The order concave in the center ([Fig. 12]) has found advocates since the day when Hannibal by its use gained the battle of Cannæ. This order may indeed be very good when the progress of the battle itself gives rise to it; that is, when the enemy attacks the center, this retires before him, and he suffers himself to be enveloped by the wings. But, if this order is adopted before the battle begins, the enemy, instead of falling on the center, has only to attack the wings, which present their extremities and are in precisely the same relative situation as if they had been assailed in flank. This order would, therefore, be scarcely ever used except against an enemy who had taken the convex order to fight a battle, as will be seen farther on.
Fig. 12 bis.
An army will rarely form a semicircle, preferring rather a broken line with the center retired, ([Fig. 12, bis.]) If several writers may be believed, such an arrangement gave the victory to the English on the famous days of Crécy and Agincourt. This order is certainly better than a semicircle, since it does not so much present the flank to attack, whilst allowing forward movement by echelon and preserving all the advantages of concentration of fire. These advantages vanish if the enemy, instead of foolishly throwing himself upon the retired center, is content to watch it from a distance and makes his greatest effort upon one wing. Essling, in 1809, is an example of the advantageous use of a concave line; but it must not be inferred that Napoleon committed an error in attacking the center; for an army fighting with the Danube behind it and with no way of moving without uncovering its bridges of communication, must not be judged as if it had been free to maneuver at pleasure.
Fig. 13.
The convex order with the center salient ([Fig. 13]) answers for an engagement immediately upon the passage of a river when the wings must be retired and rested on the river to cover the bridges; also when a defensive battle is to be fought with a river in rear, which is to be passed and the defile covered, as at Leipsic; and, finally, it may become a natural formation to resist an enemy forming a concave line. If an enemy directs his efforts against the center or against a single wing, this order might cause the ruin of the whole army.[[26]]
The French tried it at Fleurus in 1794, and were successful, because the Prince of Coburg, in place of making a strong attack upon the center or upon a single extremity, divided his attack upon five or six diverging lines, and particularly upon both wings at once. Nearly the same convex order was adopted at Essling, and during the second and third days of the famous battle of Leipsic. On the last occasion it had just the result that might have been expected.