THE PRINCIPLE OF NUMBEPt. 9 



The degradation of the corolla is likewise very common. 

 As its enhancement has been due to insect agency, so, 

 conversely, its reduction in size, colour, etc., is presumably 

 often the result of the neglect of insects. Consequently 

 inconspicuousness becomes a characteristic feature of self- 

 fertilising flowers. By increased degradation the corolla may 

 disappear entirely, as in Sagina apetala, some cleistogamous 

 flowers, and in the Incomjjleto' generally. Such degradation 

 is also characteristic of wind-fertilised flowers. 



As both calyx and corolla maybe degraded and disappear, 

 so may the stamens and carpels, unisexual and neuter flowers 

 beiug the result. 



Further observations, however, will be made upon this 

 subject when treating of the several whorls respectively, and 

 especially when discussing the phenomenon of degeneracy. 



The Oeigin of Different Numbers. The number of parts 

 constituting the floral whorls is, without doubt, primarily 

 due to phyllotaxis ; and therefore, to understand why certain 

 numbers, such as fives, fours, and threes prevail, it is needful 

 to give some preliminary remarks on the principles of leaf 

 arrangement. It has long been observed that these are 

 referable to two kinds — one in which two or more leaves are 

 situated on the same node, when they are decussate,* that 

 is to say, each pair or whorl of three or more leaves alternates 

 in position with the whorl immediately above and below it. 

 The second system is when only one leaf occurs at a node ; 

 the leaves are then said to be alternate. The leaves are then 

 arranged on a continuous spiral line, and can be represented 

 by the fractions of the well-known series 4-, i, -|, f , tj, /y, etc. 

 Of these fractions the denominator represents the number of 



* Rare exceptions occur in species of Poiamogeton, in which alternate 

 internodes between the distichously arranged leaves are suppressed, so 

 that they become opposite, but are all in the same plane. 



