186 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



to equality of the ratios, there is a distinct sign of symmetrical 

 construction, in that any change involving a rise or fall in the 

 system must, in order to retain the bijugate construction, take 

 place by adding or losing two curves simultaneously, since if a 

 single path be gained or lost, the ratio may become divisible by 

 unity only and thus work out as a single genetic spiral. 



Prom the point of view that a decussate system represents a 

 doubled construction, (2 + 2) = 2 (1 + 1), the possibility of the 

 secondary reversion to the doubled spiral construction implied in 

 bijugate systems is very apparent. The examples met with in the 

 inflorescence of Verbena and the flower of Galycanthus might be 

 thus explained ; but it must be pointed out that the rule does not 

 hold for Jlelianthios annuus, which, though decussate at first, reverts 

 to normal Fibonacci ratios with almost perfect constancy ; nor, again, 

 does it apply to II. rigidus and II. strmnosus, which are decussate 

 almost to the terminal capitulum. The fact that the more obvious 

 parastichies of garden Fer6e?ias may vary from (5 + 8) to (6 + 10), 

 and the floral members of Galycanthus in the same manner, is quite 

 independent of the decussate phyllotaxis of the vegetative shoot, 

 and comparable with similar variation in Sedum elegans, Podocarpus 

 japonica, etc. 



Again, the distinction between a truly decussate (2 + 2) system 

 and the bijugate variant (2+4) is often indistinguishable to the eye, 

 so far as the general appearance of the adult shoot is concerned. 

 That very considerable displacements may take place in the former 

 symmetrical construction is shown, for example, by taking sections 

 of a decussate bud of Epilohium angustifolium (perennating shoot) : 

 on cutting a section a little above the actual apex (fig. 71, 1), very 

 considerable changes may be seen to follow irregular growth and 

 twisting of the older leaves. Such distortion is very general in 

 decussate leafy shoots, and requires to be carefully separated from 

 bijugate construction. Thus in the typically decussate family of 

 the Labiatae, this external deformation of the symmetrical con- 

 struction is very common, and the original case of Ajuga genevensis 

 evidently comes under this head: in rosette - forming mem- 

 bers of this and other families, or in their seedlings and peren- 

 nating foliage shoots,, the apparent reversion to an asymmetrical 



