Symmetry 149 



any fundamental similarity between the two is uncertain. For a discussion 

 of this problem the reader is referred to the work of Haeckel (1866) and 

 others. 



Although many symmetries in cells and minute multicellular structures 

 resemble those in inorganic systems under the control of surface forces, 

 organic symmetries are conspicuous in much larger bodies where these 

 forces are not operative. Organic bodies are semiliquid systems which are 

 subject to continual loss and replacement of material, as is shown by 

 tagged isotopes and in other ways, and in this respect are unlike crystal- 

 line structures, which are usually fixed and static. This semiliquid char- 

 acter is also reflected in the almost universal presence of curved lines and 

 surfaces in organic bodies as compared with the systems of straight lines 

 and planes which distinguish molecular and crystalline forms. This is 

 what makes possible the infinite number of similar planes of symmetry 

 around an organic axis instead of the limited number of two, three, four, 

 and six found in crystals. 



Aside from these differences from the inorganic, the symmetries shown 

 by living plant structures also possess two distinctive features of their 

 own which provide the key to an understanding of their nature. 



First, they are often expressed in multiple parts. A typical plant body 

 consists of an indeterminate series of repeated, essentially similar parts, 

 laterally dispersed along a continuous axis. These are leaves, branches, 

 and lateral roots in higher plants and analogous repetitive structures in 

 lower ones. The most conspicuous examples of organic symmetry are 

 found in the relations of these repeated structures to the axis from which 

 they arise. This is a type of symmetrv unlike that found in most inorganic 

 systems. 



Second, many plant axes, particularly those of the aerial portions of the 

 plant, have either a spiral twist or a spiral arrangement of their parts. 

 This complicates the expression of symmetry and, in the case of phyllo- 

 taxy, has given rise to a great deal of speculation. Spirality seems to be a 

 characteristic feature of protoplasmic behavior in many cases. The course 

 of streaming is often spiral in a cell and thus may be reflected in the 

 structure of the cell itself, as in the familiar cases of Chara and Nitella. 

 Cell growth may be spiral, as has been shown by Castle ( 1936 ) in the 

 hyphae of Phycomyces, and there are many other examples. 



These two traits— multiple parts and spirality— make the symmetry of 

 plant parts radically different, at least in external expression, from the 

 symmetries of the inorganic world. 



A few single-celled forms and some colonies like those of Volvox may 

 be spherical and completely symmetrical around a point. This seems to 

 be primarily an expression of surface forces, however, rather than of in- 

 herent symmetry. Most single-celled plants, however, like the desmids, 



