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