NOTE: This version of Clausewitz's On War is the long-obsolete J.J. Graham translation published in London in 1873. The 1976/84 Howard/Paret version is the  standard translation today.


 
 

Chapter IX

Plan of War when the Destruction of the Enemy is the Object

HAVING characterised in detail the different aims to which war may be directed, we shall go through the organisation of war as a whole for each of the three separate gradations corresponding to these aims.

In conformity with all that has been said on the subject up to the present, two fundamental principles reign throughout the whole plan of the war, and serve as a guide for everything else.

The first is: to reduce the weight of the enemy's power into as few centres of gravity as possible, into one if it can be done; again, to confine the attack against these centres of force to as few principal undertakings as possible, to one if possible; lastly, to keep all secondary undertakings as subordinate as possible. In a word, the first principle is, to act concentrated as much as possible.

The second principle runs thus—to act as swiftly as possible; therefore, to allow of no delay or detour without sufficient reason.

The reducing the enemy's power to one central point depends—

1. On the nature of its political connection. If it consists of armies of one Power, there is generally no difficulty; if of allied armies, of which one is acting simply as an ally without any interest of its own, then the difficulty is not much greater; if of a coalition for a common object, then it depends on the cordiality of the alliance; we have already treated of this subject.

2. On the situation of the theatre of war upon which the different hostile armies make their appearance.

If the enemy's forces are collected in one army upon one theatre of war, they constitute in reality a unity, and we need not inquire further; if they are upon one theatre of war, but in separate armies, which belong to different Powers, there is no longer absolute unity; there is, however, a sufficient interdependence of parts for a decisive blow upon one part to throw down the other in the concussion. If the armies are posted in theatres of war adjoining each other, and not separated by any great natural obstacles, then there is in such case also a decided influence of the one upon the other; but if the theatres of war are wide apart, if there is neutral territory, great mountains, etc., intervening between them, then the influence is very doubtful and improbable as well; if they are on quite opposite sides of the State against which the war is made, so that operations directed against them must diverge on eccentric lines, then almost every trace of connection is at an end.

If Prussia was attacked by France and Russia at the same time, it would be as respects the conduct of the war much the same as if there were two separate wars; at the same time the unity would appear in the negotiations.

Saxony and Austria, on the contrary, as military powers in the Seven Years' War, were to be regarded as one; what the one suffered the other felt also, partly because the theatres of war lay in the same direction for Frederick the Great, partly because Saxony had no political independence.

Numerous as were the enemies of Buonaparte in Germany in 1813, still they all stood very much in one direction in respect to him, and the theatres of war for their armies were in close connection, and reciprocally influenced each other very powerfully. If by a concentration of all his forces he had been able to overpower the main army, such a defeat would have had a decisive effect on all the parts. If he had beaten the Bohemain grand army, and marched upon Vienna by Prague, Blucher, however willing, could not have remained in Saxony, because he would have been called upon to co-operate in Bohemia, and the Crown Prince of Sweden as well would have been unwilling to remain in the Mark.

On the other hand, Austria, if carrying on war against the French on the Rhine and Italy at the same time, will always find it difficult to give a decision upon one of those theatres by means of a successful stroke on the other. Partly because Switzerland, with its mountains, forms too strong a barrier between the two theatres, and partly because the direction of the roads on each side is divergent. France, again, can much sooner decide in the one by a successful result in the other, because the direction of its forces in both converges upon Vienna, the centre of the power of the whole Austrian empire; we may add further, that a decisive blow in Italy will have more effect on the Rhine theatre than a success on the Rhine would have in Italy, because the blow from Italy strikes nearer to the centre, and that from the Rhine more upon the flank, of the Austrian dominions.

It proceeds from what we have said that the conception of separated or connected hostile power extends through all degrees of relationship, and that therefore, in each case, the first thing is to discover the influence which events in one theatre may have upon the other, according to which we may then afterwards settle how far the different forces of the enemy may be reduced into one centre of force.

There is only one exception to the principle of directing all our strength against the centre of gravity of the enemy's power, that is, if ancillary expeditions promise extraordinary advantages, and still, in this case, it is a condition assumed, that we have such a decisive superiority as enables us to undertake such enterprises without incurring too great risk at the point which forms our great object.

When General Bulow marched into Holland in 1814, it was to be foreseen that the thirty thousand men composing his corps would not only neutralise the same number of Frenchmen, but would, besides, give the English and the Dutch an opportunity of entering the field with forces which otherwise would never have been brought into activity.

Thus, therefore, the first consideration in the combination of a plan for a war, is to determine the centres of gravity of the enemy's power, and, if possible, to reduce them to one. The second is to unite the forces which are to be employed against the centre of force into one great action.

Here now the following grounds for dividing our forces may present themselves:—

1. The original position of the military forces, therefore also the situation of the States engaged in the offensive.

If the concentration of the forces would occasion detours and loss of time, and the danger of advancing by separate lines is not too great, then the same may be justifiable on those grounds; for to effect an unnecessary concentration of forces, with great loss of time, by which the freshness and rapidity of the first blow is diminished, would be contrary to the second leading principle we have laid down. In all cases in which there is a hope of surprising the enemy in some measure, this deserves particular attention.

But the case becomes still more important if the attack is undertaken by allied States which are not situated on a line directed towards the State attacked—not one behind the other—but situated side by side. If Prussia and Austria undertook a war against France, it would be a very erroneous measure, a squandering of time and force if the armies of the two powers were obliged to set out from the same point, as the natural line for an army operating from Prussia against the heart of France is from the Lower Rhine, and that of the Austrians is from the Upper Rhine. Concentration, therefore, in this case, could only be effected by a sacrifice; consequently in any particular instance, the question to be decided would be, Is the necessity for concentration so great that this sacrifice must be made?

2. The attack by separate lines may offer greater results.

As we are now speaking of advancing by separate lines against one centre of force, we are, therefore, supposing an advance by converging lines. A separate advance on parallel or eccentric lines belongs to the rubric of accessory undertakings, of which we have already spoken.

Now, every convergent attack in strategy, as well as in tactics, holds out the prospect of great results; for if it succeeds, the consequence is not simply a defeat, but more or less the cutting off of the enemy. The concentric attack is, therefore, always that which may lead to the greatest results; but on account of the separation of the parts of the force, and the enlargement of the theatre of war, it involves also the most risk; it is the same here as with attack and defence, the weaker form holds out the greater results in prospect.

