1912] on the Pressure of a Blow. 279 



through the galvanometer and produces a proportionate deflection 

 iu it. It has been found that the time of contact measured in this 

 way for steel balls is exactly that predicted by theory, and it may 

 be inferred that the theory is correct in all its details, and that the 

 pressure calculated by its aid corresponds with the facts. This 

 method was first used by Pouillet in 1845, and has recently been 

 brought to great perfection by Mr. J. B. Sears,* who showed, among 

 other things, that the relation between pressure and deformation of 

 steel is almost exactly the same when the pressure is applied for an 

 excessively short time, as in the case of impact, as it is when applied 

 steadily, as in a testing machine. The assumption that this is the 

 case lies of course at the root of the calculations, and its verification 

 was therefore a matter of considerable importance. 



When one billiard ball strikes another the effect of the blow is 

 practically instantaneously transmitted to every portion of the col- 

 liding balls, or, to speak more precisely, the time taken to transmit 

 the pressure is short compared with the total time of contact. 

 Except for the minute relative displacement near the point of 

 contact the balls move as a whole, every part having the same 

 velocity at each instance of time and coming to rest at the same 

 moment. In many cases of impact, however, and in those possessing 

 the most interest from a practical point of view, this is by no means 

 the case. We may consider, for instance, the impact of an elongated 

 lead rifle bullet against a hard steel plate. Under the enormous 

 pressures developed lead flows almost like water, and in the absence 

 of lateral support it is as little capable of transmitting those pressures. 

 Thus, when the nose of the bullet strikes, the metal thus brought 

 into contact with the plate immediately flows out laterally, its forward 

 motion being destroyed, but the hind parts of the bullet know 

 nothing of what has happened to the nose because the pressure 

 cannot be transmitted to them, and they continue to travel on with 

 the original velocity until they in their turn come up to the plate 

 and have their momentum destroyed. The process of stopping the 

 bullet is complete when its tail reaches the plate, and the time 

 required is simply that taken by the bullet to travel its own length. 

 Thus a Lee-Metford bullet is 1^ inch in length, or, say, yV of a 

 foot, and if moving at 1800 feet per second, which is about the 

 velocity given with a rifle, it would be stopped in y^^oo- of a second. 

 The bullet weighs approximately "03 lb., and possesses with this 

 velocity about 1-7 lb. second units of momentum. The force 

 required to destroy this in ysooo o^ ^ second is 18,000 multiplied by 

 1-7 lb., or, say, 15 tons. This acts over the sectional area of the 

 bullet, which is yV of a square inch, giving a pressure of about 210 

 tons per square inch. This is the average pressure throughout the 

 impact, but the pressure is probably nearly constant. It is to be 

 noted that the pressure per square inch depends only upon the 



* Camb. Phil. Soc. Proc ;. vol. xiv. p. 257. 



