362 ON THE THEORY OF VEGETABLE SPIRALS. 



elusion established inductively by Schimper and Braun, namely, 

 that these are the only numbers which present themselves in 

 vegetable spirals. I believe at least I am justified in saying so, 

 for though Professor Henslow*, in giving an account of Braun's 

 researches, does not say that no other numbers occur than those 

 of the series, yet all his examples belong to it, and the principle 

 is broadly stated as a general law by linger in his Botanical 

 Letters|. To this numerical law we can now append an equi- 

 valent statement, which not being numerical brings us a good 

 deal nearer to a theory of the actual genesis of vegetable spirals, 

 for we may substitute the following as an equivalent law, namely, 

 that every vegetable spiral is resoluble into antagonistic portions, 

 actually unsymmetrical but potentially symmetrical. In this 

 form the law serves to give morphological significance to many 

 obvious phenomena ; as for instance, the three larger petals of 

 the pansy stand in opposition to the two smaller, the balance of 

 symmetry not having been fully established. Again, the five 

 petals of papilionaceous flowers present us with two petals op- 

 posed to three, the three latter containing a sub-system of two 

 petals opposed to one. Thus perhaps too we are led to recognise 

 a certain duplicity in the structure of cruciferous flowers ; but 

 I will not venture to enter on any but obvious examples. 



It is interesting to observe how consciously or unconsciously 

 we are always influenced by the forms of nature. That man is 

 her minister and interpreter is true, not only of his knowledge 

 and his power, but in that which combines both, his works of 

 art. That volutes and tracery reproduce the forms of the vege- 

 table world is obvious, but we may be reminded of the numerical 

 relations of which we have been speaking when we recollect 

 how often three lights in a western window are opposed to five 

 in an eastern: the higher symmetry in the holier place and 

 related to the lower as the flower to the leaf. 



Sed fugit interea, fugit irreparabile tempus; 

 Singula dum capti circumvectamur amore. 



3. The result at which we have arrived may perhaps be 

 more clearly expressed by saying that every natural spiral can 

 be resolved into two parts, of which the smaller stands in the 



* In Lardner's Cabinet Cyclopaedia. 



t Naumann appears to have recognised a spiral of 377 elements, thus reaching 

 the thirteenth term of the series. 



