even of the battle, are too little known. Bonaparte had at Dresden 120,000 against 220,000, therefore not the double. At Kollin, Frederick the Great did not succeed, with 30,000 against 50,000 Austrians, neither did Bonaparte in the desperate battle of Leipsic, where he was 160,000 strong, against 280,000.

From this we may infer, that it is very difficult in the present state of Europe, for the most talented general to gain a victory over an enemy double his strength. Now if we see double numbers prove such a weight in the scale against the greatest generals, we may be sure, that in ordinary cases, in small as well as great combats, an important superiority of numbers, but which need not be over two to one, will be sufficient to ensure the victory, however disadvantageous other circumstances may be. Certainly we may imagine a defile which even tenfold would not suffice to force, but in such a case it can be no question of a battle at all.

We think, therefore, that under our conditions, as well as in all similar ones, the superiority at the decisive point is a matter of capital importance, and that this subject, in the generality of cases, is decidedly the most important of all. The strength at the decisive point depends on the absolute strength of the army, and on skill in making use of it.

The first rule is therefore to enter the field with an army as strong as possible. This sounds very like a commonplace, but still it is really not so.

In order to show that for a long time the strength of forces was by no means regarded as a chief point, we need only observe that in most, and even in the most detailed histories of the wars in the eighteenth century, the strength of the armies is either not given at all, or only incidentally, and in no case is any special value laid upon it. Tempelhof in his history of the Seven Years’ War is the earliest writer who gives it regularly, but at the same time he does it only very superficially.

Even Massenbach, in his manifold critical observations on the Prussian campaigns of 1793--4 in the Vosges, talks a great deal about hills and valleys, roads and footpaths, but does not say a syllable about mutual strength.

Another proof lies in a wonderful notion which haunted the heads of many critical historians, according to which there was a certain size of an army which was the best, a normal strength, beyond which the forces in excess were burdensome rather than serviceable.

Lastly, there are a number of instances to be found, in which all the available forces were not really brought into the battle, or into the war, because the superiority of numbers was not considered to have that importance which in the nature of things belongs to it.

If we are thoroughly penetrated with the conviction that with a considerable superiority of numbers everything possible is to be effected, then it cannot fail that this clear conviction reacts in the preparations for the war, so as to make us appear in the field with as many troops as possible, and either to give us ourselves the superiority, or at least to guard against the enemy obtaining it. So much for what concerns the absolute force with which the war is to be conducted.

The measure of this absolute force is determined by the government; and although with this determination the real action of war commences, and it forms an essential part of the strategy of the war, still in most cases the general who is to command these forces in the war must regard their absolute strength as a given quantity, whether it be that he has had no voice in fixing it, or that circumstances prevented a sufficient expansion being given to it.

There remains nothing, therefore, where an absolute superiority is not attainable, but to produce a relative one at the decisive point, by making skilful use of what we have.

The calculation of space and time appears as the most essential thing to this end -- and this has caused that subject to be regarded as one which embraces nearly the whole art of using military forces. Indeed,