The several fronts ofafortification may be all dissimilar, both in their proportions and in their extent ; as also in the number and construction of their several out works ; yet the whole cannot be termed irregular. Thus the two ends of a long oval may be constructed on the second, i e. the mean system ; while each of the two long sides may be upon the third, or great system. One end may have a horn work ; the other a crown-work : the late ral faces being strengthened with rave lines, lunettes, tenailles, or other works, all these are evidently regular members of a perfect whole, and when duly combin ed according to the rules of art, form a complete and regular defence, founded on approved systems.
When the number of faces has been ad justed and laid, down, it is proper to de cide whether the works are to be planned outwards, or inwards, from the line laid down. In the former case much space is gained by keeping all clear within that line, which by this means becomes the in terior side : in the latter instance the line becomes the exterior side, all the works being raised within it, which considerably diminishes the area within them. It is to be remembered, that in laying down the plan of a tbrtification, the several lines, describing the outer part of each ram part, exhibit the situation of a semicircu lar projection of masonry, called the cor don, which is, with few exceptions, made at the top of their respective facings of stone, brick, &c. called revetements. The line thus following the direction of the cordon, as it proceeds along the works, is called the principal.
A reference to rig. 1, Plate Fortifica tion, will illustrate the foregoing descrip tion. The half of a hexagon, or polygon of six equal sides, is selected, as being the most appropriate to this occasion. The line, AD, is the diameter of the circle ; which circle having been divided into six equal parts, each equal to the radius, or semidiameter, AE, or ED, gives the faces formed by the passage of the rays BE, and CE, through the points of equal divi sion, B and C. Let us suppose the fortifi cation to proceed inwards : in such case the lines AB, BC, CD, will be termed ex terior sides, and all the principal will be formed within them; whereas, had it been intended to cover more ground, and to keep the whole of the area contained within the lines AB, BC, CD, and DC, clear, the principal would have been pro jected outwards, and the lines AB, BC, Cl). would then have been termed the in. terior side. The former mode is in use when the exterior el the defences is first marked out, and has its separate mode of formation ; and the latter is adopted, where the interior of the works is estab lished by any pre-existing circumstances, such as fortifying an old town, &c. ; and proceeds on a suitable plan of projection. The two modes correspond perfectly, giv ing the same angles and proportions ; the former on a diminished, the latter on an extended scale.
The interior lines FG, GH, HI, form parallel faces with those on the exterior lines AB, BC, CD. If it were required to fortify outwards, they would be the bases oftheir several defences respective ly, and the measurements would be taken from them, in lieu of from the exterior line. We shall proceed according to the latter mode, it being the most common and the most familiar.
To fortify inwards from an exterior line.
—Let the exterior line BC be 18u toises, (each toise being one fathom, or six feet,) bisect it in d, and draw the perpendicular d8 equal to one sixth of the exterior line BC, namely, 30 toises. Now from B draw the line B v, passing through the point n; and from C draw the line C u, intersecting B v in n. Set off 50 toises from the points B and C, on their respective lines, which are called the lines of defence, giv ing B t and C w for the faces of the two bastions. With the w, measure t v and w u, on the lines of defence, to de termine their proper lengths, so as to give 91 V for the length and position of the cur tain ; next draw the lines t v and me v, eir ther curved or straight, for the flanks of the bastions. If they are to be curved, which are generally preferred, the points t and w will be the centres of equal cir cles, whereof the two flanks will be equal segments.
Proceed in the same manner with the other two fronts, AB and CD ; you will thus complete two bastions, 3 and 4, and the halves of two more, 2 and 5. Next measure off 15 toises, and draw something less than quadrants, or quarters of circles, from the points B and C ; the centres of those quadrants being exactly opposite thereto, place your scale so that you may draw lines from the ends of the quadrants towards the shoulders of the bastions, but draw no further than suffices to touch upon the perpendicular of 30 toises : thus your scale would give the direction, 1w, but your line would stop a little below d. This being done in both directions, and throughout the three faces, will give the width of the ditch, and the interior lines or re-entering angles of the ravelines 0, N, K. The body of the raveline is form ed by measuring 10 toises on the face of each bastion, setting off from the shoul ders t w towards the saliant, or projecting angles, (here called flanked angles,) B and C. An opening of the compasses equal to u w, (or to i v,) with the ten toises included, will give the distance of the saliant angle o, of the raveline from the centre 5, of the curtain u v. The sides or faces of the ravelines, are determined by lines, drawn from the sa liant angle to those points on the faces of the bastion 3 and 4, already set off at 10 toises each, from their respective shoul ders t and Tv.