THE AERODYNAMICS OF A SPINNING SHELL. 
353 
Since y and q 2 are both small over the range of the experiments, the formula 
becomes 
(4.124) 
h —k + 2y = 
-1 
(t'J — tl) 
a. 
The three equations (4.121), (4.122), (4.124) for k, h, and 2y are in theory 
sufficient to determine their values completely. It may be noted again that 2y is 
probably negligible and Ji — k + 2y is always positive, so that q 2 continually increases 
with the time, and AAa continually decreases. The constant j is always very 
small, but may be positive or negative. If it is positive, (3 1 is initially positive, 
giving the larger average rate of increase of <p, which changes to the smaller rate of 
increase when /3 1 becomes negative. If j is negative, <j> increases at the slower rate 
from the beginning. Exactly the opposite results would be obtained if h—K + 2y 
were negative. The values of Ji + k and Ji—k + 2y, obtained in this manner, are 
given in Table VII. 
In order to illustrate the actual path traced out by the axis of the shell, it is 
necessary to plot 3 and <p as polar co-ordinates. This is done for three rounds in 
fig. 14. The resulting curves are roughly equivalent to the path of a point on the 
axis of the shell relative to the centre of gravity. They illustrate the decrease of a u 
the algebraic decrease of /3 U and the tendency to change from quick to slow precession 
and to settle down to a steady slow precession. 
The process described above was evolved gradually during the work of analysing 
the results, so that a number of observations were analysed before it was fully 
developed. It is probable that if the calculations were to be repeated ab initio a 
number of periods and minima of 3 would be slightly altered, but it is unlikely that 
any serious systematic errors remain. 
4.13. Details of Tables V. to VII. —The information contained in the General 
Table of Results, Table V., has been compiled by analysis of the original standard 
diagrams. As first constructed these were drawn with the time t as abscissa and not 
Qt as in fig. 12. It contains practically all the information of importance provided 
by the more stable shells. In the unstable cases, a number of which occurred during the 
trial (see for example fig. 12), a detailed study of the whole yaw curve is required 
which will not be undertaken in this paper. 
Column 5 gives the values of the periods of the yaw curve in units of ywuo second. 
The periods are read off from positions of the minima and sometimes of the maxima. 
They are entered to the nearest 2 ( ) 00 second. They are in doubt by more than this 
quantity in many cases, but mainly in the case of the longer periods, in which small 
errors are of less importance. 
Column 6 gives the values of the maxima of the yaw in degrees and decimals to one 
place of decimals. These values are read straight from the curves and represent 
roughly the accuracy to which the maxima are in most cases determined by the 
observations. 
3 c 2 
