration: FIG. 69.] The works communicated with each other by posterns. As the fortress of La Roche-Pont was only assailable on one side, the number of cannon necessary for its defence might be, it appeared, in proportion to its extent, inconsiderable. The number amounted to thirty twenty-four pounders, ten twelve-and four-pounders to arm the demi-lunes. At the end of the reign of Louis XIV., the efforts of the coalition were directed towards the north-eastern frontiers, and the garrison of La Roche-Pont did not get a view of the enemy. However, during the course of the eighteenth century, this fortress was kept in passable condition. FOOTNOTES: [Footnote 57: See Fig. 60.] [Footnote 58: See Fig. 65.]