The question, therefore, is, whether the assailant feels strong enough to try for this great result.

When Frederick the Great advanced upon Bohemia, in the year 1757, he set out from Saxony and Silesia with his forces divided. The two principal reasons for his doing so were, first, that his forces were so cantoned in the winter that a concentration of them at one point would have divested the attack of all the advantages of a surprise; and next, that by this concentric advance, each of the two Austrian theatres of war was threatened in the flanks and the rear. The danger to which Frederick the Great exposed himself on that occasion was that one of his two armies might have been completely defeated by superior forces; should the Austrians not see this, then they would have to give battle with their centre only, or run the risk of being thrown off their line of communication, either on one side or the other, and meeting with a catastrophe; this was the great result which the king hoped for by this advance. The Austrians preferred the battle in the centre, but Prague, where they took up their position, was in a situation too much under the influence of the convergent attack, which, as they remained perfectly passive in their position, had time to develop its efficacy to the utmost. The consequence of this was that when they lost the battle, it was a complete catastrophe; as is manifest from the fact that two-thirds of the army with the commander-in-chief were obliged to shut themselves up in Prague.

This brilliant success at the opening of the campaign was attained by the bold stroke with a concentric attack. If Frederick considered the precision of his own movements, the energy of his generals, the moral superiority of his troops, on the one side, and the sluggishness of the Austrians on the other, as sufficient to ensure the success of his plan, who can blame him? But as we cannot leave these moral advantages out of consideration, neither can we ascribe the success solely to the mere geometrical form of the attack. Let us only think of the not less brilliant campaign of Buonaparte's, in the year 1796, when the Austrians were so severely punished for their concentric march into Italy. The means which the French general had at command on that occasion, the Austrian general had also at his disposal in 1757 (with the exception of the moral), indeed, he had rather more, for he was not, like Buonaparte, weaker than his adversary. Therefore, when it is to be apprehended that the advance on separate converging lines may afford the enemy the means of counteracting the inequality of numerical forces by using interior lines, such a form of attack is not advisable; and if on account of the situation of the belligerents, it must be resorted to, it can only be regarded as a necessary evil.

If, from this point of view, we cast our eyes on the plan which was adopted for the invasion of France in 1814, it is impossible to give it approval. The Russian, Austrian, and Prussian armies were concentrated at a point near Frankfort on the Maine, on the most natural and most direct line to the centre of the force of the French monarchy. These armies were then separated, that one might penetrate into France from Mayence, the other from Switzerland. As the enemy's force was so reduced that a defence of the frontier was out of the question, the whole advantage to be expected from this concentric advance, if it succeeded, was that while Lorraine and Alsace were conquered by one army, Franche-Comte would be taken by the other. Was this trifling advantage worth the trouble of marching into Switzerland?—We know very well that there were other (but just as insufficient) grounds which caused this march; but we confine ourselves here to the point which we are considering.

On the other side, Buonaparte was a man who thoroughly understood the defensive to oppose to a concentric attack, as he had already shown in his masterly campaign of 1796; and although the Allies were very considerably superior in numbers, yet the preponderance due to his superiority as a general was on all occasions acknowledged. He joined his army too late near Chalons, and looked down rather too much, generally, on his opponents, still he was very near hitting the two armies separately; and what was the state he found them in at Brienne? Blucher had only 27,000 of his 65,000 men with him, and the great army, out of 200,000, had only 100,000 present. It was impossible to make a better game for the adversary. And from the moment that active work began, no greater want was felt than that of re-union.

After all these reflections, we think that although the concentric attack is in itself a means of obtaining greater results, still it should generally only proceed from a previous separation of the parts composing the whole force, and that there are few cases in which we should do right in giving up the shortest and most direct line of operation for the sake of adopting that form.

3. The breadth of a theatre of war can be a motive for attacking on separate lines.

If an army on the offensive in its advance from any point, penetrates with success to some distance into the interior of the enemy's country, then, certainly, the space which it commands is not restricted exactly to the line of road by which it marches, it will command a margin on each side; still that will depend very much, if we may use the figure, on the solidity and cohesion of the opposing State. If the State only hangs loosely together, if its people are an effeminate race unaccustomed to war, then, without our taking much trouble, a considerable extent of country will open behind our victorious army; but if we have to deal with a brave and loyal population, the space behind our army will form a triangle, more or less acute.

In order to obviate this evil, the attacking force requires to regulate its advance on a certain width of front. If the enemy's force is concentrated at a particular point, this breadth of front can only be preserved so long as we are not in contact with the enemy, and must be contracted as we approach his position: that is easy to understand.

But if the enemy himself has taken up a position with a certain extent of front, then there is nothing absurd in a corresponding extension on our part. We speak here of one theatre of war, or of several, if they are quite close to each other. Obviously this is, therefore, the case when, according to our view, the chief operation is, at the same time, to be decisive on subordinate points

But now can we always run the chance of this? And may we expose ourselves to the danger which must arise if the influence of the chief operation is not sufficient to decide at the minor points? Does not the want of a certain breadth for a theatre of war deserve special consideration?

Here as well as everywhere else it is impossible to exhaust the number of combinations which may take place; but we maintain that, with few exceptions, the decision on the capital point will carry with it the decision on all minor points. Therefore, the action should be regulated in conformity with this principle, in all cases in which the contrary is not evident.

When Buonaparte invaded Russia, he had good reason to believe that by conquering the main body of the Russian army he would compel their forces on the Upper Dwina to succumb. He left at first only the corps of Oudinot to oppose them, but Wittgenstein assumed the offensive, and Buonaparte was then obliged to send also the sixth corps to that quarter.

On the other hand, at the beginning of the campaign, he directed a part of his forces against Bagration; but that general was carried along by the influence of the backward movement in the centre, and Buonaparte was enabled then to recall that part of his forces. If Wittgenstein had not had to cover the second capital, he would also have followed the retreat of the great army under Barclay.

In the years 1805 and 1809, Buonaparte's victories at Ulm and Ratisbon decided matters in Italy and also in the Tyrol, although the first was rather a distant theatre, and an independent one in itself. In the year 1806, his victories at Jena and Auerstadt were decisive in respect to everything that might have been attempted against him in Westphalia and Hesse, or on the Frankfort road.

Amongst the number of circumstances which may have an influence on the resistance at secondary points, there are two which are the most prominent.

