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 soon begin to take part in the action. But when you are dealing with half a dozen army corps--240,000 men--it is quite another matter. The turning of any one of these great bodies through a whole right angle is a lengthy business. You cannot put a quarter of a million men into one column--they would take ages to deploy--so you must, as we have seen, make each unit of them overlap the next before the turn can begin. [Illustration: Sketch 29.] [Illustration: Sketch 30.] Nor is that all the delay involved. It would never do for these six separate corps to come up in driblets and get defeated in detail; 10, 11, and 12 will have to wait until 13, 14, 15, and even 16, have got up abreast of them--and that is the third cause of delay. Here are three causes of delay which, between them and accumulated, have disastrous effect; and in general we may be certain that where very large bodies and very extensive stretches of territory are concerned, that wing of Black which has been left out in the cold can never come up in time to retrieve the situation created by White's twelve pinning Black's engaged wing of only nine. If the square has worked, and if the twelve White have pinned the right-hand wing of Black, 1 to 9 inclusive, there is nothing for Black to do but to order his right wing, 1 to 9, to retreat as fast as possible before superior numbers, and to order his left wing, 10 to 16, to fall back at the same time and keep in line; and you then have the singular spectacle of twelve men compelling the retreat of and pursuing sixteen.