DISTRIBUTION OF THE GEEEN LEAVES ON THE STEM. 397 



as, for example, in the Oleander, these are separated from one another in a 

 horizontal direction by one-third of the circumference of the circle (120) Several 

 leaves springing from the same height form together a whorl, and the distance of 

 the individual members of a whorl from one another is called the horizontal 

 distance, or the divergence. The divergence amounts to i in fig 98 ' and i in 

 fig. 98 \ of the circumference of the circle, and can be thus shortly expressed b v 

 means of these fractions. 



It is very remarkable that the whorls which follow after and above one 

 another according to their age on one and the same shoot do not originate at 

 corresponding places of the circumference, but are displaced regularly with regard 

 to one another. Thus the point of origin of the second two-membered whorl in 



Fig. 98. -Plan of Whorled Phyllotaxis. 

 i Two-membered WhorL a Three-mem bered WhorL 



fig. 98 * is shifted through a quarter of the circumference (i.e. through 90, a rig} it 

 angle) from the point of origin of the first, oldest, and lowest two-membered whorl. 

 The third whorl is again shifted through a right angle with regard to the second, 

 and so it continues up the stem as far, generally speaking, as foliage-leaves are to 

 be found on it. If the stem is elongated in the case described, four rectilineal lines 

 (orthostichies) appear to be developed on it (fig. 98 J ). If a whorl is composed of 

 three leaves, and if the successive whorls be displaced through one-sixth of the 

 circumference, as, for example, in the Oleander (see fig. 98 2 ), six rectilineal series of 

 leaves or orthostichies originate, running parallel to one another down the stem. 



The leafy stem can also be imagined as divided into stories, each of which 

 displays the same number, position, and distribution of the leaves, and agrees 

 completely in the plan of its construction with the adjoining story. In one such 

 case (fig. 98 1 ), each story possesses four leaves in the form of a cross; in another 

 case (fig. 98 *), it possesses two sets of three leaves separated from one another by 

 a distance of 60. If the stories standing above one another are separated, they 

 would be so alike in arrangement as to be easily mistaken for one another. Each 



