558 Prof. J. W. Nicholson on the High-frequency 

 and its orbit is given by 



r-r6 2 = - Aite- ~ SA r*0= Const., 

 mr- \ 4 /' 



which leads as usual to the ellipse. If a is the semi-axis 

 major of any orbit, the mean angular velocity co satisfies 



CO 



ma 3 \ 4 /' 



as in a circular orbit of radius a. 



When a circular orbit ceases to be stable, as in Bohr's 

 theory when n is greater than 8, there may be stable sets of 

 elliptic orbits, and if there are to be many electrons in the 

 atom, this is a probable configuration; though perhaps a more 

 probable one consists of parallel rings, or even parallel 

 arrangements describing elliptic orbits. 



Returning to the lithium atom, we see that, since an 

 inner ring of two electrons is not possible, the attempt to 

 treat the atom from a point of view which assumes that the 

 outer part of the atom contains a number of electrons equal 

 to the normal valency of the element, breaks down. For 

 there seems to be no method of disposing of one electron in 

 order to endow it with peculiar properties. For lithium, 

 there are presumed to be three electrons, and no arrangement 

 not in one plane can satisfy Bohr's conditions. Yet the only 

 coplanar arrangement is that of a single ring. We must 

 accept one of two alternatives. Either the number of 

 electrons most remote from the nucleus does not represent 

 the chemical valency, as has been generally supposed, except 

 by Bohr, or the lithium atom does not contain 3 electrons. 

 To accept the second alternative gives up van den Broek's 

 hypothesis in its present form. 



Bohr rejects the first alternative, as for example in his 

 model of the helium atom with two electrons, and has treated 

 the problem of valency from a new and convincing point of 

 view, which we shall adopt in the next section. In the case 

 of lithium, he adopted the configuration already discussed, 

 not because his theory definitely required it, but because it 

 seemed most likely to lead to the chemical properties of 

 lithium. Since, however, lithium, if it has 3 electrons, must 

 have only one ring, its valency, together with those of 

 beryllium and boron, must be re-examined. 



The Valencies of Elements, 



Bohr has given a partial analysis of this question, which, 

 in so far as it relates to hydrogen and helium, is complete. 



