SO Dr. Eva von Bahr on the Quantum-theory and 



The wave-lengths and the accompanying number, repre- 

 senting order in occurrence as calculated by A. Eucken, are 

 given in Table II. cols. 4-7. Their agreement with my values 

 is not particularly close for the longer wave-lengths, and for 

 some of my maxima there are no corresponding values in 

 Eucken's series. However, ii must be borne in mind that 

 my values rtannot be very exact just in the case of the longer 

 wave-lengths, and that it is not impossible that one or two 

 maxima in fig. 2 do not belong to the water- vapour band 

 at 6'26 /jb. Judging from the fact that absorption is stronger 

 in the long-wave part of the band, it is even probable that 

 we are here in the presence of another, weaker absorption- 

 band, lying over the principal band. Another possibility is 

 that in reality there are three series, but that the third series 

 presents itself so feebly that it is noticeable only in the 

 neighbourhood of a rotation wave-length of about 40-60 /j,. 

 The most serious objection to Eucken's series is that they 

 postulate an absorption-band at 87 fi } where Rubens has even 

 found great transparency for water-vapour. 



In the case of the diatomic hydrochloric acid there is 

 reason to anticipate a simpler composition of the absorption- 

 band than in the case of water-vapour, and to judge from the 

 curves given in fig. 4 such is also the case. As appears from 



Table III. col. 5, - is not, however, constant, as it ought to be 



•according to Bjerrum's formula, but decreases with increasing 

 frequencies. It is true that the determinations are not very 

 exact, and we can hardly claim that the divergencies of the 

 particular values from the mean value lie outside the margin 

 of error, but the steadiness of the decrease indicates that 

 here we have probably an actual divergence. It is possible, 

 however, that this divergence does not depend on the falsity 

 of the formula, but — as Eucken suggests — upon the moment 

 of inertia of the molecules (I) increasing with increased 

 velocity of rotation. 



If, as first approximation, we assume that the rotation- 

 frequencies of the hydrochloric-acid molecules, as well as 

 those of the water-vapour molecules, form arithmetical 

 series, as anticipated by formula (1), then it still remains to 

 enquire whether the formula still holds quantitatively. The 

 possibility of such a test is afforded by the calculation of the 

 moment of inertia, on the one hand from formula (1), and on 

 the other from the Kinetic theory of Gases. Similar calcula- 

 tions have already been made for water-vapour by Bjerrum,* 

 who found correspondence in respect of order of greatness. 

 * N. Bjerrum, I. c. 



