DE. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
41 
(a) of the denominators which give the doublet separations. Here, liowever, t)-iplets 
enter and two constants Aj and Ag appear. It is found tliat the Zn, Cd, Ilg grouj) 
follows the same rule if W is taken to be Aa, wliicli is rOughly one-half of Aj, hut, as 
in the case of Cs, a modification is recjiiired for the liigh separations of Hg. Using 
the numbers given in Table I., it will be found that the following forms for the 
denominators hold :—■ 
Zn . . . m+l-W(l-m-')-h-290534(l--21558m-'), 
Cd . . . m-M-W(l-w-')-U359854 (l--21537w-'), 
Eu . . . m-M-W(l-?>r')+-3U993()(l--2124G?n-'),* 
Hg. . . m+l-W/4 -h'317077 (1--21534^1-1). 
The numbers in hi’ackets after each formula give respectively the possible limits of 
variatioii of the k. It is clear that, as in the alkalies, k can easily he the same for all. 
In Mg and the Ca sub-group we have the complication of the additional terms in 
or of the modified form of the sexpience itself with only. In the first case 
/3, as we have seen, is a multiple of A^,. The constant ratio k does not enter now 
unless we nse f3 in place of Ag, in which case ther-e results 
Mg. . 
. 777 + 1 - /3( 1 -777-i) +-382402 (I-- 21533777 - 1 ) +/8777--. 
/3 = 
20As 
Ca . 
. 777 + 1 - /3(I-777-i )+-574797 (l--215727r7-i)+/3777-k 
14As 
S . . 
. 777+ 1 -2/3(1 -777-1) +-070150 (1--21404777-1) +/ 3777 - 11 . 
/3- 
3 As 
Ba . 
1 
The modified form does not so naturally fall into line. It is, of course, only a 
matter of calculation to put in a term such that the ratio of a//x left over 
is the same constant as in the other cases. If we confine ourselves to multiples of As 
or of A = Ai-f As = 3 A 2 roughly, and use multiples of these to give aj/j. as nearly as 
possible constant, we get the following results :— 
Mg. . . r/i+l-i5A (l-m-')+'399010 (I--21G247>?-'), 
wi+l-45As (I-7 u-')+-398GU5(1-'215457^-0, 
Ca . . . 77i-fl— 9A (l -I- 4)09908 (l—'2 1 5 8 5777“^), 
7H+l-27As(l-7i7-') +-G09413 (1--215227 >d'), 
Sr . . . 7U + 1- 3A (1-777-1) +-092393 (l--21G027n^'), 
777+1- 9As(1-W7-i) + -G90053 (1--2133G777-1), 
Ba . . . 777+1- 2A (I- 777 - 1 )+ -77574G (1--21584777-1), 
777 + 1 - 7As (1- 777 - 1 ) +-770744 (1--21085777-1). 
* Might quite possibly be '215, see Appendix 1. [also note at end]. 
VOL. ccxri.-A. 
Cr 
