50 
DR. W. M. HICKS; A CRITICAL STUDY OF SPECTRAL SERIES. 
to complete the series. It is, however, difficult to be certain, as to any identification 
proposed, as there is a maze of lines in this portion of the spectrum. Below I propose 
certain changes in his identification, for reasons which will he given. 
If we now discuss the series for Zn, Cd, Al, and T1 we find that the limits of the 
series, as found from the lines as a whole, agree very closely with the values of VS (l), 
hut the calculated values of VP (1) deviate very consideralily from the values of 
S (oo). Tills is in agreement with the deduction already drawn that the S series 
depend on what was called the p-sequence in Part I., and the P series on the 
.s-sequence. When, however, we attempt to find the constants ^ and a in the usual 
way we get formuhe which reproduce the lines witli fair accuracy in the case of Zn 
only. It is possible to modify the form so as to get good agreement within 
observational errors, but it seems preferable to proceed in another way and attempt 
to discover the connection between the Pi, P^, and Pg terms and the relationship 
which undoiilitedly exists betvv^een the S and P series by direct compai'lson of 
their values. Such relationship will most probably show itself between the values 
of corresponding denominators. The values obtained, on the supposition of constant 
N, are given below. For comparative study the corresponding numbers are given for 
the alkalies. 
As in previous cases figures in brackets after a number give the greatest possible 
variations in the last digits of the number, so far as the variation depends on errors 
of observations. Other systematic variations may enter by the possilile changes in 
the limits P ('^) or S ( oo). With the exception of the alkalies the values for S are 
calculated from the formulm (see Table I.). Then VS(l) (or ^^(l)) is taken to be 
P(oo)j and using this as the limit the denominators for the P lines are calculated 
direct from their observed values. This metliod, therefore, assumes the validity of 
the relation P('») =p(l) = VS(l). In the cases in question, as we have seen, this 
has always been found to be the case. In the case of the alkalies, however, one of 
the relations indicated does not liold unless we use tlie limit found directly from the 
series (see Table II., Part L), and that accordingly has been done. Since, however, 
the top lines in the alkalies are so ill determined the value of P ( oo ) is used for 
VS(1). OsS(2 ) is so iincertain that the value from the foi'inula is also inserted. 
IIbS(2) is also from the formula, as Bergmann’s observed vahie is very considerably 
in erro]'. Tlie difference between corresponding numbers are entered between 
them. 
Arranged in this way a number of facts emerge at once. Begarding Zn, Cd, Al, 
and Tl, they all with one or two exceptions clearly indicate a general law that from 
m — 2 onwards the denominators for the different triplets or doublets in each element 
differ by the same amount, and that this amount is somewhere about 7 to ‘8 times 
tlie corresponding difference for m = 1, which gives the values of Aj, Ag, or the 
atomic weight terms. We may feel justified, tlierefore, in using this as a test to 
apply to Paschen’s allocation of the upper lines of the P series for Hg. The values 
