256 Dr. L. Vegard on the X-Ray Spectra 



From the periodic variation of the properties of the 

 elements we come (as we sh;ill see later on) to the conclusion 

 that we shall most likely in addition have an increase of the 

 quant-number of the surface ring when we pass the element 

 Argon. If, however, for a moment we look away from this 

 possibility, we still have to consider the changes of frequency 

 which are due to the variation of the number of electrons in 

 the system of departure (system from which recombination 

 starts). As we have seen, these changes are not large ; but 

 still they may be great enough to affect the curve v=f(N) 

 and give to it a characteristic curvature, which also should 

 be found for the experimental curve. 



In order to carry out this test, we shall calculate the 

 frequencies for all atomic numbers between 11 and 30. We 

 shall consider the quantity : 



A = ^-^N 2 - -BN + C + e. . . . (22) 



In Table XII. are oiven the values of B and C for values 

 of qs varying from 1 to 12. 







Table XII. 







ffs- 



B. 



c. 



9v 



B. 



C. 



1 



3-962 



8-7 



7 



4-146 



11-5 



2 



4073 



9-8 



8 



4-117 



11-6 



3 



4-133 



10-5 



9 



4 071 



11-6 



4 



4-163 



109 



10 



4-034 



11-5 



5 



4-173 



11 2 



11 



3-974 



11-3 



6 



4166 



11-4 



12 



3911 



11-0 



From these values of B and C, and from the values of e 

 for K a and L a , we can determine A for various atomic 

 numbers. The results are given in Table XIII. 



The variation of A with the atomic number is represented 

 in fig. 2. 



Curve I. is drawn from Debye's values, which are cal- 

 culated on the assumption of recombination from a secondary 

 circle. 



The curves II. and III. represent the above values of A 

 for </3=12 and §'3 = 8 respectively. Curve IV. is drawn so 

 as to represent the observed values of A. It should be 

 remembered that errors may be attached to the observed 

 frequencies, and that the absolute error of frequency will 

 greatly increase with increase of atomic number. Thus the 

 curve A bs can be drawn with a considerable accuracy up to 



