DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 389 



(2) 18466-47 



7313-17 



(1) 28341-62 4425-90 



F! 1863-92 Fj 829-69 F, 4426-43(2)31035-76 



(4)28047-34 4131'62 



1975-86 1974-70 1970-10 



(4)25891-58 1862-76 (2)27754-34 825-09 (4)28579-43 1864-94^- 



Here Fj, 25891, 27754 form a series inequality with d + 2, v t 2 ; F! forms a parallel 

 inequality with 28341 and 28047 with u-2, v-2 ; 18466, F,, 277 54 a series inequality 

 with d, e ; and F 3 a parallel inequality with v 2,-d 2. 



As a rule in the list only displaced lines are dealt with and only occasionally linked 

 ones. The evidence is strong for the existence of possible series with limits 30725 

 (+XS,) especially x = 2 and that for each order most of the energy goes to a line 

 with one of these limits, not necessarily the same for different orders nor for the same 

 triplet set, nor for the same F or F type. 



Notes. A displacement <?, produces 4'97 on F,(oc). 5'43 on F, (<x), and 5'65 on 

 F,(oo). 



m = 1. The shortest sounder to reach from the calculated F (l) to the observed 

 region is 2e, giving values in the neighbourhood of 17700. In this neighbourhood we 

 tind a triplet (No. 2 of the sets on p. 38')) 



(6) 17638-55 1864-64 (3) 1950.T29 829'93 (l) 2<)3:J:5"22, 



which in separation and order of intensity corresponds precisely to the values required. 

 With the normal value of e they indicate lines with wave-numbers at 3010"35, 

 4875'09, 5705'02. In connection with the question of satellite effect it may be worth 

 noting that lines in the neighbourhood of the above may be arranged with them thus 



(6)176:18 1864-64 (3)19503 829*93 (1)20333 



12-52 



(3) 19515'Sl 



25-53 



(5) 17664-07 



To complete the set there should be a line at 17651 "31, but it was not observed 

 by BALY. A sequence displacement iny(l) of 3(5, produces a change of 12"76 and 

 of 6^1 of 25 '53. These are practically exact and correspond to the diffuse satellite 

 arrangement with this difference, that the triplet appears as a main set in which the 

 first line is strongest. They depend on 3<^, 6^, displacements, so that the mantissa 

 of the doublet set, that of 19515, is exceedingly close to 90A 2 , viz., 90 x 10997'17. 



With F, (l) = 3010 should go F,(l) = 58440'17. This is outside the observed 

 region on the other side, in the ultra-violet, and requires even larger sounders than 

 F(l). The treble link 3e = 21 942 '30 requires a line at 36497 "87- There is no line 



