244 



Dr. L. Vegard on tlie X-Bay Spectra 



place between successive rings, we have to put k = i-\-l, and 

 l=k-l 

 2 qil^i 2 = 0. Then the equation (10) takes the simpler foim 



</>fe +1 )-? i+ i= (~ff [*^)+^]-^ + i- 1 /2Bn i+ /. (Ik) 



From equation (4) we see that p i+l is independent of q i+l . 

 But p. x depends on q. and the number of electrons between 

 the q { ring and the nucleus. In order to get an equation of 

 condition between q i+l and q i we must know the rings inside 

 the i ring, or p.. Thus, the natural procedure will be to 

 begin with the ring next to the nucleus and proceed out- 

 wards, as done in my previous paper. 



Putting p. +l = q i -l r p i equation (11a) takes the form 



<M? i+1 ) -a+i- ( v) 2<#,(9i) ~ 9i+A =fi9i) 



where A is a constant independent of q i and q i+v 



A=7- 



ni+i 



11 c 



l/2Bn, +1 2 . 



(116) 



(lie) 



If we have calculated once for all the values of the 

 function <f)(q) — q for various values (whole numbers) of q, 

 we have then in any particular case to determine the term to 

 the right for various values of % and we have to see whether 

 any of the values of the right term equals any of the values 

 found for cf)(q) — q. 



The values of <f>(q) and <j>(q)- q corresponding to q=l, 2, 



Table I. 



'*. 



• . JLU tilt? 



<p(q)-q 



1 



o-ooo 



-1000 



; 2 



0-500 



-1-500 



3 



1-231 



-1-769 



4 



2-097 



-1-903 



5 



3-052 



-1-948 



6 



4-082 



-1-918 



7 



5-173 



-1-827 



8 



6-305 



-1-695 



From the variation shown by <f>(q) 

 general conclusions. 



Q> 



0(9). 



tp(g)-g. 



9 



7-512 



-1-488 



10 



8-678 



-1-322 



11 



9946 



-1-054 



12 



11-232 



-0-768 



13 



12537 



- 0-463 



14 



13-881 



-0-119 



15 



15-234 



+ 0234 



16 



16 604 



+0-604 



;<?)- 



— q we can 



draw some 



