ments, should an attack be expected; in this case, it will suffice to regulate the size of the redoubt in such a manner that the number of men intended for its defence can man the parapet properly, without being crowded and obstructed in their motions; but if the garrison is to reside in the work, its interior surface must be larger.

Various methods have been proposed for calculating the necessary length of the interior sides of a redoubt, according to the strength of its garrison; but most have the double defect of not being applicable to small detachments, as the redoubts would then be considerably too little, and to increase beyond measure the interior surfaces of those works, when their garrison exceeds a certain number of men.

The method proposed by Noizé de St. Paul, a French engineer, is better in general than any we have seen. We shall observe, however, that it is rather complicated, as it varies according to the strength of the detachments; it contains, besides, several inaccuracies; we point out the two following: :

This author says, No. 32, page 39, of his work on field-fortification, if the detachment which you intend to place in a redoubt, is composed of more than ninety men, and does not exceed 120. take cue-fourth of the number of men for a reserve, which you may make equal to one-third of that number, if the detachment consists of 130 men or thereabout: then divide the remainder by eight, and the quotient will give the length in toises, &c., of each interior side.'-According to this rule, a detachment of 100 men requires that the length of the interior sides should be nearly nine toises and three feet; whereas it is proved by experience, that eight toises and three feet, or thereabout, are enough; thus Noizé de St. Paul's rule increases, without necessity, the size of the redoubt, which requires thereby more time, and a greater quantity of materials for its construction:-besides, the author is inconsistent with himself; for he says, p. 44, note k, in the same work, that a detachment of 100 men requires a redoubt, whose interior sides should have from eight to nine toises at most. But let us proceed further, and suppose that the detachment consists of 120 men; according to the same rule, the interior sides of the redoubt should be eleven toises one foot and six inches: but Noizé de St. Paul recommends the same length for those of a redoubt constructed for 180 men; since he says, p. 39, if the number of men exceeds 150, as they will be able to man in two ranks the parapet of a redoubt capable of containing them, the length of the interior sides will be found by dividing the detachment by sixteen. Now, why should a redoubt, calculated for 120 men, be exactly of the same size as a redoubt constructed for 180? And is it not evident, that Noizé de St. Paul's method, which may give satisfactory results in some other instances is very defective in these two? Indeed it appears that he was aware of its insufficiency with regard to certain detachments; for he says, No. 32, p. 40, that he proposes it as a scale of comparison, which should be used merely as a guide in practice,

since it is very difficult, not to say impossible, to give a general rule of computing the, necessary length of the interior sides of redoubts according to the strength of the detachments, and that trying is the only way.' This author's work, however, in which he has collected and generally exposed with perspicuity, most of the modern principles on which field-fortification is grounded, deserves no small degree of praise.

M. Malortie de Martimont proposes the following rule, supposing the redoubts to be square, and that the garrison is to reside within them :

1. Multiply by ten the number of men of which the detachment is composed, and the product will give, in square feet, the necessary extent of the surface contained between the foot of the slopes of the banquettes.

2. Extract the square root of that product to one decimal, and it will give in feet and tenths of a foot, the lengths of one of the sides which enclose the above-mentioned surface.

3. Add to this length twice the number of feet which the base of the interior slope of the parapet, the breadth of the banquette, and the base of its slope, are to have, and the sum will be the length, in feet and tenths of a foot, of one of the interior sides of the redoubt.

Let us suppose, for instance, that you have to construct a square redoubt a b c d, plate VI. fig. 4, for ninety men: multiply ninety by ten, and the product 900 will show that the surface i k l m, which is contained between the foot of the slopes of the banquettes, ought to be 900 square feet: extract the square root, thirty, of that product for the length of feet in the side i k, which is represented by a b in the profile fig. 5. Now supposing the base of the slope c of the banquette to be six feet, the breadth of the banquette d three feet, and the base of the interior slope e of the parapet one foot; multiply the sum of those dimensions by two, and add the product twenty to the square root thirty which you have found before; then will the sun fifty be the length in feet of the interior side e e fig. 5, and ef fig. 4. It is evident, that in all redoubts constructed by this simple method, every man of the detachment has for himself ten square feet of the clear surface which is contained between the foot of the slopes of the banquettes; and ten feet, in addition to the space afforded by the banquettes and their slopes, as this writer contends, will suffice in all redoubts, let their size and figure be what they may.

