DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
365 
(c) This example involves the c, d links wliose 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. 
20S^S‘^7ee-2Q- 
2 / - yr2Z428 
■ 224-^2 
2/64-2 
,66- 
10 8J/ — fs&ss - 2/d6o‘^a$-5s—^2241/3 - B2S-8^- 
.[2/^/2]' 
-2//4f 
•‘t®' 
-252J4 
It may be noted that in this fragment of a linkage all the links involved are 
p-links. A similar preponderance of these in linkages connected with D lines is a 
marked feature also in Ag and An [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 (oc 
e.g., in the case of 19928 considered below. Further support to (3) is given l)y the 
F separations (p. 370). 
The Satellites. —Any allocation of satellites which may he regarded as fiiinly 
established is a matter of some difficulty on account of the large number of p.j 
separations which enter indirectly as links, and the })revalence of sets depending on 
displaced limits and displaced d secj[uences. The lines in the list for 771 — 1 ai'e placed 
there provisionally and for special discussion, although other lines certainly belong to 
the system. Consequently, the denotation Di„ is to be regarded simply as a means 
of referring to the different sets considered in this communication oidy, the 7 i giving 
the ordinal position starting from 20976 as Dj,. 
The criteria that these lines should be possible D satellites with the same are 
that the differences of their mantissm from that of should be multiples of the oun. 
Should any belong to another group with limit {yS^) D(co) their mantissm will be 
modified, but the qualification test will still hold with reference to the difference 
between their mantissag thus modified and that of the original D^, for they must all 
belong to d sequents and so be oun multiples. Nor will the test be affected l)y the 
