SPECTRA OF OTHER ELEMENTS Series Formulae.—Evidence that series more or less resembling those of hydrogen occur in the spectra of other elements came from the pioneer investigations of J. R. Rydberg, H. Kayser and C. Runge. The spectra of the alkali metals (lithium, sodium, po tassium, etc.) in particular can be almost completely analysed into series having the same general characteristics of convergence to limiting wave-numbers and continuous decrease of intensity, as the hydrogen series. (See Plate II., Nos. 8, 9, 2b.) A similar structure has been found in many other spectra also. None of these series, however (with one or two important exceptions which will be de scribed later) can be represented by formulae quite so simple or so exact as those for hydrogen, although very close approximations can often be made. Rydberg's formula v.= A — R/ (m+ (where A is the limit of the series ; R—the "Rydberg constant"— has approximately the same value as for hydrogen; in takes suc cessive integral values ; and A is a fraction, constant for each series) is sufficiently accurate for descriptive purposes, and will be so employed here, but more exact representation is given by the inclusion of an additional constant (a) as in the formula of W. M. Hicks— v.= A Types of Series.—The series which were found intermingled in the various spectra were classified by Rydberg into types, characterised by the general appearance of the lines. Thus, in each of several spectra, a principal, a diffuse and a sharp series were found ; a fourth series, the fundamental, was isolated later. The significance of these names has now almost disappeared, although the names themselves are still sometimes used, and the initial letters P, D, S, F are in general use to distinguish the different types of terms, and occasionally the series themselves. Other types of terms, which have been recognized only in recent times, are represented by the letters, G, H, . . . in alphabetical order, with no corresponding names.
The various series occurring in a spectrum are not independent of one another. Thus the S and D series converge to the same limit, and the difference between this and the limit of the P series is equal to the wave-number of the first P line. In other words,
the first 'term of the P series is the common limit of the S and D series, and the first term of the S series is the limit of the P series. These reciprocal relations between the S and P series are known as the Rydberg-Schuster law. Again, the limit of the F series is the first term of the D series—a relation known as Runge's law. The four series are thus interconnected.
We may therefore express the various formulae, in the order in which they are now usually given, as follows :— cerned, but for other reasons a definite scheme has been generally adopted, which is given in the following table for multiplicities up to 8:— Here s, p, d, f, are the values ofµ for the respective series, and it has been assumed, for simplicity of representation, that the value of m yielding the limit of each series is unity. For brevity the formulae are mostly written :— It appears, therefore, that, as with hydrogen, the consideration of the spectrum may be simplified by the substitution of terms for lines, the wave-number of each line taking part in a series being given by the difference of two terms. Instead, however, of a single sequence, of terms, there are in general four sequences—S, P, D, F—and possibly more. As before, there is no fundamental reason why the particular differences of terms constituting the prominent series should be differentiated from other differences of terms. This was first realized by Ritz, whose well-known "combination principle" asserts that in addition to the series already described, a spectrum might contain lines represented by such expressions as m1S—m2P, —m2F, etc. Many such lines have been observed. There appears, however, to be a restriction on the possible combinations, which is ex pressed by what is called a selection rule. For the alkali spectra it may be stated as follows: If the sequences of terms be written in the order, S, P, D, F, G, H . . . , then a term of any sequence may combine only with a term of either of the neighbouring sequences. Thus, any S term may combine with any P term, but not with another S term or with any term of the other sequences. A P term, however, may combine with an S or a D term; and so on.