Manchester Memoirs, Vol. xlvi. (1901), No. 3. 3 



on opening the boiler stop-valve, the plug of water would 

 be shot along the pipe to the engine, and would shatter 

 the end of the pipe. 



To understand the action of a water-hammer, we have 

 to study the question of an elastic blow ; this has been 

 been done by many mathematicians, notably M. de Saint- 

 Venant, whose view that the velocities of sound-waves and 

 pressure-waves are the same have been generally accepted, 

 but he does not help one over the difficulty pointed out by 

 Dr. A. Ritter^ that waves are undulatory, while a pressure- 

 wave implies at least the possibility of absolute dis- 

 continuity of motion, i.e., that a particle of matter may 

 have its velocity changed with absolute suddenness by a 

 definite pressure According to Saint-Venant", the pres- 

 sure in a bar travels at a uniform velocity ; and, as far as the 

 pressure extends, the bar will shorten ; hence he finds a 

 velocity for the propagation of the pressure which agrees 

 with the velocity of sound, but he does not deal with the 

 shape of the front (as it were) of the pressure-wave, nor 

 does he say whether the pressure grows suddenly or only 

 fairly suddenly, and it might well be that a gradual 

 pressure might travel as fast as sound, while a very sudden 

 pressure might have another velocity. In 1871, Dr. John 

 Hopkinson read two papers before the Society on the 

 conditions under which wires can be ruptured by a falling 

 weight, while Dr. A. Ritter's paper deals with adiabatic 

 expansion ; in both papers the leading idea is the same, 

 viz., that the pressure can be estimated by a comparison 

 of the velocity of the object as a whole with the velocity 

 of the pressure-wave in the object. 



Dr. Hopkinson considers that pressure-waves travel 

 v/ith the velocity of sound in the wire, while Dr. Ritter 



^ Wiedemann's Aniialeit, Bd. 37 (1889), p. 634. 

 " Comptes Rendtis, Tome 64 (1867), p. 1192. 



