DETONATION OF HIGH EXPLOSIVES OR BY THE IMPACT OF BULLETS. 445 



small distance between the plane CC and the end of the rod, the constant of integra- 



tion is 



p 

 bt'> + - 



\ 



and we have 



x* 2P, / 

 1 -- , = -log-. 

 t' u 8 At'* " ./ 



From this x can be plotted in terms of x, and thence in terms of t. 'IV total pressure 

 P + Xcc 3 is then plotted in terms of the time. 



As an example, take X = 0'35 Ibs. per foot, I = 1'05 inches which correspond to a 

 bullet having the same mean density diameter and total mass as those used in the 

 experiments. The pressure required to stop such a bullet at 2000 feet per second, if 

 fluid, would be constant and equal to 43,500 Ibs. If P be taken as ^ of this, or 

 2170 Ibs., and the curve plotted as described, it will be found that when x = 0'3/ the 

 hydrodynamical pressure Xc a has dropped 12 per cent, making, after allowing the 

 addition of 5 per cent, for the rigidity, a nett drop of 7 per cent. Furthermore, 

 the momentum still left after a fluid bullet would have been completely set up is about 

 4 per cent, of the whole. 



If corrections of this amount were applied to the calculated figures in the last section. 

 the effect would be to make the observed maximum pressure about 4 per cent, too 

 high, while the observed time of impact would" be still slightly too long. It was found 

 that to crush the cylindrical part of the service bullet in a testing machine required 

 an end pressure of about 1800 Ibs., but the nickel casing failed by buckling, where!* 

 in the impact it apparently bursts and is torn into strips along the length of the 

 bullet. The pressure required to deform the bullet in the latter case, after rupture is 

 once started, is probably less than 2000 Ibs. Thus, while the difference between the 

 observed and calculated times of impact may undoubtedly be referred in part to 

 rigidity, it is unlikely that the whole can be accounted for in this way. 



Discussion of Errors Inherent in the Method of Experiment. 



In calculating the pressure from the momentum in the piece which is tin-own off 

 the end of the rod it is assumed that the pressure wave transmitted along the rod 

 represents exactly the sequence of pressures applied at the end, that it travels along 

 the rod and through the joint without change of type, and that it is perfectly 

 reflected at the other end. These assumptions are correct if the wave is long 

 compared with the diameter of the rod, and if the pressure is uniformly distributed 

 over the end, but are subject to certain qualifications in so far as these conditions are 



not fulfilled. 



(a) Effect of Length of the Rod The mathematical theory of the longitudinal 

 oscillations of a cylinder shows that a pressure wave of simple harmonic type is 

 propagated without change, but the velocity of propagation depends on the wave- 

 length. Because of the kinetic energy involved in the radial displacements, which is 



