1920. No. 2. ON THE X-RAY SPECTRA. 5 



The ettective nucleus charge of the ring considered will be (N — p) e, 

 and the energ\- of the ring : 



A-=C-^''-^^' 



O 



]/i-^^^ (A^-^^-ÅV-j - c- n-{n,p,'j) ..(2) 



In this formula the variation of mass with velocity is taken into 

 account. 



R is Rydberg's constant, Ji Plack's constant, o a constant equal to 

 5,30. 10° and 



i=q-l 



i = i sin Î 

 9 



For a given value of X, IT is a function of )i, p, q and for the 

 sake of convenience we introduce: 



W{n,p,q) 

 h M 



V[n,p,q)= -^ r,_ j;,_^^(A7_p_.s/j ...(3a) 



If we do not take into account the variation og mass we get : 



T'ol^'W^'i) f (^V-^>-5'/ ...(3 b) 



''2 



As o is a small tjuantity the expression to the right of (3 a) can 

 be expanded into series, and to the first approximation: 



l'(.",i^'?)= ^0+ ;|l'o- .••(3 c) 



The hypothesis of preservation of energy means that even after an 

 electron is removed from a system inside the ring considered, the energy 

 remains unaltered (' — T' (",i^, 7), where j; is the the number of electrons 

 inside the 7 ring before the removal of the electron. 



If we suppose the angular momentum to be preserved, the energy 

 of the ring after the removal of a internal electron will be 



C- ]V{)i,p-\,q). 



The correctness of this statement is evident from the fact, that the 

 formula (2) gives the energy of the ring when each electron has an an- 

 gular momentum of — and an effective nucleus charge [X — p)e. The 



explusion of an electron from an interior system will change the effec- 

 tive nucleus charge of the ring to [.V — [p — i]). 



