Dr. Eva von Bahr on the Quantum-theoryland 

 Table III. 



n. 



v. 10-n 



x in (a. 



n 



1 



75 



74 



403 



7-45 



2 



146 



13-3 



215 



6-98 



3 



20-3 



20 



149 



6-72 



4 



261 



263 



115 



6-55 



5 



31-4 



326 



94 



6-40 



6 



36-8 



— 



82 



613 



7 



40-8 



— 



74 



5-83 



The numbers appearing in the first column give the order 

 o£ occurrence reckoned from the mid-point of the band. For 

 hydrochloric acid no absorption-bands in the long-wave 

 spectrum have yet been measured directly, but from the 

 determinations of Rubens and v. Wartenberg* it appears 

 that between 100 and 350 yu hydrochloric acid shows strong 

 absorption, which is stronger between 100 and 200yit than in 

 the case of longer wave-lengths. 



Figs. 2-4 show as clearly as can be desired that, if we 

 wish to maintain Bjerrum's view as to the origin of the 

 ultra-red absorption, we must assume that the rotation 

 frequencies of the molecules (at least of the absorbing mole- 

 cules) do not vary continuously according to Maxwell's or 

 any similar law of distribution. Hence it readily suggests- 

 itself to try with hypotheses from the quantum-theory, and 

 this Bjerrum has in fact done in his above-mentioned work. 

 He starts — as Ehrenfest does later on — from a distribution 

 of the rotation-energy according to quanta and puts 



~(27TZ/) 2 .I = 71. ll.V, 



(1) 



where I is the molecules' moment of inertia, n a whole 

 number,, and h Planck's constant. 



From this we get v — n ^ 2 j ; that is to say that when I 



is constant v can only have certain fixed values, which form 

 an arithmetical progression with the constant difference =■ 



h 



27T 2 f 



* L.c. 



