DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
35 
logarithms of these modified atomic volumes and of the Ihrdts of the S series he 
plotted, then, with the exception of Zn and In, the corresponding points lie roughly 
on a straight line. 
The p-sequence. —In determining the formulm constants for the Sharp series, it 
immediately becomes evident that they are based on the P-sequence, viz., that which 
in the alkalies give the Principal series. It is impossible to get constants based on 
the S-sequence to reproduce the lines within considerable multiples of the possible 
errors. Not only does the P-sequence do so, but it will be found in correspondence 
that the Principal series are formed on the S-sequence, viz., that which in the alkalies 
gives the Sharp series. Confirmatory evidence is also afforded from the facts that 
the relationships between the constants are of a similar kind to those found in the 
alkalies and that the limit of the Principal series (S-sequence) is the same as the 
variable part of the first line of the Sharp whilst that of the Sharp is not rigorously 
the same as the variable part of the first line of the Principal. In other words, VP 
and VS denoting sequences, the limit of the Principal series is VP(l), whilst that for 
the Sharp series deviates considerably from VS (l). This fact renders the notation of 
the sequences introduced in Part I. confusing. The confusion may, however, to some 
extent be avoided if small letters are used to denote sequences and large letters the 
lines or series. Thus, in these elements VP {m) = s {ni) and VS {m) — p) {m). 
The features of the p-sequence, as developed in Part I., are (l) ju = I+/where/is 
a fraction (2) if the denominator be written in the form 1—W {l—m~^) + iu + a7n~^, 
where W is the atomic weight term, a. is negative, ajm is a constant (’215), /x is 
proportional to the atomic volume of the element, andp (l) = S(co). The s-sequence 
has (l) /x =/ a negative, /u about '5 less than the corresponding value for the 
principal and s (l) is not P ( go) but very nearly so, being always slightly less. 
In the alkalies it was found necessary, if Rydbeeg’s relations between the limits of 
the S and P series were to be valid, that a very small term in had to be applied, 
although it was unnecessary, so far as reproducing the lines within observational 
error was concerned. In the present case, also, no term in is required for the 
Zn or T1 groups. In the alkaline earths themselves such a term is required, 
/3, however, being a small fraction of a. 
The formulse constants determined for the various elements are given in Table I. 
They are determined, as a rule, by taking the measures of the first three lines as 
having no observational errors, the limits of variation of constants due to these 
possible observational errors Joeing given in brackets, as in Part I. It is found, 
however, that in the case of Zn, Cd, Hg, Sr it is necessary to allow for these errors if 
the subsequent lines are to come within observational limits. In these cases the 
constants have been slightly modified within permissible limits so as to bring all 
within, and the numbers attached to the constants in the tables are limits allowable 
on these modified constants. There is some uncertainty in the case of Ba. The 
series is ill defined. No lines were assigned by Kayser and Runge to the S series— 
F 2 
