DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
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— 921'42 + 963*80 + 3778 (see map) as real. Again the succession of links through 30806 
of 3778 — 919'5 8 + 963’91 — 91978 + 959 "6 9 would appear to signify a real succession. 
There would then remain the two u links — 2456'66 and —2457'69. To make the latter 
correct 29358 should be 1'49 less. This would bring 921 and 3774 nearer their normal 
values, but would make 92075 too large. On the other hand 2456 is about 
a S displacement on u. Provisionally, therefore, tlie false link is located between 29358 
and 31815. The evidence for this allocation is not strong, but it is strengthened 
somewhat from the formulae. These show (No. 41) that the two e links introduced 
after S x (3) are now cut out by the others, pointing to their being parallel sequences. 
Further the set of modified p links stretching from 30806 produce in the end a change 
— 2p + 4jp ( — A) — 2p ( — 2A) or 2(6 —c) in which all modification has disappeared. 
Nos. 41, 42, and 43 afford an example of series inequality. The odd links attached as 
tags to the lines here considered fall naturally into the formulae. Those given for 
Nos. 46 and 49 depend directly on the formulae for the lines to which they are attached. 
They can, however, take the simpler alternative forms given if displacements are 
allowed in the other terms. The line 29803 (No. 35) is 3777'54 ahead of S 2 (4), so 
that it might possibly be the commencing line of a S (4) linkage, in analogy with all 
the other lines. But the line falls in so naturally in its present position that the 
connection with S (4) is possibly accidental (but see below under S (4, 5)). From 
33179 (No. 37) a side chain starts which apparently leads into the P linkage. As 
will be seen below when the P linkages are considered, the links up to 33179 seem 
good. 33179 would seem a good S (3) line and possibly one of the p links near it may 
be spurious, viz., 96P23 or 960'83, or again 2456'66. The difficulty must at present be 
left open. 
AgS (4). S x (4) = 25106'89, S 2 (4) = 26025'60. 
The only apparent link from these is that referred to in the foregoing, viz., 3777 54 
from S 2 (4). S 2 (4) is not a good observation (possible error = 13'5). If it be corrected 
from S, (4), which is much better ('9) by adding 920'44, the link becomes 377 5*81, 
which is e( — 2<5) — *31, and '31 gives d\ — 03. It is thus so close to the usual link 
which starts from the series lines as to make it very probable that it is a real link. 
If so, other lines from those allocated above to S (3) will probably be linked up, and 
another spurious link will exist amongst the S (3) set. 
From Si (5) a link 377676, e(-2d) + '58 goes to 30722, which occurs also in the 
S (3) linkage next to that related to S 2 (4) to which it is connected by a link 919'58. 
Now S x (5) -So (4) is 920'36 or an exact b link, the exactness of which, owing to the 
uncertainties of the measurements, must be pure chance. If S 2 be corrected as abo\ e, 
the difference would be 918'63, still within limits of S 1 (5). There is then foimed a 
mesh :—- 
So (4) 26025 3777-54 29803 
920-36 919-58 
(?) S; (5) 
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VOL. OCXVII.—A. 
3776'76 
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30722 
