Absorption and Fluorescence. 577 



frequency which is the least common multiple of the atomic 

 frequency of all its atoms. The molecule also exhibits as 

 subsidiary frequencies both the least common multiples of 

 the frequencies of groups of atoms forming a component part 

 of itself and also the atomic frequencies themselves. 1 am 

 of opinion that development along these lines affords much 

 greater promise than either Bjerrum's theory of rotational 

 velocities or Kriiger's theory of precessional motions. 



Before leaving the subject of the so-called rotational 

 frequencies of water, attention may be drawn to a statement 

 which is now becoming general in the literature — namely, 

 that the central wave-length of the water band at 3"06 /t is 

 3*26 /jl. It is nothing of the kind. The most accurate 

 observations by Coblentz, Paschen, Rubens, and others 

 show the centre to be at 3*06 fi. The 3*26 //, value is due 

 to Miss von Bahr and is based not on measurements but on 

 a misconception. In his early paper Bjerrum stated that 

 the central line of an absorption-band should be the mean of 

 the two central sub-groups. In this, he was wrong, because 

 it is now well known from the study of some hundred 

 absorption-bands that there is one central sub-group and 

 that the central line of this group is the central line of the 

 whole band. In the case of water the central sub-group has 

 its central line at 3'06 \x and this is therefore the true centre 

 of the whole band. Confusion will undoubtedly arise if this 

 error is not corrected, and I therefore venture to draw 

 attention to it. Indeed, the fact the molecular rotation 

 theory leads to an erroneous value for the molecular or true 

 central frequency of an absorption-band undoubtedly argues 

 against the theory. 



In conclusion, it may be said that the criticism I have 

 given of the Bjerrum and Kriiger theories must in no way 

 be interpreted against the validity of the energy quantum 

 theory or its application. It would, indeed, seem that the 

 material now at hand foims an excellent opportunity for 

 the application of the quantum theory, since a well-ordered 

 discontinuity in the frequency shown by a molecule has 

 been established. This, however, is reserved for another 

 paper. 



The University, Liverpool 



