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In a line with the face M L of the ravelin, draw gr', and, after making equal to seven tises, draw t'u directed towards the extremity L of this face. For the retirade, v'w's', set off four toises from l' to v', and make v'w' perpendicular to 'l'; then draw 'w', and produce gr until it meets it.

The method of fortifying just explained, evidently has a great superiority over Vauban's first system, but is still liable to material defects, the principal of which are the following:

First, with the exception of the superior polygons, and of the fronts disposed either in a straight line or on a concave-curve, the body of the place is not better secured than any other part of the fortification from the ricochet fire, which the besieger can use from the beginning of the siege; and no portion of the ground, within the sphere of the works, is sufficiently re-entering to render the attacks subject to a very effectual fire from them, in flank and in reverse; whilst the sallies are but feebly protected, and the besieger can crown at one time the whole covert-way of the front of attack, without much risk from this operation. Secondly, this system is as much deficient as that of Vauban, in places of security for the artillery and troops; the consequences of which are that no batteries can be preserved entire, for the most important period of the siege; whilst the troops after having felt the destructive effect of the ricochet fire, kept up by the besieger from the commencement of his operations, become still further exposed to such a vertical fire from his nearer batteries as must render the terrepleins almost untenable, if not entirely so.

Thirdly, although the larger size of the re-entering places of arms, besides their substantial redoubts, much improves the defence of the covert-way, yet this work can be stormed; and further improvements in its disposition are still requisite, to enable the garrison to defend it with great obstinacy.

Fourthly, the besieger can breach the body of the place through the ditch of the ravelin, even before he has taken this work; and after taking it he can execute the same operation through the ditch of the redoubt. The body of the place is also liable to be breached from the terreplein of the redoubts in the re-entering places of arms, through the openings between the profiles of the tenaille and the flanks of the bastions; and it is to be observed, likewise, that the besieger has it in his power to dislodge the garrison of the re-entering places of arms and their redoubts without making any direct attack upon these works, as, after taking the ravelin and destroying its coupures, he can advance in the rear of the above places of arms and redoubts, by means of a single sap which he constructs in the parapet of the ravelin, in order to keep up from this sap a plunging and reverse fire upon the troops stationed in them.

Fifthly, the flanking defence that the ditches of the ravelin and its redoubt receive from the faces of the bastions, is not so effectual as might be wished; and, as has been previously remarked, the ditch along the escarp of the tenaille is but imperfectly defended.

Lastly, this system has the same inconveniences as that of Vauban, with respect to the retrenchments in the bastions, the requisite quantity of timber during the siege, &c.

The duration of the defence which the system. just described can afford, consists of thirty-six days in such inferior polygons as allow the besieger to carry on the attacks upon a ravelin and the two collateral bastions, but it may be extended to forty-two or forty-four days in the other polygons.

Besides the modifications which have been effected in Cormontaingne's original system, several engineers of eminence, amongst whom are Virgin, La Chiche, Montalembert, Bousmard, Mouzé, and Carnot, have some years since published methods of their own; but notwithstanding the great ingenuity, profound views and considerable degree of professional knowledge, which these engineers have displayed in their productions, yet they have not entirely solved the very difficult problem of contriving a system of fortification to which no well-founded objections can be made. The reader, however, will derive much benefit from making himself acquainted with the several systems, according to his professional or other connexions with this art, as well as with the reasonings of their authors in order to support them; and particularly, if not being yet sufficiently proficient in fortification to trust to his own discrimination, he consults the judicious analysis of those systems which men of experience have given.

