GEOMETRICAL RELATIONS OF CLEAVAGE-FORMS 



367 



and Lamarle have shown, assume a polyhedral form and tend toward 

 such an arrangement that tJic area of surface-contact between them is 

 a mininmni. Spheres in a mass thus tend to assume the form of 

 interlocking polyhedrons so arranged that three planes intersect in 

 a line, while four lines and six planes meet at a point. If arranged 

 in a single layer on an extended surface, they assume the form of 



C D 



Fig. 170. — Cleavage of Polygordius, from life. 

 A. Four-cell stage, from above. B. Corresponding view of eight-cell stage. C. Side view of 

 the same (contrast Fig. 169, C) . D. Sixteen-cell stage from the side. 



hexagonal prisms, three planes meeting along a line as before. Both 

 these forms are commonly shown in the arrangement of the cells of 

 plant and animal tissues; and Berthold {^"i^) and Errera ('86, '87), 

 carefully analyzing the phenomena, have endeavoured to show that 

 not only the form and relative position of cells, but also the direction 

 of cell-division, is, partially at least, thus determined. 



It is through displacements of the cells of this type that many of 