The first is: that in a country of vast extent, and also relatively of great power, like Russia, we can put off the decisive blow at the chief point for some time, and are not obliged to do all in a hurry.

The second is: when a minor point (like Silesia in the year 1806), through a great number of fortresses, possesses an extraordinary degree of independent strength. And yet Buonaparte treated that point with great contempt, inasmuch as, when he had to leave such a point completely in his rear on the march to Warsaw, he only detached 20,000 men under his brother Jerome to that quarter.

If it happens that the blow at the capital point, in all probability, will not shake such a secondary point, or has not done so, and if the enemy has still forces at that point, then to these,—as a necessary evil,—an adequate force must be opposed, because no one can absolutely lay open his line of communication from the very commencement.

But prudence may go a step further; it may require that the advance upon the chief point shall keep pace with that on the secondary points, and consequently the principal undertaking must be delayed whenever the secondary points will not succumb.

This principle does not directly contradict ours as to uniting all action as far as possible in one great undertaking, but the spirit from which it springs is diametrically opposed to the spirit in which ours is conceived. By following such a principle there would be such a measured pace in the movements, such a paralysation of the impulsive force, such room for the freak of chance, and such a loss of time, as would be practically perfectly inconsistent with an offensive directed to the complete overthrow of the enemy.

The difficulty becomes still greater if the forces stationed at these minor points can retire on divergent lines.—What would then become of the unity of our attack?

We must, therefore, declare ourselves completely opposed in principle to the dependence of the chief attack on minor attacks, and we maintain that an attack directed to the destruction of the enemy which has not the boldness to shoot, like the point of an arrow, direct at the heart of the enemy's power, can never hit the mark.

4. Lastly, there is still a fourth ground for a separate advance in the facility which it may afford for subsistence.

It is certainly much pleasanter to march with a small army through an opulent country, than with a large army through a poor one; but by suitable measures, and with an army accustomed to privations, the latter is not impossible, and, therefore, the first should never have such an influence on our plans as to lead us into a great danger.

We have now done justice to the grounds for a separation of forces which divides the chief operation into several, and if the separation takes place on any of these grounds, with a distinct conception of the object, and after due consideration of the advantages and disadvantages, we shall not venture to find fault.

But if, as usually happens, a plan is drawn out by a learned general staff, merely according to routine; if different theatres of war, like the squares on a chess board, must each have its piece first placed on it before the moves begin, if these moves approach the aim in complicated lines and relations by dint of an imaginary profundity in the art of combination, if the armies are to separate to-day in order to apply all their skill in reuniting at the greatest risk in fourteen days—then we have a perfect horror of this abandonment of the direct simple common-sense road to rush intentionally into absolute confusion. This folly happens more easily the less the general-in-chief directs the war, and conducts it in the sense which we have pointed out in the first chapter as an act of his individuality invested with extraordinary powers; the more, therefore, the whole plan is manufactured by an inexperienced staff, and from the ideas of a dozen smatterers.

We have still now to consider the third part of our first principle; that is, to keep the subordinate parts as much as possible in subordination.

Whilst we endeavour to refer the whole of the operations of a war to one single aim, and try to attain this as far as possible by one great effort, we deprive the other points of contact of the States at war with each other of a part of their independence; they become subordinate actions. If we could concentrate everything absolutely into one action, then those points of contact would be completely neutralised; but this is seldom possible, and, therefore, what we have to do is to keep them so far within bounds, that they shall not cause the abstraction of too many forces from the main action.

Next, we maintain that the plan of the war itself should have this tendency, even if it is not possible to reduce the whole of the enemy's resistance to one point; consequently, in case we are placed in the position already mentioned, of carrying on two almost quite separate wars at the same time, the one must always be looked upon as the principal affair to which our forces and activity are to be chiefly devoted.

In this view, it is advisable only to proceed offensively against that one principal point, and to preserve the defensive upon all the others. The attack there being only justifiable when invited by very exceptional circumstances.

Further we are to carry on this defensive, which takes place at minor points, with as few troops as possible, and to seek to avail ourselves of every advantage which the defensive form can give.

This view applies with still more force to all theatres of war on which armies come forward belonging to different powers really, but still such as will be struck when the general centre of force is struck.

But against the enemy at whom the great blow is aimed, there must be, according to this, no defensive on minor theatres of war. The chief attack itself, and the secondary attacks, which for other reasons are combined with it, make up this blow, and make every defensive, on points not directly covered by it, superfluous. All depends on this principal attack; by it every loss will be compensated. If the forces are sufficient to make it reasonable to seek for that great decision, then the possibility of failure can be no ground for guarding oneself against injury at other points in any event; for just by such a course this failure will become more probable, and it therefore constitutes here a contradiction in our action.

This same predominance of the principal action over the minor, must be the principle observed in each of the separate branches of the attack. But as there are generally ulterior motives which determine what forces shall advance from one theatre of war, and what from another against the common centre of the enemy's power, we only mean here that there must be an effort to make the chief action over-ruling, for everything will become simpler and less subject to the influence of chance events the nearer this state of preponderance can be attained.

The second principle concerns the rapid use of the forces.

Every unnecessary expenditure of time, every unnecessary detour, is a waste of power, and therefore contrary to the principles of strategy.

It is most important to bear always in mind that almost the only advantage which the offensive possesses, is the effect of surprise at the opening of the scene. Suddenness and irresistible impetuosity are its strongest pinions; and when the object is the complete overthrow of the enemy, it can rarely dispense with them.

By this, therefore, theory demands the shortest way to the object, and completely excludes from consideration endless discussions about right and left here and there.

If we call to mind what was said in the chapter on the subject of the strategic attack respecting the pit of the stomach in a state, and further, what appears in the fourth chapter of this book, on the influence of time, we believe no further argument is required to prove that the influence which we claim for that principle really belongs to it.

Buonaparte never acted otherwise. The shortest high road from army to army, from one capital to another, was always the way he loved best.

And in what will now consist the principal action to which we have referred everything, and for which we have demanded a swift and straightforward execution?

In the fourth chapter we have explained as far as it is possible in a general way what the total overthrow of the enemy means, and it is unnecessary to repeat it. Whatever that may depend on at last in particular cases, still the first step is always the same in all cases, namely: The destruction of the enemy's combatant force, that is, a great victory over the same and its dispersion. The sooner, which means the nearer our own frontiers, this victory is sought for, the easier it is; the later, that is, the further in the heart of the enemy's country it is gained, the more decisive it is. Here, as well as everywhere, the facility of success and its magnitude balance each other.

