ed for.
Namur, as we have already seen, fell, not in three or four days, but
instantly--the moment it was attacked. And the result was that,
instead of an orderly and slow retirement, sufficiently tardy to
permit of the swinging up of the rest of the French "square"--that is,
of the arrival of the other armies or manoeuvring masses--there came
as a fact the necessity for very rapid retirement of the operative
corner over more than one hundred miles and the immediate peril for
days of total disaster to it.

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 s