DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
347 
s(l) = 94120'27 + ^ = N/{l'079474 — 573^}^. From this the links, viz., 
u = s(l) —s(l) (Aj), V = s {l) ( —Ai) —s (l) can be calculated. The results are 
u = 1884-03 + 2-33(ij/i--02^, 
V = 1942-44 + 2-48c?ri--03^, 
with 
e = 3183-34 + 4-096 dri--006^. 
The occurrency curves for these are shown in Plate 2 (fig. l). It will be seen at 
once that the maximum occurrences appear with sharp peaks in close agreement with 
the calculated values. 
The calculated lines for m > 4 are outside the observation region, but their 
existence can be indicated by using the above links as sounders. At the same time, 
in order to give more confidence in the application of the method, the similar linkages 
are examined for the lines which are observed. It is, of course, understood that the 
existence of a single link is no conclusive evidence of the existence of the unseen 
line, as it may be a coincidence. The evidence is cumulative and is seen at a glance 
in the diagram in Plate 3 (fig. l). The actual data are given here. In the appli¬ 
cation of this the frequent link modification must be allowed for, as well as the effect 
of observation errors. Consequently separations deviating by not more than two 
or three units from the values determined above are admitted. As a fact, this will 
exclude a number of real link connections as well as include a certain number of 
pseudo ones. But by limiting the deviations to these small amounts the conclusions 
drawn will be more reliable. 
Sounding Data. 
S(l). 
(2) 37340 (1) 39799 1882-57 
1944-49 
(1) 39284 3184-49 Si (In) 38497 3185-23 S 2 
1882 * 11 
(3) 41166 (1) 39741 1940-62 
S3 
Here the u, v links form a series inequality in Si with 39284 and a corresponding parallel inequality 
with S 2 . The -e link with S 2 is probably spurious, since 38497 will later be shown to be Di 5 ( 2 ) (p. 371), 
and the link as shown is excessive. It is omitted in the diagram. No links are seen with S 3 ; 
S(2). 
(1) 21332 
1994-17 
(2) 23276 3183-57 Si 
(5) 24578 1881-95 
(4) 24062 
1940-68 
(2n) 26003 
1884-03 (1) 29130 (5) 31726 
1886-73 
3183-70 S 2 3183-38 (1) 30430 318311 (3) 33613 
1940-93 
(2) 35554 
Here is present a chain of e links in S 2 so frequent in Ag and Au [IV.]. Also, as in the case of m = 1 , 
are found the same modification effect of about 2 in the «, v links. It may be noted that in addition to 
