THE AERODYNAMICS OF A SPINNING SHELL. 
315 
that OA is level with OP, and that S is given by (1.342), lead to a determination of the 
drift which is sufficiently accurate for all trajectories of elevation less than 30 degrees. 
The drift is produced by the cross-wind force resulting from the above value of 
the yaw. 
In the neighbourhood of the vertex of a trajectory of high elevation, both the 
velocity and the couple M become very small, so that S becomes large. A calculation 
has been made, by a step-by-step process, of the angular motion and drift of a shell 
fired at an elevation of 70 degrees. The yaw, soon after the vertex, reaches the 
value 60 degrees, while the axis lags behind the tangent to the path by more than 
45 degrees. 
1.35. The effect of gravity as described in the last section completes the list of 
factors which have an appreciable effect on the motion, and it remains to consider 
the way in which they combine. It will be shown in § 3.2 that the motion of the 
axis of a stable shell is determined, to a good approximation, when the yaw is not 
too large, by a linear differential equation of the second order. The effect of gravity 
is to produce the type of motion described in § 1.34, given the proper initial conditions 
in which the yaw and its rate of increase are both very small. The complete motion 
under arbitrary initial conditions may be obtained by superposing the appropriate 
type of initial oscillatory motion, which is unaffected by gravity. The superposed 
oscillations will ultimately be damped out, leaving the motion of the last section 
only. The motion of the centre of gravity will be appreciably affected by alteration 
of the initial conditions only in so far as they produce a certain small sideways 
displacement and velocity (§ 4.2), and increase the drag to an extent which is not yet 
known. 
More detailed results are reserved for Part IV., following the discussion of the 
mathematical theory. Actual examples of the observed motion of the shell’s axis can 
be studied in fig. 14. 
Part II.— Details of the Experimental Arrangements and Material. 
§2.0. General Arrangements. 
We propose, in this part, to explain the details of the experiments in so far 
as is necessary to enable the reader to understand the method used, and to 
form an estimate of the accuracy obtained, or capable of being obtained, in this 
manner. 
The experiments were carried out as the weather served in January and February, 
1919, four different types of 3-inch shells being fired, at various velocities, from each 
of two differently rifled guns. The constants of the shells used are given in Table IIP, 
