"The one part of his forces, V and W, will find it difficult to act in co-operation with the other part of his forces, Y and Z, because Y and Z (acting as they are on an outside circumference split by the fortified zone SSS) will be separated, or only able to connect in a long and roundabout way. The two lots, V and W, and Y and Z, could only join hands by stretching round an awkward angle--that is, by stretching round the bulge which SSS makes, SSS being the ring of forts round Namur. Part of their forces (that along the arrow X) will further be used up in trying to break down the resistance of SSS. That will take a good deal of time. If our horizontal line AB holds its own, naturally defended as it is, against the attack from V and W, while our perpendicular line BC holds its own still more firmly (relying on its much better natural obstacle) against YZ, we shall have ample time to break the first and worst shock of the enemy's attack, and to allow, once we have concentrated that attack upon ourselves, the rest of our forces, the masses of manoeuvre, or at any rate a sufficient portion of them, to come up and give us a majority in _this_ part of the field. We shall still be badly outnumbered on the line as a whole; but the resistance of our operative corner, relying on the Sambre and Meuse and the fortress of Namur, will gather much of the enemy unto itself. It will thus make of this part of the field the critical district of the whole campaign. Our masses, arriving while we resist, will give us a local superiority here which will hold up the whole German line. We may even by great good luck so break the shock of the attack as ourselves to begin taking the counter-offensive after a little while, and to roll back either Y and Z or V and W by the advance of our forces across the rivers when the enemy has exhausted himself." It will be clear that this calculation (whether of the expected and probable least favourable issue--a lengthy defence followed by an orderly and slow retreat designed to allow the rest of the armies to come up--or of the improbable and more favourable issue--the taking of the counter-offensive) depended upon two presumptions which the commander of the Allies had taken for granted: (1) that the German shock would not come in more than a certain admitted maximum, say thirty per cent. superiority at the most over the Allied forces at this particular point; (2) that the ring of forts round Namur would be able to hold out for at least three or four days, and thus absorb the efforts of part of the enemy as well as awkwardly divide his forces, while that enemy's attack was being delivered.