AEPINUS ATOMIZED. 



845 



one plane, and the electrions are equally spacecl round one great circle 

 of the sphère. This is the sole configuration for two electrions or for 

 three electrions : but for any number exceeding three it is easily proved 

 to be unstable, and is thereforce not the sole configuration of equili- 

 brium. For four electrions it is easily seen that, besides the unstable 

 equilibrium in one plane, there is only the stable configuration, and in 

 this the four electrions are at the four corners of an equilateral tetra- 

 hedron. 



§ 18. For five electrions we have clearly stable equilibrium with 

 three of them in one plane through C, and the other two at the ends of 

 the diameter perpendicular to this plane. There is also at least one 

 other configuration of equilibrium : this we see by imagining four of 

 the electrions constrained to remain in a freely movable plane, which 

 gives stable equilibrium with tins plane at some distance from the 

 centre and the fifth electrion at the far end of the diameter perpendi- 

 cular to it. And similarly for any greater number of electrions, we fmd 

 a configuration of equilibrium by imagining ail but one of them to be 

 constrained to remain in a freely movable plane. But it is not easy, 

 without calculation, to see, at ail events for the case of only five elec- 

 trions, whether that equilibrium would be stable if the constraint of ail 

 of them but one to one plane is annulled. For numbers greater than 

 five it seems certain that that equilibrium is unstable. 



§ 19. For six we have a configuration of stable equilibrium with the 

 electrions at the six corners of a regular octahedron; for eight at the 

 corners of a cube. For ten, as for any even number, we should have two 

 configurations of equilibrium (both certainly unstable for large numbers) 

 with two halves of the number in two planes at equal distances on the 

 two sides of the centre. For twelve we have a configuration of stable 

 equilibrium with the electrions at positions of the twelve nearest neigh- 

 bours to C in an equilateral homogeneous assemblage of points; l ) for 

 twenty at the twenty corners of a pentagonal dodecahedron. Ail thèse 

 configurations of § 19 except those for ten electrions are stable if, as 

 we are now supposing, the electrions are constrained to a spherical 

 surface on which they are free to move. 



*) „Molecnlar Tactics of a CrystaV\ § 4. 



