It is noticed below that a decrease of pitch at the limits met with in 
practice does not influence sensibly the accuracy. 
However, from the reasons explained further on and confirmed by the 
shooting from a 3*4" mortar, with twists at muzzle of 15 and 5 calibres, 
it is seen an excessive rapid twist might, with vertical fire and small 
initial velocity, lessen somewhat the accuracy. 
By far the most interesting work of the problem now touched upon, 
belongs to Greenhill, Professor at the Woolwich Artillery College. 
Greenhill* assumes the projectile is an ellipsoid, and moves equably 
and rectilineally, in an incompressible fluid, the velocity of the parts 
of which has a potential, subordinate to certain conditions. 
Our investigations show two methods for deducing the equation (7) 
which solves the problem. One method is based on the geometrical 
theories of the motion of a solid body and the other on Euler’s formulae. 
II. 
We will suppose that the uniform acting air resistance is in the plane 
of the tangent and axis of figure, and that the centre of air resistance 
lies in front of the C. of G. The rotation of projectile is from right to left, 
looking from the point towards the C. of G. 
In the expression for its moment, the air resistance is taken to act 
only normally to the surface, the air friction being neglected, as also, 
variations of pressure on the surface. 
With these suppositions we may assume that the couple of the air 
resistance 
K = h. R. p sin 8 cos Sf . (1). 
Here R is radius of projectile, 
p is air resistance, 
h is a numerical co-efficient. 
For small angles SJ 
K=h. R. p. 8 . (2). 
III. 
Let Ox, Oy, Oz, (Fig. 1.) be the central axes of moments of inertia, Ox 
coinciding with axis of figure, Oy with direction of the principal linear 
moment of air resistance AT§ (axis of couple of air resistance), which is 
perpendicular to Ox and a tangent to trajectory. The projectile, with 
its principal axes, is referred to axes Ox Y , 0y\, Oz\ fixed in space, where 
Ox x is the direction of the tangent supposed to be fixed, Oz 1 is in the 
vertical plane, 0y\ is evidently perpendicular to plane passing through 
Ox i, Ox, Oz. 
# Professor A. G. Greenhill “On the rotation required for the stability of an elongated 
projectile,” Proceedings, Royal Artillery Institution, 1879, in whose treatment the couple 
is due to the slight disturbance of the adjacent stream lines of the air, due to the 
sidelong oscillations of the projectile. (Translator). 
f Majevski’s “ Traite de Balistique Exterieure,” p. 170. 
J Majevski “ On solution of problems of direct and vertical fire,” p. 66. 
§ The positive direction of axis of rotation is here contrary to that usually assumed. 