Square redoubts are more simple and easy to construct than any other; but the configuration of the ground, and the number and situation of the points which a redoubt may have to defend, &c., frequently require that its figure should not be square; in this case, plant staves at all the points, where, in your opinion, the vertex of the angles, formed by the interior sides of the work, can be placed to the greatest advantage; and after taking, with the plain table, or by any other means which you have at hand, the plan of the figure delineated by lines which you suppose to join those staves, consider it as representing the interior contour of the parapet: measure the angles formed by those lines, in order to ascertain whether they are sufficiently open, Max. 1,

and if some are not, rectify them: inside of the plan draw a parallel to its outline, and at a distance from it, equal to the number of feet which you intend to allow to the base of the interior slope of the parapet, the breadth of the banquette, and to the base of its stope: and, as the figure described by this parallel represents that of the space which is contained between the foot of the slopes of the banquettes, compute its area in square feet; if it appears from your calculations, that the redoubt will be considerably too large, according to its garrison and artillery, this defect may be remedied by shortening the interior sides, or diminishing their number when it exceeds four, or by giving a smaller opening to the angles: but, if the work is small beyond measure, the contrary should be done.

Should a redoubt be circular, compute the radius of the circle, bounded by the foot of the slope of the banquette, so that the enclosed surface may allow ten square feet to each man, and 324 square feet to each piece of cannon: add to this radius twice the base of the interior slope of the parapet, twice the breadth of the banquette, and twice the base of its slope; then drive a picket at the centre of the redoubt, and fasten to it one end of a cord equal to the radius thus increased; and with the other end, to which a pointed picket is fastened, describe a circumference upon the ground.

To ascertain how many men and guns a redoubt which is constructed can contain :-Compute the area in square feet of the surface contained between the foot of the slopes of the banquettes, and divide it by ten if no artillery is to be placed in the redoubt; the quotient will give the number of men that can be lodged in the work but, should the redoubt be supplied with cannon, subtract 324 square feet for each piece from the above area, and divide the remainder by ten, which will give the number of

men.

Of fortins or field-forts.-Two kinds of fortins or field-forts are most generally used, when the ground, the intended object of the work you have to construct, and the strength of its detachment, will allow you to make it regular, or nearly sa; these are the forts with tenailles or star-forts, and the forts with bastions; but sometimes you are compelled to construct a fort which is composed of different figures at once, and in this case no particular name can be given to it.

Field-forts take a particular name also from their number of saliants; thus, a fort is said to be square, pentagonal, or hexagonal, &c., according as it has four, five, or six saliants.

Star forts, or forts à tenaille, are such as form a regular suite of saliant and re-entering angles. They are, in fact, polygons, whose sides are broken so as to form the re-entering angles. If possible, the saliant angles should never be less than seventy degrees, and the nearer they approach to ninety the better, as a rectangular defence is always the best. The brisures, or faces, forming the re-entering angle, should not be less than fifty feet, or more than 100. If they are longer they require a numerous garrison to defend them, and it would therefore be better,

in such cases, to construct a small fortress, especially if you have guns to use. Star forts are seldom constructed either in the triangular or square form, a redoubt being almost always preferable to either. In a triangle there can be no brisures, in a square their angles are 150°. A pentagon is somewhat superior to both, the defence of its saliant angles being better, and the angles of the brisure 132°. The hexagon is still better than the pentagon, though its saliants are by no means well defended. The heptagon has saliant angles of 128°, and those of the brisures 112. This form might therefore be used with considerable advantage, were the construction not difficult; the most convenient, however, as well as the most advantageous polygon for works of this kind, is the octagon. The construction is made either upon the interior polygon, by placing equilateral triangles on its sides, or on the exterior side, by means of the perpendiculars from the saliant and re-entering angles.

Bastion forts have often been proposed, but are inferior to star forts; the triangular half bastion particularly. They are difficult to construct; the saliants are too acute and ill-defended; the faces of the demi-lunes are without cover, and the interior surface is too small. The square half-bastion is little better than the triangular, but it encloses a larger space. When the bastions are full, the work may sometimes be very advantageous, and the construction is the same as in permanent fortification. In bastion forts the sides should not be less than 100, nor more than 200 yards, that the flanked parts may be within musket shot: 130 yards is a good medium. The best form of the curtain is to break it twice, by which a very advantageous fire is obtained.

