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:--

First, because the largest howitzers capable of movement and of being
brought up against any fortress and shifted from one place of
concealment to another were so small that their range was
insignificant. Therefore the circumference on which they could be used
was also a small one; their opportunities for hiding were consequently
reduced; the chances of their emplacement being immediately spotted
from the fortress wer