FORTIFICATION 429 should have aslope of 1 in 12. The command of the crest of the parapet over that of the glacis should be such that an assailant, standing on the crest of the latter, should not be able to fire into the interior of the work, a condition which requires a command over the glacis of 5i feet, so that with a parapet 7 feet high the maximum height of glacis would be 1^ feet. The minimum height of the glacis is determined by another condition, viz., that the fire from the parapet should pass at no greater distance than 2 feet above its surface ; and in no case should the plunge or slope of the glacis be greater than that of the parapet. An advanced glacis is sometimes adopted either to render the cover more effectual, or to occupy a favourable line for first opposing the progress of the enemy. Fig. 20 shows this arrangement, gg l , being the first or ordinary glacis, and g~y 3 the second or advanced glacis. The slope of these glacis should not be such as to withdraw the assailants from the grazing fire of the parapet, and if it be not possible to extend the slope of g 2 g 3 so far as to keep it in the prolongation of the line eg 2 , it should be so arranged that no point of the slope should be more than 2 feet below that line or the plane corresponding to it, namely, the plane passing through the crest of the parapet and the crest of the advanced glacis. To form the advanced glacis, the slope at g is prolonged below the surface of the ground to g l , the earth excavated in doing this supplying the material for the glacis. When it is intended that the defence of this advanced glacis shall be derived solely from the parapet, either an abattis or rows of stakes may be placed im mediately behind it, so as to stop the advance of the enemy when at the point of maximum exposure, but advanced glacis may often assume the character of successive in- trenchments, and be defended with vigour and success. This figure will be again referred to when treating on defence by mines. The height of the parapet being deter mined by the amount of cover required, and the thickness by the nature of projectile to which it is exposed, the whole profile or section is necessarily completed on the principles pointed out, and the bulk therefore of earth contained in any portion of the parapet will be equal to the area of the mean or average profile multiplied by the length of that portion. Now, as this earth must be obtained from the ditch, the dimensions of the latter depend on those of the former ; and the volume of any portion of the excavated ditch will also be equal to the mean section of that portion multiplied by its length. If, therefore, F represent the area of the mean section of this portion of the parapet, D the area of the mean section of the corresponding portion of the ditch, and L the length of this portion, then LP = LD, provided the earth be of the same bulk after as before ex cavation ; but this is not the case, for after having been broken up from its previously closely packed condition, it is found that the "remblai" or earth built up exceeds the "deblai" or earth exca vated by a coefficient varying with the nature of the soil, being in sandy soil nearly 0. Thus if represent the coefficient, in sand it is 0, in earth of medium tenacity T , and in very strong and naturally compressed earth ; so that to render the earth of the ditch just equal to that of the parapet, the above equation should , or - ~ P. , . As, however, the earth resulting from this excess, even allowing for the greater length of the ditch in polygonal works, will be required for forming the glacis, or for making up the banks, called "barbettes," in the salients constructed for raising guns sufficiently high to fire over the parapet, the dimensions of the ditch may be safely esti mated without reference to the excess, as follows : Let x be the breadth of the bottom of the ditch, and y its depth ; and let the sum of the bases of the slopes of the escarp and counter scarp be represented as a function of the depth by the fraction - y ; v then x + -y will be equal to the breadth of the ditch at top, and D = D r x + x + - y ) , whence x = _ y, and y J I y 2s Now, as the defensive object of the ditch requires that it should be both deep and wide enough to form a decided obstacle to an enemy, the width ought not to be less than 18 feet, whilst the depth should have no other limit than that arising from the difficulty of raising the earth, which r fixes 12 feet as about the maximum. Taking y =12 feet, ~ = | , and D=108 square feet, then # = 9-9 = 0, and the width of the ditch therefore -^ -| of 12 = 18 feet, the ditch being triangular. Assuming a profile area of 70, corresponding to a parapet 7 feet high and only 6 feet thick, and making x = Q fora triangular ditch, I = 9 ft. 7 in. , and the width of the ditch = 14 foet ; with a profile area of 116 feet corresponding to a parapet 7 feet high and 12 feet thick, the depth of the ditch, if triangular, is 12^ feet, and the width 18J feet ; so that this profile appears about the maximum for a triangular ditch with a profile area of 163 feet, corresponding to a parapet 8 feet high and 18 feet thick. With a banquette 4 feet wide a triangular ditch would give 7/ = 14f feet, so that such a form would be inconvenient ; but taking x = 4 feet as the width of the bottom of the ditch, y or the depth becomes 12 ft. 4 in. , and the width of the top of the ditch 22 feet a very well-proportioned ditch. In the preceding cases the base of the slope of the escarp has been assumed as equal to its height, and that of the slope of the counterscarp as equal to half its height. Should the nature of the soil be such as to require the base to be equal T to the height in both escarp and counterscarp, - y = 2y; and s should the soil be sufficisntly firm to admit of a base of rt one-half in both, -y = y. In the first of these cases, even with the large profile area last named, the ditch may be made triangular with a depth of 12J feet, and a breadth of 25 feet ; and in the second a triangular ditch is inadmis sible with a profile area of 110 feet, as the depth would be more than 15 feet; indeed it would be inadmissible with pro file areas beyond 85 square feet, for which a depth of 13 feet would be required. Before leaving this subject, a few words may be said respecting the " berm." The most effec tual escarp for defence is that which forms one continuous plane with the exterior slope, or at least which commences immediately where the other ends, as the absolute relief of the parapet is then a maximum, and there is no berm ; but in many cases it would be imprudent to carry the parapet to the edge of the escarp, as injury to the latter would occa sion the fall of part of the parapet, while the difficulty of
