formula of Rrrz that the succession of the lines is irregular, is quite 
removed by the introduction of the negative frequencies and the 
continuity obtained through it. 
Further our plate of the Natrium system throws light on the so- 
called summational and differential series, discussed by MoGrNporrr '). 
We find two P-series in the spectrum of Na; viz. P, Pr and S, Pr. 
The corresponding terms of the two series show the constant diffe- 
rence of frequency S, P,, which also represents the frequency of 
the first term of the P series with S, asymptote. 
According to Mocrnporrr *) the series P, Pe is now a differential 
series of S, Lw and S, P,, or as we may briefly write: 
So Pc SP =P Pe 
Such a relation can also be easily shown between other trans- 
lation series e. g. 
7 Dao PPP ND 
Here it are the two D series: P, Dr and P, Dr, of which the 
corresponding terms show the constant difference in frequency which 
exists between their asymptotes, viz. P, P,, which is also the 2nd 
term of P, Pe; according to Mocrnporrr the 1* line of the diffe- 
rential series. As appears from the plate, however, (the observed 
lines are indicated by 0), this line has not yet been observed, though 
it (4 7510) lies in a region very well accessible to observation. So 
it will probably have a very slight intensity. That this line would 
give rise to a whole series of differential vibrations, seems, indeed, 
somewhat strange to me. From the asymptotes of one Translation 
group we can write all kinds of constant differences of frequency, 
for which a line is often to be found then. In this way we can 
indicate the members of one Translation group in all kinds of ways 
as summational and differential series. So we get simply here 
Rrrz’s “Kombinationsprinzip”’, in somewhat modified form, for which 
PascHEN *) has already given a scheme for the Potassium spectrum, 
according to which scheme Dunz*) has calculated the systems of 
series for different elements. These systems, however, share the 
drawback of Mogrnporrr’s system of being confusing and difficult 
to survey, which drawback is entirely removed by the introduction 
of the Translation series. 
*) Summational and differential vibrations in line spectra. Proc. Kon. Akad. 
v. Wet. Amsterdam. 25 November 1911 p. 470. 
2) Le. p. 474. 
35) Jahrbuch der Radioaktivität und Elektronik Bd 8 p. 174. 1911. 
dink ver th: 89, 
