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.