DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
373 
modification just considered. If only separations varying by one or two units from the 
calculated links are allowed, most of these difficulties, if not all, would disappear. In 
the maps in certain cases a suggested false link is placed in square brackets. The 
various cases are more definitely treated in the notes attached to each map as they 
occur. Another way in which the presence of spurious links is indicated is that of a 
complete cycle of links in which the links do not each cancel out with another of the 
same kind. Of true cycles, some examples have been given in Plate 6. 
Another very long one is found in the map AuX, ii. and is considered on p. 388. 
Meshes also form a very numerous class of such small cycles. Of false cycles a few 
examples may here be cited for illustration from the general discussion below— 
(l) In the AgP linkage there occurs the cycle 
32974 
2460-84 
35435 
2617-67 
2461-00 
30357 
37896 
3768-75 
34125 
3770-86 
This could only be a true linkage if s ( — A) + s — 2s (A) = 2 { p (— 3A) — p (A)} 
which cannot be. The numerical values happen to be nearly equal in the case of Ag 
only. The link 2617 is not good, 3770-86 is practically exact and the 2460 belong to 
the long series (l) on p. 366. It is probable, therefore, that 376875 or 2617 is the 
false link in this case, most probably 2617. 
(2) In AgS (3) there is the mesh 
29358 
92P42 1004-42 
28436 30362 
963-50 962-04 
29400, 
where apparently 2 c = b + d. This cannot hold exactly, but it must necessarily be 
approximately true for any metal, since by their constitution c must be near the mean 
of b and d. Clearly in this case 1004'42 is the difference 2c — b and is not a true 
link. 
(3) Another similar but longer cycle occurs in AgD(4), which may be written 
29084 + r; — d+v+u+u+e—v+c—u—u+c—e—v— b = 29084. 
In this case most of the links cancel and the set reduce to 2c —(b + d) as in the last 
case. The actual sequence can be followed on the map of AgD (4). 
