278 Scientific Intelligence. 



end-piece when it flies off from the longer steel rod. With this 

 assemblage of apparatus it is easy to determine the momenta of 

 the steel rod and of its extension after an impulsive force has 

 been applied to the end of the rod (the free end) which is more 

 remote from the auxiliary ballistic pendulum. 



The following outline of the elementary theory of the action of 

 the steel rods may not be superfluous. When a rifle bullet is fired 

 against the end of a steel rod, or when some gun-cotton is 

 detonated near this end, a wave of pressure is propagated along 

 the rod with the speed of sound in steel. This compressional 

 wave travels practically unchanged across the plane of contact of 

 the rod and its end-piece, provided the pieces of metal are in 

 good, firm contact. At the free end of the shorter rod the dis- 

 turbance is reflected as a wave of tension, and hence the pressure 

 at any cross-section is obtained by adding the effects of the 

 pressure and tension waves. At the interface of the rods the 

 pressure persists until the head of the tension wave arrives there. 

 If the tail of the pressure wave has then passed the joint the end- 

 piece flies off, having trapped within it the whole of the momen- 

 tum of the blow, and the longer rod is left completely at rest. 

 The length of end-piece which is just sufficient to entirely stop 

 the main rod is equal to half the length of the compressional 

 wave, and the duration of the blow is twice the time taken by 

 this wave to travel the length of the steel extension. Further, it 

 can be proved that the momentum trapped in very short end- 

 pieces w T ill be equal to the maximum pressure multiplied b}>" twice 

 the time taken by the wave in traversing the end-piece. Thus 

 by experimenting with different lengths of end-pieces and deter- 

 mining the momentum with which each flies off the rod as a 

 result of the blow, it is possible to measure both the duration of 

 the blow and the maximum pressure developed by it. 



The method was first tested by firing lead projectiles against 

 the free end of the steel-rod pendulum. With speeds of 700, 

 1240, and 2000 feet per second the observed " maximum pres- 

 sures" were found to be 5320, 16700, and 42600 "lb." respec- 

 tively. The corresponding calculated values are given as 5450, 

 15700, and 43500 "lb." The computations are based on the 

 assumption that a lead bullet behaves on impact as a fluid. It 

 then follows that the time required to completely stop the bullet, 

 which is the duration of the blow, is equal to the time taken by 

 the projectile to travel its own length, and also that the maximum 

 pressure is equal to the mass per unit length in the section of 

 greatest area multiplied by the square of the speed. In the case 

 of the highest speed used the observed duration of the blow is 

 about 6 per cent, greater than the time taken by the missile to 

 travel its own length. This discrepancy can be accounted for on 

 the ground that the conditions postulated in the simple theory 

 are not entirely fulfilled by the experimental tests. For example, 

 the lead does not act as a perfect fluid, and the pressure exerted 

 by the bullet is not uniformly distributed over the end. Experi- 