As to irregular fortifications the great variety of combinations which they require evidently shows, as colonel Malortie observes, that any expectation of acquiring an effectual knowledge of it from such general explanations, accompanied by few plates, as might be given in an ordinary treatise, or in other works of the same moderate extent, would be visionary. Indeed, the best and even the only method of gaining real information on this subject, is to learn at first the general principles of fortification, together with the use of the works most commonly employed, and the proper method of disposing them in a fortress perfectly regular. The learner is then to examine attentively plans of irregular fortresses situated in various kinds of ground, particularly those of the most celebrated fortresses, and to avail himself of any verbal explanation which experienced professional men may give him, in respect to the intended purposes and the merits of the works composing the fortresses in question; he may undoubtedly also consult the publications of such authors as have treated of irregular fortifications; and, if circumstances should allow him to visit fortresses, he certainly will derive great advantage from viewing upon the spot the fortifications and the country round them.'

We refer to the few observations of this gentleman in his treatise on Permanent Fortifications, chap. x., as well worthy the learner's particular attention.

SECT. V.-M. CARNOT'S SYSTEM.

But it is due to the reputation of Carnot, he fore we close this part of our subject, to notice

distinctly his New Principles of Fortification His Treatise on the Defence of Fortified Places is in very general circulation; it has been translated into our language, and the unquestionable talents of the author as a mathematician and an engineer have powerfully patronised his theory, that a fortified place may be renderea impregnable by a general use of vertical fire.

M. Carnot tells us, that he had long been convinced of the vast advantages which would result from adopting vertical fire as the basis of defence, instead of using it as an accessory mean; but that he did not make his theory known, lest the discovery should be practised against the of fensive operations of his countrymen. 'But now,' he observes, that our enemies have few places left to defend, I no longer hesitate to render my ideas public, since any improvement in the defensive art must turn, almost exclusively, to the advantage of the French frontiers.'

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That is, as Sir Howard Douglas remarks, 'when France had succeeded in establishing almost universal dominion over the continent of Europe, M. Carnot promulgated his new doctrine, in obedience, as he informs us, to the commands of Buonaparte, to show the military intrusted with the defence of the bulwarks of the state, the importance of their functions, and the extent of their obligations-the glory which attends the faithful discharge of their duties, and the misfortunes which those, who either neglect or betray them, must draw upon themselves and upon their country. This appeal was particularly addressed to the troops occupying the fortresses which the French retained in foreign territory, and to the garrisons of their frontier and interior places, at the time Napoleon began to prepare his mighty means for the Russian war. To stimulate to the utmost the defensive energies of his garrisons, the work contains succinct and very partial accounts of memorable sieges, together with a code of imperial laws detailing the circumstarces, and evidences of extremity, under which, only, governors or commandants of fortresses and places should be justified in capitulating, without incurring the severe and summary penalties denounced against those who should surrender their posts without full compliance with the terms of this decree.

Before Napoleon entered on the remote enterprise which his insatiable ambition impelled him to undertake, it became essentially necessary to adopt every possible precaution to enforce the constancy of his allies, maintain the internal tranquillity of his empire, and stimulate elsewhere a defensive system, during the absence of the grand army; and to urge to the last extremity the defence of his frontier places, in the event of any failure in his external operations. These great objects, he rightly considered, would all be best promoted by giving to public opinion, from high professional authority, such impressions of the security in which these strong-holds were left, and of the impossibility of reducing them, as might deter enterprises of defection and conspiracy, and give enthusiastic confidence in the means of resistance. To effect this, it was necessary to assert the discovery of some fallacy in

the well known balance which, since the days of Vauban, has remained decidedly, and with calcu. lable certainty, in favor of attack; but as such a revolution in public opinion could not be established by any new arrangement of known or ordinary means, M. Carnot boldly and ingeniously proclaimed the discovery of a new mode of defence, by which fortresses might be rendered absolutely impregnable, and by means so simple as to be easily adapted to all places. In promulgating this new doctrine the author has filled-in some useful materials and observations calculated to excite protracted defence; but his general reasoning is quite delusive. He wrote as a political engineer; or rather he compiled the treatise which, he informs us, Napoleon sketched; and the deduction drawn from it is, perhaps, one of the most curious and interesting passages that has every emanated from the imperial press. From what we have just read,' says our author, results, I think, very evidently, this tranquillising truth, that the barriers of the French empire are absolutely inexpugnable by any power, or coalition of powers, whatever, if well defended.'

