A.— MATHEMATICAL AND PHYSICAL SCIENCES. 21 



The azimuthal quantum number is the same for all terms of the 

 same sequence, and, in accordance with the previous empirical deductions, 

 considerations based upon Bohr's correspondence principle indicated 

 theoretical reasons for the restriction imposed on combinations of terms 

 of different types, namely, that terms of different types combine in 

 ordinary circumstances only when their h values differ by unity. 



When a series consists of doublets or triplets, ' inner ' quantum 

 numbers, usually represented by j, are introduced to distinguish the 

 individual components ; the accepted physical interpretation is that 

 jhj'Iiz represents the resultant angular momentum of the entire atom, and 

 fixes the orientation of the orbit of the series electron relative to the axis 

 of the remainder of the atom (the atom core). 



The theory also indicated an important relation between the ionisa- 

 tion potential of an element and the highest spectroscopic term, repre- 

 senting the normal state of the corresponding atom, which has been 

 verified experimentally for numerous elements.'^ Indeed, the ionisation 

 potentials of many elements can be determined with greater accuracy 

 from series data than by direct measurements. 



Other earlier successes of the quantum theory of spectra which should 

 not be passed over without mention are Sommerfeld's derivation of a 

 formula for the normal Zeeman effect in 1916, and the theoretical interpre- 

 tation of the Stark effect, which was given independently by Schwarzschild 

 and Epstein in the same year. The latter is rightly regarded as one of the 

 greatest triumphs of the quantum theory, since classical electrodynamics 

 had failed to give any explanation at all. 



Following the pioneer work of Schwarzschild, Lenz and Heurlinger, 

 the quantum theory has also been applied with conspicuous success to 

 the highly complex band spectra of molecules by several workers, notably 

 by Kratzer, Curtis, Jevous, and Midliken. The underlying idea is that 

 each component line of such a spectrum results from the simultaneous 

 occurrence of three distinct quantum transitions, involving the electronic 

 energy, the energy of nuclear vibration, and the energy of molecular 

 rotation. In general, the quantum number of each may change by integral 

 steps, and the complexity of the spectrum results from the great variety 

 of possible changes. Of special interest is the application of the theory 

 to the investigation of the isotopes of a given element." 



It will have been observed that while certain experimental data were 

 essential for the formulation of the quantum theory of spectra, the theory 

 has sometimes been in advance and has suggested new observations. I 

 shall next refer to new discoveries in experimental work which have given 

 a great impetus to theoretical investigations of a far-reaching character. 



Apart from the first two groups and the aluminium sub-group of the 

 periodic table, the spectra of the elements, with few exceptions, are 

 extremely complex and long defied analysis. It is true that certain 

 ' constant differences ' had been noted in many of these spectra by Kayser 

 and Runge, Paulson, and others, but these gave little knowledge of the 

 real structure of the spectra. It was not until 1922 that a key to the 



^ See Foote .and Mohler's Origin of Specira. uhap. 3 (1922). 



' MuUikeu, Phys. Rei\, vol. 2.5, p. 119 (192.5), and other papers. 



