DR. W. M. HICKS: A CRITICAL STUDT OF SPECTRAL SERIES. 
367 
group with a limit ( —2^i) D(co) or with a limit ( + 4^i) D(co), decreasing by ^ the 
mantissas of the sequents and requiring 
•6-... = 0 ; 3-5-... = 0 ; 8-9-... ; 
which again are easily satisfied within observation errors. With regard, however, 
to (2), (3), it is not common to find two satellites so close together, and as they both 
belong to doublet sets we should suspect that they belong to different groups, and 
in fact the condition is satisfied by regarding the limit of 20875 as displaced by — 
on that of 20871. 
We shall consider the conditions more fully later in connection with the more 
accurate determination of the oun. The preceding results are sufficient to show 
that (l), (4), (5) are a definite normal D satellite on the basis of Ag = 4680 ±. That 
(7) (8) belong to a series probably based on A'2 = 4243 ±1, and 2, 3, 6 to a parallel 
system based on the limit { — 2S^) D ( 00) or ((5) D ( 00). 
I omit details about the satellite e. u, v links, but the following points are interesting. 
The line 19116 affords an example of the two displaced D2 lines analogous to that 
given in 3(a) as explaining the source of the abnormal separations. In addition 
the linked line 2e + Dig shows the same effect with two lines (2) 25380’26, (l) 25382‘58. 
D]6, Dgg are curious as showing successive abnormal u links. Thus 
(1) 18780 
1888‘61 
Die 
(2)20669 
1888-37 
(4) 22557 
(1) 19881 
1885-31 
D 36 
(3n) 21766 
1885-71 
(3) 23652-29 
1889-40 
3-69 
(3) 23655-98 
3-31 
(1) 23659-29 
The two lines Djg, 
Di 3 which 
have been shown to 
have a relative displacement 
of 2(5^ show u, V links to a mid-line displaced from each. Thus (3) 22815'84 is 
1942T5 or -y—’29 below their mean; whilst (l) 19778'52 is 1883'69 or w —'34 below 
the mean of D22 and D23. 
The satellites for m = 2 are more doubtful on account of the large changes in the 
mantissm produced by observation errors. The line 38531 has a mantissa difference 
from that of of exactly the same as in Di3(l). It should, however, be one of 
a doublet with the second line stronger. The others show mantissse differences of 
28(1, 103^, 124(1, 224f^, which, allowing for the usual changes in the second order, 
clearly point to the sets as indicated in the table. There appears, however, no 
analogue in m = 1 for 38324. In this case it is important to notice that the V 2 
VOL. CCXX.-A. 3 E 
