384 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
from this, but with increasing doubt as to spurious links. In fact the long succession 
of links in series in the lower part would seem to point to connection with a diffuse 
linkage. The presence of such a spurious link is shown directly also by the appearance 
of the line 27783 in two places, cols, d and g indicating a cycle. 
AuP. Pj (1) = 41172-94, P 2 (l) = 37357*62, P ( oo) = 70638*12. The linkage as 
shown in the map is much smaller than in the case of Ag. This is doubtless due to the 
fact that in both cases the chains start with the long series of e links. In Ag several 
of these in succession lead up to the ultra-violet region from which chains run back 
again towards longer wave-lengths. In the case of Au, however, two of these 
long e links carry right across the observed region, and if the Au linkage is analogous 
to that of Ag, the points from which linkages would run back again are beyond the 
observed. Possibly some may exist amongst Handke’s ultra-violet, but the observed 
possible errors in n are so excessive, due to the very large multiple of dX as well as to 
large possible values of dX, that it is best to neglect them. There are several links in 
the neighbourhood of 17260, where e ( — ci : ) = 17264'03, and of 17258. It is possible 
these may be e links modified in some way not yet known. In the lists, however, 
the attempt has been made to explain all these modifications by displacements on the 
links in general. 
Starting from P 2 (l), if the first link is e without any modification, there must be 
an error d\ = 7 in the line 20100 which is hardly credible. If, however, p ( A) and 
•p { — A) in the formula have displacements — S 1} the error in this line is reduced to 
dX = —‘25. The line 60270 is from Handke. As the dn — 36 d\, it is just possible 
that the link from it to the previous line might be a normal e or e (— 7 : ) link. The 
link 11332‘4 from 54617 is about 10 in deficit and may be spurious, and in fact it 
leads on into the X linkage. It is, however, rt(^) + '62, but this and those beyond 
have been excluded from the list. In support of this further evidence is available 
from the consideration of the D 2 linkage below. A mesh with clear e ( —^) links is 
based on P x (l) and P 2 (l). The formulae seem to run naturally down to 18432, which 
as in several cases ends the chain by annulling all the displacements. From 34669 a 
chain leads to the AuX map. It would seem impossible at present to determine 
where the spurious link comes. It may be noted that whilst 34669 contains 
— e + e ( — c\) there are lines on either side linked by +e and — e ( — <^). 
The curious double mesh attached to 40305 contains very abnormal links, but with 
the calculated error —'8 which the formula gives to 40305, the links from it form two 
pairs of parallel inequalities, viz., 11345'92 and 14933*8, which deviate equally in 
opposite directions from their normal values. The lines are probably really connected. 
The D Linkages. In [III] the lines, allotted to D (2) are D n (2) = 17125, 
D 21 (2) = 20858 with the satellite too faint to be observed, but giving a satellite 
separation of 82*11. Linkages start from both these lines. In addition there are the 
three lines of a D type corresponding to similar ones in Cu and Ag already referred 
to (p. 372). 
