432 DE. W. M. HICKS : A CRITICAL STUDY OF SPECTRAL SERIES. 



therefore be a real connection. In (10) Vl is a normal 49 with error 2 and v 2 with 

 p 1 is 00= 14 14 or the oun displacement in the last line. In (12) also the oun 

 displacement in the last line makes v 2 = 16. No. 13 can be explained by the oun 

 displacement on the middle line alone. They can all then with the exception of one be 

 explained by /, = 5635 or 5649, and v 2 = 2816 within limits of about 1. The 

 consideration of their source is postponed until the D sequents have been touched 

 upon (p. 441). 



An examination of the spectral list shows values of ^ varying between 5361 and 

 5388 with v 2 from 2639 to 2685. In many cases two lines are separated by about 

 5371 and a line approximately midway with separations 2680 . Now in the other 

 gases the appearance of such fa separations is so common as to be almost the rule. 

 This lends weight on the one side to the assumption that 537 1 is v l and on the 

 other that 2680 is not i/ 2 but corresponds to ^ v v Values therefore in the neighbour- 

 hood of 2686 may be left out of account in the search for v 2 which is always less 

 than fa. 



There are a considerable number of separations in the neighbourhood of 5380 

 which again suggest the analogous modified i/, related to the D satellites in Kr and X. 

 In those cases the explanation was adopted that at least in the main they arose from 

 displacements of small multiples of the oun in the sequence term. No exact value of 

 these displacements can be obtained until the value of the limit itself is known, but it is 

 possible to arrive at an approximate estimate by employment of a value of the limit 

 which may be a few hundreds wrong. Such an estimate will be of great value in 

 guiding our search. 



The values of S(oo) for A, Kr, X are respectively 51731, 51651, 51025. From 

 analogy, that for Ra, Em would be in the neighbourhood of 50500, say 50500 + 

 With i/j in the neighbourhood of 5371 + 1 calculation shows that a displacement of (5, 

 will produce a change in the limit of 30'86 + '0011 and in the ^ of 472. The D 

 sequence terms vary with each satellite set. One such sequence set has already been 

 found in the F series already discussed, viz., 29964. Here the oun displacements 

 produces a change in n of 13 '96. But higher values than this for d(\] sequents are 

 to be allowed for up to even 31000. For 30500 the oun displacement produces a 

 change of 14'88. It is safe therefore to take the oun displacement on the sequent as 

 producing a change varying from 14 to 15. 



If now the 5370+ separations be analysed it will be found that three lie at 71'4'4, 



eight at 74'2 + '6, five at 80 + '5, six at 84'2 + l and a group at 88 with none between. 



There is a clear majority about 74 with a set at 88, or about 14 ahead (i.e., ^ on the 



sequent) and a few about 61, or 14 behind. Whilst the 71'7 and 78 sets suggest the 



Si displacements in the limits, definitely seen to exist in Kr and X. 



For the v 2 , the oun changes on the sequent are the same and on the limit are about half 

 the previous, say, about 2 or 3. In this case are found a majority near 2649 with 

 some about 14 on either side, and another few about 2652. 



