451) 



again suppose Debije's method to be approximately valid. According to 

 that method the "spectrum" is determined without taking account 

 of the molecular structure, and then it is cut off on the side of the 

 high frequencies at a value Vmax whicii is found by putting the total 

 number of such modes of vibration equal to the number of degrees 

 of freedom. 



We may imagine that the energy of the radiation is transferred 

 to the molecular rotations by means of the radiation pressure and 

 hence and b}' analogy with the molecular translatory motion (cf. Suppl. 

 N". 30cz § 2) suppose, that we have to take energy elements of 

 magnitnde ^ hv^), if r is the frequency of the considered mode of 

 vibration. A different supposition concerning the coefficient of hv 

 would, moreover, not cause any change in the general results of 

 this communication. 



As was done for the translatory motion (Suppl. N". ^Oa § 3) we 

 will for this free rotatory motion suppose, that the velocity of propa- 

 gation c of the wave motions considered here, for the small wave- 

 lengths which are the most important, at states which deviate only 

 little from the state of thermodynamic equilibrium, is for each mode 

 of vibration proportional to the square root of the energy Uy., ^) of 

 that mode of vibration. We then obtain as in Suppl. N°. 30a § 4: 



%v = è U- H-èAr (1) 



ekf—1 



This expression is adopted also by Eiisstein and SterxN for the 

 energy of rotation with "frequency" v for one degree of freedom. 

 The supposition concerning c may provisionalTy be further justified 

 by the remark that by it we obtain that for high temperatures the 

 ratio of the energy for one degree of freedom to ^ kT approaches 

 to 1, as must be the case for these free rotations. 



We will suppose that in this communication, where the contrary 

 is not mentioned explicitly, we have to deal with the rotations round 

 two equivalent axes. For the mean energy of rotation for these two 

 degrees of freedom we then find 



''max 



3 ri hv ) 



>h = 3 \ \~-r^ [-^.hvlv'dv, (2) 



ï'max nJ ( ^ ] 



IcT _ 1 



^) Gf. also 1^. Ehrenfest i. c, p, 453 note 1. 



') The index r will indicate that the quantity relates to the rotatory motion. 



