DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
307 
They are excerpted from the maps of some of the linkages given later. In these 
the dots represent wave-numbers of spectral lines, the small circle corresponds to the 
wave-number which is given in the notes to the figures, and the letters denote the 
links. We shall call a collocation of four lines connected in parallel—as for example 
the two sets in fig. (a )—a mesh. The number of these is very large and the Au 
spectrum contains some very complicated examples. 
In a very large number of cases a correction on a single line will render all the links 
attached to it correct. Thus, for instance, in the AgP (ii.) and (iii.) maps, the line 
42203 (see fig. I, Plate 6) differs from two preceding lines by 964'89, 2818'83 and from 
two succeeding lines by 959'62, 2456'44. If this be corrected by — 2'2 (d\ = '12) the 
differences become the links 962'69, 2616'G3, 96P82, 2458'64 —practically exact. 
Another example may be taken from the line 40353, which occurs in the first of the 
long sequences given on p. 366. In addition to the link 2457'26 there shown, it forms 
part of a mesh which may be written :— 
41891 
2461-66 
39430 
959-00 923-99 
38471 40353 
919-69 963-29 
39390 
If 39430 be 3'5 larger (cl A = — '23) the three links converging on it are made 
simultaneously exact, viz., 962'50, 920'49, 2458'41, the outstanding variations being 
only small fractions of possible observation errors. The u link also becomes the same 
as that just before 40353 in the long sequence to which the abnormal 2460 of the 
others have returned. In these two instances the first may be due either to an 
observation error or to another cause. The second, however, is too large to be explained 
as due to an error, but is probably due to the same cause that produces the double 
peaks in the frequency curves. That such causes exist has been already pointed out 
by the many long sequences of equal and abnormal links. As additional evidence 
the following examples out of a large number of similar ones may be taken. In the 
AuX linkage the following mesh occurs— 
41320 
3192-47 3197-75 
38127 44517 
3197-76 3192-46 
41325 
Here alterations of 2'6 ( d\ = — T5) on 41320 and — 2'6 on 41325 make the 
differences two exact-a links. But it would also make the two lines coincide, whilst 
