A Critical Study of Spectral Series. Part III: The Atomic Weight Term and Its Import in the Constitution of Spectra

The doublet and triplet separations in the spectra of elements are, as has long been known, roughly proportional to the squares of their atomic weights, at least whenelements of the same group of the periodic table are compared. In the formulae which give the series lines these separations arise by certain terms being deducted from the denominator of the typical sequences. For instance, in the alkalies if the p -sequence be written N/D m 2, where D m = m +μ+α/ m the p -sequence for the second principal series has denominator D—Δ, and we get converging doublets; whereas the constant separations for the S and D series are formed by taking S1(∞) = D1(∞) = N/D12 and S2(∞) = D2(∞)= N/(D1—Δ)2. It is clear that the values of Δ for the various elements will also be roughly proportional to the squares of the atomic weights. For this reason it is convenient to refer to them as the atomic weight terms. We shall denote them by Δ in the case of doublets and Δ1 and Δ2 in the case of triplets, using v as before to denote the separations. Two questions naturally arise. On the one hand what is the real relation between them and the atomic weights, and on the other what relation have they to the constitution of the spectra themselves ? The present communication is an attempt to throw some light on both these problems.