386 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
a map Y is given starting from 18069 which is 599'41 behind 18668 in An X. i., and 
is also attached to a typical v link. No formulae, however, from this map have been 
discussed. 
In the map X. i. appears a congery of meshes, two of which seem to afford some 
support for the suggestion as to the connection between 600 and 625. The meshes in 
question may be represented as follows :— 
22253 
11342-36 
33595 
1493477 
14935-17 
37188 
11342-76 
48530 
-14914-64 
-14911-43 
22273 
11345-79 
33619 
The value 14911 would never have have been admitted were it not for the evidence 
of the numerous u, v meshes in this region. Their values may be explained as 
follows. The line 33595 depends on the d 12 (i.e., the X 12 ) sequence. The line 33619 
is 2374 greater, and this is the value of a displacement on the d 12 term. If d x 
remains unchanged, and the D 12 , D 21 [i.e., the lines depending on d 12 ) are thus 
displaced, the satellite separation d l2 —d n becomes 2374 less, i.e., about 601. In this 
case the 14911 are not modified links, but are normal v links with a simultaneous 
displacement on the d 12 or VD 2 . The F type separation of 600 is produced by the 
new d 12 and the unchanged d n . 
A very common difference found in the Au spectrum is 1000. Where it enters an 
arrow is attached to the number representing the line, to indicate its existence. If 
D (2) be the first diffuse line, VD U (2) = D ( oo) — D n (2) = 12340 = Fj ( o°), the limit 
of one of the F series. It is noticeable that F x ( — A) — F x = 1000‘4. The 1000 is 
therefore a link based on the diffuse sequences, the consideration of which has been 
excluded from the present paper. There are also a very large number of separations 
equal to that of the D (2) satellites, viz., 82. 
It will be instructive to write down the formulae for short regions of the X maps, but 
no useful purpose would be served by attempting to do this throughout. Starting 
from the X 21 line 15923 in AuX. ii., we find the long series of d links already referred to 
(No. 4 on p. 366). It. is noticeable that the last three sum to 16905'87 = 3x5635'29or 
three exact d links. At 38457 the chain passes to AuX. iii., and 38457 is a starting 
point for the very remarkable congeries of meshes already referred to (fig. c, Plate 6). 
The formulae for only one of these is written down, but all the e links cluster round 
17257, and it looks as if they are sums of single displaced p links. The link 4612'68 
from 21201 (No. 8) has only been admitted on account of the mesh. It also comes 
naturally from the formula for 21201 by annulling displacements, viz., in the 3rd and 
4th columns of the formulae tables from — (2<^), 3— ( — <^) to —2, — 4 + ( — <^). At 38457 
also a chain links on to D 21 (2) by a b link = 381378. This link, however, is one of three 
