422 
TRAJECTORIES OF FIELD GUNS. 
In order to ensure the successive first and second differences of these 
times being fairly regular, it was necessary in the first place to obtain 
the velocities to decimals of a foot, and to employ proportional parts in 
taking out the times from the time-integral table. The heights of the 
trajectories at a hundred yards from the muzzle for each range were 
then deduced by successive application of the formula 
s=\gt (T-t ); 
where t = time from muzzle to a hundred yds. distance, 
T — whole time of flight for the particular range. 
This was then repeated for all the other distances from the muzzle. 
In these tables, the vertical column on the left shows the ranges fired 
at, and the horizontal column at the top distances in yds. from the 
muzzle. 
Their intersections give the heights of the paths above the muzzle in 
feet. 
With regard to the angle of descent I find that it can be expressed 
as a function of the range of the form 
Arfi + Bn + C, 
where n is the range in hundreds, and decimals of a hundred yards, 
and A, B, and C are constants readily determined for any particular 
gun. 
Take, for instance, the 13-pr. M.L.R. gun. In this case 
A — *38, B = 6*25, (7=1*5, 
and the formula becomes— 
angle of descent in minutes = *38« 2 4- 6*2 5n -f 1*5. 
Suppose we require the angle for 3360 yds. range; we get 
•38 X (33-6) 2 + 6-25 x 33*6 + 1*5 
= 428*9 + 210 -1- 1*5, 
= 640*4 minutes. 
Therefore, the required angle is 10° 40'. 
For the 16-pr. gun the formula is— 
angle of descent in minutes = *38 n 2 + 10*45^ — 4*5, 
and *44^ 2 — 10*34^ — 6 
for the 9-pr, 
