DE. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 377 



m = 2. To the only two direct F there appear two direct E with the same mean 30674-77 and 

 modified separation 301-8. Also there is a direct line to F 4 . To the linked F 4 .e corresponds a linked 

 e.F.|. In this connection it must be remembered that all the F are large, over 44000, and an e link would 

 reach to lines outside the region of observation. Three other sets are included in the list, which involve 

 displaced / sequerits. The second pair give a mean 30674 77 + 102 10 and belong therefore to the limit 

 midway between F 2 and F 3 . But the sequent = half the difference = 13399-95 in place of 13353-26, 

 on the supposition of a common limit. So also the pairs for F 7i8 show / sequents 13362-41 and 13339-01 

 on the same supposition. 



If the observed 44028 is really (38i) FI, where Fj has the same limit as FI, and may he called the 

 normal FI, the mean of the observed FI and of FI is 30677-80, and should give the true value of the limit 

 subject only to observation errors on the two lines, i.e., within maximum error of 1 1 with d\ = -05, 

 and within a probable error much less. 



m = 3. FI corresponds to Y\ with mean 30677-27 + 1. Ther'e are some cases of displaced /(3) as in 

 m = 2, The 10A' 2 set appear also in F, and as they contain several examples they are placed in the list. 

 There are two lines 37836-36 and 38050-15 (separation 213-79) which as Fj and F 5 give a mean 

 30671 "71. The lines in the list show an unobserved line for Fj, which is the basis for the others, its 

 actual value is taken as - 3<5i displacement on 37836. The mean is 30674-76 which, on the supposition 

 adopted above, corresponds to a (38j) F ( oo). Since F 3 = ( - 28^ F 2 , the line 37946 may be written as 

 normal F 2 , giving mean limit = 30676" 79 1. In the 4A'.> set is a line 39799-89 = F S (4A' 2 ), giving with 

 F 8 (4A'.j) a mean 1860-19 + 30678-78. 



m = 4. There appear no direct F to the F lines. But they occur in the parallel set F' ; but as F'^ 

 (28^ F' 4) (3!) F' 5) (2Si) F 7 , F' 8 . The mean is 30677 -16. 



m = 5. Here F! and Fj appear, but as the mean depends only on calculated F : it is not reliable. If 

 FI be taken from the observed line 26727-89 by the -a link, the P\ line would be 27496-83, giving 

 mean 30677-25. There are also lines connected with the parallel series F\ which has a limit 16 below 

 Fj. F\ = 27482-72 and F'j = 33838-09, gives mean 30660-40, which is about the proper amount below 

 F ( oo ) = 30677 80. With this goes 34146 82 as F' with separation 308 73. 



m = 6. The unobserved lines supposed for the first pair are calculated respectively from the observed 

 F 6 , F 8 , and F 4 . The line 33297 is (28,) FO. Corresponding to 33076-55 as F' 3 , the mean limit with F' t is 

 30658 in place of 30660. With this might possibly go 34018-93 as (3^) F' 7 . 



m = 7. Fj + e = 35624-97 gives a mean limit 30674-71. Also with Fj + 6 = 33228-89 gives a mean 

 limit 30675 12. Also 3351 1 22 an exact F' 7 with mean 30677 34. 



m = 8. Fj + e = 35249-74 gives mean 30676-36, but F t is uncertain. 



m = 9. I have not found F 1( but 32015-37 as F 5 gives Fj = 31802-00, which gives mean limit 

 30677-10. 



m = 10. No F! found, but 31726-38 as F 3 and 31841-05 as ( -6,) F 5 gives FI the same value 31625-5. 

 This gives a mean limit = 30676 75. 



The evidence seems therefore clear for the existence of this type of series. 

 The Value of the Oun. For the evaluation of the oun there are at disposal : 



(l) The A 15 A-; as determined from the S separations. These have given (p. 346) for 

 A first approximation to , the value 249'30 from j, and 249'6 from the two alternative 

 1/2, i/ 2 . The i/s are so ill-determined that these might possibly refer to values giving 

 the same S. But the fact that the value of e calculated from A t agrees so closely 

 with the maximum ordinate in the corresponding occurrency curve (Plate 2, fig. l) 

 shows that A! must be exceedingly close to the true yalue, in which case it is 



3 F 2 



