Whether a target will be struck by a bullet when the range has not been correctly estimated depends entirely upon the danger space. In pointing at the bottom line of the target, the aiming position (_i.e._, the height at which the piece is held) does not affect the danger space. When pointing at the center of the target the danger space changes, increasing for low rear sight elevations and tall targets, and decreasing for high rear sight elevations and low targets, as compared with aim taken at the bottom line of a target. “The evil effects of errors in estimating the range decrease as the ‘danger space’ increases, which, by the way, is wholly dependent upon the ballistic properties of the rifle, upon the range, and the height of the target. The danger on the ground in rear of the target fired upon, and the difficulty of bringing up reinforcements and ammunition over it, increases directly as the beaten zone, which in addition depends upon the inclination of the ground to the line of sight.” The importance of this circumstance is frequently so magnified in the French infantry that sight is lost of tactical requirements. For example, they employ formulae to ascertain the point from which a height can be covered with grazing fire, or propose to defend the ascent to a plateau by evacuating the military crest and occupying the reverse slope, keeping the slope facing the enemy under a grazing fire with the tail ends of the trajectories. Let A B B¹, in the accompanying figure, represent a horizontal plane pierced by trajectories C B and C¹ B¹, at an angle α, forming the beaten zone B B¹. If now the ground falls from B in the direction B D, it is obvious from the figure, that the angle of fall β decreases and the beaten zone B D increases. The limit of this increase is reached when the angle of slope is greater than the angle of fall of the projectile. In this case there is a dead angle beyond B and toward D. If, on the other hand, the ground be rising, the angle of fall will be C¹ D¹ B and the beaten zone[170] decreases to B D¹. The smaller the angle of fall of the projectile the greater the influence of the ground. [Illustration] [170] The computation of beaten zones is based upon the formula deduced by Lieutenant-General ROHNE in his work _Schieszlehre für Infanterie_, p. 127: Let α = angle of fall; γ = angle of slope (rising or falling); β = beaten zone on level ground; then α ----- β = beaten zone on falling ground; α - γ α ----- β = beaten zone on rising ground. α + γ