and the Constitution of the Atom. 249 



quant-number 2 and that recombination takes place between 

 successive systems. On this assumption we have 



i = 2, n 2 = 2, rc 3 =3, /> 2 = 3, p3 = '/2 + 3, B = 2*06 (approx.), 



and the equation (11 b) takes the form 



cf>(q 3 )-q 3 =9/±cl>(q 2 )-q 2 -5-52=f(q 2 ). . . (13) 



Values of f(q 2 ) corresponding to various values of q 2 are 

 given in Table V. 



Table V. 



q 2 ... 1 2 3 4 5 6 7 8 



f(q 2 )... -6-50 -6-40 -5-98 -4'80 -3-65 -2-34 -0-88 +0-67 



Comparing the values of f(q 2 ) with those of (f>(qs) — qz 

 (Table I.) we see that the equation of condition (13) is 

 approximately fulfilled by the following two combinations : 



q 2 = 7, q 3 =l-*12, 



The first solution corresponds to the one found in Paper I. 

 and given by 



q 2 =l and q z = l. 



The second solution q 2 = 8, q 3 =16 must be considered as 

 improbable on account of the large number of electrons in 

 the third system. Further, the application of the theory to 

 K^ and M a makes the assumption of q^—16 impossible. 

 The only possibility is to assume 7 electrons in the second 

 ring, and the coefficients B and C are determined by the 

 equations 



B = 1-865 -| (Ma) -ft), 



G=14-30-^[^(20+^ 8 + S ?3 _ 1 )(S 2 3-S ?3 „ 1 ) 



+ (10 + S ?3 _ 1 ) 2 -2^ 3 (S 93 + 9-5)]. 



Values of B and C corresponding to various values of q z are 

 given in Table VI. 



The relative change of B and C with variation of q z in the 

 case of L a is even smaller than for K a ; and, although the 



