Dft. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
380 
parallel inequality correcting both the links attached to it. In this chain it is to be 
noted that the several u, v links are all normal with the exception of that between 
Nos. 2 and 7, which requires a displacement 2(5j on a d link. The X. iii. map contains 
a large number of symmetries showing meshes involving the 1000 and 14333 
separations, or the dfftuse links indicated.by arrows and broken lines—see, e.g., the 
neighbourhood of ( e . l) and (f 6). A very striking illustration of such symmetry is 
afforded by the system attached to 27758 (c. 7). It is represented in the following 
scheme:— 
28755 . . 
14941-33 
43697 
997-14 
1002-22 
27758 . . . 
14936-25 
42694 
31804 
14936-44 
17263-02 . . . 46020 
1002-30 
17259-63 
1002-53 
30082 
14936-21 
. . . 45018 
The agreement in the values of each separation is very close and would be wholly 
so if 28755 were about 5 larger. As the X. iii. map contains the D 12 linkage the term 
YD occurs in the formula for 27758 and the 1002 is due to a A displacement in this. 
We have in fact two parallel linkages depending on D ]2 (2) and D ]2 ( — A) respectively. 
A similar case is seen in the neighbourhood of X. iv. k. The close equality of the 
differences between 26842 and the next lines, viz., 46'46 and 46'49, is noticeable and 
has been already referred to. Now 46'46 is caused by a displacement +4(5 on YD n and 
46T9 by —4(5 on the same. As the YD enters in the formula as a negative quantity, 
the smaller wave-number would be due to YD n ( — 4(5) and the larger to YD n ( + 4(5). 
The maps bring out certain general peculiarities quite clearly. Amongst these may 
be mentioned :— 
(1) The majority of the strong lines are connected to the e link either directly or 
by an intermediary p link. More especially so in the case of Ag. 
(2) The curious frequency with which, in a mesh involving the e link, a u or v 
link is attached at one angle. In many cases we find u or v links attached 
to an e link as if the whole of a mesh has not been observed. 
(3) The fact that where a large number of links converge on a line, that line is 
in general of small intensity—suggesting that the number of configurations 
present emitting the frequency is small, because it is only slightly stable and 
splits up into others related to it by the link relation. 
(4) The large number of^> links of normal value entering in the D linkages. 
