e 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