A.— MATHEMATICAL AND PHYSICAL SCIENCES. 



23 



or more values according as the term is single or multiple ; r represents the 

 maximum muUiplicity of terms in the system to which the term belongs, 

 so that r= 1 for singlets, 2 for doublets, 3 for triplets, and so on. Correspond- 

 ing members of successive terms of the same sequence have the same values 

 of j. Values of r, k, j different from those mentioned are used in certain 

 theoretical discussions, but the above suffice for expressing the empirical 

 results obtained in the anah'sis of spectra. 



In practice the azimuthal quantum number is most conveniently indi- 

 cated by retaining the old designations S, P, D, F for the term 



sequences, and the value of r representing the multiplicity of the system 

 is now, by general agreement," written on the upper left of the term 

 symbol ; for example, T, represents a term of the triplet system for which 

 k—2 and_^=l. The values oi j corresponding to the various terms and 

 systems are collected in Table I. 



Table I. 



Inner Quantum Numbeks. 

 Odd Multiplicities. 



Even Multiplicities. 



There is theoretically no limit to the number of types of terms, and other 



types H are found for which k>b. In each system, however, 



the number of components in these additional types of terms never exceeds 

 the maximum indicated by the value of r for the system. 



It is to be noted that since differences of j values are alone embodied in 

 the combination rules for inner quantum numbers, there is a certain 

 arbitrariness in the values tabulated. With j'=0 for the singlet S term and 

 j=l for the doublet S term, however, all the other values follow from the 

 combinations indicated by observational data. 



The selection rules regulating the term combinations of most general 



occurrence are : 



For different types of terms : Ak- 



:1. 



>* Aslrophys. Journ., vol. 61, p. 66 (1925). 



