THE PRINCIPLE OF NUMBER. 85 



4 with 5-6-ineroas, and 1 with. 4-6-merous whorls in the 

 different species. In Olacinere, of 36 genera, 17 have altei'- 

 nate leaves and 5-merous flowers ; 7 have 4-5-meroiis ; 4, 

 5-6-merous ; 2, 6-merous, and 1, 4-6-merous. 



As six leaves cannot form a cycle of any of the ordinary 

 kinds of phyllotaxis, this will account for its rarity in 

 nature ; and indeed it may probably, without exception, be 

 divisible into two whorls of three members each, except in 

 the case of symmetrical increase from five. 



Heptamerous Whorls. — Like the number 6, 7 is a very 

 rare one ; and when present appears to be due to its being a 

 primitive number or to symmeti'ical change. If any whorls 

 are deducible from decussating verticils of threes, a cycle 

 may contain seven parts, as the phyllo tactical series arising 

 from the breaking up of such verticils into a continuous 

 spiral arrangement is represented by i, i, f , y\, etc. So that 

 if leaves on a plant were in whorls of threes, as occurs in 

 some instances, and not opposite, as in the primitive type 

 amongst Dicotyledons, then a heptamerous arrangement 

 would occur. If, therefore, there be any existing illustra- 

 tion, it must, by the very nature of the case, be exceedingly 

 rare. It sometimes occurs in Trientalls ; and when this is 

 the case, it may possibly have arisen as here suggested. 

 According to the description given of this plant in the 

 Genera Plantarum, the numbers of the three outer whorls 

 range from 5 to 9, the capsule being 5-valved. The leaves, 

 on the other hand, are " saepe tot quot petala subverti- 

 cillata." 



A second cause is arrest. This obviously accounts for 

 the 7 anthers in Felargonium, for the 10 filaments are present. 



A third cause is symmetrical change. Lythrum Salicaria 

 illustrates this as already mentioned. This flower is some- 

 times described as 6-merous, but it is not always so. The 



