582 DR J. HALM ON 
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both cases. It is not the object of this communication to enter upon a discussion of — 
the constants, but merely to show in a number of typical cases the extraordinary 
accuracy of our formula. I shall therefore not discuss the other series of the Oxygen- 
bands, and reserve this particular investigation for another paper. One point, however, 
in connection with the second bands seems to require special mention. It is noticed 
that in these bands the index (m + «) of the first visible line is a comparatively high 
number. According to the formula other lines before the one which “apparently” 
forms the head or beginning should be possible, but these lines are in fact not present 
in the spectrum. Instances of such “missing” lines are by no means rare among the 
band-spectra. Bands with “hypothetical” heads have indeed already been pointed out 
by Professor THIELE in his investigation of the Hydrocarbon-band. It is interesting to’ 
find at least one similar occurrence also among the line-series. According to Professor 
Kayser the first observed double line of the 2nd Subsidiary Series of Potassium should 
be preceded by a strong pair at X = 6985, which, however, has not been observed. 
Professor Kayser remarks that this is the only case among all the line-series where 
computed lines seem to be actually missing. I am inclined to think that we have here 
a (so far) unique instance of a line-series with a hypothetical head. Perhaps the lines 
are not altogether absent, but are too faint to be noticed. It is quite a common 
feature in band-spectra that the intensity, instead of changing gradually from line to 
line, sometimes falls off abruptly. This abnormal phenomenon usually occurs in the 
tails, but there is no reason why it should not also be possible near the heads. We 
shall have to return to this interesting feature later on when we consider the struc- 
ture of the Cyanogen-band. 
Mr Lester shows that the measured wave-frequencies of the Oxygen-band can be 
represented by an equation 
v=v,—am—bm?. 
He lays particular stress on the existence of a term depending on the first power of m. 
Evidently his formula is a first approximation to the RypBERG-THIELE equation, which 
may be written : 
(m+ p)? Gy) 
a1 + Am + )) o 
b 6,2 : 
V-Vy= ah te) — g(t pw)? eS a 95 
4 4 
and can therefore be brought to Mr Lesrsr’s form if m be counted from the first 
observed line. Thus we find in the case of the second band (second series) of the 
B-group from the constants of the RypBeRG-THIELE equation : 
whereas Mr Lester has : 
v= 14526°27 — 5°86m —0°2611m?. 
The examples here given are in my opinion quite sufficient to demonstrate the appli- 
eability of the RypBerc-TuHre.e formula to both line- and band-spectra. The difference 
between these two types is seen to be solely due to the difference in the constants of our 
