228 Theory of a Non-Conservative Gas [CH. x 



Further experimental data will be found in Meyer's Kinetic Theory of 

 Gases. 



276. There are two further complications which ought to be mentioned, 

 although it seems probable that the magnitude of their effect must be 

 considered small in comparison with those just discussed. 



We have assumed that it is legitimate to neglect the cohesion-factor. 

 This is certainly not negligible as regards its influence on the boundary- 

 pressure and ought therefore to be taken into account in the calculation 

 of C p . On the other hand, it seems improbable that it could affect the value 

 of 7 to an extent comparable with the difference between the observed values 

 of 7 and those given by assigning integral values to n. 



277. In discussing the values obtained experimentally for 7, it ought 

 to be remembered that most of these values have been obtained indirectly 

 by observation of the velocity of propagation of sound through the gas in 

 question. Now in arriving at Laplace's value for the velocity of propagation 

 of sound in a gas *, it is assumed that the ratio of the two specific heats of 

 a gas has a definite value, 7, which depends solely upon the nature of the 

 gas. This of course amounts to assuming the hypothesis of 200, namely 

 that the mean internal energy of a molecule bears, at every instant, a 

 constant ratio to the mean energy of translation. 



After the lapse of infinite time, a gas tends to assume a steady state 

 in which the two mean energies may be, as we have seen, supposed to bear 

 to one another this constant ratio ; but the case is different with a gas in 

 which the value of one of the quantities in question is continually caused 

 to vary owing to the passage of a wave of sound. For the mechanism 

 by which the balance of energy is adjusted cannot be supposed to work with 

 infinite rapidity, so that the ratio in question will never have the actual value 

 which must be assigned to it in order to arrive at the Laplacean velocity of 

 sound. The question as to whether or not this want of steadiness in the 

 ratio of the two energies is sufficient to influence appreciably the trans- 

 mission of sound, is therefore seen to be one requiring investigation. 



A full investigation of this question is reserved for a later chapter. For 

 the present, we may notice that since there are about 3 x 10 9 collisions per 

 molecule per second in normal air, and 3 x 10 2 vibrations per second for 

 sound of average pitch, therefore each molecule must undergo about 10 7 

 collisions for each wave of sound. It therefore appears that there will be 

 ample opportunity for an approximate adjustment of the ratio of different 

 kinds of energy. We should accordingly expect the value of 7 to have very 

 approximately the same values, whether calculated from the velocity of 

 sound or. by direct methods. 



* Lord Rayleigh, Theory of Sound, 246. 



