Theoretical Evaluation of y. 639 



Experimentally the value of 7 is best found indirectly by 

 observation of the velocity of sound ; and this introduces a 

 further complication into the question. This complication 

 arises as follows. 



In arriving at Laplace's value for the velocity 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, as can easily be verified, amounts to 

 assuming that the mean internal energy of a molecule bears, 



at every instant, a constant ratio '^ — T\~^ *° ^ ne mearL 

 energy of translation. \/~ ) 



Ndw, after the lapse of infinite time, a gas tends to assume 

 a steady state in which the two mean energies may, perhaps, 

 be legitimately 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 transmission of sound, is therefore 

 seen to be one requiring investigation. 



General Theory, 



§ 2. Let us, for the sake of simplicity, consider a gas of 

 which the molecules possess only one kind of freedom in 

 addition to the freedom to move in space. Let the mean 

 energy of translation in space be denoted by E, and the mean 

 total energy by E + F, the energy F arising from the re- 

 maining kind of freedom, which may be either a rotation or 

 an internal vibration. 



The quantities E and F will be capable of variation owing- 

 to the transfer of energy which is effected by collisions between 

 the molecules of the gas. In order to obtain sufficiently 

 general results we find it necessary to imagine a second path 

 for the transfer of energy, namely a?ther-vibrations. Regarding 

 the molecule as an electromagnetic system, the vibrations or 

 rotation of the system will send out electromagnetic waves 

 into the aether, and collision of the two molecules will also 

 send out a system of irregular electromagnetic waves or 



* Lord Eayleigh, « Theory of Sound,' § 246, 



