and the Constitution of the Atom. 251 



C. On the Possibility of two L-systems. 



§ 7. In Paper I. I was led to assume a second L-ring of 

 8 electrons. Building on the assumption of recombination 

 from secondaries I was able by means of this assumption to 

 indicate an explanation of the Z-series. Now it would be of 

 interest to see how far the assumption of two L-systems is 

 consistent with our present hypothesis with regard to the 

 process of recombination, and how far this hypothesis is able 

 to yield any satisfactory explanation of the /-series. 



In this case we must apply equation (10) because the 

 recombination does not take place between successive rings. 



Putting in equation (10) 



i = 2, £=4, n 2 = 2, ?i 3 = 2, t? 4 = 3, /> 2 = 3 > 

 p 3 =z3 + q 2 , /v=3 + 2 2 + g 3? 



the equation of condition takes the form 



<M&)-&=/fe)+i?3, .... (14) 



where f(q 2 ) is the same function as in equation (13). 



From the Tables I. and V. we find that we get a fairly 

 satisfactory solution of (14) for a number of values of q 2 

 and q z . 



The values of /(g 2 ) + 5/4 ^ 3 for the possible combinations 

 (#2> #3) are given in Table VIII. 



Table VIII. 



q 2 6 5 4 3 2 1 



g 3 12 3 4 4 4 



f(q 2 )+5/4q s . -1'09 -115 -T05 -0'98 -1-40 -150 



With the exception of the last two combinations the total 

 number of electrons in. the L-systems (q 2 + qz) is equal to 7. 



From a mere numerical point of view the above combi- 

 nations would give a fairly satisfactory agreement, and we 

 may say that our hypothesis of recombination between pri- 

 maries and conservation of momentum is not against the 

 assumption of two L-systems ; but in this case — as far as I 

 can see at present — such an assumption only leads to compli- 

 cations ; for it does not lead to any satisfactory explanation 

 of the /-series. 



Putting into the equation (5 c) 



i = 3, & = 4, n 3 = 2, n 4 = 3, p 3 =3 + q 2 , p 4 =3 + ? 2 + ?3, 

 we shall find that for all the combinations (q 2 , q s ) given in 