If we are not so superior to the enemy that the victory is beyond doubt, then we should, when possible, seek him out, that is his principal force. We say when possible, for if this endeavour to find him led to great detours, false directions, and a loss of time, it might very likely turn out a mistake. If the enemy's principal force is not on our road, and our interests otherwise prevent our going in quest of him, we may be sure we shall meet with him hereafter, for he will not fail to place himself in our way. We shall then, as we have just said, fight under less advantageous circumstances—an evil to which we must submit. However, if we gain the battle, it will be so much the more decisive.

From this it follows that, in the case now assumed, it would be an error to pass by the enemy's principal force designedly, if it places itself in our way, at least if we expect thereby to facilitate a victory.

On the other hand, it follows from what precedes, that if we have a decided superiority over the enemy's principal force, we may designedly pass it by in order at a future time to deliver a more decisive battle.

We have been speaking of a complete victory, therefore of a thorough defeat of the enemy, and not of a mere battle gained. But such a victory requires an enveloping attack, or a battle with an oblique front, for these two forms always give the result a decisive character. It is therefore an essential part of a plan of a war to make arrangements for this movement, both as regards the mass of forces required and the direction to be given them, of which more will be said in the chapter on the plan of campaign.

It is certainly not impossible, that even Battles fought with parallel fronts may lead to complete defeats, and cases in point are not wanting in military history; but such an event is uncommon, and will be still more so the more armies become on a par as regards discipline and handiness in the field. We no longer take twenty-one battalions in a village, as they did at Blenheim.

Once the great victory is gained, the next question is not about rest, not about taking breath, not about considering, not about reorganising, etc., etc., but only of pursuit of fresh blows wherever necessary, of the capture of the enemy's capital, of the attack of the armies of his allies, or of whatever else appears to be a rallying point for the enemy.

If the tide of victory carries us near the enemy's fortresses, the laying siege to them or not will depend on our means. If we have a great superiority of force, it would be a loss of time not to take them as soon as possible; but if we are not certain of the further events before us, we must keep the fortresses in check with as few troops as possible, which precludes any regular formal sieges. The moment that the siege of a fortress compels us to suspend our strategic advance, that advance, as a rule, has reached its culminating point. We demand, therefore, that the main body should press forward rapidly in pursuit without any rest; we have already condemned the idea of allowing the advance towards the principal point being made dependent on success at secondary points; the consequence of this is, that in all ordinary cases, our chief army only keeps behind it a narrow strip of territory which it can call its own, and which therefore constitutes its theatre of war. How this weakens the momentum at the head, and the dangers for the offensive arising therefrom, we have shown already. Will not this difficulty, will not this intrinsic counterpoise come to a point which impedes further advance? Certainly that may occur; but just as we have already insisted that it would be a mistake to try to avoid this contracted theatre of war at the commencement, and for the sake of that object to rob the advance of its elasticity, so we also now maintain, that as long as the commander has not yet overthrown his opponent, as long as he considers himself strong enough to effect that object, so long must he also pursue it. He does so perhaps at an increased risk, but also with the prospect of a greater success. If he reaches a point which he cannot venture to go beyond, where, in order to protect his rear, he must extend himself right and left—well, then, this is most probably his culminating point. The power of flight is spent, and if the enemy is not subdued, most probably he will not be now.

All that the assailant now does to intensify his attack by conquest of fortresses, defiles, provinces, is no doubt still a slow advance, but it is only of a relative kind, it is no longer absolute. The enemy is no longer in flight, he is perhaps preparing a renewed resistance, and it is therefore already possible that, although the assailant still advances intensively, the position of the defence is every day improving. In short, we come back to this, that, as a rule, there is no second spring after a halt has once been necessary.

Theory, therefore, only requires that, as long as there is an intention of destroying the enemy, there must be no cessation in the advance of the attack; if the commander gives up this object because it is attended with too great a risk, he does right to stop and extend his force. Theory only objects to this when he does it with a view to more readily defeating the enemy.

We are not so foolish as to maintain that no instance can be found of States having been gradually reduced to the utmost extremity. In the first place, the principle we now maintain is no absolute truth, to which an exception is impossible, but one founded only on the ordinary and probable result; next, we must make a distinction between cases in which the downfall of a State has been effected by a slow gradual process, and those in which the event was the result of a first campaign. We are here only treating of the latter case, for it is only in such that there is that tension of forces which either overcomes the centre of gravity of the weight, or is in danger of being overcome by it. If in the first year we gain a moderate advantage, to which in the following we add another, and thus gradually advance towards our object, there is nowhere very imminent danger, but it is distributed over many points. Each pause between one result and another gives the enemy fresh chances: the effects of the first results have very little influence on those which follow, often none, often a negative only, because the enemy recovers himself, or is perhaps excited to increased resistance, or obtains foreign aid; whereas, when all is done in one march, the success of yesterday brings on with itself that of to-day, one brand lights itself from another. If there are cases in which States have been overcome by successive blows—in which, consequently, Time, generally the patron of the defensive, has proved adverse—how infinitely more numerous are the instances in which the designs of the aggressor have by that means utterly failed. Let us only think of the result of the Seven Years' War, in which the Austrians sought to attain their object so comfortably, cautiously, and prudently, that they completely missed it.

In this view, therefore, we cannot at all join in the opinion that the care which belongs to the preparation of a theatre of war, and the impulse which urges us onwards, are on a level in importance, and that the former must, to a certain extent, be a counterpoise to the latter; but we look upon any evil which springs out of the forward movement, as an unavoidable evil which only deserves attention when there is no longer hope for us a-head by the forward movement.

Buonaparte's case in 1812, very far from shaking our opinion, has rather confirmed us in it.

His campaign did not miscarry because he advanced too swiftly, or too far, as is commonly believed, but because the only means of success failed. The Russian Empire is no country which can be regularly conquered, that is to say, which can be held in possession, at least not by the forces of the present States of Europe, nor by the 500,000 men with which Buonaparte invaded the country. Such a country can only be subdued by its own weakness, and by the effects of internal dissension. In order to strike these vulnerable points in its political existence, the country must be agitated to its very centre. It was only by reaching Moscow with the force of his blow that Buonaparte could hope to shake the courage of the Government, the loyalty and steadfastness of the people. In Moscow he expected to find peace, and this was the only rational object which he could set before himself in undertaking such a war.

