372 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
has not been found possible to exhibit on the maps in such a way that they can be 
seen at a glance. There are clear indications that these are due in many cases to 
displacements of the known kind in one of the terms. In the maps the differences of 
the wave-numbers from the nearest lines before and after a given one are indicated. 
Although these are intended for a different purpose, they indicate such displacements 
by the frequent appearance of the same separations, and in many cases the same on 
both sides, e.#., in Ag, the mesh with one angle at 37233 (AgP i., j 7) is one striking 
example. Amongst such separations in Ag may be given as illustrations 52, 43, 37, 
28, 16, where 4<5 on p ( — A) is 52'16. 38 on p (— A) is 4278, 8 on S (A) is 3675, 2<5 on 
p{ — A) is 28‘52, 8 on p ( — 3 A) is 16. But also 42 is the double link, c — b, and may 
indicate an unobserved line. As corresponding examples from Au may be taken the 
chain from 18449 (AuS (3). e . 12). A very exact example of lines at equal distances 
on either side is given by 26842 (AuX iii., d 14). The adjacent lines differ from it 
by —4679* and 4679 on either side. Now a displacement of 2<h on VX 12 produces 
4674. They are therefore ordinary displacements ±2<h on either side of 26842. A 
complete discussion of the whole spectrum must take account of these possibilities. 
The present paper only deals with the establishment of the truth of the linkages 
effect. 
The majority of the linkages observed are represented in sixteen maps. This 
method is in fact the only wa}^ in which the general connection can be visualised and 
realised. They are based on the differences as found and consequently must contain 
a considerable number of chance coincidences, although for the reason given above 
(p. 363) the number will be less than that given by the probability formula. In the 
present state of our knowledge there is little to decide where they occur. In a few 
cases the existence of a coincidence may be evident and be traced. For example, the 
lines 15923, 19113, in the AuX linkage which differ by 319073, or apparently by a 
modified a link, really belong to a doublet of the D type, referred to in more detail 
later. They are respectively the D 21 and D n terms. The satellite D 12 is 19738, 
which gives the normal separation 3815‘54 with 15923. They are in inverse order—or 
their formula gives negative values. The satellite separation D 12 — D u = 62571 and 
as it chances 3815'54 — 62571 = 319073. Thus the apparent a link is not really so, 
it is a pure coincidence. It is further possible that links attached to these lines maj r 
reproduce other examples of this pseudo link. As a fact 15923 has a separation 
17243 to 33165'51 and 19113 a link e — 1725470 to 36367, which suggests a spurious 
link a = 3202'25 between 33165 and 36367. 
In many cases it is easy to see that a spurious link must occur somewhere in a 
certain region. For instance, if a linkage starting from one series line runs on into 
that of another by a certain sequence of links, one at least in that sequence must be a 
chance coincidence. There are several cases of this, but astonishingly few when 
regard is had to the enormous number of links which exist. One chief difficulty in 
settling the true sequence in a case like this is due to the existence of the link 
