82 Quantum-theory and Rotation-Energy of Molecules. 



that v lies between 20 and 40 x 10 11 . The mean value 30 x 10 11 

 gives a mean moment of inertia = 3*3x 10~ 40 . 



For gases other than hydrochloric acid and water-vapour 

 there are not yet any experimental determinations of the 

 frequency difference. On the other hand, we have more or 

 less exact values of v, as noticed above,, and by means of 

 the kinetic formula we can approximately calculate the 

 moments of inertia for these gases also. In Table IV. are 

 brought together — besides the values worked out above — 

 the moments of inertia (I) for several di- and tri-atomic gases. 



Table IV. 



Gas. 



v.10- 11 . 



I.1040(k.t.) 



1 . 10-io (q. t.) 



A.10 8 . 



HC1 



20-15 

 16-7 

 8-3 

 30 

 3-8 

 25 



4-9 



67 



29 



33 



205 



480 



51 

 V9; 4-4 



1-8 

 23 

 1-6 



HBr 



CO 



H 2 



N 2 



co 2 





It is striking that the moment of inertia of carbon monoxide 

 is more than four times as large as that of hydrobromic acid 

 although the molecular weight is three times less. But if we 

 assume the Rutherford atom-model, and, by means of the 

 moments of inertia given in the table, calculate the distance 

 (A) between the atoms, we get the values given in the fifth 

 column of the table, which are well reconcilable with mole- 

 cular sizes determined by other methods. 



According to formula (1) the frequency differences (^— ^ ) 



are inversely proportional to the moments of inertia. If the 

 formula holds, the separate lines in the absorption-band of 

 e. g. the carbon-monoxide, must lie six times as close together 

 as those of the hydrochloric-acid band. The poly-atomic 

 gases generally have moments of inertia much greater than 

 those of carbon monoxide, and, further, as they—- like water- 

 vapour — probably have at least two frequency series, there is 

 good reason to believe that their absorption-lines lie very 

 close together. From this would be explained the fact that 

 the influence of the pressure on the absorption generally 

 ceases the sooner, the greater the molecules, and that it has 

 not been possible to demonstrate any pressure-effect at ail in 



