This system admits of two varieties, according as the centre is attractive or repulsive. In either case, for the maintenance of equilibrium the force of the centre must always be less than half that of the vertices combined, as the author shows, (giving the values for each polyhedron;) and it would seem that the first supposition would therefore be untenable, since the attractive force in each molecule, as just stated, necessarily exceeds the repulsive. Equilibrium certainly cannot be maintained in this case; but this will not involve the permanent collapse of the molecule, but merely a continual vibration of its elements back and forward through the centre.
The second hypothesis, on the other hand, requires either a centre so weak as to produce very little repulsion outside of the molecule, or else a continual tendency to expand under a central power too great for equilibrium. Both will tend to bring the molecular envelopes near to each other, and produce adhesion or mixing among them; also, it may perhaps be added, that the envelopes themselves will, on account of the mutual attraction of their elements, be unstable.
Of these two constructions, then, the first would seem most probable; but both are open to objection on account of there being no internal resistance in the individual molecules to a change of diameter proportional to a change produced by external action in that of a mass of them; and if such a change should take place, the mass would be in just the same statical conditions as before, only differing in the relative dimensions of its parts, and the resistance to pressure which is exhibited more or less by all matter would not be accounted for. But it does not seem quite certain that pressure or traction of the mass would operate upon the separate molecules in the same sense.
We are not, however, restricted to such a simple structure; for there may be several envelopes instead of only one, and of these some may be attractive and others repulsive; the centre also may be repulsive. There would have to be an absolute predominance of attractivity, of course, as in the previous more simple supposition. It seems probable that in this supposition the envelopes would be all tetrahedric, or that either the cube and octahedron, or the other two, which are similarly counterparts of each other, would alternate. Many of these forms are examined mathematically by the author, as to their internal action.