6±6 Mr. J. H. Jeans on the 



The result seems, however, to suggest that part of the damp- 

 ing of sound in air may be assignable to causes other than 

 pure viscosity. 



The value of a is roughly 



so that ^(E ) might vary largely from our numerical estimate 

 of equation (20) before any appreciable difference could be 

 expected between the true and apparent values of 7. 



Subsidiary Degrees of Freedom. 



§ 8. We have supposed, in dealing with rotatory energy 

 in the last section, that the energy of rotation is, in the steady 

 state, equal to the value which Boltzm ami's theorem would 

 assign to it. In other words, we have assumed that in equa- 

 tion (1) the term $(E, F) is so large as to outweigh the 

 term i|r(E, F). 



In addition to degrees of freedom of this kind, there may 

 be other degrees of freedom, for which <£(E, F) will be com- 

 parable with ^(E, F), the transfer of energy being deter- 

 mined as much by the aether-reactions as by collisions. It is 

 convenient to refer to these two kinds of degrees of freedom 

 as " principal" and ''subsidiary " respectively. 



Let us suppose that a molecule possesses, in addition to its 

 freedom to move in space, n " principal " degrees of freedom 

 and m " subsidiary " degrees of freedom, the energy of each 

 of the latter being supposed to have the same mean value F 

 [e. g., for a single internal vibration, m = 2 ; for a single 

 spectral line which can be separated into s lines, we pro- 

 bably have m = 2s]. 



If we ignore the u lag " in the energy of the principal 

 degrees of freedom, we may write (cf. equation 14) 



r=i + 



3 + n4-3m/'(E)frl-h-^)' " " 



(21) 



and the value of 7 may be deduced by putting p=6. 



We must now try to evaluate /(E) and %(E). 



The transfer of energy due to collisions will be jointly pro- 

 portional to the number of collisions, and to the mean transfer 

 at each collision. Let us therefore take, in equation 1, 



<f(E, F) = -x VE(F-JE), . . . (22) 



