and the Constitution of the Atom. 269 



circuit to be inside the atomic rings with quant-number 



n ^ — T - 



There is, however, the possibility to consider, that the re- 

 combining electron is taken up in the atomic ring k, which 

 has the quant-number n k = r. If q k is the number of elec- 

 trons in the normal ring q^ + l would be the number just 

 before recombination. 



This hypothesis may also be considered as a higher 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 pre- 

 viously treated will be apparent from the fact that the 

 frequency formula is simply deduced from equation (5) by 

 replacing qu with gfc+1. 



From the fact that the change of number of electrons in 

 the ring of departure has a very small influence on the fre- 

 quency, we conclude that also the present hypothesis leads 

 to the same number of electrons in the various rings, and 

 that it will give a very good numerical agreement with 

 observations. 



In the case of K a the agreement will be even better than 

 that obtained on the assumption of recombination between 

 primaries (Table IV.)' a * an } r ra ^ e f° r sma U atomic numbers. 

 And for higher atomic numbers it will give a better agree- 

 ment than the formula of Debye based on the hypothesis of 

 recombination from secondaries. 



Just as in the case of recombination between primaries, 

 considerations with regard to K# will show that we cannot 

 assume one M-system with 12 or 13 electrons. Two M- 

 sy stems, 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 the expression : 



hs +©;-©; 



=Y(nj,pj, qj)-V(nj,pj, Qj-1) 



-Y(nj, pj-1, #+l)-V(fi* Pi-1, 9j)> 



To get approximate values of d we may put V = V ; then 

 in the case of K^, K a , L a we get : 



d = 0'066N + O53. 



Phil. Maq. S. 6. Vol. 37. No. 219. March 1919. U 



(27) 



