562 Prof. J. W. Nicholson on the High-frequency 



X-ray Sjiectra. 



The considerations already given may evidently be applied 

 in a general way to rings of electrons which are not coplanar, 

 and we may conclude, — a conclusion supported by a further 

 analysis not given in this paper, — that any such rings,, 

 preserving equality of angular momentum of all electrons, 

 must as a rule be of the same radius. 



Let us assume, in the preliminary consideration of Moseley's- 

 results, referred to in the introductory paragraph, that the 

 X-ray spectra come from a ring of electrons not greatly 

 disturbed by other rings, and treat this ring from the point 

 of view of Bohr's theory, for Moseley, in applying this theory, 

 has used an erroneous formula, to which the theory does not 

 naturally lead. 



If everv electron in the ring has an angular momentum 

 T/i/277, where r is a whole number, we have, in the usual 

 notation, if o> and a are the angular velocitv and radius o£ 

 the ring 



2 / 1 \ 



&r= — A N — 7-S»|, ina 2 (D = T]tl27r. 

 ma \ 4 / 



The total kinetic energy of the electrons is 



TT T J- 9 9 



\\ = -mna-co~, 



and W is the energy which is radiated in the passage of the 

 ring from a state of infinite dispersion into its present 

 configuration. We find 



w 2ttW / n 1^\ 2 



In passing between two stationary states, the frequency 

 emitted is 



where 2irme^\l^ is the constant which agrees so closely with 

 the universal constant of spectra. 



The formula used by Moseley in his interpretation is, on the 

 other hand, 



-O'-Wfe-a 



2ir 2 me 

 v 



and omits the factor n. This has a vital effect on the con- 

 clusions which he has drawn. For he takes Ti=l, t 2 = 2 as 



