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



ring, it would be difficult on the basis of the hypothesis men- 

 tioned to convey any clear conception as to the process o£ 

 light-emission ; the secondary stability circles could hardly 

 have any real existence. 



It is, however, possible to modify the hypothesis of 

 recombination from secondaries in such a way that these 

 difficulties are avoided. 



Just as in the case of recombination between primaries, 

 we may assume that the energy changes of the intermediate 

 rings which accompany the recombination process enter into the 

 energy-quantum which is emitted as the result of the recom- 

 bination. 



Proceeding in the same way as before, and using the 

 same designations, we easily deduce the following general 

 frequency formula : 



g = V(?i t , p t , ql)—Y{ni, p}, Qi—1) 

 l=zk— 1 



2 [V(«,,j*0)-VKn,-i,8rt > • (25) 



l=i + 1 



-V(T,/*-l, 1)]. 



Comparing the equation (25) with (da), we see that the 

 first can be derived from the latter simply by putting 



n k = r and </* = l. 



In order to see the significance of this statement, we shall 

 consider the recombination to the i-ring. In one case we 

 suppose the electron to recombine from the primary &-ring 

 with quant-number n&. (If there is more than one ring with 

 the same quant-number we suppose recombination to occur 

 from the ring nearest to the nucleus.) The resulting fre- 

 quency we call v p . In the second case we consider the 

 recombination from a secondary with quant-number t=t?^ 

 which results in a frequency v s . From what has been said 

 about the position of the secondary circle relative to the 

 primary ones we conclude that in both cases the recom- 

 piling electron passes the same intermediate primary 

 systems, and we get : 



1 - 1 = V(t,P*, ?*-1)-V(t, p k -l, q k ) +V(t, Pk -l, 1). 



Thus the difference is ojily due to the change of number of 

 electrons of the system from which recombination takes 



