455 



valuable data for a more detailed treatment of the question ^) as to 

 the way in which the quantuni-tlieorj has to be applied to the 

 molecular rotations. 



As far as the general character is concerned, Einstein and Stern '^) 

 obtain a good agreement with Eucken's measurements by the sup- 

 position, that the mean energy of rotation of a molecule at the 

 temperature T is determined by the formula which Planck recently "') 

 has given for the mean energy at the temperature Tof an oscillator 

 with definite frequency. In this formula the hypothesis of a kinetic 

 energy at the absolute zero is included. As frequency they accept 

 for the rotating molecule the number of revolutions per unit of time. 

 Hence the frequency is immediately connected with the energy 

 by a second relation. 



Although generally speaking the agreement is very satisfactory, 

 still at ordinary and at not very low temperatures differences exist, 

 which justify a closer investigation as to the way in which the 

 quantum-theory has to be applied to the molecular rotations. Einstein 

 and Stern themselves already indicated that their calculations are 

 not complete in so far as ihey suppose only one frequency of 

 rotation to be present in the gas at a given temperature. Sackur*), 

 who independently of Einstein and Stern also applied the quantum- 

 theory, but in a somewhat different manner, to the rotatory motion 

 of the molecules, had gone farther in this matter in including 

 different possible velocities of rotation in his considerations. The 

 same was done by Ehrenfest^), who applied the rules of statistical 

 mechanics in a way which more closely corresponds to the consi- 

 derations by Planck. In both modes of treatment the principle 

 of finite energy elements, respectively of finite elementary regions 

 of equal probability, is applied to each of the rotating molecules 

 separately in a corresponding way as Pi-anck does for an oscillator. 

 As, however, the rotatory motion of a molecule, in the absence of 

 a directing force and therefore of a potential energy coming into 

 play in this motion, differs in principle from the motion of a Planck's 

 oscillator, the immediate transfer of Planck's considerations to the 

 rotatory motion of each of the molecules separately does not seem 

 to me to be very obvious. 



1) This question is also of importance for the thermal equation of state, cf. 

 Suppl. W. 25 § 3 /■ (Sept. 1912). 



2) A. Einstein and 0. Stern. Ann. d. Phys. (4) 40 (1913), p. 551. 

 s) Gf. M. Planck. Warmestrahlung, 2to Aufl., p. 140. 



^) 0. Sagkur. Jaliresber. der Schles. Ges. fiir vaterl. Gultur. Febr. 1918. 

 5) P. Ehrenfest. Verb d. D. physik. Ges. 1913, p. 451. 



