d is trifling;
but when the campaign is just opening, and the two opposing armies are
about equal, the case is very different.

If one hundred thousand Frenchmen pass the Rhine at Strasbourg or at
Manheim in presence of one hundred thousand Austrians, the first thing
to be done will be to drive the enemy in three directions,--first,
before them as far as the Black Forest, secondly, by the right in order
to cover the bridges on the Upper Rhine, and thirdly, by the left to
cover the bridges of Mayence and the Lower Rhine. This necessity is the
cause of an unfortunate division of the forces; but, to make the
inconveniences of this subdivision as few as possible, the idea must be
insisted on that it is by no means essential for the army to be
separated into three equal parts, nor need these detachments remain
absent longer than the few days required for taking possession of the
natural point of concentration of the enemy's forces.

The fact cannot be concealed, however, that the case supposed is one in
which the general finds his position a most trying one; for if he
divides his army to protect his bridges he may be obliged to contend
with one of his subdivisions against the whole of the enemy's force, and
have it overwhelmed; and if he moves his army upon a single line, the
enemy may divide his army and reassemble it at some unexpected point,
the bridges may be captured or destroyed, and the general may find
himself compromised before he has had time or opportunity to gain a
victory.

The best course to be pursued is to place the bridges near a city which
will afford a strong defensive point for their protection, to infuse all
possible vigor and activity into the first operations after the passage,
to fall upon the subdivisions of the enemy's army in succession, and to
beat them in such a way that they will have no further desire of
touching the bridges. In some cases eccentric lines of operations may be
used. If the enemy has divided his one hundred thousand men into several
corps, occupying posts of observation, a passage may be effected with
one hundred thousand men at a single point near the center of the line
of posts, the isolated defensive corps at this position may be
overwhelmed, and two masses of fifty thousand men each may then be
formed, which, by taking diverging lines of operations, can certainly
drive off the successive portions of the opposing army, prevent them
from reuniting, and remove them farther an