Absorption and Fluorescence. 569 



3, etc. Sleator, however, only measured the lines in a 

 portion of" one side of the band, and all the central sub- 

 group lines measured by him are given by 981216 X 10 13 

 + mx l'7301xl0 12 , where m equals 4, 5, . . . 12, and 

 9-81216 xl0 ls + ?iX 7*5 X 10 11 , where n equals 9, 10,. ..27. 



Then, again, there are the component lines in each sub- 

 group, the frequencies of which are given by compounding 

 the central frequency of each sub-group with the atomic 

 frequencies. There are four such series of lines possible, 

 two in each series of sub-groups, but the number of lines 

 in any one of- the sub-groups must be small, since the sub- 

 groups are very narrow and closely situated in the band. 

 The maximum number of lines in any one sub-group 

 without overlapping is seven — namely, the central line and 

 three on each side of it. In the second series of sub- 

 groups, the central frequencies of which are given by 

 9'81216 X 10 13 + n X 75 x 10 11 , there should be two series of 

 constant differences 1-0635 x 10 n and 2*1159 x 10 u , since 

 7*5 x 10 11 is the least common multiple of these two atomic 

 frequencies. But 2'1159 is very nearly twice 1*0635 and 

 therefore it will be sufficient only to calculate the series 

 with constant frequency difference 10635 x 10 11 , and the 

 formula for all the lines in tlie sub-groups will obviously 

 be 9*81216 x 10 13 + «x 7-5 xlO n ±px 1*0635 xlO 11 , where 

 /2 = 9, 10, . . . 27, and p = Q, 1, 2, 3. 



Similarly, in the first series of sub-groups there should 

 also be two series of lines with constant frequency dif- 

 ference, but it happens that the frequencies calculated 

 are very nearly the same as those calculated for the second 

 series of sub-groups. For the present purpose therefore 

 thev may be neglected. J n Table I. are given the calculated 

 values of all the lines in the second series of sub-groups 

 and the central lines only of the first series, together with 

 Sleator's measurements. In the first column are given the 

 wave numbers (1/V) for all the lines in the second series of 

 sub-groups calculated from the above formula. The sixth 

 column contains the wave numbers of the central lines of 

 the first series of subgroups calculated from the frequencv 

 formula 9'81216 x 10 13 -f m x 1*7301, where m = 4, 5, . . . 12. 

 The second and fourth columns contain the corresponding- 

 wave-lengths, and in the fifth column are given the wave- 

 lengths as observed b}' Sleator. 



The agreement, on the whole, between the calculated and 

 observed values is remarkably good, the maximum difference 

 being 0-0022 yu,, whilst the general average is +000074 jj.. 



Phil. Mag. S. 6. Yol. 39. No. 233. May 1920. 2 P 



