THE PRINCIPLE OF NUMBER. 13 



leaf type, that they hav^e undergone such wonderful transfor- 

 mations and adaptations to insect and other agencies and to 

 their environing conditions, so that the simple and original 

 laws governing the arrangement of the leaves, here pro- 

 pounded for the origin of what may be called the " primitive 

 symmetry" of the floral organs, have become in many cases, 

 masked or interfered with. Hence, to deduce those original 

 laws from the present structure of flowers, it is not only neces- 

 sary to consider the floral symmetry of an immense number 

 of genera, and so ascertain what are the relative proportions 

 of certain numbers when associated with alternate and oppo- 

 site leaves respectively, but to discover what may have been 

 the interfering causes which have modified what would 

 have been the immediate effects of the fundamental laws of 

 phyllotaxis. 



Thus, it will be found that the numbers of the parts 

 of whorls are liable to vary on their own account, while 

 the arrangement of the foliage varies independently at the 

 same time ; so that where the floral symmetry of a plant 

 does not tally with the leaf arrangement, the discrepancy 

 may be due either to subsequent changes occurring in the 

 flowers or in the leaves, or perhaps in both. 



For example, a quaternary floral type may be, and often 

 is, associated with alternate leaves ; where there is reason 

 to suspect that the former was established from a primitive 

 opposition in the leaf organs, but that the foliage has subse- 

 quently differentiated into a spiral arrangement, leaving the 

 original 4-merous symmetry of the flowers unaffected, as in 

 many of the Onagracece ; Epilohium, indeed, often furnishing 

 ocular demonstration, as, while the lower leaves may be 

 opposite, the upper are often alternate. 



On the other hand a quinary arrangement is often 



associated with what may be called a persistent opposition 

 4 



