FLUORINE: 8 spikes of 15 atoms 120 2 balloons 220 ---- Total 340 ---- Atomic weight 18.90 Number weight 340/18 18.88 MANGANESE (Plate XVII, 2) has fourteen spikes radiating from a central "balloon." 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]