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 tln^ir practically exact values, and so give evidence for the reality of each. 
Thus, — 1‘2 on al give c, — 1'5 on a2 give u, and the mean of 1^3, i/g. (or the line 
(—<li)Fo or (dj) Fg = F23, say); —'5 {d\ = *08) on ci* gives c, v^; —1'5 on c5 gives d, 
i'4, i/g. These new sets give ns representatives of all the lines missing from the direct 
normal lines. It is noticeable how the fg sequent persists. 
Certain displaced sets are given in the tables. If 23418 is ‘5 less {dX = ’08) the 
1/3, 1^8 become exact and it is Fj (3) (4A'3). 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„, n = I, 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 he due to some displacement it is probably 2^i on the 
limit and some onus on the sequence, or all by onus on the sequence. The order is so 
high {711 = 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 y, u links exact, and that here again the x appears. Symmetry 
would seem to indicate that the true F^ (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 
calcidated S ( 00). 
For 711 — b... 10 the values for Fj calculated from the formula are 27498’81, 
28357-47, 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 lirst 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. 
711 — b. No line has been observed at 27498, but there are lines with it for Fg, Fg, 
and others for F^g^ by a link—a. A value of F^ 27497 is Fg—1860-19 and reduces it 
PI as just suggested.! 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 771 — 5, this starts from 27482-72 as Fj. 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 
Fp We may explain its source as a displaced (2(5) F (00), as the difference of two 
p-links, 6-c, or as the direct congeries of F lines dejDending on 20991 as an independent 
Djj 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 Dn.e. The suggested change makes the e link worse^ whicli 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 clearff^ 
