352 DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



of examining the lines of the blue 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 731 5 '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 4'23d!i' 1 = 1'2, or d } about '30, d\ = '04 

 distributed between the two S lt 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 Sj (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'! 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 ( o) or s (l). From this the values 

 of the u, v links are found. The complete set are 



Links. Changes per Sj displacement. 

 u = 4133 i 18--049+2'19d>> 1 177, 



r = 4428'00--061+2-51di' 1 1'84, 



e = 7314-l-'0056 + 4-23di/ 1 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 S 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 Sj (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 d\ are given on the right, the observed or 

 line being regarded as the observed sounded line -I- the link as given above. The value 

 entered in the table of S lines above is, however, not the line as calculated from the 

 formula, but the most probable vahie 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. 



8(1). 



[-42153-39] -40375-49 -39561-50 



-e(<l)34836 -15, '07 -e(5)33061 -01, - -06 -(3)32248 - -07, - -14 



-2(4)27523 -13, --02 -2(1)25747 -00, - -15 -e-u(l) 28113 "04, - -07 



-e-w(3) 30700 -37, -11 -e-w(l) 28928 -00, - -11 -e + u(S) 36379 -11, -05 



-e-v(l) 27819 '00, - '12 



