Absorption and Fluorescence. 567 



1*05972 x 10 13 , which is the least common multiple of another 

 pair of the atomic frequencies, namely 8*19 xlO 11 and 

 1*296 x 10 12 . Lastly, in each sub-group of the less re- 

 frangible band the component lines form a series with 

 constant frequency difference of 8*19 x 10 11 , which is one 

 of those atomic frequencies compounded in the constant 

 frequency difference of the series of* the central lines of 

 the sub-groups. The component lines of the sub-groups 

 of the more refrangible band of sulphur dioxide have not 

 yet been accurately measured. 



It will thus be seen that, whilst the central frequencies 

 of all the absorption-bands of sulphur dioxide are based 

 on a molecular frequency which is the least common 

 multiple of all three atomic frequencies, the sub-groups 

 of the bands are due to the least common multiples of 

 two out of the three atomic frequencies, and the component 

 lines of the sub-groups are due to the atomic frequencies 

 themselves. Each complete absorption - band therefore 

 consists of a central or true molecular frequency, com- 

 pounded with intra-molecular frequencies in the central 

 lines of the sub-groups and with atomic frequencies in the 

 component lines of the sub-groups. 



Sulphur dioxide was the first substance in which these 

 relations were completely worked out, since it was the first 

 instance for which accurate measurements had been made 

 both for the infra-red and for the individual lines com- 

 posing one of the absorption-bands. Recently, however, 

 Sleatqr * has published highly accurate measurements of 

 water vapour at 6 /x and 3 /a, and it becomes possible to 

 test whether a structure similar to that found in sulphur 

 dioxide exists in the absorption-spectrum of water vapour. 

 Further, if the atomic frequency 2*4531 x 10 u is trulv 

 characteristic of the oxygen atom, this value should form 

 one of the atomic frequencies which is active in the case of 

 the molecule of water. 



It is well known from the works of: Bjerrum and of 

 Miss von Bahr that the two great absorption-bands of 

 water at 6 /x and 3 /u, consist of sub-groups and that the 

 central frequencies of these sub-groups can be arranged in 

 two series with constant frequency differences of 7*5 x 10 11 

 and 1*7301 X 10 1 ' 2 respectively. By analogy with sulphur 

 dioxide these differences u ill be intra-molecular frequencies, 

 and therefore will be the least common multiples of two 



* W, W. Sieator. Astiophys. Journ. vol. xlviii. p. 125 (19]8). 



