stract 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.

[Illustration: Sketch 40.]

The situation of that force was as follows:--

[Illustration: Sketch 41.]

Along and behind {~GREEK SMALL LETTER BETA~}{~GREEK SMALL LETTER
GAMMA~} stretched the 5th Army of the French, prolonged on its left by
the British contingent. I have marked the first in the diagram with the
figure 5, the second with the letters Br, and the latter portion I have
also shaded. At right angles to the French 5th Army stretched the
French 4th Army, which I have marked with the figure 4. It depended
upon the obstacle of the Meuse {~GREEK SMALL LETTER BETA~}{~GREEK SMALL
LETTER DELTA~} for its defence, just as the French 5th Army depended
upon the Sambre, {~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER
BETA~}. It must, of course, be understood that when one says these
forces "lay along" the aforesaid lines, one does not mean that they
merely lay behind them. One means that they held the bridges and
prepared to dispute the crossing of them.

Now, the French plan was as follows. They said to themselves: "There
will come against us an enemy acting along the arrows VWXYZ, and this
enemy will certainly be in superior force to our own. He will perhaps
be as much as fifty per cent. stronger than we are. But he will suffer
under these disadvantages:--

"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, a