680 ON CONCRETIONS, SPICULES, ETC. [ch. 



We have already studied in an elementary way, but enough for 

 our purpose, the manner in which three, four or more cells, or 

 bubbles, meet together under the influence of surface-tension, in 

 configurations geometrically similar to what may be brought about 

 by a uniform distribution of mechanical pressure. And we have 

 seen how surface-energy leads to the adsorption of certain chemical 

 substances, first at the corners, then at the edges, lastly in the 

 partition- walls, of such an assemblage of cells. A spicule formed 

 in the interior of such a mass, starting at a corner where four cells 

 meet and extending along the adjacent edges, would then (in theory) 

 have the characteristic form which the geometry of the bee's cell 

 has taught us, of four rays radiating from a point, and set at co-equal 

 angles to one another of 109°, approximately. Precisely such 

 " tetractinellid " spicules are often formed. 



But when we confine ourselves to a plane assemblage of cells, or 

 to the outer surface of a mass, we need only deal with the simpler 

 geometry of the hexagon. In such a plane assemblage we find the 

 cells meeting one another in threes ; when the cells are uniform in 

 size the partitions are straight lines, and combine to form regular 

 hexagons; but when the cells are unequal, the partitions tend to be 

 curved, and to' combine to form other and less regular polygons. 

 Accordingly, a skeletal secretion originating in a layer or surface 

 of cells will begin at the corners and extend to the edges of the cells, 

 and will thus take the form of triradiate spicules, whose rays (in a 

 typical case) will be set at co-equal angles of 120° (Fig. 313, F). This 

 latter condition of inequahty will be open to modification in various 

 ways. It will be modified by any inequality in the specific tensions 

 of adjacent cells ; as a special case, it will be apt to be greatly modified 

 at the surface of the system, where a spicule happens to be formed 

 in a plane perpendicular to the cell-layer, so that one of its three rays 

 lies between two adjacent cells and the other two are associated 

 with the surface of contact between the cells and the surrounding 

 medium; in such a case (as in the cases considered in connection 

 with the forms of the cells themselves on p. 494), we shall tend to 

 obtain a spicule with two equal angles and one unequal (Fig. 313, 

 A, C) ; in the last case, the two outer, or superficial rays, will tend 

 to be markedly curved. Again, the equiangular condition will be 

 departed from, and more or less curvature will be imparted to the 



