206 Theory of a Non-Conservative Gas [CH. ix 



so that the ratio to the total number of collisions, of the number of collisions 

 for which V is greater than F , is 



rV=ao 



.. ...(497) 



F=F O 



= I e~ x xdx 



[>-* H 4- v\\ 



L 6 \ x + x !\. 



This quantity vanishes with extreme rapidity as F increases, so that the 

 number of collisions for which F is great forms an extremely small fraction of 

 the whole. If, as in 242, we take (7 = 5 x 10 4 we must put 



3 



m = w* ~ 



Still using the figures of the last two sections, it appears that to obtain a collision 

 of duration comparable with that of a vibration of light (p = 2 x 10 15 ), the 

 value of F must be comparable with 2 x 10 7 cm. per sec. Giving this value 

 to F and putting hm = 6 x 10~ 10 the value of expression (498) becomes 



120,001 x 6-120,000. 



Even if we give to F a value ten times as small as this, the value of 

 expression (498) is 



1201 xe- 12(X > (499), 



which is equal to about 10~ B18 , a quantity which is quite negligible for our 

 present purpose. 



245. To recapitulate, we have seen that there are two cases of transfer 

 of energy to be considered, the first arising from the common collisions in 

 which the duration of the collision is great in comparison with the periods of 

 vibration of the molecule, and the second from the rare collisions in which 

 the duration of the collision is comparable only with that of a vibration. We 

 have seen that in the former case the transfer of energy is infinitesimal 

 on account of the high frequency of the vibrations, and in the latter case 

 the transfer is infinitesimal on account of the extreme rarity of these 

 collisions. 



Here, then, we have a sufficient explanation of the slow transfer, and 

 consequently slow dissipation of energy, which is necessary in order that 

 a normal state may exist. In this respect the analogy with the two 

 mechanical illustrations of the preceding chapter is complete. Our hypo- 

 thetical view of the structure of the atom having so far led to a satis- 

 factory result, we shall proceed in the next chapter to investigate the 

 calorimetry of a gas upon these hypotheses. 