He therefore led his main body against that of the Russians, which fell back before him, trudged past the camp at Drissa, and did not stop until it reached Smolensk. He carried Bagration along in his movement, beat the principal Russia army, and took Moscow.

He acted on this occasion as he had always done: it was only in that way that he made himself the arbiter of Europe, and only in that way was it possible for him to do so.

He, therefore, who admires Buonaparte in all his earlier campaigns as the greatest of generals, ought not to censure him in this instance.

It is quite allowable to judge an event according to the result, as that is the best criticism upon it (see fifth chapter, 2nd book), but this judgment derived merely from the result, must not then be passed off as evidence of superior understanding. To seek out the causes of the failure of a campaign, is not going the length of making a criticism upon it; it is only if we show that these causes should neither have been overlooked nor disregarded that we make a criticism and place ourselves above the General.

Now we maintain that any one who pronounces the campaign of 1812 an absurdity merely on account of the tremendous reaction in it, and who, if it had been successful, would look upon it as a most splendid combination, shows an utter incapacity of judgment.

If Buonaparte had remained in Lithuania, as most of his critics think he should, in order first to get possession of the fortresses, of which, moreover, except Riga, situated quite at one side, there is hardly one, because Bobruisk is a small insignificant place of arms, he would have involved himself for the winter in a miserable defensive system: then the same people would have been the first to exclaim, This is not the old Buonaparte! How is it, he has not got even as far as a first great battle? he who used to put the final seal to his conquests on the last ramparts of the enemy's states, by victories such as Austerlitz and Friedland. Has his heart failed him that he has not taken the enemy's capital, the defenceless Moscow, ready to open its gates, and thus left a nucleus round which new elements of resistance may gather themselves? He had the singular luck to take this far-off and enormous colossus by surprise, as easily as one would surprise a neighbouring town, or as Frederick the Great entered the little state of Silesia, lying at his door, and he makes no use of his good fortune, halts in the middle of his victorious career, as if some evil spirit laid at his heels!—This is the way in which he would have been judged of after the result, for this is the fashion of critics' judgments in general.

In opposition to this, we say, the campaign of 1812 did not succeed because the government remained firm, the people loyal and steadfast, because it therefore could not succeed. Buonaparte may have made a mistake in undertaking such an expedition; at all events, the result has shown that he deceived himself in his calculations, but we maintain that, supposing it necessary to seek the attainment of this object, it could not have been done in any other way upon the whole.

Instead of burthening himself with an interminable costly defensive war in the east, such as he had on his hands in the west, Buonaparte attempted the only means to gain his object: by one bold stroke to extort a peace from his astonished adversary. The destruction of his army was the danger to which he exposed himself in the venture; it was the stake in the game, the price of great expectations. If this destruction of his army was more complete than it need have been through his own fault, this fault was not in his having penetrated too far into the heart of the country, for that was his object, and unavoidable; but in the late period at which the campaign opened, the sacrifice of life occasioned by his tactics, the want of due care for the supply of his army, and for his line of retreat, and lastly, in his having too long delayed his march from Moscow.

That the Russians were able to reach the Beresina before him, intending regularly to cut off his retreat, is no strong argument against us. For in the first place, the failure of that attempt just shows how difficult it is really to cut off an army, as the army which was intercepted in this case under the most unfavourable circumstances that can be conceived, still managed at last to cut its way through; and although this act upon the whole contributed certainly to increase its catastrophe, still it was not essentially the cause of it. Secondly, it was only the very peculiar nature of the country which afforded the means to carry things as far as the Russians did; for if it had not been for the marshes of the Beresina, with its wooded impassable borders lying across the great road, the cutting off would have been still less possible. Thirdly, there is generally no means of guarding against such an eventuality except by making the forward movement with the front of the army of such a width as we have already disapproved; for if we proceed on the plan of pushing on in advance with the centre and covering the wings by armies detached right and left, then if either of these detached armies meets with a check, we must fall back with the centre, and then very little can be gained by the attack.

Moreover, it cannot be said that Buonaparte neglected his wings. A superior force remained fronting Wittgenstein, a proportionate siege-corps stood before Riga which at the same time was not needed there, and in the south Schwarzenberg had 50,000 men with which he was superior to Tormasoff and almost equal to Tschitschagow: in addition, there were 30,000 men under Victor, covering the rear of the centre. Even in the month of November, therefore, at the decisive moment when the Russian armies had been reinforced, and the French were very much reduced, the superiority of the Russians in rear of the Moscow army was not so very extraordinary. Wittgenstein, Tschitschagow, and Sacken, made up together a force of 100,000. Schwartzenberg, Regmer, Victor, Oudinot, and St. Cyr, had still 80,000 effective. The most cautious general in advancing would hardly devote a greater proportion of his force to the protection of his flanks.

If out of the 600,000 men who crossed the Niemen in 1812, Buonaparte had brought back 250,000 instead of the 50,000 who repassed it under Schwartzenberg, Regmer, and Macdonald, which was possible, by avoiding the mistakes with which he has been reproached, the campaign would still have been an unfortunate one, but theory would have had nothing to object to it, for the loss of half an army in such a case is not at all unusual, and only appears so to us in this instance on account of the enormous scale of the whole enterprize.

So much for the principal operation, its necessary tendency, and the unavoidable risks. As regards the subordinate operations, there must be, above all things, a common aim for all; but this aim must be so situated as not to paralyse the action of any of the individual parts. If we invade France from the upper and middle Rhine and Holland, with the intention of uniting at Paris, neither of the armies employed to risk anything on the advance, but to keep itself intact until the concentration is effected, that is what we call a ruinous plan. There must be necessarily a constant comparison of the state of this threefold movement causing delay, indecision, and timidity in the forward movement of each of the armies. It is better to assign to each part its mission, and only to place the point of union wherever these several activities become unity of themselves.

Therefore, when a military force advances to the attack on separate theatres of war, to each army should be assigned an object against which the force of its shock is to be directed. Here the point is that these shocks should be given from all sides simultaneously, but not that proportional advantages should result from all of them.

If the task assigned to one army is found too difficult because the enemy has made a disposition of his force different to that which was expected, if it sustains a defeat, this neither should, nor must have, any influence on the action of the others, or we should turn the probability of the general success against ourselves at the very outset. It is only the unsuccessful issue of the majority of enterprises or of the principal one, which can and must have an influence upon the others: for then it comes under the head of a plan which has miscarried.

