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



examples where small changes (errors or displacements) in lines make all the allied 

 links take their practically exact values, and so give evidence for the reality of each. 

 Thus, 1'2 on al give c, v 8 ; 1'5 on a2 give u, v 1 and the mean of v a , v 3 . (or the line 



(-(?,) F 2 or (S^ F, = F 2:i , say) ; -*5 (d\ = *08) on c4* gives c, v s ; -1*5 on c5 gives d, 

 i/ 4 , v s . These new sets give us representatives of all the lines missing from the direct 

 normal lines. It is noticeable how the/ 8 sequent persists. 



Certain displaced sets are given in the tables. If 23418 is '5 less (d\ = '08) the 

 i/ 2 , V B become exact and it is Y l (3) (4A' 2 ). The numerical proofs of these allocations are 

 not given, as these displacements have no importance at present beyond the fact that 

 they exist. 



m = 4. Direct lines are found for F B , n = 1, 2, 4, 6, whilst 5 appears displaced 

 5*01 = 2 x 2*50, to observed lines 26265, -26275. There is also a line 26067 ahead of 

 26065 by 2'51. If this 2'50 be due to some displacement it is probably 2^ on the 

 limit and some onus on the sequence, or all by ouns on the sequence. The order is so 

 high (m = 4) that it is not possible to decide, and it is shown in the tables as a 

 difference x = 2'50. Linked lines are shown in the map (Plate 5). Again note that 

 2'5 on Fj makes the v, u links exact, and that here again the x appears. Symmetry 

 would seem to indicate that the true Fj (4) or 26057 should be about x less. This 

 would diminish the calculated limit of the series to a value nearer that given by the 

 calculated S ( oo ). 



For m = 5 ... 10 the values for F, calculated from the formula are 27498*81, 

 28'i57'47, 28909*97, 29286*33, 29554*21, 29730*00. With = -1*34 as determined 

 later, we should expect values less than these from about 1 for the first varying to 

 2 for the last. None of these appear but they have linked lines whilst other of the 

 parallel F sets also appear directly. 



m = 5. No line has been observed at 27498, but there are lines with it for F 5 , F 8 , 

 and others for F i;i7 by a link-. A value of F t 27497 is F 8 - 1860*19 and reduces it 

 1*1 as just suggested, f The connections are exhibited in the map (Plate 4). From 

 this order and beyond there appears to be a parallel set at a distance 16 units less. 

 For m = 5, this starts from 27482*72 as F,. As is seen in the map (c9) it has a 

 very large linkage to F lines with similar sets to those connected with the calculated 

 FJ. We may explain its source as a displaced (2(5) F ( oo ), as the difference of two 

 p-links, b c, or as the direct congeries of F lines depending on 20991 as an independent 

 D n line. In the map the notation depending on the second is adopted. In the list 

 27482 is written as F', leaving the question of the origin open. The p-links are 

 particularly prevalent. This was found to be the case also in Ag and Au, the only 

 elements in which the linkages have been examined with any thoroughness. In 

 particular the series of successive + and links from 27497 recalls a similar 



This has been given as a bad D n .e. The suggested change makes the e link worse, which increases 

 the improbability of its belonging to the D system. 



t The calculated is retained however in the map, as the links show the repetitions more clearly. 



