It is evident to all who study closely the map of France that her eastern frontier falls into two sharply contrasted divisions, the north-eastern which reaches from the sea to the valley of the Sambre, and the south-eastern which extends from that river to, and along the Swiss boundary. The former is flat country, easy for military operations; the latter is mountainous, intersected with many deep valleys. After the loss of Alsace-Lorraine, the French set to work to rectify artificially the strategical weakness of their frontier; and in a chain of fortresses behind the Vosges Mountains they erected a rampart which has the reputation of being impregnable. This is the line Belfort, Épinal, Toul, Verdun. A German attack launched upon this line without violating neutral territory would have to be frontal, for on the north the line is covered by the neutral states of Belgium and Luxemburg, while on the south, although the gap between the Vosges and the Swiss frontier apparently gives a chance of out-flanking the French defences, the fortress of Belfort, which was never reduced even in the war of 1870-1, was considered too formidable an obstacle against which to launch an invading army. A rapid advance on Paris was therefore deemed impossible if respect were to be paid to the neutrality of Belgium and Luxemburg, and it was for this purely military reason that Germany has to-day violated her promises to regard the neutrality of these states. This was frankly admitted by Herr von Jagow to Sir Edward Goschen: 'if they had gone by the more southern route they could not have hoped, in view of the paucity of roads and the strength of the fortresses, to have got through without formidable opposition entailing great loss of time'.[8] In the case of Belgium a very easy road was afforded into French territory up the Valley of the Meuse, past Liège and thence into France past Namur and through what is known as the Gap of Namur. A German army could debouch into France through this gap the more easily inasmuch as the French, relying on the neutrality of these two states, had not strongly fortified the frontier from the sea to Maubeuge. Moreover, as the country to the west of the Sambre was very easy country for manoeuvring and furnished with good roads and railways, it was reckoned that the formidable French lines to the south could be turned in this manner, and the German army could march upon Paris from the north-east. As to Luxemburg, plainly it could not in such a scheme remain neutral. It would lie between the two wings of the German army, and controlling as it did the roads to Brussels, Metz, and Aix-la-Chapelle, it could not be allowed to cause such inconvenience as to prevent easy communication between one portion of the German army and another.