and the Constitution of the Atom. 271 



At an infinite distance the quant-number r is infinitely 

 great, and Y(rj>q) vanishes. Putting in equation (25) 

 t = oo , we get : 



S = R = Y ( n '» Pi> #) — V (*fc pi, qi-1) 



+ X [ V ( w fc Ph qi) ~ V(ni, pi - 1, ?*)]> 



j=»+i 



(28) 



where m is the total number of electronic systems of the 

 atom considered. 



In order to calculate v± we must know the constitution of 

 all the electronic systems surrounding the nucleus, but we 

 only know with certainty the K- and L-system. 



The best way of testing the correctness of the equation (28) 

 would be to calculate v± for the K-absorption edge and for 

 very low atomic numbers. In that case we know those 

 systems which contribute most to the frequency va, and 

 differences with regard to the outer systems will not have 

 any great effect on the frequency. 



The lowest atomic numbers for which I have found deter- 

 minations of the absorption edges are N = 26 (Fe) and 

 28 (Ni). 



Wagner * gives the following values : — 



Fe X A = 1'759 10 8 cm. 



Ni X A = 1-502 „ „ 



Now we assume a constitution of the electronic system 

 similar to the one indicated in fig. 2 of my previous paper, but 

 with a change of the quant-number of the third and fourth 

 rings. 



The following constitution is adopted : — 



Ring 



q(Fe) 

 Z(Ni) 



V 



1. 



2. 



3. 



4. 



1 



2 



3 



4 



3 



7 



8 



8 



3 



7 



8 



10 







3 



10 



18 



These values of (??, p, q) give us all we want for the 

 determination of va from (28). 



Values of ^ calculated from (28) and corrected for varia- 



IX 



tion of mass with velocity, as also the values calculated from 

 observations, are given in Table XIX. 



* E. Wagner, Phys. Zeitschr. xviii. p. 436 (1917). 



U2 



