Suppose two lines perpendicular one to the other, and therefore forming a right angle, AB and BC. Suppose at their junction, B, a considerable zone or segment, SSS, of a circle, as shaded in the following diagram. Supposing the line AB to be protected along the outer half of it, AK, by no natural obstacle--the state of affairs which I have represented by a dotted line αγ; but suppose the second half of it, KB, should be protected by a natural obstacle, though not a very formidable one--such as I have represented by the continuous line γβ. Supposing the perpendicular line BC to be protected by a really formidable natural obstacle βδ, and supposing the shaded segment of the circle at B to represent a fortified zone (1) accessible to any one within the angle KBC, as from the arrow M; (2) inaccessible (until it was captured or forced) to any one coming from outside the angle, as from the arrows NNN; (3) containing within itself, protected by its ring of fortifications, passages, PP, for traversing the two natural obstacles, γβ and βδ, which meet at the point β. [Illustration: Sketch 38.] There you have the elements of the position in which the advance corner of the great French square was situated just before it took the shock of the main German armies. The two lines AB and BC are the French and British armies lying behind the Sambre, γβ, and the Middle Meuse, βδ, respectively; but the line of the Sambre ceases to protect eastward along the dotted line αγ beyond the point up to which the river forms a natural obstacle, while from K to B the line is protected by the river Sambre itself. The more formidable obstacle, βδ, represents the great trench or ravine of the Meuse which stretches south from Namur. The town of Namur itself is at B, the junction of the two rivers; and the fortified zone, SSS, is the ring of forts lying far out all round Namur; while the passages, PP, over the obstacles contained within that fortified zone, and accessible to the people _inside_ the angle from M, but not to the people _outside_ the angle from NNN, are the bridges across both the Sambre and the Meuse at Namur. All this is, of course, put merely diagrammatically, and a diagram is something very distant from reality. The "open strategic square" in practice comes to mean little more than two main elements--one the operative corner, the other a number of separate units disposed in all sorts of different places behind, and generally denominated "the manoeuvring mass." If you had looked down from above at all the French armies towards the end of August, when the first great shock came, you would have seen nothing remotely resembling a square. [Illustration: Sketch 39.]