PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 83 



of a new series e.g., not only is there the sharp series VP(l) VS, but there may 

 also he VP(2) VS. RITZ has given several examples of this. As the matter is 

 thus open the formula as determined on each supposition is entered in Table II. 



In the P and S series a is negative. It is positive in the D series, not only in the 

 alkalies, but in other typical D series ; in fact, so general is the rule, that if any 

 new series gives a positive it may be taken at least provisionally as a D series. 



(M). If we write down the values of p. of P + /M of D and of //, + for D, we find 

 the following : 



Na . . . 2'126987(1164) 1-004918 



K . . . l'987273 + (6592) -997538-(l7150) 



-(32938) +(103360) 



Rb . . . 1'987783(14827) '861570(27275) 



Cs . . . 1 -980930 ? -543920 ? 



The numbers for Na look abnormal. We shall see later that the D series here 

 belongs to a sequence of a new type, for which the notation F is proposed. It need 

 not, therefore, be here further considered. The values of fj. p + /J. lt for the others point 

 to a constant value, which suggests that fi p is of the form AB and fj. c/ of the form 

 A + B. Now we have seen that /J, P is of the form A B. If we calculate the values 

 of A + B we get the following values for K, Rb, Cs, using the mean value of />, 

 viz., '074560, 



700294, -620756, '536373. 



The first two agree with the values found for p., for K, and Rb well within the 

 limits of error. The third is obtained on the supposition that the atomic weight term 

 is W as for the others, and it is clearly too large. But in the P series we saw that 

 apparently the W term had fallen out. If this missing term be put in here, i.e., 2\V 

 deducted from unity in place of W, the value of /x comes out to '520205, well within 

 permissible limits of the fj. of D 21 or D 12 . The /x of D n (2) is '008168 greater than that 

 of D 12 (2) as calculated from the observed lines (see Table II ). Now '008109 is W. 

 Hence, with the satellite series of Cs, the D's are given by 



-r / 1 \ 



m+1 3W 1 66 forDii, 



\ ml 



m+l-4W(l--)-66 for D 18 or 1) 21 , 



\ 'Wl) 



_-w(i-L\- s b. 



the values for K and Rb being 



The cases of K and Rb, both for P and D, falling into analogous forms, while in 

 that of Cs both P and D show a difference, although depending on the same kinds of 



M 2 



