L. VEGARD M.-N. Kl. 



I. 



On the Recombination between 'Primaries'. 



In order to deduce the frequency formula on the assumption of 

 recombination between primary systems we must introduce some addi- 

 tional 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 ß-rsLys) 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 especialh' those outside 

 the broken system will have their motion changed. 



The change taking place must be a very definite one if we shall 

 get homogeneous radiation. 



We have mainlv two possibilities to consider. 



i) The motion is changed in such a way that the foigular momen- 

 tum 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 systems remains unchanged. 



A priori we cannot tell which of these hypotheses is the right one. 



As the preservation 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, I gave up 

 the assumption of preservation of momentum because I found it do 

 disagree by far too much with Kossel's empirical relation : 



V — V ^ ^^ V (approximatel)-) . . . (ij 



Ko Kft Lfi 



The frequencies were therefore calculated on the assumption of 

 preservation of energy, which is in accordance with the relation (i). 



To fix the idea, let us recall to memory the way in which the 

 frequenc)- formulæ are deduced. 



Let the element considered have an atomic number X. Let us con- 

 sider a certain ring-system with quant-numper )i consisting of q elec- 

 trons. Let the total number of electrons between the nucleus and the 

 ring be ^;, when the atom is in its normal state. 



