MULTIJUGATE TYPES. 193 



a fall apparently commences at about 101, and the curves are 

 evidently dropped out with the regularity postulated for "dis- 

 continuous phyllotaxis" in the Fibonacci ratio. 



Such a diagram presents, in fact, an elegant epitome of the 

 phenomena which any theory of phyllotaxis is called upon 

 to interpret, and if possible explain. It includes a bijugate con- 

 struction, rising from a known constant system of (2 + 4) to an 

 equally definite (10-1-16) system, as shown by the contact lines 

 of the rhomboid members, and then falling equally symmetrically 

 towards the close of the construction to two leaves placed opposite 

 each other in the median line, just like the initial pair of the 

 series. 



Treated as the product of a spiral ontogenetic line of de- 

 velopment, or an oscillating growth movement across the apex, 

 laying down new growth-centres at an approximately equal 

 divergence angle, it is clear that two such genetic paths must 

 be in operation, producing members in diametrically opposed 

 pairs, and that the adjustment of members with a progressively 

 lowered bulk-ratio must also involve slight changes in the 

 oscillation-angle, since the angle which builds a (2 + 4) system is 

 not the same as th^t which builds a (10 -f- 16); how these angular 

 changes may be controlled by the plant is at present quite 

 inexplicable. 



Treated, on the other hand, as a system in which new growth- 

 centres are formed at the points of intersection of indefinitely 

 continued asymmetrical construction curves, among which new 

 paths may be opened up or subsequently closed according to a 

 simple law for the spacing out of the added members around the 

 axis, as already hypothecated for Bipsacus, the number of " genetic 

 spirals " which work out the system in point of time, as also the 

 exact oscillation-angle, becomes immaterial, and the subject admits 

 of clearer expression and is easier to handle. Such a standpoint is 

 here put forward solely on account of these reasons ; it is sufficiently 

 obvious that it does not follow that the simplest method of dealing 

 with facts necessarily involves any account of their actual evolu- 

 tion or causation. To suggest that the plant knows what it is doing 

 in laying down a stated number of curved paths is of course as futile 



