120 



frequencies of the individual molecules begin to [day a part for the 

 energy distribution. 



This theoi-y involves that for smaller densities Uy is no longer 

 determined by the relations of Suppl. N". 32r/, equations f4) and 

 (5) of this paper. Notwithstanding that, in consequence of the relative 

 insensibility of the way in which u,- depejids on T for the special 

 assumption about the distribution of the fre(piencies (cf. Suppl. N". 31 

 § 7 by OosTERHUis), a good agreement may still be obtained l)y 

 those relations with the observations considered in this paper, but 

 then the values of (\, which give such an agreement, do not have 

 the meaning laid down by the theory in Suppl. N". 32«. 



Meanwhile the part for the smaller densities (o<^0.J5) of the 



0^ ,0-curve of Fig. 2 may be given a simple meaning by supposing 



15 

 the curve for this region to represent — A, if A is determined 



by the fact that the ^^i-, T-curve on the side of the high temperatures 

 approaches asymptotically to 



u, = k{T-\-L). 



As according to the relations of Suppl. N". 32^^ § 2 (cf. Snppl. 



15 

 N". 32A § 5) 0^ = — A, the curve has also this meaning tor 



(J ^ J . For a nearer interpretation of the intermediate region the 

 theory will have to be further developed. 



On the side of the small densities the curve in Fig. 2 has been 

 extrapolated (indicated by dots) to a parr that terminates parallel 

 to the (,--axis, in agreement with the theory given above, that at 

 small densities the frequencies of rotation are no longer dependent 

 on the density. 



In this region of densities the rotatory energy is determined as in 

 the simplified scheme of Einstein and Stkrn or of Oosterhuis, in 

 which to all the molecules the same velocity of rotation Avas ascribed, 

 or better in the more elaborate thsory of Holm^), in which the 



1) E. Holm. Ann. d. Phys. (4; 42 (1913), p, 1311. This theory, in which in the 



system of rotating niolecules all frequencies occur, and for the distribution of the 



molecules according to the frequencies, in a way analogous to that which Planck 



in his recent theory followed for linear oscillators, the plane in which the condition 



of a molecule rotating about one axis is represented by the values of its azimuth 



and moment of momentum, is divided into regions of constant probability limited 



hv 

 bv enprQ;v curves ii — n—^ , is consistent with the resu ts of Bjerrum and E. 

 J --• 2 



V. Bahr concerning the discontinuous character of absorption spectra in the 

 infra-red of gases of not loo high densities, if it is assumed that the absorption 



