possible by taking advantage of the ground, continually falling
back upon the principal army.

8. A double line is applicable in the case of a decided superiority of
force, when each army will be a match for any force the enemy can bring
against it. In this case this course will be advantageous,--since a
single line would crowd the forces so much as to prevent them all from
acting to advantage. However, it will always be prudent to support well
the army which, by reason of the nature of its theater and the
respective positions of the parties, has the most important duty to
perform.

9 The principal events of modern wars demonstrate the truth of two other
maxims. The first is, that two armies operating on interior lines and
sustaining each other reciprocally, and opposing two armies superior in
numbers, should not allow themselves to be crowded into a too contracted
space, where the whole might be overwhelmed at once. This happened to
Napoleon at Leipsic.[17] The second is, that interior lines should not
be abused by extending them too far, thus giving the enemy the
opportunity of overcoming the corps of observation. This risk, however,
may be incurred if the end pursued by the main forces is so decisive as
to conclude the war,--when the fate of these secondary bodies would be
viewed with comparative indifference.

10. For the same reason, two converging lines are more advantageous than
two divergent. The first conform better to the principles of strategy,
and possess the advantage of covering the lines of communication and
supply; but to be free from danger they should be so arranged that the
armies which pass over them shall not be separately exposed to the
combined masses of the enemy, before being able to effect their
junction.

11. Divergent lines, however, may be advantageous when the center of the
enemy has been broken and his forces separated either by a battle or by
a strategic movement,--in which case divergent operations would add to
the dispersion of the enemy. Such divergent lines would be interior,
since the pursuers could concentrate with more facility than the
pursued.

12. It sometimes happens that an army is obliged to change its line of
operations in the middle of a campaign. This is a very delicate and
important step, which may lead to great successes, or to equally great
disasters if not applied with sagacity, and is used only to extricate an
army from an embarrassing position. Napoleon proje