the disturbances in the initial motion of a shell 313 



(3) Consequences of the barrel vibration theory. On the other 

 Jiand, if the main cause of the disturbances Hes in the vibration of 

 the barrel, which constrains the base of the shell to follow its move- 

 ments so long as the driving band is engaged in the rifling, we can 

 draw at once very different deductions. For a gun is not a figure 

 of revolution, and its vibrations may well be expected to take 

 ]>lace in or nearly in the same plane from round to round, and to 

 be in or nearly in the same phase each time when the dridng band 

 disengages*. This effect might be expected to be all the more 

 marked and give rise to larger disturbances when the gun has a 

 considerable curvature (technically droop). It appears in such 

 cases that the gun temporarily straightens more or less while the 

 shell is travelling down the bore. 



It follows then as a consequence of this theory that cf)^ should 

 be roughly constant from round to round fired under similar con- 

 ditions, or at least that the values of ^q should be highly correlated. 

 Again, in this case the twist of the rifling may play a fundamental 

 part in the phenomenon. For there will at least be stresses in the 

 barrel proportional to the twist of the rifling, and we cannot say 

 that the theory demands a value of Sq independent of the twist of 

 the rifling. The further discussion of this case is unfortunately 

 somewnat speculative at present and requires a little mathematical 

 analysis. It is postponed until we have described the experimental 

 evidence. 



(4) The experimental evidence. The evidence available is deduced 

 almost entirely from the experiments previously referred to. The 

 following table gives the mean values of Sq' and SoV^t which can 

 be deduced from that experiment, for groups fired under similar 

 conditions from guns of two different riflings. The other entries 

 are the reference numbers of the observations J, Q. itself, the muzzle 

 velocity and the twist of the rifling. The values of Sq for the various 

 rounds in any one group are reasonably consistent. 



It can be seen at once, by inspection of the columns for Sq and 

 Sq'/D., that So' is distinctly greater for the gun rifled 1 turn in 30 

 diameters — that is, with the sharper twist of rifling — than for the 

 gun rifled 1 in 40. On the other hand Sq'/D. appears to be practi- 

 cally the same (to the accuracy of the experiment) for both twists 

 of rifling in each group. The disturbing impulse, other things being 



* The case of a rifle is well-known, in which the direction of departure of the 

 bullet is very largely affected by barrel vibrations, which are themselves affected 

 by the presence or absence of the bayonet. 



t The notation is that of our previous paper loc. cit. 12 =AN/B, where A and B 

 are respectively the axial and transverse moments of inertia of the shell and N' is 

 the axial spin in radians per sec. The twist of the rifling is specified as 1 complete 

 turn in n diameters of the bore, il and N are inversely proportional to n. 



X Loc. cit. 



