THE AERODYNAMICS OF A SPINNING SHELL. 
323 
§ 2.2. Determination of the Dynamical Constants. 
All the shells used in these experiments were weighed before firing, and their 
overall lengths were measured. The variations from shell to shell were small, and 
the mean values given in the tables may be assumed to be correct for all purposes. 
No appreciable change in these quantities is likely to occur on firing. 
The moments of inertia were determined, before firing, for a selection of about 
25 per cent, of the shells of each type. The probable error of any determination was 
about 1 part in 2000. The mean values for the different types of shell are given in 
the table. The extreme variation of any transverse moment of inertia from the mean 
was 1 • 8 per cent., and of the axial moment of inertia was 0-8 per cent. The errors in 
assuming that the mean value of the sample is the correct value for each round may 
therefore be appreciable at times, but should not seriously affect the final mean 
results. The general accuracy of the experiments was, contrary to expectation, 
sufficient to warrant the refinement of determining and using the individual values 
for each shell. 
The centres of gravity were also determined, before firing, for the same selection of 
shells, and the mean value of the distance of the centre of gravity from the base is 
given, in the same table, for each type. The determination was made with a 
probable error of 0*003 inches. The values were fairly constant for the shells of any 
one type, the extreme variation from the mean being 0*022 inches. 
It is by no means certain a priori that the values of A and B and the position of 
the centre of gravity may not be changed appreciably in some of the shells by the 
stresses set up when the gun is fired. No change is at all likely in the empty shells 
of types I. and IV., or in the bodies of the other shells; they may be confidently 
relied upon not to be stressed beyond their elastic limit; but the lead and wood filling 
in the shells of types II. and III. is decidedly suspect. To test this point, two shells 
of each of the types II. and III., after the determination of their dynamical constants, 
were fired* over water for recovery, and their constants were then re-determined. In 
the case of the shells of type III., with a filling of lead at the back and wood in front, 
there was no appreciable change. In the case of the shells of type II. with lead in 
front and wood behind, the wood block, as might have been expected, was crushed, 
and the lead had moved back about three inches in the case of the high velocity and 
one inch in the case of the low. The axial moments of inertia, A, were unaltered, but 
the transverse moments of inertia B and the positions of the centre of gravity were 
of course seriously affected. It was found, however, *that the observed changes in 
both could be satisfactorily accounted for by the observed movement of the lead 
block, of weight 1 • 9 lb. When the centre of gravity of the shell of type II. is 
4*727 inches from the base, so that it coincides with the centre of gravity of a shell of 
* One of each type at a muzzle velocity of 1950 f.s. and one at 1530 f.s. 
