xiv] 



OR PHYLLOTAXIS 



925 



many in the other. Accordingly, in our diagrammatic construction, 

 the spirals AO and aO must, and always can, be so taken that m 

 spirals parallel to aO, and n spirals parallel to AO, shall separately 

 include all the leaves upon the stem or cone. 



If m and n have a common factor, I, it can easily be shewn that 

 the arrangement is composite, and that there are I fundamental, 

 or genetic spirals, and I leaves (including A) which are situated 



Fig. 451. 



exactly on the line. Aa. That is to say, we have here a whorled 

 arrangement, which we have agreed to leave unconsidered in favour 

 of the simpler case. We restrict ourselves, accordingly, to the cases 

 where there is but one genetic spiral, and when therefore m and n 

 are prime to one another. 



Our fundamental, or genetic, spiral, as we have seen, is that which 

 passes from A (or a) to the leaf which is situated nearest to the 

 base-line Aa. The fundamental spiral will thus be right-handed 

 (A, P, etc.) if F, which is nearer to A than to a, be this leaf — left- 

 handed if it be jo. That is to say, we make it a convention that we 



