ON THE KINETIC THEORY OF GASES. 211 



whose molecules are stable and have n degrees of freedom, 

 the ratio of the specific heat at constant pressure to that at 



n + 2 n 4- 2 + e 



constant volume is 7 = , or , where e is 



a small quantity necessarily positive, that is 7 is, or is 



rather less than, . 



11 



Now it would seem that the molecules (or atoms) of 



any gas may have, in addition to three degrees of freedom 



of motion in space, perhaps as many more as the spectrum 



11+2 

 of the gas contains lines. And if that be the case, 



can on no probable hypothesis be made to represent the 

 observed values of 7. 



16. One possible solution of this difficulty is, I think, 

 the following : in deducing the value of 7 from the 

 law £~ h (x + T) we have assumed that our gas consists only 

 of stable molecules, each having the given number of 

 degrees of freedom. Each molecule is then a system 

 which, when left to itself, is in stationary motion. On 

 that hypothesis the virial equation may be put in the 



»-3 



form — fiv = - T + 

 2 r n 



T -* ESRr 



the terms within 



u 



the bracket denoting respectively the energy of relative 

 motion of the constituent parts of the molecules, and the 

 mutual forces acting between them, R being now positive 

 when attractive. If the molecule be stable, the two terms 

 within the bracket cancel each other, and we have left 



1 -> 



pv = - T, which leads us into difficulties in the form 

 2 r n ' 



n + 2 n - 3 



7= — . But if the molecule be unstable \ E2Rr< T. 



' 11 11 



And therefore - ■pv > - T. We thus get rid of the particu- 



lar difficulty, only perhaps to introduce others which may 

 prove as formidable. On this view the gas will consist not 

 of stable molecules only, but of molecules with a considerable 

 admixture of dissociated atoms. 



1 7. The following has also been suggested as a mode of 



15 



