(3) Before some of its forts fell, Namur must have been entirely isolated, and attacked not only from the north but also from the south; and the French armies were not in a position to reinforce the garrison unless they sent forward some detachments before the Germans crossed the Sambre. (4) In the fighting between August 18th and 22nd or 23rd it was the French armies who attacked and not the German--except in the neighbourhood of Mons. Reference has been made to the triangle of which Namur is the apex. This, it was generally believed by the military critics, was the angle which the French were ready to occupy, if they had not, indeed, already occupied it, before the fighting at Charleroi began. The discovery that this triangle was really in possession of the Germans came as a shock. Exaggerated hopes gave way to exaggerated fears; and it was even held that the Germans had a reasonable chance of breaking through the French lines in the north and advancing on Paris before the Russians could advance much further into Germany. It is to be presumed that these fears are exaggerated, and that General Joffre can shift his men from Alsace to the north. One gathered that eighteen German army corps had advanced through Belgium, and that only three or four had been left to watch over Alsace-Lorraine. It would be unwise to hazard any conjecture as to the strength of the French; but if it were said that the proportions were just the reverse the statement might not be far out. At any rate, the fact remains that at the time of writing the French advance has been entirely checked; and the Allies are now on the defensive. If General Joffre had chosen to remain on the defensive from the first instead of advancing into Alsace; or, on the other hand, if he had considerably strengthened his force in the north and advanced in that direction with the object of establishing himself at Namur, the position would have been totally different. The numbers of the opposing forces would, at least, have been better proportioned, and the "human tidal wave" could have been held back.