DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 365 



(c) This example involves the c, d links whose values are respectively 804'59, 

 823'29. It belongs to the D(l) system. The lines enclosed in [ ] are hypothetical 

 and introduced to indicate the transitions. The relations are indicated by the 

 accompanying schematic arrangement, starting with 20875 = Dj. 



20S7f ?68- 





It may be noted that in this fragment of a linkage all the links involved arc 

 >-links. A similar preponderance of these in linkages connected with D lines is a 

 marked feature also in Ag and Au [IV., p. 389]. 



The conclusion is to be drawn that there is very considerable evidence in favour 

 of (3) as explaining the origin of these modified separations. It does not, of course, 

 follow that the effect indicated in (l) does not exist amongst the lines of a spectrum. 

 "We know also that the effect indicated in (2) is existent, and we shall find clear 

 evidence"of it in the existence of lines depending on limits which are displaced S ( o ), 

 e.g., in the case of 19928 considered below. Further support to (3) is given by the 

 F separations (p. 370). 



The Satellites. Any allocation of satellites which may be regarded as firmly 

 established is a matter of some difficulty on account of the large number of i/,, v. 2 

 separations which enter indirectly as links, and the prevalence of sets depending on 

 displaced limits and displaced d sequences. The lines in the list for m = 1 are placed 

 there provisionally and for special discussion, although other lines certainly belong to 

 the system. Consequently, the denotation D lB is to be regarded simply as a means 

 of referring to the different sets considered in this communication only, the n giving 

 the ordinal position starting from 20976 as D n . 



The criteria that these lines should be possible D satellites with the same D n are 

 that the differences of their mantissas from that of D n should be multiples of the oun. 

 Should any belong to another group with limit (yS t ) D(o), their mantissae will be 

 modified, but the qualification test will still hold with reference to the difference 

 between their mantissae thus modified and that of the original D U) for they must all 

 belong to d sequents and so be oun multiples. Nor will the test be affected by the 



