119 



It is luitui'iil to as('ril)c tins agreement at higher, and tliis deviiilion 

 at lower densities to the following ^). At larger densities the rotations 

 of the oxygen niolecnles ai-e continually disturbed by collisions, or 

 at least interactions with the other oxygen molecules, so that the 

 periods of revolution of the oxygen molecules cannot play a part 

 in the determination of the frequencies in the system which govern 

 the distribution of energy. 



For those densities the frequencies are determined by the analysis 

 according to Jeans of the molecular rotatory motions in the system 

 into natural vibrations; the relations given in Suppl. N". 32a ^ 2 are 

 then valid as approximations. 



At small densities, however, at which every molecule performs 

 in the mean a certain number of revolutions before its rotation is 

 disturbed by the collision (interaction) with another molecule, it is 

 the numbers of revolutions of the individual molecules in the unit 

 of time which govern the distribution of energy. These frequencies 

 are then determined at the limit by Einstein's relation^). 



?«,, = h J (2jtvY 



and are independent of the density; 



Between these two extremes a transition range lies. 



If (for I' =85) the number of collisions, which an oxygen molecule 

 undei'goes in 'J sec. at <> ;= 1 (the molecular diameter o- = 3.I0— ^'^ 

 derived from the viscosity), is compared with the number of revolutions 

 per sec. (distance of the oxygen atoms being assumed = 0.7.10—^'^, 

 derived from the moment of inertia calculated according to Holm') 

 from Zi = J, which value was assumed according to Fig. 2 for 

 oxygen in the gaseous state), one finds that in the mean the oxygen 

 molecule makes 0.4 revolution between two successive collisions. It 

 is, however, not necessary to assume that the number of times that 

 the rotatory motion is disturbed in a second, coincides with the 

 number of times that this is the case with the translatory motion. 

 Some room is thus left for an average number of revolutions between 

 two successive disturbances of the rotatory motion other than the 

 number just mentioned. But if we assume that the order of magnitude 

 will not be essentially different, the result of the calculation mentioned 

 above is such as to be quite consistent with the theory developed 

 above that at (.> = 1 a transitional region begins in which the 



q Gf. the note quoted p. 112 note 1. 



~) Rapports conseil Solvay 1911, p. 433. 



3) E. Holm. Ann. d. Phys. (4) 42 (1913, p. 1319. The 6 used by Hulm 

 corresponds to a in this paper. 



