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corps d'armée passes over in attaining its object; the front of operations is the front formed by the army as it advances on this line.

When an army acts as a single mass, without forming independent corps, the line it follows is denominated a simple line of operations.

If two or more corps act in an isolated manner, but against the same opposing force, they are said to follow double or multiple lines.

The lines by which Moreau and Jourdan entered Germany in 1796, were double lines; but Napoleon's advance by Bamberg and Gera, in 1806, although moving in seven distinct corps d'armée, formed but a single line of operations.

Interior lines of operations are those followed by an army which operates between the enemy's lines in such a way as to be able to concentrate his forces on one of these lines before the other can be brought to its assistance. For example, Napoleon's line of operations in 1814, between the Marne and the Seine, where he manœuvred with so much skill and success against the immensely superior forces of the allies.

Exterior lines present the opposite results; they are those which an army will form in moving on the extremities of the opposing masses. For example, the lines of the Marne and the Seine, followed by the army of Silesia and the grand Austro-Russian army, in the campaign of 1814. Burgoyne's line of operations, in 1777, was double and exterior.

Concentric lines are such as start from distant points, and are directed towards the same object, either in the rear or in advance of their base.

If a mass leaves a single point and separates into several distinct corps, taking divergent directions, it is said to pursue eccentric lines.

Lines are said to be deep, when the end to be attained is very distant from the base.

The lines followed by a secondary or auxiliary force are denominated secondary lines.

The lines pursued by the army of the Sombre-et-Meuse in 1796, and by Bagration in 1812, were secondary lines, as the former were merely secondary to the army of the Rhine, and the latter to that of Barclay.

Accidental lines are those which result from a change in the primitive plan of campaign, which give a new direction to the operations. These are of rare occurrence, but they sometimes lead to important results.

The direction given to a line of operations depends not only on the geographical situation of the country, but also on the positions occupied by the enemy. The general plan of campaign is frequently determined on previous to beginning operations, but the choice of lines and positions must ordinarily result from the ulterior events of the war, and be made by the general as these events occur.

As a general rule, a line of operations should be directed upon the centre, or one of the extremities of the enemy's line of defence; unless our forces be infinitely superior in number, it would be absurd to act against the front and extremities at the same time.

If the configuration of the theatre of operations be favorable to a movement against the extremity of the enemy's line of defence, this direction maybe best calculated to lead to important results. (Fig.4.)

In 1800 the army of the Rhine was directed against the extreme left of the line of the Black Forest; the army of reserve was directed by the St. Bernard and Milan on the extreme right and rear of Melas's line of defence: both operations were most eminently successful. (Fig. 5.)

It may be well to remark that it is not enough merely to gain the extremity and rear of the enemy, for in that case it may be possible for him to throw himself on our communications and place us in the very dilemma in which we had hoped to involve him. To avoid this danger it is necessary to give such a direction to the line of operations that our army shall preserve its communications and be able to reach its base.

Thus, if Napoleon, in 1800, after crossing the Alps, had marched by Turin on Alexandria and received battle at Marengo, without having first secured Lombardy and the left of the Po, his own line of retreat would have been completely cut off by Melas; whereas, by the direction which he gave to his line of operations he had, in case of reverse, every means for reaching either the Var or the Valois. (Fig. 6.) Again, in 1806, if he had marched directly from Gera to Leipsic, he would have been cut off from his base on the Rhine; whereas, by turning from Gera towards Weimar, he not only cut off the Prussians from the Elbe, but at the same time secured to himself the roads of Saalfield, Schleitz, and Hoff, thus rendering perfectly safe his communications in his rear. (Fig. 7.)

We have said that the configuration of the ground and the position of the hostile forces may sometimes render it advisable to direct our line of operations against the extremity of the enemy's line of defence; but, as a general rule a central direction will lead to more important results. This severs the enemy's means of resistance, and enables the assailant to strike, with the mass of his force, upon the dissevered and partially paralyzed members of the hostile body. (Fig. 8.)

Such a plan of operations enabled Napoleon, in the Italian campaigns of 1796 and 1797, to pierce and destroy, with a small force, the large and successive armies which Austria sent against him. In 1805 his operations were both interior and central: in 1808 they were most eminently central: in 1809, by the central operations in the vicinity of Ratisbonne, he defeated the large and almost victorious army of the Archduke Charles: in 1814, from his central position between the Marne and Seine, with only seventy thousand men against a force of more than two hundred thousand, he gained numerous victories, and barely failed of complete success. Again in 1815, with an army of only one hundred and twenty thousand men against an allied force of two hundred and twenty thousand, by his central advance on Charleroi and Ligny, he gained a most decided advantage over the enemy—an advantage lost by the eccentric movement of Grouchy: and even in 1813, his central position at Dresden would have secured him most decisive advantages, had not the faults of his lieutenants lost these advantages in the disasters of Kulm and the Katzbach.

