36 L. VEGARD M.-N. Kl. 



A third Modification of the Hypothesis of Recombination 

 from Secondaries. 



§ M- 



In our previous treatment of recombination from secondaries we 

 assumed the electron before starting recombination to be moving a stability 

 circuits of its own with quant-number t. We further assumed the secondary 

 circuit to be inside the atomic rings with quant-number n^ = T. 



There is, however, the possibility to consider, that the recombining 

 electron is taken up in the atomic ring k, which has the quantnumber 

 n/g = r. If 5^ is the number of electrons in the normal ring q^ + i, 

 would be the number just before recombination. 



This hypothesis may also be considered as a heigher union of the 

 hypothesis of recombination between primaries and that of recombination 

 from secondaries; because we may say that recombination takes place 

 from a deformed primary circle. 



The analogy between this hypothesis and the two previously treated 

 will be apparent from the fact that the frequency formula is simply deduced 

 from equation (5) by replacing g^ with g^+ i. 



From the fact that the change of number of electrons in the ring 

 of depart has a very small influence on the frequency, we conclude that 

 also the present hypothesis leads to the same number of electrons in the 

 various rings, and that it will give an equally good numerical agreement 

 with observations. 



In the case of K^ the agreement will be even better that obtained 

 on the assumption of recombination between primaries (Tacle IV) at any 

 rate for small atomic numbers. And for heigher atomic numbers it will 

 give a better agreement than the formula of Debye based on the hypo- 

 thesis of recombination from secondaries. 



Just as in the case of recombination between primaries considerations 

 with regard to Ko will show, that we cannot assume one Ji-system 

 with 12 or 13 electrons. Two J/-systems one with 8 another with 7, 

 however, may still be possible. 



With regard to Kossel's relation it is not identically, but merely 

 approximately fulfilled, in fact the quantity d is given by expression: 



rf = i^V + 



y ("y, Vj — I ,-(lj 4- I ) — F (wy, i^j — I , q) 



