THE USES AND ORIGIN OF THE ARRANGEMENTS OP LEAVES IN PLANTS. 401 



or the indirect agency of utility in producing adaptations, cannot, so far 

 have yet seen, be appealed to for the explanation of the 



a~ 



spir 



general ; nor for the explanation of the verticil arrangements ; though the character 

 in the latter, in which they resemble the alternate system, may come within the range 

 of this explanation through the utility I have pointed out. The only ground 

 for the action of Natural Selection which I have yet shown is in the choice 

 there is among possible spiral arrangements with reference to this utility; and 

 it appears that the principle is fully competent to account for the relative 

 frequency of these, and the entire absence of some of them from the actual 

 forms of nature. 



We now come to the special study of two other features which have ap- 

 peared in these arrangements, namely, the spiral character itself and the sim- 

 plicity of their cycles. The cyclic character is entirely wanting in the ideal 

 arrangement of the interval k ; but, as I have saipl, this interval cannot be proved 



to exist in nature; for even if it did, it would be indistinguishable even from 



the simple fraction f. This very fact, however, makes the interval f, a sulli- 

 ciently exact realization of the distributive property, according to the degree of 



exactness with which actual plants are constructed. But £ is also a compara- 



tively simple cycle, though there would not be sufficient evidence that its cyclic 

 character is an essential one, or other than incidental to the scale of exactness 

 in the structure of plants, if there did not exist several distinguishable and 

 simpler cycles, namely, J, f, and }. The cyclic character of leaf arrangements 

 is, indeed, a more noticeable feature in plants generally than the distributive 

 one. It is obviously essential, and involves on the theory of adaptation some 

 important utility. Whatever this may be, it is clear that it has to be gained 

 by means directly opposed to those which secure distribution; that is, its utility 

 depends on leaves coming together in direction, or being brought nearer to 

 each other than they would otherwise be; instead of their being dispersed as 

 widely .and as thoroughly as possible. This utility is obviously to be sought in 

 the internal relations of leaves to each other, or their connections through the 



cause of the structure, or as the pattern which guides the bees' instinct towards an ideally perfect economy. But 

 a plainer order of economy, a simple housewifely one, saving at every turn, together with the conveniences and 

 utilities which govern the work of social nest-building insects in general, would result, if carried out to perfection, 

 in the very same form. Hence the theory of 'adaptation regards the honey-cells as modifications of similar but 

 rougher structures of the same sort, determined by the further utility of simple saving in working with a costly 

 material ; and whatever evidence there is that the bees' instinct is determined toward the ideally perfect type of 

 *u„ u 11 • j.- . .1 iL i. -l r„ >u» ;♦ U «n Hfttprmined bv these simple conveniences and utilities. 