The chief recommendation of this writer is, that the besieged should begin to make use of vertical fire upon the commencement of the construction of the third parallel, and from that stage of the siege keep up an incessant discharge of musketry and four-ounce iron balls, at great elevation, upon the enemy's works, so as to form a rain (pluie) of shot upon the trenches. The iron balls to be discharged from a number of twelve-inch mortars, two of which are placed in the saliants of each bastion and ravelin in the front or fronts attacked each mortar throwing 600 balls at every discharge. He introduces his theory of the effect of these balls by observing, that of any number which fall in the trenches, the number that take effect will depend upon the proportion which the unoccupied part of the trench bears to the part which is covered by the men posted and working in it. Thus, supposing a man standing upon an horizontal plane to cover a space of about a foot square, and a man in the attitude of working somewhat more, M. Carnot calculates that the projections of the bodies of the men usually working and posted in the trenches will occupy about part of their surface; from which he infers, that of every 180 balls that fall in the trench, one should, according to the doctrine of chances, hit a man; and he does not doubt that it will put him 'hors de combat.'

The distribution which M. Carnot proposes to make of his mortars and pierriers for vertical fire, on a front of fortification, is as follows:

Three mortars in the saliant angle of each bastion and demi-lune.

Three to fire d'écharpe on each of the four branches of the covered way.

The mortars or pierriers are placea behind the ramparts in small bomb-proof casemates, each large enough to contain a mortar and two or three men. The casemates, or as M. Carnot calls them, 'petites cases blindées à l'épreuve,' for the defence of the capitals, are placed perpendicularly to the capitals of the bastions or

demi-lune; and those to defend the four bran ches of the covered way are placed parallel to the works behind which they are erected, forming a sort of interior enclosure at the foot of the interior slope of the rampart. A large port, or embrasure, is left in the end of each casemate to admit of the discharge of the mortar.

By this disposition the terre-plein of the rampart is left free for the reception of the ordinary artillery and musketry, which however, he says, should not be used at the same time with the ❝ batteries-blindées,' but, according to circumstances, in alternation with them. The artillery in the saliants are mounted en barbette, protected by merlons of sand-bags, until the ricochet batteries of attack are established; after which the ordnance of the place is to be withdrawn from the ramparts, until the fire of the ricochet batteries is masked by the advanced works of the attack. Thus, as soon as the enemy's ricochet batteries gain ascendancy over the artillery of the place, M. Carnot withdraws his ordnance and troops, and brings into action his batteries blindées, two-thirds of which are, at this stage of the siege, furnished with guns or howitzers to fire à ricochet, and the other third armed with mortars. This arrangement of ordnance in the casemates is to continue until the third parallel be finished, when the guns and howitzers in the batteries blindées' are to be replaced by pierriers, which, together with the mortars, are then to discharge small iron balls, pieces of iron, case shot, shells, and stones, on the enemy's approaches.

This writer presses the importance of ricochet fire for defence, and says, it is not sufficiently practised. He recommends its more general application both from behind the ramparts and dry ditches: and thinks it even more important in defending than in attacking a place.

'The enemy's troops,' says he, ' are every night exposed, without shelter, in constructing their works and covering their parties. Now a bullet which grazes five or six times will be much more likely to do execution than a direct shot, which may either strike short of the mark, and in the next bound pass far beyond the trenches, or go over without touching at all.'

He also gravely recommends a revival of the ancient weapons, particularly the cross-bow, in the defence of fortified places, and quotes many instances of brilliant defence, in ancient and modern history, to support his doctrine of the efficacy of armes blanches.' 'A man,' says he, 'armed with a cross-bow, may easily discharge an arrow every minute, which is 1440 in twentyfour hours. Supposing then that the besieged employ 200 cross-bow men, there would be 288,000 arrows discharged from the ramparts in that time. But it has been shown,' he adds, that at least one arrow in every 180 will take effect, whence, of the whole number thrown, 1600 will do execution, from which it follows that 1600 men will be put hors de combat daily. Supposing this défense rapprochée to continue only ten days, the besiegers he calculates will have lost 16,000 men, and it would be easy to double the result by augmenting the number of cross-bowmen.'

