THE AERODYNAMICS OF A SPINNING SHELL. 
357 
The figures in Table VII. were obtained from the sufficiently stable rounds fired 
from either gun. In the one comparative pair of groups available the results for the 
two different stability factors and values of Q were in agreement. 
Fig. 14c. Path of nose of shell. Round IV.15. 
Path described, relative to the centre of gravity, by a point on the axis of the shell in front of the 
centre of gravity, shown on an enlarged scale. 
The total time taken from 0 to K is O'5502 second. On the scale used, 2 cm. distance from 0 
represents 1° yaw (very nearly), and corresponds to a linear displacement of O' 143 inch for the nose 
of the shell from the line of motion of the centre of gravity. 
Note that the first loop encloses 0, corresponding to the “ stepped up ” motion in <f>. Subsequent 
loops do not, as the motion in <£ has changed to the “ stepped down ” motion. (See fig. 12.) 
§ 4.2. Determination of the Motion of the Shell in Space. 
We now proceed to make use of the results of the experiments to determine the 
true path of the centre of gravity of a shell projected in a given manner. The 
solution of the equations of type a is sufficient for this purpose so long as the yaw 
does not exceed 0*1 radian ; the values of y* L , f u , f Ry &c., which we have obtained, 
are sufficient to determine the motion completely in this case. Assuming that the 
maximum yaw due to the initial disturbances is less than 0 • 1 radian in the first 
period, it will remain so throughout the trajectory; the yaw arising from the 
particular integral will not exceed 0 • 1 radian until the velocity has fallen considerably 
