DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 439 



from an observed line. Thus in m = 3, the observed is entered as v.(3) 3897212, 

 whereas the actually observed is v less. 



m. Calculated. Observed. d\. 



1 -{(2) 201637 (W.) + Vl + V2 \.v * 



2 (0) 25432-35 (W.) * 



3 38972-54 u(3) 3897212 (R) "02 



4 43873-80 e.(4) 43874'02 (W.) -'01 



5 4618476 see Note "07 



6 47454-96 



7 48227-14 u.v.(l) 48227'00 (W.) '00 



8 48731-22 see Note 



Note. For m = 3 the e sounder is too large, and for m = 4 the v is too small to 

 act. 



The agreement is so good that the chosen low intensity lines for Sj (l) are justified. 

 The low intensity may be explained by the supposition that the energy of the normal 

 line has been partly transferred to other displaced ones, in the way indicated above 

 for m = 3 and as shown also by higher orders. For m 4 together with 20195 the 

 line sounded from W. only observes (2) 201637, and K only (0) 20133'0. These 

 differ successively from the first by 30 . For m = 4 the oun displacement produces 

 1'42 on the sequent and the normal 30 "5 on the limit. They are therefore possibly 

 e.(^) S t (4) and e.(2^) S, (4). In m = 5 the e sounder requires 22506, not observed by 

 either, but there is an isolated group, 22516'9 by both, (5) 22535'5 (W.), (3) 22540'4 

 (R.), of which 22535 is 30 ahead of the required line and 22540 is 35, so that the 

 former is ( <^) on the limit. The latter, however, sounds to 4621871 for ( ^) ^(S) 

 and gives Sj (5) = 46183'25. The d\ = '07 of the list is based on this. For m = 6 

 the e requires 23776'65 with observed (0) 23760'9 (W.) and (10) 2378375. In m = 8 

 the u + v link = 2487T8 requires 23859'5. The only observed are (2) 2384T9 (W.) 

 and (4) 2387T3 (W.) or (5) 70'00 (E.), about equally displaced on either side of the 

 normal line. 



Some space has been devoted to the consideration of the S series as on it depends 

 the determination of the important u, v links as well as the limit for the D series. 

 The latter is perhaps in general the more important as it affords with the F, the 

 means of obtaining accurate determinations of the oun. In the present case, however, 

 the measures have such large possible observation errors that they do not add to the 

 accuracy already found in the foregoing discussion. A few points only will therefore 

 be here referred to. Both the D satellites for m = \ and the F lines for m = 2 with 

 related lines form the majority of the lines in the long wave end of the spectrum 

 (n < 20000). One clue as to a distinction between the two sets may be found in 

 the fact that where the 5640 link occurs on a D line it links backwards, while in 

 the F it links forward. Consequently where a line has a link forward it is probably 



VOL. ccxx. A. 3 o 



