for it was the perpendicularity of this base to that of the
French army which enabled the allies to neutralize the immense
advantages which the line of the Elbe would otherwise have afforded
Napoleon, and turned the advantages of the campaign in their favor.
Likewise, in 1812, by establishing their base perpendicularly upon the
Oka and Kalouga, the Russians were able to execute their flank march
upon Wiazma and Krasnoi.

If any thing further be required to establish these truths, it will only
be necessary to consider that, if the base be perpendicular to that of
the enemy, the front of operations will be parallel to his line of
operations, and that hence it will be easy to attack his communications
and line of retreat.

It has been stated that perpendicular bases are particularly favorable
in the case of a double frontier, as in the last figures. Critics may
object to this that it does not agree with what is elsewhere said in
favor of frontiers which are salient toward the enemy, and against
double lines of operations with equality of force. (Art. XXI.) The
objection is not well founded; for the greatest advantage of a
perpendicular base consists in the fact that it forms such a salient,
which takes in reverse a portion of the theater of operations. On the
other hand, a base with two faces by no means requires that both should
be occupied in force: on the contrary, upon one of them it will be
sufficient to have some fortified points garrisoned by small bodies,
while the great bulk of the force rests upon the other face,--as was
done in the campaigns of 1800 and 1806. The angle of nearly ninety
degrees formed by the portion of the Rhine from Constance to Basel, and
thence to Kehl, gave General Moreau one base parallel and another
perpendicular to that of his antagonist. He threw two divisions by his
left toward Kehl on the first base, to attract the attention of the
enemy to that point, while he moved with nine divisions upon the
extremity of the perpendicular face toward Schaffhausen, which carried
him in a few days to the gates of Augsburg, the two detached divisions
having already rejoined him.

In 1806, Napoleon had also the double base of the Rhine and Main,
forming almost a right re-entrant angle. He left Mortier upon the first
and parallel one, while with the mass of his forces he gained the
extremity of the perpendicular base, and thus intercepted the Prussians
at Gera and Naumburg by reaching their line of r