Têtes de pont are thrown up for covering a communication across a river, and favoring the movements of an army or detachment, either when advancing into the enemy's country, or retreating from it. The form, size, and strength of a tête de pont, ought to be regulated according to various circumstances, and before you fix upon them it is necessary to consider; 1. The importance of the communication which it is to cover, and the probable length of time, during which the communication is to be kept up; for its utility may be confined to a temporary movement of the troops, or extended to the sequel of operations for a long time: 2. The breadth and form of the river at the point where the tête de pont is to be thrown up; and, likewise, the nature of the country on both banks: 3. Whether the tête de pont can be supported by musketry from the opposite banks, or by artillery only, or by neither; 4. Whether the river has only one arm, or forms an island; and in this case, what is the breadth of its arms, and the form of the ground in the island itself, so that you may determine, with more certainty, the defensive dispositions which can be made to the greatest advantage: 5. When you are to construct a tête de pont for covering the retreat of an army, or strong detachment, you ought to consider, whether, according to their composition and the state of things, that retreat is likely to be executed with celerity or slowness; whether there is any fear that the retreating troops will be

closely followed up by considerable forces, or whether they can retire quietly, and without being exposed to any attack which may endanger them: 6, and lastly, you ought to examine what is the strength of the army, or detachment, its number of cannon, the quantity of stores, and equipage, &c., and regulate accordingly the size of the tête de pont, as well as the passages through it, in order that the whole may file off without stoppage and confusion; all these various circumstances oblige us to make a difference in the size, form, and strength of a tête de pont. If an army or considerable detachment, for instance, is closely pursued by a great force, and can retreat but slowly, either on account of its composition, or because it is compelled to take particular precautions, which require time, the tête de pont, which is intended to favor its passage across the river, ought to be of a certain extent, and capable of making a good defence; for then, not only the troops, artillery, &c., must file off through it without any obstruction or confusion, but it ought to check the enemy, should he attempt to approach it: on the contrary, if a tête de pont has to cover a communication of no great importance, or the passage across a river, of an army or detachment which is not closely pursued, and can retreat quietly and speedily, it will not require as much extent and strength as the former.

The bridge or bridges, which a tête de pont covers, should be concealed as much as possible from the enemy's sight, as he would batter and ruin them with his cannon; and that, in general, the most advantageous points for constructing those works are where the river bends in

wards.

and de, the direction of which ought, in general to be as perpendicular as possible, to ef and df, which they defend. Care must be taken, however, that they are not exposed to be enfiladed, which depends, of course, on the configuration of the river, and the disposition of the surrounding ground.

Sometimes, also, a tête de pont may be composed of a horn work, the inside and branches of which are defended by batteries a, erected on the opposite bank. When the ground does not allow you to construct these batteries, the branches of the horn work may be broken.

Half a square fort, with bastions, makes a strong tête de pont, particularly when you can construct on the opposite bank batteries and intrenchments. Half a star-fort, or redoubts so disposed as to flank each other, may also be used for a tête de pont.

Of intrenchments of armies.-The whole of the works and obstacles by which an army or a considerable body of troops cover themselves, for their own defence, may be called intrenchments of armies. In general the object is, to interpose between themselves and the enemy a defensive line, whose protection may compensate for their inferiority in number; this line may be composed of parts so connected together, that no uncovered space is left between them, in which case it is called a continued line; or those parts may be isolated from each other, and uncovered intervals left between them; and then it is named a line with intervals.

Intrenchments of armies can seldom be composed of regular and similar works, nor even of works different in their nature, but symmetrically disposed, and so constructed, that all those of the same kind may have the same dimensions; for, on account of the ground, or because of a necessity to direct more fire to certain points than to others, some irregularities will be requisite; thus it is impossible to foresee all the variations that may occur in the tracing of intrenchments of armies; wherefore no particular rules can be given for every case; there are, however, general principles which ought to guide an engineer.

The works most commonly used for intrenchments of armies, in a continued line, are redans, tenailles, or queues d'hironde, cremaillères and bastions; hence intrenchments take the name of intrenchments with redans, intrenchments with tenailles, or queues d'hironde, intrenchments with cremaillères, and intrenchments with bastions; sometimes also lunettes are placed in front and to a certain distance from a main intrenchment, which is then called intrenchment with lunettes.

For the detailed construction of these works, we must refer the reader to the professional publications on the subject.

The following general principles should be observed, as much as possible, in the formation of intrenchments of armies.

1. Their flanks must be supported, and not exposed to be turned; for, of what avail would be the defence in front which intrenchments afford, could they be attacked in the rear?

2. Their extent should be proportionate to the

strength of the army which they cover, since they are to be defended by it.

