150 MILITARY SCIENCES. 



the last construction an effective fire is obtained in front of the faces from 

 the line ef. 



c. Fortified Lines. When the ground to be defended has a great 

 extent in one direction this long line must be intrenched. This may be 

 done by lines without or by lines with flanks, forming salient and re-entering 

 angles. Merely straight or curved lines not flanked present a very poor 

 defence, wherefore they are broken, like the teeth of a saw {en cremaiHiere)j 

 by which they are flanked towards one side. Let it be the line N (pi. 47, 

 Jig. I) which is to be defended ; it is first divided into lengths of 360 or 

 140 feet, according as a single defence, as at A, or a double one, as at B, is 

 desired. Then at d, perpendiculars are erected, da = 48 feet, and the 

 lines b a drawn, upon which, at a, the perpendiculars, h a, are erected as 

 flanks. Cremaillieres have, however, many disadvantages, and it is prefer- 

 able, therefore, to break the long lines by simple redans {jig. 2^). The 

 lengths, dd, amount to 720 feet, the perpendiculars, da, are 130 feet, and 

 the half gorge of the redan, d b, is 90 feet. Here, however, the defence is 

 good only before Y, and in front of a lies a dead angle. It is better, there- 

 fore, to make d d only 480 feet {fig. 2 *), while d a and d b maintain the 

 same dimensions as above, whereby not only X but the angles in front of a 

 are defended. A still better defence is obtained by the arrangement on the 

 line M N {fig. 3), where the curtains lying between the redans, bd,ba, are 

 broken to the front, a perpendicular, cb= 180 feet, being erected at c, 

 upon the lines constructed as in fig. 2 ^ and the new faces, c b and b c, 

 drawn. Is the time so limited that redans cannot be constructed the line 

 M N {fig- 4) is broken only into salient and re-entering angles, db, dbd, 

 by means of the perpendiculars, c6=180 feet, where dd is 720 feet. 

 Here, however, dead angles are made at X. Wherever time and ground 

 permit the bastioned line, that is always the most advantageous arrange- 

 ment {fig. 8), but the distance between the salients must be at least 300 

 feet and not over 720. To fortify the line M N in this manner, at the 

 centre, c, of the polygon side, a a, the perpendicular, c = } a a, is erected, 

 the lines, a b.x, drawn, the faces, ah = ^aa, laid off, and the flanks hm ; let 

 fall the perpendiculars upon the lines of defence, abx; then mm are the 

 curtains, which can Hkewise be broken forward, as in the front B, or even 

 twice, as at Y, in the front C. For the straight curtains, as at D, the 

 ditches must be dug out at c P F and at c O, else the shot coming from O P 

 and F will not effectually sweep the salient, X. 



d. The Profile. The chief part in fortification is the breastwork, dc 

 bafa{fig. 21), which is to protect the defenders from the hostile shot. 

 Its thickness is regulated by the penetration of balls into earth, and against 

 musket balls must be not less than three feet, but against 12-pounder balls 

 as much as 12 to 14 feet. The exterior slope, /a, is regulated according to 

 the consistency of the earth, the steeper it can be the better. In front 

 of the breastwork lies the ditch, and its profile Z is governed by the 

 profile Y, as it is to furnish the material for the embankment ; it is desi- 

 rable, however, to give it depth rather than breadth. The slopes may 

 be steep, as they are cut in the solid earth. The outer slope is called the 

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