For the same frontier it is objectionable to form more than one army; grand detachments and corps of observation may frequently be used with advantage, but double or multiple lines of operation are far less favorable than one simple line. It may however sometimes occur that the position of the enemy's forces will be such as to make this operation the preferable one. In that case, interior lines should always be adopted, unless we have a vast superiority in number. Double exterior lines, with corps several days' march asunder, must be fatal, if the enemy, whether acting on single or double interior lines, take advantage of his position to concentrate his masses successively against our isolated forces. The Roman armies under the consuls Flaminius and Servilius opposed Hannibal on exterior lines, the one by Florence and Arrezzio, and the other by Modena and Ariminum. Hannibal turned the position of Flaminius and attacked the Roman armies separately, gaining a complete and decisive victory. Such also was the character of the operations of the French in 1795, under Pichegru and Jourdan; they met with a bloody and decisive defeat. Again in 1796, the French armies under Jourdan and Moreau, pursued exterior lines; the Archduke Charles, from his interior position, succeeded in defeating both the opposing generals, and forcing them to retreat. If the two armies united had pursued a single line, the republican flag had been carried in triumph to Vienna.

Converging lines of operation are preferable, under most circumstances, to diverging lines. Care should be taken, however, that the point of meeting be such that it may not be taken as a strategic position by the enemy, and our own forces be destroyed in detail, before they can effect a junction. In 1797 the main body of the Austrians, under Alvinzi, advanced against Napoleon, on three separate lines, intending to concentrate at Rivoli, and then attack the French in mass; but Napoleon took his strategic position at Rivoli, and overthrew the enemy's corps as they successively appeared. In the same way the Archduke Charles took an interior position, between Moreau and Jourdan, in 1796, and prevented them from concentrating their forces on a single point. Wurmser and Quasdanowich attempted to concentrate their forces on the Mincio, by moving on the opposite shores of Lake Garda; but Napoleon took an interior position and destroyed them. In 1815 Blucher and Wellington, from their interior position, prevented the junction of Napoleon and Grouchy.

Diverging lines may be employed with advantage against an enemy immediately after a successful battle or strategic manœuvre; for by this means we separate the enemy's forces, and disperse them; and if occasion should require it, may again concentrate our forces by converging lines. Such was the manœuvre of Frederick the Great, in 1757, which produced the battles of Rosbach and Leuthen; such also was the manœuvre of Napoleon at Donawert in 1805, at Jena in 1806, and at Ratisbon in 1809.

Interior lines of operations, when properly conducted, have almost invariably led to success: indeed every instance of failure may be clearly traced to great unskilfulness in their execution, or to other extraneous circumstances of the campaign. There may, however, be cases where it will be preferable to direct our forces on the enemy's flank; the geographical character of the theatre of war, the position of other collateral forces, &c., rendering such a direction necessary. But as a general rule, interior and central lines, for an army of moderate forces, will lead to decisive results.

Napoleon's Italian campaigns in 1796 and 1797, the campaign of the Archduke Charles in 1796, Napoleon's campaigns of 1805 and 1809 against Austria, and of 1806 and 1807 against Prussia and Russia, of 1808 in Spain, his manœuvres in 1814, between the battle of Brienne and that of Paris, and his operations previous to the Battle of Ligny in 1815, are all brilliant examples under this head.

To change the line of operations, in the middle of a campaign, and follow accidental lines, is always a delicate affair, and can only be resorted to by a general of great skill, and with disciplined troops. In such a case it may be attended with important results. It was one of Napoleon's maxims, that "a line of operations, when once chosen, should never be abandoned." This maxim, however, must sometimes be disregarded by an army of undisciplined troops, in order to avoid entire destruction; but the total abandonment of a line of operations is always attended with great loss, and should be regarded as a mere choice of evils. A regular army can always avoid this result, by changing the direction of its line; thus frequently gaining superior advantages in the new theatre of action. If the plan of this change be the result of a good coup d'oeil, and it be skilfully executed, the rear of the operating army will be secure from the enemy; and moreover, he will be left in doubt respecting its weak points. But such is the uncertainty of this manœuvre, that it is very rarely taken by the best troops, unless actually forced upon them. If the army be of incongruous materials, generally a change of direction will be less advantageous than to entirely abandon the line, and save as many as possible of the troops for some new plan of operations. (Maxim 20.) If, however, the undisciplined army be sustained by fortifications, it can take up the accidental line of operations in the same manner, and with the same probability of success, as is done by a regular force.

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