LEWIS: PRODUCTION OF TETRAKAIDECAHEDRA 5 



Cell division extends the difference in the number of facets both above 

 and below the afore-mentioned range of 12 to 18. Yet if the average plane 

 of division is hexagonal (which would be expected when division bisects a 

 cell rather than cuts off a corner) it will not affect the average of 14 facets. 

 It causes a diversity in cell size, incompatible with a full realization of the 

 Kelvin pattern. Yet if division occurs in a prevailing plane, it can orient 

 the cells, and orientation makes possible an approach to Kelvin's orthic 14— 

 hedron, which approximation is indubitably present in the oriented pith of 

 Eiipatoriwn and in similar tissue. 



We conclude, therefore, that an average of 14 facets can be due to chance, 

 or to tension, or a combination of both. The mathematical solution of the 

 problem of dividing space into uniform bodies of least surface area and of 

 maximum stability has been solved by Lord Kelvin's minimal 14-hedron (or 

 its close approach, — his orthic 14-hedron). Since such diverse forms as the 

 stellate 12-rayed cells of J uncus, and the prosenchymal tracheids of the pine 

 with from 18 to 22 facets apiece, are accountable as derivatives of the Kelvin 

 14-hedron, as well as all the forms in cork and pith, it may properly be 

 regarded as the typical shape of cells in masses. There is no rival uniform 

 pattern. But it is only through absolute uniformity in size, precision in align- 

 ment, and the dominance of surface tension (3 factors at least) that a foam 

 of minimal 14-hedra may be expected. These conditions have apparently 

 not yet been realized in any cells or any froth. The typical shape thus remains 

 a mathematical abstraction, whereas the actual shapes are coming to be well 

 understood, and haphazard is a factor. 



Harvard Medical School 

 Boston, Massachusetts 



