VIIl] 



THE PARTITIONING OF SPACE 



389 



case of the other two we may fairly assume that their proper 

 and original arrangement was that of our type 6 b (Fig. 158), 

 though the central intermediate partition has been crowded out 

 by partial coalescence. When with increasing age the septa 

 become more numerous, their arrangement becomes exceedingly 

 variable ; for the simple reason that, from the mathematical 

 point of view, the number of possible arrangements, of 10, 12 

 or more cellular partitions in triple contact, tends to increase 

 with great rapidity, and there is little to choose between many 



Fig. 174. Heterophyllia sp. (After Martin Duncan.) 



of them in regard to symmetry and equilibrium. But while, 

 mathematically speaking, each particular case among the multi- 

 tude of possible cases is an orderly and definite arrangement, 

 from the purely biological point of view on the other hand no 

 law or order is recognisable ; and so McCoy described the genus 

 as being characterised by the possession of septa " destitute of any 

 order of arrangement, but irregularly branching and coalescing in 

 their passage from the solid external walls towards some indefinite 

 point near the centre where the few main lamellae irregularly 

 anastomose." 



