(_c_) Further, the war proved even more conclusively that the wastage was not worth while. The immense expense in men only succeeded where there was an overwhelming superiority in number. The strategical result was not arrived at quickly (as the Germans had expected) through this tactical method, and after six months of war, the enemy had thrown away more than twice and nearly three times as many men as he need have sacrificed had he judged sanely the length of time over which operations might last. II. Another German theory had maintained that modern high explosives fired from howitzers and the accuracy of their aim controlled by aircraft would rapidly and promptly dominate permanent fortification. This theory requires explanation. Its partial success in practice was the most startling discovery and the most unpleasant one to the Allies of the early part of the war. In the old days, say up to ten years ago or less, permanent fortification mounting heavy guns was impregnable to direct assault if it were properly held and properly munitioned. It could hold out for months. Its heavy guns had a range superior to any movable guns that could be brought against it--indeed, so very heavily superior that movable guns, even if they were howitzers, would be smashed or their crews destroyed long before the fortress was seriously damaged by them. A howitzer is but a form of mortar, and all such pieces are designed to lob a projectile instead of throwing it. The advantage of using these instruments when you are besieging permanent works is that you can hide them behind an obstacle, such as a hill, and that the heavy gun in the fortress cannot get its shell on to them because that shell has a flatter trajectory. The disadvantage is that the howitzer has a very much shorter range than the gun size for size. [Illustration: Sketch 19.] Here is a diagram showing how necessarily true this is. The howitzer, lobbing its shell with a comparatively small charge, has the advantage of being able to hide behind a steep bit of ground, but on such a trajectory the range is short. The gun in the fortress does not lob its shell, but throws it. The course of the gun shell is much more straight. It therefore can only hit the howitzer and its crew indirectly by exploding its shell just above them. Until recently, the gun was master of the howitzer for three reasons:--