and the Constitution of the Atom. 239 



The frequencies were therefore calculated on the assump- 

 tion of conservation of energy, which is in accordance with 

 the relation (1). 



To fix the idea, let us recall to memory the way in which 

 the frequency formulae are deduced. 



Let the element considered have an atomic number N. 

 Let us consider a certain ring-system with quant-number n, 

 consisting of q electrons. Let the total number of electrons 

 between the nucleus and the ring be p, when the atom is in 

 its normal state. 



The effective nucleus charge of the ring considered will be 

 (N —p)e, and the energy of the ring 



E = C-M?{l- X /l-i(N- P -S } )4 = C-¥(» lPl? ). 



9 L • • • (2) 



In this formula the variation of mass with velocity is taken 

 into account. 



B, is Rydberg's constant, h Planck's constant, p a constant 

 equal to 5'30 . 10 5 , and 



i=q-l I 



S 2 = \ 2 ~T7V 



q 4 ^ smi- 

 *•=! q 



For a given value of N, W is a function of n,p, q, and for 

 the sake of convenience we introduce 



. . . (3 a) 



If we do not take into account the variation of the mass, 

 we get 



V (»,P,?)=f 2 (N-p-S 2 ) 2 . . . . (3 b) 



As p is a small quantity, the expression to the right 

 of (3 a) can be expanded into series, and to the first 

 approximation : 



Y(n,.p,q) = V +£-Y^ (3c) 



The hypothesis of maintenance ot energy means that even 

 after an electron is removed from a system inside the ring 

 considered the energy remains unaltered and equal to 

 C - W(n, p, q), where p is the number of electrons inside the 

 q ring before the removal of the electron. 



S 2 



