PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



85 



recognised as forming a doublet series. We have seen that this value 97 '1 is the 

 difference between the D n (2) and D 12 (2) calculated from the formula, D (2) not having 

 yet been observed. It is natural, therefore, to look to the D series as generating 

 those in question in the same way as the S depends on the P, i.e., the limits of the 

 new series should be VD n (2) and VD 12 (2) or VD 31 (2), i.e., about 17000. If we 

 employ this, however, it is at once seen to be too large. If the lines 8082, 7280, 6872 

 are used to calculate the constants, there results 



N = 16783-52 ( + v)-N/(m+l'038603-m- 1 x -219539)*, 



which is of the S type. The formula does not look right, the limit is rather far from 

 VD (2), and, moreover, it is the first case where there has appeared a value of /x a/m 

 which passes from < 1 to > 1 as m increases. The formula which bounds, so to say, 

 the change from the S type to the D type, i.e., a = 0, and satisfies the two lines 

 8082 and 7280 exactly, is 



16810-N/(m+-968295) 2 , 



and it gives a better agreement with the other lines, as is shown by the following 

 table, in which only the values for the first of each doublet is given for the former 

 formula. The differences are for obs. calc. and v is taken to be 97 '5 : 



For the last, the measurements of S give v = 84'5 or 13 too small, i.e., a wave- 

 length difference 5'2 A.U. too small. If the second line is correct, showing good 

 agreement with the formula, the first would therefore be 2 wrong instead of 7 '15. 

 As is seen, the second formula gives extremely good agreement. If the limit is 

 higher than 16810 the series becomes a D type. In these inexact measurements, 

 however, it is probably best to use RYDBERG'S form without the a. Even now the 

 limit is not that calculated for VD (2) ; there may be a small error in the latter, but 

 hardly to the extent of 200. We may feel as certain, however, that the limit and 

 VD (2) are the same as for the corresponding case of P( oo) and VS (1), in which the 

 " error" is also considerable. The strongest evidence is in the striking fact that the 

 D n and D 13 series generate the doublet separation. For m = 2, X = 22920, which 

 would be far outside BEKGMANN'S region of observation. 



The only lines now left unaccounted for in Cs are 13711 B. and 5209 R. The wave- 



