ECCENTRIC GROWTH. 269 



which may still be practically circular in section. The term 

 dorsiventral thus became applied by Sachs as indicating a definitely 

 physiological conception of plant symmetry, which might be ex- 

 pressed by a morphological hilaterality, but the bilaterality must 

 not be " double," that is to say, a dorsiventral organ must have 

 two unlike surfaces. 



It is clear that not only have several special cases been included 

 under the same terms, but the existing terms are not very strictly 

 defined. Thus the case of a symmetrical (1 + 1) leafy shoot pre- 

 sents little difficulty ; there is no need to regard it as bilateral 

 any more than a (5-f 5) shoot would gain by being called ten- 

 sided. The cases of the cladode and the fasciated stem are again 

 only special cases of radial symmetry, while the latter has much 

 in common with the often-quoted type of Marchantia and Algal 

 forms, as F'Mus. Two cases remain, the lifacial foliage leaf, and 

 the " dorsiventral " shoot bearing leaves on the so-called dorsal 

 surface: the former presenting a phenomenon which is the 

 property of an appendage without reference to the symmetry of 

 the axis bearing it, the latter a special case of axis construction. 

 In fact, it now becomes apparent that the so-called dorsiventrality 

 of these structures may be due to entirely different causes, and 

 that two distinct phenomena have been included under the same 

 metaphorical expression. The bilaterality of an appendage is a 

 mathematical property of the primordium, and may be expressed 

 as either a bifacial or isdbilateral flattening ; while the so-called 

 dorsiventraUty of a leafy shoot system is merely the expression 

 of its structural eccentricity. The term dorsiventral may be there- 

 fore conveniently eliminated from botanical phraseology altogether ; 

 the physiological conception of Sachs being clearly defined by his 

 later expression plagiotropism. At any rate, before committing 

 oneself too far to the pursuit of academic abstractions as to the 

 symmetrical relations of living and growing organisms, it will be 

 well to consider the mathematical consequences of certain simple 

 types of growth. 



Eeturning to the original proposition of growth, it is obvious 

 that mathematically centric growth is only a special and ideal 

 case, which is possibly extremely rare in nature. If perfect radial 