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M. Carnot has imbibed many of M. Follard's prejudices in favor of the defensive powers of ancient arms. The latter says 'all prejudice apart, this arm (the cross-bow) is infinitely more destructive than our musket, its force being at least equal, and its effect more certain.' But our author's assertion that 200 arbalétriers would put 1600 men of the besiegers 'hors de combat' daily, is going much further than ever the prejudiced Follard ventured to retrograde upon the path of improvement.

M. Guichard gives more correct readings of the practice and character of ancient sieges; and to all those on whom the reasoning of Carnot, supported by the fancies of Follard, have had any effect, we recommend the perusal of that work, as a sensible antidote, M. Guichard says, page 13, 'I have examined in the original language, the passages upon which he (M. Follard) appuys his system, and soon convinced myself that there is no authority for what he asserts, and that the authors express themselves very clearly upon the subjects they have undertaken to explain. We might extract many other observations bearing with equal force upon the erroneous conclusions M. Follard has drawn; but it is quite idle to compare modern and ancient modes of warfare for any purpose of practical utility. The invention of gunpowder turned the balance in favor of attack, and the introduction of the ricochet system has confirmed this superiority. All M. Carnot's theory and ingenuity are insufficient to restore the equilibrium of this settled preponderance. His suggestions, if strictly followed, would on the contrary turn the scale more in the direction of their present inequality, from the little vigor he excites in the first stages of defence. The introduction of artillery gives a momentum, equal to that of a battering-ram, to a cannon ball which may be projected with such a degree of accuracy, as to enable us to injure defences at very com siderable distances. The largest battering-ram we read of was 120 feet long, and, including a head of cast iron of one ton and a half, was about 35,000lbs. weight. Supposing it to te worked by 500 men, each exerting a force of 70lbs. the force of momentum produced by ther action, when the ram moves one foot per second, is about 35,000lbs.-The momentum of a 241b. shot, moving with a velocity of 1500 feet pe second, is about 36,000lbs. The invention of gunpowder thus proved utterly destructive of all former modes of war; and the gradual irprovements made in artillery, and in the scien of attack, explain the causes of what M. Carr considers so extraordinary, when he says, pai 327, from what cause does it happen that t strongest places are commonly taken in sie which rarely exceed six weeks, and genera last only twenty-two or twenty-three days These are the causes which have produced short duration of modern sieges: and it is qu useless and absurd, as colonel Douglas we observes, to attempt any comparison betwee the obsolete and the existing practices, with hope of improvement.

M. Carnot closes this part of his treatise! noticing, and certainly favoring (p. 349%

singular idea of a M. Flachon de la Jomarière, who proposes to pour upon the besiegers, when they are about to crown the covered-way, an enormous quantity of water from powerful engines, which, he says, will make the soil so liquid that it cannot be worked.

His New System of Improving Fortifications is, of course, grounded on these principles. The spirit,' says A. Carnot, of the new system of fortification, consists in procuring, by the particular combination of the parts which compose it, numerous debouches on all the avenues of the place, so that the besiegers may not be able to establish themselves near it without being exposed to be suddenly attacked, at all times, by all the garrison. From this the enemy will not be able to present himself any where, without keeping troops constantly drawn out, ready to repulse any sortie the besieged may unexpectedly make, and which they may renew whenever they please. The besiegers will therefore be obliged to accumulate troops on all parts of the immense circumference which they must occupy, to embrace the defences of the place; and as in the défense raprochée all this development of force is within the influence of vertical fire, showers of projectiles will carry off some men every moment, and at length entirely crush the besiegers.'

