mber against Black on his right, White's left, and the remaining
part of Black's line (10 to 16 inclusive), is out in the cold.

If it were a tactical problem, and all this were taking place in a
small field, Black's left wing, 10-16, would, of course, come up at
once and redress the balance. But being a strategical problem, and
involving very large numbers and very great distances, Black's left
wing, 10-16, can do nothing of the kind. For Black's left wing, 10-16,
_cannot possibly get up in time_. Long before it has arrived on the
scene, White's 12 will have broken Black's 9 along Black's right wing.

[Illustration: Sketch 27.]

There are three elements which impose this delay upon Black's left
wing.

First, to come round in aid of the right wing means the marching
forward of one unit after another, so that each shall overlap the
last, and so allow the whole lot to come up freely. This means that
the last unit will have to go forward six places before turning, and
that means several days' marching. For with very large bodies, and
with a matter of 100 miles to come up, all in one column, it would be
an endless business (Sketch 28).

[Illustration: Sketch 28.]

Next you have the delay caused by the _conversion of direction_
through a whole right angle. That cause of delay is serious. For when
you are dealing with very large bodies of men, such as half a dozen
army corps, to change suddenly from the direction S (see Sketch 29)
for which your Staff work was planned, and to break off at a moment's
notice in direction E, while you are on the march towards S, is
impossible. You have to think out a whole new set of dispositions,
and to re-order all your great body of men. White was under no such
compulsion, for though he had to swing, the swing faced the same
general direction as his original dispositions. And the size of the
units and the distances to be traversed--the fact that the problem is
strategical and not tactical--is the essence of the whole thing. If,
for instance, you have (as in Sketch 30) half a dozen, not army corps,
but mere battalions of 1,000 men, deployed over half a dozen miles of
ground, AB, and advancing in the direction SS, and they are suddenly
sent for in the direction E, it is simple enough. You form your 6,000
men into column; in a few hours' delay they go off in the direction
E, and when they get to the place where they are wanted, the column
can spread out quickly again on the front CD, and