550 LEWIS. 



site sides of the original hexagon, owing to the vertical division of the 

 adjoining cells. The two tetrahedral angles produced by these 

 vertical divisions have slipped into pairs of closely adjacent trihedrals. 

 Among other irregularities this cell has an additional surface — nine- 

 teen instead of eighteen — but on the whole it is remarkably close to 

 the theoretical pattern. 



Another instance of this sort is seen in Figure 21 in connection with 

 the large cell at the left of the group. Its two facets a and b result 

 from the subdivision of a quadrilateral surface, caused by the vertical 

 division of an adjoining cell. The constriction following this division 

 drew out the angle between a and b on the top surface, and contributed 

 one of the two extra sides possessed by the octagon. It may be noted 

 that the plane of the ridge between a and b is continued downward by 

 the plane of a vertical division which produced the surface c, but in 

 such a way that the formation of a tetrahedral angle is avoided, as the 

 surface b is pentagonal instead of quadrilateral. The large cell with 

 the octagonal top in Figure 21, is in relation with similar large flat 

 cells both above and below, thus forming a column which could be 

 split, by vertical division, into two columns of cells of average size, 

 with hexagonal instead of octagonal bases and tops. But the restora- 

 tion of the tetrakaidecahedral form after vertical divisions is a com- 

 plex process of readjustment, which cannot be explained by any simple 

 scheme. 



Thus far cells have been considered individually or in pairs. As a 

 concluding observation, the mutual relations of cells in a group of 

 seven (Figure 21) may be compared with those of a cluster of orthic 

 tetrakaidecahedra shown in Figure 20. The pattern-group needs no 

 explanation other than to note that the lowest cell in the midline has 

 been cut in halves transversely. It could not, in wax, be made to 

 constrict at its plane of division, so that it presents in the figure rela- 

 tively a much larger upper surface than would occur in actual cells. 

 The relative heights of the top surfaces of the cells in this pattern 

 should he carefully observed. That of the central cell is at the lowest 

 level. The distance from the central cell to the top of the half -cell in 

 the midline below may be described as a half-step. Thence it is a 

 half-step further up to the top of the cells on either side of it, which 

 rise above the central cell by the width of a square. The distance 

 from these to the tops of the cells seen above them in the figure, is a 

 full-step, for these cells rise above the central cell by the width of a 

 hexagon. They mark the highest plane in the drawing. Finally it is 

 a step down from them to the top of the cell in the midline above. 



