48 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



magnetons not in groups of eight), the average magnetic energy per 

 magneton is higher and the average attractions between the mag- 

 netons are less. Since the valence magnetons are distinct from the 

 others (as an average effect at all events), this will show itself chiefly 

 in the existence of a rather less compressed outer layer in which the 

 valence magnetons lie, but partly also in an expansion of the groups 

 of eight in the atom owing to the disturbing effect described in §11. 

 The total result is thus an expansion of the atom, 

 the amount of which must be roughly propor- 

 tional to the number of valence magnetons in it. 

 Hence we would expect a periodic fluctuation of 

 the atom's normal volume just like that in the 

 curve given above. There, the maximum volumes 

 are about three times as great as the minimum, but 

 it should be borne in mind that this only means a 

 45 per cent increase in the radius of the atom for the transfer of 

 about one-third of its magnetons from a closely to a loosely bound 

 condition. 



The abnormally high value of p— I for Hydrogen is not entirely 

 unexpected, because, although the positive spheres of all atoms are 

 internally compressed to the same extent by electrostatic forces (§7), 

 the Hydrogen atom is the only one that is not further compressed 

 by internal magnetic forces, for it contains only one magneton. Even 

 in the H 2 molecule the compression cannot be nearly so great as in 

 the Helium atom ; so that the volume of the positive sphere of the 

 atom of gaseous Hydrogen may be expected to be abnormally great — 

 if not quite so great as the fi— 1 relation indicates. 



§15. Atomic Volumes in the Liquid and Solid States 



In considering now the volumes of atoms in liquids and solids, it 

 might loosely be taken for granted that the action of valence mag- 

 netons on atoms such as I have hitherto described could produce the 

 differences in volume that are observed. This involves a fallacy, the 

 avoidance of which leads to an important conclusion about the distri- 

 bution of the atom's positive sphere, which up to the present has been 

 assumed to be uniform in the absence of magnetons. 



If a naturally uniform positive sphere contains magnetons propor- 

 tional in number to its charge (and normal volume), which are not 

 attached to it except by electrostatic forces, the average compression 

 in a cluster of such spheres must be about the same whether the 

 magnetic forces are acting almost entirely within the separate 



