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MEMOIRS OF THE AMERICAN ACADEMY. 



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which this name is applied to the spiral arrangements ; and in respect to their 

 distributive and cyclic characters, whorls are thus most closely related to the i, 

 or alternate system. But there is, as I have said, no fundamental or genetic 

 relationship between them and this particular form of the spiral arrangement. 

 The relationship is rather an adaptive or analogical one. They are, so to speak, 

 two distinct solutions of the same problem, two modes of realizing the same utili- 

 ties, or securing the same advantages; like the wings of birds and bats. 



One of these utilities we have now sufficiently considered, namely, that which 

 the theoretical angle k would realize most perfectly; by which the leaves would 

 be distributed most thoroughly and rapidly around the stem, exposed 

 completely to light and air, and provided with the greatest freedom for sym- 

 metrical expansion, together with a compact arrangement in the bud. Neither 

 this property, nor an exact cyclical arrangement, ought, as I have said, to be 

 found, or expected, in the incipient parts at the centre of the bud, any more 

 in the perfected proportions and adaptations of the mature animal could be 

 expected, or are found, in the embryo. Both are fully determined, no doubt, 

 in the vital forces of the individual's growth. Our question is, what has de- 

 termined such an action in these vital forces? "Their very nature, or an 

 ultimate creative power," is the answer which the theory of types gives to this 

 question. « The necessities of their lives, both outward and inward, or the 

 conditions past and present of their existence," is the answer of the theory 

 of adaptation. Science ought to be entirely neutral between these theories, and 

 ready to receive any confirmation of either of them which can "be adduced; 

 though, from this point of view, the theory of adaptation has a decided advan- 

 tage ; since the theory of types can have no confirmation from observation 

 except of a negative sort, the failure of its rival to show conclusive proofs. 

 But we have seen that whatever can be said in favor of the view, that there 

 is a unity of type in the intervals of spiral arrangements, is directly convertible 

 to the advantage of the theory of adaptation; since this unity consists in the 

 distributive property common to these arrangements * Natural Selection, however, 



* There is a remarkable analogy between this relation and that of the two tbeories of the structure of the 

 honey-cell. The work of the bees suggests to the geometrician a perfectly definite and regular form, which he 

 finds to be the most economical form o( compartments into which space can be divided j or he finds that the 

 honeycomb would be the lightest, or be composed of the least material for the same capacity and number of com- 

 partments, if part,t,oned into such figures as the typical cell. From the definition of this figure he is able to com- 

 pute its angles and Dronortinn* wifK * A a ~*. a „ ~e • • , t- . ., , . . . ° . . . 



often deviates widely. The 



