The situation at this moment can best be understood by a glance at the sketch map on p. 178. Two great French advances had been made in the winter of 1792-93; the one a northern advance, which we have just detailed, the over-running of Belgium; the other an eastern advance right up to the Rhine and to the town of Mayence. Both had failed. The failure in Belgium, culminating in the treason of Dumouriez, has been read. On the Rhine (where Mayence had been annexed by the French Parliament just as Belgium had been) the active hostility of the population and the gathering of the organised forces of the Allies had the same effect as had been produced in the Low Countries. It was on March 21, 1793, that the Prussians crossed the Rhine at Bacharach, and within that week the French commander, Custine, began to fall back. On the first of April he was back again in French territory, leaving the garrison of Mayence, somewhat over twenty thousand men, to hold out as best it could; a fortnight later the Prussians had surrounded the town and the siege had begun. On the north-eastern front, stretching from the Ardennes to the sea, a similar state of things was developing. There, a barrier of fortresses stood between the Allies and Paris, and a series of sieges corresponding to the siege of Mayence in the east had to be undertaken. At much the same time as the investment of Mayence, on April 9, the first step in this military task was taken by the Allies moving in between the fortress of Condé and the fortress of Valenciennes. Thenceforward it was the business of the Austrians under Coburg, with the Allies that were to reach him, to reduce the frontier fortresses one by one, and when his communications were thus secure, to march upon Paris. It is here necessary for the reader unacquainted with military history to appreciate two points upon which not a little of contemporary historical writing may mislead him. The first is that both in the Rhine valley and on the Belgian frontier the forces of the Allies in their numbers and their organisation were conceived to be overwhelming. The second is that no competent commander on the spot would have thought of leaving behind him the garrison of even one untaken fortress. It is important to insist upon these points, because the political passions roused by the Revolution are still so strong that men can hardly write of it without prejudice and bias, and two errors continually present in these descriptions of the military situation in the spring of 1793, are, first, that the Allies were weakened by the Polish question, which was then active, and secondly, that the delay of their commanders before the French fortresses was unnecessary.