When superior numbers have passed one end of an obstacle it is obvious that the rest of the obstacle gradually becomes useless.[3] At what hour the French knew that they had to retire, we have not been told.  As we have seen, the enemy was right within Namur on the early afternoon of Saturday, the 22nd, and it is to be presumed that the French retirement was in full swing by the Sunday morning, in which case the British contingent, which this retirement left in peril upon the western extreme of the line, ought to have been warned many hours before five o’clock in the afternoon.

To what the delay was due we are again as yet in ignorance, but probably to the confusion into which the unexpected fall of Namur and the equally unexpected strength of the enemy beyond the Sambre and the Meuse had thrown the French General Staff.

At any rate, the news did come thus late, and its lateness was of serious consequence to the British contingent, and might have been disastrous to it.

The second piece of news, on the other hand, was the saving of it; and that second piece of news was the information that Sir John French had in front of him not one German army corps, and possibly part or even the whole of a second, but at least three.  As the matter turned out, the British contingent was really dealing first and last with four army corps, and the essential part of the news conveyed was that the extreme western portion of this large German force was attempting to turn the flank of the whole army.

It was not only attempting to do so, it was in number sufficient to do so; and unless prompt measures were taken, what was now discovered to be the general German plan would succeed, and the campaign in the West would be in two days decided adversely to the Allies—­the same space of time in which the campaign of 1815 was decided adversely to Napoleon in just these same country-sides.

It is here necessary to describe what this German plan was.

The reader has already seen, when the general principles of the open strategic square were described on a previous page, that everything depends upon the fate of the operative corner.  This operative corner in the present campaign had turned out to be the two French armies, the 4th and the 5th, upon the Lower Sambre and the Meuse, and the British contingent lying to the left of the 5th on the Upper Sambre and by Mons.

If the operative corner of a strategic open square is annihilated as a military force, or so seriously defeated that it can offer no effective opposition for some days, then the whole plan of a strategic square breaks to pieces, and the last position of the inferior forces which have adopted it is worse than if they had not relied upon the manoeuvre at all, but had simply spread out in line to await defeat in bulk at the hands of their superior enemy.

Now there are two ways in which a military force can be disposed of by its opponent.  There are two ways in which it can be—­to use the rather exaggerated language of military history—­“annihilated.”