3. In tracing those intrenchments, you ought to avail yourself of every natural accident of the ground which they traverse; a low and marshy spot, a stream whose banks may be overflowed, a ravine, a wood where an abatis may be formed, and other natural obstacles, frequently afford great advantages, when properly connected with the other defences; either by increasing the strength of some parts of the line, or, when they suffice to stop the assailants, by saving you the time and labor, which, without them, the construction of works would require.

4. The line formed by intrenchments of armies should occupy, as much as possible, the elevated parts of the ground which it crosses, and border the summits of the heights or hills in its direction; by which means the intrenchments will have a superiority over the assailants, who cannot approach them without passing through uneven and difficult ground.

5. Every point of the ground, in front of an intrenchment, must be seen and defended by some of its parts.

6. The habitations in front of the line should be occupied and fortified, when they are sufficiently near to be supported by it; but should they be too distant, and so situated as to conceal the movements of the enemy, they must be destroyed.

7. For the same reason, a wood, which the line can support, must be occupied; but should its distance prevent it, and its situation be such as to conceal the movements of the assailants, it requires to be cut down.

8. The line ought to cover all the habitations in its direction, so as to make them serve as points of support, and to reap advantage from their reverse fire.

9. The number and strength of the respective works, depend on the greater or less danger to which the part of the line where they stand may be exposed; if, for instance, the enemy could scarcely approach it, and should he not be able to bring his cannon against it, the works thrown up for its defence, would undoubtedly not require the same extent and strength as they would, in case the assailants could easily approach and batter it.

10. All obstacles which may obstruct the communications of the line, with such parts in its front as must be protected by it, or which may impede the retreat of the army, should the intrenchinents be carried, must be removed.

Intrenchments with intervals are now preferred to those which form a continued line. The following are the reasons which are assigned for it; 1st, the former require less troops for their defence than the latter; so that, with an equal number of men, a greater force can be placed at the most exposed points, or stronger reserves kept; 2dly, the intrenched army can form in such order as will not impede its movements; wherefore it will be able to pass successively from the defensive to the offensive, and vice versa, according as circumstances may require whereas, on the contrary, an army placed behind continued intrenchments must be de

ployed; and, as it can scarcely execute any movements outside of them, it is reduced to defend passively, if I may use that expression, the works which cover it, and are sometimes very imperfect: 3dly, a line with intervals requires less labor than a continued line; therefore, the works which compose it can be constructed with greater care in the same time, and with the same number of workmen. Lastly, the former line is more easily adapted to the ground than the latter; as the engineer, who is not confined to a fixed tracing whose parts must all be connected, can place the works at the most essential parts of defence.

In the late continental wars frontiers of countries have been the frequent objects of attack and defence. They constitute important objects of field fortification. M. Malorti furnishes some excellent directions for forming the principal works of this kind.

i. Of lines of frontiers.-The works and obstacles disposed along some open parts of a frontier, to shut up the country from one place, or post, to another, are called lines of frontiers.

These lines may answer very useful purposes; first, they protect the army which defends the country behind them, and also to secure its movements; secondly, they prevent the incursions of the enemy's parties, and the devastation which they would occasion; thirdly, they remove the fears of the inhabitants, who then attend to agriculture. Lastly, they connect the defences of the frontier, and therefore increase the resistance which can be made. Indeed, a line of frontiers will not afford those advantages, unless it be considered in its proper light and used accordingly; for should the army consider it, as forming its own intrenchments, and actually defend it, as lines of frontiers have in general a greater extent than is proportionate to the strength of the army, it follows that the troops would be weak every where; and that they would undoubtedly be crushed by the columns which the enemy would march to several points at once; thus the line would be disadvantageous rather than useful; but on the contrary should the army support it only with a limited number of troops, and occupy a position behind, from which it could repair rapidly to all points, and take in flank the enemy's columns when they begin to advance, no doubt can be entertained, in this case, of the utility of the line, and particularly when its extent is not so great as to preclude the army from the possibility of supporting all its parts; for the enemy will be compelled to form partial attacks, and therefore to weaken himself by dividing his forces. The following are the general rules to be attended to, in the construction of lines of frontiers.

1. They require, like intrenchments of armies, that the extremities should be supported, and not exposed to be turned. Should a line of frontiers be very extensive, it must be directed from one fortress to another, when there are any on the frontier.

2. Their front ought not to present any unprotected openings, by means of which the enemy may penetrate into the country which they are intended to cover. The reason is evident,