THE ROYAL ARTILLERY INSTITUTION. 
51 
In both formulas. 
tan a = 
Vi -y* 
if both the points JD and T lie above the horizontal plane passing- 
through M. If T lies below it we have 
tana = A+Al. 
— x x 
In the rarely-occurring case in which both points lie below this plane 
we shall have 
tan a 
Vi-Vi 
Lastly, should it happen that the point of impact T lay in this plane, 
we should have y x = o } and 
In the above the values of y 1 and y 2 are always taken with reference 
to the horizontal plane through the muzzle of the gun. 
In all these cases, the numerator (y x =p y 2 ) of the fraction is inva¬ 
riably the difference in height of the two points; the denominator, on 
the contrary (x 2 — x) } their horizontal distance. If we call the first u 
and the last a , we shall have 
, u 
tan a = -; 
a 
in which expression it is all the same whether the points D and T lie 
above or below the horizontal plane through muzzle of the gun. 
The requisite data for the calculation of the angle of descent must 
either be taken from such plans as are forthcoming or be determined 
approximately by reconnaissances and suitable combinations. The 
heights indicated in plans of fortifications are always referable to an 
assumed plane of comparison. If a plan is available there will be no 
difficulty in fixing the difference in height (u) between the top of the 
cover and the point of impact, as also the horizontal distance (a) 
between these points. - ^ The measurements u and expressed in 
similar terms and divided one bv the other, give the tangent of the 
angle a. 
The considerations which are decisive in determining the point of 
impact will be discussed in parts 4, 5, and 6. 
The distance of the top of the cover and its height above the gun's 
muzzle (in other words, the groundf angle, of the top of the 
cover), if not already known, can be measured by means of practical 
geometry. These two data will be, in general, the only available 
sources of information; the others which are still required for the com- 
* If the line of fire is not perpendicular to the line of the protecting crest, the distance of the 
above-mentioned points must either be calculated, or he inferred from a bird’s-eye view. 
f Terrainwinkel. To avoid confusion of terms I have translated this word “ground angle ” 
instead of “ angle of elevation.”—T b. 
