128 
DERIVATION, OR DRIFT, OF ELONGATED PROJECTILES. 
Magnus began by trying to explain the drift as due to the differences 
of pressure in consequence of the existence of a vortex round the shot; 
but this would make the shot drift to the left. 
In the January, 1880, number of the “Messenger of Mathematics” 
it is shown that a horizontal cylinder of density <r, revolving with 
angular velocity w in infinite liquid of density />, and surrounded by a 
vortex, would, if left to itself, describe a cycloid from right to left, with 
mean velocity —~, and that if projected with this velocity would 
describe a horizontal straight line. 
When a gas-check becomes ’detached from the base of a shot, the 
forward motion is soon destroyed, but the angular velocity remains, and 
the gas-check behaves in a similar manner to the above cylinder, and 
drifts to the left, with mean velocity ~ - - p £ . 
For instance, in the 16-in. 80-ton gun 
TV V 7T 
n a 50 
and for copper. 
<x — 8*6, 
while for air, 
p = -001276, 
therefore 
01 “P 9 _ 715 . 
2 p o) 
1600 
= 48tt } 
the mean velocity with which the gas-check will drift to the left, if it 
becomes detached from the base of the shell. 
It is only in such a case as this, then, that we can assert (as on p. 589, 
Yol. X., “Proceedings, R.A. Institution”) that the drift diminishes 
as w the angular velocity increases; and the paradoxical result that the 
velocity of drift is infinite when the angular velocity is zero, only means 
that we should require to project the cylinder from right to left with 
infinite velocity in order that the path should not be curved. 
From the preceding explanation we see that the drift is proportional 
to the angular velocity. This explanation is rendered necessary by 
the unfortunate mis-statement on p. 589, which was written down 
hastily, and of which the incorrectness escaped notice till after the 
paper was printed. 
We can gain an approximate idea of the amount of deflection of the 
point to the right, and above the tangent to the trajectory, by con¬ 
sidering them separately, each being supposed small. For if a! denote 
the angle between the axis of the shot and the vertical plane through 
the tangent of the trajectory, then ° 
tan a' = A tan a, 
