DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
389 
in the sequent terms of F series has been referred to above. One good illustration of 
double displacements fully established is found in the KrS series (p. 349), in which the 
indications are shown for m = 1, 2, 3 . A knowledge of the laws governing displace¬ 
ments is much to be desired. Very little is known at present. 
Linkages. —-Arc spectra are distinguished, as a rule, by the presence of well-defined 
series, depending on single groups of P.S.D.F. type. In spark and vacuum tube 
spectra, however, these seem to be weakened, and a very large number of other lines 
appear which are related to one another by certain constant separations (links) to 
form congeries of linkages each connected to a series line. These links can be 
calculated when the values of A, or of A^, A2, are known. The evidence for these was 
given in [IV.]. There appear to be links of several types. Those already discussed 
are of two types : (l) separations between successive double displacements of A^ on 
either side of 82(00) or ^>2(1) ; ( 2 ) displacements of Aj on either side of P (00 ) or 
s(l). Of these, use is confined almost entirely in the present communication to one 
only of type (l) and both of type (2). They are 
e = (-2 Ai)p2(1)-(2Ai)p2(1), 
or 
= (- 3 Ai) Si(oo)_(Ai) Si(cx)), 
u = s(l)-(Ai) s(l), V = (-Ai) s(l)- 5 (l). 
These links themselves may also be subject to small displacements by having their 
sources on, say, (xS^) ( 00 ) instead of Sj ( 00 ). For the present purpose, however, 
no use can be made of these. 
In [IV.] the prevalence of these separations in a spectrum in excess of their 
occurrence from mere chance was exhibited in a series of curves with abscissae 
= separation and ordinates = number of occurrences within a given small amount 
on each side. Such occurrency curves are also given here for the e links and for the 
u, V of Kr in Plate 2. The e links seem to be a normal accompaniment to series lines 
(often displaced, however, when directly attached to those of low order). A further 
peculiarity of these linkages is the prevalence of the combination e±u, or e ± v. 
They are indicated by writing the letter denoting the link to the left of the line 
when deducted and to -the right when added. Thus, in the example below, 
44236 = e. 47419 , or 47419 = 44236 .e. 
Sounding. —In the following pages the unravelling of the complete series of 
linkages has not been touched upon, but the e, u, v links have been used for testing 
the existence of lines outside the observed region, a method we may call sounding. 
A link thus used may be referred to as a sounder. In this way it is possible to 
obtain evidence of the existence, or of the exact value, of a calculated line which 
lies beyond the region observed. It may even serve as evidence for the real existence 
of a line in the observed region too weak to have been observed, for it was shown 
