XIV] • OR PHYLLOTAXIS 651 



is to vary, to make blind shots at constructions, or to 'mutate 

 as it is now termed ; and the most suitable of these constructions 

 will in the long run be isolated by the action of Natural Selection.' 

 Finally, and this is the most concrete objection of all, the supposed 

 isolation of the leaves, or their most complete "distribution to 

 the action of the surrounding atmosphere" is manifestly very little 

 affected by any conditions which are confined to the angle of 

 azimuth. If we could imagine a case in which all the leaves of 

 the stem, or all the scales of a fir-cone, were crushed down to one 

 and the same level, into a simple ring or whorl of leaves, then 

 indeed they would have their most equable distribution under 

 the condition of the "ideal angle," that is to say of the "golden 

 mean." But if it be (so to speak) Nature's object to set them 

 further apart than they actually are, to give them freer exposure 

 to the air than they actually have, then it is surely manifest that 

 the simple way to do so is to elongate the axis, and to set the 

 leaves further apart, lengthways on the stem. This has at once 

 a far more potent effect than any nice manipulation of the "angle 

 of divergence." For it is obvious that in i^(^ . sin 6) we have a 

 greater range of variation by altering 6 than by altering 4>. We 

 come then, without more ado, to the conclusion that the "Fibon- 

 acci series," and its supposed usefulness, and the hypothesis of 

 its introduction into plant-structure through natural selection, 

 are all matters which deserve no place in the plain study ol 

 botanical phenomena. As Sachs shrewdly recognised years ago. 

 all such speculations as these hark back to a school of mystical 

 idealism. 



