20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



atom into groups of eight, with a remainder of valence magnetons, 

 would give an ideal explanation of the " Law of Octaves." Indeed, 

 no other arrangement of the magnetons — as, for example, in one 

 large group — could give a picture of the facts, chemical and mag- 

 netic, that even approaches this in fidelity. What follows, therefore, 

 is an attempt to analyze the behavior of large numbers of magnetons 

 in a positive sphere with a view to finding conditions which could 

 lead to' such a grouping. 



Any number of magnetons within a sphere of equivalent positive 

 electrification must arrange themselves so as to secure an equilibrium 

 between the two tendencies of the magnetic energy and the electric 

 energy, respectively, to be at a minimum. The first would be satisfied 

 by a gathering of all the magnetons into one very compact group, 

 the second by an even distribution of single magnetons ; and in view 

 of the fact that magnetic forces increase more rapidly than electric 

 forces as the distance diminishes, it might be thought that a likely 

 compromise between the two tendencies would be the formation of 

 groups containing the smallest number of magnetons that is com- 

 patible with a low magnetic energy, and at the same time with sym- 

 metry and mobility, in the group — that is, groups of eight. But more 

 careful study of the matter shows that when a magneton is displaced 

 from the position it would occupy in a plan of even distribution, the 

 electrostatic forces of restitution are greater than the opposing mag- 

 netic forces ; so that the stable condition is one of even distribution. 



What has been said, however, implies the assumption that the 

 positive sphere is rigid; if, on the contrary, it is compressible, we 

 have a set of conditions that requires further consideration. This 

 compressibility of the positive electricity will be found necessary to 

 explain atomic volume relations and also the phenomena of gaseous 

 collisions and a-particle scattering (see the note at the end of §16) : 

 it will therefore be introduced here. 



The hypothetical positive sphere we are using must be supposed to 

 possess two distinct sets of properties. In the first place it is a 

 uniform charge of positive electricity, and on that account tends to 

 expand indefinitely into space. Secondly, it has a coherence due to 

 forces; something like elastic forces, which are in equilibrium with 

 the expansive electrostatic forces. Thus when isolated from mag- 

 netons it would be in a state of distension, and very compressible. 

 Further, to preserve the individualities of the positive spheres of 

 different atoms we need to assume an internal structure like that of 

 an elastic solid rather than that of a fluid. What has been said does 

 not, as might seem at first, burden the positive sphere with more 



