MANGANESE:  14 spikes of 63 atoms 882
           Central balloon 110
                                         ——­
                           Total 992
                                         ——­
           Atomic weight 54.57
           Number weight 992/18 55.11
       * * * * *

IX.

We have now to consider the breaking up of the octahedral groups, and more and more, as we proceed, do we find that the most complicated arrangements are reducible to simple elements which are already familiar.

CARBON (Plate III, 5, and XV, 1).

[Illustration]

Carbon is the typical octahedron, and a clear understanding of this will enable us to follow easily the constitution and disintegration of the various members of these groups.  Its appearance as a chemical atom is shown on Plate III, and see XV, 1.  On the proto level the chemical atom breaks up into four segments, each consisting of a pair of funnels connected by a single atom; this is the proto element which appears at the end of each arm of the cross in titanium and zirconium.  On the meta level the five six-atomed “cigars” show two neutral combinations, and the truncated “cigar” of five atoms is also neutral; the “leaves” yield two forms of triplet, five different types being thus yielded by each pair of funnels, exclusive of the linking atom.  The hyper level has triplets, duads and units.

TITANIUM (Plate III, 6, and XV, 2, 3).

[Illustration]

On the proto level, the cross breaks up completely, setting free the pairs of funnels with the linking atom (a and b), as in carbon, the four bodies marked c, the twelve marked d, and the central globe marked e.  The latter breaks up again, setting free its five intersecting cigar-bearing tetrahedra, which follow their usual course (see Occultum, p. 44).  The eight-atomed body in the centre makes a ring of seven atoms round a central one, like that in occultum (see p. 44, diagram B), from which it only differs in having the central atom, and breaks up similarly, setting the central atom free.  The ovoid c sets free its four contained globes, and the ovoid d sets free the three within it.  Thus sixty-one proto elements are yielded by titanium.  On the meta level, c (titanium 3) breaks up into star-like and cruciform bodies; the component parts of these are easily followed; on the hyper level, of the four forms of triplets one behaves as in carbon, and the others are shown, a, b and f; the cruciform quintet yields a triplet and a duad, c and d; the tetrahedra yield two triplets g and h, and two units; the septet, a triplet k and a quartet j.  On the meta level, the bodies from d behave like their equivalents in sodium, each d shows two quartets and a sextet, breaking up, on the hyper level, into four duads and two triads.