396 DK. W. M. HICKS : A CRITICAL STUDY OF SPECTRAL SERIES. 



Further, the conditions for/(l) require -67-a;-'4f+ 'dn = 0, or dn = -1'8-'056 

 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 result 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)19942-53 1775-45 (10)21717-98 



2. (1)19989-72 1780-27 (6) 21769-99 



(1)20017-46 1783-71 

 (1)20021-66 1779-51 



(10) 21801-17 



4. (10)20636-301767-09 (20) 22403-39 813' 66->(<l) 



5. (2)20688-961785-54 (10)22474-44 



6. (1)20859-231784-57 (7)22643-80 



7. (4)20962-071780-09 (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 17 79 '51 also occurs. 



In (l) the separation 1775'45 is v l 2'45. It differs from the displaced ($)t>i by '29 

 which is within error limits. In this case the limit would be (<S) D ( oo) which is 42'48 

 less than D(oo) and = 50982'8l. With this limit the mantissa of 19942 comes to 

 879711 = 80x 10998'3-(S 1 or 80A 2 -<$, 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 A 2 = 10998'2 + x its true value is 80A 2 ^ + 8 

 30'28f+30dn 80x. The observation error dn is < '2 in this region and is 

 probably <1. 



In (2) 19989 is 47'19 above (l). The change due to the displacement <S in the limit 

 is 42'55, whilst <5, in the sequent gives 5'05 suggesting that the limit of (2) is the 

 normal D(oo), with sequent 80A 3 . With this limit the mantissa is found to be 

 879853 = 80 x 10998'! 6, or with small corrections 80A 2 -3'2-30'29f +30dn-SOx. 



In (3) we have the modified 178371 with the clearly real separation 177 9 '51 or 

 j^ + 1'61. Now the displacement due to 3<J 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 = 80A 2 -l'4-30'29+30cfa,-80;r. The line 20017'46 is 4'20 

 behind the other. A displacement of S l in the sequent term produces 5 '05. Thus 

 20017 is very close to a line with mantissa = 80A 2 $ lt but the difference '85, 

 corresponding to dX '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. 



