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
withstand by a careful choice of position the first shock of enemies
who would certainly be numerically superior. It was the whole business
of the German commanders to make the shock overwhelming, in order that
the operative corner should be pounded to pieces, or should be
surrounded and annihilated before the manoeuvring masses could swing
up in aid. Should this destruction of the operative corner take place
before the manoeuvring masses behind it could swing, the campaign in
the West was lost to the Allies, and the Germans pouring in between
the still separated corners of the square were the masters for good.

It behoves us, therefore, if we desire to understand the campaign, to
grasp how this operative corner stood, upon what defences it relied,
in what force it was, what numbers it thought were coming against it,
and what numbers were, as a fact, coming against it.

To get all this clear, it is best to begin with a diagram.

Suppose two lines perpendicular one to the other, and therefore
forming a right angle, AB and BC. Suppose at their junction, B, a
considerable zone or segment, SSS, of a circle, as shaded in the
following diagram. Supposing the line AB to be protected along the
outer half of it, AK, by no natural obstacle--the state of affairs
which I have represented by a dotted line {~GREEK SMALL LETTER
ALPHA~}{~GREEK SMALL LETTER GAMMA~}; but suppose the second half of it,
KB, should be protected by a natural obstacle, though not a very
formidable one--such as I have represented by the continuous line
{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER BETA~}. Supposing the
perpendicular line BC to be protected by a really formidable natural
obstacle {~GREEK SMALL LETTER BETA~}{~GREEK SMALL LETTER DELTA~}, and
supposing the shaded segment of the circle at B to represent a
fortified zone (1) accessible to any one within the angle KBC, as from
the arrow M; (2) inaccessible (until it was captured or forced) to any
one comi