161 



leaves are called orthostichies , while the parallel spirals are named 

 parastichies. The cycle is indicated by a numeral symbol in the 



form of a fraction, 

 like: fa fa f ff etc., 

 the numerator of 

 which indicates the 

 number of turns of 

 the spiral in each 

 cycle, while its de- 

 nominator indica- 

 tes the number of 

 members inserted 

 in each cycle. As 

 an instance of this, 

 we have in fig. i2j 



reproduced the 

 plane projection 

 of such a spiral 

 Fig. 127. arrangement on a 



Plane projection of a spiral arrangement ( \ on a cone. COnical Surface, in 



which five mem- 



Genetic spiral 



Parastichies. 



bets are included 

 in a cycle of two revolutions (|). The orthostichies (e. g.,*2-7-12) are 

 projected as the radii of the system 

 of circles, while for some members 

 a right-, and a left-handed wound 

 parastichy has been drawn, to the 

 significance of which we will draw 

 attention afterwards. 



Bravais determined Braun's 

 "divergence" of two consecutive 

 leaves by angular measurements, 

 expressed in degrees of arc, the 

 magnitude of this angle being, 

 of course, directly related to the 

 fractional symbols mentioned in 

 the above. As beautiful examples 

 of such spiral arrangements may 

 be mentioned: the ripened car- 



pellary cones of Pinus, the fruitbearing capitulum of the ordinary 



ii 



Fig. 128. 



Fruits in the capitulum of 

 the sunflower. 



