VII 



OF HEXAGONAL SYMMETRY 



515 



Fig. 195. 



Female cone 



of Zamia. 



A beautiful hexagonal pattern is seen in the male and female 

 cones of Zamia, where the scales which bear the pollen-sacs or the 

 ovules are crowded together, and are so formed and circumstanced 

 that they cannot protrude and overlap. They become 

 compressed accordingly into regular hexagons*, smaller 

 and more regular in the male cone than in the female, 

 in which latter the cone as a whole has tended to grow 

 more in breadth than in length, and the hexagons are 

 somewhat broader than they are long. In a cob of 

 maize the hexagonal form of the grains, such as should 

 result from close-packing and mutual compression, is 

 exhibited faintly if at all; for growth and elongation 

 of the spike itself has reheved, or helped to reheve, the 

 mutual pressure of the grains. 



The pine-cone shews a simple, but unusual mode of 

 close-packing. The spiral arrangement causes each 

 scale to lie, to right and to left, on two prmcipal spirals; 

 it has close neighbours on four sides, and mutual 

 compression leads to a square or rhomboidal, instead of an hexa- 

 gonal, configuration*. On the other hand, the scales of the larch - 

 cone overlap: therefore they are not subject to compression, but 

 grow more freely into leaf- like curves. 



The story of the hexagon leads us far afield, and in many directions, 

 but it begins with something simpler even than the hexagon. We 

 have seen that in a soapy froth three films, and three only, meet 

 in an edge, a phenomenon capable of explanation by the law of 

 areae minirnae. But the conjunction, three by three, of almost any 

 assemblage of partitions, of cracks in drying mud, of varnish on an 

 old picture, of the various cellular systems we have described, is a 

 general tendency, to be explained more simply still. It would be 

 a complex pattern indeed, and highly improbable, were all the cracks 

 (for instance) to meet one another six by six; four by four would 

 be less so, but still too much; and three by three is nature's way, 

 simply because it is the simplest and the least. When the partitions 

 meet three by three, the angles by which they do so may vary 

 indefinitely, but their average will be 120°; and if all be on the 



* In some small, few-scaled cones the packing remains incomplete, and the scales 

 are four-, five-, or six-sided, as the case may be. 



