596 DR J. HALM ON 
known, Professor RypBERG had assumed that the factor = should be a constant for all 
1 
the line-series. Kayser, however, showed that this assumption had to be abandoned 
because it led to quite inadmissible discrepancies in the computed wave-lengths. In 
his own formula the value of ie ranges between 109625 for Li and 155562 for Al, and 
ah 
thus ‘‘ varies only within narrow limits for the various elements” (Handbuch, vol. ii. 
p. 516). At another place he remarks that ‘‘ probably in the true formula, which neither 
he nor RyppeRG had found, this factor may indeed be a constant.” Let us now see how 
far = changes if the RypBerG-THIELE formula is employed. In this comparison 
1 
between the various elements we must confine our attention to the subsidiary series, 
because so far principal series are only known for the elements of the group of alkalis 
and for Helium. Now we notice at once that the values of = are certainly not the 
1 
same for different spectra, since they range between 109575 for Li and 124020 for Cs. 
But the variations are doubtless much smaller than in Professor Kayssr’s formula. 
Since the a priori presumption may perhaps be admitted that the changes of ~ may 
1 
be connected with the position of the element in MENDELEJEF’s system, I have arranged 
the following table, which shows the constants in this order : 
I, II. Til. VI. 
} 
1. H: 109704 
2. In: LO9STS O: 110118 
3. Na: 110788 Mg: 112512 Al: 114590 S: 110567 
4. K: 116430 Ca: 111363 
5. Cu: 109726 Zn: 114265 Se: 109345 
6. Rb: 123572 Sr: 117292 
7. Ag: 109410 Cd: 114250 In: 117398 | 
8 Cs: 124020 
9, eae 
10. 
ie Hg: 112838 Tl: 114015 
The system is that published in vol. 71 of Nature, p. 66. In all cases where more 
than one subsidiary series is known, I have taken the arithmetical mean of the 
constants computed from each series. One interesting fact is at once revealed by the 
figures of this table, viz. that the changes are greatest in the first vertical column, the 
difference between the largest and smallest values of a being respectively, column I. ; 
a 
1 
14445; column I[].: 5929; column III.: 2808; column VI.: 1022. But another 
important feature is shown if we compare the horizontal rows 1, 2,3... 11. In the 
odd rows 3, 5,7 and 11 the numbers increase at first, reach a maximum, and then 
