THE USES AND ORIGIN OF THE ARRANGEMENTS OF LEAVES IN 1 TS. 3 



of Phyllotaxy is concerned. The latter, or the verticil imngemeul' thou h 

 presenting a great variety of forms, are so obviously all of the name general 

 and simple type, that they present no difficulties or problems for the < \- reise 

 of mathematical skill. Their varieties consist simply in the number of Iee\< in 

 the whorl. From two leaves placed oppositely, these whorii vary throu h all 

 numbers to very large ones, and in all these vaiicti the simple law holds* that 

 the leaves of successive whorls, being of the one Dumber and placed in each 



whorl at equal distances around the stem, like the spokes of a wheel, are mi 

 disposed that the leaves of the upper whorl stand directly over lie angular 

 spaces between those of the lower one. These features ol 

 obviously the same adaptations as those we shall fad in the more complicated 

 spiral arrangements, that I will consider them both together. Th. appear to 

 be two solutions of the same problem in the economy of the high 

 fe; though it is probable that the wh 



ife]mMit ii re so 



r 



the inferior one. H 



pproaches in simplicity most nearly to the alternate system among the spit 



perfectly distinct from this. An opposition of leav m th 



form 



horl is an accident or trivial circumstance dependent on the fact that the 



f leaves in the whorl is in many cases an even one; while in the 



mber 



alternate arrangement this opposition is an essential character. Tin- would not 

 be strietly the case, indeed, if the theory were tree .hat the ah, mate u «dl 

 as the other spiral arrangements are only modifications of a s.ngle typ.ca. one. 

 But an examination of the evidence will show very slight ground, for tins 

 opinion. No donbt, in the doctrine of development, all .1,,-e ,n,nge„,, , mu- 

 be considered as modifications of some single ancent ,„nn, t.mng , -. - 

 quite likely, was very diiferent from the typical arrangement, or the p. , 



,n the theory of Phyllotaxy. The important pom., however to be 



that on 



nection betw 



the theory of development .here i- properly no ( n, , ron- 

 L opposLn of leaves in whorls and those „ the ahernaW 



— . 7 . f\ !n . tlie three-leaved systems of .he two types the 



arrangement. And, m eed m ^* \ J~b a whorl stand over the 



contrast is very marked; for the three letu ^ 



angnlar spaces between the three of he who 1 b low J ^ 



ments of this type ; while the three *£ of £ * V J "^ ^ ^ 

 severally directly over the three helo« th cm . I S rf 



two great types will be specially cons.dercd « hen we c 



the origin of both from *££*£ Jjso properly applicable to group. 

 The names "system "and cycle 



