A.— MATHEMATICAL ANJJ PHYSICAL SCIENCES. 27 



In the actual analysis of a spectrum, the selection rules which have 

 been indicated for the combination of terms are supplemented in a very 

 practical way by Sommerfeld's ' intensity rule ' and to a less degree bj 

 Landc's ' interval rule.' 



The intensity rule was indicated in the first instance in connection witl 

 the simpler spectra, but has since been found to be of general application. 

 It is to the effect that lines for which the changes in j and Ic are in the 

 same direction are the strongest, while those for which the changes are of 

 opposite sign are the weakest. Thus, in the 'DT combination previously 

 shown, where ^ is 3 for D and 2 for P, the strongest line is DjP.„ while 

 the weakest is D.^P,, ; the same rule holds good for the combination 

 ■"D'^P'. In combinations of ordinary and anomalous (or ' primed ') 

 terms, however, such as ^D'^D' previously tabulated, k is the same for 

 both, and the strongest line is that resulting from the terms having the 

 largest (identical) j values (D'^DJ. The detailed relations may easily 

 be gathered from the examples of multiplet structures given above. 



The whole question of intensities in related groups of lines has recently 

 been placed on a quantitative basis through photometric measurements 

 initiated by Ornstein, Burger and Dorgelo at Utrecht. It results that the 

 intensities in such groups are in the ratio of integers, and it may accordingly 

 be concluded that intensities, like frequencies, are determined by quantum 

 considerations. In an application of the correspondence principle Sommer- 

 feld and Heisenberg had already investigated the probabilities of emission, 

 and formulae for computing the relative intensities in multiplets on this 

 basis have since been deduced.'** Russell has found excellent agreement 

 between calculated and observed values in an extensive comparison with 

 the approximate experimental data available. Further photometric 

 measurements to test the formulae are much to be desired. The constancy 

 or otherwise of the intensity relations in the same multiplet imder different 

 conditions of excitation is a question which also calls for the attention of 

 experimental workers. 



In general the separations between successive components of a multiple 

 term increase as the inner quantum number j increases. In systems of 

 odd multiplicity these separations are approximately proportional to the 

 larger values of ^ ; thus in a triplet P term with_^'=2, 1, 0, the separations 

 are in the ratio 2:1. In a group of terms of even multiplicity the separa- 

 tions are proportional to the means of the j values ; in a quartet P term, 

 for example, j'=3, 2, 1, and the separations are in the ratio 5:3; for a 

 sextet system the rule gives the ratio 7 : 5 for the P separations. The 

 interval rule in its present form, however, frequently breaks down, as is 

 emphasised especially by Hicks. '^ 



The characteristics of the various systems and types of terms which 

 are outlined above are sufficient for the classification of the lines of most 

 spectra in a form adapted for theoretical investigations. The quantum 

 numbers which have been assigned, however, may be considered entirely 



" Ornstein and Burger, Zeit. /. Phys., voL 31, p. 355 (1925). Kronig, Zeit. f. 

 Phys., vol. 31, p. 885 ; vol. 32, p. 261 (1925). Sommeifeld and Honl, Sitz. Preuss. 

 Akad. Wiss., vol. 9, p. 141 (1925). Russell, Proc. Nat. Acad. Wash., vol. 11, p. 31-t 

 (1925). 



i» Phil Mag., vol. 48, p. 1036 (1924). 



