126 derivation, or drift, of elongated projectiles: 
and this, acting on the resultant angular momentum of the shot (which 
may be taken to be c 6 r, and indifferently about the axis PC or PT, 
since they are very nearly coincident), will cause the point of the shot 
C to descend so as always to be very nearly in the tangent to the 
trajectory; and therefore if the tangent at P makes an angle p with 
the horizon, 
dz Ccf dip' 
dt Z dt’ 
the negative sign being taken with ~, because ip is diminishing. 
ctt 
The resultant momentum Z may be put equal to Wv; where v is the 
resultant velocity in the trajectory, neglecting the momentum due 
to the motion of the air, which is small compared with PFv, the 
momentum of the shot; and therefore 
dz 
dt 
c 6 r dip 
Wv dt 
v dt 
If the angular velocity r died away at the same rate as the linear 
V 
velocity v, the fraction - would be constant, and equal to the value it 
^ 7T 
has at the muzzle—namely, —; 2 a being the calibre. 
Then 
dz 
dt 
d\p 
dt 
and 
2 =- 
n a 
if <p is the circular measure of the angle of projection. 
On this assumption the drift would be proportional to the change of 
direction of the motion, and the total drift to the sum of the angles of 
ascent and descent. 
Using u now to denote the horizontal component of the velocity, 
