He has no choice but to _fall back upon shorter lines_. That is, having only six units left he must retire to some such point as the line F-G, Diagram VII, where his remaining six units will be just sufficient to hold the line, and if the six dwindle to four he must again fall back to a yet shorter line, such as C-D. Note carefully that this does not concern proportionate numbers. We are not here considering the relative strength of the defence and of the offence; we are dealing with absolute numbers, with a minimum below which the defensive _cannot_ hold a certain line at all, but _must_ seek a shorter one. [Illustration: DIAGRAM VIII. The Germans are now holding, roughly, the line A-B, from the North Sea to the Swiss Mountains--500 miles long in all its twists and turns. If dwindling numbers force them to take up a shorter line they could either abandon Alsace-Lorraine and substitute C-G for C-B, or abandon most of Belgium and Northern France and substitute E-C for A-C. With still failing numbers they would have to take up the still shorter line F-B. It would be no shortening of the German line to fall back upon the Rhine, D-D-D.] Now that is precisely the state of affairs upon the French and Belgian frontiers at this moment. The Germans are holding a line, which is roughly that shown in Diagram VIII, between the Swiss mountains and the sea near Nieuport, the line A-B about 400 miles long in all its twists and turns. If their numbers fall below a certain level they cannot hold that line at all, and they must take up a shorter line. How could they do this? Either by abandoning Alsace-Lorraine and substituting C-G for the present C-B, or by abandoning most of Belgium and all northern France, and falling back upon the line Antwerp-Namur-The Ardennes and the Vosges, substituting E-C for A-C. With failing numbers they would have to take up a still shorter line from Liege southwards, just protecting German territory, the line F-B. As for the line of the Rhine lying immediately behind F-B, the line D-D-D, it is a great deal longer than the shortest line they could take up. F-B, and though heavily fortified at five important points and with slighter fortifications elsewhere, it would need quite as many men to defend it as a corresponding line of trenches. Thus it would be no shortening of the German line to fall back upon the Rhine. So much for an illustration of what is meant by absolute numbers and of their importance in the present phase of the campaign. (2) Now what of _Proportionate_ numbers? That is a point upon which even closer attention must be fixed, because upon it will depend the issue of the campaign. The first thing we have to see clearly is that Austria and Germany began the war with a very great preponderance in numbers of trained and equipped men ready to take the field within the first six weeks. They had here a great advantage over Russia and France combined, and to see what that advantage was look at Diagram IX.