This same rule applies to those armies and portions of them which have originally acted on the defensive, and, owing to the successes gained, have assumed the offensive, unless we prefer to attach such spare forces to the principal offensive, a point which will chiefly depend on the geographical situation of the theatre of war.

But under these circumstances, what becomes of the geometrical form and unity of the whole attack, what of the flanks and rear of corps when those corps next to them are beaten.

That is precisely what we wish chiefly to combat. This glueing down of a great offensive plan of attack on a geometrical square, is losing one's way in the regions of fallacy.

In the fifteenth chapter of the Third Book we have shown that the geometrical element has less influence in strategy than in tactics; and we shall only here repeat the deduction there obtained, that in the attack especially, the actual results at the various points throughout deserve more attention than the geometrical figure, which may gradually be formed through the diversity of results.

But in any case, it is quite certain, that looking to the vast spaces with which strategy has to deal, the views and resolutions which the geometrical situation of the parts may create, should be left to the general-in-chief; that, therefore, no subordinate general has a right to ask what his neighbour is doing or leaving undone, but each is to be directed peremptorily to follow out his object. If any serious incongruity really arises from this, a remedy can always be applied in time by the supreme authority. Thus, then, may be obviated the chief evil of this separate mode of action, which is, that in the place of realities, a cloud of apprehensions and suppositions mix themselves up in the progress of an operation, that every accident affects not only the part it comes immediately in contact with, but also the whole, by the communication of impressions, and that a wide field of action is opened for the personal failings and personal animosities of subordinate commanders.

We think that these views will only appear paradoxical to those who have not studied military history long enough or with sufficient attention, who do not distinguish the important from the unimportant, nor make proper allowance for the influence of human weaknesses in general.

If even in tactics there is a difficulty, which all experienced soldiers admit there is, in succeeding in an attack in separate columns where it depends on the perfect connection of the several columns, how much more difficult, or rather how impossible, must this be in strategy, where the separation is so much wider. Therefore, if a constant connection of all parts was a necessary condition of success, a strategic plan of attack of that nature must be at once given up. But on the one hand, it is not left to our option to discard it completely, because circumstances, which we cannot control, may determine in favour of it; on the other hand, even in tactics, this constant close conjunction of all parts at every moment of the execution, is not at all necessary, and it is still less so in strategy. Therefore in strategy we should pay the less attention to this point, and insist the more upon a distinct piece of work being assigned to each part.

We have still to add one important observation: it relates to the proper allotment of parts.

In the year 1793 and 1794 the principal Austrian army was in the Netherlands, that of the Prussians, on the upper Rhine. The Austrians marched from Vienna to Condé and Valenciennes, crossing the line of march of the Prussians from Berlin to Landau. The Austrians had certainly to defend their Belgian provinces in that quarter, and any conquests made in French Flanders would have been acquisitions conveniently situated for them, but that interest was not strong enough. After the death of Prince Kaunitz, the Minister Thugut carried a measure for giving up the Netherlands entirely, for the better concentration of the Austrian forces. In fact, Austria is about twice as far from Flanders as from Alsace; and at a time when military resources were very limited, and everything had to be paid for in ready money, that was no trifling consideration. Still, the Minister Thugut had plainly something else in view; his object was, through the urgency of the danger to compel Holland, England, and Prussia, the powers interested in the defence of the Netherlands and Lower Rhine, to make greater efforts. He certainly deceived himself in his calculations, because nothing could be done with the Prussian cabinet at that time, but this occurrence always shows the influence of political interests on the course of a war.

Prussia had neither anything to conquer nor to defend in Alsace. In the year 1792 it had undertaken the march through Lorraine into Champagne in a sort of chivalrous spirit. But as that enterprise ended in nothing, through the unfavourable course of circumstances, it continued the war with a feeling of very little interest. If the Prussian troops had been in the Netherlands, they would have been in direct communication with Holland, which they might look upon almost as their own country, having conquered it in the year 1787; they would then have covered the Lower Rhine, and consequently that part of the Prussian monarchy which lay next to the theatre of war. Prussia on account of subsidies would also have had a closer alliance with England, which, under these circumstances, would not so easily have degenerated into the crooked policy of which the Prussian cabinet was guilty at that time.

A much better result, therefore, might have been expected if the Austrians had appeared with their principal force on the Upper Rhine, the Prussians with their whole force in the Netherlands, and the Austrians had left there only a corps of proportionate strength.

If, instead of the enterprising Blücher, General Barclay had been placed at the head of the Silesian army in 1814, and Blucher and Schwartzenberg had been kept with the grand army, the campaign would perhaps have turned out a complete failure.

If the enterprising Laudon, instead of having his theatre of war at the strongest point of the Prussian dominions, namely, in Silesia, had been in the position of the German States' army, perhaps the whole Seven Years' War would have had quite a different turn. In order to examine this subject more narrowly, we must look at the cases according to their chief distinctions.

The first is, if we carry on war in conjunction with other powers, who not only take part as our allies, but also have an independent interest as well.

The second is, if the army of the ally has come to our assistance.

The third is, when it is only a question with regard to the personal characteristics of the General.

In the two first cases, the point may be raised, whether it is better to mix up the troops of the different powers completely, so that each separate army is composed of corps of different powers, as was done in the wars 1813 and 1814, or to keep them separate as much as possible, so that the army of each power may continue distinct and act independently.

Plainly, the first is the most salutary plan; but it supposes a degree of friendly feeling and community of interests which is seldom found. When there is this close good fellowship between the troops, it is much more difficult for the cabinets to separate their interests; and as regards the prejudicial influence of the egotistical views of commanders, it can only show itself under these circumstances amongst the subordinate Generals, therefore, only in the province of tactics, and even there not so freely or with such impunity as when there is a complete separation. In the latter case, it affects the strategy, and therefore, makes decided marks. But, as already observed, for the first case there must be a rare spirit of conciliation on the part of the Governments. In the year 1813, the exigencies of the time impelled all Governments in that direction; and yet we cannot sufficiently praise this in the Emperor of Russia, that although he entered the field with the strongest army, and the change of fortune was chiefly brought about by him, yet he set aside all pride about appearing at the head of a separate and an independent Russian army, and placed his troops under the Prussian and Austrian Commanders.

