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SCIENTIFIC RECREATIONS. 



arithmetical exactitude ; and for those who love calculations and " fractions /' 

 the determination of the spirals, their continuity and intermixture, supplies 

 abundance of curious entertainment. All three modes of leaf-arrangement are 

 found in certain herbaceous plants, none disclosing this particular kind of 

 playfulness more plainly than the common pyramidal Loosestrife, Lysimachia 

 vulgaris, and the purple Lythrum of the waterside, in each of which very hand- 



Fig. 768. Branch of horse chestnut. 



some wild flowers, alternate, opposite, and whorled leaves may be found in near 

 neighbourhood. Alternate and opposite leaves are also met with, side by 

 side, in various species of Myrtaceae ; and imperfectly, upon young shoots 

 of the common ash-tree. The rule is, nevertheless, that there shall be 

 uniformity, and in many of the largest natural orders the rule is never 

 broken. In the Rosaceae the stem leaves are invariably alternate ; in the 

 Gentianaceae they are invariably opposite." 



