40 L. VEGARD. M.-N. Kl. 



The assumption I. b does not lead to any satisfactory result. Although 

 we were able to get a fearly good formula for the A'^-line, the assump- 

 tion does not seem to give room for further extensions to the other 

 X-ray series. Thus we cannot explain L^ by means of the electronic 

 rings which were given through the calculation of K^,. For the same 

 reason an assumption II. b must be abandoned. In the case of recombina- 

 tion from secondaries the difference between III, a and III. b would^ not 

 come in as long as we only treat the principal (a)-line of each series. But 

 the difference is very marked indeed, when we are considering the {ß)- 

 lines and we find that the assumption of preservation of momentum gives 

 by far the better agreement for these lines. 



Thus we come to the following conclusion: 



Whether ive assume recomhination from a normal or deformed primary 

 system or recomhination from a secondary one, we have alivays to assume, 

 that the angular momentum of the electrons left behind in the atom 

 remains unchanged. And, further, we have to assume that the changes 

 of energy of the systems situated hetioeen the broken ring and the ring 

 of depart enters into the energy quantum of radiation tvhich is emitted 

 as the result of the recomhination. 



When we assume preservation of momentum the three assumptions I, 

 II, III will all give a very close agreement between calculated and 

 observed values, and all three assumptions lead to the same values of 

 the number of electrons in the various ring systems. This is due to the 

 fact that the energy changes which accompany the recombination is 

 very little effected by a change of the number of electrons in the system 

 of depart. 



If we were merely regarding the numerical agreement for each line 

 separately, it would be very difficult indeed to decide in favour of any 

 of the three possibilities (I, II, III). All of them explain the principal 

 (a)-lines as well as the second (/i).lines almost equally well when each 

 line is seen separately; but still we found, that the assumptions I. and 

 II. meet with considerable difficulties. 



First of all we found that the assumptions I. and II. in the case of 

 Kß led to a characteristic form of the curve v = f {N) which was not 

 indicated by the experimental values. At any rate the assumptions I. 

 and II. are not consistent with the assumption of only one M-nng. The 

 assumption III., however, gave the right curvature. 



The strongest argument in favour of the assumption III we got from 

 considerations with regard to the deviation from Kossel's relation. The 

 assumption of recombination from secondaries gave just the right values 



