352 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
of examining the lines of the bine spectrum for separations of this magnitude is 
shown in Plate 2 , fig. 2 . It is distinguished from those of elements hitherto discussed 
by showing one definite maximum alone at about 7315’3, although there are indica¬ 
tions of the appearance of another peak beyond 7317. The displaced e (^j) link shows 
a difference of 2’32, so that a second peak might be expected at 7317‘62. If the 
actual value is at 7315'3 it would require 4'23di/i = 1’2, or dv^ about ’30, d\ = '04 
distributed between the two 81 , 2 ( 2 ) lines. This is possible with +'02 on each line, 
but probably excessive for an error on one of them. Both values are tested as links 
below for the observed lines, and the results show that with the exception of Si (l) 
the value of e, calculated from the original is extraordinarily exact. For this 
reason, and because the exact position of the peak of the frequency curve depends 
on several disturbing conditions, the original value e = 7314‘1 will be used for 
sounding purposes on lines outside observed regions. Again the first line —42153 
and the limit 51025 gives 93178 as the value of P ( co) or s (l). From this the values 
of the u, V links are found. The complete set are 
Links. Changes per 81 displacement. 
M = 4133-18--049f+2-19di/i 177, 
V = 4428-00--061^-t2-51 di^i r84, 
e = 7314-l--0056 + 4-23 dri 2-32. 
The results obtained by sounding are shown at a glance in diagram Plate 3, 
which embraces orders up to m = 13. The cumulative weight of the evidence is 
overwhelming in support of the general application of this method. The existence 
of a series parallel to the normal 8 at a distance — e is proved, whilst the presence of 
other linked lines is rendered extremely probable by succession of similar linking in 
the same set, and in neighbouring orders. Compare, for instance, the triplets in 
m = 1, 3, 4, 7, 8 and the sets for m = 8 , 9, 10. 
Detailed Discussion. —In the following discussion the starting point for the con¬ 
sideration of each triplet set is—after m = 3—the value of 8 ^ (m) calculated from 
the series formula obtained above. The sounders are indicated to the left of each 
observed line and the values O —C in dX are given on the right, the observed or 0 
line being regarded as the observed sounded line + the link as given above. The value 
entered in the table of 8 lines above is, however, not the line as calcidated from the 
formula, but the most probable value as deduced from sounding. They are indicated 
below by asterisks. For the first three orders the values of dX obtained by using 
e = 7315'3 are placed to the right of those depending on e = 7314‘1. 
S(l). 
[- 42153-39] 
• 
-40375-49 
-39561-50 
-e(<l) 34836 
•15, 
•07 
-e(5) 33061 
•01, - 
•06 
-e(3) 32248 
I 
0 
1 
•14 
- 2e (4) 27523 
•13, 
- -02 
-2e(l) 25747 
•00, - 
•15 
-e-M(l) 28113 
•04, - 
•07 
-e-u (3) 30700 
•37, 
•11 
-e-u{]) 28928 
•00, - 
•11 
-e + u{3) 36379 
-e-v{l) 27819 
•11, 
•00, - 
•05 
•12 
