396 
DR. W. M. HICKS : A CRITICAL STUDY OF SPECTRAL SERIES. 
Further, the conditions forI) require ‘67—x—‘4^+Adti = 0, or dn = —1'8 —'OSGf. 
If the sounder 2e was exactly normal this dn must be due to observation errors in 
17638 of d\ = ‘5. but the value of e is also subject to some small uncertainty. In any 
case the residt shows that the reference line does not depend on a displaced 30725, 
for if so dn would be at least 4"97. 
Returning now to the discussion of the D series let us consider first this second 
group of clearly analogous series of lines :— 
1. (1)19912-53 1775-45 
2. (1) 19989-72 1780-27 
1(1) 20017-46 1783-71 
3 . <^ 
[(1) 20021-66 1779-51 
(10) 21717-98 4. (10) 20636-30 1767-09 (20) 22403-39 813-66->(<l) 
(6ft) 21769-99 5. (2) 20688-96 1785-54 (10) 22474-44 
6 . (1) 20859-23 1784-57 (7) 22643-80 
(10) 21801-17 j7_ (4) 20962-07 1780-09 (10) 22742-16 813-80^(1) 
They all, with the doubtful exception of 4, 7 have the appearance of belonging to 
first, or doublet, satellite sets, in which the second line is always the stronger. The 
1780 separations are clearly associated with the now well recognised mid-triplet 
abnormality. That it is not itself a normal separation is indicated by No. 3 in which 
the 1779'51 also occurs. 
In (l) the separation 1775'45 is —2'45. It differs from the displaced (^) by '29 
which is within error limits. In this case the limit would be (d) D ( oo) which is 42'48 
less than D(oo) and = 50982'81. With this limit the mantissa of 19942 comes to 
879711 = 80 X 10998'3 —^1 or 80 A 2 —^i within error limits. This is the typical form 
for the second satellite set of a triplet D series, but modified by the displacement, 
so common in this group of elements, though here it appears in an apparently first 
satellite set instead of the second. We note at present that taking account of the 
small corrections, and writing as before As = 10998'2-l-a; its true value is 8 OA 2 —(^i-l -8 
— 30'28^+30cZn —80x. The observation error dii is < '2 in this region and f is 
probably < 1 . 
In ( 2 ) 19989 is 47'19 above (l). The change due to the displacement ^ in the limit 
is 42'55, whilst dj in the sequent gives 5'05 suggesting that the limit of (2) is the 
normal D( 00 ), with sequent 8 OA 2 . With this limit the mantissa is found to be 
879853 = 80x 10998'16, or with small corrections 8 OA 2 —3'2 —30'29^+30(iw —80a;. 
In ( 3 ) we have the modified 1783'71 with the clearly real separation 1779'51 or 
i'i-l-l'61. Now the displacement due to —3^ on the v is 1'60 which is practically 
exact. This gives a limit 31'88 larger or 51057'17, and the mantissa becomes 879855, 
the same as for ( 2 ) and = 8 OA 2 —l'4 — 30'29^-l-30(7??, —80a;. The line 20017'46 is 4'20 
behind the other. A displacement of dj in the sequent term produces 5'05. Thus 
20017 is very close to a line with mantissa = 8 OA 2 —(^i, but the difference '85, 
corresponding to d\ = ‘21, is too great to render the relation exact. 
Nos. 4 to 7, although much further towards the violet should not be put aside. 
They all show the exceptional separations. 
