648 Mr. J. H. Jeans on the 



found for it npon the assumption of 6 = 0. Also as E in- 

 creases, the influence of the " lag " in the energy of subsidiary 

 vibrations will increase, being nil when E = 0, and infinite 

 when E = go . 



Summary and Conclusion. 



§ 9. From an inspection of the results which have been 

 obtained, the following general conclusions may be drawn : — 



(i.) The value o£ 7 is not restricted to having a value 

 given by the formula 1 4-2/n. It will, however, have such a 

 value if the internal (i. e. vibratory) energy is vanishingly 

 small. 



(ii.) When the value of 7 is different from a value given by 

 the formula 1 4- 2/n, the value will, in general, vary with the 

 temperature. In general 7 will decrease as the temperature 

 increases. 



We may conveniently refer to the two kinds of gases 

 mentioned in (i.) and (ii.) as "regular" and " irregular." 

 For a completely regular gas, r and 7 become identical, so 

 that the true value of 7 will be found from sound-observa- 

 tions, and there will be no damping of sound caused by the 

 il lag " in subsidiary degrees of freedom. 



(iii.) The general value for 7 is 



2 



where the summation extends over all subsidiary degrees of 

 freedom. 



§ 10. It appears that air is almost completely regular. 

 The value of y is almost exactly 1|, and this same value is 

 found by either method of experiment *. Leduc's values for 

 7 at temperatures of 0° and 100° are | 



0°. 100°. 



7 = 1-4040 1-4031. 



The value of 7 it will be noticed is slightly in excess of the 

 value If, whereas we should certainly expect 2/ '(E) to be 

 positive. The explanation probably lies in the fact that the 

 rotations of the molecules are not entirely free from reaction 

 with the asther, so that n in equation (24) must be slightly 

 less than 2. 



As other instances of regular gases may be mentioned 



* Rayleigh, < Theory of Sound/ § 246. 

 t Comptes Mendus, cxxvii. p. 661. 



