ch the Saale in time to be of any use, and
that another force Of 25,000 men belonging to this power remained
in East and South Prussia, destined only to be put on a war-footing
afterwards as a reserve.

After these examples we cannot be accused of having been fighting with
windmills.

CHAPTER XIV. ECONOMY OF FORCES

THE road of reason, as we have said, seldom allows itself to be reduced
to a mathematical line by principles and opinions. There remains always
a certain margin. But it is the same in all the practical arts of life.
For the lines of beauty there are no abscissae and ordinates; circles
and ellipses are not described by means of their algebraical formulae.
The actor in War therefore soon finds he must trust himself to the
delicate tact of judgment which, founded on natural quickness of
perception, and educated by reflection, almost unconsciously seizes upon
the right; he soon finds that at one time he must simplify the law (by
reducing it) to some prominent characteristic points which form his
rules; that at another the adopted method must become the staff on which
he leans.

As one of these simplified characteristic points as a mental appliance,
we look upon the principle of watching continually over the co-operation
of all forces, or in other words, of keeping constantly in view that
no part of them should ever be idle. Whoever has forces where the enemy
does not give them sufficient employment, whoever has part of his forces
on the march--that is, allows them to lie dead--while the enemy's are
fighting, he is a bad manager of his forces. In this sense there is
a waste of forces, which is even worse than their employment to no
purpose. If there must be action, then the first point is that all parts
act, because the most purposeless activity still keeps employed and
destroys a portion of the enemy's force, whilst troops completely
inactive are for the moment quite neutralised. Unmistakably this idea is
bound up with the principles contained in the last three chapters, it
is the same truth, but seen from a somewhat more comprehensive point of
view and condensed into a single conception.

CHAPTER XV. GEOMETRICAL ELEMENT

THE length to which the geometrical element or form in the disposition
of military force in War can become a predominant principle, we see in
the art of fortification, where geometry looks after the great and
the little. Also in tactics it plays a great part. It is the basis of