302 MESSRS. R. H. FOWLER, E. G. GALLOP, C. N. H. LOCK AND H. AY. RICHMOND: 
It aims at determining the exact angular motion, as well as the motion of the centre 
of gravity. It confirms the classical theory of the plane trajectory (in accordance 
with the results of experiment), by showing that the divergences of the axis of the 
shell from the tangent to its path are generally small, but it aims, further, at 
determining the magnitude and effect of these divergences. 
In this general case the force system to be specified is more elaborate than in the 
case of the classical theory. In accordance with aerodynamical 
usage, we call the angle between the axis of symmetry of the 
shell and the direction of motion of its centre of gravity the 
yaw , and denote it by <L When the shell, regarded for the 
moment as without axial spin, has a yaw S, and the axis of the 
shell OA and the direction of motion OP remain in the same 
relative positions, the force system can by symmetry be repre¬ 
sented, as shown in fig. 1, by the following components, specified 
according to aerodynamical usage. 
(l) The drag , R, acting through the centre of gravity 0, in 
the direction of motion OP reversed. 
L, at right angles to R, called the cross wind force, which acts 
through O in the plane of yaw POA, and is positive when it tends to move O in the 
direction from P to A. 
(3) A moment M about 0, which acts in the plane of yaw, and is positive when 
it tends to increase the yaw. 
By analogy with § 1.0, we assume the following forms for R, L, and M :— 
(1.101) R = pv 2 r 2 f R {v/a, S), 
(1.102) L = pv 2 r 2 sin Sf L {v/a, <■)), 
(1.103) M = pv 2 r s sin d f u {v/a, S). 
These equations are of the most natural forms to make f l{ , f L , and f M of no physical 
dimensions. The arguments of § 1.01, by which the form of equation (l.OOl) was 
justified to some extent, probably apply with equal force in this more general case. 
The form chosen is suggested by the aerodynamical treatment of the force system on 
an aeroplane. Since L and M, by symmetry, vanish with S, the factor sin S is 
explicitly included in (1.102) and (1.103), in order that the cross wind force and moment 
coefficients,/^ and //, may have non-zero limits as de^O. We shall use the symbols 
4 (''/«),/l {v/a), / M {v/a) for f R {v/a, 0), Lt / L {v/a, S), and Lt/ M {v/a, S) respectively, 
«->-0 S -^-0 
and shall omit the explicit mention of the argument r/a when no confusion can arise 
by so doing. 
In view of the evidence mentioned in § 1.01, we may confidently expect that, for 
all values of S, all three coefficients will be nearly independent of v/a in the region 
0*1 < v/a <0-7, and shall, when required, assume their absolute independence of v/a 
p 
Fig. 1. 
(2) A component 
