156 



for some members a right, and a lefthanded wound parastichy 



has been drawn, 

 to the significance 

 of which we will 

 draw attention 

 afterwards. 



Bravais deter- 

 mined B r a u n ' s 

 "divergence" of 

 two consecutive 

 leaves by angular 

 measurements, ex- 

 pressed in degrees 

 of arc, the magni- 

 tude of this angle 

 being of course 

 directly related to 

 the fractional sym- 

 bols mentioned in 

 the above. As 

 beautiful examples 



of such spiral arrangements may be mentioned: the ripened car- 



pellary cones of Pinus, the fruit- 

 bearing capitulum of the ordinary 



sunflower (fig. 126) (Church), the 



multiple fruit of Ananassa (fig. 



127) with its consolidated mass 



of berries, and with their bracts 



round the axis, and finally the 



phyllotaxis of Euphorbia Wul- 



feni, according to Church. The 



number can be easily augmented. 

 Such a periodical arrangement 



evidently possesses the characte- 

 ristics of a space-lattice wound 



upon a cylindrical surface. There 



Fig. 125. 



Plane projection of a spiral arrangement f I on a cone. 

 .... Genetic spiral. Parastichies. 



Fig. 126. 



Fruits in the capitulum of 

 the sunflower. 



are thus definite translations, by 

 which the fundamental space- 

 lattice is determined as by a special kind of symmetrical operations. 

 If rolled round the cylindrical surface, the divergence of consecutive 



