30 L. VEGARD. M.-N. Kl. 



and 12 had only a comparatively small influence on the frequency. 

 Further we saw that always 7^ = i was among the values which gave 

 the best agreement with observations. 



Hence we conclude that the determinations of the ring-systems from 

 the rontfjen-raij spectra wJiich was undertaken in the first part of the 

 present pajjer (dso appihj to this modified form of recombination from 

 secondaries. There is, however, the difference that some of those com- 

 binations of 7 values which were possible when 7^ was variable, will 

 be much less good when 7^ has the fixed value i. Thus the last two 

 combinations of Table \TII. (72 = 2, 73 = 4) and (70 =1. 7a "= 4) do not 

 any longer give a satisfactory agreement. 



Comparing the equation (25) with equation (15) of my previous 

 paper, we notice that they are identical if: 



/,• = /• -f I 



Thus the modified and tJie original hypothesis of recombination from 

 secondaries ivill be identical in all those cases in whicJi there is no elec- 

 tronic system betiveen tJie secondary circle and the broken ring. Conse- 

 quently the equation for the frequency og A',^ will be the same in both 

 cases and equal to that of Debve. As regards />^ we also get the same 

 equation of the frequency in the two cases provided we give up the 

 assumption of two /.-rings with 7 and 8 electrons. From the treatment 

 ot the L^^-line on the hypethesis of recombination between primaries we 

 conclude that also the modified hypotheses of recombination from se- 

 condaries may be consistent with two Z-systems, for which 72 -[- 73 = 7 ; 

 but such an assumption was found to be of no use for the explanation 

 of the /-line, and we shall also for the recombination from secondaries 

 assume that there is only one ring with quantnumber 2. If so, the equation 

 (25) gives the same frequency for L^ as the equation (15) of Paper I., and 



the calculations of ( ^, j of my previous paper also apply to the modified 



hypothesis. 



With regard to M^ there will be principally the same possibilities as 

 in the case of recombination between primaries. There may be ttvo 

 M-systems or only one. 



In the latter case of the .V-ring should consist of 12 or 13 electrons. 



Now we saw Irom the treatment of 7v^ in the first part of this paper 

 that if we would stick to ihe hypothesis of recombination between pri- 

 maries, the assumption of one J/-ring with 12 or 13 electrons had to be 

 abondoned. 



