Absorption and Fluorescence. 575 



extend his observations beyond 13 /u,, he did not discover 

 the great band which must exist with its centre at 

 21-22 fi. 



It is evident from the results given above that the obser- 

 vations are in direct conflict with the theory that molecular 

 rotational frequencies play a fundamentally important role 

 in absorption-spectra. According to this theory the mole- 

 cules possess definite velocities of rotation, and Bjerrum 

 pointed out that on the energy quantum theory the fre- 

 quencies of rotation are given by ' where h is the 



Planck constant, G'56 X 10 -27 , I is the moment of inertia, 

 and n = l, 2, 3, etc. These so-called rotational frequencies 

 exhibit themselves as a series of absorption-bands in the 

 long-wave infra-red and also as frequency differences 

 within the short-wave infra-red bands. The width of the 



hn 

 rotational frequency bands is explained by saying that 9 ~ ^r 



only represents a most probable value exhibited by the 

 majority of the molecules. Two criticisms at once may 

 be made of this theory as it stands. In the first place, 

 the inexactness of the rotational frequencies is thoroughly 

 unsatisfactory, for the variations that have to be allowed 

 in these frequencies are very great indeed. In the case 

 of water the so-called rotational frequency series of bands 

 have actually been observed, their frequencies being given 

 by 1-7301 xmXlO 12 and 7-5x?iXlO u . Now in each of 

 these two series the consecutive bands overlap one another, 

 and it follows therefore that the difference between the 

 extreme values of any given molecular rotation must, at 

 any rate, be equal to the difference between any two con- 

 secutive mean values. In the case, for example, of the 



A 7 



molecular rotational frequencv t=— wr, if x be the variation 

 1 J 2tt 2 1 



the extreme values will be -5— 2T±^- Now observation 



6h 

 shows that 9^-77 + ^ must be equal to or greater than 



7 7 

 ^— 2j — x, a conclusion which deprives the theory of any 



exact basis. 



In the second place, it has been shown above and in 

 previous papers that the sub-groups due to the so-called 

 rotational frequencies have also a structure arising from 



