22 RELATION OP PHYLLOTAXIS TO MECHANICAL LAWS. 



plotted out on a rubber-tube, and this greatly extended, it can be 

 made to fall as low as one pleases. The mechanical effect of such 

 tension or compression has been noted by Schwendener and Weisse. 

 Now, in this plant, the expansions and contractions of the 

 system are due to varying rates of growth in the main axis. The 

 spiral itself is constant and the same genetic spiral runs uniformly 

 through the whole shoot, including different sets of parastichy 

 curves, which, when marked out along the axis, present the appear- 

 ance of a spiral spring expanded and contracted at different points. 



The actual arrangement of the members on the stem is, in fact, 

 here quite secondary ; varying phyllotaxis phenomena are produced 

 by varying rates of growth, a conclusion already reached by Bravais 

 from the study of the rosette of Sempervivvmi and its flowering 

 axis. The spiral arrangement is not an end at which the plant 

 is aiming, but the mere retention of a uniform system impressed 

 on it in the terminal bud. 



It follows, then, that phyllotaxis is the obvious and visible 

 expression of more obscure phenomena in the growing apex, and 

 must be referred to the first Zova of Growth, since in passing through 

 the Zone of Elongation it may be fundamentally altered in appear- 

 ance. 



Confirmation of the view that the spiral is only the relic of 

 the effect of certain agencies at the growing point, and is not 

 directly essential to the welfare of the plant, is shown by the 

 general occurrence of cases in which the originally spirally arranged 

 leaves become secondarily dorsiventral in arrangement by torsion 

 of the leaf-stalks ; i.e., the effect of the spiral becomes secondarily 

 corrected as soon as it becomes a distinct disadvantage to the plant. 



It follows again that, for any spiral leaf arrangement that has 

 passed through this second zone of elongation, no expression 

 which is not a purely arbitrary and conventional one can be 

 formulated.* 



Phyllotaxis is to be studied in the growing apex itself, or in 

 structures which have undergone so little elongation that the 



* Transverse sections of the apices of shoots of Euphorbia Wulfemi {cf. figs. 

 90, 91) show systems in which the contact parastichies are (8 + 13), (5 + 8), and 

 in very weak shoots (3 + 5). 



