It will be seen from these remarks that lines of defence are not necessarily bases of operation.

Strategic positions are such as are taken up during the operations of a war, either by a corps d’armee or grand detachment, for the purpose of checking or observing an opposing force; they are named thus to distinguish them from tactical positions or fields of battle.  The positions of Napoleon at Rivoli, Verona, and Legnano, in 1796 and 1797, to watch the Adige; his positions on the Passarge, in 1807, and in Saxony and Silesia in front of his line of defence, in 1813; and Massena’s positions on the Albis, along the Limmat and the Aar, in 1799, are examples under this head.

Before proceeding further it may be well to illustrate the strategic relations of lines and positions by the use of diagrams.

(Fig. 1.) The army at A covers the whole of the ground in rear of the line DC perpendicular to the line AB, the position of the enemy being at B.

(Fig. 2.) AJ being equal to BJ, A will still cover every thing in rear of DC.

(Fig. 3.) If the army A is obliged to cover the point a, the army B will cover all the space without the circle whose radius is a B; and of course A continues to cover the point a so long as it remains within this circle a B.

A line of operations embraces that portion of the theatre of war which an army or corps d’armee 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’armee, 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 manoeuvred 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.