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100 yards, nor greater than 200; for the flanked parts, if farther distant, would be beyond the defence of musket shot.


280. Intrenchments of armies are the works constructed for the purpose of defending an army in the field. These works are seldom regular, different points requiring different degrees of artificial protection, as the natural defence varies with every accident of the occupied ground; marshes, rivers, ravines, and other natural obstacles, when skilfully connected with the works, not only strengthen the defence, but save time and labour in the construction of the defensive line. Intrenchments with intervals are preferred, and they are made to occupy the summits of high grounds and hills that lie in its direction, as they afford a better defence, and a greater command of the surrounding country.


281. There are four methods of attacking a fortress. The first is by surprise; the second by assault (escalade, or open attack); the third, by blockade, or starving it out; and the fourth, by the attack in form, regular attack, or strong bombardment.

There are three kinds of batteries used-dismounting, ricochetting, and breaching batteries. The first kind are intended to dismount or damage guns on the parapet; the second, for enfilading the faces and fronts that are attacked, that is, for sweeping along the inside of the works in the direction of their length, and have therefore a small angle of elevation; and the third, for making breaches in the rampart, or otherwise destroying it.

When the direction of a battery is perpendicular to the line of a parapet, so that its fire may sweep along the rampart or covert way, the fire is said to be enfilading; but when the charge is small, and the guns are fired at a slight elevation, so that the shot may graze and bound over any intervening parapets along its range, the fire is said to be ricochetting.

Operations of a Regular Siege.

The attack is made upon a bastion and its collateral ravelins. The works of the siege are approaches and parallels, with their batteries and redoubts.

The approaches are trenches from 15 to 18 feet wide, made in a zig-zag form towards the point of attack, as Aab, Bcd, and the branches of it are so inclined, that they cannot be enfiladed from any of the works of the fortress; and the excavated earth is made to form a sort of parapet on the side of the trenches next to the fortress.

The parallels, or places of arms, are trenches joining every two collateral approaches, as ACB, DE, and their direction is perpendicular to the capital of the work attacked.

The first parallel, ACB, is usually traced at the distance of 300 fathoms from the covert way, the most advanced point of defence. Two batteries at the extremities of this parallel are constructed to enfilade the nearer faces of the adjoining bastions, I and K, which lie in the direction of IX and KW, on the prolongation of the first parallel, which is extended in front of all the works that can influence the attack; and other two batteries are erected on this parallel in the direction of MZ, LZ', which are intended to enfilade the faces of the adjoining ravelins. The barbette batteries in the salients of the ravelins are now removed, as they would soon be destroyed by the two latter batteries.

While these ricochet batteries are constructing, the approaches are carried forward in the direction of the capitals of the ravelins; and by the time that the batteries are in full activity, the second parallel, DE, is begun.

The preceding batteries are mounted only with guns, the former with 7, and the two latter with 4 guns; but a battery may now be erected about the middle of the first parallel, mounted with howitzers and heavy mortars, with shells filled with lead or 68 lb. shot, to destroy the escarpe wall of the bastion.

On the completion of the second parallel, the batteries, F

and G, are erected to enfilade the faces and ditch and other works of the bastion, and the remote faces of the adjacent ravelins; and each extremity of this parallel is then to be secured by a redoubt of a circular or other form, R, N, mounted with field artillery.

When these two batteries are in active operation, the trenches ES, Dr, called half parallels, are run out from the flanks of these batteries, and batteries at r, S, are established on them to enfilade the nearer faces of the collateral ravelins. These half parallels are now extended to O and P, and batteries are erected there in the prolongation of the nearer flanks of the adjoining bastions, I, K.


During the construction of the half parallels, approaches, mn, are pushed forward from the second parallel; and when the batteries r, S, are in activity, the third parallel, res, is traced, connecting the three adjoining salients of the glacis, and batteries are then erected to enfilade the faces of the bastion.

When the third parallel is completed, lodgements—that is, works to enable the besiegers to maintain their position-are to be constructed on the crest of the glacis by saps—that is, trenches made under cover of musketry-branching outwards from the capitals around the salients, and also parallel to the edge of the glacis, represented by dotted lines in the figure; also traverses and epaulements are to be erected wherever they are required for the purpose of defilading, that is, defending the interior of the trenches against an enfilading fire. At the same time, saps are cut forwards from the third parallel, and an advanced parallel, ui, is run right and left to connect the couronnement, that is, the lodgment on the glacis.

Various batteries are now constructed, as at k, l, to batter the faces of the bastion attacked, and the other adjoining works. The troops defending the ravelins will now have suffered so much that they may generally be easily taken by assault. When a breach is made in the bastion by the breaching batteries, a lodgment may then be made in it, either by assault or by sapping under the cover of the adjacent batteries, and then the garrison can no longer oppose an efficient resistance. Generally, when a sufficient breach is effected in the bastion, the garrison is summoned to surrender, as further resistance is useless, and then a capitulation is made, on such terms as may appear proper under the existing circumstances.

The greater the number of sides of the polygon, the greater is the garrison that can be contained in it, and the larger must be the investing army. A fortress, containing a garrison of 4000 men, would require an investing force of more than 20,000 men, in order that a sufficient number of troops might be furnished for the working parties, for guarding the trenches, and for the camp and line duties. The force employed in guarding the trenches ought not to be less than three-fourths of the garrison, otherwise the works would be interrupted, and sometimes destroyed.



282. The representation on a plane, of the important points and lines of an object, as they appear to the eye when situated in a particular position, is called the projection of the object.

283. The plane on which the delineation is made, is called the plane of projection, or primitive.

284. The point where the eye is situated, is called the point of sight, or the projecting point.

285. The point on the plane of projection, where a perpendicular to it from the point of sight meets the plane, is called its centre.

286. The line joining the point of sight and the centre, is called the axis of the primitive.

287. Any point, line, or other object to be projected, is called the original in reference to its projection.

288. A straight line drawn from the point of sight to any original point, is called a projecting line.

289. The surface which contains the projecting lines of all the points of any original line, is called a projecting surface. When the original line is straight, the projecting surface will be a projecting plane.

COR. The projection of any point is the intersection of its projecting line with the primitive.



290. The stereographic projection of the sphere is that in which a great circle is assumed as the plane of projection, and one of its poles as the projecting point.

291. The great circle, upon whose plane the projection is made, is called the primitive.

292. By the semi-tangent of an arc, is meant the tangent of half that arc.

293. By the line of measures of any circle of the sphere, is meant that diameter of the primitive, produced indefinitely, which is perpendicular to the line of common section of the circle and the primitive.

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