A.— MATHEMATICAL AND PHYSICAL SCIENCES. 31 



It is not improbable that such systematic relations will be of con- 

 siderable assistance in the unravelling of the numerous complicated spectra 

 which remain to be investigated. 



The more recent results of the analysis of complex spectra have pro- 

 vided an ordered knowledge of a multitude of facts which have an 

 important bearing upon the development of the theory of spectra and the 

 arrangement of electrons in the outer parts of normal atoms. Theoretical 

 workers have not been slow to utilise the new data, and have, indeed, 

 frequently been able to forge ahead of experimental results. I shall not 

 attempt to discuss in detail these theoretical developments, more 

 especially as a critical discussion by Prof. J. H. Van Vleck has been 

 published very recently.'"'' It will suffice to refer briefly to the more 

 important steps in the interpretation of the empirically known spectra, as 

 supplementing the interpretation of the simpler spectra previously given 

 by Bohr. 



Among the principal problems immediately resulting from the analysis 

 of the more complex spectra are those indicated by the existence of 

 anomalous terms, the absence of extended sequences of terms in most of 

 the complex spectra, and the question of reconciling our ideas of the 

 arrangement of electrons in the outer parts of atoms with the structure 

 of the spectra — in particular with the occurrence as ground terms of such 

 types as 'F. 



These problems, however, are not independent of one another. It 

 will be recalled that the existence of sequences of terms involving the 

 Rydberg constant, in the spectra of elements whose atoms contain more 

 than one electron, was explained by Bohr on the assumption that the 

 spectra were generated by the transitions of a single electron between 

 orbits in an approximately Coulomb field arising from the unchanged 

 remainder of the atom. This, however, is not a process which, in the 

 absence of experimental evidence, would be expected to take place in all 

 atoms. Excitation of a complex atom might well be expected to involve 

 simultaneous disturbances of more than one electron, and the fact that 

 many spectra do not appear to exhibit Rydberg sequences naturally 

 leads to a consideration of the possibility that such simultaneous dis- 

 turbances actually take place. Again, the occurrence of unexpected 

 ground terms is a matter for surprise only when the ground term of a 

 spectrum is directly associated with the innermost orbit of the series 

 electron. If there is no uniquely characterised ' series electron,' there is 

 no reason to expect any particular type of term to be the highest, and the 

 problem of determining the ground term is merged into that of deducing 

 the spectroscopic terms (anomalous as well as regular) from the simul- 

 taneous movements of the disturbed electrons. The problems of complex 

 spectra thus resolve themselves into two — first, the distribution of the 

 electrons among the various possible types of orbit ; and, second, the 

 deduction of spectroscopic terms from a given distribution of electrons. 



In the consideration of the first problem we are not confined to the 

 evidence afforded by optical spectra. Other data towards this end are 



^* ' Quantum Principles and Line Spectra.' Bulletin No. 54, Nat. Ees. Council, 

 Washington {1926). 



