﻿Quantum^ Orbit Tlieory of Spectra. 347 



achievement. In the present note I wish to illustrate this 

 by drawing attention to certain assumptions as to actual 

 spectral data, which have been made and which do not 

 appear to be justified. The criticisms may not affect 

 essential points, but they would appear to require some 

 modification in the presentment of the tlieory. References 

 will be made to Sommerfeld' , s 'Atombau und Spektrallinien,' 

 2nd edition (1921). 



1. Sommerfeld (pp. 27G, 50b') takes a configuration of 

 a central nucleus, surrounded by a ring of equally-spaced 

 electrons, and at a considerable distance furl her out one 

 electron revolving in a quantized orbit. On fhe assumption 

 — here justified — that the ring can be treated as if the 

 w r hole charge of the electrons on it were continuously 

 distributed along it, he obtains as an approximation the 

 same form for a sequence function (or term) p as that' 

 suggested by Ritz, viz.* : 



He says that this is the actual true form, as already deter- 

 mined by observation. This is, however, by no means the 

 case. No form has yet been found which will fit in for all 

 series, and indeed the form N/(m + /u. + a/m) 2 is in general 

 rather superior to that of Ritz. It is to be noted that the 

 assumption made above leads to the same result as if the 

 force to the centre depended only on forces inversely as 

 even powers of the distance, and forces depending on odd 

 powers — say l/r' d — are excluded. It may also be noted in 

 passing that the theory so developed applies only to the 

 case of a single external electron and one internal ring, 

 that is, on the usually assumed configuration of eight- 

 electron rings, only to the spectra of the fluorine group, 

 or the ionized rare gases, or the doubly-ionized alkalies, etc. 

 By taking his E as (k—sj^e in place of ke, the formula 

 would meet the more general case. This modification, 

 however, would only slightly affect the order of magnitude 

 of the quantities /a, a. 



In the formula m=n-\-n', where n, n are respectively 

 azimuthal and radial quantum numbers, and //,, a arc 

 functions of n and not of n'. 



* As a result of successive approximation, « being small, -this means 

 for a complete approximation the form 



which, as is well known, is capable of reproducing- practically all cases 

 if /*, a, {3 . . . are all at disposal, and are not related necessarily to 

 one another, as here. 