If such a fusion of armies cannot be effected, a complete separation of them is certainly better than a half-and-half state of things; the worst of all is when two independent Commanders of armies of different powers find themselves on the same theatre of war, as frequently happened in the Seven Years' War with the armies of Russia, Austria, and the German States. When there is a complete separation of forces, the burdens which must be borne are also better divided, and each suffers only from what is his own, consequently is more impelled to activity by the force of circumstances; but if they find themselves in close connection, or quite on the same theatre of war, this is not the case, and besides that the ill will of one paralyses also the powers of the other as well.

In the first of the three supposed cases, there will be no difficulty in the complete separation, as the natural interest of each State generally indicates to it a separate mode of employing its force; this may not be so in the second case, and then, as a rule, there is nothing to be done but to place oneself completely under the auxiliary army, if its strength is in any way proportionate to that measure, as the Austrians did in the latter part of the campaign of 1815, and the Prussians in the campaign of 1807.

With regard to the personal qualifications of the General, everything in this passes into what is particular and individual; but we must not omit to make one general remark, which is, that we should not, as is generally done, place at the head of subordinate armies the most prudent and cautious Commanders, but the most enterprising; for we repeat that in strategic operations conducted separately, there is nothing more important than that every part should develop its powers to the full, in that way faults committed at one part may be compensated for by successes at others. This complete activity at all points, however, is only to be expected when the Commanders are spirited, enterprising men, who are urged forwards by natural impulsiveness by their own hearts, because a mere objective, coolly reasoned out, conviction of the necessity of action seldom suffices.

Lastly, we have to remark that, if circumstances in other respects permit, the troops and their commanders, as regards their destination, should be employed in accordance with their qualities and the nature of the country—that is regular armies; good troops; numerous cavalry; old, prudent, intelligent generals in an open country;—Militia; national levies; young enterprising commanders in wooded country, mountains and defiles; auxiliary armies in rich provinces where they can make themselves comfortable.

What we have now said upon a plan of a war in general, and in this chapter upon those in particular which are directed to the destruction of the enemy, is intended to give special prominence to the object of the same, and next to indicate principles which may serve as guides in the preparation of ways and means. Our desire has been in this way to give a clear perception of what is to be, and should be, done in such a war. We have tried to emphasise the necessary and general, and to leave a margin for the play of the particular and accidental; but to exclude all that is arbitrary, unfounded, trifling, fantastical; or sophistical. If we have succeeded in this object, we look upon our problem as solved.

Now, if any one wonders at finding nothing here about turning rivers, about commanding mountains from their highest points, about avoiding strong positions, and finding the keys of a country, he has not understood us, neither does he as yet understand war in its general relations according to our views.

In preceding books we have characterised these subjects in general, and we there arrived at the conclusion, they are much more insignificant in their nature than we should think from their high repute. Therefore, so much the less can or ought they to play a great part, that is, so far as to influence the whole plan of a war, when it is a war which has for its object the destruction of the enemy.

At the end of the book we shall devote a chapter specially to the consideration of the chief command; the present chapter we shall close with an example.

If Austria, Prussia, the German Con-federation, the Netherlands and England, determine on a war with France, but Russia remains neutral—a case which has frequently happened during the last one hundred and fifty years—they are able to carry on an offensive war, having for its object the overthrow of the enemy. For powerful and great as France is, it is still possible for it to see more than half its territory overrun by the enemy, its capital occupied, and itself reduced in its means to a state of complete inefficiency, without there being any power, except Russia, which can give it effectual support. Spain is too distant and too disadvantageously situated; the Italian States are at present too brittle and powerless.

The countries we have named have, exclusive of their possessions out of Europe, above 75,000,000 inhabitants,1 whilst France has only 30,000,000; and the army which they could call out for a war against France really meant in earnest, would be as follows, without exaggeration:—
 
Austria 250,000
Prussia 200,000
The rest of Germany 150,000
Netherlands 75,000
England 50,000
Total 725,000

Should this force be placed on a warfooting it would, in all probability, very much exceed that which France could oppose; for under Buonaparte the country never had an army of the like strength. Now, if we take into account the deductions required as garrisons for fortresses and depôts, to watch the coasts, etc., there can be no doubt the allies would have a great superiority in the principal theatre of war, and upon that the object or plan of overthrowing the enemy is chiefly founded.

The centre of gravity of the French power lies in its military force and in Paris. To defeat the former in one or more battles, to take Paris and drive the wreck of the French across the Loire, must be the object of the allies. The pit of the stomach of the French monarchy is between Paris and Brussels, on that side the frontier is only thirty miles from the capital. Part of the allies; the English, Netherlanders, Prussian, and North German States have their natural point of assembly in that direction, as these States lie partly in the immediate vicinity, partly in a direct line behind it. Austria and South Germany can only carry on their war conveniently from the upper Rhine. Their natural direction is upon Troyes and Paris, or it may be Orleans. Both shocks, therefore, that from the Netherlands and the other from the upper Rhine, are quite direct and natural, short and powerful; and both fall upon the centre of gravity of the enemy's power. Between these two points, therefore, the whole invading army should be divided.

But there are two considerations which interfere with the simplicity of this plan.

The Austrians would not lay bare their Italian dominions, they would wish to retain the mastery over events there, in any case, and therefore would not incur the risk of making an attack on the heart of France, by which they would leave Italy only indirectly covered. Looking to the political state of the country, this collateral consideration is not to be treated with contempt; but it would be a decided mistake if the old and oft-tried plan of an attack from Italy, directed against the South of France, was bound up with it, and if on that account the force in Italy was increased to a size not required for mere security against contingencies in the first campaign. Only the number needed for that security should remain in Italy, only that number should be withdrawn from the great undertaking, if we would not be unfaithful to that first maxim, Unity of plan, concentration of force. To think of conquering France by the Rhone, would be like trying to lift a musket by the point of its bayonet; but also as an auxiliary enterprise, an attack on the South of France is to be condemned, for it only raises new forces against us. Whenever an attack is made on distant provinces, interests and activities are roused, which would otherwise have lain dormant. It would only be in case that the forces left for the security of Italy were in excess of the number required, and, therefore, to avoid leaving them unemployed, that there would be any justification for an attack on the South of France from that quarter.

We therefore repeat that the force left in Italy must be kept down as low as circumstances will permit; and it will be quite large enough if it will suffice to prevent the Austrians from losing the whole country in one campaign. Let us suppose that number to be 50,000 men for the purpose of our illustration.

