566 Prof. E. C. C. Baly on Light 



to be of great importance, for it affords a very complete 

 example of the least common multiple principle which 

 forms the basis of the frequencies of absorption-bands, 

 as has been pointed out in the earlier papers of this series. 

 The least common multiple of the three frequencies of 

 oxygen and sulphur given above is 2*89299 x 10 12 , and 

 this number multiplied by 10, 12, 14, 18, 26, and 33 

 gives the exact central frequencies of all the absorption - 

 bands which have been observed for sulphur dioxide in 

 the infra-red region between the wave-lengths 12 fx and 3 //,. 

 Then, again, of these absorption-bands the one with the 

 central frequency 2*89299 X 14 x 10 12 has the greatest 

 intensity, and this central frequency multiplied by 25 

 gives the exact central frequency of the less refrangible 

 band in the ultra-violet, the central frequency of the 

 more refrangible band not having been observed. 



It is well known that the effect of cooling is to decrease 

 the width of absorption-bands and that at very low tempe- 

 ratures only the central frequency remains, this persisting 

 at the lowest temperature yet reached. It is evident 

 therefore that the central frequency is the only one which 

 is truly characteristic of the molecules, the subsidiary 

 frequencies to which the breadth of the bands is due being- 

 connected in some way with the temperature of the mole- 

 cules. These central frequencies are thus true molecular 

 frequencies, and therefore it may be concluded that the 

 fundamental molecular frequency of sulphur dioxide is 

 the least common multiple of the frequencies characteristic 

 of the sulphur and oxygen atoms it contains. . 



It was also shown that the subsidiary frequencies of 

 sulphur dioxide to which the breadth of the absorption- 

 bands is due are also derived from the three atomic fre- 

 quencies of sulphur and oxygen. In the less refrangible 

 absorption-band there are a number of sub-groups symme- 

 trically distributed with respect to a central sub-group, and, 

 further, each sub-group contains a central line of maximum 

 absorptive power with a series of lines symmetrically 

 arranged on either side of it. In the less refrangible 

 absorption-band of sulphur dioxide the central lines of 

 the sub-groups form a series with a constant frequency 

 difference of 6*69696 x 10 12 which is the least common 

 multiple of two of the atomic frequencies, namely 8*19 x 10 u 

 and 2*4531 x 10 11 . Again, in the more refrangible band 

 there exist sub-groups the central frequencies of 'which 

 form a series with the constant frequency difference of 



