360 ON THE THEORY OF VEGETABLE SPIRALS. 



and the same line. The spiral in the figure has for its angle 

 of divergence the fraction -j^-, that is, it consists of 11 leaves 

 and goes 7 times round the axis ; counting always from left to 

 right the successive leaves are found at intervals of 7 cells. 

 Now if we blot out all that lies to the right of the line DD and 

 consider the first 7 cells by themselves as having been unwound 

 from a smaller cylinder, the leaves will be found to stand at 

 equal intervals from each other, namely, at intervals of 3 cells. 

 There is indeed a dislocation as to height, but height is through- 

 out the Theory of Vegetable Spirals an unessential, or at least 

 very variable element. Similarly what lies to the right of the 

 line DD forms a system of 4 leaves, similarly arranged at in- 

 tervals of 3 cells. Thus the spiral ^ is resolved into two whose 

 angles of divergence are respectively f and f . The former is 

 of course the same as a spiral whose angle of divergence is % 

 only running in the opposite direction ; and as it is usual to 

 give the name of Fundamental Spiral to the flattest or most 

 sloping spiral which can be drawn through the leaves of a given 

 system, the resolution we have effected may be described by 

 saying that the original system has been divided into two, whose 

 fundamental lines run in opposite directions, thus suggesting 

 the notion of two opposing or antagonistic growths, making up, 

 by the mutual influence of their antagonism, one symmetrical 

 whole. Now I would propose, as a sort of postulate, the assump- 

 . tion that every system which forms a part of a system actually 

 existing in nature is capable of independent existence, that it 

 only wants, if the expression may be used, to be allowed to get 

 possession of the whole axis of growth in order to shape itself 

 into a symmetrical spiral. The consequences of this assumption 

 are sufficiently interesting to make it worth while to trace them 

 in detail. They afford a remarkable instance of the confirmation 

 by facts of an a priori principle : the principle in question being, 

 so to speak, an interpretation of Schelling's celebrated maxim*, 

 that the whole is in every part and every part in the whole ; 

 a maxim which, though it may have led Oken wrong (I allude 

 of course to his speculations as to the significance of the bones 

 of the skull), yet enabled him to lead others right. 



2. Let us in the second place make an assumption naturally 



* Thi& maxim is in effect equivalent to the fundamental principle of Leibnitz's 

 philosophy, that each monad represents the universe. 



