and the Constitution of the Atom. 241 



Applying this formula to the lines K^, K a , L a , we find : 



(sl,-(al.-(fik =V(2 ' ?l - 1,?s) - V(2 ' !?1 ' ?j) - 



If KossePs relation (1) 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 may 

 assume quite considerable values. This disagreement between 

 theory and observation made me prefer the assumption of 

 conservation of energy. 



Later on I found that if we gave up the assumption that 

 it is only the energy-changes of qi and q k which are engaged 

 in the production of the X-ray line, the assumption of 

 conservation of angular momentum can be made to agree 

 with KosseFs relation. 



During recombination the rings between qi and q k will 

 undergo a change of energy, because the effective nucleus 

 charge is diminished by one elementary unit, and we might 

 assume that also the change of energy of the intermediate rings 

 enters into the energy quantum of radiation which is emitted 

 as the result of recombination . 



On this assumption the expression for the frequency takes 

 the form : 



ax 



k 

 = Y(ni,pi, qi)—V(n h pi, q { — 1) 



:jfc-l 



Y (&0 



+ X t Y ( n " P'> id-Vim, pt-h gi)] 



l=i+l 



+ Y(n*,p k , q k -l)-V{n h p k -l, q k ). 



Let us now suppose that another time the electron re- 

 combines from a ring qj, where i<j<k, to the same ring q^ 



Then we get a frequency (^) . 



Finall}- we imagine the electron to be removed from the 

 ./-ring, and that the recombining electron comes from the 



&-ring ; then we get a frequency ( tt ) • 



Applying equation (5 c) in all cases, we easily deduce the 

 identitv: 



©:-©:-©:•••■■■(«) 



Applied to the K^, K a , and L a lines, this equation is 

 identical with (1), and KossePs relation is fulfilled. 



