174 The Phenomena of Morphogenesis 



is larger than the outer, and its blade often reaches farther down the 

 midrib. In the beech, on the other hand, it is the outer part of the leaf 

 which is the larger. Many cases of leaf asymmetry, notably the conspicu- 

 ous examples in species of Begonia, are related to the position of the 

 leaf on the stem, although here the stem is often short and inconspicuous. 

 Somewhat similar expressions of apparent asymmetry are evident in 

 the branch pattern of plagiotropic shoots. In some cases, the branches 

 which arise on lateral shoots are larger on the inside, toward the apex 

 of the shoot, as in flat stems of Thuja. More commonly those on the out- 

 side, away from the axis, are larger, a phenomenon which Wiesner 

 (1892a, 1895) has called exotrophy and which he explains as due to nu- 

 tritional causes. Leaves on the outside of lateral shoots are often larger 

 than those on the inside, a special type of anisophylly. 



Fig. 7-13. Anisophylly in Goldfussia. Diagram, of shoot from above. The leaves are 

 opposite but the pairs are somewhat displaced. One member of each pair is larger 

 than the other, and one side 'of each leaf is larger than the other side. In the axillary 

 shoot, position with reference to the symmetry of the whole determines leaf size. 

 ( From Goebel. ) 



All such structures, which in a strict sense are asymmetric, are really 

 complex patterns of symmetry induced when a fundamentally radial 

 system becomes dorsiventral. What the factors are— whether nutritional, 

 hormonal, or other— which determine these differences is not known. This 

 is evidently the point where the relatively simple phenomenon of sym- 

 metry merges into the more complex one of organic pattern in general. 

 In flat, dorsiventral shoots, which are essentially structures in two di- 

 mensions only, there is an excellent opportunity to analyze the problem 

 of pattern in one of its simplest expressions. 



The external dorsiventrality of stems is often accompanied by dorsi- 

 ventrality of internal structure. Where the stem is flattened, the vascular 

 cylinder is likely to be so as well. Sometimes the symmetry changes do 



