A line of operations embraces that portion of the theatre of war which an army or 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.