DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
377 
m = 2. To the only two direct F there appear two direct F 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 
c.F.j. 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 / sequents. 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 Fj-g show / sequents 13362'41 and 13339'01 
on the same supposition. 
If the observed 44028 is really (38i) Fi, where Fi has the same limit as Fi, and may be called the 
normal Fi, the mean of the observed Fj 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 dk = ± '05, 
and within a probable error much less. 
ni = 3. Fi corresponds to Fj with mean 30677'27 ± 1. There are some cases of displaced /(3) as in 
m = 2 . The lOA'g 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 Fi and F 5 give a mean 
30671'71. The lines in the list show an unobserved line for Fi, which is the basis for the others, its 
actual value is taken as - 38i displacement on 37836. The mean is 30674'76 which, on the supposition 
adopted above, corresponds to a (SSj) F ( 00 ). Since Fg = (- 2 Si)F 2 , the line 37946 may be written as 
normal F 2 , giving mean limit = 30676'79 ±1. In the lA'o set is a line 39799'89 = F 8 ( 4 A' 2 ), giving with 
F 8 ( 4 A' 2 ) a mean I860'19 + 30678'78. 
m = 4. There appear no direct F to the F lines. But they occur in the parallel set F' ■, but as F'l 
( 2 Si) F' 4 , (38i) F 5 , (2Si) FV, F'g. The mean is 30677'16. 
m = 5. Here Fj and F 5 appear, but as the mean depends only on calculated Fj it is not reliable. If 
Fi be taken from the observed line 26727'89 by the -a link, the Fi line v/ould be 27496'83, giving 
mean 30677'25. There are also lines connected with the parallel series F'^ which has a limit 16 below 
F 4 . F'^ = 27482'72 and F'j = 33838'09, gives mean 30660'40, which is about the proper amount below 
F ( co) = 30677'80. With this goes 34146'82 as F '5 with separation 308'73. 
m — 6 . The unobserved lines supposed for the first pair are calculated respectively from the observed 
Fg, Fg, and F 4 . The line 33297 is ( 2 Sj)F 6 . Corresponding to 33076'55 as F'j, the mean limit with F\ is 
30658 in place'of 30660. With this might possibly go 34018'93 as (38^) F' 7 . 
m = 7. F^ + e = 35624'97 gives a mean limit 30674'71. Also with F^ + S = 33228'89 gives a mean 
limit 30675'12. Also 33511'22 an exact F '7 with mean 30677'34. 
m = 8 . Fj + e = 35249'74 gives mean 30676'36, but F^ is uncertain. 
m = 9. I have not found Fj, but 32015'37 fts F 5 gives Fj = 31802'00, which gives mean limit 
30677'10. 
m = 10 . No Fj found, but 31726'38 as Fj and 31841'05 as (- 8 ^) F 5 gives Fi the same value 31625'5. 
This gives a mean limit = 30676'75., 
The evidence seems therefore cleap for the existence of this type of series. 
The Value of the Oun .—For the evaluation of the oun there are at disposal:— 
( 1 ) The Ai, A 2 as determined from the S separations. These have given (p. 346) for 
a first approximation to the value 249'30from vi and 249‘6 from the two alternative 
4, rg. The v’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 Aj 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 value, in which case it is 
3 F 2 
