Spectra of the Elements, and Structur-e of the Atom. 561 



where W is also the energy required to remove the electrons 

 to infinite distances from the nucleus and from each other. 

 Eliminating a and co from these equations, we find 



W= 87 ^-sin 4 a (3-4227) 2 



= 4W sin^(3'4227) 2 , 



where W is the corresponding energy for a hydrogen atom. 

 This leads on calculation to 



W = 32'732W , 



whereas, by a previous result, when the four electrons move 

 in the same orbit, 



W = 37-037W . 



Although the value in the present case is smaller, we may 

 suppose, as Bohr does in the case of his models for the lithium 

 and beryllium atoms, that it corresponds to a possible neutral 

 system. When one electron is removed, the remaining three 

 must form one ring with, as already calculated, 



W=/(3,4) =35-142 W , 



which is larger. Thus, such a system can lose an electron. 

 Moreover, since 



2 



/(2,4)=2(4-i) =28-12, 



we find that it cannot, in the same way, lose two electrons. 

 The present atom is accordingly metallic, with a unit valency, 

 and would be capable, from this point of view, of representing 

 the lithium atom. 



Although, accordingly, it is difficult to imagine what the 

 chemical element with atomic number N=3 can be, unless 

 we postulate the existence of an unknown element between 

 helium and lithium, with similar properties to helium, we see 

 that with suitable modifications, Bohr's theory of the more 

 complex atoms can apparently continue to represent the facts 

 for at least some distance in its development, but in order to 

 do so, it must abandon van den Broek's hypothesis. But, of 

 course, outstanding difficulties remain. For example, if such 

 a lithium atom ever lost an electron, it seems more probable 

 that when the electron returned, the atom would take up the 

 chemically inert configuration with a single ring. Even on 

 Bohr's original lithium model, a chemically inert form must 

 be regarded as the more usual one, it' the method of estimating 

 valency is to retain its meaning. 



