DE. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
57 
observed also by him be taken for Pj, the separations become 1995, 963, and quite in 
order, being both about 7 times the first set. In the table above I liave, tlierefore, 
ventured to insert it in place of his selection, althougli it coincides with an undoubted 
D line. The denominator of this triplet is '5733 above the corresponding one for S. 
His next is ‘6510 above it, which is far out and cannot be made normal by any 
reasonable change in the limits. If the line 9694"5 be taken the difference becomes 
’5990, which is better but still too large. This is the only other available line 
observed in the neighbourhood, so that it is probable that the first line of the next 
triplet has not been observed. 
Summary. 
1 . The most important result of the discussion would seem to be tlie considerable 
weight of evidence, in addition to that afforded in Part I., that the series lines—at 
least the Principal and Sharp—depend in a very definite way on a certain physical 
quantity peculiar to each element which is approximately measured by what is 
generally understood as its atomic volume. The numerical evidence afforded from a 
study of the low melting-point elements of the first three groups of the Periodic 
Table is remarkably exact. The numerous lines of all these series are represented 
within limits of error, and as a rule with extreme closeness, by the formula adopted. 
The argument is based on the denominator of p(l), and this is determinable with 
great exactness ; in fact, any possible error in this due either to error of observation 
or error in the limit chosen for the series will exert practically no infiuence on the 
result."^ A change in N might do so to some extent. Any uncertainty is due to 
uncertainty in the values used for the atomic volume, which might amount to as 
much as 1 per cent., e.g., changing 2740 by 30. The high melting-point elements of 
Group II. do not show the law with such certainty, but there are clear indications of it. 
In these elements the type of formula has required a modification, and, in addition, 
the series are not well developed in the higher members Sr, Ba and Ba. Consequently 
the limits are not determined with such certainty as in the other cases. Nevertlieless 
Mg and Ca quite fall into line with the others, and even in Ba it is possible to give 
some indications of the value of the density of the solid metal. 
The fact that the terms depend on multiples of atomic volumes as ordinarily 
calculated may be interpreted in one of two ways. Either that the periods of the 
vibrating configurations do actually depend on multiples of the essential atomic 
volumes or that multiples do not enter here, but that the packing together of the 
configurations when they are aggregated into solid masses is closer or less close. 
E.g., compare Zn with factor 9 and Hg with factor 6. The period of Zn may depend 
* An increase of ^ in the limit of Zn would alter the ratio by (1 - '00022^), and ^ cannot be more than 
a few units. In the case of Ba only is 'q indeterminate to the extent of so much as 170, and for Ba the 
corresponding factor is (1 - '00013^), large enough to require a change in the multiple of v. 
VOL. CCXII.-A. I 
