CONTEMPORARY ADVANCES IN PHYSICS, XXIX 297 



to be presumed that s and / are constantly revolving or precessing 

 around the direction of j, — the triangle aforesaid is constantly re- 

 volving around its side j as a fixed axis, while retaining its size and 

 shape unchanged. If we resolve the resultant angular momentum 

 into a component parallel to j and another component perpendicular 

 to j, the latter will be forever changing in direction and its average 

 will vanish, leaving only the former as a perpetual constant. But this 

 former component we can evaluate by projecting separately upon the 

 j-direction the magnetic moments associated with orbital motion and 

 spin, and adding the two projections. Thus for the magnetic moment 

 of the atom-as-a-whole we get an effective average which is a vector 

 parallel to the angular momentum of the atom-as-a-whole, and it is of 

 the magnitude: 



Ma = CV/(/ + l) cos di, J + 2V^(7TT) cos Os, y]y^ :f (11) 



(where I have restored the factor h/lir). If we work this out with the 

 aid of (10) and the similar equation for cos ds, /, and then divide it by 

 the angular momentum {h/2Tr)^j{j -+- 1) and by e/2mc, we get the 

 g-factor for the atom-as-a-whole — commonly denoted by gj — in terms of 

 the quantum-numbers s, I and j: 



, _ . I Kj + 1) + s{s + 1) - /(/ -f 1) 



^' ^ 2JU +1) ' ^ -^ 



and this is the celebrated g-formula, which is tested by applying 

 magnetic fields H to atoms, splitting their stationary states into 

 clusters of levels, measuring the separation between successive levels 

 of a cluster, equating it to a? = g(e{2mc)H, evaluating g and compar- 

 ing it with the value which the right-hand member of (12) assumes 

 when in it s, I and j are given the values appropriate to the state from 

 which the cluster of levels was formed. So great is the variety of 

 atomic states, so great the number of different triads of values of 

 5, l,j represented among them, that the study of even a single element 

 like sodium produces many different checks of the validity of (12); 

 and since many different elements have been studied, the total of the 

 available verifications of the g-formula, and therefore of the intricate 

 network of its underlying ideas, is considerably impressive. 



The temptation of going onward and onward into the details of these 

 properties of the extranuclear electrons and their orbits is difficult to 

 resist, but it must be overcome, for the field is practically endless. 

 I must add only, that when an atom possesses two or more valence- 



