GEOMETRICAL RELATIONS OF CLEAVAGE-FORMS 



363 



Sachs has shown in the most beautiful manner that all the above 

 ideal types are closely approximated in nature, and Rauber has applied 

 the same principle to the cleavage of animal-cells. The discoid or 

 spheroid form is more or less nearly realized in the thalloid growths of 



Fig. 168. Geometrical relations of cleavage-planes in growing plant-tissues. [From SACHS, 

 after various authors.] 



A. Flat ellipsoidal germ-disc of Melobesia (Rosanoff) ; nearly typical relation of elliptic 

 periclines and hyperbolic anticlines. B, C. Apical view of terminal knob on epidermal hair of 

 Pinguicola. B, shows the ellipsoid type, C. the circular (spherical type), somewhat modified 

 (only anticlines present). D. Growing point of Salvinia (Pringsheim), typical ellipsoid type; 

 the single pericline is, however, incomplete. E. Growing point of Azolla (Strasburger) ; circular 

 or spheroidal type transitional to ellipsoidal. F. Root-cap of Equisetum (Nageli and Leitgeb) ; 

 modified circular type. G. Cross-section of leaf-vein, Trichomanes (Prantl) ; ellipsoidal type with 

 incomplete periclines. H. Embryo of Alisma ; typical ellipsoid type, pericline incomplete only 

 at lower side. /. Growing point of bud of the pine (Abies} ; typical paraboloid type, both anti- 

 clines and periclines having the form of parabolas (Sachs) . 



various lower plants, in the embryos of flowering plants, and else- 

 where (Fig. 1 68). The paraboloid form is according to Sachs charac- 

 teristic of the growing points of many higher plants ; and here, too, 

 the actual form is remarkably similar to the ideal scheme (Fig. 168, /). 



