288 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



spiral construction must be involved. Since the members are 

 few and the calyx apparently normal (3 + 5), there appears little 

 reason to doubt that Tropaeolum is a spiral (3 + 5) type throughout 

 all its parts, retaining 5 sepals, 5 petals, 8 stamens, and usually 

 3 carpels (less frequently 4-5) in normal spiral sequence, which 

 is, however, affected in so far as the numerical order of apparent 

 development is concerned by a pronounced degree of eccentricity. 



Thus, according to the diagrams, figs. 98, 99 show that the 

 amount of eccentricity of the developing flower lies between these 

 two figures ; the former shows eccentricity proceeding at a greater 

 rate, while in the latter it has affected a greater range of members. 

 The agreement of fig. 98 with the data of Eichler and Rohrbach is 

 not only very close, but it conveys in itself the reason why the 

 data may slightly vary (Eohrbach, Bot. Zeit., 1869, p. 848, figs. 

 1, 5 16, 17); while observation of the error of the geometrical 

 construction shows the difficulty of accurately gauging the relative 

 size of the primordia by the eye, the error of the geometrical 

 method being again less than that of observation of the protuber- 

 ances on the actual shoot apex. Thus in fig. 98 the sequence of 

 apparent origin would be considered to be 12, 11, 13, 14, 15, 16, 

 17, 18 ; or 



8 

 3 



6 

 2 



5 

 1 

 7 



4 



while in fig. 99 it would be 12, 13, 15, 11, 14, 18, 16, 17 ; or 



3 



6 

 2 



7 

 4 



1 

 8 

 5 



It is clear that if the eccentricity of the former diagram had proceeded 

 further 13 would have become larger than 11, that is, 3 would have 

 replaced 2 in the first scheme ; while if the eccentricity of the latter 

 had not been carried so far 15 would not have appeared larger than 

 11 and 18 would not have been larger than 16 and 17, these being 

 the changes required to bring either scheme into agreement with 

 that of Eohrbach. 



