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 manœuvring 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.

Sketch 39.

You would have seen something like Sketch 31 where the bodies enclosed under the title A were the operative corner; various garrisons and armies in the field, enclosed under the title B, were the manœuvring mass. But it is only by putting the matter quite clearly in the abstract diagrammatic form that its principle can be grasped.

With this digression I will return and conclude with the main points of debate in the use of the open strategic square.

We have seen that the operative corner is in this scheme deliberately imperilled at the outset.

The following is a sketch map of the actual position, and it will be seen that the topographical features of this countryside are fairly represented by Sketch 39; while this other sketch shows how these troops that were about to take the shock stood to the general mass of the armies.

But to return to the diagram (which I repeat and amplify as Sketch 41), let us see how the Allied force in the operative corner before Namur stood with relation to this angle of natural obstacles, the two rivers Sambre and Meuse, and the fortified zone round the point where they met.