DERIVATION, OR DRIFT, OF ELONGATED PROJECTILES. 
125 
Take 0, the origin, at the muzzle of the gun. Ox horizontal in the 
vertical plane of departure, Oy vertical, and Oz horizontal to the right 
of the plane of fire. 
Let P be the centre of gravity of the shot; x , y , z the co-ordinates 
of P •, PC the axis of the shot; and PT the tangent to the path of P. 
If there were no air, then PC would remain parallel to the tangent of 
the curve OP at 0. 
But the air causes a couple to act on the shot, tending to set the 
axis of the shot across the direction of motion; and this couple, acting 
on the shot (supposed to have angular momentum c 6 r) about PC, will 
deflect the axis PC to the right; and after a few gyrations, which are 
destroyed by the friction of the air, the shot will move steadily, with its 
point permanently deflected slightly to the right. 
Plan. 
PZ (the direction of the resultant momentum Z of the body and the 
medium) will remain constantly parallel to the plane xOy , because there 
is no impressed force perpendicular to this plane; and if a be the angle 
the axis of the shot makes with the plane xOy, and if u , w be the com¬ 
ponent velocities of P along PA and PC\ then, as before, 
c x u— — Z sin a, 
cyx a= Z cos a, 
and therefore the velocity of P in the direction Oz , 
dz 
-77 == u cos a + w sm a 
at 
»/l 1\ . 
= Z (-- — 1 sm a cos a. 
Vs Cl/ 
Now, the couple acting On the body in the plane APC is 
(c-, — Co) uw = Z 2 ^ sin a cos a; 
Vs c \) 
