PRINCIPLES OP GUNNERY. 
277 
the distance integrals, £ -—- (/5 — a) must be subtracted, and for the 
• . 7) — Q P ' i 
time integrals, (/3—a) must be subtracted. 
The equations and steps will now be written in the order oe 
CALCULATION. 
( p 1 = —^r^- for low angles of elevation, 
A 
or tan — - a ~- a - an ^ for high angles of elevation. 
If V is the muzzle velocity of the projectile, and « the angle of 
departure, then 
p = V cos a, and p sec (p 1 = V cos a sec <jh; 
then # sec q can be found from Table III. by equation (B) thus : 
d Q - 
Bq sec ^ ~ — B sec </>! H~ Bp Sec ^ \ 
where B = « — P in degrees. 
The correct value of <j> can be found in the ascending branch thus : 
then X can be found from equation (A) thus : 
w __ 
X —— ^2 COS (j) (S q S ec ^ ~~~ gee (j))j 
and Y can be found from equation (B) thus : 
qjQ _ 
Y “ sin (f> (Sq gee ^ ~ $p sec $)• 
For the correct determination of the time, 
but as the value of does not occur outside the equation in the time 
integral, the value ^ may be taken, and will give accurate results. 
Then T can be found from equation (C) thus : 
