54 
DE. W. M. HICKS; A CRITICAL STUDY OF SPECTRAL SERIES. 
of the denominators calculated for his lines, the first line being, of couise, taken to be 
also the first of the S series, are as follows:— 
P,3 ■ 
. 1-535163 ? 
3-764993 
4-775856 
5-780490 
6-782813 
30002 
4944 
18593 
13165 
10837 
P. . 
. 1-565165 2-734512 
3-769937 
4-794449 
5-793655 
6-793650 
87815 
9763 
84538 
96441 
96760 
P, . 
. 1-652980 ? 
3-860174 
4-878987 
5-890106 
6-890410 
The numbers clearly do not follow the law. It is possible, however, to select a set 
which do so, but oidy by supposing tliat the Pg lines from m = 4 and beyond do not 
occur. Tliey are given in the table above, where the agreement with the law is 
evident. Paschen also suggests another set for 7)i = 2, in which the separations are 
still more out of order, viz.: 
2734512 
13667 
2748179 
159052 
2-907231 
He supports tliis with a considerable list of combination terms, which, though 
striking, do not prove that the lines in question belong to the direct P series. In 
fact, there is evidence that some of tliese combinations are related to the D series. 
Further, I hope to show, in the next part, that ids P^ (2) here is a collateral of the 
singlet P series discovered by him and published in tlie same paper. A comparative 
list of the lines is given in Appendix II. 
A similar rule is seen to hold (as was indeed known from the results of Part I.) in 
the case of the alkalies, except that here the difference of the Pj and Pg is the same 
for all orders. In this group, it will be remembered, the principal series is based on 
the jp-sequence. 
Another law also appears in the relation of the Sharp series to the Principal, viz., 
that the denominators for the Sharp series of any element are found by deducting a 
constant value from the corresponding denominator of the Principal series, except 
that the difference is a greater one for the first term, they are roughly as follows :— 
Zn . . -5283,-5249; Cd . . ‘5263, -5224 ; A1 . . -4893,-4844 ; IT . . '5949, -5891 ; 
Na . . -4901; K-. . -4660; Pb . . ‘4856; Cs . . -4880; 
a similar arrangement also is shown by the suggested allocation in Hg, vi^., ‘6036, 
59, an additional evidence in its favour. The differences Ijetween P and S in the list 
do not appear to be rigorously constant after m = 2. This can be easily explained 
by very small changes in the limits P(oc.) or S(go). In fact, as has been seen 
already, Rydeebcis law does not appear to be quite rigorousl}^ exact. Paschen’s 
