35 MAXWELL'S LAW 73 



from without, but is forced by its own pressure to rush 

 along an opened pipe. In this case the amount of energy 

 of the mass of gas remains unaltered. If, then, the gas 

 were under the pressure- 



when at rest, and its kinetic energy per unit volume were 

 therefore 



*o = */><?' 



before the flow began, the whole energy of molecular motion 

 and flow in the exit pipe, viz. 



K = 



must be the same as before. We have, therefore, 

 G 2 = G 2 - a\ 



or the molecular speed G of the flowing gas is less than 

 the molecular speed G of the gas at rest. The cross- 

 pressure 



P = i/><? 2 



of the gas when flowing is, therefore, less than the pressure 

 when the gas was at rest. This lowering of the pressure 

 by the flow depends, as the formulae show, on cooling being 

 produced. 



Since these formulae contain the velocity only in its 

 square, they are independent of the direction of the motion, 

 and hold, therefore, as well for to-and-fro oscillations as for 

 the propagation of the longitudinal waves of sound. On 

 this depend the apparent attractions and repulsions in air 

 when sounding and in the ribbed dust-figures of Kundt. 1 



36. Propagation of Sound 



When we develop the theory of sound according to the 

 kinetic hypothesis we have also to consider two sorts of 

 motion which exist without disturbing each other. In 

 addition to the molecular motion which is present even in a 

 gas at rest there are the to-and-fro motions which constitute 



1 See W. Konig, Wied. Ann. xlii. 1891, p. 353 ; Zeitschr. f. phys. u. chem. 

 Unterr. 8. Jahrg. 1895, p. 191. 



