DK. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 339 



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 1; A 2 , 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 S 2 (co) or p 2 (l) ; (2) displacements of A, on either side of P(oo) 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 



or 



u = s\-^sl v = -^sl-sl. 



These links themselves may also be subject to small displacements by having their 

 sources on, say, (xS,) S x ( co ) instead of S! ( CD ). 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 ev. 

 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 