This torrent of vertical fire' is thrown from casemated mortar-batteries, the positions of which are determined from an acknowledged defect in Vauban's systems, viz. the deficiency of fire on the prolongations of the capitals of the bastions, but which faul M. Cormontaingne has remedied by constructing redoubts in the reentering places of arms.

M. Carnot's ideas of the irresistible effect, and exclusive advantage, of this profusion of vertical fire in defence, are such, he asserts, p. 445, that it will change entirely the character of the operations of a siege. According to the existing practice,' he says, 'the besiegers are covered, and the besieged exposed. In the new system, on the contrary, the besieged are covered, but the besiegers exposed to a profusion of feux verticaux, which will reach them behind their parapets and lodgments, enabling the besieged to defend their out-works, without occupying them, merely by pouring upon them torrents of vertical ire when the assailants move forward to the ttack."

M. Carnot then arranges his new system; the asemated mortar-batteries are placed in interior nclosures in the gorges of the bastions, so as to re in the direction of their capitals. There re nine casemates in each battery: of these, even contain mortars or pierriers, two in each; e other two (the extreme casemates) are each med with three guns, for the defence of the tch of the retranchement général. The escarpe the retranchement général is a detached wall aced in front of the rampart, leaving a chemin s rondes eighteen feet wide. The exterior pes of the ramparts are all forty-five degrees. e bastions are also covered by a detached wall cted near the base of the exterior slope of the apart, leaving a chemin des rondes six feet de.

The ditch of the bastion is thirty-six feet wide. Counterguards are placed before the bastions. The demi-lunes are works of the same profile as the counterguards. Sometimes M. Carnot calls his counterguards and demi-lunes glacis coupés, and under this name recommends them for improving the defences of existing places. The cavaliers are placed in front of the tenailles, and communicate with them by caponnières.

The counterguards and demi-lunes have ditches thirty-six feet wide at bottom, the counter slopes forming a reverse glacis of forty-three yards which M, Carnot calls glacis en contrepente.

In old fortresses M. Carnot proposes to convert a portion of each bastion into a counterguard, by making a ditch, about thirty-six feet wide across the bastion, from the middle of each flank, in the directions of lines of defence; the two branches of the ditch meeting, consequently, on the capital. The part thus enclosed is formed into a bastion, by making parapets upon the interior lines of the ditch, which thus become the faces of a bastion so small that its flanks are but sixty feet long-sufficient only to receive three guns. The new ditch is consequently very little defended by flank-fire; but this, consistently with the principles already noticed, M. Carnot has here also sacrificed to the superiority of vertical fire.

For the purpose, chiefly, of being able to make sorties with facility, M. Carnot proposes to convert the glacis into a glacis en contrepente, and, with the earth furnished by the excavation, to form the upper part of the old glacis into a counterguard or glacis coupé, raised nearly as high as the body of the place. The interior slope of the new work occupies the greater part of the old covered-way. The traverses are removed; and, instead of palisades, a brick wall furnished with loop-holes is constructed very near the counterscarp. The exterior slope of the glacis coupé is so abrupt that no part of it can be seen from the body of the place; and the greater part of the advanced ditch formed by this alteration cannot be seen at all.

Colonel Sir Howard Douglas has published some spirited and scientific Observations on the Motives, Errors, and Tendency of M. Carnot's Principles. We have already quoted this writer, and it is but fair to add, that he seems to make a formidable attack upon the principles and constructions of that able engineer. We abstract a sufficient portion of his remarks and experiments to place the whole subject fairly before the reader.

