DR. W. M. HICKS; A CRITICAL STUDY CF SPECTRAL SERIES. 
43 
constant ratio is at least suggestive. A similar arrangement does not hold for Tl, hut 
we have been led not to expect it in the highest at(unic weiglit of a group. If we 
define W as before, viz., 2W = A, we can write for the fornnd® 
A1 = 771+1-50W +'294286 (1 --21526^1-’), 
Ga = 77r+T-10W+'359895 (l-'2148377i-'), 
In =771+1- 2W + '325202(1-'2U78777-’), 
Tl = 777+1- W + '331405 (l-'21248777-'). 
Ga and In may give '21520 within observation limits. 
The foregoing results, combined with those previously (7btained for the alkalies, 
produce a strong conviction that the number '21520 is an essential constant—-possibly 
for all elements—-but at the same time raise the question of the cause why they do 
not follow precisely the forms shown by the alkalies, the Zn group, and to some extent 
by the alkaline earths. 
Atomic Volume Tei'm .—In the spectra of the alkalies it was found that when the 
^-sequence was thrown into the form considered above the fx was very nearly propor¬ 
tional to the atomic volume, and still more nearl}^ so if the denominators were written 
777 + '987...+ , &c. Since the atomic weight term disappears when m = 1 the same 
result should hold for the denominator of ^^(l), with the advantage that this can be 
determined much more precisely than /j.. The value of the atomic volume of an 
element as calculated from its atomic weight and density must have some degree of 
indefiniteness, depending as it does on the temperature and physical state of the 
substance when its density is measured. Nevertheless there must be some physical 
property peculiar to each element of which the atomic volume as usually determined 
is a rough measure, and it is this which would occur in the spectral formulse if the 
relation indicated in the alkalies is a reality. Probably the relation between this 
physical constant and the atomic volume would be exact if tlie latter were determined 
at absolute zero. Failing the possibility of doing this we might try to extrapolate 
downwards by using the coefficient of expansion determined at ordinary temperatures, 
or compare the substances in corresponding states, say at tlie melting-points. In this 
first survey, however, it is needless to attempt such refinement, and we shall confine 
ourselves to seeing what evidence there is that such relationships do enter, and try to 
get a rough idea of the way in which they do. 
It will be better to discuss the relationship on the basis of the denominator of 
rather than the former being less dependent on errors of observation. In Part I. 
the quantities in question were considered as being proportional to the atomic volume, 
but as a result of the discussion below it will be found best to consider them as 
proportional to twice the atomic volume. The constant of the ratio for the alkalies 
was not determined ; but the values of the denominators there given, combined with 
G 2 
