6 L. VEGARD. M.-N. Kl. 



When the momentum is maintained the expulsion of an electron is 

 accompanied with a sudden change of energy of all the ring systems 

 outside the broken one. As a matter of fact the energy of such a ring 

 is diminished and with the amount, 



This energy might either disappear in the form af radiation or it 

 might be spent on the escaping electron on its way out of the atom. 



The Frequency Formula. 



§ 3. 



The general expression for the frequency on the assumption of pre- 

 servation of energy was given in ny previous paper, and we easily see 

 that Kossel's relations are fulfilled. 



On the second assumption of preservation of momentum the matter 

 is not quite so simple. 



Let the ring-systems — beginning from the nucleus — be indicated 



by the indices; I, 2, 3 Let the broken ring have an index i and 



the ring from which recombination takes place be /r — The effective 

 nucleus charge of any ring i is (N — p.). where: 



Now originally I supposed that it vas only the energies of the rings 

 q. and q between which recombination took place, which were engaged 

 in the production of an A'-ray line. On this assumption we get for the 

 frequency : 



Applying this formula to the lines A'^. A'^^, L„, we find: 



ß a a 



If Kossel's relation (i| should be fulfilled the expression on the right 

 should be approximately equal to Zero; but as a matter of fact it is 

 equal to a positive quantity which nia}- assume quite considerable values. 

 This disagreement between theor}' and observation made me prefer the 

 assumption of preservation of energy. 



