ON THE THEORY OF VEGETABLE SPIRALS. 369 



points of the spiral next below it falls short of this limit, and 

 vice versa. In consequence of this, under the influence of circum- 

 stances, which we cannot appreciate, the last eight points may 

 repeat themselves in a symmetrical position, and maintain this 

 form of symmetry permanently. On the contrary, if after having 

 thus repeated themselves they are again subjected to the in- 

 fluence of the thirteen preceding points, a sort of compromise 

 is effected, of which the result is a spiral of twenty-one points. 

 The two cases resemble a contest between the constitution of 

 a whole kingdom and that of a particular province ; the pro- 

 vince may revolt and succeed in establishing its own law 

 universally, or a mixture of the two may become the common 

 law of the land. Thirdly, things may remain as they are and 

 the provincial law be altogether abrogated. Thus the opposi- 

 tion of the greater part to the whole may under varying cir- 

 cumstances produce an increase or a decrease in the complexity 

 of the system, and the same cause, namely the rhythmical ten- 

 dency which seems to belong to all growth, may be at one time 

 a cause of change, and at another of permanence. If we try to go 

 beyond this, " ad ulteriora tendentes ad proximiora recidemus," 

 our explanations must become vaguer and yet more unsatis- 

 factory. Something might be said of the contest between the 

 principles of recurrence and opposition, but it would too much 

 resemble the Us and amicitia of Empedocles 1 . 



6. The attempt I am about to make to trace the general 

 characters of vegetable arrangement in the structure of leaves 

 is based upon so simple a remark that I can hardly suppose it 

 has escaped observation. As however I have not met with it, it 

 seemed worth while to set it down here though I cannot trace 

 its consequences in detail. The primary division of the nerves 

 of leaves is into anguli-form and curvi-form nerves, 'that is, 

 those which have a straight portion at their base and those 

 which exhibit curvature throughout. Now just as the straight 



divergence, namely, this limiting one; and that if botanists have thought they 

 recognised distinct systems, it has teen because they have stopped sometimes at 

 one degree of approximation to it and sometimes at another; but this doctrine ap- 

 pears to be opposed to ascertained facts, the real unity of nature does not in this 

 way exclude variety. 



1 When the spiral passes into a whorl, the tendency to rhythmical recurrence 

 seems generally to cease and to be replaced by a tendency to symmetrical anti- 

 thesis or alternation, as if, speaking mathematically, positions of equilibrium pre- 

 viously stable had become unstable, and vice vend. 



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