264 
PRINCIPLES OP GUNNERY. 
The action of gravity must now be considered. 
For low angles of elevation the vertical velocity of the projectile is 
small, and the resistance of the air to the projectile in the vertical 
direction may be neglected; so that all the conditions shown to hold 
in the vertical plane in the case of an unresisted projectile hold also 
in this case. 
The projectile will ascend approximately for half the time of flight, 
T 
— -, and descend for the same time. It will be at its maximum 
2 T 
height (PI) at the time ; so that, as before. 
In the same way, by Table II. the time over OP and PB may be 
found, when the velocity at 0 and the distances ON and NB are 
known. 
Suppose 
time over OP = i, 
„ OB = T ; 
then „ PB = T — t = t\ suppose; 
tlien height NP — ~t (T — t), from equation (6), 
z 
Example 1.—A common shell, fired from a 64-pr. M.L. siege gun 
with a charge of 12 lbs. of powder, was observed to strike the crest of 
a traverse in 3‘2 secs. Find approximately the range, and what ver¬ 
tical distance below the crest of the traverse the shell would strike an 
escarp 200 ft. beyond. Muzzle velocity = 1457 f.s., weight of shell 
= 64 lbs., diameter of shell — 6'22 ins. 
The remaining velocity at P can be found thus: 
= •6834 + 1-9344 = 2-6178 ; 
v = 1064 f.s. (Table II.) 
The distance ON can then be found thus : 
S-= 
S v — >Sy 3455-2 — 1075-1 
d? 
■6045 
= 3937-3 ft. = ON, 
the distance of the traverse from the gun, 
