Light Absorption and Fluorescence. 511 



If this be proved to be correct, then it would follow that the 

 results given in my last paper represent a portion of the 

 complete relation, for the frequencies of the absorption bands 

 in the short-wave region of the infra-red must themselves 

 represent certain definite values of 



Jin 



2tt 2 I 



It would seem to be established from further investigation 

 that the complete Bjerrum relation does hold good, and that 

 the whole of the absorption-band groups in the short-wave 

 infra-red, visible, and ultra-violet regions can be calculated 

 on the basis of Bjerrum's theory. 



The first point to be considered is whether it is possible to 

 find the values of 



hn 

 2tt 2 I 



for any compounds simply from the measurements of their 

 infra-red absorption bands. 



In dealing with oscillation frequencies the values are 

 inconveniently large, and where a number of calculations 

 have to be made, it is simpler to use the reciprocals of the 

 wave-lengths, that is to say the oscillation frequencies divided 

 by the velocity of light. This practice will be adopted in 

 what follows, and the reciprocals employed represent the 

 number of waves contained in a length of 1 mm., and in 

 order to convert them into true oscillation frequencies they 

 must be multiplied by 3 x TO 8 . 



Now Eucken* showed that the infra-red absorption bands 

 of water vapour of longer wave-length than about 10 ix can 

 be expressed by the Bjerrum formula; that is to say, their 

 frequencies for m consecutive multiples of two constants (he 

 having assumed two degrees of freedom) which, if wave- 

 length reciprocals be used, are 5' 78 and 2 5 respectively. 

 Eucken, however, entirely failed to explain the very remark- 

 able variations in the relative intensities of the infra-red 

 absorption bands of water. He only extended his second 

 series to 10*0 /x, and offered no explanation of the extra- 

 ordinary intensity of the great absorption bands of G'O/a, 

 3 yLt, 2ytt, and 1*5 jj,. The whole essence of Bjerrum's theory 

 is that the frequencies of the centres of the infra-red hands 

 are consecutive multiples of a fundamental constant or basis. 

 His theory in no way accounts for the fact that certain select 



* Deutsch. Phys. Ges., Vcrh. xv. p. 1159 (1913). 



