312 MESSES. R. H. FOWLER, E. G. GALLOP, C. N. H. LOCK AND H. W. RICHMOND: 
angular motion for both shell and top consists of a small oscillation, composed ot 
periodic terms with two distinct periods. The values of these two periods are 
uniquely determined by the values of s and AN/B or Q ; conversely s and Q, and 
hence /u and f yi are uniquely determined by the values of the periods. The main 
object of the jump card experiment, described in this paper, is to determine the two 
periods of the initial angular oscillations of a shell, fired horizontally from a gun. 
As H depends only on the spin N (known in terms of the muzzle velocity) and the 
moments of inertia, there is in general an independent check on the observation. # 
By firing the shell at a series of different muzzle velocities, values of f M are 
determined for different values of the variable v/a, resulting in the curves of § 1.21. 
1.32. The success, of the experiments depends entirely on the occurrence of 
accidental disturbances at the muzzle, in order to produce oscillations of sufficient 
amplitude to be measurable. The methods of observation used were capable of 
giving accurate results, provided that the maximum yaw exceeded 1 degree. In the 
actual trial, no round was fired which developed a maximum yaw of less than 
2 degrees, and it is probable that with almost any type of shell the initial disturbance 
would be sufficient for observations of this nature to be made. It may be noticed 
that, for a given initial disturbance, the amplitude of the oscillations is greater, the 
smaller the value of s, until, as s approaches and becomes smaller than the value unity, 
the amplitude of the oscillations increases very rapidly. For this reason it was at 
first considered preferable to deal with a shell and gun for which s was only just 
greater than unity, but the experiments described in this paper indicate that a value 
of 5 in the neighbourhood of 1 • 5 will give the best general results. 
It is to be expected a priori , and is confirmed by the experiment, that the initial 
yaw of a shell, on leaving the muzzle of a gun, is very small, and that the angular 
oscillations are due mainly to an initial angular velocity about a transverse axis. 
The shell is completely unstable under the very large pressures of the powder gases on 
its base, so that as soon as it is released from the barrel it is disturbed from its 
position of unstable equilibrium by an amount, and in a direction, which depend 
largely on accidental circumstances, t The pressure of the powder gases probably 
continue to influence the motion over a short interval after the shell has left the gun, 
but the whole effect on the shell must approximate to that of an impulsive couple 
about a transverse axis. 
The angular motion of the shell, for some distance from the muzzle, approximates, 
therefore, to the type of motion of a spinning top known as rosette motion, in which 
the axis of the top passes periodically through the vertical. 
* This check is especially important in the case of shells of type II., as the shift of the lead 
block on firing alters the values of the dynamical constants as determined by laboratory experiments 
(§ 2 . 2 ). 
t \_Note added July 31, 1920. In view of further analysis of the initial circumstances of shells in this 
trial, this account of the matter is probably incomplete.] 
