1!)12] on the Pressure of a Blow. 281 



traversed by the wave will be at rest and in compression (as indicated 

 on a greatly exaggerated scale by the shoitening and thickening on the 

 diagram), while the remainder which has not yet been reached by the 

 wave, and accordingly as yet knows nothing of the impact, will still 

 be moving forward with the old velocity. Each section continues to 

 move on until the wave reaches it, when it is stopped with a jerk, 

 the sections thus pulling up successively until the whole rod is at 

 rest, which happens when the wave has travelled to the free end. 

 From the momentum of the rod, and the time taken to stop it, the 

 pressure can be calculated by the use of the principles already illus- 

 trated. Thus a rod 10 inches long is stopped, as we have seen, in 

 jTiooTr second, and if it be moving with the moderate velocity of 

 17 feet per second, the pressure required to pull it up in this time is 

 13 tons per square inch. This pressure is constant throughout the 

 impact, and it is obvious that here again the intensity of pressure is 

 dependent only upon the velocity and not on the weight of the rod. 

 For if with the same velocity the length is increased, the corresponding 

 increase of momentum to be destroyed is cancelled by the greater 

 time required for the transmission of the pressure wave, and if the 

 area is increased, the total pressure is merely increased in proportion, 

 the pressure per unit area remaining the same. For a hard elastic 

 body the pressure is proportional to the velocity, a principle which is 

 probably generally applicable in the initial stage of all impacts. 



At the instant of greatest compression, when the rod is reduced 

 to rest, it is like a compressed spring, and there being no pressure 

 acting at its free end to keep it compressed, it proceeds to expand 

 again. Starting at the free end a wave of expansion travels down 

 the rod, the several portions being successively jerked into motion 

 with approximately the original velocity. The whole process of 

 restoring motion to the rod is completed when this wave reaches the 

 impinging end, when the rod rebounds as a whole with the original 

 velocity. The whole time of contact is then that taken by a wave of 

 sound to travel twice the length of the rod. Here, again, by electrical 

 measurement of the time of contact, it is possible to check the theory. 

 It is found that the actual time is longer than that predicted. This 

 is due to the fact that one cannot in practice make the rods hit 

 absolutely true all over the ends ; they strike at one point tirst, and 

 the metal near that point has to be flattened out before the ends 

 come into contact all over and initiate the simple plane pressure wave 

 of the theory. The complete analysis of the discrepancies between 

 theory and experiment so caused was long a puzzle to physicists 

 interested in these matters. It was linally effected by Mr. J. E. 

 Sears, who determined mathematically the corrections necessary on 

 this account, and submitted his tlieory to experimental test with 

 entirely satisfactory results.* 



Another simple instance of the propagation of waves along rods 



Camb. Phil. Soc. Trans, vol. xxi. p. 49. 



