642 Mr. J. H. Jeans on the 



remains constant. This gives the equation * 



f(8E + SF)+f>ES(-\ =0, 



in which 8 denotes excess above the mean value. Substituting 

 for E, F, and p, this gives 



|(E 1 + F I )-^=0: 



Po 



or, by equation (6), 



4(i+0.J- , -£=o. 



E p 

 Combining this with equation (11), we find 



-where 



! *ra, (12) 



o Po v ' 



r = 1+ 3(I+^) ••••••••• d3) 



= 1+— ? : \r tz^t- ■ ■ (14) 



3{l+/(E)/(l+^)} 



If we had supposed the gas to obey the ordinarily-assumed 

 equation for adiabatic motion, viz. 



we should have obtained 



§ 5. Comparing this with equation (12), we see that the 

 quantity T given by equation (13) is a generalized form of 

 the usual quantity y. When the variation in E is infinitely 

 slow (i. e. whenj9 = 0), the ratio between F and E is always 

 the equilibrium ratio, and F becomes identical with y. So 

 that we find, in this case, that equations (14) and (5) become 

 identical. When, on the other hand, the variation in E is 

 of infinite rapidity, the value of F is unaffected by variations 

 in E, and maintains a constant value corresponding to the 

 mean value of E. For this reason, the gas will behave like a 

 gas of which the molecules possess only the three trans- 

 lational degrees of freedom, i. e. like a gas for which y = lf. 



* Boltzmann, Vorlesungen iiber Gastheorie, i. p. 56. 



