The first is this:  You can break up its cohesion by a smashing blow delivered somewhere along its line, and preferably near its centre.  But if you do that, the results will never be quite complete, and may be incomplete in any degree according to the violence and success of your blow.

The second way is to get round the enemy with your superior numbers, to get past his flank, to the back of him, and so envelop him.  If that manoeuvre is carried out successfully, you bag his forces entire.  It is to this second manoeuvre that modern Prussian strategy and tactics are particularly attached.  It is obvious that its fruits are far more complete than those of the first manoeuvre, when, or if, it is wholly successful.  For to get round your enemy and bag him whole is a larger result than merely to break him up and leave some of him able to re-form and perhaps fight again.  Two things needful to such success are (a) superior numbers, save in case of gross error upon the part of the opponents; (b) great rapidity of action on the part of the outflanking body, coupled, if possible, with surprise.  That rapidity of action is necessary is obvious; for the party on the flank has got to go much farther than the rest of the army.  It has to go all the length of the arrow (1), and an element of surprise is usually necessary.  For if the army AA which BB was trying to outflank learned of the manoeuvre in time he only has to retreat upon his left by the shorter arrow (2) to escape from the threatened clutch.

[Illustration:  Sketch 45.]

Now, von Kluck with his five army corps, four of which were in operation against Sir John French, was well able to count on all these elements.  He had highly superior numbers, his superiority had not been discovered until it was almost too late, and for rapidity of action he had excellent railways and a vast equipment of petrol vehicles.

What he proposed to do was, while engaging the British contingent of less than two army corps with three full army corps of his own, to swing his extreme western army corps right round, west through Tournai, and so turn the British line.  If he succeeded in doing that, he had at the same time succeeded in turning the whole of the Franco-British forces on the Sambre and Meuse.  In other words, he was in a fair way to accomplishing the destruction of the operative corner of the great square, and consequently, as a last result, the destruction of the whole Allied force in the West.

The thing may be represented on a sketch map in this form.

Of von Kluck’s five corps, 1 is operating against the junction of the English and French lines beyond Binche, 2, 3, and 4 are massing against the rather more than one and a half of Sir John French at AA, and 5, after the capture of Tournai, is going to take a big sweep round in the direction of the arrow towards Cambrai, and so to turn the whole line.  Meanwhile, the cavalry, still farther west, acting independently, is to sweep the country right out to Arras and beyond.