1920. No. 2. ON THE X-RAY SPECTRA 2g 



If there are systems between the secondary and the broken ring it 

 would be difficult on the basis of the hypothesis mentioned to convey- 

 any clear conception to the process of light emission, the secondarj- 

 stabilitycircles could hardh* have an\' 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, wJnch accompaug 

 the recombination process, enter into the energg quantum ïvJiich is emitted 

 as the result of the recombination. 



Proceeding in the same way as before and using the same designa- 

 tions, we easily deduce the following general frequency formula: 



j^,= I' ('',. ]>,' '/,' — T'(»,, p,. </, — I) 



2 ^^{>'e>Pe>'h)- ^'i^'e'Ve- ^ ' 'le) 

 /=•+1 



Comparing the equation (25) vith (5 a) we see that the first can be 

 derived from the latter simply by putting: 



n^ = r and (^^ = i. 



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 /r-ring with quant number >/^. (If there is 

 more than one ring with the same quant-number we suppose recombina- 

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

 quency we call Vp. In the second case we consider the recombination 

 from a socondary with quant number r=n^, which results in a frequency v^. 

 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- 

 bining electron passes the same intermediate primary systèmes, and 

 Ave set : 



V . V 



Thus the difference is onl\- due to the change of numl)er of electrons 

 of the system from which recombination takes place from r/^ to i, and 

 as we saw in the first part of this paper the change of 7^ between i 



