in 1796, the army of the Sambre and Meuse was
secondary to the army of the Rhine, and, in 1812, the army of Bagration
was secondary to that of Barclay.

_Accidental lines_ are those brought about by events which change the
original plan and give a new direction to operations. These are of the
highest importance. The proper occasions for their use are fully
recognized only by a great and active mind.

There may be, in addition, _provisional_ and _definitive lines of
operations_. The first designate the line adopted by an army in a
preliminary, decisive enterprise, after which it is at liberty to select
a more advantageous or direct line. They seem to belong as much to the
class of temporary or eventual strategic lines as to the class of lines
of operations.

These definitions show how I differ from those authors who have preceded
me. Lloyd and Bulow attribute to these lines no other importance than
that arising from their relations to the depots of the army: the latter
has even asserted that when an army is encamped near its depots it has
no lines of operations.

The following example will disprove this paradox. Let us suppose two
armies, the first on the Upper Rhine, the second in advance of
Dusseldorf or any other point of this frontier, and that their large
depots are immediately behind the river,--certainly the safest, nearest,
and most advantageous position for them which could possibly be adopted.
These armies will have an offensive or defensive object: hence they
will certainly have lines of operations, arising from the different
proposed enterprises.

1. Their defensive territorial line, starting from their positions, will
extend to the second line which they are to cover, and they would both
be cut off from this second line should the enemy establish himself in
the interval which separates them from it. Even if Melas[13] had
possessed a year's supplies in Alessandria, he would none the less have
been cut off from his base of the Mincio as soon as the victorious enemy
occupied the line of the Po.

2. Their line would be double, and the enemy's single if he concentrated
his forces to defeat these armies successively; it would be a double
exterior line, and the enemy's a double interior, if the latter divided
his forces into two masses, giving them such directions as to enable him
to concentrate all his forces before the two armies first referred to
could unite.

Bulow would have been more nearly right had