Let us suppose that A has _political_ reasons for particularly desiring to save from invasion four districts, the importance of which I have indicated on Sketch 12 by shading, and which I have numbered 1, 2, 3, 4. [Illustration: Sketch 11.] Let us suppose that those four districts happen to lie at the four exposed corners of the area which A has to defend. The Government of A knows it to be essential to success in the war that his territory should not be invaded. Or, at least, if it is invaded, it must not, under peril of collapse, be invaded in the shaded areas. It is apparent upon the very face of such a diagram, that with the all-important shaded areas situated in the corners of his quadrilateral, A is heavily embarrassed. He must disperse his forces in order to protect all four. If wastage of men compels him to shorten his line on the right against M, he will be immediately anxious as to whether he can dare sacrifice 4 to save 2, or whether he should run the dreadful risk of sacrificing 2 to save 4. [Illustration: Sketch 12.] If wastage compels him to shorten his defensive line upon the left, he is in a similar quandary between 1 and 3. The whole situation is one in which he is quite certain that a defensive war, long before he is pushed to extremities, will compel him to "scrap" one of the four corners, yet each one is, for some political reason, especially dear to him and even perhaps necessary to him. Each he desires, with alternating anxieties and indecisions, to preserve at all costs from invasion; yet he cannot, as he is forced upon the defensive, preserve all four. Here, again, the ideal situation for him would be to possess against the invader some such arrangement as is suggested by Sketch 11. In this arrangement, if one were compelled unfortunately to consider four special districts as more important than the mass of one's territory, one would have the advantage of knowing that they were clearly distinguishable into less and more important, and the further advantage of knowing that the more important the territory was, the more central it was and the better protected against invasion. Thus, in this diagram, the government of the general oblong, A, may distinguish four special zones, the protection of which from invasion is important, but which vary in the degree of their importance. The least important is the outermost, 1; the more important is an inner one, 2; still more important is 3; and most important of all is the black core of the whole. Some such arrangement has been the salvation of France time and time again, notably in the Spanish wars, and in the wars of Louis XIV., and in the wars of the Revolution. To some extent you have seen the same thing in the present war. To save Paris was exceedingly important, next came the zone outside Paris, and so on up to the frontier.