374 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
The Linkages.* 
It is found that, starting from any link belonging to the ordinarily recognised 
series, a series of other lines can be linked up to them in succession. These linkages 
are exhibited in a diagrammatic form in the maps appended. In these the wave- 
numbers increase towards the right. They are arranged in vertical columns for easy 
reference, the small p links stretch from one column to the next, the s links from one 
to the second from it, and the long e link over three. In this way the distance gives 
a general idea of the magnitude, and as a rule each column will contain wave-numbers 
of the same order of magnitude, although not always, especially when the links run 
forward and backward several times. The links are represented by straight lines, 
with the actual observed separations placed over them. Intensities are indicated by 
small figures over and to the left of each wave-number. These maps contain all the 
links noted to be related. In addition certain more abnormal ones, which other 
evidence, such as meshes or other regularity, render it advisable to put in evidence, 
are also shown. Also in many cases abnormal links are shown when they end a chain. 
In this case their presence can lead to no errors in succeeding lines. From these 
maps lists (pp. 391-410) are formed of some of the lines expressed as sums of multiples 
of the p (a*A), 5 (xA) by considering them in succession with their links. These lists 
explain themselves. The first column is an ordinal number for reference. When a 
chain ends the wave-number is printed in italics. In that case the next line will 
start a new chain branching from a previous line. The numbers attached in brackets 
to its ordinal number refer either back to a previous line from which it starts or 
forwards to the branching off of a fresh chain. Figures in brackets after a wave- 
number give the small changes in it required to make the links correct, the last 
column of all headed d\ giving the corresponding O —C of wave-length. The 
numbers in heavy type between the wave-numbers give the exact observed separa¬ 
tions. The numbers in the columns under p (A), &c., give the multiples of these 
quantities on which the wave-number depends, and when the modified values with 
or xS enter, they are entered as ( x ). For instance under the column-for p ( — 2A), 
l + ( —l) would mean in Ag, p ( — 2A)+_p ( — — 2A). The columns headed s' or d' refer 
to the variable part of the series line from which the linkage starts. For example, in 
the S (3) linkage s' stands for VS (3). 
I. Silver. 
AgS(2). Sj (2) = 12082T3, S 2 (2) = 13003'42. Wave-lengths 8274T, 7688T 
observed by Randall! in the ultra-red. The separation is 92079 or '25 too large. 
If S 2 is taken as correct, s' = VS (2) = 18561 "61. Any single link attached to increase 
these values lands us in a region which has not been observed. If a linkage exists it 
is therefore necessary to try the sum of two links. It is found that there are two 
* This portion of the text should be read in combination with the respective maps (Plates 7 to 18) and 
formulae tables (pp. 391-410). 
f ‘Ann. d. Phys.,’ 33, p. 742 ; ‘ Astro. Jour.,’ XXXIV., p. 10. 
