m 



DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 369 



or say, < 18491,- or X >5408. This region is examined for the separations in question 

 and lists made. It is then found that some depend on the same first line, in which 

 case, they clearly refer to F or related lines. Several sets are found connected by 

 one of the ordinary links, which excludes at least one of them as a direct F line. It 

 is now easy to select a few sets from the lists which seem suitable for the F, line. 

 This with the given Fj oo gives /(2), and then RYDBERG'S tables give a rough 

 approximation to F (3). It is then only necessary to examine the lines near these for 

 the separations, in order to find the actual Fj (3). The result of this examination is 

 to show that for the first three orders m = 2, 3, 4, the only sets which exist without 

 displacements in any correspond to the separation 301, with Y 1 lines (l) 17321'51, 

 (In) 23353'84, (3) 26057'20. The formula calculated from these gives as the limit 

 30678 '64. This is only '29 less than d n and is thus in very satisfactory agreement 

 with the rule. Using the value of d n as found from the D series withD(oo) 

 = 51655'56 + ' the actual formula is given by 



877406-577 '8'- 



InthisifD(oo) = S(oo), ^ = -4-27, but if D( oo ) = (-$,) S( 

 The mantissa of the first line F a (2) is 



865448-107'26f+16/> = 185 (4G78'1-'580' + '034p) = 185A L * 



within error limits. The lines have been selected as showing the given separations. 

 Quite independently they give a formula with the proper limit and with the first 

 sequence mantissa a multiple of A*. The evidence therefore for the correctness of the 

 allocation is incontrovertible. 



In the consideration of the notation for the various parallel F series it will be 

 necessary to determine what is to be understood by the normal separations. If the 

 latter are to be decided directly from the D n (l) lines, the separations must be those 

 given above. But a glance at the table of F lines will show that there is a consider- 

 able variation from these, and indeed from one another due as we have seen to the 

 great variability in the oun displacements. Especially is this noticeable in the 

 separations given by the Dj (l) satellites as 213'38 and 307'27. In place of these we 

 find values about 2, 4 or 6 less, corresponding to 1, 2 and 3 oun displacements. The 

 separation 301 is the most frequent displacement from 307 '27. Now ^ alters the 

 separation by 2'03, and therefore 3^ alters 307'27 to 30118. That these deviations 

 from normal values correspond to real F separations can be seen by their frequent 

 repetition in connection with F lines. See for instance the maps for F, especially 

 F(5), in Plate 4. 



* 185A 2 = 204A' 2 + 3S!. 

 3 E 2 



