21 



latory motions. The characteristic temperatures ((5„, cf. Siippl. N^ 32a). 

 which according to that hypothesis govern tlie rotatory energy, are, 

 however, owing to the small moment of inerlia of the monatomic 

 molecules, so high, that at the ternperatures mentioned the energy 

 of rotation of the molecules does not yet deviate appreciably from 

 the corresponding zero i)oint energy. The same applies to the motions 

 within the atom. The contributions to the entropy due to these 

 rotations of and motions within the atom may then be counted as 

 zero. We limit ourselves to the temperature range within which this 

 is the case '). 



We shall further assume that we are dealing with an ideal 

 monatomic gas, so that terms due to the intluence of the real 

 volume or of the mutual attraction of the molecules need not to be 

 considered. 



The entropy of such a gas is then, on the basis of the hypotheses 

 of Suppl. N". 30a, determined by the expressions given in Suppl. 

 NV 33 § 2a. 



§ 3. In the first place, as was already observed in Su[)pl. N". 33 

 ^ '2a/i, the introduction of the zero i)oint energy makes no change 

 in the value which is found for the chemical constant. Hence a 

 comparison of the value calculated for this constant, e.g. with the 

 value which was found by Sackur to agree with experimental data, 

 cannot furnish a test between Planck's formula with or without 

 zero point energy ^). 



§ 4. If the development of S for high temperatures: equation (J 4) 

 Suppl, N". 33, is written in the form 



then 



6' = Cs + Nk In V + V, Ak In r + j 



! 7 • • • • (1) 



-j- terms of smaller order of magnitude I ' ' ' 



Cs = Nk{i + ~lnii]\A (2) 



1) According to measurements by Pier of the specific heat of argon, this tem- 

 perature range extends for this gas to at least 2300° G. As Prof, Einstein pointed 

 out in a discussion, the investigation at high temperatures of the specific heat of 

 a monatomic gas with high atomic weight, such as mercury, would be of great 

 interest. 



2) Prof. SoMMERPELD asks me to say, that lie wishes the sentence: "Nebenbei 

 sei bemerkt etc. on p. 139 of: Vorlriige liber die kinetische Theorie der Materie 

 und der Eleklrizitat," Leipzig und Berlin 1913, to be omitted. 



