(Figure 21.) The concave order may be used with advantage in certain cases, and in particular localities.  Hannibal employed it at the battle of Cannae, the English at Crecy and Agincourt, and the Austrians at Essling, in 1809.

(Figure 22.) The convex order is sometimes formed to cover a defile, to attack a concave line, or to oppose an attack before or after the passage of a river.  The Romans formed this order at the battle of Cosilinum; the French at Ramilies in 1706, at Fleurus in 1794, at Essling in 1809, and at the second and third days of Leipsic in 1813, and at Brienne in 1814.

(Figure 23.) The order by echelon on one wing may be frequently employed with advantage; but if the echelon be made on both wings, there is the same objection to its use as to the perpendicular order on both wings.  At Dresden, Napoleon attacked both wings at the same time; this is the only instance in his whole history of a similar attack, and this was owing to peculiar circumstances in the ground and in the position of his troops.

(Figure 24.) The echelon order on the centre alone may be employed with success against an army formed in a thin or too extended line of battle, for it would be pretty certain to penetrate and break the line.

The echelon order possesses in general very great advantages.  The several corps composing the army may manoeuvre separately, and consequently with greater ease.  Each echelon covers the flank of that which precedes it; and all may be combined towards a single object, and extended with the necessary ensemble.  At the battle of the Pyramids, Napoleon formed the oblique order in echelon by squares.  Portions of his forces were arranged in echelon in some of his other battles.

(Figure 25.) The combined order in columns on the centre and one extremity at the same time, is better suited than either of the preceding for attacking a strong contiguous line.  Napoleon employed this order at Wagram, Ligny, Bautzen, Borodino, and Waterloo.

It is impossible to lay down, as a general rule, which of these orders of battle should be employed, or that either should be exclusively followed throughout the whole battle.  The question must be decided by the general himself on the ground, where all the circumstances may be duly weighed.  An order well suited to one position might be the worst possible in another.  Tactics is in this respect the very reverse of strategy—­the latter being subject to more rigid and invariable rules.

But whatever the plan adopted by the attacking force, it should seek to dislodge the enemy, either by piercing or turning his line.  If it can conceal its real intentions, and deceive him respecting the true point of attack, success will be more certain and decisive.  A turning manoeuvre may frequently be employed with advantage at the same time with the main attack on the line.  The operations of Davoust at Wagram, and Richepanse at Hohenlinden, are good examples under this head.  The manoeuvre is, however, a difficult one, and unless executed with skill, may lead to disasters like the turning manoeuvres of the Austrians at Rivoli and Austerlitz, and of the French under Jourdan at Stackach, and under Marmont at Salamanca.