and the Constitution of the Atom. 243 



On the Determination of the Quant-number and Number 

 of Electrons of the Ring-systems from the observed 

 Frequencies. 



§ 4. The problem before us is to find such whole numbers 

 n, p, and q, that the calculated and observed frequencies of 

 the various X-ray spectra are in agreement with each other. 

 The procedure in the present case is the same as the one 

 followed in my previous paper, only the equations and some 

 of the results will be different. 



From equations (5) we see that also the assumption of 

 unchangeable momentum leads to an equation of the right 

 type; for, as we know, the frequency of an X-ray line varies 

 with the atomic number in such a way as to approximately 

 satisfy an equation of the form 



Hi-i) N2 - BN+c (8) 



At any rate tins equation will hold for small atomic 

 numbers. 



Now the quant-numbers iii and nt will be determined from 

 the coefficient of N 2 . 



The number of electrons in the rings must be determined 

 from the coefficients B and C. To make the final test we 

 can calculate € by means of the known for possible) values 



of n, p, q, and thus find the value of -ry corrected for 

 variation of mass. 



As mentioned in Paper L, we have first of all to find such 

 values of q that we get the right value of the coefficient B. 



Putting as before : 



<M?)=<M^?)-p=?(S s -s s -i) + s,-i, • • (9) 



our principal equation of condition now takes the form 



y 2B ^(-^ + P< _fM^Z^ + 'V?l. . (10) 



* k i=i+i l 



In the case of conservation of energy the corresponding 

 equation of condition is (see Paper I., equation 16) 



1/t7R <!>(&)+ Pi $(qd+Pk 



1/2 B= — - — • 



ni 2 n k 2 



Taking first the important case when recombination takes 