'It is quite clear,' observes this writer, 'that M. Carnot has formed his theory upon the parabolic hypothesis, which, I must inform such readers as are not acquainted with these matters, is the theory of a projectile's flight in a non-resisting medium. This theory, considerably erroneous in all cases, is particularly and greatly so with small projectiles; and its deductions, as applied to the velocity of descent of small balls used in very elevated short ranges, are quite fallacious. The velocity of the ball in a horizontal direction (which by this theory would be constant, and to the projectile velocity as radius to t

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of the angle of elevation) being inconsiderable, it is evident that the effect of vertical fire must depend upon the velocity of descent in the direction of the curve. Estimating this according to the parabolic theory (as the secant of the angle of elevation), the motion would be slowest at the vertex of the curve, and the velocities of the projectile be equal at equal distances from that point. According to this supposition we should assign to the descent of small balls, discharged at an elevation of seventy-five degrees, or eighty degrees, such accelerated velocities, as would, if true, be quite sufficient to do good service in the way M. Carnot suggests; but the fact is, that there can be no acceleration beyond a limit which, with small balls, is very much less than is generally imagined. From the vertex of the curve, where all the vertical motion is lost, the ball begins to descend by an urging force which is nearly constant, viz. its own weight. This force would produce equal increments of velocity, in equal times in vacuo, but in air, the descent of the ball being resisted more and more as the velocity accelerates, the urging force will, at a certain velocity, be opposed by an equal resistance of air, after which there can be no further acceleration of motion, and the ball will continue to descend with a velocity nearly terminal.

"When I began to consider this interesting problem, as applied to vertical fire, I was soon satisfied that M. Carnot had entirely overlooked terminal velocity; and I shall show, from his own words, that this is the case. It is not necessary to exhibit here the investigations by which I have established the impotency of M. Carnot's vertical fire; I shall only state the results, not to embarrass the conclusions with abstruse matter. The solutions are computed from the theorems given in Dr. Hutton's tracts, and, although the results may differ a little from the truth, yet it is quite clear, that in the descent of the balls there can be no acceleration of motion beyond a certain limit; that with small balls this velocity is very much less than persons who have not investigated this curious problem would imagine; and that M. Carnot has evidently overlooked this circumstance.

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The velocity which a musket ball has acquired when the resistance becomes equal to the weight, or urging force of descent, is only about 180 feet in a second. The potential altitude, or the height from which the ball must descend in vacuo, to acquire a velocity equal nearly to the terminal velocity, is 523 feet. Hence, in the first place, it would be a waste of means to use the full charge; for a musket ball fired upwards, with the ordinary quantity of powder, would be projected to a greater height than 523 feet; and it is evident that all above this is unnecessary. The indentation which a musket ball, moving with a velocity of 180 feet per second, makes on a piece of elm timber, is about of an inch this might, perhaps, be sufficient to knock a man down, if by great chance it were to fall upon his head; but in no other case would it put him hors de combat.'

'Now, as to the four-ounce balls. The diameter of a French four-ounce ball is one

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The potential altitude of the cast-iron ball is about

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201 feet

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. 631 650 'M. Carnot recommends that the balls should be made of hammered iron; but adds, that, as the charge of powder for a mortar is sinall, balls of cast-iron may resist the explosion without breaking, and will answer as well. Now this observation shows that the author had not considered the effect of the air's resistance, nor doubted a sufficiency of force in his vertical fire: for the weight of a ball of hammered iron is greater than that of a ball of cast-iron of equal diameter, and the superior weight or urging force of the former would generate greater terminal velocity than a lighter ball of the same size could acquire; the momenta of the two balls in question would be as nineteen to eighteen.

'Four-ounce balls, discharged at elevations even considerably above forty-five degrees, to the distance of 120 yards, would not inflict a mortal wound, excepting upon an uncovered head. They would not have force sufficient to break any principal bone; there would be no penetration, but merely a contusion. This certainly would not oblige the besiegers to cover themselves with blindages, as M. Carnot imagines; for a strong cap or hat, and a cover of thick leather for the back and shoulders, would be sufficient protection from the effects of his vertical fire with small balls. As the quantity of balls required to feed mortars discharging coc balls at a time would be very considerable, M Carnot observes that cubes of iron of eight er ten lines side, cut from square bars of this d mension, may be substituted. These, he says may be fired from mortars, howitzers, or store mortars, and will produce the same effect as bala (page 491, Carnot).

'Let us consider this:

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