238 Dr. L. Vegard on the X-Ray Spectra 



General formulae for the calculation of the frequency were 

 given for both the possibilities mentioned (Equations 15 

 and 16, Paper I.), It should, however, be remembered 

 that either of these two assumptions needs some additional 

 hypothesis, if the frequency formula is to be derived without 

 ambiguity. 



It is my intention in this paper to give a more complete 

 discussion of the various possibilities with regard to the 

 process of recombination, and to draw some of the con- 

 sequences to which they lead. 



I. 



On the Recombination between " Primaries ." 



§ 2. In order to deduce the frequency formula on the 

 assumption of recombination between primary systems 

 we must introduce some additional hypothesis with regard 

 to the change of the electronic systems which accompanies 

 the expulsion of an electron from one of the rings. 



When an electron by some agency (X- or /3-rays) is 

 driven out from one of the rings the electrons left behind 

 in the atom will change their motion, and not only those 

 which belong to the broken ring-system, but also those 

 belonging to the other rings and especially those outside 

 the broken system, will have their motion changed. 



The change taking place must be a veiy definite one 

 if we are to get homogeneous radiation. 



We have mainly two possibilities to consider : — 



(1) The motion is changed in such a way that the angular 



momentum of each electron preserves its value 

 unaltered, or it remains the same as in the normal 

 state of: the atom. 



(2) The motion is changed in such a way that the energy 



of the unbroken electronic system remains un- 

 changed. 



A priori we cannot tell which of these hypotheses is the 

 right one. 



As the maintenance of a definite angular momentum of 

 the electron seems to be a fundamental property of the 

 atom, the first assumption might seem the more probable ; 

 still, in my previous paper, 1 gave up the assumption of 

 unchangeable momentum because I found it to disagree by 

 far too much with KossePs empirical relation : 



v K —v K = v^ (approximately). . . . (1) 



