DERIVATION; OR DRIFT; OF ELONGATED PROJECTILES. 
129 
and the couple acting on the shot about the axis normal to the tra¬ 
jectory in this vertical plane 
= (<?! — c 3 ) v 2 sin a cos a'; 
which must therefore = — c,r ~ 
at 
and therefore 
sin 2a' = 
2 c 6 r 1 d\f/ 
c 1 — c 3 v 2 dt 
2 c & r g cos if/ 
c i “ v?> 
Again, if p 1 be the angle between the axis of the shot and the plane 
through the tangent of the trajectory perpendicular to the plane xOy, 
the couple acting on the shot about the axis PA 
— ( c i — c 3 ) v 2 sin P' cos P '; 
and this with our approximations must be put 
da. 
and therefore 
sin 2 P' = 
dt * 
2 CnT da 
c 1 — c 3 dt 
If the rifling at the muzzle be just sufficient for stability; 
2 CnT 
g C 3 C 4 y 
c i c e> 77 
Q ^ ^ 1 ^ TT 
= 8 - ^ 
7r K l 
with the approximations employed; and then 
sm 
3a'= 8 l*£ a r*S%±. 
7r k* v 6 
• n ni _ o ^ tcA j--r da 
sm 2p =8 — j- aV - 
7r I 2 
and with our approximations we may put 
dt 
aW 
dt 
1 d?z 
v dt 2 
