364 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
in a set was found to be very large and it is only possible to visualize their mutual 
connection by exhibiting them on a diagram. They appeared connected to one 
another by links of a few definite species. It will be convenient to refer to these sets 
as linkages, and a constant difference as a link. The vast majority of the spark lines 
are thus connected. As a rule the linkages are attached to—or related to—one of the 
ordinary series lines. It will be convenient for shortness of statement to denote the 
various links by definite letters. The following will be used—- 
p-p{A) = a, p(-2A)-p(-A) = c, 
p(-A)-p = b , p(-3A)-p(-2A) = d, 
p(~3A) — p (A) = e, 
s—s (A) — u, s( — A) — s = v. 
From the constitution of a linkage it is clear that if p — X denote the wave-number 
of the first—or any one—of the linkages, that of another can be expressed in the 
form— 
Wave-number = — X + ap (A) + yp + zp ( — A) + x'p { — 2A) + y l p ( — 3A) 
+ #S ( A ) + tjS -f £s (— A ) 
where x, y, z ... are integers. From the way in which the links appear as the difference 
of two terms the sum x + y+ ... must be odd. The existence of lines in which this sum 
is even is not excluded, as the method adopted would not isolate them and no attempt 
has been made to test for them. Tables for certain of these linkages are given below. 
We now proceed to give the evidence on which the above statements are made. 
The data for p, s, A, 8 are taken from Part III. of this series of papers.* They 
are 
Ag- 
An. 
8 
do 
II 
30644‘60 + # 
29465"18 + # 
= N/(l'891897) 2 
= N/(l"929298) 3 
.5 = P ( 00 ) 
61116*33 -4-^ 
70638‘12 + f 
= N/(l‘339600) 2 
- N/(l"246047) 2 
V 
920-435 —-0014£ 
3815-54 
A 
27786*57-1*29# 
113961-5-46# 
<? 
42P0087 —‘0196# 
1406-93 —-047# 
The values of the different links 
as calculated from 
these are as follows : — 
a 
880-77 
3195-14 
b 
920-44 
3815-54 
c 
962-54 
4607-77 
d 
1007-26 
5635-33 
e 
377P00 
1725378 
u 
2458-64 
11342-19 
V 
2616-61 
14937-24 
* 
‘ Phil. Trans.,’ A, vol. 
213. 
