578 
DR J. HALM ON 
we obtain the values (A —A,) shown in the third column of the following table : 
1 2 3 4 5 6 
Ist Triplet Series Diff 
Cyanogen-band. L—l, A-2, d of Oxygen Ons Con 
(1st Comp.). ee 
Ly = 3866°95 81°53 1634°70 6158-41 - 6158-41 0:00 
1, = 3857°82 72°40 80714 5330°84 5330°84 0:00 
Igo = 3846°79 61:37 445-31 4969:01 4968-94 — 0:07 
1,) = 3833'93 48°51 250°18 477388 477394 + 0:06 
Iz, = 3819°36 33°94 131°83 465553 465554 +0:01 
Igy = 3803°16 17°74 54:07 4577-77 457784 + 0:07 
Ly99 = 378542 0-00 | 0:00 4523°70 4523°70 ii 
Adding to each figure of column 3 the constant 4523°70 we find the values of 2 in 
column 4. The 5th column, on the other hand, contains the observed wave-lengths of 
the first triplet series (1st component) of Oxygen according to the measurements by 
RuncE and PascHEN (see p. 564). The very close agreement between 4 and 5 shows 
conclusively that the RypBERG-THIELE equation satisfies the conditions of both series, 
Instead of the Oxygen-series we might, of course, have selected any series of the 
group «=0. 
In my introductory remarks I have alluded to Professor THIELE’s investigation 
of the third band of the Carbon-spectrum (Astrophysical Journal, vol. viii. 
p. 1). I have mentioned that Professor TuiELe found himself obliged to reject 
the simple formula here used, although he had been the first to notice some of its 
remarkable properties. His contention, however, that the formula does not sufficiently | 
satisfy the observations, is not acceptable, as will be conclusively shown in the 
computations which follow. Indeed, if we study more closely the conditions under 
which Professor THIELE made use of the formula, we come to the conclusion that his 
negative result is due not so much to a deficiency in the equation employed, as to a 
particular extra demand imposed upon it. For Professor THIELE introduces an assump- 
tion which, though it may have some mathematical probability, has certainly so far no 
physical foundation. He assumes that all the series of the band should appear coupled 
in pairs, and that each pair should be represented by one and the same equation, the 
two branches being obtained by assigning to m either its positive or negative value. 
This hypothesis necessitates equations of great complexity, involving at least eight 
constants. It must appear difficult, if not altogether impracticable, to use cumbersome 
formulz such as those obtained by Professor THIELE as a basis for theoretical investi- 
gations, nor are they of use as purely empirical expressions of the law of the spectral 
structures. But this complexity disappears as soon as we abandon Mr THIELES 
assumption. If we consider by itself each of the many series which he has so success- 
fully unravelled by his masterly treatment of the Carbon-band here considered, we 
