Page:Encyclopædia Britannica, Ninth Edition, v. 9.djvu/452

 438 FORTIFICATION lieve them. The rules may therefore be laid down, that in all detached works the mode and time of relief should be palpable to the garrison ; that the nature of the construc tions should inspire the garrison with confidence in its power of resistance for a reasonable time ; and, above all, that the garrisons of such works should be composed of the best soldiers. Redoubts, as has been said, may be either regular or irregular polygons of any number of sides, but the square redoubt is the most simple (see fig. 40). All redoubts have the disadvantage of &quot; dead &quot; salient angles ; and it is usual, therefore, to place the guns used in their defence in the salients, so that their fire may be along the capitals or lines bisecting the salient angles, as well as upon the dead space in front of them. The sides should be made to front the probable line of approach, and, as shown in one half of fig. 55, which represents a Rectangular Redoubt, the FIG. 55. Rectum Redoubt. escarp is sometimes sloped gently down to the bottom of the ditch, and covered with abattis or other obstacles, which can then be seen and defended in front by direct fire. It is indeed impossible to repeat too often that in all works the efficiency of defence must mainly depend on the power of arresting the progress of the assailants at those points which are under the fire of the defenders. The entrance to a redoubt should be made in the least exposed side, and be protected by a parapetted traverse placed behind it, as in fig. 55, where an arrangement of palisades is shown by which the traverse may be connected with the parapet of the works, and the entrance closed by gates or barriers. Traverses may be also constructed either for the purpose FIG. 56. Plan and Section of Magazine behind a Gabion Traverse. of defilade or for affording additional cover to the troops. They may be formed, when the work is sufficiently capacious, of long parallel epaulements, with a space be tween them, which can be covered over or blinded when it is likely that the work will be held for a considerable time, and when, in consequence, a more secure and comfortable lodging is desirable for the garrison. Maga zines for ammunition may be constructed either against or in such traverses ; and fig. 56 represents, in plan and sec tion, a magazine behind a gabion traverse, and isolated from the parapet in front of it. This magazine is partly sunk in the ground, with sides of plank and a roof of strong timbers forming a ridge in the centre, covered first with fascines and then with 4 or 5 feet of earth. Its dimensians are length 8 feet, breadth 5 feet, height 6 feet. Having thus generally described this portion of the sub ject, it is necessary to determine the least size which can be given to redoubts, so as to ensure interior space sufficient to ac commodate the garri son required for the defence of the parapet, remembering that in works not provided with flanking defences the whole parapet, un less secured in part by some insurmountable natural obstacle, must be defended. A general formula may be easily obtained for determining the least regular polygonal trace in the following manner : Let x be the side in feet of any regular polygon, n the number of sides, A the interior surface reckoned from the foot of the ban quette, y the number of men forming the garrison, / the number of linear feet allotted to each soldier, F the number of square feet occupied by each man in the interior, then nx A n F x fynx, and YyA., or7/=y = Y w &quot; ence ~ y-=A. Again, let the perpendicular Cd, from the centre of the polygon (tig. 57) to its side AB, be/&amp;gt;, and let the distance db from the side AB to the boundary line of the available interior space mn be d ; ikenCb=p-d; andasCo!: AB : : Cb : mn,p:x : :p-d: mn,ormn*=* - - = x Now, the value of p expressed as a function of P P x and of the angle of the centre &amp;lt;, which is = x cot. &amp;lt;/&amp;gt;, varies with the nature of the polygon ; and replacing therefore the variable coefficient cot. | &amp;lt;f&amp;gt; by 0, we have p = frx, and mn, the side of the interior space mnpo, = x-- - =-- x - jr^ x James500 (talk)o Fi ant ^ ^ = mn x 4 cot. J $&amp;gt;&quot;- whence also Cb is thus = n F x = n /3 / _ _d 2 -- = ~ 1 The surface of the interior triangle - ) P J and A = -- rfV. = ^ cot. ^ &amp;lt;f&amp;gt; are as follows: In the triangle,, , square, and thence by reduction The values of the variable 0-288 0-500 pentagon, 6SS ,, hexagon, 866 the square, and supposing we have d=12 feet, /=3, = 6x3 = 18, a; = 62 -81 feet (21 yards), which may therefore be taken as the side of the smallest square redoubt to be defended by one rank only of soldiers, the garrison being 84 men in single rank, and a reserve equal to one-third of the garrison ; if /= 2, then x = 76 66 feet, or nearly 26 yards, the garrison being 15(5 men. If there are to be two ranks, /=!, and 2 = 89 6 = 30 yards nearly, the garrison being 240 men; and if two ranks, with a reserve equal to one-third of the whole garrison, /=! and z -115 feet, or about 38 yards, the garrison being 456 men, Triangular Redoubts are rarely used, as their interior space is small and out of proportion to the length of parapet: thus the smallest triangular redoubt to be de-
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