To appreciate how superior the enemy proved to be in number, and how heavy the miscalculation here was, we must first see what the numbers of this Allied operative corner were.

I have in Sketch 42 indicated the approximate positions and relative sizes of the three parts of the Allied forces.

Beginning from the left, we have barely two army corps actually present of the British contingent in the fighting line:  for certain contingents of the outermost army corps had not yet arrived.  We may perhaps call the numbers actually present at French’s command when contact was taken 70,000 men, but that is probably beyond the mark.  To the east lay the 5th French Army, three army corps amounting, say, to 120,000 men, and immediately south of this along the Meuse lay the 4th French Army, another three army corps amounting to at the most another 120,000 men.

We may then call the whole of the operative corner (if we exclude certain cavalry reserves far back, which never came into play) just over 300,000 men.  That there were as many as 310,000 is improbable.

The French calculation was that against these 300,000 men there would arrive at the very most 400,000.

That, of course, meant a heavy superiority in number for the enemy; but, as we have seen, the scheme allowed for such an inconvenience at the first contact.

That more than 400,000 could strike in the region of Namur no one believed, for no one believed that the enemy could provision and organize transport for more than that number.

A very eminent English critic had allowed for seven army corps of first-line men as all that could be brought across the Belgian Plain.  The French went so far as to allow for ten, a figure represented by the 400,000 men of the enemy they expected.

We had then the Allied forces expecting an attack in about the superiority indicated upon this diagram, where the British contingent and the two French armies are marked in full, and the supposed enemy in dotted lines.

[Illustration:  Sketch 42.]

Roughly speaking, the Allies were allowing for a thirty per cent. superiority.

Now, lying as they did behind the rivers, and with the ring of forts around Namur to shield their point of junction and to split the enemy’s attack, this superiority, though heavy, was not crushing.  The hopes of the defensive that it would stand firm, or at least retire slowly so as to give time for the manoeuvring masses to come up was, under this presumption, just.  It was even thought possible that, if the enemy attacked too blindly and spent himself too much, the counter-offensive might be taken after the first two or three days.

As for the remainder of the German forces, it was believed that they were stretched out very much in even proportion, without any thin places, from the Meuse to Alsace.