arely able to maintain a communication
by couriers with his base, and he certainly would have been obliged to
cut his way out or to surrender in case he had not been reinforced.]

[Footnote 14: The capture of Paris by the allies decided the fate of
Napoleon; but he had no army, and was attacked by all Europe, and the
French people had, in addition, separated their cause from his. If he
had possessed fifty thousand more old soldiers, he would have shown that
the capital was at his head-quarters.]

[Footnote 15: The inferiority of an army does not depend exclusively
upon the number of soldiers: their military qualities, their _morale_,
and the ability of their commander are also very important elements.]

[Footnote 16: When the fractions of an army are separated from the main
body by only a few marches, and particularly when they are not intended
to act separately throughout the campaign, these are central strategic
positions, and not lines of operations.]

[Footnote 17: In the movements immediately preceding the battle of
Leipsic, Napoleon, strictly speaking, had but a single line of
operations, and his armies were simply in central strategic positions;
but the principle is the same, and hence the example is illustrative of
lines of operations.]

[Footnote 18: I am well aware that it is not always possible to avoid a
combat without running greater risks than would result from a check; but
Macdonald might have fought Bluecher to advantage if he had better
understood Napoleon's instructions.]

[Footnote 19: It will not be thought strange that I sometimes approve of
concentric, and at other times divergent, maneuvers, when we reflect
that among the finest operations of Napoleon there are some in which he
employed these two systems alternately within twenty-four hours; for
example, in the movements about Ratisbon in 1809.]

ARTICLE XXII.

Strategic Lines.

Mention has already been made of strategic lines of maneuvers, which
differ essentially from lines of operations; and it will be well to
define them, for many confound them. We will not consider those
strategic lines which have a great and permanent importance by reason of
their position and their relation to the features of the country, like
the lines of the Danube and the Meuse, the chains of the Alps and the
Balkan. Such lines can best be studied by a detailed and minute
examination of the topography of Europe; and an excellent model for this
kind of