RECREATIVE SCIENCE. 



141 



grow. In Fig. B, if we begin with No. 1, we 

 have to go three times round the stem before 

 we come to No. 8, which is exactly above it. 

 This arrangement of leaf, therefore, would be 

 marked by the fraction f ; if you look at the 

 circle on the top of the stem, you will seo at 

 once that Nos. 1 and 2, which represent the 

 position of the first two leaves, are fths of a 

 circle apart. In Fig. C, where we have only 

 to go once round the stem before coming to 



age are expressed by the following fractions : 

 h i. h i A. 2^>. ih H, etc. It will be seen 

 that these numbers bear a singular relation 

 to each other, for the numerator of each 

 fraction is the sum of the two preceding, and 

 the denominator, in the same way, is the sum 

 of the two preceding denominators ; besides 

 this, you will find that the denominator of 

 one is the numerator of the next but one 

 after it. This shows a very curious mathe- 



Fio. B. 



Fig. a. 



Fig. C. 



the leaf exactly above No. 1, the fraction is 1 , 

 and at the top it is manifest that Nos. 1 and 

 2 are ^th of a circle apart. Although the 

 phyllotaxis is invariably the same in the same 

 species, it is sometimes different in different 

 species of the same genus ; thus in the Euro- 

 pean larch it is i-^, while in the American 

 larch it is |. Botanists have discovered, too, 

 that the most common arrangements of leaf- 



matical order, where we should least expect 

 to find it, in the myriads of leaves which are 

 tossed about in wild confusion by the summer 

 breeze. 



But a discovery, almost more wonderful 

 than this, has been made by Mr. M'Cosh, for 

 he has found out that " the leaf is a typical 

 plant or branch, and that every tree or 

 branch is a typical leaf." This resemblance, 



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