Now, as a matter of fact, the German forces were in no such disposition. 1.  The Germans had added to every army corps a reserve division. 2.  They had brought through the Belgian plains a very much larger number than seven army corps:  they had brought nine. 3.  They had further brought against Namur yet another four army corps through the Ardennes, the woods of which helped to hide their progress from air reconnaissance.  To all this mass of thirteen army corps, each army corps half as large again as the active or first line allowed for, add some imperfectly trained but certainly large bodies of independent cavalry.  We cannot accurately say what the total numbers of this vast body were, but we can be perfectly certain that more than 700,000 men were massed in this region of Namur.  The enemy was coming on, not four against three, but certainly seven against three, and perhaps eight or even nine against three.

The real situation was that given in the accompanying diagram (Sketch 43).

Five corps, each with its extra division, were massed under von Kluck, and called the 1st German Army.  Four more, including the Guards, were present with von Buelow, and stretched up to and against the first defences of Namur.  Now, around the corner of that fortress, two Saxon corps, a Wurtemberg corps, a Magdeburg corps, and a corps of reserve under the Duke of Wurtemberg formed the 3rd Army, the right wing of which opposed the forts of Namur, the rest of which stretched along the line of the Meuse.

Even if the forts of Namur had held out, the position of so hopelessly inferior a body as was the Franco-British force, in face of such overwhelming numbers, would have been perilous in the extreme.  With the forts of Namur abandoned almost at the first blow, the peril was more than a peril.  It had become almost certain disaster.

[Illustration:  Sketch 43.]

With the fall of Namur, the angle between the rivers—­that is, the crossings of the rivers at their most difficult part where they were broadest—­was in the hands of the enemy, and the whole French body, the 4th and 5th Armies, was at some time on that Saturday falling back.

The exact hour and the details of that movement we do not yet know.  We do not know what loss the French sustained, we do not know whether any considerable bodies were cut off.  We do not know even at what hour the French General Staff decided that the position was no longer tenable, and ordered the general retreat.

All we know is that, so far from being able to hold out two or three days against a numerical superiority of a third and under the buttress of Namur, the operative corner, with Namur fallen and, not 30 per cent., but something more like 130 per cent. superiority against it, began not the slow retreat that had been envisaged, but a retirement of the most rapid sort.

Such a retirement was essential if the cohesion of the Allied forces was to be maintained at all, and if the combined 4th and 5th French Armies and British contingent were to escape being surrounded or pierced.