444 MR. B. HOPKINSON ON MEASURING THE PRESSURE PRODUCED IN THE 



The differences between the calculated and observed figures in this table are 

 probably rather outside experimental errors. Especially is this the case as regards 

 the 5-inch and 6-inch pieces. The impact seems to last appreciably longer than it 

 ought. 



The Effect of the Rigidity of the Bullet. 



In the simple theory it is assumed that the bullet is absolutely fluid. In fact, it 

 possesses a certain rigidity, partly because of the nickel casing and partly because of 

 the viscosity of the lead the effects of which may be quite appreciable at such high 

 speeds of deformation. The general effect of rigidity may be represented by saying 

 that any section of the bullet requires to be subjected to an end-pressure P before it 

 begins to deform at all, and this pressure must act across the section CC (fig. 4) where 

 deformation is just beginning and where, if the bullet were really fluid, there would be 

 no pressure. To a first approximation, P will be proportional to the area of the cross- 

 section of the bullet which is undergoing deformation, that is to X the mass per unit 

 length in the plane CC. The pressure P is added to that due to the destruction ot 

 momentum, making a total pressure P + Xv 2 where X is the mass per foot of the section 

 of the bullet in the plane CC, v the velocity of that section. Further, the part of the 

 bullet behind CC is being continually retarded by the pressure P, with the result that 

 the hinder parts do not come up with unimpaired velocity v a , as they would if the 

 bullet were quite fluid, but with a diminishing velocity. 



The general effect of this is obvious. In the early stages of the impact there has 

 not been time for much retardation, and the pressure will be increased above the 

 theoretical value 1 by nearly the amount P. As the hinder parts come up, however, 

 with less and less velocity, the fluid pressure term diminishes until the pressure falls 

 below the theoretical value in spite of the rigidity term P. Applying this correction 

 to a pressure curve such as that in fig. 7 in which the maximum pressure occurs 

 somewhat late in the impact, it will be seen that the general effect will be to reduce 

 that maximum, and also to make it flatter. Furthermore, since the tail of the bullet 

 takes longer to reach the end of the rod, the impact will be prolonged beyond the 

 theoretical time. 



It is easy to get a rough idea of the magnitude of these effects. Assume that the 

 bullet is cylindrical and of mass X per unit length and that the deforming pressure is 

 constant. Let x be the length of the bullet behind the plane CC (fig. 4). This 

 portion is moving as a rigid body with acceleration x and its equation of motion is 



\xx = P, 

 which integrates in the form 



p 



?x 2 = log x + const. 



X 



If I be the length of the bullet and 1 its velocity on striking, and if we neglect the 



