106 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



Fibonacci ratios which have 1 only as a common factor, it becomes 

 possible to draw a single genetic-spiral throughout tbe entire 

 series. 



It will be noticed that the formation of lateral appendages one 

 at a time, which was put forward as being possibly a phylogenetic 

 reason for asymmetrical growth, is not wholly satisfactory ; but if 

 it will not hold, it leaves no clear justification for regarding the 

 tendency of plants, in the more general case, to grow asymmetrically 

 rather than symmetrically, as anything beyond the mere expression 

 of the mathematical fact that symmetrical construction is only to 

 be regarded as a special case of the proposition of growth. This 

 phylogenetic conception was based on the observation that m the 

 great bulk of lower cellular forms, the segmentation of the plant- 

 body into component cells is relatively on so large a scale that it 

 apparently controls the space-form of the entire organism, although 

 it is still possible to regard it as the mere mechanism by which the 

 space-form is divided into units. The range of bulk-variation in 

 the working cells of green plants is remarkably restricted in 

 comparison with the range of bulk-variation in- the adult organisms ; 

 and just as in building a small house the size of the bricks may 

 become an important factor, while in a large one it would be 

 negligible, so in the construction of a small plant, histological 

 details are more striking than in immense plant forms. In these 

 simpler constructions, the mechanism of which is apparently 

 controlled by a single apical ceU, the practical details of karyo- 

 kinesis and cell-formation require that new members initiated as 

 single eeUs should be formed one at a time from the initial cell, 

 and it is quite possible to regard this mode of production of a 

 space-form comprised of serially produced members as becoming 

 fixed, and then being retained even after the relative increase in 

 the bulk of the organism and its growth activities would admit of 

 the formation of massive members in which the cell segmentation 

 would be of subsidiary importance. By starting from this first 

 standpoint of a controlling genetic growth movement, which comes 

 into line with the theories of Schimper and Braun, the strength or 

 weakness of the hypothesis should become manifest. It is true 

 that the genetic spiral apparently never reverses, although a 



