To make this very simple principle intelligible at a glance, suppose (Fig. 76) a circular enclosure containing forty defenders separated from each other about a yard apart; a hand-to-hand struggle can only be carried on with a number equal to that of the defenders--or nearly so--and these under cover. It is no use for the assailants to assemble as at _A_, they can only present a front equal to that of the defence, and if this is energetic, the triangle _a_, _b_, _c_, will be effective only at _c_. [Illustration: FIG. 77.] But let us suppose the attacking body to possess projectile arms (Fig. 77), and instead of encountering the circular enclosure, the assailants to set up their engines between _A_ and _B_ within fair range. They will overwhelm the segment _d_, _c_, _e_, of the circle with projectiles, while the defenders will be able to oppose only an inferior number of engines to the convergent fire. [Illustration: FIG. 78.] To compensate in part for this inferiority the defending party adds appendages to the enclosure (Fig. 78 A), which allow an almost equal front of defence to be opposed to the attacking front, as regards the number of projectile weapons, and very superior in point of elevation and protection. But the attacking force will thus naturally arrange its engines as seen at B. Thus the projectiles sent from _a_, _b_, _c_, _d_, _e_, converge upon the salient C. The defence adds the new appendages D D, and if the engines are well protected, it can make the projectiles _g_, _h_, _i_, converge on the engine K and crush it, secondly the projectiles _l_, _g_, _h_, on engine _m_ and destroy it, and so on. Besides, these appendages have the further advantage of giving side views over the circumvallation itself and masking its foot. This principle regulates and will always regulate attack and defence; distances alone modify its applications. The more eccentric the defence is, the more distant must be the attack, and the wider the perimeter it must occupy; but it should be observed, that the more widely the defence is extended, the more open its flanks are to attack; these flanks therefore must also be capable of being defended, for every obstacle that offers only its own resisting force, without being protected by the action of a neighbouring obstacle, is soon destroyed. Whether fortifications or plans of battle are in question, the same principle comes into play. "Every part should defend its neighbour and be defended by it." It is clear that the solution of the problem becomes more and more difficult in proportion to the enlargement of the range of projectile weapons, and the extent of fronts of fortification or lines of battle. Vauban, and most of the engineers who were his rivals and successors, had resolved the problem in view of the range of the artillery of the period.