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 αγ; 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 γβ. Supposing the perpendicular line BC to be protected by a
really formidable natural obstacle βδ, 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 coming from