Light Absorption and Fluorescence. 513 



the relationship between the absorption bands in the ultra- 

 violet and visible regions and one band in the infra-red 

 dealt with in the previous paper. Similarly it explains the 

 existence of harmonics in the infra-red noted by Coblentz 

 and others. 



Again, due regard being paid to the fact that the multiples 

 of the least common multiple can only form the central line 

 of the absorption bands in the short-wave regions, it would 

 follow that the complete system of absorption lines in any 

 one ultra-violet band group can be calculated. The central 

 line of the group must have a frequency which is a multiple 

 of the least common multiple of the basis constants, and in 

 the case of water this must be some multiple of 166*6. The 

 complete system of absorption lines in any one band group 

 of water will be given by the expressions 166'6^±nK 1 and 

 166' 6x ±wK 2 , where x is some whole number, Kj and K 2 

 are the basis constants 2*5 and 6 6, and n is 1, 2, 3, 4, ... . &c. 

 This follows naturally from an application of Bjerrum's 

 principle to any absorption band whether in the short-wave 

 infra-red, the visible, or the ultra-violet region. Nothing, 

 however, is known about the absorption bands of water in 

 the ultra-violet region, and therefore the calculation in this 

 case cannot be put to the test. 



Attention may be drawn here to the influence of tempe- 

 rature on the breadth of absorption bands, it being a well- 

 known fact that they tend to become narrower with fall of 

 temperature. At the boiling-point of hydrogen it has been 

 shown that the bands appear only as fine lines. In all pro- 

 bability the effect of temperature is to change the molecular 

 rotational energy, and as the temperature falls the effective 

 values of n in the Bjerrum formula 



hn 



will become smaller in number, and indeed at very low 

 temperatures only the lowest multiples of: 



2tt 2 I 



will be active. If the breadth of an absorption band group 

 is due to 



A hn 



v± 2^r 



Phil. Mag. S. 6. Vol. 30. No. 178. Oct. 1915. 2 L 



