An army of 200,000 men in ten divisions, the divisions composed of five brigades each, would give brigades 4,000 strong. We see here no disproportion. Certainly this army might also be divided into five corps, the corps into four divisions, and the division into four brigades, which makes the brigade 2,500 men strong; but the first distribution, looked at in the abstract, appears to us preferable, for besides that, in the other, there is one more gradation of rank, five parts are too few to make an army manageable; four divisions, in like manner, are too few for a corps, and 2,500 men is a weak brigade, of which, in this manner, there are eighty, whereas the first formation has only fifty, and is therefore simpler. All these advantages are given up merely for the sake of having only to send orders to half as many generals. Of course the distribution into corps is still more unsuitable for smaller armies. This is the abstract view of the case. The particular case may present good reasons for deciding otherwise. Likewise, we must admit that, although eight or ten divisions may be directed when united in a level country, in widely extended mountain positions the thing might perhaps be impossible. A great river which divides an army into halves, makes a commander for each half indispensable; in short, there are a hundred local and particular objects of the most decisive character, before which all rules must give way. But still, experience teaches us, that these abstract grounds come most frequently into use and are seldomer overruled by others than we should perhaps suppose. We wish further to explain clearly the scope of the foregoing considerations by a simple outline, for which purpose we now place the different points of most importance next to each other. As we mean by the term numbers, or parts of a whole, only those which are made by the primary, therefore the immediate division, we say. 1. If a whole has too few members it is unwieldy. 2. If the parts of a whole body are too large, the power of the superior will is thereby weakened. 3. With every additional step through which an order has to pass, it is weakened in two ways: in one way by the loss of force, which it suffers in its passage through an additional step; in another way by the longer time in its transmission. The tendency of all this is to show that the number of co-ordinate divisions should be as great, and the gradational steps as few as possible; and the only limitation to this conclusion is, that in armies no more than from eight to ten, and in subordinate corps no more than from four or at most six, subdivisions can be conveniently directed. 2.—Combination of Arms.