368 MESSRS. R. H. FOWLER, E. G. GALLOP, G. N. H. LOCK AND H. W. RICHMOND: 
could be made with the data of the present trial, but we cannot undertake this in 
this paper. 
In Part III., we have arrived at two separate solutions of the equations of motion 
of a shell treated as a rigid body, which together cover practically all types of motion 
which are likely to occur in practical shooting. (We ignore here the case of an 
unstable shell, since it is of no practical use.) A general solution of the equations of 
motion of tj^pe a has been developed, which applies with sufficient accuracy to the 
most general type of motion of a shell whose angle of yaw $ and inclination of the 
tangents of true and plane trajectories do not exceed (say) 0 • 1 radian. The solution 
of the equations of type /3 can be applied with sufficient accuracy to the steady (non- 
oscillatory) motion of a shell at any angle of yaw. In practice the large angles of 
yaw (> O’l radian) only occur in the neighbourhood of or beyond the vertex of a 
high angle trajectory, and by this stage the initial angular oscillations of the shell 
have been completely damped out so that the condition for the applicability of the 
solution of type fB is satisfied. Thus the solutions we have obtained, though 
theoretically inadequate, are probably sufficient to cover all cases likely to occur in 
practice. 
In order to make use of these solutions to determine the complete motion of 
a shell, information is necessary as to the complete force system acting on the 
shell. Our information, as we have seen, is fairly complete for angles of yaw up 
to 10 degrees, and can be applied to calculate the true trajectory of any shell for 
which the angle of yaw does not exceed this value, if the loss of spin and increase of 
drag with yaw can be ignored. 
Larger angles of yaw (exceeding 10 degrees) occur in general only as a consequence 
of the low velocity of the shell near the vertex of a high angle trajectory. The force 
system is then mainly covered by wind channel observations. The information as to 
the force system obtained by our methods is thus adequate for the calculation of a 
complete set of twisted trajectories at all elevations, at any rate for a 3-inch shell. 
§ 5.1. Problems for Further Discussion. 
5.11. Unstable Rounds. —We have already mentioned that further information 
about and f h , at yaws greater than 10 degrees, could be obtained by analysis of the 
unstable rounds. This requires the application of the exact top equation with a 
variable value of p. (§ 3.7) to the discussion. No means' of introducing damping effects 
into these equations has yet been devised. It should, however, be possible to obtain 
fairly reliable information as to the variation of f M and jf L with yaw between the angles 
of 10 degrees and 30 degrees by the analysis of the unstable rounds fired in this trial 
(Table IV.). 
5.12. Initial Conditions. —By extrapolating the (bcurve and 0 -curve backwards 
to the gun muzzle (t = 0 ) information may be obtained as to the way in which the 