Another consideration deserving attention, is the relation of France in respect to its sea-coast. As England has the upper hand at sea, it follows that France must, on that account, be very susceptible with regard to the whole of her Atlantic coast; and, consequently, must protect it with garrisons of greater or less strength. Now, however weak this coast-defence may be, still the French frontiers are tripled by it; and large drafts, on that account, cannot fail to be withdrawn from the French army on the theatre of war. Twenty or thirty thousand troops disposable to effect a landing, with which the English threaten France, would probably absorb twice or three times the number of French troops; and, further, we must think not only of troops, but also of money, artillery, etc., etc., required for ships and coast batteries. Let us suppose that the English devote 25,000 to this object.

Our plan of war would then consist simply in this:—

1. That in the Netherlands:—

         200,000 Prussians,
           75,000 Netherlanders,
           25,000 English,
           50,000 North German Confederation,
          Total. 350,000 be assembled,

of whom about 50,000 should be set aside to garrison frontier fortresses, and the remaining 300,000 should advance against Paris, and engage the French Army in a decisive battle.

2. That 200,000 Austrians and 100,000 South German troops should assemble on the Upper Rhine to advance at the same time as the army of the Netherlands, their direction being towards the Upper Seine, and from thence towards the Loire, with a view, likewise, to a great battle. These two attacks would, perhaps, unite in one on the Loire.

By this the chief point is determined. What we have to add is chiefly intended to root out false conceptions, and is as follows:—

1. To seek for the great battle, as prescribed, and deliver it with such a relation, in point of numerical strength and under such circumstances, as promise a decisive victory, is the course for the chief commanders to follow; to this object everything must be sacrificed; and as few men as possible should be employed in sieges, blockades, garrisons, etc. If, like Schwartzenberg in 1814, as soon as they enter the enemy's provinces they spread out in eccentric rays all is lost. That this did not take place in 1814 the Allies may thank the powerless state of France alone. The attack should be like a wedge well driven home, not like a soap bubble, which distends itself till it bursts.

2. Switzerland must be left to its own forces. If it remains neutral it forms a good point d'appui on the Upper Rhine; if it is attacked by France, let her stand up for herself, which in more than one respect she is very well able to do. Nothing is more absurd than to attribute to Switzerland a predominant geographical influence upon events in war because it is the highest land in Europe. Such an influence only exists under certain very restricted conditions, which are not to be found here. When the French are attacked in the heart of their country they can undertake no offensive from Switzerland, either against Italy or Swabia, and, least of all, can the elevated situation of the country come into consideration as a decisive circumstance. The advantage of a country which is dominating in a strategic sense, is, in the first place, chiefly important in the defensive, and any importance which it has in the offensive may manifest itself in a single encounter. Whoever does not know this has not thought over the thing and arrived at a clear perception of it, and in case that at any future council of potentates and generals, some learned officer of the general staff should be found, who, with an anxious brow, displays such wisdom, we now declare it beforehand to be mere folly, and wish that in the same council some true Blade, some child of sound common-sense may be present who will stop his mouth.

3. The space between two attacks we think of very little consequence. When 600,000 assemble thirty or forty miles from Paris to march against the heart of France, would any one think of covering the middle Rhine as well as Berlin, Dresden, Vienna, and Munich? There would be no sense in such a thing. Are we to cover the communications? That would not be unimportant; but then we might soon be led into giving this covering the importance of an attack, and then, instead of advancing on two lines, as the situation of the States positively requires, we should be led to advance upon three, which is not required. These three would then, perhaps, become five, or perhaps seven, and in that way the old rigmarole would once more become the order of the day.

Our two attacks have each their object; the forces employed on them are probably very superior to the enemy in numbers. If each pursues his march with vigour, they cannot fail to react advantageously upon each other. If one of the two attacks is unfortunate because the enemy has not divided his force equally, we may fairly expect that the result of the other will of itself repair this disaster, and this is the true interdependence between the two. An interdependence extending to (so as to be affected by) the events of each day is impossible on account of the distance; neither is it necessary, and therefore the immediate, or, rather the direct connection, is of no such great value.

Besides, the enemy attacked in the very centre of his dominions will have no forces worth speaking of to employ in interrupting this connection; all that is to be apprehended is that this interruption may be attempted by a co-operation of the inhabitants with the partisans, so that this object does not actually cost the enemy any troops. To prevent that, it is sufficient to send a corps of 10,000 or 15,000 men, particularly strong in cavalry, in the direction from Trèves to Rheims. It will be able to drive every partisan before it, and keep in line with the grand army. This corps should neither invest nor watch fortresses, but march between them, depend on no fixed basis, but give way before superior forces in any direction, no great misfortune could happen to it, and if such did happen, it would again be no serious misfortune for the whole. Under these circumstances, such a corps might probably serve as an intermediate link between the two attacks.

4. The two subordinate undertakings, that is, the Austrian army in Italy, and the English army for landing on the coast, might follow their object as appeared best. If they do not remain idle, their mission is fulfilled as regards the chief point, and on no account should either of the two great attacks be made dependent in any way on these minor ones.

We are quite convinced that in this way France may be overthrown and chastised whenever it thinks fit to put on that insolent air with which it has oppressed Europe for a hundred and fifty years. It is only on the other side of Paris, on the Loire, that those conditions can be obtained from it which are necessary for the peace of Europe. In this way alone the natural relation between 30 millions of men and 75 millions will quickly make itself known, but not if the country from Dunkirk to Genoa is to be surrounded in the way it has been for 150 years by a girdle of armies, whilst fifty different small objects are aimed at, not one of which is powerful enough to overcome the inertia, friction, and extraneous influences which spring up and reproduce themselves everywhere, but more especially in allied armies.

How little the provisional organisation of the German federal armies is adapted to such a disposition, will strike the reader. By that organisation the federative part of Germany forms the nucleus of the German power, and Prussia and Austria thus weakened, lose their natural influence. But a federative state is a very brittle nucleus in war—there is in it no unity, no energy, no rational choice of a commander, no authority, no responsibility.

Austria and Prussia are the two natural centres of force of the German empire; they form the pivot (or fulcrum), the forte of the sword; they are monarchical states, used to war; they have well-defined interests, independence of power; they are predominant over the others. The organisation should follow these natural lineaments, and not a false notion about unity, which is an impossibility in such a case; and he who neglects the possible in quest of the impossible is a fool.

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1 This chapter was probably written in 1828, since which time the numerical relations have considerably changed.—A. d. H.



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