DE. W. M. HICKS: A CEITICAL STUDY OF SPECTRAL SERIES. 
47 
dependence of the value required on the F-sequence of Al, whilst the corresponding 
value from T1 is very different, viz., '962661. For suppose tlie F-sequence takes tlie 
form m-1-group constant + A (l—m“^) (see Part I.). The A for Al and Tl are 
respectively '001754 and '134153, whilst m is always 2 for the first line of the 
F series. Hence the difference of the values of the denominators of the F sei'ies 
of Al and Tl is |('134153-'001754) = '06620, whilst the values found are 
'962611— '956239 = '006372, sufficiently close to show that the above explanation 
may be on the right lines. The fact that '014 and '0437 are in the ratio 1 : 3, he., of 
the valencies of the Groups I. and III., may be a coincidence, but should he borne in 
mind for future testing. The results for these two groups suggest a similar kind of 
group constant for Zn and the Mg sub-groups of II., but if so no F series have yet 
been observed to determine them. It is at least to the point to notice that such a 
term would raise the coefficients of the Zn set ('002715) more to an equality with the 
values ('002755) of the Al set. 
The evidence for the dependence of the p-sequence on the atomic volume is 
therefore strong from all the cases in combination. The actual value of the constant 
('002740) cannot be accurately determined as yet, because we have no knowledge of 
the actual value for any element of the physical quantity we denote by “ atomic 
volume”; but it is probably not far from '002740. The results of the foregoing 
discussion therefore point to they>-sequence being of the form sv, where a 
and h are constants for all elements, not very diflerent from '002740/(l —A:) and 
'21520 respectively; v is tlie essential atomic volume of the element (possibly sphere 
of activity), and s is a whole number. How s depends on the position of the element 
in its group is a problem which it is to be hoped further knowledge may solve. 
Putting /.’ = '21520 makes a approximately = '003490. 
Tlie values of s for the elements so far considered are as follows :— 
Na 2 
Mg 8 
Zn 9 
Al 8 
Ga 8 
K 2 
Ca 7 
Cd 8 
Sc ? 
In 6 
Pb 2 
Sr 6 
Eu 7 ? 
Y ? 
? 
Cs 2 
Ba ? 5 or 6 
Hg6 
La ? 
Tl 5 
Yb ? 
Pa ? 5 or 6 
The Term in W(l— 7 n“^).—This term does not affect the first line in the series, and 
its appearance would seem to indicate the possibility of some modification of the 
formula. In the course of some calculations connected with the Zn series, it was 
noticed that tlie lines could be reproduced when this term was absent provided the 
value of N was slightly altered for all terms beyond the first. It seemed worth while 
to test whether a similar connection held for other elements. The method adopted 
was to use the limit obtained by the eailier formulae, calculate the denominator in 
VS(l), throw it into the form (1 —'2152Um'^) (m = l), use this as the denominator 
