those lines remain only in the idea of the scheme of the whole, and
are not to be discovered save in the loosest way from the actual
positions of men upon the map.

We have seen that this "open strategic square" involved essentially
two conceptions--the fixed "operative corner" and the swinging
"manoeuvring masses."

The manoeuvring masses, at this moment when the great German blow fell
upon the Sambre and the Meuse, and when Namur went down immediately
before it, were (_a_) upon the frontiers of Alsace and Lorraine, (_b_)
in the centre of the country, (_c_) near the capital and to the west
of it, and even, some of them, upon the sea.

The operative corner was this group of armies before Namur on the
Sambre and Meuse, the 4th French Army under Langle, the 5th French
Army under Lanrezac, the British contingent under French.

We know from what has been written above in this book that it is the
whole business of an operative corner to "take on" superior numbers,
and to hold them as well as possible, even though compelled to
retreat, until the manoeuvring masses can swing and come up in aid,
and so pin the enemy.

We further know from what has gone before that the whole crux of this
manoeuvre lies in the power of the operative corner to stand the
shock.

It was the business of the French in this operative corner before
Namur and of their British Allies there to await and, if possible, to