APPLICATION OF SPIRAL- VORTEX CONSTRUCTION. 45 



IV. Application of Spiral-vortex Construction, 

 1. AEKAJSfGEMENT A. 



Under this heading may be comprised the simplest construction in 

 which the lateral members are formed in a free circular vortex, and 

 present the appearance known as "superposed whorls." If the 

 members are formed freely on the paraboloid surface of the cone of 

 growth and exert no pressure whatever on each other, they will, if 

 destined to produce radially symmetrical organs, tend to assume 

 the shape of spheres, and may be thus represented by concentric 

 series of circles. 



Such a construction is, however, rarely met with ; it occurs in 

 flowers (c/. Primula), and is in such cases commonly regarded as 

 of secondary origin. Expressed in terms of single cells, it occurs 

 frequently in the endocortex of roots {cf. Zea Mais), in which the 

 absence of any considerable pressure from the peripheral layers 

 enables the cells to retain the original orthogonal system in which 

 they were developed. 



The mechanical construction of the system, again, as expressed 

 geometrically, indicates that if the mutual pressures of the component 

 members are equal for every member, no disturbance of the system 

 can take place. The circles will tend to become squares, this being 

 again well seen in Zea root; but no hexagonal packing can be 

 initiated unless some additional force is brought into requisition ; 

 such, for example, as may be seen in the Zea root, where unequal 

 growth and the pressure of the outer layers induce hexagonal pack- 

 ing in the exocortex when the endocortex may stUl remain' 

 unaffected. 



