he third was that of Bernadotte
from Berlin by Dessau to the same objective point. Each of these armies
marched upon two or more adjacent parallel routes, but it could not be
said that there were as many lines of operations as roads. The principal
line of operations is that followed by the bulk of the army, and upon
which depots of provisions, munitions, and other supplies are echeloned,
and over which, if compelled, it would retreat.

If the choice of a zone of operations involves no extensive
combinations, since there can never be more than two or three zones on
each theater, and the advantages generally result from the localities,
it is somewhat different with lines of operations, as they are divided
into different classes, according to their relations to the different
positions of the enemy, to the communications upon the strategic field,
and to the enterprises projected by the commander.

_Simple lines of operations_ are those of an army acting from a
frontier when it is not subdivided into large independent bodies.

_Double lines of operations_ are those of two independent armies
proceeding from the same frontier, or those of two nearly equal armies
which are commanded by the same general but are widely separated in
distance and for long intervals of time.[11]

_Interior lines of operations_ are those adopted by one or two armies to
oppose several hostile bodies, and having such a direction that the
general can concentrate the masses and maneuver with his whole force in
a shorter period of time than it would require for the enemy to oppose
to them a greater force.[12] _Exterior lines_ lead to the opposite
result, and are those formed by an army which operates at the same time
on both flanks of the enemy, or against several of his masses.

_Concentric lines of operations_ are those which depart from
widely-separated points and meet at the same point, either in advance
of or behind the base.

_Divergent lines_ are those by which an army would leave a given point
to move upon several distinct points. These lines, of course,
necessitate a subdivision of the army.

There are also _deep lines_, which are simply _long lines_.

The term _maneuver-lines_ I apply to momentary strategic lines, often
adopted for a single temporary maneuver, and which are by no means to be
confounded with the real _lines of operations_.

_Secondary lines_ are those of two armies acting so as to afford each
other mutual support,--as,