shall then proceed to do the same in respect to their relations to the other two. Therefore, first, the direct defence, that is, such a defence as is to prevent the passage of the enemy’s army itself.
This can only come into the question in relation to large rivers, that is, great bodies of water.
The combinations of space, time, and force, which require to be looked into as elements of this theory of defence, make the subject somewhat complicated, so that it is not easy to gain a sure point from which to commence. The following is the result at which every one will arrive on full consideration.
The time required to build a bridge determines the distance from each other at which the corps charged with the defence of the river should be posted. If we divide the whole length of the line of defence by this distance, we get the number of corps required for the defence; if with that number we divide the mass of troops disposable, we shall get the strength of each corps. If we now compare the strength of each single corps with the number of troops which the enemy, by using all the means in his power, can pass over during the construction of his bridge, we shall be able to judge how far we can expect a successful resistance. For we can only assume the forcing of the passage to be impossible when the defender is able to attack the troops passed over with a considerable numerical superiority, say the double, before the bridge is completed. An illustration will make this plain.
If the enemy requires twenty-four hours for the construction of a bridge, and if he can by other means only pass over 20,000 men in those twenty-four hours, whilst the defender within twelve hours can appear at any point whatever with 20,000 men, in such case the passage cannot be forced; for the defender will arrive when the enemy engaged in crossing has only passed over the half of 20,000. Now as in twelve hours, the time