450 
PRINCIPLES OF GUNNERY. 
Suppose, then, W = weight of projectile in lbs., 
V = velocity on impact in feet per second, 
B = resistance in lbs., 
s t = number of feet penetrated, 
WV% 
then —-— = Rs ; ...(1) 
2 g 
if the resistance be supposed uniform. 
But if the projectile has sufficient energy to perforate, the remaining 
in . velocity can be measured after perforation by means of a chronograph, 
and the energy absorbed in perforating the resisting medium 
where is the remaining velocity immediately after perforation. 
Hence, in this case, 
~(r*-v?) = R S , ..( 2 ) 
But if B (the resistance to the projectile) be variable , the equation 
must be written 
¥ 9 ^~^=C Rds . (3) 
Differentiating (3), considering v and s as variable, 
„ W dv Wdv 
R= — — v — = — — , 
(j as (j at 
then / Rdt = — - dv\ 
Jt, 0 Jv, 
or if t t — the time of perforation through the resisting medium (resist¬ 
ance supposed uniform ), 
'- 7 ^).“> 
Substituting in (2), then 
W f jT-a 2 , W(V-v\ 
_(^_V)= 7 (—') s ,, 
or <,= B i ( r +»,) 5 . (5) 
or the time of passing through the resisting medium 
_ thickness of resisting medium 
mean velocity of projectile in passing through the resisting medium 
If v n is the velocity which would be required just to perforate the 
resisting medium, it follows that 
W v*-Rs- 
¥g V " ~ liS ” 
W 
but Rs, = — {V 2 — vj) from (2), 
*9 
hence v tl — < 
